Finite Group Databasebeta

← #28292801

Subgroups — #28292801

Order 13568.

6538 conjugacy classes of subgroups.

The subgroup lattice has 1612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289339C214yesmaximal, complemented
2#20289333C214yesmaximal, complemented
3#20289321C212yesmaximal, complemented
4#20289318C212yesmaximal, complemented
5#20289287C212yesmaximal, complemented
6#20289285C212yesmaximal, complemented
7#20289168C214yesmaximal, complemented
8#20289160C212yesmaximal, complemented
9#20289152C212yesmaximal, complemented
10#20288811C212yesmaximal, complemented
11#20288809C212yesmaximal, complemented
12#20288766C212yesmaximal, complemented
13#20288764C212yesmaximal, complemented
14#20288704C214yesmaximal, complemented
15#20288698C214yesmaximal, complemented
16#20288554C212yesmaximal, complemented
17#20288549C212yesmaximal, complemented
18#20288518C212yesmaximal, complemented
19#20288511C212yesmaximal, complemented
20#20288467C214yesmaximal, complemented
21#20288455C214yesmaximal, complemented
22#20288411C214yesmaximal, complemented
23C2×#16811180C211yesmaximal, characteristic, complemented
24C2×#16811157C211yesmaximal, characteristic, complemented
25C2×C53×#529C211yesmaximal, characteristic, complemented
26C53⋊#564C2214yescomplemented
27#16811377C2214yescomplemented
28#16811375C2218yescomplemented
29#16811375C2218yescomplemented
30#16811373C2214yescomplemented
31#16811367C2214yescomplemented
32#16811352C2212yescomplemented
33#16811351C2214yescomplemented
34#16811351C2212yescomplemented
35#16811350C2214yescomplemented
36#16811346C2214yescomplemented
37#16811346C2212yescomplemented
38#16811343C2212yescomplemented
39#16811342C2214yescomplemented
40#16811341C2218yescomplemented
41#16811340C2218yescomplemented
42#16811332C2218yescomplemented
43#16811332C2218yescomplemented
44#16811331C2214yescomplemented
45#16811330C2214yescomplemented
46#16811330C2214yescomplemented
47#16811328C2214yescomplemented
48#16811328C2218yescomplemented
49#16811327C2218yescomplemented
50#16811325C2214yescomplemented
51#16811322C2218yescomplemented
52#16811319C2214yescomplemented
53#16811316C2218yescomplemented
54#16811313C2214yescomplemented
55#16811313C2214yescomplemented
56#16811312C2218yescomplemented
57#16811311C2214yescomplemented
58#16811310C2218yescomplemented
59#16811310C2218yescomplemented
60#16811309C2218yescomplemented
61#16811308C2214yescomplemented
62#16811308C2218yescomplemented
63#16811308C2218yescomplemented
64#16811306C2218yescomplemented
65#16811306C2218yescomplemented
66#16811302C2218yescomplemented
67#16811299C2218yescomplemented
68#16811299C2218yescomplemented
69#16811299C2218yescomplemented
70#16811296C2218yescomplemented
71#16811296C2218yescomplemented
72Q8×D212C2212yescomplemented
73D4×Dic106C2214yescomplemented
74D4×Dic106C2214yescomplemented
75D4×Dic106C2212yescomplemented
76Q8×C22⋊D53C2214yescomplemented
77#16811286C2214yescomplemented
78#16811282C2214yescomplemented
79#16811282C2214yescomplemented
80#16811281C2214yescomplemented
81#16811279C2214yescomplemented
82#16811278C2212yescomplemented
83#16811277C2212yescomplemented
84#16811269C2214yescomplemented
85#16811267C2214yescomplemented
86#16811254C2214yescomplemented
87#16811253C2214yescomplemented
88#16811252C2214yescomplemented
89#16811251C2214yescomplemented
90#16811249C2214yes—
91#16811249C2214yescomplemented
92#16811248C2214yescomplemented
93#16811244C2214yescomplemented
94#16811244C2214yescomplemented
95#16811242C2214yescomplemented
96#16811239C2218yescomplemented
97#16811238C2214yescomplemented
98#16811237C2218yescomplemented
99#16811236C2214yescomplemented
100#16811235C2214yescomplemented
101#16811235C2214yescomplemented
102#16811232C2218yescomplemented
103#16811231C2218yescomplemented
104#16811231C2214yescomplemented
105#16811230C2218yescomplemented
106#16811230C2218yescomplemented
107#16811220C2214yes—
108#16811218C2214yes—
109#16811217C2218yescomplemented
110#16811217C2218yescomplemented
111#16811215C2218yescomplemented
112#16811214C2218yescomplemented
113#16811211C2214yes—
114#16811210C2214yes—
115#16811199C2214yescomplemented
116#16811193C2214yescomplemented
117#16811182C2214yes—
118#16811180C2212yescomplemented
119#16811180C2212yescomplemented
120#16811180C2212yescomplemented
121#16811180C2212yescomplemented
122#16811180C2212yescomplemented
123#16811180C2212yescomplemented
124#16811180C2212yescomplemented
125#16811180C2212yescomplemented
126#16811180C2214yescomplemented
127#16811175C2214yescomplemented
128C2×#13133217C2211yescharacteristic, complemented
129C2×#13133217C2211yescharacteristic, complemented
130#16811157C2212yes—
131#16811157C2214yes—
132#16811157C2212yes—
133#16811157C2212yes—
134#16811157C2212yes—
135#16811157C2212yescomplemented
136#16811157C2212yescomplemented
137#16811157C2212yescomplemented
138#16811157C2212yescomplemented
139#16811154C2214yes—
140#16811150C2218yescomplemented
141#16811150C2218yescomplemented
142C2×#13133211C2212yescomplemented
143C2×#13133209C2212yescomplemented
144C2×#13133209C2211yescharacteristic, complemented
145C2×#13133205C2211yescharacteristic, complemented
146#16811134C2214yes—
147#16811133C2214yes—
148C2×#13133200C2212yes—
149C2×#13133196C2212yes—
