Finite Group Databasebeta

← #47981556

Subgroups — #47981556

Order 35456.

312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 83 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#31800054C211yesmaximal, characteristic, complemented
3#31800053C211yesmaximal, 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—
10C4×D1108C2211yescharacteristic
11D4×Dic277C411yescharacteristic
12#22579842C411yescharacteristic
13C4×C22⋊D277—21no—
14#22579840—21no—
15C4⋊C4×D277C411yescharacteristic
16C22⋊C4×D277—21no—
17C42×D277C2211yescharacteristic
18C4⋊#14555660C2211yescharacteristic, complemented
19#22579809—21no—
20#22579792—21no—
21#22579792—21no—
22C4×#14555660C2211yescharacteristic, complemented
23C8×Dic277—21no—
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×D277C814yescomplemented
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
41C2×#14555660—21no—
42C2×#14555660—21no—
43C4⋊Dic277C2×C411yescharacteristic
44#17984542—21no—
45C22⋊Dic277—21no—
46#17984540—21no—
47#17984540—21no—
48C4×Dic277C2×C411yescharacteristic
49C4×Dic277D411yescharacteristic
50C4×Dic277D411yescharacteristic
51C2×D4×C277C2×C411yescharacteristic
52C22×C4×C277—21no—
53C2×C8×C277—21no—
54C2×C8×C277—21no—
55C4⋊C4×C277C2×C411yescharacteristic
56C22⋊C4×C277—21no—
57C42×C277C2311yescharacteristic
58C22×D277—21no—
59C22×D277—24no—
60C22×D277—42no—
61C22×D277—42no—
62C22×D277C22⋊C411yescharacteristic
63D1108—21no—
64D1108C2×C812yes—
65C22⋊D277—24no—
66C2×Dic277—21no—
67C2×Dic277—42no—
68C2×Dic277C22⋊C411yescharacteristic
69C2×Dic277C22⋊C411yescharacteristic
70C2×Dic277C22⋊C411yescharacteristic
71C4×D277—21no—
72C4×D277—21no—
73C4×D277—41no—
74C4×D277—42no—
75C4×D277—42no—
76C4×D277—41no—
77C4×D277—41no—
78C4×D277C2×C812yes—
79C4×D277M1612yes—
80#14555660—41no—
81#14555660—41no—
82C23×C277—21no—
83D4×C277—21no—
84D4×C277C2×C812yes—
85C2×C4×C277—21no—
86C2×C4×C277—41no—
87C2×C4×C277—41no—
88C2×C4×C277C22×C411yescharacteristic
89C2×C4×C277C2×D411yescharacteristic
90C2×C4×C277C2×D411yescharacteristic
91C8×C277—41no—
92C8×C277—41no—
93C22×C277—22no—
94C22×C277—41no—
95C22×C277—41no—
96C22×C277C2×C22⋊C411yescharacteristic
97C2×D277—21no—
98C2×D277—21no—
99C2×D277—22no—
100C2×D277—48no—
101C2×D277—41no—
102C2×D277—41no—
103C2×D277C22⋊C812yes—
104C4×C277—21no—
105C4×C277—41no—
106C4×C277C22×C811yescharacteristic
107C4×C277C2×M1611yescharacteristic
108C4×C277AGL(1,ℤ/8)11yescharacteristic
109C4×C277AGL(1,ℤ/8)11yescharacteristic
110Dic277—21no—
111Dic277—21no—
112Dic277—41no—
113Dic277C22⋊C812yes—
114C2×C277—42no—
115C2×C277C2×C22⋊C811yescharacteristic
116C2×C277#41811yescharacteristic
117C2×C277#42111yescharacteristic
118D277—22no—
119D277—42no—
120C277#147811yescharacteristic, complemented, Sylow
121#1478—2771nomaximal, Sylow
122C2×C4×D4—2771no—
123#431—2771no—
124#431—2771no—
125D4⋊C8—2771no—
126D4⋊C8—2771no—
127D4⋊C8—2771no—
128D4⋊C8D27711yescharacteristic, complemented
129C22×D4—2771no—
130C23×C4—5541no—
131C4×D4—2771no—
