Finite Group Databasebeta

← #46837411

Subgroups — #46837411

Order 34688.

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×#22576190C212yesmaximal, complemented
2C2×#22576087C212yesmaximal, complemented
3#31773802C211yesmaximal, characteristic, complemented
4#31773666C211yesmaximal, characteristic, complemented
5#537×C271C211yesmaximal, characteristic
6C22×Dic542C2211yescharacteristic
7#22576190—24no—
8#22576190—24no—
9C2×#16864644—22no—
10C2×#16864642—22no—
11C2×#16864638C2212yes—
12C2×C4×Dic271C2211yescharacteristic
13#22576087—24no—
14C271⋊#95—22no—
15C2×#41×C271C2212yes—
16C22⋊Q8×C271—22no—
17#121×C271—22no—
18#121×C271—22no—
19C2×C4⋊C4×C271C2211yescharacteristic
20C2×Dic542—22no—
21C2×Dic542—22no—
22C2×Dic542—21no—
23C2×Dic542D412yescomplemented
24C22×Dic271—21no—
25C22×Dic271—21no—
26#16864644—28no—
27#16864642—28no—
28#16864638—22no—
29#16864638D414yescomplemented
30C2×C271⋊C8—22no—
31C4×Dic271—22no—
32#41×C271—22no—
33#41×C271—22no—
34#41×C271—22no—
35#41×C271—22no—
36C2×Q8×C271D412yes—
37C2×D4×C271—22no—
38C2×D4×C271—22no—
39C2×D4×C271D412yes—
40C22×C4×C271—22no—
41C22×C4×C271D412yes—
42C22×C4×C271C2311yescharacteristic
43C4⋊C4×C271—22no—
44C4⋊C4×C271—22no—
45C22⋊C4×C271—24no—
46Dic542—24no—
47Dic542—42no—
48C2×Dic271—22no—
49C2×Dic271—22no—
50C2×Dic271—41no—
51C2×Dic271—41no—
52C2×Dic271—41no—
53C2×Dic271—41no—
54C271⋊C8—24no—
55C23×C271—22no—
56C23×C271C2×D411yescharacteristic
57Q8×C271—22no—
58Q8×C271—22no—
59D4×C271—22no—
60D4×C271—22no—
61D4×C271—42no—
62D4×C271—42no—
63D4×C271—82no—
64C2×C4×C271—22no—
65C2×C4×C271—22no—
66C2×C4×C271—42no—
67C2×C4×C271—42no—
68C2×C4×C271—42no—
69C2×C4×C271C2×D411yescharacteristic
70C2×C4×C271C2×D412yes—
71C2×C4×C271C2×D412yes—
72C2×C4×C271#4111yescharacteristic
73C22×C271—21no—
74C22×C271—21no—
75C22×C271—42no—
76C22×C271—42no—
77C22×C271—42no—
78C22×C271#12011yescharacteristic
79C22×C271#12111yescharacteristic
80C22×C271#12711yescharacteristic
81C4×C271—42no—
82C4×C271—42no—
83C4×C271#12012yes—
84C4×C271#12112yes—
85Dic271—42no—
86Dic271—42no—
87C2×C271—21no—
88C2×C271—21no—
89C2×C271—82no—
90C2×C271#39211yescharacteristic
91C2×C271#45511yescharacteristic
92C2×C271#45611yescharacteristic
93C271#200711yescharacteristic, complemented, Sylow
94#2007—2711nomaximal, Sylow
95C2×#137—2712no—
96#537D27111yescharacteristic
97C2×#104—2712no—
98#391—2711no—
99#343—2711no—
100C2×#41C2×D27112yes—
101C22×Q8—2711no—
102#137—5424no—
103#137—5424no—
104C2×Q16—5422no—
105C2×SD16—5422no—
106C2×M16—2712no—
107C22⋊Q8—22no—
108#121—22no—
109#121—22no—
110C2×C4⋊C4C2×D27111yescharacteristic
111C2×C42—2711no—
112#104—5424no—
113#95—5422no—
114#41—22no—
115#41—22no—
116#41—22no—
117#41—22no—
118C2×Q8—2712no—
119C2×Q8—5421no—
120C2×Q8—5422no—
121C2×Q8—5422no—
122C2×Q8C22⋊D27112yes—
123C2×D4—22no—
124C2×D4—22no—
125C2×D4C22⋊D27112yes—
126C22×C4—22no—
127C22×C4—5421no—
128C22×C4—5421no—
129C22×C4C22⋊D27112yes—
130C22×C4C22×D27111yescharacteristic
131Q16—5428no—
132SD16—5428no—
133M16—2714no—
134M16—5422no—
135C2×C8—5422no—
136C4⋊C4—22no—
137C4⋊C4—22no—
138C22⋊C4—24no—
139C42—5422no—
140C23—22no—
141C23C2×C22⋊D27111yescharacteristic
142Q8—22no—
143Q8—22no—
144Q8—5424no—
145Q8—10842no—
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—5422no—
157C2×C4—5422no—
158C2×C4—10841no—
159C2×C4—10841no—
160C2×C4—10841no—
161C2×C4—10841no—
162C2×C4D4×D27111yescharacteristic
163C2×C4D4×D27112yes—
164C2×C4C2×C22⋊D27112yes—
165C2×C4#1686465311yescharacteristic
166C8—5424no—
167C22—21no—
168C22—21no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22#2257612911yescharacteristic
173C22#2257613111yescharacteristic
174C22#2257615611yescharacteristic
175C4—42no—
176C4—42no—
177C4—10842no—
178C4—10842no—
179C4#2257612812yes—
180C4#2257613212yes—
181C2—21no—
182C2—21no—
183C2—82no—
184C2#3177380511yescharacteristic
185C2#3177407511yescharacteristic
186C2#3177408011yescharacteristic
subgroupG/H
centerC22#22576129
commutator, cosocleC22×C4×C271C23
FrattiniC22×C4C22×D271
Fitting, prime radical#537×C271C2
socleC22×C271#120
hypercenter#537D271
hypocenterC271#2007
LCSG ▷ C22×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#22576190C2semidirect
2. C2×#22576087C2semidirect
3. #31773802C2semidirect
4. #31773666C2semidirect
23. C2×Dic542D4semidirect
29. #16864638D4semidirect
93. C271#2007semidirect

Maximal subgroups

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

subgroupindex
C2×#225761902
C2×#225760872
#317738022
#317736662
#537×C2712
#2007271