Finite Group Databasebeta

← #29646586

Subgroups — #29646586

Order 15616.

984 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459240C211yesmaximal, characteristic
2#21454927C211yesmaximal, characteristic, complemented
3#21454783C211yesmaximal, characteristic, complemented
4#21444235C211yesmaximal, characteristic, complemented
5#21444234C211yesmaximal, characteristic, complemented
6#21444232C211yesmaximal, characteristic, complemented
7#21444231C211yesmaximal, characteristic, complemented
8#21444226C211yesmaximal, characteristic, complemented
9#21444219C211yesmaximal, characteristic, complemented
10#21444216C211yesmaximal, characteristic, complemented
11#21444208C211yesmaximal, characteristic, complemented
12#21444205C211yesmaximal, characteristic, complemented
13#21444200C211yesmaximal, characteristic, complemented
14D4⋊C8×D61C211yesmaximal, characteristic, complemented
15C61×#1482C211yesmaximal, characteristic, complemented
16#16840392C411yescharacteristic
17#16840385C411yescharacteristic
18#16840381C411yescharacteristic
19#16840378—21no—
20#16840368C411yescharacteristic
21#16840365C411yescharacteristic
22#16840364—21no—
23#16840351—21no—
24#16840348—21no—
25#16840342C411yescharacteristic
26#16840330C411yescharacteristic
27#16840328C411yescharacteristic
28#16840312C2211yescharacteristic
29#16840309—21no—
30#16840309C2211yescharacteristic
31#16840299C2211yescharacteristic
32#16840290—21no—
33#16840274—21no—
34#16840271—21no—
35C4×#11758226C2211yescharacteristic
36C4×#11758222C2211yescharacteristic
37C4×D4×D61C2211yescharacteristic
38#16839891—21no—
39C8×Dic122—21no—
40#16839837—21no—
41#16839836—21no—
42#16839832—21no—
43C8×D244—21no—
44#16839825—21no—
45#16839825—21no—
46#16839814C2211yescharacteristic
47#16839814C2211yescharacteristic, complemented
48#16839813C2211yescharacteristic
49#16839813C2211yescharacteristic, complemented
50C2×C4⋊#92418C2211yescharacteristic, complemented
51C4⋊C8×D61C2211yescharacteristic
52C4⋊C8×D61C2211yescharacteristic, complemented
53C4×#11758194C2211yescharacteristic, complemented
54C4×#11758189C2211yescharacteristic, complemented
55C4×C8×D61C2211yescharacteristic
56Q8⋊#92418C2211yescharacteristic, complemented
57Q8⋊#92418C2211yescharacteristic, complemented
58#16839491C2211yescharacteristic
59#16839491C2211yescharacteristic
60#16839491C2211yescharacteristic, complemented
61#16839491C2211yescharacteristic, complemented
62D4⋊#92418C2211yescharacteristic
63D4⋊#92418C2211yescharacteristic
64#16839489C2211yescharacteristic
65#16839489C2211yescharacteristic
66#16839489C2211yescharacteristic, complemented
67#16839489C2211yescharacteristic, complemented
68C61×#529C2211yescharacteristic
69C61×#431C2211yescharacteristic, complemented
70C61×#431C2211yescharacteristic, complemented
71C61×Q8⋊C8C2211yescharacteristic, complemented
72C61×Q8⋊C8C2211yescharacteristic, complemented
73C61×D4⋊C8C2211yescharacteristic
74C61×D4⋊C8C2211yescharacteristic
