Finite Group Databasebeta

← #30619358

Subgroups — #30619358

Order 15616.

722 conjugacy classes of subgroups.

The subgroup lattice has 618 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#21461873C211yesmaximal, characteristic, complemented
7#21461872C211yesmaximal, characteristic, complemented
8#21461872C211yesmaximal, characteristic, complemented
9#21461767C211yesmaximal, characteristic
10#21461765C211yesmaximal, characteristic
11#21461678C211yesmaximal, characteristic
12#21461553C211yesmaximal, characteristic
13#21461553C211yesmaximal, characteristic
14#21461486C211yesmaximal, characteristic
15#21449096C211yesmaximal, characteristic
16C22×#11758213C2211yescharacteristic
17C22×D61⋊C8C2211yescharacteristic
18C2×#14519844C2211yescharacteristic
19C2×#14519844C2211yescharacteristic
20C2×#14519844C2211yescharacteristic
21C2×C4⋊#92420C2211yescharacteristic
22C2×C4⋊#92420C2211yescharacteristic
23C2×C4⋊#92420C2211yescharacteristic
24C2×#14519834C2211yescharacteristic
25C2×#14519834C2211yescharacteristic
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×#14519742C2211yescharacteristic
45C2×#14519735C2211yescharacteristic
46#16839704C411yescharacteristic
47#16839697C411yescharacteristic
48#16839695C411yescharacteristic
49#16839684C411yescharacteristic
50#16839684C411yescharacteristic
51#16839683C411yescharacteristic
52#16839675C411yescharacteristic
53C4⋊C4×Dic61C2211yescharacteristic
54C4⋊C4×Dic61C2211yescharacteristic
55#16839613C2211yescharacteristic
56#16839609C2211yescharacteristic
57#16839609C2211yescharacteristic
58C61×#398C411yescharacteristic
59C2×#11758213—22no—
60C2×#11758213—41no—
61C2×#11758213—41no—
62C2×D61⋊C8—41no—
63C2×D61⋊C8—41no—
64C2×D61⋊C8Q814yescomplemented
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—
76C4⋊#92420—41no—
77C4⋊#92420—41no—
78C4⋊#92420—41no—
79#14519834—22no—
80#14519834—22no—
81C4×#92420—41no—
82C4×#92420—41no—
83C4×#92420—41no—
84C4×#92420—41no—
85C22×Dic122C2×C411yescharacteristic
86C22×C4×D61C2311yescharacteristic
87#14519742—41no—
88#14519742—41no—
89#14519735—41no—
90#14519735—41no—
91C2×C4⋊Dic61C2×C411yescharacteristic
92C2×C4⋊Dic61C2×C411yescharacteristic
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×#11758196C2×C411yescharacteristic
95C2×#11758196C2×C411yescharacteristic
96C2×#11758196C2×C411yescharacteristic
97C2×#11758196C2×C411yescharacteristic
98C2×#11758198C2×C411yescharacteristic
99C2×#11758198C2×C411yescharacteristic
100C2×#11758198C2×C411yescharacteristic
101C2×#11758198C2×C411yescharacteristic
102C2×#11758198C2×C411yescharacteristic
103C2×#11758198C2×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
117C2×C4⋊C4×C61C2×C411yescharacteristic
118C2×C4⋊C4×C61C2×C411yescharacteristic
119C2×C4⋊C4×C61C2×C411yescharacteristic
120C2×C4⋊C4×C61C2×C411yescharacteristic
121#95×C61C2×C411yescharacteristic
122#95×C61C2×C411yescharacteristic
123#95×C61C2×C411yescharacteristic
124C23×D61C22×C411yescharacteristic
125C22×C4×C61C22×C411yescharacteristic
