Finite Group Databasebeta

← #37583891

Subgroups — #37583891

Order 24448.

348 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 113 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
1#27133218C211yesmaximal, characteristic, complemented
2#27133200C211yesmaximal, characteristic
3#27132968C212yesmaximal, complemented
4#27132958C211yesmaximal, characteristic, complemented
5#27132954C211yesmaximal, characteristic, complemented
6#27132918C212yesmaximal, complemented
7#27132912C212yesmaximal
8#27132887C212yesmaximal, complemented
9#27132865C211yesmaximal, characteristic, complemented
10#27132685C211yesmaximal, characteristic, complemented
11#462×C191C211yesmaximal, characteristic, complemented
12C2×#15690274C2212yes—
13C2×#15690270C2212yes—
14#20259322C2211yescharacteristic
15#20259317—21no—
16#20259313—21no—
17#20259313C2211yescharacteristic
18#20259311C2211yescharacteristic
19#20259307—21no—
20#20259302—21no—
21#20259298C2211yescharacteristic
22#20259298C2212yes—
23#20259297C2211yescharacteristic
24Q8×Dic191C2212yes—
25#20259287—21no—
26C4×D764—21no—
27C4×D764C2211yescharacteristic
28#20259280—21no—
29#20259279—21no—
30C42×D191C2211yescharacteristic
31#20259255C2212yes—
32#20259254C2212yes—
33C4⋊(C191⋊C8)C2211yescharacteristic
34Dic191⋊C8C2212yes—
35#20259246C2212yes—
36#20259246C2212yes—
37#20259244C2212yes—
38C2×Q16×C191C2212yes—
39C4⋊Q8×C191C2211yescharacteristic
40C4×Q8×C191C2211yescharacteristic
41C4⋊C8×C191C2211yescharacteristic
42#103×C191C2212yes—
43C2×Dic382—21no—
44C2×D764—21no—
45C2×D764C2311yescharacteristic
46C2×C4×D191—21no—
47C2×C4×D191D411yescharacteristic
48C2×C4×D191D411yescharacteristic
49C2×C4×D191C2311yescharacteristic
50#15690274—42no—
51#15690270—42no—
52C2×C191⋊C8C2312yes—
53C4⋊Dic191—21no—
54C4⋊Dic191—22no—
55C4⋊Dic191—21no—
56C4⋊Dic191C2312yes—
57C4⋊Dic191C2311yescharacteristic
58Dic191⋊C4—21no—
59Dic191⋊C4—21no—
60Dic191⋊C4—22no—
61(C2×D191)⋊C4—22no—
62(C2×D191)⋊C4—21no—
63(C2×D191)⋊C4—21no—
64(C2×D191)⋊C4—21no—
65(C2×D191)⋊C4—21no—
66(C2×D191)⋊C4—21no—
67C4×Dic191—22no—
68C4×Dic191D411yescharacteristic
69C4×Dic191D411yescharacteristic
70C4×Dic191C2311yescharacteristic
71C2×Q8×C191C2312yes—
72C2×Q8×C191C2311yescharacteristic
73Q16×C191—42no—
74C2×C8×C191C2312yes—
75C4⋊C4×C191—21no—
76C4⋊C4×C191—21no—
77C4⋊C4×C191—21no—
78C4⋊C4×C191C2311yescharacteristic
79C42×C191—21no—
80C42×C191C2311yescharacteristic
81C22×D191—21no—
82C22×D191C2×D411yescharacteristic
83Dic382—42no—
84D764—21no—
85D764—21no—
86D764—42no—
87C2×Dic191—22no—
88C2×Dic191—21no—
89C2×Dic191C2×D411yescharacteristic
90C2×Dic191C2×D411yescharacteristic
91C2×Dic191C2×D411yescharacteristic
92C4×D191—22no—
93C4×D191—21no—
94C4×D191—21no—
95C4×D191—41no—
96C4×D191—42no—
97C191⋊C8—22no—
98Q8×C191—21no—
99Q8×C191—22no—
100Q8×C191—22no—
101Q8×C191—21no—
102C2×C4×C191—21no—
103C2×C4×C191—21no—
104C2×C4×C191—22no—
105C2×C4×C191C2×D411yescharacteristic
106C2×C4×C191C2×D411yescharacteristic
107C2×C4×C191C2411yescharacteristic
108C8×C191—22no—
109C22×C191C22×D411yescharacteristic
110C2×D191—21no—
111C2×D191—21no—
112C2×D191—21no—
113C2×D191—41no—
114C2×D191—41no—
115C2×D191—41no—
116C4×C191—21no—
117C4×C191—41no—
118C4×C191—42no—
119C4×C191—41no—
120C4×C191#13712yes—
121C4×C191H(5,𝔽2)11yescharacteristic
122C4×C1912−1+411yescharacteristic
123Dic191—21no—
124Dic191—21no—
125Dic191—21no—
126Dic191—41no—
127Dic191—42no—
