Finite Group Databasebeta

← C2×#27132795 #37581694

Subgroups — C2×#27132795 #37581694

Order 24448.

1048 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D191C211yesmaximal, characteristic, complemented
2C22×#15690272C211yesmaximal, characteristic, complemented
3C2×#20259293C211yesmaximal, characteristic, complemented
4#27132795C218yesmaximal, direct product factor
5C2×#20259244C211yesmaximal, characteristic, complemented
6C2×#20259243C211yesmaximal, characteristic, complemented
7C2×(C2×D191)⋊C8C211yesmaximal, characteristic, complemented
8C22×D8×C191C211yesmaximal, characteristic, complemented
9C24×D191—21no—
10C22×D764C2211yescharacteristic
11C22×C22⋊D191—21no—
12C22×C22⋊D191—21no—
13C2×D4×D191—24no—
14C2×D4×D191—22no—
15C2×D4×D191—24no—
16C2×D4×D191C2214yescomplemented
17C22×C4×D191C2211yescharacteristic
18C2×#15690272—24no—
19C2×#15690272C2214yescomplemented
20C22×C191⋊C8C2211yescharacteristic, complemented
21#20259293—22no—
22#20259293C2214yescomplemented
23C2×C4⋊Dic191C2211yescharacteristic, complemented
24C2×C22⋊Dic191—21no—
25#20259244C2214yescomplemented
26#20259243C2214yescomplemented
27(C2×D191)⋊C8C2214yescomplemented
28C22×D4×C191C2211yescharacteristic
29C22×D4×C191C2211yescharacteristic, complemented
30C2×D8×C191—24no—
31C2×D8×C191C2214yescomplemented
32C22×C8×C191C2211yescharacteristic, complemented
33C23×D191—28no—
34C23×D191—24no—
35C23×D191—21no—
36C23×D191—44no—
37C23×D191—44no—
38C23×D191D411yescharacteristic
39C2×D764—21no—
40C2×D764—22no—
41C2×D764D414yescomplemented
42C2×D764C2312yes—
43C2×C22⋊D191—28no—
44C2×C22⋊D191—24no—
45C2×C22⋊D191—24no—
46C2×C22⋊D191—44no—
47D4×D191—216no—
48D4×D191—28no—
49D4×D191—28no—
50C22×Dic191—21no—
51C22×Dic191D411yescharacteristic
52C2×C4×D191—22no—
53C2×C4×D191—22no—
54C2×C4×D191D412yes—
55C2×C4×D191C2312yes—
56#15690272—28no—
57C2×C191⋊C8—22no—
58C2×C191⋊C8C2312yescomplemented
59C4⋊Dic191—21no—
60C4⋊Dic191C2312yescomplemented
61C22⋊Dic191—24no—
62C24×C191—21no—
63C24×C191—21no—
64C2×D4×C191—21no—
65C2×D4×C191—22no—
66C2×D4×C191—22no—
67C2×D4×C191—22no—
68C2×D4×C191—21no—
69C2×D4×C191D414yescomplemented
70C2×D4×C191C2312yes—
71C2×D4×C191C2312yescomplemented
72C22×C4×C191C2311yescharacteristic
73D8×C191—28no—
74C2×C8×C191—22no—
75C2×C8×C191C2312yescomplemented
76C22×D191—22no—
77C22×D191—22no—
78C22×D191—216no—
79C22×D191—24no—
80C22×D191—22no—
81C22×D191—48no—
82C22×D191—432no—
83C22×D191—42no—
84C22×D191—42no—
85C22×D191—48no—
86C22×D191D814yescomplemented
87C22×D191C2×D412yes—
88D764—24no—
89D764—22no—
90D764C2×D414yescomplemented
91C22⋊D191—216no—
92C22⋊D191—48no—
93C2×Dic191—22no—
94C2×Dic191—22no—
95C2×Dic191—42no—
96C2×Dic191C2×D412yes—
97C4×D191—24no—
98C4×D191—22no—
99C4×D191—22no—
100C191⋊C8—22no—
101C23×C191—24no—
102C23×C191—22no—
103C23×C191—22no—
104C23×C191—42no—