126C22×C4×C61C22×C411yescharacteristic
127C22×C4×C61C22×C411yescharacteristic
128C22×C4×C61C22×C411yescharacteristic
129C22×C4×C61C22×C411yescharacteristic
130C22×C4×C61C22×C411yescharacteristic
131C22×C4×C61C22×C411yescharacteristic
132C22×Dic61C22×C411yescharacteristic
133C22×Dic61C22×C411yescharacteristic
134C22×Dic61C22×C411yescharacteristic
135C22×Dic61C22×C411yescharacteristic
136C22×Dic61C22×C411yescharacteristic
137C22×Dic61C22×C411yescharacteristic
138C22×Dic61C2411yescharacteristic
139C2×C4×D61—21no—
140C2×C4×D61—21no—
141C2×C4×D61—21no—
142C2×C4×D61—21no—
143C2×C4×D61C2×Q812yes—
144C2×C4×D61#4112yes—
145C2×Dic122—22no—
146C2×Dic122—22no—
147C2×Dic122—41no—
148C2×#92420—21no—
149C2×#92420—21no—
150C2×#92420—21no—
151C2×#92420—21no—
152C2×#92420—21no—
153C2×#92420—21no—
154C2×#92420—21no—
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×#92420C2×Q812yes—
171C2×#92420C2×Q812yes—
172#11758213—44no—
173D61⋊C8—44no—
174C4⋊C4×C61—22no—
175C4⋊C4×C61—22no—
176C4⋊C4×C61—41no—
177C4⋊C4×C61—41no—
178#11758198—22no—
179#11758198—22no—
180#11758198—22no—
181#11758198—22no—
182#11758198—41no—
183#11758198—41no—
184C4⋊Dic61—22no—
185C4⋊Dic61—22no—
186C4⋊Dic61—41no—
187#11758196—22no—
188#11758196—22no—
189#11758196—41no—
190#11758196—41no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—21no—
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—
203C23×C61C23×C411yescharacteristic
204C22×D61—21no—
205C22×D61—21no—
206C22×D61—21no—
207C22×D61—21no—
208C22×D61—21no—
209C22×D61—21no—
210C22×D61C4×Q812yes—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
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×C61C4×Q812yes—
230C2×C4×C61#13112yes—
231C2×C4×C61#13112yes—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
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—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61#13112yes—
249C2×Dic61#13112yes—
250C2×Dic61C22×Q811yescharacteristic
251C2×Dic61C2×#4111yescharacteristic
252C2×Dic61H(5,𝔽2)11yescharacteristic
253C2×Dic61H(5,𝔽2)11yescharacteristic
254C2×Dic61H(5,𝔽2)11yescharacteristic
255C2×Dic612−1+411yescharacteristic
256C4×D61—22no—
257C4×D61—22no—
258C4×D61—22no—
259C4×D61—22no—
260Dic122—44no—
261#92420—22no—
262#92420—22no—
263#92420—41no—
264#92420—41no—
265#92420—41no—
266#92420—41no—
267#92420—41no—
268#92420—41no—
269#22288—611nomaximal, Sylow
270C22×C61C2×C4×Q811yescharacteristic
271C22×C61#51811yescharacteristic
272C22×C61#52011yescharacteristic
273C22×C61C2×#13111yescharacteristic
274C22×C61C2×#13111yescharacteristic
275C22×C61C2×#13111yescharacteristic
276C22×C61C2×#13111yescharacteristic
277C2×D61—22no—
278C2×D61—22no—
279C2×D61—22no—
280C2×D61—41no—
281C2×D61—41no—
282C2×D61—41no—
283C2×D61—41no—
284C4×C61—22no—
285C4×C61—22no—
286C4×C61—22no—
287C4×C61—41no—
288C4×C61—41no—
289C4×C61—41no—
290C4×C61—41no—
291Dic61—22no—
292Dic61—22no—
293Dic61—41no—
294Dic61—41no—
295Dic61—41no—
296Dic61—41no—
297Dic61#53811yescharacteristic
298Dic61#53911yescharacteristic