150C2×#13133196C2212yes—
151C2×#13133196C2211yescharacteristic
152C2×#13133196C2214yescomplemented
153C22⋊Q8×D53C2214yescomplemented
154C2×#13133191C2211yescharacteristic
155#16811103C2214yescomplemented
156#16811102C2214yescomplemented
157#16811100C2214yescomplemented
158#16811099C2214yescomplemented
159#16811098C2214yes—
160#16811096C2214yes—
161C2×C4×Dic106C2212yescomplemented
162C2×C4×Dic106C2212yescomplemented
163C2×C4×Dic106C2211yescharacteristic, complemented
164C2×C4×D212C2211yescharacteristic, complemented
165C2×C4×C22⋊D53C2212yes—
166C2×#13133176C2212yes—
167C2×#13133174C2212yescomplemented
168C53×#529C2212yes—
169C53×#529C2212yes—
170C53×#529C2212yes—
171C53×#529C2212yes—
172C53×#529C2212yescomplemented
173C53×#529C2212yescomplemented
174C53×#529C2212yescomplemented
175C53×#529C2212yescomplemented
176C2×#126×C53C2212yescomplemented
177C2×#125×C53C2211yescharacteristic, complemented
178C2×#124×C53C2211yescharacteristic, complemented
179C2×#123×C53C2212yes—
180C2×C22⋊Q8×C53C2211yescharacteristic
181C2×#121×C53C2211yescharacteristic
182C2×C4×Q8×C53C2211yescharacteristic, complemented
183C2×C4×D4×C53C2212yes—
184C2×C4×D4×C53C2211yescharacteristic, complemented
185C2×#117×C53C2212yescomplemented
186C22×C42×C53C2211yescharacteristic
187C2×#11719945C2314yes—
188C2×#11719947C2314yes—
189C22×Dic106C2312yes—
190C22×Dic106C2312yes—
191C22×Dic106C2314yes—
192C22×Dic106C2311yescharacteristic
193C2×Q8×D53C2314yes—
194C22×D212C2311yescharacteristic
195C22×C22⋊D53C2312yes—
196C22×C4×D53C2312yes—
197#13133217C2312yes—
198#13133217C2312yes—
199#13133217C2314yes—
200#13133217C2314yes—
201#13133217C2312yes—
202#13133217C2312yes—
203#13133217C2312yes—
204#13133217C2312yes—
205#13133217C2312yes—
206#13133217C2312yes—
207#13133216C2318yes—
208#13133216C2314yes—
209#13133216C2318yes—
210#13133216C2318yes—
211#13133215C2314yes—
212#13133215C2318yes—
213#13133212C2318yes—
214#13133212C2318yes—
215#13133212C2318yes—
216#13133212C2318yes—
217#13133212C2318yes—
218#13133212C2318yes—
219#13133211C2318yes—
220#13133211C2314yes—
221#13133211C2314yes—
222#13133211C2314yes—
223#13133211C2314yes—
224#13133210C2318yes—
225#13133210C2318yes—
226#13133210C2318yes—
227#13133210C2318yes—
228#13133210C2318yes—
229#13133210C2318yes—
230#13133210C2318yes—
231#13133209C2314yes—
232#13133209C2318yes—
233#13133209C2312yes—
234#13133209C2314yes—
235#13133209C2314yes—
236#13133209C2312yes—
237#13133209C2312yes—
238#13133209C2312yes—
239#13133209C2314yes—
240#13133209C2314yes—
241#13133208C2318yes—
242#13133208C2318yes—
243#13133208C2314yes—
244#13133208C2318yes—
245#13133208C2318yes—
246#13133207C2318yes—
247#13133207C2318yes—
248#13133207C2318yes—
249#13133207C2318yes—
250#13133207C2318yes—
251#13133207C2318yes—
252#13133207C2318yes—
253#13133207C2318yes—
254#13133207C2318yes—
255#13133205C2314yes—
256#13133205C2312yes—
257#13133205C2312yes—
258#13133205C2312yes—
259#13133205C2312yes—
260#13133204C2314yes—
261#13133203C2318yes—
262#13133203C2318yes—
263#13133203C2318yes—
264#13133203C2318yes—
265#13133202C2318yes—
266#13133201C2318yes—
267#13133201C2318yes—
268#13133201C2318yes—
269#13133200C2314yes—
270#13133200C2314yes—
271#13133200C2318yes—
272#13133200C2318yes—
273#13133200C2314yes—
274#13133200C2314yes—
275#13133199C2318yes—
276#13133199C2318yes—
277#13133199C2318yes—
278#13133199C2318yes—
279#13133198C2318yes—
280#13133198C2318yes—
281#13133197C2314yes—
282#13133197C2314yes—
283#13133197C2318yes—
284#13133197C2318yes—
285#13133197C2318yes—
286#13133196C2314yes—
287#13133196C2314yes—
288#13133196C2314yes—
289#13133196C2314yes—
290#13133196C2314yes—
291#13133196C2318yes—
292#13133196C2312yes—
293#13133196C2314yes—
294#13133196C2318yes—
295#13133196C2314yes—
296#13133196C2318yes—
297#13133196C2312yes—
298#13133196C2314yes—
299#13133196C2312yes—
300#13133196C2314yes—
301#13133196C2312yes—
302#13133196C2314yes—
303#13133196C2314yes—
304#13133195C2318yes—
305#13133195C2318yes—
306#13133195C2318yes—
307#13133195C2318yes—
308#13133194C2318yes—
309#13133194C2318yes—
310#13133194C2318yes—
311#13133194C2318yes—
312#13133194C2318yes—
313#13133194C2318yes—
314#13133194C2318yes—
315#13133194C2318yes—
316#13133194C2318yes—
317#13133194C2318yes—
318#13133194C2318yes—
319#13133193C2314yes—
320#13133193C2318yes—
321#13133191C2314yes—
322#13133191C2312yes—
323#13133191C2312yes—
324#13133191C2312yes—
325#13133191C2312yes—
326#13133190C2318yes—
327#13133189C2318yes—
328#13133189C2318yes—
329#13133189C2318yes—
330#13133188C2314yes—
331#13133186C2318yes—
332#13133185C2318yes—
333Q8×Dic53C2314yes—
334C4×Dic106C2314yes—
335C4×Dic106C2314yes—
336C4×Dic106C2314yes—
337C4×Dic106C2314yes—
338C4×Dic106C2314yes—
339C4×Dic106C2312yes—
340C4×Dic106C2314yes—
341C4×Dic106C2318yes—
342C4×Dic106C2314yes—
343C4×Dic106C2312yes—
344C4×Dic106C2314yes—
345C4×Dic106C2312yes—
346C4×Dic106C2314yes—
347C4×Dic106C2312yes—
348C4×Dic106C2314yes—
349C4×Dic106C2314yes—
350#13133182C2314yes—
351#13133182C2314yes—
352#13133182C2318yes—
353#13133182C2318yes—
354#13133182C2318yes—
355C4×D212C2314yes—
356C4×D212C2312yes—
357C4×D212C2312yes—
358C4×D212C2312yes—
359C4×D212C2312yes—
360D4×Dic53C2314yes—
361D4×Dic53C2318yes—
362D4×Dic53C2318yes—
363D4×Dic53C2318yes—