105C23×C191—42no—
106C23×C191—42no—
107C23×C191—42no—
108C23×C191—42no—
109C23×C191C2×D411yescharacteristic
110D4×C191—24no—
111D4×C191—22no—
112D4×C191—22no—
113D4×C191—22no—
114D4×C191—42no—
115D4×C191C2×D414yescomplemented
116C2×C4×C191C2×D411yescharacteristic
117C2×C4×C191C2×D412yes—
118C2×C4×C191C2×D412yes—
119C2×C4×C191C2411yescharacteristic
120C8×C191—22no—
121C22×C191—24no—
122C22×C191—42no—
123C22×C191—42no—
124C22×C191—48no—
125C22×C191—42no—
126C22×C191—42no—
127C22×C191—42no—
128C22×C191—84no—
129C22×C191#12012yes—
130C22×C191C2×D812yes—
131C22×C191AGL(1,ℤ/8)12yes—
132C22×C191C22×D411yescharacteristic
133C2×D191—22no—
134C2×D191—22no—
135C2×D191—28no—
136C2×D191—24no—
137C2×D191—432no—
138C2×D191—42no—
139C2×D191—42no—
140C2×D191—48no—
141C2×D191C2×D814yescomplemented
142C4×C191#12012yes—
143C4×C191C22×D411yescharacteristic
144C4×C191C22×D411yescharacteristic
145Dic191—22no—
146Dic191—42no—
147C2×C191—44no—
148C2×C191—82no—
149C2×C191#44714yescomplemented
150C2×C191C2×#12011yescharacteristic
151C2×C191C22×D811yescharacteristic
152C2×C191C2×AGL(1,ℤ/8)11yescharacteristic
153D191—24no—
154D191—44no—
155C191C2×#44711yescharacteristic, complemented, Sylow
156C2×#447—1911nomaximal, Sylow
157C23×D4—1911no—
158C22×D8—1911no—
159C22×D8D19111yescharacteristic, complemented
160C2×#121—1911no—
161#447—1918no—
162C2×#102—1911no—
163C2×#102—1911no—
164C2×C22⋊C8—1911no—
165C25—3821no—
166C22×D4—3824no—
167C22×D4—3824no—
168C22×D4—3821no—
169C22×D4—3822no—
170C22×D4—3821no—
171C22×D4—1914no—
172C22×D4—1911no—
173C22×D4C2×D19111yescharacteristic
174C22×D4C2×D19111yescharacteristic, complemented
175C23×C4—1911no—
176C2×D8—24no—
177C2×D8—3824no—
178C2×D8—1914no—
179C2×D8C2×D19114yescomplemented
180C22×C8—1911no—
181C22×C8C2×D19111yescharacteristic, complemented
182#121—3822no—
183#121—1914no—
184C2×C4⋊C4—1911no—
185C2×C22⋊C4—3821no—
186#102—1914no—
187#102—1914no—
188C22⋊C8—1914no—
189C24—21no—
190C24—21no—
191C24—3828no—
192C24—3824no—
193C24—3821no—
194C24—1911no—
195C24—7644no—
196C24—7644no—
197C2×D4—22no—
198C2×D4—21no—
199C2×D4—22no—
200C2×D4—21no—
201C2×D4—22no—
202C2×D4—38216no—
203C2×D4—3828no—
204C2×D4—3828no—
205C2×D4—3828no—
206C2×D4—3824no—
207C2×D4—3824no—
208C2×D4—3821no—
209C2×D4—3822no—
210C2×D4—1914no—
211C2×D4—1912no—
212C2×D4—7644no—
213C2×D4C22⋊D19114yescomplemented
214C2×D4C22×D19112yes—
215C2×D4C22×D19112yescomplemented
216C22×C4—3822no—
217C22×C4—3822no—
218C22×C4—3821no—
219C22×C4—1911no—
220C22×C4—1912no—
221C22×C4—1912no—
222C22×C4C22×D19111yescharacteristic
223D8—28no—
224D8—3828no—
225C2×C8—22no—
226C2×C8—3822no—
227C2×C8—1912no—
228C2×C8C22×D19112yescomplemented
229C4⋊C4—3821no—
230C4⋊C4—1912no—
231C22⋊C4—3824no—
232C23—22no—
233C23—24no—
234C23—22no—
235C23—42no—
236C23—42no—
237C23—42no—
238C23—42no—
239C23—42no—
