Finite Group Databasebeta

← #27352990

Subgroups — #27352990

Order 13568.

926 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288626C211yesmaximal, characteristic
2#20283840C211yesmaximal, characteristic, complemented
3#20273443C211yesmaximal, characteristic, complemented
4#20273438C211yesmaximal, characteristic, complemented
5#20273433C211yesmaximal, characteristic, complemented
6#20273426C211yesmaximal, characteristic, complemented
7#20273418C211yesmaximal, characteristic, complemented
8#20273411C211yesmaximal, characteristic, complemented
9#20273408C211yesmaximal, characteristic, complemented
10#20273403C211yesmaximal, characteristic, complemented
11#20273393C211yesmaximal, characteristic, complemented
12#20273370C211yesmaximal, characteristic, complemented
13#20273365C211yesmaximal, characteristic, complemented
14C2×#16810370C211yesmaximal, characteristic, complemented
15C53×#2990C211yesmaximal, characteristic, complemented
16#16811346—21no—
17#16811338—21no—
18#16811333—21no—
19#16811319—21no—
20#16811319—21no—
21#16811282—21no—
22#16811282—21no—
23#16811278—21no—
24#16811244C412yes—
25#16811244C412yes—
26#16811201C412yes—
27#16811180C2211yescharacteristic
28#16811180C2211yescharacteristic
29#16811173C2211yescharacteristic
30#16811173C2211yescharacteristic
31#16811173C2211yescharacteristic
32C2×#13133217C2211yescharacteristic
33#16811103C412yes—
34#16810754—21no—
35#16810695—21no—
36#16810695—21no—
37D4×#88322—21no—
38#16810680C2211yescharacteristic
39#16810680C2211yescharacteristic
40#16810676C2211yescharacteristic
41#16810647C2211yescharacteristic
42C2×C4⋊#88322C2211yescharacteristic
43C2×C4⋊#88322C2211yescharacteristic
44#16810371C2211yescharacteristic
45#16810371C2211yescharacteristic
46#16810371C2211yescharacteristic
47#16810371C2211yescharacteristic
48#16810370C2211yescharacteristic
49#16810370C2211yescharacteristic
50#16810370C2211yescharacteristic
51#16810370C2211yescharacteristic
52#16810370C2211yescharacteristic
53#16810370C2211yescharacteristic
54#16810370C2211yescharacteristic
55#16810370C2211yescharacteristic
56#16810366C2211yescharacteristic
57#16810366C2211yescharacteristic
58#16810366C2211yescharacteristic
59#16810366C2211yescharacteristic
60C4×#41×C53C2211yescharacteristic
61C53×#446—21no—
62C53×#435—21no—
63C53×#435—21no—
64C8×D4×C53—21no—
65C53×#432C2211yescharacteristic
66C53×#432C2211yescharacteristic
67C53×#431C2211yescharacteristic
68C53×#423C2211yescharacteristic
69C2×C4⋊C8×C53C2211yescharacteristic
70C2×C4⋊C8×C53C2211yescharacteristic
71C2×#11719945—21no—
72C2×#11719945—21no—
73C2×#11719945C2×C412yes—
74C22×Dic106—21no—
75C2×#11719917—21no—
76C22×#88322—21no—
77C22×#88322—21no—
78#13133217—21no—
79#13133217—21no—
80#13133217C2×C412yes—
81#13133217C2311yescharacteristic
82#13133217C2311yescharacteristic
83#13133217C2311yescharacteristic
84#13133214C2311yescharacteristic
85#13133212—22no—
86#13133212—22no—
87#13133209—21no—
88#13133209—21no—
89#13133205—21no—
90#13133205—21no—
