Finite Group Databasebeta

← #16787379

Subgroups — #16787379

Order 3328.

326 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 92 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#13131196C211yesmaximal, characteristic, complemented
2C4×#88098C211yesmaximal, characteristic, complemented
3#13129803C212yesmaximal, complemented
4D4⋊#6092C212yesmaximal, complemented
5#13123814C211yesmaximal, characteristic
6#11719262C411yescharacteristic
7C2×#88098—21no—
8C13×#436C411yescharacteristic
9#11718788—21no—
10#11718783—21no—
11D4×#1055C2211yescharacteristic
12#11718496C411yescharacteristic
13#11718491C2211yescharacteristic
14#11718386—21no—
15#11718381—21no—
16C4×C8×D13C2211yescharacteristic
17#11718340C411yescharacteristic
18#11718259—21no—
19#11718258—21no—
20#11718257—21no—
21C4⋊#6092C2212yes—
22C4×#6092C2212yes—
23C2×C13×M16—21no—
24C4×D4×C13C2×C411yescharacteristic
25#88192C811yescharacteristic
26#88190C811yescharacteristic
27C4×C22⋊D13—21no—
28#88180—21no—
29C22×#1055—21no—
30C2×C8×D13D411yescharacteristic
31C2×C8×D13D411yescharacteristic
32#88151C811yescharacteristic
33#88144C811yescharacteristic
34#88137—21no—
35#88133—21no—
36C42×D13C2×C411yescharacteristic
37C4×Dic26C2×C411yescharacteristic
38C2×#6092—22no—
39C2×#6092—22no—
40#88098—24no—
41C13×C4⋊C8C2×C411yescharacteristic
42C13×C22⋊C8—21no—
43C4×C8×C13C2×C411yescharacteristic
44C22⋊#1055—21no—
45#88060—21no—
46#88055—21no—
47#88055—21no—
48#88054—21no—
49#88054—21no—
50C8×Dic13—21no—
51C8×Dic13D411yescharacteristic
52C8×Dic13D411yescharacteristic
53C4⋊#1055C2×C411yescharacteristic
54C4×#1055C2311yescharacteristic
55#11614—131nomaximal, Sylow
56C2×D4×C13C2×C811yescharacteristic
57C22×C4×C13—21no—
58C2×C22⋊D13—21no—
59C2×C4×D13C22⋊C411yescharacteristic
60C2×C4×D13C2×C811yescharacteristic
61C2×C4×D13M1611yescharacteristic
62C2×Dic26C2×C811yescharacteristic
63C13×M16—42no—
64C2×C8×C13—21no—
65C2×C8×C13C22⋊C411yescharacteristic
66C2×C8×C13C22⋊C411yescharacteristic
67C13×C4⋊C4C2×C811yescharacteristic
68C13×C22⋊C4—21no—
69C42×C13C22×C411yescharacteristic
70C22⋊Dic13—21no—
71C22⋊Dic13—21no—
72C22⋊Dic13—21no—
73#6103—21no—
74C4⋊Dic13—21no—
75C4⋊Dic13—21no—
76C4⋊Dic13C2×C811yescharacteristic
77#6101—21no—
78#6101—21no—
79C4×Dic13—21no—
80C4×Dic13C22⋊C411yescharacteristic
81C4×Dic13C2×C811yescharacteristic
82C4×Dic13M1611yescharacteristic
83C2×#1055—21no—
84C2×#1055—42no—
85C2×#1055C2×D411yescharacteristic
86C2×#1055C2×D411yescharacteristic
87C8×D13—22no—
88C8×D13—22no—
89#6092—24no—
90#6092—42no—
91#2966—131no—
92#2162—131no—
93C4×M32—131no—
94Q8⋊C16—132no—
95D4⋊C16—132no—
96C23×C13—21no—
97C22×D13C22⋊C811yescharacteristic
98D4×C13—22no—
99C2×C4×C13—21no—
100C2×C4×C13—41no—
101C2×C4×C13—41no—
102C2×C4×C13C2×C22⋊C411yescharacteristic
103C2×C4×C13C22×C811yescharacteristic
104C2×C4×C13C2×M1611yescharacteristic
105C22⋊D13—42no—
106C2×Dic13—21no—
107C2×Dic13—21no—
108C2×Dic13C22⋊C811yescharacteristic
109C2×Dic13C22⋊C811yescharacteristic
110C2×Dic13C22⋊C811yescharacteristic
111C4×D13—21no—
112C4×D13—21no—
113C4×D13—22no—
114C4×D13—41no—
115Dic26—22no—
116C8×C13—21no—
117C8×C13—41no—
118C8×C13#10412yes—
119#1055—21no—
120#1055—41no—
121#1055#13512yes—
122#529—131no—
123C2×M32—261no—
124#446—131no—
125C8×Q8—131no—
126#436#26111yescharacteristic
127#435—261no—
128C8×D4—131no—
