Finite Group Databasebeta

← #30615219

Subgroups — #30615219

Order 15616.

1338 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#432C211yesmaximal, characteristic, complemented
2#21462266C211yesmaximal, characteristic, complemented
3#21461724C212yesmaximal, complemented
4#21461690C212yesmaximal, complemented
5#21461689C212yesmaximal, complemented
6#21461659C212yesmaximal
7#21461591C212yesmaximal, complemented
8#21461589C212yesmaximal, complemented
9C4×#41×D61C211yesmaximal, characteristic
10#16840785—21no—
11#16840784—21no—
12#16840783—21no—
13#16840782—21no—
14D61⋊(C4⋊C8)C2212yes—
15C2×#14519840C2214yes—
16C2×#14519839C2214yes—
17D61⋊(C22⋊C8)C2212yes—
18#16840721C2212yes—
19#16840707—21no—
20#16840706C2212yes—
21#16840705—21no—
22#16840704C2212yes—
23C4×C4⋊#6923C2212yes—
24C4×C22⋊#6923—21no—
25#16840698—21no—
26#16840635C2214yes—
27#16840635C2214yes—
28C2×#41×D61C2211yescharacteristic
29#41×Dic61C411yescharacteristic, complemented
30C4×#11758226C411yescharacteristic, complemented
31C4×#11758226C411yescharacteristic, complemented
32C4×#11758222—21no—
33C4×#11758222C411yescharacteristic, complemented
34#16840230—21no—
35#16840230C411yescharacteristic, complemented
36C4×#11758224—21no—
37C4×#11758224—21no—
38C4×#11758224C411yescharacteristic, complemented
39C4×#11758224C411yescharacteristic, complemented
40C4×Q8×D61C2211yescharacteristic
41C4×Q8×D61C2211yescharacteristic
42C4×D4×D61—21no—
43C4×D4×D61—21no—
44C4×D4×D61C2211yescharacteristic
45C4×D4×D61C2211yescharacteristic
46#117×D61—21no—
47#117×D61C2211yescharacteristic
48C2×C42×D61—21no—
49C2×C42×D61C2211yescharacteristic
50C4×#41×C61C411yescharacteristic, complemented
51C2×D61⋊C8C2314yes—
52C2×C4⋊#6923C2314yes—
53C2×C22⋊#6923—22no—
54C2×C4×#6923—22no—
55#14519844—22no—
56C4⋊#92420—22no—
57#14519840—28no—
58#14519839—28no—
59#14519834—22no—
60C22⋊#92420—22no—
61#14519832—22no—
62#14519832—22no—
63(C2×#6923)⋊C4—22no—
64(C2×#6923)⋊C4—22no—
65(C2×#6923)⋊C4—22no—
66(C2×#6923)⋊C4—22no—
67C2×#11758226C2×C411yescharacteristic
68C2×#11758222—21no—
69C2×#11758222C2×C411yescharacteristic
70C2×#11758224—21no—
71C2×#11758224C2×C411yescharacteristic
72#41×D61—24no—
73#41×D61—24no—
74C2×Q8×D61C2311yescharacteristic
75C2×D4×D61—21no—
76C2×D4×D61C2311yescharacteristic
77C22×C4×D61—21no—
78C22×C4×D61—21no—
79C22×C4×D61—21no—
80C22×C4×D61D411yescharacteristic
81C22×C4×D61D411yescharacteristic
82C22×C4×D61C2311yescharacteristic
83Q8×Dic61C2×C411yescharacteristic
84Q8×Dic61C2×C411yescharacteristic
85C4×Dic122—21no—
86C4×Dic122—21no—
87C4×Dic122C2×C411yescharacteristic
88C4×Dic122C2×C411yescharacteristic
89#14519742—21no—
90#14519742—21no—
91#14519742C2×C411yescharacteristic
92#14519742C2×C411yescharacteristic
93C4×D244—21no—
94C4×D244—21no—
95C4×D244C2×C411yescharacteristic
96C4×D244C2×C411yescharacteristic
97D4×Dic61—21no—
98D4×Dic61—21no—
99D4×Dic61C2×C411yescharacteristic
100D4×Dic61C2×C411yescharacteristic
101#14519739—21no—
102#14519739—21no—
103#14519739C2×C411yescharacteristic
104#14519739C2×C411yescharacteristic
105C4×C22⋊D61—21no—
106C4×C22⋊D61—21no—
107C4×C22⋊D61—21no—
108C4×C22⋊D61—21no—
