Finite Group Databasebeta

← #28293118

Subgroups — #28293118

Order 13568.

7102 conjugacy classes of subgroups.

The subgroup lattice has 1574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288582C211yesmaximal, characteristic, complemented
2#20288577C211yesmaximal, characteristic, complemented
3#20288576C214yesmaximal, complemented
4#20288573C212yesmaximal, complemented
5#20288572C214yesmaximal, complemented
6#20288567C211yesmaximal, characteristic, complemented
7#20288566C212yesmaximal, complemented
8#20288563C214yesmaximal, complemented
9#20288559C214yesmaximal, complemented
10#20288431C214yesmaximal, complemented
11#20288430C214yesmaximal, complemented
12#20288426C214yesmaximal, complemented
13#20288419C214yesmaximal, complemented
14#20288417C214yesmaximal, complemented
15#20288416C214yesmaximal, complemented
16#20288126C214yesmaximal, complemented
17#20288122C214yesmaximal, complemented
18#20288118C211yesmaximal, characteristic, complemented
19#20288046C212yesmaximal, complemented
20#20288042C211yesmaximal, characteristic, complemented
21C2×#16811102C211yesmaximal, characteristic, complemented
22#520×D53C212yesmaximal, complemented
23C53×#3506C211yesmaximal, characteristic, complemented
24C22×#11719947C2211yescharacteristic
25C2×#41×D53C2212yes—
26#16811359C2212yescomplemented
27#16811359C2214yescomplemented
28#16811358C2212yescomplemented
29#16811356C2214yescomplemented
30#16811356C2214yescomplemented
31#16811355C2214yescomplemented
32#16811352C2212yescomplemented
33#16811351C2214yescomplemented
34#16811348C2212yescomplemented
35#16811347C2212yescomplemented
36#16811346C2214yescomplemented
37#16811345C2214yescomplemented
38#16811343C2214yescomplemented
39#16811343C2212yescomplemented
40#16811343C2212yescomplemented
41#16811342C2214yescomplemented
42#16811342C2214yescomplemented
43#16811342C2218yescomplemented
44#16811341C2214yescomplemented
45#16811340C2218yescomplemented
46#16811338C2212yescomplemented
47#16811337C2218yescomplemented
48#16811337C2214yescomplemented
49#16811335C2218yescomplemented
50#16811334C2212yescomplemented
51#16811332C2218yescomplemented
52#16811330C2212yescomplemented
53#16811328C2214yescomplemented
54#16811327C2218yescomplemented
55#16811325C2214yescomplemented
56#16811323C2214yescomplemented
57#16811322C2218yescomplemented
58#16811320C2214yescomplemented
59#16811318C2218yescomplemented
60#16811316C2218yescomplemented
61#16811316C2218yescomplemented
62#16811313C2214yescomplemented
63#16811312C2214yescomplemented
64#16811311C2214yescomplemented
65#16811310C2218yescomplemented
66#16811310C2218yescomplemented
67#16811309C2218yescomplemented
68#16811308C2214yescomplemented
69#16811306C2218yescomplemented
70#16811294C2212yescomplemented
71#16811293C2214yescomplemented
72#16811278C2212yescomplemented
73#16811273C2214yescomplemented
74#16811272C2218yescomplemented
75#16811271C2218yescomplemented
76#16811253C2212yescomplemented
77#16811253C2212yescomplemented
78#16811252C2212yescomplemented
79#16811252C2212yescomplemented
80#16811250C2212yescomplemented
81#16811250C2212yescomplemented
82#16811248C2212yes—
83#16811248C2212yes—
84#16811222C2214yescomplemented
85#16811219C2218yescomplemented
86#16811218C2214yescomplemented
87#16811216C2218yescomplemented
88#16811216C2218yescomplemented
89#16811215C2218yescomplemented
90#16811214C2218yescomplemented
91#16811211C2214yescomplemented
92#16811209C2218yescomplemented
93#16811208C2218yescomplemented
94#16811207C2218yescomplemented
95#16811205C2218yescomplemented
96#16811205C2218yescomplemented
97#16811202C2214yes—
98#16811202C2214yes—
99#16811200C2212yes—
100#16811200C2212yes—
101#16811199C2212yescomplemented
102#16811198C2212yescomplemented
103#16811194C2212yescomplemented
104#16811193C2212yescomplemented
105#16811193C2214yescomplemented
106#16811191C2212yescomplemented
107#16811190C2212yescomplemented
108#16811186C2212yescomplemented
109#16811186C2214yescomplemented
110#16811183C2218yes—
111#16811181C2212yes—
112#16811181C2212yes—
113#16811180C2211yescharacteristic, complemented
114#16811177C2214yescomplemented
115#16811177C2214yescomplemented
116#16811176C2212yescomplemented
117#16811173C2211yescharacteristic
118#16811172C2214yes—
119#16811171C2214yes—
120#16811169C2212yes—
121#16811159C2214yescomplemented
122#16811156C2218yescomplemented
123#16811155C2218yescomplemented
124#16811154C2214yescomplemented
125#16811153C2218yescomplemented
126#16811152C2218yescomplemented
127#16811151C2218yescomplemented
128#16811134C2214yescomplemented
129#16811133C2214yescomplemented
130#16811133C2214yescomplemented
131#16811133C2218yescomplemented
132#16811132C2214yescomplemented
133#16811132C2214yescomplemented
134#16811132C2218yescomplemented
135#16811131C2218yescomplemented
136#16811130C2218yescomplemented
137#16811129C2218yescomplemented
138#16811129C2218yescomplemented
139#16811106C2212yescomplemented
140#16811105C2214yescomplemented
