Finite Group Databasebeta

← #16787439

Subgroups — #16787439

Order 3328.

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

normal subgroups only

This group has 430 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, complemented
2#13131195C211yesmaximal, characteristic, complemented
3#13129787C212yesmaximal, complemented
4D4⋊#6092C212yesmaximal, complemented
5C8×D4×D13C211yesmaximal, characteristic
6C22×C8×D13—21no—
7C4×D4×D13C411yescharacteristic
8C8×D4×C13C411yescharacteristic
9C8×C22⋊D13—21no—
10D4×#1055C2211yescharacteristic
11#11718495C2211yescharacteristic
12D13×C4⋊C8C411yescharacteristic
13#11718386—21no—
14D13×C22⋊C8—21no—
15C8×D52C411yescharacteristic
16C4×C8×D13C2211yescharacteristic
17#11718260—21no—
18#11718259—21no—
19#11718259—21no—
20#11718257—21no—
21C4⋊#6092C2212yescomplemented
22C4×#6092C2212yescomplemented
23C2×D4×D13C811yescharacteristic
24C22×C4×D13—21no—
25C22×C8×C13—21no—
26C4×D4×C13C2×C411yescharacteristic
27D4×Dic13C811yescharacteristic
28C4×C22⋊D13—21no—
29C22×#1055—21no—
30C2×C8×D13—21no—
31C2×C8×D13—21no—
32C2×C8×D13—21no—
33C2×C8×D13—44no—
34C2×C8×D13D411yescharacteristic
35C2×C8×D13D411yescharacteristic
36#88147C811yescharacteristic
37C4⋊C4×D13C811yescharacteristic
38#88135—21no—
39C22⋊C4×D13—21no—
40C4×D52C2×C411yescharacteristic
41C42×D13C2×C411yescharacteristic
42C2×#6092—22no—
43C2×#6092—22no—
44C13×C4⋊C8C2×C411yescharacteristic
45C13×C22⋊C8—21no—
46C4×C8×C13C2×C411yescharacteristic
47C22⋊#1055—21no—
48#88060—21no—
49#88060—21no—
50#88054—21no—
51C8×Dic13D411yescharacteristic
52C8×Dic13D411yescharacteristic
53C4⋊#1055C2×C411yescharacteristic
54C4×#1055C2311yescharacteristic
55#11629—131nomaximal, Sylow
56C23×D13—21no—
57C2×D4×C13C2×C811yescharacteristic
58C22×C4×C13—21no—
59C2×C22⋊D13—21no—
60C22×Dic13—21no—
61D4×D13—22no—
62D4×D13C1614yescomplemented
63C2×D52C2×C811yescharacteristic
64C2×C4×D13—21no—
65C2×C4×D13—21no—
66C2×C4×D13—21no—
67C2×C4×D13—42no—
68C2×C4×D13—42no—
69C2×C4×D13C22⋊C411yescharacteristic
70C2×C4×D13C2×C811yescharacteristic
71C2×C4×D13M1611yescharacteristic
72C2×C8×C13—21no—
73C2×C8×C13—42no—
74C2×C8×C13C22⋊C411yescharacteristic
75C2×C8×C13C22⋊C411yescharacteristic
76C13×C4⋊C4C2×C811yescharacteristic
77C13×C22⋊C4—21no—
78C42×C13C22×C411yescharacteristic
79C22⋊Dic13—21no—
80#6103—21no—
81#6103—21no—
82C4⋊Dic13C2×C811yescharacteristic
83#6101—21no—
84C4×Dic13C22⋊C411yescharacteristic
85C4×Dic13C2×C811yescharacteristic
86C4×Dic13M1611yescharacteristic
87C2×#1055—21no—
88C2×#1055—42no—
89C2×#1055C2×D411yescharacteristic
90C2×#1055C2×D411yescharacteristic
91C8×D13—22no—
92C8×D13—41no—
93C8×D13—42no—
94C8×D13—42no—
95C8×D13—42no—
96#6092—42no—
97#6092—42no—
98C2×C8×D4—131no—
99#2162—131no—
100#2162—131no—
101D4⋊C16—132no—
102D4⋊C16—132no—
103C23×C13—21no—
104C22×D13—21no—
105C22×D13—24no—
106C22×D13—42no—
107C22×D13—42no—
108C22×D13C22⋊C811yescharacteristic
109D4×C13—21no—
110D4×C13C2×C1612yes—
111C2×C4×C13—21no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13C2×C22⋊C411yescharacteristic
115C2×C4×C13C22×C811yescharacteristic
116C2×C4×C13C2×M1611yescharacteristic
117C22⋊D13—24no—
118C2×Dic13—21no—
119C2×Dic13—42no—
120C2×Dic13C22⋊C811yescharacteristic
121C2×Dic13C22⋊C811yescharacteristic
