Finite Group Databasebeta

← #16858375

Subgroups — #16858375

Order 3968.

362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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#14521785C211yesmaximal, characteristic, complemented
2#14521756C211yesmaximal, characteristic, complemented
3#14521402C212yesmaximal, complemented
4#14521395C211yesmaximal, characteristic, complemented
5#14521347C212yesmaximal, complemented
6#14521345C211yesmaximal, characteristic, complemented
7#14521262C212yesmaximal, complemented
8#14521173C211yesmaximal, characteristic, complemented
9C4×#92480C211yesmaximal, characteristic, complemented
10D8×Dic31C212yesmaximal, complemented
11C31×#459C211yesmaximal, characteristic
12C2×D8×C31C2212yes—
13C31×#127C2211yescharacteristic
14C4×D4×C31C2211yescharacteristic
15#11758513—21no—
16#11758513C2212yes—
17#11758512—22no—
18D4×Dic31—21no—
19D4×Dic31C2212yes—
20D4×Dic31C2212yes—
21C2×#92480C2211yescharacteristic
22C2×C4⋊Dic31—21no—
23#11758501—21no—
24#11758467C2212yes—
25#11758455—22no—
26#11758446C2211yescharacteristic
27C4×Dic62C2211yescharacteristic
28C4×Dic62C2211yescharacteristic
29C31×C4⋊C8C2211yescharacteristic
30C31×#102C2212yes—
31#11758420C2212yes—
32#11758420C2211yescharacteristic
33#11758420C2212yes—
34#11758406C2212yes—
35#11758404C2212yes—
36Dic31⋊C8C2212yes—
37C8×Dic31C2212yes—
38#11758398C2211yescharacteristic
39#11758396C2211yescharacteristic
40C4×C31⋊C8C2211yescharacteristic
41C2×D4×C31—21no—
42C2×D4×C31—21no—
43C2×D4×C31C2312yes—
44C2×D4×C31C2311yescharacteristic
45C22×C4×C31—21no—
46C22×Dic31—22no—
47C22×Dic31—22no—
48C2×Dic62—21no—
49C2×Dic62D411yescharacteristic
50C2×Dic62C2311yescharacteristic
51D8×C31—24no—
52C2×C8×C31C2312yes—
53C4⋊C4×C31C2311yescharacteristic
54C22⋊C4×C31—21no—
55C42×C31C2311yescharacteristic
56C22⋊Dic31—22no—
57C22⋊Dic31—22no—
58C22⋊Dic31—22no—
59C22⋊Dic31—22no—
60#92480—22no—
61C4⋊Dic31—21no—
62C4⋊Dic31—22no—
63C4⋊Dic31D411yescharacteristic
64C4⋊Dic31C2311yescharacteristic
65C4⋊Dic31C2312yes—
66Dic31⋊C4—21no—
67Dic31⋊C4—22no—
68Dic31⋊C4D412yes—
69C4×Dic31—21no—
70C4×Dic31C2312yes—
71C2×C31⋊C8C2311yescharacteristic
72C2×C31⋊C8C2311yescharacteristic
73C23×C31—21no—
74C23×C31—22no—
75D4×C31—22no—
76D4×C31—21no—
77D4×C31—22no—
78D4×C31—42no—
79D4×C31—81no—
80D4×C31#4112yes—
81C2×C4×C31—21no—
82C2×C4×C31—42no—
83C2×C4×C31C2×D411yescharacteristic
84C2×C4×C31C2×D411yescharacteristic
85C2×C4×C31C2411yescharacteristic
86C2×Dic31—21no—
87C2×Dic31—21no—
88C2×Dic31—22no—
89C2×Dic31—82no—
90C2×Dic31—82no—
91C2×Dic31C2×D412yes—
92C2×Dic31C2×D412yes—
93Dic62—22no—
94Dic62—21no—
95Dic62—21no—
96Dic62—81no—
97C8×C31—22no—
98C31⋊C8—21no—
99C31⋊C8—21no—
100#3361—311nomaximal, Sylow
101C22×C31—22no—
102C22×C31—41no—
103C22×C31—41no—
104C22×C31—42no—
105C22×C31—42no—
106C22×C31—42no—
107C22×C31C22×D411yescharacteristic
108C4×C31—21no—
109C4×C31—41no—
110C4×C31#13512yes—
111C4×C31C2×#4111yescharacteristic
112C4×C312−1+411yescharacteristic
113Dic31—22no—
114Dic31—22no—
115Dic31—41no—
116Dic31—42no—
117Dic31—41no—
