Finite Group Databasebeta

← #38769863

Subgroups — #38769863

Order 25472.

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×#20263980C211yesmaximal, characteristic, complemented
2C2×#20263951C211yesmaximal, characteristic, complemented
3C2×#20263882C211yesmaximal, characteristic, complemented
4#27164022C211yesmaximal, characteristic, complemented
5C2×#20263872C211yesmaximal, characteristic, complemented
6#27163777C211yesmaximal, characteristic, complemented
7#535×C199C211yesmaximal, characteristic, complemented
8C22×D796C2211yescharacteristic
9C22×C22⋊D199—22no—
10#20263980—22no—
11#20263980—22no—
12C2×#15691873—21no—
13C2×#15691871—21no—
14C2×#15691870C2211yescharacteristic
15C2×#15691870C2211yescharacteristic
16#20263951—22no—
17#20263951—22no—
18C2×C4×Dic199C2211yescharacteristic
19#20263882—22no—
20#20263875—22no—
21#20263872—22no—
22C2×#41×C199C2211yescharacteristic
23C22×D4×C199C2211yescharacteristic
24#127×C199—21no—
25#124×C199—21no—
26#121×C199—22no—
27#120×C199—22no—
28#117×C199C2211yescharacteristic
29C23×D199—21no—
30C2×D796—21no—
31C2×D796—21no—
32C2×D796—21no—
33C2×D796—21no—
34C2×D796—21no—
35C2×D796D412yescomplemented
36C2×C22⋊D199—28no—
37C2×C22⋊D199—48no—
38C22×Dic199—21no—
39#15691873—24no—
40#15691871—24no—
41#15691870—21no—
42#15691870—21no—
43#15691870—21no—
44#15691870D412yescomplemented
45C2×C199⋊C8—21no—
46C2×C199⋊C8—21no—
47C4×Dic199—21no—
48C4×Dic199D412yescomplemented
49C24×C199D412yes—
50#41×C199—21no—
51#41×C199—21no—
52#41×C199—21no—
53#41×C199—21no—
54C2×Q8×C199D411yescharacteristic, complemented
55C2×D4×C199—21no—
56C2×D4×C199—24no—
57C2×D4×C199—21no—
58C2×D4×C199—21no—
59C2×D4×C199—21no—
60C2×D4×C199—21no—
61C2×D4×C199—21no—
62C2×D4×C199—21no—
63C2×D4×C199D411yescharacteristic, complemented
64C22×C4×C199—21no—
65C22×C4×C199C2311yescharacteristic
66C4⋊C4×C199D412yescomplemented
67C22⋊C4×C199—24no—
68C22⋊C4×C199—21no—
69C42×C199—21no—
70C22×D199—22no—
71C22×D199—44no—
72C22×D199—41no—
73C22×D199—41no—
74D796—22no—
75D796—22no—
76D796—41no—
77D796—41no—
78C22⋊D199—416no—
79C2×Dic199—24no—
80C2×Dic199—22no—
81C199⋊C8—22no—
82C199⋊C8—41no—
83C23×C199—22no—
84C23×C199—21no—
85C23×C199—22no—
86C23×C199—22no—
87C23×C199—44no—
88C23×C199C2×D411yescharacteristic
89Q8×C199—21no—
90Q8×C199—21no—
91D4×C199—21no—
92D4×C199—21no—
93D4×C199—41no—
94D4×C199—41no—
95D4×C199—41no—
96D4×C199—41no—
97D4×C199—41no—
98D4×C199—41no—
99D4×C199—84no—
100C2×C4×C199—22no—
101C2×C4×C199—21no—
102C2×C4×C199—41no—
103C2×C4×C199—41no—
104C2×C4×C199C2×D411yescharacteristic
105C2×C4×C199C2×D411yescharacteristic
106C2×C4×C199C2×D411yescharacteristic
107C2×C4×C199C2×D411yescharacteristic
108C2×C4×C199C2×D411yescharacteristic
109C2×C4×C199#4111yescharacteristic
110C22×C199—22no—
111C22×C199—44no—
112C22×C199—41no—
113C22×C199—42no—
114C22×C199—42no—
115C22×C199—44no—
116C22×C199—82no—
117C22×C199#12011yescharacteristic
118C22×C199#12011yescharacteristic
119C22×C199#12111yescharacteristic
120C2×D199—44no—
121C2×D199—42no—
122C2×D199—82no—
123C2×D199—82no—
124C4×C199—41no—
125C4×C199—42no—
126C4×C199#12011yescharacteristic
127C4×C199#12111yescharacteristic
128C4×C199#12111yescharacteristic
129C4×C199#12711yescharacteristic
130Dic199—24no—
131C2×C199—21no—
132C2×C199—21no—
133C2×C199—81no—
134C2×C199—82no—
135C2×C199#39211yescharacteristic
136C2×C199#45312yes—
137D199—82no—
138C199#200211yescharacteristic, complemented, Sylow
139#2002—1991nomaximal, Sylow
140C2×AGL(1,ℤ/8)—1991no—
