Finite Group Databasebeta

← D61×#2077 #29708837

Subgroups — D61×#2077 #29708837

Order 15616.

1270 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#106×D61C211yesmaximal, characteristic, complemented
2C2×C22⋊C8×D61C211yesmaximal, characteristic
3#380×D61C211yesmaximal, characteristic
4#380×D61C211yesmaximal, characteristic
5#21447258C211yesmaximal, characteristic, complemented
6#21447257C211yesmaximal, characteristic, complemented
7#21447256C211yesmaximal, characteristic, complemented
8#21447255C211yesmaximal, characteristic, complemented
9#21447254C211yesmaximal, characteristic, complemented
10#21447253C211yesmaximal, characteristic, complemented
11#21447252C211yesmaximal, characteristic, complemented
12#340×D61C211yesmaximal, characteristic, complemented
13#340×D61C211yesmaximal, characteristic, complemented
14#340×D61C211yesmaximal, characteristic, complemented
15C61×#2077C211yesmaximal, characteristic, complemented
16C23×C4×D61C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C2×C4⋊C4×D61C2211yescharacteristic
20C2×C4⋊C4×D61C2211yescharacteristic
21C2×C4⋊C4×D61C2211yescharacteristic
22C2×C4⋊C4×D61C2211yescharacteristic
23C2×C22⋊C4×D61—21no—
24C2×C22⋊C4×D61—21no—
25C2×#14519709C2211yescharacteristic, complemented
26C2×#14519708C2211yescharacteristic, complemented
27C2×#14519708C2211yescharacteristic, complemented
28#106×D61—24no—
29C2×C22⋊#92418C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C22⋊C8×D61—24no—
33#16839622C2211yescharacteristic
34#16839622C2211yescharacteristic
35#16839621—21no—
36#16839621—21no—
37#16839620—21no—
38#16839620—21no—
39#16839619C2211yescharacteristic
40#16839619C2211yescharacteristic
41#16839619C2211yescharacteristic
42#16839619C2211yescharacteristic
43#95×D61—21no—
44#95×D61—21no—
45#16839525C2211yescharacteristic, complemented
46#16839525C2211yescharacteristic, complemented
47#16839525C2211yescharacteristic, complemented
48#16839524C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53#16839524C2211yescharacteristic, complemented
54C2×#106×C61C2211yescharacteristic, complemented
55C2×C22⋊C8×C61C2211yescharacteristic
56C61×#380C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#340C2211yescharacteristic, complemented
59C61×#340C2211yescharacteristic, complemented
60C61×#340C2211yescharacteristic, complemented
61C24×D61D411yescharacteristic
62C23×Dic61D411yescharacteristic
63C22×C4×D61—22no—
64C22×C4×D61—22no—
65C22×C4×D61—22no—
66C22×C4×D61—22no—
67C22×C4×D61—22no—
68C22×C4×D61—22no—
69C22×C4×D61—21no—
70C22×C4×D61—21no—
71C22×C4×D61—21no—
72C22×C4×D61—21no—
73C22×C4×D61D411yescharacteristic
74C22×C4×D61D411yescharacteristic
75C22×C4×D61C2311yescharacteristic
76C22×C4×D61C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C2×C8×D61—22no—
80C2×C8×D61—22no—
81C2×C8×D61—22no—
82C2×C8×D61—22no—
83C2×C8×D61—22no—
84C2×C8×D61D414yes—
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×#11758196—21no—
90C2×#11758196—21no—
91C2×#11758196—21no—
92C2×#11758196—21no—
93C4⋊C4×D61—22no—
94C4⋊C4×D61—22no—
95C4⋊C4×D61—22no—
96C4⋊C4×D61—22no—
97C4⋊C4×D61—22no—
98C4⋊C4×D61—22no—
99C4⋊C4×D61—22no—
100C4⋊C4×D61—22no—
101C2×C22⋊Dic61—21no—
102C2×C22⋊Dic61—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C22⋊C4×D61—44no—
108C22⋊C4×D61—44no—
109#14519709—22no—
110#14519708—22no—
111#14519708—22no—
112C22⋊#92418—22no—
113#14519689—22no—
114#14519689—22no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120#14519684—21no—
121C23×C4×C61C2311yescharacteristic
122C22×C8×C61C2311yescharacteristic
123C22×C8×C61C2311yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130#106×C61—22no—
131C22⋊C8×C61—22no—
132#95×C61—21no—
133#95×C61—21no—
134C24×C61C2×D411yescharacteristic
135C23×D61—22no—
136C23×D61—22no—
137C23×D61—22no—
138C23×D61—22no—
139C23×D61—22no—
140C23×D61—22no—
141C23×D61SD1614yes—
142C23×D61C2×D411yescharacteristic
143C23×D61C2×D411yescharacteristic
144C22×C4×C61—21no—
145C22×C4×C61—21no—
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×C61C2×D411yescharacteristic
155C22×C4×C61C2411yescharacteristic
156C22×Dic61—22no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61C2×D411yescharacteristic
164C22×Dic61C2×D411yescharacteristic
165C2×C4×D61—22no—
166C2×C4×D61—22no—
167C2×C4×D61—22no—
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—22no—
175C2×C4×D61—22no—
176C2×C4×D61—22no—
177C2×C4×D61—44no—
178C2×C4×D61—44no—
179C2×C4×D61—44no—
180C2×C4×D61—44no—
181C2×C4×D61—42no—
182C2×C4×D61—42no—
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×D61—42no—
190C2×C4×D61—42no—
191C2×C4×D61—42no—
192C2×C4×D61—42no—
193C2×C4×D61C2×D412yes—
194C2×C4×D61#4112yes—
195C2×C4×D61#4112yes—
196C2×C4×D61#4112yes—
197C2×C4×D61#4112yes—
