Finite Group Databasebeta

← #29681266

Subgroups — #29681266

Order 15616.

1778 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840335C211yesmaximal, characteristic
2C2×#16840242C211yesmaximal, characteristic
3C2×#16839769C211yesmaximal, characteristic, complemented
4C2×#103×D61C211yesmaximal, characteristic, complemented
5C2×#16839727C211yesmaximal, characteristic
6#21446131C211yesmaximal, characteristic, complemented
7#21446130C211yesmaximal, characteristic, complemented
8#21446128C211yesmaximal, characteristic, complemented
9#21446127C211yesmaximal, characteristic, complemented
10#21446125C211yesmaximal, characteristic, complemented
11#21446124C211yesmaximal, characteristic, complemented
12#21446123C211yesmaximal, characteristic, complemented
13#21445537C211yesmaximal, characteristic, complemented
14#21445534C211yesmaximal, characteristic, complemented
15C61×#1873C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840335—24no—
21#16840335C418yescomplemented
22C2×#14519776—21no—
23C2×#14519763—21no—
24C2×#14519762—21no—
25C2×#14519759—21no—
26C2×#14519757C2211yescharacteristic
27C2×#14519756C2211yescharacteristic
28C2×#14519753C2211yescharacteristic
29#16840242—24no—
30#16840242—24no—
31C2×C4×Dic122—21no—
32C2×C4×D244—21no—
33C2×#14519737—21no—
34C2×#14519737—21no—
35C2×#14519735C2211yescharacteristic
36C2×#14519735C2211yescharacteristic
37C2×#14519735C2211yescharacteristic
38C22×C4⋊Dic61C2211yescharacteristic
39C2×C4⋊C4×D61C2211yescharacteristic
40C2×C4⋊C4×D61C2211yescharacteristic
41#16839769—24no—
42C2×#14519702C2211yescharacteristic
43C2×#14519702C2211yescharacteristic
44C2×#14519701C2211yescharacteristic
45C2×#14519701C2211yescharacteristic
46C2×#14519700C2211yescharacteristic
47C2×#14519700C2211yescharacteristic
48#103×D61—24no—
49#16839727—24no—
50C2×C22⋊#92418C2211yescharacteristic
51C2×#14519689C2211yescharacteristic
52C2×#14519689C2211yescharacteristic
53#16839525C2211yescharacteristic
54#16839525C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57#16839524C2211yescharacteristic
58#16839524C2211yescharacteristic
59C2×C22⋊Q8×C61C2211yescharacteristic
60C2×#117×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×#103×C61C2211yescharacteristic
63C2×C22⋊C8×C61C2211yescharacteristic
64C61×#340C2211yescharacteristic
65C61×#340C2211yescharacteristic
66C2×#11758222—22no—
67C2×#11758222—22no—
68C2×#11758222—22no—
69C2×#11758222—22no—
70C2×#11758222C2×C414yes—
71C2×#11758222D414yes—
72C22×Dic122—21no—
73C22×Dic122D411yescharacteristic
74C22×Dic122C2311yescharacteristic
75C2×Q8×D61—22no—
76C2×Q8×D61—22no—
77C2×Q8×D61—22no—
78C2×Q8×D61—22no—
79C2×Q8×D61—22no—
80C2×Q8×D61C2×C414yescomplemented
81C22×D244D411yescharacteristic
82C22×C22⋊D61D411yescharacteristic
83C22×C22⋊D61D411yescharacteristic
84C23×Dic61—21no—
85C22×C4×D61—21no—
86C22×C4×D61—21no—
87C22×C4×D61—21no—
88C22×C4×D61C2311yescharacteristic
89C22×C4×D61C2311yescharacteristic
90C2×#11758189—22no—
91C2×#11758189—22no—
92C2×#11758189—22no—
93C22×#92418C2311yescharacteristic
