Finite Group Databasebeta

← #27187866

Subgroups — #27187866

Order 12928.

502 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15692342C211yesmaximal, characteristic, complemented
2C2×D101⋊M16C211yesmaximal, characteristic, complemented
3#20266211C211yesmaximal, characteristic, complemented
4#20266210C211yesmaximal, characteristic, complemented
5#20266209C211yesmaximal, characteristic, complemented
6#20266207C211yesmaximal, characteristic, complemented
7#20266207C211yesmaximal, characteristic, complemented
8#20266206C211yesmaximal, characteristic, complemented
9#20266205C211yesmaximal, characteristic, complemented
10#20266204C211yesmaximal, characteristic, complemented
11#20266183C211yesmaximal, characteristic, complemented
12#20266150C211yesmaximal, characteristic, complemented
13C2×#15692312C211yesmaximal, characteristic, complemented
14#20266141C211yesmaximal, characteristic, complemented
15#20265685C211yesmaximal, characteristic
16#15692342—24no—
17C2×#13108084C2211yescharacteristic
18C2×#13108084C2211yescharacteristic
19C2×#13108084C2211yescharacteristic, complemented
20D101⋊M16—24no—
21C2×#13108083C2211yescharacteristic
22C2×#13108083C2211yescharacteristic
23C2×#13108083C2211yescharacteristic, complemented
24C2×D101⋊C8C2211yescharacteristic
25C2×D101⋊C8C2211yescharacteristic
26C2×D101⋊C8C2211yescharacteristic, complemented
27C22×#11717581C2211yescharacteristic
28C22×#11717581C2211yescharacteristic
29C22×#11717581C2211yescharacteristic, complemented
30#15692322C2211yescharacteristic, complemented
31#15692322C2211yescharacteristic, complemented
32C4⋊#11717581C2211yescharacteristic, complemented
33C4⋊#11717581C2211yescharacteristic, complemented
34#15692312C2211yescharacteristic
35#15692312C2211yescharacteristic
36#15692312C2211yescharacteristic
37#15692312C2211yescharacteristic
38#15692312C2211yescharacteristic, complemented
39#15692312C2211yescharacteristic, complemented
40C22⋊#11717581C2211yescharacteristic, complemented
41C22⋊#11717581C2211yescharacteristic, complemented
42#15692310C2211yescharacteristic, complemented
43#15692310C2211yescharacteristic, complemented
44C4×#11717581C2211yescharacteristic, complemented
45C4×#11717581C2211yescharacteristic, complemented
46C2×#13108073C2211yescharacteristic
47C22×C4×D101C2211yescharacteristic
48#15692238C411yescharacteristic
49#15692233C411yescharacteristic
50#15692233C411yescharacteristic
51#15692228C411yescharacteristic
52#15692228C411yescharacteristic
53#15692225C411yescharacteristic
54#15692223C411yescharacteristic
55#15692217C2211yescharacteristic
56#15692217C2211yescharacteristic
57#15692215C2211yescharacteristic
58#15692215C2211yescharacteristic
59#15692211C2211yescharacteristic
60#123×C101C411yescharacteristic
61#13108084—22no—
62#13108084—22no—
63#13108084—22no—
64#13108083—22no—
65#13108083—22no—
66#13108083D414yescomplemented
67D101⋊C8—22no—
68D101⋊C8—22no—
69D101⋊C8—22no—
