Finite Group Databasebeta

← #29647556

Subgroups — #29647556

Order 15616.

996 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459870C211yesmaximal, characteristic
2#21454853C211yesmaximal, characteristic, complemented
3#21448450C211yesmaximal, characteristic, complemented
4#21444389C211yesmaximal, characteristic, complemented
5#21444384C211yesmaximal, characteristic, complemented
6#21444372C211yesmaximal, characteristic, complemented
7#21444369C211yesmaximal, characteristic, complemented
8#21444359C211yesmaximal, characteristic, complemented
9#21444357C211yesmaximal, characteristic, complemented
10#21444350C211yesmaximal, characteristic, complemented
11#21444337C211yesmaximal, characteristic, complemented
12#21444320C211yesmaximal, characteristic, complemented
13#21444307C211yesmaximal, characteristic, complemented
14#328×D61C211yesmaximal, characteristic, complemented
15C61×#1521C211yesmaximal, characteristic, complemented
16#16840485C411yescharacteristic, complemented
17#16840469—21no—
18#16840450C411yescharacteristic, complemented
19#16840450C411yescharacteristic, complemented
20#16840435—21no—
21#16840435—21no—
22Q8×D244C411yescharacteristic, complemented
23#16840420C411yescharacteristic, complemented
24#16840420C411yescharacteristic, complemented
25#16840417C411yescharacteristic, complemented
26#16840416C411yescharacteristic, complemented
27#16840408—21no—
28#16840383—21no—
29#16840353—21no—
30#16840353—21no—
31#16840319C2211yescharacteristic
32#16840272C2211yescharacteristic
33#16840272C2211yescharacteristic
34C22⋊Q8×D61C2211yescharacteristic
35C22⋊Q8×D61C2211yescharacteristic
36#16840242—21no—
37C2×C4×D244C2211yescharacteristic
38#16839841—21no—
39#16839832—21no—
40#16839832—21no—
41C8×D244—21no—
42#16839819C2211yescharacteristic
43#16839724C2211yescharacteristic
44#16839724C2211yescharacteristic
45C22⋊C8×D61C2211yescharacteristic
46C22⋊C8×D61C2211yescharacteristic
47#16839654—21no—
48#16839645—21no—
49#16839640—21no—
50#16839636—21no—
51#16839628C2211yescharacteristic
52#16839624C2211yescharacteristic
53#16839621C2211yescharacteristic
54#16839609C2211yescharacteristic
55#95×D61C2211yescharacteristic
56#16839500C2211yescharacteristic
57#16839500C2211yescharacteristic
58#16839500C2211yescharacteristic
59#16839500C2211yescharacteristic
60#16839499C2211yescharacteristic
61#16839499C2211yescharacteristic
62#16839498C2211yescharacteristic
63#16839498C2211yescharacteristic
64#16839498C2211yescharacteristic
65#16839498C2211yescharacteristic
66#16839496C2211yescharacteristic
67#16839496C2211yescharacteristic
68C61×#529C2211yescharacteristic
69C61×#431C2211yescharacteristic
70C61×#383C2211yescharacteristic
71C61×#328C2211yescharacteristic
72C61×#328C2211yescharacteristic
73C61×#327C2211yescharacteristic
74C61×#327C2211yescharacteristic
75C2×#11758222—21no—
76C2×#11758224C2×C411yescharacteristic
77C2×#11758224C2×C411yescharacteristic, complemented
78C2×Q8×D61C2×C411yescharacteristic
79C2×Q8×D61C2×C411yescharacteristic, complemented
80C22×D244D411yescharacteristic
81C22×C4×D61—21no—
82C22×C4×D61C2311yescharacteristic
83C22×C4×D61C2311yescharacteristic
