Finite Group Databasebeta

← #30619521

Subgroups — #30619521

Order 15616.

672 conjugacy classes of subgroups.

The subgroup lattice has 606 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#21461891C211yesmaximal, characteristic
4#21461891C211yesmaximal, characteristic
5#21461890C211yesmaximal, characteristic
6#21461890C211yesmaximal, characteristic
7#21461879C211yesmaximal, characteristic, complemented
8#21461877C211yesmaximal, characteristic, complemented
9#21461875C211yesmaximal, characteristic, complemented
10#21461872C211yesmaximal, characteristic, complemented
11#21461713C211yesmaximal, characteristic
12#21461611C211yesmaximal, characteristic, complemented
13C4⋊C4×#92420C211yesmaximal, characteristic, complemented
14#21461548C211yesmaximal, characteristic
15#21449096C211yesmaximal, characteristic
16C2×#14519844C2211yescharacteristic
17C2×#14519844C2211yescharacteristic
18C2×C4⋊#92420C2211yescharacteristic
19C2×C4⋊#92420C2211yescharacteristic
20C2×#14519834C2211yescharacteristic
21C2×#14519834C2211yescharacteristic
22C2×#14519834C2211yescharacteristic
23C2×#14519834C2211yescharacteristic
24C2×#14519832C2211yescharacteristic
25C2×C4×#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×#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
59C22×#92420C2311yescharacteristic
60C22×#92420C2311yescharacteristic
61C22×#92420C2311yescharacteristic
62C22×#92420C2311yescharacteristic
63C22×#92420C2311yescharacteristic
64C22×#92420C2311yescharacteristic
65C22×#92420C2311yescharacteristic
66C22×#92420C2311yescharacteristic
67#14519844—22no—
68#14519844—41no—
69C4⋊#92420—22no—
70C4⋊#92420—41no—
71#14519834—22no—
72#14519834—22no—
73#14519834—41no—
74#14519834—41no—
75#14519832—41no—
76C4×#92420—22no—
77C4×#92420—22no—
78C4×#92420—41no—
79C4×#92420—41no—
80C4×#92420—41no—
81C22×Dic122C2×C411yescharacteristic
82C22×C4×D61C2311yescharacteristic
83#14519742—41no—
84#14519742—41no—
85#14519735—41no—
86#14519735—41no—
87C2×C4⋊Dic61C2×C411yescharacteristic
88C2×C4⋊Dic61C2×C411yescharacteristic
89C2×C4⋊Dic61C2×C411yescharacteristic
90C2×#11758196C2×C411yescharacteristic
91C2×#11758196C2×C411yescharacteristic
92C2×#11758196C2×C411yescharacteristic
93C2×#11758196C2×C411yescharacteristic
94C2×#11758198C2×C411yescharacteristic
95C2×#11758198C2×C411yescharacteristic
96C2×#11758198C2×C411yescharacteristic
97C2×#11758198C2×C411yescharacteristic
98C2×#11758198C2×C411yescharacteristic
99C2×#11758198C2×C411yescharacteristic
100C2×C4×Dic61C2311yescharacteristic
101C2×C4×Dic61C2311yescharacteristic
102C2×C4×Dic61C2311yescharacteristic
103C2×C4×Dic61C2311yescharacteristic
104C2×C4×Dic61C2311yescharacteristic
105C2×C4×Dic61C2311yescharacteristic
106#14519684C2×C411yescharacteristic
107#14519684C2×C411yescharacteristic
108#14519684C2×C411yescharacteristic
109#14519684C2×C411yescharacteristic
110#14519684C2×C411yescharacteristic
111#14519684C2×C411yescharacteristic
112#14519684C2×C411yescharacteristic
113C2×C4⋊C4×C61C2×C411yescharacteristic