70C2×#11717581—22no—
71C2×#11717581—22no—
72C2×#11717581—22no—
73C2×#11717581C2311yescharacteristic
74C2×#11717581C2311yescharacteristic
75C2×#11717581C2311yescharacteristic
76C2×#11717581C2311yescharacteristic
77C2×#11717581C2311yescharacteristic
78C2×#11717581C2311yescharacteristic
79C2×#11717581C2311yescharacteristic
80C2×#11717581C2311yescharacteristic
81C23×D101C2×C411yescharacteristic
82#13108073—22no—
83#13108073—22no—
84C2×Dic202C2×C411yescharacteristic
85C2×D404C2×C411yescharacteristic
86C2×D404C2×C411yescharacteristic
87C2×C22⋊D101C2×C411yescharacteristic
88C2×C22⋊D101C2×C411yescharacteristic
89C2×C22⋊D101C2×C411yescharacteristic
90C2×C22⋊D101C2×C411yescharacteristic
91C22×Dic101C2311yescharacteristic
92C22×Dic101C2311yescharacteristic
93C2×C4×D101—22no—
94C2×C4×D101—22no—
95C2×C4×D101C2×C411yescharacteristic
96C2×C4×D101C2×C411yescharacteristic
97C2×C4×D101C2311yescharacteristic
98C2×C4×D101C2311yescharacteristic
99C2×C4×D101C2311yescharacteristic
100#13108053C2×C411yescharacteristic
101#13108053C2×C411yescharacteristic
102#13108053C2×C411yescharacteristic
103#13108053C2×C411yescharacteristic
104C22⋊Dic101C2×C411yescharacteristic
105#13108051C2×C411yescharacteristic
106#13108051C2×C411yescharacteristic
107#13108051C2×C411yescharacteristic
108#13108051C2×C411yescharacteristic
109#13108051C2×C411yescharacteristic
110#13108051C2×C411yescharacteristic
111C4×Dic101C2311yescharacteristic
112C4×Dic101C2311yescharacteristic
113C2×D4×C101C2×C411yescharacteristic
114C22×C4×C101C2×C411yescharacteristic
115C4⋊C4×C101C2×C411yescharacteristic
116C4⋊C4×C101C2×C411yescharacteristic
117C22⋊C4×C101C2×C411yescharacteristic
118C22⋊C4×C101C2×C411yescharacteristic
119C22⋊C4×C101C2×C411yescharacteristic
120C23×C101C22×C411yescharacteristic
121C23×C101C22×C411yescharacteristic
122C22×D101—22no—
123C22×D101—22no—
124C22×D101—41no—
125C22×D101C22×C411yescharacteristic
126C22×D101C22×C411yescharacteristic
127C22×D101C22×C411yescharacteristic
128D4×C101—22no—
129C2×C4×C101—22no—
130C2×C4×C101C22×C411yescharacteristic
131C2×C4×C101C22×C411yescharacteristic
132C2×C4×C101C22×C411yescharacteristic
133C2×C4×C101C22×C411yescharacteristic
134C2×C4×C101C22×C411yescharacteristic
135C22⋊D101—22no—
136C22⋊D101—22no—
137C22⋊D101—22no—
138C22⋊D101—41no—
139C2×Dic101—21no—
140C2×Dic101—21no—
141C2×Dic101C22×C411yescharacteristic
142C2×Dic101C22×C411yescharacteristic
143C2×Dic101C22×C411yescharacteristic
144C2×Dic101C22×C411yescharacteristic
145C2×Dic101C2×D412yes—
146C2×Dic101#4112yes—
147C2×Dic101C2411yescharacteristic
148D404—22no—
149D404—41no—
150C4×D101—22no—
151C4×D101—22no—
152C4×D101—21no—
153C4×D101—21no—
154C4×D101—21no—
155C4×D101—21no—
156C4×D101—21no—
157C4×D101—21no—
158Dic202—22no—
159#11717581—21no—
160#11717581—21no—
161#11717581—21no—
162#11717581—21no—
163#11717581—21no—
164#11717581—21no—
165#11717581C2×D412yes—
166#11717581C2×D412yes—
167C22×C101—21no—
