Finite Group Databasebeta

← #47982223

Subgroups — #47982223

Order 35456.

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

normal subgroups only

This group has 336 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, complemented
2#31800379C211yesmaximal, characteristic, complemented
3#31800198C211yesmaximal, characteristic, complemented
4#31800197C211yesmaximal, characteristic, complemented
5#31799745C211yesmaximal, characteristic, complemented
6#31799731C211yesmaximal, characteristic, complemented
7D4⋊C8×C277C211yesmaximal, characteristic, complemented
8C22×D1108—21no—
9C2×D4×D277—21no—
10C2×D2216—22no—
11C2×D2216—21no—
12C2×#17984548—21no—
13#22579877C2211yescharacteristic
14#22579877C2211yescharacteristic, complemented
15#22579855—21no—
16#22579854—21no—
17#22579850—22no—
18C4×D1108C2211yescharacteristic
19C4⋊#14555660C2211yescharacteristic, complemented
20#22579802—21no—
21#22579800—21no—
22C4×D4×C277C2211yescharacteristic
23C4⋊C8×C277C2211yescharacteristic, complemented
24C4×C8×C277C2211yescharacteristic, complemented
25C23×D277—22no—
26C2×D1108—22no—
27C2×D1108—21no—
28C2×D1108—21no—
29C2×D1108—21no—
30C2×D1108—21no—
31C2×D1108—21no—
32C2×D1108—42no—
33C2×D1108—42no—
34C2×D1108D411yescharacteristic
35C2×D1108D412yes—
36C2×C22⋊D277—22no—
37D4×D277—42no—
38D4×D277—42no—
39C2×C4×D277—21no—
40D2216—44no—
41D2216—42no—
42#17984548—42no—
43C2×#14555660—21no—
44C4⋊Dic277D411yescharacteristic
45#17984540—22no—
46#17984540—21no—
47C2×D4×C277D411yescharacteristic
48C22×C4×C277—21no—
49C2×C8×C277—21no—
50C2×C8×C277—21no—
51C4⋊C4×C277D411yescharacteristic
52C22⋊C4×C277—21no—
53C42×C277C2311yescharacteristic
54C22×D277—21no—
55C22×D277—22no—
56C22×D277—44no—
57C22×D277—44no—
58C22×D277—41no—
59C22×D277—82no—
60D1108—21no—
61D1108—42no—
62D1108—42no—
63D1108—44no—
64D1108—41no—
65D1108—41no—
66D1108—41no—
67D1108—41no—
68D1108—41no—
69D1108—41no—
70D1108—41no—
71D1108—41no—
72D1108D812yescomplemented
73C22⋊D277—44no—
74C2×Dic277—21no—
75C4×D277—41no—
76C4×D277—41no—
77#14555660—41no—
78C23×C277—21no—
79D4×C277—21no—
80D4×C277D812yescomplemented
81C2×C4×C277—21no—
82C2×C4×C277—41no—
83C2×C4×C277—41no—
84C2×C4×C277C2×D411yescharacteristic
85C2×C4×C277C2×D411yescharacteristic
86C2×C4×C277C2×D411yescharacteristic
87C8×C277—22no—
88C8×C277—41no—
89C22×C277—22no—
90C22×C277—41no—
91C22×C277—41no—
92C22×C277#12011yescharacteristic
93C2×D277—22no—
94C2×D277—41no—
95C2×D277—41no—
96C2×D277—42no—
97C2×D277—42no—
98C2×D277—42no—
99C2×D277—88no—
100C2×D277—81no—
101C2×D277—81no—
102C2×D277—81no—
103C4×C277—21no—
104C4×C277—41no—
105C4×C277C2×D811yescharacteristic
106C4×C277C2×D811yescharacteristic
107C4×C277AGL(1,ℤ/8)11yescharacteristic
108C4×C277AGL(1,ℤ/8)11yescharacteristic
109Dic277—41no—
110C2×C277—42no—
111C2×C277#44711yescharacteristic
112C2×C277#44711yescharacteristic
113C2×C277#45311yescharacteristic
114D277—42no—
115D277—82no—
116D277—161no—
117C277#161911yescharacteristic, complemented, Sylow
118#1619—2771nomaximal, Sylow
119D42—2771no—
120#493—2771no—
121#459—2771no—