141#16811104C2212yescomplemented
142#16811104C2214yescomplemented
143#16811103C2212yescomplemented
144#16811103C2214yescomplemented
145#16811102C2214yescomplemented
146#16811102C2214yescomplemented
147#16811102C2214yescomplemented
148#16811102C2218yescomplemented
149#16811102C2214yescomplemented
150#16811102C2214yescomplemented
151C2×C4×Dic106C2211yescharacteristic, complemented
152C2×#13133182C2211yescharacteristic, complemented
153C4×Q8×D53C2214yescomplemented
154C2×D4×Dic53C2211yescharacteristic, complemented
155C2×C4×C22⋊D53C2212yes—
156C2×#13133177C2212yes—
157C4×D4×D53C2218yes—
158C4×D4×D53C2214yescomplemented
159C2×#13133174C2211yescharacteristic
160C2×#13133173C2212yescomplemented
161#117×D53C2212yes—
162#117×D53C2214yescomplemented
163C22×#11719919C2212yescomplemented
164C2×C4⋊C4×D53C2211yescharacteristic
165C2×C4⋊C4×D53C2214yescomplemented
166C53×#559C2214yescomplemented
167C53×#556C2212yescomplemented
168C53×#555C2212yescomplemented
169C53×#553C2214yescomplemented
170C53×#550C2212yescomplemented
171C53×#547C2212yescomplemented
172C53×#538C2214yescomplemented
173C53×#535C2212yescomplemented
174C53×#533C2211yescharacteristic, complemented
175C53×#532C2211yescharacteristic
176C53×#525C2214yescomplemented
177C53×#520C2212yescomplemented
178C2×C4×D4×C53C2211yescharacteristic, complemented
179C2×#11719949C2312yes—
180C2×#11719945C2314yes—
181C2×#11719945C2312yes—
182C2×#11719945C2314yes—
183C2×#11719947—28no—
184C2×#11719947C2314yes—
185C2×#11719947C2314yes—
186C2×#11719947C2312yes—
187C2×#11719947C2314yes—
188C2×#11719947C2318yes—
189#41×D53—216no—
190C22×Dic106C2311yescharacteristic
191C2×Q8×D53C2312yes—
192C22×C22⋊D53C2312yes—
193C2×D4×D53C2314yes—
194C2×D4×D53C2312yes—
195C23×Dic53C2312yes—
196C23×Dic53C2312yes—
197C22×C4×D53C2314yes—
198C22×C4×D53C2312yes—
199C22×C4×D53C2318yes—
200C22×C4×D53C2311yescharacteristic
201#13133217C2311yescharacteristic
202#13133217C2311yescharacteristic
203#13133217C2311yescharacteristic
204#13133217C2314yes—
205#13133216C2314yes—
206#13133216C2312yes—
207#13133216C2314yes—
208#13133216C2312yes—
209#13133215C2314yes—
210#13133215C2314yes—
211#13133215C2312yes—
212#13133215C2314yes—
213#13133214C2311yescharacteristic
214#13133213C2312yes—
215#13133213C2314yes—
216#13133212C2318yes—
217#13133212C2318yes—
218#13133212C2318yes—
219#13133211C2318yes—
220#13133210C2318yes—
221#13133210C2318yes—
222#13133210C2318yes—
223#13133210C2318yes—
224#13133210C2318yes—
225#13133210C2318yes—
226#13133210C2318yes—
227#13133209C2318yes—
228#13133209C2312yes—
229#13133208C2312yes—
230#13133208C2314yes—
231#13133208C2314yes—
232#13133208C2318yes—
233#13133208C2312yes—
234#13133207C2314yes—
235#13133207C2318yes—
236#13133207C2318yes—
237#13133207C2314yes—
238#13133207C2318yes—
239#13133207C2314yes—
240#13133207C2314yes—
241#13133206C2314yes—
242#13133206C2312yes—
243#13133205C2314yes—
244#13133205C2312yes—
245#13133204C2318yes—
246#13133204C2314yes—
247#13133204C2314yes—
248#13133204C2314yes—
249#13133204C2312yes—
250#13133203C2318yes—
251#13133203C2318yes—
252#13133203C2318yes—
253#13133202C2318yes—
254#13133202C2314yes—
255#13133202C2314yes—
256#13133201C2318yes—
257#13133201C2318yes—
258#13133200C2318yes—
259#13133200C2318yes—
260#13133199C2318yes—
261#13133199C2318yes—
262#13133199C2318yes—
263#13133199C2314yes—
264#13133199C2314yes—
265#13133199C2318yes—
266#13133199C2318yes—
267#13133198C2318yes—
268#13133198C2318yes—
269#13133198C2318yes—
270#13133198C2318yes—
271#13133197C2314yes—
272#13133197C2314yes—
273#13133197C2314yes—
274#13133197C2314yes—
275#13133196C2318yes—
276#13133196C2314yes—
277#13133196C2314yes—
278#13133196C2314yes—
279#13133196C2312yes—
280#13133196C2312yes—
281#13133195C2318yes—
282#13133195C2314yes—
283#13133195C2314yes—
284#13133195C2314yes—
285#13133195C2314yes—
286#13133195C2314yes—
287#13133195C2314yes—
288#13133194C2318yes—
289#13133194C2318yes—
290#13133194C2318yes—
291#13133194C2318yes—
292#13133194C2314yes—
293#13133194C2314yes—
294#13133194C2314yes—
295#13133194C2314yes—
296#13133193C2318yes—
297#13133193C2314yes—
298#13133193C2314yes—
299#13133191C2314yes—
300#13133191C2312yes—
301#13133191C2312yes—
302#13133190C2314yes—
303#13133190C2318yes—
304#13133190C2314yes—
305#13133190C2318yes—
306#13133190C2318yes—
307#13133189C2318yes—
308#13133189C2314yes—
309#13133189C2318yes—
310#13133189C2318yes—
311#13133189C2314yes—
312#13133189C2318yes—
313#13133189C2314yes—
314#13133189C2314yes—
315#13133188C2314yes—
316#13133188C2318yes—
317#13133188C2314yes—
318#13133188C2318yes—
319#13133188C2318yes—
320#13133187C2314yes—
321#13133187C2314yes—
322#13133186C2318yes—
323#13133185C2314yes—
324#13133185C2318yes—
325#13133185C2314yes—
326#13133185C2318yes—
327Q8×Dic53C2314yes—
328Q8×Dic53C2314yes—
329C4×Dic106C2314yes—
330C4×Dic106C2312yes—
331C4×Dic106C2318yes—
332C4×Dic106C2312yes—
333C4×Dic106C2312yes—
334C4×Dic106C2318yes—