94C22×#92418C2311yescharacteristic
95C2×C8×D61—22no—
96C2×C8×D61—22no—
97C2×C8×D61—22no—
98#14519776—28no—
99#14519763—28no—
100#14519762—28no—
101#14519759—28no—
102#14519757—22no—
103#14519757C2×C414yescomplemented
104#14519756—22no—
105#14519756C2×C414yescomplemented
106#14519753—22no—
107#14519753C2×C414yescomplemented
108C4×Dic122—28no—
109C4×D244—28no—
110#14519737—28no—
111#14519737—28no—
112#14519735—22no—
113#14519735—22no—
114#14519735—22no—
115#14519735—22no—
116#14519735C2×C414yescomplemented
117#14519735D414yes—
118C2×C4⋊Dic61—21no—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61—22no—
121C2×C4⋊Dic61—22no—
122C2×C4⋊Dic61C2311yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C4⋊C4×D61—22no—
130C4⋊C4×D61—22no—
131C4⋊C4×D61—22no—
132C4⋊C4×D61D414yes—
133C2×C22⋊Dic61—21no—
134C2×#11758198—21no—
135C2×#11758198—21no—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61—21no—
142#14519702—22no—
143#14519702—22no—
144#14519701—22no—
145#14519701—22no—
146#14519700—22no—
147#14519700—22no—
148C22⋊#92418—22no—
149#14519689—22no—
150#14519689—22no—
151C22×Q8×C61C2311yescharacteristic
152C23×C4×C61C2311yescharacteristic
153C22×C8×C61C2311yescharacteristic
154C22×C8×C61C2311yescharacteristic
155C22⋊Q8×C61—22no—
156C22⋊Q8×C61C2×C414yescomplemented
157#117×C61—22no—
158#117×C61—22no—
159C2×C4⋊C4×C61—21no—
160C2×C4⋊C4×C61C2311yescharacteristic
161C2×C4⋊C4×C61C2311yescharacteristic
162C2×C4⋊C4×C61C2311yescharacteristic
163C2×C22⋊C4×C61—21no—
164C2×C22⋊C4×C61—21no—
165C2×C42×C61—21no—
166#103×C61—22no—
167#103×C61—22no—
168C22⋊C8×C61—22no—
169C24×C61C2×D411yescharacteristic
170C23×D61C2×D411yescharacteristic
171C23×D61C2×D411yescharacteristic
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61—21no—
175C2×Q8×C61—21no—
176C2×Q8×C61—21no—
177C2×Q8×C61C22×C412yes—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61C22×C412yes—
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D412yes—
189C22×C4×C61C2411yescharacteristic
190C2×C22⋊D61—22no—
191C2×C22⋊D61—22no—
192C2×C22⋊D61—22no—
193C2×C22⋊D61—22no—
194C2×C22⋊D61C22⋊C414yes—
195C2×C22⋊D61C22⋊C414yes—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—24no—
201C22×Dic61—81no—
202C22×Dic61—81no—
203C22×Dic61C2×D411yescharacteristic
204C22×Dic61C2×D411yescharacteristic
205Q8×D61—28no—
206Q8×D61—28no—
207Q8×D61—44no—
208Q8×D61—44no—
209#11758222—28no—
210#11758222—28no—
211#11758222—28no—
212#11758222—28no—
213C2×D244—22no—
214C2×D244—22no—
215C2×D244C22⋊C414yes—
216C2×C4×D61—21no—
217C2×C4×D61—21no—
218C2×C4×D61—21no—
219C2×C4×D61—21no—
220C2×C4×D61—24no—
221C2×C4×D61—24no—
222C2×C4×D61—24no—
223C2×C4×D61—42no—
224C2×C4×D61—42no—
225C2×C4×D61—81no—
226C2×C4×D61—81no—
227C2×C4×D61—81no—
228C2×C4×D61—81no—
229C2×C4×D61C22×C412yes—
230C2×C4×D61C22×C412yes—
231C2×C4×D61C2×D412yes—
232C2×C4×D61C2×D412yes—
233C2×C4×D61C2×D412yes—
234C2×C4×D61C2×D412yes—
235C2×C4×D61#4112yes—
236C2×C4×D61#4112yes—
237C2×Dic122—22no—
238C2×Dic122—22no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122—21no—
