Finite Group Databasebeta

← #29646940

Subgroups — #29646940

Order 15616.

958 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459375C211yesmaximal, characteristic
2#21454785C211yesmaximal, characteristic, complemented
3#21454486C211yesmaximal, characteristic, complemented
4#21444290C211yesmaximal, characteristic, complemented
5#21444281C211yesmaximal, characteristic, complemented
6#21444260C211yesmaximal, characteristic, complemented
7#21444257C211yesmaximal, characteristic, complemented
8#21444251C211yesmaximal, characteristic, complemented
9#21444238C211yesmaximal, characteristic, complemented
10#21444229C211yesmaximal, characteristic, complemented
11#21444227C211yesmaximal, characteristic, complemented
12#21444208C211yesmaximal, characteristic, complemented
13#21444205C211yesmaximal, characteristic, complemented
14#21444202C211yesmaximal, characteristic, complemented
15C61×#1494C211yesmaximal, characteristic, complemented
16#16840481C411yescharacteristic
17#16840476C411yescharacteristic
18#16840468C411yescharacteristic
19#16840457—21no—
20#16840450C411yescharacteristic
21#16840448—21no—
22#16840446C411yescharacteristic
23#16840440—21no—
24#16840437—21no—
25#16840414C411yescharacteristic
26#16840409C411yescharacteristic
27#16840405C411yescharacteristic
28#16840316C2211yescharacteristic
29#16840294—21no—
30#16840294C2211yescharacteristic
31#16840290—21no—
32#16840271—21no—
33C4×#11758226C2211yescharacteristic
34C4×#11758222C2211yescharacteristic
35C4×#11758222C2211yescharacteristic
36C4×D4×D61C2211yescharacteristic
37#117×D61—21no—
38#16839892—21no—
39#16839841—21no—
40#16839833—21no—
41#16839833—21no—
42#16839824—21no—
43#16839820—21no—
44#16839818C2211yescharacteristic
45#16839815C2211yescharacteristic, complemented
46#16839815C2211yescharacteristic, complemented
47#16839814C2211yescharacteristic
48#16839813C2211yescharacteristic
49#16839813C2211yescharacteristic, complemented
50#16839784C2211yescharacteristic, complemented
51C4⋊C8×D61C2211yescharacteristic, complemented
52#16839727—21no—
53#16839719—21no—
54C4×#11758189C2211yescharacteristic
55C4×#11758189C2211yescharacteristic, complemented
56#16839494C2211yescharacteristic, complemented
57#16839494C2211yescharacteristic, complemented
58Q8⋊#92418C2211yescharacteristic, complemented
59Q8⋊#92418C2211yescharacteristic, complemented
60#16839492C2211yescharacteristic, complemented
61#16839492C2211yescharacteristic, complemented
62#16839491C2211yescharacteristic
63#16839491C2211yescharacteristic
64D4⋊#92418C2211yescharacteristic
65D4⋊#92418C2211yescharacteristic
66#16839489C2211yescharacteristic
67#16839489C2211yescharacteristic
68C61×#529C2211yescharacteristic
69C61×#432C2211yescharacteristic, complemented
70C2×C4×C8×C61C2211yescharacteristic, complemented
71C61×Q8⋊C8C2211yescharacteristic, complemented
72C61×Q8⋊C8C2211yescharacteristic, complemented
73C61×D4⋊C8C2211yescharacteristic
74C61×D4⋊C8C2211yescharacteristic
