Finite Group Databasebeta

← #29680737

Subgroups — #29680737

Order 15616.

1590 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D61C211yesmaximal, characteristic
2C2×#16839799C211yesmaximal, characteristic, complemented
3C2×#16839797C211yesmaximal, characteristic, complemented
4C2×C22⋊C8×D61C211yesmaximal, characteristic
5#21448201C211yesmaximal, characteristic
6#21446020C211yesmaximal, characteristic, complemented
7#21446018C211yesmaximal, characteristic, complemented
8#21446016C211yesmaximal, characteristic, complemented
9#21446013C211yesmaximal, characteristic, complemented
10#21446010C211yesmaximal, characteristic, complemented
11#21446008C211yesmaximal, characteristic, complemented
12#21446005C211yesmaximal, characteristic, complemented
13#21445534C211yesmaximal, characteristic, complemented
14#21445534C211yesmaximal, characteristic, complemented
15C61×#1854C211yesmaximal, characteristic, complemented
16C23×C4×D61C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C2×#14519736C2211yescharacteristic
20C2×#14519735C2211yescharacteristic
21C2×#14519735C2211yescharacteristic
22C2×#14519735C2211yescharacteristic
23C2×#14519735C2211yescharacteristic
24C2×#14519734—21no—
25C2×#14519733—21no—
26#117×D61—24no—
27#117×D61—24no—
28C2×C4⋊C4×D61C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30C2×C22⋊C4×D61—21no—
31C2×C42×D61—21no—
32#16839799—24no—
33#16839797—24no—
34C2×#14519711C2211yescharacteristic, complemented
35C2×#14519710C2211yescharacteristic, complemented
36C2×#14519710C2211yescharacteristic, complemented
37C2×#14519709C2211yescharacteristic, complemented
38C2×#14519708C2211yescharacteristic, complemented
39C2×#14519708C2211yescharacteristic, complemented
40C2×C22⋊#92418C2211yescharacteristic
41C2×#14519689C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C22⋊C8×D61C418yescomplemented
44#16839624—21no—
45#16839622C2211yescharacteristic
46#16839619C2211yescharacteristic
47#16839619C2211yescharacteristic
48#16839617—21no—
49C22⋊C4×Dic61—21no—
50#16839609—21no—
51#16839525C2211yescharacteristic, complemented
52#16839525C2211yescharacteristic, complemented
53#16839524C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57C2×#117×C61C2211yescharacteristic
58C2×#107×C61C2211yescharacteristic, complemented
59C2×#106×C61C2211yescharacteristic, complemented
60C2×C22⋊C8×C61C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C61×#340C2211yescharacteristic, complemented
63C61×#340C2211yescharacteristic, complemented
64C24×D61D411yescharacteristic
65C23×Dic61D411yescharacteristic
66C22×C4×D61—22no—
67C22×C4×D61—22no—
68C22×C4×D61—22no—
69C22×C4×D61—22no—
70C22×C4×D61—21no—
71C22×C4×D61—21no—
72C22×C4×D61C2×C414yes—
73C22×C4×D61D411yescharacteristic
74C22×C4×D61D411yescharacteristic
75C22×C4×D61Q814yes—
76C22×C4×D61C2311yescharacteristic
77C22×C4×D61C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C2×C8×D61—22no—
81C2×C8×D61—22no—
82C2×C8×D61—22no—
83C2×C8×D61—22no—
84C2×C8×D61C2×C414yescomplemented
85C2×C8×D61C2×C414yescomplemented
86#14519736—22no—
87#14519736—22no—
88#14519735—22no—
89#14519735—22no—
90#14519735—22no—
91#14519735—22no—
92#14519735—22no—
93#14519735—22no—
94#14519735D414yes—
95#14519735D414yes—
96#14519734—28no—
97#14519733—28no—
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×C4⋊Dic61C2311yescharacteristic
101C2×C4⋊Dic61C2311yescharacteristic
102C2×#11758196—21no—
