Finite Group Databasebeta

← #29647600

Subgroups — #29647600

Order 15616.

938 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459902C211yesmaximal, characteristic
2#21454906C211yesmaximal, characteristic, complemented
3#21448469C211yesmaximal, characteristic, complemented
4#21444395C211yesmaximal, characteristic, complemented
5#21444380C211yesmaximal, characteristic, complemented
6#21444377C211yesmaximal, characteristic, complemented
7#21444365C211yesmaximal, characteristic, complemented
8#21444364C211yesmaximal, characteristic, complemented
9#21444357C211yesmaximal, characteristic, complemented
10#21444356C211yesmaximal, characteristic, complemented
11#21444343C211yesmaximal, characteristic, complemented
12#21444325C211yesmaximal, characteristic, complemented
13#21444312C211yesmaximal, characteristic, complemented
14#21444304C211yesmaximal, characteristic, complemented
15C61×#1521C211yesmaximal, characteristic, complemented
16#16840497C411yescharacteristic, complemented
17#16840494C411yescharacteristic, complemented
18#16840494C411yescharacteristic, complemented
19Q8×Dic122C411yescharacteristic, complemented
20#16840469C411yescharacteristic, complemented
21#16840468C411yescharacteristic, complemented
22#16840468C411yescharacteristic, complemented
23#16840433C411yescharacteristic, complemented
24#16840421—21no—
25#16840416—21no—
26#16840410—21no—
27#16840410—21no—
28#16840383—21no—
29#16840378—21no—
30#16840378—21no—
31#16840312C2211yescharacteristic
32#16840307C2211yescharacteristic
33#16840307C2211yescharacteristic
34#16840298C2211yescharacteristic
35#16840298C2211yescharacteristic
36#16840242—21no—
37C2×C4×Dic122C2211yescharacteristic
38#16839892—21no—
39#16839891—21no—
40#16839891—21no—
41C8×Dic122—21no—
42#16839819C2211yescharacteristic
43#16839816C2211yescharacteristic
44#16839816C2211yescharacteristic
45#16839812C2211yescharacteristic
46#16839812C2211yescharacteristic
47#16839666—21no—
48#16839659—21no—
49#16839649—21no—
50#16839647—21no—
51#16839629C2211yescharacteristic
52#16839628C2211yescharacteristic
53#16839626C2211yescharacteristic
54#16839613C2211yescharacteristic
55#16839607C2211yescharacteristic
56#16839499C2211yescharacteristic
57#16839499C2211yescharacteristic
58#16839497C2211yescharacteristic
59#16839497C2211yescharacteristic
60#16839497C2211yescharacteristic
61#16839497C2211yescharacteristic
62#16839496C2211yescharacteristic
63#16839496C2211yescharacteristic
64#16839495C2211yescharacteristic
65#16839495C2211yescharacteristic
66#16839495C2211yescharacteristic
67#16839495C2211yescharacteristic
68C61×#529C2211yescharacteristic
69C61×#431C2211yescharacteristic
70C61×#383C2211yescharacteristic
71C61×#328C2211yescharacteristic
72C61×#328C2211yescharacteristic
73C61×#327C2211yescharacteristic
74C61×#327C2211yescharacteristic
75C2×#11758222—21no—