364D4×Dic53C2318yes—
365C4×C22⋊D53C2314yes—
366C4×C22⋊D53C2314yes—
367C4×C22⋊D53C2318yes—
368C4×C22⋊D53C2314yes—
369C4×C22⋊D53C2318yes—
370C4×C22⋊D53C2318yes—
371C4×C22⋊D53C2314yes—
372#13133177C2318yes—
373#13133177C2318yes—
374#13133177C2318yes—
375#13133177C2318yes—
376#13133177C2318yes—
377#13133176C2314yes—
378#13133176C2314yes—
379#13133176C2314yes—
380#13133176C2314yes—
381#13133176C2318yes—
382#13133176C2314yes—
383#13133175C2318yes—
384#13133175C2318yes—
385#13133175C2314yes—
386#13133174C2318yes—
387#13133174C2314yes—
388#13133174C2314yes—
389#13133174C2314yes—
390#13133174C2314yes—
391#13133173C2318yes—
392#13133173C2318yes—
393#13133173C2318yes—
394#13133173C2318yes—
395C2×C4⋊Dic53C2314yes—
396C2×C4⋊Dic53C2311yescharacteristic
397C2×C4⋊Dic53C2312yes—
398C2×C4⋊Dic53C2312yes—
399C2×C4⋊Dic53C2311yescharacteristic
400C2×C4⋊Dic53C2312yes—
401C2×C4⋊Dic53C2312yes—
402C2×#11719919C2318yes—
403C2×#11719919C2312yes—
404C2×#11719919C2312yes—
405C2×#11719919C2314yes—
406C2×#11719919C2314yes—
407C2×#11719919C2312yes—
408C2×#11719919C2312yes—
409C4⋊C4×D53C2314yes—
410C4⋊C4×D53C2318yes—
411C2×C22⋊Dic53C2318yes—
412C2×C22⋊Dic53C2314yes—
413C2×C22⋊Dic53C2312yes—
414C2×#11719921C2312yes—
415C2×#11719921C2312yes—
416C2×#11719921C2312yes—
417C2×#11719921C2312yes—
418C22⋊C4×D53C2318yes—
419C2×C4×Dic53C2312yes—
420C2×C4×Dic53C2314yes—
421C22×Q8×C53C2311yescharacteristic
422C22×D4×C53C2312yes—
423C22×D4×C53C2311yescharacteristic
424C23×C4×C53C2311yescharacteristic
425C23×C4×C53C2311yescharacteristic
426C23×C4×C53C2311yescharacteristic
427C23×C4×C53C2312yes—
428#126×C53C2314yes—
429#126×C53C2314yes—
430#126×C53C2314yes—
431#126×C53C2314yes—
432#125×C53C2312yes—
433#125×C53C2312yes—
434#125×C53C2312yes—
435#125×C53C2312yes—
436#124×C53C2312yes—
437#124×C53C2312yes—
438#124×C53C2312yes—
439#124×C53C2312yes—
440#123×C53C2314yes—
441#123×C53C2314yes—
442#123×C53C2314yes—
443#123×C53C2314yes—
444C22⋊Q8×C53C2312yes—
445C22⋊Q8×C53C2312yes—
446C22⋊Q8×C53C2312yes—
447C22⋊Q8×C53C2312yes—
448#121×C53C2312yes—
449#121×C53C2312yes—
450#121×C53C2312yes—
451#121×C53C2312yes—
452C4×Q8×C53C2312yes—
453C4×Q8×C53C2312yes—
454C4×Q8×C53C2312yes—
455C4×Q8×C53C2312yes—
456C4×D4×C53C2314yes—
457C4×D4×C53C2312yes—
458C4×D4×C53C2312yes—
459C4×D4×C53C2314yes—
460C4×D4×C53C2314yes—
461C4×D4×C53C2314yes—
462C4×D4×C53C2312yes—
463C4×D4×C53C2312yes—
464#117×C53C2314yes—
465#117×C53C2314yes—
466#117×C53C2314yes—
467#117×C53C2314yes—
468C2×C4⋊C4×C53C2312yes—
469C2×C4⋊C4×C53C2312yes—
470C2×C4⋊C4×C53C2312yes—
471C2×C4⋊C4×C53C2311yescharacteristic
472C2×C4⋊C4×C53C2311yescharacteristic
473C2×C4⋊C4×C53C2312yes—
474C2×C22⋊C4×C53C2312yes—
475C2×C22⋊C4×C53C2312yes—
476C2×C22⋊C4×C53C2312yes—
477C2×C22⋊C4×C53C2312yes—
478C2×C22⋊C4×C53C2312yes—
479C2×C42×C53C2311yescharacteristic
480C2×C42×C53C2311yescharacteristic
481C2×C42×C53C2311yescharacteristic
482C2×C42×C53C2311yescharacteristic
483C2×C42×C53C2311yescharacteristic
484C2×C42×C53C2311yescharacteristic
485C2×C42×C53C2311yescharacteristic
486C2×C42×C53C2311yescharacteristic
487C2×C42×C53C2311yescharacteristic
488C2×C42×C53C2311yescharacteristic
489C2×C42×C53C2311yescharacteristic
490C2×C42×C53C2311yescharacteristic
491C2×C42×C53C2312yes—
492C24×C53C2412yes—
493C24×C53C2411yescharacteristic
494C23×D53C2412yes—
495C2×Q8×C53—42no—
496C2×Q8×C53C2412yes—
497C2×Q8×C53C2412yes—
498C2×D4×C53—28no—
499C2×D4×C53—42no—
500C2×D4×C53C2414yes—
501C2×D4×C53C2414yes—
502C2×D4×C53C2412yes—
503C2×D4×C53C2412yes—
504C22×C4×C53—24no—
505C22×C4×C53—42no—
506C22×C4×C53—42no—
507C22×C4×C53—44no—
508C22×C4×C53C2411yescharacteristic
509C22×C4×C53C2411yescharacteristic
510C22×C4×C53C2411yescharacteristic
511C22×C4×C53C2411yescharacteristic
512C22×C4×C53C2411yescharacteristic
513C22×C4×C53C2411yescharacteristic
514C22×C4×C53C2411yescharacteristic
515C22×C4×C53C2411yescharacteristic
516C22×C4×C53C2411yescharacteristic
517C22×C4×C53C2411yescharacteristic
518C22×C4×C53C2411yescharacteristic
519C22×C4×C53C2411yescharacteristic
520C22×C4×C53C2412yes—
521C22×C4×C53C2414yes—
522C22×C4×C53C2411yescharacteristic
523C22×C4×C53C2411yescharacteristic
524C22×C4×C53C2411yescharacteristic
525C22×C4×C53C2411yescharacteristic
526C22×C4×C53C2411yescharacteristic
527C22×C4×C53C2411yescharacteristic
528C22×C4×C53C2412yes—
529C22×C4×C53C2412yes—
530C22×C4×C53C2414yes—
531C2×C22⋊D53—28no—
532C2×C22⋊D53C2414yes—
533C2×C22⋊D53C2414yes—
534C2×C22⋊D53C2418yes—
535C2×C22⋊D53C2418yes—
536C22×Dic53C2412yes—
537C22×Dic53C2412yes—
538C22×Dic53C2414yes—
539C22×Dic53C2414yes—
540C22×Dic53C2412yes—
541C22×Dic53C2418yes—
542C22×Dic53C2418yes—
543Q8×D53—48no—
544#11719947—48no—
545#11719945—48no—
546C2×D212—42no—
547C2×D212C2412yes—
548C2×D212C2412yes—
549C2×C4×D53—44no—
550C2×C4×D53C2414yes—
551C2×C4×D53C2418yes—
552C2×C4×D53C2418yes—
553C2×C4×D53C2414yes—
554C2×Dic106—42no—
555C2×Dic106—48no—
556C2×Dic106—44no—
557C2×Dic106—44no—
558C2×Dic106C2414yes—
559C2×Dic106C2412yes—
560C2×Dic106C2414yes—
561C2×Dic106C2418yes—
562C2×Dic106C2418yes—
563C2×Dic106C2412yes—
564C2×Dic106C2414yes—
565C2×Dic106C2414yes—
566C4⋊C4×C53C2414yes—
567C4⋊C4×C53C2414yes—
568C4⋊C4×C53C2414yes—
569C4⋊C4×C53C2414yes—
570C4⋊C4×C53C2412yes—
571C4⋊C4×C53C2412yes—