168C22×C101—21no—
169C22×C101—21no—
170C22×C101—21no—
171C22×C101—21no—
172C22×C101C4×D412yes—
173C22×C101C23×C411yescharacteristic
174C2×D101—21no—
175C2×D101—21no—
176C2×D101—21no—
177C2×D101—21no—
178C2×D101—21no—
179C2×D101—21no—
180C2×D101—21no—
181C2×D101—21no—
182C2×D101—44no—
183C2×D101#13112yescomplemented
184C4×C101—21no—
185C4×C101—21no—
186C4×C101—21no—
187C4×C101—21no—
188C4×C101—21no—
189Dic101—21no—
190Dic101—21no—
191Dic101—21no—
192Dic101C4×D412yes—
193Dic101C22×D411yescharacteristic
194Dic101C2×#4111yescharacteristic
195C2×C101—22no—
196C2×C101—41no—
197C2×C101C2×C4×D411yescharacteristic
198C2×C101C2×#13111yescharacteristic
199C2×C101#56811yescharacteristic
200D101—22no—
201D101—41no—
202D101—41no—
203#2933—1011nomaximal, Sylow
204C101#293311yescharacteristic, complemented, Sylow
205C2×#131—1011no—
206C22×M16—1011no—
207#525—1011no—
208#436—1011no—
209#436—1011no—
210#435—1011no—
211#435—1011no—
212#435—1011no—
213#435—1011no—
214C8×D4—1011no—
215C8×D4—1011no—
216#424—1011no—
217#408—1011no—
218C2×C22⋊C8—1011no—
219#405—1011no—
220C2×#41—1011no—
221C23×C4—1011no—
222#131—2024no—
223C2×M16—1011no—
224C2×M16—1011no—
225C2×M16—1011no—
226C2×M16—1011no—
227C2×M16—1011no—
228C2×M16—1011no—
229C2×M16—2024no—
230C22×C8—1011no—
231C22×C8—1011no—
232C22×C8—1011no—
233C22×C8—1011no—
234C22×C8—1011no—
235C22×C8—1011no—
236#123—1011no—
237#123#8793811yescharacteristic
238C22⋊Q8—1011no—
239C22⋊Q8—1011no—
240#121—1011no—
241#121—1011no—
242#120—1011no—
243#120—1011no—
244C4×D4—1011no—
245C4×D4—1011no—
246C4×D4—1011no—
247C4×D4—1011no—
248#117—1011no—
249C4⋊C8—1011no—
250C4⋊C8—1011no—
251C4⋊C8—1011no—
252C4⋊C8—1011no—
253C22⋊C8—1011no—
254C22⋊C8—1011no—
255C22⋊C8—1011no—
256C22⋊C8—1011no—
257C22⋊C8—1011no—
258C22⋊C8—1011no—
259C22⋊C8—1011no—
260C22⋊C8—1011no—
261#97—1011no—
262#97—1011no—
263C4×C8—1011no—
264C4×C8—1011no—
265C24—1011no—
266#41—2022no—
267#41—2022no—
268C2×Q8—1011no—
269C2×D4—1011no—
270C2×D4—1011no—
271C2×D4—1011no—
272C2×D4—1011no—
273C2×D4—1011no—
274C2×D4—1011no—
275C2×D4C2×#8793811yescharacteristic
276C22×C4—1011no—
277C22×C4—1011no—
278C22×C4—1011no—
279C22×C4—1011no—
280C22×C4—1011no—
281C22×C4—1011no—
282C22×C4—1011no—
283C22×C4—2022no—
284C22×C4—2022no—
285C22×C4C2×#8793811yescharacteristic
286M16—1014no—
287M16—2022no—
288M16—2022no—
289M16—2022no—
290M16—2022no—
291M16—2022no—
292C2×C8—1011no—
293C2×C8—1011no—
294C2×C8—1011no—
295C2×C8—1011no—
296C2×C8—1011no—
297C2×C8—1011no—
298C2×C8—1011no—
299C2×C8—1011no—
300C2×C8—2022no—
301C2×C8—2022no—
302C2×C8—2022no—
303C2×C8—2022no—
304C2×C8—2022no—
305C2×C8—2022no—
306C4⋊C4—1011no—
307C4⋊C4—1011no—
308C4⋊C4—1011no—
309C4⋊C4—1011no—
310C4⋊C4C2×#8793811yescharacteristic
311C4⋊C4C2×#8793811yescharacteristic
312C22⋊C4—1011no—
313C22⋊C4—1011no—
314C22⋊C4—1011no—
315C22⋊C4—1011no—
316C22⋊C4—1011no—
317C22⋊C4—1011no—
318C22⋊C4—1011no—
319C22⋊C4C2×#8793811yescharacteristic