76C2×#11758222—21no—
77C2×#11758224—21no—
78C2×#11758224—21no—
79C22×Dic122D411yescharacteristic
80#14519777—21no—
81#14519777C2×C411yescharacteristic
82#14519776—21no—
83#14519776—21no—
84#14519776C2×C411yescharacteristic
85#14519776C2×C411yescharacteristic
86#14519774C2×C411yescharacteristic
87#14519773C2×C411yescharacteristic
88#14519773C2×C411yescharacteristic
89#14519772—21no—
90#14519772—21no—
91#14519768C2×C411yescharacteristic
92#14519768C2×C411yescharacteristic
93#14519766C2×C411yescharacteristic
94#14519766C2×C411yescharacteristic
95#14519765—21no—
96#14519765—21no—
97#14519763—21no—
98#14519763—21no—
99#14519763—21no—
100#14519763—21no—
101#14519762—21no—
102#14519762—21no—
103#14519761—21no—
104#14519761—21no—
105#14519761—21no—
106#14519761—21no—
107#14519759—21no—
108#14519759—21no—
109#14519757—21no—
110#14519757—21no—
111#14519756—21no—
112#14519755—21no—
113#14519755—21no—
114#14519755—21no—
115#14519755—21no—
116#14519754—21no—
117#14519754—21no—
118#14519751—21no—
119#14519751—21no—
120#14519751C2311yescharacteristic
121#14519751C2311yescharacteristic
122#14519750—21no—
123#14519750—21no—
124#14519749—21no—
125#14519749—21no—
126Q8×Dic61C2×C411yescharacteristic
127Q8×Dic61C2×C411yescharacteristic
128C4×Dic122—21no—
129C4×Dic122C2×C411yescharacteristic
130C4×Dic122C2×C411yescharacteristic
131C4×Dic122C2×C411yescharacteristic
132C4×Dic122C2×C411yescharacteristic
133C4×Dic122D411yescharacteristic
134C4×Dic122D411yescharacteristic
135C4×Dic122D411yescharacteristic
136C4×Dic122D411yescharacteristic
137C4×D244—21no—
138C4×D244—21no—
139C4×D244C2×C411yescharacteristic
140C4×D244C2×C411yescharacteristic
141D4×Dic61C2×C411yescharacteristic
142D4×Dic61C2×C411yescharacteristic
143#14519739C2×C411yescharacteristic
144#14519739C2×C411yescharacteristic
145#14519739C2×C411yescharacteristic
146#14519739C2×C411yescharacteristic
147#14519737—21no—
148#14519737—21no—
149#14519737—21no—
150#14519737—21no—
151#14519737—21no—
152#14519737—21no—
153#14519735—21no—
154#14519735—21no—
155C2×C4⋊Dic61—21no—
156C2×C4⋊Dic61—21no—
157C2×C4⋊Dic61D411yescharacteristic
158C2×#11758196—21no—
159C2×#11758196—21no—
160C2×#11758196D411yescharacteristic
161C2×#11758196D411yescharacteristic
162C4⋊C4×D61—21no—
163C4⋊C4×D61—21no—
164C2×C4×Dic61—21no—
165C2×C4×Dic61—21no—
166C2×C4×Dic61C2311yescharacteristic
167C2×C4×Dic61C2311yescharacteristic
168C4⋊#92418—21no—
169#14519706—21no—
170#14519706—21no—
171#14519706—21no—
172#14519706—21no—
173C22⋊#92418C2311yescharacteristic
174C22⋊#92418C2311yescharacteristic
175#14519688—21no—
176#14519687—21no—
177#14519687—21no—
178C8×Dic61—21no—
179C8×Dic61—21no—
180#14519684—21no—
181#14519684—21no—
182#14519684—21no—
183#14519684—21no—
184#14519684—21no—
185#14519684C2311yescharacteristic
186#14519684C2311yescharacteristic
187#126×C61—21no—