122#459—2771no—
123#331—2771no—
124D4⋊C8—2771no—
125D4⋊C8D27711yescharacteristic, complemented
126C22×D4—5541no—
127C22×D4—5541no—
128C2×D8—5541no—
129C2×D8—5542no—
130C2×D8—5541no—
131#127—2771no—
132#127—2771no—
133#121—5541no—
134#121—5541no—
135#120—5542no—
136C4×D4—2771no—
137C4×D4C2×D27711yescharacteristic
138C4⋊C8—2771no—
139C4⋊C8C2×D27711yescharacteristic, complemented
140#102—5541no—
141#102—5541no—
142C4×C8C2×D27711yescharacteristic, complemented
143C24—5542no—
144C2×D4—2771no—
145C2×D4—2772no—
146C2×D4—5542no—
147C2×D4—5542no—
148C2×D4—5541no—
149C2×D4—5541no—
150C2×D4—5541no—
151C2×D4—5541no—
152C2×D4—5541no—
153C2×D4—11082no—
154C2×D4—11082no—
155C2×D4—11082no—
156C2×D4—11082no—
157C2×D4D110811yescharacteristic
158C22×C4—21no—
159C22×C4—5541no—
160D8—11084no—
161D8—11082no—
162D8—11082no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—5541no—
166C4⋊C4—2771no—
167C4⋊C4D110811yescharacteristic
168C22⋊C4—21no—
169C22⋊C4—5542no—
170C22⋊C4—5541no—
171C42C22×D27711yescharacteristic
172C23—21no—
173C23—5541no—
174C23—5542no—
175C23—11084no—
176C23—11084no—
177C23—11081no—
178C23—22162no—
179D4—21no—
180D4—2772no—
181D4—5541no—
182D4—11082no—
183D4—11082no—
184D4—11084no—
185D4—11084no—
186D4—11081no—
187D4—11081no—
188D4—11081no—
189D4—11081no—
190D4—11081no—
191D4—11081no—
192D4—11081no—
193D4—11081no—
194D4D221612yescomplemented
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—5541no—
199C2×C4—11081no—
200C2×C4—11081no—
201C2×C4D4×D27711yescharacteristic
202C2×C4D4×D27711yescharacteristic
203C2×C4C2×D110811yescharacteristic
204C8—22no—
205C8—41no—
206C8—11081no—
207C22—22no—
208C22—41no—
209C22—41no—
210C22—5542no—
211C22—11081no—
212C22—11081no—
213C22—11082no—
214C22—11082no—
215C22—11082no—
216C22—22168no—
217C22—22161no—
218C22—22161no—
219C22—22161no—
220C22#2257985011yescharacteristic
221C4—21no—
222C4—41no—
223C4—11081no—
224C4D8×D27711yescharacteristic
225C4C2×D221611yescharacteristic
226C4#2257990711yescharacteristic
227C4#2257990811yescharacteristic
228C2—42no—
229C2—44321no—
230C2—11082no—
231C2—22162no—
232C2#3180013711yescharacteristic
233C2#3180013811yescharacteristic
234C2#3180017111yescharacteristic
subgroupG/H
centerC22#22579850
commutator, cosocleC42×C277C23
FrattiniC42C22×D277
FittingD4⋊C8×C277C2
socleC22×C277#120
hypercenterD4⋊C8D277
hypocenterC277#1619
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
1. D4×D1108C2semidirect
2. #31800379C2semidirect
3. #31800198C2semidirect
4. #31800197C2semidirect
5. #31799745C2semidirect
6. #31799731C2semidirect
7. D4⋊C8×C277C2semidirect
14. #22579877C22semidirect
19. C4⋊#14555660C22semidirect
23. C4⋊C8×C277C22semidirect
24. C4×C8×C277C22semidirect
72. D1108D8semidirect
80. D4×C277D8semidirect
117. C277#1619semidirect
125. D4⋊C8D277semidirect
139. C4⋊C8C2×D277semidirect
142. C4×C8C2×D277semidirect
194. D4D2216semidirect

Maximal subgroups

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

subgroupindex
D4×D11082
#318003792
#318001982
#318001972
#317997452
#317997312
D4⋊C8×C2772
#1619277