Finite Group Databasebeta

← #16787409

Subgroups — #16787409

Order 3328.

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

normal subgroups only

This group has 362 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#13131195C211yesmaximal, characteristic, complemented
2D13⋊(C4⋊C16)C211yesmaximal, characteristic, complemented
3Q8⋊#6092C212yesmaximal, complemented
4#13129787C212yesmaximal, complemented
5C8×#6131C211yesmaximal, characteristic
6C4×#6131C411yescharacteristic
7C2×D13⋊C16—21no—
8C8×Q8×C13C411yescharacteristic
9Q8×#1055C2211yescharacteristic
10#11718495—21no—
11#11718495C2211yescharacteristic
12#11718494—21no—
13#11718494C411yescharacteristic
14C8×D52—21no—
15C8×D52C411yescharacteristic
16C4×C8×D13—21no—
17C4×C8×D13C2211yescharacteristic
18#11718260—21no—
19#11718260—21no—
20#11718259—21no—
21C4⋊#6092C2212yes—
22C4×#6092C2212yes—
23C2×#6131C811yescharacteristic
24C4×Q8×C13C2×C411yescharacteristic
25Q8×Dic13C811yescharacteristic
26C2×C8×D13—21no—
27C2×C8×D13—21no—
28C2×C8×D13D411yescharacteristic
29C2×C8×D13D411yescharacteristic
30#88147—21no—
31#88147C811yescharacteristic
32#88146—21no—
33#88146C811yescharacteristic
34C4×D52—21no—
35C4×D52C2×C411yescharacteristic
36C42×D13—21no—
37C42×D13C2×C411yescharacteristic
38C2×#6092—22no—
39C2×#6092—22no—
40D13⋊C16—42no—
41C13×C4⋊C8—21no—
42C13×C4⋊C8C2×C411yescharacteristic
43C4×C8×C13—21no—
44C4×C8×C13C2×C411yescharacteristic
45#88060—21no—
46#88060—21no—
47#88060—21no—
48C8×Dic13—21no—
49C8×Dic13D411yescharacteristic
50C8×Dic13D411yescharacteristic
51C4⋊#1055—21no—
52C4⋊#1055C2×C411yescharacteristic
53C4×#1055—21no—
54C4×#1055C2311yescharacteristic
55#11621—131nomaximal, Sylow
56C2×Q8×C13C2×C811yescharacteristic
57#6131—22no—
58#6131C1614yescomplemented
59C2×D52—21no—
60C2×D52C2×C811yescharacteristic
61C2×C4×D13—21no—
62C2×C4×D13—21no—
63C2×C4×D13—21no—
64C2×C4×D13C22⋊C411yescharacteristic
65C2×C4×D13C2×C811yescharacteristic
66C2×C4×D13M1611yescharacteristic
67C2×C8×C13—21no—
68C2×C8×C13C22⋊C411yescharacteristic
69C2×C8×C13C22⋊C411yescharacteristic
70C13×C4⋊C4—21no—
71C13×C4⋊C4C2×C811yescharacteristic
72C42×C13—21no—
73C42×C13C22×C411yescharacteristic
74#6103—21no—
75#6103—21no—
76#6103—21no—
77C4⋊Dic13—21no—
78C4⋊Dic13C2×C811yescharacteristic
79C4×Dic13—21no—
80C4×Dic13—21no—
81C4×Dic13C22⋊C411yescharacteristic
82C4×Dic13C2×C811yescharacteristic
83C4×Dic13M1611yescharacteristic
84C2×#1055—21no—
85C2×#1055C2×D411yescharacteristic
86C2×#1055C2×D411yescharacteristic
87C8×D13—21no—
88C8×D13—21no—
89C8×D13—41no—
90C8×D13—42no—
91C8×D13—41no—
92C8×D13—41no—
93#6092—42no—
94#6092—42no—
95C8×#41—131no—
96#2162—131no—
97C2×C4⋊C16—131no—
98Q8⋊C16—132no—
99D4⋊C16—132no—
100C22×D13—21no—
101C22×D13C22⋊C811yescharacteristic
102Q8×C13—21no—
103Q8×C13C2×C1612yescomplemented
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13C2×C22⋊C411yescharacteristic
107C2×C4×C13C22×C811yescharacteristic
108C2×C4×C13C2×M1611yescharacteristic
109C2×Dic13—21no—
110C2×Dic13C22⋊C811yescharacteristic
111C2×Dic13C22⋊C811yescharacteristic
112C2×Dic13C22⋊C811yescharacteristic
113D52—24no—
114D52—21no—
115D52C2×C1612yescomplemented
116C4×D13—21no—
117C4×D13—21no—
118C4×D13—24no—
119C4×D13—41no—
120C4×D13—42no—
121C4×D13—41no—
122C4×D13—41no—
123C4×D13C2×C1612yes—
124C4×D13M3212yes—
125C8×C13—21no—
126C8×C13—21no—
127C8×C13—41no—
128#1055—21no—
129#1055—41no—
130#1055AGL(1,ℤ/8)11yescharacteristic
131#1055#13711yescharacteristic
132C4×#41—131no—
133C22×C16—261no—
134C8×Q8—131no—
135C8×Q8#26111yescharacteristic
136C8×D4—131no—
137C8×D4—131no—
138C8×D4—261no—
139C8×D4—261no—
140#431—131no—
141#431—261no—
142C2×C4×C8—131no—
