Finite Group Databasebeta

← #47981608

Subgroups — #47981608

Order 35456.

316 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C4×D4×D277C211yesmaximal, characteristic
2#31800058C211yesmaximal, characteristic, complemented
3C4×#17984546C211yesmaximal, characteristic, complemented
4#31799731C211yesmaximal, characteristic, complemented
5D4⋊#14555660C211yesmaximal, characteristic, complemented
6#31799729C211yesmaximal, characteristic, complemented
7D4⋊C8×C277C211yesmaximal, characteristic, complemented
8C2×D4×D277C411yescharacteristic
9C22×C4×D277—21no—
10C2×#17984546—21no—
11C4×D1108C2211yescharacteristic
12D4×Dic277C411yescharacteristic
13#22579842C411yescharacteristic
14C4×C22⋊D277—21no—
15#22579840—21no—
16C4⋊C4×D277C411yescharacteristic
17C22⋊C4×D277—21no—
18C42×D277C2211yescharacteristic
19C4⋊#14555660C2211yescharacteristic, complemented
20#22579792—21no—
21#22579790—21no—
22#22579790—21no—
23C4×#14555660C2211yescharacteristic, complemented
24C4×D4×C277C2211yescharacteristic
25C4⋊C8×C277C2211yescharacteristic, complemented
26C4×C8×C277C2211yescharacteristic, complemented
27C23×D277—21no—
28C2×D1108C2×C411yescharacteristic
29C2×C22⋊D277—21no—
30D4×D277—22no—
31D4×D277—22no—
32C22×Dic277—21no—
33C2×C4×D277—21no—
34C2×C4×D277—21no—
35C2×C4×D277—21no—
36C2×C4×D277—42no—
37C2×C4×D277—42no—
38C2×C4×D277C2×C411yescharacteristic
39C2×C4×D277D411yescharacteristic
40C2×C4×D277D411yescharacteristic
41#17984546—24no—
42C2×#14555660—21no—
43C2×#14555660—21no—
44C4⋊Dic277C2×C411yescharacteristic
45#17984542—21no—
46C22⋊Dic277—21no—
47#17984540—21no—
48#17984540—21no—
49C4×Dic277C2×C411yescharacteristic
50C4×Dic277D411yescharacteristic
51C4×Dic277D411yescharacteristic
52C2×D4×C277C2×C411yescharacteristic
53C22×C4×C277—21no—
54C2×C8×C277—21no—
55C2×C8×C277—21no—
56C4⋊C4×C277C2×C411yescharacteristic
57C22⋊C4×C277—21no—
58C42×C277C2311yescharacteristic
59C22×D277—24no—
60C22×D277—21no—
61C22×D277—42no—
62C22×D277—42no—
63C22×D277C22⋊C411yescharacteristic
64D1108—21no—
65D1108M1612yescomplemented
66C22⋊D277—24no—
67C2×Dic277—21no—
68C2×Dic277—42no—
69C2×Dic277C22⋊C411yescharacteristic
70C2×Dic277C22⋊C411yescharacteristic
71C2×Dic277C22⋊C411yescharacteristic
72C4×D277—22no—
73C4×D277—21no—
74C4×D277—21no—
75C4×D277—21no—
76C4×D277—21no—
77C4×D277—42no—
78C4×D277—42no—
79C4×D277—41no—
80C4×D277—41no—
81#14555660—22no—
82#14555660—41no—
83C23×C277—21no—
84D4×C277—21no—
85D4×C277M1612yescomplemented
86C2×C4×C277—21no—
87C2×C4×C277—41no—
88C2×C4×C277—41no—
89C2×C4×C277C22×C411yescharacteristic
90C2×C4×C277C2×D411yescharacteristic
91C2×C4×C277C2×D411yescharacteristic
92C8×C277—22no—
93C8×C277—41no—
94C22×C277—22no—
95C22×C277—41no—
96C22×C277—41no—
97C22×C277C2×C22⋊C411yescharacteristic
98C2×D277—21no—
99C2×D277—21no—
100C2×D277—22no—
101C2×D277—48no—
102C2×D277—41no—
103C2×D277—41no—
104C2×D277#10412yes—
105C4×C277—21no—
106C4×C277—41no—
107C4×C277C2×M1611yescharacteristic
108C4×C277C2×M1611yescharacteristic
109C4×C277AGL(1,ℤ/8)11yescharacteristic
110C4×C277AGL(1,ℤ/8)11yescharacteristic
111Dic277—21no—
112Dic277—21no—
113Dic277—21no—
114Dic277—41no—
115C2×C277—42no—
116C2×C277#40711yescharacteristic
117C2×C277#41811yescharacteristic
118C2×C277C2×#10411yescharacteristic
119D277—22no—
120D277—42no—
121C277#149011yescharacteristic, complemented, Sylow