103C2×#11758196—21no—
104C4⋊C4×D61—22no—
105C4⋊C4×D61—22no—
106C4⋊C4×D61—22no—
107C4⋊C4×D61—22no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61—21no—
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C22⋊C4×D61—28no—
117C2×C4×Dic61—21no—
118C2×C4×Dic61—21no—
119C2×C4×Dic61—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122C42×D61—28no—
123#14519711—22no—
124#14519710—22no—
125#14519710—22no—
126#14519709—22no—
127#14519708—22no—
128#14519708—22no—
129C22⋊#92418C2×C414yescomplemented
130#14519689C2×C414yes—
131#14519689C2×C414yes—
132#14519684—21no—
133#14519684—21no—
134#14519684—21no—
135C23×C4×C61C2311yescharacteristic
136C22×C8×C61C2311yescharacteristic
137C22×C8×C61C2311yescharacteristic
138#117×C61—22no—
139#117×C61—22no—
140C2×C4⋊C4×C61C2311yescharacteristic
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C22⋊C4×C61—21no—
145C2×C22⋊C4×C61—21no—
146C2×C42×C61—21no—
147#107×C61—22no—
148#106×C61—22no—
149C22⋊C8×C61C2×C414yescomplemented
150#95×C61—21no—
151C24×C61C2×D411yescharacteristic
152C23×D61—22no—
153C23×D61—22no—
154C23×D61—22no—
155C23×D61—22no—
156C23×D61—41no—
157C23×D61—41no—
158C23×D61C4⋊C414yes—
159C23×D61C2×D411yescharacteristic
160C23×D61C2×D411yescharacteristic
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61C22×C412yes—
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2×Q812yes—
172C22×C4×C61C2411yescharacteristic
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61C4⋊C414yes—
180C22×Dic61C2×D411yescharacteristic
181C22×Dic61C2×D411yescharacteristic
182C2×C4×D61—22no—
183C2×C4×D61—22no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—22no—
189C2×C4×D61—22no—
190C2×C4×D61—28no—
191C2×C4×D61—28no—
192C2×C4×D61—28no—
193C2×C4×D61—28no—
194C2×C4×D61—24no—
195C2×C4×D61—24no—
196C2×C4×D61—42no—
197C2×C4×D61—42no—
198C2×C4×D61—42no—
199C2×C4×D61—42no—
200C2×C4×D61C4⋊C414yes—
201C2×C4×D61C4⋊C414yes—
202C2×C4×D61C22×C412yes—
203C2×C4×D61C22×C412yes—
204C2×C4×D61C2×D412yes—
205C2×C4×D61C2×D412yes—
206C2×C4×D61C2×Q812yes—
207C2×C4×D61C2×Q812yes—
208C2×C4×D61#4112yes—
209C2×C4×D61#4112yes—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61C22×C412yes—
215C2×C8×C61C22×C412yes—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61C2×D412yes—
223C4⋊C4×C61C2×D412yes—
224C22⋊C4×C61—24no—
225C22⋊C4×C61—42no—
226C42×C61—24no—
227C22⋊Dic61—24no—
228C22⋊Dic61—42no—
229#11758198—24no—
230#11758198—24no—
231#11758198—42no—
232#11758198—42no—
233#11758198—42no—
234#11758198—42no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61—21no—
240C4⋊Dic61—21no—
241C4⋊Dic61C2×D412yes—
242C4⋊Dic61C2×D412yes—
243#11758196—24no—
244#11758196—24no—
245C4×Dic61—24no—
246C4×Dic61—24no—
247C4×Dic61—24no—
248C4×Dic61—42no—
249C4×Dic61—42no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418C22×C412yes—
255C2×#92418C22×C412yes—
256C8×D61—28no—
257C8×D61—28no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61C2×C4⋊C412yes—
265C23×C61C22×D411yescharacteristic
266C22×D61—21no—
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—28no—
275C22×D61—28no—
276C22×D61—44no—
277C22×D61—44no—
278C22×D61—44no—
279C22×D61—44no—
280C22×D61—44no—
281C22×D61C2×C4⋊C412yes—
282C22×D61C2×C4⋊C412yes—
283C22×D61#12012yes—
284C22×D61#12312yes—
285C22×D61#13512yes—
286C22×D61#13512yes—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61C2×C4⋊C412yes—
306C2×C4×C61C23×C411yescharacteristic