299Dic61#54311yescharacteristic
300Dic61#54411yescharacteristic
301#2396—611no—
302#1984—611no—
303#1984—611no—
304#1939—611no—
305#1939—611no—
306#1916—611no—
307#1916—611no—
308#1916—611no—
309#1916—611no—
310#1851—611no—
311#1851—611no—
312#1798—611no—
313C8×C22⋊C4—611no—
314C8×C22⋊C4—611no—
315#1729—611no—
316C2×C61#232911yescharacteristic
317C2×C61#296011yescharacteristic
318C2×C61#296011yescharacteristic
319C2×C61#297711yescharacteristic
320C2×C61#297911yescharacteristic
321C2×C61#299411yescharacteristic
322C2×C61#299411yescharacteristic
323D61—42no—
324C22×M16—611no—
325C23×C8—611no—
326C2×C4×Q8—611no—
327C2×#117—611no—
328C2×C4⋊C8—611no—
329C2×C4⋊C8—611no—
330C2×C4⋊C8—611no—
331C2×C4⋊C8—611no—
332C2×C4⋊C8—611no—
333C2×C4⋊C8—611no—
334C2×C22⋊C8—611no—
335C2×C22⋊C8—611no—
336C2×C4×C8—611no—
337C2×C4×C8—611no—
338C2×C4×C8—611no—
339C2×C4×C8—611no—
340#400—611no—
341#399—611no—
342#398—611no—
343#398#692311yescharacteristic
344#396—611no—
345#396—611no—
346#395—611no—
347#393—611no—
348C4×C4⋊C4—611no—
349C4×C4⋊C4—611no—
350C4×C4⋊C4—611no—
351C4×C22⋊C4—611no—
352C4×C22⋊C4—611no—
353#336—611no—
354#336—611no—
355#336—611no—
356#336—611no—
357#336—611no—
358#336—611no—
359#336—611no—
360#336—611no—
361#336—611no—
362#336—611no—
363#336—611no—
364#336—611no—
365#336—611no—
366#336—611no—
367C61#2228811yescharacteristic, complemented, Sylow
368C22×Q8—611no—
369C23×C4—611no—
370C2×M16—1222no—
371C2×M16—2441no—
372C2×M16—2441no—
373C22×C8—611no—
374C22×C8—611no—
375C22×C8—614no—
376C22×C8—611no—
377C22×C8—611no—
378C22×C8—611no—
379C22×C8—611no—
380C22×C8—611no—
381C22×C8—611no—
382C22×C8—2441no—
383C22×C8—2441no—
384C4×Q8—2441no—
385C4×Q8—2441no—
386#117—2441no—
387#117—2441no—
388C2×C4⋊C4—611no—
389C2×C4⋊C4—611no—
390C2×C4⋊C4—611no—
391C2×C4⋊C4—611no—
392C2×C4⋊C4—611no—
393C2×C4⋊C4—611no—
394C2×C4⋊C4—611no—
395C2×C4⋊C4C2×#692311yescharacteristic
396C2×C4⋊C4C2×#692311yescharacteristic
397C2×C4⋊C4C2×#692311yescharacteristic
398C2×C4⋊C4C2×#692311yescharacteristic
399C2×C22⋊C4—611no—
400C2×C22⋊C4—611no—
401C2×C22⋊C4—611no—
402C2×C22⋊C4—611no—
403C2×C22⋊C4—611no—
404C2×C22⋊C4—611no—
405C2×C42—611no—
406C2×C42—611no—
407C2×C42—611no—
408C2×C42—611no—
409C2×C42—611no—
410C2×C42—611no—
411C4⋊C8—2441no—
412C4⋊C8—2441no—
413C4⋊C8—2441no—
414C4⋊C8—2441no—
415C4⋊C8—2441no—
416C4⋊C8—2441no—
417C22⋊C8—1222no—
418C22⋊C8—1222no—
419C4×C8—2441no—
420C4×C8—2441no—
421C4×C8—2441no—
422C4×C8—2441no—
423#95—611no—
424#95—611no—
425#95—611no—
426#95—611no—
427#95—611no—
428#95—611no—
429#95—611no—
430#95C2×#692311yescharacteristic
431#95C2×#692311yescharacteristic
432#95C2×#692311yescharacteristic
433C24—611no—
434C2×Q8—1222no—
435C2×Q8—1222no—
436C2×Q8—2441no—
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—611no—
440C22×C4—612no—
441C22×C4—612no—
442C22×C4—611no—
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—1221no—
447C22×C4—1221no—
448C22×C4—1221no—
449C22×C4—1221no—
450C22×C4C22×#692311yescharacteristic
451C22×C4C22×#692311yescharacteristic