188#125×C61C2×C411yescharacteristic
189#124×C61C2×C411yescharacteristic
190#123×C61—21no—
191C22⋊Q8×C61C2311yescharacteristic
192#121×C61C2311yescharacteristic
193C4×Q8×C61C2×C411yescharacteristic
194C4×D4×C61—21no—
195C4×D4×C61C2×C411yescharacteristic
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
206C2×Q8×C61C22×C411yescharacteristic
207C2×D4×C61—21no—
208C2×D4×C61C22×C411yescharacteristic
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2411yescharacteristic
215C2×C22⋊D61—21no—
216C2×C22⋊D61—21no—
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
227C22×Dic61C2×D411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229#11758224—81no—
230#11758224—81no—
231#11758224—81no—
232#11758224—81no—
233#11758222—44no—
234#11758222—81no—
235#11758222—81no—
236C2×D244—21no—
237C2×D244—21no—
238C2×D244C22×C411yescharacteristic
239C2×D244C22×C411yescharacteristic
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×Dic122—21no—
247C2×Dic122—21no—
248C2×Dic122—21no—
249C2×Dic122—42no—
250C2×Dic122C22⋊C411yescharacteristic
251C2×Dic122C22⋊C411yescharacteristic
252C2×Dic122C22⋊C411yescharacteristic
253C2×Dic122C22⋊C411yescharacteristic
254C2×C8×C61—21no—
255C2×C8×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61C22×C411yescharacteristic
261C4⋊C4×C61C22×C411yescharacteristic
262C22⋊C4×C61—21no—
263C22⋊C4×C61—21no—
264C22⋊C4×C61—21no—
265C22⋊C4×C61—21no—
266C22⋊C4×C61—21no—
267C42×C61—21no—
268C42×C61C22×C411yescharacteristic
269C42×C61C22×C411yescharacteristic
270C42×C61C2×D411yescharacteristic
271C42×C61C2×D411yescharacteristic
272C22⋊Dic61—21no—
273C22⋊Dic61—21no—
274#11758198—21no—
275#11758198—21no—
276#11758198—21no—
277#11758198—21no—
278#11758198—21no—
279#11758198—21no—
280#11758198—21no—
281#11758198—21no—
282#11758198—21no—
283#11758198—21no—
284#11758198—21no—
285#11758198—21no—
286C4⋊Dic61—21no—
287C4⋊Dic61—21no—
288C4⋊Dic61—21no—
289C4⋊Dic61—21no—
290C4⋊Dic61—21no—
291C4⋊Dic61—81no—
292C4⋊Dic61C22⋊C411yescharacteristic
293C4⋊Dic61C22⋊C411yescharacteristic
294C4⋊Dic61C22⋊C411yescharacteristic
295C4⋊Dic61C22⋊C411yescharacteristic
296C4⋊Dic61C22×C411yescharacteristic
297C4⋊Dic61C22×C411yescharacteristic
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—42no—
303#11758196—81no—
304#11758196C22⋊C411yescharacteristic
305#11758196C22⋊C411yescharacteristic
306#11758196C22⋊C411yescharacteristic
307#11758196C22⋊C411yescharacteristic
308#11758196C22⋊C411yescharacteristic
309#11758196C22⋊C411yescharacteristic
310#11758196C22⋊C411yescharacteristic
311#11758196C22⋊C411yescharacteristic
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61—42no—
315C4×Dic61—81no—
316C4×Dic61C22×C411yescharacteristic
317C4×Dic61C22×C411yescharacteristic
318C4×Dic61C22×C411yescharacteristic
319C4×Dic61C22×C411yescharacteristic