109C4×C22⋊D61—21no—
110C4×C22⋊D61—21no—
111#14519737—21no—
112#14519737—21no—
113#14519737—21no—
114#14519737—21no—
115#14519737—21no—
116#14519737—21no—
117#14519736—21no—
118#14519736C2×C411yescharacteristic
119#14519735—21no—
120#14519735—21no—
121#14519735C2×C411yescharacteristic
122#14519735C2×C411yescharacteristic
123#14519734—21no—
124#14519734—21no—
125#14519734—21no—
126#14519733—21no—
127#14519733—21no—
128#14519733—21no—
129C4⋊C4×D61—21no—
130C4⋊C4×D61—21no—
131C4⋊C4×D61C2311yescharacteristic
132C4⋊C4×D61C2311yescharacteristic
133C22⋊C4×D61—21no—
134C22⋊C4×D61—21no—
135C22⋊C4×D61—21no—
136C2×C4×Dic61—21no—
137C2×C4×Dic61—21no—
138C2×C4×Dic61—21no—
139C2×C4×Dic61C2×C411yescharacteristic
140C2×C4×Dic61D411yescharacteristic
141C2×C4×Dic61D411yescharacteristic
142C42×D61—21no—
143C42×D61—21no—
144C42×D61—21no—
145C42×D61—21no—
146C42×D61—21no—
147C42×D61—21no—
148C42×D61—21no—
149C42×D61C2×C411yescharacteristic
150C42×D61C2×C411yescharacteristic
151C42×D61D411yescharacteristic
152C42×D61D411yescharacteristic
153C42×D61D411yescharacteristic
154C42×D61D411yescharacteristic
155C42×D61C2311yescharacteristic
156C42×D61C2311yescharacteristic
157C2×#41×C61C2×C411yescharacteristic
158C4×Q8×C61C2×C411yescharacteristic
159C4×Q8×C61C2×C411yescharacteristic
160C4×D4×C61—21no—
161C4×D4×C61—21no—
162C4×D4×C61C2×C411yescharacteristic
163C4×D4×C61C2×C411yescharacteristic
164#117×C61—21no—
165#117×C61C2×C411yescharacteristic
166C2×C42×C61—21no—
167C2×C42×C61C2×C411yescharacteristic
168C23×D61—21no—
169C23×D61C2×D411yescharacteristic
170C22×#6923—24no—
171#41×C61—22no—
172#41×C61—22no—
173C2×Q8×C61C22×C411yescharacteristic
174C2×D4×C61—21no—
175C2×D4×C61C22×C411yescharacteristic
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61C22⋊C411yescharacteristic
180C22×C4×C61C22⋊C411yescharacteristic
181C22×C4×C61C22×C411yescharacteristic
182C2×C22⋊D61—21no—
183C2×C22⋊D61—21no—
184C2×C22⋊D61—21no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61C22⋊C411yescharacteristic
189C22×Dic61C22⋊C411yescharacteristic
190C22×Dic61C2×D411yescharacteristic
191#11758226—22no—
192#11758226—22no—
193Q8×D61—22no—
194Q8×D61#4114yes—
195#11758224—28no—
196#11758224—22no—
197#11758224—22no—
198D4×D61—28no—
199D4×D61—22no—
200D4×D61#4114yes—
201#11758222—28no—
202#11758222—22no—
203#11758222—22no—
204C2×D244—21no—
205C2×D244C22×C411yescharacteristic
206C2×C4×D61—28no—
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—22no—
211C2×C4×D61—22no—
212C2×C4×D61—21no—
213C2×C4×D61—21no—
214C2×C4×D61—21no—
215C2×C4×D61—21no—
216C2×C4×D61—21no—
217C2×C4×D61—21no—
218C2×C4×D61—42no—
219C2×C4×D61—42no—
220C2×C4×D61—44no—
221C2×C4×D61—44no—
222C2×C4×D61C22⋊C411yescharacteristic
223C2×C4×D61C22⋊C411yescharacteristic
224C2×C4×D61C22⋊C411yescharacteristic
225C2×C4×D61C22⋊C411yescharacteristic
226C2×C4×D61C22×C411yescharacteristic
227C2×C4×D61C2×D411yescharacteristic
228C2×C4×D61C2×D411yescharacteristic
229C2×C4×D61C2×D411yescharacteristic
230C2×C4×D61C2×D411yescharacteristic
231C2×C4×D61C2×D411yescharacteristic
232C2×C4×D61C2×D411yescharacteristic
233C2×C4×D61C2411yescharacteristic
