Finite Group Databasebeta

← D61×#1854 #29680727

Subgroups — D61×#1854 #29680727

Order 15616.

1662 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D61C211yesmaximal, characteristic
2C2×#107×D61C211yesmaximal, characteristic, complemented
3C2×#106×D61C211yesmaximal, characteristic, complemented
4C2×C22⋊C8×D61C211yesmaximal, characteristic
5#380×D61C211yesmaximal, characteristic
6#21446021C211yesmaximal, characteristic, complemented
7#21446020C211yesmaximal, characteristic, complemented
8#21446019C211yesmaximal, characteristic, complemented
9#21446018C211yesmaximal, characteristic, complemented
10#21446017C211yesmaximal, characteristic, complemented
11#21446016C211yesmaximal, characteristic, complemented
12#21446015C211yesmaximal, characteristic, complemented
13#340×D61C211yesmaximal, characteristic, complemented
14#340×D61C211yesmaximal, characteristic, complemented
15C61×#1854C211yesmaximal, characteristic, complemented
16C23×C4×D61C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C2×#14519736C2211yescharacteristic
20C2×#14519735C2211yescharacteristic
21C2×#14519735C2211yescharacteristic
22C2×#14519734—21no—
23C2×#14519733—21no—
24#117×D61—24no—
25#117×D61—24no—
26C2×C4⋊C4×D61C2211yescharacteristic
27C2×C4⋊C4×D61C2211yescharacteristic
28C2×C4⋊C4×D61C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30C2×C22⋊C4×D61—21no—
31C2×C22⋊C4×D61—21no—
32C2×C42×D61—21no—
33C2×#14519711C2211yescharacteristic, complemented
34C2×#14519710C2211yescharacteristic, complemented
35C2×#14519710C2211yescharacteristic, complemented
36#107×D61—24no—
37C2×#14519709C2211yescharacteristic, complemented
38C2×#14519708C2211yescharacteristic, complemented
39C2×#14519708C2211yescharacteristic, complemented
40#106×D61—24no—
41C2×C22⋊#92418C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C22⋊C8×D61C418yescomplemented
45#16839622C2211yescharacteristic
46#16839621—21no—
47#16839620—21no—
48#16839619C2211yescharacteristic
49#16839619C2211yescharacteristic
50#95×D61—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×D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61C2×C414yes—
75C22×C4×D61D411yescharacteristic
76C22×C4×D61D411yescharacteristic
77C22×C4×D61Q814yes—
78C22×C4×D61C2311yescharacteristic
79C22×C4×D61C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C2×C8×D61—22no—
83C2×C8×D61—22no—
84C2×C8×D61—22no—
85C2×C8×D61—22no—
86C2×C8×D61C2×C414yes—
87C2×C8×D61C2×C414yes—
88#14519736—22no—
89#14519736—22no—
90#14519735—22no—
91#14519735—22no—
92#14519735—22no—
93#14519735—22no—
94#14519734—28no—
95#14519733—28no—
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×#11758196—21no—
104C4⋊C4×D61—22no—
105C4⋊C4×D61—22no—
106C4⋊C4×D61—22no—
107C4⋊C4×D61—22no—
108C4⋊C4×D61—22no—
109C4⋊C4×D61—22no—
110C4⋊C4×D61D414yes—
111C4⋊C4×D61D414yes—
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C22⋊C4×D61—28no—
119C22⋊C4×D61—44no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61—21no—
123C42×D61—28no—
124#14519711—22no—
125#14519710—22no—
126#14519710—22no—
127#14519709—22no—
128#14519708—22no—
129#14519708—22no—
130C22⋊#92418C2×C414yescomplemented
131#14519689C2×C414yescomplemented
132#14519689C2×C414yescomplemented
133#14519684—21no—
134#14519684—21no—
135#14519684—21no—
136C23×C4×C61C2311yescharacteristic
