Finite Group Databasebeta

← #37573548

Subgroups — #37573548

Order 24448.

394 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C2×#20259352C211yesmaximal, characteristic, complemented
2#27133227C211yesmaximal, characteristic
3C2×#20259310C211yesmaximal, characteristic, complemented
4#27132673C211yesmaximal, characteristic, complemented
5C2×#20259238C211yesmaximal, characteristic, complemented
6#27132423C211yesmaximal, characteristic, complemented
7C2×#104×C191C211yesmaximal, characteristic, complemented
8C22×Dic382C2211yescharacteristic
9C22×D764C2211yescharacteristic
10#20259352—22no—
11#20259352—22no—
12C2×#15690277—21no—
13C2×#15690275—21no—
14C2×#15690271C2211yescharacteristic
15#20259318—21no—
16#20259311—21no—
17#20259310—22no—
18#20259310—22no—
19#20259296—22no—
20#20259290—22no—
21#20259281C2211yescharacteristic
22C2×(C2×D191)⋊C4—22no—
23#20259247—22no—
24#20259238—22no—
25C2×#41×C191C2211yescharacteristic
26C2×M16×C191C2211yescharacteristic
27C2×C42×C191C2211yescharacteristic
28#104×C191—22no—
29C23×D191D412yes—
30C2×Dic382—21no—
31C2×Dic382—21no—
32C2×Dic382—21no—
33C2×Dic382—21no—
34C2×Dic382—21no—
35C2×Dic382D412yescomplemented
36C2×D764—21no—
37C2×D764—21no—
38C2×D764—21no—
39C2×D764—21no—
40C2×D764—21no—
41C2×D764—21no—
42C2×C22⋊D191—24no—
43C22×Dic191—21no—
44#15690277—24no—
45#15690275—24no—
46#15690271—21no—
47#15690271D412yescomplemented
48C2×C191⋊C8—21no—
49C4⋊Dic191D412yes—
50C22⋊Dic191—21no—
51(C2×D191)⋊C4—28no—
52(C2×D191)⋊C4—24no—
53C4×Dic191—21no—
54#41×C191—21no—
55#41×C191—21no—
56#41×C191—21no—
57#41×C191—21no—
58C2×Q8×C191D411yescharacteristic
59C2×D4×C191—21no—
60C2×D4×C191D411yescharacteristic
61C22×C4×C191—21no—
62C22×C4×C191—21no—
63C22×C4×C191C2311yescharacteristic
64M16×C191—21no—
65M16×C191—21no—
66C2×C8×C191—21no—
67C42×C191—21no—
68C42×C191D412yescomplemented
69C22×D191—22no—
70C22×D191—22no—
71C22×D191—22no—
72C22×D191—44no—
73Dic382—22no—
74Dic382—22no—
75Dic382—41no—
76Dic382—41no—
77D764—41no—
78D764—41no—
79D764—41no—
80D764—41no—
81C22⋊D191—84no—
82C2×Dic191—22no—
83C2×Dic191—22no—
84C2×Dic191—41no—
85C2×Dic191—41no—
86C191⋊C8—22no—
87C23×C191—21no—
88C23×C191C2×D411yescharacteristic
89Q8×C191—21no—
90Q8×C191—21no—
91D4×C191—21no—
92D4×C191—21no—
93D4×C191—41no—
94D4×C191—41no—
95C2×C4×C191—22no—
96C2×C4×C191—21no—
97C2×C4×C191—42no—
98C2×C4×C191—41no—
99C2×C4×C191—41no—
100C2×C4×C191C2×D411yescharacteristic
101C2×C4×C191C2×D411yescharacteristic
102C2×C4×C191C2×D411yescharacteristic
103C2×C4×C191C2×D411yescharacteristic
104C2×C4×C191C2×D411yescharacteristic
105C2×C4×C191#4111yescharacteristic
106C8×C191—41no—
107C22×C191—22no—
108C22×C191—41no—
109C22×C191—42no—
110C22×C191#12011yescharacteristic
111C22×C191#12011yescharacteristic
112C22×C191#12111yescharacteristic
113C2×D191—44no—
114C2×D191—42no—
115C2×D191—44no—
116C2×D191—82no—
117C4×C191—42no—
118C4×C191—41no—
119C4×C191#12011yescharacteristic
120C4×C191#12111yescharacteristic
121C4×C191#12111yescharacteristic
122C4×C191#12711yescharacteristic
123Dic191—42no—
124Dic191—42no—
125C2×C191—21no—
126C2×C191—21no—
127C2×C191—81no—
128C2×C191#39211yescharacteristic
129C2×C191#45512yes—
130D191—82no—
131C191#200411yescharacteristic, complemented, Sylow