234C2×Dic122—21no—
235C2×Dic122C22×C411yescharacteristic
236C22⋊#6923—44no—
237C2×#92420—24no—
238C4⋊#6923—24no—
239C4⋊#6923—24no—
240C4×#6923—44no—
241D61⋊C8—24no—
242D61⋊C8—24no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61C22×C411yescharacteristic
246C4⋊C4×C61C22×C411yescharacteristic
247C22⋊C4×C61—21no—
248C22⋊C4×C61—21no—
249C22⋊C4×C61—21no—
250C42×C61—21no—
251C42×C61—21no—
252C42×C61—21no—
253C42×C61C22⋊C411yescharacteristic
254C42×C61C22⋊C411yescharacteristic
255C42×C61C22×C411yescharacteristic
256C42×C61C22×C411yescharacteristic
257C22⋊Dic61—21no—
258C22⋊Dic61—21no—
259C22⋊Dic61—21no—
260#11758198—21no—
261#11758198—21no—
262#11758198—21no—
263#11758198—21no—
264#11758198—21no—
265#11758198—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61C22×C411yescharacteristic
269C4⋊Dic61C22×C411yescharacteristic
270#11758196—21no—
271#11758196—21no—
272#11758196—21no—
273#11758196—21no—
274#11758196—21no—
275#11758196—21no—
276C4×Dic61—21no—
277C4×Dic61—21no—
278C4×Dic61—21no—
279C4×Dic61—21no—
280C4×Dic61—21no—
281C4×Dic61—21no—
282C4×Dic61—21no—
283C4×Dic61—21no—
284C4×Dic61—21no—
285C4×Dic61C22⋊C411yescharacteristic
286C4×Dic61C22⋊C411yescharacteristic
287C4×Dic61C22⋊C411yescharacteristic
288C4×Dic61C22⋊C411yescharacteristic
289C4×Dic61C22⋊C411yescharacteristic
290C4×Dic61C22⋊C411yescharacteristic
291C4×Dic61C22×C411yescharacteristic
292C4×Dic61C22×C411yescharacteristic
293C4×Dic61C2×D411yescharacteristic
294C4×Dic61C2×D411yescharacteristic
295C4×Dic61C2×D411yescharacteristic
296C4×Dic61C2×D411yescharacteristic
297C23×C61—21no—
298C23×C61C2×C22⋊C411yescharacteristic
299C22×D61—21no—
300C22×D61—22no—
301C22×D61—24no—
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—42no—
305C22×D61—42no—
306C22×D61C2×C22⋊C411yescharacteristic
307C22×D61C22×D411yescharacteristic
308C2×#6923—44no—
309C2×#6923—44no—
310C2×#6923—44no—
311Q8×C61—21no—
312Q8×C61#11712yes—
313D4×C61—24no—
314D4×C61—21no—
315D4×C61#11712yes—
316C2×C4×C61—24no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—42no—
325C2×C4×C61—42no—
326C2×C4×C61C2×C22⋊C411yescharacteristic
327C2×C4×C61C2×C22⋊C411yescharacteristic
328C2×C4×C61C2×C22⋊C411yescharacteristic
329C2×C4×C61C2×C22⋊C411yescharacteristic
330C2×C4×C61C2×C22⋊C411yescharacteristic
331C2×C4×C61C23×C411yescharacteristic
332C22⋊D61—24no—
333C22⋊D61—24no—
334C22⋊D61—24no—
335C2×Dic61—24no—
336C2×Dic61—21no—
337C2×Dic61—22no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—42no—
343C2×Dic61—42no—
344C2×Dic61C2×C22⋊C411yescharacteristic
345C2×Dic61C2×C22⋊C411yescharacteristic
346C2×Dic61C2×C22⋊C411yescharacteristic
347C2×Dic61C2×C22⋊C411yescharacteristic
348C2×Dic61C2×C22⋊C411yescharacteristic
349C2×Dic61C22×D411yescharacteristic
350D244—24no—
351D244—21no—
352D244#11712yes—
353C4×D61—24no—
354C4×D61—24no—
355C4×D61—22no—
356C4×D61—24no—
357C4×D61—22no—
358C4×D61—22no—
359C4×D61—22no—
360C4×D61—22no—
361C4×D61—21no—
362C4×D61—21no—
363C4×D61—22no—
364C4×D61—41no—
365C4×D61—41no—
366C4×D61—41no—
367C4×D61—41no—
368C4×D61—42no—
369C4×D61—42no—
370C4×D61—42no—
371C4×D61—42no—
372C4×D61—42no—
