Finite Group Databasebeta

← #47982349

Subgroups — #47982349

Order 35456.

308 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×D1108C211yesmaximal, characteristic
2#31800349C211yesmaximal, characteristic, complemented
3#31800282C211yesmaximal, characteristic, complemented
4#31800208C211yesmaximal, characteristic, complemented
5#31799745C211yesmaximal, characteristic, complemented
6#31799731C211yesmaximal, characteristic, complemented
7D4⋊C8×C277C211yesmaximal, characteristic, complemented
8C22×D1108—21no—
9C2×D4×D277—21no—
10C2×#17984552—21no—
11#22579880C2211yescharacteristic, complemented
12#22579877C2211yescharacteristic
13#22579855—21no—
14#22579854—21no—
15#22579850—22no—
16C4×D1108C2211yescharacteristic
17#22579813—21no—
18C4⋊#14555660C2211yescharacteristic, complemented
19#22579805—21no—
20#22579802—22no—
21#22579801—21no—
22C4×D4×C277C2211yescharacteristic
23C4⋊C8×C277C2211yescharacteristic, complemented
24C4×C8×C277C2211yescharacteristic, complemented
25C23×D277—22no—
26C2×Dic554—21no—
27C2×D1108—22no—
28C2×D1108—21no—
29C2×D1108—21no—
30C2×D1108—42no—
31C2×D1108—42no—
32C2×D1108D411yescharacteristic
33C2×D1108D412yes—
34C2×C22⋊D277—22no—
35D4×D277—42no—
36D4×D277—42no—
37C2×C4×D277—21no—
38#17984552—42no—
39C2×#14555660—21no—
40C4⋊Dic277—21no—
41C4⋊Dic277—21no—
42C4⋊Dic277D411yescharacteristic
43#17984540—22no—
44#17984540—21no—
45C2×D4×C277D411yescharacteristic
46C22×C4×C277—21no—
47C2×C8×C277—21no—
48C2×C8×C277—21no—
49C4⋊C4×C277D411yescharacteristic
50C22⋊C4×C277—21no—
51C42×C277C2311yescharacteristic
52C22×D277—21no—
53C22×D277—22no—
54C22×D277—44no—
55C22×D277—44no—
56C22×D277—82no—
57Dic554—41no—
58Dic554—41no—
59D1108—21no—
60D1108—42no—
61D1108—44no—
62D1108—41no—
63D1108—41no—
64D1108—41no—
65D1108—41no—
66D1108D812yes—
67C22⋊D277—44no—
68C2×Dic277—21no—
69C2×Dic277—41no—
70C4×D277—41no—
71C4×D277—41no—
72#14555660—41no—
73C23×C277—21no—
74D4×C277—21no—
75D4×C277SD1612yescomplemented
76C2×C4×C277—21no—
77C2×C4×C277—41no—
78C2×C4×C277—41no—
79C2×C4×C277C2×D411yescharacteristic
80C2×C4×C277C2×D411yescharacteristic
81C2×C4×C277C2×D411yescharacteristic
82C8×C277—41no—
83C8×C277—41no—
84C22×C277—22no—
85C22×C277—41no—
86C22×C277—41no—
87C22×C277#12011yescharacteristic
88C2×D277—22no—
89C2×D277—41no—
90C2×D277—41no—
91C2×D277—42no—
92C2×D277—42no—
93C2×D277—42no—
94C2×D277—88no—
95C4×C277—21no—
96C4×C277—41no—
97C4×C277C2×D811yescharacteristic
98C4×C277C2×SD1611yescharacteristic
99C4×C277AGL(1,ℤ/8)11yescharacteristic
100C4×C277AGL(1,ℤ/8)11yescharacteristic
101Dic277—41no—
102Dic277—81no—
103C2×C277—42no—
104C2×C277#44711yescharacteristic
105C2×C277#45011yescharacteristic
106C2×C277#45511yescharacteristic
107D277—42no—
108D277—82no—
109C277#163911yescharacteristic, complemented, Sylow
110#1639—2771nomaximal, Sylow
111D42—2771no—
112#486—2771no—
113#474—2771no—
114#461—2771no—
115#331—2771no—