244C2×Dic122—24no—
245C2×Dic122—42no—
246C2×Dic122—42no—
247C2×Dic122C22⋊C414yes—
248C2×Dic122C22×C412yes—
249C2×C8×C61—21no—
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C2×C8×C61—21no—
253C2×C8×C61—21no—
254C2×C8×C61—21no—
255C4⋊C4×C61—24no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61C22×C412yes—
260C4⋊C4×C61C2×D412yes—
261C4⋊C4×C61C2×D412yes—
262C22⋊C4×C61—24no—
263C22⋊C4×C61—24no—
264C42×C61—24no—
265C22⋊Dic61—24no—
266#11758198—24no—
267#11758198—24no—
268#11758198—24no—
269#11758198—24no—
270#11758198—24no—
271C4⋊Dic61—24no—
272C4⋊Dic61—21no—
273C4⋊Dic61—21no—
274C4⋊Dic61—21no—
275C4⋊Dic61—24no—
276C4⋊Dic61C22×C412yes—
277C4⋊Dic61C2×D412yes—
278C4⋊Dic61C2×D412yes—
279#11758196—24no—
280#11758196—24no—
281#11758196—24no—
282#11758196—24no—
283C4×Dic61—24no—
284C4×Dic61—24no—
285C4×Dic61—24no—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292#11758189—44no—
293C8×D61—44no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61C2×C22⋊C412yes—
301C23×C61C22×D411yescharacteristic
302C22×D61—21no—
303C22×D61—21no—
304C22×D61—21no—
305C22×D61—21no—
306C22×D61—21no—
307C22×D61—21no—
308C22×D61—21no—
309C22×D61—21no—
310C22×D61—21no—
311C22×D61—21no—
312C22×D61C2×C22⋊C412yes—
313C22×D61C2×C22⋊C412yes—
314C22×D61#12012yes—
315C22×D61#12312yes—
316Q8×C61—22no—
317Q8×C61—22no—
318Q8×C61—41no—
319Q8×C61—41no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61C2×C22⋊C412yes—
339C2×C4×C61C23×C411yescharacteristic
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C2×#4111yescharacteristic
344C2×C4×C61C2×#4111yescharacteristic
345C22⋊D61—28no—
346C22⋊D61—28no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—84no—
362C2×Dic61C2×C22⋊C412yes—
363C2×Dic61C2×C22⋊C412yes—
364C2×Dic61#12012yes—
365C2×Dic61#12312yes—
366D244—28no—
367C4×D61—22no—
368C4×D61—22no—
369C4×D61—22no—
370C4×D61—22no—
371C4×D61—48no—
372C4×D61—84no—
373C4×D61—84no—
374C4×D61C4×D414yes—
375C4×D61C4×D414yes—
376C4×D61#12114yes—
377C4×D61#12114yes—
378Dic122—28no—
379Dic122—22no—
380Dic122—22no—
381Dic122—41no—
382Dic122—41no—
383Dic122—48no—
384C8×C61—41no—
385C8×C61—41no—
386#92418—41no—
387#92418—41no—
388#20913—611nomaximal, Sylow
389C22×C61—22no—
390C22×C61—22no—
391C22×C61—22no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61C22×C22⋊C411yescharacteristic
397C22×C61C2×#12011yescharacteristic
398C22×C61C2×#12311yescharacteristic
399C22×C61#57711yescharacteristic
400C22×C61#57711yescharacteristic
401C22×C61#57811yescharacteristic
402C22×C61#57811yescharacteristic
403C2×D61—22no—
404C2×D61—22no—
405C2×D61—22no—
406C2×D61—22no—
407C2×D61—22no—
408C2×D61—22no—
409C2×D61—22no—
410C2×D61—22no—
411C2×D61—22no—
412C2×D61—41no—
413C2×D61—41no—
414C2×D61—41no—
415C2×D61—41no—
416C2×D61#38614yes—
417C4×C61—22no—
418C4×C61—42no—
419C4×C61—42no—
420C4×C61—42no—
421C4×C61—42no—
422C4×C61C2×C4×D411yescharacteristic
423C4×C61C2×C4×D411yescharacteristic
424C4×C61C2×#12111yescharacteristic
425C4×C61C2×#12111yescharacteristic
426Dic61—22no—
427Dic61—42no—
428Dic61—42no—