91#13133205C2×C412yes—
92#13133203—22no—
93#13133203—22no—
94#13133199—22no—
95#13133199—22no—
96#13133196—21no—
97#13133196—21no—
98#13133196C2×C412yes—
99#13133196C2×C412yes—
100#13133195—22no—
101#13133195—22no—
102#13133193—22no—
103#13133191—21no—
104#13133191—21no—
105#13133191—21no—
106#13133191—21no—
107#13133191C2×C412yes—
108#13133191C2×C412yes—
109#13133189—22no—
110#13133189—22no—
111#13133188—22no—
112C4×Dic106—21no—
113C4×Dic106—21no—
114C4×Dic106C2×C412yes—
115C4×Dic106C2×C412yes—
116C4×D212—21no—
117C4×D212—21no—
118C4×D212—21no—
119C4×D212—21no—
120C4×D212C2×C412yes—
121C4×D212C2×C412yes—
122#13133177—22no—
123#13133177—22no—
124#13133176—21no—
125#13133176—21no—
126#13133175—22no—
127C2×C4⋊Dic53—21no—
128C2×C4⋊Dic53C2×C412yes—
129C4⋊C4×D53—22no—
130C4⋊#88322—21no—
131C4⋊#88322—21no—
132C4⋊#88322—21no—
133C4⋊#88322C2311yescharacteristic
134C4⋊#88322C2311yescharacteristic
135C4⋊#88322C2311yescharacteristic
136C4⋊#88322C2311yescharacteristic
137C22⋊#88322—21no—
138C22⋊#88322—21no—
139C22⋊#88322—21no—
140#13133128—21no—
141#13133128—21no—
142C4×#88322—21no—
143C2×#41×C53C2×C411yescharacteristic
144C2×M16×C53—21no—
145C22×C8×C53—21no—
146C22×C8×C53—21no—
147C4×Q8×C53D411yescharacteristic
148C4×Q8×C53D411yescharacteristic
149C4×D4×C53D411yescharacteristic
150C4×D4×C53D411yescharacteristic
151C4×D4×C53D411yescharacteristic
152C4×D4×C53D411yescharacteristic
153C4×D4×C53D411yescharacteristic
154C4×D4×C53D411yescharacteristic
155#117×C53C2×C411yescharacteristic
156#117×C53C2×C411yescharacteristic
157#117×C53C2×C411yescharacteristic
158C2×C42×C53C2311yescharacteristic
159C2×C42×C53C2311yescharacteristic
160C2×C42×C53C2311yescharacteristic
161C4⋊C8×C53—21no—
162C4⋊C8×C53—21no—
163C4⋊C8×C53—21no—
164C4⋊C8×C53C2311yescharacteristic
165C4⋊C8×C53C2311yescharacteristic
166C4⋊C8×C53C2311yescharacteristic
167C4⋊C8×C53C2311yescharacteristic
168C22⋊C8×C53—21no—
169C22⋊C8×C53—21no—
170C22⋊C8×C53—21no—
171#97×C53—21no—
172#97×C53—21no—
173C4×C8×C53—21no—
174#41×C53—42no—
175C2×Q8×C53C22⋊C411yescharacteristic
176C2×D4×C53C22⋊C411yescharacteristic
177C2×D4×C53C22⋊C411yescharacteristic
178C2×D4×C53C22⋊C411yescharacteristic
179C22×C4×C53C22×C411yescharacteristic
180C22×C4×C53C22×C411yescharacteristic
181C22×C4×C53C22×C411yescharacteristic
182C22×C4×C53C2×D411yescharacteristic
183C22×C4×C53C2×D411yescharacteristic
184C22×C4×C53C2×D411yescharacteristic
185C22×C4×C53C2×D411yescharacteristic
186C22×C4×C53C2×D411yescharacteristic
187C22×C4×C53C2×D411yescharacteristic
188C2×C22⋊D53—22no—
189C2×C22⋊D53—22no—
190C2×C22⋊D53—22no—
191C22×Dic53—22no—
192#11719945—44no—
193#11719945—81no—
194#11719945—81no—
195#11719945—81no—
196#11719945—81no—
197C2×D212—21no—
198C2×D212—21no—
199C2×D212C22×C412yes—
200C2×C4×D53—22no—
201C2×C4×D53—22no—
202C2×C4×D53—22no—
203C2×Dic106—21no—
204C2×Dic106—21no—
205C2×Dic106—22no—
206C2×Dic106—81no—
207C2×Dic106—81no—
208C2×Dic106C22×C412yes—
209M16×C53—81no—
210C2×C8×C53—21no—
211C2×C8×C53—21no—
212C2×C8×C53—21no—
