Finite Group Databasebeta

← #37573538

Subgroups — #37573538

Order 24448.

478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 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×#20259350C211yesmaximal, characteristic, complemented
2#27133232C211yesmaximal, characteristic, complemented
3C2×#20259319C211yesmaximal, characteristic, complemented
4C2×#20259250C211yesmaximal, characteristic, complemented
5#27132667C211yesmaximal, characteristic, complemented
6C2×#20259238C211yesmaximal, characteristic, complemented
7#339×C191C211yesmaximal, characteristic, complemented
8C2×#15690287C2211yescharacteristic
9C22×D764—22no—
10C22×D764C2211yescharacteristic
11C22×D764C2211yescharacteristic
12#20259350—22no—
13#20259350—22no—
14C2×#15690276—21no—
15C2×D1528—21no—
16C2×#15690271C2211yescharacteristic
17#20259319—22no—
18#20259319—21no—
19#20259319—22no—
20#20259310—21no—
21#20259297—22no—
22#20259292—22no—
23#20259250—22no—
24#20259242—22no—
25#20259238—22no—
26C2×M16×C191C2211yescharacteristic
27#117×C191C2211yescharacteristic
28C2×C42×C191C2211yescharacteristic
29C23×D191—21no—
30C23×D191D412yes—
31#15690287—21no—
32#15690287—21no—
33#15690287—21no—
34#15690287—21no—
35C2×Dic382D411yescharacteristic, complemented
36C2×D764—28no—
37C2×D764—24no—
38C2×D764—21no—
39C2×D764—21no—
40C2×D764—21no—
41C2×D764—21no—
42C2×D764—21no—
43C2×D764—21no—
44C2×D764—21no—
45C2×D764—21no—
46C2×D764—21no—
47C2×D764—21no—
48C2×D764—21no—
49C2×D764—48no—
50C2×D764D411yescharacteristic, complemented
51C2×D764D412yescomplemented
52C2×C22⋊D191—21no—
53C2×C4×D191—21no—
54#15690276—24no—
55D1528—24no—
56#15690271—21no—
57#15690271—21no—
58C2×C191⋊C8—21no—
59(C2×D191)⋊C4—24no—
60C22×C4×C191—21no—
61C22×C4×C191C2311yescharacteristic
62M16×C191—21no—
63M16×C191D412yescomplemented
64C2×C8×C191—21no—
65C4⋊C4×C191D412yescomplemented
66C22⋊C4×C191—21no—
67C42×C191—21no—
68C42×C191—21no—
69C42×C191D412yescomplemented
70C22×D191—22no—
71C22×D191—21no—
72C22×D191—22no—
73C22×D191—22no—
74C22×D191—22no—
75C22×D191—44no—
76C22×D191—44no—
77C22×D191—41no—
78C22×D191—41no—
79Dic382—21no—
80Dic382—21no—
81D764—21no—
82D764—22no—
83D764—22no—
84D764—21no—
85D764—416no—
86D764—41no—
87D764—41no—
88D764—41no—
89D764—41no—
90D764—41no—
91D764—41no—
92D764—84no—
93C22⋊D191—41no—
94C22⋊D191—41no—
95C2×Dic191—21no—
96C4×D191—41no—
97C4×D191—41no—
98C191⋊C8—41no—
99C23×C191C2×D411yescharacteristic
100C2×C4×C191—24no—
101C2×C4×C191—22no—
102C2×C4×C191—22no—
103C2×C4×C191C2×D411yescharacteristic
104C2×C4×C191C2×D411yescharacteristic
105C2×C4×C191C2×D411yescharacteristic
106C2×C4×C191C2×D411yescharacteristic
107C2×C4×C191C2×D411yescharacteristic
108C2×C4×C191#4111yescharacteristic
109C8×C191—22no—
110C22×C191—22no—
111C22×C191#12011yescharacteristic
112C22×C191#12011yescharacteristic
113C22×C191#12111yescharacteristic
114C2×D191—44no—
115C2×D191—44no—
116C2×D191—41no—
117C2×D191—42no—
118C2×D191—42no—
119C2×D191—42no—
120C2×D191—44no—
121C2×D191—82no—
122C2×D191—82no—
123C2×D191—82no—
124C4×C191—24no—
125C4×C191—42no—
126C4×C191#12011yescharacteristic
127C4×C191#12111yescharacteristic
128C4×C191#12111yescharacteristic
129C4×C191#12711yescharacteristic
130Dic191—41no—
131C2×C191—21no—
132C2×C191—21no—
133C2×C191#39211yescharacteristic
134C2×C191#45312yes—
135D191—81no—
136D191—82no—
137D191—82no—
138C191#200211yescharacteristic, complemented, Sylow
139#2002—1911nomaximal, Sylow
140C2×AGL(1,ℤ/8)—1911no—
141#535—1911no—
