Finite Group Databasebeta

← #29690303

Subgroups — #29690303

Order 15616.

1162 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839725C211yesmaximal, characteristic
2#21448201C211yesmaximal, characteristic
3#380×D61C211yesmaximal, characteristic
4#21446021C211yesmaximal, characteristic, complemented
5#21446019C211yesmaximal, characteristic, complemented
6#21446017C211yesmaximal, characteristic, complemented
7#21446015C211yesmaximal, characteristic, complemented
8#21446013C211yesmaximal, characteristic, complemented
9#21446010C211yesmaximal, characteristic, complemented
10#21446008C211yesmaximal, characteristic, complemented
11#21446005C211yesmaximal, characteristic, complemented
12#21445852C211yesmaximal, characteristic, complemented
13#21445850C211yesmaximal, characteristic, complemented
14#21445850C211yesmaximal, characteristic, complemented
15C61×#1809C211yesmaximal, characteristic, complemented
16C23×C4×D61C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C2×#14519735C2211yescharacteristic
19C2×#14519735C2211yescharacteristic
20C2×C4⋊C4×D61C2211yescharacteristic
21C2×C4⋊C4×D61C2211yescharacteristic
22C2×C22⋊C4×D61—21no—
23C2×#14519711C2211yescharacteristic, complemented
24C2×#14519710C2211yescharacteristic, complemented
25C2×#14519710C2211yescharacteristic, complemented
26C2×#14519709C2211yescharacteristic, complemented
27C2×#14519708C2211yescharacteristic, complemented
28C2×#14519708C2211yescharacteristic, complemented
29#16839725C418yescomplemented
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34#16839624—21no—
35#16839622C2211yescharacteristic
36#16839622C2211yescharacteristic
37#16839621—21no—
38#16839620—21no—
39#16839619C2211yescharacteristic
40#16839619C2211yescharacteristic
41#16839619C2211yescharacteristic
42#16839619C2211yescharacteristic
43#16839617—21no—
44C22⋊C4×Dic61—21no—
45#16839609—21no—
46#95×D61—21no—
47#16839525C2211yescharacteristic, complemented
48#16839525C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53C22×M16×C61C2211yescharacteristic
54C2×#107×C61C2211yescharacteristic, complemented
55C2×#106×C61C2211yescharacteristic, complemented
56C61×#380C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#340C2211yescharacteristic, complemented
59C61×#340C2211yescharacteristic, complemented
60C24×D61D411yescharacteristic
61C23×Dic61D411yescharacteristic
62C22×C4×D61—21no—
63C22×C4×D61—21no—
64C22×C4×D61—41no—
65C22×C4×D61—41no—
66C22×C4×D61—41no—
67C22×C4×D61—41no—
68C22×C4×D61C2×C414yes—
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61Q814yes—
72C22×C4×D61C2311yescharacteristic
73C22×C4×D61C2311yescharacteristic
74C2×#11758194—41no—
75C2×#11758194—41no—
76C2×#11758194C2×C414yescomplemented
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79#14519735—41no—
80#14519735—41no—
81#14519735—41no—
82#14519735—41no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×#11758196—21no—
88C2×#11758196—21no—
89C4⋊C4×D61—41no—
90C4⋊C4×D61—41no—
91C4⋊C4×D61—41no—
92C4⋊C4×D61—41no—
93C2×C22⋊Dic61—21no—
94C2×C22⋊Dic61—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C22⋊C4×D61—44no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61—21no—
104#14519711—41no—
105#14519710—41no—
106#14519710—41no—
107#14519709—41no—
108#14519708—41no—
109#14519708—41no—
110#14519689C2×C414yes—
111#14519689C2×C414yes—
112#14519689C2×C414yescomplemented
113#14519689C2×C414yescomplemented
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120C23×C4×C61C2311yescharacteristic
121C2×M16×C61—41no—
122C2×M16×C61—41no—
123C2×M16×C61C2×C414yescomplemented
124C22×C8×C61C2311yescharacteristic
125C22×C8×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132#107×C61—41no—
133#106×C61—41no—
134#95×C61—21no—
135#95×C61—21no—
136C24×C61C2×D411yescharacteristic
137C23×D61—22no—
138C23×D61—22no—
139C23×D61—41no—