132C4×D4—2771no—
133C4×D4—2771no—
134C4×D4—5541no—
135C4×D4—5541no—
136C4×D4C2×D27711yescharacteristic
137C2×C4⋊C4—2771no—
138C2×C22⋊C4—5541no—
139C2×C42—2771no—
140C4⋊C8—2771no—
141C4⋊C8—5541no—
142C4⋊C8C2×D27711yescharacteristic, complemented
143C22⋊C8—5541no—
144C22⋊C8—5541no—
145C4×C8—2771no—
146C4×C8—5541no—
147C4×C8C2×D27711yescharacteristic, complemented
148C24—5541no—
149C2×D4—2774no—
150C2×D4—2771no—
151C2×D4—5542no—
152C2×D4—5541no—
153C2×D4C4×D27711yescharacteristic
154C22×C4—21no—
155C22×C4—2771no—
156C22×C4—2771no—
157C22×C4—2771no—
158C22×C4—5541no—
159C22×C4—5541no—
160C22×C4—5541no—
161C22×C4—5541no—
162C22×C4—11082no—
163C22×C4—11082no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—5541no—
167C2×C8—5541no—
168C4⋊C4—2771no—
169C4⋊C4—5541no—
170C4⋊C4C4×D27711yescharacteristic
171C22⋊C4—21no—
172C22⋊C4—5541no—
173C22⋊C4—5541no—
174C22⋊C4—5541no—
175C42—2771no—
176C42—2771no—
177C42—2771no—
178C42C22×D27711yescharacteristic
179C23—21no—
180C23—2771no—
181C23—5544no—
182C23—5541no—
183C23—11082no—
184C23—11082no—
185D4—21no—
186D4—2772no—
187D4—5544no—
188D4—5541no—
189D4C8×D27712yes—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—2771no—
194C2×C4—2772no—
195C2×C4—2772no—
196C2×C4—2771no—
197C2×C4—2771no—
198C2×C4—5541no—
199C2×C4—5541no—
200C2×C4—5541no—
201C2×C4—11081no—
202C2×C4—11082no—
203C2×C4—11082no—
204C2×C4—11082no—
205C2×C4—11081no—
206C2×C4—11081no—
207C2×C4C2×C4×D27711yescharacteristic
208C2×C4D4×D27711yescharacteristic
209C2×C4D4×D27711yescharacteristic
210C8—41no—
211C8—41no—
212C8—11081no—
213C8—11081no—
214C22—22no—
215C22—41no—
216C22—41no—
217C22—2772no—
218C22—5541no—
219C22—5541no—
220C22—5542no—
221C22—11088no—
222C22—11081no—
223C22—11081no—
224C22C22⋊C4×D27711yescharacteristic
225C4—21no—
226C4—41no—
227C4—2772no—
228C4—5541no—
229C4—5541no—
230C4—11081no—
231C4C2×C8×D27711yescharacteristic
232C4M16×D27711yescharacteristic
233C4#2257990411yescharacteristic
234C4#2257990711yescharacteristic
235C2—42no—
236C2—5542no—
237C2—11082no—
238C2C22⋊C8×D27711yescharacteristic
239C2#3180000511yescharacteristic
240C2#3180001711yescharacteristic
subgroupG/H
centerC2×C4D4×D277
commutatorC4×C277C22×C8
FrattiniC42C22×D277
FittingD4⋊C8×C277C2
socleC22×C277C2×C22⋊C4
prime radicalC2×D4×D277C4
cosocleC42×C277C23
hypercenterD4⋊C8D277
hypocenterC277#1478
LCSG ▷ 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. #31800054C2semidirect
3. #31800053C2semidirect
4. #31799731C2semidirect
5. D4⋊#14555660C2semidirect
6. #31799729C2semidirect
7. D4⋊C8×C277C2semidirect
18. C4⋊#14555660C22semidirect
22. C4×#14555660C22semidirect
25. C4⋊C8×C277C22semidirect
26. C4×C8×C277C22semidirect
31. D4×D277C8semidirect
120. C277#1478semidirect
128. D4⋊C8D277semidirect
142. C4⋊C8C2×D277semidirect
147. C4×C8C2×D277semidirect

Maximal subgroups

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

subgroupindex
C4×D4×D2772
#318000542
#318000532
#317997312
D4⋊#145556602
#317997292
D4⋊C8×C2772
#1478277