Finite Group Databasebeta

← #27351757

Subgroups — #27351757

Order 13568.

944 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283373C211yesmaximal, characteristic, complemented
2#20277575C211yesmaximal, characteristic, complemented
3#20273292C211yesmaximal, characteristic, complemented
4#20273279C211yesmaximal, characteristic, complemented
5#20273271C211yesmaximal, characteristic
6#20273266C211yesmaximal, characteristic, complemented
7#20273253C211yesmaximal, characteristic, complemented
8#20273248C211yesmaximal, characteristic, complemented
9#20273240C211yesmaximal, characteristic, complemented
10#20273227C211yesmaximal, characteristic, complemented
11#20273219C211yesmaximal, characteristic
12#20273214C211yesmaximal, characteristic, complemented
13#20273201C211yesmaximal, characteristic, complemented
14C2×#16810360C211yesmaximal, characteristic, complemented
15C53×#3495C211yesmaximal, characteristic
16#16810684—21no—
17#16810684—21no—
18#16810680C2211yescharacteristic
19#16810680C2211yescharacteristic
20#16810676C2211yescharacteristic
21#16810676C2211yescharacteristic
22#16810650—21no—
23#16810587C2211yescharacteristic
24C2×C22⋊#88322C2211yescharacteristic
25#16810579—21no—
26#16810509—21no—
27#16810509—21no—
28#16810498—21no—
29#16810491C2211yescharacteristic
30#16810489C2211yescharacteristic
31#16810486C2211yescharacteristic
32C4×C4⋊Dic53C2211yescharacteristic
33C22⋊C4×Dic53—21no—
34#16810469C2211yescharacteristic
35C2×#13133124C2211yescharacteristic
36#16810360C2211yescharacteristic
37#16810360C2211yescharacteristic
38#16810360C2211yescharacteristic
39#16810360C2211yescharacteristic
40#16810360C2211yescharacteristic
41#16810360C2211yescharacteristic
42#16810360C2211yescharacteristic
43#16810360C2211yescharacteristic
44#16810360C2211yescharacteristic
45#16810360C2211yescharacteristic
46#16810360C2211yescharacteristic
47#16810360C2211yescharacteristic
48#16810357C2211yescharacteristic
49#16810357C2211yescharacteristic
50#16810357C2211yescharacteristic
51#16810357C2211yescharacteristic
52C53×#556—21no—
53C53×#554—21no—
54C53×#552—21no—
55C53×#552—21no—
56C53×#552—21no—
57C53×#552—21no—
58C53×#551—21no—
59C53×#551—21no—
60C53×#544C411yescharacteristic, complemented
61C53×#542C411yescharacteristic, complemented
62C53×#542C411yescharacteristic, complemented
63C53×#541C411yescharacteristic, complemented
64C53×#541C411yescharacteristic, complemented
65C53×#536C411yescharacteristic, complemented
66C53×#533C2211yescharacteristic
67C53×#533C2211yescharacteristic
68C53×#529C2211yescharacteristic
69C53×#529C2211yescharacteristic
70C53×#525C2211yescharacteristic
71C2×C22⋊Q8×C53C2211yescharacteristic
72C53×#520C411yescharacteristic, complemented
73C53×#519C411yescharacteristic, complemented
74C2×#117×C53C2211yescharacteristic
75C23×Dic53—21no—
76C2×#11719917—21no—
77C22×#88322—21no—
78C2×C4⋊Dic53—21no—
