Finite Group Databasebeta

← #27187947

Subgroups — #27187947

Order 12928.

380 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20266229C211yesmaximal, characteristic, complemented
2#20266226C211yesmaximal, characteristic, complemented
3#20266210C211yesmaximal, characteristic, complemented
4#20266208C211yesmaximal, characteristic, complemented
5#20266206C211yesmaximal, characteristic, complemented
6#20266204C211yesmaximal, characteristic, complemented
7#20266204C211yesmaximal, characteristic, complemented
8D4×#11717581C211yesmaximal, characteristic, complemented
9#20266202C211yesmaximal, characteristic, complemented
10#20266201C211yesmaximal, characteristic, complemented
11#20266197C211yesmaximal, characteristic, complemented
12#20266142C211yesmaximal, characteristic, complemented
13#20266141C211yesmaximal, characteristic, complemented
14C2×C4×#11717581C211yesmaximal, characteristic, complemented
15#20265704C211yesmaximal, characteristic
16C2×#13108084C2211yescharacteristic
17C2×#13108083C2211yescharacteristic
18C2×D101⋊C8C2211yescharacteristic
19C22×#11717581C2211yescharacteristic
20C22×#11717581C2211yescharacteristic
21C22×#11717581C2211yescharacteristic
22#15692322C2211yescharacteristic
23#15692322C2211yescharacteristic
24#15692322C2211yescharacteristic
25#15692322C2211yescharacteristic
26C4⋊#11717581C2211yescharacteristic
27C4⋊#11717581C2211yescharacteristic
28#15692312C2211yescharacteristic
29#15692312C2211yescharacteristic
30C22⋊#11717581C2211yescharacteristic
31C22⋊#11717581C2211yescharacteristic
32C22⋊#11717581C2211yescharacteristic
33C22⋊#11717581C2211yescharacteristic
34#15692310C2211yescharacteristic
35#15692310C2211yescharacteristic
36#15692310C2211yescharacteristic
37#15692310C2211yescharacteristic
38C4×#11717581C2211yescharacteristic
39C4×#11717581C2211yescharacteristic
40C4×#11717581C2211yescharacteristic
41C4×#11717581C2211yescharacteristic
42C4×#11717581C2211yescharacteristic
43C4×#11717581C2211yescharacteristic
44#15692250C411yescharacteristic
45#15692248C411yescharacteristic
46#15692245C411yescharacteristic
47#15692241C411yescharacteristic
48#15692238C411yescharacteristic
49#15692232C411yescharacteristic
50#15692227C411yescharacteristic
51#15692220C2211yescharacteristic
52D4×Dic101C2211yescharacteristic
53#15692215C2211yescharacteristic
54#15692215C2211yescharacteristic
55#15692213C2211yescharacteristic
56#15692211C2211yescharacteristic
57C2×C4×Dic101C2211yescharacteristic
58#123×C101C411yescharacteristic
59#13108084—22no—
60#13108083—22no—
61D101⋊C8—22no—
62C2×#11717581—22no—
63C2×#11717581—22no—
64C2×#11717581—22no—
65C2×#11717581C2311yescharacteristic
66C2×#11717581C2311yescharacteristic
67C2×#11717581C2311yescharacteristic
68C2×#11717581C2311yescharacteristic
69C2×#11717581C2311yescharacteristic
70C2×#11717581C2311yescharacteristic
71C2×#11717581C2311yescharacteristic
72C2×#11717581C2311yescharacteristic
73C2×Dic202C2×C411yescharacteristic
74C2×C22⋊D101C2×C411yescharacteristic
75C2×C22⋊D101C2×C411yescharacteristic
76C22×Dic101C2×C411yescharacteristic
77C22×Dic101C2311yescharacteristic
78C22×Dic101C2311yescharacteristic
79C2×C4×D101C2311yescharacteristic
80C4⋊Dic101C2×C411yescharacteristic
81C4⋊Dic101C2×C411yescharacteristic
82#13108053C2×C411yescharacteristic
