Finite Group Databasebeta

← #46822321

Subgroups — #46822321

Order 34432.

370 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 109 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#31771208C212yesmaximal, complemented
2#31770907C212yesmaximal, complemented
3#31770904C212yesmaximal, complemented
4#31770858C211yesmaximal, characteristic, complemented
5#31770839C212yesmaximal, complemented
6#31770799C212yesmaximal, complemented
7#31770798C212yesmaximal, complemented
8#31770633C211yesmaximal, characteristic, complemented
9#469×C269C211yesmaximal, characteristic, complemented
10C2×D2152C2211yescharacteristic
11C2×#16864387C2212yes—
12C22×#14524130C2211yescharacteristic
13#22575449C2212yes—
14#22575444C2212yes—
15#22575437—22no—
16#22575435—22no—
17#22575427C2212yes—
18#22575425—22no—
19#22575424—22no—
20D4×Dic269C2212yes—
21#22575415C2212yes—
22#22575412C2211yescharacteristic
23#22575386C2212yes—
24#22575385C2211yescharacteristic
25#22575382C2212yes—
26#22575382C2212yes—
27#22575375C2212yes—
28#22575374C2212yes—
29#22575373C2212yes—
30C2×D8×C269C2211yescharacteristic
31C2×M16×C269C2211yescharacteristic
32#121×C269C2212yes—
33#106×C269C2211yescharacteristic
34#102×C269C2212yes—
35C2×D1076C2312yes—
36C2×C22⋊D269—22no—
37C2×C22⋊D269—22no—
38C2×C22⋊D269—22no—
39C22×Dic269—22no—
40C2×C4×D269—22no—
41D2152—41no—
42#16864387—42no—
43C2×#14524130—41no—
44C2×#14524130C2312yes—
45C4⋊Dic269—22no—
46C4⋊Dic269D412yes—
47C4⋊Dic269C2312yes—
48#16864381—22no—
49C22⋊Dic269—22no—
50C22⋊Dic269D411yescharacteristic
51C22⋊Dic269D411yescharacteristic
52#16864379—22no—
53#16864379—22no—
54C4×Dic269C2312yes—
55C2×D4×C269—22no—
56C2×D4×C269C2312yes—
57C22×C4×C269C2311yescharacteristic
58D8×C269—41no—
59M16×C269—41no—
60C2×C8×C269C2311yescharacteristic
61C2×C8×C269C2311yescharacteristic
62C4⋊C4×C269C2312yes—
63C22⋊C4×C269—22no—
64C22×D269—22no—
65D1076—22no—
66D1076—22no—
67C22⋊D269—82no—
68C22⋊D269—82no—
69C22⋊D269—82no—
70C2×Dic269—22no—
71C2×Dic269—82no—
72C2×Dic269C2×D412yes—
73C2×Dic269C2×D412yes—
74C4×D269—82no—
75#14524130—22no—
76C23×C269—22no—
77C23×C269C2×D411yescharacteristic
78D4×C269—22no—
79D4×C269—22no—
80D4×C269—82no—
81C2×C4×C269—21no—
82C2×C4×C269—21no—
83C2×C4×C269—22no—
84C2×C4×C269C2×D411yescharacteristic
85C2×C4×C269C2411yescharacteristic
86C8×C269—21no—
87C8×C269—21no—
88C22×C269—21no—
89C22×C269—22no—
90C22×C269—42no—
91C22×C269—42no—
92C22×C269—42no—
93C22×C269C22×D411yescharacteristic
94C2×D269—42no—
95C2×D269—42no—
96C2×D269—42no—
97C4×C269—21no—
98C4×C269—42no—
99C4×C269H(5,𝔽2)11yescharacteristic
100C4×C2692−1+411yescharacteristic
101Dic269—22no—
102Dic269—22no—
103Dic269—42no—
104C2×C269—41no—
105C2×C269—82no—
106C2×C269#53711yescharacteristic
107C2×C269#57612yes—
108D269—82no—
109C269#325911yescharacteristic, complemented, Sylow
110#3259—2691nomaximal, Sylow
111#540—2692no—
112#478—2692no—
113#478—2692no—
114#469—2691no—
115#469D26911yescharacteristic, complemented
116#466—2692no—
117#459—2692no—
118#459—2692no—
119#424—2691no—
120C2×D8—2692no—
121C2×D8—2691no—
122C2×D8C2×D26911yescharacteristic
123C2×M16C2×D26911yescharacteristic
124C22×C8—2691no—
125#127—2692no—
126#125—2692no—
127#123—5382no—
128#123—5382no—
129#121—2692no—
130#121—5382no—
131#121—5382no—
132#121C2×D26912yes—
133C4×D4—2692no—
134C4×D4—2692no—
135#117—2691no—
136#107—2692no—
137#106—2691no—
138#106C2×D26911yescharacteristic
139C4⋊C8—2692no—
140C4⋊C8—2692no—
141#102—2692no—
142#102—2692no—
143#102—2692no—
144#102C2×D26912yes—
145C2×D4—22no—
146C2×D4—2692no—
147C2×D4—5382no—
148C2×D4—5382no—
149C2×D4—5382no—
150C2×D4C22×D26912yes—
151C22×C4—5382no—
152C22×C4—5382no—
153C22×C4C22×D26911yescharacteristic
154D8—41no—
155D8—10761no—
156D8—10762no—
157M16—41no—
158C2×C8—2692no—
159C2×C8—10761no—
160C2×C8C22×D26911yescharacteristic
161C2×C8C22×D26911yescharacteristic
162C4⋊C4—2692no—
163C4⋊C4—2692no—
164C4⋊C4—5382no—
165C4⋊C4—5382no—
166C4⋊C4C22×D26912yes—
167C22⋊C4—22no—
168C22⋊C4—2691no—
169C22⋊C4—2691no—
170C22⋊C4—5382no—
171C22⋊C4—5382no—
172C22⋊C4—5382no—
173C42—2692no—
174C23—22no—
175C23—5382no—
176C23D4×D26911yescharacteristic
177D4—22no—
178D4—22no—
179D4—82no—
180D4—5382no—
181D4—5382no—
182D4—21522no—
183D4—21522no—
184D4—21522no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—2692no—
189C2×C4—2692no—
190C2×C4—5382no—
191C2×C4—21522no—
192C2×C4—21522no—
193C2×C4D4×D26911yescharacteristic
194C2×C4C23×D26911yescharacteristic
195C8—21no—
196C8—21no—
197C8—5382no—
198C22—22no—
199C22—21no—
200C22—42no—
201C22—42no—
202C22—42no—
203C22—10762no—
204C22—10762no—
205C22—10762no—
206C22C2×D4×D26911yescharacteristic
207C4—21no—
208C4—42no—
209C4—5382no—
210C4—5382no—
211C4—10762no—
212C4#2257549811yescharacteristic
213C4#2257550011yescharacteristic
214C2—41no—
215C2—82no—
216C2—21522no—
217C2#3177118211yescharacteristic
218C2#3177140912yes—
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#469×C269C2
socleC22×C269C22×D4
hypercenter#469D269
hypocenterC269#3259
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #31771208C2semidirect
2. #31770907C2semidirect
3. #31770904C2semidirect
4. #31770858C2semidirect
5. #31770839C2semidirect
6. #31770799C2semidirect
7. #31770798C2semidirect
8. #31770633C2semidirect
9. #469×C269C2semidirect
109. C269#3259semidirect
115. #469D269semidirect

Maximal subgroups

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

subgroupindex
#317712082
#317709072
#317709042
#317708582
#317708392
#317707992
#317707982
#317706332
#469×C2692
#3259269