Finite Group Databasebeta

← #16787429

Subgroups — #16787429

Order 3328.

328 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 88 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#13131199C211yesmaximal, characteristic, complemented
2D13⋊(C4⋊C16)C211yesmaximal, characteristic, complemented
3#13129804C212yesmaximal, complemented
4#13129789C212yesmaximal, complemented
5#13123801C211yesmaximal, characteristic
6C4×#6131C411yescharacteristic
7C2×D13⋊C16—21no—
8C13×#446C411yescharacteristic
9#11718685C2211yescharacteristic
10#11718499C2211yescharacteristic
11#11718497—21no—
12#11718494—21no—
13#11718494C411yescharacteristic
14#11718368—21no—
15#11718367—21no—
16#11718349C411yescharacteristic
17C4×C8×D13C2211yescharacteristic
18#11718260—21no—
19#11718260—21no—
20#11718259—21no—
21#11718231C2212yes—
22C4⋊#6092C2212yes—
23C2×#6131C811yescharacteristic
24C4×Q8×C13C2×C411yescharacteristic
25Q8×Dic13C811yescharacteristic
26C2×#6094—21no—
27C2×#6094—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
43C13×#97—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
53#88043—21no—
54C4×#1055C2311yescharacteristic
55#11626—131nomaximal, Sylow
56C2×Q8×C13C2×C811yescharacteristic
57#6131—42no—
58C2×D52—21no—
59C2×D52C2×C811yescharacteristic
60C2×C4×D13—21no—
61C2×C4×D13—21no—
62C2×C4×D13—21no—
63C2×C4×D13C22⋊C411yescharacteristic
64C2×C4×D13C2×C811yescharacteristic
65C2×C4×D13M1611yescharacteristic
66C2×C8×C13—21no—
67C2×C8×C13C22⋊C411yescharacteristic
68C2×C8×C13C22⋊C411yescharacteristic
69C13×C4⋊C4—21no—
70C13×C4⋊C4C2×C811yescharacteristic
71C42×C13—21no—
72C42×C13C22×C411yescharacteristic
73#6103—21no—
74#6103—21no—
75#6103—21no—
76C4⋊Dic13—21no—
77C4⋊Dic13C2×C811yescharacteristic
78C4×Dic13—21no—
79C4×Dic13—21no—
80C4×Dic13C22⋊C411yescharacteristic
81C4×Dic13C2×C811yescharacteristic
82C4×Dic13M1611yescharacteristic
83C2×#1055—21no—
84C2×#1055C2×D411yescharacteristic
85C2×#1055C2×D411yescharacteristic
86#6094—42no—
87#6094—41no—
88#6094—41no—
89C8×D13—21no—
90C8×D13—21no—
91C8×D13—41no—
92#6092—42no—
93#6092—42no—
94#2965—131no—
95#2163—131no—
96C2×C4⋊C16—131no—
97#1338—132no—
98#1330—132no—
99C22×D13—21no—
100C22×D13C22⋊C811yescharacteristic
101Q8×C13—41no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13C2×C22⋊C411yescharacteristic
105C2×C4×C13C22×C811yescharacteristic
106C2×C4×C13C2×M1611yescharacteristic
107C2×Dic13—21no—
108C2×Dic13C22⋊C811yescharacteristic
109C2×Dic13C22⋊C811yescharacteristic
110C2×Dic13C22⋊C811yescharacteristic
111D52—41no—
112D52—42no—
113C4×D13—22no—
114C4×D13—21no—
115C4×D13—21no—
116C4×D13—22no—
117C4×D13—42no—
118C4×D13—41no—
119C4×D13—41no—
120C4×D13—42no—
121C8×C13—21no—
122C8×C13—21no—
123C8×C13—41no—
124#1055—21no—
125#1055—41no—
126#1055AGL(1,ℤ/8)11yescharacteristic
127#1055#13711yescharacteristic
128C4×#41—131no—
129C22×C16—261no—
130#446—131no—
131#446#26111yescharacteristic
132#436—131no—
133#436—131no—
134#435—261no—
135#435—261no—
136#431—131no—
137#431—261no—
138C4×M16—261no—
139C2×C4×C8—131no—
140C4⋊C16—132no—
141C4⋊C16—261no—
142C4⋊C16—261no—
143C22⋊C16—261no—
144#346—132no—
145C22×C13C2×C22⋊C811yescharacteristic
146C2×D13—21no—