429Dic61—42no—
430Dic61—42no—
431Dic61#38614yes—
432C2×#536—611no—
433C2×#520—611no—
434C2×#419—611no—
435C22×#103—611no—
436C2×#408—611no—
437#1873—611no—
438#1873—611no—
439#1873—611no—
440#1873D6111yescharacteristic, complemented
441#1872—611no—
442#1872—611no—
443#1872—611no—
444#1872—611no—
445#1736—611no—
446#1735—611no—
447C2×C61—42no—
448C2×C61C2×#38611yescharacteristic
449C2×C61#289811yescharacteristic
450C2×C61#289811yescharacteristic
451C2×C61#300911yescharacteristic
452C2×C61#301111yescharacteristic
453C2×C61#309711yescharacteristic
454C2×C61#309711yescharacteristic
455D61—24no—
456D61—42no—
457C22×#41—611no—
458C23×Q8—611no—
459C22×M16—611no—
460C23×C8—611no—
461#536—618no—
462#536—1224no—
463C2×C4⋊Q8—1221no—
464C2×#124—1221no—
465C2×#123—1221no—
466C2×#123—1221no—
467C2×C22⋊Q8—611no—
468C2×C22⋊Q8—611no—
469C2×C22⋊Q8—611no—
470C2×C22⋊Q8C2×D6111yescharacteristic
471#520—1224no—
472#520—1224no—
473C2×C4×Q8—1221no—
474C2×C4×D4—1221no—
475C2×C4×D4—1221no—
476C2×C4×D4—1221no—
477C2×#117—611no—
478C2×#117—611no—
479C2×#117—611no—
480C2×#117C2×D6111yescharacteristic
481C22×C4⋊C4—611no—
482C22×C4⋊C4—611no—
483C22×C4⋊C4—611no—
484#419—1224no—
485C2×#103—611no—
486C2×#103—611no—
487C2×#103—611no—
488C2×#103—611no—
489C2×#103—611no—
490C2×#103—611no—
491C2×#103—1224no—
492C2×#103C2×D6111yescharacteristic
493C2×#103C2×D6111yescharacteristic
494#408—1224no—
495C2×C22⋊C8—611no—
496C2×C22⋊C8—611no—
497C2×C22⋊C8—611no—
498C2×C22⋊C8C2×D6111yescharacteristic
499#340—611no—
500#340—611no—
501#340—611no—
502#340—611no—
503#340—611no—
504#340—611no—
505#340C2×D6111yescharacteristic
506#340C2×D6111yescharacteristic
507C61#2091311yescharacteristic, complemented, Sylow
508C2×#41—614no—
509C2×#41—614no—
510C2×#41—1222no—
511C2×#41—1222no—
512C2×#41—1222no—
513C2×#41—1222no—
514C22×Q8—611no—
515C22×Q8—614no—
516C22×Q8—611no—
517C22×Q8—1221no—
518C22×Q8—1222no—
519C22×Q8—1222no—
520C22×Q8—1222no—
521C22×Q8—1222no—
522C22×Q8—1222no—
523C22×Q8C22×D6111yescharacteristic
524C22×D4—611no—
525C22×D4—611no—
526C22×D4—611no—
527C23×C4—611no—
528C23×C4—611no—
529C23×C4—1221no—
530C23×C4—1221no—
531C23×C4—1221no—
532C23×C4—1221no—
533C23×C4C22×D6111yescharacteristic
534C2×M16—1222no—
535C2×M16—1222no—
536C2×M16—1222no—
537C22×C8—611no—
538C22×C8—611no—
539C22×C8—1222no—
540C22×C8—1222no—
541C22×C8—1222no—
542C22×C8C22×D6111yescharacteristic
543C22×C8C22×D6111yescharacteristic
544C4⋊Q8—1228no—
545#124—1228no—
546#123—1228no—
547#123—1228no—
548C22⋊Q8—22no—
549C22⋊Q8—614no—
550C22⋊Q8—614no—
551C22⋊Q8—614no—
552C22⋊Q8—1222no—
553C22⋊Q8—1222no—
554C22⋊Q8—1222no—
555C22⋊Q8C4×D6114yescomplemented
556C4×Q8—1228no—
557C4×D4—1228no—
558C4×D4—1228no—
559C4×D4—1228no—
560#117—22no—
561#117—22no—
562#117—614no—
563#117—614no—
564#117—1222no—
565#117—1222no—
566#117—1222no—
567#117—1222no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—611no—
570C2×C4⋊C4—611no—
571C2×C4⋊C4—611no—
572C2×C4⋊C4—614no—
573C2×C4⋊C4—1222no—
574C2×C4⋊C4—1222no—
575C2×C4⋊C4—1222no—
576C2×C4⋊C4—1222no—
