Finite Group Databasebeta

← #46811268

Subgroups — #46811268

Order 34432.

332 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 89 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#31771151C211yesmaximal, characteristic
2#31770621C212yesmaximal, complemented
3#31770579C211yesmaximal, characteristic, complemented
4#31770366C212yesmaximal, complemented
5#568×C269C211yesmaximal, characteristic, complemented
6C2×#16864402C2211yescharacteristic
7#22575451C411yescharacteristic, complemented
8#22575449C411yescharacteristic, complemented
9#22575442C411yescharacteristic, complemented
10#22575440C411yescharacteristic, complemented
11#22575425—22no—
12C4×C22⋊D269—22no—
13#22575412C2212yes—
14C2×C4×Dic269C2211yescharacteristic
15#22575379—24no—
16#22575368—22no—
17C2×#41×C269C2211yescharacteristic
18#131×C269—24no—
19C2×M16×C269—22no—
20C2×M16×C269C2212yes—
21#16864402—22no—
22#16864402—22no—
23C2×Dic538C2×C411yescharacteristic
24C2×D1076C2×C411yescharacteristic
25C2×C22⋊D269—22no—
26C2×C22⋊D269—21no—
27C22×Dic269—21no—
28C2×C4×D269—21no—
29C4⋊Dic269—22no—
30#16864381—22no—
31C22⋊Dic269—22no—
32C22⋊Dic269—22no—
33#16864379—22no—
34C4×Dic269—21no—
35C4×Dic269—22no—
36C4×Dic269C2×C411yescharacteristic
37C4×Dic269C2×C411yescharacteristic
38#41×C269—22no—
39#41×C269—22no—
40C2×Q8×C269C2×C411yescharacteristic
41C2×D4×C269C2×C411yescharacteristic
42C2×D4×C269D412yes—
43C22×C4×C269D412yes—
44C22×C4×C269C2311yescharacteristic
45M16×C269—24no—
46M16×C269—22no—
47M16×C269D414yescomplemented
48C2×C8×C269—24no—
49C2×C8×C269—22no—
50C22×D269—21no—
51Dic538—22no—
52D1076—22no—
53C22⋊D269—44no—
54C22⋊D269—42no—
55C2×Dic269—21no—
56C2×Dic269—21no—
57C2×Dic269—21no—
58C2×Dic269—42no—
59C2×Dic269—42no—
60C4×D269—41no—
61C4×D269—41no—
62C23×C269C22⋊C412yes—
63C23×C269C2×D411yescharacteristic
64Q8×C269—22no—
65D4×C269—24no—
66D4×C269—22no—
67C2×C4×C269—22no—
68C2×C4×C269—22no—
69C2×C4×C269C22⋊C412yes—
70C2×C4×C269C22×C411yescharacteristic
71C2×C4×C269C2×D412yes—
72C2×C4×C269C2×D411yescharacteristic
73C2×C4×C269#4112yes—
74C8×C269—24no—
75C22×C269—22no—
76C22×C269—41no—
77C22×C269—42no—
78C22×C269C2×C22⋊C411yescharacteristic
79C22×C269#12112yes—
80C2×D269—42no—
81C2×D269—41no—
82C4×C269—22no—
83C4×C269C4×D412yes—
84C4×C269#12011yescharacteristic
85C4×C269#12311yescharacteristic
86Dic269—22no—
87Dic269—41no—
88Dic269—41no—
89Dic269—82no—
90C2×C269—21no—
91C2×C269—22no—
92C2×C269—42no—
93C2×C269#38611yescharacteristic
94D269—81no—
95C269#188411yescharacteristic, complemented, Sylow
96#1884—2691nomaximal, Sylow
97#568D26911yescharacteristic, complemented
98#532—2691no—
99#421—2692no—
100#410—2691no—
101#339—2692no—
102C2×#41—2691no—
103C2×#41C2×D26911yescharacteristic
104#131—24no—
105C2×M16—22no—
106C2×M16C2×D26912yes—
107C4⋊Q8—2691no—
108#127—2691no—
109#124—2691no—
110#124—2691no—
111#121—5382no—
112C4×D4—5382no—
113#117—2692no—
114C2×C42—2691no—
115#104—5384no—
116#99—5382no—
117#41—22no—
118#41—22no—
119#41—5382no—
120#41—5382no—
121C2×Q8—2691no—
122C2×Q8C4×D26911yescharacteristic
123C2×D4—2691no—
124C2×D4—5382no—
125C2×D4—5381no—
126C2×D4C4×D26911yescharacteristic
127C2×D4D107612yes—
128C22×C4—5381no—
129C22×C4—5381no—
130C22×C4C22⋊D26912yes—
131C22×C4C22×D26911yescharacteristic
132M16—24no—
133M16—22no—
134M16C22⋊D26914yescomplemented
135C2×C8—24no—
136C2×C8—22no—
137C4⋊C4—5382no—
138C4⋊C4—5382no—
139C22⋊C4—5382no—
140C22⋊C4—5382no—
141C22⋊C4—5382no—
142C42—2691no—
143C42—2691no—
144C42—5381no—
145C42—5382no—
146C23—5381no—
147C23#1686437912yes—
148C23C2×D107611yescharacteristic
149Q8—22no—
150Q8—5382no—
151D4—24no—
152D4—22no—
153D4—5382no—
154D4—10764no—
155D4—10762no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—5381no—
159C2×C4—5381no—
160C2×C4—5381no—
161C2×C4—10762no—
162C2×C4—10761no—
163C2×C4—10761no—
164C2×C4—10762no—
165C2×C4#1686437912yes—
166C2×C4C2×C4×D26911yescharacteristic
167C2×C4C2×C22⋊D26912yes—
168C2×C4C2×C22⋊D26911yescharacteristic
169C2×C4#1686440212yes—
170C8—24no—
171C22—22no—
172C22—41no—
173C22—42no—
174C22—10762no—
175C22—10761no—
176C22C2×#1686437911yescharacteristic
177C22#2257542712yes—
178C4—22no—
179C4—5382no—
180C4—10761no—
181C4—10761no—
182C4—21522no—
183C4C4×C22⋊D26912yes—
184C4#2257542211yescharacteristic
185C4#2257543611yescharacteristic
186C2—21no—
187C2—22no—
188C2—42no—
189C2—21521no—
190C2#3177048411yescharacteristic
subgroupG/H
centerC4#22575422
commutatorC2×C4×C269C22×C4
FrattiniC22×C4C22×D269
Fitting#568×C269C2
socleC2×C269#386
prime radical#31771151C2
cosocleC22×C4×C269C23
hypercenter#568D269
hypocenterC269#1884
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C4 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #31770621C2semidirect
3. #31770579C2semidirect
4. #31770366C2semidirect
5. #568×C269C2semidirect
7. #22575451C4semidirect
8. #22575449C4semidirect
9. #22575442C4semidirect
10. #22575440C4semidirect
47. M16×C269D4semidirect
95. C269#1884semidirect
97. #568D269semidirect
134. M16C22⋊D269semidirect

Maximal subgroups

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

subgroupindex
#317711512
#317706212
#317705792
#317703662
#568×C2692
#1884269