75C2×#11758226C2×C411yescharacteristic
76C2×#11758222—21no—
77C2×#11758222—21no—
78C2×#11758222C2×C411yescharacteristic
79C2×D4×D61C2×C411yescharacteristic
80C22×C4×D61—21no—
81C2×#11758194—21no—
82C2×#11758189—21no—
83C22×#92418—21no—
84C2×C8×D61—21no—
85C2×C8×D61—21no—
86C2×C8×D61—21no—
87#14519777C2×C411yescharacteristic
88#14519776—21no—
89#14519776C2×C411yescharacteristic
90#14519774C2×C411yescharacteristic
91#14519773—21no—
92#14519773C2×C411yescharacteristic
93#14519772—21no—
94#14519772—21no—
95#14519770—21no—
96#14519768C2×C411yescharacteristic
97#14519767—21no—
98#14519766C2×C411yescharacteristic
99#14519765—21no—
100#14519763—21no—
101#14519763—21no—
102#14519763—21no—
103#14519763—21no—
104#14519762—21no—
105#14519762—21no—
106#14519762—21no—
107#14519761—21no—
108#14519761—21no—
109#14519759—21no—
110#14519759—21no—
111#14519757—21no—
112#14519757—21no—
113#14519755—21no—
114#14519755—21no—
115#14519754—21no—
116#14519753C2×C411yescharacteristic
117#14519752—21no—
118#14519752—21no—
119#14519752—21no—
120#14519752C2×C411yescharacteristic
121#14519752C2×C411yescharacteristic
122#14519751—21no—
123#14519751C2×C411yescharacteristic
124#14519751C2×C411yescharacteristic
125#14519750—21no—
126#14519750—21no—
127#14519750—21no—
128#14519750—21no—
129#14519750—21no—
130#14519749—21no—
131#14519748—21no—
132#14519748C2×C411yescharacteristic
133#14519747—21no—
134#14519747—21no—
135#14519747—21no—
136#14519745—21no—
137Q8×Dic61C2×C411yescharacteristic
138C4×Dic122D411yescharacteristic
139C4×Dic122D411yescharacteristic
140C4×D244—21no—
141C4×D244—21no—
142C4×D244—21no—
143C4×D244D411yescharacteristic
144C4×D244D411yescharacteristic
145C4×D244C2311yescharacteristic
146C4×D244C2311yescharacteristic
147D4×Dic61C2×C411yescharacteristic
148#14519739—21no—
149#14519739C2×C411yescharacteristic
150#14519739C2×C411yescharacteristic
151C4×C22⋊D61—21no—
152C4×C22⋊D61—21no—
153C4×C22⋊D61D411yescharacteristic
154C4×C22⋊D61D411yescharacteristic
155C4×C22⋊D61D411yescharacteristic
156C4×C22⋊D61D411yescharacteristic
157#14519737—21no—
158#14519736C2×C411yescharacteristic
159#14519735—21no—
160#14519735C2×C411yescharacteristic
161#14519734—21no—
162#14519734C2×C411yescharacteristic
163#14519734C2×C411yescharacteristic
164C4⋊C4×D61C2×C411yescharacteristic
165C22⋊C4×D61—21no—
166C42×D61—21no—
167C42×D61C2311yescharacteristic
168C42×D61C2311yescharacteristic
169C4⋊#92418—21no—
170C4⋊#92418C2311yescharacteristic
171C4⋊#92418C2311yescharacteristic
172#14519706—21no—
173#14519706—21no—
174#14519706—21no—
175#14519706—21no—
176#14519689—21no—
177#14519689—21no—
178#14519689—21no—
179#14519689—21no—
180#14519688—21no—
181#14519687—21no—
182C4×#92418C2311yescharacteristic
183C4×#92418C2311yescharacteristic
184C8×Dic61—21no—
185C8×Dic61—21no—
186C8×Dic61—21no—
187#126×C61—21no—
188#125×C61C2×C411yescharacteristic
189#124×C61C2×C411yescharacteristic
190#123×C61—21no—
