Finite Group Databasebeta

← #30619353

Subgroups — #30619353

Order 15616.

814 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461990C211yesmaximal, characteristic, complemented
2#21461989C211yesmaximal, characteristic, complemented
3#21461918C211yesmaximal, characteristic, complemented
4#21461917C211yesmaximal, characteristic, complemented
5#21461875C211yesmaximal, characteristic, complemented
6#21461874C211yesmaximal, characteristic, complemented
7#21461874C211yesmaximal, characteristic, complemented
8#21461873C211yesmaximal, characteristic, complemented
9#21461763C211yesmaximal, characteristic
10#21461762C211yesmaximal, characteristic
11#21461675C211yesmaximal, characteristic
12C22⋊C4×#92420C211yesmaximal, characteristic
13C22⋊C4×#92420C211yesmaximal, characteristic
14C2×#16840628C211yesmaximal, characteristic
15#21448351C211yesmaximal, characteristic
16C23×#92420C2211yescharacteristic
17C23×#92420C2211yescharacteristic
18C2×#14519844C2211yescharacteristic
19C2×#14519844C2211yescharacteristic
20C2×#14519844C2211yescharacteristic
21C2×#14519844C2211yescharacteristic
22C2×C4⋊#92420C2211yescharacteristic
23C2×C4⋊#92420C2211yescharacteristic
24C2×C22⋊#92420C2211yescharacteristic
25C2×C22⋊#92420C2211yescharacteristic
26C2×C4×#92420C2211yescharacteristic
27C2×C4×#92420C2211yescharacteristic
28C2×C4×#92420C2211yescharacteristic
29C2×C4×#92420C2211yescharacteristic
30#16840628C2211yescharacteristic
31#16840628C2211yescharacteristic
32#16840628C2211yescharacteristic
33#16840628C2211yescharacteristic
34#16840628C2211yescharacteristic
35#16840628C2211yescharacteristic
36#16840628C2211yescharacteristic
37#16840628C2211yescharacteristic
38#16840628C2211yescharacteristic
39#16840628C2211yescharacteristic
40#16840628C2211yescharacteristic
41#16840628C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44C2×#14519754C411yescharacteristic
45C2×#14519742C2211yescharacteristic
46C22×C4×Dic61C2211yescharacteristic
47#16839666C411yescharacteristic
48#16839657C411yescharacteristic
49#16839647C411yescharacteristic
50#16839643C411yescharacteristic
51#16839635C411yescharacteristic
52#16839620C411yescharacteristic
53C4⋊C4×Dic61C2211yescharacteristic
54#16839613C2211yescharacteristic
55#16839613C2211yescharacteristic
56C22⋊C4×Dic61C2211yescharacteristic
57C22⋊C4×Dic61C2211yescharacteristic
58C61×#385C411yescharacteristic
59C22×#92420—22no—
60C22×#92420—41no—
61C22×#92420—41no—
62C22×#92420—41no—
63C22×#92420—41no—
64C22×#92420Q814yescomplemented
65C22×#92420C2311yescharacteristic
66C22×#92420C2311yescharacteristic
67C22×#92420C2311yescharacteristic
68C22×#92420C2311yescharacteristic
69C22×#92420C2311yescharacteristic
70C22×#92420C2311yescharacteristic
71C22×#92420C2311yescharacteristic
72C22×#92420C2311yescharacteristic
73#14519844—41no—
74#14519844—41no—
75#14519844—41no—
76#14519844—41no—
77C4⋊#92420—41no—
78C4⋊#92420—41no—
79C22⋊#92420—22no—
80C22⋊#92420—22no—