84C2×#11758189—21no—
85C2×#11758189—21no—
86C2×C8×D61—21no—
87C2×C8×D61—21no—
88#14519777—21no—
89#14519777C2×C411yescharacteristic, complemented
90#14519777C2×C411yescharacteristic, complemented
91#14519772—21no—
92#14519772—21no—
93#14519772—21no—
94#14519772—21no—
95#14519769—21no—
96#14519768—21no—
97#14519768—21no—
98#14519765—21no—
99#14519763—21no—
100#14519763—21no—
101#14519762—21no—
102#14519762—21no—
103#14519761—21no—
104#14519761—21no—
105#14519759—21no—
106#14519759—21no—
107#14519759—21no—
108#14519759—21no—
109#14519757—21no—
110#14519757—21no—
111#14519757C2×C411yescharacteristic
112#14519757C2×C411yescharacteristic
113#14519757C2×C411yescharacteristic, complemented
114#14519757C2×C411yescharacteristic, complemented
115#14519756—21no—
116#14519756—21no—
117#14519756C2311yescharacteristic
118#14519756C2311yescharacteristic
119#14519755—21no—
120#14519755—21no—
121#14519754—21no—
122#14519754—21no—
123#14519754—21no—
124#14519754—21no—
125#14519753C2×C411yescharacteristic
126#14519753C2×C411yescharacteristic, complemented
127#14519751—21no—
128#14519750—21no—
129#14519750—21no—
130#14519748C2×C411yescharacteristic
131#14519748C2×C411yescharacteristic, complemented
132#14519745—21no—
133#14519745—21no—
134C4×Dic122—21no—
135C4×Dic122—21no—
136C4×Dic122C2×C411yescharacteristic, complemented
137C4×Dic122C2×C411yescharacteristic, complemented
138C4×D244—21no—
139C4×D244C2×C411yescharacteristic
140C4×D244C2×C411yescharacteristic
141C4×D244C2×C411yescharacteristic
142C4×D244C2×C411yescharacteristic
143C4×D244D411yescharacteristic
144C4×D244D411yescharacteristic
145C4×D244D411yescharacteristic
146C4×D244D411yescharacteristic
147D4×Dic61—21no—
148D4×Dic61—21no—
149#14519737—21no—
150#14519737—21no—
151#14519737—21no—
152#14519737—21no—
153#14519736—21no—
154#14519735—21no—
155#14519735—21no—
156#14519735C2×C411yescharacteristic
157#14519735C2×C411yescharacteristic, complemented
158C2×C4⋊Dic61—21no—
159C2×C4⋊Dic61—21no—
160C2×C4⋊Dic61D411yescharacteristic
161C2×#11758196—21no—
162C4⋊C4×D61—21no—
163C4⋊C4×D61—21no—
164C4⋊C4×D61C2×C411yescharacteristic
165C4⋊C4×D61C2×C411yescharacteristic, complemented
166C2×#11758198—21no—
167C2×#11758198—21no—
168C2×#11758198—21no—
169C2×#11758198D411yescharacteristic
170C2×#11758198D411yescharacteristic
171C22⋊C4×D61—21no—
172C22⋊C4×D61—21no—
173C2×C4×Dic61—21no—
174C4⋊#92418—21no—
175C22⋊#92418C2311yescharacteristic
176C22⋊#92418C2311yescharacteristic
177#14519689—21no—
178#14519689—21no—
179#14519689—21no—
180#14519689—21no—
181#14519688—21no—
182#14519684—21no—
183#14519684—21no—
184#14519684—21no—
185#14519684C2311yescharacteristic
186#14519684C2311yescharacteristic
187#126×C61—21no—
188#125×C61C2×C411yescharacteristic, complemented
189#124×C61C2×C411yescharacteristic, complemented
190#123×C61—21no—
191C22⋊Q8×C61C2311yescharacteristic
192#121×C61C2311yescharacteristic
193C4×Q8×C61C2×C411yescharacteristic, complemented
194C4×D4×C61—21no—
195C4×D4×C61C2×C411yescharacteristic, complemented
196#117×C61—21no—
197C2×C42×C61C2311yescharacteristic
198C4⋊C8×C61—21no—
199C22⋊C8×C61C2311yescharacteristic
200C22⋊C8×C61C2311yescharacteristic
