Finite Group Databasebeta

← #37573536

Subgroups — #37573536

Order 24448.

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

normal subgroups only

This group has 478 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×#20259348C211yesmaximal, characteristic, complemented
2#27133232C211yesmaximal, characteristic, complemented
3C2×#20259318C211yesmaximal, characteristic, complemented
4C2×#20259248C211yesmaximal, characteristic, complemented
5C2×#20259238C211yesmaximal, characteristic, complemented
6#27132422C211yesmaximal, characteristic, complemented
7#418×C191C211yesmaximal, characteristic, complemented
8C2×#15690287C2211yescharacteristic
9C22×D764C2211yescharacteristic
10C22×C22⋊D191—22no—
11#20259348—22no—
12#20259348—22no—
13C2×#15690275—21no—
14C2×#15690272—21no—
15C2×#15690271C2211yescharacteristic
16#20259319—21no—
17#20259318—22no—
18#20259318—22no—
19#20259310—21no—
20#20259297—22no—
21#20259292—22no—
22C2×C4×Dic191C2211yescharacteristic
23#20259248—22no—
24#20259238—22no—
25C22×D4×C191C2211yescharacteristic
26C2×M16×C191C2211yescharacteristic
27#117×C191C2211yescharacteristic
28#102×C191—22no—
29C23×D191D412yes—
30#15690287—21no—
31#15690287—21no—
32#15690287—21no—
33#15690287—21no—
34C2×Dic382D411yescharacteristic, complemented
35C2×D764—24no—
36C2×D764—21no—
37C2×D764—21no—
38C2×D764—21no—
39C2×D764—21no—
40C2×D764—21no—
41C2×D764—21no—
42C2×D764D411yescharacteristic, complemented
43C2×C22⋊D191—28no—
44C2×C22⋊D191—21no—
45C2×C22⋊D191—48no—
46C22×Dic191—21no—
47C2×C4×D191—21no—
48#15690275—24no—
49#15690272—24no—
50#15690271—21no—
51#15690271D412yescomplemented
52C2×C191⋊C8—21no—
53(C2×D191)⋊C4—24no—
54C4×Dic191—21no—
55C4×Dic191D412yescomplemented
56C24×C191—21no—
57C2×D4×C191—21no—
58C2×D4×C191—21no—
59C2×D4×C191—21no—
60C2×D4×C191—21no—
61C2×D4×C191—21no—
62C2×D4×C191D412yescomplemented
63C22×C4×C191C2311yescharacteristic
64M16×C191—21no—
65M16×C191—21no—
66C2×C8×C191—21no—
67C4⋊C4×C191D412yescomplemented
68C22⋊C4×C191—21no—
69C42×C191—21no—
70C22×D191—22no—
71C22×D191—21no—
72C22×D191—22no—
73C22×D191—22no—
74C22×D191—44no—
75Dic382—21no—
76Dic382—21no—
77D764—21no—
78D764—21no—
79D764—41no—
80D764—41no—
81D764—41no—
82D764—41no—
83D764—84no—
84C22⋊D191—416no—
85C22⋊D191—41no—
86C22⋊D191—41no—
87C2×Dic191—24no—
88C2×Dic191—22no—
89C2×Dic191—21no—
90C4×D191—41no—
91C4×D191—41no—
92C191⋊C8—22no—
93C23×C191—22no—
94C23×C191—44no—
95C23×C191—41no—
96C23×C191—41no—
97C23×C191C2×D411yescharacteristic
98D4×C191—22no—
99D4×C191—22no—
100D4×C191—41no—
101D4×C191—41no—
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—41no—
110C22×C191—22no—
111C22×C191—44no—
112C22×C191—42no—
113C22×C191—82no—
114C22×C191—82no—
115C22×C191#12011yescharacteristic
116C22×C191#12011yescharacteristic
117C22×C191#12111yescharacteristic
118C2×D191—44no—
119C2×D191—41no—
120C2×D191—42no—
121C2×D191—42no—
122C2×D191—44no—
123C2×D191—82no—
124C4×C191—42no—
125C4×C191#12011yescharacteristic
126C4×C191#12111yescharacteristic
127C4×C191#12111yescharacteristic
128C4×C191#12711yescharacteristic
129Dic191—24no—
130Dic191—41no—
131C2×C191—21no—
132C2×C191—21no—
133C2×C191—82no—
134C2×C191#39211yescharacteristic
135C2×C191#45312yes—
136D191—81no—
