Finite Group Databasebeta

← #30610484

Subgroups — #30610484

Order 15616.

1138 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462741C211yesmaximal, characteristic, complemented
2#21462630C211yesmaximal, characteristic, complemented
3#21461162C211yesmaximal, characteristic, complemented
4#21461161C211yesmaximal, characteristic, complemented
5#21461157C211yesmaximal, characteristic, complemented
6#21461156C211yesmaximal, characteristic, complemented
7#21461153C211yesmaximal, characteristic, complemented
8#21461152C211yesmaximal, characteristic, complemented
9#21461148C211yesmaximal, characteristic, complemented
10#21461147C211yesmaximal, characteristic, complemented
11#21461122C211yesmaximal, characteristic, complemented
12#21461117C211yesmaximal, characteristic, complemented
13#21461113C211yesmaximal, characteristic, complemented
14D61⋊(Q8⋊C8)C211yesmaximal, characteristic, complemented
15#21459028C211yesmaximal, characteristic
16#16840814—21no—
17#16840814—21no—
18#16840795—21no—
19#16840795—21no—
20#16840794—21no—
21#16840794—21no—
22#16840792—21no—
23#16840792—21no—
24#16840784C2211yescharacteristic
25#16840783C2211yescharacteristic
26#16840781C2211yescharacteristic
27#16840781C2211yescharacteristic
28#16840780C2211yescharacteristic
29#16840779C2211yescharacteristic
30#16840766C2211yescharacteristic
31#16840765C2211yescharacteristic
32D61⋊(C4⋊C8)C2211yescharacteristic
33C4×#11758213C2211yescharacteristic
34C4×#11758217C2211yescharacteristic
35C4×D61⋊C8C2211yescharacteristic
36#16840612C2211yescharacteristic
37#16840612C2211yescharacteristic
38#16840612C2211yescharacteristic
39#16840612C2211yescharacteristic
40Q8⋊#92420C2211yescharacteristic
41Q8⋊#92420C2211yescharacteristic
42Q8⋊#92420C2211yescharacteristic
43Q8⋊#92420C2211yescharacteristic
44Q8⋊#92420C2211yescharacteristic
45Q8⋊#92420C2211yescharacteristic
46Q8⋊#92420C2211yescharacteristic
47Q8⋊#92420C2211yescharacteristic
48#16840610C2211yescharacteristic
49#16840610C2211yescharacteristic
50#16840610C2211yescharacteristic
51#16840610C2211yescharacteristic
52C2×#14519825C411yescharacteristic
53#16840244—21no—
54#16840244C411yescharacteristic
55#16840244C411yescharacteristic
56#16840242—21no—
57#16840242—21no—
58#16840242C411yescharacteristic
59#16840242C411yescharacteristic
60#16840238—21no—
61#16840238C411yescharacteristic
62#16840238C411yescharacteristic
63C4×#11758226—21no—
64C4×#11758226C2211yescharacteristic
65C4×#11758226C2211yescharacteristic
66#16840230—21no—
67#16840230—21no—
68#16840230C2211yescharacteristic
69#16840230C2211yescharacteristic
70C2×Q8×Dic61C2211yescharacteristic
71C4×Q8×D61—21no—
72C4×Q8×D61C2211yescharacteristic
73C4×Q8×D61C2211yescharacteristic
74C61×#519C411yescharacteristic
75C2×#11758213—21no—
76C2×#11758213—21no—
77C2×#11758217—21no—
78C2×#11758217—21no—
79C2×D61⋊C8—21no—
80C2×D61⋊C8—21no—
81#14519844—21no—
82#14519844—21no—
83#14519844—21no—
