Finite Group Databasebeta

← #47986330

Subgroups — #47986330

Order 35456.

464 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C2×#22579859C211yesmaximal, characteristic
2#31799906C212yesmaximal, complemented
3#31799897C212yesmaximal, complemented
4#31799896C212yesmaximal
5#31799890C212yesmaximal
6#31799885C212yesmaximal, complemented
7#31799883C212yesmaximal, complemented
8#31799865C211yesmaximal, characteristic
9#380×C277C211yesmaximal, characteristic
10C22×Dic554C2211yescharacteristic
11#22579859C418yescomplemented
12C2×C4⋊Dic277C2211yescharacteristic
13C2×#17984542C2212yes—
14C2×#17984542C2212yes—
15C2×#17984542C2212yes—
16C2×C22⋊Dic277C2212yes—
17C2×C22⋊Dic277C2212yes—
18C2×C4×Dic277C2212yes—
19C2×C4×Dic277C2212yes—
20#22579787C2211yescharacteristic
21#22579787C2212yes—
22#22579787C2211yescharacteristic
23#22579787C2212yes—
24#22579787C2212yes—
25#22579787C2212yes—
26#22579787C2212yes—
27C23×C4×C277C2211yescharacteristic
28C2×C4⋊C4×C277C2212yes—
29C2×C22⋊C4×C277C2211yescharacteristic
30C2×C22⋊C4×C277C2211yescharacteristic
31#95×C277C2212yes—
32C2×Dic554—42no—
33C2×Dic554C2×C414yes—
34C22×Dic277C2312yes—
35C22×Dic277C2312yes—
36C22×Dic277C2312yes—
37C22×Dic277C2312yes—
38C4⋊Dic277C2×C414yes—
39#17984542—42no—
40#17984542—42no—
41#17984542C2×C418yes—
42C22⋊Dic277—42no—
43C22⋊Dic277C2×C418yes—
44C4×Dic277—42no—
45C4×Dic277—42no—
46C24×C277C2311yescharacteristic
47C22×C4×C277—42no—
48C22×C4×C277C2×C414yes—
49C22×C4×C277C2312yes—
50C22×C4×C277C2312yes—
51C22×C4×C277C2311yescharacteristic
52C22×C4×C277C2311yescharacteristic
53C4⋊C4×C277—42no—
54C22⋊C4×C277—41no—
55C22⋊C4×C277—41no—
56Dic554—44no—
57C2×Dic277—22no—
58C2×Dic277—22no—
59C2×Dic277—22no—
60C2×Dic277—22no—
61C2×Dic277—22no—
62C2×Dic277—22no—
63C2×Dic277—22no—
64C2×Dic277—22no—
65C2×Dic277—22no—
66C2×Dic277—22no—
67C2×Dic277C22×C414yes—
68C2×Dic277C22×C414yes—
69C23×C277—21no—
70C23×C277—22no—
71C23×C277—22no—
72C23×C277—21no—
73C23×C277C22×C412yes—
74C23×C277C2411yescharacteristic
75C2×C4×C277—22no—
76C2×C4×C277—22no—
77C2×C4×C277—22no—
78C2×C4×C277—22no—
79C2×C4×C277—22no—
80C2×C4×C277—22no—
81C2×C4×C277—22no—
82C2×C4×C277—22no—
83C2×C4×C277—44no—
84C2×C4×C277C22×C412yes—
85C2×C4×C277C22×C412yes—
86C22×C277—22no—
87C22×C277—22no—
88C22×C277—22no—
89C22×C277—42no—
90C22×C277—42no—
91C22×C277C23×C411yescharacteristic
92C22×C277H(5,𝔽2)12yes—
93C22×C277H(5,𝔽2)11yescharacteristic
94C22×C2772−1+412yes—
95C22×C2772−1+411yescharacteristic
96C4×C277—22no—
97C4×C277—22no—
98C4×C277—42no—
99C4×C277—42no—
100Dic277—24no—
101Dic277—24no—
102Dic277—42no—
103Dic277—42no—
104C2×C277—42no—
105C2×C277#51811yescharacteristic
106C2×C277#51911yescharacteristic
107C2×C277#52011yescharacteristic
108C2×C277#56212yes—