373C4×D61—42no—
374C4×D61C2×#4112yes—
375C4×D61C2×#4112yes—
376Dic122—21no—
377Dic122—24no—
378Dic122#11712yes—
379#92420—44no—
380#20742—611nomaximal, Sylow
381C22×C61—21no—
382C22×C61—21no—
383C22×C61—21no—
384C22×C61—22no—
385C22×C61—41no—
386C22×C61—41no—
387C22×C61C22×C22⋊C411yescharacteristic
388C2×D61—21no—
389C2×D61—21no—
390C2×D61—21no—
391C2×D61—22no—
392C2×D61—41no—
393C2×D61—41no—
394C2×D61—44no—
395C2×D61—48no—
396C2×D61#52512yes—
397C2×D61#57512yes—
398C2×D61#57512yes—
399#6923—84no—
400C4×C61—21no—
401C4×C61—21no—
402C4×C61—21no—
403C4×C61—21no—
404C4×C61—22no—
405C4×C61—21no—
406C4×C61—41no—
407C4×C61—41no—
408C4×C61C2×#11711yescharacteristic
409C4×C61C2×#11711yescharacteristic
410Dic61—21no—
411Dic61—21no—
412Dic61—21no—
413Dic61—21no—
414Dic61—22no—
415Dic61—21no—
416Dic61—41no—
417Dic61—41no—
418Dic61#52512yes—
419C2×C4×#41—611no—
420C2×#432—611no—
421#2283—611no—
422#1825—612no—
423#1805—612no—
424#1804—612no—
425#1788—612no—
426#1763—612no—
427#1762—612no—
428C2×C61—41no—
429C2×C61—42no—
430C2×C61#228011yescharacteristic
431C2×C61#289611yescharacteristic
432C2×C61#289611yescharacteristic
433D61—41no—
434D61—42no—
435D61#311114yes—
436C22×#41—611no—
437C4×#41—611no—
438C4×#41—611no—
439C4×#41—611no—
440C4×#41—611no—
441C4×#41—611no—
442C4×#41—611no—
443C4×#41—611no—
444C4×#41—1221no—
445C4×#41—1221no—
446C4×#41—1221no—
447C4×#41—1221no—
448C4×#41#692311yescharacteristic, complemented
449C2×C4×Q8—611no—
450C2×C4×Q8—611no—
451C2×C4×D4—611no—
452C2×C4×D4—611no—
453C2×C4×D4—1221no—
454C2×C4×D4—1221no—
455C2×#117—611no—
456C2×#117—1221no—
457C22×C42—611no—
458C22×C42—1221no—
459#432—1221no—
460#432—1221no—
461#432—1221no—
462#432—1221no—
463C2×C4⋊C8—612no—
464C2×#103—614no—
465C2×#102—614no—
466C2×C22⋊C8—612no—
467C2×#97—612no—
468#383—1221no—
469#382—612no—
470#381—1221no—
471#380—612no—
472C4×C4⋊C4—612no—
473C4×C22⋊C4—1221no—
474#376—1221no—
475#340—614no—
476#340—614no—
477C61#2074211yescharacteristic, complemented, Sylow
478C2×#41—611no—
479C2×#41—611no—
480C2×#41—611no—
481C2×#41—1221no—
482C2×#41—1221no—
483C2×#41—1224no—
484C2×#41—1224no—
485C2×#41C2×#692311yescharacteristic
486C22×Q8—611no—
487C22×D4—611no—
488C22×D4—1221no—
489C23×C4—611no—
490C23×C4—611no—
491C23×C4—611no—
492C23×C4—1221no—
493C23×C4—1221no—
494C23×C4—1221no—
495C22×C8—614no—
496C4×Q8—611no—
497C4×Q8—611no—
498C4×Q8—611no—
499C4×Q8—611no—
500C4×Q8—611no—
501C4×Q8—611no—
502C4×Q8—1221no—
503C4×Q8—1221no—
504C4×Q8—1221no—
505C4×Q8—1221no—
506C4×Q8C2×#692311yescharacteristic
507C4×Q8C2×#692311yescharacteristic
508C4×D4—21no—
509C4×D4—21no—
510C4×D4—611no—
511C4×D4—611no—
512C4×D4—611no—
513C4×D4—611no—
514C4×D4—611no—
515C4×D4—611no—
516C4×D4—1221no—
517C4×D4—1221no—
518C4×D4—1221no—
519C4×D4—1221no—
520C4×D4—1221no—
521C4×D4—1221no—
522C4×D4—1221no—
523C4×D4—1221no—
524C4×D4—1221no—
525C4×D4—1221no—
526C4×D4—1221no—
527C4×D4—1221no—
528C4×D4—1221no—
529C4×D4—1221no—
530C4×D4—1221no—
531C4×D4—1221no—
532C4×D4—1221no—
533C4×D4—1221no—
534C4×D4C2×#692311yescharacteristic
535C4×D4C2×#692311yescharacteristic
536#117—21no—
537#117—611no—
538#117—611no—