75C2×#11758226C2×C411yescharacteristic
76C2×#11758222C2×C411yescharacteristic
77C2×#11758222D411yescharacteristic
78C2×D4×D61C2×C411yescharacteristic
79C22×C4×D61—21no—
80C2×#11758189—21no—
81C2×#11758189—21no—
82C2×#11758189—21no—
83C2×C8×D61—21no—
84#14519776C2×C411yescharacteristic
85#14519775C2×C411yescharacteristic
86#14519772—21no—
87#14519770—21no—
88#14519770—21no—
89#14519770—21no—
90#14519770—21no—
91#14519768—21no—
92#14519768C2×C411yescharacteristic
93#14519767—21no—
94#14519767—21no—
95#14519764—21no—
96#14519764C2×C411yescharacteristic
97#14519763—21no—
98#14519762—21no—
99#14519762—21no—
100#14519759—21no—
101#14519759—21no—
102#14519759—21no—
103#14519759—21no—
104#14519759—21no—
105#14519757—21no—
106#14519757C2×C411yescharacteristic
107#14519757C2×C411yescharacteristic
108#14519755—21no—
109#14519755—21no—
110#14519755—21no—
111#14519754—21no—
112#14519753C2×C411yescharacteristic
113#14519750—21no—
114#14519750—21no—
115#14519749—21no—
116#14519748—21no—
117#14519748C2×C411yescharacteristic
118#14519747—21no—
119#14519745—21no—
120Q8×Dic61C2×C411yescharacteristic
121C4×Dic122—21no—
122C4×Dic122C2×C411yescharacteristic
123C4×Dic122C2×C411yescharacteristic
124C4×Dic122D411yescharacteristic
125C4×Dic122C2311yescharacteristic
126C4×D244—21no—
127C4×D244C2×C411yescharacteristic
128C4×D244C2×C411yescharacteristic
129C4×D244D411yescharacteristic
130C4×D244C2311yescharacteristic
131D4×Dic61C2×C411yescharacteristic
132#14519739—21no—
133#14519739C2×C411yescharacteristic
134#14519739C2×C411yescharacteristic
135C4×C22⋊D61—21no—
136C4×C22⋊D61—21no—
137C4×C22⋊D61—21no—
138C4×C22⋊D61—21no—
139C4×C22⋊D61C2×C411yescharacteristic
140C4×C22⋊D61C2×C411yescharacteristic
141C4×C22⋊D61D411yescharacteristic
142C4×C22⋊D61D411yescharacteristic
143#14519737—21no—
144#14519736—21no—
145#14519736C2×C411yescharacteristic
146#14519736D411yescharacteristic
147#14519735—21no—
148#14519735—21no—
149#14519735—21no—
150#14519735C2×C411yescharacteristic
151#14519734—21no—
152#14519734—21no—
153#14519734D411yescharacteristic
154#14519734D411yescharacteristic
155#14519733—21no—
156#14519733—21no—
157C4⋊C4×D61—21no—
158C4⋊C4×D61—21no—
159C4⋊C4×D61C2×C411yescharacteristic
160C22⋊C4×D61—21no—
161C22⋊C4×D61—21no—
162C22⋊C4×D61—21no—
163C42×D61—21no—
164C42×D61—21no—
165C42×D61C2311yescharacteristic
166C42×D61C2311yescharacteristic
167C4⋊#92418—21no—
168C4⋊#92418C2311yescharacteristic
169C4⋊#92418C2311yescharacteristic
170#14519706—21no—
171#14519706—21no—
172#14519706—21no—
173#14519706—21no—
174C22⋊#92418—21no—
175C22⋊#92418—21no—
176#14519689—21no—
177#14519689—21no—
178#14519689—21no—
179#14519689—21no—
180#14519687—21no—
181#14519687—21no—
182#14519687—21no—
183C4×#92418—21no—
184C4×#92418C2311yescharacteristic
185C4×#92418C2311yescharacteristic
186C8×Dic61—21no—
187C22×C8×C61—21no—
188#126×C61—21no—
189#125×C61C2×C411yescharacteristic
190#124×C61C2×C411yescharacteristic