572C4⋊C4×C53C2414yes—
573C4⋊C4×C53C2414yes—
574C4⋊C4×C53C2412yes—
575C4⋊C4×C53C2412yes—
576C4⋊C4×C53C2414yes—
577C4⋊C4×C53C2414yes—
578C22⋊C4×C53C2414yes—
579C22⋊C4×C53C2414yes—
580C22⋊C4×C53C2414yes—
581C22⋊C4×C53C2414yes—
582C22⋊C4×C53C2414yes—
583C22⋊C4×C53C2414yes—
584C22⋊C4×C53C2414yes—
585C22⋊C4×C53C2414yes—
586C22⋊C4×C53C2414yes—
587C22⋊C4×C53C2414yes—
588C42×C53C2411yescharacteristic
589C42×C53C2411yescharacteristic
590C42×C53C2411yescharacteristic
591C42×C53C2411yescharacteristic
592C42×C53C2411yescharacteristic
593C42×C53C2411yescharacteristic
594C42×C53C2411yescharacteristic
595C42×C53C2411yescharacteristic
596C42×C53C2411yescharacteristic
597C42×C53C2411yescharacteristic
598C42×C53C2411yescharacteristic
599C42×C53C2411yescharacteristic
600C42×C53C2411yescharacteristic
601C42×C53C2411yescharacteristic
602C42×C53C2411yescharacteristic
603C42×C53C2411yescharacteristic
604C42×C53C2414yes—
605C42×C53C2414yes—
606C22⋊Dic53C2418yes—
607C22⋊Dic53C2414yes—
608C22⋊Dic53C2418yes—
609C22⋊Dic53C2414yes—
610C22⋊Dic53C2418yes—
611C22⋊Dic53C2418yes—
612C22⋊Dic53C2418yes—
613C22⋊Dic53C2418yes—
614#11719921C2418yes—
615#11719921C2418yes—
616#11719921C2414yes—
617#11719921C2414yes—
618#11719921C2414yes—
619#11719921C2414yes—
620#11719921C2414yes—
621#11719921C2414yes—
622#11719921C2414yes—
623#11719921C2414yes—
624#11719921C2418yes—
625#11719921C2418yes—
626C4⋊Dic53C2414yes—
627C4⋊Dic53C2418yes—
628C4⋊Dic53C2412yes—
629C4⋊Dic53C2414yes—
630C4⋊Dic53C2412yes—
631C4⋊Dic53C2414yes—
632C4⋊Dic53C2414yes—
633C4⋊Dic53C2414yes—
634C4⋊Dic53C2414yes—
635C4⋊Dic53C2412yes—
636C4⋊Dic53C2412yes—
637C4⋊Dic53C2414yes—
638C4⋊Dic53C2414yes—
639C4⋊Dic53C2418yes—
640C4⋊Dic53C2418yes—
641C4⋊Dic53C2418yes—
642#11719919C2418yes—
643#11719919C2418yes—
644#11719919C2418yes—
645#11719919C2414yes—
646#11719919C2418yes—
647#11719919C2414yes—
648#11719919C2414yes—
649#11719919C2414yes—
650#11719919C2414yes—
651#11719919C2418yes—
652#11719919C2414yes—
653#11719919C2414yes—
654#11719919C2418yes—
655#11719919C2418yes—
656#11719919C2414yes—
657#11719919C2418yes—
658#11719919C2418yes—
659#11719919C2418yes—
660#11719919C2418yes—
661#11719919C2418yes—
662C4×Dic53C2414yes—
663C4×Dic53C2418yes—
664C4×Dic53C2418yes—
665C4×Dic53C2414yes—
666C4×Dic53C2418yes—
667C4×Dic53C2418yes—
668C4×Dic53C2418yes—
669C4×Dic53C2418yes—
670C23×C53—24no—
671C23×C53—41no—
672C23×C53—41no—
673C23×C53—42no—
674C23×C53—42no—
675C23×C532−1+414yes—
676C23×C53C2514yes—
677C23×C53C2511yescharacteristic
678C23×C53C2511yescharacteristic
679C23×C53C2511yescharacteristic
680C22×D53—24no—
681C22×D53—42no—
682C22×D53—42no—
683C22×D53C2514yes—
684Q8×C53—24no—
685Q8×C53—42no—
686D4×C53—28no—
687D4×C53—28no—
688D4×C53—24no—
689D4×C53—42no—
690C2×C4×C53—22no—
691C2×C4×C53—22no—
692C2×C4×C53—22no—
693C2×C4×C53—22no—
694C2×C4×C53—22no—
695C2×C4×C53—22no—
696C2×C4×C53—24no—
697C2×C4×C53—22no—
698C2×C4×C53—22no—
699C2×C4×C53—22no—
700C2×C4×C53—28no—
701C2×C4×C53—22no—
702C2×C4×C53—22no—
703C2×C4×C53—22no—
704C2×C4×C53—41no—
705C2×C4×C53—41no—
706C2×C4×C53—41no—
707C2×C4×C53—41no—
708C2×C4×C53—42no—
709C2×C4×C53—44no—
710C2×C4×C53—41no—
711C2×C4×C53—41no—
712C2×C4×C53—42no—
713C2×C4×C53C2511yescharacteristic
714C2×C4×C53C2511yescharacteristic
715C2×C4×C53C2514yes—
716C2×C4×C53C2514yes—
717C2×C4×C53C2511yescharacteristic
718C2×C4×C53C2511yescharacteristic
719C2×C4×C53C2511yescharacteristic
720C2×C4×C53C2511yescharacteristic
721C2×C4×C53C2511yescharacteristic
722C2×C4×C53C2511yescharacteristic
723C2×C4×C53C2511yescharacteristic
724C2×C4×C53C2511yescharacteristic
725C2×C4×C53C2514yes—
726C2×C4×C53C2511yescharacteristic
727C2×C4×C53C2511yescharacteristic
728C22⋊D53—28no—
729C22⋊D53—28no—
730C22⋊D53—48no—
731C22⋊D53—48no—
732C2×Dic53—24no—
733C2×Dic53—42no—
734C2×Dic53—48no—
735C2×Dic53—44no—
736C2×Dic53—44no—
737C2×Dic53—42no—
738C2×Dic53—48no—
739C2×Dic53C2514yes—
740C2×Dic53C2518yes—
741C2×Dic53C2518yes—
742C2×Dic53C2514yes—
743C2×Dic53C2514yes—
744D212—24no—
745D212—42no—
746C4×D53—28no—
747C4×D53—44no—
748C4×D53—48no—
749C4×D53—48no—
750Dic106—24no—
751Dic106—28no—
752Dic106—28no—
753Dic106—42no—
754Dic106—48no—
755Dic106—44no—
756Dic106—44no—
757Dic106—48no—
758#62823—531nomaximal, Sylow
759C22×C53—21no—
760C22×C53—21no—
761C22×C53—21no—
762C22×C53—21no—
763C22×C53—21no—
764C22×C53—21no—
765C22×C53—24no—
766C22×C53—24no—
767C22×C53—24no—
768C22×C53—44no—
769C22×C53—84no—
770C22×C53C2×2−1+412yes—
771C22×C53C2×2−1+412yes—
772C22×C53C2×2−1+412yes—
773C22×C53C2611yescharacteristic
774C2×D53—24no—
775C2×D53—24no—
776C2×D53—24no—
777C2×D53—84no—
778C4×C53—21no—
779C4×C53—21no—
780C4×C53—21no—
781C4×C53—21no—
782C4×C53—24no—
783C4×C53—21no—
784C4×C53—21no—
785C4×C53—24no—
786C4×C53—24no—
787C4×C53—21no—
788C4×C53—21no—
789C4×C53—21no—
790C4×C53—21no—
791C4×C53#58512yes—
792C4×C53#58512yes—
793Dic53—24no—
794Dic53—24no—
795Dic53—28no—
796Dic53—28no—
797Dic53—24no—
798#3564—534no—
799#3564—534no—
800#3563—532no—
801#3563—532no—
802#3561—532no—
803#3561—532no—
804#3553—534no—
805#3552—532no—
806#3552—532no—
807#3523—532no—
808#3523—532no—
809#3520—532no—
810#3520—532no—
811#3516—534no—
812#3516—534no—
813#3505—532no—
814#3505—532no—
815#3501—532no—
816#3501—532no—