539#117—611no—
540#117—1221no—
541#117—1221no—
542#117—1221no—
543#117—1221no—
544#117—1221no—
545#117—1221no—
546#117—1221no—
547#117—1221no—
548#117—1221no—
549#117C2×#692311yescharacteristic
550C2×C4⋊C4—611no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—614no—
553C2×C4⋊C4—1221no—
554C2×C4⋊C4—1221no—
555C2×C22⋊C4—1221no—
556C2×C22⋊C4—1221no—
557C2×C22⋊C4—1221no—
558C2×C22⋊C4—1222no—
559C2×C42—21no—
560C2×C42—611no—
561C2×C42—611no—
562C2×C42—611no—
563C2×C42—611no—
564C2×C42—611no—
565C2×C42—611no—
566C2×C42—611no—
567C2×C42—611no—
568C2×C42—611no—
569C2×C42—611no—
570C2×C42—611no—
571C2×C42—1221no—
572C2×C42—1221no—
573C2×C42—1221no—
574C2×C42—1221no—
575C2×C42—1221no—
576C2×C42—1221no—
577C2×C42—1221no—
578C2×C42—1221no—
579C2×C42—1221no—
580C2×C42—1221no—
581C2×C42—1222no—
582C2×C42C2×#692311yescharacteristic
583C4⋊C8—1222no—
584C4⋊C8—1222no—
585#103—1228no—
586#102—1228no—
587C22⋊C8—1222no—
588C22⋊C8—1222no—
589#97—1222no—
590#97—1222no—
591#95—1222no—
592#95—1222no—
593#95—1222no—
594#95—1222no—
595C24—611no—
596C24—1221no—
597#41—22no—
598#41—22no—
599#41—1222no—
600#41—1222no—
601#41—1228no—
602#41—1222no—
603#41—1228no—
604#41—1222no—
605#41—1222no—
606#41—1222no—
607C2×Q8—614no—
608C2×Q8—611no—
609C2×Q8—1221no—
610C2×Q8—1222no—
611C2×Q8C22×#692311yescharacteristic
612C2×D4—21no—
613C2×D4—614no—
614C2×D4—611no—
615C2×D4—1221no—
616C2×D4—1222no—
617C2×D4—1221no—
618C2×D4—1228no—
619C2×D4—1221no—
620C2×D4—1221no—
621C2×D4C22×#692311yescharacteristic
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—611no—
626C22×C4—611no—
627C22×C4—611no—
628C22×C4—611no—
629C22×C4—611no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—611no—
636C22×C4—611no—
637C22×C4—611no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—1221no—
641C22×C4—1222no—
642C22×C4—1222no—
643C22×C4—1221no—
644C22×C4—1221no—
645C22×C4—1221no—
646C22×C4—1228no—
647C22×C4—1221no—
648C22×C4—1221no—
649C22×C4—1221no—
650C22×C4—1221no—
651C22×C4—1221no—
652C22×C4—1221no—
653C22×C4—1221no—
654C22×C4—1221no—
655C22×C4—1224no—
656C22×C4—2442no—
657C22×C4—2442no—
658C22×C4—2444no—
659C22×C4—2444no—
660C22×C4C22⋊#692311yescharacteristic
661C22×C4C22⋊#692311yescharacteristic
662C22×C4C22×#692311yescharacteristic
663C2×C8—1224no—
664C2×C8—1224no—
665C2×C8—1224no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—611no—
669C4⋊C4—611no—
670C4⋊C4—1221no—
671C4⋊C4—1221no—
672C4⋊C4—1221no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4—1224no—
677C4⋊C4—1224no—
678C4⋊C4—1221no—
679C4⋊C4—1221no—
680C4⋊C4C22×#692311yescharacteristic
681C4⋊C4C22×#692311yescharacteristic
682C22⋊C4—21no—
683C22⋊C4—21no—
684C22⋊C4—21no—
685C22⋊C4—1221no—
686C22⋊C4—1221no—
687C22⋊C4—1221no—
688C22⋊C4—1221no—
689C22⋊C4—1221no—
690C22⋊C4—1221no—
691C22⋊C4—1221no—
692C22⋊C4—1221no—
693C22⋊C4—1221no—
694C22⋊C4—2444no—
695C42—21no—
696C42—21no—
697C42—21no—
698C42—611no—
699C42—611no—
700C42—611no—
701C42—611no—
702C42—611no—
703C42—611no—
704C42—611no—
705C42—611no—
706C42—611no—
707C42—611no—
708C42—611no—
709C42—611no—
710C42—1221no—
711C42—1221no—
712C42—1221no—
713C42—1221no—