122#1490—2771nomaximal, Sylow
123C2×C4×D4—2771no—
124#432—2771no—
125C4×M16—2771no—
126D4⋊C8—2771no—
127D4⋊C8—2771no—
128D4⋊C8—2771no—
129D4⋊C8D27711yescharacteristic, complemented
130C22×D4—2771no—
131C23×C4—5541no—
132C2×M16—5541no—
133C4×D4—2771no—
134C4×D4—2771no—
135C4×D4—2771no—
136C4×D4—5541no—
137C4×D4—5541no—
138C4×D4C2×D27711yescharacteristic
139C2×C4⋊C4—2771no—
140C2×C22⋊C4—5541no—
141C2×C42—2771no—
142C4⋊C8—2771no—
143C4⋊C8C2×D27711yescharacteristic, complemented
144C22⋊C8—5541no—
145#97—5541no—
146#97—5541no—
147C4×C8—2771no—
148C4×C8C2×D27711yescharacteristic, complemented
149C24—5541no—
150C2×D4—2771no—
151C2×D4—5541no—
152C2×D4—5542no—
153C2×D4—5542no—
154C2×D4C4×D27711yescharacteristic
155C22×C4—21no—
156C22×C4—2771no—
157C22×C4—2771no—
158C22×C4—2771no—
159C22×C4—5541no—
160C22×C4—5541no—
161C22×C4—5541no—
162C22×C4—5541no—
163C22×C4—11082no—
164C22×C4—11082no—
165M16—5544no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—5541no—
169C2×C8—5541no—
170C4⋊C4—2771no—
171C4⋊C4—5541no—
172C4⋊C4C4×D27711yescharacteristic
173C22⋊C4—21no—
174C22⋊C4—5541no—
175C22⋊C4—5541no—
176C22⋊C4—5541no—
177C42—2771no—
178C42—2771no—
179C42—2771no—
180C42C22×D27711yescharacteristic
181C23—21no—
182C23—2771no—
183C23—5544no—
184C23—5541no—
185C23—11082no—
186C23—11082no—
187D4—21no—
188D4—2772no—
189D4—5544no—
190D4—5541no—
191D4#1798454612yescomplemented
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—2771no—
196C2×C4—2771no—
197C2×C4—2771no—
198C2×C4—5542no—
199C2×C4—5541no—
200C2×C4—5541no—
201C2×C4—5541no—
202C2×C4—5541no—
203C2×C4—5541no—
204C2×C4—11082no—
205C2×C4—11082no—
206C2×C4—11082no—
207C2×C4—11081no—
208C2×C4—11081no—
209C2×C4C2×C4×D27711yescharacteristic
210C2×C4D4×D27711yescharacteristic
211C2×C4D4×D27711yescharacteristic
212C8—22no—
213C8—41no—
214C8—5542no—
215C8—11081no—
216C22—22no—
217C22—41no—
218C22—41no—
219C22—2772no—
220C22—5541no—
221C22—5541no—
222C22—5542no—
223C22—11088no—
224C22—11081no—
225C22—11081no—
226C22C22⋊C4×D27711yescharacteristic
227C4—21no—
228C4—41no—
229C4—5541no—
230C4—5541no—
231C4—5541no—
232C4—11081no—
233C4M16×D27711yescharacteristic
234C4C2×#1798454611yescharacteristic
235C4#2257990411yescharacteristic
236C4#2257990711yescharacteristic
237C2—42no—
238C2—5542no—
239C2—11082no—
240C2#3179996411yescharacteristic
241C2#3180000511yescharacteristic
242C2#104×D27711yescharacteristic
subgroupG/H
centerC2×C4D4×D277
commutatorC2×C4×C277C22×C4
FrattiniC42C22×D277
FittingD4⋊C8×C277C2
socleC22×C277C2×C22⋊C4
prime radicalC2×D4×D277C4
cosocleC42×C277C23
hypercenterD4⋊C8D277
hypocenterC277#1490
LCSG ▷ C2×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #31800058C2semidirect
3. C4×#17984546C2semidirect
4. #31799731C2semidirect
5. D4⋊#14555660C2semidirect
6. #31799729C2semidirect
7. D4⋊C8×C277C2semidirect
19. C4⋊#14555660C22semidirect
23. C4×#14555660C22semidirect
25. C4⋊C8×C277C22semidirect
26. C4×C8×C277C22semidirect
65. D1108M16semidirect
85. D4×C277M16semidirect
121. C277#1490semidirect
129. D4⋊C8D277semidirect
143. C4⋊C8C2×D277semidirect
148. C4×C8C2×D277semidirect
191. D4#17984546semidirect

Maximal subgroups

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

subgroupindex
C4×D4×D2772
#318000582
C4×#179845462
#317997312
D4⋊#145556602
#317997292
D4⋊C8×C2772
#1490277