320C4×Dic61C2×D411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C4×Dic61C2×D411yescharacteristic
323C4×Dic61C2×D411yescharacteristic
324C2×#92418—21no—
325C2×#92418—21no—
326C23×C61—21no—
327C23×C61C22×D411yescharacteristic
328C22×D61—21no—
329C22×D61—21no—
330Q8×C61—41no—
331D4×C61—41no—
332D4×C61—41no—
333D4×C61—41no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—42no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61C2×C22⋊C411yescharacteristic
349C2×C4×C61C2×C22⋊C411yescharacteristic
350C2×C4×C61C2×C22⋊C411yescharacteristic
351C2×C4×C61C2×C22⋊C411yescharacteristic
352C2×C4×C61C23×C411yescharacteristic
353C2×C4×C61C22×D411yescharacteristic
354C22⋊D61—42no—
355C22⋊D61—41no—
356C22⋊D61—41no—
357C22⋊D61—41no—
358C22⋊D61—41no—
359C22⋊D61—42no—
360C22⋊D61—81no—
361C22⋊D61—81no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—21no—
365C2×Dic61—21no—
366C2×Dic61—22no—
367C2×Dic61—21no—
368C2×Dic61—21no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—41no—
373C2×Dic61—41no—
374C2×Dic61—41no—
375C2×Dic61—41no—
376C2×Dic61—81no—
377C2×Dic61—81no—
378C2×Dic61C2×C22⋊C411yescharacteristic
379C2×Dic61C2×C22⋊C411yescharacteristic
380C2×Dic61C2×C22⋊C411yescharacteristic
381C2×Dic61C2×C22⋊C411yescharacteristic
382C2×Dic61C2×C22⋊C411yescharacteristic
383C2×Dic61C2×C22⋊C411yescharacteristic
384C2×Dic61C2×C22⋊C411yescharacteristic
385C2×Dic61C2×C22⋊C411yescharacteristic
386D244—41no—
387D244—41no—
388D244—42no—
389D244—81no—
390C4×D61—42no—
391C4×D61—42no—
392C4×D61—81no—
393C4×D61—81no—
394C4×D61—81no—
395C4×D61—81no—
396Dic122—22no—
397Dic122—22no—
398Dic122—41no—
399Dic122—41no—
400Dic122—81no—
401Dic122—81no—
402Dic122—81no—
403C8×C61—41no—
404C8×C61—41no—
405#92418—41no—
406#92418—41no—
407#17602—611nomaximal, Sylow
408C22×C61—21no—
409C22×C61—21no—
410C22×C61—41no—
411C22×C61—41no—
412C22×C61—41no—
413C22×C61C22×C22⋊C411yescharacteristic
414C22×C61#57611yescharacteristic
415C22×C61#57711yescharacteristic
416C2×D61—41no—
417C2×D61—41no—
418C2×D61—41no—
419C2×D61—41no—
420C2×D61—41no—
421C2×D61—41no—
422C4×C61—21no—
423C4×C61—21no—
424C4×C61—21no—
425C4×C61—21no—
426C4×C61—21no—
427C4×C61—21no—
428C4×C61—41no—
429C4×C61—41no—
430C4×C61—41no—
431C4×C61—81no—
432C4×C61—81no—
433Dic61—21no—
434Dic61—21no—
435Dic61—21no—
436Dic61—21no—
437Dic61—21no—
438Dic61—21no—
439Dic61—21no—
440Dic61—41no—
441Dic61—41no—
442Dic61—81no—
443Dic61—81no—
444Dic61#42112yes—
445#3522—611no—
446#2984—611no—
447#2320—611no—
448#1521—611no—
449#1521D6111yescharacteristic, complemented
450#1517—611no—
451#1517—611no—
452#1514—611no—
453#1514—611no—
454#1512—611no—
455#1512—611no—
456#1509—611no—
457#1505—611no—
458#1502—611no—
459#1500—611no—
460C2×C61—21no—
461C2×C61—21no—
462C2×C61—81no—
463C2×C61#288411yescharacteristic
464C2×C61#289711yescharacteristic
465C2×C61C2×#42111yescharacteristic
466D61—81no—