213C2×C8×C53—21no—
214C2×C8×C53—81no—
215C2×C8×C53—81no—
216C4⋊C4×C53C22⋊C411yescharacteristic
217C4⋊C4×C53C22⋊C411yescharacteristic
218C4⋊C4×C53C22⋊C411yescharacteristic
219C4⋊C4×C53C22⋊C411yescharacteristic
220C4⋊C4×C53C22⋊C411yescharacteristic
221C4⋊C4×C53C22⋊C411yescharacteristic
222C22⋊C4×C53C22⋊C411yescharacteristic
223C22⋊C4×C53C22⋊C411yescharacteristic
224C22⋊C4×C53C22⋊C411yescharacteristic
225C22⋊C4×C53C22⋊C411yescharacteristic
226C22⋊C4×C53C22⋊C411yescharacteristic
227C22⋊C4×C53C22⋊C411yescharacteristic
228C42×C53C22×C411yescharacteristic
229C42×C53C22×C411yescharacteristic
230C42×C53C22×C411yescharacteristic
231C42×C53C2×D411yescharacteristic
232C42×C53C2×D411yescharacteristic
233C42×C53C2×D411yescharacteristic
234C42×C53C2×D411yescharacteristic
235C42×C53C2×D411yescharacteristic
236C42×C53C2×D411yescharacteristic
237C42×C53C2411yescharacteristic
238C22⋊Dic53—22no—
239C22⋊Dic53—22no—
240#11719921—22no—
241#11719921—22no—
242#11719921—22no—
243#11719921—22no—
244#11719921—22no—
245#11719921—22no—
246C4⋊Dic53—22no—
247C4⋊Dic53—22no—
248C4⋊Dic53—21no—
249C4⋊Dic53—21no—
250C4⋊Dic53—21no—
251C4⋊Dic53—21no—
252C4⋊Dic53C22×C412yes—
253C4⋊Dic53C22×C412yes—
254#11719919—22no—
255#11719919—22no—
256#11719919—22no—
257#11719919—22no—
258C4×Dic53—22no—
259C4×Dic53—22no—
260#11719917—81no—
261C2×#88322—21no—
262C2×#88322—21no—
263C2×#88322—21no—
264C2×#88322—21no—
265C2×#88322—81no—
266C2×#88322—81no—
267C23×C53C2×C22⋊C411yescharacteristic
268C23×C53C2×C22⋊C411yescharacteristic
269C23×C53C2×C22⋊C411yescharacteristic
270C22×D53—22no—
271Q8×C53—41no—
272D4×C53—22no—
273D4×C53—22no—
274D4×C53—41no—
275C2×C4×C53—22no—
276C2×C4×C53—21no—
277C2×C4×C53—21no—
278C2×C4×C53—21no—
279C2×C4×C53—21no—
280C2×C4×C53—21no—
281C2×C4×C53—21no—
282C2×C4×C53—21no—
283C2×C4×C53—21no—
284C2×C4×C53—21no—
285C2×C4×C53—21no—
286C2×C4×C53—21no—
287C2×C4×C53—21no—
288C2×C4×C53—41no—
289C2×C4×C53—41no—
290C2×C4×C53C2×C22⋊C411yescharacteristic
291C2×C4×C53C2×C22⋊C411yescharacteristic
292C2×C4×C53C2×C22⋊C411yescharacteristic
293C2×C4×C53C2×C22⋊C411yescharacteristic
294C2×C4×C53C2×C22⋊C411yescharacteristic
295C2×C4×C53C2×C22⋊C411yescharacteristic
296C2×C4×C53C2×C22⋊C411yescharacteristic
297C2×C4×C53C2×C22⋊C411yescharacteristic
298C2×C4×C53C2×C22⋊C411yescharacteristic
299C2×C4×C53C23×C411yescharacteristic
300C2×C4×C53C22×D411yescharacteristic
301C2×C4×C53C22×D411yescharacteristic
302C22⋊D53—44no—
303C22⋊D53—82no—
304C22⋊D53—82no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—82no—
309D212—42no—
310D212—41no—
311D212—41no—
312D212—41no—
313D212—41no—
314C4×D53—44no—
315C4×D53—82no—
316C4×D53—82no—
317Dic106—41no—
318Dic106—41no—
319Dic106—41no—
320Dic106—41no—
321Dic106—42no—
322Dic106—82no—
323C8×C53—41no—
324C8×C53—41no—
325C8×C53—41no—
326C8×C53—41no—
327#88322—41no—
328#88322—41no—
329#88322—41no—
330#88322—41no—
331#17775—531nomaximal, Sylow
332C22×C53—21no—
333C22×C53—21no—
334C22×C53—21no—
335C22×C53—21no—
336C22×C53—21no—
337C22×C53—21no—
338C22×C53—21no—