140C23×D61—41no—
141C23×D61—41no—
142C23×D61—41no—
143C23×D61C4⋊C414yes—
144C23×D61C2×D411yescharacteristic
145C23×D61C2×D411yescharacteristic
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61C22×C412yes—
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×Q812yes—
157C22×C4×C61C2411yescharacteristic
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—41no—
163C22×Dic61—41no—
164C22×Dic61C4⋊C414yes—
165C22×Dic61C2×D411yescharacteristic
166C22×Dic61C2×D411yescharacteristic
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—21no—
174C2×C4×D61—21no—
175C2×C4×D61—44no—
176C2×C4×D61—44no—
177C2×C4×D61—44no—
178C2×C4×D61—44no—
179C2×C4×D61—41no—
180C2×C4×D61—41no—
181C2×C4×D61—41no—
182C2×C4×D61—41no—
183C2×C4×D61—42no—
184C2×C4×D61—42no—
185C2×C4×D61—42no—
186C2×C4×D61—42no—
187C2×C4×D61—42no—
188C2×C4×D61—42no—
189C2×C4×D61C4⋊C414yes—
190C2×C4×D61C4⋊C414yes—
191C2×C4×D61C22×C412yes—
192C2×C4×D61C22×C412yes—
193C2×C4×D61C2×Q812yes—
194C2×C4×D61C2×Q812yes—
195M16×C61—44no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61C22×C412yes—
201C2×C8×C61C22×C412yes—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C22⋊C4×C61—42no—
211C22⋊C4×C61—42no—
212C22⋊Dic61—42no—
213C22⋊Dic61—42no—
214#11758198—42no—
215#11758198—42no—
216#11758198—42no—
217#11758198—42no—
218#11758198—42no—
219#11758198—42no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228#11758196—42no—
229#11758196—42no—
230C4×Dic61—42no—
231C4×Dic61—42no—
232#11758194—44no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418C22×C412yes—
238C2×#92418C22×C412yes—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61C2×C4⋊C412yes—
246C23×C61C22×D411yescharacteristic
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—28no—
258C22×D61—44no—
259C22×D61—44no—
260C22×D61—44no—
261C22×D61—44no—
262C22×D61—44no—
263C22×D61—44no—
264C22×D61C2×C4⋊C412yes—
265C22×D61C2×C4⋊C412yes—
266C22×D61AGL(1,ℤ/8)12yes—
267C22×D61#13712yes—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61C2×C4⋊C412yes—
287C2×C4×C61C23×C411yescharacteristic
288C2×C4×C61C22×Q811yescharacteristic
289C2×C4×C61H(5,𝔽2)11yescharacteristic
290C2×C4×C61H(5,𝔽2)11yescharacteristic
291C2×C4×C61H(5,𝔽2)11yescharacteristic
292C2×C4×C61H(5,𝔽2)11yescharacteristic
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—44no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61C2×C4⋊C412yes—
311C2×Dic61C2×C4⋊C412yes—
312C4×D61—22no—
313C4×D61—22no—
314C4×D61—22no—
315C4×D61—22no—
316C4×D61—22no—
317C4×D61—22no—
318C4×D61—22no—
319C4×D61—22no—
320C4×D61—44no—
321C4×D61—44no—
322C4×D61—84no—
323C4×D61—84no—
324C8×C61—22no—
325C8×C61—22no—
326#92418—22no—
327#92418—22no—
328#21944—611nomaximal, Sylow
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61C22×C4⋊C411yescharacteristic
337C22×C61#53411yescharacteristic
338C22×C61#53411yescharacteristic
339C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
340C22×C61C2×#13711yescharacteristic
341C22×C61#57511yescharacteristic
342C22×C61#57511yescharacteristic
343C2×D61—22no—
344C2×D61—22no—
345C2×D61—22no—
346C2×D61—22no—
347C2×D61—22no—
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—22no—
351C2×D61—22no—
352C2×D61—416no—
353C2×D61—41no—
354C2×D61—41no—
355C2×D61—41no—
356C2×D61—41no—
357C2×D61#42814yes—
358C4×C61—22no—
359C4×C61—81no—
360C4×C61—81no—
361C4×C61—81no—
362C4×C61—81no—
363C4×C61#51811yescharacteristic
364C4×C61#51811yescharacteristic
365C4×C61#54311yescharacteristic
366C4×C61#54311yescharacteristic
367Dic61—22no—
368Dic61—22no—
369Dic61—81no—
370Dic61—81no—
371Dic61—81no—
372Dic61—81no—
373C2×#407—611no—
374#2280—611no—
375C2×#380—611no—
376#1854—611no—
377#1854—611no—
378#1854—611no—
379#1854—611no—
380#1853—611no—
381#1853—611no—
382#1852—611no—
383#1852—611no—
384#1809—611no—
385#1809—611no—
386#1809—611no—
387#1809D6111yescharacteristic, complemented