79C2×C4⋊Dic53—21no—
80C2×C22⋊Dic53—21no—
81C2×C4×Dic53—21no—
82C2×C4×Dic53—21no—
83C4⋊#88322—21no—
84C4⋊#88322—21no—
85C4⋊#88322—21no—
86C4⋊#88322—21no—
87C22⋊#88322—21no—
88C22⋊#88322—21no—
89C22⋊#88322C2311yescharacteristic
90C22⋊#88322C2311yescharacteristic
91C22⋊#88322C2311yescharacteristic
92C22⋊#88322C2311yescharacteristic
93#13133128—21no—
94#13133128—21no—
95C4×#88322—21no—
96C4×#88322—21no—
97#13133124—21no—
98#13133124—21no—
99#13133124—21no—
100#13133124—21no—
101#13133124—21no—
102#13133124—21no—
103#13133124C2311yescharacteristic
104#13133124C2311yescharacteristic
105#13133124C2311yescharacteristic
106#13133124C2311yescharacteristic
107C2×#41×C53C2×C411yescharacteristic
108C22×Q8×C53C2×C411yescharacteristic
109C23×C4×C53C2311yescharacteristic
110C4⋊Q8×C53—21no—
111C4⋊Q8×C53C2×C411yescharacteristic, complemented
112C4⋊Q8×C53C2×C411yescharacteristic, complemented
113C4⋊Q8×C53C2×C411yescharacteristic, complemented
114C4⋊Q8×C53C2×C411yescharacteristic, complemented
115#126×C53—21no—
116#126×C53—21no—
117#126×C53—21no—
118#126×C53—21no—
119#126×C53—21no—
120#126×C53—21no—
121#126×C53—21no—
122#126×C53—21no—
123#125×C53—21no—
124#125×C53—21no—
125#125×C53—21no—
126#125×C53—21no—
127#125×C53—21no—
128#125×C53—21no—
129#125×C53—21no—
130#125×C53C2×C411yescharacteristic, complemented
131#125×C53C2×C411yescharacteristic, complemented
132#124×C53—21no—
133#124×C53—21no—
134#124×C53C2×C411yescharacteristic, complemented
135#124×C53C2×C411yescharacteristic, complemented
136#123×C53—21no—
137#123×C53—21no—
138#123×C53—21no—
139#123×C53—21no—
140#123×C53—21no—
141#123×C53—21no—
142#123×C53—21no—
143C22⋊Q8×C53—21no—
144C22⋊Q8×C53—21no—
145C22⋊Q8×C53—21no—
146C22⋊Q8×C53—21no—
147C22⋊Q8×C53—21no—
148C22⋊Q8×C53—21no—
149C22⋊Q8×C53—21no—
150C22⋊Q8×C53—21no—
151C22⋊Q8×C53—21no—
152C22⋊Q8×C53—21no—
153C22⋊Q8×C53C2×C411yescharacteristic
154C22⋊Q8×C53C2×C411yescharacteristic
155C22⋊Q8×C53C2×C411yescharacteristic
156C22⋊Q8×C53C2311yescharacteristic
157C22⋊Q8×C53C2311yescharacteristic
158C22⋊Q8×C53C2311yescharacteristic
159#121×C53C2×C411yescharacteristic
160#121×C53C2311yescharacteristic
161#120×C53—21no—
162C4×Q8×C53—21no—
163C4×Q8×C53—21no—
164C4×Q8×C53—21no—
165C4×Q8×C53—21no—
166C4×Q8×C53C2×C411yescharacteristic, complemented
167C4×Q8×C53C2×C411yescharacteristic, complemented
168C4×Q8×C53C2×C411yescharacteristic, complemented
169C4×Q8×C53C2×C411yescharacteristic, complemented
170C4×Q8×C53C2×C411yescharacteristic, complemented
171C4×Q8×C53C2×C411yescharacteristic, complemented
172C4×D4×C53—21no—
173C4×D4×C53—21no—
174C4×D4×C53—21no—
175C4×D4×C53—21no—
176C4×D4×C53—21no—
177C4×D4×C53—21no—
178C4×D4×C53C2×C411yescharacteristic, complemented
179C4×D4×C53C2×C411yescharacteristic, complemented
180#117×C53—21no—
181#117×C53—21no—
182#117×C53—21no—
183#117×C53—21no—
184#117×C53—21no—
185#117×C53—21no—
186#117×C53—21no—