132#2004—1911nomaximal, Sylow
133C2×#137—1911no—
134#535—1911no—
135C2×#124—1911no—
136C2×#104D19111yescharacteristic, complemented
137#419—1911no—
138C2×#100—1911no—
139#339—1911no—
140C2×#41C2×D19111yescharacteristic
141C22×Q8—1911no—
142C22×D4—1911no—
143#137—3822no—
144#137—3822no—
145C2×Q16—3821no—
146C2×SD16—3821no—
147C2×M16—1911no—
148C2×M16C2×D19111yescharacteristic
149#127—3821no—
150#124—3822no—
151#124—3821no—
152#124—3822no—
153#121—3822no—
154#120—3822no—
155#117—1911no—
156C2×C22⋊C4—3822no—
157C2×C42C2×D19111yescharacteristic
158#104—22no—
159#103—3822no—
160#100—3822no—
161C24—1912no—
162#41—21no—
163#41—21no—
164#41—21no—
165#41—21no—
166C2×Q8—3821no—
167C2×Q8—3821no—
168C2×Q8—3821no—
169C2×Q8—3821no—
170C2×Q8—3821no—
171C2×Q8—1912no—
172C2×Q8D76411yescharacteristic
173C2×D4—21no—
174C2×D4—3824no—
175C2×D4—3821no—
176C2×D4—3821no—
177C2×D4—3821no—
178C2×D4—3821no—
179C2×D4—3821no—
180C2×D4—3821no—
181C2×D4D76411yescharacteristic
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—3821no—
185C22×C4C22×D19111yescharacteristic
186Q16—3824no—
187SD16—3824no—
188M16—21no—
189M16—21no—
190M16—3821no—
191M16—1912no—
192C2×C8—21no—
193C2×C8—3821no—
194C4⋊C4—1912no—
195C22⋊C4—3828no—
196C22⋊C4—3824no—
197C22⋊C4—3821no—
198C42—21no—
199C42—3821no—
200C42C22⋊D19112yescomplemented
201C23—21no—
202C23—3822no—
203C23—3822no—
204C23—3822no—
205C23—7644no—
206C23D4×D19111yescharacteristic
207Q8—21no—
208Q8—21no—
209Q8—3822no—
210Q8—3822no—
211Q8—7641no—
212Q8—7641no—
213D4—21no—
214D4—21no—
215D4—41no—
216D4—41no—
217D4—15284no—
218D4—7641no—
219D4—7641no—
220D4—7641no—
221D4—7641no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—42no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—3822no—
228C2×C4—3822no—
229C2×C4—7641no—
230C2×C4—7641no—
231C2×C4D4×D19111yescharacteristic
232C2×C4D4×D19111yescharacteristic
233C2×C4D4×D19111yescharacteristic
234C2×C4C2×C22⋊D19111yescharacteristic
235C2×C4C2×D76411yescharacteristic
236C2×C4#1569028711yescharacteristic
237C8—41no—
238C8—3822no—
239C22—22no—
240C22—41no—
241C22—42no—
242C22—15282no—
243C22—7644no—
244C22—7642no—
245C22—7644no—
246C22#2025929011yescharacteristic
247C22#2025929211yescharacteristic
248C22#2025929511yescharacteristic
249C4—42no—
250C4—41no—
251C4—7642no—
252C4—7642no—
253C4#2025929211yescharacteristic
254C4#2025929511yescharacteristic
255C4#2025929611yescharacteristic
256C4#2025931811yescharacteristic
257C2—21no—
258C2—21no—
259C2—81no—
260C2—15282no—
261C2#2713257211yescharacteristic
262C2#2713284212yes—
subgroupG/H
centerC22#20259292
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
FittingC2×#104×C191C2
socleC22×C191#120
prime radical#27133227C2
hypercenterC2×#104D191
hypocenterC191#2004
LCSG ▷ C22×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×#20259352C2semidirect
3. C2×#20259310C2semidirect
4. #27132673C2semidirect
5. C2×#20259238C2semidirect
6. #27132423C2semidirect
7. C2×#104×C191C2semidirect
35. C2×Dic382D4semidirect
47. #15690271D4semidirect
68. C42×C191D4semidirect
131. C191#2004semidirect
136. C2×#104D191semidirect
200. C42C22⋊D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593522
#271332272
C2×#202593102
#271326732
C2×#202592382
#271324232
C2×#104×C1912
#2004191