116D4⋊C8—2771no—
117D4⋊C8D27711yescharacteristic, complemented
118C22×D4—5541no—
119C22×D4—5541no—
120C2×SD16—5541no—
121C4⋊Q8—2771no—
122#127—2771no—
123#121—5541no—
124#121—5541no—
125#120—5542no—
126C4×D4—2771no—
127C4×D4C2×D27711yescharacteristic
128#107—5541no—
129C4⋊C8—2771no—
130C4⋊C8C2×D27711yescharacteristic, complemented
131#103—5541no—
132#102—5542no—
133#102—5541no—
134C4×C8C2×D27711yescharacteristic, complemented
135C24—5542no—
136C2×Q8—5541no—
137C2×D4—2771no—
138C2×D4—2772no—
139C2×D4—5542no—
140C2×D4—5542no—
141C2×D4—5541no—
142C2×D4—5541no—
143C2×D4—11082no—
144C2×D4—11082no—
145C2×D4—11082no—
146C2×D4—11082no—
147C2×D4D110811yescharacteristic
148C22×C4—21no—
149C22×C4—5541no—
150SD16—11082no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—5541no—
154C4⋊C4—2771no—
155C4⋊C4—5541no—
156C4⋊C4—5541no—
157C4⋊C4D110811yescharacteristic
158C22⋊C4—21no—
159C22⋊C4—5542no—
160C22⋊C4—5541no—
161C42C22×D27711yescharacteristic
162C23—21no—
163C23—5541no—
164C23—5542no—
165C23—11084no—
166C23—11084no—
167C23—22162no—
168Q8—11081no—
169Q8—11081no—
170D4—21no—
171D4—2772no—
172D4—5541no—
173D4—11082no—
174D4—11084no—
175D4—11084no—
176D4—11081no—
177D4—11081no—
178D4—11081no—
179D4—11081no—
180D4#1798455212yescomplemented
181C2×C4—21no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—5541no—
185C2×C4—11081no—
186C2×C4—11081no—
187C2×C4—11081no—
188C2×C4D4×D27711yescharacteristic
189C2×C4D4×D27711yescharacteristic
190C2×C4C2×D110811yescharacteristic
191C8—41no—
192C8—41no—
193C8—11081no—
194C22—22no—
195C22—41no—
196C22—41no—
197C22—5542no—
198C22—11081no—
199C22—11081no—
200C22—11082no—
201C22—11082no—
202C22—11082no—
203C22—22168no—
204C22#2257985011yescharacteristic
205C4—21no—
206C4—41no—
207C4—11081no—
208C4—22161no—
209C4D8×D27711yescharacteristic
210C4C2×#1798455211yescharacteristic
211C4#2257990711yescharacteristic
212C4#2257990811yescharacteristic
213C2—42no—
214C2—11082no—
215C2—22162no—
216C2#3180013711yescharacteristic
217C2#3180015511yescharacteristic
218C2#3180018111yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
FittingD4⋊C8×C277C2
socleC22×C277#120
prime radicalD4×D1108C2
hypercenterD4⋊C8D277
hypocenterC277#1639
LCSG ▷ C42×C277 ▷ C22×C277 ▷ C277
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #31800349C2semidirect
3. #31800282C2semidirect
4. #31800208C2semidirect
5. #31799745C2semidirect
6. #31799731C2semidirect
7. D4⋊C8×C277C2semidirect
11. #22579880C22semidirect
18. C4⋊#14555660C22semidirect
23. C4⋊C8×C277C22semidirect
24. C4×C8×C277C22semidirect
75. D4×C277SD16semidirect
109. C277#1639semidirect
117. D4⋊C8D277semidirect
130. C4⋊C8C2×D277semidirect
134. C4×C8C2×D277semidirect
180. D4#17984552semidirect

Maximal subgroups

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

subgroupindex
D4×D11082
#318003492
#318002822
#318002082
#317997452
#317997312
D4⋊C8×C2772
#1639277