187#117×C53C2×C411yescharacteristic
188#117×C53C2×C411yescharacteristic
189#117×C53C2×C411yescharacteristic
190#117×C53C2×C411yescharacteristic
191#117×C53C2×C411yescharacteristic
192#117×C53D411yescharacteristic
193#117×C53D411yescharacteristic
194#117×C53D411yescharacteristic
195#117×C53D411yescharacteristic
196C2×C4⋊C4×C53—21no—
197C2×C4⋊C4×C53—21no—
198C2×C4⋊C4×C53C2×C411yescharacteristic
199C2×C4⋊C4×C53D411yescharacteristic
200C2×C4⋊C4×C53D411yescharacteristic
201C2×C22⋊C4×C53—21no—
202C2×C22⋊C4×C53D411yescharacteristic
203C2×C22⋊C4×C53D411yescharacteristic
204C2×C42×C53C2311yescharacteristic
205C2×C42×C53C2311yescharacteristic
206C24×C53C2×D411yescharacteristic
207#41×C53—42no—
208C2×Q8×C53—21no—
209C2×Q8×C53—21no—
210C2×Q8×C53—21no—
211C2×Q8×C53—42no—
212C2×Q8×C53C22×C411yescharacteristic
213C2×Q8×C53C22×C411yescharacteristic
214C2×Q8×C53C22×C411yescharacteristic
215C2×D4×C53—21no—
216C2×D4×C53—21no—
217C2×D4×C53—21no—
218C2×D4×C53C22×C411yescharacteristic
219C22×C4×C53—21no—
220C22×C4×C53—21no—
221C22×C4×C53—21no—
222C22×C4×C53—21no—
223C22×C4×C53—21no—
224C22×C4×C53—42no—
225C22×C4×C53C22×C411yescharacteristic
226C22×C4×C53C22×C411yescharacteristic
227C22×C4×C53C2×D411yescharacteristic
228C22×C4×C53C2×D411yescharacteristic
229C22×C4×C53C2×D411yescharacteristic
230C22×C4×C53C2×D411yescharacteristic
231C22×C4×C53C2×D411yescharacteristic
232C22×C4×C53C2×D411yescharacteristic
233C22×C4×C53C2×D411yescharacteristic
234C22×C4×C53C2411yescharacteristic
235C22×Dic53—21no—
236C22×Dic53—21no—
237C22×Dic53—21no—
238C22×Dic53—21no—
239C22×Dic53—42no—
240C22×Dic53—42no—
241C22×Dic53—81no—
242C4⋊C4×C53—21no—
243C4⋊C4×C53—21no—
244C4⋊C4×C53—21no—
245C4⋊C4×C53—21no—
246C4⋊C4×C53—21no—
247C4⋊C4×C53—21no—
248C4⋊C4×C53—21no—
249C4⋊C4×C53—21no—
250C4⋊C4×C53—21no—
251C4⋊C4×C53—21no—
252C4⋊C4×C53—21no—
253C4⋊C4×C53—21no—
254C4⋊C4×C53—21no—
255C4⋊C4×C53—21no—
256C4⋊C4×C53—21no—
257C4⋊C4×C53—21no—
258C4⋊C4×C53—21no—
259C4⋊C4×C53—21no—
260C4⋊C4×C53—21no—
261C4⋊C4×C53—21no—
262C4⋊C4×C53—21no—
263C4⋊C4×C53—21no—
264C4⋊C4×C53—21no—
265C4⋊C4×C53C22⋊C411yescharacteristic
266C4⋊C4×C53C22⋊C411yescharacteristic
267C4⋊C4×C53C22⋊C411yescharacteristic
268C4⋊C4×C53C22⋊C411yescharacteristic
269C4⋊C4×C53C22⋊C411yescharacteristic
270C4⋊C4×C53C22⋊C411yescharacteristic
271C4⋊C4×C53C22⋊C411yescharacteristic
272C4⋊C4×C53C22⋊C411yescharacteristic
273C4⋊C4×C53C22×C411yescharacteristic
274C4⋊C4×C53C22×C411yescharacteristic
275C4⋊C4×C53C22×C411yescharacteristic
276C4⋊C4×C53C22×C411yescharacteristic
277C22⋊C4×C53—21no—
278C22⋊C4×C53—21no—
279C22⋊C4×C53—21no—
280C22⋊C4×C53—21no—
281C22⋊C4×C53—21no—
282C22⋊C4×C53—21no—
283C22⋊C4×C53—21no—
284C22⋊C4×C53—21no—
285C22⋊C4×C53—21no—
286C22⋊C4×C53—21no—
287C22⋊C4×C53—21no—
288C22⋊C4×C53—21no—
289C22⋊C4×C53—21no—
290C22⋊C4×C53—21no—
291C22⋊C4×C53—21no—
292C22⋊C4×C53C22⋊C411yescharacteristic