335C4×Dic106C2314yes—
336C4×Dic106C2312yes—
337C4×Dic106C2312yes—
338C4×Dic106C2312yes—
339C4×Dic106C2314yes—
340#13133182C2314yes—
341#13133182C2318yes—
342#13133182C2314yes—
343#13133182C2314yes—
344#13133182C2314yes—
345C4×D212C2312yes—
346C4×D212C2314yes—
347C4×D212C2312yes—
348C4×D212C2318yes—
349D4×Dic53C2318yes—
350D4×Dic53C2314yes—
351D4×Dic53C2314yes—
352D4×Dic53C2314yes—
353D4×Dic53C2314yes—
354D4×Dic53C2318yes—
355D4×Dic53C2318yes—
356D4×Dic53C2318yes—
357#13133179C2314yes—
358#13133179C2314yes—
359#13133179C2318yes—
360C4×C22⋊D53C2318yes—
361C4×C22⋊D53C2314yes—
362C4×C22⋊D53C2318yes—
363C4×C22⋊D53C2318yes—
364C4×C22⋊D53C2314yes—
365C4×C22⋊D53C2318yes—
366C4×C22⋊D53C2318yes—
367C4×C22⋊D53C2318yes—
368C4×C22⋊D53C2318yes—
369#13133177C2318yes—
370#13133177C2318yes—
371#13133177C2318yes—
372#13133177C2318yes—
373#13133177C2318yes—
374#13133177C2318yes—
375#13133177C2318yes—
376#13133177C2318yes—
377#13133176C2318yes—
378#13133176C2314yes—
379#13133176C2314yes—
380#13133176C2312yes—
381#13133175C2314yes—
382#13133175C2318yes—
383#13133175C2314yes—
384#13133175C2312yes—
385#13133175C2312yes—
386#13133174C2318yes—
387#13133174C2318yes—
388#13133174C2314yes—
389#13133174C2312yes—
390#13133174C2312yes—
391#13133174C2312yes—
392#13133174C2312yes—
393#13133173C2318yes—
394#13133173C2318yes—
395#13133173C2318yes—
396#13133173C2318yes—
397#13133173C2318yes—
398#13133173C2314yes—
399C2×C4⋊Dic53C2314yes—
400C2×C4⋊Dic53C2311yescharacteristic
401C2×#11719919C2318yes—
402C2×#11719919C2318yes—
403C2×#11719919C2318yes—
404C2×#11719919C2312yes—
405C2×#11719919C2311yescharacteristic
406C2×#11719919C2312yes—
407C2×#11719919C2312yes—
408C2×#11719919C2311yescharacteristic
409C4⋊C4×D53C2318yes—
410C4⋊C4×D53C2314yes—
411C4⋊C4×D53C2314yes—
412C4⋊C4×D53C2314yes—
413C4⋊C4×D53C2314yes—
414C4⋊C4×D53C2312yes—
415C4⋊C4×D53C2318yes—
416C4⋊C4×D53C2312yes—
417C2×C22⋊Dic53C2312yes—
418C2×#11719921C2311yescharacteristic
419C2×#11719921C2311yescharacteristic
420C22⋊C4×D53C2314yes—
421C22⋊C4×D53C2318yes—
422C2×C4×Dic53C2312yes—
423C2×C4×Dic53C2312yes—
424C2×C4×Dic53C2311yescharacteristic
425C42×D53C2314yes—
426C42×D53C2318yes—
427C2×#41×C53C2312yes—
428C2×#41×C53C2314yes—
429C22×D4×C53C2311yescharacteristic
430C23×C4×C53C2312yes—
431C4⋊Q8×C53C2311yescharacteristic
432C4⋊Q8×C53C2311yescharacteristic
433C4⋊Q8×C53C2311yescharacteristic
434#127×C53C2314yes—
435#127×C53C2311yescharacteristic
436#126×C53C2318yes—
437#125×C53C2312yes—
438#124×C53C2312yes—
439#124×C53C2314yes—
440#124×C53C2318yes—
441#123×C53C2318yes—
442#123×C53C2318yes—
443C22⋊Q8×C53C2312yes—
444C22⋊Q8×C53C2314yes—
445C22⋊Q8×C53C2312yes—
446#121×C53C2314yes—
447#121×C53C2312yes—
448#121×C53C2314yes—
449#121×C53C2312yes—
450#121×C53C2314yes—
451#121×C53C2318yes—
452#120×C53C2318yes—
453C4×Q8×C53C2314yes—
454C4×Q8×C53C2312yes—
455C4×Q8×C53C2312yes—
456C4×D4×C53C2312yes—
457C4×D4×C53C2312yes—
458C4×D4×C53C2312yes—
459C4×D4×C53C2312yes—
460C4×D4×C53C2318yes—
461C4×D4×C53C2314yes—
462C4×D4×C53C2318yes—
463C4×D4×C53C2312yes—
464C4×D4×C53C2312yes—
465#117×C53C2312yes—
466#117×C53C2314yes—
467#117×C53C2314yes—
468C2×C4⋊C4×C53C2311yescharacteristic
469C2×C4⋊C4×C53C2314yes—
470C2×C22⋊C4×C53C2312yes—
471C2×C42×C53C2311yescharacteristic
472C24×C53C2412yes—
473C23×D53C2414yes—
474C23×D53C2411yescharacteristic
475#41×C53—28no—
476#41×C53—84no—
477C2×Q8×C53C2412yes—
478C2×Q8×C53C2412yes—
479C2×Q8×C53C2412yes—
480C2×D4×C53—24no—
481C2×D4×C53C2414yes—
482C2×D4×C53C2412yes—
483C2×D4×C53C2412yes—
484C2×D4×C53C2412yes—
485C2×D4×C53C2418yes—
486C2×D4×C53C2412yes—
487C2×D4×C53C2412yes—
488C2×D4×C53C2418yes—
489C22×C4×C53—82no—
490C22×C4×C53C2414yes—
491C22×C4×C53C2411yescharacteristic
492C22×C4×C53C2411yescharacteristic
493C22×C4×C53C2412yes—
494C22×C4×C53C2418yes—
495C22×C4×C53C2414yes—
496C22×C4×C53C2414yes—
497C22×C4×C53C2411yescharacteristic
498C2×C22⋊D53—28no—
499C2×C22⋊D53C2414yes—
500C2×C22⋊D53C2418yes—
501C2×C22⋊D53C2414yes—
502C2×C22⋊D53C2414yes—
503C2×C22⋊D53C2418yes—
504C2×C22⋊D53C2418yes—
505C2×C22⋊D53C2414yes—
506C2×C22⋊D53C2414yes—
507C22×Dic53—28no—
508C22×Dic53—82no—
509C22×Dic53C2412yes—
510C22×Dic53C2418yes—
511C22×Dic53C2414yes—
512C22×Dic53C2411yescharacteristic
513C22×Dic53C2411yescharacteristic
514C22×Dic53C2412yes—
515C22×Dic53C2418yes—
516C22×Dic53C2418yes—
517C22×Dic53C2411yescharacteristic
518#11719949—28no—
519Q8×D53—28no—
520#11719947—216no—
521#11719947—28no—
522#11719947—216no—
523#11719947—216no—
524#11719947—88no—
525D4×D53—216no—
526D4×D53—28no—
527#11719945—28no—
528#11719945—216no—
529#11719945—84no—
530C2×D212C2414yes—
531C2×D212C2412yes—
532C2×D212C2412yes—
533C2×D212C2412yes—
534C2×C4×D53—216no—
535C2×C4×D53—82no—
536C2×C4×D53—88no—
537C2×C4×D53#4118yescomplemented
538C2×C4×D53C2414yes—
539C2×C4×D53C2414yes—
540C2×C4×D53C2414yes—
541C2×C4×D53C2414yes—
542C2×C4×D53C2418yes—
543C2×C4×D53C2414yes—
544C2×C4×D53C2418yes—
545C2×C4×D53C2418yes—
