Finite Group Databasebeta

← #16787463

Subgroups — #16787463

Order 3328.

342 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 106 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
2#13131195C211yesmaximal, characteristic
3#13129803C212yesmaximal, complemented
4Q8⋊#6092C212yesmaximal, complemented
5C8×Q8×D13C211yesmaximal, characteristic
6C4×Q8×D13C411yescharacteristic
7C8×Q8×C13C411yescharacteristic
8Q8×#1055C2211yescharacteristic
9D13×C4⋊C8—21no—
10D13×C4⋊C8C411yescharacteristic
11#11718491—21no—
12#11718491C2211yescharacteristic
13C4×C8×D13—21no—
14C4×C8×D13C2211yescharacteristic
15C8×Dic26—21no—
16C8×Dic26C411yescharacteristic
17#11718260—21no—
18#11718259—21no—
19#11718259—21no—
20#11718257—21no—
21C4⋊#6092C2212yes—
22C4×#6092C2212yes—
23C2×Q8×D13C811yescharacteristic
24C4×Q8×C13C2×C411yescharacteristic
25Q8×Dic13C811yescharacteristic
26C2×C8×D13—21no—
27C2×C8×D13D411yescharacteristic
28C2×C8×D13D411yescharacteristic
29C4⋊C4×D13—21no—
30C4⋊C4×D13C811yescharacteristic
31#88141—21no—
32#88141C811yescharacteristic
33C42×D13—21no—
34C42×D13C2×C411yescharacteristic
35C4×Dic26—21no—
36C4×Dic26C2×C411yescharacteristic
37C2×#6092—22no—
38C2×#6092—22no—
39C13×C4⋊C8—21no—
40C13×C4⋊C8C2×C411yescharacteristic
41C4×C8×C13—21no—
42C4×C8×C13C2×C411yescharacteristic
43#88054—21no—
44#88054—21no—
45#88054—21no—
46C8×Dic13—21no—
47C8×Dic13—21no—
48C8×Dic13D411yescharacteristic
49C8×Dic13D411yescharacteristic
50C4⋊#1055—21no—
51C4⋊#1055C2×C411yescharacteristic
52C4×#1055—21no—
53C4×#1055C2311yescharacteristic
54#11637—131nomaximal, Sylow
55C2×Q8×C13C2×C811yescharacteristic
56Q8×D13—22no—
57Q8×D13C1614yescomplemented
58C2×C4×D13—21no—
59C2×C4×D13—21no—
60C2×C4×D13C22⋊C411yescharacteristic
61C2×C4×D13C2×C811yescharacteristic
62C2×C4×D13M1611yescharacteristic
63C2×Dic26—21no—
64C2×Dic26C2×C811yescharacteristic
65C2×C8×C13—21no—
66C2×C8×C13C22⋊C411yescharacteristic
67C2×C8×C13C22⋊C411yescharacteristic
68C13×C4⋊C4—21no—
69C13×C4⋊C4C2×C811yescharacteristic
70C42×C13—21no—
71C42×C13C22×C411yescharacteristic
72C4⋊Dic13—21no—
73C4⋊Dic13C2×C811yescharacteristic
74#6101—21no—
75#6101—21no—
76#6101—21no—
77C4×Dic13—21no—
78C4×Dic13—21no—
79C4×Dic13—21no—
80C4×Dic13C22⋊C411yescharacteristic
81C4×Dic13C2×C811yescharacteristic
82C4×Dic13M1611yescharacteristic
83C2×#1055—21no—
84C2×#1055C2×D411yescharacteristic
85C2×#1055C2×D411yescharacteristic
86C8×D13—22no—
87C8×D13—41no—
88C8×D13—42no—
89#6092—42no—
90#6092—42no—
91C2×C8×Q8—131no—
92#2162—131no—
93#2162—131no—
94Q8⋊C16—132no—
95Q8⋊C16—132no—
96C22×D13C22⋊C811yescharacteristic
97Q8×C13—21no—
98Q8×C13C2×C1612yes—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13C2×C22⋊C411yescharacteristic
102C2×C4×C13C22×C811yescharacteristic
103C2×C4×C13C2×M1611yescharacteristic
104C2×Dic13—21no—
105C2×Dic13—21no—
106C2×Dic13C22⋊C811yescharacteristic
107C2×Dic13C22⋊C811yescharacteristic
108C2×Dic13C22⋊C811yescharacteristic
109C4×D13—24no—
110C4×D13—21no—
111C4×D13—21no—
112C4×D13—41no—
113C4×D13—42no—
114C4×D13C2×C1612yes—
115C4×D13M3212yes—
116Dic26—21no—
117Dic26—24no—
118Dic26C2×C1612yes—
119C8×C13—21no—
120C8×C13—21no—
121C8×C13—41no—
122#1055—21no—
123#1055—41no—
124#1055#13712yes—
125C2×C4×Q8—131no—
126C8×Q8—131no—
127C8×Q8—131no—
128C8×Q8—131no—
129C8×Q8—261no—
130C8×Q8—261no—
131C8×Q8#26111yescharacteristic
132C2×C4⋊C8—131no—
133C2×C4⋊C8—261no—
134C2×C4×C8—131no—
135C2×C4×C8—261no—
