Finite Group Databasebeta

← #38770533

Subgroups — #38770533

Order 25472.

250 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 65 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#27164564C211yesmaximal, characteristic
2#27164002C211yesmaximal, characteristic, complemented
3#27163816C212yesmaximal, complemented
4#27163814C212yesmaximal, complemented
5#413×C199C211yesmaximal, characteristic, complemented
6C2×#15691886C411yescharacteristic
7C2×#15691870—21no—
8#20263953C2211yescharacteristic
9#20263951C411yescharacteristic
10#20263944C2211yescharacteristic
11#20263942C411yescharacteristic
12#20263927—21no—
13#20263927—21no—
14C4×C22⋊D199—21no—
15C4×C22⋊D199—21no—
16C2×C4×Dic199C411yescharacteristic
17#20263874C2212yes—
18#20263872—21no—
19C2×#41×C199C2211yescharacteristic
20C2×M16×C199—21no—
21#101×C199C2212yes—
22#100×C199—21no—
23#15691886—41no—
24#15691886—41no—
25C2×Dic398C2×C411yescharacteristic
26C2×D796C2×C411yescharacteristic
27C2×C22⋊D199—21no—
28C2×C22⋊D199—21no—
29C2×C22⋊D199—21no—
30C22×Dic199—21no—
31C2×C4×D199—21no—
32#15691870—22no—
33#15691870—41no—
34C2×C199⋊C8—41no—
35Dic199⋊C4—21no—
36Dic199⋊C4—21no—
37C22⋊Dic199—21no—
38C22⋊Dic199—21no—
39(C2×D199)⋊C4—21no—
40(C2×D199)⋊C4—21no—
41C4×Dic199—21no—
42C4×Dic199C2×C411yescharacteristic
43C4×Dic199C2×C411yescharacteristic
44#41×C199—41no—
45#41×C199—41no—
46C2×Q8×C199C2311yescharacteristic
47C2×D4×C199C2×C411yescharacteristic
48C2×D4×C199D411yescharacteristic
49C2×D4×C199D411yescharacteristic
50C22×C4×C199C2×C411yescharacteristic
51C22×C4×C199D411yescharacteristic
52C22×C4×C199D411yescharacteristic
53M16×C199—22no—
54M16×C199—41no—
55C2×C8×C199—41no—
56C22×D199—21no—
57Dic398—41no—
58D796—41no—
59C22⋊D199—42no—
60C22⋊D199—42no—
61C22⋊D199—42no—
62C2×Dic199—21no—
63C2×Dic199—21no—
64C2×Dic199—21no—
65C2×Dic199—42no—
66C4×D199—41no—
67C4×D199—41no—
68C199⋊C8—42no—
69C23×C199C22⋊C411yescharacteristic
70C23×C199C22⋊C411yescharacteristic
71C23×C199C22⋊C411yescharacteristic
72Q8×C199—41no—
73D4×C199—41no—
74D4×C199—41no—
75D4×C199—41no—
76C2×C4×C199—21no—
77C2×C4×C199—21no—
78C2×C4×C199—21no—
79C2×C4×C199—21no—
80C2×C4×C199—21no—
81C2×C4×C199—21no—
82C2×C4×C199C22⋊C411yescharacteristic
83C2×C4×C199C22×C411yescharacteristic
84C2×C4×C199C2×D411yescharacteristic
85C2×C4×C199C2×D411yescharacteristic
86C8×C199—42no—
87C22×C199—21no—
88C22×C199—21no—
89C22×C199—21no—
90C22×C199—41no—
91C22×C199—41no—
92C22×C199—41no—
93C22×C199C2×C22⋊C411yescharacteristic
94C2×D199—41no—
95C2×D199—41no—
96C2×D199—41no—
97C4×C199—21no—
98C4×C199—21no—
99C4×C199—21no—
100C4×C199#9911yescharacteristic
101C4×C199#9911yescharacteristic
102Dic199—22no—
103Dic199—41no—
104Dic199—41no—
105C2×C199—21no—
106C2×C199—41no—
107C2×C199—41no—
108C2×C199—41no—
