Finite Group Databasebeta

← #16857628

Subgroups — #16857628

Order 3968.

386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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#14521769C211yesmaximal, characteristic, complemented
2#14521399C211yesmaximal, characteristic, complemented
3#14521387C212yesmaximal, complemented
4#14521329C211yesmaximal, characteristic, complemented
5#14521288C212yesmaximal, complemented
6#14521256C211yesmaximal, characteristic, complemented
7#14521211C212yesmaximal, complemented
8C4×#92480C211yesmaximal, characteristic, complemented
9D4×C31⋊C8C211yesmaximal, characteristic, complemented
10#14521045C212yesmaximal, complemented
11C31×#547C211yesmaximal, characteristic
12C2×#41×C31C2212yes—
13C31×C4⋊Q8C2211yescharacteristic
14C31×#123—22no—
15C31×C22⋊Q8C2212yes—
16C31×#121—21no—
17C4×D4×C31C2211yescharacteristic
18C4×D4×C31C2211yescharacteristic
19C2×C4⋊C4×C31—21no—
20C2×#92482C2212yes—
21#11758513—21no—
22C2×#92480C2211yescharacteristic
23#11758503C2212yes—
24#11758501C2212yes—
25C22×C31⋊C8C2212yes—
26#11758464—21no—
27#11758456—22no—
28#11758446C2211yescharacteristic
29C4×Dic62C2211yescharacteristic
30#11758423C2212yes—
31#11758423C2212yes—
32#11758423C2212yes—
33#11758420C2211yescharacteristic
34#11758420C2212yes—
35C22⋊(C31⋊C8)C2212yes—
36#11758398C2211yescharacteristic
37#11758396C2211yescharacteristic
38#11758395C2212yes—
39C4⋊(C31⋊C8)C2211yescharacteristic
40C4×C31⋊C8C2211yescharacteristic
41#41×C31—24no—
42#41×C31—42no—
43C2×Q8×C31C2312yes—
44C2×D4×C31—22no—
45C2×D4×C31D411yescharacteristic
46C2×D4×C31C2311yescharacteristic
47C22×C4×C31—21no—
48C22×C4×C31—22no—
49C22×C4×C31C2312yes—
50C2×Dic62—21no—
51C2×Dic62C2311yescharacteristic
52C4⋊C4×C31—21no—
53C4⋊C4×C31—22no—
54C4⋊C4×C31—21no—
55C4⋊C4×C31D411yescharacteristic
56C4⋊C4×C31C2311yescharacteristic
57C22⋊C4×C31—22no—
58C22⋊C4×C31—21no—
59C22⋊C4×C31D412yes—
60C42×C31C2311yescharacteristic
61C22⋊Dic31—22no—
62C22⋊Dic31—22no—
63#92482—42no—
64#92480—22no—
65C4⋊Dic31—21no—
66C4⋊Dic31C2312yes—
67C4⋊Dic31C2311yescharacteristic
68Dic31⋊C4—21no—
69Dic31⋊C4—22no—
70C4×Dic31—21no—
71C4×Dic31—22no—
72C2×C31⋊C8—42no—
73C2×C31⋊C8C2311yescharacteristic
74C2×C31⋊C8C2311yescharacteristic
75C2×C31⋊C8C2312yes—
76C23×C31—21no—
77C23×C31C2×D412yes—
78Q8×C31—22no—
79Q8×C31—22no—
80D4×C31—22no—
81D4×C31—21no—
82D4×C31—44no—
83D4×C31#4112yes—
84C2×C4×C31—22no—
85C2×C4×C31—22no—
86C2×C4×C31—21no—
87C2×C4×C31—22no—
88C2×C4×C31—44no—
89C2×C4×C31—42no—
90C2×C4×C31C2×D412yes—
91C2×C4×C31C2×D411yescharacteristic
92C2×C4×C31C2×D411yescharacteristic
93C2×C4×C31C2411yescharacteristic
94C2×Dic31—21no—
95C2×Dic31—21no—
96C2×Dic31—22no—
97Dic62—21no—
98Dic62—21no—
99Dic62—42no—
100C31⋊C8—21no—
101C31⋊C8—21no—
102C31⋊C8—22no—
103#3302—311nomaximal, Sylow
104C22×C31—22no—
105C22×C31—22no—
106C22×C31—22no—
107C22×C31—22no—
108C22×C31—41no—
109C22×C31—41no—
110C22×C31C22×D411yescharacteristic
111C4×C31—22no—
112C4×C31—21no—
113C4×C31—42no—
114C4×C31—41no—
115C4×C31#13512yes—
116C4×C31C2×#4111yescharacteristic
117C4×C31H(5,𝔽2)11yescharacteristic
118Dic31—41no—
119Dic31—42no—
120Dic31—41no—
