Finite Group Databasebeta

← #28293119

Subgroups — #28293119

Order 13568.

7102 conjugacy classes of subgroups.

The subgroup lattice has 1582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288578C214yesmaximal, complemented
2#20288575C214yesmaximal, complemented
3#20288574C214yesmaximal, complemented
4#20288565C214yesmaximal, complemented
5#20288561C214yesmaximal, complemented
6#20288558C214yesmaximal, complemented
7#20288433C214yesmaximal, complemented
8#20288432C212yesmaximal, complemented
9#20288431C214yesmaximal, complemented
10#20288428C212yesmaximal, complemented
11#20288425C211yesmaximal, characteristic, complemented
12#20288424C211yesmaximal, characteristic, complemented
13#20288423C214yesmaximal, complemented
14#20288422C211yesmaximal, characteristic, complemented
15#20288417C214yesmaximal, complemented
16#20288123C214yesmaximal, complemented
17#20288122C214yesmaximal, complemented
18#20288119C211yesmaximal, characteristic, complemented
19#20288045C212yesmaximal, complemented
20#20288043C211yesmaximal, characteristic, complemented
21C2×#16811104C211yesmaximal, characteristic, complemented
22#520×D53C212yesmaximal, complemented
23C53×#3492C211yesmaximal, characteristic, complemented
24C22×#11719945C2211yescharacteristic
25C2×#41×D53C2212yes—
26#16811357C2218yescomplemented
27#16811357C2218yescomplemented
28#16811356C2218yescomplemented
29#16811350C2218yescomplemented
30#16811346C2214yescomplemented
31#16811344C2214yescomplemented
32#16811344C2218yescomplemented
33#16811344C2214yescomplemented
34#16811343C2214yescomplemented
35#16811341C2214yescomplemented
36#16811341C2214yescomplemented
37#16811340C2218yescomplemented
38#16811340C2218yescomplemented
39#16811338C2214yescomplemented
40#16811338C2214yescomplemented
41#16811337C2214yescomplemented
42#16811337C2214yescomplemented
43#16811336C2214yescomplemented
44#16811336C2214yescomplemented
45#16811334C2214yescomplemented
46#16811331C2214yescomplemented
47#16811328C2214yescomplemented
48#16811327C2218yescomplemented
49#16811326C2214yescomplemented
50#16811323C2214yescomplemented
51#16811322C2218yescomplemented
52#16811321C2214yescomplemented
53#16811321C2214yescomplemented
54#16811320C2214yescomplemented
55#16811320C2214yescomplemented
56#16811319C2214yescomplemented
57#16811318C2218yescomplemented
58#16811314C2214yescomplemented
59#16811313C2214yescomplemented
60#16811311C2214yescomplemented
61#16811310C2218yescomplemented
62#16811308C2214yescomplemented
63#16811308C2214yescomplemented
64#16811307C2214yescomplemented
65#16811307C2214yescomplemented
66#16811305C2218yescomplemented
67#16811292C2214yescomplemented
68#16811291C2214yescomplemented
69#16811276C2214yescomplemented
70#16811275C2214yescomplemented
71#16811274C2214yescomplemented
72#16811273C2214yescomplemented
73#16811272C2214yescomplemented
74#16811254C2211yescharacteristic, complemented
75#16811253C2214yescomplemented
76#16811251C2212yescomplemented
77#16811250C2214yescomplemented
78#16811248C2214yes—
79#16811222C2214yescomplemented
80#16811221C2218yescomplemented
81#16811220C2214yescomplemented
82#16811219C2218yescomplemented
83#16811219C2218yescomplemented
84#16811218C2214yescomplemented
85#16811216C2218yescomplemented
86#16811212C2218yescomplemented
87#16811209C2218yescomplemented
88#16811209C2218yescomplemented
89#16811208C2218yescomplemented
90#16811206C2218yescomplemented
91#16811205C2218yescomplemented
92#16811204C2211yescharacteristic
93#16811203C2212yes—
94#16811203C2212yes—
95#16811202C2212yes—
96#16811202C2212yes—
97#16811201C2212yes—
98#16811196C2214yescomplemented
99#16811196C2212yescomplemented
100#16811196C2212yescomplemented
101#16811195C2214yescomplemented
102#16811189C2214yescomplemented
103#16811189C2212yescomplemented
104#16811189C2212yescomplemented
105#16811188C2214yescomplemented
106#16811184C2214yes—
107#16811183C2214yes—
108#16811181C2214yes—
109#16811179C2214yescomplemented
110#16811178C2214yescomplemented
111#16811175C2214yescomplemented
112#16811170C2214yes—
113#16811170C2214yes—
114#16811168C2214yes—
115#16811158C2218yescomplemented
116#16811156C2218yescomplemented
117#16811155C2218yescomplemented
118#16811153C2218yescomplemented
119#16811151C2218yescomplemented
120#16811150C2218yescomplemented
121#16811136C2214yescomplemented
122#16811136C2214yescomplemented
123#16811136C2218yescomplemented
124#16811135C2212yescomplemented
125#16811134C2212yescomplemented
126#16811134C2214yescomplemented
127#16811133C2214yescomplemented
128#16811133C2214yescomplemented
129#16811132C2214yescomplemented
130#16811132C2214yescomplemented
131#16811132C2218yescomplemented
132#16811131C2218yescomplemented
133#16811130C2212yescomplemented
134#16811130C2218yescomplemented
135#16811106C2212yescomplemented
136#16811105C2214yescomplemented
137#16811104C2214yescomplemented