143C2×C4×C8—261no—
144C4⋊C16—132no—
145C4⋊C16—261no—
146C4⋊C16—261no—
147C22⋊C16—261no—
148C4×C16—132no—
149C22×C13C2×C22⋊C811yescharacteristic
150C2×D13—21no—
151C2×D13—21no—
152C2×D13—22no—
153C2×D13—41no—
154C2×D13—41no—
155C2×D13C22⋊C1612yes—
156C4×C13—22no—
157C4×C13—21no—
158C4×C13—41no—
159C4×C13#41711yescharacteristic
160C4×C13#42111yescharacteristic
161C4×C13C22×C1611yescharacteristic
162C4×C13C2×M3211yescharacteristic
163Dic13—21no—
164Dic13—21no—
165Dic13—41no—
166Dic13C22⋊C1612yes—
167C2×#41—131no—
168C22×C8—131no—
169C22×C8—131no—
170C22×C8—261no—
171C22×C8—261no—
172C4×Q8—131no—
173C4×Q8C2×#26111yescharacteristic
174C4×D4—131no—
175C4×D4—131no—
176C4×D4—261no—
177C4×D4—261no—
178#117—131no—
179#117—261no—
180C2×C42—131no—
181C2×C42—261no—
182C2×C16—262no—
183C2×C16—262no—
184C2×C16—522no—
185C4⋊C8—21no—
186C4⋊C8—131no—
187C4⋊C8—261no—
188C4⋊C8C2×#26111yescharacteristic
189C22⋊C8—261no—
190C22⋊C8—261no—
191C22⋊C8—261no—
192C4×C8—21no—
193C4×C8—131no—
194C4×C8—131no—
195C4×C8—131no—
196C4×C8—261no—
197C4×C8—261no—
198C4×C8C2×#26111yescharacteristic
199C2×C13#147711yescharacteristic
200C2×C13C2×C22⋊C1611yescharacteristic
201C2×C13#211711yescharacteristic
202D13—22no—
203D13—42no—
204#41—134no—
205#41—262no—
206C2×Q8D13⋊C811yescharacteristic
207C2×D4—131no—
208C2×D4—261no—
209C22×C4—131no—
210C22×C4—131no—
211C22×C4—131no—
212C22×C4—261no—
213C22×C4—261no—
214C22×C4—261no—
215C2×C8—21no—
216C2×C8—131no—
217C2×C8—131no—
218C2×C8—261no—
219C2×C8—261no—
220C2×C8—261no—
221C2×C8—521no—
222C2×C8—522no—
223C2×C8—521no—
224C2×C8—521no—
225C2×C8C22⋊#26111yescharacteristic
226C2×C8C22⋊#26111yescharacteristic
227C4⋊C4—21no—
228C4⋊C4—131no—
229C4⋊C4—261no—
230C4⋊C4D13⋊C811yescharacteristic
231C22⋊C4—261no—
232C22⋊C4—261no—
233C22⋊C4—261no—
234C42—21no—
235C42—131no—
236C42—131no—
237C42—131no—
238C42—261no—
239C42—261no—
240C42C22×#26111yescharacteristic
241C16—522no—
242C16—522no—
243C13#1162111yescharacteristic, complemented, Sylow
244C23—131no—
245C23—261no—
246Q8—21no—
247Q8D13⋊C1612yescomplemented
248D4—132no—
249D4—264no—
250D4—261no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—131no—
254C2×C4—132no—
255C2×C4—132no—
256C2×C4—131no—
257C2×C4—131no—
258C2×C4—264no—
259C2×C4—261no—
260C2×C4—261no—
261C2×C4—261no—
262C2×C4—521no—
263C2×C4—522no—
264C2×C4—521no—
265C2×C4—521no—
266C2×C4C2×D13⋊C811yescharacteristic
267C2×C4D13⋊M1611yescharacteristic
268C2×C4C2×C22⋊#26111yescharacteristic
269C8—21no—
270C8—21no—
271C8—41no—
272C8—131no—
273C8—131no—
274C8—261no—
275C8—521no—
276C22—132no—
277C22—261no—
278C22—261no—
279C22—262no—
280C22—521no—
281C22—521no—
282C22D13⋊(C22⋊C8)11yescharacteristic
283C4—22no—
284C4—21no—
285C4—41no—
286C4—132no—
287C4—261no—
288C4—261no—
289C4—521no—
290C4C2×D13⋊C1611yescharacteristic
291C4D13⋊M3211yescharacteristic
292C4#1171915511yescharacteristic
293C4#1171916411yescharacteristic
294C2—262no—
295C2—522no—
296C2#1313013411yescharacteristic
297C2D13⋊(C22⋊C16)11yescharacteristic
298C2#1313107911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC4×C13C22×C16
FrattiniC42C22×#261
FittingC8×Q8×C13C4
socleC22×C13C2×C22⋊C8
prime radicalC2×#6131C8
cosocleC4×#1055C23
hypercenterC8×Q8#261
hypocenterC13#11621
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
1. #13131195C2semidirect
2. D13⋊(C4⋊C16)C2semidirect
3. Q8⋊#6092C2semidirect
4. #13129787C2semidirect
58. #6131C16semidirect
103. Q8×C13C2×C16semidirect
115. D52C2×C16semidirect
243. C13#11621semidirect
247. Q8D13⋊C16semidirect

Maximal subgroups

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

subgroupindex
#131311952
D13⋊(C4⋊C16)2
Q8⋊#60922
#131297872
C8×#61312
#1162113