293C22⋊C4×C53C22⋊C411yescharacteristic
294C22⋊C4×C53C22⋊C411yescharacteristic
295C22⋊C4×C53C22⋊C411yescharacteristic
296C22⋊C4×C53C22⋊C411yescharacteristic
297C22⋊C4×C53C22⋊C411yescharacteristic
298C22⋊C4×C53C22⋊C411yescharacteristic
299C22⋊C4×C53C22⋊C411yescharacteristic
300C42×C53—21no—
301C42×C53—21no—
302C42×C53—21no—
303C42×C53—21no—
304C42×C53—21no—
305C42×C53—21no—
306C42×C53—21no—
307C42×C53C22×C411yescharacteristic
308C42×C53C22×C411yescharacteristic
309C42×C53C22×C411yescharacteristic
310C42×C53C22×C411yescharacteristic
311C42×C53C2×D411yescharacteristic
312C42×C53C2×D411yescharacteristic
313C42×C53C2×D411yescharacteristic
314C42×C53C2×D411yescharacteristic
315C22⋊Dic53—42no—
316C4⋊Dic53—42no—
317C4⋊Dic53—81no—
318C4×Dic53—42no—
319C4×Dic53—81no—
320#11719917—42no—
321C2×#88322—21no—
322C2×#88322—21no—
323C2×#88322—21no—
324C2×#88322—21no—
325C2×#88322—42no—
326C23×C53—21no—
327C23×C53—21no—
328C23×C53—22no—
329C23×C53—21no—
330C23×C53—41no—
331C23×C53C2×C22⋊C411yescharacteristic
332C23×C53C2×C22⋊C411yescharacteristic
333C23×C53C22×D411yescharacteristic
334Q8×C53—42no—
335Q8×C53—41no—
336Q8×C53—41no—
337Q8×C53—41no—
338Q8×C53—81no—
339Q8×C53—81no—
340D4×C53—41no—
341D4×C53—41no—
342D4×C53—41no—
343D4×C53—42no—
344D4×C53—81no—
345C2×C4×C53—21no—
346C2×C4×C53—21no—
347C2×C4×C53—21no—
348C2×C4×C53—21no—
349C2×C4×C53—22no—
350C2×C4×C53—22no—
351C2×C4×C53—21no—
352C2×C4×C53—21no—
353C2×C4×C53—21no—
354C2×C4×C53—21no—
355C2×C4×C53—21no—
356C2×C4×C53—21no—
357C2×C4×C53—21no—
358C2×C4×C53—41no—
359C2×C4×C53—41no—
360C2×C4×C53—41no—
361C2×C4×C53—41no—
362C2×C4×C53—41no—
363C2×C4×C53—41no—
364C2×C4×C53—42no—
365C2×C4×C53—42no—
366C2×C4×C53—81no—
367C2×C4×C53—81no—
368C2×C4×C53—81no—
369C2×C4×C53C2×C22⋊C411yescharacteristic
370C2×C4×C53C2×C22⋊C411yescharacteristic
371C2×C4×C53C2×C22⋊C411yescharacteristic
372C2×C4×C53C2×C22⋊C411yescharacteristic
373C2×C4×C53C2×C22⋊C411yescharacteristic
374C2×C4×C53C2×C22⋊C411yescharacteristic
375C2×C4×C53C2×C22⋊C411yescharacteristic
376C2×C4×C53C2×C22⋊C411yescharacteristic
377C2×C4×C53C2×C22⋊C411yescharacteristic
378C2×C4×C53C2×C22⋊C411yescharacteristic
379C2×C4×C53C23×C411yescharacteristic
380C2×C4×C53C22×D411yescharacteristic
381C2×Dic53—22no—
382C2×Dic53—41no—
383C2×Dic53—41no—
384C2×Dic53—41no—
385C2×Dic53—41no—
386C2×Dic53—41no—
387C2×Dic53—41no—
388C2×Dic53—41no—
389C2×Dic53—41no—
390C2×Dic53—41no—
391C2×Dic53—41no—
392C2×Dic53—41no—
393C2×Dic53—84no—
394#88322—41no—
395#88322—41no—
396#88322—41no—
397#88322—41no—
398#17609—531nomaximal, Sylow
399C22×C53—21no—
400C22×C53—21no—
401C22×C53—21no—
402C22×C53—21no—
403C22×C53—21no—
404C22×C53—21no—
405C22×C53—21no—
406C22×C53—42no—
407C22×C53—42no—
408C22×C53—41no—
409C22×C53—41no—
410C22×C53—41no—
411C22×C53#41012yes—
412C22×C53C22×C22⋊C411yescharacteristic
413C22×C53#57711yescharacteristic
414C22×C53#57811yescharacteristic
415C4×C53—21no—