83#13108053C2×C411yescharacteristic
84#13108053C2×C411yescharacteristic
85#13108053C2×C411yescharacteristic
86#13108053C2×C411yescharacteristic
87#13108053C2×C411yescharacteristic
88C22⋊Dic101C2×C411yescharacteristic
89C22⋊Dic101C2×C411yescharacteristic
90C22⋊Dic101C2×C411yescharacteristic
91#13108051C2×C411yescharacteristic
92#13108051C2×C411yescharacteristic
93#13108051C2×C411yescharacteristic
94#13108051C2×C411yescharacteristic
95C4×Dic101C2×C411yescharacteristic
96C4×Dic101C2×C411yescharacteristic
97C4×Dic101C2311yescharacteristic
98C4×Dic101C2311yescharacteristic
99C4×Dic101C2311yescharacteristic
100C4×Dic101C2311yescharacteristic
101C2×D4×C101C2×C411yescharacteristic
102C22×C4×C101C2×C411yescharacteristic
103C4⋊C4×C101C2×C411yescharacteristic
104C4⋊C4×C101C2×C411yescharacteristic
105C22⋊C4×C101C2×C411yescharacteristic
106C22⋊C4×C101C2×C411yescharacteristic
107C22⋊C4×C101C2×C411yescharacteristic
108C23×C101C22×C411yescharacteristic
109C23×C101C22×C411yescharacteristic
110C22×D101C22×C411yescharacteristic
111D4×C101—22no—
112C2×C4×C101—22no—
113C2×C4×C101C22×C411yescharacteristic
114C2×C4×C101C22×C411yescharacteristic
115C2×C4×C101C22×C411yescharacteristic
116C2×C4×C101C22×C411yescharacteristic
117C2×C4×C101C22×C411yescharacteristic
118C22⋊D101—22no—
119C22⋊D101—22no—
120C2×Dic101—22no—
121C2×Dic101—21no—
122C2×Dic101—21no—
123C2×Dic101—21no—
124C2×Dic101—21no—
125C2×Dic101C22×C411yescharacteristic
126C2×Dic101C22×C411yescharacteristic
127C2×Dic101C22×C411yescharacteristic
128C2×Dic101C22×C411yescharacteristic
129C2×Dic101C22×C411yescharacteristic
130C2×Dic101C22×C411yescharacteristic
131C2×Dic101C2411yescharacteristic
132C4×D101—21no—
133C4×D101—21no—
134Dic202—22no—
135#11717581—21no—
136#11717581—21no—
137#11717581—21no—
138#11717581—21no—
139#11717581—21no—
140#11717581—21no—
141#11717581#4112yes—
142#11717581#4112yes—
143C22×C101—21no—
144C22×C101—21no—
145C22×C101—21no—
146C22×C101—21no—
147C22×C101—21no—
148C22×C101#13112yes—
149C22×C101C23×C411yescharacteristic
150C2×D101—21no—
151C2×D101—21no—
152C2×D101—21no—
153C4×C101—21no—
154C4×C101—21no—
155C4×C101—21no—
156C4×C101—21no—
157C4×C101—21no—
158Dic101—21no—
159Dic101—21no—
160Dic101—21no—
161Dic101—21no—
162Dic101—21no—
163Dic101#13112yes—
164Dic101C2×#4111yescharacteristic
165Dic101C2×#4111yescharacteristic
166C2×C101—22no—
167C2×C101—41no—
168C2×C101C4×#4111yescharacteristic
169C2×C101C2×#13111yescharacteristic
170C2×C101C2×#13111yescharacteristic
171D101—41no—
172#2966—1011nomaximal, Sylow
173C101#296611yescharacteristic, complemented, Sylow
174#529—1011no—
175#446—1011no—
176C8×Q8—1011no—
177#436—1011no—
178#435—1011no—
179#435—1011no—
180C8×D4—1011no—
181C8×D4—1011no—
182C8×D4—1011no—
183#433—1011no—
184#433—1011no—
185#432—1011no—
186#405—1011no—
187#405—1011no—
188C2×C4×C8—1011no—
189C2×M16—1011no—
190C2×M16—1011no—
191C22×C8—1011no—
192C22×C8—1011no—
193C22×C8—1011no—
194C22×C8—1011no—
195#126—1011no—
196#126—1011no—
197#125—1011no—
198#124—1011no—
199#123—1011no—
200#123#8793811yescharacteristic
201C22⋊Q8—1011no—
202#121—1011no—
203C4×Q8—1011no—
204C4×D4—1011no—
205C4×D4—1011no—
206C4×D4—1011no—
207#117—1011no—
208#117—1011no—
209C2×C42—1011no—
210C4⋊C8—1011no—
211C4⋊C8—1011no—
212C4⋊C8—1011no—
213C4⋊C8—1011no—
214C4⋊C8—1011no—
215C4⋊C8—1011no—