546C2×C4×D53C2412yes—
547C2×C4×D53C2412yes—
548C2×Dic106—24no—
549C2×Dic106C2414yes—
550C2×Dic106C2412yes—
551C2×Dic106C2412yes—
552C2×Dic106C2412yes—
553C2×Dic106C2412yes—
554C2×Dic106C2414yes—
555C2×Dic106C2412yes—
556C2×Dic106C2414yes—
557C4⋊C4×C53C2412yes—
558C4⋊C4×C53C2412yes—
559C4⋊C4×C53C2412yes—
560C4⋊C4×C53C2418yes—
561C4⋊C4×C53C2412yes—
562C4⋊C4×C53C2412yes—
563C4⋊C4×C53C2412yes—
564C4⋊C4×C53C2414yes—
565C4⋊C4×C53C2412yes—
566C4⋊C4×C53C2414yes—
567C4⋊C4×C53C2412yes—
568C22⋊C4×C53C2414yes—
569C22⋊C4×C53C2414yes—
570C22⋊C4×C53C2414yes—
571C22⋊C4×C53C2418yes—
572C22⋊C4×C53C2418yes—
573C22⋊C4×C53C2414yes—
574C22⋊C4×C53C2418yes—
575C22⋊C4×C53C2414yes—
576C42×C53C2411yescharacteristic
577C42×C53C2411yescharacteristic
578C42×C53C2411yescharacteristic
579C42×C53C2411yescharacteristic
580C42×C53C2418yes—
581C42×C53C2414yes—
582C22⋊Dic53C2414yes—
583C22⋊Dic53C2418yes—
584C22⋊Dic53C2418yes—
585C22⋊Dic53C2418yes—
586C22⋊Dic53C2418yes—
587C22⋊Dic53C2414yes—
588C22⋊Dic53C2418yes—
589C22⋊Dic53C2414yes—
590C22⋊Dic53C2418yes—
591#11719921C2414yes—
592#11719921C2418yes—
593#11719921C2414yes—
594#11719921C2418yes—
595#11719921C2412yes—
596#11719921C2412yes—
597#11719921C2412yes—
598#11719921C2412yes—
599#11719921C2414yes—
600#11719921C2418yes—
601#11719921C2414yes—
602#11719921C2414yes—
603#11719921C2418yes—
604#11719921C2414yes—
605C4⋊Dic53C2412yes—
606C4⋊Dic53C2412yes—
607C4⋊Dic53C2412yes—
608C4⋊Dic53C2418yes—
609C4⋊Dic53C2412yes—
610C4⋊Dic53C2418yes—
611C4⋊Dic53C2412yes—
612C4⋊Dic53C2414yes—
613C4⋊Dic53C2412yes—
614C4⋊Dic53C2414yes—
615C4⋊Dic53C2412yes—
616C4⋊Dic53C2418yes—
617C4⋊Dic53C2412yes—
618#11719919C2418yes—
619#11719919C2414yes—
620#11719919C2418yes—
621#11719919C2418yes—
622#11719919C2414yes—
623#11719919C2412yes—
624#11719919C2412yes—
625#11719919C2418yes—
626#11719919C2414yes—
627#11719919C2414yes—
628#11719919C2412yes—
629#11719919C2412yes—
630#11719919C2414yes—
631#11719919C2414yes—
632#11719919C2414yes—
633#11719919C2418yes—
634#11719919C2414yes—
635#11719919C2414yes—
636#11719919C2418yes—
637#11719919C2414yes—
638#11719919C2414yes—
639#11719919C2414yes—
640C4×Dic53C2418yes—
641C4×Dic53C2418yes—
642C4×Dic53C2418yes—
643C4×Dic53C2414yes—
644C4×Dic53C2414yes—
645C4×Dic53C2414yes—
646C4×Dic53C2414yes—
647C4×Dic53C2418yes—
648C4×Dic53C2414yes—
649C4×Dic53C2412yes—
650C4×Dic53C2412yes—
651C23×C53—24no—
652C23×C53—42no—
653C23×C53—42no—
654C23×C53C2514yes—
655C23×C53C2514yes—
656C23×C53C2511yescharacteristic
657C22×D53—28no—
658C22×D53—41no—
659C22×D53—44no—
660C22×D53—41no—
661C22×D53—44no—
662C22×D53C2×#4114yes—
663C22×D53C2514yes—
664C22×D53C2512yes—
665Q8×C53—24no—
666Q8×C53—42no—
667Q8×C53—42no—
668D4×C53—28no—
669D4×C53—24no—
670D4×C53—24no—
671D4×C53—24no—
672D4×C53—48no—
673D4×C53—42no—
674D4×C53—48no—
675D4×C53—42no—
676C2×C4×C53—28no—
677C2×C4×C53—42no—
678C2×C4×C53—48no—
679C2×C4×C53—44no—
680C2×C4×C53—41no—
681C2×C4×C53—44no—
682C2×C4×C53—41no—
683C2×C4×C53C2×#4114yes—
684C2×C4×C53C2511yescharacteristic
685C2×C4×C53C2511yescharacteristic
686C2×C4×C53C2514yes—
687C2×C4×C53C2514yes—
688C2×C4×C53C2514yes—
689C2×C4×C53C2514yes—
690C2×C4×C53C2511yescharacteristic
691C2×C4×C53C2511yescharacteristic
692C2×C4×C53C2511yescharacteristic
693C2×C4×C53C2511yescharacteristic
694C22⋊D53—28no—
695C22⋊D53—28no—
696C22⋊D53—216no—
697C22⋊D53—28no—
698C22⋊D53—48no—
699C22⋊D53—44no—
700C22⋊D53—48no—
701C22⋊D53—44no—
702C2×Dic53—24no—
703C2×Dic53—28no—
704C2×Dic53—216no—
705C2×Dic53—48no—
706C2×Dic53—42no—
707C2×Dic53—48no—
708C2×Dic53—41no—
709C2×Dic53—41no—
710C2×Dic53C2×#4114yes—
711C2×Dic53C2514yes—
712C2×Dic53C2514yes—
713C2×Dic53C2514yes—
714C2×Dic53C2512yes—
715C2×Dic53C2514yes—
716C2×Dic53C2512yes—
717C2×Dic53C2514yes—
718C2×Dic53C2512yes—
719D212—28no—
720D212—24no—
721D212—42no—
722D212—42no—
723C4×D53—28no—
724C4×D53—28no—
725C4×D53—28no—
726C4×D53—44no—
727C4×D53—48no—
728C4×D53—48no—
729C4×D53—48no—
730C4×D53—44no—
731C4×D53C2×#4118yes—
732C4×D53C2×#4118yes—
733Dic106—24no—
734Dic106—24no—
735Dic106—24no—
736Dic106—28no—
737Dic106—42no—
738Dic106—44no—
739Dic106—42no—
740Dic106—44no—
741#62845—531nomaximal, Sylow
742C22×C53—21no—
743C22×C53—21no—
744C22×C53—24no—
745C22×C53—24no—
746C22×C53—24no—
747C22×C53—24no—
748C22×C53—24no—
749C22×C53—24no—
750C22×C53—48no—
751C22×C53C22×#4112yes—
752C22×C53C2611yescharacteristic
753C2×D53—22no—
754C2×D53—22no—
755C2×D53—24no—
756C2×D53—24no—
757C2×D53—24no—
758C2×D53—44no—
759C2×D53—416no—
760C2×D53C22×#4114yes—
761C4×C53—24no—
762C4×C53—21no—
763C4×C53—24no—
764C4×C53—24no—
765C4×C53—21no—
766C4×C53—21no—
767C4×C53—24no—
768C4×C53—21no—
769C4×C53C22×#4112yes—
770C4×C53C22×#4112yes—
771Dic53—24no—
772Dic53—24no—
773Dic53—24no—
774Dic53—22no—
775Dic53—24no—
776Dic53—24no—
777Dic53—22no—
778Dic53C22×#4114yes—
779#3507—534no—
780#3507—534no—
781#3507—531no—
782#3507—531no—
783#3507—532no—
784#3506—534no—
785#3506—534no—
786#3506—532no—
