Finite Group Databasebeta

← #38769864

Subgroups — #38769864

Order 25472.

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×#20263980C211yesmaximal, characteristic, complemented
2#27164582C211yesmaximal, characteristic, complemented
3C2×#20263952C211yesmaximal, characteristic, complemented
4#27164024C211yesmaximal, characteristic, complemented
5C2×#20263871C211yesmaximal, characteristic, complemented
6#27163778C211yesmaximal, characteristic, complemented
7C2×#104×C199C211yesmaximal, characteristic, complemented
8C22×D796—22no—
9C22×D796C2211yescharacteristic
10C22×D796C2211yescharacteristic
11#20263980—22no—
12#20263980—22no—
13C2×#15691873—21no—
14C2×#15691871—21no—
15C2×#15691870C2211yescharacteristic
16#20263952—22no—
17#20263952—22no—
18#20263951—21no—
19#20263944—21no—
20#20263929—22no—
21#20263923—22no—
22#20263914C2211yescharacteristic
23#20263877—22no—
24#20263871—22no—
25C2×#41×C199C2211yescharacteristic
26C2×M16×C199C2211yescharacteristic
27C2×C42×C199C2211yescharacteristic
28#104×C199—22no—
29C23×D199—21no—
30C23×D199D412yes—
31C2×D796—28no—
32C2×D796—21no—
33C2×D796—21no—
34C2×D796—21no—
35C2×D796—21no—
36C2×D796—21no—
37C2×D796—21no—
38C2×D796—21no—
39C2×D796—21no—
40C2×D796—21no—
41C2×D796—21no—
42C2×D796—21no—
43C2×D796—48no—
44C2×D796D412yescomplemented
45C2×C22⋊D199—24no—
46#15691873—24no—
47#15691871—24no—
48#15691870—21no—
49#15691870D412yescomplemented
50C2×C199⋊C8—21no—
51C4⋊Dic199D412yescomplemented
52C22⋊Dic199—21no—
53(C2×D199)⋊C4—24no—
54C4×Dic199—21no—
55#41×C199—21no—
56#41×C199—21no—
57#41×C199—21no—
58#41×C199—21no—
59C2×Q8×C199D411yescharacteristic, complemented
60C2×D4×C199—21no—
61C2×D4×C199D411yescharacteristic, complemented
62C22×C4×C199—21no—
63C22×C4×C199—21no—
64C22×C4×C199C2311yescharacteristic
65M16×C199—21no—
66M16×C199—21no—
67C2×C8×C199—21no—
68C42×C199—21no—
69C42×C199D412yescomplemented
70C22×D199—22no—
71C22×D199—22no—
72C22×D199—22no—
73C22×D199—22no—
74C22×D199—44no—
75C22×D199—44no—
76C22×D199—41no—
77C22×D199—41no—
78D796—22no—
79D796—22no—
80D796—416no—
81D796—41no—
82D796—41no—
83D796—41no—
84D796—41no—
85D796—41no—
86D796—41no—
87C22⋊D199—84no—
88C2×Dic199—22no—
89C199⋊C8—22no—
90C23×C199—21no—
91C23×C199C2×D411yescharacteristic
92Q8×C199—21no—
93Q8×C199—21no—
94D4×C199—21no—
95D4×C199—21no—
96D4×C199—41no—
97D4×C199—41no—
98C2×C4×C199—24no—
99C2×C4×C199—22no—
100C2×C4×C199—21no—
101C2×C4×C199—41no—
102C2×C4×C199—41no—
103C2×C4×C199C2×D411yescharacteristic
104C2×C4×C199C2×D411yescharacteristic
105C2×C4×C199C2×D411yescharacteristic
106C2×C4×C199C2×D411yescharacteristic
107C2×C4×C199C2×D411yescharacteristic
108C2×C4×C199#4111yescharacteristic
109C8×C199—41no—
110C22×C199—22no—
111C22×C199—41no—
112C22×C199—42no—
113C22×C199#12011yescharacteristic
114C22×C199#12011yescharacteristic
115C22×C199#12111yescharacteristic
116C2×D199—44no—
117C2×D199—44no—
118C2×D199—42no—
119C2×D199—42no—
120C2×D199—44no—
121C2×D199—82no—
122C2×D199—82no—
123C2×D199—82no—
124C4×C199—24no—
125C4×C199—41no—
126C4×C199#12011yescharacteristic
127C4×C199#12111yescharacteristic
128C4×C199#12111yescharacteristic
129C4×C199#12711yescharacteristic
130Dic199—42no—
131C2×C199—21no—
132C2×C199—21no—
133C2×C199—81no—
134C2×C199#39211yescharacteristic
135C2×C199#45312yes—
136D199—82no—
137D199—82no—
138C199#200211yescharacteristic, complemented, Sylow
139#2002—1991nomaximal, Sylow
140C2×AGL(1,ℤ/8)—1991no—
141#535—1991no—
142C2×#127—1991no—