137C22×C8×C61C2311yescharacteristic
138C22×C8×C61C2311yescharacteristic
139#117×C61—22no—
140#117×C61—22no—
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C22⋊C4×C61—21no—
146C2×C22⋊C4×C61—21no—
147C2×C42×C61—21no—
148#107×C61—22no—
149#106×C61—22no—
150C22⋊C8×C61C2×C414yescomplemented
151#95×C61—21no—
152C24×C61C2×D411yescharacteristic
153C23×D61—22no—
154C23×D61—22no—
155C23×D61—22no—
156C23×D61—22no—
157C23×D61—22no—
158C23×D61—22no—
159C23×D61C4⋊C414yes—
160C23×D61C2×D411yescharacteristic
161C23×D61C2×D411yescharacteristic
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×C61—21no—
170C22×C4×C61C22×C412yes—
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2×Q812yes—
173C22×C4×C61C2411yescharacteristic
174C22×Dic61—22no—
175C22×Dic61—22no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61C4⋊C414yes—
181C22×Dic61C2×D411yescharacteristic
182C22×Dic61C2×D411yescharacteristic
183C2×C4×D61—22no—
184C2×C4×D61—22no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—22no—
190C2×C4×D61—22no—
191C2×C4×D61—28no—
192C2×C4×D61—28no—
193C2×C4×D61—28no—
194C2×C4×D61—28no—
195C2×C4×D61—24no—
196C2×C4×D61—24no—
197C2×C4×D61—42no—
198C2×C4×D61—42no—
199C2×C4×D61—42no—
200C2×C4×D61—42no—
201C2×C4×D61—42no—
202C2×C4×D61—42no—
203C2×C4×D61—42no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61—42no—
207C2×C4×D61C4⋊C414yes—
208C2×C4×D61C4⋊C414yes—
209C2×C4×D61C22×C412yes—
210C2×C4×D61C22×C412yes—
211C2×C4×D61C2×D412yes—
212C2×C4×D61C2×D412yes—
213C2×C4×D61C2×Q812yes—
214C2×C4×D61C2×Q812yes—
215C2×C4×D61#4112yes—
216C2×C4×D61#4112yes—
217C2×C8×C61—21no—
218C2×C8×C61—21no—
219C2×C8×C61—21no—
220C2×C8×C61—21no—
221C2×C8×C61C22×C412yes—
222C2×C8×C61C22×C412yes—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61C2×D412yes—
230C4⋊C4×C61C2×D412yes—
231C22⋊C4×C61—24no—
232C22⋊C4×C61—42no—
233C42×C61—24no—
234C22⋊Dic61—24no—
235C22⋊Dic61—42no—
236#11758198—24no—
237#11758198—24no—
238#11758198—42no—
239#11758198—42no—
240C4⋊Dic61—21no—
241C4⋊Dic61—21no—
242C4⋊Dic61—21no—
243C4⋊Dic61—21no—
244C4⋊Dic61—21no—
245C4⋊Dic61—21no—
246C4⋊Dic61C2×D412yes—
247C4⋊Dic61C2×D412yes—
248#11758196—24no—
249#11758196—24no—
250#11758196—42no—
251#11758196—42no—
252C4×Dic61—24no—
253C4×Dic61—24no—
254C4×Dic61—24no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418C22×C412yes—
260C2×#92418C22×C412yes—
261C8×D61—28no—
262C8×D61—28no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61C2×C4⋊C412yes—
270C23×C61C22×D411yescharacteristic
271C22×D61—21no—
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—28no—
278C22×D61—28no—
279C22×D61—28no—
280C22×D61—44no—
281C22×D61—44no—
282C22×D61—44no—
283C22×D61—44no—
284C22×D61C2×C4⋊C412yes—
285C22×D61C2×C4⋊C412yes—
286C22×D61#12012yes—
287C22×D61#12312yes—
288C22×D61#13512yes—
289C22×D61#13512yes—
290C22×D61AGL(1,ℤ/8)12yes—
291C22×D61#13712yes—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61C2×C4⋊C412yes—
311C2×C4×C61C23×C411yescharacteristic
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C22×D411yescharacteristic
314C2×C4×C61C22×Q811yescharacteristic
315C2×C4×C61C2×#4111yescharacteristic
316C2×C4×C61C2×#4111yescharacteristic
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—28no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61C2×C4⋊C412yes—