138#16811104C2214yescomplemented
139#16811104C2214yescomplemented
140#16811104C2214yescomplemented
141#16811104C2212yescomplemented
142#16811104C2214yescomplemented
143#16811103C2214yescomplemented
144#16811103C2212yescomplemented
145#16811102C2218yescomplemented
146#16811102C2214yescomplemented
147C2×#13133182C2212yescomplemented
148C4×Q8×D53C2214yescomplemented
149C2×#13133179C2212yes—
150C2×C4×C22⋊D53C2212yes—
151C2×C4×C22⋊D53C2212yescomplemented
152C4×D4×D53C2218yes—
153C4×D4×D53C2214yescomplemented
154C2×#13133176C2211yescharacteristic, complemented
155C2×#13133175C2211yescharacteristic
156C2×#13133175C2211yescharacteristic, complemented
157#117×D53C2212yes—
158#117×D53C2214yescomplemented
159C2×C4⋊C4×D53C2211yescharacteristic
160C2×C4⋊C4×D53C2214yescomplemented
161C2×C4⋊C4×D53C2211yescharacteristic, complemented
162C53×#554C2214yescomplemented
163C53×#553C2214yescomplemented
164C53×#552C2214yescomplemented
165C53×#547C2214yescomplemented
166C53×#544C2211yescharacteristic, complemented
167C53×#539C2214yescomplemented
168C53×#537C2211yescharacteristic
169C53×#525C2212yescomplemented
170C53×#525C2214yescomplemented
171C53×#520C2212yescomplemented
172C22×C4⋊C4×C53C2211yescharacteristic, complemented
173C2×#11719949C2312yes—
174C2×#11719949C2314yes—
175C2×#11719945—28no—
176C2×#11719945C2312yes—
177C2×#11719945C2314yes—
178C2×#11719945C2312yes—
179C2×#11719945C2312yes—
180C2×#11719945C2312yes—
181C2×#11719945C2312yes—
182C2×#11719945C2314yes—
183C2×#11719947C2312yes—
184C2×#11719947C2314yes—
185C2×#11719947C2314yes—
186#41×D53—216no—
187C22×Dic106C2311yescharacteristic
188C2×Q8×D53C2312yes—
189C22×D212C2311yescharacteristic
190C22×C22⋊D53C2311yescharacteristic
191C22×C22⋊D53C2311yescharacteristic
192C2×D4×D53C2314yes—
193C2×D4×D53C2312yes—
194C22×C4×D53C2314yes—
195C22×C4×D53C2311yescharacteristic
196C22×C4×D53C2312yes—
197C22×C4×D53C2318yes—
198C22×C4×D53C2312yes—
199C22×C4×D53C2311yescharacteristic
200#13133217C2314yes—
201#13133216C2314yes—
202#13133216C2314yes—
203#13133216C2314yes—
204#13133216C2314yes—
205#13133216C2314yes—
206#13133216C2314yes—
207#13133215C2314yes—
208#13133213C2314yes—
209#13133213C2314yes—
210#13133213C2314yes—
211#13133212C2318yes—
212#13133212C2318yes—
213#13133212C2318yes—
214#13133212C2318yes—
215#13133212C2318yes—
216#13133211C2318yes—
217#13133210C2318yes—
218#13133210C2318yes—
219#13133210C2318yes—
220#13133210C2318yes—
221#13133210C2318yes—
222#13133209C2314yes—
223#13133208C2314yes—
224#13133208C2314yes—
225#13133208C2318yes—
226#13133207C2318yes—
227#13133207C2318yes—
228#13133207C2318yes—
229#13133207C2318yes—
230#13133207C2318yes—
231#13133205C2318yes—
232#13133204C2318yes—
233#13133203C2318yes—
234#13133203C2318yes—
235#13133203C2318yes—
236#13133203C2318yes—
237#13133203C2314yes—
238#13133203C2318yes—
239#13133203C2314yes—
240#13133203C2314yes—
241#13133203C2314yes—
242#13133202C2318yes—
243#13133202C2318yes—
244#13133202C2318yes—
245#13133202C2318yes—
246#13133202C2314yes—
247#13133202C2314yes—
248#13133202C2318yes—
249#13133201C2314yes—
250#13133200C2318yes—
251#13133200C2318yes—
252#13133200C2314yes—
253#13133199C2318yes—
254#13133199C2318yes—
255#13133199C2314yes—
256#13133199C2314yes—
257#13133199C2318yes—
258#13133198C2318yes—
259#13133198C2318yes—
260#13133198C2314yes—
261#13133197C2314yes—
262#13133197C2312yes—
263#13133197C2314yes—
264#13133197C2312yes—
265#13133197C2318yes—
266#13133196C2314yes—
267#13133196C2312yes—
268#13133196C2314yes—
269#13133196C2312yes—
270#13133196C2314yes—
271#13133195C2318yes—
272#13133195C2314yes—
273#13133195C2314yes—
274#13133195C2318yes—
275#13133195C2318yes—
276#13133194C2318yes—
277#13133194C2314yes—
278#13133194C2314yes—
279#13133194C2318yes—
280#13133193C2314yes—
281#13133193C2318yes—
282#13133193C2312yes—
283#13133193C2314yes—
284#13133193C2312yes—
285#13133193C2318yes—
286#13133192C2314yes—
287#13133192C2312yes—
288#13133192C2314yes—
289#13133192C2312yes—
290#13133192C2314yes—
291#13133192C2314yes—
292#13133191C2312yes—
293#13133191C2314yes—
294#13133191C2318yes—
295#13133191C2314yes—
296#13133191C2312yes—
297#13133191C2314yes—
298#13133190C2314yes—
299#13133190C2318yes—
300#13133190C2314yes—
301#13133190C2314yes—
302#13133190C2314yes—
303#13133190C2314yes—
304#13133190C2314yes—
305#13133189C2314yes—
306#13133189C2318yes—
307#13133189C2314yes—
308#13133189C2318yes—
309#13133188C2312yes—
310#13133188C2318yes—
311#13133188C2314yes—
312#13133188C2312yes—
313#13133188C2314yes—
314#13133188C2314yes—
315#13133188C2314yes—
316#13133187C2314yes—
317#13133187C2318yes—
318#13133187C2314yes—
319#13133187C2314yes—
320#13133186C2314yes—
321#13133185C2314yes—
322#13133185C2318yes—
323#13133185C2314yes—
324#13133185C2314yes—
325Q8×Dic53C2314yes—
326Q8×Dic53C2314yes—
327C4×Dic106C2314yes—
328C4×Dic106C2318yes—
329C4×Dic106C2318yes—