118#559—311no—
119#554—311no—
120#488—312no—
121#486—311no—
122#478—312no—
123#477—311no—
124#463—312no—
125#459D3111yescharacteristic
126C8×Q8—311no—
127C4×SD16—311no—
128C4×D8—312no—
129C2×C31—42no—
130C2×C31—82no—
131C2×C31#54811yescharacteristic
132C2×C31C2×#13511yescharacteristic
133C2×C31#57611yescharacteristic
134C2×SD16—311no—
135C2×D8C2×D3112yes—
136C4⋊Q8—311no—
137#127C2×D3111yescharacteristic
138#125—312no—
139#124—312no—
140#124—621no—
141#123—622no—
142C22⋊Q8—622no—
143C22⋊Q8—621no—
144C4×Q8—311no—
145C4×Q8—311no—
146C4×D4—312no—
147C4×D4—312no—
148C4×D4—621no—
149C4×D4C2×D3111yescharacteristic
150C2×C4⋊C4—621no—
151#107—312no—
152#106—311no—
153C4⋊C8—312no—
154C4⋊C8C2×D3111yescharacteristic
155#103—312no—
156#103—311no—
157#102—311no—
158#102—312no—
159#102—312no—
160#102C2×D3112yes—
161C4×C8—312no—
162C4×C8—311no—
163C31#336111yescharacteristic, complemented, Sylow
164C2×Q8—311no—
165C2×Q8—311no—
166C2×Q8—621no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4C22×D3112yes—
170C2×D4C22×D3111yescharacteristic
171C22×C4—21no—
172C22×C4—622no—
173C22×C4—622no—
174SD16—622no—
175D8—24no—
176C2×C8—311no—
177C2×C8—311no—
178C2×C8C22×D3112yes—
179C4⋊C4—312no—
180C4⋊C4—311no—
181C4⋊C4—312no—
182C4⋊C4—311no—
183C4⋊C4—622no—
184C4⋊C4—622no—
185C4⋊C4—621no—
186C4⋊C4—621no—
187C4⋊C4C22×D3111yescharacteristic
188C22⋊C4—21no—
189C22⋊C4—622no—
190C22⋊C4—622no—
191C22⋊C4—622no—
192C22⋊C4—622no—
193C42—312no—
194C42—621no—
195C42C22×D3111yescharacteristic
196C23—21no—
197C23—22no—
198Q8—622no—
199Q8—621no—
200Q8—621no—
201Q8—2481no—
202D4—22no—
203D4—21no—
204D4—22no—
205D4—42no—
206D4—81no—
207D4#9249712yes—
208C2×C4—21no—
209C2×C4—42no—
210C2×C4—312no—
211C2×C4—312no—
212C2×C4—621no—
213C2×C4—621no—
214C2×C4—622no—
215C2×C4—2482no—
216C2×C4—2482no—
217C2×C4D4×D3111yescharacteristic
218C2×C4D4×D3111yescharacteristic
219C2×C4C23×D3111yescharacteristic
220C8—22no—
221C8—621no—
222C8—621no—
223C22—22no—
224C22—41no—
225C22—41no—
226C22—42no—
227C22—42no—
228C22—42no—
229C22C2×D4×D3111yescharacteristic
230C4—21no—
231C4—41no—
232C4—622no—
233C4—622no—
234C4—1241no—
235C4—1241no—
236C4—1242no—
237C4#1175848912yes—
238C4C2×#9249711yescharacteristic
239C4#1175856711yescharacteristic
240C2—42no—
241C2—82no—
242C2#1452170511yescharacteristic
243C2C2×#1175848911yescharacteristic
244C2#1452185311yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
Fitting, prime radicalC31×#459C2
socleC22×C31C22×D4
hypercenter#459D31
hypocenterC31#3361
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #14521785C2semidirect
2. #14521756C2semidirect
3. #14521402C2semidirect
4. #14521395C2semidirect
5. #14521347C2semidirect
6. #14521345C2semidirect
7. #14521262C2semidirect
8. #14521173C2semidirect
9. C4×#92480C2semidirect
10. D8×Dic31C2semidirect
163. C31#3361semidirect

Maximal subgroups

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

subgroupindex
#145217852
#145217562
#145214022
#145213952
#145213472
#145213452
#145212622
#145211732
C4×#924802
D8×Dic312
C31×#4592
#336131