307C2×C4×C61C22×D411yescharacteristic
308C2×C4×C61C22×D411yescharacteristic
309C2×C4×C61C22×Q811yescharacteristic
310C2×C4×C61C2×#4111yescharacteristic
311C2×C4×C61C2×#4111yescharacteristic
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—28no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61C2×C4⋊C412yes—
328C2×Dic61C2×C4⋊C412yes—
329C2×Dic61#12012yes—
330C2×Dic61#12312yes—
331C4×D61—28no—
332C4×D61—22no—
333C4×D61—22no—
334C4×D61—22no—
335C4×D61—22no—
336C4×D61—28no—
337C4×D61—48no—
338C4×D61—48no—
339C4×D61C4×D414yes—
340C4×D61C4×D414yes—
341C4×D61C22⋊Q814yes—
342C4×D61C22⋊Q814yes—
343C8×C61—22no—
344C8×C61—22no—
345#92418—22no—
346#92418—22no—
347#20843—611nomaximal, Sylow
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—22no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61C22×C4⋊C411yescharacteristic
356C22×C61C2×#12011yescharacteristic
357C22×C61C2×#12311yescharacteristic
358C22×C61C2×#13511yescharacteristic
359C22×C61C2×#13511yescharacteristic
360C22×C61#57511yescharacteristic
361C22×C61#57511yescharacteristic
362C2×D61—22no—
363C2×D61—22no—
364C2×D61—22no—
365C2×D61—22no—
366C2×D61—22no—
367C2×D61—22no—
368C2×D61—22no—
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—22no—
372C2×D61—22no—
373C2×D61—22no—
374C2×D61—416no—
375C2×D61#38514yes—
376C2×D61#42714yescomplemented
377C4×C61—22no—
378C4×C61—42no—
379C4×C61—42no—
380C4×C61—81no—
381C4×C61—81no—
382C4×C61C2×C4×D411yescharacteristic
383C4×C61C2×C4×D411yescharacteristic
384C4×C61C2×C22⋊Q811yescharacteristic
385C4×C61C2×C22⋊Q811yescharacteristic
386Dic61—22no—
387Dic61—42no—
388Dic61—42no—
389Dic61—81no—
390Dic61—81no—
391Dic61#38514yes—
392C22×#117—611no—
393C2×#427—611no—
394C2×#427—611no—
395C22×C22⋊C8—611no—
396#2280—611no—
397#1854—611no—
398#1854—611no—
399#1854—611no—
400#1854D6111yescharacteristic, complemented
401#1853—611no—
402#1853—611no—
403#1852—611no—
404#1852—611no—
405#1735—611no—
406#1735—611no—
407C2×C61—42no—
408C2×C61C2×#38511yescharacteristic
409C2×C61C2×#42711yescharacteristic
410C2×C61#291111yescharacteristic
411C2×C61#300211yescharacteristic
412C2×C61#300211yescharacteristic
413C2×C61#309111yescharacteristic
414C2×C61#309111yescharacteristic
415D61—24no—
416D61—24no—
417C24×C4—611no—
418C23×C8—611no—
419C23×C8—611no—
420C2×#117—611no—
421C2×#117—611no—
422C2×#117—611no—
423C2×#117—611no—
424C2×#117—611no—
425C2×#117—1221no—
426C2×#117—1221no—
427C2×#117—1224no—
428C2×#117—1224no—
429C2×#117C2×D6111yescharacteristic
430C22×C4⋊C4—611no—
431C22×C4⋊C4—611no—
432C22×C22⋊C4—1221no—
433C22×C42—1221no—
434#427—1224no—
435#427—1224no—
436C2×#107—611no—
437C2×#107—611no—
438C2×#107—611no—
439C2×#107C2×D6111yescharacteristic, complemented
440C2×#106—611no—
441C2×#106—611no—
442C2×#106—611no—
443C2×#106C2×D6111yescharacteristic, complemented
444C2×C22⋊C8—611no—
445C2×C22⋊C8—611no—
446C2×C22⋊C8—611no—
447C2×C22⋊C8—618no—
448C2×C22⋊C8C2×D6111yescharacteristic
449#381—1221no—
450#380—611no—
451#380—611no—
452#380—611no—
453#380C2×D6111yescharacteristic
454#379—1221no—
455C4×C22⋊C4—1221no—
456C4×C22⋊C4—1221no—
457#340—611no—
458#340—611no—
459#340—611no—
460#340—611no—
461#340—611no—
462#340—611no—
463#340C2×D6111yescharacteristic, complemented
464#340C2×D6111yescharacteristic, complemented
465C61#2084311yescharacteristic, complemented, Sylow
466C25—611no—
467C23×C4—611no—
468C23×C4—611no—
469C23×C4—614no—