114C2×C4⋊C4×C61C2×C411yescharacteristic
115C2×C4⋊C4×C61C2×C411yescharacteristic
116C2×C4⋊C4×C61C2×C411yescharacteristic
117#95×C61C2×C411yescharacteristic
118#95×C61C2×C411yescharacteristic
119#95×C61C2×C411yescharacteristic
120C23×D61C22×C411yescharacteristic
121C22×C4×C61C22×C411yescharacteristic
122C22×C4×C61C22×C411yescharacteristic
123C22×C4×C61C22×C411yescharacteristic
124C22×C4×C61C22×C411yescharacteristic
125C22×C4×C61C22×C411yescharacteristic
126C22×C4×C61C22×C411yescharacteristic
127C22×C4×C61C22×C411yescharacteristic
128C22×Dic61C22×C411yescharacteristic
129C22×Dic61C22×C411yescharacteristic
130C22×Dic61C22×C411yescharacteristic
131C22×Dic61C22×C411yescharacteristic
132C22×Dic61C22×C411yescharacteristic
133C22×Dic61C22×C411yescharacteristic
134C22×Dic61C2411yescharacteristic
135C2×C4×D61—21no—
136C2×C4×D61—21no—
137C2×C4×D61—21no—
138C2×C4×D61—21no—
139C2×C4×D61—21no—
140C2×C4×D61—21no—
141C2×Dic122—22no—
142C2×Dic122—22no—
143C2×Dic122—41no—
144C2×#92420—21no—
145C2×#92420—21no—
146C2×#92420—21no—
147C2×#92420—21no—
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#4112yes—
167C2×#92420#4112yes—
168C4⋊C4×C61—22no—
169C4⋊C4×C61—22no—
170C4⋊C4×C61—41no—
171C4⋊C4×C61—41no—
172#11758198—22no—
173#11758198—22no—
174#11758198—22no—
175#11758198—22no—
176#11758198—41no—
177#11758198—41no—
178C4⋊Dic61—22no—
179C4⋊Dic61—22no—
180C4⋊Dic61—41no—
181#11758196—22no—
182#11758196—22no—
183#11758196—41no—
184#11758196—41no—
185C4×Dic61—21no—
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—21no—
195C4×Dic61—21no—
196C4×Dic61—21no—
197C23×C61C23×C411yescharacteristic
198C22×D61—21no—
199C22×D61—21no—
200C22×D61—21no—
201C22×D61—21no—
202C22×D61—21no—
203C22×D61—21no—
204C22×D61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
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#13112yes—
225C2×C4×C61#13112yes—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
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#13112yes—
243C2×Dic61#13112yes—
244C2×Dic61C2×#4111yescharacteristic
245C2×Dic61C2×#4111yescharacteristic
246C2×Dic61H(5,𝔽2)11yescharacteristic
247C2×Dic61H(5,𝔽2)11yescharacteristic
248C2×Dic612−1+411yescharacteristic
249C2×Dic612−1+411yescharacteristic
250C4×D61—41no—
251C4×D61—41no—
252C4×D61—41no—
253C4×D61—41no—
254Dic122—44no—
255#92420—22no—
256#92420—22no—
257#92420—41no—
258#92420—41no—
259#92420—41no—
260#92420—41no—
261#92420—41no—
262#92420—41no—
263#22318—611nomaximal, Sylow
264C22×C61C4×#4111yescharacteristic
265C22×C61#51811yescharacteristic
266C22×C61#51911yescharacteristic
267C22×C61C2×#13111yescharacteristic
268C22×C61C2×#13111yescharacteristic
269C22×C61C2×#13111yescharacteristic
270C22×C61C2×#13111yescharacteristic
271C2×D61—41no—
272C2×D61—41no—
273C2×D61—41no—
274C2×D61—41no—
275C2×D61—41no—
276C2×D61—41no—
277C2×D61—41no—
278C4×C61—22no—
279C4×C61—22no—
280C4×C61—41no—
281C4×C61—41no—
282C4×C61—41no—
283C4×C61—41no—
284C4×C61—41no—
285Dic61—22no—
286Dic61—22no—
287Dic61—41no—
288Dic61—41no—