330#13133182C2314yes—
331#13133182C2318yes—
332#13133182C2314yes—
333#13133182C2318yes—
334#13133182C2318yes—
335#13133182C2318yes—
336#13133182C2318yes—
337C4×D212C2314yes—
338C4×D212C2314yes—
339C4×D212C2314yes—
340C4×D212C2318yes—
341D4×Dic53C2314yes—
342D4×Dic53C2314yes—
343D4×Dic53C2318yes—
344#13133179C2314yes—
345#13133179C2314yes—
346#13133179C2318yes—
347#13133179C2318yes—
348#13133179C2318yes—
349#13133179C2318yes—
350C4×C22⋊D53C2314yes—
351C4×C22⋊D53C2314yes—
352C4×C22⋊D53C2314yes—
353C4×C22⋊D53C2314yes—
354C4×C22⋊D53C2314yes—
355C4×C22⋊D53C2318yes—
356C4×C22⋊D53C2314yes—
357C4×C22⋊D53C2318yes—
358C4×C22⋊D53C2314yes—
359C4×C22⋊D53C2314yes—
360C4×C22⋊D53C2318yes—
361C4×C22⋊D53C2318yes—
362C4×C22⋊D53C2318yes—
363C4×C22⋊D53C2318yes—
364C4×C22⋊D53C2318yes—
365#13133177C2318yes—
366#13133177C2318yes—
367#13133177C2318yes—
368#13133177C2318yes—
369#13133177C2318yes—
370#13133177C2318yes—
371#13133176C2314yes—
372#13133176C2314yes—
373#13133176C2314yes—
374#13133176C2318yes—
375#13133176C2314yes—
376#13133176C2312yes—
377#13133175C2318yes—
378#13133175C2314yes—
379#13133175C2314yes—
380#13133175C2314yes—
381#13133175C2314yes—
382#13133175C2314yes—
383#13133175C2314yes—
384#13133175C2312yes—
385#13133175C2312yes—
386#13133175C2314yes—
387#13133175C2314yes—
388#13133174C2318yes—
389#13133174C2318yes—
390#13133174C2314yes—
391#13133173C2318yes—
392#13133173C2318yes—
393#13133173C2314yes—
394C2×C4⋊Dic53C2314yes—
395C2×C4⋊Dic53C2311yescharacteristic
396C2×C4⋊Dic53C2311yescharacteristic
397C2×#11719919C2318yes—
398C2×#11719919C2312yes—
399C2×#11719919C2312yes—
400C4⋊C4×D53C2314yes—
401C4⋊C4×D53C2314yes—
402C4⋊C4×D53C2318yes—
403C4⋊C4×D53C2314yes—
404C4⋊C4×D53C2314yes—
405C4⋊C4×D53C2314yes—
406C4⋊C4×D53C2314yes—
407C4⋊C4×D53C2312yes—
408C4⋊C4×D53C2318yes—
409C4⋊C4×D53C2312yes—
410C2×C22⋊Dic53C2312yes—
411C2×#11719921C2312yes—
412C2×#11719921C2312yes—
413C22⋊C4×D53C2314yes—
414C22⋊C4×D53C2318yes—
415C2×C4×Dic53C2312yes—
416C2×C4×Dic53C2312yes—
417C2×C4×Dic53C2312yes—
418C42×D53C2314yes—
419C42×D53C2318yes—
420C2×#41×C53C2312yes—
421C2×#41×C53C2314yes—
422C23×C4×C53C2311yescharacteristic
423C23×C4×C53C2312yes—
424C4⋊Q8×C53C2314yes—
425#126×C53C2318yes—
426#125×C53C2318yes—
427#125×C53C2314yes—
428#123×C53C2314yes—
429#123×C53C2318yes—
430#123×C53C2318yes—
431C22⋊Q8×C53C2314yes—
432C22⋊Q8×C53C2312yes—
433C22⋊Q8×C53C2314yes—
434C22⋊Q8×C53C2312yes—
435C22⋊Q8×C53C2314yes—
436C22⋊Q8×C53C2318yes—
437#121×C53C2314yes—
438#121×C53C2314yes—
439#121×C53C2314yes—
440#121×C53C2312yes—
441#121×C53C2312yes—
442#120×C53C2314yes—
443C4×Q8×C53C2314yes—
444C4×D4×C53C2318yes—
445C4×D4×C53C2314yes—
446C4×D4×C53C2314yes—
447C4×D4×C53C2314yes—
448C4×D4×C53C2318yes—
449#117×C53C2312yes—
450#117×C53C2314yes—
451#117×C53C2314yes—
452C2×C4⋊C4×C53C2314yes—
453C2×C4⋊C4×C53C2311yescharacteristic
454C2×C4⋊C4×C53C2311yescharacteristic
455C2×C4⋊C4×C53C2312yes—
456C2×C4⋊C4×C53C2314yes—
457C2×C4⋊C4×C53C2314yes—
458C24×C53C2411yescharacteristic
459C23×D53C2414yes—
460C23×D53C2411yescharacteristic
461C23×D53C2411yescharacteristic
462#41×C53—28no—
463#41×C53—84no—
464C2×Q8×C53C2412yes—
465C2×Q8×C53C2414yes—
466C2×D4×C53C2414yes—
467C2×D4×C53C2412yes—
468C2×D4×C53C2414yes—
469C2×D4×C53C2414yes—
470C2×D4×C53C2414yes—
471C22×C4×C53—24no—
472C22×C4×C53—82no—
473C22×C4×C53C2412yes—
474C22×C4×C53C2412yes—
475C22×C4×C53C2411yescharacteristic
476C22×C4×C53C2414yes—
477C22×C4×C53C2414yes—
478C22×C4×C53C2412yes—
479C22×C4×C53C2414yes—
480C22×C4×C53C2412yes—
481C22×C4×C53C2418yes—
482C22×C4×C53C2411yescharacteristic
483C2×C22⋊D53—24no—
484C2×C22⋊D53—24no—
485C2×C22⋊D53C2414yes—
486C2×C22⋊D53C2414yes—
487C2×C22⋊D53C2414yes—
488C2×C22⋊D53C2412yes—
489C2×C22⋊D53C2412yes—
490C2×C22⋊D53C2411yescharacteristic
491C2×C22⋊D53C2411yescharacteristic
492C2×C22⋊D53C2411yescharacteristic
493C2×C22⋊D53C2411yescharacteristic
494C2×C22⋊D53C2414yes—
495C2×C22⋊D53C2418yes—
496C2×C22⋊D53C2414yes—
497C2×C22⋊D53C2414yes—
498C2×C22⋊D53C2414yes—
499C22×Dic53C2411yescharacteristic
500C22×Dic53C2414yes—
501C22×Dic53C2412yes—
502C22×Dic53C2412yes—
503C22×Dic53C2418yes—
504C22×Dic53C2411yescharacteristic
505#11719949—28no—
506#11719949—84no—
507Q8×D53—28no—
508#11719947—216no—
509#11719947—28no—
510#11719947—84no—
511D4×D53—216no—
512D4×D53—28no—
513#11719945—28no—
514#11719945—216no—
515#11719945—28no—
516#11719945—28no—
517#11719945—28no—
518#11719945—28no—
519#11719945—84no—
520C2×D212—24no—
521C2×D212C2412yes—
522C2×D212C2412yes—
523C2×D212C2414yes—
524C2×D212C2412yes—
525C2×D212C2414yes—
526C2×D212C2414yes—
527C2×D212C2414yes—
528C2×C4×D53—24no—
529C2×C4×D53—216no—
530C2×C4×D53—82no—
531C2×C4×D53—88no—
532C2×C4×D53—82no—
533C2×C4×D53#4118yescomplemented
534C2×C4×D53C2414yes—
535C2×C4×D53C2414yes—
536C2×C4×D53C2412yes—
537C2×C4×D53C2414yes—
538C2×C4×D53C2412yes—
539C2×C4×D53C2414yes—
