Finite Group Databasebeta

← #47983128

Subgroups — #47983128

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×#22579806C212yesmaximal, complemented
3#31800004C212yesmaximal, complemented
4#31799909C211yesmaximal, characteristic, complemented
5C2×#101×C277C211yesmaximal, characteristic, complemented
6#22579928—24no—
7#22579928—22no—
8#22579928C414yescomplemented
9C2×#17984564—22no—
10C2×#17984563—22no—
11C2×#17984563C2212yes—
12C2×Q8×D277—22no—
13C2×C4⋊Dic277C2211yescharacteristic
14C2×C4×Dic277C2211yescharacteristic
15#22579806—24no—
16#22579805—22no—
17#22579802—22no—
18#22579787—22no—
19C22×Q8×C277C2211yescharacteristic
20C2×M16×C277C2212yes—
21#101×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—
37C22×Dic277—21no—
38C22×Dic277—21no—
39C2×C4×D277—24no—
40C2×C4×D277—22no—
41C4⋊Dic277—22no—
42C4×Dic277—22no—
43C2×Q8×C277—22no—
44C2×Q8×C277—22no—
45C2×Q8×C277C2×C412yes—
46C2×Q8×C277D412yes—
47C22×C4×C277D412yes—
48C22×C4×C277C2311yescharacteristic
49M16×C277—22no—
50M16×C277—22no—
51C2×C8×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—
62C2×Dic277—22no—
63C2×Dic277—41no—
64C2×Dic277—41no—
65C2×Dic277—42no—
66C2×Dic277—41no—
67C4×D277—216no—
68C4×D277—24no—
69C4×D277—24no—
70C23×C277C2×D411yescharacteristic
71Q8×C277—24no—
72Q8×C277—24no—
73C2×C4×C277—22no—
74C2×C4×C277—22no—
75C2×C4×C277C22⋊C414yes—
76C2×C4×C277C22×C411yescharacteristic
77C2×C4×C277C2×D412yes—
78C2×C4×C277C2×D412yes—
79C2×C4×C277C2×D411yescharacteristic
80C8×C277—42no—
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×C277C2×C22⋊C412yes—
91C4×C277#12012yes—
92Dic277—24no—
93Dic277—42no—
94Dic277—81no—
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×#101D27711yescharacteristic, complemented
107#391—2771no—
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×M16C2×D27712yes—
117C2×C4⋊C4—2771no—
118C2×C42—2771no—
119#104—5544no—
120#103—5542no—
121#102—5542no—
122#101—22no—
123#95—5542no—
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×Q8C22⋊D27712yes—
140C2×D4—2772no—
141C2×D4—5542no—
142C2×D4—5542no—
143C22×C4—5544no—
144C22×C4—5542no—
145C22×C4—5541no—
146C22×C4—5541no—
147C22×C4D110812yes—
148C22×C4C22×D27711yescharacteristic
149M16—22no—
150M16—22no—
151C2×C8—22no—
152C4⋊C4—5542no—
153C42—5542no—
154C23—5542no—
155C23C2×D110811yescharacteristic
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—55416no—
169C2×C4—5542no—
170C2×C4—5544no—
171C2×C4—5544no—
172C2×C4—5542no—
173C2×C4—11081no—
174C2×C4—11081no—
175C2×C4—11082no—
176C2×C4—11081no—
177C2×C4#1798454014yes—
178C2×C4C2×C4×D27711yescharacteristic
179C2×C4D4×D27712yes—
180C2×C4D4×D27712yes—
181C2×C4C2×C22⋊D27711yescharacteristic
182C8—42no—
183C22—21no—
184C22—21no—
185C22—5544no—
186C22—11082no—
187C22—11082no—
188C22C2×#1798454011yescharacteristic
189C22#2257985011yescharacteristic
190C22#2257985011yescharacteristic
191C4—24no—
192C4—5544no—
193C4—11082no—
194C4—22161no—
195C4C22⋊C4×D27712yes—
196C4#2257984812yes—
197C2—21no—
198C2—21no—
199C2—11084no—
200C2#3179985711yescharacteristic
201C2#3180017711yescharacteristic
202C2#3180018711yescharacteristic
subgroupG/H
centerC22#22579850
commutatorC2×C4×C277C22×C4
FrattiniC22×C4C22×D277
FittingC2×#101×C277C2
socleC22×C277#120
prime radicalC2×#22579928C2
cosocleC22×C4×C277C23
hypercenterC2×#101D277
hypocenterC277#1793
LCSG ▷ C2×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#22579806C2semidirect
3. #31800004C2semidirect
4. #31799909C2semidirect
5. C2×#101×C277C2semidirect
8. #22579928C4semidirect
101. C277#1793semidirect
106. C2×#101D277semidirect

Maximal subgroups

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

subgroupindex
C2×#225799282
C2×#225798062
#318000042
#317999092
C2×#101×C2772
#1793277