577C2×C4⋊C4—1221no—
578C2×C4⋊C4—1221no—
579C2×C4⋊C4—1221no—
580C2×C4⋊C4—1221no—
581C2×C4⋊C4—1221no—
582C2×C4⋊C4—1221no—
583C2×C4⋊C4—1222no—
584C2×C4⋊C4C22×D6111yescharacteristic
585C2×C4⋊C4C22×D6111yescharacteristic
586C2×C4⋊C4C22×D6111yescharacteristic
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—1221no—
590C2×C22⋊C4—1221no—
591C2×C22⋊C4—1221no—
592C2×C22⋊C4—1221no—
593C2×C22⋊C4—1221no—
594C2×C22⋊C4—1221no—
595C2×C42—21no—
596C2×C42—1221no—
597C2×C42—1221no—
598C2×C42—1221no—
599#103—22no—
600#103—22no—
601#103—1222no—
602#103—1222no—
603#103—1222no—
604#103—1222no—
605#103—1222no—
606#103—1222no—
607C22⋊C8—22no—
608C22⋊C8—1222no—
609C22⋊C8—1222no—
610C22⋊C8—1222no—
611C24—611no—
612C24—611no—
613C24D4×D6111yescharacteristic
614#41—1228no—
615#41—1228no—
616#41—1228no—
617#41—1228no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—614no—
624C2×Q8—612no—
625C2×Q8—1222no—
626C2×Q8—1222no—
627C2×Q8—1224no—
628C2×Q8—1228no—
629C2×Q8—1228no—
630C2×Q8—1221no—
631C2×Q8—1221no—
632C2×Q8—1221no—
633C2×Q8—1221no—
634C2×Q8—1221no—
635C2×Q8—2442no—
636C2×Q8—2442no—
637C2×Q8—2444no—
638C2×Q8—2444no—
639C2×Q8C2×C4×D6112yes—
640C2×D4—614no—
641C2×D4—614no—
642C2×D4—614no—
643C2×D4—1222no—
644C2×D4—1222no—
645C2×D4—1222no—
646C2×D4—1222no—
647C2×D4—1222no—
648C2×D4—1222no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—611no—
658C22×C4—612no—
659C22×C4—612no—
660C22×C4—612no—
661C22×C4—612no—
662C22×C4—612no—
663C22×C4—612no—
664C22×C4—611no—
665C22×C4—612no—
666C22×C4—612no—
667C22×C4—1224no—
668C22×C4—1224no—
669C22×C4—1224no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—1224no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—4881no—
680C22×C4—4881no—
681C22×C4—4881no—
682C22×C4—4881no—
683C22×C4—4881no—
684C22×C4—4881no—
685C22×C4—2442no—
686C22×C4—2442no—
687C22×C4C2×C4×D6112yes—
688C22×C4D4×D6112yes—
689C22×C4D4×D6111yescharacteristic
690C22×C4C23×D6111yescharacteristic
691M16—2444no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—1221no—
699C2×C8—1221no—
700C2×C8—1221no—
701C2×C8—1221no—
702C2×C8—1221no—
703C2×C8—1221no—
704C2×C8—2444no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—24no—
709C4⋊C4—612no—
710C4⋊C4—612no—
711C4⋊C4—612no—
712C4⋊C4—1224no—
713C4⋊C4—1224no—
714C4⋊C4—1224no—
715C4⋊C4—1224no—
716C4⋊C4—1224no—
717C4⋊C4—1221no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—1224no—
721C4⋊C4C2×C4×D6112yes—
722C4⋊C4D4×D6112yes—
723C4⋊C4D4×D6112yes—
724C22⋊C4—24no—
725C22⋊C4—24no—
726C22⋊C4—1224no—
727C22⋊C4—1224no—
728C22⋊C4—1224no—
729C22⋊C4—1224no—
730C22⋊C4—1224no—
731C22⋊C4—1224no—
732C42—24no—
733C42—1224no—
734C42—1224no—
735C42—1224no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—612no—
743C23—612no—
744C23—612no—
745C23—612no—
746C23—1221no—
747C23—1221no—
748C23—1221no—
749C23—1221no—
750C23—1221no—
751C23—1221no—
752C23—1221no—
753C23—1221no—
754C23—1221no—
755C23—1221no—
756C23C22⋊C4×D6112yes—
757C23C2×D4×D6111yescharacteristic
758Q8—22no—
759Q8—22no—
760Q8—41no—
761Q8—41no—
762Q8—1228no—
763Q8—1222no—