191C22⋊Q8×C61C2×C411yescharacteristic
192#121×C61C2×C411yescharacteristic
193C4×Q8×C61C2311yescharacteristic
194C4×D4×C61—21no—
195C4×D4×C61C2311yescharacteristic
196#117×C61—21no—
197C2×C42×C61C2311yescharacteristic
198C4⋊C8×C61—21no—
199C4⋊C8×C61C2311yescharacteristic
200C4⋊C8×C61C2311yescharacteristic
201C22⋊C8×C61—21no—
202C22⋊C8×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⋊D61—21no—
218C2×C22⋊D61—21no—
219C2×C22⋊D61—21no—
220C2×C22⋊D61C22⋊C411yescharacteristic
221C2×C22⋊D61C22⋊C411yescharacteristic
222C22×Dic61—21no—
223#11758226—24no—
224D4×D61—24no—
225#11758222—24no—
226#11758222—81no—
227#11758222—81no—
228#11758222—81no—
229#11758222—81no—
230C2×D244—21no—
231C2×D244—21no—
232C2×D244—21no—
233C2×D244—21no—
234C2×D244—21no—
235C2×D244C22⋊C411yescharacteristic
236C2×D244C22×C411yescharacteristic
237C2×D244C22×C411yescharacteristic
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—81no—
245C2×C4×D61—81no—
246C2×C4×D61C22×C411yescharacteristic
247C2×C4×D61C22×C411yescharacteristic
248C2×C4×D61C2×D411yescharacteristic
249C2×C4×D61C2×D411yescharacteristic
250C2×C4×D61C2×D411yescharacteristic
251C2×C4×D61C2×D411yescharacteristic
252C2×Dic122—21no—
253C2×Dic122—21no—
254C2×Dic122C22⋊C411yescharacteristic
255C2×C8×C61—21no—
256C2×C8×C61—21no—
257C2×C8×C61—21no—
258C2×C8×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61—21no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61C22×C411yescharacteristic
264C4⋊C4×C61C22×C411yescharacteristic
265C22⋊C4×C61—21no—
266C22⋊C4×C61—21no—
267C22⋊C4×C61—21no—
268C22⋊C4×C61—21no—
269C22⋊C4×C61—21no—
270C42×C61—21no—
271C42×C61C22×C411yescharacteristic
272C42×C61C2×D411yescharacteristic
273C42×C61C2×D411yescharacteristic
274C42×C61C2411yescharacteristic
275C22⋊Dic61—21no—
276C22⋊Dic61—21no—
277C22⋊Dic61C22⋊C411yescharacteristic
278C22⋊Dic61C22⋊C411yescharacteristic
279#11758198—21no—
280#11758198—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—21no—
290#11758198—21no—
291#11758198C22⋊C411yescharacteristic
292#11758198C22⋊C411yescharacteristic
293#11758198C22⋊C411yescharacteristic
294#11758198C22⋊C411yescharacteristic
295C4⋊Dic61—21no—
296C4⋊Dic61—21no—
297C4⋊Dic61—21no—
298C4⋊Dic61C22⋊C411yescharacteristic
299C4⋊Dic61C22⋊C411yescharacteristic
300C4⋊Dic61C22×C411yescharacteristic
301C4⋊Dic61C22×C411yescharacteristic
302#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305#11758196—21no—
306#11758196C22⋊C411yescharacteristic
307#11758196C22⋊C411yescharacteristic
308#11758196C22⋊C411yescharacteristic
309#11758196C22⋊C411yescharacteristic
310C4×Dic61—21no—
311C4×Dic61—21no—
312C4×Dic61C22×C411yescharacteristic
313C4×Dic61C22×C411yescharacteristic
314C4×Dic61C2×D411yescharacteristic
315C4×Dic61C2×D411yescharacteristic
316C4×Dic61C2×D411yescharacteristic
317C4×Dic61C2×D411yescharacteristic
318#11758194—42no—
319C2×#92418—21no—
320C2×#92418—21no—
321C2×#92418—21no—
322C2×#92418—21no—
323C2×#92418—81no—
324#11758189—42no—
