Finite Group Databasebeta

← #47983135

Subgroups — #47983135

Order 35456.

588 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 97 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×#22579926C211yesmaximal, characteristic
2#31800020C212yesmaximal, complemented
3#31800006C212yesmaximal, complemented
4#31799986C211yesmaximal, characteristic, complemented
5#410×C277C211yesmaximal, characteristic, complemented
6#22579926—24no—
7#22579926—24no—
8C2×#17984564—21no—
9C2×#17984563C412yescomplemented
10C2×#17984563C2211yescharacteristic
11C22×D1108C412yescomplemented
12C22×D1108C2211yescharacteristic
13C2×D4×D277—22no—
14C2×D4×D277—21no—
15C2×#17984547C2212yescomplemented
16#22579808—24no—
17#22579800—24no—
18#22579799—21no—
19#22579797—21no—
20C2×#41×C277C2211yescharacteristic
21#117×C277C2212yescomplemented
22#99×C277—22no—
23C23×D277—22no—
24C23×D277—21no—
25#17984564—28no—
26#17984563—24no—
27#17984563—24no—
28#17984563—22no—
29#17984563D414yes—
30C2×Dic554C2×C411yescharacteristic
31C2×D1108—24no—
32C2×D1108—24no—
33C2×D1108—22no—
34C2×D1108—21no—
35C2×D1108—22no—
36C2×D1108C2×C411yescharacteristic
37C2×D1108C2×C412yes—
38C2×D1108D414yes—
39C2×C22⋊D277—22no—
40C2×C22⋊D277—21no—
41D4×D277—216no—
42D4×D277—28no—
43C2×C4×D277—22no—
44C2×C4×D277—21no—
45#17984547—22no—
46#17984547—22no—
47C2×#14555660—22no—
48#41×C277—22no—
49#41×C277—22no—
50C2×Q8×C277D411yescharacteristic
51C2×D4×C277D412yes—
52C2×D4×C277D411yescharacteristic
53C22×C4×C277C2×C412yes—
54C22×C4×C277C2311yescharacteristic
55C4⋊C4×C277—22no—
56C22⋊C4×C277—22no—
57C42×C277—22no—
58C22×D277—22no—
59C22×D277—21no—
60C22×D277—28no—
61C22×D277—24no—
62C22×D277—82no—
63C22×D277—84no—
64Dic554—21no—
65Dic554C22⋊C412yes—
66D1108—28no—
67D1108—22no—
68D1108—21no—
69D1108—24no—
70D1108C22⋊C412yes—
71D1108C22⋊C414yes—
72C22⋊D277—28no—
73C22⋊D277—24no—
74C2×Dic277—21no—
75C4×D277—28no—
76C4×D277—24no—
77#14555660—42no—
78C23×C277C22⋊C412yes—
79C23×C277C2×D411yescharacteristic
80Q8×C277—22no—
81D4×C277—24no—
82D4×C277—22no—
83C2×C4×C277—22no—
84C2×C4×C277—22no—
85C2×C4×C277—42no—
86C2×C4×C277C22⋊C412yes—
87C2×C4×C277C22×C411yescharacteristic
88C2×C4×C277C2×D412yes—
89C2×C4×C277C2×D412yes—
90C2×C4×C277C2×D411yescharacteristic
91C22×C277—22no—
92C22×C277—41no—
93C22×C277—42no—
94C22×C277C2×C22⋊C411yescharacteristic
95C22×C277#12012yes—
96C2×D277—24no—
97C2×D277—22no—
98C2×D277—44no—
99C2×D277—42no—
100C2×D277—84no—
101C2×D277—88no—
102C4×C277—22no—
103C4×C277—82no—
104C4×C277C2×C22⋊C411yescharacteristic
105C4×C277C2×C22⋊C411yescharacteristic
106C4×C277#12012yes—
107Dic277—22no—
108C2×C277—22no—
109C2×C277—21no—
110C2×C277—42no—
111C2×C277#37911yescharacteristic
112D277—44no—
113D277—42no—
114C277#179511yescharacteristic, complemented, Sylow
115#1795—2771nomaximal, Sylow
116C2×H(5,𝔽2)—2771no—