817#3495—534no—
818#3495—534no—
819#3491—534no—
820C2×#533—531no—
821C2×#529—531no—
822C2×#529D5311yescharacteristic, complemented
823C2×C53—22no—
824C2×C53—22no—
825C2×C53—22no—
826C2×C53—44no—
827C2×C53C22×2−1+411yescharacteristic
828C2×C53C2×#58511yescharacteristic
829C2×C53C2×#58511yescharacteristic
830D53—44no—
831#564—534no—
832#563—538no—
833#563—538no—
834#563—534no—
835#563—534no—
836#562—534no—
837#557—534no—
838#557—534no—
839#557—532no—
840#557—532no—
841#556—538no—
842#556—534no—
843#556—534no—
844#556—532no—
845#556—532no—
846#556—538no—
847#554—538no—
848#554—534no—
849#554—534no—
850#554—534no—
851#554—538no—
852#554—538no—
853#554—538no—
854#554—534no—
855#553—538no—
856#553—534no—
857#553—534no—
858#553—538no—
859#552—538no—
860#552—534no—
861#552—538no—
862#552—538no—
863#552—534no—
864#552—534no—
865#552—538no—
866#552—538no—
867#552—538no—
868#552—538no—
869#552—538no—
870#552—534no—
871#551—538no—
872#551—538no—
873#551—538no—
874#551—538no—
875#551—538no—
876#551—538no—
877D4×Q8—534no—
878D4×Q8—534no—
879D4×Q8—532no—
880D4×Q8—534no—
881D4×Q8—534no—
882D4×Q8—532no—
883#548—534no—
884#548—534no—
885#548—534no—
886#548—534no—
887#547—532no—
888#547—532no—
889#546—534no—
890#546—534no—
891#544—534no—
892#544—534no—
893#544—534no—
894#544—534no—
895#543—534no—
896#543—534no—
897#543—534no—
898#542—538no—
899#542—534no—
900#542—538no—
901#542—534no—
902#542—534no—
903#542—534no—
904#541—538no—
905#541—538no—
906#541—534no—
907#541—538no—
908#541—534no—
909#541—538no—
910#541—534no—
911#541—534no—
912#539—538no—
913#539—538no—
914#539—538no—
915#539—534no—
916#539—538no—
917#539—534no—
918#538—534no—
919#538—534no—
920#536—534no—
921#536—534no—
922#534—534no—
923#533—534no—
924#533—532no—
925#533—532no—
926#533—532no—
927#533—532no—
928#533—532no—
929#533—532no—
930#533—532no—
931#533—532no—
932#533—534no—
933C2×C4⋊Q8—531no—
934C2×C4⋊Q8—531no—
935#529—538no—
936#529—538no—
937#529—534no—
938#529—532no—
939#529—532no—
940#529—532no—
941#529—532no—
942#529—532no—
943#529—532no—
944#529—532no—
945#529—532no—
946#529—534no—
947#529C2×D5312yes—
948#529C2×D5312yes—
949#529C2×D5312yes—
950#529C2×D5312yes—
951#529C2×D5312yescomplemented
952#529C2×D5312yescomplemented
953#529C2×D5312yescomplemented
954#529C2×D5312yescomplemented
955C2×#126—532no—
956C2×#126C2×D5312yescomplemented
957C2×#125—531no—
958C2×#125—532no—
959C2×#125C2×D5311yescharacteristic, complemented
960C2×#124—531no—
961C2×#124C2×D5311yescharacteristic, complemented
962#525—534no—
963#525—534no—
964C2×#123—532no—
965C2×#123C2×D5312yes—
966C2×C22⋊Q8—531no—
967C2×C22⋊Q8—532no—
968C2×C22⋊Q8—532no—
969C2×C22⋊Q8—534no—
970C2×C22⋊Q8—534no—
971C2×C22⋊Q8C2×D5311yescharacteristic
972C2×#121—531no—
973C2×#121C2×D5311yescharacteristic
974#520—534no—
975#520—534no—
976#519—534no—
977#519—534no—
978#518—534no—
979#518—534no—
980C2×C4×Q8—531no—
981C2×C4×Q8—532no—
982C2×C4×Q8—532no—
983C2×C4×Q8C2×D5311yescharacteristic, complemented
984C2×C4×D4—532no—
985C2×C4×D4—531no—
986C2×C4×D4C2×D5312yes—
987C2×C4×D4C2×D5311yescharacteristic, complemented
988C2×#117—532no—
989C2×#117—532no—
990C2×#117C2×D5312yescomplemented
991C22×C42C2×D5311yescharacteristic
992C53#6282311yescharacteristic, complemented, Sylow
993C2×#41—534no—
994C2×#41—534no—
995C22×Q8—534no—
996C22×Q8—531no—
997C22×Q8—532no—
998C22×Q8—532no—
999C22×Q8—534no—
1000C22×Q8C22×D5311yescharacteristic
1001C22×D4—532no—
1002C22×D4—531no—
1003C22×D4C22×D5312yes—
1004C22×D4C22×D5311yescharacteristic
1005C23×C4—532no—
1006C23×C4C22×D5311yescharacteristic
1007C23×C4C22×D5312yes—
1008C23×C4C22×D5311yescharacteristic
1009C23×C4C22×D5311yescharacteristic
1010C4⋊Q8—534no—
1011C4⋊Q8—538no—
1012C4⋊Q8—534no—
1013C4⋊Q8—538no—
1014C4⋊Q8—538no—
1015C4⋊Q8—538no—
1016C4⋊Q8—532no—
1017C4⋊Q8—532no—
1018C4⋊Q8—532no—
1019C4⋊Q8—532no—
1020C4⋊Q8—532no—
1021C4⋊Q8—532no—
1022C4⋊Q8—532no—
1023C4⋊Q8—532no—
1024C4⋊Q8—534no—
1025C4⋊Q8—534no—
1026#126—538no—
1027#126—538no—
1028#126—538no—
1029#126—538no—
1030#126—538no—
1031#126—538no—
1032#126—538no—
1033#126—538no—
1034#126—538no—
1035#126—538no—
1036#126—538no—
1037#126—538no—
1038#126—538no—
1039#126—534no—
1040#126—534no—
1041#126—534no—
1042#126—534no—
1043#126—538no—
1044#126C22×D5314yes—
1045#126C22×D5314yes—
1046#126C22×D5314yes—
1047#126C22×D5314yes—
1048#125—538no—
1049#125—538no—
1050#125—534no—
1051#125—538no—
1052#125—538no—
1053#125—538no—
1054#125—538no—
1055#125—538no—
1056#125—538no—
1057#125—538no—
1058#125—538no—
1059#125—538no—
1060#125—538no—
1061#125—538no—
1062#125—532no—
1063#125—532no—
1064#125—532no—
1065#125—532no—
1066#125—534no—
1067#125—534no—
1068#125—534no—
1069#125—534no—
1070#125—534no—
1071#125—538no—
1072#125C22×D5312yes—
1073#125C22×D5312yes—
1074#125C22×D5312yes—
1075#125C22×D5312yes—
1076#124—534no—
1077#124—538no—
1078#124—538no—
1079#124—538no—
1080#124—538no—
1081#124—532no—
1082#124—532no—
1083#124—532no—
1084#124—532no—
1085#124—534no—
1086#124C22×D5312yes—
1087#124C22×D5312yes—
1088#124C22×D5312yes—
1089#124C22×D5312yes—
1090#123—538no—
1091#123—538no—
1092#123—534no—
1093#123—534no—
1094#123—534no—
1095#123—534no—
1096#123—538no—
1097#123—538no—
1098#123—538no—
1099#123—538no—
1100#123—538no—