198C2×C4×D61#4112yes—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61C2×D412yes—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C22⋊C4×C61—42no—
214C22⋊C4×C61—42no—
215C22⋊Dic61—42no—
216C22⋊Dic61—42no—
217#11758198—42no—
218#11758198—42no—
219#11758198—42no—
220#11758198—42no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229#11758196—42no—
230#11758196—42no—
231#11758196—42no—
232#11758196—42no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418C2×D412yes—
239C8×D61—28no—
240C8×D61—44no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61C2×SD1612yes—
248C23×C61C22×D411yescharacteristic
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—28no—
256C22×D61—28no—
257C22×D61—28no—
258C22×D61—44no—
259C22×D61—44no—
260C22×D61—44no—
261C22×D61—44no—
262C22×D61#12112yes—
263C22×D61#12312yes—
264C22×D61#12312yes—
265C22×D61C2×SD1612yes—
266C22×D61C2×SD1612yes—
267C22×D61#13512yes—
268C22×D61AGL(1,ℤ/8)12yes—
269C22×D61#13712yes—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—41no—
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×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61C22×D411yescharacteristic
290C2×C4×C61C2×#4111yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×C4×C61C2×#4111yescharacteristic
294C2×C4×C61C2×#4111yescharacteristic
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—44no—
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×Dic61—41no—
311C2×Dic61#12112yes—
312C2×Dic61#12312yes—
313C2×Dic61#12312yes—
314C4×D61—44no—
315C4×D61—41no—
316C4×D61—41no—
317C4×D61—41no—
318C4×D61—41no—
319C4×D61—44no—
320C4×D61—84no—
321C4×D61—84no—
322C4×D61—84no—
323C4×D61—84no—
324C4×D61#12314yes—
325C4×D61#12414yes—
326C4×D61#12614yes—
327C4×D61#12614yes—
328C8×C61—22no—
329C8×C61—41no—
330#92418—22no—
331#92418—41no—
332C2×#2077—611nomaximal, Sylow
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61C2×#12111yescharacteristic
341C22×C61C2×#12311yescharacteristic
342C22×C61C2×#12311yescharacteristic
343C22×C61C22×SD1611yescharacteristic
344C22×C61C2×#13511yescharacteristic
345C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
346C22×C61C2×#13711yescharacteristic
347C2×D61—22no—
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—41no—
351C2×D61—41no—
352C2×D61—41no—
353C2×D61—41no—
354C2×D61—416no—
355C2×D61#39714yes—
356C2×D61#46514yes—
357C2×D61#46814yes—
358C2×D61#48114yes—
359C2×D61#48214yes—
360C2×D61#48314yes—
361C2×D61#48514yes—
362C4×C61—41no—
363C4×C61—81no—
364C4×C61—81no—
365C4×C61—81no—
366C4×C61—81no—
367C4×C61C2×#12311yescharacteristic
368C4×C61C2×#12411yescharacteristic
369C4×C61C2×#12611yescharacteristic
370C4×C61C2×#12611yescharacteristic
371Dic61—41no—
372Dic61—81no—
373Dic61—81no—
374Dic61—81no—
375Dic61—81no—
376Dic61#39714yes—
377C22×#106—611no—
378C22×C22⋊C8—611no—
379C2×#380—611no—
380C2×#380—611no—
381#2077—611no—
382#2077—611no—
383#2077—611no—
384#2077—611no—
385#2077—611no—
386#2077—611no—
387#2077—611no—
388#2077D6111yescharacteristic, direct product factor
389C2×#340—611no—
390C2×#340—611no—
391C2×#340—611no—
392C2×C61—42no—
393C2×C61C2×#39711yescharacteristic
394C2×C61C2×#46511yescharacteristic
395C2×C61C2×#46811yescharacteristic
396C2×C61C2×#48311yescharacteristic
397C2×C61C2×#48211yescharacteristic
398C2×C61C2×#48511yescharacteristic
399C2×C61C2×#48111yescharacteristic
400D61—42no—
401D61#207718yesdirect product factor
402C24×C4—611no—
403C23×C8—611no—
404C23×C8—611no—
405C22×C4⋊C4—611no—
406C22×C4⋊C4—611no—
407C22×C4⋊C4—611no—
408C22×C4⋊C4—611no—
409C22×C22⋊C4—1221no—
410C22×C22⋊C4—1221no—
411C2×#106—611no—
412C2×#106—611no—
413C2×#106—611no—
414C2×#106—1224no—
415C2×#106C2×D6111yescharacteristic, complemented
416C2×C22⋊C8—611no—
417C2×C22⋊C8—611no—
418C2×C22⋊C8—611no—
419C2×C22⋊C8—1224no—
420C2×C22⋊C8C2×D6111yescharacteristic
421#380—611no—
422#380—611no—
423#380—611no—
424#380—611no—
425#380—611no—
426#380—611no—
427#380—1221no—
428#380—1221no—
429#380—1221no—
430#380—1221no—
431#380C2×D6111yescharacteristic
432#380C2×D6111yescharacteristic
433C2×#95—1221no—
434C2×#95—1221no—
435#340—611no—
436#340—611no—
437#340—611no—
438#340—611no—
439#340—611no—
440#340—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444#340C2×D6111yescharacteristic, complemented
445#340C2×D6111yescharacteristic, complemented
446#340C2×D6111yescharacteristic, complemented
447C61C2×#207711yescharacteristic, complemented, Sylow
448C25—611no—
449C23×C4—611no—
450C23×C4—611no—
451C23×C4—611no—
452C23×C4—611no—
453C23×C4—611no—
454C23×C4—1222no—
455C23×C4—1222no—
456C23×C4—1222no—
457C23×C4—1222no—
458C23×C4—1222no—
459C23×C4—1222no—
460C23×C4—1221no—
461C23×C4—1221no—
462C23×C4—1221no—
463C23×C4—1221no—
464C23×C4C22×D6111yescharacteristic
465C22×C8—611no—
466C22×C8—614no—
467C22×C8—611no—
468C22×C8—1222no—
469C22×C8—1222no—