109C2×C277#56312yes—
110C277#237811yescharacteristic, complemented, Sylow
111#2378—2771nomaximal, Sylow
112C2×C22⋊Q8—2771no—
113#391—2772no—
114#389—2772no—
115#388—2772no—
116#388—2772no—
117#387—2772no—
118#387—2772no—
119#381—2771no—
120#380D27711yescharacteristic
121C22×Q8—2771no—
122C23×C4C2×D27711yescharacteristic
123C22⋊Q8—2778no—
124C2×C4⋊C4—2772no—
125C2×C4⋊C4—2771no—
126C2×C4⋊C4—2772no—
127C2×C4⋊C4—2772no—
128C2×C4⋊C4C2×D27712yes—
129C2×C22⋊C4—2772no—
130C2×C22⋊C4—2772no—
131C2×C22⋊C4C2×D27711yescharacteristic
132C2×C22⋊C4C2×D27711yescharacteristic
133C2×C42—2772no—
134C2×C42—2772no—
135#95—2771no—
136#95—2772no—
137#95—2771no—
138#95—2772no—
139#95—2772no—
140#95—2772no—
141#95—2772no—
142#95C2×D27712yes—
143C24C22×D27711yescharacteristic
144C2×Q8—2774no—
145C2×Q8—11082no—
146C22×C4—42no—
147C22×C4—2772no—
148C22×C4—2772no—
149C22×C4—2772no—
150C22×C4—2772no—
151C22×C4C4×D27714yes—
152C22×C4C22×D27712yes—
153C22×C4C22×D27712yes—
154C22×C4C22×D27711yescharacteristic
155C22×C4C22×D27711yescharacteristic
156C4⋊C4—42no—
157C4⋊C4—2778no—
158C4⋊C4—2774no—
159C4⋊C4—11082no—
160C4⋊C4—11082no—
161C22⋊C4—41no—
162C22⋊C4—41no—
163C22⋊C4—2778no—
164C22⋊C4—11082no—
165C42—11082no—
166C42—11082no—
167C23—21no—
168C23—22no—
169C23—22no—
170C23—21no—
171C23C2×C4×D27712yes—
172C23C23×D27711yescharacteristic
173Q8—11084no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—44no—
183C2×C4—2774no—
184C2×C4—2774no—
185C2×C4—5542no—
186C2×C4—5542no—
187C2×C4—5542no—
188C2×C4—5542no—
189C2×C4—5542no—
190C2×C4—5542no—
191C2×C4—5542no—
192C2×C4—5542no—
193C2×C4—5542no—
194C2×C4—5542no—
195C2×C4C2×C4×D27712yes—
196C2×C4C2×C4×D27712yes—
197C22—22no—
198C22—22no—
199C22—22no—
200C22—42no—
201C22—42no—
202C22C22×C4×D27711yescharacteristic
203C22#2257992512yes—
204C22#2257992511yescharacteristic
205C22#2257992712yes—
206C22#2257992811yescharacteristic
207C4—22no—
208C4—22no—
209C4—42no—
210C4—42no—
211C4—5544no—
212C4—5544no—
213C4—11082no—
214C4—11082no—
215C2—42no—
216C2#3180047511yescharacteristic
217C2#3180047911yescharacteristic
218C2#3180048311yescharacteristic
219C2#3180074712yes—
220C2#3180075312yes—
subgroupG/H
center, FrattiniC23C23×D277
commutatorC22×C277C23×C4
Fitting#380×C277C2
socle, cosocleC23×C277C24
prime radicalC24×C277C23
hypercenter#380D277
hypocenterC277#2378
LCSG ▷ C22×C277 ▷ C277
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. #31799906C2semidirect
3. #31799897C2semidirect
6. #31799885C2semidirect
7. #31799883C2semidirect
11. #22579859C4semidirect
110. C277#2378semidirect

Maximal subgroups

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

subgroupindex
C2×#225798592
#317999062
#317998972
#317998962
#317998902
#317998852
#317998832
#317998652
#380×C2772
#2378277