109C2×C199C2×#9911yescharacteristic
110D199—81no—
111C199#213211yescharacteristic, complemented, Sylow
112#2132—1991nomaximal, Sylow
113#532—1991no—
114#413—1991no—
115#413D19911yescharacteristic, complemented
116#356—1992no—
117#355—1992no—
118C2×#41—1991no—
119C2×#41C2×D19911yescharacteristic
120C2×M16—21no—
121C2×M16—3981no—
122C4⋊Q8—1991no—
123#127—1991no—
124#124—1991no—
125#124—1991no—
126#121—3981no—
127#121—3981no—
128C4×D4—3981no—
129C4×D4—3981no—
130C2×C42—1991no—
131#101—1992no—
132#101C2×D19912yes—
133#100—21no—
134#100—3981no—
135#41—41no—
136#41—41no—
137#41—7961no—
138#41—7961no—
139C2×Q8—1991no—
140C2×Q8C22×D19911yescharacteristic
141C2×D4—3981no—
142C2×D4—3981no—
143C2×D4—3981no—
144C2×D4—1991no—
145C2×D4C4×D19911yescharacteristic
146C2×D4C22⋊D19911yescharacteristic
147C2×D4D79611yescharacteristic
148C22×C4—3981no—
149C22×C4—3981no—
150C22×C4C4×D19911yescharacteristic
151C22×C4C22⋊D19911yescharacteristic
152C22×C4D79611yescharacteristic
153M16—22no—
154M16—41no—
155M16—7961no—
156M16—3982no—
157C2×C8—41no—
158C2×C8—7961no—
159C4⋊C4—3981no—
160C4⋊C4—3981no—
161C22⋊C4—3981no—
162C22⋊C4—3981no—
163C22⋊C4—3981no—
164C22⋊C4—3981no—
165C42—3981no—
166C42—1991no—
167C42—1991no—
168C23—3981no—
169C23(C2×D199)⋊C411yescharacteristic
170C23(C2×D199)⋊C411yescharacteristic
171C23(C2×D199)⋊C411yescharacteristic
172Q8—41no—
173Q8—7961no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—7961no—
178D4—7962no—
179D4—7962no—
180D4—7962no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—7962no—
188C2×C4—7961no—
189C2×C4—7961no—
190C2×C4—3981no—
191C2×C4—3981no—
192C2×C4—3981no—
193C2×C4(C2×D199)⋊C411yescharacteristic
194C2×C4C2×C4×D19911yescharacteristic
195C2×C4C2×C22⋊D19911yescharacteristic
196C2×C4C2×D79611yescharacteristic
197C8—42no—
198C8—7962no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—7961no—
206C22—7961no—
207C22—7961no—
208C22C2×(C2×D199)⋊C411yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—7961no—
213C4—7961no—
214C4—3982no—
215C4#2026386911yescharacteristic
216C4#2026386911yescharacteristic
217C2—21no—
218C2—41no—
219C2—41no—
220C2—41no—
221C2—15921no—
222C2C2×#2026386911yescharacteristic
subgroupG/H
centerC4#20263869
commutatorC2×C4×C199C22×C4
FrattiniC2×Q8C22×D199
Fitting#413×C199C2
socleC2×C199C2×#99
prime radical#27164564C2
cosocleC2×Q8×C199C23
hypercenter#413D199
hypocenterC199#2132
LCSG ▷ C2×C4×C199 ▷ C22×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #27164002C2semidirect
3. #27163816C2semidirect
4. #27163814C2semidirect
5. #413×C199C2semidirect
111. C199#2132semidirect
115. #413D199semidirect

Maximal subgroups

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

subgroupindex
#271645642
#271640022
#271638162
#271638142
#413×C1992
#2132199