Finite Group Databasebeta

← #37583887

Subgroups — #37583887

Order 24448.

348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 121 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#27133197C211yesmaximal, characteristic
2#27132970C212yesmaximal, complemented
3#27132955C211yesmaximal, characteristic, complemented
4#27132950C211yesmaximal, characteristic, complemented
5#27132919C212yesmaximal, complemented
6#27132911C212yesmaximal
7#27132885C212yesmaximal, complemented
8#27132870C211yesmaximal, characteristic, complemented
9#27132865C211yesmaximal, characteristic, complemented
10#27132687C211yesmaximal, characteristic, complemented
11#533×C191C211yesmaximal, characteristic, complemented
12C2×#15690277C2212yes—
13C2×#15690274C2212yes—
14C2×#15690271C2212yes—
15#20259316—21no—
16#20259314C2211yescharacteristic
17#20259310C2211yescharacteristic
18#20259305—21no—
19#20259301C2211yescharacteristic
20#20259296C2211yescharacteristic
21C4×Dic382C2211yescharacteristic
22C4×D764C2211yescharacteristic
23C4×C22⋊D191—21no—
24#20259279—21no—
25#20259255C2212yes—
26#20259253C2212yes—
27C4⋊(C191⋊C8)C2211yescharacteristic
28C4⋊(C191⋊C8)C2211yescharacteristic
29C4⋊(C191⋊C8)C2212yes—
30#20259246C2212yes—
31#20259246C2212yes—
32#20259245C2212yes—
33#20259242C2212yes—
34C4⋊Q8×C191C2211yescharacteristic
35C4⋊Q8×C191C2211yescharacteristic
36#125×C191—21no—
37C22⋊Q8×C191—21no—
38C22⋊Q8×C191C2212yes—
39C4×Q8×C191—21no—
40C4×Q8×C191C2212yes—
41#117×C191—21no—
42C2×C42×C191C2211yescharacteristic
43C2×Dic382C2311yescharacteristic
44C2×D764C2311yescharacteristic
45C2×C22⋊D191—21no—
46C2×C4×D191—21no—
47#15690277—42no—
48#15690274—42no—
49#15690271—42no—
50C2×C191⋊C8C2312yes—
51C2×C191⋊C8C2312yes—
52C4⋊Dic191C2311yescharacteristic
53C4⋊Dic191C2311yescharacteristic
54Dic191⋊C4—21no—
55Dic191⋊C4—21no—
56Dic191⋊C4—21no—
57Dic191⋊C4—21no—
58C22⋊Dic191—21no—
59(C2×D191)⋊C4—21no—
60(C2×D191)⋊C4—21no—
61(C2×D191)⋊C4—21no—
62(C2×D191)⋊C4—21no—
63C4×Dic191—21no—
64C2×Q8×C191—21no—
65C2×Q8×C191C2312yes—
66C22×C4×C191D411yescharacteristic
67C22×C4×C191D411yescharacteristic
68C22×C4×C191C2311yescharacteristic
69C4⋊C4×C191—21no—
70C4⋊C4×C191—21no—
71C4⋊C4×C191—21no—
72C4⋊C4×C191—22no—
73C4⋊C4×C191—22no—
74C4⋊C4×C191C2312yes—
75C22⋊C4×C191—22no—
76C42×C191—22no—
77C42×C191D411yescharacteristic
78C42×C191D411yescharacteristic
79C42×C191C2311yescharacteristic
80C42×C191C2311yescharacteristic
81C22×D191—21no—
82Dic382—21no—
83Dic382—21no—
84D764—21no—
85D764—21no—
86C22⋊D191—42no—
87C2×Dic191—21no—
88C2×Dic191—21no—
89C2×Dic191—21no—
90C4×D191—42no—
91C191⋊C8—22no—
92C191⋊C8—22no—
93C23×C191C2×D411yescharacteristic
94Q8×C191—22no—
95Q8×C191—22no—
96Q8×C191—42no—
97C2×C4×C191—22no—
98C2×C4×C191—21no—
99C2×C4×C191—21no—
100C2×C4×C191—22no—
101C2×C4×C191—22no—
102C2×C4×C191—41no—
103C2×C4×C191C2×D411yescharacteristic
104C2×C4×C191C2×D411yescharacteristic
105C2×C4×C191C2×D411yescharacteristic
106C2×C4×C191C2×D411yescharacteristic
107C2×C4×C191C2×D411yescharacteristic
108C2×C4×C191C2411yescharacteristic
109C22×C191—21no—
110C22×C191—21no—
111C22×C191—21no—
112C22×C191C22×D411yescharacteristic
113C2×D191—41no—
114C2×D191—41no—
115C2×D191—41no—
116C4×C191—21no—
117C4×C191—21no—
118C4×C191—21no—
119C4×C191—21no—
120C4×C191—42no—
121C4×C191—42no—
122C4×C191#13712yes—
123C4×C191H(5,𝔽2)11yescharacteristic
124C4×C1912−1+411yescharacteristic
125Dic191—41no—
126Dic191—41no—
127Dic191—41no—
128C2×C191—41no—