333C2×Dic61C2×C4⋊C412yes—
334C2×Dic61#12012yes—
335C2×Dic61#12312yes—
336C4×D61—28no—
337C4×D61—22no—
338C4×D61—22no—
339C4×D61—22no—
340C4×D61—22no—
341C4×D61—28no—
342C4×D61—48no—
343C4×D61—48no—
344C4×D61—84no—
345C4×D61—84no—
346C4×D61C4×D414yes—
347C4×D61C4×D414yes—
348C4×D61C22⋊Q814yes—
349C4×D61C22⋊Q814yes—
350C8×C61—22no—
351C8×C61—22no—
352#92418—22no—
353#92418—22no—
354C2×#1854—611nomaximal, Sylow
355C22×C61—22no—
356C22×C61—22no—
357C22×C61—22no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61C22×C4⋊C411yescharacteristic
363C22×C61C2×#12011yescharacteristic
364C22×C61C2×#12311yescharacteristic
365C22×C61C2×#13511yescharacteristic
366C22×C61C2×#13511yescharacteristic
367C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
368C22×C61C2×#13711yescharacteristic
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—22no—
372C2×D61—41no—
373C2×D61—41no—
374C2×D61—41no—
375C2×D61—41no—
376C2×D61—416no—
377C2×D61#38514yes—
378C2×D61#42714yes—
379C2×D61#42814yes—
380C2×D61#44914yes—
381C2×D61#45214yes—
382C2×D61#48214yes—
383C2×D61#48514yes—
384C4×C61—22no—
385C4×C61—42no—
386C4×C61—42no—
387C4×C61—81no—
388C4×C61—81no—
389C4×C61C2×C4×D411yescharacteristic
390C4×C61C2×C4×D411yescharacteristic
391C4×C61C2×C22⋊Q811yescharacteristic
392C4×C61C2×C22⋊Q811yescharacteristic
393Dic61—22no—
394Dic61—42no—
395Dic61—42no—
396Dic61—81no—
397Dic61—81no—
398Dic61#38514yes—
399C22×#117—611no—
400C22×#107—611no—
401C22×#106—611no—
402C22×C22⋊C8—611no—
403C2×#380—611no—
404#1854—611no—
405#1854—611no—
406#1854—611no—
407#1854—611no—
408#1854—611no—
409#1854—611no—
410#1854—611no—
411#1854D6111yescharacteristic, direct product factor
412C2×#340—611no—
413C2×#340—611no—
414C2×C61—42no—
415C2×C61C2×#38511yescharacteristic
416C2×C61C2×#42711yescharacteristic
417C2×C61C2×#42811yescharacteristic
418C2×C61C2×#44911yescharacteristic
419C2×C61C2×#45211yescharacteristic
420C2×C61C2×#48211yescharacteristic
421C2×C61C2×#48511yescharacteristic
422D61—42no—
423D61#185418yesdirect product factor
424C24×C4—611no—
425C23×C8—611no—
426C23×C8—611no—
427C2×#117—611no—
428C2×#117—611no—
429C2×#117—611no—
430C2×#117—1221no—
431C2×#117—1221no—
432C2×#117—1224no—
433C2×#117—1224no—
434C2×#117C2×D6111yescharacteristic
435C22×C4⋊C4—611no—
436C22×C4⋊C4—611no—
437C22×C4⋊C4—611no—
438C22×C4⋊C4—611no—
439C22×C22⋊C4—1221no—
440C22×C22⋊C4—1221no—
441C22×C42—1221no—
442C2×#107—611no—
443C2×#107—611no—
444C2×#107—611no—
445C2×#107—1224no—
446C2×#107C2×D6111yescharacteristic, complemented
447C2×#106—611no—
448C2×#106—611no—
449C2×#106—611no—
450C2×#106—1224no—
451C2×#106C2×D6111yescharacteristic, complemented
452C2×C22⋊C8—611no—
453C2×C22⋊C8—611no—
454C2×C22⋊C8—611no—
455C2×C22⋊C8—618no—
456C2×C22⋊C8C2×D6111yescharacteristic
457#380—611no—
458#380—611no—
459#380—611no—
460#380—1221no—
461#380—1221no—
462#380C2×D6111yescharacteristic
463C2×#95—1221no—
464#340—611no—
465#340—611no—
466#340—611no—
467#340—611no—
468#340—611no—
469#340—611no—
470#340C2×D6111yescharacteristic, complemented
471#340C2×D6111yescharacteristic, complemented
472C61C2×#185411yescharacteristic, complemented, Sylow
473C25—611no—
474C23×C4—611no—
475C23×C4—611no—
476C23×C4—614no—
477C23×C4—611no—
478C23×C4—611no—
479C23×C4—614no—
480C23×C4—611no—