1101#123—538no—
1102#123—538no—
1103#123—538no—
1104#123—538no—
1105#123—538no—
1106#123C22×D5314yes—
1107#123C22×D5314yes—
1108#123C22×D5314yes—
1109#123C22×D5314yes—
1110C22⋊Q8—534no—
1111C22⋊Q8—538no—
1112C22⋊Q8—532no—
1113C22⋊Q8—534no—
1114C22⋊Q8—534no—
1115C22⋊Q8—532no—
1116C22⋊Q8—532no—
1117C22⋊Q8—532no—
1118C22⋊Q8—534no—
1119C22⋊Q8—534no—
1120C22⋊Q8—534no—
1121C22⋊Q8—534no—
1122C22⋊Q8—534no—
1123C22⋊Q8—534no—
1124C22⋊Q8—538no—
1125C22⋊Q8—534no—
1126C22⋊Q8—534no—
1127C22⋊Q8—538no—
1128C22⋊Q8—534no—
1129C22⋊Q8—538no—
1130C22⋊Q8—538no—
1131C22⋊Q8—534no—
1132C22⋊Q8—534no—
1133C22⋊Q8—538no—
1134C22⋊Q8—538no—
1135C22⋊Q8—538no—
1136C22⋊Q8—538no—
1137C22⋊Q8—538no—
1138C22⋊Q8—538no—
1139C22⋊Q8—538no—
1140C22⋊Q8—538no—
1141C22⋊Q8—538no—
1142C22⋊Q8—538no—
1143C22⋊Q8—538no—
1144C22⋊Q8—538no—
1145C22⋊Q8—538no—
1146C22⋊Q8—538no—
1147C22⋊Q8—538no—
1148C22⋊Q8—538no—
1149C22⋊Q8—538no—
1150C22⋊Q8C22×D5312yes—
1151C22⋊Q8C22×D5312yes—
1152C22⋊Q8C22×D5312yes—
1153C22⋊Q8C22×D5312yes—
1154#121—534no—
1155#121—538no—
1156#121—538no—
1157#121—538no—
1158#121—532no—
1159#121—532no—
1160#121—532no—
1161#121—532no—
1162#121—534no—
1163#121—538no—
1164#121C22×D5312yes—
1165#121C22×D5312yes—
1166#121C22×D5312yes—
1167#121C22×D5312yes—
1168#120—538no—
1169#120—538no—
1170C4×Q8—534no—
1171C4×Q8—534no—
1172C4×Q8—538no—
1173C4×Q8—538no—
1174C4×Q8—538no—
1175C4×Q8—534no—
1176C4×Q8—532no—
1177C4×Q8—534no—
1178C4×Q8—534no—
1179C4×Q8—532no—
1180C4×Q8—532no—
1181C4×Q8—532no—
1182C4×Q8—534no—
1183C4×Q8—534no—
1184C4×Q8—534no—
1185C4×Q8—534no—
1186C4×Q8—534no—
1187C4×Q8—534no—
1188C4×Q8—534no—
1189C4×Q8—538no—
1190C4×Q8—534no—
1191C4×Q8—534no—
1192C4×Q8C22×D5312yes—
1193C4×Q8C22×D5312yes—
1194C4×Q8C22×D5312yes—
1195C4×Q8C22×D5312yes—
1196C4×D4—538no—
1197C4×D4—538no—
1198C4×D4—538no—
1199C4×D4—538no—
1200C4×D4—534no—
1201C4×D4—534no—
1202C4×D4—534no—
1203C4×D4—534no—
1204C4×D4—534no—
1205C4×D4—538no—
1206C4×D4—538no—
1207C4×D4—538no—
1208C4×D4—538no—
1209C4×D4—538no—
1210C4×D4—538no—
1211C4×D4—538no—
1212C4×D4—538no—
1213C4×D4—532no—
1214C4×D4—532no—
1215C4×D4—532no—
1216C4×D4—532no—
1217C4×D4—534no—
1218C4×D4C22×D5314yes—
1219C4×D4C22×D5314yes—
1220C4×D4C22×D5314yes—
1221C4×D4C22×D5314yes—
1222C4×D4C22×D5312yes—
1223C4×D4C22×D5312yes—
1224C4×D4C22×D5312yes—
1225C4×D4C22×D5312yes—
1226#117—534no—
1227#117—534no—
1228#117—534no—
1229#117—534no—
1230#117—538no—
1231#117—534no—
1232#117—534no—
1233#117—538no—
1234#117—538no—
1235#117—538no—
1236#117—538no—
1237#117—538no—
1238#117—538no—
1239#117—534no—
1240#117—534no—
1241#117—534no—
1242#117—534no—
1243#117—538no—
1244#117C22×D5314yes—
1245#117C22×D5314yes—
1246#117C22×D5314yes—
1247#117C22×D5314yes—
1248C2×C4⋊C4—532no—
1249C2×C4⋊C4—532no—
1250C2×C4⋊C4—532no—
1251C2×C4⋊C4—532no—
1252C2×C4⋊C4—531no—
1253C2×C4⋊C4—532no—
1254C2×C4⋊C4—531no—
1255C2×C4⋊C4—534no—
1256C2×C4⋊C4—534no—
1257C2×C4⋊C4—532no—
1258C2×C4⋊C4—532no—
1259C2×C4⋊C4—532no—
1260C2×C4⋊C4—538no—
1261C2×C4⋊C4—534no—
1262C2×C4⋊C4—538no—
1263C2×C4⋊C4—534no—
1264C2×C4⋊C4C22×D5312yes—
1265C2×C4⋊C4C22×D5312yes—
1266C2×C4⋊C4C22×D5312yes—
1267C2×C4⋊C4C22×D5311yescharacteristic
1268C2×C4⋊C4C22×D5311yescharacteristic
1269C2×C4⋊C4C22×D5312yes—
1270C2×C22⋊C4—534no—
1271C2×C22⋊C4—532no—
1272C2×C22⋊C4—538no—
1273C2×C22⋊C4—532no—
1274C2×C22⋊C4—532no—
1275C2×C22⋊C4—532no—
1276C2×C22⋊C4—532no—
1277C2×C22⋊C4—538no—
1278C2×C22⋊C4C22×D5312yes—
1279C2×C22⋊C4C22×D5312yes—
1280C2×C22⋊C4C22×D5312yes—
1281C2×C22⋊C4C22×D5312yes—
1282C2×C22⋊C4C22×D5312yes—
1283C2×C42—532no—
1284C2×C42—534no—
1285C2×C42C22×D5311yescharacteristic
1286C2×C42C22×D5311yescharacteristic
1287C2×C42C22×D5312yes—
1288C2×C42C22×D5311yescharacteristic
1289C2×C42C22×D5311yescharacteristic
1290C2×C42C22×D5311yescharacteristic
1291C2×C42C22×D5311yescharacteristic
1292C2×C42C22×D5311yescharacteristic
1293C2×C42C22×D5311yescharacteristic
1294C2×C42C22×D5311yescharacteristic
1295C2×C42C22×D5311yescharacteristic
1296C2×C42C22×D5311yescharacteristic
1297C2×C42C22×D5311yescharacteristic
1298C24—532no—
1299C24C23×D5312yes—
1300C24C23×D5311yescharacteristic
1301#41—2128no—
1302#41—2128no—
1303C2×Q8—42no—
1304C2×Q8—532no—
1305C2×Q8—534no—
1306C2×Q8—534no—
1307C2×Q8—538no—
1308C2×Q8—538no—
1309C2×Q8—532no—
1310C2×Q8—534no—
1311C2×Q8—534no—
1312C2×Q8—2122no—
1313C2×Q8—2124no—
1314C2×Q8—2124no—
1315C2×Q8—2128no—
1316C2×Q8—2128no—
1317C2×Q8C23×D5312yes—
1318C2×Q8C23×D5312yes—
1319C2×D4—28no—
1320C2×D4—42no—
1321C2×D4—534no—
1322C2×D4—534no—
1323C2×D4—538no—
1324C2×D4—538no—
1325C2×D4—532no—
1326C2×D4—532no—
1327C2×D4—1068no—
1328C2×D4—2122no—
1329C2×D4C23×D5314yes—
1330C2×D4C23×D5314yes—
1331C2×D4C23×D5312yes—
1332C2×D4C23×D5312yes—
1333C22×C4—24no—
1334C22×C4—42no—
1335C22×C4—44no—
1336C22×C4—42no—
1337C22×C4—532no—
1338C22×C4—532no—
1339C22×C4—534no—
1340C22×C4—534no—
1341C22×C4—532no—
1342C22×C4—538no—
1343C22×C4—538no—
1344C22×C4—534no—
1345C22×C4—538no—
1346C22×C4—538no—
1347C22×C4—534no—
1348C22×C4—2124no—
1349C22×C4C23×D5311yescharacteristic
1350C22×C4C23×D5311yescharacteristic
1351C22×C4C23×D5311yescharacteristic
1352C22×C4C23×D5311yescharacteristic
1353C22×C4C23×D5311yescharacteristic
1354C22×C4C23×D5311yescharacteristic
1355C22×C4C23×D5311yescharacteristic
