Finite Group Databasebeta

← #38767968

Subgroups — #38767968

Order 25472.

314 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×D796C211yesmaximal, characteristic
2#27164391C211yesmaximal, characteristic, complemented
3#27164309C211yesmaximal, characteristic, complemented
4#27164308C211yesmaximal, characteristic, complemented
5#27163761C211yesmaximal, characteristic, complemented
6#27163747C211yesmaximal, characteristic, complemented
7D4⋊C8×C199C211yesmaximal, characteristic, complemented
8C22×D796—21no—
9C2×D4×D199—21no—
10C2×#15691875—22no—
11#20263955C2211yescharacteristic, complemented
12#20263952C2211yescharacteristic
13#20263930—21no—
14#20263929—21no—
15#20263925—22no—
16C4×D796C2211yescharacteristic
17#20263887—21no—
18#20263886—21no—
19C4⋊(C199⋊C8)C2211yescharacteristic, complemented
20#20263877—21no—
21#20263876—21no—
22C4×D4×C199C2211yescharacteristic
23C4⋊C8×C199C2211yescharacteristic, complemented
24C4×C8×C199C2211yescharacteristic, complemented
25C23×D199—22no—
26C2×Dic398—21no—
27C2×D796—22no—
28C2×D796—21no—
29C2×D796—21no—
30C2×D796—42no—
31C2×D796—42no—
32C2×D796D411yescharacteristic
33C2×D796D412yes—
34C2×C22⋊D199—22no—
35D4×D199—42no—
36D4×D199—42no—
37C2×C4×D199—21no—
38#15691875—44no—
39C2×C199⋊C8—21no—
40C4⋊Dic199—21no—
41C4⋊Dic199—21no—
42C4⋊Dic199D411yescharacteristic
43(C2×D199)⋊C4—22no—
44(C2×D199)⋊C4—21no—
45C2×D4×C199D411yescharacteristic
46C22×C4×C199—21no—
47C2×C8×C199—21no—
48C2×C8×C199—21no—
49C4⋊C4×C199D411yescharacteristic
50C22⋊C4×C199—21no—
51C42×C199C2311yescharacteristic
52C22×D199—21no—
53C22×D199—22no—
54C22×D199—44no—
55C22×D199—44no—
56C22×D199—82no—
57Dic398—42no—
58D796—21no—
59D796—42no—
60D796—44no—
61D796—41no—
62D796—41no—
63D796—41no—
64D796—41no—
65D796SD1612yescomplemented
66C22⋊D199—44no—
67C2×Dic199—21no—
68C2×Dic199—41no—
69C4×D199—41no—
70C4×D199—41no—
71C199⋊C8—41no—
72C23×C199—21no—
73D4×C199—21no—
74D4×C199SD1612yescomplemented
75C2×C4×C199—21no—
76C2×C4×C199—41no—
77C2×C4×C199—41no—
78C2×C4×C199C2×D411yescharacteristic
79C2×C4×C199C2×D411yescharacteristic
80C2×C4×C199C2×D411yescharacteristic
81C8×C199—22no—
82C8×C199—41no—
83C22×C199—22no—
84C22×C199—41no—
85C22×C199—41no—
86C22×C199#12011yescharacteristic
87C2×D199—22no—
88C2×D199—41no—
89C2×D199—41no—
90C2×D199—42no—
91C2×D199—42no—
92C2×D199—42no—
93C2×D199—88no—
94C4×C199—21no—
95C4×C199—41no—
96C4×C199C2×SD1611yescharacteristic
97C4×C199C2×SD1611yescharacteristic
98C4×C199AGL(1,ℤ/8)11yescharacteristic
99C4×C199AGL(1,ℤ/8)11yescharacteristic
100Dic199—41no—
101Dic199—81no—
102C2×C199—42no—
103C2×C199#45011yescharacteristic
104C2×C199#45011yescharacteristic
105C2×C199#45311yescharacteristic
106D199—42no—
107D199—82no—
108C199#162911yescharacteristic, complemented, Sylow
109#1629—1991nomaximal, Sylow
110D42—1991no—
111#492—1991no—
112#476—1991no—
113#476—1991no—
114#331—1991no—