470C22×C8—1222no—
471C22×C8—1222no—
472C22×C8—1222no—
473C22×C8C22×D6111yescharacteristic
474C22×C8C22×D6111yescharacteristic
475C2×C4⋊C4—611no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—1222no—
480C2×C4⋊C4—1222no—
481C2×C4⋊C4—1222no—
482C2×C4⋊C4—1222no—
483C2×C4⋊C4—1222no—
484C2×C4⋊C4—1222no—
485C2×C4⋊C4—1222no—
486C2×C4⋊C4—1222no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4C22×D6111yescharacteristic
492C2×C4⋊C4C22×D6111yescharacteristic
493C2×C4⋊C4C22×D6111yescharacteristic
494C2×C4⋊C4C22×D6111yescharacteristic
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—2444no—
504C2×C22⋊C4—2444no—
505#106—22no—
506#106—1222no—
507#106—1222no—
508#106—1222no—
509C22⋊C8—22no—
510C22⋊C8—1222no—
511C22⋊C8—1222no—
512C22⋊C8—1222no—
513#95—21no—
514#95—21no—
515#95—1221no—
516#95—1221no—
517#95—1221no—
518#95—1221no—
519#95—1221no—
520#95—1221no—
521C24—611no—
522C24—611no—
523C24—614no—
524C24—1222no—
525C24—1222no—
526C24—1222no—
527C24—1222no—
528C24—1222no—
529C24—1222no—
530C24D4×D6111yescharacteristic
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—611no—
542C22×C4—612no—
543C22×C4—612no—
544C22×C4—612no—
545C22×C4—612no—
546C22×C4—612no—
547C22×C4—612no—
548C22×C4—611no—
549C22×C4—1222no—
550C22×C4—1222no—
551C22×C4—1222no—
552C22×C4—1222no—
553C22×C4—1222no—
554C22×C4—1222no—
555C22×C4—1222no—
556C22×C4—1222no—
557C22×C4—1222no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—2444no—
569C22×C4—2444no—
570C22×C4—2444no—
571C22×C4—2444no—
572C22×C4—2442no—
573C22×C4—2442no—
574C22×C4—2442no—
575C22×C4—2442no—
576C22×C4—2442no—
577C22×C4—2442no—
578C22×C4—2442no—
579C22×C4—2442no—
580C22×C4—2442no—
581C22×C4—2442no—
582C22×C4—2442no—
583C22×C4—2442no—
584C22×C4D4×D6111yescharacteristic
585C22×C4C23×D6111yescharacteristic
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—612no—
592C2×C8—1228no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—2444no—
599C2×C8D4×D6112yes—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—1221no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—1221no—
612C4⋊C4—1221no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—2442no—
617C4⋊C4—2442no—
618C4⋊C4—2442no—
619C4⋊C4—2442no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—2442no—
623C22⋊C4—2442no—
624C22⋊C4—2442no—
625C22⋊C4—2442no—
626C22⋊C4—2442no—
627C22⋊C4—2442no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—612no—
635C23—612no—
636C23—612no—
637C23—612no—
638C23—612no—
639C23—612no—
640C23—612no—
641C23—612no—
642C23—1228no—
643C23—1228no—
644C23—1228no—
645C23—1221no—
646C23—1221no—
647C23—1221no—
648C23—1221no—
649C23—1221no—
650C23—1221no—
651C23—2444no—
652C23—2444no—
653C23—2444no—
654C23—2444no—
655C23SD16×D6112yes—
656C23C2×D4×D6111yescharacteristic
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
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—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—612no—
677C2×C4—612no—
678C2×C4—612no—
679C2×C4—614no—
680C2×C4—614no—
681C2×C4—614no—
682C2×C4—614no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—4884no—
687C2×C4—4884no—
688C2×C4—4884no—
689C2×C4—4884no—
690C2×C4—2444no—
691C2×C4—2444no—
692C2×C4—2444no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4C2×D4×D6111yescharacteristic
710C2×C4#41×D6111yescharacteristic
711C2×C4#41×D6111yescharacteristic
712C2×C4#41×D6111yescharacteristic
713C2×C4#41×D6111yescharacteristic
714C2×C4#41×D6111yescharacteristic
715C8—22no—
716C8—41no—
717C8—1222no—
718C8—2441no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—614no—
727C22—614no—
728C22—614no—
729C22—614no—
730C22—614no—
731C22—614no—
732C22—614no—
733C22—1222no—
734C22—1222no—
735C22—1222no—
736C22—24416no—
737C22—2441no—
738C22—2441no—
739C22—2441no—
740C22—2441no—
741C22#121×D6111yescharacteristic
742C22#123×D6111yescharacteristic
743C22#123×D6111yescharacteristic
744C22C2×SD16×D6111yescharacteristic
745C22#135×D6111yescharacteristic
746C22AGL(1,ℤ/8)×D6111yescharacteristic
747C22#137×D6111yescharacteristic
748C4—41no—
749C4—81no—
750C4—81no—
751C4—81no—
752C4—81no—
753C4—614no—
754C4—4881no—
755C4—4881no—
756C4—4881no—
757C4—4881no—
758C4—2441no—
759C4#123×D6111yescharacteristic
760C4#124×D6111yescharacteristic
761C4#126×D6111yescharacteristic
762C4#126×D6111yescharacteristic
763C2—42no—
764C2—618no—
765C2—2442no—
766C2#397×D6111yescharacteristic
767C2#465×D6111yescharacteristic
768C2#468×D6111yescharacteristic
769C2#483×D6111yescharacteristic
770C2#482×D6111yescharacteristic
771C2#485×D6111yescharacteristic
772C2#481×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2077C2
socleC23×C61C22×D4
prime radicalC24×D61D4
hypercenter#2077D61
hypocenterC61C2×#2077
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2077