416C4×C53—21no—
417C4×C53—21no—
418C4×C53—21no—
419C4×C53—21no—
420C4×C53—21no—
421C4×C53—21no—
422C4×C53—21no—
423C4×C53—21no—
424C4×C53—21no—
425C4×C53—21no—
426C4×C53—21no—
427C4×C53—41no—
428C4×C53—41no—
429C4×C53—41no—
430C4×C53—41no—
431C4×C53—41no—
432C4×C53—41no—
433C4×C53—41no—
434Dic53—42no—
435Dic53—81no—
436Dic53—81no—
437Dic53—81no—
438#3495D5311yescharacteristic
439#2924—531no—
440#2343—531no—
441#1521—531no—
442#1518—531no—
443#1516—531no—
444#1515—531no—
445#1512—531no—
446#1511—531no—
447#1509—531no—
448#1506—531no—
449#1504—531no—
450#1503—531no—
451#1500—531no—
452C2×#328—531no—
453C2×C53—21no—
454C2×C53—21no—
455C2×C53—22no—
456C2×C53—41no—
457C2×C53—81no—
458C2×C53C2×#41011yescharacteristic
459C2×C53#289811yescharacteristic
460C2×C53#290111yescharacteristic
461#556—21no—
462#554—21no—
463#552—21no—
464#552—21no—
465#552—21no—
466#552—21no—
467#551—21no—
468#551—21no—
469#544Dic5311yescharacteristic, complemented
470#542Dic5311yescharacteristic, complemented
471#542Dic5311yescharacteristic, complemented
472#541Dic5311yescharacteristic, complemented
473#541Dic5311yescharacteristic, complemented
474#536Dic5311yescharacteristic, complemented
475#533C2×D5311yescharacteristic
476#533C2×D5311yescharacteristic
477#529C2×D5311yescharacteristic
478#529C2×D5311yescharacteristic
479#525C2×D5311yescharacteristic
480C2×C22⋊Q8C2×D5311yescharacteristic
481#520Dic5311yescharacteristic, complemented
482#519Dic5311yescharacteristic, complemented
483C2×#117C2×D5311yescharacteristic
484#433—1061no—
485#433—1061no—
486#432—531no—
487#432—531no—
488#431—531no—
489#431—531no—
490#424—1061no—
491#407—531no—
492C2×C22⋊C8—531no—
493#405—1061no—
494#387—1061no—
495#387—1061no—
496#385—1061no—
497#383—531no—
498#382—531no—
499#381—531no—
500C4×C4⋊C4—531no—
501C4×C22⋊C4—1061no—
502#376—531no—
503C2×#95—531no—
504#328—531no—
505#328—531no—
506#328—531no—
507#328—531no—
508#328—531no—
509#328—531no—
510#328—531no—
511#328—531no—
512#328—531no—
513#328—531no—
514#328—531no—
515#328—531no—
516#327—531no—
517#327—531no—
518#327—531no—
519#327—531no—
520C53#1760911yescharacteristic, complemented, Sylow
521C2×#41C2×Dic5311yescharacteristic
522C22×Q8C2×Dic5311yescharacteristic
523C23×C4—1061no—
524C23×C4C22×D5311yescharacteristic
525C2×M16—1061no—
526C22×C8—1061no—
527C4⋊Q8—21no—
528C4⋊Q8C2×Dic5311yescharacteristic, complemented
529C4⋊Q8C2×Dic5311yescharacteristic, complemented
530C4⋊Q8C2×Dic5311yescharacteristic, complemented
531C4⋊Q8C2×Dic5311yescharacteristic, complemented
532#126—21no—
533#126—21no—
534#126—21no—
535#126—21no—
536#126—21no—
537#126—21no—
538#126—21no—
539#126—21no—
540#125—21no—
541#125—21no—
542#125—21no—
543#125—21no—
544#125—21no—
545#125—21no—
546#125—21no—
547#125C2×Dic5311yescharacteristic, complemented
548#125C2×Dic5311yescharacteristic, complemented
549#124—21no—
550#124—21no—