320C22⋊C4C2×#8793811yescharacteristic
321C22⋊C4C2×#8793811yescharacteristic
322C42—1011no—
323C42—1011no—
324C23—1011no—
325C23—1011no—
326C23—1011no—
327C23—4041no—
328C23—2022no—
329C23—2022no—
330C23C22×#8793811yescharacteristic
331C23C22×#8793811yescharacteristic
332Q8—2022no—
333D4—22no—
334D4—4041no—
335D4—4041no—
336D4—2022no—
337D4—2022no—
338D4—2022no—
339D4—2022no—
340C2×C4—22no—
341C2×C4—1012no—
342C2×C4—1012no—
343C2×C4—1011no—
344C2×C4—1011no—
345C2×C4—1011no—
346C2×C4—1011no—
347C2×C4—1011no—
348C2×C4—2021no—
349C2×C4—2021no—
350C2×C4—2021no—
351C2×C4—2021no—
352C2×C4—2021no—
353C2×C4—2022no—
354C2×C4—2022no—
355C2×C4—2021no—
356C2×C4—2021no—
357C2×C4—2021no—
358C2×C4C22×#8793811yescharacteristic
359C2×C4C22×#8793811yescharacteristic
360C2×C4C22×#8793811yescharacteristic
361C2×C4C22×#8793811yescharacteristic
362C2×C4C22×#8793811yescharacteristic
363C8—1012no—
364C8—1012no—
365C8—2021no—
366C8—2021no—
367C8—2021no—
368C8—2021no—
369C8—2021no—
370C8—2021no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—1012no—
377C22—4044no—
378C22—2021no—
379C22—2021no—
380C22—2021no—
381C22—2021no—
382C22—2021no—
383C22—2021no—
384C22—2021no—
385C22—2021no—
386C22D4×#8793812yes—
387C22C23×#8793811yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—1011no—
394C4—1011no—
395C4—1012no—
396C4—2021no—
397C4—2021no—
398C4—2021no—
399C2—22no—
400C2—41no—
401C2—4041no—
402C2—4041no—
403C2—2022no—
404C2C2×D4×#8793811yescharacteristic
405C2D101⋊#13111yescharacteristic
406C2#2026625611yescharacteristic
subgroupG/H
center, FrattiniC22C23×#87938
commutator, socleC22×C101C23×C4
Fitting#123×C101C4
prime radical#20265685C2
cosocleC2×Dic101C24
hypercenter#123#87938
hypocenterC101#2933
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×#15692342C2semidirect
2. C2×D101⋊M16C2semidirect
3. #20266211C2semidirect
4. #20266210C2semidirect
5. #20266209C2semidirect
6. #20266207C2semidirect
7. #20266207C2semidirect
8. #20266206C2semidirect
9. #20266205C2semidirect
10. #20266204C2semidirect
11. #20266183C2semidirect
12. #20266150C2semidirect
13. C2×#15692312C2semidirect
14. #20266141C2semidirect
19. C2×#13108084C22semidirect
23. C2×#13108083C22semidirect
26. C2×D101⋊C8C22semidirect
29. C22×#11717581C22semidirect
30. #15692322C22semidirect
31. #15692322C22semidirect
32. C4⋊#11717581C22semidirect
33. C4⋊#11717581C22semidirect
38. #15692312C22semidirect
39. #15692312C22semidirect
40. C22⋊#11717581C22semidirect
41. C22⋊#11717581C22semidirect
42. #15692310C22semidirect
43. #15692310C22semidirect
44. C4×#11717581C22semidirect
45. C4×#11717581C22semidirect
66. #13108083D4semidirect
183. C2×D101#131semidirect
204. C101#2933semidirect

Maximal subgroups

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

subgroupindex
C2×#156923422
C2×D101⋊M162
#202662112
#202662102
#202662092
#202662072
#202662062
#202662052
#202662042
#202661832
#202661502
C2×#156923122
#202661412
#202656852
#2933101