339C22×C53—21no—
340C22×C53#41312yes—
341C22×C53C22×C22⋊C411yescharacteristic
342C2×D53—42no—
343C2×D53—42no—
344C2×D53—42no—
345C4×C53—21no—
346C4×C53—21no—
347C4×C53—21no—
348C4×C53—21no—
349C4×C53—21no—
350C4×C53—21no—
351C4×C53—21no—
352C4×C53—21no—
353C4×C53—21no—
354C4×C53—21no—
355C4×C53#57611yescharacteristic
356C4×C53#57711yescharacteristic
357C4×C53#57711yescharacteristic
358C4×C53#57811yescharacteristic
359Dic53—42no—
360Dic53—42no—
361Dic53—42no—
362#3511—531no—
363#2990—531no—
364#2990D5311yescharacteristic, complemented
365#1559—531no—
366#1557—531no—
367#1556—531no—
368#1554—531no—
369#1553—531no—
370#1551—531no—
371#1551—531no—
372#1550—531no—
373#1547—531no—
374#1542—531no—
375#1540—531no—
376C2×#332—531no—
377C2×C53—22no—
378C2×C53—41no—
379C2×C53—41no—
380C2×C53C2×#41311yescharacteristic
381C2×C53#289711yescharacteristic
382C2×C53#289811yescharacteristic
383D53—82no—
384#556—1061no—
385#555—1061no—
386#554—1061no—
387#553—1061no—
388#553—1061no—
389#548—1061no—
390#548—1061no—
391#547—1061no—
392#542—532no—
393#542—532no—
394#537—532no—
395#533—531no—
396#533—531no—
397#532—531no—
398#532—531no—
399#532—531no—
400C2×C4⋊Q8—531no—
401#520—532no—
402C4×#41C2×D5311yescharacteristic
403#446—21no—
404#446—1061no—
405#435—21no—
406#435—21no—
407#435—1061no—
408#435—1061no—
409C8×D4—21no—
410C8×D4—1061no—
411#432—531no—
412#432—531no—
413#432C2×D5311yescharacteristic
414#432C2×D5311yescharacteristic
415#431—531no—
416#431C2×D5311yescharacteristic
417#423—531no—
418#423C2×D5311yescharacteristic
419C2×C4⋊C8—531no—
420C2×C4⋊C8—531no—
421C2×C4⋊C8C2×D5311yescharacteristic
422C2×C4⋊C8C2×D5311yescharacteristic
423#333—531no—
424#333—531no—
425#333—531no—
426#333—531no—
427#332—531no—
428#332—531no—
429#332—531no—
430#332—531no—
431#332—531no—
432#332—531no—
433#332—531no—
434#332—531no—
435#331—531no—
436#331—531no—
437#331—531no—
438#331—531no—
439C53#1777511yescharacteristic, complemented, Sylow
440C2×#41—532no—
441C2×#41—1061no—
442C2×#41—1061no—
443C2×#41C4×D5311yescharacteristic
444C22×Q8—1061no—
445C2×M16—21no—
446C2×M16—1061no—
447C22×C8—21no—
448C22×C8—21no—
449C22×C8—1061no—
450C22×C8—1061no—
451C4⋊Q8—532no—
452C4⋊Q8—531no—
453C4⋊Q8—531no—
454C4⋊Q8—531no—
455C4⋊Q8—1061no—
456C4⋊Q8—1061no—
457#127—531no—
458#126—1062no—
459#126—1062no—
460#125—1061no—
461#125—1061no—
462#124—532no—
463#124—1062no—
464#124—1062no—
465#124—1061no—
466#124—1061no—
467#123—1062no—
468#123—1062no—
469C22⋊Q8—532no—
470C22⋊Q8—532no—
471C22⋊Q8—1062no—
472C22⋊Q8—1061no—
473C22⋊Q8—1061no—
474C22⋊Q8—1062no—
475C22⋊Q8—1062no—
476#121—532no—
477#121—532no—
478#121—1062no—
479#121—1062no—
480#121—1062no—
481#121—1061no—
482#121—1061no—
483#121—1061no—
484#121—1061no—
485C4×Q8—532no—
486C4×Q8—532no—
487C4×Q8—1061no—
488C4×Q8—1061no—
489C4×Q8D21211yescharacteristic
490C4×Q8C22⋊D5311yescharacteristic
491C4×D4—532no—
492C4×D4—532no—
493C4×D4—1062no—
494C4×D4—1062no—
495C4×D4—1061no—
496C4×D4—1061no—
497C4×D4—1061no—
498C4×D4—1061no—
