Finite Group Databasebeta

← #46834848

Subgroups — #46834848

Order 34688.

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

normal subgroups only

This group has 238 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
1#31774431C211yesmaximal, characteristic
2#31773950C211yesmaximal, characteristic, complemented
3#31773633C212yesmaximal, complemented
4#31773630C212yesmaximal
5#376×C271C211yesmaximal, characteristic, complemented
6#22576154—21no—
7#22576152C411yescharacteristic, complemented
8#22576148C411yescharacteristic, complemented
9#22576143—21no—
10#22576139C2211yescharacteristic
11#22576134C2211yescharacteristic
12C4×Dic542C411yescharacteristic, complemented
13C4×D1084C411yescharacteristic, complemented
14C4×C22⋊D271—21no—
15#22576117—21no—
16C4⋊(C271⋊C8)—21no—
17C22⋊(C271⋊C8)C2212yes—
18C4×C271⋊C8—21no—
19C2×C42×C271—21no—
20C2×C42×C271C2211yescharacteristic
21#95×C271—21no—
22#95×C271C2212yes—
23C2×Dic542C2×C411yescharacteristic
24C2×D1084C2×C411yescharacteristic
25C2×C22⋊D271—21no—
26C2×C4×D271—21no—
27C2×C271⋊C8—22no—
28C4⋊Dic271C2×C411yescharacteristic
29C4⋊Dic271C2×C411yescharacteristic
30Dic271⋊C4—21no—
31Dic271⋊C4—21no—
32Dic271⋊C4—21no—
33Dic271⋊C4—21no—
34C22⋊Dic271—21no—
35(C2×D271)⋊C4—21no—
36(C2×D271)⋊C4—21no—
37(C2×D271)⋊C4—21no—
38(C2×D271)⋊C4—21no—
39C4×Dic271—21no—
40C22×C4×C271—22no—
41C22×C4×C271D411yescharacteristic
42C22×C4×C271D411yescharacteristic
43C22×C4×C271C2311yescharacteristic
44C42×C271—24no—
45C42×C271C2×C411yescharacteristic
46C42×C271C2×C411yescharacteristic
47C42×C271D411yescharacteristic
48C42×C271D411yescharacteristic
49C22×D271—21no—
50Dic542—41no—
51D1084—41no—
52C22⋊D271—42no—
53C2×Dic271—21no—
54C2×Dic271—21no—
55C2×Dic271—21no—
56C4×D271—42no—
57C271⋊C8—42no—
58C23×C271C2×D411yescharacteristic
59C2×C4×C271—22no—
60C2×C4×C271—22no—
61C2×C4×C271—24no—
62C2×C4×C271—41no—
63C2×C4×C271—42no—
64C2×C4×C271—42no—
65C2×C4×C271C22⋊C411yescharacteristic
66C2×C4×C271C22⋊C411yescharacteristic
67C2×C4×C271C22⋊C411yescharacteristic
68C2×C4×C271C22⋊C411yescharacteristic
69C2×C4×C271C22×C411yescharacteristic
70C2×C4×C271C2×D411yescharacteristic
71C22×C271—21no—
72C22×C271—21no—
73C22×C271C2×C22⋊C411yescharacteristic
74C22×C271#13512yes—
75C2×D271—41no—
76C2×D271—41no—
77C2×D271—41no—
78C4×C271—21no—
79C4×C271—21no—
80C4×C271—21no—
81C4×C271—21no—
82C4×C271—21no—
83C4×C271—44no—
84C4×C271#10412yes—
85Dic271—41no—
86Dic271—41no—
87Dic271—41no—
88C2×C271—22no—
89C2×C271#41011yescharacteristic
90C2×C271#41611yescharacteristic
91C2×C271C2×#10411yescharacteristic
92D271—81no—
93C271#150011yescharacteristic, complemented, Sylow
94#1500—2711nomaximal, Sylow
95#529—2711no—
96#431—2711no—
97#376D27111yescharacteristic, complemented
98#328—2712no—
99#327—2712no—
100#126—5421no—
101#125—2711no—
102#124—2711no—
103#123—5421no—
104C22⋊Q8—2711no—
105#121—2711no—
106C4×Q8—2711no—
107C4×D4—2711no—
108C4×D4—5421no—
109#117—5421no—
110C2×C42—21no—
111C2×C42C2×D27111yescharacteristic
112C4⋊C8—5421no—
113C22⋊C8—2712no—
114C4×C8—5421no—
115#95—21no—
116#95C2×D27112yes—
117C2×Q8—2711no—
118C2×D4—2711no—
119C2×D4—5421no—
120C22×C4—22no—
121C22×C4—5421no—
122C22×C4C22⋊D27111yescharacteristic
123C22×C4C22⋊D27111yescharacteristic
124C22×C4C22×D27111yescharacteristic
125C2×C8—5422no—
126C4⋊C4—2711no—
127C4⋊C4—2711no—
128C4⋊C4—5421no—
129C4⋊C4—5421no—
130C4⋊C4—5421no—
131C4⋊C4—5421no—
132C22⋊C4—5421no—
133C22⋊C4—5421no—
134C22⋊C4—5421no—
135C22⋊C4—5421no—
136C22⋊C4—5421no—
137C42—24no—
138C42—5421no—
139C42C4×D27111yescharacteristic
140C42C4×D27111yescharacteristic
141C42D108411yescharacteristic
142C42D108411yescharacteristic
143C23—5421no—
144C23C2×C22⋊D27111yescharacteristic
145Q8—10841no—
146D4—10841no—
147D4—10842no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—24no—
151C2×C4—41no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4—5421no—
155C2×C4—5421no—
156C2×C4—5421no—
157C2×C4—10842no—
158C2×C4(C2×D271)⋊C411yescharacteristic
159C2×C4(C2×D271)⋊C411yescharacteristic
160C2×C4(C2×D271)⋊C411yescharacteristic
161C2×C4(C2×D271)⋊C411yescharacteristic
162C2×C4C2×C4×D27111yescharacteristic
163C2×C4C2×D108411yescharacteristic
164C8—10842no—
165C22—21no—
166C22—21no—
167C22—10841no—
168C22—10841no—
169C22—10841no—
170C22C2×(C2×D271)⋊C411yescharacteristic
171C22#2257618012yes—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—44no—
178C4—10841no—
179C4—10841no—
180C4—10841no—
181C4#2257608812yes—
182C2—22no—
183C2—21681no—
184C2#3177387011yescharacteristic
185C2#3177389111yescharacteristic
186C2C2×#2257608811yescharacteristic
subgroupG/H
centerC2×C4(C2×D271)⋊C4
commutatorC2×C4×C271C22×C4
FrattiniC22×C4C22×D271
Fitting#376×C271C2
socleC22×C271C2×C22⋊C4
prime radical#22576134C22
cosocleC22×C4×C271C23
hypercenter#376D271
hypocenterC271#1500
LCSG ▷ C2×C4×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
2. #31773950C2semidirect
3. #31773633C2semidirect
5. #376×C271C2semidirect
7. #22576152C4semidirect
8. #22576148C4semidirect
12. C4×Dic542C4semidirect
13. C4×D1084C4semidirect
93. C271#1500semidirect
97. #376D271semidirect

Maximal subgroups

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

subgroupindex
#317744312
#317739502
#317736332
#317736302
#376×C2712
#1500271