551#124C2×Dic5311yescharacteristic, complemented
552#124C2×Dic5311yescharacteristic, complemented
553#123—21no—
554#123—21no—
555#123—21no—
556#123—21no—
557#123—21no—
558#123—21no—
559#123—21no—
560C22⋊Q8—21no—
561C22⋊Q8—21no—
562C22⋊Q8—21no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566C22⋊Q8—21no—
567C22⋊Q8—21no—
568C22⋊Q8—21no—
569C22⋊Q8—21no—
570C22⋊Q8C2×Dic5311yescharacteristic
571C22⋊Q8C2×Dic5311yescharacteristic
572C22⋊Q8C2×Dic5311yescharacteristic
573C22⋊Q8C22×D5311yescharacteristic
574C22⋊Q8C22×D5311yescharacteristic
575C22⋊Q8C22×D5311yescharacteristic
576#121C2×Dic5311yescharacteristic
577#121C22×D5311yescharacteristic
578#120—21no—
579C4×Q8—21no—
580C4×Q8—21no—
581C4×Q8—21no—
582C4×Q8—21no—
583C4×Q8C2×Dic5311yescharacteristic, complemented
584C4×Q8C2×Dic5311yescharacteristic, complemented
585C4×Q8C2×Dic5311yescharacteristic, complemented
586C4×Q8C2×Dic5311yescharacteristic, complemented
587C4×Q8C2×Dic5311yescharacteristic, complemented
588C4×Q8C2×Dic5311yescharacteristic, complemented
589C4×D4—21no—
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—21no—
595C4×D4C2×Dic5311yescharacteristic, complemented
596C4×D4C2×Dic5311yescharacteristic, complemented
597#117—21no—
598#117—21no—
599#117—21no—
600#117—21no—
601#117—21no—
602#117—21no—
603#117—21no—
604#117C2×Dic5311yescharacteristic
605#117C2×Dic5311yescharacteristic
606#117C2×Dic5311yescharacteristic
607#117C2×Dic5311yescharacteristic
608#117C2×Dic5311yescharacteristic
609#117C22⋊D5311yescharacteristic
610#117C22⋊D5311yescharacteristic
611#117C22⋊D5311yescharacteristic
612#117C22⋊D5311yescharacteristic
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—1061no—
616C2×C4⋊C4—1061no—
617C2×C4⋊C4C2×Dic5311yescharacteristic
618C2×C4⋊C4C22⋊D5311yescharacteristic
619C2×C4⋊C4C22⋊D5311yescharacteristic
620C2×C22⋊C4—21no—
621C2×C22⋊C4—1061no—
622C2×C22⋊C4C22⋊D5311yescharacteristic
623C2×C22⋊C4C22⋊D5311yescharacteristic
624C2×C42—1061no—
625C2×C42—1061no—
626C2×C42C22×D5311yescharacteristic
627C2×C42C22×D5311yescharacteristic
628C4⋊C8—1061no—
629C4⋊C8—1061no—
630C4⋊C8—1061no—
631C4⋊C8—1061no—
632C22⋊C8—531no—
633C22⋊C8—531no—
634C22⋊C8—531no—
635C22⋊C8—531no—
636C22⋊C8—1061no—
637C22⋊C8—1061no—
638#97—1061no—
639#97—1061no—
640C4×C8—1061no—
641C4×C8—1061no—
642#95—531no—
643#95—531no—
644#95—531no—
645#95—531no—
646#95—1061no—
647#95—1061no—
648#95—1061no—
649#95—1061no—
650#95—1061no—
651#95—1061no—
652C24C2×C22⋊D5311yescharacteristic
653#41—42no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—42no—
658C2×Q8C22×Dic5311yescharacteristic
659C2×Q8C22×Dic5311yescharacteristic
660C2×Q8C22×Dic5311yescharacteristic
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4C22×Dic5311yescharacteristic
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—42no—
671C22×C4—1061no—
672C22×C4—1061no—
673C22×C4—1061no—
674C22×C4—1061no—
675C22×C4—4241no—
