Finite Group Databasebeta

← #46838026

Subgroups — #46838026

Order 34688.

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

normal subgroups only

This group has 258 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#31774445C211yesmaximal, characteristic
2#31773869C212yesmaximal, complemented
3#31773691C212yesmaximal, complemented
4#31773690C211yesmaximal, characteristic, complemented
5#353×C271C211yesmaximal, characteristic, complemented
6C2×#16864653C411yescharacteristic, complemented
7C2×#16864653C2211yescharacteristic
8#22576160C411yescharacteristic, complemented
9#22576147C411yescharacteristic, complemented
10#22576147C2211yescharacteristic
11#22576131—22no—
12D4×Dic271—22no—
13#22576116—22no—
14C42×D271C411yescharacteristic, complemented
15#22576075C2212yes—
16#22576074—22no—
17#127×C271C2211yescharacteristic
18#99×C271C2212yes—
19#16864653—41no—
20#16864653—41no—
21#16864653—41no—
22#16864653—41no—
23C2×Dic542C2×C411yescharacteristic
24C2×Dic542C2×C411yescharacteristic
25C2×C22⋊D271—21no—
26C2×C22⋊D271D412yes—
27C22×Dic271—21no—
28C22×Dic271D412yes—
29C2×C4×D271—21no—
30C2×C4×D271C2×C411yescharacteristic
31C4⋊Dic271—22no—
32Dic271⋊C4—42no—
33C22⋊Dic271—22no—
34C22⋊Dic271—22no—
35C22⋊Dic271—22no—
36C4×Dic271—21no—
37C4×Dic271—42no—
38C4×Dic271C2×C411yescharacteristic
39C2×D4×C271—22no—
40C2×D4×C271C2×C411yescharacteristic
41C2×D4×C271C2311yescharacteristic
42C22⋊C4×C271—22no—
43C42×C271C2×C411yescharacteristic
44C22×D271C22⋊C411yescharacteristic
45Dic542—41no—
46Dic542—41no—
47C22⋊D271—42no—
48C22⋊D271—42no—
49C2×Dic271—22no—
50C2×Dic271—22no—
51C2×Dic271—21no—
52C2×Dic271—21no—
53C2×Dic271—41no—
54C2×Dic271—41no—
55C2×Dic271—42no—
56C2×Dic271C22⋊C412yes—
57C2×Dic271C22⋊C411yescharacteristic
58C4×D271—21no—
59C4×D271—21no—
60C4×D271—42no—
61C23×C271—21no—
62C23×C271C2×D412yes—
63D4×C271—41no—
64D4×C271—41no—
65D4×C271—44no—
66C2×C4×C271—21no—
67C2×C4×C271—42no—
68C2×C4×C271C22×C411yescharacteristic
69C22×C271—22no—
70C22×C271—42no—
71C22×C271—42no—
72C22×C271—41no—
73C22×C271C2×C22⋊C411yescharacteristic
74C2×D271—21no—
75C2×D271—41no—
76C4×C271—22no—
77C4×C271—21no—
78C4×C271—82no—
79Dic271—22no—
80Dic271—41no—
81Dic271—41no—
82Dic271—82no—
83Dic271#9911yescharacteristic
84Dic271#9911yescharacteristic
85C2×C271—21no—
86C2×C271—42no—
87C2×C271—81no—
88C2×C271C2×#9911yescharacteristic
89D271—41no—
90C271#212611yescharacteristic, complemented, Sylow
91#2126—2711nomaximal, Sylow
92#532—2711no—
93#410—2712no—
94#354—2712no—
95#353—2711no—
96#353D27111yescharacteristic, complemented
97C2×#41—2711no—
98C2×#41—2711no—
99C4⋊Q8—2711no—
100#127C2×D27111yescharacteristic
101#124—2711no—
102#124—2711no—
103#121—5422no—
104C4×D4—5422no—
105#117—5422no—
106C2×C42—2711no—
107#99—2712no—
108#99—5422no—
109#99C2×D27112yes—
110#41—10841no—
111#41—10841no—
112#41—10841no—
113#41—10841no—
114C2×Q8—2711no—
115C2×Q8—2711no—
116C2×D4—22no—
117C2×D4—2712no—
118C2×D4—5421no—
119C2×D4C4×D27111yescharacteristic
120C2×D4C22×D27111yescharacteristic
121C22×C4—2712no—
122C22×C4—2711no—
123C22×C4—5421no—
124C22×C4—5421no—
125C4⋊C4—5422no—
126C4⋊C4—10842no—
127C22⋊C4—22no—
128C22⋊C4—5422no—
129C22⋊C4—5422no—
130C22⋊C4—5422no—
131C42—2711no—
132C42—5421no—
133C42—10842no—
134C42C4×D27111yescharacteristic
135C23—21no—
136C23—2711no—
137C23D4×D27112yes—
138Q8—10841no—
139Q8—10841no—
140D4—41no—
141D4—41no—
142D4—44no—
143D4—10842no—
144D4—10842no—
145C2×C4—21no—
146C2×C4—42no—
147C2×C4—2711no—
148C2×C4—2712no—
149C2×C4—5421no—
150C2×C4—5421no—
151C2×C4—5422no—
152C2×C4—5422no—
153C2×C4—5421no—
154C2×C4—5421no—
155C2×C4—10842no—
156C2×C4—10841no—
157C2×C4—10841no—
158C2×C4—10842no—
159C2×C4C2×C4×D27111yescharacteristic
160C22—22no—
161C22—42no—
162C22—42no—
163C22—41no—
164C22—5421no—
165C22—10841no—
166C22C22⋊C4×D27111yescharacteristic
167C4—22no—
168C4—21no—
169C4—82no—
170C4—2711no—
171C4—2711no—
172C4—5422no—
173C4—10841no—
174C4—10841no—
175C4—21682no—
176C2—21no—
177C2—42no—
178C2—81no—
179C2—10841no—
180C2#99×D27111yescharacteristic
subgroupG/H
centerC2#99×D271
commutatorC2×C4×C271C22×C4
FrattiniC2×D4C22×D271
Fitting#353×C271C2
socleC2×C271C2×#99
prime radical#31774445C2
cosocleC2×D4×C271C23
hypercenter#353D271
hypocenterC271#2126
LCSG ▷ C2×C4×C271 ▷ C22×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #31773869C2semidirect
3. #31773691C2semidirect
4. #31773690C2semidirect
5. #353×C271C2semidirect
6. C2×#16864653C4semidirect
8. #22576160C4semidirect
9. #22576147C4semidirect
14. C42×D271C4semidirect
90. C271#2126semidirect
96. #353D271semidirect

Maximal subgroups

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

subgroupindex
#317744452
#317738692
#317736912
#317736902
#353×C2712
#2126271