325C8×D61—42no—
326C8×D61—81no—
327C8×D61—81no—
328C23×C61—21no—
329C23×C61C2×C22⋊C411yescharacteristic
330C22×D61—21no—
331C22×D61—21no—
332C22×D61—42no—
333C22×D61—81no—
334C22×D61—81no—
335C22×D61C2×C22⋊C411yescharacteristic
336C22×D61C2×C22⋊C411yescharacteristic
337Q8×C61—22no—
338D4×C61—22no—
339D4×C61—81no—
340C2×C4×C61—22no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61C2×C22⋊C411yescharacteristic
350C2×C4×C61C2×C22⋊C411yescharacteristic
351C2×C4×C61C2×C22⋊C411yescharacteristic
352C2×C4×C61C23×C411yescharacteristic
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C22×D411yescharacteristic
355C22⋊D61—22no—
356C22⋊D61—22no—
357C22⋊D61—42no—
358C22⋊D61—81no—
359C22⋊D61—81no—
360C22⋊D61—81no—
361C22⋊D61—81no—
362C22⋊D61—81no—
363C2×Dic61—21no—
364C2×Dic61—21no—
365C2×Dic61—81no—
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—22no—
373D244—22no—
374D244—22no—
375D244—42no—
376D244—81no—
377D244—81no—
378D244—81no—
379D244—81no—
380C4×D61—22no—
381C4×D61—21no—
382C4×D61—21no—
383C4×D61—21no—
384C4×D61—21no—
385C4×D61—41no—
386C4×D61—41no—
387C4×D61—41no—
388C4×D61—41no—
389C4×D61—41no—
390C4×D61—41no—
391C4×D61—42no—
392C4×D61—81no—
393C4×D61—81no—
394C4×D61—81no—
395C4×D61#13114yes—
396Dic122—22no—
397Dic122—81no—
398Dic122—81no—
399C8×C61—41no—
400C8×C61—41no—
401C8×C61—41no—
402C8×C61—41no—
403#92418—22no—
404#92418—41no—
405#92418—41no—
406#92418—41no—
407#17468—611nomaximal, Sylow
408C22×C61—21no—
409C22×C61—21no—
410C22×C61—21no—
411C22×C61—41no—
412C22×C61—41no—
413C22×C61—41no—
414C22×C61C22×C22⋊C411yescharacteristic
415C2×D61—21no—
416C2×D61—21no—
417C2×D61—21no—
418C2×D61—21no—
419C2×D61—21no—
420C2×D61—41no—
421C2×D61—41no—
422C2×D61—41no—
423C2×D61—41no—
424C2×D61—41no—
425C2×D61—41no—
426C2×D61—84no—
427C2×D61#40812yes—
428C4×C61—21no—
429C4×C61—21no—
430C4×C61—21no—
431C4×C61—21no—
432C4×C61—41no—
433C4×C61—41no—
434C4×C61—41no—
435C4×C61C2×#13112yes—
436C4×C61#57611yescharacteristic
437C4×C61#57711yescharacteristic
438Dic61—21no—
439Dic61—21no—
440Dic61—21no—
441Dic61—21no—
442Dic61—21no—
443Dic61—41no—
444Dic61—41no—
445Dic61#40812yes—
446#3460—611no—
447#2988—611no—
448#2965—611no—
449#1484—611no—
450#1484—611no—
451#1483—611no—
452#1483—611no—
453#1482—611no—
454#1482D6111yescharacteristic, complemented
455#1480—611no—
456#1480—611no—
457#1478—611no—
458#1477—611no—
459#1476—611no—
460C2×D4⋊C8—611no—
461C2×C61—41no—
462C2×C61—81no—
463C2×C61C2×#40811yescharacteristic
464C2×C61#289711yescharacteristic
465C2×C61#290111yescharacteristic
466D61—22no—
467D61—41no—
468D61—81no—
469D61—81no—
470#544—611no—
471#542—611no—
472#542—611no—
473#542—1221no—
474#540—611no—
475#540—611no—
476#540—1221no—
477#538—1221no—
478#538—1221no—
479#537—611no—
480#535—611no—
481#535—611no—
482#532—611no—
483#532—611no—
484#532—1221no—
485#529—611no—
486#529—1221no—
487#529C2×D6111yescharacteristic
488#525—1221no—
489#525—1221no—
490C4×#41—611no—