191#123×C61—21no—
192C22⋊Q8×C61C2×C411yescharacteristic
193#121×C61C2×C411yescharacteristic
194C4×Q8×C61C2311yescharacteristic
195C4×D4×C61—21no—
196C4×D4×C61C2311yescharacteristic
197#117×C61—21no—
198C2×C42×C61C2311yescharacteristic
199C4⋊C8×C61C2311yescharacteristic
200C4⋊C8×C61C2311yescharacteristic
201C22⋊C8×C61—21no—
202#97×C61—21no—
203C4×C8×C61—21no—
204C4×C8×C61C2311yescharacteristic
205C4×C8×C61C2311yescharacteristic
206C23×D61—21no—
207C2×Q8×C61C22×C411yescharacteristic
208C2×D4×C61—21no—
209C2×D4×C61C22×C411yescharacteristic
210C22×C4×C61—21no—
211C22×C4×C61C22×C411yescharacteristic
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2×D411yescharacteristic
214C2×C22⋊D61—21no—
215C2×C22⋊D61—21no—
216C2×C22⋊D61—21no—
217C2×C22⋊D61C22⋊C411yescharacteristic
218C2×C22⋊D61C22⋊C411yescharacteristic
219C22×Dic61—21no—
220#11758226—22no—
221#11758226—41no—
222D4×D61—22no—
223D4×D61—41no—
224#11758222—22no—
225#11758222—41no—
226#11758222—41no—
227#11758222—41no—
228C2×D244—21no—
229C2×D244C22⋊C411yescharacteristic
230C2×D244C22×C411yescharacteristic
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—42no—
239C2×C4×D61—42no—
240C2×C4×D61C22×C411yescharacteristic
241C2×C4×D61C22×C411yescharacteristic
242C2×C4×D61C2×D411yescharacteristic
243C2×C4×D61C2×D411yescharacteristic
244C2×C4×D61C2×D411yescharacteristic
245C2×C4×D61C2×D411yescharacteristic
246C2×Dic122—21no—
247C2×Dic122C22⋊C411yescharacteristic
248C2×Dic122C22×C411yescharacteristic
249C2×C8×C61—21no—
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C2×C8×C61—21no—
253C2×C8×C61—42no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61C22×C411yescharacteristic
259C4⋊C4×C61C22×C411yescharacteristic
260C22⋊C4×C61—21no—
261C22⋊C4×C61—21no—
262C22⋊C4×C61—21no—
263C22⋊C4×C61—21no—
264C22⋊C4×C61—21no—
265C42×C61—21no—
266C42×C61C22×C411yescharacteristic
267C42×C61C2×D411yescharacteristic
268C42×C61C2×D411yescharacteristic
269C42×C61C2411yescharacteristic
270C22⋊Dic61—21no—
271C22⋊Dic61—21no—
272C22⋊Dic61—21no—
273C22⋊Dic61—21no—
274C22⋊Dic61—21no—
275C22⋊Dic61C22⋊C411yescharacteristic
276C22⋊Dic61C22⋊C411yescharacteristic
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#11758198C22⋊C411yescharacteristic
286#11758198C22⋊C411yescharacteristic
287#11758198C22⋊C411yescharacteristic
288#11758198C22⋊C411yescharacteristic
289C4⋊Dic61—21no—
290C4⋊Dic61—21no—
291C4⋊Dic61—21no—
292C4⋊Dic61—21no—
293C4⋊Dic61C22⋊C411yescharacteristic
294C4⋊Dic61C22⋊C411yescharacteristic
295C4⋊Dic61C22×C411yescharacteristic
296C4⋊Dic61C22×C411yescharacteristic
297#11758196—21no—
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305#11758196C22⋊C411yescharacteristic
306#11758196C22⋊C411yescharacteristic
307#11758196C22⋊C411yescharacteristic
308#11758196C22⋊C411yescharacteristic
309C4×Dic61—21no—
310C4×Dic61—21no—
311C4×Dic61—21no—
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61C22×C411yescharacteristic
315C4×Dic61C22×C411yescharacteristic