201C4×C8×C61—21no—
202#95×C61—21no—
203#95×C61—21no—
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206C23×D61C2×D411yescharacteristic
207C23×D61C2×D411yescharacteristic
208C2×Q8×C61C22×C411yescharacteristic
209C2×D4×C61—21no—
210C2×D4×C61C22×C411yescharacteristic
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2411yescharacteristic
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C2×C22⋊D61—21no—
220C2×C22⋊D61—21no—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61C2×D411yescharacteristic
226C22×Dic61C2×D411yescharacteristic
227Q8×D61—81no—
228Q8×D61—81no—
229#11758224—81no—
230#11758224—81no—
231#11758222—44no—
232C2×D244—42no—
233C2×D244C22⋊C411yescharacteristic
234C2×D244C22⋊C411yescharacteristic
235C2×D244C22⋊C411yescharacteristic
236C2×D244C22⋊C411yescharacteristic
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—42no—
242C2×C4×D61—81no—
243C2×C4×D61—81no—
244C2×C4×D61—81no—
245C2×C4×D61—81no—
246C2×C4×D61C22×C411yescharacteristic
247C2×C4×D61C22×C411yescharacteristic
248C2×C4×D61C22×C411yescharacteristic
249C2×C4×D61C22×C411yescharacteristic
250C2×C4×D61C2×D411yescharacteristic
251C2×C4×D61C2×D411yescharacteristic
252C2×C4×D61C2×D411yescharacteristic
253C2×C4×D61C2×D411yescharacteristic
254C2×Dic122—21no—
255C2×Dic122—21no—
256C2×Dic122—21no—
257C2×Dic122C22×C411yescharacteristic
258C2×Dic122C22×C411yescharacteristic
259C2×C8×C61—21no—
260C2×C8×C61—21no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61C22×C411yescharacteristic
266C4⋊C4×C61C22×C411yescharacteristic
267C22⋊C4×C61—21no—
268C22⋊C4×C61—21no—
269C22⋊C4×C61—21no—
270C22⋊C4×C61—21no—
271C22⋊C4×C61—21no—
272C42×C61—21no—
273C42×C61C22×C411yescharacteristic
274C42×C61C22×C411yescharacteristic
275C42×C61C2×D411yescharacteristic
276C42×C61C2×D411yescharacteristic
277C22⋊Dic61—21no—
278C22⋊Dic61—21no—
279C22⋊Dic61—21no—
280C22⋊Dic61—21no—
281#11758198—21no—
282#11758198—21no—
283#11758198—21no—
284#11758198—21no—
285#11758198—21no—
286#11758198—21no—
287#11758198—21no—
288#11758198—21no—
289#11758198—42no—
290#11758198—81no—
291#11758198—81no—
292#11758198C22⋊C411yescharacteristic
293#11758198C22⋊C411yescharacteristic
294#11758198C22⋊C411yescharacteristic
295#11758198C22⋊C411yescharacteristic
296#11758198C22⋊C411yescharacteristic
297#11758198C22⋊C411yescharacteristic
298#11758198C22⋊C411yescharacteristic
299#11758198C22⋊C411yescharacteristic
300C4⋊Dic61—21no—
301C4⋊Dic61—21no—
302C4⋊Dic61—21no—
303C4⋊Dic61—21no—
304C4⋊Dic61—21no—
305C4⋊Dic61—21no—
306C4⋊Dic61—21no—
307C4⋊Dic61—81no—
308C4⋊Dic61C22⋊C411yescharacteristic
309C4⋊Dic61C22⋊C411yescharacteristic
310C4⋊Dic61C22⋊C411yescharacteristic
311C4⋊Dic61C22⋊C411yescharacteristic
312C4⋊Dic61C22×C411yescharacteristic
313C4⋊Dic61C22×C411yescharacteristic
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320#11758196—21no—
321#11758196—21no—
322#11758196—81no—
323C4×Dic61—21no—
324C4×Dic61—21no—
325C4×Dic61—21no—
326C4×Dic61—21no—
327C4×Dic61—81no—
328C2×#92418—21no—
329C2×#92418—21no—
330#11758189—81no—
331#11758189—81no—
332C8×D61—81no—
333C8×D61—81no—
334C23×C61—21no—
335C23×C61C22×D411yescharacteristic