467D61—81no—
468#559—611no—
469#559—611no—
470#559—611no—
471Q82—611no—
472#554—611no—
473#554—611no—
474#554—611no—
475#550—611no—
476#548—1221no—
477#547—1221no—
478#547—1221no—
479#547—1221no—
480#542—1221no—
481#542—1221no—
482#542—1221no—
483#532—611no—
484#532—611no—
485#532—611no—
486#529—611no—
487#529—611no—
488#529C2×D6111yescharacteristic
489#520—1221no—
490C2×C4×Q8—611no—
491#446—1221no—
492#446—1221no—
493#446—1221no—
494C8×Q8—1221no—
495#432—611no—
496#432—611no—
497#432—611no—
498#431—611no—
499#431—611no—
500#431C2×D6111yescharacteristic
501#391—1221no—
502#389—1221no—
503#387—1221no—
504#387—1221no—
505#383—611no—
506#383C2×D6111yescharacteristic
507#382—611no—
508#382—611no—
509C4×C4⋊C4—611no—
510#376—611no—
511#328—611no—
512#328—611no—
513#328C2×D6111yescharacteristic
514#328C2×D6111yescharacteristic
515#327—611no—
516#327—611no—
517#327—611no—
518#327—611no—
519#327—611no—
520#327—611no—
521#327—611no—
522#327—611no—
523#327—611no—
524#327—611no—
525#327C2×D6111yescharacteristic
526#327C2×D6111yescharacteristic
527C61#1760211yescharacteristic, complemented, Sylow
528C2×#41—1221no—
529C2×#41—1221no—
530C2×#41—1221no—
531C2×#41—1221no—
532C22×Q8—611no—
533C4⋊Q8—611no—
534C4⋊Q8—611no—
535C4⋊Q8—611no—
536C4⋊Q8—1221no—
537C4⋊Q8—1221no—
538C4⋊Q8—1221no—
539#127—611no—
540#127—611no—
541#127—611no—
542#126—21no—
543#126—1221no—
544#126—1221no—
545#125—611no—
546#125—611no—
547#125C4×D6111yescharacteristic
548#124—611no—
549#124—611no—
550#124—1221no—
551#124—1221no—
552#124—1221no—
553#124—1221no—
554#124—1221no—
555#124—1221no—
556#124C4×D6111yescharacteristic
557#123—21no—
558#123—1221no—
559#123—1221no—
560#123—1221no—
561#123—1221no—
562#123—1221no—
563#123—1221no—
564#123—1221no—
565#123—1221no—
566C22⋊Q8—1221no—
567C22⋊Q8—1221no—
568C22⋊Q8—1221no—
569C22⋊Q8—1221no—
570C22⋊Q8—1221no—
571C22⋊Q8—1221no—
572C22⋊Q8—1221no—
573C22⋊Q8—1221no—
574C22⋊Q8—1221no—
575C22⋊Q8C22×D6111yescharacteristic
576#121—611no—
577#121—611no—
578#121—1221no—
579#121—1221no—
580#121—1221no—
581#121—1221no—
582#121—1221no—
583#121—1221no—
584#121C22×D6111yescharacteristic
585C4×Q8—611no—
586C4×Q8—611no—
587C4×Q8—611no—
588C4×Q8—611no—
589C4×Q8—611no—
590C4×Q8—611no—
591C4×Q8—611no—
592C4×Q8—611no—
593C4×Q8—611no—
594C4×Q8—611no—
595C4×Q8—1221no—
596C4×Q8C4×D6111yescharacteristic
597C4×D4—21no—
598C4×D4—611no—
599C4×D4—611no—
600C4×D4—611no—
601C4×D4—611no—
602C4×D4—611no—
603C4×D4—611no—
604C4×D4—611no—
605C4×D4—611no—
606C4×D4—1221no—
607C4×D4—1221no—
608C4×D4—1221no—
609C4×D4—1221no—
610C4×D4—1221no—
611C4×D4—1221no—
612C4×D4—1221no—
613C4×D4—1221no—
614C4×D4C4×D6111yescharacteristic
615#117—21no—
616#117—1221no—
617#117—1221no—
618C2×C4⋊C4—611no—
619C2×C4⋊C4—611no—
620C2×C4⋊C4—611no—
621C2×C4⋊C4—1221no—
622C2×C4⋊C4—1221no—
623C2×C4⋊C4—1221no—
624C2×C4⋊C4—1221no—