81C4×#92420—41no—
82C4×#92420—41no—
83C4×#92420—41no—
84C4×#92420—41no—
85C22×Dic122C2×C411yescharacteristic
86C23×Dic61C2×C411yescharacteristic
87C23×Dic61C2311yescharacteristic
88#14519754C818yescomplemented
89#14519742—41no—
90#14519742—41no—
91C2×C4⋊Dic61C2×C411yescharacteristic
92C2×#11758196C2×C411yescharacteristic
93C2×#11758196C2×C411yescharacteristic
94C2×#11758196C2×C411yescharacteristic
95C2×#11758196C2×C411yescharacteristic
96C2×#11758196C2×C411yescharacteristic
97C2×#11758196C2×C411yescharacteristic
98C2×C22⋊Dic61C2×C411yescharacteristic
99C2×C22⋊Dic61C2×C411yescharacteristic
100C2×C4×Dic61—41no—
101C2×C4×Dic61—41no—
102C2×C4×Dic61C2×C411yescharacteristic
103C2×C4×Dic61C2×C411yescharacteristic
104C2×C4×Dic61C2311yescharacteristic
105C2×C4×Dic61C2311yescharacteristic
106C2×C4×Dic61C2311yescharacteristic
107C2×C4×Dic61C2311yescharacteristic
108C2×C4×Dic61C2311yescharacteristic
109C2×C4×Dic61C2311yescharacteristic
110#14519684C2×C411yescharacteristic
111#14519684C2×C411yescharacteristic
112#14519684C2×C411yescharacteristic
113#14519684C2×C411yescharacteristic
114#14519684C2×C411yescharacteristic
115#14519684C2×C411yescharacteristic
116#14519684C2×C411yescharacteristic
117#14519684C2×C411yescharacteristic
118C23×C4×C61C2×C411yescharacteristic
119C2×C4⋊C4×C61C2×C411yescharacteristic
120C2×C4⋊C4×C61C2×C411yescharacteristic
121C2×C22⋊C4×C61C2×C411yescharacteristic
122C2×C22⋊C4×C61C2×C411yescharacteristic
123#95×C61C2×C411yescharacteristic
124#95×C61C2×C411yescharacteristic
125C24×C61C22×C411yescharacteristic
126C22×C4×C61—22no—
127C22×C4×C61—41no—
128C22×C4×C61—41no—
129C22×C4×C61C22×C411yescharacteristic
130C22×C4×C61C22×C411yescharacteristic
131C22×C4×C61C22×C411yescharacteristic
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C22×C411yescharacteristic
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61—21no—
138C22×Dic61—21no—
139C22×Dic61—41no—
140C22×Dic61—41no—
141C22×Dic61C2×C814yes—
142C22×Dic61C22×C411yescharacteristic
143C22×Dic61C22×C411yescharacteristic
144C22×Dic61C22×C411yescharacteristic
145C22×Dic61C22×C411yescharacteristic
146C22×Dic61C22×C411yescharacteristic
147C22×Dic61C22×C411yescharacteristic
148C22×Dic61C22×C411yescharacteristic
149C22×Dic61C2×Q812yes—
150C22×Dic61#4112yes—
151C22×Dic61C2411yescharacteristic
152C2×Dic122—41no—
153C2×Dic122—41no—
154C2×Dic122C2×C814yescomplemented
155C2×#92420—21no—
156C2×#92420—21no—
157C2×#92420—21no—
158C2×#92420—21no—
159C2×#92420—21no—
160C2×#92420—21no—
161C2×#92420—21no—
162C2×#92420—21no—
163C2×#92420—21no—
164C2×#92420—21no—
165C2×#92420—21no—
166C2×#92420—21no—
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420—21no—
172C2×#92420—21no—
173C2×#92420—21no—
174C2×#92420—21no—
175C2×#92420—21no—
176C2×#92420—21no—
177C2×#92420—44no—
178C2×#92420—44no—
179C2×#92420C2×Q812yes—
180C2×#92420C2×Q812yes—
181C4⋊C4×C61—41no—
182C4⋊C4×C61—41no—
183C22⋊C4×C61—22no—