481C23×C4—1222no—
482C23×C4—1222no—
483C23×C4—1222no—
484C23×C4—1222no—
485C23×C4—1221no—
486C23×C4—1221no—
487C23×C4—1221no—
488C23×C4—1221no—
489C23×C4C22×D6111yescharacteristic
490C22×C8—611no—
491C22×C8—611no—
492C22×C8—614no—
493C22×C8—614no—
494C22×C8—1222no—
495C22×C8—1222no—
496C22×C8—1222no—
497C22×C8—1222no—
498C22×C8C22×D6111yescharacteristic
499C22×C8C22×D6111yescharacteristic
500#117—22no—
501#117—22no—
502#117—1228no—
503#117—1228no—
504#117—1222no—
505#117—1222no—
506#117—1222no—
507#117—1222no—
508#117—1222no—
509#117—1222no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—614no—
513C2×C4⋊C4—614no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—1222no—
517C2×C4⋊C4—1222no—
518C2×C4⋊C4—1222no—
519C2×C4⋊C4—1222no—
520C2×C4⋊C4—1222no—
521C2×C4⋊C4—1222no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4C22×D6111yescharacteristic
527C2×C4⋊C4C22×D6111yescharacteristic
528C2×C4⋊C4C22×D6111yescharacteristic
529C2×C4⋊C4C22×D6111yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—1228no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—2444no—
540C2×C42—21no—
541C2×C42—1228no—
542C2×C42—1221no—
543C2×C42—1221no—
544C2×C42—1221no—
545#107—22no—
546#107—1222no—
547#107—1222no—
548#107—1222no—
549#106—22no—
550#106—1222no—
551#106—1222no—
552#106—1222no—
553C22⋊C8—614no—
554C22⋊C8—614no—
555C22⋊C8—614no—
556C22⋊C8C4×D6114yescomplemented
557#95—21no—
558#95—1221no—
559#95—1221no—
560#95—1221no—
561C24—611no—
562C24—611no—
563C24—614no—
564C24—1222no—
565C24—1222no—
566C24—1222no—
567C24—1222no—
568C24—1222no—
569C24—1222no—
570C24D4×D6111yescharacteristic
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—611no—
580C22×C4—612no—
581C22×C4—612no—
582C22×C4—612no—
583C22×C4—612no—
584C22×C4—612no—
585C22×C4—612no—
586C22×C4—611no—
587C22×C4—614no—
588C22×C4—612no—
589C22×C4—612no—
590C22×C4—614no—
591C22×C4—614no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4—1228no—
595C22×C4—1228no—
596C22×C4—1228no—
597C22×C4—1228no—
598C22×C4—1222no—
599C22×C4—1222no—
600C22×C4—1224no—
601C22×C4—1224no—
602C22×C4—1222no—
603C22×C4—1222no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—2442no—
613C22×C4—2442no—
614C22×C4—2442no—
615C22×C4—2442no—
616C22×C4—2442no—
617C22×C4—2442no—
618C22×C4—2442no—
619C22×C4—2442no—
620C22×C4—2442no—
621C22×C4—2442no—
622C22×C4C2×C4×D6112yes—
623C22×C4D4×D6111yescharacteristic
624C22×C4Q8×D6112yes—
625C22×C4C23×D6111yescharacteristic
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—612no—
631C2×C8—612no—
632C2×C8—1228no—
633C2×C8—1228no—
634C2×C8—1221no—
635C2×C8—1221no—
636C2×C8—1221no—
637C2×C8—1221no—
638C2×C8C2×C4×D6112yes—
639C2×C8C2×C4×D6112yes—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—612no—
647C4⋊C4—612no—
648C4⋊C4—1224no—
649C4⋊C4—1224no—
650C4⋊C4—1221no—
651C4⋊C4—1221no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1221no—
656C4⋊C4—2442no—
657C4⋊C4—2442no—
658C4⋊C4D4×D6112yes—
659C4⋊C4D4×D6112yes—
660C22⋊C4—24no—
661C22⋊C4—42no—
662C22⋊C4—1224no—
663C22⋊C4—1224no—
664C22⋊C4—1224no—
665C22⋊C4—2442no—
666C22⋊C4—2442no—
667C22⋊C4—2442no—
668C42—24no—
669C42—1224no—
670C42—1224no—
671C42—1224no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—612no—
679C23—612no—
680C23—612no—
681C23—612no—
682C23—612no—
683C23—612no—
