Finite Group Databasebeta

← #46822319

Subgroups — #46822319

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#31770908C212yesmaximal, complemented
3#31770903C212yesmaximal, complemented
4#31770856C212yesmaximal, complemented
5#31770841C211yesmaximal, characteristic, complemented
6#31770799C212yesmaximal, complemented
7#31770798C212yesmaximal, complemented
8#31770631C211yesmaximal, characteristic, complemented
9#466×C269C211yesmaximal, characteristic, complemented
10C2×D2152C2211yescharacteristic
11C2×#16864387C2212yes—
12C2×#16864386C2211yescharacteristic
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#22575387C2211yescharacteristic
24#22575384C2212yes—
25#22575382C2212yes—
26#22575382C2212yes—
27#22575375C2212yes—
28#22575374C2212yes—
29#22575373C2212yes—
30C2×D8×C269C2211yescharacteristic
31C22×C8×C269C2211yescharacteristic
32#121×C269C2212yes—
33#107×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—
43#16864386—41no—
44C2×#14524130C2312yes—
45C4⋊Dic269—22no—
46C4⋊Dic269D411yescharacteristic
47C4⋊Dic269D411yescharacteristic
48C4⋊Dic269C2312yes—
49#16864381—22no—
50C22⋊Dic269—22no—
51C22⋊Dic269D412yes—
52#16864379—22no—
53#16864379—22no—
54C4×Dic269C2312yes—
55C2×D4×C269—22no—
56C2×D4×C269C2312yes—
57C22×C4×C269C2311yescharacteristic
58D8×C269—41no—
59C2×C8×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—21no—
90C22×C269—21no—
91C22×C269—42no—
92C22×C269—42no—
93C22×C269—42no—
94C22×C269C22×D411yescharacteristic
95C2×D269—42no—
96C2×D269—42no—
97C2×D269—42no—
98C4×C269—21no—
99C4×C269—42no—
100C4×C269H(5,𝔽2)11yescharacteristic
101C4×C2692−1+411yescharacteristic
102Dic269—22no—
103Dic269—22no—
104Dic269—42no—
105C2×C269—41no—
106C2×C269—82no—
107C2×C269#53711yescharacteristic
108C2×C269#57611yescharacteristic
109C2×C269#57611yescharacteristic
110D269—82no—
111C269#325911yescharacteristic, complemented, Sylow
112#3259—2691nomaximal, Sylow
113#540—2692no—
114#478—2692no—
115#478—2692no—
116#469—2692no—
117#466—2691no—
118#466D26911yescharacteristic, complemented
119#459—2692no—
120#459—2692no—
121#424—2691no—
122C2×D8—2692no—
123C2×D8—2691no—
124C2×D8C2×D26911yescharacteristic
125C2×M16—2691no—
126C22×C8C2×D26911yescharacteristic
127#127—2692no—
128#125—2692no—
129#123—5382no—
130#123—5382no—
131#121—2692no—
132#121—5382no—
133#121—5382no—
134#121C2×D26912yes—
135C4×D4—2692no—
136C4×D4—2692no—
137#117—2691no—
138#107—2691no—
139#107C2×D26911yescharacteristic
140#106—2692no—
141C4⋊C8—2692no—
142C4⋊C8—2692no—
143#102—2692no—
144#102—2692no—
145#102—2692no—
146#102C2×D26912yes—
147C2×D4—22no—
148C2×D4—2692no—
149C2×D4—5382no—
150C2×D4—5382no—
151C2×D4—5382no—
152C2×D4C22×D26912yes—
153C22×C4—5382no—
154C22×C4—5382no—
155C22×C4C22×D26911yescharacteristic
156D8—41no—
157D8—10761no—
158D8—10762no—
159M16—10761no—
160C2×C8—41no—
161C2×C8—2692no—
162C2×C8C22×D26911yescharacteristic
163C2×C8C22×D26911yescharacteristic
164C4⋊C4—2691no—
165C4⋊C4—2691no—
166C4⋊C4—2692no—
167C4⋊C4—5382no—
168C4⋊C4—5382no—
169C4⋊C4C22×D26912yes—
170C22⋊C4—22no—
171C22⋊C4—2692no—
172C22⋊C4—5382no—
173C22⋊C4—5382no—
174C22⋊C4—5382no—
175C42—2692no—
176C23—22no—
177C23—5382no—
178C23D4×D26911yescharacteristic
179D4—22no—
180D4—22no—
181D4—82no—
182D4—5382no—
183D4—5382no—
184D4—21522no—
185D4—21522no—
186D4—21522no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—2692no—
191C2×C4—2692no—
192C2×C4—5382no—
193C2×C4—21522no—
194C2×C4—21522no—
195C2×C4D4×D26911yescharacteristic
196C2×C4C23×D26911yescharacteristic
197C8—21no—
198C8—21no—
199C8—5382no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—42no—
204C22—42no—
205C22—42no—
206C22—10762no—
207C22—10762no—
208C22—10762no—
209C22C2×D4×D26911yescharacteristic
210C4—21no—
211C4—42no—
212C4—5382no—
213C4—5382no—
214C4—10762no—
215C4#2257549811yescharacteristic
216C4#2257550011yescharacteristic
217C2—41no—
218C2—82no—
219C2—21522no—
220C2#3177118211yescharacteristic
221C2#3177140611yescharacteristic
222C2#3177140711yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#466×C269C2
socleC22×C269C22×D4
hypercenter#466D269
hypocenterC269#3259
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #31771208C2semidirect
2. #31770908C2semidirect
3. #31770903C2semidirect
4. #31770856C2semidirect
5. #31770841C2semidirect
6. #31770799C2semidirect
7. #31770798C2semidirect
8. #31770631C2semidirect
9. #466×C269C2semidirect
111. C269#3259semidirect
118. #466D269semidirect

Maximal subgroups

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

subgroupindex
#317712082
#317709082
#317709032
#317708562
#317708412
#317707992
#317707982
#317706312
#466×C2692
#3259269