Finite Group Databasebeta

← #46834940

Subgroups — #46834940

Order 34688.

218 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 61 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#31774433C211yesmaximal, characteristic
2#31773947C211yesmaximal, characteristic, complemented
3#31773764C211yesmaximal, characteristic, complemented
4#31773634C211yesmaximal, characteristic, complemented
5#31773632C211yesmaximal, characteristic
6#31773630C211yesmaximal, characteristic
7#328×C271C211yesmaximal, characteristic, complemented
8#22576155—21no—
9#22576151C411yescharacteristic, complemented
10#22576149C411yescharacteristic, complemented
11#22576144—21no—
12#22576134C2211yescharacteristic
13Q8×Dic271C411yescharacteristic, complemented
14#22576122C411yescharacteristic, complemented
15(C22⋊D271)⋊C4—21no—
16#22576118—21no—
17C2×C4×Dic271C2211yescharacteristic
18Dic271⋊C8—21no—
19C22⋊(C271⋊C8)C2211yescharacteristic
20C8×Dic271—21no—
21C271⋊#95—21no—
22C271⋊#95—21no—
23C271⋊#95C2211yescharacteristic
24C22⋊Q8×C271C2211yescharacteristic
25C22⋊C8×C271C2211yescharacteristic
26#95×C271C2211yescharacteristic
27C2×D1084C2×C411yescharacteristic
28C2×C22⋊D271—21no—
29C22×Dic271—21no—
30C22×Dic271D411yescharacteristic
31C22×Dic271D411yescharacteristic
32C2×C4×D271—21no—
33C2×C271⋊C8—21no—
34C4⋊Dic271—21no—
35C4⋊Dic271—21no—
36C4⋊Dic271C2×C411yescharacteristic
37Dic271⋊C4—21no—
38(C2×D271)⋊C4—21no—
39(C2×D271)⋊C4—21no—
40(C2×D271)⋊C4—21no—
41(C2×D271)⋊C4—21no—
42C4×Dic271—21no—
43C4×Dic271C2×C411yescharacteristic
44C4×Dic271C2×C411yescharacteristic
45C4×Dic271D411yescharacteristic
46C4×Dic271D411yescharacteristic
47C2×Q8×C271C2×C411yescharacteristic
48C22×C4×C271—21no—
49C22×C4×C271C2311yescharacteristic
50C2×C8×C271—21no—
51C4⋊C4×C271—21no—
52C4⋊C4×C271C2×C411yescharacteristic
53C22⋊C4×C271—21no—
54C22×D271—21no—
55D1084—41no—
56C22⋊D271—41no—
57C22⋊D271—41no—
58C2×Dic271—21no—
59C2×Dic271—21no—
60C2×Dic271—21no—
61C2×Dic271—41no—
62C2×Dic271—41no—
63C2×Dic271—41no—
64C2×Dic271—41no—
65C2×Dic271C22⋊C411yescharacteristic
66C2×Dic271C22⋊C411yescharacteristic
67C2×Dic271C22⋊C411yescharacteristic
68C2×Dic271C22⋊C411yescharacteristic
69C4×D271—42no—
70C271⋊C8—41no—
71C23×C271C2×D411yescharacteristic
72Q8×C271—41no—
73C2×C4×C271—21no—
74C2×C4×C271—21no—
75C2×C4×C271—41no—
76C2×C4×C271—41no—
77C2×C4×C271—41no—
78C2×C4×C271—41no—
79C2×C4×C271C22×C411yescharacteristic
80C2×C4×C271C2×D411yescharacteristic
81C8×C271—41no—
82C22×C271—21no—
83C22×C271—21no—
84C22×C271C2×C22⋊C411yescharacteristic
85C22×C271#13511yescharacteristic
86C22×C271#13511yescharacteristic
87C2×D271—41no—
88C2×D271—41no—
89C2×D271—41no—
90C4×C271—21no—
91C4×C271—21no—
92C4×C271—41no—
93C4×C271—41no—
94C4×C271—81no—
95Dic271—21no—
96Dic271—21no—
97Dic271—21no—
98Dic271—21no—
99Dic271—41no—
100Dic271—81no—
101C2×C271—21no—
102C2×C271—21no—
