Finite Group Databasebeta

← #46835083

Subgroups — #46835083

Order 34688.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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#31773953C211yesmaximal, characteristic, complemented
3#31773919C211yesmaximal, characteristic, complemented
4#31773644C211yesmaximal, characteristic, complemented
5#31773642C211yesmaximal, characteristic, complemented
6#31773641C211yesmaximal, characteristic, complemented
7#331×C271C211yesmaximal, characteristic, complemented
8C2×#16864653—21no—
9C2×#16864637—21no—
10#22576160C2211yescharacteristic
11#22576147—21no—
12#22576131—21no—
13#22576131C412yes—
14D4×Dic271—21no—
15D4×Dic271C412yes—
16C42×D271C2211yescharacteristic
17C4⋊(C271⋊C8)C2211yescharacteristic
18C4⋊(C271⋊C8)C2211yescharacteristic
19Dic271⋊C8—21no—
20(C2×D271)⋊C8—21no—
21#22576070—21no—
22#127×C271C2211yescharacteristic
23C4⋊C8×C271C2211yescharacteristic
24C4⋊C8×C271C2211yescharacteristic
25#16864653—42no—
26#16864653—42no—
27C2×Dic542—21no—
28C2×C22⋊D271—22no—
29C22×Dic271—22no—
30C2×C4×D271C2×C411yescharacteristic
31C2×C4×D271D411yescharacteristic
32C2×C4×D271D411yescharacteristic
33#16864637—42no—
34C2×C271⋊C8—21no—
35C2×C271⋊C8—21no—
36C4⋊Dic271—21no—
37C4⋊Dic271C2×C412yes—
38C22⋊Dic271—22no—
39C22⋊Dic271—22no—
40C4×Dic271C2×C411yescharacteristic
41C4×Dic271D411yescharacteristic
42C4×Dic271D411yescharacteristic
43C2×D4×C271—21no—
44C2×D4×C271—21no—
45C2×D4×C271C2×C412yes—
46C2×C8×C271—21no—
47C2×C8×C271—21no—
48C42×C271C2311yescharacteristic
49C22×D271C22⋊C411yescharacteristic
50Dic542—41no—
51Dic542—41no—
52C22⋊D271—44no—
53C2×Dic271—22no—
54C2×Dic271—44no—
55C2×Dic271C22⋊C411yescharacteristic
56C2×Dic271C22⋊C411yescharacteristic
57C2×Dic271C22⋊C411yescharacteristic
58C4×D271—21no—
59C4×D271—21no—
60C4×D271—21no—
61C4×D271—21no—
62C4×D271—41no—
63C271⋊C8—41no—
64C271⋊C8—41no—
65C23×C271—22no—
66D4×C271—42no—
67D4×C271—41no—
68D4×C271—41no—
69D4×C271—41no—
70D4×C271—41no—
71C2×C4×C271C22×C411yescharacteristic
72C2×C4×C271C2×D411yescharacteristic
73C2×C4×C271C2×D411yescharacteristic
74C8×C271—41no—
75C8×C271—41no—
76C22×C271—42no—
77C22×C271—42no—
78C22×C271—42no—
79C22×C271C2×C22⋊C411yescharacteristic
80C2×D271—21no—
81C2×D271—21no—
82C2×D271—21no—
83C4×C271—21no—
84C4×C271AGL(1,ℤ/8)11yescharacteristic
85C4×C271AGL(1,ℤ/8)11yescharacteristic
86C4×C271AGL(1,ℤ/8)11yescharacteristic
87C4×C271#13711yescharacteristic
88Dic271—21no—
89Dic271—21no—
90Dic271—21no—
91Dic271—42no—
92C2×C271—82no—
93C2×C271#41311yescharacteristic
94C2×C271#41711yescharacteristic
95C2×C271#41811yescharacteristic
96D271—41no—
97C271#155711yescharacteristic, complemented, Sylow
98#1557—2711nomaximal, Sylow
99#532—2711no—
100#432—2711no—
101#423—2711no—
102#332—2711no—
103#332—2711no—
104#331—2711no—
105#331D27111yescharacteristic, complemented
106C2×#41—5421no—
107C2×M16—5421no—
108C4⋊Q8—2711no—
109#127C2×D27111yescharacteristic
110#124—5421no—
111#121—2712no—
112#121—5421no—
113C4×D4—2712no—
114C4×D4—5421no—
115C2×C42—2711no—
116C4⋊C8—2711no—
117C4⋊C8—2711no—
118C4⋊C8—5421no—
119C4⋊C8C2×D27111yescharacteristic
120C4⋊C8C2×D27111yescharacteristic
121C22⋊C8—5421no—
122#97—5421no—
123#41—10842no—
124#41—10842no—
125C2×Q8—5421no—
126C2×D4—21no—
127C2×D4—21no—
128C2×D4—5422no—
129C2×D4C4×D27112yes—
130C22×C4—2711no—
131C22×C4—2711no—
132C22×C4—2711no—
133C22×C4—5422no—
134M16—10842no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—5421no—
138C2×C8—5421no—
139C4⋊C4—2712no—
140C4⋊C4—5421no—
141C22⋊C4—5422no—
142C22⋊C4—5422no—
143C42—2711no—
144C42—2711no—
145C42—2711no—
146C42C22×D27111yescharacteristic
147C23—22no—
148C23—2711no—
149Q8—10841no—
150Q8—10841no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—10844no—
157C2×C4—2711no—
158C2×C4—2711no—
159C2×C4—2711no—
160C2×C4—5421no—
161C2×C4—5421no—
162C2×C4—5421no—
163C2×C4—5421no—
164C2×C4—5422no—
165C2×C4—10841no—
166C2×C4—10844no—
167C2×C4C2×C4×D27111yescharacteristic
168C2×C4D4×D27111yescharacteristic
169C2×C4D4×D27111yescharacteristic
170C8—41no—
171C8—41no—
172C8—10841no—
173C8—10841no—
174C22—42no—
175C22—42no—
176C22—42no—
177C22—5421no—
178C22—5421no—
179C22—5421no—
180C22C22⋊C4×D27111yescharacteristic
181C4—21no—
182C4—5421no—
183C4—5421no—
184C4—5421no—
185C4—10842no—
186C4#2257618411yescharacteristic
187C4#2257618411yescharacteristic
188C4#2257618711yescharacteristic
189C4#2257618911yescharacteristic
190C2—82no—
191C2—10841no—
192C2#3177387811yescharacteristic
193C2#3177389511yescharacteristic
194C2#3177390011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D271
commutatorC2×C4×C271C22×C4
FrattiniC42C22×D271
Fitting#331×C271C2
socleC22×C271C2×C22⋊C4
prime radical#31774445C2
cosocleC42×C271C23
hypercenter#331D271
hypocenterC271#1557
LCSG ▷ C2×C4×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #31773953C2semidirect
3. #31773919C2semidirect
4. #31773644C2semidirect
5. #31773642C2semidirect
6. #31773641C2semidirect
7. #331×C271C2semidirect
97. C271#1557semidirect
105. #331D271semidirect

Maximal subgroups

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

subgroupindex
#317744452
#317739532
#317739192
#317736442
#317736422
#317736412
#331×C2712
#1557271