540C2×C4×D53C2418yes—
541C2×C4×D53C2414yes—
542C2×C4×D53C2418yes—
543C2×C4×D53C2414yes—
544C2×C4×D53C2418yes—
545C2×C4×D53C2414yes—
546C2×C4×D53C2412yes—
547C2×C4×D53C2412yes—
548C2×Dic106—24no—
549C2×Dic106C2412yes—
550C2×Dic106C2412yes—
551C2×Dic106C2412yes—
552C2×Dic106C2414yes—
553C2×Dic106C2418yes—
554C2×Dic106C2414yes—
555C4⋊C4×C53C2414yes—
556C4⋊C4×C53C2414yes—
557C4⋊C4×C53C2418yes—
558C4⋊C4×C53C2412yes—
559C4⋊C4×C53C2418yes—
560C4⋊C4×C53C2412yes—
561C4⋊C4×C53C2414yes—
562C4⋊C4×C53C2414yes—
563C4⋊C4×C53C2414yes—
564C4⋊C4×C53C2418yes—
565C4⋊C4×C53C2414yes—
566C22⋊C4×C53C2414yes—
567C22⋊C4×C53C2414yes—
568C22⋊C4×C53C2418yes—
569C22⋊C4×C53C2414yes—
570C22⋊C4×C53C2418yes—
571C22⋊C4×C53C2414yes—
572C22⋊C4×C53C2414yes—
573C42×C53C2418yes—
574C42×C53C2414yes—
575C22⋊Dic53C2414yes—
576C22⋊Dic53C2418yes—
577C22⋊Dic53C2414yes—
578C22⋊Dic53C2414yes—
579C22⋊Dic53C2418yes—
580C22⋊Dic53C2414yes—
581C22⋊Dic53C2414yes—
582C22⋊Dic53C2414yes—
583C22⋊Dic53C2414yes—
584#11719921C2414yes—
585#11719921C2418yes—
586#11719921C2414yes—
587#11719921C2418yes—
588#11719921C2418yes—
589#11719921C2414yes—
590#11719921C2414yes—
591#11719921C2414yes—
592#11719921C2418yes—
593#11719921C2414yes—
594#11719921C2414yes—
595#11719921C2414yes—
596#11719921C2414yes—
597#11719921C2414yes—
598#11719921C2418yes—
599#11719921C2414yes—
600#11719921C2414yes—
601C4⋊Dic53C2414yes—
602C4⋊Dic53C2412yes—
603C4⋊Dic53C2418yes—
604C4⋊Dic53C2412yes—
605C4⋊Dic53C2414yes—
606C4⋊Dic53C2414yes—
607C4⋊Dic53C2418yes—
608C4⋊Dic53C2414yes—
609C4⋊Dic53C2414yes—
610C4⋊Dic53C2414yes—
611#11719919C2414yes—
612#11719919C2414yes—
613#11719919C2414yes—
614#11719919C2418yes—
615#11719919C2418yes—
616#11719919C2418yes—
617#11719919C2414yes—
618#11719919C2414yes—
619#11719919C2418yes—
620#11719919C2414yes—
621#11719919C2418yes—
622#11719919C2418yes—
623#11719919C2418yes—
624#11719919C2414yes—
625#11719919C2414yes—
626C4×Dic53C2418yes—
627C4×Dic53C2418yes—
628C4×Dic53C2414yes—
629C4×Dic53C2414yes—
630C4×Dic53C2418yes—
631C4×Dic53C2414yes—
632C4×Dic53C2418yes—
633C4×Dic53C2418yes—
634C4×Dic53C2414yes—
635C4×Dic53C2414yes—
636C23×C53—22no—
637C23×C53—41no—
638C23×C53—41no—
639C23×C53C2514yes—
640C23×C53C2511yescharacteristic
641C23×C53C2511yescharacteristic
642C23×C53C2511yescharacteristic
643C22×D53—22no—
644C22×D53—28no—
645C22×D53—41no—
646C22×D53—44no—
647C22×D53—41no—
648C22×D53—41no—
649C22×D53—44no—
650C22×D53—41no—
651C22×D53C2×#4114yes—
652C22×D53C2511yescharacteristic
653C22×D53C2514yes—
654C22×D53C2511yescharacteristic
655C22×D53C2512yes—
656Q8×C53—24no—
657Q8×C53—44no—
658D4×C53—28no—
659D4×C53—24no—
660D4×C53—44no—
661D4×C53—44no—
662D4×C53—44no—
663C2×C4×C53—22no—
664C2×C4×C53—28no—
665C2×C4×C53—24no—
666C2×C4×C53—24no—
667C2×C4×C53—42no—
668C2×C4×C53—42no—
669C2×C4×C53—48no—
670C2×C4×C53—44no—
671C2×C4×C53—44no—
672C2×C4×C53C2×#4114yes—
673C2×C4×C53C2514yes—
674C2×C4×C53C2512yes—
675C2×C4×C53C2514yes—
676C2×C4×C53C2514yes—
677C2×C4×C53C2514yes—
678C2×C4×C53C2514yes—
679C2×C4×C53C2512yes—
680C22⋊D53—28no—
681C22⋊D53—24no—
682C22⋊D53—24no—
683C22⋊D53—28no—
684C22⋊D53—22no—
685C22⋊D53—22no—
686C22⋊D53—22no—
687C22⋊D53—22no—
688C22⋊D53—28no—
689C22⋊D53—44no—
690C22⋊D53—44no—
691C22⋊D53—44no—
692C22⋊D53—44no—
693C22⋊D53—48no—
694C2×Dic53—22no—
695C2×Dic53—28no—
696C2×Dic53—42no—
697C2×Dic53—48no—
698C2×Dic53—42no—
699C2×Dic53C2×#4114yes—
700C2×Dic53C2514yes—
701C2×Dic53C2512yes—
702C2×Dic53C2514yes—
703C2×Dic53C2514yes—
704C2×Dic53C2514yes—
705C2×Dic53C2514yes—
706C2×Dic53C2511yescharacteristic
707C2×Dic53C2511yescharacteristic
708D212—24no—
709D212—24no—
710D212—28no—
711D212—24no—
712D212—44no—
713D212—44no—
714D212—44no—
715C4×D53—28no—
716C4×D53—24no—
717C4×D53—24no—
718C4×D53—28no—
719C4×D53—28no—
720C4×D53—44no—
721C4×D53—48no—
722C4×D53—48no—
723C4×D53—44no—
724C4×D53—44no—
725C4×D53—48no—
726C4×D53—44no—
727C4×D53C2×#4118yes—
728C4×D53C2×#4118yes—
729Dic106—24no—
730Dic106—24no—
731Dic106—24no—
732Dic106—28no—
733Dic106—48no—
734Dic106—44no—
735#62845—531nomaximal, Sylow
736C22×C53—21no—
737C22×C53—21no—
738C22×C53—24no—
739C22×C53—21no—
740C22×C53—21no—
741C22×C53—24no—
742C22×C53—21no—
743C22×C53—21no—
744C22×C53—21no—
745C22×C53—24no—
746C22×C53—21no—
747C22×C53—44no—
748C22×C53C22×#4112yes—
749C22×C53C2611yescharacteristic
750C2×D53—22no—
751C2×D53—22no—
752C2×D53—21no—
753C2×D53—21no—
754C2×D53—24no—
755C2×D53—21no—
756C2×D53—24no—
757C2×D53—21no—
758C2×D53—21no—
759C2×D53—24no—
760C2×D53—21no—
761C2×D53—44no—
762C2×D53—416no—
763C2×D53—44no—
764C2×D53C22×#4114yes—
765C4×C53—22no—
766C4×C53—24no—
767C4×C53—24no—
768C4×C53—24no—
769C4×C53—24no—
770C4×C53—24no—
771C4×C53C22×#4114yes—
772Dic53—24no—
773Dic53—22no—
774Dic53—24no—
775Dic53—24no—
776Dic53—24no—
777Dic53—24no—
778Dic53C22×#4112yes—
779Dic53C22×#4112yes—
780#3507—534no—
781#3507—534no—
782#3507—534no—