184C22⋊C4×C61C2×C814yes—
185C22⋊Dic61—22no—
186C22⋊Dic61C2×C814yes—
187C4⋊Dic61C2×C814yescomplemented
188#11758196—41no—
189#11758196—41no—
190#11758196—41no—
191#11758196—41no—
192#11758196C2×C814yescomplemented
193#11758196C2×C814yescomplemented
194C4×Dic61—21no—
195C4×Dic61—21no—
196C4×Dic61—21no—
197C4×Dic61—21no—
198C4×Dic61—21no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61—21no—
203C4×Dic61—21no—
204C4×Dic61—21no—
205C4×Dic61—21no—
206C4×Dic61—41no—
207C4×Dic61—41no—
208C23×C61—21no—
209C23×C61—21no—
210C23×C61—21no—
211C23×C61—21no—
212C23×C61C4×Q812yes—
213C23×C61C22×C812yes—
214C23×C61#13112yes—
215C23×C61C23×C411yescharacteristic
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
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—21no—
231C2×C4×C61—21no—
232C2×C4×C61—44no—
233C2×C4×C61C22×C812yes—
234C2×C4×C61C22×C812yes—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—22no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—44no—
256C2×Dic61C4×Q812yes—
257C2×Dic61C22×C812yes—
258C2×Dic61C22×C812yes—
259C2×Dic61C22×C812yes—
260C2×Dic61C22×C812yes—
261C2×Dic61C22×Q811yescharacteristic
262C2×Dic61C2×#4111yescharacteristic
263C2×Dic61H(5,𝔽2)11yescharacteristic
264C2×Dic61H(5,𝔽2)11yescharacteristic
265C2×Dic61H(5,𝔽2)11yescharacteristic
266C2×Dic612−1+411yescharacteristic
267Dic122—44no—
268#92420—22no—
269#92420—22no—
270#92420—41no—
271#92420—41no—
272#92420—41no—
273#92420—41no—
274#92420—41no—
275#92420—41no—
276#22287—611nomaximal, Sylow
277C22×C61—22no—
278C22×C61—22no—
279C22×C61—22no—
280C22×C61—22no—
281C22×C61—22no—
282C22×C61—22no—
283C22×C61C8×Q814yes—
284C22×C61C2×C4×Q811yescharacteristic
285C22×C61#51811yescharacteristic
286C22×C61#52011yescharacteristic
287C22×C61C23×C811yescharacteristic
288C22×C61C2×#13111yescharacteristic
289C22×C61#56811yescharacteristic
290C22×C61#56811yescharacteristic
291C4×C61—22no—
292C4×C61—22no—
293C4×C61—41no—
294C4×C61—41no—
295C4×C61—41no—
296C4×C61—41no—
297Dic61—22no—
298Dic61—22no—
299Dic61—22no—
300Dic61—22no—
301Dic61—22no—
302Dic61—41no—
303Dic61—41no—
304Dic61#53811yescharacteristic
305Dic61#53911yescharacteristic
306Dic61#54311yescharacteristic
307Dic61#54411yescharacteristic
308C4×C22⋊Q8—611no—
309#1984—611no—
310#1984—611no—
311#1939—611no—
312#1939—611no—
313#1916—611no—
314#1916—611no—
315#1916—611no—
316#1916—611no—
317#1850—611no—
318#1850—611no—
319#1797—611no—
320C8×C22⋊C4—611no—
321C8×C22⋊C4—611no—
322C2×#336—611no—
323C2×C61—24no—
324C2×C61#232911yescharacteristic
325C2×C61C2×C8×Q811yescharacteristic
326C2×C61#296111yescharacteristic
327C2×C61#297211yescharacteristic
328C2×C61#297611yescharacteristic
329C2×C61#298811yescharacteristic
330C2×C61#299211yescharacteristic
331C23×C8—611no—
332C23×C8—611no—
333C2×C22⋊Q8—611no—
334C2×C4×Q8—611no—
335C22×C42—611no—
336C2×C4⋊C8—611no—
337C2×C4⋊C8—611no—
338C2×C4⋊C8—611no—
339C2×C4⋊C8—611no—
340C2×C4⋊C8—611no—
341C2×C4⋊C8—611no—