491C4×#41—611no—
492C2×C4×D4—611no—
493#446—1221no—
494C8×Q8—1221no—
495#436—1221no—
496#435—1221no—
497#435—1221no—
498C8×D4—1221no—
499C8×D4—1221no—
500C8×D4—1221no—
501#431—611no—
502#431—611no—
503#431—611no—
504#431—611no—
505#431C2×D6111yescharacteristic, complemented
506#431C2×D6111yescharacteristic, complemented
507C2×C4⋊C8—611no—
508C2×C4⋊C8—611no—
509C2×C4⋊C8—611no—
510C4×M16—611no—
511C4×M16—611no—
512C2×C4×C8—611no—
513Q8⋊C8—611no—
514Q8⋊C8—611no—
515Q8⋊C8C2×D6111yescharacteristic, complemented
516Q8⋊C8C2×D6111yescharacteristic, complemented
517D4⋊C8—611no—
518D4⋊C8—611no—
519D4⋊C8—611no—
520D4⋊C8—611no—
521D4⋊C8—611no—
522D4⋊C8—611no—
523D4⋊C8—611no—
524D4⋊C8—611no—
525D4⋊C8—611no—
526D4⋊C8—611no—
527D4⋊C8C2×D6111yescharacteristic
528D4⋊C8C2×D6111yescharacteristic
529C61#1746811yescharacteristic, complemented, Sylow
530C2×#41—611no—
531C2×#41—611no—
532C2×#41—1221no—
533C2×#41—1221no—
534C22×D4—611no—
535C23×C4—1221no—
536C2×M16—1221no—
537C2×M16—1221no—
538C22×C8—1221no—
539C22×C8—1221no—
540C22×C8—1221no—
541C22×C8—1221no—
542C4⋊Q8—611no—
543C4⋊Q8—611no—
544C4⋊Q8—1221no—
545#127—611no—
546#127—611no—
547#127—1221no—
548#126—21no—
549#126—1221no—
550#126—1221no—
551#126—1221no—
552#125—611no—
553#125—1221no—
554#125C4×D6111yescharacteristic
555#124—611no—
556#124—1221no—
557#124—1221no—
558#124—1221no—
559#124—1221no—
560#124—1221no—
561#124C4×D6111yescharacteristic
562#123—21no—
563#123—1221no—
564#123—1221no—
565#123—1221no—
566#123—1221no—
567#123—1221no—
568#123—1221no—
569#123—1221no—
570C22⋊Q8—611no—
571C22⋊Q8—1221no—
572C22⋊Q8—1221no—
573C22⋊Q8—1221no—
574C22⋊Q8—1221no—
575C22⋊Q8—1221no—
576C22⋊Q8C4×D6111yescharacteristic
577#121—611no—
578#121—611no—
579#121—611no—
580#121—611no—
581#121—611no—
582#121—1221no—
583#121—1221no—
584#121—1221no—
585#121—1221no—
586#121—1221no—
587#121—1221no—
588#121—1221no—
589#121—1221no—
590#121—1221no—
591#121—1221no—
592#121—1221no—
593#121C4×D6111yescharacteristic
594#120—1221no—
595#120—1221no—
596#120—1221no—
597#120—1221no—
598C4×Q8—611no—
599C4×Q8—611no—
600C4×Q8—611no—
601C4×Q8C22×D6111yescharacteristic
602C4×D4—21no—
603C4×D4—611no—
604C4×D4—611no—
605C4×D4—611no—
606C4×D4—611no—
607C4×D4—611no—
608C4×D4—611no—
609C4×D4—611no—
610C4×D4—611no—
611C4×D4—611no—
612C4×D4—611no—
613C4×D4—611no—
614C4×D4—1221no—
615C4×D4—1221no—
616C4×D4—1221no—
617C4×D4—1221no—
618C4×D4—1221no—
619C4×D4—1221no—
620C4×D4—1221no—
621C4×D4C22×D6111yescharacteristic
622#117—21no—
623#117—611no—
624#117—611no—
625#117—611no—
626#117—611no—
627#117—1221no—
628#117—1221no—
629C2×C4⋊C4—611no—
630C2×C22⋊C4—1221no—
631C2×C42—611no—
632C2×C42—611no—
633C2×C42—1221no—
634C2×C42C22×D6111yescharacteristic
635C4⋊C8—21no—
636C4⋊C8—611no—
637C4⋊C8—611no—
638C4⋊C8—1221no—
639C4⋊C8—1221no—
640C4⋊C8—1221no—
641C4⋊C8—1221no—
642C4⋊C8—1221no—
643C4⋊C8C22×D6111yescharacteristic
644C4⋊C8C22×D6111yescharacteristic
645C22⋊C8—21no—
646C22⋊C8—21no—
