Finite Group Databasebeta

← #16846014

Subgroups — #16846014

Order 3968.

376 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#92474C211yesmaximal, characteristic, complemented
2C2×#11758425C212yesmaximal, complemented
3C4×C22⋊Dic31C211yesmaximal, characteristic, complemented
4#14520808C212yesmaximal, complemented
5C31×#525C211yesmaximal, characteristic
6C2×#41×C31C2211yescharacteristic
7C23×C4×C31C2211yescharacteristic
8C31×#123—21no—
9C31×C22⋊Q8C411yescharacteristic, complemented
10C31×C22⋊Q8C411yescharacteristic, complemented
11C31×#121C411yescharacteristic, complemented
12C31×#121C411yescharacteristic, complemented
13C31×#120—21no—
14C4×D4×C31—21no—
15C4×D4×C31—21no—
16C31×#117C2211yescharacteristic
17C2×C22⋊Dic31—21no—
18C2×C4×Dic31C2212yes—
19C2×#92474—21no—
20C2×#92474—24no—
21C2×#92474C2212yes—
22C22×C31⋊C8—21no—
23#11758425—24no—
24C31⋊#95—21no—
25C24×C31D411yescharacteristic
26#41×C31—22no—
27#41×C31—22no—
28C2×Q8×C31C2×C411yescharacteristic
29C2×D4×C31—21no—
30C2×D4×C31—21no—
31C2×D4×C31—21no—
32C2×D4×C31C2×C411yescharacteristic
33C22×C4×C31—22no—
34C22×C4×C31—22no—
35C22×C4×C31—21no—
36C22×C4×C31C2×C411yescharacteristic
37C22×C4×C31C2×C411yescharacteristic
38C22×C4×C31D411yescharacteristic
39C22×C4×C31D411yescharacteristic
40C22×C4×C31D411yescharacteristic
41C22×C4×C31C2311yescharacteristic
42C22×Dic31—22no—
43C4⋊C4×C31—21no—
44C4⋊C4×C31—21no—
45C4⋊C4×C31C2×C411yescharacteristic
46C4⋊C4×C31C2×C411yescharacteristic
47C22⋊C4×C31—21no—
48C22⋊C4×C31—21no—
49C22⋊C4×C31—21no—
50C22⋊C4×C31—21no—
51C22⋊C4×C31—21no—
52C42×C31—21no—
53C22⋊Dic31—24no—
54C4×Dic31—22no—
55C4×Dic31—22no—
56#92474—24no—
57#92474—22no—
58#92474D414yescomplemented
59C2×C31⋊C8—24no—
60C2×C31⋊C8—22no—
61C23×C31—22no—
62C23×C31—22no—
63C23×C31—21no—
64C23×C31—41no—
65C23×C31C22⋊C411yescharacteristic
66C23×C31C22⋊C411yescharacteristic
67C23×C31C2×D411yescharacteristic
68Q8×C31—22no—
69D4×C31—22no—
70D4×C31—42no—
71D4×C31—42no—
72D4×C31—42no—
73C2×C4×C31—22no—
74C2×C4×C31—22no—
75C2×C4×C31—22no—
76C2×C4×C31—21no—
77C2×C4×C31—21no—
78C2×C4×C31—21no—
79C2×C4×C31—21no—
80C2×C4×C31—21no—
81C2×C4×C31—21no—
82C2×C4×C31—21no—
83C2×C4×C31—41no—
84C2×C4×C31—41no—
85C2×C4×C31C22⋊C411yescharacteristic
86C2×C4×C31C22⋊C411yescharacteristic
87C2×C4×C31C22×C411yescharacteristic
88C2×C4×C31C2×D412yes—
89C2×C4×C31C2×D411yescharacteristic
90C2×C4×C31#4112yes—
91C2×Dic31—24no—
92C2×Dic31—42no—
93C2×Dic31—42no—
94C31⋊C8—24no—
95#1871—311nomaximal, Sylow
96C22×C31—21no—
97C22×C31—21no—
98C22×C31—21no—
99C22×C31—21no—
100C22×C31—21no—
101C22×C31—21no—
102C22×C31—21no—
103C22×C31—44no—
104C22×C31—41no—
105C22×C31—41no—
106C22×C31—41no—
107C22×C31#10412yescomplemented
108C22×C31C2×C22⋊C411yescharacteristic
109C22×C31#12112yes—
110C4×C31—21no—
111C4×C31—21no—
112C4×C31—41no—
113C4×C31—41no—
114C4×C31—41no—
115C4×C31C4×D412yes—
116C4×C31#12011yescharacteristic
117C4×C31#12311yescharacteristic
118Dic31—44no—
119C22×M16—311no—
120#525D3111yescharacteristic
121C2×#104—312no—
122C4×C22⋊C4—311no—
123#339—312no—
124C2×C31—22no—
125C2×C31—22no—
126C2×C31—41no—
127C2×C31—81no—
128C2×C31#38611yescharacteristic
129C2×C31C2×#10411yescharacteristic