452C22×C4C22×#692311yescharacteristic
453C22×C4C22×#692311yescharacteristic
454C22×C4C22×#692311yescharacteristic
455C22×C4C22×#692311yescharacteristic
456C22×C4C22×#692311yescharacteristic
457M16—2444no—
458C2×C8—612no—
459C2×C8—612no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—1221no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8—1221no—
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—2444no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—1222no—
488C4⋊C4—1222no—
489C4⋊C4—1222no—
490C4⋊C4—1222no—
491C4⋊C4—2441no—
492C4⋊C4—2441no—
493C4⋊C4—2441no—
494C22⋊C4—1222no—
495C22⋊C4—1222no—
496C22⋊C4—1222no—
497C22⋊C4—1222no—
498C22⋊C4—2441no—
499C22⋊C4—2441no—
500C42—1221no—
501C42—1221no—
502C42—1221no—
503C42—1221no—
504C42—1221no—
505C42—1221no—
506C42—1221no—
507C42—1221no—
508C42—1221no—
509C42—1221no—
510C42—1221no—
511C42—1221no—
512C23—612no—
513C23—1221no—
514C23—1221no—
515C23—1221no—
516C23—1221no—
517C23—1221no—
518C23—1221no—
519C23C23×#692311yescharacteristic
520Q8—2444no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—611no—
540C2×C4—611no—
541C2×C4—611no—
542C2×C4—611no—
543C2×C4—611no—
544C2×C4—611no—
545C2×C4—612no—
546C2×C4—612no—
547C2×C4—1222no—
548C2×C4—1222no—
549C2×C4—1222no—
550C2×C4—1222no—
551C2×C4—1221no—
552C2×C4—1221no—
553C2×C4—1221no—
554C2×C4—1221no—
555C2×C4—1221no—
556C2×C4—1221no—
557C2×C4—1221no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—1221no—
566C2×C4—1221no—
567C2×C4Q8×#692312yes—
568C2×C4#1451986412yes—
569C2×C4#1451986512yes—
570C8—1222no—
571C8—1222no—
572C8—2441no—
573C8—2441no—
574C8—2441no—
575C8—2441no—
576C8—2441no—
577C8—2441no—
578C22—1222no—
579C22—1222no—
580C22—1222no—
581C22—2441no—
582C22—2441no—
583C22—2441no—
584C22—2441no—
585C22C2×Q8×#692311yescharacteristic
586C22#1684082911yescharacteristic
587C22#1684083111yescharacteristic
588C22C2×#1451986411yescharacteristic
589C22D61⋊#13111yescharacteristic
590C22D61⋊#13111yescharacteristic
591C22C2×#1451986511yescharacteristic
592C4—22no—
593C4—22no—
594C4—22no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—611no—
600C4—611no—
601C4—611no—
602C4—611no—
603C4—1222no—
604C4—1222no—
605C4—2441no—
606C4—2441no—
607C4—2441no—
608C4—2441no—
609C2—2442no—
610C2#2146231211yescharacteristic
611C2#2146260811yescharacteristic
612C2#2146260911yescharacteristic
613C2#2146269411yescharacteristic
614C2#2146269911yescharacteristic
615C2#2146276711yescharacteristic
616C2#2146277111yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#398C4
prime radicalC23×D61C22×C4
cosocleC22×Dic61C24
hypercenter#398#6923
hypocenterC61#22288
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #398

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. #21461873C2semidirect
7. #21461872C2semidirect
8. #21461872C2semidirect
64. C2×D61⋊C8Q8semidirect
367. C61#22288semidirect

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
#214618732
#214618722
#214617672
#214617652
#214616782
#214615532
#214614862
#214490962
#2228861