Finite Group Databasebeta

← #29689564

Subgroups — #29689564

Order 15616.

970 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839823C211yesmaximal, characteristic
2#21448428C211yesmaximal, characteristic
3#21446793C211yesmaximal, characteristic, complemented
4#21446789C211yesmaximal, characteristic, complemented
5#21446785C211yesmaximal, characteristic, complemented
6#21446781C211yesmaximal, characteristic, complemented
7#21446777C211yesmaximal, characteristic, complemented
8#21446777C211yesmaximal, characteristic, complemented
9#21446772C211yesmaximal, characteristic, complemented
10#21446768C211yesmaximal, characteristic, complemented
11#21445914C211yesmaximal, characteristic
12#21445914C211yesmaximal, characteristic
13#21445909C211yesmaximal, characteristic
14#21445905C211yesmaximal, characteristic
15C2×C61×#544C211yesmaximal, characteristic
16#16839823—24no—
17C2×C4⋊#92418C2211yescharacteristic
18C2×C4⋊#92418C2211yescharacteristic
19C2×C22⋊#92418C2211yescharacteristic
20C2×C22⋊#92418C2211yescharacteristic
21C2×#14519688C2211yescharacteristic
22C2×C4×#92418C2211yescharacteristic
23#16839655—21no—
24#16839655—21no—
25#16839648—21no—
26#16839648—21no—
27#16839632C2211yescharacteristic
28#16839628C2211yescharacteristic
29#16839622C2211yescharacteristic
30#16839622C2211yescharacteristic
31C4×C4⋊Dic61C2211yescharacteristic
32C4×C4⋊Dic61C2211yescharacteristic
33#16839524C2211yescharacteristic
34#16839524C2211yescharacteristic
35#16839524C2211yescharacteristic
36#16839524C2211yescharacteristic
37#16839524C2211yescharacteristic
38#16839524C2211yescharacteristic
39#16839524C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49C61×#544—24no—
50C61×#544C418yescomplemented
51C2×C4⋊Q8×C61—21no—
52C2×C4⋊Q8×C61C2211yescharacteristic
53C2×C4⋊Q8×C61C2211yescharacteristic
54C2×#125×C61—21no—
55C2×#125×C61C2211yescharacteristic
56C2×#125×C61C2211yescharacteristic
57C2×C22⋊Q8×C61—21no—
58C2×C22⋊Q8×C61—21no—
59C2×#117×C61C2211yescharacteristic
60C2×#117×C61C2211yescharacteristic
61C22×C4⋊C4×C61C2211yescharacteristic
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C2×C4⋊Dic61—21no—
67C2×C4⋊Dic61—21no—
68C2×C4⋊Dic61C2311yescharacteristic
69C2×C4⋊Dic61C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C22⋊Dic61—21no—
73C2×C22⋊Dic61—21no—
74C2×C4×Dic61—21no—
75C2×C4×Dic61—21no—
76C4⋊#92418—22no—
77C4⋊#92418—22no—
78C22⋊#92418—22no—
79C22⋊#92418—22no—
80#14519688—22no—
81C4×#92418—22no—
82#14519684—21no—
83#14519684—21no—
84#14519684—21no—
85#14519684—21no—
86#14519684—21no—
87#14519684—21no—
88C22×Q8×C61—21no—
89C22×Q8×C61—21no—
90C23×C4×C61—21no—
91C23×C4×C61C2311yescharacteristic
92C4⋊Q8×C61—28no—
93C4⋊Q8×C61—22no—
94C4⋊Q8×C61—22no—
95C4⋊Q8×C61C2×C414yes—
96C4⋊Q8×C61C2×C414yes—
97#125×C61—28no—
98#125×C61—22no—
99#125×C61—22no—
100#125×C61C2×C414yes—
101#125×C61C2×C414yes—
102C22⋊Q8×C61—28no—
103C22⋊Q8×C61—28no—
104#117×C61—22no—
105#117×C61C2×C414yes—
106#117×C61C2×C414yes—
107#117×C61D414yes—
108C2×C4⋊C4×C61—21no—
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61—21no—
111C2×C4⋊C4×C61—21no—
112C2×C4⋊C4×C61—21no—
113C2×C4⋊C4×C61—22no—
114C2×C4⋊C4×C61—21no—