130C2×C31#42111yescharacteristic
131C2×#41C2×D3111yescharacteristic
132C23×C4C2×D3111yescharacteristic
133C2×M16—312no—
134C2×M16—624no—
135C2×M16—621no—
136C22×C8—621no—
137#123—21no—
138C22⋊Q8Dic3111yescharacteristic, complemented
139C22⋊Q8Dic3111yescharacteristic, complemented
140#121Dic3111yescharacteristic, complemented
141#121Dic3111yescharacteristic, complemented
142#120—21no—
143C4×D4—21no—
144C4×D4—21no—
145#117C2×D3111yescharacteristic
146C2×C22⋊C4—621no—
147C2×C42—312no—
148#104—624no—
149#95—621no—
150C31#187111yescharacteristic, complemented, Sylow
151C24C22⋊D3111yescharacteristic
152#41—22no—
153#41—22no—
154C2×Q8C2×Dic3111yescharacteristic
155C2×D4—21no—
156C2×D4—21no—
157C2×D4—21no—
158C2×D4C2×Dic3111yescharacteristic
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—21no—
162C22×C4—622no—
163C22×C4C2×Dic3111yescharacteristic
164C22×C4C2×Dic3111yescharacteristic
165C22×C4C22⋊D3111yescharacteristic
166C22×C4C22⋊D3111yescharacteristic
167C22×C4C22⋊D3111yescharacteristic
168C22×C4C22×D3111yescharacteristic
169M16—314no—
170M16—624no—
171M16—622no—
172C2×C8—624no—
173C2×C8—622no—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4C2×Dic3111yescharacteristic
177C4⋊C4C2×Dic3111yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—21no—
180C22⋊C4—21no—
181C22⋊C4—21no—
182C22⋊C4—21no—
183C22⋊C4—624no—
184C42—21no—
185C42—622no—
186C42—622no—
187C23—22no—
188C23—22no—
189C23—21no—
190C23—41no—
191C23C22⋊Dic3111yescharacteristic
192C23C22⋊Dic3111yescharacteristic
193C23C2×C22⋊D3111yescharacteristic
194Q8—22no—
195D4—22no—
196D4—42no—
197D4—42no—
198D4—42no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—624no—
212C2×C4—1242no—
213C2×C4—1242no—
214C2×C4C22⋊Dic3111yescharacteristic
215C2×C4C22⋊Dic3111yescharacteristic
216C2×C4D4×D3112yes—
217C2×C4#9249712yes—
218C2×C4C22×Dic3111yescharacteristic
219C2×C4C2×C22⋊D3111yescharacteristic
220C8—624no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—44no—
229C22—41no—
230C22—41no—
231C22—41no—
232C22#1175842512yescomplemented
233C22#1175851612yes—
234C22C2×C22⋊Dic3111yescharacteristic
235C4—21no—
236C4—21no—
237C4—41no—
238C4—41no—
239C4—41no—
240C4—1244no—
241C4D4×Dic3112yes—
242C4#1175851211yescharacteristic
243C4#1175851411yescharacteristic
244C2—22no—
245C2—22no—
246C2—41no—
247C2—81no—
248C2#1452092911yescharacteristic
249C2C2×#1175842511yescharacteristic
250C2#1452106611yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
Fitting, prime radicalC31×#525C2
socleC22×C31C2×C22⋊C4
cosocleC22×C4×C31C23
hypercenter#525D31
hypocenterC31#1871
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C22×#92474C2semidirect
2. C2×#11758425C2semidirect
3. C4×C22⋊Dic31C2semidirect
4. #14520808C2semidirect
9. C31×C22⋊Q8C4semidirect
10. C31×C22⋊Q8C4semidirect
11. C31×#121C4semidirect
12. C31×#121C4semidirect
58. #92474D4semidirect
107. C22×C31#104semidirect
138. C22⋊Q8Dic31semidirect
139. C22⋊Q8Dic31semidirect
140. #121Dic31semidirect
141. #121Dic31semidirect
150. C31#1871semidirect
232. C22#11758425semidirect

Maximal subgroups

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

subgroupindex
C22×#924742
C2×#117584252
C4×C22⋊Dic312
#145208082
C31×#5252
#187131