783#3506—534no—
784#3506—534no—
785#3506—534no—
786#3493—534no—
787#3493—534no—
788#3493—532no—
789#3493—532no—
790#3492—534no—
791#3492—534no—
792#3492—531no—
793#3492—531no—
794#3492—531no—
795#3492D5311yescharacteristic, complemented
796#3459—534no—
797#3459—534no—
798#3458—531no—
799#3449—531no—
800#3449—532no—
801C2×#520—532no—
802C2×#520—531no—
803C2×C53—22no—
804C2×C53—44no—
805C2×C53—41no—
806C2×C53—41no—
807C2×C53C23×#4111yescharacteristic
808C2×C53H(7,𝔽2)11yescharacteristic
809C2×C532−1+611yescharacteristic
810D53—24no—
811D53—41no—
812D53—44no—
813D53—41no—
814C22×#41—532no—
815C22×#41—531no—
816#559—538no—
817#559—538no—
818#559—538no—
819#557—538no—
820#556—538no—
821#556—538no—
822#556—534no—
823#556—538no—
824#556—534no—
825#556—534no—
826#556—534no—
827#556—534no—
828#556—534no—
829#555—534no—
830#555—534no—
831#555—534no—
832#555—534no—
833#555—534no—
834#555—534no—
835#554—534no—
836#554—538no—
837#554—534no—
838#554—534no—
839#554C2×D5314yescomplemented
840#553—534no—
841#553—538no—
842#553—534no—
843#553—534no—
844#553—534no—
845#553—538no—
846#553—534no—
847#553—534no—
848#553—534no—
849#553C2×D5314yescomplemented
850#552—538no—
851#552—534no—
852#552—538no—
853#552—534no—
854#552—534no—
855#552—534no—
856#552—534no—
857#552—534no—
858#552—534no—
859#552C2×D5314yescomplemented
860#550—534no—
861#550—534no—
862#547—534no—
863#547—534no—
864#547—534no—
865#547—534no—
866#547—534no—
867#547C2×D5314yescomplemented
868#544—534no—
869#544—534no—
870#544—532no—
871#544—531no—
872#544C2×D5311yescharacteristic, complemented
873#543—534no—
874#539—538no—
875#539—538no—
876#539—538no—
877#539—538no—
878#539—534no—
879#539—534no—
880#539—534no—
881#539C2×D5314yescomplemented
882#538—538no—
883#538—538no—
884#538—538no—
885#538—538no—
886#538—538no—
887#538—538no—
888#537—532no—
889#537—532no—
890#537—532no—
891#537—532no—
892#537—532no—
893#537—531no—
894#537C2×D5311yescharacteristic
895#536—534no—
896#536—532no—
897#536—534no—
898#536—532no—
899#535—532no—
900#535—534no—
901#535—532no—
902#535—534no—
903#534—534no—
904#534—534no—
905#534—534no—
906#533—534no—
907#533—534no—
908#533—534no—
909#532—534no—
910#532—534no—
911#532—534no—
912#529—538no—
913#529—538no—
914#529—538no—
915#529—538no—
916#529—538no—
917#529—538no—
918#525—532no—
919#525—538no—
920#525—532no—
921#525—534no—
922#525—538no—
923#525—534no—
924#525—538no—
925#525—534no—
926#525—534no—
927#525—534no—
928#525—534no—
929#525—534no—
930#525—538no—
931#525—532no—
932#525C2×D5312yescomplemented
933#525C2×D5314yescomplemented
934#520—532no—
935#520—534no—
936#520—534no—
937#520—538no—
938#520—532no—
939#520—534no—
940#520—534no—
941#520—534no—
942#520—532no—
943#520—534no—
944#520—534no—
945#520—534no—
946#520C2×D5312yescomplemented
947C2×C4×Q8—534no—
948C2×C4×Q8—532no—
949C2×C4×D4—532no—
950C2×C4×D4—532no—
951C2×C4×D4—538no—
952C2×C4×D4—534no—
953C2×C4×D4—532no—
954C2×#117—531no—
955C2×#117—532no—
956C2×#117—534no—
957C2×#117—531no—
958C2×#117—531no—
959C22×C4⋊C4—531no—
960C22×C4⋊C4—531no—
961C22×C4⋊C4—534no—
962C22×C4⋊C4C2×D5311yescharacteristic, complemented
963C53#6284511yescharacteristic, complemented, Sylow
964C2×#41—532no—
965C2×#41—534no—
966C2×#41—532no—
967C2×#41—534no—
968C2×#41—534no—
969C2×#41—532no—
970C2×#41—532no—
971C2×#41—532no—
972C2×#41—534no—
973C2×#41—532no—
974C2×#41—532no—
975C2×#41—534no—
976C2×#41—1068no—
977C2×#41—10616no—
978C2×#41C22×D5312yes—
979C2×#41C22×D5314yes—
980C22×Q8—532no—
981C22×Q8—531no—
982C22×D4—531no—
983C22×D4—531no—
984C22×D4—534no—
985C22×D4—532no—
986C22×D4—531no—
987C23×C4—531no—
988C23×C4—534no—
989C23×C4—531no—
990C23×C4—532no—
991C23×C4—532no—
992C23×C4—538no—
993C23×C4C22×D5311yescharacteristic
994C23×C4C22×D5312yes—
995C4⋊Q8—534no—
996C4⋊Q8—534no—
997C4⋊Q8—534no—
998C4⋊Q8—534no—
999C4⋊Q8—534no—
1000C4⋊Q8—534no—
1001C4⋊Q8—534no—
1002C4⋊Q8—534no—
1003C4⋊Q8C22×D5314yes—
1004#127—534no—
1005#127—534no—
1006#127—534no—
1007#126—538no—
1008#126—538no—
1009#126—538no—
1010#126—538no—
1011#126—538no—
1012#126—538no—
1013#126—538no—
1014#126—538no—
1015#126—538no—
1016#126—538no—
1017#126—538no—
1018#126C22×D5318yes—
1019#125—538no—
1020#125—538no—
1021#125—538no—
1022#125—538no—
1023#125—538no—
1024#125—538no—
1025#125—534no—
1026#125—534no—
1027#125—534no—
1028#125C22×D5318yes—
1029#125C22×D5314yes—
1030#124—538no—
1031#124—538no—
1032#124—538no—
1033#124—538no—
1034#124—538no—
1035#124—534no—
1036#124—538no—
1037#124—534no—
1038#124—534no—
1039#124—534no—
1040#124—538no—
1041#123—534no—
1042#123—538no—
1043#123—538no—
1044#123—534no—
1045#123—538no—
1046#123—538no—
1047#123—534no—
1048#123—534no—
1049#123—538no—
1050#123—538no—
1051#123—538no—
1052#123—538no—
1053#123—538no—
1054#123—538no—
1055#123—534no—
1056#123—534no—
1057#123—534no—
1058#123—538no—
1059#123—538no—
1060#123C22×D5318yes—