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61C2×C414yes—
117C2×C4⋊C4×C61D411yescharacteristic
118C2×C4⋊C4×C61D411yescharacteristic
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C4⋊C4×C61C2311yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C22⋊C4×C61—21no—
124C2×C22⋊C4×C61D411yescharacteristic
125C2×C22⋊C4×C61D411yescharacteristic
126C2×C42×C61—21no—
127C2×C42×C61C2311yescharacteristic
128C2×C42×C61C2311yescharacteristic
129C24×C61C2×D411yescharacteristic
130C2×Q8×C61—24no—
131C2×Q8×C61—24no—
132C2×Q8×C61—81no—
133C2×Q8×C61—81no—
134C2×Q8×C61—81no—
135C2×Q8×C61—81no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—24no—
145C22×C4×C61—81no—
146C22×C4×C61—81no—
147C22×C4×C61C22×C412yes—
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D412yes—
154C22×C4×C61C2411yescharacteristic
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C4⋊C4×C61—24no—
160C4⋊C4×C61—24no—
161C4⋊C4×C61—24no—
162C4⋊C4×C61—24no—
163C4⋊C4×C61—24no—
164C4⋊C4×C61—24no—
165C4⋊C4×C61—24no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61C22⋊C414yes—
171C4⋊C4×C61C22⋊C414yes—
172C4⋊C4×C61C22×C412yes—
173C4⋊C4×C61C22×C412yes—
174C4⋊C4×C61C22×C412yes—
175C4⋊C4×C61C22×C412yes—
176C22⋊C4×C61—24no—
177C22⋊C4×C61C22⋊C414yes—
178C22⋊C4×C61C22⋊C414yes—
179C42×C61—24no—
180C42×C61C22×C412yes—
181C42×C61C22×C412yes—
182C42×C61C2×D412yes—
183C42×C61C2×D412yes—
184C22⋊Dic61—81no—
185C22⋊Dic61—81no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—81no—
195C4⋊Dic61—81no—
196C4×Dic61—81no—
197C4×Dic61—81no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C23×C61—21no—
211C23×C61—21no—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61C2×C22⋊C412yes—
217C23×C61C22×D411yescharacteristic
218Q8×C61—84no—
219Q8×C61—84no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—84no—
247C2×C4×C61C2×C22⋊C412yes—
248C2×C4×C61C2×C22⋊C412yes—
249C2×C4×C61C2×C22⋊C412yes—
250C2×C4×C61C2×C22⋊C412yes—
251C2×C4×C61C2×C22⋊C412yes—
252C2×C4×C61C23×C411yescharacteristic
253C2×C4×C61C22×D411yescharacteristic
254C2×C4×C612−1+411yescharacteristic
255C2×C4×C612−1+411yescharacteristic
256C2×C4×C612−1+411yescharacteristic
257C2×C4×C612−1+411yescharacteristic
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270#92418—41no—
271#92418—41no—
272#92418—41no—
273#92418—41no—
274#21843—611nomaximal, Sylow
275C22×C61—22no—
276C22×C61—22no—
277C22×C61—22no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61C22×C22⋊C411yescharacteristic
283C22×C61#53611yescharacteristic
284C22×C61#53611yescharacteristic
285C22×C61#57611yescharacteristic
286C22×C61#57711yescharacteristic
287C22×C61#57711yescharacteristic
288C22×C61#57811yescharacteristic
289C4×C61—22no—
290C4×C61—22no—
291C4×C61—22no—
292C4×C61—22no—
293C4×C61—22no—
294C4×C61—42no—
295C4×C61—42no—
296C4×C61—42no—
297C4×C61—42no—
298C4×C61#51911yescharacteristic
299C4×C61#51911yescharacteristic
300C4×C61#53611yescharacteristic
301C4×C61#53611yescharacteristic
302Dic61—81no—
303Dic61—81no—
304Dic61—81no—
305Dic61—81no—
306C2×#544D6111yescharacteristic
307C2×#433—611no—
308#2314—611no—
309#1993—611no—
310#1992—611no—
311#1991—611no—
312#1990—611no—
313#1989—611no—
314#1989—611no—
315#1988—611no—