787#3506—531no—
788#3506D5311yescharacteristic, complemented
789#3493—534no—
790#3493—534no—
791#3493—534no—
792#3492—534no—
793#3492—534no—
794#3492—534no—
795#3459—534no—
796#3459—534no—
797#3458—531no—
798#3449—532no—
799#3449—531no—
800C2×#520—532no—
801C2×#520—531no—
802C2×C53—22no—
803C2×C53—44no—
804C2×C53—44no—
805C2×C53C23×#4111yescharacteristic
806C2×C53H(7,𝔽2)11yescharacteristic
807C2×C532−1+611yescharacteristic
808D53—24no—
809D53—44no—
810C22×#41—532no—
811C22×#41—531no—
812#559—534no—
813#559—532no—
814#559—534no—
815#559—532no—
816#559—534no—
817#559—534no—
818#559C2×D5314yescomplemented
819#557—532no—
820#557—534no—
821#557—532no—
822#556—532no—
823#556—538no—
824#556—538no—
825#556—534no—
826#556—534no—
827#556—534no—
828#556—534no—
829#556—532no—
830#556—534no—
831#556—532no—
832#556—534no—
833#556C2×D5312yescomplemented
834#555—538no—
835#555—534no—
836#555—538no—
837#555—532no—
838#555C2×D5312yescomplemented
839#554—532no—
840#554—538no—
841#554—532no—
842#554—538no—
843#554—534no—
844#553—538no—
845#553—538no—
846#553—538no—
847#553—534no—
848#553—534no—
849#553—538no—
850#553—534no—
851#553C2×D5314yescomplemented
852#552—538no—
853#552—534no—
854#552—538no—
855#552—538no—
856#552—534no—
857#552—538no—
858#552—534no—
859#552—534no—
860#550—534no—
861#550—532no—
862#550C2×D5312yescomplemented
863#547—538no—
864#547—538no—
865#547—534no—
866#547—532no—
867#547C2×D5312yescomplemented
868#544—532no—
869#544—532no—
870#544—532no—
871#544—532no—
872#544—532no—
873#544—532no—
874#543—532no—
875#543—532no—
876#539—538no—
877#539—538no—
878#539—538no—
879#539—538no—
880#539—534no—
881#539—534no—
882#539—538no—
883#538—538no—
884#538—538no—
885#538—538no—
886#538—538no—
887#538—538no—
888#538—534no—
889#538C2×D5314yescomplemented
890#537—532no—
891#537—534no—
892#537—532no—
893#537—534no—
894#536—532no—
895#536—532no—
896#536—534no—
897#536—532no—
898#536—532no—
899#535—532no—
900#535—534no—
901#535—532no—
902#535—532no—
903#535C2×D5312yescomplemented
904#534—532no—
905#534—532no—
906#534—538no—
907#533—534no—
908#533—534no—
909#533—532no—
910#533—531no—
911#533C2×D5311yescharacteristic, complemented
912#532—532no—
913#532—534no—
914#532—534no—
915#532—531no—
916#532C2×D5311yescharacteristic
917#529—538no—
918#529—538no—
919#529—534no—
920#529—534no—
921#529—538no—
922#529—538no—
923#529—538no—
924#525—538no—
925#525—534no—
926#525—538no—
927#525—534no—
928#525—534no—
929#525—538no—
930#525—538no—
931#525—538no—
932#525—534no—
933#525—534no—
934#525—538no—
935#525C2×D5314yescomplemented
936#520—532no—
937#520—534no—
938#520—538no—
939#520—534no—
940#520—534no—
941#520—534no—
942#520—534no—
943#520—534no—
944#520—534no—
945#520—532no—
946#520—534no—
947#520—532no—
948#520C2×D5312yescomplemented
949C2×C4×Q8—534no—
950C2×C4×Q8—531no—
951C2×C4×Q8—531no—
952C2×C4×D4—531no—
953C2×C4×D4—532no—
954C2×C4×D4—538no—
955C2×C4×D4—534no—
956C2×C4×D4—532no—
957C2×C4×D4C2×D5311yescharacteristic, complemented
958C2×#117—532no—
959C2×#117—534no—
960C2×#117—532no—
961C2×#117—531no—
962C22×C4⋊C4—532no—
963C22×C4⋊C4—531no—
964C22×C4⋊C4—534no—
965C53#6284511yescharacteristic, complemented, Sylow
966C2×#41—532no—
967C2×#41—534no—
968C2×#41—534no—
969C2×#41—532no—
970C2×#41—534no—
971C2×#41—538no—
972C2×#41—534no—
973C2×#41—532no—
974C2×#41—534no—
975C2×#41—1068no—
976C2×#41—10616no—
977C2×#41C22×D5312yes—
978C2×#41C22×D5314yes—
979C22×Q8—532no—
980C22×Q8—531no—
981C22×D4—532no—
982C22×D4—534no—
983C22×D4—532no—
984C22×D4C22×D5311yescharacteristic
985C23×C4—531no—
986C23×C4—532no—
987C23×C4—532no—
988C23×C4—534no—
989C23×C4—532no—
990C23×C4—538no—
991C23×C4C22×D5312yes—
992C4⋊Q8—532no—
993C4⋊Q8—534no—
994C4⋊Q8—534no—
995C4⋊Q8—534no—
996C4⋊Q8—534no—
997C4⋊Q8—532no—
998C4⋊Q8—534no—
999C4⋊Q8—532no—
1000C4⋊Q8—534no—
1001C4⋊Q8—531no—
1002C4⋊Q8—531no—
1003C4⋊Q8—531no—
1004C4⋊Q8C22×D5311yescharacteristic
1005C4⋊Q8C22×D5311yescharacteristic
1006C4⋊Q8C22×D5311yescharacteristic
1007#127—532no—
1008#127—534no—
1009#127—531no—
1010#127C22×D5314yes—
1011#127C22×D5311yescharacteristic
1012#126—538no—
1013#126—538no—
1014#126—538no—
1015#126—538no—
1016#126—538no—
1017#126—538no—
1018#126—538no—
1019#126—538no—
1020#126—538no—
1021#126—538no—
1022#126—538no—
1023#126C22×D5318yes—
1024#125—538no—
1025#125—538no—
1026#125—538no—
1027#125—534no—
1028#125—538no—
1029#125—534no—
1030#125—534no—
1031#125—534no—
1032#125—534no—
1033#125—534no—
1034#125—532no—
1035#125—532no—
1036#125—538no—
1037#125—532no—
1038#125C22×D5312yes—
1039#124—534no—
1040#124—532no—
1041#124—534no—
1042#124—538no—
1043#124—532no—
1044#124—534no—
1045#124—534no—
1046#124—538no—
1047#124—538no—
1048#124—538no—
1049#124—534no—
1050#124—532no—
1051#124C22×D5318yes—
1052#124C22×D5314yes—
1053#124C22×D5312yes—
1054#123—538no—
1055#123—538no—
1056#123—538no—
1057#123—538no—
1058#123—538no—
1059#123—538no—
1060#123—534no—
1061#123—534no—
1062#123—538no—
