Finite Group Databasebeta

← #46839656

Subgroups — #46839656

Order 34688.

504 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 163 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
1C2×#22576125C211yesmaximal, characteristic
2C2×#22576125C211yesmaximal, characteristic
3#31773831C212yesmaximal
4#31773828C211yesmaximal, characteristic
5#31773818C211yesmaximal, characteristic
6#31773817C212yesmaximal
7#31773817C211yesmaximal, characteristic
8C4⋊C4×Dic271C212yesmaximal
9#31773748C212yesmaximal
10#31773742C211yesmaximal, characteristic
11#398×C271C211yesmaximal, characteristic
12C22×Dic542C2211yescharacteristic
13C22×Dic542C2211yescharacteristic
14#22576125—24no—
15#22576125—24no—
16C2×C4⋊Dic271C2212yes—
17C2×Dic271⋊C4C2212yes—
18C2×Dic271⋊C4C2212yes—
19C2×Dic271⋊C4C2212yes—
20C2×Dic271⋊C4C2211yescharacteristic
21C2×Dic271⋊C4C2211yescharacteristic
22C2×C4×Dic271C2211yescharacteristic
23C2×C4×Dic271C2212yes—
24C2×C4×Dic271C2211yescharacteristic
25C2×C4×Dic271C2211yescharacteristic
26C2×C4×Dic271C2212yes—
27C271⋊#95C2211yescharacteristic
28C271⋊#95C2212yes—
29C271⋊#95C2212yes—
30C271⋊#95C2212yes—
31C271⋊#95C2212yes—
32C2×C4⋊C4×C271C2212yes—
33C2×C4⋊C4×C271C2211yescharacteristic
34C2×C4⋊C4×C271C2211yescharacteristic
35#95×C271C2211yescharacteristic
36#95×C271C2212yes—
37C2×Dic542—22no—
38C2×Dic542—22no—
39C2×Dic542—24no—
40C2×Dic542—22no—
41C2×Dic542—22no—
42C22×Dic271C2311yescharacteristic
43C22×Dic271C2311yescharacteristic
44C22×Dic271C2312yes—
45C22×Dic271C2311yescharacteristic
46C22×Dic271C2312yes—
47C22×Dic271C2311yescharacteristic
48C4⋊Dic271—24no—
49Dic271⋊C4—24no—
50Dic271⋊C4—22no—
51Dic271⋊C4—24no—
52Dic271⋊C4—24no—
53Dic271⋊C4—22no—
54C4×Dic271—22no—
55C4×Dic271—22no—
56C4×Dic271—24no—
57C4×Dic271D414yes—
58C4×Dic271Q818yescomplemented
59C22×C4×C271C2311yescharacteristic
60C22×C4×C271C2312yes—
61C22×C4×C271C2311yescharacteristic
62C22×C4×C271C2312yes—
63C22×C4×C271C2311yescharacteristic
64C4⋊C4×C271—22no—
65C4⋊C4×C271—22no—
66C4⋊C4×C271—24no—
67Dic542—28no—
68Dic542—28no—
69C2×Dic271—22no—
70C2×Dic271—21no—
71C2×Dic271—22no—
72C2×Dic271—22no—
73C2×Dic271—21no—
74C2×Dic271—22no—
75C2×Dic271—21no—
76C2×Dic271—21no—
77C2×Dic271—21no—
78C2×Dic271—22no—
79C2×Dic271C2×D412yes—
80C2×Dic271C2×D412yes—
81C2×Dic271C2×Q814yes—
82C2×Dic271C2×Q814yes—
83C2×Dic271#4112yes—
84C2×Dic271#4114yes—
85C23×C271C2411yescharacteristic
86C2×C4×C271—21no—
87C2×C4×C271—22no—
88C2×C4×C271—22no—
89C2×C4×C271—22no—
90C2×C4×C271—21no—
91C2×C4×C271—21no—
92C2×C4×C271—22no—
93C2×C4×C271—22no—
94C2×C4×C271—22no—
95C2×C4×C271—22no—
96C2×C4×C271C2×D412yes—
97C2×C4×C271C2×Q814yes—
98C2×C4×C271#4112yes—
99C22×C271C22×D411yescharacteristic
100C22×C271C22×Q812yes—
101C22×C271C2×#4112yes—
102C22×C271C2×#4111yescharacteristic
103C22×C271C2×#4111yescharacteristic
104C4×C271—22no—
105C4×C271—22no—
106C4×C271—24no—
107C4×C271—41no—
108C4×C271—42no—
109Dic271—22no—
110Dic271—24no—
111Dic271—22no—
112Dic271—24no—