336C22×D61—21no—
337C22×D61—21no—
338C22×D61—21no—
339C22×D61—21no—
340C22×D61—22no—
341C22×D61—41no—
342C22×D61—41no—
343C22×D61—41no—
344C22×D61C2×C22⋊C411yescharacteristic
345C22×D61C2×C22⋊C411yescharacteristic
346C22×D61C2×C22⋊C411yescharacteristic
347C22×D61C2×C22⋊C411yescharacteristic
348Q8×C61—41no—
349D4×C61—41no—
350D4×C61—41no—
351D4×C61—41no—
352C2×C4×C61—21no—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61—21no—
356C2×C4×C61—21no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—42no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61C2×C22⋊C411yescharacteristic
367C2×C4×C61C2×C22⋊C411yescharacteristic
368C2×C4×C61C2×C22⋊C411yescharacteristic
369C2×C4×C61C2×C22⋊C411yescharacteristic
370C2×C4×C61C23×C411yescharacteristic
371C2×C4×C61C22×D411yescharacteristic
372C22⋊D61—42no—
373C22⋊D61—42no—
374C22⋊D61—81no—
375C22⋊D61—81no—
376C2×Dic61—21no—
377C2×Dic61—21no—
378C2×Dic61—21no—
379C2×Dic61—21no—
380C2×Dic61—41no—
381C2×Dic61—41no—
382C2×Dic61—41no—
383C2×Dic61—41no—
384C2×Dic61—41no—
385C2×Dic61—41no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61—81no—
389C2×Dic61—81no—
390C2×Dic61C2×C22⋊C411yescharacteristic
391C2×Dic61C2×C22⋊C411yescharacteristic
392C2×Dic61C2×C22⋊C411yescharacteristic
393C2×Dic61C2×C22⋊C411yescharacteristic
394D244—22no—
395D244—22no—
396D244—41no—
397D244—41no—
398C4×D61—41no—
399C4×D61—41no—
400C4×D61—41no—
401C4×D61—41no—
402C4×D61—41no—
403C4×D61—41no—
404C4×D61—41no—
405C4×D61—41no—
406C4×D61—42no—
407C4×D61—42no—
408C4×D61—81no—
409C4×D61—81no—
410C4×D61—84no—
411Dic122—42no—
412Dic122—41no—
413Dic122—41no—
414Dic122—81no—
415Dic122—81no—
416C8×C61—41no—
417C8×C61—41no—
418#92418—41no—
419#92418—41no—
420#17598—611nomaximal, Sylow
421C22×C61—21no—
422C22×C61—21no—
423C22×C61—41no—
424C22×C61—41no—
425C22×C61—41no—
426C22×C61C22×C22⋊C411yescharacteristic
427C22×C61#57711yescharacteristic
428C22×C61#57811yescharacteristic
429C2×D61—21no—
430C2×D61—21no—
431C2×D61—21no—
432C2×D61—21no—
433C2×D61—21no—
434C2×D61—21no—
435C2×D61—21no—
436C2×D61—21no—
437C2×D61—21no—
438C2×D61—21no—
439C2×D61—21no—
440C2×D61—42no—
441C2×D61—42no—
442C2×D61—81no—
443C2×D61—81no—
444C2×D61#42112yes—
445C4×C61—21no—
446C4×C61—21no—
447C4×C61—21no—
448C4×C61—21no—
449C4×C61—21no—
450C4×C61—21no—
451C4×C61—41no—
452C4×C61—41no—
453C4×C61—41no—
454C4×C61—81no—
455C4×C61—81no—
456Dic61—21no—
457Dic61—21no—
458Dic61—21no—
459Dic61—21no—
460Dic61—41no—
461Dic61—41no—
462Dic61—41no—
463Dic61—41no—
464Dic61—81no—
465Dic61—81no—
466#3520—611no—
467#2974—611no—
468#2318—611no—
469#1521D6111yescharacteristic, complemented
470#1520—611no—
471#1518—611no—
472#1516—611no—
473#1515—611no—
474#1513—611no—
475#1512—611no—
476#1511—611no—
477#1508—611no—
478#1504—611no—
479#1501—611no—
480C2×#328—611no—
481C2×C61—21no—
482C2×C61—21no—
483C2×C61—81no—
484C2×C61#288311yescharacteristic
485C2×C61#289811yescharacteristic
486C2×C61C2×#42111yescharacteristic
487D61—22no—
488D61—41no—
489D61—41no—
490D61—41no—
491#556—611no—
492#554—1221no—
493#552—611no—
494#552—611no—
495#551—1221no—
496#551—1221no—
497D4×Q8—611no—
498#548—611no—
499#548—611no—
500#547—611no—