470C23×C4—611no—
471C23×C4—611no—
472C23×C4—614no—
473C23×C4—611no—
474C23×C4—1222no—
475C23×C4—1222no—
476C23×C4—1222no—
477C23×C4—1222no—
478C23×C4—1221no—
479C23×C4—1221no—
480C23×C4C22×D6111yescharacteristic
481C22×C8—611no—
482C22×C8—611no—
483C22×C8—614no—
484C22×C8—614no—
485C22×C8—1222no—
486C22×C8—1222no—
487C22×C8—1222no—
488C22×C8—1222no—
489C22×C8C22×D6111yescharacteristic
490C22×C8C22×D6111yescharacteristic
491#117—22no—
492#117—22no—
493#117—614no—
494#117—614no—
495#117—1228no—
496#117—1228no—
497#117—1222no—
498#117—1222no—
499#117—1222no—
500#117—1222no—
501#117—1222no—
502#117—1222no—
503#117—1222no—
504#117—1222no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—1222no—
510C2×C4⋊C4—1222no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1222no—
514C2×C4⋊C4—1222no—
515C2×C4⋊C4C22×D6111yescharacteristic
516C2×C4⋊C4C22×D6111yescharacteristic
517C2×C4⋊C4C22×D6111yescharacteristic
518C2×C4⋊C4C22×D6111yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—1228no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C42—21no—
531C2×C42—1228no—
532C2×C42—1221no—
533C2×C42—1221no—
534C2×C42—1221no—
535C2×C42—1221no—
536C2×C42—1221no—
537#107—22no—
538#107—1222no—
539#107—1222no—
540#107—1222no—
541#106—22no—
542#106—1222no—
543#106—1222no—
544#106—1222no—
545C22⋊C8—614no—
546C22⋊C8—614no—
547C22⋊C8—614no—
548C22⋊C8C4×D6114yescomplemented
549#95—21no—
550#95—1221no—
551#95—1221no—
552#95—1221no—
553C24—611no—
554C24—611no—
555C24—614no—
556C24—1222no—
557C24—1222no—
558C24—1222no—
559C24—1222no—
560C24—2441no—
561C24—2441no—
562C24D4×D6111yescharacteristic
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—611no—
572C22×C4—612no—
573C22×C4—612no—
574C22×C4—612no—
575C22×C4—612no—
576C22×C4—612no—
577C22×C4—612no—
578C22×C4—611no—
579C22×C4—614no—
580C22×C4—612no—
581C22×C4—612no—
582C22×C4—614no—
583C22×C4—614no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1228no—
587C22×C4—1228no—
588C22×C4—1228no—
589C22×C4—1228no—
590C22×C4—1222no—
591C22×C4—1222no—
592C22×C4—1224no—
593C22×C4—1224no—
594C22×C4—1222no—
595C22×C4—1222no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—2442no—
605C22×C4—2442no—
606C22×C4—2442no—
607C22×C4—2442no—
608C22×C4C2×C4×D6112yes—
609C22×C4D4×D6111yescharacteristic
610C22×C4Q8×D6112yes—
611C22×C4C23×D6111yescharacteristic
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—612no—
617C2×C8—612no—
618C2×C8—1228no—
619C2×C8—1228no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8C2×C4×D6112yes—
625C2×C8C2×C4×D6112yes—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—612no—
633C4⋊C4—612no—
634C4⋊C4—1224no—
635C4⋊C4—1224no—
636C4⋊C4—1221no—
637C4⋊C4—1221no—
638C4⋊C4—1221no—
639C4⋊C4—1221no—
640C4⋊C4—1221no—
641C4⋊C4—1221no—
642C4⋊C4D4×D6112yes—
643C4⋊C4D4×D6112yes—
644C22⋊C4—24no—
645C22⋊C4—42no—
646C22⋊C4—1224no—
647C22⋊C4—1224no—
648C22⋊C4—1224no—
649C22⋊C4—2442no—
650C22⋊C4—2442no—
651C22⋊C4—2442no—
652C22⋊C4—2442no—
653C22⋊C4—2442no—
654C42—24no—
655C42—1224no—
656C42—1224no—
657C42—1224no—
658C42—2442no—
659C42—2442no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—612no—
667C23—612no—
668C23—612no—
669C23—612no—
670C23—612no—
671C23—612no—
672C23—1228no—
673C23—1228no—
674C23—1221no—
675C23—1221no—
676C23—1221no—
677C23—1221no—
678C23—1221no—
679C23—1221no—
680C23—1221no—
681C23—1221no—
682C23—2444no—
683C23—2444no—
684C23—2444no—
