Finite Group Databasebeta

← #16856232

Subgroups — #16856232

Order 3968.

348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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#14521605C211yesmaximal, characteristic
2#14521604C211yesmaximal, characteristic
3#14521459C211yesmaximal, characteristic, complemented
4#14521458C211yesmaximal, characteristic, complemented
5#14521457C212yesmaximal, complemented
6#14521456C212yesmaximal, complemented
7#14521455C211yesmaximal, characteristic, complemented
8#14521086C212yesmaximal
9#14521084C212yesmaximal
10#97×D31C211yesmaximal, characteristic
11C31×#501C211yesmaximal, characteristic, complemented
12C31×C4⋊Q8C2211yescharacteristic
13C31×#125C2211yescharacteristic
14#11758523—21no—
15Q8×Dic31—21no—
16C2×C8×D31C2212yes—
17#11758474—21no—
18#11758473—21no—
19#11758473—21no—
20#11758469C2212yes—
21#11758469C2211yescharacteristic
22#11758469C2211yescharacteristic
23#11758467C2212yes—
24#11758465C2211yescharacteristic
25#11758465C2211yescharacteristic
26#11758464—21no—
27#11758464—21no—
28#11758464—21no—
29C42×D31C2211yescharacteristic
30#11758447C2211yescharacteristic
31#11758446C2211yescharacteristic
32C31×#107C2212yes—
33C31×#106C2212yes—
34C31×#97C2211yescharacteristic
35#11758406C2212yes—
36#11758405C2212yes—
37#11758403C2212yes—
38#11758396C2212yes—
39#11758396C2212yes—
40#11758395C2212yes—
41#11758395C2212yes—
42#11758391C2211yescharacteristic
43C2×Q8×C31—21no—
44C2×C4×D31D411yescharacteristic
45C2×C4×D31D411yescharacteristic
46C2×C4×D31C2311yescharacteristic
47C2×Dic62—21no—
48C2×Dic62—21no—
49C2×Dic62—21no—
50C2×C8×C31C2312yes—
51C4⋊C4×C31—21no—
52C4⋊C4×C31—21no—
53C4⋊C4×C31—21no—
54C4⋊C4×C31C2311yescharacteristic
55C4⋊C4×C31C2312yes—
56C4⋊C4×C31C2311yescharacteristic
57C42×C31C2311yescharacteristic
58(C2×D31)⋊C4—21no—
59(C2×D31)⋊C4—21no—
60(C2×D31)⋊C4—22no—
61C4⋊Dic31—21no—
62C4⋊Dic31—22no—
63C4⋊Dic31C2311yescharacteristic
64C4⋊Dic31C2312yes—
65C4⋊Dic31C2311yescharacteristic
66Dic31⋊C4—21no—
67Dic31⋊C4—21no—
68Dic31⋊C4—21no—
69Dic31⋊C4—21no—
70Dic31⋊C4—22no—
71C4×Dic31—21no—
72C4×Dic31—21no—
73C4×Dic31—22no—
74C4×Dic31D411yescharacteristic
75C4×Dic31D411yescharacteristic
76C4×Dic31C2311yescharacteristic
77C2×C31⋊C8C2312yes—
78C8×D31Q818yescomplemented
79C22×D31C2×D411yescharacteristic
80Q8×C31—42no—
81C2×C4×C31—22no—
82C2×C4×C31—21no—
83C2×C4×C31—21no—
84C2×C4×C31C2×D411yescharacteristic
85C2×C4×C31C2×D411yescharacteristic
86C2×C4×C31C2411yescharacteristic
87C2×Dic31—21no—
88C2×Dic31—21no—
89C2×Dic31—22no—
90C2×Dic31C2×D411yescharacteristic
91C2×Dic31C2×D411yescharacteristic
92C2×Dic31C2×D411yescharacteristic
93C4×D31—41no—
94C4×D31—41no—
95C4×D31C2×Q814yes—
96Dic62—42no—
97Dic62—42no—
98Dic62—42no—
99C8×C31C2×Q814yes—
100C31⋊C8C2×Q814yes—
101#3162—311nomaximal, Sylow
102C22×C31C22×D411yescharacteristic
103C2×D31—21no—
104C2×D31—21no—
105C2×D31C4⋊Q812yes—
106C4×C31—21no—
107C4×C31—21no—
108C4×C31—41no—
109C4×C31—41no—
110C4×C31—42no—
111C4×C31C22×Q812yes—
112Dic31—21no—
113Dic31—21no—