84#14519844—21no—
85C4⋊#92420—21no—
86C4⋊#92420—21no—
87C4⋊#92420C2311yescharacteristic
88C4⋊#92420C2311yescharacteristic
89C4⋊#92420C2311yescharacteristic
90C4⋊#92420C2311yescharacteristic
91#14519834—21no—
92#14519834—21no—
93#14519834—21no—
94#14519834—21no—
95C22⋊#92420—21no—
96C22⋊#92420—21no—
97#14519832—21no—
98#14519832—21no—
99#14519832—21no—
100#14519832—21no—
101C4×#92420—21no—
102C4×#92420—21no—
103C4×#92420C2311yescharacteristic
104C4×#92420C2311yescharacteristic
105C4×#92420C2311yescharacteristic
106C4×#92420C2311yescharacteristic
107#14519825—24no—
108#14519825—24no—
109C2×#11758226—21no—
110C2×#11758226C2×C411yescharacteristic
111C2×#11758226C2×C411yescharacteristic
112C2×#11758222—21no—
113C2×#11758222—21no—
114C2×#11758222C2×C411yescharacteristic
115C2×#11758222C2×C411yescharacteristic
116C2×Q8×D61—21no—
117C2×Q8×D61C2×C411yescharacteristic
118C2×Q8×D61C2×C411yescharacteristic
119Q8×Dic61—21no—
120Q8×Dic61—21no—
121Q8×Dic61C2×C411yescharacteristic
122Q8×Dic61C2×C411yescharacteristic
123Q8×Dic61C2311yescharacteristic
124Q8×Dic61C2311yescharacteristic
125C4×Dic122—21no—
126C4×Dic122—21no—
127C4×Dic122—21no—
128C4×Dic122—21no—
129C4×Dic122—21no—
130C4×Dic122C2×C411yescharacteristic
131C4×Dic122C2×C411yescharacteristic
132#14519742—21no—
133#14519742—21no—
134#14519742—21no—
135#14519742—21no—
136#14519742C2×C411yescharacteristic
137#14519742D411yescharacteristic
138#14519742D411yescharacteristic
139#14519742C2311yescharacteristic
140C4×D244—21no—
141C4×D244—21no—
142C4×D244—21no—
143C4×D244—21no—
144C4×D244—21no—
145C4×D244C2×C411yescharacteristic
146C4×D244C2×C411yescharacteristic
147#14519739—21no—
148#14519739—21no—
149#14519739—21no—
150#14519739—21no—
151#14519739C2×C411yescharacteristic
152#14519739D411yescharacteristic
153#14519739D411yescharacteristic
154#14519739C2311yescharacteristic
155#14519737—21no—
156#14519737—21no—
157#14519737—21no—
158#14519737—21no—
159#14519737—21no—
160#14519737—21no—
161#14519737D411yescharacteristic
162#14519737D411yescharacteristic
163#14519737D411yescharacteristic
164#14519737D411yescharacteristic
165#14519735—21no—
166#14519735—21no—
167#14519735—21no—
168#14519735—21no—
169#14519735—21no—
170#14519735C2×C411yescharacteristic
171#14519735C2×C411yescharacteristic
172#14519734—21no—
173#14519734—21no—
174#14519734—21no—
175#14519734—21no—
176#14519734—21no—
177#14519734C2×C411yescharacteristic
178#14519734C2×C411yescharacteristic
179C2×C4⋊Dic61—21no—
180C2×C4⋊Dic61C2×C411yescharacteristic
181C4⋊C4×D61—21no—
182C4⋊C4×D61—21no—
183C4⋊C4×D61—21no—
184C4⋊C4×D61—21no—
185C4⋊C4×D61—21no—
186C4⋊C4×D61C2×C411yescharacteristic
187C4⋊C4×D61C2×C411yescharacteristic
188C2×C4×Dic61—21no—
189C2×C4×Dic61C2311yescharacteristic
190C42×D61—21no—
191C42×D61—21no—
192C42×D61—21no—
193C42×D61—21no—
194C42×D61—21no—
195C42×D61C2311yescharacteristic
196C42×D61C2311yescharacteristic
197C22×Q8×C61C2×C411yescharacteristic