1356C22×C4C23×D5311yescharacteristic
1357C22×C4C23×D5311yescharacteristic
1358C22×C4C23×D5311yescharacteristic
1359C22×C4C23×D5311yescharacteristic
1360C22×C4C23×D5311yescharacteristic
1361C22×C4C23×D5312yes—
1362C22×C4C23×D5314yes—
1363C22×C4C23×D5311yescharacteristic
1364C22×C4C23×D5311yescharacteristic
1365C22×C4C23×D5311yescharacteristic
1366C22×C4C23×D5311yescharacteristic
1367C22×C4C23×D5311yescharacteristic
1368C22×C4C23×D5311yescharacteristic
1369C22×C4C23×D5312yes—
1370C22×C4C23×D5312yes—
1371C22×C4C23×D5314yes—
1372C4⋊C4—534no—
1373C4⋊C4—532no—
1374C4⋊C4—534no—
1375C4⋊C4—534no—
1376C4⋊C4—538no—
1377C4⋊C4—538no—
1378C4⋊C4—538no—
1379C4⋊C4—538no—
1380C4⋊C4—534no—
1381C4⋊C4—532no—
1382C4⋊C4—534no—
1383C4⋊C4—534no—
1384C4⋊C4—534no—
1385C4⋊C4—534no—
1386C4⋊C4—534no—
1387C4⋊C4—534no—
1388C4⋊C4—534no—
1389C4⋊C4—532no—
1390C4⋊C4—534no—
1391C4⋊C4—534no—
1392C4⋊C4—538no—
1393C4⋊C4—538no—
1394C4⋊C4—532no—
1395C4⋊C4—538no—
1396C4⋊C4—538no—
1397C4⋊C4—534no—
1398C4⋊C4—534no—
1399C4⋊C4—534no—
1400C4⋊C4—538no—
1401C4⋊C4—538no—
1402C4⋊C4—538no—
1403C4⋊C4—538no—
1404C4⋊C4—538no—
1405C4⋊C4—538no—
1406C4⋊C4—538no—
1407C4⋊C4—538no—
1408C4⋊C4C23×D5314yes—
1409C4⋊C4C23×D5312yes—
1410C4⋊C4C23×D5314yes—
1411C4⋊C4C23×D5312yes—
1412C4⋊C4C23×D5314yes—
1413C4⋊C4C23×D5314yes—
1414C4⋊C4C23×D5314yes—
1415C4⋊C4C23×D5312yes—
1416C4⋊C4C23×D5314yes—
1417C4⋊C4C23×D5314yes—
1418C4⋊C4C23×D5312yes—
1419C4⋊C4C23×D5314yes—
1420C22⋊C4—534no—
1421C22⋊C4—538no—
1422C22⋊C4—538no—
1423C22⋊C4—534no—
1424C22⋊C4—538no—
1425C22⋊C4—538no—
1426C22⋊C4—538no—
1427C22⋊C4—538no—
1428C22⋊C4—534no—
1429C22⋊C4—534no—
1430C22⋊C4—534no—
1431C22⋊C4—534no—
1432C22⋊C4—534no—
1433C22⋊C4—534no—
1434C22⋊C4—538no—
1435C22⋊C4—538no—
1436C22⋊C4—534no—
1437C22⋊C4—534no—
1438C22⋊C4—538no—
1439C22⋊C4—538no—
1440C22⋊C4C23×D5314yes—
1441C22⋊C4C23×D5314yes—
1442C22⋊C4C23×D5314yes—
1443C22⋊C4C23×D5314yes—
1444C22⋊C4C23×D5314yes—
1445C22⋊C4C23×D5314yes—
1446C22⋊C4C23×D5314yes—
1447C22⋊C4C23×D5314yes—
1448C22⋊C4C23×D5314yes—
1449C22⋊C4C23×D5314yes—
1450C42—534no—
1451C42—538no—
1452C42—538no—
1453C42—534no—
1454C42—538no—
1455C42—538no—
1456C42—538no—
1457C42—538no—
1458C42C23×D5311yescharacteristic
1459C42C23×D5311yescharacteristic
1460C42C23×D5311yescharacteristic
1461C42C23×D5311yescharacteristic
1462C42C23×D5311yescharacteristic
1463C42C23×D5311yescharacteristic
1464C42C23×D5311yescharacteristic
1465C42C23×D5311yescharacteristic
1466C42C23×D5311yescharacteristic
1467C42C23×D5311yescharacteristic
1468C42C23×D5311yescharacteristic
1469C42C23×D5311yescharacteristic
1470C42C23×D5311yescharacteristic
1471C42C23×D5311yescharacteristic
1472C42C23×D5311yescharacteristic
1473C42C23×D5311yescharacteristic
1474C42C23×D5314yes—
1475C42C23×D5314yes—
1476C23—24no—
1477C23—41no—
1478C23—41no—
1479C23—42no—
1480C23—42no—
1481C23—534no—
1482C23—1064no—
1483C23—2122no—
1484C23—2122no—
1485C23#1313326414yes—
1486C23C24×D5314yes—
1487C23C24×D5311yescharacteristic
1488C23C24×D5311yescharacteristic
1489C23C24×D5311yescharacteristic
1490Q8—24no—
1491Q8—42no—
1492Q8—1064no—
1493Q8—1068no—
1494Q8—1068no—
1495Q8—2128no—
1496Q8—2122no—
1497Q8—2124no—
1498Q8—2124no—
1499Q8—2128no—
1500D4—28no—
1501D4—28no—
1502D4—24no—
1503D4—42no—
1504D4—1068no—
1505D4—1068no—
1506D4—1064no—
1507D4—2122no—
1508D4—2128no—
1509D4—2128no—
1510C2×C4—22no—
1511C2×C4—22no—
1512C2×C4—22no—
1513C2×C4—22no—
1514C2×C4—22no—
1515C2×C4—22no—
1516C2×C4—24no—
1517C2×C4—22no—
1518C2×C4—22no—
1519C2×C4—22no—
1520C2×C4—22no—
1521C2×C4—22no—
1522C2×C4—22no—
1523C2×C4—28no—
1524C2×C4—44no—
1525C2×C4—41no—
1526C2×C4—41no—
1527C2×C4—41no—
1528C2×C4—41no—
1529C2×C4—42no—
1530C2×C4—41no—
1531C2×C4—41no—
1532C2×C4—42no—
1533C2×C4—534no—
1534C2×C4—534no—
1535C2×C4—538no—
1536C2×C4—538no—
1537C2×C4—534no—
1538C2×C4—1064no—
1539C2×C4—1068no—
1540C2×C4—2124no—
1541C2×C4—2128no—
1542C2×C4—2128no—
1543C2×C4—2122no—
1544C2×C4—2124no—
1545C2×C4—2124no—
1546C2×C4—2128no—
1547C2×C4—2122no—
1548C2×C4—2128no—
1549C2×C4C24×D5311yescharacteristic
1550C2×C4C24×D5311yescharacteristic
1551C2×C4C24×D5311yescharacteristic
1552C2×C4C24×D5314yes—
1553C2×C4C24×D5314yes—
1554C2×C4C24×D5314yes—
1555C2×C4C24×D5311yescharacteristic
1556C2×C4C24×D5311yescharacteristic
1557C2×C4C24×D5311yescharacteristic
1558C2×C4C24×D5311yescharacteristic
1559C2×C4C24×D5311yescharacteristic
1560C2×C4C24×D5311yescharacteristic
1561C2×C4C24×D5311yescharacteristic
1562C2×C4C24×D5311yescharacteristic
1563C2×C4C24×D5311yescharacteristic
1564C22—21no—
1565C22—21no—
1566C22—21no—
1567C22—21no—
1568C22—21no—
1569C22—21no—
1570C22—24no—
1571C22—24no—
1572C22—24no—
1573C22—44no—
1574C22—84no—
1575C22—1064no—
1576C22—1064no—
1577C22—1064no—
1578C22—4244no—
1579C22C2×#1313326412yes—
1580C22C2×#1313326412yes—
1581C22C2×#1313326412yes—
1582C22C25×D5311yescharacteristic
1583C4—21no—
1584C4—21no—
1585C4—21no—
1586C4—21no—
1587C4—24no—
1588C4—21no—
1589C4—21no—
1590C4—24no—
1591C4—21no—
1592C4—21no—
1593C4—21no—
1594C4—21no—
1595C4—24no—
1596C4—1064no—
1597C4—1064no—
1598C4—1068no—
1599C4—1068no—
1600C4—1064no—
1601C4#1681145912yes—
1602C4#1681145912yes—
1603C2—22no—
1604C2—22no—
1605C2—22no—
1606C2—44no—
1607C2—2124no—
1608C2C22×#1313326411yescharacteristic
