Finite Group Databasebeta

← #47984214

Subgroups — #47984214

Order 35456.

370 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 75 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×#22579910C212yesmaximal, complemented
2C2×#22579807C212yesmaximal, complemented
3#31799907C211yesmaximal, characteristic, complemented
4#31799771C211yesmaximal, characteristic, complemented
5#537×C277C211yesmaximal, characteristic
6C22×Dic554C2211yescharacteristic
7#22579910—24no—
8#22579910—24no—
9C2×#17984553—22no—
10C2×#17984551—22no—
11C2×#17984547C2212yes—
12C2×C4×Dic277C2211yescharacteristic
13#22579807—24no—
14#22579787—22no—
15C2×#41×C277C2212yes—
16C22⋊Q8×C277—22no—
17#121×C277—22no—
18#121×C277—22no—
19C2×C4⋊C4×C277C2211yescharacteristic
20C2×Dic554—22no—
21C2×Dic554—22no—
22C2×Dic554—21no—
23C2×Dic554D412yescomplemented
24C22×Dic277—21no—
25C22×Dic277—21no—
26#17984553—28no—
27#17984551—28no—
28#17984547—22no—
29#17984547D414yescomplemented
30C2×#14555660—22no—
31C4×Dic277—22no—
32#41×C277—22no—
33#41×C277—22no—
34#41×C277—22no—
35#41×C277—22no—
36C2×Q8×C277D412yes—
37C2×D4×C277—22no—
38C2×D4×C277—22no—
39C2×D4×C277D412yes—
40C22×C4×C277—22no—
41C22×C4×C277D412yes—
42C22×C4×C277C2311yescharacteristic
43C4⋊C4×C277—22no—
44C4⋊C4×C277—22no—
45C22⋊C4×C277—24no—
46Dic554—24no—
47Dic554—42no—
48C2×Dic277—22no—
49C2×Dic277—22no—
50C2×Dic277—41no—
51C2×Dic277—41no—
52C2×Dic277—41no—
53C2×Dic277—41no—
54#14555660—24no—
55C23×C277—22no—
56C23×C277C2×D411yescharacteristic
57Q8×C277—22no—
58Q8×C277—22no—
59D4×C277—22no—
60D4×C277—22no—
61D4×C277—42no—
62D4×C277—42no—
63D4×C277—82no—
64C2×C4×C277—22no—
65C2×C4×C277—22no—
66C2×C4×C277—42no—
67C2×C4×C277—42no—
68C2×C4×C277—42no—
69C2×C4×C277C2×D411yescharacteristic
70C2×C4×C277C2×D412yes—
71C2×C4×C277C2×D412yes—
72C2×C4×C277#4111yescharacteristic
73C22×C277—21no—
74C22×C277—21no—
75C22×C277—42no—
76C22×C277—42no—
77C22×C277—42no—
78C22×C277#12011yescharacteristic
79C22×C277#12111yescharacteristic
80C22×C277#12711yescharacteristic
81C4×C277—42no—
82C4×C277—42no—
83C4×C277#12012yes—
84C4×C277#12112yes—
85Dic277—42no—
86Dic277—42no—
87C2×C277—21no—
88C2×C277—21no—
89C2×C277—82no—
90C2×C277#39211yescharacteristic
91C2×C277#45511yescharacteristic
92C2×C277#45611yescharacteristic
93C277#200711yescharacteristic, complemented, Sylow
94#2007—2771nomaximal, Sylow
95C2×#137—2772no—
96#537D27711yescharacteristic
97C2×#104—2772no—
98#391—2771no—
99#343—2771no—
100C2×#41C2×D27712yes—
101C22×Q8—2771no—
102#137—5544no—
103#137—5544no—
104C2×Q16—5542no—
105C2×SD16—5542no—
106C2×M16—2772no—
107C22⋊Q8—22no—
108#121—22no—
109#121—22no—
110C2×C4⋊C4C2×D27711yescharacteristic
111C2×C42—2771no—
112#104—5544no—
113#95—5542no—
114#41—22no—
115#41—22no—
116#41—22no—
117#41—22no—
118C2×Q8—2772no—
119C2×Q8—5541no—
120C2×Q8—5542no—
121C2×Q8—5542no—
122C2×Q8C22⋊D27712yes—
123C2×D4—22no—
124C2×D4—22no—
125C2×D4C22⋊D27712yes—
126C22×C4—22no—
127C22×C4—5541no—
128C22×C4—5541no—
129C22×C4C22⋊D27712yes—
130C22×C4C22×D27711yescharacteristic
131Q16—5548no—
132SD16—5548no—
133M16—2774no—
134M16—5542no—
135C2×C8—5542no—
136C4⋊C4—22no—
137C4⋊C4—22no—
138C22⋊C4—24no—
139C42—5542no—
140C23—22no—
141C23C2×C22⋊D27711yescharacteristic
142Q8—22no—
143Q8—22no—
144Q8—5544no—
145Q8—11082no—
146D4—22no—
147D4—22no—
148D4—42no—
149D4—42no—
150D4—82no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—42no—
156C2×C4—5542no—
157C2×C4—5542no—
158C2×C4—11081no—
159C2×C4—11081no—
160C2×C4—11081no—
161C2×C4—11081no—
162C2×C4D4×D27711yescharacteristic
163C2×C4D4×D27712yes—
164C2×C4C2×C22⋊D27712yes—
165C2×C4#1798456211yescharacteristic
166C8—5544no—
167C22—21no—
168C22—21no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22#2257984911yescharacteristic
173C22#2257985111yescharacteristic
174C22#2257987611yescharacteristic
175C4—42no—
176C4—42no—
177C4—11082no—
178C4—11082no—
179C4#2257984812yes—
180C4#2257985212yes—
181C2—21no—
182C2—21no—
183C2—82no—
184C2#3179991011yescharacteristic
185C2#3180018011yescharacteristic
186C2#3180018511yescharacteristic
subgroupG/H
centerC22#22579849
commutator, cosocleC22×C4×C277C23
FrattiniC22×C4C22×D277
Fitting, prime radical#537×C277C2
socleC22×C277#120
hypercenter#537D277
hypocenterC277#2007
LCSG ▷ C22×C4×C277 ▷ C2×C277 ▷ C277
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#22579910C2semidirect
2. C2×#22579807C2semidirect
3. #31799907C2semidirect
4. #31799771C2semidirect
23. C2×Dic554D4semidirect
29. #17984547D4semidirect
93. C277#2007semidirect

Maximal subgroups

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

subgroupindex
C2×#225799102
C2×#225798072
#317999072
#317997712
#537×C2772
#2007277