113Dic271—41no—
114Dic271C4⋊Q814yes—
115C2×C271#52511yescharacteristic
116C2×C271#52511yescharacteristic
117C2×C271C2×C4⋊Q811yescharacteristic
118C2×C271#53312yes—
119C2×C271#53312yes—
120C271#239911yescharacteristic, complemented, Sylow
121#2399—2711nomaximal, Sylow
122C2×C4×Q8—2711no—
123C2×C4×Q8—2711no—
124#398—2711no—
125#398—2712no—
126#398D27111yescharacteristic
127#395—2712no—
128#395—2711no—
129#395—2711no—
130C4×C4⋊C4—2712no—
131C4×C4⋊C4—2712no—
132#376—2711no—
133C22×Q8—2711no—
134C22×Q8—2711no—
135C4×Q8—5424no—
136C4×Q8—5424no—
137C2×C4⋊C4—2712no—
138C2×C4⋊C4—2711no—
139C2×C4⋊C4—2711no—
140C2×C4⋊C4—2712no—
141C2×C4⋊C4—2712no—
142C2×C4⋊C4—2712no—
143C2×C4⋊C4C2×D27111yescharacteristic
144C2×C4⋊C4C2×D27111yescharacteristic
145C2×C4⋊C4C2×D27112yes—
146C2×C42—2711no—
147C2×C42—2712no—
148C2×C42—2712no—
149C2×C42—2711no—
150C2×C42—2711no—
151#95—2711no—
152#95—2712no—
153#95—2712no—
154#95—2712no—
155#95—2712no—
156#95C2×D27111yescharacteristic
157#95C2×D27112yes—
158C2×Q8—5422no—
159C2×Q8—5424no—
160C2×Q8—5422no—
161C2×Q8—5422no—
162C2×Q8—5422no—
163C22×C4—2711no—
164C22×C4—2712no—
165C22×C4—2711no—
166C22×C4—2712no—
167C22×C4—2711no—
168C22×C4—2711no—
169C22×C4C22×D27112yes—
170C22×C4C22×D27111yescharacteristic
171C22×C4C22×D27111yescharacteristic
172C22×C4C22×D27112yes—
173C22×C4C22×D27111yescharacteristic
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—24no—
177C4⋊C4—5424no—
178C4⋊C4—5422no—
179C4⋊C4—5424no—
180C4⋊C4—5424no—
181C4⋊C4—5424no—
182C4⋊C4—5422no—
183C42—2714no—
184C42—2718no—
185C42—5422no—
186C42—5422no—
187C42—5424no—
188C23C23×D27111yescharacteristic
189Q8—5428no—
190Q8—5428no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—2712no—
202C2×C4—2714no—
203C2×C4—2712no—
204C2×C4—2714no—
205C2×C4—2714no—
206C2×C4—2712no—
207C2×C4—5422no—
208C2×C4—5421no—
209C2×C4—5422no—
210C2×C4—5422no—
211C2×C4—5422no—
212C2×C4—5421no—
213C2×C4—5421no—
214C2×C4—5421no—
215C2×C4—5421no—
216C2×C4—5422no—
217C2×C4D4×D27112yes—
218C2×C4Q8×D27114yes—
219C2×C4#1686465312yes—
220C22C2×D4×D27111yescharacteristic
221C22C2×Q8×D27112yes—
222C22#41×D27112yes—
223C22#41×D27111yescharacteristic
224C22C2×#1686465311yescharacteristic
225C4—22no—
226C4—22no—
227C4—24no—
228C4—41no—
229C4—42no—
230C4—2714no—
231C4—5424no—
232C4—5422no—
233C4—5422no—
234C4—5424no—
235C4—10841no—
236C2#3177440511yescharacteristic
237C2#3177440711yescharacteristic
238C2C4⋊Q8×D27111yescharacteristic
239C2#3177444912yes—
240C2#3177445312yes—
subgroupG/H
center, FrattiniC23C23×D271
commutator, socle, prime radical, cosocleC23×C271C24
Fitting#398×C271C2
hypercenter#398D271
hypocenterC271#2399
LCSG ▷ C23×C271 ▷ C271
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
58. C4×Dic271Q8semidirect
120. C271#2399semidirect

Maximal subgroups

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

subgroupindex
C2×#225761252
#317738312
#317738282
#317738182
#317738172
C4⋊C4×Dic2712
#317737482
#317737422
#398×C2712
#2399271