625C2×C4⋊C4—1221no—
626C2×C4⋊C4—1221no—
627C2×C42—611no—
628C2×C42—611no—
629C2×C42—1221no—
630C2×C42—1221no—
631C2×C42C22×D6111yescharacteristic
632C4⋊C8—21no—
633C4⋊C8—1221no—
634C4⋊C8—1221no—
635C4⋊C8—1221no—
636C4⋊C8—1221no—
637C4⋊C8—1221no—
638C22⋊C8—611no—
639C22⋊C8—611no—
640C22⋊C8C22×D6111yescharacteristic
641C22⋊C8C22×D6111yescharacteristic
642#97—1221no—
643#97—1221no—
644#97—1221no—
645C4×C8—21no—
646C4×C8—1221no—
647C4×C8—1221no—
648#95—21no—
649#95—21no—
650#95—611no—
651#95—611no—
652#95—1221no—
653#95—1221no—
654#95—1221no—
655#95—1221no—
656#95—1221no—
657#95C22×D6111yescharacteristic
658#95C22×D6111yescharacteristic
659#41—4881no—
660#41—4881no—
661#41—4881no—
662#41—4881no—
663#41—4881no—
664#41—4881no—
665#41—2444no—
666C2×Q8—611no—
667C2×Q8—611no—
668C2×Q8—611no—
669C2×Q8—611no—
670C2×Q8—1221no—
671C2×Q8—1221no—
672C2×Q8—1221no—
673C2×Q8—2442no—
674C2×Q8C2×C4×D6111yescharacteristic
675C2×D4—21no—
676C2×D4—611no—
677C2×D4—611no—
678C2×D4—1221no—
679C2×D4—1221no—
680C2×D4—1221no—
681C2×D4—1221no—
682C2×D4—1221no—
683C2×D4—1221no—
684C2×D4—1221no—
685C2×D4—1221no—
686C2×D4C2×C4×D6111yescharacteristic
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—611no—
691C22×C4—611no—
692C22×C4—611no—
693C22×C4—611no—
694C22×C4—1221no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4D4×D6111yescharacteristic
705C22×C4D4×D6111yescharacteristic
706C22×C4C23×D6111yescharacteristic
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—1221no—
710C2×C8—1221no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—611no—
716C4⋊C4—611no—
717C4⋊C4—611no—
718C4⋊C4—611no—
719C4⋊C4—611no—
720C4⋊C4—611no—
721C4⋊C4—611no—
722C4⋊C4—611no—
723C4⋊C4—611no—
724C4⋊C4—611no—
725C4⋊C4—611no—
726C4⋊C4—611no—
727C4⋊C4—611no—
728C4⋊C4—611no—
729C4⋊C4—1221no—
730C4⋊C4—1221no—
731C4⋊C4—1221no—
732C4⋊C4—1221no—
733C4⋊C4—1221no—
734C4⋊C4—1221no—
735C4⋊C4—1221no—
736C4⋊C4—1221no—
737C4⋊C4—1221no—
738C4⋊C4—4881no—
739C4⋊C4—4881no—
740C4⋊C4—2442no—
741C4⋊C4C2×C4×D6111yescharacteristic
742C4⋊C4C2×C4×D6111yescharacteristic
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—1221no—
749C22⋊C4—1221no—
750C22⋊C4—1221no—
751C22⋊C4—1221no—
752C22⋊C4—1221no—
753C22⋊C4—1221no—
754C22⋊C4—1221no—
755C22⋊C4—1221no—
756C22⋊C4—1221no—
757C22⋊C4—1221no—
758C22⋊C4—1221no—
759C22⋊C4—1221no—
760C22⋊C4—1221no—
761C22⋊C4—1221no—
762C42—21no—
763C42—611no—
764C42—611no—
765C42—611no—
766C42—611no—
767C42—611no—
768C42—611no—
769C42—611no—
770C42—611no—
771C42—1221no—
772C42—1221no—
773C42—4881no—
774C42—2442no—
775C42C2×C4×D6111yescharacteristic
776C42C2×C4×D6111yescharacteristic
777C42D4×D6111yescharacteristic
778C42D4×D6111yescharacteristic
779C23—21no—
780C23—1221no—
781C23—1221no—
782C23C2×D4×D6111yescharacteristic
783Q8—41no—
784Q8—1222no—
785Q8—1222no—
786Q8—4881no—
787Q8—4881no—
788Q8—4881no—