647C22⋊C8—1221no—
648C22⋊C8—1221no—
649C22⋊C8—1221no—
650C22⋊C8—1221no—
651#97—1221no—
652#97—1221no—
653C4×C8—21no—
654C4×C8—611no—
655C4×C8—611no—
656C4×C8—1221no—
657C4×C8—1221no—
658C4×C8—1221no—
659C4×C8C22×D6111yescharacteristic
660C4×C8C22×D6111yescharacteristic
661C24—1221no—
662#41—1224no—
663#41—1224no—
664#41—4881no—
665#41—4881no—
666#41—4881no—
667#41—4881no—
668C2×Q8—611no—
669C2×Q8—1221no—
670C2×Q8—1221no—
671C2×Q8C2×C4×D6111yescharacteristic
672C2×D4—21no—
673C2×D4—611no—
674C2×D4—611no—
675C2×D4—611no—
676C2×D4—611no—
677C2×D4—611no—
678C2×D4—1221no—
679C2×D4—1221no—
680C2×D4—1221no—
681C2×D4—1224no—
682C2×D4—1221no—
683C2×D4—1221no—
684C2×D4—1221no—
685C2×D4—1221no—
686C2×D4—1221no—
687C2×D4—1221no—
688C2×D4—1221no—
689C2×D4—1221no—
690C2×D4C2×C4×D6111yescharacteristic
691C22×C4—21no—
692C22×C4—611no—
693C22×C4—611no—
694C22×C4—611no—
695C22×C4—611no—
696C22×C4—611no—
697C22×C4—611no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—4881no—
706C22×C4—4881no—
707C22×C4C2×C4×D6111yescharacteristic
708C22×C4D4×D6111yescharacteristic
709C22×C4D4×D6111yescharacteristic
710M16—2442no—
711M16—2442no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—1221no—
717C2×C8—1221no—
718C2×C8—1221no—
719C2×C8—1221no—
720C2×C8—4881no—
721C2×C8—4881no—
722C2×C8—4881no—
723C2×C8—2442no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—611no—
729C4⋊C4—611no—
730C4⋊C4—611no—
731C4⋊C4—611no—
732C4⋊C4—611no—
733C4⋊C4—611no—
734C4⋊C4—611no—
735C4⋊C4—611no—
736C4⋊C4—1221no—
737C4⋊C4—1221no—
738C4⋊C4—1221no—
739C4⋊C4—1221no—
740C4⋊C4—1221no—
741C4⋊C4—1221no—
742C4⋊C4—1221no—
743C4⋊C4C2×C4×D6111yescharacteristic
744C4⋊C4C2×C4×D6111yescharacteristic
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—611no—
751C22⋊C4—611no—
752C22⋊C4—611no—
753C22⋊C4—611no—
754C22⋊C4—611no—
755C22⋊C4—611no—
756C22⋊C4—1221no—
757C22⋊C4—1221no—
758C22⋊C4—1221no—
759C22⋊C4—1221no—
760C22⋊C4—1221no—
761C22⋊C4—1221no—
762C22⋊C4—1221no—
763C22⋊C4—1221no—
764C22⋊C4—1221no—
765C22⋊C4—1221no—
766C22⋊C4—1221no—
767C22⋊C4—1221no—
768C22⋊C4—1221no—
769C22⋊C4—1221no—
770C42—21no—
771C42—611no—
772C42—611no—
773C42—611no—
774C42—611no—
775C42—611no—
776C42—611no—
777C42—1221no—
778C42—1221no—
779C42C2×C4×D6111yescharacteristic
780C42D4×D6111yescharacteristic
781C42D4×D6111yescharacteristic
782C42C23×D6111yescharacteristic
783C23—21no—
784C23—611no—
785C23—611no—
786C23—1221no—
787C23—1221no—
788C23—4881no—
789C23—4881no—
790C23—2442no—
791C23C22⋊C4×D6111yescharacteristic
792Q8—22no—
793Q8—1222no—
794Q8—4881no—
795Q8—4881no—
796D4—22no—
797D4—81no—
798D4—1222no—
799D4—1222no—
800D4—1222no—
801D4—1222no—
802D4—1222no—
803D4—4881no—
804D4—4881no—
805D4—4881no—
806D4—4881no—
807D4—4881no—
808D4—4881no—
809D4—4881no—
810D4—4881no—
811D4—4881no—
812D4—2442no—
813D4—2442no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—611no—
824C2×C4—614no—
825C2×C4—611no—
826C2×C4—611no—
827C2×C4—611no—