764Q8—1222no—
765Q8—2448no—
766Q8—2441no—
767Q8—2441no—
768D4—1228no—
769D4—1228no—
770D4—1228no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—612no—
790C2×C4—612no—
791C2×C4—612no—
792C2×C4—614no—
793C2×C4—614no—
794C2×C4—614no—
795C2×C4—614no—
796C2×C4—612no—
797C2×C4—1221no—
798C2×C4—1221no—
799C2×C4—1222no—
800C2×C4—1222no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1222no—
806C2×C4—1222no—
807C2×C4—4884no—
808C2×C4—4884no—
809C2×C4—4884no—
810C2×C4—2448no—
811C2×C4—2441no—
812C2×C4—2441no—
813C2×C4—2441no—
814C2×C4—2441no—
815C2×C4—2441no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4—2441no—
819C2×C4C22⋊C4×D6112yes—
820C2×C4C22×C4×D6111yescharacteristic
821C2×C4C2×D4×D6111yescharacteristic
822C2×C4C2×D4×D6111yescharacteristic
823C2×C4C2×D4×D6111yescharacteristic
824C2×C4#41×D6111yescharacteristic
825C2×C4#41×D6111yescharacteristic
826C8—41no—
827C8—41no—
828C8—2441no—
829C8—2441no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—614no—
838C22—1222no—
839C22—1222no—
840C22—1222no—
841C22—1222no—
842C22—1222no—
843C22—1222no—
844C22—1222no—
845C22—1222no—
846C22—1222no—
847C22—2441no—
848C22—2441no—
849C22—2441no—
850C22—2441no—
851C22C2×C22⋊C4×D6111yescharacteristic
852C22#120×D6111yescharacteristic
853C22#123×D6111yescharacteristic
854C22#1684056911yescharacteristic
855C22#1684057111yescharacteristic
856C22#1684057611yescharacteristic
857C22#1684057811yescharacteristic
858C4—22no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—42no—
863C4—614no—
864C4—1222no—
865C4—2442no—
866C4—2442no—
867C4—2442no—
868C4—2442no—
869C4C4×D4×D6111yescharacteristic
870C4C4×D4×D6111yescharacteristic
871C4#121×D6111yescharacteristic
872C4#121×D6111yescharacteristic
873C2—42no—
874C2—1224no—
875C2—2442no—
876C2#386×D6111yescharacteristic
877C2#2145434811yescharacteristic
878C2#2145435111yescharacteristic
879C2#2145509311yescharacteristic
880C2#2145511111yescharacteristic
881C2#2145578311yescharacteristic
882C2#2145578511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1873C2
socleC23×C61C22×D4
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenter#1873D61
hypocenterC61#20913
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
3. C2×#16839769C2semidirect
4. C2×#103×D61C2semidirect
6. #21446131C2semidirect
7. #21446130C2semidirect
8. #21446128C2semidirect
9. #21446127C2semidirect
10. #21446125C2semidirect
11. #21446124C2semidirect
12. #21446123C2semidirect
13. #21445537C2semidirect
14. #21445534C2semidirect
15. C61×#1873C2semidirect
21. #16840335C4semidirect
80. C2×Q8×D61C2×C4semidirect
103. #14519757C2×C4semidirect
105. #14519756C2×C4semidirect
107. #14519753C2×C4semidirect
116. #14519735C2×C4semidirect
156. C22⋊Q8×C61C2×C4semidirect
440. #1873D61semidirect
507. C61#20913semidirect
555. C22⋊Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403352
C2×#168402422
C2×#168397692
C2×#103×D612
C2×#168397272
#214461312
#214461302
#214461282
#214461272
#214461252
#214461242
#214461232
#214455372
#214455342
C61×#18732
#2091361