Finite Group Databasebeta

← #46838046

Subgroups — #46838046

Order 34688.

250 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 55 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#31774446C211yesmaximal, characteristic
2#31773880C212yesmaximal, complemented
3#31773695C212yesmaximal, complemented
4#31773694C211yesmaximal, characteristic, complemented
5#355×C271C211yesmaximal, characteristic, complemented
6C2×#16864655C2211yescharacteristic
7C2×#16864653C411yescharacteristic
8M16×D271—22no—
9#22576158C2211yescharacteristic
10#22576156C411yescharacteristic
11#22576148C411yescharacteristic
12#22576133—22no—
13(C22⋊D271)⋊C4—22no—
14C42×D271C411yescharacteristic
15#22576079C2212yes—
16#22576076—22no—
17#124×C271C2211yescharacteristic
18#101×C271C2212yes—
19#16864655—41no—
20#16864655—41no—
21#16864653—41no—
22#16864653—41no—
23C2×Dic542C2×C411yescharacteristic
24C2×D1084C2×C411yescharacteristic
25C2×D1084D412yes—
26C2×C22⋊D271—21no—
27C2×C22⋊D271—22no—
28C22×Dic271—21no—
29C2×C4×D271—21no—
30C2×C4×D271C2×C411yescharacteristic
31C2×C4×D271D412yes—
32#16864638—22no—
33#16864637—42no—
34C8×D271—42no—
35Dic271⋊C4—22no—
36(C2×D271)⋊C4—22no—
37C4×Dic271—21no—
38C4×Dic271C2×C411yescharacteristic
39C2×Q8×C271C2311yescharacteristic
40C2×D4×C271C2×C411yescharacteristic
41M16×C271—22no—
42C22⋊C4×C271—22no—
43C42×C271C2×C411yescharacteristic
44C22×D271C22⋊C412yes—
45C22×D271C22⋊C411yescharacteristic
46Dic542—41no—
47D1084—41no—
48D1084—42no—
49C22⋊D271—44no—
50C22⋊D271—42no—
51C2×Dic271—21no—
52C2×Dic271—21no—
53C2×Dic271—41no—
54C2×Dic271—41no—
55C2×Dic271C22⋊C411yescharacteristic
56C4×D271—22no—
57C4×D271—22no—
58C4×D271—21no—
59C4×D271—21no—
60C4×D271—42no—
61C271⋊C8—42no—
62C23×C271—21no—
63Q8×C271—41no—
64D4×C271—41no—
65C2×C4×C271—21no—
66C2×C4×C271C22×C411yescharacteristic
67C2×C4×C271C2×D412yes—
68C8×C271—42no—
69C22×C271—42no—
70C22×C271—41no—
71C22×C271C2×C22⋊C411yescharacteristic
72C2×D271—21no—
73C2×D271—22no—
74C2×D271—41no—
75C2×D271—42no—
76C4×C271—22no—
77C4×C271—21no—
78C4×C271—41no—
79Dic271—22no—
80Dic271—41no—
81Dic271#9911yescharacteristic
82Dic271#9911yescharacteristic
83C2×C271—21no—
84C2×C271—81no—
85C2×C271C2×#9911yescharacteristic
86D271—41no—
87D271—42no—
88C271#213211yescharacteristic, complemented, Sylow
89#2132—2711nomaximal, Sylow
90#532—2711no—
91#413—2712no—
92#356—2712no—
93#355—2711no—
94#355D27111yescharacteristic, complemented
95C2×#41—2711no—
96C2×#41—2711no—
97C2×M16—5422no—
98C4⋊Q8—2711no—
99#127—2711no—
100#124—2711no—
101#124C2×D27111yescharacteristic
102#121—5422no—
103C4×D4—5422no—
104C2×C42—2711no—
105#101—2712no—
106#101C2×D27112yes—
107#100—5422no—
108#41—10841no—
109#41—10841no—
110#41—10841no—
111#41—10841no—
112C2×Q8—2711no—
113C2×Q8C22×D27111yescharacteristic
114C2×D4—2711no—
115C2×D4—2712no—
116C2×D4—5422no—
117C2×D4—5421no—
118C2×D4C4×D27111yescharacteristic
119C22×C4—2711no—
120C22×C4—2712no—
121C22×C4—5421no—
122C22×C4—5421no—
123M16—22no—
124M16—5422no—
125M16—10842no—
126C2×C8—10842no—
127C4⋊C4—5422no—
128C22⋊C4—22no—
129C22⋊C4—5422no—
130C42—2711no—
131C42—5421no—
132C42C4×D27111yescharacteristic
133C23—21no—
134C23—2712no—
135C23—2711no—
136Q8—41no—
137Q8—10841no—
138D4—41no—
139D4—10842no—
140D4—10841no—
141D4—10844no—
142D4—10842no—
143C2×C4—21no—
144C2×C4—2711no—
145C2×C4—5422no—
146C2×C4—5422no—
147C2×C4—5421no—
148C2×C4—5421no—
149C2×C4—5421no—
150C2×C4—5421no—
151C2×C4—10842no—
152C2×C4—10841no—
153C2×C4—10841no—
154C2×C4C2×C4×D27111yescharacteristic
155C2×C4D4×D27112yes—
156C8—42no—
157C8—10842no—
158C22—42no—
159C22—41no—
160C22—5421no—
161C22—5422no—
162C22—10841no—
163C22—10842no—
164C22C22⋊C4×D27111yescharacteristic
165C4—22no—
166C4—21no—
167C4—41no—
168C4—2711no—
169C4—2711no—
170C4—5422no—
171C4—10841no—
172C2—21no—
173C2—81no—
174C2—10841no—
175C2—10842no—
176C2#99×D27111yescharacteristic
subgroupG/H
centerC2#99×D271
commutatorC2×C4×C271C22×C4
FrattiniC2×Q8C22×D271
Fitting#355×C271C2
socleC2×C271C2×#99
prime radical#31774446C2
cosocleC2×Q8×C271C23
hypercenter#355D271
hypocenterC271#2132
LCSG ▷ C2×C4×C271 ▷ C22×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #31773880C2semidirect
3. #31773695C2semidirect
4. #31773694C2semidirect
5. #355×C271C2semidirect
88. C271#2132semidirect
94. #355D271semidirect

Maximal subgroups

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

subgroupindex
#317744462
#317738802
#317736952
#317736942
#355×C2712
#2132271