240C23—38216no—
241C23—3822no—
242C23—3822no—
243C23—3822no—
244C23—3824no—
245C23—1914no—
246C23—1912no—
247C23—7648no—
248C23—76432no—
249C23—7648no—
250C23—7642no—
251C23—7642no—
252C23D4×D19111yescharacteristic
253D4—22no—
254D4—22no—
255D4—22no—
256D4—24no—
257D4—42no—
258D4—38216no—
259D4—3822no—
260D4—3824no—
261D4—1914no—
262D4—7648no—
263D4C2×C22⋊D19114yescomplemented
264C2×C4—3822no—
265C2×C4—3822no—
266C2×C4—3822no—
267C2×C4—3824no—
268C2×C4—3822no—
269C2×C4—1912no—
270C2×C4—7642no—
271C2×C4D4×D19112yes—
272C2×C4D4×D19111yescharacteristic
273C2×C4C2×C22⋊D19112yes—
274C2×C4C23×D19111yescharacteristic
275C8—22no—
276C8—3822no—
277C22—24no—
278C22—42no—
279C22—48no—
280C22—42no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—84no—
285C22—3822no—
286C22—3828no—
287C22—3822no—
288C22—3824no—
289C22—1914no—
290C22—76432no—
291C22—7642no—
292C22—7648no—
293C22—7642no—
294C22#2025929012yes—
295C22D8×D19112yes—
296C22#2025934612yes—
297C22C2×D4×D19111yescharacteristic
298C4—3822no—
299C4—7642no—
300C4#2025929012yes—
301C4C2×D4×D19111yescharacteristic
302C4C22×C22⋊D19111yescharacteristic
303C2—44no—
304C2—82no—
305C2—3824no—
306C2—7644no—
307C2#2713279514yesdirect product factor
308C2C2×#2025929011yescharacteristic
309C2C2×D8×D19111yescharacteristic
310C2C2×#2025934611yescharacteristic
subgroupG/H
centerC23D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
FittingC22×D8×C191C2
socleC23×C191C2×D4
hypercenterC22×D8D191
hypocenterC191C2×#447
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×D4×D191C2semidirect
2. C22×#15690272C2semidirect
3. C2×#20259293C2semidirect
4. #27132795C2direct (N × H)
5. C2×#20259244C2semidirect
6. C2×#20259243C2semidirect
7. C2×(C2×D191)⋊C8C2semidirect
8. C22×D8×C191C2semidirect
16. C2×D4×D191C22semidirect
19. C2×#15690272C22semidirect
20. C22×C191⋊C8C22semidirect
22. #20259293C22semidirect
23. C2×C4⋊Dic191C22semidirect
25. #20259244C22semidirect
26. #20259243C22semidirect
27. (C2×D191)⋊C8C22semidirect
29. C22×D4×C191C22semidirect
31. C2×D8×C191C22semidirect
32. C22×C8×C191C22semidirect
41. C2×D764D4semidirect
58. C2×C191⋊C8C23semidirect
60. C4⋊Dic191C23semidirect
69. C2×D4×C191D4semidirect
71. C2×D4×C191C23semidirect
75. C2×C8×C191C23semidirect
86. C22×D191D8semidirect
90. D764C2×D4semidirect
115. D4×C191C2×D4semidirect
141. C2×D191C2×D8semidirect
149. C2×C191#447semidirect
155. C191C2×#447semidirect
159. C22×D8D191semidirect
174. C22×D4C2×D191semidirect
179. C2×D8C2×D191semidirect
181. C22×C8C2×D191semidirect
213. C2×D4C22⋊D191semidirect
215. C2×D4C22×D191semidirect
228. C2×C8C22×D191semidirect
263. D4C2×C22⋊D191semidirect
307. C2#27132795direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D1912
C22×#156902722
C2×#202592932
#271327952
C2×#202592442
C2×#202592432
C2×(C2×D191)⋊C82
C22×D8×C1912
C2×#447191