Finite Group Databasebeta

← #15756374

Subgroups — #15756374

Order 3328.

404 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 99 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#13117333C211yesmaximal, characteristic
2#13113148C212yesmaximal
3#13112669C211yesmaximal, characteristic, complemented
4#13112664C212yesmaximal, complemented
5C13×#1276C211yesmaximal, characteristic, complemented
6C2×#88126C2211yescharacteristic
7C13×#431C2212yes—
8C43×C13C2211yescharacteristic
9#11718601—22no—
10C4×#6103C412yes—
11#11718594—22no—
12#11718593C2211yescharacteristic
13C4×#6101C412yes—
14#11718586C2212yes—
15#11718061—22no—
16#11718060—22no—
17C22×C4×D13C2×C411yescharacteristic
18C2×C42×C13—22no—
19C2×C42×C13C2×C412yes—
20C2×C42×C13C2311yescharacteristic
21C2×#6103—22no—
22C2×#6103D412yes—
23C2×#6101—22no—
24C2×#6101D412yes—
25C2×C4×Dic13C2×C412yes—
26C2×C4×Dic13C2×C411yescharacteristic
27#88126—22no—
28#88126—21no—
29#88126—21no—
30C13×C4⋊C8—22no—
31C13×C22⋊C8—22no—
32C4×C8×C13—22no—
33#88071—22no—
34#88071—22no—
35#88071—22no—
36C22⋊#1055—22no—
37C4⋊#1055—22no—
38C4×#1055—22no—
39#8733—131nomaximal, Sylow
40C23×D13C22⋊C411yescharacteristic
41C22×C4×C13—22no—
42C22×C4×C13C22×C411yescharacteristic
43C22×C4×C13C2×D412yes—
44C22×Dic13—22no—
45C22×Dic13C22⋊C411yescharacteristic
46C22×Dic13C22⋊C412yes—
47C2×C4×D13—21no—
48C2×C4×D13—21no—
49C2×C4×D13—22no—
50C2×C4×D13—22no—
51C2×C8×C13—42no—
52C42×C13—22no—
53C42×C13—22no—
54C42×C13—44no—
55C42×C13#4112yes—
56C42×C13#4111yescharacteristic
57C42×C13#4111yescharacteristic
58#6103—22no—
59#6103—22no—
60#6103—44no—
61#6101—22no—
62#6101—22no—
63#6101—44no—
64C4×Dic13—21no—
65C4×Dic13—21no—
66C4×Dic13—22no—
67C4×Dic13—22no—
68C2×#1055—42no—
69#2298—131no—
70#1458—132no—
71#1276—131no—
72#1276D1311yescharacteristic, complemented
73#1274—132no—
74C23×C13C2×C22⋊C411yescharacteristic
75C22×D13—21no—
76C22×D13—22no—
77C22×D13—42no—
78C2×C4×C13—24no—
79C2×C4×C13—42no—
80C2×C4×C13—42no—
81C2×C4×C13—42no—
82C2×C4×C13#11711yescharacteristic
83C2×C4×C13#11711yescharacteristic
84C2×C4×C13#12312yes—
85C2×C4×C13#12312yes—
86C2×C4×C13#13112yes—
87C2×C4×C13#13112yes—
88C2×Dic13—22no—
89C2×Dic13—21no—
90C2×Dic13—22no—
91C2×Dic13—42no—
92C2×Dic13—42no—
93C2×Dic13—42no—
94C2×Dic13—42no—
95C4×D13—42no—
96C4×D13—41no—
97C4×D13—41no—
98C8×C13—82no—
99#1055—82no—
100C2×#117—131no—
101#431—132no—
102#431C2×D1312yes—
103#388—262no—
104#387—262no—
105C4×C4⋊C4—132no—
106C4×C22⋊C4—132no—
107#376—131no—
108C43C2×D1311yescharacteristic
109#324—262no—
110#323—262no—
111C22×C13—22no—
112C22×C13#38111yescharacteristic
113C22×C13#40812yes—
114C2×D13—41no—
115C2×D13—42no—
116C2×D13—82no—
117C4×C13—22no—
118C4×C13—22no—
119C4×C13—44no—
120C4×C13#43312yes—
121C4×C13#43311yescharacteristic
122C4×C13#43311yescharacteristic
123Dic13—41no—
124Dic13—42no—
125Dic13—82no—
126C23×C4—131no—
127#117—262no—
128#117—261no—
129#117—261no—
130C2×C4⋊C4—132no—
131C2×C4⋊C4—262no—
132C2×C22⋊C4—132no—
133C2×C22⋊C4—262no—
134C2×C42—22no—
135C2×C42—131no—
136C2×C42—132no—
137C2×C42C4×D1312yes—
138C2×C42C22×D1311yescharacteristic
139C4⋊C8—22no—
140C4⋊C8—262no—
141C22⋊C8—22no—
142C22⋊C8—262no—
143C4×C8—22no—
144C4×C8—262no—
145#95—262no—
146#95—262no—
147#95—262no—
148C2×C13—22no—
149C2×C13#181811yescharacteristic
150C2×C13#182712yes—
151D13—81no—
152C24—131no—
153C22×C4—22no—
154C22×C4—131no—
155C22×C4—132no—
156C22×C4—261no—
157C22×C4—261no—
158C22×C4—262no—
159C22×C4—262no—
160C22×C4—262no—
161C22×C4C2×C4×D1311yescharacteristic
162C22×C4D4×D1312yes—
163C2×C8—42no—
164C2×C8—522no—
165C4⋊C4—262no—
166C4⋊C4—262no—
167C4⋊C4—524no—
168C22⋊C4—262no—
169C22⋊C4—262no—
170C22⋊C4—524no—
171C42—22no—
172C42—22no—
173C42—44no—
174C42—261no—
175C42—261no—
176C42—262no—
177C42—262no—
178C42#612712yes—
179C42#612911yescharacteristic
180C42#613111yescharacteristic
181C13#873311yescharacteristic, complemented, Sylow
182C23—261no—
183C23—262no—
184C23—522no—
185C23C22⋊C4×D1311yescharacteristic
186C2×C4—24no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—262no—
191C2×C4—261no—
192C2×C4—262no—
193C2×C4—522no—
194C2×C4—521no—
195C2×C4—521no—
196C2×C4—522no—
197C2×C4—522no—
198C2×C4—522no—
199C2×C4—522no—
200C2×C4#8812611yescharacteristic
201C2×C4#8813712yes—
202C2×C4#8814611yescharacteristic
203C2×C4#8814812yes—
204C2×C4#8815512yes—
205C2×C4#8816112yes—
206C8—82no—
207C8—1042no—
208C22—22no—
209C22—521no—
210C22—522no—
211C22—1042no—
212C22#1171832511yescharacteristic
213C22#1171838812yes—
214C4—22no—
215C4—22no—
216C4—44no—
217C4—521no—
218C4—522no—
219C4—1042no—
220C4#1171835111yescharacteristic
221C4#1171837011yescharacteristic
222C4#1171850112yes—
223C2—22no—
224C2—1041no—
225C2#1311490611yescharacteristic
226C2#1311493912yes—
subgroupG/H
centerC2×C4#88146
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1276C2
socleC22×C13#381
prime radicalC23×D13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1276D13
hypocenterC13#8733
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
3. #13112669C2semidirect
4. #13112664C2semidirect
5. C13×#1276C2semidirect
72. #1276D13semidirect
181. C13#8733semidirect

Maximal subgroups

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

subgroupindex
#131173332
#131131482
#131126692
#131126642
C13×#12762
#873313