216C22⋊C8—1011no—
217C22⋊C8—1011no—
218C22⋊C8—1011no—
219C22⋊C8—1011no—
220C22⋊C8—1011no—
221C22⋊C8—1011no—
222#97—1011no—
223#97—1011no—
224#97—1011no—
225#97—1011no—
226C4×C8—1011no—
227C4×C8—1011no—
228C4×C8—1011no—
229C4×C8—1011no—
230C4×C8—1011no—
231C4×C8—1011no—
232C2×Q8—1011no—
233C2×D4—1011no—
234C2×D4—1011no—
235C2×D4C2×#8793811yescharacteristic
236C22×C4—1011no—
237C22×C4—1011no—
238C22×C4—1011no—
239C22×C4—1011no—
240C22×C4C2×#8793811yescharacteristic
241M16—2022no—
242M16—2022no—
243C2×C8—1011no—
244C2×C8—1011no—
245C2×C8—1011no—
246C2×C8—1011no—
247C2×C8—1011no—
248C2×C8—1011no—
249C2×C8—1011no—
250C2×C8—1011no—
251C2×C8—2022no—
252C2×C8—2022no—
253C2×C8—2022no—
254C2×C8—2022no—
255C4⋊C4—1011no—
256C4⋊C4—1011no—
257C4⋊C4—1011no—
258C4⋊C4—1011no—
259C4⋊C4—1011no—
260C4⋊C4—1011no—
261C4⋊C4—1011no—
262C4⋊C4—1011no—
263C4⋊C4C2×#8793811yescharacteristic
264C4⋊C4C2×#8793811yescharacteristic
265C22⋊C4—1011no—
266C22⋊C4—1011no—
267C22⋊C4—1011no—
268C22⋊C4—1011no—
269C22⋊C4—1011no—
270C22⋊C4—1011no—
271C22⋊C4—1011no—
272C22⋊C4C2×#8793811yescharacteristic
273C22⋊C4C2×#8793811yescharacteristic
274C22⋊C4C2×#8793811yescharacteristic
275C42—1011no—
276C42—1011no—
277C42—1011no—
278C42—1011no—
279C42—1011no—
280C42—1011no—
281C23—1011no—
282C23C22×#8793811yescharacteristic
283C23C22×#8793811yescharacteristic
284Q8—2022no—
285D4—22no—
286D4—2022no—
287D4—2022no—
288C2×C4—22no—
289C2×C4—1011no—
290C2×C4—1011no—
291C2×C4—1011no—
292C2×C4—1011no—
293C2×C4—1011no—
294C2×C4—1011no—
295C2×C4—1011no—
296C2×C4—2021no—
297C2×C4—2021no—
298C2×C4—2021no—
299C2×C4—2021no—
300C2×C4—2021no—
301C2×C4—2021no—
302C2×C4—2022no—
303C2×C4C22×#8793811yescharacteristic
304C2×C4C22×#8793811yescharacteristic
305C2×C4C22×#8793811yescharacteristic
306C2×C4C22×#8793811yescharacteristic
307C2×C4C22×#8793811yescharacteristic
308C8—1012no—
309C8—1012no—
310C8—2021no—
311C8—2021no—
312C8—2021no—
313C8—2021no—
314C8—2021no—
315C8—2021no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—2021no—
322C22—2021no—
323C22—2021no—
324C22#1569234212yes—
325C22C23×#8793811yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—1011no—
332C4—1011no—
333C4—1012no—
334C4—2021no—
335C4—2021no—
336C4—2021no—
337C4—2021no—
338C4—2021no—
339C2—22no—
340C2—41no—
341C2—4041no—
342C2#41×#8793811yescharacteristic
343C2C2×#1569234211yescharacteristic
344C2D101⋊#13111yescharacteristic
subgroupG/H
center, FrattiniC22C23×#87938
commutator, socleC22×C101C23×C4
Fitting#123×C101C4
prime radical#15692227C4
cosocleC2×Dic101C24
hypercenter#123#87938
hypocenterC101#2966
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #20266229C2semidirect
2. #20266226C2semidirect
3. #20266210C2semidirect
4. #20266208C2semidirect
5. #20266206C2semidirect
6. #20266204C2semidirect
7. #20266204C2semidirect
8. D4×#11717581C2semidirect
9. #20266202C2semidirect
10. #20266201C2semidirect
11. #20266197C2semidirect
12. #20266142C2semidirect
13. #20266141C2semidirect
14. C2×C4×#11717581C2semidirect
173. C101#2966semidirect

Maximal subgroups

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

subgroupindex
#202662292
#202662262
#202662102
#202662082
#202662062
#202662042
D4×#117175812
#202662022
#202662012
#202661972
#202661422
#202661412
C2×C4×#117175812
#202657042
#2966101