Finite Group Databasebeta

← #37573535

Subgroups — #37573535

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×#20259348C211yesmaximal, characteristic, complemented
2#27133230C211yesmaximal, characteristic, complemented
3C2×#20259250C211yesmaximal, characteristic, complemented
4#27132668C211yesmaximal, characteristic, complemented
5C2×#20259239C211yesmaximal, characteristic, complemented
6#27132423C211yesmaximal, characteristic, complemented
7C2×#127×C191C211yesmaximal, characteristic, complemented
8C2×#15690287C2211yescharacteristic
9#20259348—22no—
10#20259348—22no—
11C2×#15690275—21no—
12C2×#15690272—21no—
13C2×#15690271C2211yescharacteristic
14C2×#15690271C2211yescharacteristic
15#20259318—21no—
16#20259309—21no—
17#20259293—22no—
18#20259291—22no—
19#20259281C2211yescharacteristic
20#20259250—22no—
21#20259243—22no—
22#20259239—22no—
23C22×D4×C191—22no—
24C22×D4×C191C2211yescharacteristic
25C22×D4×C191C2211yescharacteristic
26#127×C191—22no—
27#127×C191—22no—
28C2×C42×C191C2211yescharacteristic
29#15690287—21no—
30#15690287—21no—
31#15690287—21no—
32#15690287—21no—
33C2×Dic382D411yescharacteristic, complemented
34C2×D764D411yescharacteristic, complemented
35C2×C22⋊D191—24no—
36C2×C22⋊D191—21no—
37C2×C4×D191—21no—
38#15690275—24no—
39#15690272—24no—
40#15690271—21no—
41#15690271—21no—
42#15690271—21no—
43#15690271D412yescomplemented
44C2×C191⋊C8—21no—
45C2×C191⋊C8—21no—
46C4⋊Dic191D412yescomplemented
47C22⋊Dic191—24no—
48C22⋊Dic191—21no—
49C4×Dic191—21no—
50C24×C191—21no—
51C24×C191D412yes—
52C2×D4×C191—28no—
53C2×D4×C191—21no—
54C2×D4×C191—21no—
55C2×D4×C191—21no—
56C2×D4×C191—21no—
57C2×D4×C191—21no—
58C2×D4×C191—21no—
59C2×D4×C191—21no—
60C2×D4×C191—21no—
61C2×D4×C191—21no—
62C2×D4×C191—21no—
63C2×D4×C191—21no—
64C2×D4×C191—48no—
65C2×D4×C191D412yescomplemented
66C22×C4×C191—21no—
67C22×C4×C191C2311yescharacteristic
68C42×C191—21no—
69C42×C191D412yescomplemented
70C22×D191—21no—
71Dic382—21no—
72Dic382—21no—
73D764—21no—
74D764—21no—
75C22⋊D191—41no—
76C22⋊D191—41no—
77C22⋊D191—84no—
78C2×Dic191—22no—
79C2×Dic191—21no—
80C4×D191—41no—
81C4×D191—41no—
82C191⋊C8—22no—
83C191⋊C8—41no—
84C23×C191—22no—
85C23×C191—22no—
86C23×C191—22no—
87C23×C191—22no—
88C23×C191—44no—
89C23×C191—44no—
90C23×C191—41no—
91C23×C191—41no—
92C23×C191C2×D411yescharacteristic
93D4×C191—22no—
94D4×C191—22no—
95D4×C191—416no—
96D4×C191—41no—
97D4×C191—41no—
98D4×C191—41no—
99D4×C191—41no—
100D4×C191—41no—
101D4×C191—41no—
102C2×C4×C191—24no—
103C2×C4×C191—22no—
104C2×C4×C191C2×D411yescharacteristic
105C2×C4×C191C2×D411yescharacteristic
106C2×C4×C191C2×D411yescharacteristic
107C2×C4×C191C2×D411yescharacteristic
108C2×C4×C191C2×D411yescharacteristic
109C2×C4×C191#4111yescharacteristic
110C22×C191—22no—
111C22×C191—44no—
112C22×C191—44no—
113C22×C191—42no—
114C22×C191—42no—
115C22×C191—44no—
116C22×C191—82no—
117C22×C191—82no—
118C22×C191—82no—
119C22×C191#12011yescharacteristic
120C22×C191#12011yescharacteristic
121C22×C191#12111yescharacteristic
122C2×D191—41no—
123C2×D191—42no—
124C4×C191—24no—
125C4×C191#12011yescharacteristic
126C4×C191#12111yescharacteristic
127C4×C191#12111yescharacteristic
128C4×C191#12711yescharacteristic
129Dic191—41no—
130Dic191—42no—
131C2×C191—21no—
132C2×C191—21no—
133C2×C191—82no—
134C2×C191—82no—