141#535D19911yescharacteristic, complemented
142C2×#127—1991no—
143C2×#104—1991no—
144#418—1991no—
145C2×#100—1991no—
146#339—1991no—
147C2×#41C2×D19911yescharacteristic
148C22×D4—3982no—
149C22×D4—1991no—
150C22×D4C2×D19911yescharacteristic
151AGL(1,ℤ/8)—3982no—
152AGL(1,ℤ/8)—3982no—
153C2×SD16—3981no—
154C2×D8—3981no—
155C2×M16—1991no—
156C2×M16—1991no—
157#127—21no—
158#127—3982no—
159#127—3982no—
160#124—21no—
161#121—22no—
162#120—22no—
163#117C2×D19911yescharacteristic
164C2×C42—1991no—
165#104—3982no—
166#102—3982no—
167#100—3982no—
168C24—3981no—
169C24C22⋊D19912yes—
170#41—21no—
171#41—21no—
172#41—21no—
173#41—21no—
174C2×Q8C22⋊D19911yescharacteristic, complemented
175C2×D4—21no—
176C2×D4—24no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—21no—
183C2×D4—7968no—
184C2×D4—3988no—
185C2×D4—3981no—
186C2×D4—3981no—
187C2×D4—3981no—
188C2×D4—3981no—
189C2×D4—3981no—
190C2×D4—1992no—
191C2×D4C22⋊D19911yescharacteristic, complemented
192C22×C4—21no—
193C22×C4—3981no—
194C22×C4C22×D19911yescharacteristic
195SD16—3984no—
196D8—3984no—
197M16—3981no—
198M16—3981no—
199M16—3981no—
200M16—1992no—
201C2×C8—3981no—
202C2×C8—3981no—
203C4⋊C4C22⋊D19912yescomplemented
204C22⋊C4—24no—
205C22⋊C4—21no—
206C42—21no—
207C42—3981no—
208C42—1992no—
209C23—22no—
210C23—22no—
211C23—21no—
212C23—22no—
213C23—44no—
214C23—7964no—
215C23—7961no—
216C23—7961no—
217C23—3982no—
218C23C2×C22⋊D19911yescharacteristic
219Q8—21no—
220Q8—21no—
221D4—21no—
222D4—21no—
223D4—41no—
224D4—41no—
225D4—41no—
226D4—41no—
227D4—41no—
228D4—41no—
229D4—84no—
230D4—79616no—
231D4—7961no—
232D4—7961no—
233D4—3982no—
234D4—3982no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—3984no—
240C2×C4—3982no—
241C2×C4D4×D19911yescharacteristic
242C2×C4D4×D19911yescharacteristic
243C2×C4D4×D19911yescharacteristic
244C2×C4C2×C22⋊D19911yescharacteristic
245C2×C4C2×C22⋊D19911yescharacteristic
246C2×C4#1569188511yescharacteristic
247C8—7961no—
248C8—3982no—
249C22—22no—
250C22—44no—
251C22—41no—
252C22—42no—
253C22—42no—
254C22—44no—
255C22—82no—
256C22—7964no—
257C22—7962no—
258C22—15922no—
259C22—15922no—
260C22#2026392311yescharacteristic
261C22#2026392411yescharacteristic
262C22#2026392711yescharacteristic
263C4—41no—
264C4—42no—
265C4—3984no—
266C4#2026392311yescharacteristic
267C4#2026392611yescharacteristic
268C4#2026392711yescharacteristic
269C4#2026395111yescharacteristic
270C2—21no—
271C2—21no—
272C2—82no—
273C2—81no—
274C2—15922no—
275C2#2716392611yescharacteristic
276C2#2716418612yes—
subgroupG/H
centerC22#20263924
commutator, cosocleC22×C4×C199C23
FrattiniC22×C4C22×D199
Fitting#535×C199C2
socleC22×C199#120
hypercenter#535D199
hypocenterC199#2002
LCSG ▷ C22×C4×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C22 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#20263980C2semidirect
2. C2×#20263951C2semidirect
3. C2×#20263882C2semidirect
4. #27164022C2semidirect
5. C2×#20263872C2semidirect
6. #27163777C2semidirect
7. #535×C199C2semidirect
35. C2×D796D4semidirect
44. #15691870D4semidirect
48. C4×Dic199D4semidirect
54. C2×Q8×C199D4semidirect
63. C2×D4×C199D4semidirect
66. C4⋊C4×C199D4semidirect
138. C199#2002semidirect
141. #535D199semidirect
174. C2×Q8C22⋊D199semidirect
191. C2×D4C22⋊D199semidirect
203. C4⋊C4C22⋊D199semidirect

Maximal subgroups

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

subgroupindex
C2×#202639802
C2×#202639512
C2×#202638822
#271640222
C2×#202638722
#271637772
#535×C1992
#2002199