Finite Group Databasebeta

← #46835433

Subgroups — #46835433

Order 34688.

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

normal subgroups only

This group has 236 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#31774608C211yesmaximal, characteristic, complemented
2#31774094C211yesmaximal, characteristic, complemented
3#31774089C211yesmaximal, characteristic
4#31773646C211yesmaximal, characteristic, complemented
5#31773629C211yesmaximal, characteristic, complemented
6#31773626C211yesmaximal, characteristic, complemented
7#492×C271C211yesmaximal, characteristic, complemented
8C2×#16864642—21no—
9C2×#16864639—21no—
10#22576151—21no—
11#22576140—21no—
12#22576136—22no—
13C4×Dic542C2211yescharacteristic
14C4×D1084C2211yescharacteristic
15#22576122—21no—
16C4⋊C4×D271—21no—
17C4⋊(C271⋊C8)C2211yescharacteristic
18C4⋊(C271⋊C8)C2211yescharacteristic
19#22576081—21no—
20#22576081—21no—
21C2×SD16×C271—22no—
22C4⋊Q8×C271C2211yescharacteristic
23#127×C271C2211yescharacteristic
24C4×C8×C271C2211yescharacteristic
25C2×Dic542D411yescharacteristic
26C2×D1084D411yescharacteristic
27C2×C4×D271—22no—
28C2×C4×D271—21no—
29#16864642—42no—
30#16864639—42no—
31C2×C271⋊C8—21no—
32C2×C271⋊C8—21no—
33C4⋊Dic271—22no—
34C4⋊Dic271D411yescharacteristic
35C4⋊Dic271D411yescharacteristic
36Dic271⋊C4—22no—
37Dic271⋊C4—21no—
38(C2×D271)⋊C4—22no—
39(C2×D271)⋊C4—21no—
40C4×Dic271—21no—
41C2×Q8×C271D412yes—
42C2×D4×C271—21no—
43C2×D4×C271—21no—
44C2×D4×C271—21no—
45SD16×C271—44no—
46C2×C8×C271—21no—
47C4⋊C4×C271—21no—
48C4⋊C4×C271—21no—
49C42×C271C2311yescharacteristic
50C22×D271—21no—
51Dic542—21no—
52Dic542—21no—
53D1084—21no—
54D1084SD1612yescomplemented
55C2×Dic271—21no—
56C2×Dic271—21no—
57C2×Dic271—21no—
58C4×D271—41no—
59C4×D271—41no—
60C4×D271—82no—
61C271⋊C8—41no—
62C271⋊C8—41no—
63C23×C271—41no—
64Q8×C271—42no—
65D4×C271—42no—
66D4×C271—41no—
67D4×C271—41no—
68D4×C271—41no—
69D4×C271—41no—
70C2×C4×C271—22no—
71C2×C4×C271C2×D411yescharacteristic
72C2×C4×C271C2×D411yescharacteristic
73C2×C4×C271C2×D411yescharacteristic
74C8×C271—22no—
75C22×C271—81no—
76C22×C271—81no—
77C22×C271—81no—
78C22×C271#12011yescharacteristic
79C2×D271—22no—
80C2×D271—41no—
81C2×D271—41no—
82C4×C271—21no—
83C4×C271—42no—
84C4×C271C2×SD1611yescharacteristic
85C4×C271#13511yescharacteristic
86C4×C271AGL(1,ℤ/8)11yescharacteristic
87C4×C271#13711yescharacteristic
88Dic271—41no—
89Dic271—41no—
90Dic271—41no—
91C2×C271—161no—
92C2×C271#44811yescharacteristic
93C2×C271#44911yescharacteristic
94C2×C271#45311yescharacteristic
95D271—42no—
96C271#162211yescharacteristic, complemented, Sylow
97#1622—2711nomaximal, Sylow
98#554—2711no—
99#492D27111yescharacteristic, complemented
100#460—2711no—
101#459—2711no—
102#333—2711no—
103Q8⋊C8—2711no—
104D4⋊C8—2711no—
105C2×SD16—22no—
106C2×SD16—5421no—
107C2×D8—5421no—
108C4⋊Q8C2×D27111yescharacteristic
109#127C2×D27111yescharacteristic
110#125—5421no—
111C22⋊Q8—5421no—
112C22⋊Q8—5422no—
113C4×Q8—2711no—
114C4×D4—2711no—
115C4×D4—5421no—
116C2×C4⋊C4—5421no—
117C4⋊C8—2711no—
118C4⋊C8—2711no—
119#102—5421no—
120#102—5421no—
121C4×C8C2×D27111yescharacteristic
122C2×Q8—2711no—
123C2×Q8C22⋊D27112yes—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—2711no—
128C22×C4—5422no—
129C22×C4—5421no—
130SD16—44no—
131SD16—10842no—
132D8—10842no—
133C2×C8—21no—
134C2×C8—5421no—
135C2×C8—5421no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—2711no—
139C4⋊C4—2711no—
140C4⋊C4—5422no—
141C4⋊C4—5422no—
142C4⋊C4—5421no—
143C22⋊C4—5422no—
144C22⋊C4—5421no—
145C42—5421no—
146C42C22×D27111yescharacteristic
147C23—41no—
148C23—5421no—
149Q8—42no—
150Q8—5421no—
151Q8—5421no—
152D4—42no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—2712no—
158D4—5421no—
159C2×C4—22no—
160C2×C4—5421no—
161C2×C4—5421no—
162C2×C4—5421no—
163C2×C4—10841no—
164C2×C4—10841no—
165C2×C4—21682no—
166C2×C4D4×D27111yescharacteristic
167C2×C4D4×D27111yescharacteristic
168C2×C4C2×C22⋊D27111yescharacteristic
169C8—22no—
170C8—10841no—
171C8—10841no—
172C22—81no—
173C22—81no—
174C22—81no—
175C22—5422no—
176C22—10841no—
177C22—10841no—
178C22#2257612811yescharacteristic
179C4—21no—
180C4—42no—
181C4—10841no—
182C4—10841no—
183C4—10841no—
184C4SD16×D27111yescharacteristic
185C4#2257618111yescharacteristic
186C4#2257618711yescharacteristic
187C4#2257618911yescharacteristic
188C2—161no—
189C2—10842no—
190C2#3177403411yescharacteristic
191C2#3177404111yescharacteristic
192C2#3177406411yescharacteristic
subgroupG/H
centerC22#22576128
commutator, cosocleC42×C271C23
FrattiniC42C22×D271
Fitting#492×C271C2
socleC22×C271#120
prime radical#31774089C2
hypercenter#492D271
hypocenterC271#1622
LCSG ▷ C42×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #31774608C2semidirect
2. #31774094C2semidirect
4. #31773646C2semidirect
5. #31773629C2semidirect
6. #31773626C2semidirect
7. #492×C271C2semidirect
54. D1084SD16semidirect
96. C271#1622semidirect
99. #492D271semidirect

Maximal subgroups

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

subgroupindex
#317746082
#317740942
#317740892
#317736462
#317736292
#317736262
#492×C2712
#1622271