129C2×C191#53711yescharacteristic
130C2×C191C2×#13711yescharacteristic
131C2×C191#57511yescharacteristic
132D191—81no—
133C191#325211yescharacteristic, complemented, Sylow
134#3252—1911nomaximal, Sylow
135#533D19111yescharacteristic, complemented
136#529—1911no—
137#479—1912no—
138#477—1911no—
139#476—1911no—
140#470—1912no—
141#468—1912no—
142#464—1912no—
143#462—1911no—
144#461—1911no—
145#423—1911no—
146C2×Q16—1912no—
147C2×SD16—1912no—
148C2×M16—1912no—
149C4⋊Q8C2×D19111yescharacteristic
150C4⋊Q8C2×D19111yescharacteristic
151#126—3821no—
152#125—21no—
153#125—1911no—
154#124—1911no—
155#123—3821no—
156C22⋊Q8—21no—
157C22⋊Q8—1911no—
158C22⋊Q8C2×D19112yes—
159#121—1911no—
160C4×Q8—21no—
161C4×Q8—1911no—
162C4×Q8C2×D19112yes—
163C4×D4—3821no—
164C4×D4—1911no—
165#117—21no—
166#117—3821no—
167C2×C42C2×D19111yescharacteristic
168#107—1912no—
169#106—1912no—
170C4⋊C8—1911no—
171C4⋊C8—1911no—
172C4⋊C8—1912no—
173#103—1912no—
174#103—1912no—
175#103—1912no—
176#102—1912no—
177C2×Q8—21no—
178C2×Q8—1911no—
179C2×Q8C22×D19112yes—
180C2×D4—3821no—
181C2×D4—1911no—
182C22×C4—3821no—
183C22×C4C22⋊D19111yescharacteristic
184C22×C4C22⋊D19111yescharacteristic
185C22×C4C22×D19111yescharacteristic
186Q16—7642no—
187SD16—7642no—
188M16—7642no—
189C2×C8—1912no—
190C2×C8—1912no—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—21no—
194C4⋊C4—22no—
195C4⋊C4—22no—
196C4⋊C4—3821no—
197C4⋊C4—3821no—
198C4⋊C4—3821no—
199C4⋊C4—3821no—
200C4⋊C4—1911no—
201C4⋊C4—1911no—
202C4⋊C4C22×D19112yes—
203C22⋊C4—22no—
204C22⋊C4—3821no—
205C22⋊C4—3821no—
206C22⋊C4—3821no—
207C22⋊C4—3821no—
208C22⋊C4—3821no—
209C42—22no—
210C42—3821no—
211C42C22⋊D19111yescharacteristic
212C42C22⋊D19111yescharacteristic
213C42C22×D19111yescharacteristic
214C42C22×D19111yescharacteristic
215C23—3821no—
216C23C2×C22⋊D19111yescharacteristic
217Q8—22no—
218Q8—22no—
219Q8—42no—
220Q8—3821no—
221Q8—3821no—
222D4—3821no—
223D4—3821no—
224D4—7642no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—41no—
231C2×C4—3821no—
232C2×C4—3821no—
233C2×C4—3821no—
234C2×C4—7642no—
235C2×C4C2×C22⋊D19111yescharacteristic
236C2×C4C2×C22⋊D19111yescharacteristic
237C2×C4C2×C22⋊D19111yescharacteristic
238C2×C4C2×C22⋊D19111yescharacteristic
239C2×C4C2×C22⋊D19111yescharacteristic
240C2×C4C23×D19111yescharacteristic
241C8—3822no—
242C8—3822no—
243C22—21no—
244C22—21no—
245C22—21no—
246C22—7641no—
247C22—7641no—
248C22—7641no—
249C22C22×C22⋊D19111yescharacteristic
250C4—21no—
251C4—21no—
252C4—21no—
253C4—21no—
254C4—42no—
255C4—42no—
256C4—7641no—
257C4—7641no—
258C4—7641no—
259C4#2025935312yes—
260C4#2025936811yescharacteristic
261C4#2025936911yescharacteristic
262C2—41no—
263C2—15281no—
264C2#2713324111yescharacteristic
265C2C2×#2025935311yescharacteristic
266C2#2713346111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#533×C191C2
socleC22×C191C22×D4
prime radical#20259296C22
hypercenter#533D191
hypocenterC191#3252
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #27132970C2semidirect
3. #27132955C2semidirect
4. #27132950C2semidirect
5. #27132919C2semidirect
7. #27132885C2semidirect
8. #27132870C2semidirect
9. #27132865C2semidirect
10. #27132687C2semidirect
11. #533×C191C2semidirect
133. C191#3252semidirect
135. #533D191semidirect

Maximal subgroups

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

subgroupindex
#271331972
#271329702
#271329552
#271329502
#271329192
#271329112
#271328852
#271328702
#271328652
#271326872
#533×C1912
#3252191