676C22×C4—2122no—
677C22×C4—2122no—
678C22×C4C22×Dic5311yescharacteristic
679C22×C4C22×Dic5311yescharacteristic
680C22×C4C2×C22⋊D5311yescharacteristic
681C22×C4C2×C22⋊D5311yescharacteristic
682C22×C4C2×C22⋊D5311yescharacteristic
683C22×C4C2×C22⋊D5311yescharacteristic
684C22×C4C2×C22⋊D5311yescharacteristic
685C22×C4C2×C22⋊D5311yescharacteristic
686C22×C4C2×C22⋊D5311yescharacteristic
687C22×C4C23×D5311yescharacteristic
688M16—2122no—
689C2×C8—1061no—
690C2×C8—1061no—
691C2×C8—1061no—
692C2×C8—1061no—
693C2×C8—2122no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—4241no—
718C4⋊C4—2122no—
719C4⋊C4C22⋊Dic5311yescharacteristic
720C4⋊C4C22⋊Dic5311yescharacteristic
721C4⋊C4C22⋊Dic5311yescharacteristic
722C4⋊C4C22⋊Dic5311yescharacteristic
723C4⋊C4C22⋊Dic5311yescharacteristic
724C4⋊C4C22⋊Dic5311yescharacteristic
725C4⋊C4C22⋊Dic5311yescharacteristic
726C4⋊C4C22⋊Dic5311yescharacteristic
727C4⋊C4C22×Dic5311yescharacteristic
728C4⋊C4C22×Dic5311yescharacteristic
729C4⋊C4C22×Dic5311yescharacteristic
730C4⋊C4C22×Dic5311yescharacteristic
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—2122no—
747C22⋊C4C22⋊Dic5311yescharacteristic
748C22⋊C4C22⋊Dic5311yescharacteristic
749C22⋊C4C22⋊Dic5311yescharacteristic
750C22⋊C4C22⋊Dic5311yescharacteristic
751C22⋊C4C22⋊Dic5311yescharacteristic
752C22⋊C4C22⋊Dic5311yescharacteristic
753C22⋊C4C22⋊Dic5311yescharacteristic
754C22⋊C4C22⋊Dic5311yescharacteristic
755C42—21no—
756C42—21no—
757C42—21no—
758C42—21no—
759C42—21no—
760C42—21no—
761C42—21no—
762C42—4241no—
763C42—2122no—
764C42C22×Dic5311yescharacteristic
765C42C22×Dic5311yescharacteristic
766C42C22×Dic5311yescharacteristic
767C42C22×Dic5311yescharacteristic
768C42C2×C22⋊D5311yescharacteristic
769C42C2×C22⋊D5311yescharacteristic
770C42C2×C22⋊D5311yescharacteristic
771C42C2×C22⋊D5311yescharacteristic
772C23—22no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—41no—
777C23C2×C22⋊Dic5311yescharacteristic
778C23C2×C22⋊Dic5311yescharacteristic
779C23C22×C22⋊D5311yescharacteristic
780Q8—41no—
781Q8—41no—
782Q8—41no—
783Q8—42no—
784Q8—81no—
785Q8—81no—
786D4—41no—
787D4—42no—
788D4—41no—
789D4—41no—
790D4—81no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—81no—
813C2×C4—81no—
814C2×C4—81no—
815C2×C4—1062no—
816C2×C4—4244no—
817C2×C4—2121no—
818C2×C4—2121no—
819C2×C4—2121no—
820C2×C4—2121no—
821C2×C4—2121no—
822C2×C4—2121no—
823C2×C4—2121no—
824C2×C4—2121no—
825C2×C4—2121no—
826C2×C4—2121no—
827C2×C4—2121no—
828C2×C4C2×C22⋊Dic5311yescharacteristic
829C2×C4C2×C22⋊Dic5311yescharacteristic
830C2×C4C2×C22⋊Dic5311yescharacteristic
831C2×C4C2×C22⋊Dic5311yescharacteristic
832C2×C4C2×C22⋊Dic5311yescharacteristic
833C2×C4C2×C22⋊Dic5311yescharacteristic
834C2×C4C2×C22⋊Dic5311yescharacteristic
835C2×C4C2×C22⋊Dic5311yescharacteristic
836C2×C4C2×C22⋊Dic5311yescharacteristic
837C2×C4C2×C22⋊Dic5311yescharacteristic
838C2×C4C23×Dic5311yescharacteristic
