Finite Group Databasebeta

← #47983246

Subgroups — #47983246

Order 35456.

316 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 81 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×C4⋊C4×D277C211yesmaximal, characteristic
2#31799965C212yesmaximal
3#31799771C211yesmaximal, characteristic, complemented
4#31799770C212yesmaximal, complemented
5#343×C277C211yesmaximal, characteristic, complemented
6C22×C4×D277C412yes—
7C22×C4×D277C2211yescharacteristic
8C2×#17984547C2212yes—
9C2×C4⋊Dic277C2211yescharacteristic
10C2×#17984542C412yes—
11C4⋊C4×D277—22no—
12C4⋊C4×D277—22no—
13#22579792—22no—
14#22579792—22no—
15C2×M16×C277C2212yes—
16C2×C4⋊C4×C277C2211yescharacteristic
17C23×D277C2×C411yescharacteristic
18C22×Dic277C2×C411yescharacteristic
19C22×Dic277C2×C412yes—
20C2×C4×D277—22no—
21C2×C4×D277—22no—
22C2×C4×D277—21no—
23C2×C4×D277—22no—
24C2×C4×D277—21no—
25C2×C4×D277—44no—
26C2×C4×D277D412yes—
27C2×C4×D277D412yes—
28#17984547—22no—
29#17984547—22no—
30C2×#14555660—22no—
31C4⋊Dic277—22no—
32#17984542—24no—
33C22×C4×C277C2×C412yes—
34C22×C4×C277C2311yescharacteristic
35M16×C277—22no—
36M16×C277—22no—
37C2×C8×C277—22no—
38C4⋊C4×C277—22no—
39C22×D277—21no—
40C22×D277—21no—
41C22×D277—22no—
42C22×D277—22no—
43C22×D277C22⋊C411yescharacteristic
44C22×D277C22⋊C411yescharacteristic
45C2×Dic277—21no—
46C2×Dic277—21no—
47C2×Dic277—22no—
48C2×Dic277—42no—
49C2×Dic277C22⋊C412yes—
50C4×D277—22no—
51C4×D277—22no—
52C4×D277—22no—
53C4×D277—22no—
54C4×D277—44no—
55C4×D277—44no—
56#14555660—42no—
57C23×C277C22×C411yescharacteristic
58C2×C4×C277—22no—
59C2×C4×C277—42no—
60C2×C4×C277C2×D412yes—
61C2×C4×C277#4111yescharacteristic
62C2×C4×C277#4112yes—
63C2×C4×C277#4111yescharacteristic
64C8×C277—42no—
65C22×C277—21no—
66C22×C277—21no—
67C22×C277C2×C22⋊C411yescharacteristic
68C22×C277#11711yescharacteristic
69C22×C277#11711yescharacteristic
70C2×D277—24no—
71C2×D277—24no—
72C2×D277—21no—
73C2×D277—21no—
74C2×D277—21no—
75C2×D277—21no—
76C2×D277#10012yes—
77C2×D277#10112yes—
78C4×C277—42no—
79C4×C277#12312yes—
80C4×C277#12312yes—
81Dic277—22no—
82Dic277—42no—
83C2×C277—21no—
84C2×C277—21no—
85C2×C277#38111yescharacteristic
86C2×C277C2×#10011yescharacteristic
87C2×C277C2×#10111yescharacteristic
88D277—22no—
89D277—22no—
90C277#182111yescharacteristic, complemented, Sylow
91#1821—2771nomaximal, Sylow
92C22×C4⋊C4—2771no—
93#407—2772no—
94#343—2772no—
95#343—2771no—
96#343D27711yescharacteristic, complemented
97C23×C4—2771no—
98C23×C4—2772no—
99C2×M16—2772no—
100C2×M16C2×D27712yes—
101C2×C4⋊C4—2772no—
102C2×C4⋊C4—2771no—
103C2×C4⋊C4—5542no—
104C2×C4⋊C4—5542no—
105C2×C4⋊C4C2×D27711yescharacteristic
106C22⋊C8—5542no—
107C22⋊C8—5542no—
108C24—2771no—
109C22×C4—2771no—
110C22×C4—2772no—
111C22×C4—2772no—
112C22×C4—2772no—
113C22×C4—5542no—
114C22×C4—5542no—
115C22×C4—5541no—
116C22×C4—5542no—
117C22×C4—5541no—
118C22×C4—11084no—
119C22×C4C4×D27712yes—
120C22×C4C22×D27711yescharacteristic
121M16—22no—
122M16—22no—
123M16—5542no—
124M16—5542no—
125C2×C8—22no—
126C2×C8—5542no—
127C4⋊C4—22no—
128C4⋊C4—5544no—
129C4⋊C4—5542no—
130C23—2771no—
131C23—2771no—
132C23—5542no—
133C23—5542no—
134C23—5541no—
135C23—5541no—
136C23C2×C4×D27711yescharacteristic
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—2772no—
140C2×C4—5541no—
141C2×C4—5541no—
142C2×C4—5542no—
143C2×C4—5542no—
144C2×C4—5542no—
145C2×C4—5542no—
146C2×C4—5542no—
147C2×C4—11084no—
148C2×C4—11084no—
149C2×C4—11082no—
150C2×C4D4×D27712yes—
151C2×C4#1798456211yescharacteristic
152C2×C4#1798456312yes—
153C2×C4#1798456411yescharacteristic
154C8—42no—
155C8—11082no—
156C22—21no—
157C22—21no—
158C22—2772no—
159C22—2772no—
160C22—5544no—
161C22—5544no—
162C22—5541no—
163C22—5541no—
164C22—5541no—
165C22—5541no—
166C22C22⋊C4×D27711yescharacteristic
167C22#2257983711yescharacteristic
168C22#2257983811yescharacteristic
169C4—42no—
170C4—5542no—
171C4—11082no—
172C4#2257986212yes—
173C4#2257986512yes—
174C2—21no—
175C2—21no—
176C2—5542no—
177C2—5542no—
178C2#3179986411yescharacteristic
179C2#100×D27711yescharacteristic
180C2#101×D27711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D277
commutatorC23×C277C22×C4
FrattiniC22×C4C22×D277
Fitting#343×C277C2
socleC22×C277C2×C22⋊C4
prime radicalC23×D277C2×C4
cosocleC22×C4×C277C23
hypercenter#343D277
hypocenterC277#1821
LCSG ▷ C23×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
3. #31799771C2semidirect
4. #31799770C2semidirect
5. #343×C277C2semidirect
90. C277#1821semidirect
96. #343D277semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D2772
#317999652
#317997712
#317997702
#343×C2772
#1821277