114Dic31—41no—
115Dic31—41no—
116Dic31—42no—
117Dic31C4⋊Q812yes—
118#533—311no—
119#533—311no—
120#501—311no—
121#501—311no—
122#501—312no—
123#501—312no—
124#501—311no—
125#501D3111yescharacteristic, complemented
126#427—312no—
127#427—312no—
128C2×#97—311no—
129C2×C31C2×C4⋊Q811yescharacteristic
130C2×C31#57511yescharacteristic
131C2×C31#57511yescharacteristic
132D31—22no—
133C22×C8—312no—
134C4⋊Q8—311no—
135C4⋊Q8—311no—
136C4⋊Q8—311no—
137C4⋊Q8C2×D3111yescharacteristic
138#125—312no—
139#125—311no—
140#125C2×D3111yescharacteristic
141C22⋊Q8—621no—
142C22⋊Q8—621no—
143C22⋊Q8—621no—
144C22⋊Q8—621no—
145C4×Q8—621no—
146C4×Q8—621no—
147C4×Q8—621no—
148C4×Q8—621no—
149#117—311no—
150#117—312no—
151#117—311no—
152C2×C42—311no—
153#107—312no—
154#107—312no—
155#107—312no—
156#107C2×D3112yes—
157#106—312no—
158#106—312no—
159#106—312no—
160#106C2×D3112yes—
161#97—312no—
162#97—311no—
163#97C2×D3111yescharacteristic
164C31#316211yescharacteristic, complemented, Sylow
165C2×Q8—21no—
166C2×Q8—621no—
167C2×Q8—621no—
168C2×Q8—621no—
169C22×C4—311no—
170C22×C4—311no—
171C22×C4—311no—
172C2×C8—312no—
173C2×C8—318no—
174C2×C8C22×D3112yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—21no—
178C4⋊C4—311no—
179C4⋊C4—312no—
180C4⋊C4—311no—
181C4⋊C4—622no—
182C4⋊C4—621no—
183C4⋊C4—621no—
184C4⋊C4—622no—
185C4⋊C4—621no—
186C4⋊C4—621no—
187C4⋊C4—621no—
188C4⋊C4C22×D3111yescharacteristic
189C4⋊C4C22×D3112yes—
190C4⋊C4C22×D3111yescharacteristic
191C22⋊C4—621no—
192C22⋊C4—621no—
193C22⋊C4—622no—
194C42—311no—
195C42—311no—
196C42—311no—
197C42—621no—
198C42—621no—
199C42—622no—
200C42C22×D3111yescharacteristic
201C23—311no—
202Q8—42no—
203Q8—1242no—
204Q8—1242no—
205Q8—1242no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—311no—
210C2×C4—314no—
211C2×C4—311no—
212C2×C4—311no—
213C2×C4—621no—
214C2×C4—621no—
215C2×C4—622no—
216C2×C4—1241no—
217C2×C4—1241no—
218C2×C4D4×D3111yescharacteristic
219C2×C4D4×D3111yescharacteristic
220C2×C4C23×D3111yescharacteristic
221C8—314no—
222C8Q8×D3114yes—
223C22—312no—
224C22—621no—
225C22—621no—
226C22C2×D4×D3111yescharacteristic
227C4—21no—
228C4—21no—
229C4—42no—
230C4—41no—
231C4—41no—
232C4—312no—
233C4—621no—
234C4—621no—
235C4—1241no—
236C4—1242no—
237C4—1241no—
238C4C2×Q8×D3112yes—
239C2—622no—
240C2C4⋊Q8×D3111yescharacteristic
241C2#1452184511yescharacteristic
242C2#1452184811yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#501C2
socleC22×C31C22×D4
prime radicalC22×D31C2×D4
hypercenter#501D31
hypocenterC31#3162
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
3. #14521459C2semidirect
4. #14521458C2semidirect
5. #14521457C2semidirect
6. #14521456C2semidirect
7. #14521455C2semidirect
11. C31×#501C2semidirect
78. C8×D31Q8semidirect
125. #501D31semidirect
164. C31#3162semidirect

Maximal subgroups

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

subgroupindex
#145216052
#145216042
#145214592
#145214582
#145214572
#145214562
#145214552
#145210862
#145210842
#97×D312
C31×#5012
#316231