Finite Group Databasebeta

← #16856311

Subgroups — #16856311

Order 3968.

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

normal subgroups only

This group has 364 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#14521583C211yesmaximal, characteristic
2#14521455C211yesmaximal, characteristic, complemented
3#14521441C211yesmaximal, characteristic, complemented
4#14521417C211yesmaximal, characteristic, complemented
5#14521411C211yesmaximal, characteristic, complemented
6#14521305C212yesmaximal, complemented
7#14521297C212yesmaximal
8C4×#92482C212yesmaximal, complemented
9C4×#92481C212yesmaximal, complemented
10C4×#92474C211yesmaximal, characteristic, complemented
11C31×#533C211yesmaximal, characteristic, complemented
12C31×C4⋊Q8C2211yescharacteristic
13C31×C4⋊Q8C2211yescharacteristic
14C31×#125—21no—
15C31×C22⋊Q8—21no—
16C31×C22⋊Q8C2212yes—
17C4×Q8×C31—21no—
18C4×Q8×C31C2212yes—
19C31×#117—21no—
20C2×C42×C31C2211yescharacteristic
21C2×#92482C2212yes—
22C2×#92481C2212yes—
23#11758507C2211yescharacteristic
24#11758506—21no—
25C4×C22⋊D31—21no—
26#11758501C2211yescharacteristic
27C2×#92474C2212yes—
28#11758453—21no—
29#11758452C2211yescharacteristic
30C4×D124C2211yescharacteristic
31#11758449—21no—
32#11758447C2211yescharacteristic
33C4×Dic62C2211yescharacteristic
34#11758423C2212yes—
35#11758423C2212yes—
36#11758398C2212yes—
37#11758397C2212yes—
38#11758396C2212yes—
39#11758395C2212yes—
40#11758391C2211yescharacteristic
41#11758391C2211yescharacteristic
42C4×C31⋊C8C2212yes—
43C2×Q8×C31—21no—
44C2×Q8×C31C2312yes—
45C22×C4×C31D411yescharacteristic
46C22×C4×C31D411yescharacteristic
47C22×C4×C31C2311yescharacteristic
48C2×C22⋊D31—21no—
49C2×D124C2311yescharacteristic
50C2×C4×D31—21no—
51C2×Dic62C2311yescharacteristic
52C4⋊C4×C31—21no—
53C4⋊C4×C31—21no—
54C4⋊C4×C31—21no—
55C4⋊C4×C31—22no—
56C4⋊C4×C31—22no—
57C4⋊C4×C31C2312yes—
58C22⋊C4×C31—22no—
59C42×C31—22no—
60C42×C31D411yescharacteristic
61C42×C31D411yescharacteristic
62C42×C31C2311yescharacteristic
63C42×C31C2311yescharacteristic
64C22⋊Dic31—21no—
65#92482—24no—
66#92481—24no—
67(C2×D31)⋊C4—21no—
68(C2×D31)⋊C4—21no—
69(C2×D31)⋊C4—21no—
70(C2×D31)⋊C4—21no—
71C4⋊Dic31C2311yescharacteristic
72C4⋊Dic31C2311yescharacteristic
73Dic31⋊C4—21no—
74Dic31⋊C4—21no—
75Dic31⋊C4—21no—
76Dic31⋊C4—21no—
77C4×Dic31—21no—
78#92474—24no—
79C2×C31⋊C8C2312yes—
80C2×C31⋊C8C2312yes—
81C23×C31C2×D411yescharacteristic
82C22×D31—21no—
83Q8×C31—22no—
84Q8×C31—22no—
85Q8×C31—42no—
86C2×C4×C31—22no—
87C2×C4×C31—22no—
88C2×C4×C31—22no—
89C2×C4×C31—22no—
90C2×C4×C31—41no—
91C2×C4×C31C2×D411yescharacteristic
92C2×C4×C31C2×D411yescharacteristic
93C2×C4×C31C2×D411yescharacteristic
94C2×C4×C31C2×D411yescharacteristic
95C2×C4×C31C2×D411yescharacteristic
96C2×C4×C31C2411yescharacteristic
97C22⋊D31—42no—
98C2×Dic31—21no—
99C2×Dic31—21no—
100C2×Dic31—21no—
101D124—22no—
102C4×D31—42no—
103Dic62—22no—
104C31⋊C8—22no—
105C31⋊C8#4114yes—
106#3172—311nomaximal, Sylow
107C22×C31—21no—
108C22×C31—21no—
109C22×C31—21no—
110C22×C31C22×D411yescharacteristic
111C2×D31—41no—
112C2×D31—41no—
113C2×D31—41no—
114C4×C31—21no—
115C4×C31—21no—
116C4×C31—21no—
117C4×C31—21no—
118C4×C31—42no—
119C4×C31—42no—
120C4×C31#13712yes—
121C4×C31C2×#4112yes—
122Dic31—41no—