501#547—611no—
502#546—1221no—
503#542—1221no—
504#539—1221no—
505#539—1221no—
506#533—611no—
507#529C2×D6111yescharacteristic
508#525—611no—
509#525—611no—
510C2×C22⋊Q8—611no—
511C2×C22⋊Q8—611no—
512#520—1221no—
513C2×C4×D4—611no—
514#436—1221no—
515#435—1221no—
516#435—1221no—
517C8×D4—1221no—
518#432—611no—
519#431C2×D6111yescharacteristic
520#407—611no—
521#407—611no—
522C2×C22⋊C8—611no—
523C2×C22⋊C8—611no—
524#388—1221no—
525#387—1221no—
526#386—1221no—
527#385—1221no—
528#383C2×D6111yescharacteristic
529#382—611no—
530#381—611no—
531#380—611no—
532C4×C22⋊C4—611no—
533C2×#95—611no—
534#328—611no—
535#328—611no—
536#328—611no—
537#328—611no—
538#328—611no—
539#328—611no—
540#328—611no—
541#328—611no—
542#328—611no—
543#328—611no—
544#328C2×D6111yescharacteristic
545#328C2×D6111yescharacteristic
546#327—611no—
547#327—611no—
548#327C2×D6111yescharacteristic
549#327C2×D6111yescharacteristic
550C61#1759811yescharacteristic, complemented, Sylow
551C2×#41—611no—
552C2×#41—611no—
553C2×#41—1221no—
554C22×Q8—611no—
555C22×Q8—611no—
556C22×D4—611no—
557C23×C4—611no—
558C23×C4—611no—
559C23×C4—1221no—
560C2×M16—1221no—
561C2×M16—1221no—
562C22×C8—1221no—
563C22×C8—1221no—
564C4⋊Q8—611no—
565C4⋊Q8—611no—
566C4⋊Q8—1221no—
567#126—21no—
568#126—1221no—
569#126—1221no—
570#126—1221no—
571#126—1221no—
572#125—1221no—
573#125—1221no—
574#125—1221no—
575#125C4×D6111yescharacteristic, complemented
576#124—1221no—
577#124—1221no—
578#124—1221no—
579#124C4×D6111yescharacteristic, complemented
580#123—21no—
581#123—1221no—
582#123—1221no—
583#123—1221no—
584#123—1221no—
585#123—1221no—
586#123—1221no—
587#123—1221no—
588#123—1221no—
589C22⋊Q8—611no—
590C22⋊Q8—611no—
591C22⋊Q8—611no—
592C22⋊Q8—611no—
593C22⋊Q8—611no—
594C22⋊Q8—611no—
595C22⋊Q8—611no—
596C22⋊Q8—611no—
597C22⋊Q8—1221no—
598C22⋊Q8—1221no—
599C22⋊Q8—1221no—
600C22⋊Q8—1221no—
601C22⋊Q8—1221no—
602C22⋊Q8—1221no—
603C22⋊Q8—1221no—
604C22⋊Q8—1221no—
605C22⋊Q8—1221no—
606C22⋊Q8—1221no—
607C22⋊Q8C22×D6111yescharacteristic
608#121—611no—
609#121—611no—
610#121—1221no—
611#121—1221no—
612#121—1221no—
613#121C22×D6111yescharacteristic
614#120—1221no—
615#120—1221no—
616C4×Q8—611no—
617C4×Q8—611no—
618C4×Q8—1221no—
619C4×Q8—1221no—
620C4×Q8C4×D6111yescharacteristic, complemented
621C4×D4—21no—
622C4×D4—611no—
623C4×D4—611no—
624C4×D4—611no—
625C4×D4—611no—
626C4×D4—611no—
627C4×D4—611no—
628C4×D4—611no—
629C4×D4—611no—
630C4×D4—1221no—
631C4×D4—1221no—
632C4×D4—1221no—
633C4×D4—1221no—
634C4×D4—1221no—
635C4×D4—1221no—
636C4×D4—1221no—
637C4×D4C4×D6111yescharacteristic, complemented
638#117—21no—
639#117—611no—
640#117—611no—
641#117—1221no—
642#117—1221no—
643#117—1221no—
644C2×C4⋊C4—611no—
645C2×C4⋊C4—611no—
646C2×C4⋊C4—611no—
647C2×C4⋊C4—1221no—
648C2×C4⋊C4—1221no—
649C2×C4⋊C4—1221no—
650C2×C4⋊C4—1221no—
651C2×C4⋊C4—1221no—
652C2×C22⋊C4—611no—
653C2×C22⋊C4—611no—
654C2×C22⋊C4—1221no—
655C2×C22⋊C4—1221no—
656C2×C22⋊C4—1221no—
657C2×C22⋊C4—1221no—
658C2×C22⋊C4—1221no—
659C2×C42—1221no—
660C2×C42C22×D6111yescharacteristic
661C4⋊C8—21no—
662C4⋊C8—1221no—
663C22⋊C8—611no—
664C22⋊C8—611no—
665C22⋊C8—1221no—
666C22⋊C8—1221no—