714C42—1221no—
715C42—1221no—
716C42—1221no—
717C42—1221no—
718C42—1221no—
719C42—2444no—
720C42C22⋊#692311yescharacteristic
721C42C22⋊#692311yescharacteristic
722C42C22×#692311yescharacteristic
723C42C22×#692311yescharacteristic
724C23—21no—
725C23—611no—
726C23—611no—
727C23—1222no—
728C23—1224no—
729C23—1222no—
730C23—1222no—
731C23—1221no—
732C23—2442no—
733C23—2442no—
734C23C2×C22⋊#692311yescharacteristic
735Q8—21no—
736Q8—612no—
737Q8—1224no—
738Q8—1221no—
739Q8#1451985612yes—
740D4—24no—
741D4—21no—
742D4—612no—
743D4—1224no—
744D4—1224no—
745D4—1224no—
746D4—1224no—
747D4—1221no—
748D4#1451985612yes—
749C2×C4—24no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—611no—
760C2×C4—612no—
761C2×C4—612no—
762C2×C4—611no—
763C2×C4—611no—
764C2×C4—611no—
765C2×C4—611no—
766C2×C4—611no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1224no—
774C2×C4—1224no—
775C2×C4—1224no—
776C2×C4—1222no—
777C2×C4—1224no—
778C2×C4—1221no—
779C2×C4—1221no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—2441no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4—2442no—
788C2×C4—2442no—
789C2×C4—2442no—
790C2×C4—2442no—
791C2×C4—2442no—
792C2×C4—2442no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4—2442no—
796C2×C4—2442no—
797C2×C4—2444no—
798C2×C4—2444no—
799C2×C4—2444no—
800C2×C4C2×C22⋊#692311yescharacteristic
801C2×C4C2×C22⋊#692311yescharacteristic
802C2×C4C2×C22⋊#692311yescharacteristic
803C2×C4C2×C22⋊#692311yescharacteristic
804C2×C4C2×C22⋊#692311yescharacteristic
805C2×C4C23×#692311yescharacteristic
806C8—2444no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—22no—
811C22—41no—
812C22—41no—
813C22—612no—
814C22—612no—
815C22—612no—
816C22—1221no—
817C22—1221no—
818C22—1222no—
819C22—1221no—
820C22—2444no—
821C22—2448no—
822C22—2441no—
823C22—2441no—
824C22C22×C22⋊#692311yescharacteristic
825C4—21no—
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—22no—
831C4—41no—
832C4—41no—
833C4—612no—
834C4—1221no—
835C4—1221no—
836C4—1221no—
837C4—1221no—
838C4—1221no—
839C4—1222no—
840C4—4884no—
841C4—2441no—
842C4—2441no—
843C4C2×#1451985611yescharacteristic
844C4C2×#1451985611yescharacteristic
845C2—41no—
846C2—42no—
847C2—614no—
848C2—2441no—
849C2—2442no—
850C2#2146226311yescharacteristic
851C2#2146243911yescharacteristic
852C2#2146243911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC4×#41×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenterC4×#41#6923
hypocenterC61#20742
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. D61⋊#432C2semidirect
2. #21462266C2semidirect
3. #21461724C2semidirect
4. #21461690C2semidirect
5. #21461689C2semidirect
7. #21461591C2semidirect
8. #21461589C2semidirect
29. #41×Dic61C4semidirect
30. C4×#11758226C4semidirect
31. C4×#11758226C4semidirect
33. C4×#11758222C4semidirect
35. #16840230C4semidirect
38. C4×#11758224C4semidirect
39. C4×#11758224C4semidirect
50. C4×#41×C61C4semidirect
448. C4×#41#6923semidirect
477. C61#20742semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4322
#214622662
#214617242
#214616902
#214616892
#214616592
#214615912
#214615892
C4×#41×D612
#2074261