684C23—612no—
685C23—612no—
686C23—1228no—
687C23—1228no—
688C23—1228no—
689C23—1221no—
690C23—1221no—
691C23—1221no—
692C23—1221no—
693C23—1221no—
694C23—1221no—
695C23—2444no—
696C23—2444no—
697C23—2444no—
698C23—2444no—
699C23C4⋊C4×D6112yes—
700C23C2×D4×D6111yescharacteristic
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—612no—
720C2×C4—612no—
721C2×C4—612no—
722C2×C4—614no—
723C2×C4—614no—
724C2×C4—614no—
725C2×C4—614no—
726C2×C4—612no—
727C2×C4—1228no—
728C2×C4—1228no—
729C2×C4—1228no—
730C2×C4—1221no—
731C2×C4—1221no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—4884no—
739C2×C4—4884no—
740C2×C4—2448no—
741C2×C4—2448no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4C4⋊C4×D6112yes—
753C2×C4C22×C4×D6111yescharacteristic
754C2×C4C2×D4×D6111yescharacteristic
755C2×C4C2×D4×D6111yescharacteristic
756C2×C4C2×Q8×D6111yescharacteristic
757C2×C4#41×D6111yescharacteristic
758C2×C4#41×D6111yescharacteristic
759C8—22no—
760C8—22no—
761C8—1222no—
762C8—1222no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—614no—
771C22—614no—
772C22—614no—
773C22—614no—
774C22—614no—
775C22—614no—
776C22—614no—
777C22—1222no—
778C22—1222no—
779C22—1222no—
780C22—24416no—
781C22—2441no—
782C22—2441no—
783C22—2441no—
784C22—2441no—
785C22C2×C4⋊C4×D6111yescharacteristic
786C22#120×D6111yescharacteristic
787C22#123×D6111yescharacteristic
788C22#135×D6111yescharacteristic
789C22#135×D6111yescharacteristic
790C22AGL(1,ℤ/8)×D6111yescharacteristic
791C22#137×D6111yescharacteristic
792C4—22no—
793C4—42no—
794C4—42no—
795C4—81no—
796C4—81no—
797C4—614no—
798C4—1222no—
799C4—4881no—
800C4—4881no—
801C4—2442no—
802C4—2442no—
803C4C4×D4×D6111yescharacteristic
804C4C4×D4×D6111yescharacteristic
805C4C22⋊Q8×D6111yescharacteristic
806C4C22⋊Q8×D6111yescharacteristic
807C2—42no—
808C2—618no—
809C2—2442no—
810C2#385×D6111yescharacteristic
811C2#427×D6111yescharacteristic
812C2#428×D6111yescharacteristic
813C2#449×D6111yescharacteristic
814C2#452×D6111yescharacteristic
815C2#482×D6111yescharacteristic
816C2#485×D6111yescharacteristic
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
hypocenterC61C2×#1854
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×#107×D61C2semidirect
3. C2×#106×D61C2semidirect
6. #21446021C2semidirect
7. #21446020C2semidirect
8. #21446019C2semidirect
9. #21446018C2semidirect
10. #21446017C2semidirect
11. #21446016C2semidirect
12. #21446015C2semidirect
13. #340×D61C2semidirect
14. #340×D61C2semidirect
15. C61×#1854C2semidirect
33. C2×#14519711C22semidirect
34. C2×#14519710C22semidirect
35. C2×#14519710C22semidirect
37. C2×#14519709C22semidirect
38. C2×#14519708C22semidirect
39. C2×#14519708C22semidirect
44. 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
130. C22⋊#92418C2×C4semidirect
131. #14519689C2×C4semidirect
132. #14519689C2×C4semidirect
150. C22⋊C8×C61C2×C4semidirect
411. #1854D61direct (N × H)
423. D61#1854direct (N × H)
446. C2×#107C2×D61semidirect
451. C2×#106C2×D61semidirect
470. #340C2×D61semidirect
471. #340C2×D61semidirect
472. C61C2×#1854semidirect
556. 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×#107×D612
C2×#106×D612
C2×C22⋊C8×D612
#380×D612
#214460212
#214460202
#214460192
#214460182
#214460172
#214460162
#214460152
#340×D612
C61×#18542
C2×#185461