Finite Group Databasebeta

← #16847363

Subgroups — #16847363

Order 3968.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#14521621C211yesmaximal, characteristic
2#14521030C211yesmaximal, characteristic
3#14521021C211yesmaximal, characteristic
4#14520840C211yesmaximal, characteristic, complemented
5#14520839C211yesmaximal, characteristic, complemented
6#14520838C211yesmaximal, characteristic, complemented
7C31×#352C211yesmaximal, characteristic, complemented
8C2×#92497C2211yescharacteristic
9C22×Dic62C411yescharacteristic, complemented
10C31×#123C2211yescharacteristic
11#11758512C2211yescharacteristic
12#11758506C411yescharacteristic, complemented
13M16×D31—21no—
14#11758473—21no—
15#11758465—21no—
16#11758463C411yescharacteristic, complemented
17#11758462—21no—
18#11758455—21no—
19#11758454—21no—
20#11758454C411yescharacteristic, complemented
21C31×#100C2211yescharacteristic
22C31×#99C2211yescharacteristic
23#11758422C2211yescharacteristic
24#11758421C2211yescharacteristic
25#11758412—21no—
26#11758394—21no—
27C2×D4×C31C2311yescharacteristic
28C22×C4×C31C2×C411yescharacteristic
29C2×C22⋊D31C2×C411yescharacteristic
30C2×C22⋊D31D411yescharacteristic
31C22×Dic31C2×C411yescharacteristic
32C22×Dic31C2×C411yescharacteristic
33C22×Dic31D411yescharacteristic
34#92497—41no—
35#92497—41no—
36C2×C4×D31D411yescharacteristic
37C2×Dic62—21no—
38C2×Dic62—21no—
39C2×Dic62—41no—
40C2×Dic62—41no—
41C2×Dic62D411yescharacteristic
42M16×C31—21no—
43C4⋊C4×C31—21no—
44C22⋊C4×C31—21no—
45C22⋊C4×C31—21no—
46C22⋊C4×C31C2×C411yescharacteristic
47C22⋊Dic31—21no—
48C22⋊Dic31—21no—
49C22⋊Dic31C2×C411yescharacteristic
50(C2×D31)⋊C4—21no—
51(C2×D31)⋊C4—21no—
52C4⋊Dic31—21no—
53Dic31⋊C4—21no—
54Dic31⋊C4—21no—
55Dic31⋊C4—21no—
56Dic31⋊C4—41no—
57C4×Dic31—21no—
58C4×Dic31—41no—
59#92474—21no—
60#92469—41no—
61C8×D31—41no—
62C23×C31C22×C411yescharacteristic
63C23×C31C2×D411yescharacteristic
64C22×D31C22⋊C411yescharacteristic
65D4×C31—41no—
66C2×C4×C31—21no—
67C2×C4×C31—21no—
68C2×C4×C31—41no—
69C2×C4×C31—41no—
70C2×C4×C31C2×D411yescharacteristic
71C22⋊D31—41no—
72C22⋊D31—41no—
73C2×Dic31—21no—
74C2×Dic31—21no—
75C2×Dic31—21no—
76C2×Dic31—21no—
77C2×Dic31—21no—
78C2×Dic31—21no—
79C2×Dic31—41no—
80C2×Dic31—41no—
81C2×Dic31C22⋊C411yescharacteristic
82C2×Dic31C22⋊C411yescharacteristic
83C2×Dic31C22⋊C411yescharacteristic
84C4×D31—21no—
85C4×D31—21no—
86Dic62—41no—
87Dic62—42no—
88Dic62—41no—
89Dic62—41no—
90C8×C31—41no—
91C31⋊C8—41no—
92#2123—311nomaximal, Sylow
93C22×C31—21no—
94C22×C31—21no—
95C22×C31—41no—
96C22×C31—41no—
97C22×C31C2×C22⋊C411yescharacteristic
98C2×D31—21no—
99C2×D31—41no—
100C4×C31—21no—
101C4×C31—41no—
102C4×C31—41no—
103C4×C31—81no—
104Dic31—21no—
105Dic31—21no—
106Dic31—41no—
107Dic31—41no—
108Dic31—81no—
109Dic31#9911yescharacteristic