316C4×Dic61C2×D411yescharacteristic
317C4×Dic61C2×D411yescharacteristic
318C4×Dic61C2×D411yescharacteristic
319C4×Dic61C2×D411yescharacteristic
320C2×#92418—21no—
321C2×#92418—21no—
322C2×#92418—21no—
323C2×#92418—21no—
324#11758189—42no—
325#11758189—42no—
326#11758189—42no—
327C8×D61—42no—
328C23×C61—21no—
329C23×C61C2×C22⋊C411yescharacteristic
330C22×D61—21no—
331C22×D61—42no—
332C22×D61—42no—
333C22×D61—81no—
334C22×D61C2×C22⋊C411yescharacteristic
335C22×D61C2×C22⋊C411yescharacteristic
336Q8×C61—21no—
337Q8×C61—21no—
338D4×C61—21no—
339D4×C61—21no—
340D4×C61—81no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61C2×C22⋊C411yescharacteristic
352C2×C4×C61C2×C22⋊C411yescharacteristic
353C2×C4×C61C2×C22⋊C411yescharacteristic
354C2×C4×C61C23×C411yescharacteristic
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C22×D411yescharacteristic
357C22⋊D61—41no—
358C22⋊D61—41no—
359C22⋊D61—42no—
360C22⋊D61—42no—
361C22⋊D61—81no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—21no—
365C2×Dic61—42no—
366C2×Dic61C2×C22⋊C411yescharacteristic
367C2×Dic61C2×C22⋊C411yescharacteristic
368C2×Dic61C2×C22⋊C411yescharacteristic
369C2×Dic61C2×C22⋊C411yescharacteristic
370C2×Dic61C2×C22⋊C411yescharacteristic
371C2×Dic61C2×C22⋊C411yescharacteristic
372D244—21no—
373D244—41no—
374D244—42no—
375D244#13112yes—
376C4×D61—21no—
377C4×D61—21no—
378C4×D61—21no—
379C4×D61—21no—
380C4×D61—21no—
381C4×D61—21no—
382C4×D61—21no—
383C4×D61—21no—
384C4×D61—41no—
385C4×D61—41no—
386C4×D61—42no—
387C4×D61—42no—
388C4×D61—42no—
389C4×D61—42no—
390C4×D61—41no—
391C4×D61—41no—
392C4×D61—81no—
393C4×D61—81no—
394Dic122—21no—
395Dic122—21no—
396Dic122—41no—
397Dic122—81no—
398C8×C61—22no—
399C8×C61—41no—
400C8×C61—41no—
401C8×C61—41no—
402#92418—41no—
403#92418—41no—
404#92418—41no—
405#92418—41no—
406#17513—611nomaximal, Sylow
407C22×C61—21no—
408C22×C61—21no—
409C22×C61—21no—
410C22×C61—41no—
411C22×C61—41no—
412C22×C61—41no—
413C22×C61C22×C22⋊C411yescharacteristic
414C2×D61—21no—
415C2×D61—21no—
416C2×D61—22no—
417C2×D61—21no—
418C2×D61—21no—
419C2×D61—21no—
420C2×D61—21no—
421C2×D61—41no—
422C2×D61—41no—
423C2×D61—84no—
424C4×C61—21no—
425C4×C61—21no—
426C4×C61—21no—
427C4×C61—21no—
428C4×C61—41no—
429C4×C61—41no—
430C4×C61—41no—
431C4×C61C2×#13111yescharacteristic
432C4×C61#56811yescharacteristic
433C4×C61#57511yescharacteristic
434C4×C61#57511yescharacteristic
435Dic61—21no—
436Dic61—21no—
437Dic61—21no—
438Dic61—21no—
439Dic61—21no—
440Dic61—21no—
441Dic61—41no—
442Dic61—41no—
443Dic61—41no—
444#3475—611no—
445#2965—611no—
446#2925—611no—
447#1497—611no—
448#1495—611no—
449#1494D6111yescharacteristic, complemented
450#1490—611no—
451#1489—611no—
452#1488—611no—
453#1485—611no—
454#1483—611no—
455#1482—611no—
456#1478—611no—
457#1477—611no—
458#1476—611no—
459C2×C61—41no—
460C2×C61—81no—
461C2×C61#288011yescharacteristic
462C2×C61#289611yescharacteristic
463C2×C61#290111yescharacteristic