1063#123—538no—
1064#123—534no—
1065#123—534no—
1066#123—538no—
1067#123—538no—
1068#123—538no—
1069#123—538no—
1070#123—538no—
1071#123—538no—
1072#123C22×D5318yes—
1073#123C22×D5318yes—
1074C22⋊Q8—534no—
1075C22⋊Q8—538no—
1076C22⋊Q8—534no—
1077C22⋊Q8—532no—
1078C22⋊Q8—534no—
1079C22⋊Q8—534no—
1080C22⋊Q8—534no—
1081C22⋊Q8—538no—
1082C22⋊Q8—532no—
1083C22⋊Q8—534no—
1084C22⋊Q8—534no—
1085C22⋊Q8—534no—
1086C22⋊Q8—534no—
1087C22⋊Q8—534no—
1088C22⋊Q8—534no—
1089C22⋊Q8—534no—
1090C22⋊Q8—538no—
1091C22⋊Q8—534no—
1092C22⋊Q8—534no—
1093C22⋊Q8—534no—
1094C22⋊Q8—534no—
1095C22⋊Q8—538no—
1096C22⋊Q8—534no—
1097C22⋊Q8—534no—
1098C22⋊Q8—538no—
1099C22⋊Q8—538no—
1100C22⋊Q8—538no—
1101C22⋊Q8—534no—
1102C22⋊Q8C22×D5312yes—
1103C22⋊Q8C22×D5314yes—
1104C22⋊Q8C22×D5312yes—
1105#121—538no—
1106#121—534no—
1107#121—534no—
1108#121—538no—
1109#121—534no—
1110#121—534no—
1111#121—534no—
1112#121—538no—
1113#121—538no—
1114#121—538no—
1115#121—538no—
1116#121—538no—
1117#121—534no—
1118#121—532no—
1119#121—534no—
1120#121—532no—
1121#121—538no—
1122#121—534no—
1123#121—534no—
1124#121—538no—
1125#121—538no—
1126#121C22×D5314yes—
1127#121C22×D5314yes—
1128#121C22×D5318yes—
1129#121C22×D5312yes—
1130#121C22×D5314yes—
1131#121C22×D5312yes—
1132#120—538no—
1133#120—538no—
1134#120—534no—
1135#120—534no—
1136#120—538no—
1137#120—534no—
1138#120—534no—
1139#120C22×D5318yes—
1140C4×Q8—534no—
1141C4×Q8—534no—
1142C4×Q8—538no—
1143C4×Q8—534no—
1144C4×Q8—534no—
1145C4×Q8—534no—
1146C4×Q8—534no—
1147C4×Q8—532no—
1148C4×Q8—532no—
1149C4×Q8—538no—
1150C4×Q8—534no—
1151C4×Q8—532no—
1152C4×Q8—532no—
1153C4×Q8—538no—
1154C4×Q8—534no—
1155C4×Q8—532no—
1156C4×Q8—534no—
1157C4×Q8—532no—
1158C4×Q8C22×D5314yes—
1159C4×Q8C22×D5312yes—
1160C4×Q8C22×D5312yes—
1161C4×D4—538no—
1162C4×D4—534no—
1163C4×D4—534no—
1164C4×D4—534no—
1165C4×D4—534no—
1166C4×D4—538no—
1167C4×D4—538no—
1168C4×D4—538no—
1169C4×D4—538no—
1170C4×D4—538no—
1171C4×D4—538no—
1172C4×D4—538no—
1173C4×D4—538no—
1174C4×D4—538no—
1175C4×D4—538no—
1176C4×D4—534no—
1177C4×D4—534no—
1178C4×D4—538no—
1179C4×D4—534no—
1180C4×D4—534no—
1181C4×D4—538no—
1182C4×D4—538no—
1183C4×D4—538no—
1184C4×D4—538no—
1185C4×D4—538no—
1186C4×D4—538no—
1187C4×D4—538no—
1188C4×D4—538no—
1189C4×D4—538no—
1190C4×D4—534no—
1191C4×D4—532no—
1192C4×D4—532no—
1193C4×D4C22×D5318yes—
1194C4×D4C22×D5314yes—
1195C4×D4C22×D5312yes—
1196C4×D4C22×D5312yes—
1197C4×D4C22×D5312yes—
1198C4×D4C22×D5312yes—
1199C4×D4C22×D5312yes—
1200C4×D4C22×D5312yes—
1201C4×D4C22×D5318yes—
1202#117—532no—
1203#117—534no—
1204#117—534no—
1205#117—538no—
1206#117—532no—
1207#117—532no—
1208#117—534no—
1209#117—534no—
1210#117—538no—
1211#117—534no—
1212#117—538no—
1213#117—538no—
1214#117—538no—
1215#117—538no—
1216#117—538no—
1217#117—532no—
1218#117—532no—
1219#117—534no—
1220#117—532no—
1221#117—532no—
1222#117—538no—
1223#117—538no—
1224#117C22×D5312yes—
1225#117C22×D5314yes—
1226#117C22×D5314yes—
1227C2×C4⋊C4—532no—
1228C2×C4⋊C4—531no—
1229C2×C4⋊C4—531no—
1230C2×C4⋊C4—532no—
1231C2×C4⋊C4—532no—
1232C2×C4⋊C4—538no—
1233C2×C4⋊C4—538no—
1234C2×C4⋊C4—538no—
1235C2×C4⋊C4—534no—
1236C2×C4⋊C4—531no—
1237C2×C4⋊C4—534no—
1238C2×C4⋊C4—532no—
1239C2×C4⋊C4—534no—
1240C2×C4⋊C4—538no—
1241C2×C4⋊C4—538no—
1242C2×C4⋊C4—534no—
1243C2×C4⋊C4—534no—
1244C2×C4⋊C4—532no—
1245C2×C4⋊C4C22×D5311yescharacteristic
1246C2×C4⋊C4C22×D5314yes—
1247C2×C22⋊C4—532no—
1248C2×C22⋊C4—531no—
1249C2×C22⋊C4—531no—
1250C2×C22⋊C4—534no—
1251C2×C22⋊C4—538no—
1252C2×C22⋊C4C22×D5312yes—
1253C2×C42—532no—
1254C2×C42—532no—
1255C2×C42—531no—
1256C2×C42—538no—
1257C2×C42—534no—
1258C2×C42C22×D5311yescharacteristic
1259C24—531no—
1260C24—534no—
1261C24C23×D5312yes—
1262#41—28no—
1263#41—84no—
1264#41—10616no—
1265#41—10616no—
1266#41—10616no—
1267#41—10616no—
1268#41—1068no—
1269#41—1068no—
1270#41—1068no—
1271#41—4244no—
1272#41—4248no—
1273C2×Q8—534no—
1274C2×Q8—532no—
1275C2×Q8—532no—
1276C2×Q8—532no—
1277C2×Q8—532no—
1278C2×Q8—534no—
1279C2×Q8—534no—
1280C2×Q8—532no—
1281C2×Q8—1068no—
1282C2×Q8—1064no—
1283C2×Q8C23×D5312yes—
1284C2×Q8C23×D5312yes—
1285C2×Q8C23×D5312yes—
1286C2×D4—24no—
1287C2×D4—534no—
1288C2×D4—538no—
1289C2×D4—534no—
1290C2×D4—534no—
1291C2×D4—534no—
1292C2×D4—538no—
1293C2×D4—534no—
1294C2×D4—538no—
1295C2×D4—534no—
1296C2×D4—532no—
1297C2×D4—532no—
1298C2×D4—532no—
1299C2×D4—1068no—
1300C2×D4—10616no—
1301C2×D4—1068no—
1302C2×D4C23×D5314yes—
1303C2×D4C23×D5312yes—
1304C2×D4C23×D5312yes—
1305C2×D4C23×D5312yes—
1306C2×D4C23×D5312yes—
1307C2×D4C23×D5318yes—
1308C2×D4C23×D5318yes—
1309C2×D4C23×D5312yes—
1310C22×C4—82no—
1311C22×C4—531no—
1312C22×C4—538no—
1313C22×C4—532no—
1314C22×C4—532no—
1315C22×C4—532no—
1316C22×C4—534no—
1317C22×C4—538no—
1318C22×C4—531no—
1319C22×C4—532no—
1320C22×C4—531no—
1321C22×C4—538no—
1322C22×C4—538no—
1323C22×C4—534no—
1324C22×C4—534no—
1325C22×C4—534no—
1326C22×C4—534no—
1327C22×C4—538no—
1328C22×C4—534no—