142C2×#127—1911no—
143C2×#104—1911no—
144#418—1911no—
145C2×#100—1911no—
146#339D19111yescharacteristic, complemented
147C2×#41—1911no—
148C22×D4—3822no—
149C22×D4—1911no—
150C22×D4—1911no—
151AGL(1,ℤ/8)—3822no—
152AGL(1,ℤ/8)—3822no—
153C2×SD16—3821no—
154C2×D8—3821no—
155C2×M16—1911no—
156C2×M16C2×D19111yescharacteristic
157#127—3822no—
158#127—3821no—
159#127—3822no—
160#124—3821no—
161#121—3822no—
162#120—3822no—
163#117C2×D19111yescharacteristic
164C2×C42C2×D19111yescharacteristic
165#104—3822no—
166#102—3822no—
167#100—3822no—
168C24—3821no—
169C24—1912no—
170#41—3821no—
171#41—3821no—
172#41—3821no—
173#41—3821no—
174C2×Q8—1911no—
175C2×D4—3824no—
176C2×D4—3828no—
177C2×D4—3821no—
178C2×D4—3821no—
179C2×D4—3821no—
180C2×D4—3821no—
181C2×D4—3821no—
182C2×D4—3821no—
183C2×D4—3821no—
184C2×D4—3821no—
185C2×D4—3821no—
186C2×D4—3821no—
187C2×D4—3821no—
188C2×D4—3821no—
189C2×D4—1911no—
190C2×D4—1912no—
191C2×D4—7648no—
192C22×C4—21no—
193C22×C4—3821no—
194C22×C4C22×D19111yescharacteristic
195SD16—3824no—
196D8—3824no—
197M16—21no—
198M16—3821no—
199M16—3821no—
200M16D76412yescomplemented
201C2×C8—21no—
202C2×C8—3821no—
203C4⋊C4D76412yescomplemented
204C22⋊C4—21no—
205C22⋊C4—3824no—
206C42—21no—
207C42—21no—
208C42D76412yescomplemented
209C23—3822no—
210C23—3822no—
211C23—3822no—
212C23—3822no—
213C23—3821no—
214C23—7644no—
215C23—7644no—
216C23—7641no—
217C23—7641no—
218C23D4×D19111yescharacteristic
219Q8—3821no—
220Q8—3821no—
221D4—3821no—
222D4—3822no—
223D4—3822no—
224D4—3821no—
225D4—15284no—
226D4—76416no—
227D4—7641no—
228D4—7641no—
229D4—7641no—
230D4—7641no—
231D4—7641no—
232D4—7641no—
233D4—7641no—
234D4—7641no—
235C2×C4—24no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—3821no—
239C2×C4—7641no—
240C2×C4—7641no—
241C2×C4D4×D19111yescharacteristic
242C2×C4D4×D19111yescharacteristic
243C2×C4C2×D76411yescharacteristic
244C2×C4C2×D76411yescharacteristic
245C2×C4C2×D76411yescharacteristic
246C2×C4#1569028811yescharacteristic
247C8—22no—
248C8—7641no—
249C22—22no—
250C22—15282no—
251C22—15282no—
252C22—15282no—
253C22—7644no—
254C22—7644no—
255C22—7641no—
256C22—7642no—
257C22—7642no—
258C22—7642no—
259C22—7644no—
260C22#2025929211yescharacteristic
261C22#2025929211yescharacteristic
262C22#2025929711yescharacteristic
263C4—24no—
264C4—42no—
265C4—7641no—
266C4#2025929211yescharacteristic
267C4#2025929711yescharacteristic
268C4#2025929711yescharacteristic
269C4#2025931911yescharacteristic
270C2—21no—
271C2—21no—
272C2—15282no—
273C2—15282no—
274C2—15281no—
275C2#2713257311yescharacteristic
276C2#2713283212yes—
subgroupG/H
centerC22#20259292
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
Fitting#339×C191C2
socleC22×C191#120
hypercenter#339D191
hypocenterC191#2002
LCSG ▷ C22×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. C2×#20259350C2semidirect
2. #27133232C2semidirect
3. C2×#20259319C2semidirect
4. C2×#20259250C2semidirect
5. #27132667C2semidirect
6. C2×#20259238C2semidirect
7. #339×C191C2semidirect
35. C2×Dic382D4semidirect
50. C2×D764D4semidirect
51. C2×D764D4semidirect
63. M16×C191D4semidirect
65. C4⋊C4×C191D4semidirect
69. C42×C191D4semidirect
138. C191#2002semidirect
146. #339D191semidirect
200. M16D764semidirect
203. C4⋊C4D764semidirect
208. C42D764semidirect

Maximal subgroups

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

subgroupindex
C2×#202593502
#271332322
C2×#202593192
C2×#202592502
#271326672
C2×#202592382
#339×C1912
#2002191