1061#123C22×D5314yes—
1062#123C22×D5318yes—
1063C22⋊Q8—538no—
1064C22⋊Q8—532no—
1065C22⋊Q8—532no—
1066C22⋊Q8—534no—
1067C22⋊Q8—538no—
1068C22⋊Q8—534no—
1069C22⋊Q8—534no—
1070C22⋊Q8—532no—
1071C22⋊Q8—534no—
1072C22⋊Q8—532no—
1073C22⋊Q8—534no—
1074C22⋊Q8—538no—
1075C22⋊Q8—534no—
1076C22⋊Q8—532no—
1077C22⋊Q8—534no—
1078C22⋊Q8—534no—
1079C22⋊Q8—532no—
1080C22⋊Q8—538no—
1081C22⋊Q8—534no—
1082C22⋊Q8—538no—
1083C22⋊Q8—538no—
1084C22⋊Q8—534no—
1085C22⋊Q8—534no—
1086C22⋊Q8—538no—
1087C22⋊Q8—538no—
1088C22⋊Q8C22×D5314yes—
1089C22⋊Q8C22×D5314yes—
1090C22⋊Q8C22×D5318yes—
1091C22⋊Q8C22×D5312yes—
1092C22⋊Q8C22×D5312yes—
1093C22⋊Q8C22×D5314yes—
1094#121—534no—
1095#121—532no—
1096#121—534no—
1097#121—532no—
1098#121—534no—
1099#121—534no—
1100#121—534no—
1101#121—538no—
1102#121—538no—
1103#121—534no—
1104#121—538no—
1105#121—534no—
1106#121—532no—
1107#121—534no—
1108#121—532no—
1109#121—538no—
1110#121—534no—
1111#121—534no—
1112#121—532no—
1113#121—534no—
1114#121—532no—
1115#121—534no—
1116#121—534no—
1117#121—534no—
1118#121—534no—
1119#121—534no—
1120#121—534no—
1121#121—538no—
1122#121—534no—
1123#121—534no—
1124#121C22×D5314yes—
1125#121C22×D5314yes—
1126#121C22×D5312yes—
1127#121C22×D5312yes—
1128#121C22×D5314yes—
1129#120—534no—
1130#120—534no—
1131#120—538no—
1132#120—534no—
1133#120—534no—
1134#120—534no—
1135#120—538no—
1136#120—534no—
1137#120—534no—
1138#120C22×D5314yes—
1139C4×Q8—534no—
1140C4×Q8—534no—
1141C4×Q8—538no—
1142C4×Q8—534no—
1143C4×Q8—538no—
1144C4×Q8—538no—
1145C4×Q8—538no—
1146C4×Q8—534no—
1147C4×Q8—538no—
1148C4×Q8—534no—
1149C4×Q8—538no—
1150C4×Q8—538no—
1151C4×Q8C22×D5314yes—
1152C4×D4—538no—
1153C4×D4—534no—
1154C4×D4—534no—
1155C4×D4—538no—
1156C4×D4—538no—
1157C4×D4—538no—
1158C4×D4—538no—
1159C4×D4—534no—
1160C4×D4—534no—
1161C4×D4—538no—
1162C4×D4—534no—
1163C4×D4—534no—
1164C4×D4—538no—
1165C4×D4—538no—
1166C4×D4—534no—
1167C4×D4—534no—
1168C4×D4—534no—
1169C4×D4—534no—
1170C4×D4—538no—
1171C4×D4—538no—
1172C4×D4—538no—
1173C4×D4—534no—
1174C4×D4—538no—
1175C4×D4—534no—
1176C4×D4—538no—
1177C4×D4—538no—
1178C4×D4—538no—
1179C4×D4—538no—
1180C4×D4—538no—
1181C4×D4—538no—
1182C4×D4—538no—
1183C4×D4—534no—
1184C4×D4—534no—
1185C4×D4—534no—
1186C4×D4C22×D5318yes—
1187C4×D4C22×D5314yes—
1188C4×D4C22×D5318yes—
1189C4×D4C22×D5314yes—
1190C4×D4C22×D5314yes—
1191#117—532no—
1192#117—534no—
1193#117—534no—
1194#117—534no—
1195#117—538no—
1196#117—534no—
1197#117—534no—
1198#117—532no—
1199#117—532no—
1200#117—534no—
1201#117—534no—
1202#117—534no—
1203#117—534no—
1204#117—534no—
1205#117—534no—
1206#117—538no—
1207#117—534no—
1208#117—534no—
1209#117—538no—
1210#117—538no—
1211#117—534no—
1212#117—538no—
1213#117—538no—
1214#117C22×D5312yes—
1215#117C22×D5314yes—
1216#117C22×D5314yes—
1217C2×C4⋊C4—531no—
1218C2×C4⋊C4—532no—
1219C2×C4⋊C4—532no—
1220C2×C4⋊C4—538no—
1221C2×C4⋊C4—534no—
1222C2×C4⋊C4—531no—
1223C2×C4⋊C4—534no—
1224C2×C4⋊C4—532no—
1225C2×C4⋊C4—534no—
1226C2×C4⋊C4—538no—
1227C2×C4⋊C4—538no—
1228C2×C4⋊C4—534no—
1229C2×C4⋊C4—534no—
1230C2×C4⋊C4—534no—
1231C2×C4⋊C4—534no—
1232C2×C4⋊C4—532no—
1233C2×C4⋊C4C22×D5311yescharacteristic
1234C2×C4⋊C4C22×D5311yescharacteristic
1235C2×C4⋊C4C22×D5314yes—
1236C2×C4⋊C4C22×D5312yes—
1237C2×C4⋊C4C22×D5314yes—
1238C2×C4⋊C4C22×D5314yes—
1239C2×C22⋊C4—532no—
1240C2×C22⋊C4—532no—
1241C2×C22⋊C4—532no—
1242C2×C22⋊C4—534no—
1243C2×C22⋊C4—538no—
1244C2×C42—532no—
1245C2×C42—532no—
1246C2×C42—532no—
1247C2×C42—538no—
1248C2×C42—534no—
1249C24—531no—
1250C24—534no—
1251C24—531no—
1252C24C23×D5311yescharacteristic
1253#41—28no—
1254#41—84no—
1255#41—1068no—
1256#41—1068no—
1257#41—1068no—
1258#41—1068no—
1259#41—10616no—
1260#41—10616no—
1261#41—1068no—
1262#41—1068no—
1263#41—1068no—
1264#41—4244no—
1265#41—4244no—
1266#41—4244no—
1267C2×Q8—532no—
1268C2×Q8—532no—
1269C2×Q8—532no—
1270C2×Q8—534no—
1271C2×Q8—538no—
1272C2×Q8—534no—
1273C2×Q8—1064no—
1274C2×Q8—1068no—
1275C2×Q8C23×D5312yes—
1276C2×Q8C23×D5314yes—
1277C2×D4—532no—
1278C2×D4—532no—
1279C2×D4—534no—
1280C2×D4—534no—
1281C2×D4—531no—
1282C2×D4—531no—
1283C2×D4—531no—
1284C2×D4—531no—
1285C2×D4—534no—
1286C2×D4—534no—
1287C2×D4—534no—
1288C2×D4—538no—
1289C2×D4—534no—
1290C2×D4—534no—
1291C2×D4—532no—
1292C2×D4—532no—
1293C2×D4—534no—
1294C2×D4—532no—
1295C2×D4—534no—
1296C2×D4—534no—
1297C2×D4—534no—
1298C2×D4—1064no—
1299C2×D4—1068no—
1300C2×D4—1064no—
1301C2×D4—10616no—
1302C2×D4—1064no—
1303C2×D4C23×D5314yes—
1304C2×D4C23×D5312yes—
1305C2×D4C23×D5314yes—
1306C2×D4C23×D5314yes—
1307C2×D4C23×D5314yes—
1308C22×C4—24no—
1309C22×C4—82no—
1310C22×C4—531no—
1311C22×C4—538no—
1312C22×C4—532no—
1313C22×C4—532no—
1314C22×C4—531no—
1315C22×C4—534no—
1316C22×C4—532no—
1317C22×C4—532no—
1318C22×C4—538no—
1319C22×C4—534no—
1320C22×C4—534no—
1321C22×C4—532no—
1322C22×C4—534no—
1323C22×C4—532no—