103C2×C271#41011yescharacteristic
104C2×C271#41611yescharacteristic
105C2×C271#42111yescharacteristic
106D271—81no—
107C271#152111yescharacteristic, complemented, Sylow
108#1521—2711nomaximal, Sylow
109#529—2711no—
110#431—2711no—
111#383—2711no—
112#328—2711no—
113#328D27111yescharacteristic, complemented
114#327—2711no—
115#327—2711no—
116#126—5421no—
117#125—2711no—
118#124—2711no—
119#123—5421no—
120C22⋊Q8C2×D27111yescharacteristic
121#121—2711no—
122C4×Q8—2711no—
123C4×D4—2711no—
124C4×D4—5421no—
125#117—5421no—
126C2×C42—2711no—
127C4⋊C8—5421no—
128C22⋊C8—2711no—
129C22⋊C8C2×D27111yescharacteristic
130C4×C8—5421no—
131#95—2711no—
132#95—5421no—
133#95—5421no—
134#95C2×D27111yescharacteristic
135C2×Q8C4×D27111yescharacteristic
136C2×D4—2711no—
137C2×D4—5421no—
138C22×C4—21no—
139C22×C4—2711no—
140C22×C4—2711no—
141C22×C4—5421no—
142C22×C4—5421no—
143C22×C4C22×D27111yescharacteristic
144C2×C8—21no—
145C2×C8—5421no—
146C4⋊C4—21no—
147C4⋊C4—2711no—
148C4⋊C4—5421no—
149C4⋊C4—5421no—
150C4⋊C4—5421no—
151C4⋊C4C4×D27111yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—5421no—
154C22⋊C4—5421no—
155C22⋊C4—5421no—
156C22⋊C4—5421no—
157C42—2711no—
158C42—2711no—
159C42—2711no—
160C42—2711no—
161C42—5421no—
162C23—5421no—
163C23D4×D27111yescharacteristic
164Q8—41no—
165D4—10841no—
166D4—10841no—
167D4—10841no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—2711no—
175C2×C4—2711no—
176C2×C4—2711no—
177C2×C4—2711no—
178C2×C4—5421no—
179C2×C4—5421no—
180C2×C4—5421no—
181C2×C4—10842no—
182C2×C4—10841no—
183C2×C4—10841no—
184C2×C4—10841no—
185C2×C4—10841no—
186C2×C4C2×C4×D27111yescharacteristic
187C2×C4D4×D27111yescharacteristic
188C8—41no—
189C8—10841no—
190C22—21no—
191C22—21no—
192C22—10841no—
193C22—10841no—
194C22—10841no—
195C22C22⋊C4×D27111yescharacteristic
196C22#2257618111yescharacteristic
197C22#2257618311yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—41no—
202C4—81no—
203C4—5421no—
204C4—5421no—
205C4—5421no—
206C4—5421no—
207C4—10841no—
208C4—21681no—
209C2—21no—
210C2—21no—
211C2—21681no—
212C2#3177386911yescharacteristic
213C2#3177389211yescharacteristic
214C2#3177391211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D271
commutatorC2×C4×C271C22×C4
FrattiniC22×C4C22×D271
Fitting#328×C271C2
socleC22×C271C2×C22⋊C4
prime radical#22576134C22
cosocleC22×C4×C271C23
hypercenter#328D271
hypocenterC271#1521
LCSG ▷ C2×C4×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #31773947C2semidirect
3. #31773764C2semidirect
4. #31773634C2semidirect
7. #328×C271C2semidirect
9. #22576151C4semidirect
10. #22576149C4semidirect
13. Q8×Dic271C4semidirect
14. #22576122C4semidirect
107. C271#1521semidirect
113. #328D271semidirect

Maximal subgroups

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

subgroupindex
#317744332
#317739472
#317737642
#317736342
#317736322
#317736302
#328×C2712
#1521271