110Dic31#9911yescharacteristic
111#536—311no—
112#413—311no—
113#410—311no—
114#352—311no—
115#352—311no—
116#352—311no—
117#352D3111yescharacteristic, complemented
118C2×C31—21no—
119C2×C31—41no—
120C2×C31—41no—
121C2×C31C2×#9911yescharacteristic
122D31—41no—
123C2×#41—311no—
124C22×Q8—311no—
125C2×M16—621no—
126C4⋊Q8—621no—
127#124—621no—
128#123—311no—
129#123—311no—
130#123—311no—
131#123C2×D3111yescharacteristic
132C22⋊Q8—621no—
133C22⋊Q8—621no—
134#117—311no—
135#117—621no—
136#101—621no—
137#100—311no—
138#100C2×D3111yescharacteristic
139#99—311no—
140#99—621no—
141#99C2×D3111yescharacteristic
142C31#212311yescharacteristic, complemented, Sylow
143#41—1241no—
144#41—1241no—
145C2×Q8—311no—
146C2×Q8—621no—
147C2×Q8—621no—
148C2×Q8—1241no—
149C2×Q8—1241no—
150C2×D4—311no—
151C2×D4—311no—
152C2×D4C22×D3111yescharacteristic
153C22×C4—311no—
154C22×C4—311no—
155C22×C4—311no—
156C22×C4—311no—
157C22×C4C4×D3111yescharacteristic
158M16—21no—
159M16—621no—
160M16—1241no—
161C2×C8—1241no—
162C4⋊C4—21no—
163C4⋊C4—621no—
164C4⋊C4—621no—
165C4⋊C4—621no—
166C4⋊C4—621no—
167C4⋊C4—1241no—
168C22⋊C4—21no—
169C22⋊C4—21no—
170C22⋊C4—311no—
171C22⋊C4—621no—
172C22⋊C4—621no—
173C22⋊C4—621no—
174C22⋊C4—621no—
175C22⋊C4C4×D3111yescharacteristic
176C42—621no—
177C42—1241no—
178C23—311no—
179C23C2×C4×D3111yescharacteristic
180C23D4×D3111yescharacteristic
181Q8—1241no—
182Q8—1241no—
183Q8—1241no—
184Q8—1242no—
185D4—41no—
186D4—1241no—
187D4—1241no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—311no—
193C2×C4—311no—
194C2×C4—311no—
195C2×C4—621no—
196C2×C4—621no—
197C2×C4—621no—
198C2×C4—621no—
199C2×C4—621no—
200C2×C4—621no—
201C2×C4—621no—
202C2×C4—621no—
203C2×C4—1241no—
204C2×C4—1241no—
205C2×C4D4×D3111yescharacteristic
206C8—41no—
207C8—1241no—
208C22—21no—
209C22—21no—
210C22—41no—
211C22—41no—
212C22—621no—
213C22—1241no—
214C22C22⋊C4×D3111yescharacteristic
215C4—21no—
216C4—41no—
217C4—41no—
218C4—81no—
219C4—311no—
220C4—311no—
221C4—621no—
222C4—621no—
223C4—1241no—
224C4—1241no—
225C4—2481no—
226C2—21no—
227C2—41no—
228C2—41no—
229C2—1241no—
230C2#99×D3111yescharacteristic
subgroupG/H
centerC2#99×D31
commutatorC23×C31C22×C4
FrattiniC2×D4C22×D31
FittingC31×#352C2
socleC2×C31C2×#99
prime radicalC2×#92497C22
cosocleC2×D4×C31C23
hypercenter#352D31
hypocenterC31#2123
LCSG ▷ C23×C31 ▷ C22×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
4. #14520840C2semidirect
5. #14520839C2semidirect
6. #14520838C2semidirect
7. C31×#352C2semidirect
9. C22×Dic62C4semidirect
12. #11758506C4semidirect
16. #11758463C4semidirect
20. #11758454C4semidirect
117. #352D31semidirect
142. C31#2123semidirect

Maximal subgroups

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

subgroupindex
#145216212
#145210302
#145210212
#145208402
#145208392
#145208382
C31×#3522
#212331