198C4×Q8×C61—21no—
199C4×Q8×C61—21no—
200C4×Q8×C61C2×C411yescharacteristic
201C4×Q8×C61C2×C411yescharacteristic
202C4×Q8×C61C2×C411yescharacteristic
203C4×Q8×C61C2×C411yescharacteristic
204#117×C61—21no—
205#117×C61—21no—
206#117×C61C2×C411yescharacteristic
207#117×C61C2×C411yescharacteristic
208C2×Q8×C61—22no—
209C2×Q8×C61—22no—
210C2×Q8×C61—21no—
211C2×Q8×C61C22×C411yescharacteristic
212C2×Q8×C61C22×C411yescharacteristic
213C22×C4×C61—21no—
214C22×C4×C61C22×C411yescharacteristic
215C2×C22⋊D61—21no—
216C2×C22⋊D61C22⋊C411yescharacteristic
217C2×C22⋊D61C22⋊C411yescharacteristic
218C22×Dic61—21no—
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221#11758226—28no—
222#11758226—22no—
223#11758226—22no—
224#11758226—22no—
225#11758226M1614yescomplemented
226Q8×D61—28no—
227Q8×D61—22no—
228Q8×D61—22no—
229Q8×D61—22no—
230Q8×D61M1614yescomplemented
231#11758222—28no—
232#11758222—28no—
233#11758222—22no—
234#11758222—22no—
235#11758222—22no—
236#11758222—22no—
237C2×D244—21no—
238C2×D244—21no—
239C2×D244C22⋊C411yescharacteristic
240C2×D244C22×C411yescharacteristic
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61C22×C411yescharacteristic
253C2×C4×D61C22×C411yescharacteristic
254C2×C4×D61C2×D411yescharacteristic
255C2×C4×D61C2×D411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×Dic122—21no—
259C2×Dic122—21no—
260C2×Dic122C22⋊C411yescharacteristic
261C2×Dic122C22×C411yescharacteristic
262#11758217—42no—
263#11758217—81no—
264C2×#92420—21no—
265C2×#92420—21no—
266C2×#92420—21no—
267C2×#92420—21no—
268C2×#92420—21no—
269C2×#92420—21no—
270C2×#92420—21no—
271C2×#92420—21no—
272#11758213—42no—
273#11758213—81no—
274D61⋊C8—42no—
275D61⋊C8—81no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61C22⋊C411yescharacteristic
281C4⋊C4×C61C22⋊C411yescharacteristic
282C4⋊C4×C61C22×C411yescharacteristic
283C4⋊C4×C61C22×C411yescharacteristic
284C22⋊C4×C61—21no—
285C22⋊C4×C61C22⋊C411yescharacteristic
286C22⋊C4×C61C22⋊C411yescharacteristic
287C42×C61—21no—
288C42×C61—21no—
289C42×C61—21no—
290C42×C61—21no—
291C42×C61—21no—
292C42×C61C22×C411yescharacteristic
293C42×C61C22×C411yescharacteristic
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198C22⋊C411yescharacteristic
301#11758198C22⋊C411yescharacteristic
302#11758198C22⋊C411yescharacteristic
303#11758198C22⋊C411yescharacteristic
304C4⋊Dic61—21no—
305C4⋊Dic61—21no—
306C4⋊Dic61—21no—
307C4⋊Dic61—21no—
308C4⋊Dic61—21no—
309C4⋊Dic61C22×C411yescharacteristic
310C4⋊Dic61C22×C411yescharacteristic
311#11758196—21no—
312#11758196—21no—
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317#11758196C22⋊C411yescharacteristic
318#11758196C22⋊C411yescharacteristic
319#11758196C22⋊C411yescharacteristic
320#11758196C22⋊C411yescharacteristic
321C4×Dic61—21no—
322C4×Dic61—21no—
323C4×Dic61—21no—
324C4×Dic61—21no—
325C4×Dic61—21no—
326C4×Dic61—21no—
327C4×Dic61—21no—
328C4×Dic61—21no—
