Finite Group Databasebeta

← #46822286

Subgroups — #46822286

Order 34432.

354 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 117 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#31771139C212yesmaximal, complemented
2#31770913C212yesmaximal, complemented
3#31770906C212yesmaximal, complemented
4#31770863C211yesmaximal, characteristic, complemented
5#31770858C211yesmaximal, characteristic
6#31770851C212yesmaximal, complemented
7#31770828C212yesmaximal, complemented
8#31770821C212yesmaximal, complemented
9#423×C269C211yesmaximal, characteristic, complemented
10C2×Dic1076C2211yescharacteristic
11C2×#16864391C2212yes—
12C2×D2152C2211yescharacteristic
13#22575447—22no—
14#22575445C2212yes—
15#22575441C2212yes—
16#22575436—22no—
17#22575432C2212yes—
18#22575427C2212yes—
19C4×Dic538C2212yes—
20C4×D1076C2212yes—
21C4×C22⋊D269—22no—
22#22575410—22no—
23#22575387C2212yes—
24#22575385C2211yescharacteristic
25#22575385C2211yescharacteristic
26#22575378C2212yes—
27#22575378C2212yes—
28#22575375C2212yes—
29#22575375C2212yes—
30C2×M16×C269C2211yescharacteristic
31C2×M16×C269C2211yescharacteristic
32C2×C42×C269C2211yescharacteristic
33C4⋊C8×C269C2212yes—
34C4⋊C8×C269C2212yes—
35C2×Dic538C2312yes—
36C2×D1076C2312yes—
37C2×C22⋊D269—22no—
38C2×C4×D269—22no—
39Dic1076—41no—
40#16864391—42no—
41D2152—41no—
42C4⋊Dic269C2312yes—
43C4⋊Dic269C2312yes—
44#16864381—22no—
45#16864381—22no—
46#16864381—22no—
47#16864381—22no—
48C22⋊Dic269—22no—
49#16864379—22no—
50#16864379—22no—
51#16864379—22no—
52#16864379—22no—
53C4×Dic269—22no—
54C22×C4×C269D412yes—
55C22×C4×C269C2311yescharacteristic
56M16×C269—41no—
57M16×C269—41no—
58C2×C8×C269C2311yescharacteristic
59C2×C8×C269C2312yes—
60C2×C8×C269C2311yescharacteristic
61C42×C269D411yescharacteristic
62C42×C269D411yescharacteristic
63C42×C269C2312yes—
64C22×D269—22no—
65Dic538—22no—
66Dic538—22no—
67D1076—22no—
68D1076—22no—
69C22⋊D269—44no—
70C2×Dic269—22no—
71C2×Dic269—22no—
72C2×Dic269—22no—
73C4×D269—44no—
74C23×C269C2×D411yescharacteristic
75C2×C4×C269—21no—
76C2×C4×C269—21no—
77C2×C4×C269—42no—
78C2×C4×C269C2×D411yescharacteristic
79C2×C4×C269C2×D412yes—
80C2×C4×C269C2×D412yes—
81C2×C4×C269C2411yescharacteristic
82C8×C269—21no—
83C8×C269—22no—
84C8×C269—21no—
85C22×C269—21no—
86C22×C269—22no—
87C22×C269C22×D411yescharacteristic
88C2×D269—42no—
89C2×D269—42no—
90C2×D269—42no—
91C4×C269—21no—
92C4×C269—22no—
93C4×C269—22no—
94C4×C269H(5,𝔽2)11yescharacteristic
95C4×C2692−1+411yescharacteristic
96Dic269—42no—
97Dic269—42no—
98Dic269—42no—
99C2×C269—41no—
100C2×C269#53711yescharacteristic
101C2×C269#57512yes—
102D269—82no—
103C269#325611yescharacteristic, complemented, Sylow
104#3256—2691nomaximal, Sylow
105#529—2692no—
106#479—2692no—
107#478—2692no—
108#470—2691no—
109#469—2691no—
110#468—2692no—
111#464—2692no—
112#463—2692no—
113#423D26911yescharacteristic, complemented
114C2×Q16—2691no—
115C2×SD16—2692no—
116C2×D8—2691no—
117C2×M16C2×D26911yescharacteristic
118C2×M16C2×D26911yescharacteristic
119#126—5382no—
120#125—2692no—
121#124—2692no—
122#123—5382no—
123C22⋊Q8—2692no—
124#121—2692no—
125C4×Q8—2692no—
126C4×D4—2692no—
127C4×D4—5382no—
128#117—5382no—
129C2×C42C2×D26911yescharacteristic
130#107—2692no—
131#106—2691no—
132#106—2691no—
133C4⋊C8C2×D26912yes—
134C4⋊C8C2×D26912yes—
135#103—2692no—
136#103—2692no—
137#102—2692no—
138#102—2692no—
139C2×Q8—2692no—
140C2×D4—2692no—
141C2×D4—5382no—
142C22×C4—5382no—
143C22×C4D107612yes—
144C22×C4C22×D26911yescharacteristic
145Q16—10761no—
146SD16—10762no—
147D8—10761no—
148M16—41no—
149M16—41no—
150C2×C8C22×D26911yescharacteristic
151C2×C8C22×D26912yes—
152C2×C8C22×D26911yescharacteristic
153C4⋊C4—2692no—
154C4⋊C4—2692no—
155C4⋊C4—5382no—
156C4⋊C4—5382no—
157C4⋊C4—5382no—
158C4⋊C4—5382no—
159C22⋊C4—5382no—
160C22⋊C4—5382no—
161C22⋊C4—5382no—
162C22⋊C4—5382no—
163C22⋊C4—5382no—
164C42—5382no—
165C42D107611yescharacteristic
166C42D107611yescharacteristic
167C42C22×D26912yes—
168C23—5382no—
169C23C2×D107611yescharacteristic
170Q8—5382no—
171Q8—5382no—
172D4—5382no—
173D4—5382no—
174D4—10764no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—42no—
178C2×C4—5382no—
179C2×C4—5382no—
180C2×C4—5382no—
181C2×C4—10764no—
182C2×C4C2×D107612yes—
183C2×C4C2×D107611yescharacteristic
184C2×C4C2×D107612yes—
185C2×C4C23×D26911yescharacteristic
186C8—21no—
187C8—22no—
188C8—21no—
189C22—22no—
190C22—21no—
191C22—10762no—
192C22—10762no—
193C22—10762no—
194C22C22×D107611yescharacteristic
195C4—22no—
196C4—22no—
197C4—21no—
198C4—10762no—
199C4—10762no—
200C4—10762no—
201C4#2257549811yescharacteristic
202C4#2257550111yescharacteristic
203C2—41no—
204C2—21522no—
205C2#3177118611yescharacteristic
206C2#3177140512yes—
subgroupG/H
centerC22C22×D1076
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#423×C269C2
socleC22×C269C22×D4
prime radical#31770858C2
hypercenter#423D269
hypocenterC269#3256
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
1. #31771139C2semidirect
2. #31770913C2semidirect
3. #31770906C2semidirect
4. #31770863C2semidirect
6. #31770851C2semidirect
7. #31770828C2semidirect
8. #31770821C2semidirect
9. #423×C269C2semidirect
103. C269#3256semidirect
113. #423D269semidirect

Maximal subgroups

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

subgroupindex
#317711392
#317709132
#317709062
#317708632
#317708582
#317708512
#317708282
#317708212
#423×C2692
#3256269