Finite Group Databasebeta

← #47983240

Subgroups — #47983240

Order 35456.

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

normal subgroups only

This group has 504 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×C22⋊C4×D277C211yesmaximal, characteristic
2#31799857C212yesmaximal
3#31799769C211yesmaximal, characteristic, complemented
4#31799768C212yesmaximal, complemented
5#342×C277C211yesmaximal, characteristic, complemented
6C24×D277C2211yescharacteristic
7C22×C4×D277C412yescomplemented
8C2×C22⋊Dic277C2212yes—
9C2×C22⋊Dic277C2211yescharacteristic
10C2×#17984540—24no—
11C2×#17984540C412yescomplemented
12C22⋊C4×D277—24no—
13C2×C22⋊C4×C277C2212yes—
14C2×C22⋊C4×C277C2211yescharacteristic
15C23×D277—21no—
16C23×D277—22no—
17C23×D277—21no—
18C23×D277—44no—
19C23×D277C2×C411yescharacteristic
20C23×D277C2×C411yescharacteristic
21C23×D277D414yes—
22C22×Dic277—22no—
23C22×Dic277C2×C412yes—
24C2×C4×D277—22no—
25C2×C4×D277—22no—
26C2×C4×D277—44no—
27C22⋊Dic277—22no—
28C22⋊Dic277—22no—
29C22⋊Dic277—22no—
30#17984540—24no—
31#17984540—48no—
32C24×C277C2311yescharacteristic
33C22×C4×C277—22no—
34C22×C4×C277C2×C412yes—
35C22⋊C4×C277—22no—
36C22⋊C4×C277—22no—
37C22⋊C4×C277—22no—
38C22×D277—21no—
39C22×D277—21no—
40C22×D277—24no—
41C22×D277—21no—
42C22×D277—21no—
43C22×D277—24no—
44C22×D277—24no—
45C22×D277—28no—
46C22×D277—42no—
47C22×D277—44no—
48C22×D277—44no—
49C22×D277—48no—
50C22×D277—44no—
51C22×D277C22⋊C412yes—
52C22×D277C22⋊C412yes—
53C2×Dic277—22no—
54C2×Dic277—42no—
55C2×Dic277—44no—
56C2×Dic277—42no—
57C4×D277—44no—
58C4×D277—44no—
59C23×C277—42no—
60C23×C277C22×C411yescharacteristic
61C23×C277C2×D412yes—
62C23×C277#4111yescharacteristic
63C23×C277#4112yes—
64C23×C277#4111yescharacteristic
65C2×C4×C277—22no—
66C2×C4×C277—42no—
67C2×C4×C277—44no—
68C2×C4×C277—42no—
69C22×C277—22no—
70C22×C277—24no—
71C22×C277—41no—
72C22×C277—42no—
73C22×C277—41no—
74C22×C277C2×C22⋊C411yescharacteristic
75C22×C277#11711yescharacteristic
76C22×C277#11711yescharacteristic
77C22×C277#12312yes—
78C22×C277#12312yes—
79C2×D277—24no—
80C2×D277—24no—
81C2×D277—22no—
82C2×D277—22no—
83C2×D277—22no—
84C2×D277—24no—
85C2×D277—48no—
86C2×D277—48no—
87C2×D277—42no—
88C2×D277—42no—
89C2×D277#9914yes—
90C4×C277—42no—
91C4×C277—82no—
92Dic277—42no—
93Dic277—82no—
94C2×C277—22no—
95C2×C277—22no—
96C2×C277—21no—
97C2×C277—21no—
98C2×C277#38111yescharacteristic
99C2×C277C2×#9912yes—
100D277—24no—
101D277—42no—
102C277#181911yescharacteristic, complemented, Sylow
103#1819—2771nomaximal, Sylow
104C22×C22⋊C4—2771no—
105#379—2772no—
106#342—2772no—
107#342—2771no—
108#342D27711yescharacteristic, complemented
109C25—2771no—
110C23×C4—2772no—
111C2×C22⋊C4—2771no—
112C2×C22⋊C4—2772no—
113C2×C22⋊C4—2772no—
114C2×C22⋊C4—5544no—
115C2×C22⋊C4—5544no—
116C2×C22⋊C4C2×D27712yes—
117C2×C22⋊C4C2×D27711yescharacteristic
118C24—2771no—
119C24—2774no—
120C24—2771no—
121C24—5541no—
122C24—5542no—
123C24—5541no—
124C24—11084no—
125C24C22×D27711yescharacteristic
126C22×C4—22no—
127C22×C4—2772no—
128C22×C4—5542no—
129C22×C4—5542no—
130C22×C4—5542no—
131C22×C4—11084no—
132C22×C4C4×D27712yes—
133C22⋊C4—22no—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C22⋊C4—5544no—
137C22⋊C4—5542no—
138C22⋊C4—5542no—
139C22⋊C4—5542no—
140C22⋊C4—11088no—
141C23—42no—
142C23—2772no—
143C23—2772no—
144C23—5544no—
145C23—5548no—
146C23—5541no—
147C23—5541no—
148C23—5541no—
149C23—5541no—
150C23—5544no—
151C23—5544no—
152C23—11082no—
153C23—11084no—
154C23—11084no—
155C23—11088no—
156C23—11084no—
157C23C2×C4×D27711yescharacteristic
158C23D4×D27712yes—
159C23#1798456211yescharacteristic
160C23#1798456312yes—
161C23#1798456411yescharacteristic
162C2×C4—22no—
163C2×C4—42no—
164C2×C4—44no—
165C2×C4—42no—
166C2×C4—5542no—
167C2×C4—11084no—
168C2×C4—11084no—
169C2×C4—11082no—
170C2×C4—11084no—
171C2×C4—11082no—
172C22—22no—
173C22—24no—
174C22—41no—
175C22—42no—
176C22—41no—
177C22—2774no—
178C22—5544no—
179C22—5544no—
180C22—5542no—
181C22—5542no—
182C22—5542no—
183C22—5544no—
184C22—11088no—
185C22—11088no—
186C22—11082no—
187C22—11082no—
188C22C22⋊C4×D27711yescharacteristic
189C22#2257983711yescharacteristic
190C22#2257983811yescharacteristic
191C22#2257986212yes—
192C22#2257986512yes—
193C4—42no—
194C4—82no—
195C4—11082no—
196C4—22162no—
197C2—22no—
198C2—22no—
199C2—21no—
200C2—21no—
201C2—5544no—
202C2—11082no—
203C2#3179986411yescharacteristic
204C2#99×D27712yes—
subgroupG/H
centerC22C22⋊C4×D277
commutatorC23×C277C22×C4
FrattiniC24C22×D277
Fitting#342×C277C2
socleC22×C277C2×C22⋊C4
prime radicalC24×D277C22
cosocleC24×C277C23
hypercenter#342D277
hypocenterC277#1819
LCSG ▷ C23×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
3. #31799769C2semidirect
4. #31799768C2semidirect
5. #342×C277C2semidirect
7. C22×C4×D277C4semidirect
11. C2×#17984540C4semidirect
102. C277#1819semidirect
108. #342D277semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×D2772
#317998572
#317997692
#317997682
#342×C2772
#1819277