464D61—41no—
465D61—41no—
466D61—42no—
467#556—611no—
468#555—611no—
469#554—611no—
470#553—1221no—
471#552—611no—
472#552—611no—
473#552—1221no—
474#551—1221no—
475#551—1221no—
476#547—611no—
477#546—611no—
478#546—611no—
479#533—611no—
480#529—611no—
481#529—1221no—
482#529—1221no—
483#529C2×D6111yescharacteristic
484#525—1221no—
485C4×#41—611no—
486C4×#41—611no—
487C4×#41—611no—
488C2×C4×D4—611no—
489C2×#117—1221no—
490#446—1221no—
491#436—1221no—
492#435—1221no—
493#435—1221no—
494#433—1221no—
495#433—1221no—
496#432—611no—
497#432C2×D6111yescharacteristic, complemented
498#431—611no—
499#431—611no—
500#431—611no—
501#431—611no—
502#431—611no—
503#423—611no—
504C2×C4⋊C8—611no—
505#408—1221no—
506#405—1221no—
507C4×M16—611no—
508C4×M16—611no—
509C2×C4×C8C2×D6111yescharacteristic, complemented
510Q8⋊C8—611no—
511Q8⋊C8—611no—
512Q8⋊C8—611no—
513Q8⋊C8—611no—
514Q8⋊C8—611no—
515Q8⋊C8—611no—
516Q8⋊C8C2×D6111yescharacteristic, complemented
517Q8⋊C8C2×D6111yescharacteristic, complemented
518D4⋊C8—611no—
519D4⋊C8—611no—
520D4⋊C8—611no—
521D4⋊C8—611no—
522D4⋊C8—611no—
523D4⋊C8—611no—
524D4⋊C8C2×D6111yescharacteristic
525D4⋊C8C2×D6111yescharacteristic
526C61#1751311yescharacteristic, complemented, Sylow
527C2×#41—611no—
528C2×#41—611no—
529C2×#41—611no—
530C22×D4—611no—
531C23×C4—1221no—
532C2×M16—1221no—
533C2×M16—1221no—
534C2×M16—1221no—
535C22×C8—21no—
536C22×C8—1221no—
537C4⋊Q8—611no—
538C4⋊Q8—611no—
539#126—21no—
540#126—1221no—
541#126—1221no—
542#126—1221no—
543#126—1221no—
544#126—1221no—
545#125—611no—
546#125—1221no—
547#125—1221no—
548#125—1221no—
549#125C4×D6111yescharacteristic
550#124—611no—
551#124—1221no—
552#124—1221no—
553#124C4×D6111yescharacteristic
554#123—21no—
555#123—1221no—
556#123—1221no—
557#123—1221no—
558#123—1221no—
559#123—1221no—
560#123—1221no—
561#123—1221no—
562C22⋊Q8—611no—
563C22⋊Q8—611no—
564C22⋊Q8—611no—
565C22⋊Q8—1221no—
566C22⋊Q8—1221no—
567C22⋊Q8—1221no—
568C22⋊Q8—1221no—
569C22⋊Q8—1221no—
570C22⋊Q8C4×D6111yescharacteristic
571#121—611no—
572#121—1221no—
573#121—1221no—
574#121—1221no—
575#121—1221no—
576#121C4×D6111yescharacteristic
577#120—1221no—
578#120—1221no—
579C4×Q8—611no—
580C4×Q8—611no—
581C4×Q8—611no—
582C4×Q8—611no—
583C4×Q8—611no—
584C4×Q8—1221no—
585C4×Q8C22×D6111yescharacteristic
586C4×D4—21no—
587C4×D4—611no—
588C4×D4—611no—
589C4×D4—611no—
590C4×D4—611no—
591C4×D4—611no—
592C4×D4—611no—
593C4×D4—611no—
594C4×D4—611no—
595C4×D4—611no—
596C4×D4—611no—
597C4×D4—611no—
598C4×D4—1221no—
599C4×D4—1221no—
600C4×D4—1221no—
601C4×D4—1221no—
602C4×D4—1221no—
603C4×D4—1221no—
604C4×D4—1221no—
605C4×D4C22×D6111yescharacteristic
606#117—21no—
607#117—611no—
608#117—611no—
609#117—611no—
610#117—611no—
611#117—611no—
612#117—1221no—
613#117—1221no—
614#117—1221no—
615#117—1221no—
616#117—1221no—
617#117—1221no—
618#117—1221no—
619#117—1221no—
620C2×C4⋊C4—611no—
621C2×C4⋊C4—1221no—
622C2×C4⋊C4—1221no—
623C2×C22⋊C4—1221no—
