Finite Group Databasebeta

← #38770009

Subgroups — #38770009

Order 25472.

246 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 69 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
1#27164646C211yesmaximal, characteristic
2#27164027C211yesmaximal, characteristic
3#27163925C211yesmaximal, characteristic
4#27163786C211yesmaximal, characteristic
5#27163779C211yesmaximal, characteristic
6#27163777C211yesmaximal, characteristic
7#419×C199C211yesmaximal, characteristic
8C2×#15691870C2211yescharacteristic
9#20263955—21no—
10#20263954—21no—
11#20263947—21no—
12#20263946—21no—
13#20263932—22no—
14#20263914C2211yescharacteristic
15C2×C4⋊Dic199C2211yescharacteristic
16C2×C4×Dic199C2211yescharacteristic
17#20263879—21no—
18#20263879—21no—
19C199⋊#95—22no—
20C22×Q8×C199C2211yescharacteristic
21C2×M16×C199C2211yescharacteristic
22#117×C199C2211yescharacteristic
23#103×C199—21no—
24#103×C199—21no—
25C2×Dic398—22no—
26C22×Dic199—21no—
27C22×Dic199D412yes—
28#15691870—21no—
29#15691870—21no—
30C2×C199⋊C8—21no—
31C4⋊Dic199—22no—
32C4⋊Dic199—21no—
33C4⋊Dic199—21no—
34C4⋊Dic199D411yescharacteristic
35C4⋊Dic199D411yescharacteristic
36Dic199⋊C4—22no—
37Dic199⋊C4—22no—
38C22⋊Dic199—21no—
39C4×Dic199—21no—
40C4×Dic199—21no—
41C4×Dic199—21no—
42C2×Q8×C199—21no—
43C2×Q8×C199—21no—
44C2×Q8×C199—21no—
45C2×Q8×C199—21no—
46C2×Q8×C199—21no—
47C2×Q8×C199Q812yescomplemented
48C22×C4×C199—21no—
49C22×C4×C199C2311yescharacteristic
50M16×C199—21no—
51M16×C199—21no—
52C2×C8×C199—21no—
53C4⋊C4×C199D411yescharacteristic
54C4⋊C4×C199D411yescharacteristic
55C22⋊C4×C199—21no—
56C42×C199—21no—
57Dic398—82no—
58C2×Dic199—22no—
59C2×Dic199—21no—
60C2×Dic199—21no—
61C2×Dic199—22no—
62C2×Dic199—41no—
63C2×Dic199—41no—
64C2×Dic199—42no—
65C199⋊C8—41no—
66C23×C199C2×D411yescharacteristic
67Q8×C199—22no—
68Q8×C199—22no—
69Q8×C199—41no—
70Q8×C199—41no—
71C2×C4×C199—21no—
72C2×C4×C199—21no—
73C2×C4×C199—22no—
74C2×C4×C199—41no—
75C2×C4×C199—41no—
76C2×C4×C199C2×D411yescharacteristic
77C2×C4×C199C2×D411yescharacteristic
78C2×C4×C199C2×Q811yescharacteristic
79C2×C4×C199#4111yescharacteristic
80C2×C4×C199#4111yescharacteristic
81C2×C4×C199#4111yescharacteristic
82C8×C199—41no—
83C22×C199—21no—
84C22×C199—21no—
85C22×C199#12011yescharacteristic
86C22×C199C22⋊Q811yescharacteristic
87C22×C199#12411yescharacteristic
88C4×C199—42no—
89C4×C199—41no—
90C4×C199—41no—
91C4×C199C22⋊Q811yescharacteristic
92C4×C199C22⋊Q811yescharacteristic
93C4×C199#12411yescharacteristic
94C4×C199#12411yescharacteristic
95Dic199—42no—
96Dic199—42no—
97Dic199—41no—
98Dic199—41no—
99C2×C199—21no—
100C2×C199—21no—
101C2×C199#39311yescharacteristic
102C2×C199#45511yescharacteristic
103C2×C199#45611yescharacteristic
104C199#202811yescharacteristic, complemented, Sylow
105#2028—1991nomaximal, Sylow
106#544—1991no—
107#419—1991no—
108#419D19911yescharacteristic
109#391—1991no—
110#343—1991no—
111#339—1991no—
112#339—1991no—
113C22×Q8C2×D19911yescharacteristic
114C2×M16—1991no—
115C2×M16C2×D19911yescharacteristic
116C4⋊Q8—3981no—
117C4⋊Q8—3981no—
118#125—3981no—
119#125—3981no—
120C22⋊Q8—3982no—
121#117—1991no—
122#117C2×D19911yescharacteristic
123C2×C4⋊C4—1991no—
124C2×C42—1991no—
125#103—21no—
126#103—21no—
127#103—3981no—
128#103—3981no—
129#95—3982no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—3982no—
136C2×Q8Dic39812yescomplemented
137C22×C4—21no—
138C22×C4—3981no—
139C22×C4—1992no—
140C22×C4C22×D19911yescharacteristic
141M16—21no—
142M16—21no—
143M16—3981no—
144M16—3981no—
145C2×C8—21no—
146C2×C8—3981no—
147C4⋊C4—3982no—
148C4⋊C4—3982no—
149C4⋊C4—3982no—
150C4⋊C4—3981no—
151C4⋊C4—3981no—
152C4⋊C4—1991no—
153C4⋊C4—1991no—
154C4⋊C4C22⋊D19911yescharacteristic
155C4⋊C4C22⋊D19911yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—3981no—
158C42—21no—
159C42—3981no—
160C42—3981no—
161C42—3981no—
162C23D4×D19911yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—41no—
166Q8—41no—
167Q8—15922no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—7961no—
174C2×C4—7961no—
175C2×C4—7962no—
176C2×C4—3982no—
177C2×C4—3981no—
178C2×C4—3981no—
179C2×C4—3982no—
180C2×C4D4×D19911yescharacteristic
181C2×C4C2×C22⋊D19911yescharacteristic
182C2×C4C2×Dic39811yescharacteristic
183C2×C4#1569188511yescharacteristic
184C2×C4#1569188511yescharacteristic
185C2×C4#1569188611yescharacteristic
186C8—41no—
187C8—7961no—
188C22—21no—
189C22—21no—
190C22#2026392311yescharacteristic
191C22#2026393211yescharacteristic
192C22#2026394111yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—7962no—
197C4—7962no—
198C4—7961no—
199C4—7961no—
200C4#2026393211yescharacteristic
201C4#2026393411yescharacteristic
202C4#2026394111yescharacteristic
203C4#2026394211yescharacteristic
204C2—21no—
205C2—21no—
206C2#2716393011yescharacteristic
207C2#2716419411yescharacteristic
208C2#2716419911yescharacteristic
subgroupG/H
centerC22#20263923
commutator, cosocleC22×C4×C199C23
FrattiniC22×C4C22×D199
Fitting#419×C199C2
socleC22×C199#120
prime radicalC23×C199C2×D4
hypercenter#419D199
hypocenterC199#2028
LCSG ▷ C22×C4×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
47. C2×Q8×C199Q8semidirect
104. C199#2028semidirect
136. C2×Q8Dic398semidirect

Maximal subgroups

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

subgroupindex
#271646462
#271640272
#271639252
#271637862
#271637792
#271637772
#419×C1992
#2028199