1609C2C2×#1681145911yescharacteristic
1610C2C2×#1681145911yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC2×C53×#529C2
hypercenterC2×#529D53
hypocenterC53#62823
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×#529

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20289339C2semidirect
2. #20289333C2semidirect
3. #20289321C2semidirect
4. #20289318C2semidirect
5. #20289287C2semidirect
6. #20289285C2semidirect
7. #20289168C2semidirect
8. #20289160C2semidirect
9. #20289152C2semidirect
10. #20288811C2semidirect
11. #20288809C2semidirect
12. #20288766C2semidirect
13. #20288764C2semidirect
14. #20288704C2semidirect
15. #20288698C2semidirect
16. #20288554C2semidirect
17. #20288549C2semidirect
18. #20288518C2semidirect
19. #20288511C2semidirect
20. #20288467C2semidirect
21. #20288455C2semidirect
22. #20288411C2semidirect
23. C2×#16811180C2semidirect
24. C2×#16811157C2semidirect
25. C2×C53×#529C2semidirect
26. C53⋊#564C22semidirect
27. #16811377C22semidirect
28. #16811375C22semidirect
29. #16811375C22semidirect
30. #16811373C22semidirect
31. #16811367C22semidirect
32. #16811352C22semidirect
33. #16811351C22semidirect
34. #16811351C22semidirect
35. #16811350C22semidirect
36. #16811346C22semidirect
37. #16811346C22semidirect
38. #16811343C22semidirect
39. #16811342C22semidirect
40. #16811341C22semidirect
41. #16811340C22semidirect
42. #16811332C22semidirect
43. #16811332C22semidirect
44. #16811331C22semidirect
45. #16811330C22semidirect
46. #16811330C22semidirect
47. #16811328C22semidirect
48. #16811328C22semidirect
49. #16811327C22semidirect
50. #16811325C22semidirect
51. #16811322C22semidirect
52. #16811319C22semidirect
53. #16811316C22semidirect
54. #16811313C22semidirect
55. #16811313C22semidirect
56. #16811312C22semidirect
57. #16811311C22semidirect
58. #16811310C22semidirect
59. #16811310C22semidirect
60. #16811309C22semidirect
61. #16811308C22semidirect
62. #16811308C22semidirect
63. #16811308C22semidirect
64. #16811306C22semidirect
65. #16811306C22semidirect
66. #16811302C22semidirect
67. #16811299C22semidirect
68. #16811299C22semidirect
69. #16811299C22semidirect
70. #16811296C22semidirect
71. #16811296C22semidirect
72. Q8×D212C22semidirect
73. D4×Dic106C22semidirect
74. D4×Dic106C22semidirect
75. D4×Dic106C22semidirect
76. Q8×C22⋊D53C22semidirect
77. #16811286C22semidirect
78. #16811282C22semidirect
79. #16811282C22semidirect
80. #16811281C22semidirect
81. #16811279C22semidirect
82. #16811278C22semidirect
83. #16811277C22semidirect
84. #16811269C22semidirect
85. #16811267C22semidirect
86. #16811254C22semidirect
87. #16811253C22semidirect
88. #16811252C22semidirect
89. #16811251C22semidirect
91. #16811249C22semidirect
92. #16811248C22semidirect
93. #16811244C22semidirect
94. #16811244C22semidirect
95. #16811242C22semidirect
96. #16811239C22semidirect
97. #16811238C22semidirect
98. #16811237C22semidirect
99. #16811236C22semidirect
100. #16811235C22semidirect
101. #16811235C22semidirect
102. #16811232C22semidirect
103. #16811231C22semidirect
104. #16811231C22semidirect
105. #16811230C22semidirect
106. #16811230C22semidirect
109. #16811217C22semidirect
110. #16811217C22semidirect
111. #16811215C22semidirect
112. #16811214C22semidirect
115. #16811199C22semidirect
116. #16811193C22semidirect
118. #16811180C22semidirect
119. #16811180C22semidirect
120. #16811180C22semidirect
121. #16811180C22semidirect
122. #16811180C22semidirect
123. #16811180C22semidirect
124. #16811180C22semidirect
125. #16811180C22semidirect
126. #16811180C22semidirect
127. #16811175C22semidirect
128. C2×#13133217C22semidirect
129. C2×#13133217C22semidirect
135. #16811157C22semidirect
136. #16811157C22semidirect
137. #16811157C22semidirect
138. #16811157C22semidirect
140. #16811150C22semidirect
141. #16811150C22semidirect
142. C2×#13133211C22semidirect
143. C2×#13133209C22semidirect
144. C2×#13133209C22semidirect
145. C2×#13133205C22semidirect
152. C2×#13133196C22semidirect
153. C22⋊Q8×D53C22semidirect
155. #16811103C22semidirect
156. #16811102C22semidirect
157. #16811100C22semidirect
158. #16811099C22semidirect
161. C2×C4×Dic106C22semidirect
162. C2×C4×Dic106C22semidirect
163. C2×C4×Dic106C22semidirect
164. C2×C4×D212C22semidirect
167. C2×#13133174C22semidirect
172. C53×#529C22semidirect
173. C53×#529C22semidirect
174. C53×#529C22semidirect
175. C53×#529C22semidirect
176. C2×#126×C53C22semidirect
177. C2×#125×C53C22semidirect
178. C2×#124×C53C22semidirect
182. C2×C4×Q8×C53C22semidirect
184. C2×C4×D4×C53C22semidirect
185. C2×#117×C53C22semidirect
822. C2×#529D53semidirect
951. #529C2×D53semidirect
952. #529C2×D53semidirect
953. #529C2×D53semidirect
954. #529C2×D53semidirect
956. C2×#126C2×D53semidirect
959. C2×#125C2×D53semidirect
961. C2×#124C2×D53semidirect
983. C2×C4×Q8C2×D53semidirect
987. C2×C4×D4C2×D53semidirect
990. C2×#117C2×D53semidirect
992. C53#62823semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202893392
#202893332
#202893212
#202893182
#202892872
#202892852
#202891682
#202891602
#202891522
#202888112
#202888092
#202887662
#202887642
#202887042
#202886982
#202885542
#202885492
#202885182
#202885112
#202884672
#202884552
#202884112
C2×#168111802
C2×#168111572
C2×C53×#5292
#6282353