Complements

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

NH ≅ G/Ntype
1. C2×#106×D61C2semidirect
5. #21447258C2semidirect
6. #21447257C2semidirect
7. #21447256C2semidirect
8. #21447255C2semidirect
9. #21447254C2semidirect
10. #21447253C2semidirect
11. #21447252C2semidirect
12. #340×D61C2semidirect
13. #340×D61C2semidirect
14. #340×D61C2semidirect
15. C61×#2077C2semidirect
25. C2×#14519709C22semidirect
26. C2×#14519708C22semidirect
27. C2×#14519708C22semidirect
45. #16839525C22semidirect
46. #16839525C22semidirect
47. #16839525C22semidirect
48. #16839524C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839524C22semidirect
53. #16839524C22semidirect
54. C2×#106×C61C22semidirect
58. C61×#340C22semidirect
59. C61×#340C22semidirect
60. C61×#340C22semidirect
388. #2077D61direct (N × H)
401. D61#2077direct (N × H)
415. C2×#106C2×D61semidirect
444. #340C2×D61semidirect
445. #340C2×D61semidirect
446. #340C2×D61semidirect
447. C61C2×#2077semidirect

Maximal subgroups

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

subgroupindex
C2×#106×D612
C2×C22⋊C8×D612
#380×D612
#214472582
#214472572
#214472562
#214472552
#214472542
#214472532
#214472522
#340×D612
C61×#20772
C2×#207761