289Dic61—41no—
290Dic61—41no—
291Dic61#53911yescharacteristic
292Dic61#53911yescharacteristic
293Dic61#54211yescharacteristic
294Dic61#54211yescharacteristic
295#2396—611no—
296#1984—611no—
297#1984—611no—
298#1923—611no—
299#1923—611no—
300#1923—611no—
301#1923—611no—
302#1917—611no—
303#1917—611no—
304#1916—611no—
305#1916—611no—
306#1818—611no—
307C8×C4⋊C4—611no—
308C8×C4⋊C4—611no—
309#1750—611no—
310C2×C61#233211yescharacteristic
311C2×C61#296611yescharacteristic
312C2×C61#296611yescharacteristic
313C2×C61#297711yescharacteristic
314C2×C61#297911yescharacteristic
315C2×C61#298611yescharacteristic
316C2×C61#298611yescharacteristic
317D61—81no—
318C2×C4×Q8—611no—
319C2×#117—611no—
320C2×C4⋊C8—611no—
321C2×C4⋊C8—611no—
322C2×C4⋊C8—611no—
323C2×C4⋊C8—611no—
324C2×C22⋊C8—611no—
325C2×C22⋊C8—611no—
326C2×C22⋊C8—611no—
327C2×C22⋊C8—611no—
328C2×#97—611no—
329C2×C4×C8—611no—
330C2×C4×C8—611no—
331C2×C4×C8—611no—
332C2×C4×C8—611no—
333C2×C4×C8—611no—
334#400—611no—
335#399—611no—
336#398—611no—
337#398#692311yescharacteristic
338#396—611no—
339#396—611no—
340#395—611no—
341#393—611no—
342C4×C4⋊C4—611no—
343C4×C4⋊C4—611no—
344C4×C4⋊C4—611no—
345C4×C22⋊C4—611no—
346C4×C22⋊C4—611no—
347#336—611no—
348#336—611no—
349#336—611no—
350#336—611no—
351#336—611no—
352#336—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—
361C61#2231811yescharacteristic, complemented, Sylow
362C22×Q8—611no—
363C23×C4—611no—
364C22×C8—611no—
365C22×C8—611no—
366C22×C8—611no—
367C22×C8—611no—
368C22×C8—611no—
369C22×C8—611no—
370C22×C8—611no—
371C22×C8—611no—
372C4×Q8—2441no—
373C4×Q8—2441no—
374#117—2441no—
375#117—2441no—
376C2×C4⋊C4—611no—
377C2×C4⋊C4—611no—
378C2×C4⋊C4—611no—
379C2×C4⋊C4—611no—
380C2×C4⋊C4—611no—
381C2×C4⋊C4—611no—
382C2×C4⋊C4—611no—
383C2×C4⋊C4C2×#692311yescharacteristic
384C2×C4⋊C4C2×#692311yescharacteristic
385C2×C4⋊C4C2×#692311yescharacteristic
386C2×C4⋊C4C2×#692311yescharacteristic
387C2×C22⋊C4—611no—
388C2×C22⋊C4—611no—
389C2×C22⋊C4—611no—
390C2×C22⋊C4—611no—
391C2×C22⋊C4—611no—
392C2×C22⋊C4—611no—
393C2×C42—611no—
394C2×C42—611no—
395C2×C42—611no—
396C2×C42—611no—
397C2×C42—611no—
398C2×C42—611no—
399C4⋊C8—1222no—
400C4⋊C8—1222no—
401C4⋊C8—2441no—
402C4⋊C8—2441no—
403C22⋊C8—1222no—
404C22⋊C8—1222no—
405C22⋊C8—2441no—
406C22⋊C8—2441no—
407#97—2441no—
408C4×C8—1222no—
409C4×C8—1222no—
410C4×C8—2441no—
411C4×C8—2441no—
412C4×C8—2441no—
413#95—611no—
414#95—611no—
415#95—611no—
416#95—611no—
417#95—611no—
418#95—611no—
419#95—611no—
420#95C2×#692311yescharacteristic
421#95C2×#692311yescharacteristic
422#95C2×#692311yescharacteristic
423C24—611no—
424C2×Q8—1222no—
425C2×Q8—1222no—
426C2×Q8—2441no—
427C22×C4—611no—
428C22×C4—611no—
429C22×C4—611no—
430C22×C4—611no—
431C22×C4—611no—
432C22×C4—611no—
433C22×C4—611no—
434C22×C4—1221no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4—1221no—
438C22×C4—1221no—
439C22×C4—1221no—
440C22×C4C22×#692311yescharacteristic
441C22×C4C22×#692311yescharacteristic
442C22×C4C22×#692311yescharacteristic
