Finite Group Databasebeta

← #37575755

Subgroups — #37575755

Order 24448.

696 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 159 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×D4×Dic191C211yesmaximal, characteristic, complemented
2C2×D4×Dic191C212yesmaximal, complemented
3C2×#20259278C211yesmaximal, characteristic, complemented
4#27132595C211yesmaximal, characteristic, complemented
5#27132588C211yesmaximal, characteristic, complemented
6#27132586C212yesmaximal, complemented
7#27132577C212yesmaximal, complemented
8#27132577C211yesmaximal, characteristic, complemented
9#27132514C211yesmaximal, characteristic, complemented
10C22⋊C4×Dic191C212yesmaximal, complemented
11#392×C191C211yesmaximal, characteristic
12C23×Dic191C2212yes—
13C23×Dic191C2211yescharacteristic
14D4×Dic191—28no—
15D4×Dic191—24no—
16#20259278—24no—
17C2×C4⋊Dic191C2212yes—
18C2×C4⋊Dic191C2211yescharacteristic
19C2×Dic191⋊C4C2212yes—
20C2×Dic191⋊C4C2211yescharacteristic
21C2×Dic191⋊C4C2211yescharacteristic
22C2×C22⋊Dic191C2212yes—
23C2×C22⋊Dic191C2211yescharacteristic
24C2×C22⋊Dic191C2212yes—
25C2×C22⋊Dic191C2212yes—
26C2×C22⋊Dic191C2212yes—
27C2×C4×Dic191C2211yescharacteristic
28C2×C4×Dic191C2212yes—
29C2×C4×Dic191C2211yescharacteristic
30C191⋊#95C2212yes—
31C191⋊#95C2212yes—
32C191⋊#95C2211yescharacteristic
33C22×D4×C191C2211yescharacteristic
34C22×D4×C191C2212yes—
35C2×C22⋊C4×C191C2212yes—
36C2×C22⋊C4×C191C2211yescharacteristic
37#95×C191C2211yescharacteristic
38C22×Dic191—22no—
39C22×Dic191—22no—
40C22×Dic191—24no—
41C22×Dic191—24no—
42C22×Dic191—24no—
43C22×Dic191D414yescomplemented
44C22×Dic191C2312yes—
45C22×Dic191C2312yes—
46C22×Dic191C2311yescharacteristic
47C22×Dic191C2311yescharacteristic
48C22×Dic191C2311yescharacteristic
49C22×Dic191C2311yescharacteristic
50C4⋊Dic191—24no—
51C4⋊Dic191—22no—
52Dic191⋊C4—22no—
53Dic191⋊C4—22no—
54Dic191⋊C4—24no—
55C22⋊Dic191—22no—
56C22⋊Dic191—24no—
57C22⋊Dic191—24no—
58C22⋊Dic191—24no—
59C22⋊Dic191—24no—
60C4×Dic191—22no—
61C4×Dic191—24no—
62C4×Dic191D414yescomplemented
63C24×C191C2311yescharacteristic
64C24×C191C2312yes—
65C2×D4×C191—24no—
66C2×D4×C191—24no—
67C2×D4×C191—24no—
68C2×D4×C191—22no—
69C2×D4×C191—24no—
70C22×C4×C191C2311yescharacteristic
71C22×C4×C191C2311yescharacteristic
72C22×C4×C191C2312yes—
73C22⋊C4×C191—22no—
74C22⋊C4×C191—24no—
75C2×Dic191—21no—
76C2×Dic191—22no—
77C2×Dic191—21no—
78C2×Dic191—28no—
79C2×Dic191—22no—
80C2×Dic191—21no—
81C2×Dic191—22no—
82C2×Dic191—22no—
83C2×Dic191—22no—
84C2×Dic191—22no—
85C2×Dic191—22no—
86C2×Dic191—22no—
87C2×Dic191—48no—
88C2×Dic191C2×D412yes—
89C2×Dic191C2×D412yes—
90C2×Dic191C2×D412yes—
91C2×Dic191C2×D412yes—
92C2×Dic191#4112yes—
93C23×C191—21no—
94C23×C191—22no—
95C23×C191—22no—
96C23×C191—22no—
97C23×C191—22no—
98C23×C191—22no—
99C23×C191—22no—
100C23×C191—22no—
101C23×C191—21no—
102C23×C191—22no—
103C23×C191C2×D412yes—
104C23×C191#4114yes—
105C23×C191C2411yescharacteristic
106D4×C191—28no—
107D4×C191—216no—
108C2×C4×C191—22no—
109C2×C4×C191—22no—
110C2×C4×C191—22no—
111C2×C4×C191—21no—
112C2×C4×C191—22no—
113C2×C4×C191C2×D412yes—
114C2×C4×C191#4114yes—
115C22×C191—22no—
116C22×C191—24no—
117C22×C191—24no—
118C22×C191—24no—
119C22×C191—24no—
120C22×C191—42no—
121C22×C191—41no—
122C22×C191—42no—
123C22×C191—42no—
124C22×C191—42no—
125C22×C191—41no—
126C22×C191—42no—
127C22×C191C22×D411yescharacteristic
128C22×C191C22×D411yescharacteristic
129C22×C191C2×#4111yescharacteristic
130C22×C191C2×#4112yes—
131C22×C191C2×#4112yes—
132C4×C191—22no—
133C4×C191—24no—
134C4×C191—41no—
135Dic191—22no—
136Dic191—22no—
137Dic191—42no—
138Dic191—42no—
139Dic191—41no—
140Dic191#12114yes—
141C2×C191—42no—