129C8×D4—261no—
130#433—261no—
131#432—131no—
132#405—261no—
133C2×C4×C8—131no—
134C4⋊C16—132no—
135C22⋊C16—261no—
136#346—261no—
137C4×C16—132no—
138C4×C16—261no—
139C22×C13—41no—
140C22×C13—41no—
141C22×C13—41no—
142C22×C13C2×C22⋊C811yescharacteristic
143C2×D13—21no—
144C2×D13—21no—
145C2×D13—21no—
146C4×C13—21no—
147C4×C13—41no—
148C4×C13#41611yescharacteristic
149C4×C13C2×#10411yescharacteristic
150C4×C13#50412yes—
151Dic13—21no—
152Dic13—21no—
153Dic13—21no—
154Dic13—41no—
155Dic13—41no—
156C2×M16—21no—
157C22×C8—131no—
158C22×C8—131no—
159C22×C8—261no—
160#126—261no—
161#125—131no—
162#124—131no—
163#123—261no—
164C22⋊Q8—131no—
165#121—131no—
166C4×Q8—131no—
167C4×D4—261no—
168C4×D4C2×#26111yescharacteristic
169#117—261no—
170C2×C42—131no—
171M32—264no—
172C2×C16—262no—
173C2×C16—262no—
174C4⋊C8—131no—
175C4⋊C8—261no—
176C4⋊C8—261no—
177C4⋊C8C2×#26111yescharacteristic
178C22⋊C8—21no—
179C22⋊C8—261no—
180C22⋊C8—261no—
181#97—261no—
182#97—261no—
183C4×C8—131no—
184C4×C8—131no—
185C4×C8—131no—
186C4×C8—261no—
187C4×C8C2×#26111yescharacteristic
188C2×C13—81no—
189C2×C13#147611yescharacteristic
190C2×C13#211311yescharacteristic
191C2×C13#211711yescharacteristic
192D13—41no—
193C2×Q8—131no—
194C2×D4—261no—
195C2×D4D13⋊C811yescharacteristic
196C22×C4—21no—
197C22×C4—131no—
198C22×C4—131no—
199C22×C4—131no—
200M16—42no—
201C2×C8—21no—
202C2×C8—131no—
203C2×C8—131no—
204C2×C8—262no—
205C2×C8—262no—
206C2×C8—261no—
207C2×C8—522no—
208C2×C8C22⋊#26111yescharacteristic
209C2×C8C22⋊#26111yescharacteristic
210C4⋊C4—131no—
211C4⋊C4—261no—
212C4⋊C4—261no—
213C4⋊C4—261no—
214C4⋊C4—261no—
215C4⋊C4D13⋊C811yescharacteristic
216C22⋊C4—21no—
217C22⋊C4—261no—
218C22⋊C4—261no—
219C22⋊C4—261no—
220C22⋊C4—261no—
221C42—131no—
222C42—131no—
223C42—131no—
224C42—261no—
225C42C22×#26111yescharacteristic
226C16—264no—
227C16—522no—
228C13#1161411yescharacteristic, complemented, Sylow
229C23—21no—
230C23—131no—
231Q8—262no—
232D4—22no—
233D4—522no—
234C2×C4—21no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—131no—
238C2×C4—131no—
239C2×C4—131no—
240C2×C4—262no—
241C2×C4—261no—
242C2×C4—261no—
243C2×C4—261no—
244C2×C4—261no—
245C2×C4—521no—
246C2×C4C2×D13⋊C811yescharacteristic
247C2×C4D13⋊M1611yescharacteristic
248C2×C4C2×C22⋊#26111yescharacteristic
249C8—21no—
250C8—41no—
251C8—132no—
252C8—261no—
253C8—521no—
254C8#8811612yes—
255C22—41no—
256C22—41no—
257C22—41no—
258C22—261no—
259C22—261no—
260C22—261no—
261C22D13⋊(C22⋊C8)11yescharacteristic
262C4—21no—
263C4—41no—
264C4—261no—
265C4—261no—
266C4—261no—
267C4—521no—
268C4—521no—
269C4#1171909612yes—
270C4C2×#8811611yescharacteristic
271C4#1171916511yescharacteristic
272C2—81no—
273C2—521no—
274C2#1313012811yescharacteristic
275C2#1313106711yescharacteristic
276C2#1313107911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC42C22×#261
FittingC13×#436C4
socleC22×C13C2×C22⋊C8
prime radical#88192C8
cosocleC4×#1055C23
hypercenter#436#261
hypocenterC13#11614
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #13131196C2semidirect
2. C4×#88098C2semidirect
3. #13129803C2semidirect
4. D4⋊#6092C2semidirect
228. C13#11614semidirect

Maximal subgroups

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

subgroupindex
#131311962
C4×#880982
#131298032
D4⋊#60922
#131238142
#1161413