121#556—311no—
122#547D3111yescharacteristic
123#487—311no—
124#485—312no—
125#474—311no—
126#467—312no—
127#462—311no—
128#452—312no—
129C4×SD16—311no—
130C8×D4—311no—
131#416—312no—
132C2×C31—42no—
133C2×C31—42no—
134C2×C31#54611yescharacteristic
135C2×C31C2×#13511yescharacteristic
136C2×C31#57811yescharacteristic
137C2×#41C2×D3112yes—
138C2×Q16—312no—
139C2×SD16—311no—
140C22×C8—312no—
141C4⋊Q8—311no—
142C4⋊Q8C2×D3111yescharacteristic
143#126—622no—
144#124—621no—
145#123—22no—
146C22⋊Q8—312no—
147C22⋊Q8C2×D3112yes—
148#121—21no—
149C4×Q8—311no—
150C4×Q8—621no—
151C4×D4C2×D3111yescharacteristic
152C4×D4C2×D3111yescharacteristic
153#117—312no—
154C2×C4⋊C4—21no—
155#107—312no—
156#106—311no—
157C4⋊C8—311no—
158#103—312no—
159#103—312no—
160#103—312no—
161#103—311no—
162#102—311no—
163#102—312no—
164C22⋊C8—312no—
165C4×C8—311no—
166C31#330211yescharacteristic, complemented, Sylow
167#41—24no—
168#41—42no—
169C2×Q8—311no—
170C2×Q8—621no—
171C2×Q8C22×D3112yes—
172C2×D4—22no—
173C2×D4C22⋊D3111yescharacteristic
174C2×D4C22×D3111yescharacteristic
175C22×C4—21no—
176C22×C4—22no—
177C22×C4C22×D3112yes—
178Q16—1242no—
179SD16—622no—
180C2×C8—311no—
181C2×C8—311no—
182C2×C8—312no—
183C2×C8—1242no—
184C4⋊C4—21no—
185C4⋊C4—22no—
186C4⋊C4—21no—
187C4⋊C4—311no—
188C4⋊C4—312no—
189C4⋊C4—621no—
190C4⋊C4—622no—
191C4⋊C4—621no—
192C4⋊C4C22⋊D3111yescharacteristic
193C4⋊C4C22×D3111yescharacteristic
194C22⋊C4—22no—
195C22⋊C4—21no—
196C22⋊C4—622no—
197C22⋊C4—622no—
198C22⋊C4C22⋊D3112yes—
199C42—622no—
200C42—621no—
201C42C22×D3111yescharacteristic
202C23—21no—
203C23C2×C22⋊D3112yes—
204Q8—22no—
205Q8—22no—
206Q8—621no—
207Q8—621no—
208Q8—1242no—
209D4—22no—
210D4—21no—
211D4—44no—
212D4#9249712yes—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—44no—
218C2×C4—42no—
219C2×C4—621no—
220C2×C4—622no—
221C2×C4—621no—
222C2×C4C2×C22⋊D3112yes—
223C2×C4C2×C22⋊D3111yescharacteristic
224C2×C4C2×C22⋊D3111yescharacteristic
225C2×C4C23×D3111yescharacteristic
226C8—621no—
227C8—621no—
228C8—622no—
229C22—22no—
230C22—22no—
231C22—22no—
232C22—22no—
233C22—41no—
234C22—41no—
235C22C22×C22⋊D3111yescharacteristic
236C4—21no—
237C4—22no—
238C4—42no—
239C4—41no—
240C4—1241no—
241C4—1241no—
242C4—1242no—
243C4#1175852712yes—
244C4C2×#9249711yescharacteristic
245C4#1175856111yescharacteristic
246C2—42no—
247C2—42no—
248C2#1452169311yescharacteristic
249C2C2×#1175852711yescharacteristic
250C2#1452186411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
Fitting, prime radicalC31×#547C2
socleC22×C31C22×D4
hypercenter#547D31
hypocenterC31#3302
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #14521769C2semidirect
2. #14521399C2semidirect
3. #14521387C2semidirect
4. #14521329C2semidirect
5. #14521288C2semidirect
6. #14521256C2semidirect
7. #14521211C2semidirect
8. C4×#92480C2semidirect
9. D4×C31⋊C8C2semidirect
10. #14521045C2semidirect
166. C31#3302semidirect

Maximal subgroups

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

subgroupindex
#145217692
#145213992
#145213872
#145213292
#145212882
#145212562
#145212112
C4×#924802
D4×C31⋊C82
#145210452
C31×#5472
#330231