443C22×C4C22×#692311yescharacteristic
444C22×C4C22×#692311yescharacteristic
445C22×C4C22×#692311yescharacteristic
446C22×C4C22×#692311yescharacteristic
447C2×C8—612no—
448C2×C8—612no—
449C2×C8—1221no—
450C2×C8—1221no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—1221no—
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—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—1222no—
476C4⋊C4—1222no—
477C4⋊C4—1222no—
478C4⋊C4—1222no—
479C4⋊C4—2441no—
480C4⋊C4—2441no—
481C4⋊C4—2441no—
482C22⋊C4—1222no—
483C22⋊C4—1222no—
484C22⋊C4—1222no—
485C22⋊C4—1222no—
486C22⋊C4—2441no—
487C22⋊C4—2441no—
488C42—1221no—
489C42—1221no—
490C42—1221no—
491C42—1221no—
492C42—1221no—
493C42—1221no—
494C42—1221no—
495C42—1221no—
496C42—1221no—
497C42—1221no—
498C42—1221no—
499C42—1221no—
500C23—1221no—
501C23—1221no—
502C23—1221no—
503C23—1221no—
504C23—1221no—
505C23—1221no—
506C23—1221no—
507C23C23×#692311yescharacteristic
508Q8—2444no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—611no—
529C2×C4—611no—
530C2×C4—611no—
531C2×C4—611no—
532C2×C4—611no—
533C2×C4—611no—
534C2×C4—612no—
535C2×C4—612no—
536C2×C4—1221no—
537C2×C4—1221no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—1221no—
543C2×C4—1221no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—1221no—
547C2×C4—1221no—
548C2×C4—1221no—
549C2×C4—1221no—
550C2×C4—1221no—
551C2×C4—1221no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4#1451986412yes—
557C2×C4#1451986512yes—
558C8—1222no—
559C8—1222no—
560C8—2441no—
561C8—2441no—
562C8—2441no—
563C8—2441no—
564C8—2441no—
565C8—2441no—
566C22—2441no—
567C22—2441no—
568C22—2441no—
569C22—2441no—
570C22—2441no—
571C22—2441no—
572C22—2441no—
573C22#41×#692311yescharacteristic
574C22#1684082911yescharacteristic
575C22#1684083011yescharacteristic
576C22C2×#1451986411yescharacteristic
577C22D61⋊#13111yescharacteristic
578C22D61⋊#13111yescharacteristic
579C22C2×#1451986511yescharacteristic
580C4—22no—
581C4—22no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—611no—
588C4—611no—
589C4—611no—
590C4—611no—
591C4—1222no—
592C4—1222no—
593C4—2441no—
594C4—2441no—
595C4—2441no—
596C4—2441no—
597C2—4881no—
598C2#2146231511yescharacteristic
599C2#2146263411yescharacteristic
600C2#2146263611yescharacteristic
601C2#2146269411yescharacteristic
602C2#2146269911yescharacteristic
603C2#2146272911yescharacteristic
604C2#2146273011yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#398C4
prime radicalC23×D61C22×C4
cosocleC22×Dic61C24
hypercenter#398#6923
hypocenterC61#22318
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
7. #21461879C2semidirect
8. #21461877C2semidirect
9. #21461875C2semidirect
10. #21461872C2semidirect
12. #21461611C2semidirect
13. C4⋊C4×#92420C2semidirect
361. C61#22318semidirect

Maximal subgroups

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

subgroupindex
#214619902
#214619892
#214618912
#214618902
#214618792
#214618772
#214618752
#214618722
#214617132
#214616112
C4⋊C4×#924202
#214615482
#214490962
#2231861