Finite Group Databasebeta

← #46822287

Subgroups — #46822287

Order 34432.

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

normal subgroups only

This group has 354 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#31771141C212yesmaximal, complemented
2#31770910C212yesmaximal, complemented
3#31770904C212yesmaximal, complemented
4#31770858C211yesmaximal, characteristic
5#31770853C212yesmaximal, complemented
6#31770829C212yesmaximal, complemented
7#31770823C212yesmaximal, complemented
8#31770628C211yesmaximal, characteristic, complemented
9#470×C269C211yesmaximal, characteristic, complemented
10C2×#16864389C2212yes—
11C2×D2152C2211yescharacteristic
12C2×#16864386C2211yescharacteristic
13#22575448—22no—
14#22575444C2212yes—
15#22575442C2212yes—
16#22575437—22no—
17#22575427C2212yes—
18Q8×Dic269C2212yes—
19#22575415C2212yes—
20#22575413—22no—
21#22575411—22no—
22C2×C4×Dic269C2211yescharacteristic
23#22575386C2212yes—
24#22575385C2211yescharacteristic
25#22575382C2212yes—
26#22575382C2212yes—
27#22575377C2212yes—
28#22575375C2212yes—
29#22575373C2212yes—
30C2×Q16×C269C2211yescharacteristic
31C2×M16×C269C2211yescharacteristic
32C22⋊Q8×C269C2212yes—
33#106×C269C2211yescharacteristic
34#103×C269C2212yes—
35C2×D1076C2312yes—
36C2×C22⋊D269—22no—
37C22×Dic269D412yes—
38C2×C4×D269—22no—
39#16864389—42no—
40D2152—41no—
41#16864386—41no—
42C2×#14524130C2312yes—
43C4⋊Dic269—22no—
44C4⋊Dic269—22no—
45C4⋊Dic269C2312yes—
46#16864381—22no—
47#16864379—22no—
48#16864379—22no—
49#16864379—22no—
50#16864379—22no—
51C4×Dic269—22no—
52C4×Dic269D411yescharacteristic
53C4×Dic269D411yescharacteristic
54C4×Dic269C2312yes—
55C2×Q8×C269C2312yes—
56C22×C4×C269C2311yescharacteristic
57Q16×C269—41no—
58M16×C269—41no—
59C2×C8×C269C2311yescharacteristic
60C2×C8×C269C2311yescharacteristic
61C4⋊C4×C269—22no—
62C4⋊C4×C269C2312yes—
63C22⋊C4×C269—22no—
64C22×D269—22no—
65D1076—22no—
66D1076—22no—
67C22⋊D269—44no—
68C2×Dic269—22no—
69C2×Dic269—42no—
70C2×Dic269C2×D412yes—
71C2×Dic269C2×D412yes—
72C4×D269—44no—
73#14524130—22no—
74C23×C269C2×D411yescharacteristic
75Q8×C269—22no—
76Q8×C269—22no—
77C2×C4×C269—21no—
78C2×C4×C269—21no—
79C2×C4×C269—22no—
80C2×C4×C269—22no—
81C2×C4×C269C2×D411yescharacteristic
82C2×C4×C269C2411yescharacteristic
83C8×C269—21no—
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—42no—
93C4×C269—42no—
94C4×C269H(5,𝔽2)11yescharacteristic
95C4×C2692−1+411yescharacteristic
96Dic269—22no—
97Dic269—22no—
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#470D26911yescharacteristic, complemented
109#469—2691no—
110#468—2692no—
111#464—2692no—
112#463—2692no—
113#423—2691no—
114C2×Q16C2×D26911yescharacteristic
115C2×SD16—2692no—
116C2×D8—2691no—
117C2×M16—2691no—
118C2×M16C2×D26911yescharacteristic
119#126—5382no—
120#125—2692no—
121#124—2692no—
122#123—5382no—
123C22⋊Q8C2×D26912yes—
124#121—2692no—
125C4×Q8—2692no—
126C4×D4—2692no—
127C4×D4—5382no—
128#117—5382no—
129C2×C42—2691no—
130#107—2692no—
131#106—2691no—
132#106C2×D26911yescharacteristic
133C4⋊C8—2692no—
134C4⋊C8—2692no—
135#103—2692no—
136#103C2×D26912yes—
137#102—2692no—
138#102—2692no—
139C2×Q8C22×D26912yes—
140C2×D4—2692no—
141C2×D4—5382no—
142C22×C4—2692no—
143C22×C4—5382no—
144C22×C4C22×D26911yescharacteristic
145Q16—41no—
146SD16—10762no—
147D8—10761no—
148M16—41no—
149M16—10761no—
150C2×C8—2692no—
151C2×C8C22×D26911yescharacteristic
152C2×C8C22×D26911yescharacteristic
153C4⋊C4—22no—
154C4⋊C4—2692no—
155C4⋊C4—5382no—
156C4⋊C4—5382no—
157C4⋊C4—5382no—
158C4⋊C4C22×D26912yes—
159C22⋊C4—22no—
160C22⋊C4—5382no—
161C22⋊C4—5382no—
162C22⋊C4—5382no—
163C22⋊C4—5382no—
164C42—2691no—
165C42—2691no—
166C42—2692no—
167C42—5382no—
168C23—5382no—
169C23D4×D26911yescharacteristic
170Q8—22no—
171Q8—22no—
172D4—5382no—
173D4—5382no—
174D4—10764no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—2692no—
180C2×C4—2692no—
181C2×C4—5382no—
182C2×C4—10764no—
183C2×C4—10762no—
184C2×C4D4×D26911yescharacteristic
185C2×C4C23×D26911yescharacteristic
186C8—21no—
187C8—21no—
188C8—5382no—
189C22—22no—
190C22—21no—
191C22—10762no—
192C22—10762no—
193C22—10762no—
194C22C2×D4×D26911yescharacteristic
195C4—21no—
196C4—42no—
197C4—42no—
198C4—5382no—
199C4—5382no—
200C4—10762no—
201C4#2257549811yescharacteristic
202C4#2257550011yescharacteristic
203C2—41no—
204C2—21522no—
205C2#3177118211yescharacteristic
206C2#3177140412yes—
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#470×C269C2
socleC22×C269C22×D4
prime radical#31770858C2
hypercenter#470D269
hypocenterC269#3256
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #31771141C2semidirect
2. #31770910C2semidirect
3. #31770904C2semidirect
5. #31770853C2semidirect
6. #31770829C2semidirect
7. #31770823C2semidirect
8. #31770628C2semidirect
9. #470×C269C2semidirect
103. C269#3256semidirect
108. #470D269semidirect

Maximal subgroups

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

subgroupindex
#317711412
#317709102
#317709042
#317708582
#317708532
#317708292
#317708232
#317706282
#470×C2692
#3256269