316#1987—611no—
317#1825—611no—
318#1825—611no—
319#1824—611no—
320#1823—611no—
321C2×C61—42no—
322C2×C61#231011yescharacteristic
323C2×C61#289711yescharacteristic
324C2×C61#289811yescharacteristic
325C2×C61#324111yescharacteristic
326C2×C61#324211yescharacteristic
327C2×C61#324311yescharacteristic
328C2×C61#324411yescharacteristic
329#544—24no—
330#544Dic6118yescomplemented
331C2×C4⋊Q8—21no—
332C2×C4⋊Q8C2×D6111yescharacteristic
333C2×C4⋊Q8C2×D6111yescharacteristic
334C2×#125—21no—
335C2×#125C2×D6111yescharacteristic
336C2×#125C2×D6111yescharacteristic
337C2×C22⋊Q8—21no—
338C2×C22⋊Q8—21no—
339C2×#117C2×D6111yescharacteristic
340C2×#117C2×D6111yescharacteristic
341C22×C4⋊C4C2×D6111yescharacteristic
342#433—1224no—
343C2×C4⋊C8—611no—
344C2×C4⋊C8—611no—
345C2×C22⋊C8—611no—
346C2×C22⋊C8—611no—
347C2×#97—611no—
348C2×C4×C8—611no—
349#388—1221no—
350#388—1221no—
351#387—1221no—
352#387—1221no—
353#384—611no—
354#382—611no—
355#380—611no—
356#380—611no—
357C4×C4⋊C4—611no—
358C4×C4⋊C4—611no—
359#340—611no—
360#340—611no—
361#340—611no—
362#340—611no—
363#340—611no—
364#340—611no—
365#340—611no—
366#340—611no—
367#340—611no—
368#340—611no—
369#340—611no—
370#340—611no—
371#340—611no—
372#340—611no—
373#340—611no—
374#340—611no—
375C61#2184311yescharacteristic, complemented, Sylow
376C22×Q8—21no—
377C22×Q8—21no—
378C23×C4—21no—
379C23×C4C22×D6111yescharacteristic
380C22×C8—611no—
381C22×C8—611no—
382C22×C8—611no—
383C22×C8—611no—
384C4⋊Q8—28no—
385C4⋊Q8—22no—
386C4⋊Q8—22no—
387C4⋊Q8C2×Dic6114yes—
388C4⋊Q8C2×Dic6114yes—
389#125—28no—
390#125—22no—
391#125—22no—
392#125C2×Dic6114yes—
393#125C2×Dic6114yes—
394C22⋊Q8—28no—
395C22⋊Q8—28no—
396#117—22no—
397#117C2×Dic6114yes—
398#117C2×Dic6114yes—
399#117C22⋊D6114yes—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—611no—
409C2×C4⋊C4—611no—
410C2×C4⋊C4—611no—
411C2×C4⋊C4—611no—
412C2×C4⋊C4—1221no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4C2×Dic6114yes—
415C2×C4⋊C4C22⋊D6111yescharacteristic
416C2×C4⋊C4C22⋊D6111yescharacteristic
417C2×C4⋊C4C22×D6111yescharacteristic
418C2×C4⋊C4C22×D6111yescharacteristic
419C2×C4⋊C4C22×D6111yescharacteristic
420C2×C4⋊C4C22×D6111yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—1221no—
423C2×C22⋊C4—1221no—
424C2×C22⋊C4C22⋊D6111yescharacteristic
425C2×C22⋊C4C22⋊D6111yescharacteristic
426C2×C42—21no—
427C2×C42—1221no—
428C2×C42—1221no—
429C2×C42C22×D6111yescharacteristic
430C2×C42C22×D6111yescharacteristic
431C4⋊C8—1222no—
432C4⋊C8—1222no—
433C22⋊C8—1222no—
434C22⋊C8—1222no—
435#97—1222no—
436C4×C8—1222no—
437#95—1221no—
438#95—1221no—
439#95—1221no—
440#95—1221no—
441#95—1221no—
442#95—1221no—
443C24C2×C22⋊D6111yescharacteristic
444C2×Q8—24no—
445C2×Q8—24no—
446C2×Q8—81no—
447C2×Q8—81no—
448C2×Q8—81no—
449C2×Q8—81no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—24no—
459C22×C4—81no—
460C22×C4—81no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4C22×Dic6112yes—
466C22×C4C2×C22⋊D6112yes—
467C22×C4C2×C22⋊D6111yescharacteristic
468C22×C4C2×C22⋊D6111yescharacteristic
469C22×C4C2×C22⋊D6111yescharacteristic
470C22×C4C2×C22⋊D6111yescharacteristic
471C22×C4C2×C22⋊D6111yescharacteristic
