Finite Group Databasebeta

← #47981504

Subgroups — #47981504

Order 35456.

316 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 69 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×#22579842C211yesmaximal, characteristic
2#31799964C212yesmaximal, complemented
3#31799728C211yesmaximal, characteristic, complemented
4#31799725C212yesmaximal, complemented
5#324×C277C211yesmaximal, characteristic, complemented
6C22×D1108C411yescharacteristic
7C22×C4×D277C411yescharacteristic
8C22×C4×D277C2211yescharacteristic
9C2×#17984546—22no—
10#22579842—22no—
11#22579842—22no—
12C2×#17984540C411yescharacteristic
13C2×#17984540C2211yescharacteristic
14C2×C4×Dic277C411yescharacteristic
15C22⋊#14555660C2212yes—
16#22579792—22no—
17C2×C4⋊C4×C277C2211yescharacteristic
18C22⋊C8×C277C2212yes—
19C23×D277C2×C411yescharacteristic
20C23×D277C2×C411yescharacteristic
21C2×D1108—22no—
22C2×D1108—22no—
23C2×D1108—22no—
24C22×Dic277C2×C411yescharacteristic
25C22×Dic277C2×C411yescharacteristic
26C2×C4×D277—21no—
27C2×C4×D277—21no—
28C2×C4×D277—42no—
29C2×C4×D277—42no—
30C2×C4×D277D412yes—
31C2×C4×D277D412yes—
32#17984546—44no—
33C2×#14555660—22no—
34#17984540—22no—
35#17984540—22no—
36C4×Dic277—21no—
37C4×Dic277—21no—
38C22×C4×C277C2×C411yescharacteristic
39C22×C4×C277C2×C411yescharacteristic
40C22×C4×C277C2311yescharacteristic
41C2×C8×C277—22no—
42C4⋊C4×C277—22no—
43C22×D277—21no—
44C22×D277—21no—
45C22×D277—21no—
46C22×D277—21no—
47C22×D277—41no—
48C22×D277—41no—
49C22×D277—41no—
50C22×D277—41no—
51C22×D277C22⋊C412yes—
52C22×D277M1612yescomplemented
53D1108—28no—
54C2×Dic277—22no—
55C2×Dic277—21no—
56C2×Dic277—41no—
57C2×Dic277C22⋊C411yescharacteristic
58C2×Dic277C22⋊C411yescharacteristic
59C4×D277—24no—
60C4×D277—42no—
61C4×D277—42no—
62C4×D277—42no—
63#14555660—42no—
64C23×C277C22×C411yescharacteristic
65C2×C4×C277—21no—
66C2×C4×C277—21no—
67C2×C4×C277—21no—
68C2×C4×C277—41no—
69C2×C4×C277—41no—
70C2×C4×C277M1612yescomplemented
71C2×C4×C277C2×D412yes—
72C8×C277—42no—
73C22×C277—21no—
74C22×C277—21no—
75C22×C277C2×C22⋊C411yescharacteristic
76C22×C277C2×M1611yescharacteristic
77C22×C277C2×M1611yescharacteristic
78C2×D277—22no—
79C2×D277—22no—
80C2×D277—22no—
81C2×D277—22no—
82C2×D277—42no—
83C2×D277—42no—
84C2×D277—42no—
85C2×D277—41no—
86C2×D277—41no—
87C2×D277—42no—
88C4×C277—22no—
89C4×C277—22no—
90C4×C277—41no—
91Dic277—21no—
92Dic277—41no—
93Dic277#9912yes—
94C2×C277—21no—
95C2×C277—21no—
96C2×C277#40711yescharacteristic
97C2×C277C2×#9911yescharacteristic
98C2×C277#41311yescharacteristic
99D277—42no—
100D277—42no—
101C277#146511yescharacteristic, complemented, Sylow
102#1465—2771nomaximal, Sylow
103C2×C4×D4—2771no—
104#407—2772no—
105#324—2771no—
106#324D27711yescharacteristic, complemented
107#323—2772no—
108C22×D4—2771no—
109C23×C4—2771no—
110C23×C4—2771no—
111C2×M16—5542no—
112C4×D4—5542no—
113C4×D4—5542no—
114C2×C4⋊C4C2×D27711yescharacteristic
115C2×C22⋊C4—2771no—
116C2×C22⋊C4—2771no—
117C2×C42—2771no—
118C22⋊C8—2772no—
119C22⋊C8—5542no—
120C22⋊C8C2×D27712yes—
121C24—2771no—
122C24—2771no—
123C2×D4—5542no—
124C2×D4—5542no—
125C2×D4—5542no—
126C22×C4—2771no—
127C22×C4—2772no—
128C22×C4—2772no—
129C22×C4—2771no—
130C22×C4—5541no—
131C22×C4—5541no—
132C22×C4—11082no—
133C22×C4—11082no—
134C22×C4C4×D27711yescharacteristic
135C22×C4C4×D27711yescharacteristic
136C22×C4C22×D27711yescharacteristic
137M16—11084no—
138C2×C8—22no—
139C2×C8—5542no—
140C4⋊C4—22no—
141C22⋊C4—5542no—
142C22⋊C4—5542no—
143C42—5541no—
144C42—5541no—
145C23—2772no—
146C23—2772no—
147C23—5541no—
148C23—5541no—
149C23—5541no—
150C23—5541no—
151C23—11081no—
152C23—11081no—
153C23—11081no—
154C23—11081no—
155C23C2×C4×D27711yescharacteristic
156D4—5548no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—2771no—
163C2×C4—2771no—
164C2×C4—5544no—
165C2×C4—5542no—
166C2×C4—5541no—
167C2×C4—11082no—
168C2×C4—11082no—
169C2×C4—11082no—
170C2×C4—11081no—
171C2×C4#1798454612yescomplemented
172C2×C4D4×D27712yes—
173C8—42no—
174C8—11082no—
175C22—21no—
176C22—21no—
177C22—5542no—
178C22—5542no—
179C22—5542no—
180C22—5542no—
181C22—11082no—
182C22—11082no—
183C22—11082no—
184C22—11082no—
185C22—11081no—
186C22—11081no—
187C22C22⋊C4×D27711yescharacteristic
188C22M16×D27711yescharacteristic
189C22C2×#1798454611yescharacteristic
190C4—22no—
191C4—22no—
192C4—41no—
193C4—2772no—
194C4—5541no—
195C4—11081no—
196C2—21no—
197C2—21no—
198C2—11082no—
199C2—11082no—
200C2#3179996411yescharacteristic
201C2#99×D27711yescharacteristic
202C2#3179998511yescharacteristic
subgroupG/H
centerC22C22⋊C4×D277
commutatorC23×C277C22×C4
FrattiniC22×C4C22×D277
Fitting#324×C277C2
socleC22×C277C2×C22⋊C4
prime radicalC22×D1108C4
cosocleC22×C4×C277C23
hypercenter#324D277
hypocenterC277#1465
LCSG ▷ C23×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #31799964C2semidirect
3. #31799728C2semidirect
4. #31799725C2semidirect
5. #324×C277C2semidirect
52. C22×D277M16semidirect
70. C2×C4×C277M16semidirect
101. C277#1465semidirect
106. #324D277semidirect
171. C2×C4#17984546semidirect

Maximal subgroups

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

subgroupindex
C2×#225798422
#317999642
#317997282
#317997252
#324×C2772
#1465277