667C22⋊C8—1221no—
668C22⋊C8—1221no—
669C22⋊C8C22×D6111yescharacteristic
670C22⋊C8C22×D6111yescharacteristic
671#97—1221no—
672C4×C8—21no—
673#95—21no—
674#95—21no—
675#95—611no—
676#95—611no—
677#95—1221no—
678#95—1221no—
679#95—1221no—
680#95C22×D6111yescharacteristic
681#95C22×D6111yescharacteristic
682C24—611no—
683C24—611no—
684#41—4881no—
685#41—4881no—
686#41—2444no—
687C2×Q8—611no—
688C2×Q8—611no—
689C2×Q8—1221no—
690C2×Q8—1221no—
691C2×Q8—1221no—
692C2×Q8—4881no—
693C2×Q8—4881no—
694C2×Q8C2×C4×D6111yescharacteristic
695C2×D4—21no—
696C2×D4—611no—
697C2×D4—611no—
698C2×D4—611no—
699C2×D4—611no—
700C2×D4—1221no—
701C2×D4—1221no—
702C2×D4—1221no—
703C2×D4—1221no—
704C2×D4—2442no—
705C2×D4C2×C4×D6111yescharacteristic
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—611no—
710C22×C4—611no—
711C22×C4—611no—
712C22×C4—611no—
713C22×C4—611no—
714C22×C4—611no—
715C22×C4—611no—
716C22×C4—611no—
717C22×C4—611no—
718C22×C4—611no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—4881no—
728C22×C4—4881no—
729C22×C4—4881no—
730C22×C4—4881no—
731C22×C4—2442no—
732C22×C4D4×D6111yescharacteristic
733C22×C4D4×D6111yescharacteristic
734C22×C4C23×D6111yescharacteristic
735M16—4881no—
736M16—4881no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—1221no—
740C2×C8—1221no—
741C2×C8—4881no—
742C2×C8—4881no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—611no—
748C4⋊C4—611no—
749C4⋊C4—611no—
750C4⋊C4—611no—
751C4⋊C4—611no—
752C4⋊C4—611no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4—1221no—
761C4⋊C4—1221no—
762C4⋊C4—1221no—
763C4⋊C4—1221no—
764C4⋊C4—1221no—
765C4⋊C4—1221no—
766C4⋊C4—1221no—
767C4⋊C4—1221no—
768C4⋊C4—4881no—
769C4⋊C4—4881no—
770C4⋊C4C2×C4×D6111yescharacteristic
771C4⋊C4C2×C4×D6111yescharacteristic
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—611no—
778C22⋊C4—611no—
779C22⋊C4—611no—
780C22⋊C4—611no—
781C22⋊C4—611no—
782C22⋊C4—611no—
783C22⋊C4—611no—
784C22⋊C4—611no—
785C22⋊C4—1221no—
786C22⋊C4—1221no—
787C22⋊C4—1221no—
788C22⋊C4—1221no—
789C22⋊C4—1221no—
790C22⋊C4—1221no—
791C22⋊C4—1221no—
792C22⋊C4—1221no—
793C22⋊C4—1221no—
794C22⋊C4—1221no—
795C22⋊C4—1221no—
796C22⋊C4—1221no—
797C22⋊C4—4881no—
798C22⋊C4—4881no—
799C22⋊C4—2442no—
800C42—21no—
801C42—1221no—
802C42—1221no—
803C42—1221no—
804C42—1221no—
805C42—4881no—
806C42C2×C4×D6111yescharacteristic
807C42C2×C4×D6111yescharacteristic
808C42D4×D6111yescharacteristic
809C42D4×D6111yescharacteristic
810C23—21no—
811C23—611no—
812C23—611no—
813C23—611no—
814C23—611no—
815C23—1222no—
816C23—1221no—
817C23—1221no—
818C23—1221no—
819C23—1221no—
820C23—2441no—
821C23—2441no—
822C23—2441no—
823C23C2×D4×D6111yescharacteristic
824Q8—41no—
825Q8—4881no—
826Q8—4881no—
827Q8—2441no—
828Q8—2441no—
829Q8—2442no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—1222no—
834D4—1222no—
835D4—4881no—
836D4—4881no—
837D4—2441no—
838D4—2441no—
839D4—2442no—
840D4—2442no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—42no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—611no—
856C2×C4—611no—
857C2×C4—611no—
858C2×C4—611no—
859C2×C4—1221no—
860C2×C4—1221no—
861C2×C4—1221no—
862C2×C4—1221no—