329C4×Dic61—21no—
330C4×Dic61—21no—
331C4×Dic61C22×C411yescharacteristic
332C4×Dic61C2×D411yescharacteristic
333C4×Dic61C2×D411yescharacteristic
334C4×Dic61C2×D411yescharacteristic
335C4×Dic61C2×D411yescharacteristic
336C4×Dic61C2×D411yescharacteristic
337C4×Dic61C2×D411yescharacteristic
338C4×Dic61C2411yescharacteristic
339C23×C61C2×C22⋊C411yescharacteristic
340C22×D61—21no—
341C22×D61C2×C22⋊C411yescharacteristic
342C22×D61C2×C22⋊C411yescharacteristic
343Q8×C61—24no—
344Q8×C61—21no—
345Q8×C61—21no—
346Q8×C61C2×M1612yes—
347Q8×C61C2×M1612yes—
348C2×C4×C61—24no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—21no—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61C2×C22⋊C411yescharacteristic
356C2×C4×C61C2×C22⋊C411yescharacteristic
357C2×C4×C61C2×C22⋊C411yescharacteristic
358C2×C4×C61C2×C22⋊C411yescharacteristic
359C2×C4×C61C2×C22⋊C411yescharacteristic
360C2×C4×C61C23×C411yescharacteristic
361C22⋊D61—24no—
362C22⋊D61—22no—
363C22⋊D61—22no—
364C2×Dic61—21no—
365C2×Dic61—21no—
366C2×Dic61—21no—
367C2×Dic61—21no—
368C2×Dic61—21no—
369C2×Dic61—41no—
370C2×Dic61—81no—
371C2×Dic61C2×C22⋊C411yescharacteristic
372C2×Dic61C2×C22⋊C411yescharacteristic
373C2×Dic61C2×C22⋊C411yescharacteristic
374C2×Dic61C2×C22⋊C411yescharacteristic
375C2×Dic61C22×D411yescharacteristic
376C2×Dic61C22×D411yescharacteristic
377D244—24no—
378D244—24no—
379D244—22no—
380D244—21no—
381D244C2×M1612yes—
382C4×D61—24no—
383C4×D61—24no—
384C4×D61—24no—
385C4×D61—24no—
386C4×D61—21no—
387C4×D61—21no—
388C4×D61—21no—
389C4×D61—21no—
390C4×D61—21no—
391C4×D61—21no—
392C4×D61—24no—
393C4×D61—41no—
394C4×D61—41no—
395C4×D61—41no—
396C4×D61—41no—
397C4×D61—81no—
398C4×D61—81no—
399C4×D61—81no—
400C4×D61—81no—
401C4×D61—81no—
402C4×D61C2×M1612yes—
403C4×D61C2×M1612yes—
404Dic122—24no—
405Dic122—21no—
406Dic122—24no—
407Dic122—22no—
408Dic122C2×M1612yes—
409#92420—22no—
410#92420—41no—
411#92420—41no—
412#92420—41no—
413#92420—41no—
414#92420—41no—
415#92420—41no—
416#92420—41no—
417#17454—611nomaximal, Sylow
418C22×C61—21no—
419C22×C61—21no—
420C22×C61—21no—
421C22×C61C22×C22⋊C411yescharacteristic
422C2×D61—21no—
423C2×D61—21no—
424C2×D61—21no—
425C2×D61—22no—
426C2×D61—21no—
427C2×D61—21no—
428C2×D61—41no—
429C2×D61—41no—
430C2×D61#40712yes—
431C4×C61—22no—
432C4×C61—22no—
433C4×C61—21no—
434C4×C61—21no—
435C4×C61—21no—
436C4×C61—21no—
437C4×C61—21no—
438C4×C61—41no—
439C4×C61—41no—
440C4×C61C22×M1611yescharacteristic
441C4×C61C22×M1611yescharacteristic
442Dic61—21no—
443Dic61—22no—
444Dic61—21no—
445Dic61—21no—
446Dic61—21no—
447Dic61—41no—
448Dic61—41no—
449Dic61#40712yes—
450Dic61#57711yescharacteristic
451Dic61#57811yescharacteristic
452C4×2−1+4—611no—
453#2989—611no—
454#2965—611no—
455#1491—611no—
456#1491—611no—
457#1489—611no—
458#1489—611no—
459#1488—611no—
460#1488—611no—
461#1487—611no—
462#1487—611no—
463#1479—611no—
464#1477—611no—
465#1476—611no—
466C2×Q8⋊C8—611no—