123Dic31—41no—
124Dic31—41no—
125#533D3111yescharacteristic, complemented
126#529—311no—
127#501—311no—
128#497—311no—
129#491—311no—
130#489—311no—
131#470—312no—
132#468—312no—
133C4×Q16—312no—
134C4×SD16—312no—
135C4×M16—311no—
136C2×C31—41no—
137C2×C31#53211yescharacteristic
138C2×C31C2×#13711yescharacteristic
139C2×C31#57511yescharacteristic
140D31—81no—
141C2×Q16—312no—
142C2×SD16—312no—
143C2×M16—312no—
144C4⋊Q8C2×D3111yescharacteristic
145C4⋊Q8C2×D3111yescharacteristic
146#126—621no—
147#125—21no—
148#125—311no—
149#124—311no—
150#123—621no—
151C22⋊Q8—21no—
152C22⋊Q8—311no—
153C22⋊Q8C2×D3112yes—
154#121—311no—
155C4×Q8—21no—
156C4×Q8—311no—
157C4×Q8C2×D3112yes—
158C4×D4—311no—
159C4×D4—621no—
160#117—21no—
161#117—621no—
162C2×C42C2×D3111yescharacteristic
163#107—312no—
164#106—312no—
165#103—312no—
166#103—312no—
167#103—312no—
168#102—312no—
169#97—311no—
170#97—311no—
171C4×C8—312no—
172C31#317211yescharacteristic, complemented, Sylow
173C2×Q8—21no—
174C2×Q8—311no—
175C2×Q8C22×D3112yes—
176C2×D4—311no—
177C2×D4—621no—
178C22×C4—621no—
179C22×C4C22⋊D3111yescharacteristic
180C22×C4C22⋊D3111yescharacteristic
181C22×C4C22×D3111yescharacteristic
182Q16—624no—
183SD16—624no—
184M16—624no—
185C2×C8—312no—
186C2×C8—312no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—311no—
193C4⋊C4—311no—
194C4⋊C4—621no—
195C4⋊C4—621no—
196C4⋊C4—621no—
197C4⋊C4—621no—
198C4⋊C4C22×D3112yes—
199C22⋊C4—22no—
200C22⋊C4—621no—
201C22⋊C4—621no—
202C22⋊C4—621no—
203C22⋊C4—621no—
204C22⋊C4—621no—
205C42—22no—
206C42—621no—
207C42C22⋊D3111yescharacteristic
208C42C22⋊D3111yescharacteristic
209C42C22×D3111yescharacteristic
210C42C22×D3111yescharacteristic
211C23—621no—
212C23C2×C22⋊D3111yescharacteristic
213Q8—22no—
214Q8—22no—
215Q8—42no—
216Q8—622no—
217D4—622no—
218D4—1242no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—621no—
225C2×C4—621no—
226C2×C4—621no—
227C2×C4—1242no—
228C2×C4C2×C22⋊D3111yescharacteristic
229C2×C4C2×C22⋊D3111yescharacteristic
230C2×C4C2×C22⋊D3111yescharacteristic
231C2×C4C2×C22⋊D3111yescharacteristic
232C2×C4C2×C22⋊D3111yescharacteristic
233C2×C4C23×D3111yescharacteristic
234C8—314no—
235C8—622no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—1241no—
240C22—1241no—
241C22—1241no—
242C22C22×C22⋊D3111yescharacteristic
243C4—21no—
244C4—21no—
245C4—21no—
246C4—21no—
247C4—42no—
248C4—42no—
249C4—1241no—
250C4—1241no—
251C4—1241no—
252C4#1175851912yes—
253C4#41×D3112yes—
254C2—41no—
255C2—2481no—
256C2#1452159511yescharacteristic
257C2C2×#1175851911yescharacteristic
258C2#1452184711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#533C2
socleC22×C31C22×D4
prime radical#11758507C22
hypercenter#533D31
hypocenterC31#3172
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #14521455C2semidirect
3. #14521441C2semidirect
4. #14521417C2semidirect
5. #14521411C2semidirect
6. #14521305C2semidirect
8. C4×#92482C2semidirect
9. C4×#92481C2semidirect
10. C4×#92474C2semidirect
11. C31×#533C2semidirect
125. #533D31semidirect
172. C31#3172semidirect

Maximal subgroups

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

subgroupindex
#145215832
#145214552
#145214412
#145214172
#145214112
#145213052
#145212972
C4×#924822
C4×#924812
C4×#924742
C31×#5332
#317231