115D4⋊C8—1991no—
116D4⋊C8D19911yescharacteristic, complemented
117C22×D4—3981no—
118C22×D4—3981no—
119C2×SD16—3982no—
120C4⋊Q8—1991no—
121#127—1991no—
122#121—3981no—
123#121—3981no—
124#120—3982no—
125C4×D4—1991no—
126C4×D4C2×D19911yescharacteristic
127#106—3981no—
128#106—3981no—
129C4⋊C8—1991no—
130C4⋊C8C2×D19911yescharacteristic, complemented
131#102—3981no—
132#102—3981no—
133C4×C8C2×D19911yescharacteristic, complemented
134C24—3982no—
135C2×Q8—3981no—
136C2×D4—7962no—
137C2×D4—7962no—
138C2×D4—7962no—
139C2×D4—7962no—
140C2×D4—3982no—
141C2×D4—3982no—
142C2×D4—3981no—
143C2×D4—3981no—
144C2×D4—1992no—
145C2×D4—1991no—
146C2×D4D79611yescharacteristic
147C22×C4—21no—
148C22×C4—3981no—
149SD16—7964no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—3981no—
153C4⋊C4—3981no—
154C4⋊C4—3981no—
155C4⋊C4—1991no—
156C4⋊C4D79611yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—3982no—
159C22⋊C4—3981no—
160C42C22×D19911yescharacteristic
161C23—21no—
162C23—7964no—
163C23—7964no—
164C23—15922no—
165C23—3982no—
166C23—3981no—
167Q8—7962no—
168D4—21no—
169D4—7962no—
170D4—7964no—
171D4—7964no—
172D4—7961no—
173D4—7961no—
174D4—7961no—
175D4—7961no—
176D4—3981no—
177D4—1992no—
178D4#1569187512yescomplemented
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—7961no—
183C2×C4—7961no—
184C2×C4—7961no—
185C2×C4—3981no—
186C2×C4D4×D19911yescharacteristic
187C2×C4D4×D19911yescharacteristic
188C2×C4C2×D79611yescharacteristic
189C8—22no—
190C8—41no—
191C8—7961no—
192C22—22no—
193C22—41no—
194C22—41no—
195C22—7961no—
196C22—7961no—
197C22—7962no—
198C22—7962no—
199C22—7962no—
200C22—15928no—
201C22—3982no—
202C22#2026392511yescharacteristic
203C4—21no—
204C4—41no—
205C4—7961no—
206C4—15921no—
207C4SD16×D19911yescharacteristic
208C4C2×#1569187511yescharacteristic
209C4#2026397911yescharacteristic
210C4#2026398311yescharacteristic
211C2—42no—
212C2—7962no—
213C2—15922no—
214C2#2716417011yescharacteristic
215C2#2716417111yescharacteristic
216C2#2716418711yescharacteristic
subgroupG/H
centerC22#20263925
commutator, cosocleC42×C199C23
FrattiniC42C22×D199
FittingD4⋊C8×C199C2
socleC22×C199#120
prime radicalD4×D796C2
hypercenterD4⋊C8D199
hypocenterC199#1629
LCSG ▷ C42×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #27164391C2semidirect
3. #27164309C2semidirect
4. #27164308C2semidirect
5. #27163761C2semidirect
6. #27163747C2semidirect
7. D4⋊C8×C199C2semidirect
11. #20263955C22semidirect
19. C4⋊(C199⋊C8)C22semidirect
23. C4⋊C8×C199C22semidirect
24. C4×C8×C199C22semidirect
65. D796SD16semidirect
74. D4×C199SD16semidirect
108. C199#1629semidirect
116. D4⋊C8D199semidirect
130. C4⋊C8C2×D199semidirect
133. C4×C8C2×D199semidirect
178. D4#15691875semidirect

Maximal subgroups

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

subgroupindex
D4×D7962
#271643912
#271643092
#271643082
#271637612
#271637472
D4⋊C8×C1992
#1629199