Finite Group Databasebeta

← #47985885

Subgroups — #47985885

Order 35456.

516 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 197 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×#22579878C211yesmaximal, characteristic
2C2×Q8×Dic277C211yesmaximal, characteristic
3C2×#22579845C211yesmaximal, characteristic
4#31799908C211yesmaximal, characteristic
5#31799889C214yesmaximal
6#31799884C214yesmaximal
7#31799867C211yesmaximal, characteristic
8#31799848C211yesmaximal, characteristic
9#391×C277C211yesmaximal, characteristic
10C22×Dic554C2211yescharacteristic
11#22579878C418yescomplemented
12Q8×Dic277—24no—
13#22579845—24no—
14C2×C4⋊Dic277C2211yescharacteristic
15C2×C4⋊Dic277C2212yes—
16C2×#17984542C2212yes—
17C2×#17984542C2214yes—
18C2×C4×Dic277C2212yes—
19C2×C4×Dic277C2212yes—
20C2×C4×Dic277C2211yescharacteristic
21C2×C4×Dic277C2211yescharacteristic
22#22579787C2212yes—
23#22579787C2212yes—
24#22579787C2214yes—
25#22579787C2214yes—
26C22×Q8×C277C2211yescharacteristic
27C2×C4⋊C4×C277C2211yescharacteristic
28C2×C42×C277C2211yescharacteristic
29#95×C277C2214yes—
30C2×Dic554—22no—
31C2×Dic554—22no—
32C2×Dic554C2×C414yes—
33C22×Dic277C2312yes—
34C22×Dic277C2312yes—
35C22×Dic277C2312yes—
36C22×Dic277C2311yescharacteristic
37C22×Dic277C2311yescharacteristic
38C4⋊Dic277—24no—
39C4⋊Dic277—22no—
40#17984542—24no—
41#17984542C2×C4116yes—
42C4×Dic277—24no—
43C4×Dic277—24no—
44C4×Dic277C2×C414yes—
45C4×Dic277D414yes—
46C2×Q8×C277—22no—
47C2×Q8×C277—22no—
48C2×Q8×C277C2×C414yes—
49C22×C4×C277C2312yes—
50C22×C4×C277C2312yes—
51C22×C4×C277C2312yes—
52C22×C4×C277C2311yescharacteristic
53C4⋊C4×C277—22no—
54C42×C277—22no—
55Dic554—28no—
56C2×Dic277—22no—
57C2×Dic277—22no—
58C2×Dic277—22no—
59C2×Dic277—22no—
60C2×Dic277—22no—
61C2×Dic277—22no—
62C2×Dic277—22no—
63C2×Dic277—24no—
64C2×Dic277C22×C414yes—
65C2×Dic277C22×C414yes—
66C2×Dic277C2×D412yes—
67C2×Dic277C2×D412yes—
68C23×C277C2411yescharacteristic
69Q8×C277—28no—
70C2×C4×C277—22no—
71C2×C4×C277—22no—
72C2×C4×C277—22no—
73C2×C4×C277—22no—
74C2×C4×C277—24no—
75C2×C4×C277—22no—
76C2×C4×C277—22no—
77C2×C4×C277C22×C414yes—
78C2×C4×C277C22×C412yes—
79C2×C4×C277C2×D412yes—
80C2×C4×C277#4112yes—
81C22×C277C23×C411yescharacteristic
82C22×C277C22×D411yescharacteristic
83C22×C277C2×#4111yescharacteristic
84C22×C2772−1+412yes—
85C22×C2772−1+412yes—
86C4×C277—24no—
87C4×C277—42no—
88C4×C277—42no—
89C4×C277C4×D414yes—
90Dic277—24no—
91Dic277—24no—
92Dic277—22no—
93Dic277—22no—
94Dic277—42no—
95C2×C277C2×C4×D411yescharacteristic
96C2×C277#51912yes—
97C2×C277#53611yescharacteristic
98C2×C277#53611yescharacteristic
99C2×C277#54112yes—
100C277#232711yescharacteristic, complemented, Sylow
101#2327—2771nomaximal, Sylow
102C2×C4⋊Q8—2771no—
103C2×C4×Q8—2771no—
104C2×C4×Q8—2771no—
105#391—2771no—
106#391D27711yescharacteristic
107#387—2774no—
108#387—2774no—
109#382—2771no—
110#376—2771no—
111C22×Q8—2771no—
112C22×Q8C2×D27711yescharacteristic
113C4⋊Q8—2778no—
114C4×Q8—5544no—
115C4×Q8—5544no—
116C2×C4⋊C4—2774no—
117C2×C4⋊C4—2772no—
118C2×C4⋊C4—2771no—
119C2×C4⋊C4—2772no—
120C2×C4⋊C4C2×D27711yescharacteristic
121C2×C42—2771no—
122C2×C42—2771no—
123C2×C42—2772no—
124C2×C42—2772no—
125C2×C42C2×D27711yescharacteristic
126#95—2772no—
127#95—2772no—
128#95—2774no—
129#95—2774no—
130#95C2×D27714yes—
131C2×Q8—22no—
132C2×Q8—22no—
133C2×Q8—2774no—
134C2×Q8—5542no—
135C2×Q8—5542no—
136C2×Q8C4×D27714yes—
137C22×C4—2772no—
138C22×C4—2771no—
139C22×C4—2771no—
140C22×C4—2772no—
141C22×C4—2772no—
142C22×C4C22×D27712yes—
143C22×C4C22×D27712yes—
144C22×C4C22×D27712yes—
145C22×C4C22×D27711yescharacteristic
146C4⋊C4—22no—
147C4⋊C4—27716no—
148C4⋊C4—5544no—
149C4⋊C4—5544no—
150C4⋊C4—5542no—
151C42—22no—
152C42—2774no—
153C42—2774no—
154C42—5544no—
155C42—5544no—
156C23C23×D27711yescharacteristic
157Q8—28no—
158Q8—5548no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—24no—
165C2×C4—22no—
166C2×C4—2774no—
167C2×C4—2774no—
168C2×C4—2772no—
169C2×C4—2772no—
170C2×C4—5542no—
171C2×C4—5542no—
172C2×C4—5542no—
173C2×C4—5542no—
174C2×C4—5542no—
175C2×C4—5542no—
176C2×C4—5542no—
177C2×C4—5544no—
178C2×C4C2×C4×D27714yes—
179C2×C4C2×C4×D27712yes—
180C2×C4D4×D27712yes—
181C2×C4#1798456212yes—
182C22C22×C4×D27711yescharacteristic
183C22C2×D4×D27711yescharacteristic
184C22C2×#1798456211yescharacteristic
185C22#2257992712yes—
186C22#2257992812yes—
187C4—24no—
188C4—42no—
189C4—42no—
190C4—5542no—
191C4—5544no—
192C4—5544no—
193C4—5542no—
194C4—11082no—
195C4#2257984014yes—
196C2C2×#2257984011yescharacteristic
197C2#3180047812yes—
198C2#3180057211yescharacteristic
199C2#3180057711yescharacteristic
200C2#3180061212yes—
subgroupG/H
center, FrattiniC23C23×D277
commutatorC22×C277C23×C4
Fitting#391×C277C2
socle, prime radical, cosocleC23×C277C24
hypercenter#391D277
hypocenterC277#2327
LCSG ▷ C22×C277 ▷ C277
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
11. #22579878C4semidirect
100. C277#2327semidirect

Maximal subgroups

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

subgroupindex
C2×#225798782
C2×Q8×Dic2772
C2×#225798452
#317999082
#317998892
#317998842
#317998672
#317998482
#391×C2772
#2327277