388C2×C61—42no—
389C2×C61#231511yescharacteristic
390C2×C61C2×#42811yescharacteristic
391C2×C61#291111yescharacteristic
392C2×C61#319411yescharacteristic
393C2×C61#319411yescharacteristic
394C2×C61#319611yescharacteristic
395C2×C61#319611yescharacteristic
396D61—24no—
397D61—42no—
398C24×C4—611no—
399C22×M16—611no—
400C22×M16C2×D6111yescharacteristic
401C2×#117—611no—
402C2×#117—611no—
403C22×C4⋊C4—611no—
404C22×C4⋊C4—611no—
405C22×C22⋊C4—1221no—
406C2×#107—611no—
407C2×#107—611no—
408C2×#107—611no—
409C2×#107C2×D6111yescharacteristic, complemented
410C2×#106—611no—
411C2×#106—611no—
412C2×#106—611no—
413C2×#106C2×D6111yescharacteristic, complemented
414#407—618no—
415C2×C22⋊C8—611no—
416C2×C22⋊C8—611no—
417C2×C22⋊C8—611no—
418C2×C22⋊C8—611no—
419#381—1221no—
420#380—611no—
421#380—611no—
422#380—611no—
423#380—611no—
424#380—611no—
425#380—611no—
426#380—1221no—
427#380—1221no—
428#380C2×D6111yescharacteristic
429#380C2×D6111yescharacteristic
430#379—1221no—
431C4×C22⋊C4—1221no—
432C4×C22⋊C4—1221no—
433C2×#95—1221no—
434#340—611no—
435#340—611no—
436#340—611no—
437#340—611no—
438#340—611no—
439#340—611no—
440#340C2×D6111yescharacteristic, complemented
441#340C2×D6111yescharacteristic, complemented
442C61#2194411yescharacteristic, complemented, Sylow
443C25—611no—
444C23×C4—611no—
445C23×C4—611no—
446C23×C4—611no—
447C23×C4—614no—
448C23×C4—611no—
449C23×C4—611no—
450C23×C4—614no—
451C23×C4—1221no—
452C23×C4—1221no—
453C23×C4—2441no—
454C23×C4—2441no—
455C23×C4—2441no—
456C23×C4—2441no—
457C23×C4C22×D6111yescharacteristic
458C2×M16—41no—
459C2×M16—41no—
460C2×M16—614no—
461C2×M16—2441no—
462C2×M16—2441no—
463C2×M16C4×D6114yescomplemented
464C22×C8—611no—
465C22×C8—611no—
466C22×C8C22×D6111yescharacteristic
467C22×C8C22×D6111yescharacteristic
468#117—2441no—
469#117—2441no—
470#117—2441no—
471#117—2441no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—611no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—1221no—
477C2×C4⋊C4—1221no—
478C2×C4⋊C4—2441no—
479C2×C4⋊C4—2441no—
480C2×C4⋊C4—2441no—
481C2×C4⋊C4—2441no—
482C2×C4⋊C4C22×D6111yescharacteristic
483C2×C4⋊C4C22×D6111yescharacteristic
484C2×C4⋊C4C22×D6111yescharacteristic
485C2×C4⋊C4C22×D6111yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4—1221no—
490C2×C22⋊C4—1221no—
491C2×C22⋊C4—1221no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—2444no—
497C2×C42—1221no—
498C2×C42—1221no—
499#107—41no—
500#107—2441no—
501#107—2441no—
502#107—2441no—
503#106—41no—
504#106—2441no—
505#106—2441no—
506#106—2441no—
507C22⋊C8—614no—
508C22⋊C8—614no—
509C22⋊C8—614no—
510C22⋊C8—614no—
511#95—21no—
512#95—21no—
513#95—1221no—
514#95—1221no—
515#95—1221no—
516#95—1221no—
517#95—1221no—
518#95—1221no—
519C24—611no—
520C24—611no—
521C24—614no—
522C24—1222no—
523C24—1222no—
524C24—2441no—
525C24—2441no—
526C24—2441no—
527C24—2441no—
528C24D4×D6111yescharacteristic
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—611no—
538C22×C4—611no—
539C22×C4—614no—
540C22×C4—612no—
541C22×C4—612no—
542C22×C4—612no—
543C22×C4—612no—
544C22×C4—614no—
545C22×C4—614no—
546C22×C4—1221no—
547C22×C4—1221no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—2444no—
559C22×C4—2444no—
560C22×C4—2444no—
561C22×C4—2444no—
562C22×C4—2441no—
563C22×C4—2441no—
564C22×C4—2441no—
565C22×C4—2441no—
566C22×C4—2442no—
567C22×C4—2442no—
568C22×C4—2442no—
569C22×C4—2442no—
570C22×C4—2442no—
571C22×C4—2442no—
572C22×C4—2441no—
573C22×C4—2441no—
574C22×C4C2×C4×D6112yes—
575C22×C4D4×D6111yescharacteristic
576C22×C4Q8×D6112yes—
577C22×C4C23×D6111yescharacteristic
578M16—44no—
579M16—2444no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—612no—
585C2×C8—612no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8C2×C4×D6112yes—