624C2×C22⋊C4—1221no—
625C2×C22⋊C4—1221no—
626C2×C42—611no—
627C2×C42—611no—
628C2×C42—1221no—
629C2×C42—1221no—
630C2×C42C22×D6111yescharacteristic
631C4⋊C8—611no—
632C4⋊C8—611no—
633C4⋊C8—1221no—
634C4⋊C8—1221no—
635C4⋊C8—1221no—
636C4⋊C8—1221no—
637C4⋊C8—1221no—
638C4⋊C8C22×D6111yescharacteristic
639C4⋊C8C22×D6111yescharacteristic
640C22⋊C8—21no—
641C22⋊C8—1221no—
642C22⋊C8—1221no—
643C22⋊C8—1221no—
644C22⋊C8—1221no—
645C22⋊C8—1221no—
646C22⋊C8—1221no—
647#97—21no—
648#97—1221no—
649#97—1221no—
650#97—1221no—
651C4×C8—21no—
652C4×C8—611no—
653C4×C8—611no—
654C4×C8—1221no—
655C4×C8—1221no—
656C4×C8C22×D6111yescharacteristic
657C4×C8C22×D6111yescharacteristic
658C24—1221no—
659#41—1222no—
660#41—1222no—
661#41—2441no—
662#41—2441no—
663#41—2441no—
664#41—2441no—
665C2×Q8—611no—
666C2×Q8—611no—
667C2×Q8—1221no—
668C2×Q8C2×C4×D6111yescharacteristic
669C2×D4—21no—
670C2×D4—611no—
671C2×D4—611no—
672C2×D4—611no—
673C2×D4—611no—
674C2×D4—1221no—
675C2×D4—1221no—
676C2×D4—1222no—
677C2×D4—1221no—
678C2×D4—1221no—
679C2×D4—2441no—
680C2×D4C2×C4×D6111yescharacteristic
681C22×C4—21no—
682C22×C4—611no—
683C22×C4—611no—
684C22×C4—611no—
685C22×C4—611no—
686C22×C4—611no—
687C22×C4—611no—
688C22×C4—1221no—
689C22×C4—1221no—
690C22×C4—1221no—
691C22×C4—1221no—
692C22×C4—1221no—
693C22×C4—1221no—
694C22×C4—1221no—
695C22×C4—1221no—
696C22×C4—2442no—
697C22×C4—2442no—
698C22×C4C2×C4×D6111yescharacteristic
699C22×C4D4×D6111yescharacteristic
700C22×C4D4×D6111yescharacteristic
701M16—2442no—
702M16—2442no—
703M16—2442no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—42no—
709C2×C8—1221no—
710C2×C8—1221no—
711C2×C8—1221no—
712C2×C8—1221no—
713C2×C8—2442no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
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—1221no—
727C4⋊C4—1221no—
728C4⋊C4—1221no—
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⋊C4C2×C4×D6111yescharacteristic
739C4⋊C4C2×C4×D6111yescharacteristic
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—611no—
746C22⋊C4—611no—
747C22⋊C4—611no—
748C22⋊C4—611no—
749C22⋊C4—611no—
750C22⋊C4—611no—
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—
762C22⋊C4—1221no—
763C22⋊C4—1221no—
764C42—21no—
765C42—611no—
766C42—611no—
767C42—611no—
768C42—611no—
769C42—611no—
770C42—611no—
771C42—1221no—
772C42—1221no—
773C42—1221no—
774C42—1221no—
775C42—1221no—
776C42C2×C4×D6111yescharacteristic
777C42D4×D6111yescharacteristic
778C42D4×D6111yescharacteristic
779C42C23×D6111yescharacteristic
780C23—21no—
781C23—611no—
782C23—611no—
783C23—1221no—
784C23—4881no—
785C23—2442no—
786C23—2442no—
787C23C22⋊C4×D6111yescharacteristic
788Q8—21no—
789Q8—21no—
790Q8—1221no—
791Q8—1221no—
792Q8—4881no—
793Q8—2441no—
794D4—21no—
795D4—21no—
796D4—81no—
797D4—612no—
798D4—1221no—
799D4—4881no—
800D4—2441no—
801D4—2442no—
802D4—2441no—
803D4—2441no—
804D4—2442no—
805D4—2442no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—611no—