135C2×C191#39211yescharacteristic
136C2×C191#45312yes—
137D191—81no—
138C191#200211yescharacteristic, complemented, Sylow
139#2002—1911nomaximal, Sylow
140C2×AGL(1,ℤ/8)—1911no—
141#535—1911no—
142C2×#127D19111yescharacteristic, complemented
143C2×#104—1911no—
144#418—1911no—
145C2×#100—1911no—
146#339—1911no—
147C2×#41—1911no—
148C22×D4—22no—
149C22×D4C2×D19111yescharacteristic
150C22×D4C2×D19111yescharacteristic
151AGL(1,ℤ/8)—3822no—
152AGL(1,ℤ/8)—3822no—
153C2×SD16—3821no—
154C2×D8—3821no—
155C2×M16—1911no—
156C2×M16—1911no—
157#127—22no—
158#127—22no—
159#127—3821no—
160#124—3821no—
161#121—3822no—
162#120—3822no—
163#117—1911no—
164C2×C42C2×D19111yescharacteristic
165#104—3822no—
166#102—3822no—
167#100—3822no—
168C24—21no—
169C24C22⋊D19112yes—
170#41—3821no—
171#41—3821no—
172#41—3821no—
173#41—3821no—
174C2×Q8—1911no—
175C2×D4—28no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—21no—
183C2×D4—21no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—21no—
187C2×D4—48no—
188C2×D4—3824no—
189C2×D4—3821no—
190C2×D4—1911no—
191C2×D4C22⋊D19112yescomplemented
192C22×C4—21no—
193C22×C4—3821no—
194C22×C4C22×D19111yescharacteristic
195SD16—3824no—
196D8—3824no—
197M16—3821no—
198M16—3821no—
199M16—3821no—
200M16—1912no—
201C2×C8—3821no—
202C2×C8—3821no—
203C4⋊C4—1912no—
204C22⋊C4—3824no—
205C22⋊C4—3821no—
206C42—21no—
207C42—3821no—
208C42C22⋊D19112yescomplemented
209C23—22no—
210C23—22no—
211C23—22no—
212C23—22no—
213C23—44no—
214C23—44no—
215C23—41no—
216C23—41no—
217C23—3821no—
218C23C2×C22⋊D19111yescharacteristic
219Q8—3821no—
220Q8—3821no—
221D4—22no—
222D4—22no—
223D4—416no—
224D4—41no—
225D4—41no—
226D4—41no—
227D4—41no—
228D4—41no—
229D4—41no—
230D4—3821no—
231D4—3821no—
232D4—15284no—
233D4—7641no—
234D4—7641no—
235C2×C4—24no—
236C2×C4—22no—
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×C22⋊D19111yescharacteristic
246C2×C4#1569028611yescharacteristic
247C8—3822no—
248C8—7641no—
249C22—22no—
250C22—44no—
251C22—44no—
252C22—42no—
253C22—42no—
254C22—44no—
255C22—82no—
256C22—82no—
257C22—82no—
258C22—7641no—
259C22—7642no—
260C22#2025929011yescharacteristic
261C22#2025929111yescharacteristic
262C22#2025929411yescharacteristic
263C4—24no—
264C4—7641no—
265C4—7642no—
266C4#2025929011yescharacteristic
267C4#2025929311yescharacteristic
268C4#2025929411yescharacteristic
269C4#2025931811yescharacteristic
270C2—21no—
271C2—21no—
272C2—82no—
273C2—82no—
274C2—15281no—
275C2#2713257111yescharacteristic
276C2#2713283012yes—
subgroupG/H
centerC22#20259290
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
FittingC2×#127×C191C2
socleC22×C191#120
hypercenterC2×#127D191
hypocenterC191#2002
LCSG ▷ C22×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#20259348C2semidirect
2. #27133230C2semidirect
3. C2×#20259250C2semidirect
4. #27132668C2semidirect
5. C2×#20259239C2semidirect
6. #27132423C2semidirect
7. C2×#127×C191C2semidirect
33. C2×Dic382D4semidirect
34. C2×D764D4semidirect
43. #15690271D4semidirect
46. C4⋊Dic191D4semidirect
65. C2×D4×C191D4semidirect
69. C42×C191D4semidirect
138. C191#2002semidirect
142. C2×#127D191semidirect
191. C2×D4C22⋊D191semidirect
208. C42C22⋊D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593482
#271332302
C2×#202592502
#271326682
C2×#202592392
#271324232
C2×#127×C1912
#2002191