142C2×C191—44no—
143C2×C191C2×#12111yescharacteristic
144C2×C191#52511yescharacteristic
145C2×C191#52512yes—
146C2×C191#52912yes—
147C2×C191#53211yescharacteristic
148C191#239211yescharacteristic, complemented, Sylow
149#2392—1911nomaximal, Sylow
150C2×C4×D4—1912no—
151C2×C4×D4—1911no—
152C2×#117—1911no—
153#398—1911no—
154#397—1911no—
155#396—1912no—
156#394—1912no—
157#394—1911no—
158#392D19111yescharacteristic
159C4×C4⋊C4—1911no—
160C4×C22⋊C4—1912no—
161C22×D4C2×D19111yescharacteristic
162C22×D4C2×D19112yes—
163C23×C4—1912no—
164C23×C4—1911no—
165C4×D4—3828no—
166C4×D4—3824no—
167#117—3824no—
168C2×C4⋊C4—1911no—
169C2×C4⋊C4—1911no—
170C2×C4⋊C4—1912no—
171C2×C4⋊C4—1911no—
172C2×C4⋊C4—1912no—
173C2×C22⋊C4—1911no—
174C2×C22⋊C4—1912no—
175C2×C22⋊C4—1912no—
176C2×C22⋊C4—1912no—
177C2×C22⋊C4—1912no—
178C2×C22⋊C4C2×D19111yescharacteristic
179C2×C22⋊C4C2×D19112yes—
180C2×C42—1911no—
181C2×C42—1912no—
182C2×C42—1911no—
183#95—1912no—
184#95—1912no—
185#95—1911no—
186#95C2×D19111yescharacteristic
187C24C22×D19111yescharacteristic
188C24C22×D19112yes—
189C2×D4—24no—
190C2×D4—24no—
191C2×D4—24no—
192C2×D4—22no—
193C2×D4—24no—
194C22×C4—3822no—
195C22×C4—3822no—
196C22×C4—3824no—
197C22×C4—3824no—
198C22×C4—3824no—
199C22×C4—1912no—
200C22×C4—1911no—
201C22×C4—1912no—
202C22×C4—1914no—
203C22×C4—1911no—
204C22×C4—1911no—
205C22×C4—1911no—
206C22×C4C22×D19111yescharacteristic
207C22×C4C22×D19111yescharacteristic
208C22×C4C22×D19112yes—
209C4⋊C4—3822no—
210C4⋊C4—3824no—
211C4⋊C4—3822no—
212C4⋊C4—3822no—
213C4⋊C4—3824no—
214C22⋊C4—22no—
215C22⋊C4—24no—
216C22⋊C4—3824no—
217C22⋊C4—3824no—
218C22⋊C4—3822no—
219C22⋊C4—3824no—
220C22⋊C4—3824no—
221C42—3822no—
222C42—3824no—
223C42—1914no—
224C23—21no—
225C23—22no—
226C23—22no—
227C23—22no—
228C23—21no—
229C23—22no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—22no—
234C23D4×D19112yes—
235C23#1569028614yes—
236C23C23×D19111yescharacteristic
237D4—28no—
238D4—216no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—3821no—
245C2×C4—3821no—
246C2×C4—3822no—
247C2×C4—3828no—
248C2×C4—3822no—
249C2×C4—3821no—
250C2×C4—3822no—
251C2×C4—3822no—
252C2×C4—3822no—
253C2×C4—3822no—
254C2×C4—3822no—
255C2×C4—3822no—
256C2×C4—1912no—
257C2×C4—1912no—
258C2×C4—1912no—
259C2×C4—1912no—
260C2×C4—1912no—
261C2×C4—7648no—
262C2×C4D4×D19112yes—
263C2×C4#1569028614yes—
264C22—24no—
265C22—22no—
266C22—24no—
267C22—24no—
268C22—24no—
269C22—42no—
270C22—42no—
271C22—41no—
272C22—42no—
273C22—42no—
274C22—41no—
275C22—42no—
276C22C2×D4×D19111yescharacteristic
277C22C2×D4×D19111yescharacteristic
278C22#41×D19111yescharacteristic
279C22C2×#1569028612yes—
280C22C2×#1569028612yes—
281C4—22no—
282C4—24no—
283C4—41no—
284C4—3822no—
285C4—3822no—
286C4—1914no—
287C4—7642no—
288C4—7642no—
289C4—7641no—
290C2—44no—
291C2—42no—
292C2#121×D19111yescharacteristic
293C2#2713316911yescharacteristic
294C2#2713316912yes—
295C2#2713319412yes—
296C2#2713321111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutator, socle, cosocleC23×C191C24
Fitting, prime radical#392×C191C2
hypercenter#392D191
hypocenterC191#2392
LCSG ▷ C23×C191 ▷ C191
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic191C2semidirect
2. C2×D4×Dic191C2semidirect
3. C2×#20259278C2semidirect
4. #27132595C2semidirect
5. #27132588C2semidirect
6. #27132586C2semidirect
7. #27132577C2semidirect
8. #27132577C2semidirect
9. #27132514C2semidirect
10. C22⋊C4×Dic191C2semidirect
43. C22×Dic191D4semidirect
62. C4×Dic191D4semidirect
148. C191#2392semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic1912
C2×#202592782
#271325952
#271325882
#271325862
#271325772
#271325142
C22⋊C4×Dic1912
#392×C1912
#2392191