342C2×C22⋊C8—611no—
343C2×C22⋊C8—611no—
344C2×C4×C8—611no—
345C2×C4×C8—611no—
346C2×C4×C8—611no—
347C2×C4×C8—611no—
348#391—611no—
349#389—611no—
350#387—611no—
351#387—611no—
352#385—611no—
353#385#692311yescharacteristic
354#380—611no—
355C4×C4⋊C4—611no—
356C4×C4⋊C4—611no—
357C4×C4⋊C4—611no—
358C4×C22⋊C4—611no—
359C4×C22⋊C4—611no—
360#336—611no—
361#336—611no—
362#336—611no—
363#336—611no—
364#336—611no—
365#336—611no—
366#336—611no—
367#336—611no—
368#336—611no—
369#336—611no—
370#336—611no—
371#336—611no—
372#336—611no—
373#336—611no—
374C61#2228711yescharacteristic, complemented, Sylow
375C22×Q8—611no—
376C23×C4—611no—
377C23×C4—611no—
378C23×C4C2×#692311yescharacteristic
379C22×C8—611no—
380C22×C8—611no—
381C22×C8—614no—
382C22×C8—611no—
383C22×C8—611no—
384C22×C8—611no—
385C22×C8—611no—
386C22×C8—611no—
387C22×C8—611no—
388C22×C8—1222no—
389C22×C8—2441no—
390C22×C8—2441no—
391C22×C8—2441no—
392C22×C8—2441no—
393C22⋊Q8—618no—
394C4×Q8—2441no—
395C4×Q8—2441no—
396C2×C4⋊C4—611no—
397C2×C4⋊C4—611no—
398C2×C4⋊C4—611no—
399C2×C4⋊C4—611no—
400C2×C4⋊C4—611no—
401C2×C4⋊C4—611no—
402C2×C4⋊C4—611no—
403C2×C4⋊C4C2×#692311yescharacteristic
404C2×C4⋊C4C2×#692311yescharacteristic
405C2×C22⋊C4—611no—
406C2×C22⋊C4—611no—
407C2×C22⋊C4C2×#692311yescharacteristic
408C2×C22⋊C4C2×#692311yescharacteristic
409C2×C42—611no—
410C2×C42—611no—
411C2×C42—611no—
412C2×C42—611no—
413C2×C42—611no—
414C2×C42—611no—
415C2×C42—611no—
416C2×C42—611no—
417C2×C42—2441no—
418C2×C42—2441no—
419C4⋊C8—2441no—
420C4⋊C8—2441no—
421C4⋊C8—2441no—
422C4⋊C8—2441no—
423C4⋊C8—2441no—
424C4⋊C8—2441no—
425C22⋊C8—1222no—
426C22⋊C8—1222no—
427C4×C8—2441no—
428C4×C8—2441no—
429C4×C8—2441no—
430C4×C8—2441no—
431#95—611no—
432#95—611no—
433#95—611no—
434#95—611no—
435#95—611no—
436#95—611no—
437#95—611no—
438#95—611no—
439#95C2×#692311yescharacteristic
440#95C2×#692311yescharacteristic
441C24C22×#692311yescharacteristic
442C2×Q8—614no—
443C2×Q8—2441no—
444C2×Q8—2441no—
445C22×C4—22no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—611no—
449C22×C4—612no—
450C22×C4—612no—
451C22×C4—611no—
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—614no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—2441no—
464C22×C4—2441no—
465C22×C4C22×#692311yescharacteristic
466C22×C4C22×#692311yescharacteristic
467C22×C4C22×#692311yescharacteristic
468C22×C4C22×#692311yescharacteristic
469C22×C4C22×#692311yescharacteristic
470C22×C4C22×#692311yescharacteristic
471C2×C8—612no—
472C2×C8—612no—
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—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8—1221no—
493C2×C8—1221no—
494C2×C8—1221no—
495C2×C8—2444no—
496C2×C8—2444no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—614no—
500C4⋊C4—614no—
501C4⋊C4—614no—
502C4⋊C4—2441no—
503C4⋊C4—2441no—
504C4⋊C4—2441no—
505C4⋊C4—2441no—
506C22⋊C4—22no—
507C22⋊C4—614no—
508C22⋊C4—1222no—
509C22⋊C4D61⋊C814yes—