789Q8—2441no—
790Q8—2441no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—4881no—
795D4—4881no—
796D4—4881no—
797D4—2441no—
798D4—2441no—
799D4—2442no—
800D4—2442no—
801D4—2442no—
802D4—2441no—
803D4—2441no—
804D4—2441no—
805D4—2441no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—611no—
821C2×C4—611no—
822C2×C4—611no—
823C2×C4—611no—
824C2×C4—611no—
825C2×C4—611no—
826C2×C4—611no—
827C2×C4—611no—
828C2×C4—1222no—
829C2×C4—1221no—
830C2×C4—1221no—
831C2×C4—1221no—
832C2×C4—1221no—
833C2×C4—1221no—
834C2×C4—1221no—
835C2×C4—4881no—
836C2×C4—4881no—
837C2×C4—4881no—
838C2×C4—4881no—
839C2×C4—4881no—
840C2×C4—4881no—
841C2×C4—2442no—
842C2×C4—2442no—
843C2×C4—2441no—
844C2×C4—2441no—
845C2×C4—2441no—
846C2×C4—2441no—
847C2×C4—2441no—
848C2×C4—2441no—
849C2×C4—2441no—
850C2×C4C22⋊C4×D6111yescharacteristic
851C2×C4C22⋊C4×D6111yescharacteristic
852C2×C4C22⋊C4×D6111yescharacteristic
853C2×C4C22⋊C4×D6111yescharacteristic
854C2×C4C22×C4×D6111yescharacteristic
855C2×C4C2×D4×D6111yescharacteristic
856C8—41no—
857C8—41no—
858C8—2441no—
859C8—2441no—
860C22—21no—
861C22—21no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—2441no—
866C22—2441no—
867C22—2441no—
868C22—2441no—
869C22—2441no—
870C22—2441no—
871C22C2×C22⋊C4×D6111yescharacteristic
872C22#1684056411yescharacteristic
873C22#1684056911yescharacteristic
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—81no—
884C4—81no—
885C4—612no—
886C4—1221no—
887C4—1221no—
888C4—1221no—
889C4—1221no—
890C4—1221no—
891C4—1221no—
892C4—1221no—
893C4—4881no—
894C4—4881no—
895C4—2441no—
896C4—2441no—
897C2—21no—
898C2—21no—
899C2—81no—
900C2—4881no—
901C2—4881no—
902C2#2145428111yescharacteristic
903C2#2145434111yescharacteristic
904C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1521C2
socleC22×C61C22×C22⋊C4
prime radical#21459902C2
cosocleC22×C4×C61C24
hypercenter#1521D61
hypocenterC61#17602
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. #21454906C2semidirect
3. #21448469C2semidirect
4. #21444395C2semidirect
5. #21444380C2semidirect
6. #21444377C2semidirect
7. #21444365C2semidirect
8. #21444364C2semidirect
9. #21444357C2semidirect
10. #21444356C2semidirect
11. #21444343C2semidirect
12. #21444325C2semidirect
13. #21444312C2semidirect
14. #21444304C2semidirect
15. C61×#1521C2semidirect
16. #16840497C4semidirect
17. #16840494C4semidirect
18. #16840494C4semidirect
19. Q8×Dic122C4semidirect
20. #16840469C4semidirect
21. #16840468C4semidirect
22. #16840468C4semidirect
23. #16840433C4semidirect
449. #1521D61semidirect
527. C61#17602semidirect

Maximal subgroups

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

subgroupindex
#214599022
#214549062
#214484692
#214443952
#214443802
#214443772
#214443652
#214443642
#214443572
#214443562
#214443432
#214443252
#214443122
#214443042
C61×#15212
#1760261