136C4⋊C16—132no—
137C4⋊C16—261no—
138C22⋊C16—261no—
139C22⋊C16—261no—
140C4×C16—132no—
141C4×C16—261no—
142C22×C13C2×C22⋊C811yescharacteristic
143C2×D13—21no—
144C2×D13—21no—
145C2×D13C22⋊C1612yes—
146C4×C13—22no—
147C4×C13—21no—
148C4×C13—41no—
149C4×C13#41911yescharacteristic
150C4×C13#42111yescharacteristic
151C4×C13C22×C1611yescharacteristic
152C4×C13C2×M3211yescharacteristic
153Dic13—22no—
154Dic13—21no—
155Dic13—21no—
156Dic13—41no—
157Dic13C22⋊C1612yes—
158C22×Q8—131no—
159C22×C8—131no—
160C22×C8—131no—
161C22×C8—261no—
162C4×Q8—131no—
163C4×Q8—131no—
164C4×Q8—131no—
165C4×Q8—261no—
166C4×Q8—261no—
167C4×Q8C2×#26111yescharacteristic
168C2×C4⋊C4—131no—
169C2×C4⋊C4—261no—
170C2×C42—131no—
171C2×C42—261no—
172C2×C16—262no—
173C2×C16—262no—
174C4⋊C8—21no—
175C4⋊C8—131no—
176C4⋊C8—261no—
177C4⋊C8—261no—
178C4⋊C8—261no—
179C4⋊C8—261no—
180C4⋊C8C2×#26111yescharacteristic
181C4×C8—21no—
182C4×C8—131no—
183C4×C8—131no—
184C4×C8—131no—
185C4×C8—261no—
186C4×C8—261no—
187C4×C8—261no—
188C4×C8C2×#26111yescharacteristic
189C2×C13#147911yescharacteristic
190C2×C13C2×C22⋊C1611yescharacteristic
191C2×C13#211711yescharacteristic
192D13—22no—
193C2×Q8—134no—
194C2×Q8—131no—
195C2×Q8—261no—
196C2×Q8—262no—
197C2×Q8D13⋊C811yescharacteristic
198C22×C4—131no—
199C22×C4—131no—
200C22×C4—131no—
201C22×C4—261no—
202C22×C4—261no—
203C2×C8—21no—
204C2×C8—131no—
205C2×C8—131no—
206C2×C8—262no—
207C2×C8—261no—
208C2×C8—521no—
209C2×C8—522no—
210C2×C8C22⋊#26111yescharacteristic
211C2×C8C22⋊#26111yescharacteristic
212C4⋊C4—21no—
213C4⋊C4—131no—
214C4⋊C4—261no—
215C4⋊C4—261no—
216C4⋊C4—261no—
217C4⋊C4—261no—
218C4⋊C4D13⋊C811yescharacteristic
219C42—21no—
220C42—131no—
221C42—131no—
222C42—131no—
223C42—261no—
224C42—261no—
225C42—261no—
226C42C22×#26111yescharacteristic
227C16—522no—
228C16—522no—
229C13#1163711yescharacteristic, complemented, Sylow
230C23—131no—
231Q8—21no—
232Q8—132no—
233Q8—264no—
234Q8—261no—
235Q8D13⋊C1612yes—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—131no—
239C2×C4—132no—
240C2×C4—132no—
241C2×C4—131no—
242C2×C4—131no—
243C2×C4—264no—
244C2×C4—261no—
245C2×C4—261no—
246C2×C4—261no—
247C2×C4—261no—
248C2×C4—521no—
249C2×C4—522no—
250C2×C4C2×D13⋊C811yescharacteristic
251C2×C4D13⋊M1611yescharacteristic
252C2×C4C2×C22⋊#26111yescharacteristic
253C8—21no—
254C8—21no—
255C8—41no—
256C8—132no—
257C8—261no—
258C8—521no—
259C22—132no—
260C22—261no—
261C22—261no—
262C22D13⋊(C22⋊C8)11yescharacteristic
263C4—22no—
264C4—21no—
265C4—41no—
266C4—132no—
267C4—262no—
268C4—261no—
269C4—261no—
270C4—521no—
271C4C2×D13⋊C1611yescharacteristic
272C4D13⋊M3211yescharacteristic
273C4#1171915311yescharacteristic
274C4#1171916611yescharacteristic
275C2—262no—
276C2#1313013911yescharacteristic
277C2D13⋊(C22⋊C16)11yescharacteristic
278C2#1313107911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC4×C13C22×C16
FrattiniC42C22×#261
FittingC8×Q8×C13C4
socleC22×C13C2×C22⋊C8
prime radicalC22×D13C22⋊C8
cosocleC4×#1055C23
hypercenterC8×Q8#261
hypocenterC13#11637
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×Q8

Complements

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

NH ≅ G/Ntype
3. #13129803C2semidirect
4. Q8⋊#6092C2semidirect
57. Q8×D13C16semidirect
229. C13#11637semidirect

Maximal subgroups

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

subgroupindex
#131311962
#131311952
#131298032
Q8⋊#60922
C8×Q8×D132
#1163713