467C2×C61—41no—
468C2×C61C2×#40711yescharacteristic
469C2×C61#289811yescharacteristic
470C2×C61#290111yescharacteristic
471D61—22no—
472D61—41no—
473D61—42no—
474C2×2−1+4—611no—
475#520—611no—
476#520—611no—
477#520—611no—
478#520—611no—
479#520—1221no—
480#520—1221no—
481#520—1221no—
482#519—611no—
483#519—611no—
484#519—1221no—
485#519#692311yescharacteristic
486C4×#41—611no—
487C4×#41—611no—
488C4×#41—611no—
489C4×#41—611no—
490C4×#41—1221no—
491C4×#41—1221no—
492C4×#41—1221no—
493C2×C4×Q8—611no—
494C2×C4×Q8—611no—
495C2×C4×Q8—611no—
496C2×C4×Q8—1221no—
497#446—1221no—
498#446—1221no—
499#436—1221no—
500#436—1221no—
501#435—1221no—
502#435—1221no—
503#435—1221no—
504#435—1221no—
505#432—611no—
506#432—611no—
507#431—611no—
508#431—611no—
509#431—611no—
510#431—611no—
511#423—611no—
512#423—611no—
513C2×C4⋊C8—611no—
514C4×M16—611no—
515C4×M16—611no—
516C2×C4×C8—611no—
517Q8⋊C8—611no—
518Q8⋊C8—611no—
519Q8⋊C8—611no—
520Q8⋊C8—611no—
521Q8⋊C8—611no—
522Q8⋊C8—611no—
523Q8⋊C8—611no—
524Q8⋊C8—611no—
525Q8⋊C8—611no—
526Q8⋊C8—611no—
527Q8⋊C8—611no—
528Q8⋊C8—611no—
529D4⋊C8—611no—
530D4⋊C8—611no—
531D4⋊C8—611no—
532D4⋊C8—611no—
533C61#1745411yescharacteristic, complemented, Sylow
5342−1+4—1224no—
5352−1+4—1224no—
536C2×#41—611no—
537C2×#41—611no—
538C2×#41—611no—
539C2×#41—611no—
540C2×#41—1221no—
541C2×#41—1221no—
542C2×#41—1221no—
543C22×Q8—611no—
544C22×Q8—611no—
545C22×Q8—1221no—
546C22×Q8C2×#692311yescharacteristic
547C2×M16—1221no—
548C2×M16—1221no—
549C2×M16—1221no—
550C2×M16—1221no—
551C22×C8—1221no—
552C22×C8—1221no—
553C4×Q8—21no—
554C4×Q8—21no—
555C4×Q8—611no—
556C4×Q8—611no—
557C4×Q8—611no—
558C4×Q8—611no—
559C4×Q8—611no—
560C4×Q8—611no—
561C4×Q8—611no—
562C4×Q8—611no—
563C4×Q8—611no—
564C4×Q8—611no—
565C4×Q8—1221no—
566C4×Q8—1221no—
567C4×Q8—1221no—
568C4×Q8—1221no—
569C4×Q8—1221no—
570C4×Q8—1221no—
571C4×Q8—1221no—
572C4×Q8—1221no—
573C4×Q8—1221no—
574C4×Q8—1221no—
575C4×Q8—1221no—
576C4×Q8C2×#692311yescharacteristic
577C4×Q8C2×#692311yescharacteristic
578C4×Q8C2×#692311yescharacteristic
579C4×Q8C2×#692311yescharacteristic
580C4×D4—611no—
581C4×D4—611no—
582C4×D4—611no—
583C4×D4—611no—
584C4×D4—611no—
585C4×D4—611no—
586C4×D4—611no—
587C4×D4—611no—
588C4×D4—611no—
589C4×D4—611no—
590C4×D4—1221no—
591C4×D4—1221no—
592C4×D4—1221no—
593C4×D4—1221no—
594C4×D4—1221no—
595C4×D4—1221no—
596C4×D4—1221no—
597C4×D4—1221no—
598C4×D4—1221no—
599C4×D4—1221no—
600C4×D4—1221no—
601C4×D4—1221no—
602C4×D4—1221no—
603C4×D4—1221no—
604C4×D4—1221no—
605#117—21no—
606#117—21no—
607#117—611no—
608#117—611no—
609#117—611no—
610#117—611no—
611#117—1221no—
612#117—1221no—
613#117—1221no—
614#117—1221no—
615#117—1221no—
616#117—1221no—
617#117—1221no—
618#117—1221no—
619#117—1221no—
620#117—1221no—
621#117C2×#692311yescharacteristic
622#117C2×#692311yescharacteristic
623C2×C4⋊C4—611no—
624C2×C4⋊C4—611no—
625C2×C4⋊C4—611no—
626C2×C4⋊C4—1221no—