1329C22×C4—538no—
1330C22×C4—538no—
1331C22×C4—10616no—
1332C22×C4—1068no—
1333C22×C4—4242no—
1334C22×C4—4248no—
1335C22×C4—4242no—
1336C22×C4C23×D5314yes—
1337C22×C4C23×D5311yescharacteristic
1338C22×C4C23×D5312yes—
1339C22×C4C23×D5311yescharacteristic
1340C22×C4C23×D5314yes—
1341C22×C4C23×D5314yes—
1342C22×C4C23×D5318yes—
1343C22×C4C23×D5311yescharacteristic
1344C4⋊C4—538no—
1345C4⋊C4—532no—
1346C4⋊C4—534no—
1347C4⋊C4—532no—
1348C4⋊C4—532no—
1349C4⋊C4—532no—
1350C4⋊C4—532no—
1351C4⋊C4—538no—
1352C4⋊C4—534no—
1353C4⋊C4—534no—
1354C4⋊C4—538no—
1355C4⋊C4—538no—
1356C4⋊C4—538no—
1357C4⋊C4—532no—
1358C4⋊C4—532no—
1359C4⋊C4—534no—
1360C4⋊C4—532no—
1361C4⋊C4—534no—
1362C4⋊C4—538no—
1363C4⋊C4—538no—
1364C4⋊C4—532no—
1365C4⋊C4—534no—
1366C4⋊C4—534no—
1367C4⋊C4—534no—
1368C4⋊C4—534no—
1369C4⋊C4—532no—
1370C4⋊C4—534no—
1371C4⋊C4—534no—
1372C4⋊C4—534no—
1373C4⋊C4—532no—
1374C4⋊C4—534no—
1375C4⋊C4—534no—
1376C4⋊C4—538no—
1377C4⋊C4—532no—
1378C4⋊C4—538no—
1379C4⋊C4C23×D5312yes—
1380C4⋊C4C23×D5312yes—
1381C4⋊C4C23×D5312yes—
1382C4⋊C4C23×D5318yes—
1383C4⋊C4C23×D5312yes—
1384C4⋊C4C23×D5314yes—
1385C4⋊C4C23×D5312yes—
1386C4⋊C4C23×D5312yes—
1387C4⋊C4C23×D5312yes—
1388C4⋊C4C23×D5314yes—
1389C4⋊C4C23×D5312yes—
1390C22⋊C4—534no—
1391C22⋊C4—538no—
1392C22⋊C4—538no—
1393C22⋊C4—534no—
1394C22⋊C4—538no—
1395C22⋊C4—538no—
1396C22⋊C4—534no—
1397C22⋊C4—538no—
1398C22⋊C4—538no—
1399C22⋊C4—534no—
1400C22⋊C4—532no—
1401C22⋊C4—532no—
1402C22⋊C4—532no—
1403C22⋊C4—532no—
1404C22⋊C4—534no—
1405C22⋊C4—538no—
1406C22⋊C4—538no—
1407C22⋊C4—534no—
1408C22⋊C4—534no—
1409C22⋊C4—538no—
1410C22⋊C4—538no—
1411C22⋊C4—534no—
1412C22⋊C4—534no—
1413C22⋊C4C23×D5314yes—
1414C22⋊C4C23×D5318yes—
1415C22⋊C4C23×D5314yes—
1416C22⋊C4C23×D5314yes—
1417C22⋊C4C23×D5314yes—
1418C22⋊C4C23×D5318yes—
1419C22⋊C4C23×D5318yes—
1420C22⋊C4C23×D5314yes—
1421C42—538no—
1422C42—538no—
1423C42—538no—
1424C42—534no—
1425C42—534no—
1426C42—538no—
1427C42—534no—
1428C42—534no—
1429C42—532no—
1430C42—532no—
1431C42—534no—
1432C42C23×D5318yes—
1433C42C23×D5314yes—
1434C42C23×D5311yescharacteristic
1435C42C23×D5311yescharacteristic
1436C42C23×D5311yescharacteristic
1437C42C23×D5311yescharacteristic
1438C23—24no—
1439C23—42no—
1440C23—42no—
1441C23—532no—
1442C23—534no—
1443C23—534no—
1444C23—1068no—
1445C23—2121no—
1446C23—2124no—
1447C23—2121no—
1448C23—2124no—
1449C23C24×D5314yes—
1450C23C24×D5314yes—
1451C23C24×D5311yescharacteristic
1452Q8—24no—
1453Q8—42no—
1454Q8—42no—
1455Q8—1068no—
1456Q8—1064no—
1457Q8—1064no—
1458Q8—1064no—
1459Q8—2122no—
1460Q8—2124no—
1461Q8—2122no—
1462Q8—2124no—
1463D4—28no—
1464D4—24no—
1465D4—24no—
1466D4—24no—
1467D4—42no—
1468D4—48no—
1469D4—42no—
1470D4—48no—
1471D4—1068no—
1472D4—1068no—
1473D4—1068no—
1474D4—10616no—
1475D4—1068no—
1476D4—1064no—
1477D4—2122no—
1478D4—2122no—
1479D4—2124no—
1480D4—2128no—
1481D4—2124no—
1482D4—2128no—
1483C2×C4—28no—
1484C2×C4—41no—
1485C2×C4—42no—
1486C2×C4—44no—
1487C2×C4—44no—
1488C2×C4—48no—
1489C2×C4—41no—
1490C2×C4—534no—
1491C2×C4—532no—
1492C2×C4—538no—
1493C2×C4—538no—
1494C2×C4—534no—
1495C2×C4—532no—
1496C2×C4—534no—
1497C2×C4—534no—
1498C2×C4—534no—
1499C2×C4—534no—
1500C2×C4—532no—
1501C2×C4—1068no—
1502C2×C4—1068no—
1503C2×C4—1068no—
1504C2×C4—10616no—
1505C2×C4—1064no—
1506C2×C4—1068no—
1507C2×C4—2124no—
1508C2×C4—2128no—
1509C2×C4—2124no—
1510C2×C4—2128no—
1511C2×C4—2128no—
1512C2×C4—2121no—
1513C2×C4—2122no—
1514C2×C4—2121no—
1515C2×C4—2128no—
1516C2×C4—2128no—
1517C2×C4#41×D5314yes—
1518C2×C4C24×D5311yescharacteristic
1519C2×C4C24×D5311yescharacteristic
1520C2×C4C24×D5314yes—
1521C2×C4C24×D5314yes—
1522C2×C4C24×D5314yes—
1523C2×C4C24×D5314yes—
1524C2×C4C24×D5311yescharacteristic
1525C2×C4C24×D5311yescharacteristic
1526C2×C4C24×D5311yescharacteristic
1527C2×C4C24×D5311yescharacteristic
1528C22—21no—
1529C22—21no—
1530C22—24no—
1531C22—24no—
1532C22—24no—
1533C22—24no—
1534C22—24no—
1535C22—24no—
1536C22—48no—
1537C22—534no—
1538C22—1062no—
1539C22—1062no—
1540C22—1064no—
1541C22—1064no—
1542C22—1064no—
1543C22—2124no—
1544C22—21216no—
1545C22C2×#41×D5312yes—
1546C22C25×D5311yescharacteristic
1547C4—24no—
1548C4—24no—
1549C4—21no—
1550C4—21no—
1551C4—24no—
1552C4—21no—
1553C4—21no—
1554C4—24no—
1555C4—534no—
1556C4—1064no—
1557C4—1064no—
1558C4—1064no—
1559C4—1064no—
1560C4—1062no—
1561C4—1064no—
1562C4—1062no—
1563C4C2×#41×D5312yes—
1564C4C2×#41×D5312yes—
1565C2—22no—
1566C2—44no—
1567C2—44no—
1568C2—1064no—
1569C2—2124no—
1570C2C22×#41×D5311yescharacteristic
1571C2#2028952511yescharacteristic
1572C2#2028952811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3506C2
hypercenter#3506D53
hypocenterC53#62845
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3506

Complements

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

NH ≅ G/Ntype
1. #20288582C2semidirect
2. #20288577C2semidirect
3. #20288576C2semidirect
4. #20288573C2semidirect
5. #20288572C2semidirect