839C2×C4C22×C22⋊D5311yescharacteristic
840C8—2121no—
841C8—2121no—
842C8—2121no—
843C8—2121no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—42no—
852C22—42no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22#1681059712yes—
857C22C22×C22⋊Dic5311yescharacteristic
858C22#1681143111yescharacteristic
859C22#1681143811yescharacteristic
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—4241no—
880C4—4241no—
881C4—4241no—
882C4—2122no—
883C2—21no—
884C2—21no—
885C2—22no—
886C2—41no—
887C2—81no—
888C2C2×#1681059711yescharacteristic
889C2#2028324811yescharacteristic
890C2#2028326211yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#3495C2
socleC22×C53C22×C22⋊C4
prime radicalC53×#525C22
cosocleC22×C4×C53C24
hypercenter#3495D53
hypocenterC53#17609
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3495

Complements

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

NH ≅ G/Ntype
1. #20283373C2semidirect
2. #20277575C2semidirect
3. #20273292C2semidirect
4. #20273279C2semidirect
6. #20273266C2semidirect
7. #20273253C2semidirect
8. #20273248C2semidirect
9. #20273240C2semidirect
10. #20273227C2semidirect
12. #20273214C2semidirect
13. #20273201C2semidirect
14. C2×#16810360C2semidirect
60. C53×#544C4semidirect
61. C53×#542C4semidirect
62. C53×#542C4semidirect
63. C53×#541C4semidirect
64. C53×#541C4semidirect
65. C53×#536C4semidirect
72. C53×#520C4semidirect
73. C53×#519C4semidirect
111. C4⋊Q8×C53C2×C4semidirect
112. C4⋊Q8×C53C2×C4semidirect
113. C4⋊Q8×C53C2×C4semidirect
114. C4⋊Q8×C53C2×C4semidirect
130. #125×C53C2×C4semidirect
131. #125×C53C2×C4semidirect
134. #124×C53C2×C4semidirect
135. #124×C53C2×C4semidirect
166. C4×Q8×C53C2×C4semidirect
167. C4×Q8×C53C2×C4semidirect
168. C4×Q8×C53C2×C4semidirect
169. C4×Q8×C53C2×C4semidirect
170. C4×Q8×C53C2×C4semidirect
171. C4×Q8×C53C2×C4semidirect
178. C4×D4×C53C2×C4semidirect
179. C4×D4×C53C2×C4semidirect
469. #544Dic53semidirect
470. #542Dic53semidirect
471. #542Dic53semidirect
472. #541Dic53semidirect
473. #541Dic53semidirect
474. #536Dic53semidirect
481. #520Dic53semidirect
482. #519Dic53semidirect
520. C53#17609semidirect
528. C4⋊Q8C2×Dic53semidirect
529. C4⋊Q8C2×Dic53semidirect
530. C4⋊Q8C2×Dic53semidirect
531. C4⋊Q8C2×Dic53semidirect
547. #125C2×Dic53semidirect
548. #125C2×Dic53semidirect
551. #124C2×Dic53semidirect
552. #124C2×Dic53semidirect
583. C4×Q8C2×Dic53semidirect
584. C4×Q8C2×Dic53semidirect
585. C4×Q8C2×Dic53semidirect
586. C4×Q8C2×Dic53semidirect
587. C4×Q8C2×Dic53semidirect
588. C4×Q8C2×Dic53semidirect
595. C4×D4C2×Dic53semidirect
596. C4×D4C2×Dic53semidirect

Maximal subgroups

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

subgroupindex
#202833732
#202775752
#202732922
#202732792
#202732712
#202732662
#202732532
#202732482
#202732402
#202732272
#202732192
#202732142
#202732012
C2×#168103602
C53×#34952
#1760953