627C2×C4⋊C4—1221no—
628C2×C4⋊C4—1221no—
629C2×C4⋊C4—1221no—
630C2×C4⋊C4—1221no—
631C2×C4⋊C4—1221no—
632C2×C42—611no—
633C2×C42—611no—
634C2×C42—611no—
635C2×C42—1221no—
636C2×C42—1221no—
637C2×C42—1221no—
638C2×C42—1221no—
639C2×C42—1221no—
640C2×C42—1221no—
641C4⋊C8—611no—
642C4⋊C8—611no—
643C4⋊C8—611no—
644C4⋊C8—611no—
645C4⋊C8—1221no—
646C4⋊C8—1221no—
647C4⋊C8—1221no—
648C4⋊C8—1221no—
649C4⋊C8—1221no—
650C4⋊C8—1221no—
651C22⋊C8—1221no—
652C22⋊C8—1221no—
653C22⋊C8—1221no—
654C22⋊C8—1221no—
655C22⋊C8—1221no—
656C22⋊C8—1221no—
657#97—1221no—
658#97—1221no—
659#97—1221no—
660#97—1221no—
661C4×C8—611no—
662C4×C8—611no—
663C4×C8—611no—
664C4×C8—611no—
665C4×C8—1221no—
666C4×C8—1221no—
667#41—614no—
668#41—1222no—
669#41—1222no—
670#41—1222no—
671#41—1222no—
672#41—1228no—
673#41—1228no—
674#41—1222no—
675#41—1222no—
676#41—1228no—
677#41—1222no—
678C2×Q8—22no—
679C2×Q8—22no—
680C2×Q8—21no—
681C2×Q8—611no—
682C2×Q8—614no—
683C2×Q8—611no—
684C2×Q8—1221no—
685C2×Q8—1221no—
686C2×Q8—1222no—
687C2×Q8—1222no—
688C2×Q8—1228no—
689C2×Q8—1222no—
690C2×Q8C22×#692311yescharacteristic
691C2×Q8C22×#692311yescharacteristic
692C2×D4—611no—
693C2×D4—611no—
694C2×D4—611no—
695C2×D4—611no—
696C2×D4—1221no—
697C2×D4—1221no—
698C2×D4—1221no—
699C22×C4—21no—
700C22×C4—611no—
701C22×C4—611no—
702C22×C4—611no—
703C22×C4—611no—
704C22×C4—611no—
705C22×C4—611no—
706C22×C4—611no—
707C22×C4—611no—
708C22×C4—1221no—
709C22×C4—1221no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4C22×#692311yescharacteristic
721M16—4881no—
722M16—4881no—
723M16—2442no—
724M16—2442no—
725C2×C8—1221no—
726C2×C8—1221no—
727C2×C8—1221no—
728C2×C8—1221no—
729C2×C8—1221no—
730C2×C8—1221no—
731C2×C8—1221no—
732C2×C8—1221no—
733C2×C8—4881no—
734C2×C8—2442no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—611no—
740C4⋊C4—611no—
741C4⋊C4—611no—
742C4⋊C4—611no—
743C4⋊C4—611no—
744C4⋊C4—611no—
745C4⋊C4—1221no—
746C4⋊C4—1221no—
747C4⋊C4—1221no—
748C4⋊C4—1221no—
749C4⋊C4—1221no—
750C4⋊C4—1221no—
751C4⋊C4—1221no—
752C4⋊C4—1221no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4C22⋊#692311yescharacteristic
757C4⋊C4C22⋊#692311yescharacteristic
758C4⋊C4C22×#692311yescharacteristic
759C4⋊C4C22×#692311yescharacteristic
760C22⋊C4—21no—
761C22⋊C4—611no—
762C22⋊C4—611no—
763C22⋊C4—611no—
764C22⋊C4—611no—
765C22⋊C4—1221no—
766C22⋊C4—1221no—
767C22⋊C4—1221no—
768C22⋊C4—1221no—
769C22⋊C4—1221no—
770C22⋊C4—1221no—
771C22⋊C4C22⋊#692311yescharacteristic
772C22⋊C4C22⋊#692311yescharacteristic
773C42—21no—
774C42—21no—
775C42—21no—
776C42—21no—
777C42—21no—
778C42—611no—
779C42—611no—
780C42—611no—
781C42—611no—
782C42—611no—
783C42—611no—
784C42—611no—
785C42—611no—
786C42—1221no—
787C42—1221no—
788C42—1221no—
789C42—1221no—
790C42—1221no—
791C42—1221no—
792C42—1221no—
793C42—1221no—
794C42—1221no—
795C42—1221no—
796C42C22×#692311yescharacteristic
797C42C22×#692311yescharacteristic
798C23—611no—
799C23—611no—