147C2×D13—21no—
148C2×D13—41no—
149C2×D13—41no—
150C2×D13—41no—
151C2×D13#34912yes—
152C4×C13—21no—
153C4×C13—21no—
154C4×C13—41no—
155C4×C13—41no—
156C4×C13#41711yescharacteristic
157C4×C13#42111yescharacteristic
158Dic13—21no—
159Dic13—21no—
160Dic13—41no—
161Dic13#35012yes—
162C2×#41—131no—
163C2×M16—261no—
164C2×M16—261no—
165C22×C8—131no—
166C22×C8—131no—
167C4×Q8—131no—
168C4×Q8C2×#26111yescharacteristic
169C4×D4—131no—
170C4×D4—131no—
171C4×D4—261no—
172C4×D4—261no—
173#117—131no—
174#117—261no—
175C2×C42—131no—
176C2×C42—261no—
177C2×C16—262no—
178C2×C16—262no—
179C2×C16—522no—
180C4⋊C8—21no—
181C4⋊C8—131no—
182C4⋊C8—261no—
183C4⋊C8C2×#26111yescharacteristic
184C22⋊C8—261no—
185C22⋊C8—261no—
186C22⋊C8—261no—
187#97—21no—
188#97—261no—
189C4×C8—131no—
190C4×C8—131no—
191C4×C8—131no—
192C4×C8—261no—
193C4×C8C2×#26111yescharacteristic
194C2×C13#147711yescharacteristic
195C2×C13C2×#34911yescharacteristic
196C2×C13C2×#35011yescharacteristic
197D13—22no—
198D13—81no—
199#41—522no—
200C2×Q8D13⋊C811yescharacteristic
201C2×D4—131no—
202C2×D4—261no—
203C22×C4—131no—
204C22×C4—131no—
205C22×C4—131no—
206C22×C4—261no—
207C22×C4—261no—
208C22×C4—261no—
209M16—522no—
210M16—521no—
211M16—521no—
212C2×C8—21no—
213C2×C8—131no—
214C2×C8—131no—
215C2×C8—261no—
216C2×C8—261no—
217C2×C8—261no—
218C2×C8—521no—
219C2×C8C22⋊#26111yescharacteristic
220C2×C8C22⋊#26111yescharacteristic
221C4⋊C4—21no—
222C4⋊C4—131no—
223C4⋊C4—261no—
224C4⋊C4D13⋊C811yescharacteristic
225C22⋊C4—261no—
226C22⋊C4—261no—
227C22⋊C4—261no—
228C42—21no—
229C42—131no—
230C42—131no—
231C42—131no—
232C42—261no—
233C42—261no—
234C42C22×#26111yescharacteristic
235C16—522no—
236C16—522no—
237C13#1162611yescharacteristic, complemented, Sylow
238C23—131no—
239C23—261no—
240Q8—41no—
241D4—521no—
242D4—522no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—131no—
246C2×C4—131no—
247C2×C4—131no—
248C2×C4—262no—
249C2×C4—262no—
250C2×C4—261no—
251C2×C4—261no—
252C2×C4—261no—
253C2×C4—522no—
254C2×C4—522no—
255C2×C4—521no—
256C2×C4—521no—
257C2×C4C2×D13⋊C811yescharacteristic
258C2×C4D13⋊M1611yescharacteristic
259C2×C4C2×C22⋊#26111yescharacteristic
260C8—21no—
261C8—21no—
262C8—41no—
263C8—131no—
264C8—131no—
265C8—261no—
266C8—521no—
267C22—132no—
268C22—261no—
269C22—261no—
270C22—521no—
271C22—521no—
272C22—521no—
273C22D13⋊(C22⋊C8)11yescharacteristic
274C4—21no—
275C4—21no—
276C4—41no—
277C4—41no—
278C4—132no—
279C4—261no—
280C4—261no—
281C4—521no—
282C4#1171915511yescharacteristic
283C4#1171916411yescharacteristic
284C2—262no—
285C2—1041no—
286C2#1313013411yescharacteristic
287C2D13⋊#34911yescharacteristic
288C2D13⋊#35011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC42C22×#261
FittingC13×#446C4
socleC22×C13C2×C22⋊C8
prime radicalC2×#6131C8
cosocleC4×#1055C23
hypercenter#446#261
hypocenterC13#11626
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #13131199C2semidirect
2. D13⋊(C4⋊C16)C2semidirect
3. #13129804C2semidirect
4. #13129789C2semidirect
237. C13#11626semidirect

Maximal subgroups

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

subgroupindex
#131311992
D13⋊(C4⋊C16)2
#131298042
#131297892
#131238012
#1162613