499C4×D4D21211yescharacteristic
500C4×D4D21211yescharacteristic
501C4×D4D21211yescharacteristic
502C4×D4C22⋊D5311yescharacteristic
503C4×D4C22⋊D5311yescharacteristic
504C4×D4C22⋊D5311yescharacteristic
505#117—1061no—
506#117—1061no—
507#117—1062no—
508#117C4×D5311yescharacteristic
509#117C4×D5311yescharacteristic
510#117C4×D5311yescharacteristic
511C2×C4⋊C4—532no—
512C2×C4⋊C4—1061no—
513C2×C4⋊C4—1062no—
514C2×C42C22×D5311yescharacteristic
515C2×C42C22×D5311yescharacteristic
516C2×C42C22×D5311yescharacteristic
517C4⋊C8—21no—
518C4⋊C8—21no—
519C4⋊C8—21no—
520C4⋊C8—531no—
521C4⋊C8—531no—
522C4⋊C8—531no—
523C4⋊C8—531no—
524C4⋊C8—1061no—
525C4⋊C8—1061no—
526C4⋊C8—1061no—
527C4⋊C8C22×D5311yescharacteristic
528C4⋊C8C22×D5311yescharacteristic
529C4⋊C8C22×D5311yescharacteristic
530C4⋊C8C22×D5311yescharacteristic
531C22⋊C8—21no—
532C22⋊C8—21no—
533C22⋊C8—21no—
534C22⋊C8—1061no—
535C22⋊C8—1061no—
536C22⋊C8—1061no—
537#97—21no—
538#97—21no—
539#97—1061no—
540#97—1061no—
541C4×C8—21no—
542C4×C8—1061no—
543#41—42no—
544#41—4241no—
545#41—4241no—
546#41—4241no—
547#41—4241no—
548#41—2124no—
549C2×Q8—532no—
550C2×Q8—1062no—
551C2×Q8—1061no—
552C2×Q8—1061no—
553C2×Q8—4241no—
554C2×Q8—4241no—
555C2×Q8#1171992111yescharacteristic
556C2×D4—532no—
557C2×D4—1062no—
558C2×D4—1062no—
559C2×D4—1062no—
560C2×D4—1061no—
561C2×D4—1061no—
562C2×D4#1171992111yescharacteristic
563C2×D4#1171992111yescharacteristic
564C2×D4#1171992111yescharacteristic
565C22×C4—1062no—
566C22×C4—1062no—
567C22×C4—1062no—
568C22×C4—1062no—
569C22×C4C2×C4×D5311yescharacteristic
570C22×C4C2×C4×D5311yescharacteristic
571C22×C4C2×C4×D5311yescharacteristic
572C22×C4C2×D21211yescharacteristic
573C22×C4C2×D21211yescharacteristic
574C22×C4C2×D21211yescharacteristic
575C22×C4C2×C22⋊D5311yescharacteristic
576C22×C4C2×C22⋊D5311yescharacteristic
577C22×C4C2×C22⋊D5311yescharacteristic
578M16—81no—
579M16—4241no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—81no—
585C2×C8—81no—
586C2×C8—1061no—
587C2×C8—1061no—
588C2×C8—1061no—
589C2×C8—1061no—
590C2×C8—4241no—
591C2×C8—4241no—
592C4⋊C4—532no—
593C4⋊C4—532no—
594C4⋊C4—1062no—
595C4⋊C4—1062no—
596C4⋊C4—1062no—
597C4⋊C4—1062no—
598C4⋊C4—1062no—
599C4⋊C4—1062no—
600C4⋊C4—1061no—
601C4⋊C4—1061no—
602C4⋊C4—1061no—
603C4⋊C4—1061no—
604C4⋊C4#1171992111yescharacteristic
605C4⋊C4#1171992111yescharacteristic
606C4⋊C4#1171992111yescharacteristic
607C4⋊C4#1171992111yescharacteristic
608C4⋊C4#1171992111yescharacteristic
609C4⋊C4#1171992111yescharacteristic
610C22⋊C4—1062no—
611C22⋊C4—1062no—
612C22⋊C4—1062no—
613C22⋊C4—1062no—
614C22⋊C4—1062no—
615C22⋊C4—1062no—
616C22⋊C4—1062no—
617C22⋊C4—1062no—
618C22⋊C4#1171992111yescharacteristic
619C22⋊C4#1171992111yescharacteristic
620C22⋊C4#1171992111yescharacteristic
621C22⋊C4#1171992111yescharacteristic
622C22⋊C4#1171992111yescharacteristic
623C22⋊C4#1171992111yescharacteristic
624C42—1062no—
625C42—1062no—
626C42C2×C4×D5311yescharacteristic
627C42C2×C4×D5311yescharacteristic
628C42C2×C4×D5311yescharacteristic