800C23—1221no—
801C23C2×C22⋊#692311yescharacteristic
802Q8—24no—
803Q8—21no—
804Q8—21no—
805Q8—612no—
806Q8—1224no—
807Q8—1222no—
808Q8—1224no—
809Q8—1221no—
810Q8D61⋊M1612yes—
811Q8D61⋊M1612yes—
812D4—612no—
813D4—1222no—
814D4—1224no—
815D4—1224no—
816D4—1222no—
817D4—1222no—
818D4—1224no—
819D4—1221no—
820C2×C4—24no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—611no—
828C2×C4—611no—
829C2×C4—612no—
830C2×C4—612no—
831C2×C4—611no—
832C2×C4—611no—
833C2×C4—611no—
834C2×C4—611no—
835C2×C4—1221no—
836C2×C4—1221no—
837C2×C4—1221no—
838C2×C4—1221no—
839C2×C4—1224no—
840C2×C4—1224no—
841C2×C4—1224no—
842C2×C4—1224no—
843C2×C4—1224no—
844C2×C4—1221no—
845C2×C4—1221no—
846C2×C4—1221no—
847C2×C4—1221no—
848C2×C4—1221no—
849C2×C4—1221no—
850C2×C4—1221no—
851C2×C4—4881no—
852C2×C4—4881no—
853C2×C4—4881no—
854C2×C4—4881no—
855C2×C4—4881no—
856C2×C4—4881no—
857C2×C4—2441no—
858C2×C4—2441no—
859C2×C4—2441no—
860C2×C4—2441no—
861C2×C4—2441no—
862C2×C4C2×C22⋊#692311yescharacteristic
863C2×C4C2×C22⋊#692311yescharacteristic
864C2×C4C2×C22⋊#692311yescharacteristic
865C2×C4C2×C22⋊#692311yescharacteristic
866C2×C4C2×C22⋊#692311yescharacteristic
867C2×C4C23×#692311yescharacteristic
868C8—1222no—
869C8—2441no—
870C8—2441no—
871C8—2441no—
872C8—2441no—
873C8—2441no—
874C8—2441no—
875C8—2441no—
876C22—21no—
877C22—21no—
878C22—21no—
879C22—612no—
880C22—1221no—
881C22—1221no—
882C22—1222no—
883C22—1221no—
884C22—1221no—
885C22—1221no—
886C22—2441no—
887C22—2441no—
888C22C22×C22⋊#692311yescharacteristic
889C4—22no—
890C4—22no—
891C4—21no—
892C4—21no—
893C4—21no—
894C4—21no—
895C4—21no—
896C4—41no—
897C4—41no—
898C4—612no—
899C4—611no—
900C4—611no—
901C4—1221no—
902C4—1222no—
903C4—1221no—
904C4—1221no—
905C4—1221no—
906C4—2441no—
907C4—2441no—
908C4C2×D61⋊M1611yescharacteristic
909C4C2×D61⋊M1611yescharacteristic
910C2—41no—
911C2—1222no—
912C2—2441no—
913C2—2442no—
914C2D61⋊#40711yescharacteristic
915C2#2146244111yescharacteristic
916C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#519C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519825C4
cosocleC4×Dic61C24
hypercenter#519#6923
hypocenterC61#17454
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
1. #21462741C2semidirect
2. #21462630C2semidirect
3. #21461162C2semidirect
4. #21461161C2semidirect
5. #21461157C2semidirect
6. #21461156C2semidirect
7. #21461153C2semidirect
8. #21461152C2semidirect
9. #21461148C2semidirect
10. #21461147C2semidirect
11. #21461122C2semidirect
12. #21461117C2semidirect
13. #21461113C2semidirect
14. D61⋊(Q8⋊C8)C2semidirect
225. #11758226M16semidirect
230. Q8×D61M16semidirect
533. C61#17454semidirect

Maximal subgroups

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

subgroupindex
#214627412
#214626302
#214611622
#214611612
#214611572
#214611562
#214611532
#214611522
#214611482
#214611472
#214611222
#214611172
#214611132
D61⋊(Q8⋊C8)2
#214590282
#1745461