591C2×C8C2×C4×D6112yes—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—1221no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—2442no—
609C4⋊C4—2442no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—2442no—
613C22⋊C4—2442no—
614C22⋊C4—2442no—
615C22⋊C4—2442no—
616C22⋊C4—2442no—
617C22⋊C4—2442no—
618C22⋊C4—2442no—
619C22⋊C4—2442no—
620C42—2442no—
621C42—2442no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—612no—
629C23—612no—
630C23—612no—
631C23—612no—
632C23—1228no—
633C23—1221no—
634C23—1221no—
635C23—1221no—
636C23—1221no—
637C23—1221no—
638C23—1221no—
639C23—1221no—
640C23—1221no—
641C23—1221no—
642C23—1221no—
643C23—2444no—
644C23—2444no—
645C23—2444no—
646C23—2444no—
647C23—2444no—
648C23—2444no—
649C23C4⋊C4×D6112yes—
650C23C2×D4×D6111yescharacteristic
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—612no—
670C2×C4—612no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—4884no—
684C2×C4—4884no—
685C2×C4—2444no—
686C2×C4—2444no—
687C2×C4—2444no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4C4⋊C4×D6112yes—
701C2×C4C22×C4×D6111yescharacteristic
702C2×C4C2×Q8×D6111yescharacteristic
703C2×C4#1451982211yescharacteristic
704C2×C4#1451982211yescharacteristic
705C2×C4#1451982311yescharacteristic
706C2×C4#1451982311yescharacteristic
707C8—22no—
708C8—22no—
709C8—1222no—
710C8—1222no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—614no—
719C22—1222no—
720C22—1222no—
721C22—1222no—
722C22—1222no—
723C22—1222no—
724C22—1222no—
725C22—1222no—
726C22—1222no—
727C22—1222no—
728C22—24416no—
729C22—2441no—
730C22—2441no—
731C22—2441no—
732C22—2441no—
733C22C2×C4⋊C4×D6111yescharacteristic
734C22#1684032011yescharacteristic
735C22#1684032011yescharacteristic
736C22AGL(1,ℤ/8)×D6111yescharacteristic
737C22#137×D6111yescharacteristic
738C22#1684055811yescharacteristic
739C22#1684056111yescharacteristic
740C4—22no—
741C4—81no—
742C4—81no—
743C4—81no—
744C4—81no—
745C4—1222no—
746C4—1222no—
747C4—4881no—
748C4—4881no—
749C4—4881no—
750C4—4881no—
751C4#1684023511yescharacteristic
752C4#1684023611yescharacteristic
753C4#1684038711yescharacteristic
754C4#1684038711yescharacteristic
755C2—42no—
756C2—1224no—
757C2—2442no—
758C2#2144843211yescharacteristic
759C2#428×D6111yescharacteristic
760C2#2145440611yescharacteristic
761C2#2145662811yescharacteristic
762C2#2145663411yescharacteristic
763C2#2145664411yescharacteristic
764C2#2145665011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1809C2
socleC23×C61C22×D4
prime radicalC24×D61D4
cosocleC22×C4×C61C24
hypercenter#1809D61
hypocenterC61#21944
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
4. #21446021C2semidirect
5. #21446019C2semidirect
6. #21446017C2semidirect
7. #21446015C2semidirect
8. #21446013C2semidirect
9. #21446010C2semidirect
10. #21446008C2semidirect
11. #21446005C2semidirect
12. #21445852C2semidirect
13. #21445850C2semidirect
14. #21445850C2semidirect
15. C61×#1809C2semidirect
23. C2×#14519711C22semidirect
24. C2×#14519710C22semidirect
25. C2×#14519710C22semidirect
26. C2×#14519709C22semidirect
27. C2×#14519708C22semidirect
28. C2×#14519708C22semidirect
29. #16839725C4semidirect
47. #16839525C22semidirect
48. #16839525C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839524C22semidirect
54. C2×#107×C61C22semidirect
55. C2×#106×C61C22semidirect
58. C61×#340C22semidirect
59. C61×#340C22semidirect
76. C2×#11758194C2×C4semidirect
112. #14519689C2×C4semidirect
113. #14519689C2×C4semidirect
123. C2×M16×C61C2×C4semidirect
387. #1809D61semidirect
409. C2×#107C2×D61semidirect
413. C2×#106C2×D61semidirect
440. #340C2×D61semidirect
441. #340C2×D61semidirect
442. C61#21944semidirect
463. C2×M16C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168397252
#214482012
#380×D612
#214460212
#214460192
#214460172
#214460152
#214460132
#214460102
#214460082
#214460052
#214458522
#214458502
C61×#18092
#2194461