510C42—1221no—
511C42—1221no—
512C42—1221no—
513C42—1221no—
514C42—1221no—
515C42—1221no—
516C42—1221no—
517C42—1221no—
518C42—1221no—
519C42—1221no—
520C42—1221no—
521C42—1221no—
522C42—2441no—
523C42—2441no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23Q8×#692312yes—
529C23C2×D61⋊C812yes—
530C23#1451986412yes—
531C23C23×#692311yescharacteristic
532Q8—2444no—
533C2×C4—21no—
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—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—44no—
550C2×C4—611no—
551C2×C4—611no—
552C2×C4—611no—
553C2×C4—611no—
554C2×C4—611no—
555C2×C4—611no—
556C2×C4—612no—
557C2×C4—612no—
558C2×C4—612no—
559C2×C4—612no—
560C2×C4—612no—
561C2×C4—1222no—
562C2×C4—1222no—
563C2×C4—1222no—
564C2×C4—1222no—
565C2×C4—1221no—
566C2×C4—1221no—
567C2×C4—1221no—
568C2×C4—1221no—
569C2×C4—1221no—
570C2×C4—1221no—
571C2×C4—1221no—
572C2×C4—1221no—
573C2×C4—1221no—
574C2×C4—1221no—
575C2×C4—1221no—
576C2×C4—1221no—
577C2×C4—1221no—
578C2×C4—1221no—
579C2×C4—1221no—
580C2×C4—1221no—
581C2×C4—2444no—
582C2×C4C2×D61⋊C812yes—
583C2×C4C2×D61⋊C812yes—
584C8—1222no—
585C8—1222no—
586C8—2441no—
587C8—2441no—
588C8—2441no—
589C8—2441no—
590C8—2441no—
591C8—2441no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—22no—
596C22—22no—
597C22—22no—
598C22#1684081114yes—
599C22C2×Q8×#692311yescharacteristic
600C22#1684082911yescharacteristic
601C22#1684083111yescharacteristic
602C22C22×D61⋊C811yescharacteristic
603C22C2×#1451986411yescharacteristic
604C22#1684084011yescharacteristic
605C22#1684084111yescharacteristic
606C4—22no—
607C4—22no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—611no—
613C4—611no—
614C4—611no—
615C4—611no—
616C4—1222no—
617C4—1222no—
618C4—1222no—
619C4—1222no—
620C4—1222no—
621C4—2441no—
622C4—2441no—
623C2—24no—
624C2#2146231211yescharacteristic
625C2C2×#1684081111yescharacteristic
626C2#2146261011yescharacteristic
627C2#2146266711yescharacteristic
628C2#2146268511yescharacteristic
629C2#2146273511yescharacteristic
630C2#2146275411yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutatorC22×C61C23×C8
FittingC61×#385C4
socleC23×C61C23×C4
prime radicalC24×C61C22×C4
cosocleC22×Dic61C24
hypercenter#385#6923
hypocenterC61#22287
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. #21461990C2semidirect
2. #21461989C2semidirect
3. #21461918C2semidirect
4. #21461917C2semidirect
5. #21461875C2semidirect
6. #21461874C2semidirect
7. #21461874C2semidirect
8. #21461873C2semidirect
64. C22×#92420Q8semidirect
88. #14519754C8semidirect
154. C2×Dic122C2×C8semidirect
187. C4⋊Dic61C2×C8semidirect
192. #11758196C2×C8semidirect
193. #11758196C2×C8semidirect
374. C61#22287semidirect

Maximal subgroups

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

subgroupindex
#214619902
#214619892
#214619182
#214619172
#214618752
#214618742
#214618732
#214617632
#214617622
#214616752
C22⋊C4×#924202
C2×#168406282
#214483512
#2228761