Finite Group Databasebeta

← #47984213

Subgroups — #47984213

Order 35456.

370 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 73 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×#22579911C212yesmaximal, complemented
2#31800583C211yesmaximal, characteristic
3C2×#22579808C212yesmaximal, complemented
4#31799771C211yesmaximal, characteristic, complemented
5#391×C277C211yesmaximal, characteristic, complemented
6C2×#17984563C2212yes—
7#22579911—24no—
8#22579911—24no—
9C2×#17984553—22no—
10C2×#17984550—22no—
11C2×#17984547C2212yes—
12#22579860—22no—
13#22579855—22no—
14#22579854—22no—
15#22579808—24no—
16C22×Q8×C277C2211yescharacteristic
17C2×C4⋊C4×C277C2211yescharacteristic
18C2×C42×C277C2211yescharacteristic
19#95×C277—22no—
20#17984563—22no—
21#17984563—22no—
22#17984563—22no—
23#17984563—22no—
24C2×Dic554D412yes—
25C2×D1108—22no—
26C2×D1108D412yes—
27C2×C22⋊D277—22no—
28C2×C4×D277—22no—
29#17984553—28no—
30#17984550—28no—
31#17984547—22no—
32#17984547D414yescomplemented
33C2×#14555660—22no—
34C4⋊Dic277—22no—
35#17984540—24no—
36C2×Q8×C277—21no—
37C2×Q8×C277—22no—
38C2×Q8×C277—22no—
39C2×Q8×C277D412yescomplemented
40C22×C4×C277—21no—
41C22×C4×C277—21no—
42C22×C4×C277D412yes—
43C22×C4×C277C2311yescharacteristic
44C4⋊C4×C277—22no—
45C42×C277—22no—
46C22×D277—22no—
47Dic554—22no—
48Dic554—22no—
49D1108—22no—
50D1108—22no—
51D1108—82no—
52C22⋊D277—42no—
53C22⋊D277—42no—
54C2×Dic277—22no—
55C4×D277—42no—
56C4×D277—42no—
57#14555660—24no—
58C23×C277C2×D411yescharacteristic
59Q8×C277—24no—
60Q8×C277—42no—
61C2×C4×C277—22no—
62C2×C4×C277—22no—
63C2×C4×C277—22no—
64C2×C4×C277—41no—
65C2×C4×C277—41no—
66C2×C4×C277—41no—
67C2×C4×C277—41no—
68C2×C4×C277—42no—
69C2×C4×C277C2×D412yes—
70C2×C4×C277C2×D412yes—
71C2×C4×C277C2×D411yescharacteristic
72C2×C4×C277#4111yescharacteristic
73C22×C277—21no—
74C22×C277—21no—
75C22×C277#12011yescharacteristic
76C22×C277#12111yescharacteristic
77C22×C277#12711yescharacteristic
78C2×D277—42no—
79C2×D277—42no—
80C2×D277—42no—
81C4×C277—42no—
82C4×C277—42no—
83C4×C277—42no—
84C4×C277#12012yes—
85C4×C277#12112yes—
86Dic277—42no—
87C2×C277—21no—
88C2×C277—21no—
89C2×C277#39211yescharacteristic
90C2×C277#45511yescharacteristic
91C2×C277#45611yescharacteristic
92D277—82no—
93C277#200711yescharacteristic, complemented, Sylow
94#2007—2771nomaximal, Sylow
95C2×#137—2772no—
96#537—2771no—
97C2×#104—2772no—
98#391D27711yescharacteristic, complemented
99#343—2771no—
100C2×#41—2772no—
101C22×Q8C2×D27711yescharacteristic
102#137—5544no—
103#137—5544no—
104C2×Q16—5542no—
105C2×SD16—5542no—
106C2×M16—2772no—
107C22⋊Q8—5542no—
108#121—5542no—
109#121—5542no—
110C2×C4⋊C4C2×D27711yescharacteristic
111C2×C42C2×D27711yescharacteristic
112#104—5544no—
113#95—22no—
114#41—5542no—
115#41—5542no—
116#41—5542no—
117#41—5542no—
118C2×Q8—21no—
119C2×Q8—22no—
120C2×Q8—22no—
121C2×Q8—2772no—
122C2×Q8D110812yescomplemented
123C2×D4—2772no—
124C2×D4—5542no—
125C2×D4—5542no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—5542no—
129C22×C4C22⋊D27712yes—
130C22×C4C22×D27711yescharacteristic
131Q16—5548no—
132SD16—5548no—
133M16—2774no—
134M16—5542no—
135C2×C8—5542no—
136C4⋊C4—22no—
137C4⋊C4—5542no—
138C22⋊C4—5544no—
139C42—22no—
140C23—5542no—
141C23C2×C22⋊D27711yescharacteristic
142Q8—24no—
143Q8—42no—
144Q8—5542no—
145Q8—5542no—
146D4—5542no—
147D4—5542no—
148D4—11082no—
149D4—11082no—
150D4—22162no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—42no—
159C2×C4—5542no—
160C2×C4—11082no—
161C2×C4—11082no—
162C2×C4D4×D27712yes—
163C2×C4D4×D27712yes—
164C2×C4C2×D110811yescharacteristic
165C2×C4#1798456311yescharacteristic
166C8—5544no—
167C22—21no—
168C22—21no—
169C22—11082no—
170C22—11082no—
171C22—11082no—
172C22#2257984811yescharacteristic
173C22#2257985411yescharacteristic
174C22#2257987611yescharacteristic
175C4—42no—
176C4—42no—
177C4—42no—
178C4—11082no—
179C4#2257985012yes—
180C4#2257985312yes—
181C2—21no—
182C2—21no—
183C2—22162no—
184C2#3179991111yescharacteristic
185C2#3180017911yescharacteristic
186C2#3180018411yescharacteristic
subgroupG/H
centerC22#22579848
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
Fitting#391×C277C2
socleC22×C277#120
prime radical#31800583C2
hypercenter#391D277
hypocenterC277#2007
LCSG ▷ C22×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#22579911C2semidirect
3. C2×#22579808C2semidirect
4. #31799771C2semidirect
5. #391×C277C2semidirect
32. #17984547D4semidirect
39. C2×Q8×C277D4semidirect
93. C277#2007semidirect
98. #391D277semidirect
122. C2×Q8D1108semidirect

Maximal subgroups

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

subgroupindex
C2×#225799112
#318005832
C2×#225798082
#317997712
#391×C2772
#2007277