128C2×C191#53711yescharacteristic
129C2×C191C2×#13711yescharacteristic
130C2×C191#57511yescharacteristic
131D191—41no—
132D191—81no—
133C191#325211yescharacteristic, complemented, Sylow
134#3252—1911nomaximal, Sylow
135#533—1911no—
136#529—1911no—
137#479—1912no—
138#477—1911no—
139#476—1911no—
140#470—1912no—
141#468—1912no—
142#464—1912no—
143#462D19111yescharacteristic, complemented
144#461—1911no—
145#423—1911no—
146C2×Q16C2×D19112yes—
147C2×SD16—1912no—
148C2×M16—1912no—
149C4⋊Q8—1911no—
150C4⋊Q8C2×D19111yescharacteristic
151#126—3821no—
152#125—3821no—
153#125—1911no—
154#124—1911no—
155#123—3821no—
156C22⋊Q8—3821no—
157C22⋊Q8—1911no—
158C22⋊Q8—1912no—
159#121—1911no—
160C4×Q8—3821no—
161C4×Q8—1912no—
162C4×Q8C2×D19111yescharacteristic
163C4×D4—3821no—
164C4×D4—1911no—
165#117—3821no—
166#117—3821no—
167C2×C42—1911no—
168#107—1912no—
169#106—1912no—
170C4⋊C8—1912no—
171C4⋊C8—1911no—
172C4⋊C8C2×D19111yescharacteristic
173#103—1912no—
174#103—1912no—
175#103C2×D19112yes—
176#102—1912no—
177C2×Q8—3821no—
178C2×Q8C22×D19111yescharacteristic
179C2×Q8C22×D19112yes—
180C2×D4—3821no—
181C2×D4—1911no—
182C22×C4—3821no—
183C22×C4—1911no—
184C22×C4—1911no—
185C22×C4—1911no—
186Q16—42no—
187SD16—7642no—
188M16—7642no—
189C2×C8—1912no—
190C2×C8C22×D19112yes—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—21no—
194C4⋊C4—3821no—
195C4⋊C4—3821no—
196C4⋊C4—3822no—
197C4⋊C4—3821no—
198C4⋊C4—3822no—
199C4⋊C4—3821no—
200C4⋊C4—1912no—
201C4⋊C4—1911no—
202C4⋊C4C22×D19111yescharacteristic
203C22⋊C4—3822no—
204C22⋊C4—3821no—
205C22⋊C4—3821no—
206C22⋊C4—3821no—
207C22⋊C4—3821no—
208C22⋊C4—3821no—
209C42—21no—
210C42—3822no—
211C42—1911no—
212C42—1911no—
213C42—1911no—
214C42C22×D19111yescharacteristic
215C23—3821no—
216C23—1911no—
217Q8—22no—
218Q8—21no—
219Q8—21no—
220Q8—22no—
221Q8—7642no—
222D4—3821no—
223D4—3821no—
224D4—7642no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—3822no—
229C2×C4—3821no—
230C2×C4—3821no—
231C2×C4—3822no—
232C2×C4—3821no—
233C2×C4—1911no—
234C2×C4—1911no—
235C2×C4—1911no—
236C2×C4—7641no—
237C2×C4—7642no—
238C2×C4D4×D19111yescharacteristic
239C2×C4D4×D19111yescharacteristic
240C2×C4C23×D19111yescharacteristic
241C8—22no—
242C8—3822no—
243C22—3821no—
244C22—3821no—
245C22—3821no—
246C22—7641no—
247C22—7641no—
248C22—7641no—
249C22C2×D4×D19111yescharacteristic
250C4—21no—
251C4—41no—
252C4—41no—
253C4—42no—
254C4—3821no—
255C4—3821no—
256C4—3821no—
257C4—7641no—
258C4—7642no—
259C4#2025935412yes—
260C4#2025936711yescharacteristic
261C4#2025936911yescharacteristic
262C2—15281no—
263C2—7641no—
264C2#2713324211yescharacteristic
265C2C2×#2025935411yescharacteristic
266C2#2713346211yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#462×C191C2
socleC22×C191C22×D4
prime radical#20259297C22
hypercenter#462D191
hypocenterC191#3252
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. #27133218C2semidirect
3. #27132968C2semidirect
4. #27132958C2semidirect
5. #27132954C2semidirect
6. #27132918C2semidirect
8. #27132887C2semidirect
9. #27132865C2semidirect
10. #27132685C2semidirect
11. #462×C191C2semidirect
133. C191#3252semidirect
143. #462D191semidirect

Maximal subgroups

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

subgroupindex
#271332182
#271332002
#271329682
#271329582
#271329542
#271329182
#271329122
#271328872
#271328652
#271326852
#462×C1912
#3252191