685C23—2444no—
686C23—2444no—
687C23C4⋊C4×D6112yes—
688C23C2×D4×D6111yescharacteristic
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—612no—
708C2×C4—612no—
709C2×C4—612no—
710C2×C4—614no—
711C2×C4—614no—
712C2×C4—614no—
713C2×C4—614no—
714C2×C4—612no—
715C2×C4—1228no—
716C2×C4—1228no—
717C2×C4—1228no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—2448no—
727C2×C4—2448no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4—2441no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4C4⋊C4×D6112yes—
739C2×C4C22×C4×D6111yescharacteristic
740C2×C4C2×D4×D6111yescharacteristic
741C2×C4C2×D4×D6111yescharacteristic
742C2×C4C2×Q8×D6111yescharacteristic
743C2×C4#41×D6111yescharacteristic
744C2×C4#41×D6111yescharacteristic
745C8—22no—
746C8—22no—
747C8—1222no—
748C8—1222no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—614no—
757C22—614no—
758C22—1222no—
759C22—1222no—
760C22—1222no—
761C22—1222no—
762C22—1222no—
763C22—1222no—
764C22—1222no—
765C22—1222no—
766C22—1222no—
767C22—1222no—
768C22—1222no—
769C22—1222no—
770C22—24416no—
771C22C2×C4⋊C4×D6111yescharacteristic
772C22#120×D6111yescharacteristic
773C22#123×D6111yescharacteristic
774C22#135×D6111yescharacteristic
775C22#135×D6111yescharacteristic
776C22#1684055811yescharacteristic
777C22#1684056111yescharacteristic
778C4—22no—
779C4—42no—
780C4—42no—
781C4—81no—
782C4—81no—
783C4—614no—
784C4—1222no—
785C4—4881no—
786C4—4881no—
787C4—2442no—
788C4—2442no—
789C4C4×D4×D6111yescharacteristic
790C4C4×D4×D6111yescharacteristic
791C4C22⋊Q8×D6111yescharacteristic
792C4C22⋊Q8×D6111yescharacteristic
793C2—42no—
794C2—1224no—
795C2—1224no—
796C2#385×D6111yescharacteristic
797C2#427×D6111yescharacteristic
798C2#2145440611yescharacteristic
799C2#2145503411yescharacteristic
800C2#2145504011yescharacteristic
801C2#2145573111yescharacteristic
802C2#2145573711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1854C2
socleC23×C61C22×D4
prime radicalC24×D61D4
cosocleC22×C4×C61C24
hypercenter#1854D61
hypocenterC61#20843
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
2. C2×#16839799C2semidirect
3. C2×#16839797C2semidirect
6. #21446020C2semidirect
7. #21446018C2semidirect
8. #21446016C2semidirect
9. #21446013C2semidirect
10. #21446010C2semidirect
11. #21446008C2semidirect
12. #21446005C2semidirect
13. #21445534C2semidirect
14. #21445534C2semidirect
15. C61×#1854C2semidirect
34. C2×#14519711C22semidirect
35. C2×#14519710C22semidirect
36. C2×#14519710C22semidirect
37. C2×#14519709C22semidirect
38. C2×#14519708C22semidirect
39. C2×#14519708C22semidirect
43. C22⋊C8×D61C4semidirect
51. #16839525C22semidirect
52. #16839525C22semidirect
53. #16839524C22semidirect
54. #16839524C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
58. C2×#107×C61C22semidirect
59. C2×#106×C61C22semidirect
62. C61×#340C22semidirect
63. C61×#340C22semidirect
84. C2×C8×D61C2×C4semidirect
85. C2×C8×D61C2×C4semidirect
129. C22⋊#92418C2×C4semidirect
149. C22⋊C8×C61C2×C4semidirect
376. C2×D61#427semidirect
400. #1854D61semidirect
439. C2×#107C2×D61semidirect
443. C2×#106C2×D61semidirect
463. #340C2×D61semidirect
464. #340C2×D61semidirect
465. C61#20843semidirect
548. C22⋊C8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D612
C2×#168397992
C2×#168397972
C2×C22⋊C8×D612
#214482012
#214460202
#214460182
#214460162
#214460132
#214460102
#214460082
#214460052
#214455342
C61×#18542
#2084361