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#418D19111yescharacteristic, complemented
145C2×#100—1911no—
146#339—1911no—
147C2×#41—1911no—
148C22×D4—3822no—
149C22×D4—1911no—
150C22×D4C2×D19111yescharacteristic
151AGL(1,ℤ/8)—3822no—
152AGL(1,ℤ/8)—3822no—
153C2×SD16—3821no—
154C2×D8—3821no—
155C2×M16—1911no—
156C2×M16C2×D19111yescharacteristic
157#127—3821no—
158#127—3822no—
159#127—3822no—
160#124—3821no—
161#121—3822no—
162#120—3822no—
163#117C2×D19111yescharacteristic
164C2×C42—1911no—
165#104—3822no—
166#102—22no—
167#100—3822no—
168C24—21no—
169C24—1912no—
170#41—3821no—
171#41—3821no—
172#41—3821no—
173#41—3821no—
174C2×Q8—1911no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—3824no—
181C2×D4—3828no—
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—7648no—
191C2×D4D76412yescomplemented
192C22×C4—3821no—
193C22×C4—3821no—
194C22×C4C22×D19111yescharacteristic
195SD16—3824no—
196D8—3824no—
197M16—21no—
198M16—21no—
199M16—3821no—
200M16—1912no—
201C2×C8—21no—
202C2×C8—3821no—
203C4⋊C4C22⋊D19112yescomplemented
204C22⋊C4—21no—
205C22⋊C4—3824no—
206C42—21no—
207C42—3821no—
208C42—1912no—
209C23—22no—
210C23—44no—
211C23—41no—
212C23—41no—
213C23—3822no—
214C23—3822no—
215C23—3821no—
216C23—3822no—
217C23—7644no—
218C23D4×D19111yescharacteristic
219Q8—3821no—
220Q8—3821no—
221D4—22no—
222D4—22no—
223D4—41no—
224D4—41no—
225D4—3821no—
226D4—3821no—
227D4—15284no—
228D4—76416no—
229D4—7641no—
230D4—7641no—
231D4—7641no—
232D4—7641no—
233D4—7641no—
234D4—7641no—
235C2×C4—22no—
236C2×C4—3824no—
237C2×C4—3822no—
238C2×C4—3821no—
239C2×C4—7641no—
240C2×C4—7641no—
241C2×C4D4×D19111yescharacteristic
242C2×C4D4×D19111yescharacteristic
243C2×C4D4×D19111yescharacteristic
244C2×C4C2×C22⋊D19111yescharacteristic
245C2×C4C2×D76411yescharacteristic
246C2×C4#1569028711yescharacteristic
247C8—41no—
248C8—3822no—
249C22—22no—
250C22—44no—
251C22—42no—
252C22—82no—
253C22—82no—
254C22—15282no—
255C22—7644no—
256C22—7641no—
257C22—7642no—
258C22—7642no—
259C22—7644no—
260C22#2025929011yescharacteristic
261C22#2025929211yescharacteristic
262C22#2025929511yescharacteristic
263C4—42no—
264C4—3824no—
265C4—7641no—
266C4#2025929211yescharacteristic
267C4#2025929511yescharacteristic
268C4#2025929611yescharacteristic
269C4#2025931811yescharacteristic
270C2—21no—
271C2—21no—
272C2—82no—
273C2—15282no—
274C2—15281no—
275C2#2713257211yescharacteristic
276C2#2713282912yes—
subgroupG/H
centerC22#20259290
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
Fitting#418×C191C2
socleC22×C191#120
hypercenter#418D191
hypocenterC191#2002
LCSG ▷ C22×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C2×#20259348C2semidirect
2. #27133232C2semidirect
3. C2×#20259318C2semidirect
4. C2×#20259248C2semidirect
5. C2×#20259238C2semidirect
6. #27132422C2semidirect
7. #418×C191C2semidirect
34. C2×Dic382D4semidirect
42. C2×D764D4semidirect
51. #15690271D4semidirect
55. C4×Dic191D4semidirect
62. C2×D4×C191D4semidirect
67. C4⋊C4×C191D4semidirect
138. C191#2002semidirect
144. #418D191semidirect
191. C2×D4D764semidirect
203. C4⋊C4C22⋊D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593482
#271332322
C2×#202593182
C2×#202592482
C2×#202592382
#271324222
#418×C1912
#2002191