863C2×C4—4881no—
864C2×C4—4881no—
865C2×C4—4884no—
866C2×C4—4881no—
867C2×C4—4881no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2442no—
877C2×C4—2442no—
878C2×C4—2441no—
879C2×C4—2441no—
880C2×C4—2441no—
881C2×C4—2441no—
882C2×C4—2441no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4C22⋊C4×D6111yescharacteristic
887C2×C4C22⋊C4×D6111yescharacteristic
888C2×C4C22⋊C4×D6111yescharacteristic
889C2×C4C22⋊C4×D6111yescharacteristic
890C2×C4C22×C4×D6111yescharacteristic
891C2×C4C2×D4×D6111yescharacteristic
892C8—41no—
893C8—41no—
894C8—2441no—
895C8—2441no—
896C22—21no—
897C22—21no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—612no—
902C22—1221no—
903C22—1221no—
904C22—1221no—
905C22—1221no—
906C22—1221no—
907C22—1221no—
908C22—1221no—
909C22—1221no—
910C22—1221no—
911C22—1221no—
912C22—1221no—
913C22—4881no—
914C22—4881no—
915C22—2442no—
916C22—2442no—
917C22C2×C22⋊C4×D6111yescharacteristic
918C22#1684056911yescharacteristic
919C22#1684057611yescharacteristic
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—41no—
927C4—41no—
928C4—41no—
929C4—81no—
930C4—81no—
931C4—1221no—
932C4—1221no—
933C4—1221no—
934C4—1221no—
935C4—4881no—
936C4—4881no—
937C4—2441no—
938C4—2441no—
939C4—2441no—
940C4—2441no—
941C2—21no—
942C2—21no—
943C2—81no—
944C2—1222no—
945C2—2441no—
946C2—2441no—
947C2—2441no—
948C2#2145427811yescharacteristic
949C2#2145434811yescharacteristic
950C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1521C2
socleC22×C61C22×C22⋊C4
prime radical#21459870C2
cosocleC22×C4×C61C24
hypercenter#1521D61
hypocenterC61#17598
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1521

Complements

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

NH ≅ G/Ntype
2. #21454853C2semidirect
3. #21448450C2semidirect
4. #21444389C2semidirect
5. #21444384C2semidirect
6. #21444372C2semidirect
7. #21444369C2semidirect
8. #21444359C2semidirect
9. #21444357C2semidirect
10. #21444350C2semidirect
11. #21444337C2semidirect
12. #21444320C2semidirect
13. #21444307C2semidirect
14. #328×D61C2semidirect
15. C61×#1521C2semidirect
16. #16840485C4semidirect
18. #16840450C4semidirect
19. #16840450C4semidirect
22. Q8×D244C4semidirect
23. #16840420C4semidirect
24. #16840420C4semidirect
25. #16840417C4semidirect
26. #16840416C4semidirect
77. C2×#11758224C2×C4semidirect
79. C2×Q8×D61C2×C4semidirect
89. #14519777C2×C4semidirect
90. #14519777C2×C4semidirect
113. #14519757C2×C4semidirect
114. #14519757C2×C4semidirect
126. #14519753C2×C4semidirect
131. #14519748C2×C4semidirect
136. C4×Dic122C2×C4semidirect
137. C4×Dic122C2×C4semidirect
157. #14519735C2×C4semidirect
165. C4⋊C4×D61C2×C4semidirect
188. #125×C61C2×C4semidirect
189. #124×C61C2×C4semidirect
193. C4×Q8×C61C2×C4semidirect
195. C4×D4×C61C2×C4semidirect
469. #1521D61semidirect
550. C61#17598semidirect
575. #125C4×D61semidirect
579. #124C4×D61semidirect
620. C4×Q8C4×D61semidirect
637. C4×D4C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214598702
#214548532
#214484502
#214443892
#214443842
#214443722
#214443692
#214443592
#214443572
#214443502
#214443372
#214443202
#214443072
#328×D612
C61×#15212
#1759861