6. #20288567C2semidirect
7. #20288566C2semidirect
8. #20288563C2semidirect
9. #20288559C2semidirect
10. #20288431C2semidirect
11. #20288430C2semidirect
12. #20288426C2semidirect
13. #20288419C2semidirect
14. #20288417C2semidirect
15. #20288416C2semidirect
16. #20288126C2semidirect
17. #20288122C2semidirect
18. #20288118C2semidirect
19. #20288046C2semidirect
20. #20288042C2semidirect
21. C2×#16811102C2semidirect
22. #520×D53C2semidirect
23. C53×#3506C2semidirect
26. #16811359C22semidirect
27. #16811359C22semidirect
28. #16811358C22semidirect
29. #16811356C22semidirect
30. #16811356C22semidirect
31. #16811355C22semidirect
32. #16811352C22semidirect
33. #16811351C22semidirect
34. #16811348C22semidirect
35. #16811347C22semidirect
36. #16811346C22semidirect
37. #16811345C22semidirect
38. #16811343C22semidirect
39. #16811343C22semidirect
40. #16811343C22semidirect
41. #16811342C22semidirect
42. #16811342C22semidirect
43. #16811342C22semidirect
44. #16811341C22semidirect
45. #16811340C22semidirect
46. #16811338C22semidirect
47. #16811337C22semidirect
48. #16811337C22semidirect
49. #16811335C22semidirect
50. #16811334C22semidirect
51. #16811332C22semidirect
52. #16811330C22semidirect
53. #16811328C22semidirect
54. #16811327C22semidirect
55. #16811325C22semidirect
56. #16811323C22semidirect
57. #16811322C22semidirect
58. #16811320C22semidirect
59. #16811318C22semidirect
60. #16811316C22semidirect
61. #16811316C22semidirect
62. #16811313C22semidirect
63. #16811312C22semidirect
64. #16811311C22semidirect
65. #16811310C22semidirect
66. #16811310C22semidirect
67. #16811309C22semidirect
68. #16811308C22semidirect
69. #16811306C22semidirect
70. #16811294C22semidirect
71. #16811293C22semidirect
72. #16811278C22semidirect
73. #16811273C22semidirect
74. #16811272C22semidirect
75. #16811271C22semidirect
76. #16811253C22semidirect
77. #16811253C22semidirect
78. #16811252C22semidirect
79. #16811252C22semidirect
80. #16811250C22semidirect
81. #16811250C22semidirect
84. #16811222C22semidirect
85. #16811219C22semidirect
86. #16811218C22semidirect
87. #16811216C22semidirect
88. #16811216C22semidirect
89. #16811215C22semidirect
90. #16811214C22semidirect
91. #16811211C22semidirect
92. #16811209C22semidirect
93. #16811208C22semidirect
94. #16811207C22semidirect
95. #16811205C22semidirect
96. #16811205C22semidirect
101. #16811199C22semidirect
102. #16811198C22semidirect
103. #16811194C22semidirect
104. #16811193C22semidirect
105. #16811193C22semidirect
106. #16811191C22semidirect
107. #16811190C22semidirect
108. #16811186C22semidirect
109. #16811186C22semidirect
113. #16811180C22semidirect
114. #16811177C22semidirect
115. #16811177C22semidirect
116. #16811176C22semidirect
121. #16811159C22semidirect
122. #16811156C22semidirect
123. #16811155C22semidirect
124. #16811154C22semidirect
125. #16811153C22semidirect
126. #16811152C22semidirect
127. #16811151C22semidirect
128. #16811134C22semidirect
129. #16811133C22semidirect
130. #16811133C22semidirect
131. #16811133C22semidirect
132. #16811132C22semidirect
133. #16811132C22semidirect
134. #16811132C22semidirect
135. #16811131C22semidirect
136. #16811130C22semidirect
137. #16811129C22semidirect
138. #16811129C22semidirect
139. #16811106C22semidirect
140. #16811105C22semidirect
141. #16811104C22semidirect
142. #16811104C22semidirect
143. #16811103C22semidirect
144. #16811103C22semidirect
145. #16811102C22semidirect
146. #16811102C22semidirect
147. #16811102C22semidirect
148. #16811102C22semidirect
149. #16811102C22semidirect
150. #16811102C22semidirect
151. C2×C4×Dic106C22semidirect
152. C2×#13133182C22semidirect
153. C4×Q8×D53C22semidirect
154. C2×D4×Dic53C22semidirect
158. C4×D4×D53C22semidirect
160. C2×#13133173C22semidirect
162. #117×D53C22semidirect
163. C22×#11719919C22semidirect
165. C2×C4⋊C4×D53C22semidirect
166. C53×#559C22semidirect
167. C53×#556C22semidirect
168. C53×#555C22semidirect
169. C53×#553C22semidirect
170. C53×#550C22semidirect
171. C53×#547C22semidirect
172. C53×#538C22semidirect
173. C53×#535C22semidirect
174. C53×#533C22semidirect
176. C53×#525C22semidirect
177. C53×#520C22semidirect
178. C2×C4×D4×C53C22semidirect
537. C2×C4×D53#41semidirect
788. #3506D53semidirect
818. #559C2×D53semidirect
833. #556C2×D53semidirect
838. #555C2×D53semidirect
851. #553C2×D53semidirect
862. #550C2×D53semidirect
867. #547C2×D53semidirect
889. #538C2×D53semidirect
903. #535C2×D53semidirect
911. #533C2×D53semidirect
935. #525C2×D53semidirect
948. #520C2×D53semidirect
957. C2×C4×D4C2×D53semidirect
965. C53#62845semidirect

Maximal subgroups

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

subgroupindex
#202885822
#202885772
#202885762
#202885732
#202885722
#202885672
#202885662
#202885632
#202885592
#202884312
#202884302
#202884262
#202884192
#202884172
#202884162
#202881262
#202881222
#202881182
#202880462
#202880422
C2×#168111022
#520×D532
C53×#35062
#6284553