Finite Group Databasebeta

← #46812556

Subgroups — #46812556

Order 34432.

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

normal subgroups only

This group has 270 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#31771169C211yesmaximal, characteristic
2#31770579C211yesmaximal, characteristic, complemented
3#31770397C214yesmaximal, complemented
4#410×C269C211yesmaximal, characteristic, complemented
5C22×D1076C411yescharacteristic, complemented
6#22575449C2212yes—
7#22575442C412yescomplemented
8#22575427—21no—
9#22575427—21no—
10#22575421—21no—
11#22575421—21no—
12#22575412—21no—
13#22575412C411yescharacteristic, complemented
14#22575368—21no—
15#22575368C2212yescomplemented
16C2×#41×C269C2211yescharacteristic
17#117×C269—21no—
18#99×C269—21no—
19#99×C269C2212yescomplemented
20C23×D269—21no—
21C2×D1076—21no—
22C2×D1076—41no—
23C2×D1076—41no—
24C2×D1076C2×C412yes—
25C2×C22⋊D269—22no—
26C2×C22⋊D269—22no—
27C4⋊Dic269—21no—
28C4⋊Dic269—41no—
29C22⋊Dic269—21no—
30C22⋊Dic269—22no—
31#16864379—22no—
32#16864379—22no—
33C4×Dic269—41no—
34C4×Dic269C2×C412yes—
35#41×C269—41no—
36#41×C269—41no—
37C2×Q8×C269C2×C411yescharacteristic
38C2×D4×C269D411yescharacteristic
39C2×D4×C269D411yescharacteristic
40C2×D4×C269C2311yescharacteristic
41C22×C4×C269C2×C411yescharacteristic
42C22×C4×C269D411yescharacteristic
43C22×C4×C269D411yescharacteristic
44C4⋊C4×C269—41no—
45C22⋊C4×C269—22no—
46C42×C269—41no—
47C22×D269—22no—
48C22×D269—42no—
49C22×D269—82no—
50D1076—42no—
51D1076—41no—
52D1076—41no—
53C22⋊D269—82no—
54C22⋊D269—82no—
55C2×Dic269—22no—
56C2×Dic269—42no—
57C23×C269C22⋊C411yescharacteristic
58C23×C269C2×D411yescharacteristic
59C23×C269C2×D411yescharacteristic
60Q8×C269—41no—
61D4×C269—41no—
62D4×C269—41no—
63D4×C269—41no—
64C2×C4×C269—21no—
65C2×C4×C269—21no—
66C2×C4×C269—21no—
67C2×C4×C269—21no—
68C2×C4×C269—21no—
69C2×C4×C269—21no—
70C2×C4×C269—42no—
71C2×C4×C269C22⋊C411yescharacteristic
72C2×C4×C269C22⋊C411yescharacteristic
73C2×C4×C269C22⋊C411yescharacteristic
74C2×C4×C269C22×C411yescharacteristic
75C22×C269—21no—
76C22×C269—21no—
77C22×C269—21no—
78C22×C269—41no—
79C22×C269—41no—
80C22×C269—41no—
81C22×C269C2×C22⋊C411yescharacteristic
82C2×D269—42no—
83C2×D269—42no—
84C2×D269—42no—
85C2×D269—84no—
86C4×C269—21no—
87C4×C269—21no—
88C4×C269—21no—
89C4×C269—82no—
90C4×C269#9911yescharacteristic
91C4×C269#9911yescharacteristic
92Dic269—42no—
93Dic269—82no—
94C2×C269—21no—
95C2×C269—41no—
96C2×C269—41no—
97C2×C269—41no—
98C2×C269C2×#9911yescharacteristic
99D269—82no—
100C269#212811yescharacteristic, complemented, Sylow
101#2128—2691nomaximal, Sylow
102#535—2691no—
103#410—2691no—
104#410D26911yescharacteristic, complemented
105#353—2694no—
106C2×#41C2×D26911yescharacteristic
107C22×D4—2691no—
108#127—2692no—
109#124—2692no—
110#121—5381no—
111#121—5381no—
112#120—5381no—
113#120—5381no—
114#117—21no—
115#117—2691no—
116#117—5381no—
117#99—21no—
118#99—2692no—
119#99—5381no—
120#99C2×D26912yescomplemented
121C24—5381no—
122#41—41no—
123#41—41no—
124C2×Q8C4×D26911yescharacteristic
125C2×D4—2692no—
126C2×D4—5382no—
127C2×D4—5382no—
128C2×D4—5381no—
129C2×D4—10761no—
130C2×D4—10761no—
131C2×D4C22⋊D26911yescharacteristic
132C2×D4D107611yescharacteristic
133C2×D4C22×D26911yescharacteristic
134C22×C4C4×D26911yescharacteristic
135C22×C4C22⋊D26911yescharacteristic
136C22×C4D107611yescharacteristic
137C4⋊C4—41no—
138C4⋊C4—5381no—
139C4⋊C4—10761no—
140C22⋊C4—22no—
141C22⋊C4—5381no—
142C22⋊C4—5382no—
143C22⋊C4—5382no—
144C22⋊C4—5382no—
145C42—41no—
146C42—2692no—
147C42—10761no—
148C23—5382no—
149C23—10762no—
150C23—21522no—
151C23#1686437911yescharacteristic
152C23C2×C22⋊D26911yescharacteristic
153C23C2×D107611yescharacteristic
154Q8—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—10762no—
159D4—10761no—
160D4—10761no—
161D4—21522no—
162D4—21522no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—42no—
170C2×C4—5382no—
171C2×C4—10762no—
172C2×C4#1686437911yescharacteristic
173C2×C4#1686437911yescharacteristic
174C2×C4#1686437911yescharacteristic
175C2×C4C2×C4×D26911yescharacteristic
176C22—21no—
177C22—21no—
178C22—21no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—10762no—
183C22—10762no—
184C22—10762no—
185C22—21524no—
186C22C2×#1686437911yescharacteristic
187C4—21no—
188C4—21no—
189C4—21no—
190C4—82no—
191C4—10762no—
192C4—21522no—
193C4#2257536711yescharacteristic
194C4#2257536711yescharacteristic
195C2—21no—
196C2—41no—
197C2—41no—
198C2—41no—
199C2—21522no—
200C2C2×#2257536711yescharacteristic
subgroupG/H
centerC2C2×#22575367
commutatorC2×C4×C269C22×C4
FrattiniC2×D4C22×D269
Fitting#410×C269C2
socleC2×C269C2×#99
prime radical#31771169C2
cosocleC2×D4×C269C23
hypercenter#410D269
hypocenterC269#2128
LCSG ▷ C2×C4×C269 ▷ C22×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #31770579C2semidirect
3. #31770397C2semidirect
4. #410×C269C2semidirect
5. C22×D1076C4semidirect
7. #22575442C4semidirect
13. #22575412C4semidirect
15. #22575368C22semidirect
19. #99×C269C22semidirect
100. C269#2128semidirect
104. #410D269semidirect
120. #99C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317711692
#317705792
#317703972
#410×C2692
#2128269