117#421—2772no—
118#418—2772no—
119#413—2771no—
120#410D27711yescharacteristic, complemented
121H(5,𝔽2)—5544no—
122H(5,𝔽2)—5544no—
123C2×#41—2772no—
124C2×#41—2771no—
125C2×#41—5541no—
126C2×#41C2×D27711yescharacteristic
127C22×D4—2772no—
128C22×D4—2771no—
129C22×D4—5542no—
130C22×D4—5541no—
131C2×M16—2772no—
132#117C2×D27712yescomplemented
133#104—5544no—
134#102—5544no—
135#101—5541no—
136#100—5541no—
137#99—22no—
138C24—5542no—
139C24—5541no—
140#41—22no—
141#41—22no—
142#41—2774no—
143#41—5544no—
144#41—5544no—
145#41—5548no—
146#41—5542no—
147C2×Q8—2771no—
148C2×Q8D110811yescharacteristic
149C2×D4—2772no—
150C2×D4—2771no—
151C2×D4—2774no—
152C2×D4—5544no—
153C2×D4—5544no—
154C2×D4—55416no—
155C2×D4—5548no—
156C2×D4—5542no—
157C2×D4—5541no—
158C2×D4—5542no—
159C2×D4—5542no—
160C2×D4—5541no—
161C2×D4C22⋊D27712yes—
162C2×D4D110811yescharacteristic
163C22×C4—5542no—
164C22×C4—5541no—
165C22×C4C4×D27712yes—
166C22×C4C22×D27711yescharacteristic
167M16—5542no—
168M16—5542no—
169C2×C8—5542no—
170C4⋊C4—22no—
171C22⋊C4—22no—
172C42—22no—
173C23—5548no—
174C23—5542no—
175C23—5541no—
176C23—5544no—
177C23—22162no—
178C23—22164no—
179C23#1798454012yes—
180C23C2×C22⋊D27711yescharacteristic
181Q8—22no—
182Q8—2772no—
183Q8—5541no—
184D4—24no—
185D4—22no—
186D4—2774no—
187D4—2772no—
188D4—5548no—
189D4—5548no—
190D4—5544no—
191D4—5541no—
192D4—5542no—
193D4—5544no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—42no—
197C2×C4—5548no—
198C2×C4—5541no—
199C2×C4—5544no—
200C2×C4#1798454012yes—
201C2×C4C2×C4×D27711yescharacteristic
202C2×C4D4×D27712yes—
203C2×C4D4×D27712yes—
204C2×C4C2×D110811yescharacteristic
205C8—11082no—
206C22—22no—
207C22—41no—
208C22—42no—
209C22—5544no—
210C22—5542no—
211C22—11084no—
212C22—11082no—
213C22—22164no—
214C22—22168no—
215C22C2×#1798454011yescharacteristic
216C22#2257984812yes—
217C4—22no—
218C4—82no—
219C4—5542no—
220C4C22⋊C4×D27711yescharacteristic
221C4C22⋊C4×D27711yescharacteristic
222C4#2257985012yes—
223C2—22no—
224C2—21no—
225C2—42no—
226C2—11084no—
227C2—11082no—
228C2#3179985711yescharacteristic
subgroupG/H
centerC2#31799857
commutatorC2×C4×C277C22×C4
FrattiniC22×C4C22×D277
Fitting#410×C277C2
socleC2×C277#379
prime radicalC2×#22579926C2
cosocleC22×C4×C277C23
hypercenter#410D277
hypocenterC277#1795
LCSG ▷ C2×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #31800020C2semidirect
3. #31800006C2semidirect
4. #31799986C2semidirect
5. #410×C277C2semidirect
9. C2×#17984563C4semidirect
11. C22×D1108C4semidirect
15. C2×#17984547C22semidirect
21. #117×C277C22semidirect
114. C277#1795semidirect
120. #410D277semidirect
132. #117C2×D277semidirect

Maximal subgroups

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

subgroupindex
C2×#225799262
#318000202
#318000062
#317999862
#410×C2772
#1795277