Finite Group Databasebeta

← #38767916

Subgroups — #38767916

Order 25472.

278 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 55 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#27164688C211yesmaximal, characteristic, complemented
2#27164394C211yesmaximal, characteristic, complemented
3#27164219C211yesmaximal, characteristic, complemented
4#27164214C211yesmaximal, characteristic, complemented
5#27163748C211yesmaximal, characteristic, complemented
6#27163745C211yesmaximal, characteristic, complemented
7#331×C199C211yesmaximal, characteristic, complemented
8C2×#15691885—21no—
9C2×#15691875—21no—
10C2×D1592—21no—
11C2×#15691871—22no—
12#20263952C2211yescharacteristic
13#20263951—21no—
14#20263927—22no—
15#20263926—21no—
16C4×Dic398C2211yescharacteristic
17C4×D796C2211yescharacteristic
18D4×Dic199—21no—
19#20263877—21no—
20#20263877—21no—
21C4×C199⋊C8C2211yescharacteristic
22#127×C199C2211yescharacteristic
23C4⋊C8×C199C2211yescharacteristic
24C4⋊C8×C199C2211yescharacteristic
25#15691885—42no—
26#15691885—42no—
27C2×Dic398D411yescharacteristic
28C2×D796—21no—
29C2×D796—21no—
30C2×D796—21no—
31C2×D796D411yescharacteristic
32C2×C22⋊D199—22no—
33C2×C22⋊D199—22no—
34C22×Dic199—22no—
35C2×C4×D199—21no—
36#15691875—42no—
37D1592—42no—
38#15691871—44no—
39C2×C199⋊C8—21no—
40C4⋊Dic199D411yescharacteristic
41C4⋊Dic199D411yescharacteristic
42Dic199⋊C4—21no—
43C22⋊Dic199—22no—
44(C2×D199)⋊C4—21no—
45C4×Dic199—21no—
46C2×D4×C199—21no—
47C2×D4×C199—21no—
48C2×D4×C199D412yes—
49C2×C8×C199—21no—
50C2×C8×C199—21no—
51C42×C199C2311yescharacteristic
52C22×D199—21no—
53C22×D199—41no—
54Dic398—21no—
55Dic398D812yescomplemented
56D796—21no—
57D796—21no—
58D796—42no—
59D796—41no—
60D796—41no—
61D796—41no—
62D796—41no—
63C22⋊D199—44no—
64C22⋊D199—82no—
65C2×Dic199—21no—
66C2×Dic199—21no—
67C2×Dic199—21no—
68C2×Dic199—44no—
69C4×D199—41no—
70C4×D199—41no—
71C199⋊C8—22no—
72C23×C199—22no—
73D4×C199—42no—
74D4×C199—41no—
75D4×C199—41no—
76D4×C199—41no—
77D4×C199—41no—
78C2×C4×C199C2×D411yescharacteristic
79C2×C4×C199C2×D411yescharacteristic
80C2×C4×C199C2×D411yescharacteristic
81C8×C199—41no—
82C8×C199—41no—
83C22×C199—42no—
84C22×C199—42no—
85C22×C199—42no—
86C22×C199#12011yescharacteristic
87C2×D199—41no—
88C2×D199—41no—
89C2×D199—41no—
90C2×D199—81no—
91C2×D199—81no—
92C2×D199—81no—
93C4×C199—21no—
94C4×C199C2×D811yescharacteristic
95C4×C199#13511yescharacteristic
96C4×C199AGL(1,ℤ/8)11yescharacteristic
97C4×C199AGL(1,ℤ/8)11yescharacteristic
98Dic199—22no—
99Dic199—41no—
100Dic199—41no—
101C2×C199—82no—
102C2×C199#44711yescharacteristic
103C2×C199#44911yescharacteristic
104C2×C199#45311yescharacteristic
105D199—81no—
106D199—161no—
107C199#162111yescharacteristic, complemented, Sylow
108#1621—1991nomaximal, Sylow
109#550—1991no—
110#493—1991no—
111#460—1991no—
112#459—1991no—
113#331D19911yescharacteristic, complemented
114Q8⋊C8—1991no—
115D4⋊C8—1991no—
116C2×#41—3981no—
117C2×SD16—3981no—
118C2×D8—3981no—
119C2×D8—3982no—
120#127—3981no—
121#127—1991no—
122#127C2×D19911yescharacteristic
123#121—3982no—
124#121—3981no—
125C4×Q8—1991no—
126C4×D4—3981no—
127C4×D4—1991no—
128C4⋊C8C2×D19911yescharacteristic
129C4⋊C8C2×D19911yescharacteristic
130#102—3981no—
131#102—3981no—
132C4×C8—1991no—
133#41—7962no—
134#41—7962no—
135C2×Q8—1991no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—3982no—
139C2×D4—3982no—
140C2×D4—3981no—
141C2×D4—3981no—
142C2×D4—3981no—
143C2×D4—1991no—
144C2×D4D79612yes—
145C22×C4—3982no—
146C22×C4—3981no—
147SD16—7962no—
148D8—7962no—
149D8—7964no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—3981no—
153C4⋊C4—3981no—
154C4⋊C4—1991no—
155C4⋊C4—1991no—
156C22⋊C4—3982no—
157C22⋊C4—3981no—
158C42—3981no—
159C42C22×D19911yescharacteristic
160C23—22no—
161C23—7961no—
162C23—3981no—
163Q8—3981no—
164Q8—1992no—
165D4—42no—
166D4—41no—
167D4—41no—
168D4—41no—
169D4—41no—
170D4—7962no—
171D4—7964no—
172D4—7961no—
173D4—7961no—
174D4—7961no—
175D4—7961no—
176D4—15922no—
177D4—3981no—
178D4—3981no—
179C2×C4—7964no—
180C2×C4—7961no—
181C2×C4—7961no—
182C2×C4—3981no—
183C2×C4—3981no—
184C2×C4—3981no—
185C2×C4D4×D19911yescharacteristic
186C2×C4D4×D19911yescharacteristic
187C2×C4C2×D79611yescharacteristic
188C8—41no—
189C8—41no—
190C8—3982no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—7961no—
195C22—7961no—
196C22—7961no—
197C22—15921no—
198C22—15921no—
199C22—15921no—
200C22#2026392511yescharacteristic
201C4—21no—
202C4—7961no—
203C4—7961no—
204C4—3982no—
205C4D8×D19911yescharacteristic
206C4#2026397611yescharacteristic
207C4#2026397911yescharacteristic
208C4#2026398211yescharacteristic
209C2—82no—
210C2—15921no—
211C2—31841no—
212C2#2716415311yescharacteristic
213C2#2716416411yescharacteristic
214C2#2716418811yescharacteristic
subgroupG/H
centerC22#20263925
commutator, cosocleC42×C199C23
FrattiniC42C22×D199
Fitting#331×C199C2
socleC22×C199#120
hypercenter#331D199
hypocenterC199#1621
LCSG ▷ C42×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
1. #27164688C2semidirect
2. #27164394C2semidirect
3. #27164219C2semidirect
4. #27164214C2semidirect
5. #27163748C2semidirect
6. #27163745C2semidirect
7. #331×C199C2semidirect
55. Dic398D8semidirect
107. C199#1621semidirect
113. #331D199semidirect

Maximal subgroups

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

subgroupindex
#271646882
#271643942
#271642192
#271642142
#271637482
#271637452
#331×C1992
#1621199