472C22×C4C23×D6111yescharacteristic
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8—1221no—
476C2×C8—1221no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1221no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—24no—
490C4⋊C4—24no—
491C4⋊C4—24no—
492C4⋊C4—24no—
493C4⋊C4—24no—
494C4⋊C4—24no—
495C4⋊C4—24no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4—1221no—
500C4⋊C4—1221no—
501C4⋊C4—1221no—
502C4⋊C4—1221no—
503C4⋊C4—1221no—
504C4⋊C4—4881no—
505C4⋊C4—4881no—
506C4⋊C4C22⋊Dic6114yes—
507C4⋊C4C22⋊Dic6114yes—
508C4⋊C4C22×Dic6112yes—
509C4⋊C4C22×Dic6112yes—
510C4⋊C4C22×Dic6112yes—
511C4⋊C4C22×Dic6112yes—
512C22⋊C4—24no—
513C22⋊C4—4881no—
514C22⋊C4—4881no—
515C22⋊C4C22⋊Dic6114yes—
516C22⋊C4C22⋊Dic6114yes—
517C42—24no—
518C42—4881no—
519C42—4881no—
520C42C22×Dic6112yes—
521C42C22×Dic6112yes—
522C42C2×C22⋊D6112yes—
523C42C2×C22⋊D6112yes—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23C2×C22⋊Dic6112yes—
531C23C22×C22⋊D6111yescharacteristic
532Q8—84no—
533Q8—84no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—84no—
561C2×C4—2441no—
562C2×C4—2441no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4C2×C22⋊Dic6112yes—
574C2×C4C2×C22⋊Dic6112yes—
575C2×C4C2×C22⋊Dic6112yes—
576C2×C4C2×C22⋊Dic6112yes—
577C2×C4C2×C22⋊Dic6112yes—
578C2×C4C23×Dic6111yescharacteristic
579C2×C4C22×C22⋊D6111yescharacteristic
580C2×C4#1451982511yescharacteristic
581C2×C4#1451982511yescharacteristic
582C2×C4#1451982511yescharacteristic
583C2×C4#1451982511yescharacteristic
584C8—2441no—
585C8—2441no—
586C8—2441no—
587C8—2441no—
588C22—22no—
589C22—22no—
590C22—22no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22C22×C22⋊Dic6111yescharacteristic
596C22#1684033611yescharacteristic
597C22#1684033611yescharacteristic
598C22#1684056511yescharacteristic
599C22#1684057011yescharacteristic
600C22#1684057311yescharacteristic
601C22#1684057711yescharacteristic
602C4—22no—
603C4—22no—
604C4—22no—
605C4—22no—
606C4—22no—
607C4—42no—
608C4—42no—
609C4—42no—
610C4—42no—
611C4—4881no—
612C4—4881no—
613C4—4881no—
614C4—4881no—
615C4#1684024011yescharacteristic
616C4#1684024011yescharacteristic
617C4#1684033611yescharacteristic
618C4#1684033611yescharacteristic
619C2—42no—
620C2#2144840511yescharacteristic
621C2#2145434511yescharacteristic
622C2#2145435211yescharacteristic
623C2#2145707211yescharacteristic
624C2#2145708711yescharacteristic
625C2#2145710211yescharacteristic
626C2#2145711711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#544C2
socleC23×C61C22×D4
prime radicalC24×C61C2×D4
cosocleC22×C4×C61C24
hypercenterC2×#544D61
hypocenterC61#21843
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
3. #21446793C2semidirect
4. #21446789C2semidirect
5. #21446785C2semidirect
6. #21446781C2semidirect
7. #21446777C2semidirect
8. #21446777C2semidirect
9. #21446772C2semidirect
10. #21446768C2semidirect
50. C61×#544C4semidirect
330. #544Dic61semidirect
375. C61#21843semidirect

Maximal subgroups

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

subgroupindex
C2×#168398232
#214484282
#214467932
#214467892
#214467852
#214467812
#214467772
#214467722
#214467682
#214459142
#214459092
#214459052
C2×C61×#5442
#2184361