828C2×C4—611no—
829C2×C4—611no—
830C2×C4—1222no—
831C2×C4—1221no—
832C2×C4—1221no—
833C2×C4—1221no—
834C2×C4—1221no—
835C2×C4—1221no—
836C2×C4—1221no—
837C2×C4—4881no—
838C2×C4—4881no—
839C2×C4—4881no—
840C2×C4—4881no—
841C2×C4—2441no—
842C2×C4—2441no—
843C2×C4—2442no—
844C2×C4—2441no—
845C2×C4—2441no—
846C2×C4—2441no—
847C2×C4—2441no—
848C2×C4C22⋊C4×D6111yescharacteristic
849C2×C4C22⋊C4×D6111yescharacteristic
850C2×C4C22⋊C4×D6111yescharacteristic
851C2×C4C22×C4×D6111yescharacteristic
852C2×C4C2×D4×D6111yescharacteristic
853C2×C4C2×D4×D6111yescharacteristic
854C8—41no—
855C8—41no—
856C8—41no—
857C8—41no—
858C8—1222no—
859C8—2441no—
860C8—2441no—
861C8—2441no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—612no—
869C22—1221no—
870C22—1221no—
871C22—1221no—
872C22—1221no—
873C22—1221no—
874C22—4884no—
875C22—2441no—
876C22—2441no—
877C22—2441no—
878C22—2441no—
879C22—2441no—
880C22—2441no—
881C22C2×C22⋊C4×D6111yescharacteristic
882C4—21no—
883C4—21no—
884C4—21no—
885C4—21no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—612no—
890C4—1221no—
891C4—1221no—
892C4—1221no—
893C4—1221no—
894C4—1221no—
895C4—2441no—
896C4—2441no—
897C4#131×D6112yes—
898C4#1684056411yescharacteristic
899C4#1684056911yescharacteristic
900C2—41no—
901C2—81no—
902C2—1222no—
903C2—4881no—
904C2—4881no—
905C2—2441no—
906C2#408×D6111yescharacteristic
907C2#2145434111yescharacteristic
908C2#2145436511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1482C2
socleC22×C61C22×C22⋊C4
prime radical#21459240C2
cosocleC42×C61C24
hypercenter#1482D61
hypocenterC61#17468
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1482

Complements

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

NH ≅ G/Ntype
2. #21454927C2semidirect
3. #21454783C2semidirect
4. #21444235C2semidirect
5. #21444234C2semidirect
6. #21444232C2semidirect
7. #21444231C2semidirect
8. #21444226C2semidirect
9. #21444219C2semidirect
10. #21444216C2semidirect
11. #21444208C2semidirect
12. #21444205C2semidirect
13. #21444200C2semidirect
14. D4⋊C8×D61C2semidirect
15. C61×#1482C2semidirect
47. #16839814C22semidirect
49. #16839813C22semidirect
50. C2×C4⋊#92418C22semidirect
52. C4⋊C8×D61C22semidirect
53. C4×#11758194C22semidirect
54. C4×#11758189C22semidirect
56. Q8⋊#92418C22semidirect
57. Q8⋊#92418C22semidirect
60. #16839491C22semidirect
61. #16839491C22semidirect
66. #16839489C22semidirect
67. #16839489C22semidirect
69. C61×#431C22semidirect
70. C61×#431C22semidirect
71. C61×Q8⋊C8C22semidirect
72. C61×Q8⋊C8C22semidirect
454. #1482D61semidirect
505. #431C2×D61semidirect
506. #431C2×D61semidirect
515. Q8⋊C8C2×D61semidirect
516. Q8⋊C8C2×D61semidirect
529. C61#17468semidirect

Maximal subgroups

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

subgroupindex
#214592402
#214549272
#214547832
#214442352
#214442342
#214442322
#214442312
#214442262
#214442192
#214442162
#214442082
#214442052
#214442002
D4⋊C8×D612
C61×#14822
#1746861