143C2×#104D19911yescharacteristic, complemented
144#418—1991no—
145C2×#100—1991no—
146#339—1991no—
147C2×#41C2×D19911yescharacteristic
148C22×D4—3982no—
149C22×D4—1991no—
150C22×D4—1991no—
151AGL(1,ℤ/8)—3982no—
152AGL(1,ℤ/8)—3982no—
153C2×SD16—3981no—
154C2×D8—3981no—
155C2×M16—1991no—
156C2×M16C2×D19911yescharacteristic
157#127—3982no—
158#127—3981no—
159#127—3982no—
160#124—3981no—
161#121—3982no—
162#120—3982no—
163#117—1991no—
164C2×C42C2×D19911yescharacteristic
165#104—22no—
166#102—3982no—
167#100—3982no—
168C24—3981no—
169C24—1992no—
170#41—21no—
171#41—21no—
172#41—21no—
173#41—21no—
174C2×Q8D79611yescharacteristic, complemented
175C2×D4—21no—
176C2×D4—7968no—
177C2×D4—3988no—
178C2×D4—3984no—
179C2×D4—3981no—
180C2×D4—3981no—
181C2×D4—3981no—
182C2×D4—3981no—
183C2×D4—3981no—
184C2×D4—3981no—
185C2×D4—3981no—
186C2×D4—3981no—
187C2×D4—3981no—
188C2×D4—3981no—
189C2×D4—3981no—
190C2×D4—1992no—
191C2×D4D79611yescharacteristic, complemented
192C22×C4—21no—
193C22×C4—21no—
194C22×C4C22×D19911yescharacteristic
195SD16—3984no—
196D8—3984no—
197M16—21no—
198M16—21no—
199M16—3981no—
200M16—1992no—
201C2×C8—21no—
202C2×C8—3981no—
203C4⋊C4—1992no—
204C22⋊C4—3984no—
205C22⋊C4—3981no—
206C42—21no—
207C42—3981no—
208C42C22⋊D19912yescomplemented
209C23—21no—
210C23—7964no—
211C23—7964no—
212C23—7961no—
213C23—7961no—
214C23—3982no—
215C23—3982no—
216C23—3982no—
217C23—3982no—
218C23D4×D19911yescharacteristic
219Q8—21no—
220Q8—21no—
221D4—21no—
222D4—21no—
223D4—41no—
224D4—41no—
225D4—79616no—
226D4—7961no—
227D4—7961no—
228D4—7961no—
229D4—7961no—
230D4—7961no—
231D4—7961no—
232D4—15924no—
233D4—3982no—
234D4—3982no—
235C2×C4—24no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—3982no—
241C2×C4D4×D19911yescharacteristic
242C2×C4D4×D19911yescharacteristic
243C2×C4D4×D19911yescharacteristic
244C2×C4C2×C22⋊D19911yescharacteristic
245C2×C4C2×D79611yescharacteristic
246C2×C4#1569188611yescharacteristic
247C8—41no—
248C8—3982no—
249C22—22no—
250C22—41no—
251C22—42no—
252C22—7964no—
253C22—7964no—
254C22—7962no—
255C22—7962no—
256C22—7964no—
257C22—15922no—
258C22—15922no—
259C22—15922no—
260C22#2026392311yescharacteristic
261C22#2026392511yescharacteristic
262C22#2026392811yescharacteristic
263C4—24no—
264C4—41no—
265C4—7962no—
266C4#2026392511yescharacteristic
267C4#2026392811yescharacteristic
268C4#2026392911yescharacteristic
269C4#2026395111yescharacteristic
270C2—21no—
271C2—21no—
272C2—81no—
273C2—15922no—
274C2—15922no—
275C2#2716392711yescharacteristic
276C2#2716418712yes—
subgroupG/H
centerC22#20263925
commutator, cosocleC22×C4×C199C23
FrattiniC22×C4C22×D199
FittingC2×#104×C199C2
socleC22×C199#120
hypercenterC2×#104D199
hypocenterC199#2002
LCSG ▷ C22×C4×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×#20263980C2semidirect
2. #27164582C2semidirect
3. C2×#20263952C2semidirect
4. #27164024C2semidirect
5. C2×#20263871C2semidirect
6. #27163778C2semidirect
7. C2×#104×C199C2semidirect
44. C2×D796D4semidirect
49. #15691870D4semidirect
51. C4⋊Dic199D4semidirect
59. C2×Q8×C199D4semidirect
61. C2×D4×C199D4semidirect
69. C42×C199D4semidirect
138. C199#2002semidirect
143. C2×#104D199semidirect
174. C2×Q8D796semidirect
191. C2×D4D796semidirect
208. C42C22⋊D199semidirect

Maximal subgroups

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

subgroupindex
C2×#202639802
#271645822
C2×#202639522
#271640242
C2×#202638712
#271637782
C2×#104×C1992
#2002199