817C2×C4—611no—
818C2×C4—611no—
819C2×C4—611no—
820C2×C4—611no—
821C2×C4—611no—
822C2×C4—1221no—
823C2×C4—1221no—
824C2×C4—1221no—
825C2×C4—1221no—
826C2×C4—1221no—
827C2×C4—1221no—
828C2×C4—1221no—
829C2×C4—1221no—
830C2×C4—1221no—
831C2×C4—1221no—
832C2×C4—1221no—
833C2×C4—4881no—
834C2×C4—4881no—
835C2×C4—2441no—
836C2×C4—2441no—
837C2×C4—2442no—
838C2×C4—2442no—
839C2×C4—2442no—
840C2×C4—2442no—
841C2×C4—2442no—
842C2×C4—2441no—
843C2×C4—2441no—
844C2×C4C22⋊C4×D6111yescharacteristic
845C2×C4C22⋊C4×D6111yescharacteristic
846C2×C4C22⋊C4×D6111yescharacteristic
847C2×C4C22×C4×D6111yescharacteristic
848C2×C4C2×D4×D6111yescharacteristic
849C2×C4C2×D4×D6111yescharacteristic
850C8—22no—
851C8—41no—
852C8—41no—
853C8—41no—
854C8—2441no—
855C8—2441no—
856C8—2441no—
857C8—2441no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—1221no—
865C22—1221no—
866C22—1221no—
867C22—1221no—
868C22—1222no—
869C22—1221no—
870C22—1221no—
871C22—4884no—
872C22—2441no—
873C22—2441no—
874C22C2×C22⋊C4×D6111yescharacteristic
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—1221no—
883C4—1221no—
884C4—1221no—
885C4—1221no—
886C4—1221no—
887C4—1221no—
888C4—2441no—
889C4—2441no—
890C4—2441no—
891C4#131×D6111yescharacteristic
892C4#1684052711yescharacteristic
893C4#1684055911yescharacteristic
894C4#1684055911yescharacteristic
895C2—41no—
896C2—81no—
897C2—2441no—
898C2—2441no—
899C2—2442no—
900C2#2145426711yescharacteristic
901C2#2145433411yescharacteristic
902C2#2145436311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1494C2
socleC22×C61C22×C22⋊C4
prime radical#21459375C2
cosocleC42×C61C24
hypercenter#1494D61
hypocenterC61#17513
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
2. #21454785C2semidirect
3. #21454486C2semidirect
4. #21444290C2semidirect
5. #21444281C2semidirect
6. #21444260C2semidirect
7. #21444257C2semidirect
8. #21444251C2semidirect
9. #21444238C2semidirect
10. #21444229C2semidirect
11. #21444227C2semidirect
12. #21444208C2semidirect
13. #21444205C2semidirect
14. #21444202C2semidirect
15. C61×#1494C2semidirect
45. #16839815C22semidirect
46. #16839815C22semidirect
49. #16839813C22semidirect
50. #16839784C22semidirect
51. C4⋊C8×D61C22semidirect
55. C4×#11758189C22semidirect
56. #16839494C22semidirect
57. #16839494C22semidirect
58. Q8⋊#92418C22semidirect
59. Q8⋊#92418C22semidirect
60. #16839492C22semidirect
61. #16839492C22semidirect
69. C61×#432C22semidirect
70. C2×C4×C8×C61C22semidirect
71. C61×Q8⋊C8C22semidirect
72. C61×Q8⋊C8C22semidirect
449. #1494D61semidirect
497. #432C2×D61semidirect
509. C2×C4×C8C2×D61semidirect
516. Q8⋊C8C2×D61semidirect
517. Q8⋊C8C2×D61semidirect
526. C61#17513semidirect

Maximal subgroups

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

subgroupindex
#214593752
#214547852
#214544862
#214442902
#214442812
#214442602
#214442572
#214442512
#214442382
#214442292
#214442272
#214442082
#214442052
#214442022
C61×#14942
#1751361