629C42C2×D21211yescharacteristic
630C42C2×D21211yescharacteristic
631C42C2×D21211yescharacteristic
632C42C2×C22⋊D5311yescharacteristic
633C42C2×C22⋊D5311yescharacteristic
634C42C2×C22⋊D5311yescharacteristic
635C42C23×D5311yescharacteristic
636C23—1062no—
637C23C2×#1171992111yescharacteristic
638C23C2×#1171992111yescharacteristic
639C23C2×#1171992111yescharacteristic
640Q8—41no—
641Q8—4242no—
642Q8—2122no—
643Q8—2121no—
644Q8—2121no—
645Q8—2121no—
646Q8—2121no—
647D4—22no—
648D4—22no—
649D4—41no—
650D4—4242no—
651D4—4242no—
652D4—2122no—
653D4—2124no—
654D4—2121no—
655D4—2121no—
656D4—2121no—
657D4—2121no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—1062no—
674C2×C4—1062no—
675C2×C4—1062no—
676C2×C4—4242no—
677C2×C4—4242no—
678C2×C4—4242no—
679C2×C4—2124no—
680C2×C4C2×#1171992111yescharacteristic
681C2×C4C2×#1171992111yescharacteristic
682C2×C4C2×#1171992111yescharacteristic
683C2×C4C2×#1171992111yescharacteristic
684C2×C4C2×#1171992111yescharacteristic
685C2×C4C2×#1171992111yescharacteristic
686C2×C4C2×#1171992111yescharacteristic
687C2×C4C2×#1171992111yescharacteristic
688C2×C4C2×#1171992111yescharacteristic
689C2×C4C22×C4×D5311yescharacteristic
690C2×C4C22×C22⋊D5311yescharacteristic
691C2×C4C22×D21211yescharacteristic
692C8—41no—
693C8—41no—
694C8—41no—
695C8—41no—
696C8—2121no—
697C8—2121no—
698C8—2121no—
699C8—2121no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—2122no—
709C22—2122no—
710C22—2122no—
711C22#1681060512yes—
712C22C22×#1171992111yescharacteristic
713C4—21no—
714C4—21no—
715C4—21no—
716C4—21no—
717C4—21no—
718C4—21no—
719C4—21no—
720C4—21no—
721C4—21no—
722C4—21no—
723C4—2122no—
724C4—2122no—
725C4—2122no—
726C4#1681142611yescharacteristic
727C4#1681143111yescharacteristic
728C4#1681143511yescharacteristic
729C4#1681144011yescharacteristic
730C2—22no—
731C2—41no—
732C2—41no—
733C2—4242no—
734C2C2×#1681060511yescharacteristic
735C2#2028323811yescharacteristic
736C2#2028324911yescharacteristic
subgroupG/H
centerC22C22×#11719921
commutatorC2×C4×C53C23×C4
FrattiniC42C23×D53
FittingC53×#2990C2
socleC22×C53C22×C22⋊C4
prime radical#20288626C2
cosocleC42×C53C24
hypercenter#2990D53
hypocenterC53#17775
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2990

Complements

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

NH ≅ G/Ntype
2. #20283840C2semidirect
3. #20273443C2semidirect
4. #20273438C2semidirect
5. #20273433C2semidirect
6. #20273426C2semidirect
7. #20273418C2semidirect
8. #20273411C2semidirect
9. #20273408C2semidirect
10. #20273403C2semidirect
11. #20273393C2semidirect
12. #20273370C2semidirect
13. #20273365C2semidirect
14. C2×#16810370C2semidirect
15. C53×#2990C2semidirect
364. #2990D53semidirect
439. C53#17775semidirect

Maximal subgroups

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

subgroupindex
#202886262
#202838402
#202734432
#202734382
#202734332
#202734262
#202734182
#202734112
#202734082
#202734032
#202733932
#202733702
#202733652
C2×#168103702
C53×#29902
#1777553