1324C22×C4—534no—
1325C22×C4—538no—
1326C22×C4—534no—
1327C22×C4—534no—
1328C22×C4—534no—
1329C22×C4—538no—
1330C22×C4—538no—
1331C22×C4—10616no—
1332C22×C4—1064no—
1333C22×C4—4242no—
1334C22×C4—4242no—
1335C22×C4—4248no—
1336C22×C4C23×D5311yescharacteristic
1337C22×C4C23×D5314yes—
1338C22×C4C23×D5312yes—
1339C22×C4C23×D5312yes—
1340C22×C4C23×D5312yes—
1341C22×C4C23×D5312yes—
1342C22×C4C23×D5318yes—
1343C22×C4C23×D5314yes—
1344C22×C4C23×D5314yes—
1345C22×C4C23×D5311yescharacteristic
1346C4⋊C4—534no—
1347C4⋊C4—534no—
1348C4⋊C4—534no—
1349C4⋊C4—532no—
1350C4⋊C4—534no—
1351C4⋊C4—538no—
1352C4⋊C4—538no—
1353C4⋊C4—538no—
1354C4⋊C4—538no—
1355C4⋊C4—534no—
1356C4⋊C4—534no—
1357C4⋊C4—532no—
1358C4⋊C4—534no—
1359C4⋊C4—534no—
1360C4⋊C4—534no—
1361C4⋊C4—534no—
1362C4⋊C4—538no—
1363C4⋊C4—534no—
1364C4⋊C4—538no—
1365C4⋊C4—538no—
1366C4⋊C4—538no—
1367C4⋊C4—534no—
1368C4⋊C4—534no—
1369C4⋊C4—538no—
1370C4⋊C4—534no—
1371C4⋊C4C23×D5314yes—
1372C4⋊C4C23×D5312yes—
1373C4⋊C4C23×D5314yes—
1374C4⋊C4C23×D5318yes—
1375C4⋊C4C23×D5312yes—
1376C4⋊C4C23×D5318yes—
1377C4⋊C4C23×D5314yes—
1378C4⋊C4C23×D5314yes—
1379C4⋊C4C23×D5314yes—
1380C4⋊C4C23×D5318yes—
1381C4⋊C4C23×D5314yes—
1382C22⋊C4—534no—
1383C22⋊C4—534no—
1384C22⋊C4—534no—
1385C22⋊C4—538no—
1386C22⋊C4—534no—
1387C22⋊C4—534no—
1388C22⋊C4—538no—
1389C22⋊C4—534no—
1390C22⋊C4—534no—
1391C22⋊C4—538no—
1392C22⋊C4—534no—
1393C22⋊C4—534no—
1394C22⋊C4—534no—
1395C22⋊C4—534no—
1396C22⋊C4—538no—
1397C22⋊C4—538no—
1398C22⋊C4—534no—
1399C22⋊C4—534no—
1400C22⋊C4—538no—
1401C22⋊C4—534no—
1402C22⋊C4—534no—
1403C22⋊C4—538no—
1404C22⋊C4—534no—
1405C22⋊C4—534no—
1406C22⋊C4—534no—
1407C22⋊C4—534no—
1408C22⋊C4C23×D5314yes—
1409C22⋊C4C23×D5318yes—
1410C22⋊C4C23×D5314yes—
1411C22⋊C4C23×D5314yes—
1412C22⋊C4C23×D5314yes—
1413C22⋊C4C23×D5318yes—
1414C22⋊C4C23×D5314yes—
1415C42—538no—
1416C42—538no—
1417C42—538no—
1418C42—538no—
1419C42—538no—
1420C42—534no—
1421C42—534no—
1422C42—534no—
1423C42—534no—
1424C42—534no—
1425C42C23×D5318yes—
1426C42C23×D5314yes—
1427C23—22no—
1428C23—41no—
1429C23—41no—
1430C23—532no—
1431C23—534no—
1432C23—534no—
1433C23—531no—
1434C23—531no—
1435C23—1068no—
1436C23—1062no—
1437C23—2121no—
1438C23—2121no—
1439C23—2124no—
1440C23—2121no—
1441C23—2121no—
1442C23—2124no—
1443C23C24×D5311yescharacteristic
1444C23C24×D5311yescharacteristic
1445C23C24×D5314yes—
1446C23C24×D5311yescharacteristic
1447Q8—24no—
1448Q8—44no—
1449Q8—1064no—
1450Q8—1064no—
1451Q8—1068no—
1452Q8—1064no—
1453Q8—2128no—
1454Q8—2124no—
1455D4—28no—
1456D4—24no—
1457D4—44no—
1458D4—44no—
1459D4—44no—
1460D4—1064no—
1461D4—1064no—
1462D4—1068no—
1463D4—1062no—
1464D4—1062no—
1465D4—1062no—
1466D4—1062no—
1467D4—1068no—
1468D4—1064no—
1469D4—1064no—
1470D4—1068no—
1471D4—1068no—
1472D4—1064no—
1473D4—2124no—
1474D4—2124no—
1475D4—2124no—
1476D4—2124no—
1477D4—2128no—
1478D4—2124no—
1479D4—2124no—
1480D4—2124no—
1481C2×C4—22no—
1482C2×C4—24no—
1483C2×C4—24no—
1484C2×C4—28no—
1485C2×C4—42no—
1486C2×C4—42no—
1487C2×C4—44no—
1488C2×C4—44no—
1489C2×C4—48no—
1490C2×C4—534no—
1491C2×C4—531no—
1492C2×C4—531no—
1493C2×C4—538no—
1494C2×C4—538no—
1495C2×C4—534no—
1496C2×C4—534no—
1497C2×C4—534no—
1498C2×C4—534no—
1499C2×C4—532no—
1500C2×C4—534no—
1501C2×C4—1068no—
1502C2×C4—1068no—
1503C2×C4—1068no—
1504C2×C4—1062no—
1505C2×C4—1068no—
1506C2×C4—1064no—
1507C2×C4—1064no—
1508C2×C4—2124no—
1509C2×C4—2128no—
1510C2×C4—2124no—
1511C2×C4—2128no—
1512C2×C4—2124no—
1513C2×C4—2124no—
1514C2×C4—2128no—
1515C2×C4—2122no—
1516C2×C4—2122no—
1517C2×C4—2128no—
1518C2×C4#41×D5314yes—
1519C2×C4C24×D5314yes—
1520C2×C4C24×D5312yes—
1521C2×C4C24×D5314yes—
1522C2×C4C24×D5314yes—
1523C2×C4C24×D5314yes—
1524C2×C4C24×D5314yes—
1525C2×C4C24×D5312yes—
1526C22—21no—
1527C22—21no—
1528C22—21no—
1529C22—21no—
1530C22—24no—
1531C22—21no—
1532C22—21no—
1533C22—24no—
1534C22—21no—
1535C22—24no—
1536C22—21no—
1537C22—44no—
1538C22—534no—
1539C22—1062no—
1540C22—1062no—
1541C22—1064no—
1542C22—1061no—
1543C22—1061no—
1544C22—1061no—
1545C22—1064no—
1546C22—1061no—
1547C22—1061no—
1548C22—1064no—
1549C22—1061no—
1550C22—2124no—
1551C22—2124no—
1552C22—21216no—
1553C22C2×#41×D5312yes—
1554C22C25×D5311yescharacteristic
1555C4—22no—
1556C4—24no—
1557C4—24no—
1558C4—24no—
1559C4—24no—
1560C4—24no—
1561C4—532no—
1562C4—532no—
1563C4—1064no—
1564C4—1062no—
1565C4—1064no—
1566C4—1064no—
1567C4—1064no—
1568C4—1064no—
1569C4C2×#41×D5314yes—
1570C2—22no—
1571C2—41no—
1572C2—41no—
1573C2—44no—
1574C2—1064no—
1575C2—2121no—
1576C2—2121no—
1577C2—2124no—
1578C2C22×#41×D5311yescharacteristic
1579C2#2028952511yescharacteristic
1580C2#2028952711yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3492C2
hypercenter#3492D53
hypocenterC53#62845
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3492

Complements

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

