Finite Group Databasebeta

← #47983125

Subgroups — #47983125

Order 35456.

552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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×#22579928C211yesmaximal, characteristic
2C2×#22579808C212yesmaximal, complemented
3#31800001C212yesmaximal, complemented
4C2×#22579799C211yesmaximal, characteristic, complemented
5#391×C277C211yesmaximal, characteristic, complemented
6#22579928—24no—
7#22579928—22no—
8#22579928C414yescomplemented
9C2×#17984564—22no—
10C2×#17984563—22no—
11C2×#17984563C2212yes—
12C2×Q8×D277—22no—
13C2×#17984547C2212yes—
14#22579808—24no—
15#22579803—22no—
16#22579800—22no—
17#22579799—22no—
18C22×Q8×C277C2211yescharacteristic
19C2×C4⋊C4×C277C2211yescharacteristic
20C2×C42×C277C2211yescharacteristic
21#95×C277—22no—
22#17984564—28no—
23#17984564—28no—
24#17984563—28no—
25#17984563—28no—
26#17984563—22no—
27#17984563—22no—
28#17984563C2×C414yes—
29#17984563D414yes—
30C2×Dic554—22no—
31C2×Dic554D412yes—
32Q8×D277—28no—
33Q8×D277—28no—
34C2×D1108—22no—
35C2×D1108D412yes—
36C2×C22⋊D277—22no—
37C2×C4×D277—24no—
38C2×C4×D277—22no—
39#17984547—22no—
40#17984547—22no—
41C2×#14555660—22no—
42C2×Q8×C277—22no—
43C2×Q8×C277—22no—
44C2×Q8×C277C2×C412yes—
45C2×Q8×C277D412yes—
46C22×C4×C277—21no—
47C22×C4×C277—21no—
48C22×C4×C277D412yes—
49C22×C4×C277C2311yescharacteristic
50C4⋊C4×C277—22no—
51C42×C277—22no—
52C22×D277—22no—
53Dic554—28no—
54Dic554—22no—
55Dic554C22⋊C414yes—
56D1108—28no—
57D1108—22no—
58D1108C22⋊C414yes—
59C22⋊D277—24no—
60C22⋊D277—24no—
61C2×Dic277—22no—
62C4×D277—216no—
63C4×D277—24no—
64C4×D277—24no—
65#14555660—42no—
66C23×C277C2×D411yescharacteristic
67Q8×C277—24no—
68Q8×C277—24no—
69C2×C4×C277—22no—
70C2×C4×C277—22no—
71C2×C4×C277—22no—
72C2×C4×C277—41no—
73C2×C4×C277—41no—
74C2×C4×C277—42no—
75C2×C4×C277—41no—
76C2×C4×C277C22⋊C414yes—
77C2×C4×C277C22×C411yescharacteristic
78C2×C4×C277C2×D412yes—
79C2×C4×C277C2×D412yes—
80C2×C4×C277C2×D411yescharacteristic
81C22×C277—21no—
82C22×C277—21no—
83C22×C277C2×C22⋊C411yescharacteristic
84C22×C277#12011yescharacteristic
85C22×C277#12011yescharacteristic
86C2×D277—24no—
87C2×D277—42no—
88C2×D277—42no—
89C4×C277—24no—
90C4×C277—42no—
91C4×C277—81no—
92C4×C277C2×C22⋊C412yes—
93C4×C277#12012yes—
94Dic277—24no—
95C2×C277—21no—
96C2×C277—21no—
97C2×C277#37911yescharacteristic
98C2×C277#45411yescharacteristic
99C2×C277#45611yescharacteristic
100D277—44no—
101C277#179311yescharacteristic, complemented, Sylow
102#1793—2771nomaximal, Sylow
103C2×2−1+4—2771no—
104C2×#104—2772no—
105#417—2772no—
106C2×#101—2771no—
107#391D27711yescharacteristic, complemented
1082−1+4—2774no—
1092−1+4—5544no—
1102−1+4—5542no—
111C2×#41—2772no—
112C2×#41—5542no—
113C2×#41—5542no—
114C22×Q8—5542no—
115C22×Q8C2×D27711yescharacteristic
116C2×M16—2772no—
117C2×C4⋊C4C2×D27711yescharacteristic
118C2×C42C2×D27711yescharacteristic
119#104—5544no—
120#103—5542no—
121#102—5542no—
122#101—5542no—
123#95—22no—
124#41—2774no—
125#41—2774no—
126#41—5548no—
127#41—5548no—
128#41—5548no—
129#41—5548no—
130#41—5542no—
131#41—5542no—
132C2×Q8—22no—
133C2×Q8—22no—
134C2×Q8—2772no—
135C2×Q8—5542no—
136C2×Q8—5548no—
137C2×Q8—5548no—
138C2×Q8C4×D27712yes—
139C2×Q8D110812yes—
140C2×D4—2772no—
141C2×D4—5542no—
142C2×D4—5542no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—5544no—
146C22×C4—5542no—
147C22×C4C22⋊D27712yes—
148C22×C4C22×D27711yescharacteristic
149M16—5542no—
150M16—5542no—
151C2×C8—5542no—
152C4⋊C4—22no—
153C42—22no—
154C23—5542no—
155C23C2×C22⋊D27711yescharacteristic
156Q8—24no—
157Q8—24no—
158Q8—2774no—
159Q8—5548no—
160Q8—5542no—
161D4—2774no—
162D4—5548no—
163D4—5544no—
164D4—5544no—
165D4—5542no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—42no—
172C2×C4—41no—
173C2×C4—55416no—
174C2×C4—5542no—
175C2×C4—5544no—
176C2×C4—5544no—
177C2×C4#1798454014yes—
178C2×C4C2×C4×D27711yescharacteristic
179C2×C4D4×D27712yes—
180C2×C4D4×D27712yes—
181C2×C4C2×D110811yescharacteristic
182C8—11082no—
183C22—21no—
184C22—21no—
185C22—5544no—
186C22—11082no—
187C22—11082no—
188C22C2×#1798454011yescharacteristic
189C22#2257984811yescharacteristic
190C22#2257984811yescharacteristic
191C4—24no—
192C4—42no—
193C4—81no—
194C4—5544no—
195C4C22⋊C4×D27712yes—
196C4#2257985012yes—
197C2—21no—
198C2—21no—
199C2—11084no—
200C2#3179985711yescharacteristic
201C2#3180017411yescharacteristic
202C2#3180018411yescharacteristic
subgroupG/H
centerC22#22579848
commutatorC2×C4×C277C22×C4
FrattiniC22×C4C22×D277
Fitting#391×C277C2
socleC22×C277#120
prime radicalC2×#22579928C2
cosocleC22×C4×C277C23
hypercenter#391D277
hypocenterC277#1793
LCSG ▷ C2×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
2. C2×#22579808C2semidirect
3. #31800001C2semidirect
4. C2×#22579799C2semidirect
5. #391×C277C2semidirect
8. #22579928C4semidirect
101. C277#1793semidirect
107. #391D277semidirect

Maximal subgroups

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

subgroupindex
C2×#225799282
C2×#225798082
#318000012
C2×#225797992
#391×C2772
#1793277