NH ≅ G/Ntype
1. #20288578C2semidirect
2. #20288575C2semidirect
3. #20288574C2semidirect
4. #20288565C2semidirect
5. #20288561C2semidirect
6. #20288558C2semidirect
7. #20288433C2semidirect
8. #20288432C2semidirect
9. #20288431C2semidirect
10. #20288428C2semidirect
11. #20288425C2semidirect
12. #20288424C2semidirect
13. #20288423C2semidirect
14. #20288422C2semidirect
15. #20288417C2semidirect
16. #20288123C2semidirect
17. #20288122C2semidirect
18. #20288119C2semidirect
19. #20288045C2semidirect
20. #20288043C2semidirect
21. C2×#16811104C2semidirect
22. #520×D53C2semidirect
23. C53×#3492C2semidirect
26. #16811357C22semidirect
27. #16811357C22semidirect
28. #16811356C22semidirect
29. #16811350C22semidirect
30. #16811346C22semidirect
31. #16811344C22semidirect
32. #16811344C22semidirect
33. #16811344C22semidirect
34. #16811343C22semidirect
35. #16811341C22semidirect
36. #16811341C22semidirect
37. #16811340C22semidirect
38. #16811340C22semidirect
39. #16811338C22semidirect
40. #16811338C22semidirect
41. #16811337C22semidirect
42. #16811337C22semidirect
43. #16811336C22semidirect
44. #16811336C22semidirect
45. #16811334C22semidirect
46. #16811331C22semidirect
47. #16811328C22semidirect
48. #16811327C22semidirect
49. #16811326C22semidirect
50. #16811323C22semidirect
51. #16811322C22semidirect
52. #16811321C22semidirect
53. #16811321C22semidirect
54. #16811320C22semidirect
55. #16811320C22semidirect
56. #16811319C22semidirect
57. #16811318C22semidirect
58. #16811314C22semidirect
59. #16811313C22semidirect
60. #16811311C22semidirect
61. #16811310C22semidirect
62. #16811308C22semidirect
63. #16811308C22semidirect
64. #16811307C22semidirect
65. #16811307C22semidirect
66. #16811305C22semidirect
67. #16811292C22semidirect
68. #16811291C22semidirect
69. #16811276C22semidirect
70. #16811275C22semidirect
71. #16811274C22semidirect
72. #16811273C22semidirect
73. #16811272C22semidirect
74. #16811254C22semidirect
75. #16811253C22semidirect
76. #16811251C22semidirect
77. #16811250C22semidirect
79. #16811222C22semidirect
80. #16811221C22semidirect
81. #16811220C22semidirect
82. #16811219C22semidirect
83. #16811219C22semidirect
84. #16811218C22semidirect
85. #16811216C22semidirect
86. #16811212C22semidirect
87. #16811209C22semidirect
88. #16811209C22semidirect
89. #16811208C22semidirect
90. #16811206C22semidirect
91. #16811205C22semidirect
98. #16811196C22semidirect
99. #16811196C22semidirect
100. #16811196C22semidirect
101. #16811195C22semidirect
102. #16811189C22semidirect
103. #16811189C22semidirect
104. #16811189C22semidirect
105. #16811188C22semidirect
109. #16811179C22semidirect
110. #16811178C22semidirect
111. #16811175C22semidirect
115. #16811158C22semidirect
116. #16811156C22semidirect
117. #16811155C22semidirect
118. #16811153C22semidirect
119. #16811151C22semidirect
120. #16811150C22semidirect
121. #16811136C22semidirect
122. #16811136C22semidirect
123. #16811136C22semidirect
124. #16811135C22semidirect
125. #16811134C22semidirect
126. #16811134C22semidirect
127. #16811133C22semidirect
128. #16811133C22semidirect
129. #16811132C22semidirect
130. #16811132C22semidirect
131. #16811132C22semidirect
132. #16811131C22semidirect
133. #16811130C22semidirect
134. #16811130C22semidirect
135. #16811106C22semidirect
136. #16811105C22semidirect
137. #16811104C22semidirect
138. #16811104C22semidirect
139. #16811104C22semidirect
140. #16811104C22semidirect
141. #16811104C22semidirect
142. #16811104C22semidirect
143. #16811103C22semidirect
144. #16811103C22semidirect
145. #16811102C22semidirect
146. #16811102C22semidirect
147. C2×#13133182C22semidirect
148. C4×Q8×D53C22semidirect
151. C2×C4×C22⋊D53C22semidirect
153. C4×D4×D53C22semidirect
154. C2×#13133176C22semidirect
156. C2×#13133175C22semidirect
158. #117×D53C22semidirect
160. C2×C4⋊C4×D53C22semidirect
161. C2×C4⋊C4×D53C22semidirect
162. C53×#554C22semidirect
163. C53×#553C22semidirect
164. C53×#552C22semidirect
165. C53×#547C22semidirect
166. C53×#544C22semidirect
167. C53×#539C22semidirect
169. C53×#525C22semidirect
170. C53×#525C22semidirect
171. C53×#520C22semidirect
172. C22×C4⋊C4×C53C22semidirect
533. C2×C4×D53#41semidirect
795. #3492D53semidirect
839. #554C2×D53semidirect
849. #553C2×D53semidirect
859. #552C2×D53semidirect
867. #547C2×D53semidirect
872. #544C2×D53semidirect
881. #539C2×D53semidirect
932. #525C2×D53semidirect
933. #525C2×D53semidirect
946. #520C2×D53semidirect
962. C22×C4⋊C4C2×D53semidirect
963. C53#62845semidirect

Maximal subgroups

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

subgroupindex
#202885782
#202885752
#202885742
#202885652
#202885612
#202885582
#202884332
#202884322
#202884312
#202884282
#202884252
#202884242
#202884232
#202884222
#202884172
#202881232
#202881222
#202881192
#202880452
#202880432
C2×#168111042
#520×D532
C53×#34922
#6284553