122C2×Dic13C22⋊C811yescharacteristic
123D52—21no—
124D52C2×C1612yes—
125C4×D13—21no—
126C4×D13—21no—
127C4×D13—41no—
128C4×D13—42no—
129C4×D13—42no—
130C4×D13—41no—
131C4×D13—41no—
132C4×D13C2×C1612yes—
133C4×D13M3212yes—
134C8×C13—21no—
135C8×C13—21no—
136C8×C13—41no—
137#1055—21no—
138#1055—41no—
139#1055AGL(1,ℤ/8)12yes—
140C23×C8—261no—
141C2×C4×D4—131no—
142C8×D4—131no—
143C8×D4—131no—
144C8×D4—131no—
145C8×D4—261no—
146C8×D4—261no—
147C8×D4#26111yescharacteristic
148C2×C4⋊C8—131no—
149C2×C22⋊C8—261no—
150C2×C4×C8—131no—
151C4⋊C16—132no—
152C4⋊C16—261no—
153C22⋊C16—261no—
154C22⋊C16—261no—
155C4×C16—132no—
156C4×C16—261no—
157C22×C13—22no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13C2×C22⋊C811yescharacteristic
161C2×D13—21no—
162C2×D13—21no—
163C2×D13—22no—
164C2×D13—48no—
165C2×D13—41no—
166C2×D13—41no—
167C2×D13C22⋊C1612yes—
168C4×C13—21no—
169C4×C13—41no—
170C4×C13#41811yescharacteristic
171C4×C13#42111yescharacteristic
172C4×C13C22×C1611yescharacteristic
173C4×C13C2×M3211yescharacteristic
174Dic13—21no—
175Dic13—21no—
176Dic13—41no—
177Dic13C22⋊C1612yes—
178C22×D4—131no—
179C23×C4—261no—
180C22×C8—21no—
181C22×C8—131no—
182C22×C8—131no—
183C22×C8—261no—
184C22×C8—261no—
185C22×C8—261no—
186C22×C8—261no—
187C22×C8—524no—
188C4×D4—131no—
189C4×D4—131no—
190C4×D4—131no—
191C4×D4—261no—
192C4×D4—261no—
193C4×D4C2×#26111yescharacteristic
194C2×C4⋊C4—131no—
195C2×C22⋊C4—261no—
196C2×C42—131no—
197C2×C16—262no—
198C2×C16—262no—
199C4⋊C8—131no—
200C4⋊C8—261no—
201C4⋊C8C2×#26111yescharacteristic
202C22⋊C8—21no—
203C22⋊C8—261no—
204C22⋊C8—261no—
205C22⋊C8—261no—
206C4×C8—131no—
207C4×C8—131no—
208C4×C8—131no—
209C4×C8C2×#26111yescharacteristic
210C2×C13—42no—
211C2×C13#147811yescharacteristic
212C2×C13C2×C22⋊C1611yescharacteristic
213C2×C13#211711yescharacteristic
214D13—22no—
215D13—42no—
216C24—261no—
217C2×D4—134no—
218C2×D4—131no—
219C2×D4—262no—
220C2×D4—261no—
221C2×D4D13⋊C811yescharacteristic
222C22×C4—21no—
223C22×C4—131no—
224C22×C4—131no—
225C22×C4—131no—
226C22×C4—261no—
227C22×C4—261no—
228C22×C4—261no—
229C22×C4—261no—
230C22×C4—522no—
231C22×C4—522no—
232C2×C8—21no—
233C2×C8—42no—
234C2×C8—131no—
235C2×C8—131no—
236C2×C8—262no—
237C2×C8—261no—
238C2×C8—521no—
239C2×C8—522no—
240C2×C8—522no—
241C2×C8—522no—
242C2×C8—522no—
243C2×C8C22⋊#26111yescharacteristic
244C2×C8C22⋊#26111yescharacteristic
245C4⋊C4—131no—
246C4⋊C4—261no—
247C4⋊C4D13⋊C811yescharacteristic
248C22⋊C4—21no—
249C22⋊C4—261no—
250C22⋊C4—261no—
251C22⋊C4—261no—
252C42—131no—
253C42—131no—
254C42—131no—
255C42C22×#26111yescharacteristic
256C16—522no—
257C16—522no—
258C13#1162911yescharacteristic, complemented, Sylow
259C23—21no—
260C23—131no—
261C23—264no—
262C23—261no—
263C23—522no—
264C23—522no—
265D4—21no—
266D4—132no—
267D4—264no—
268D4—261no—
269D4D13⋊C1612yes—
270C2×C4—21no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—131no—
274C2×C4—132no—
275C2×C4—132no—
276C2×C4—131no—
277C2×C4—131no—
278C2×C4—261no—
279C2×C4—261no—
280C2×C4—261no—
281C2×C4—521no—
282C2×C4—522no—
283C2×C4—522no—
284C2×C4—522no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4C2×D13⋊C811yescharacteristic
288C2×C4D13⋊M1611yescharacteristic
289C2×C4C2×C22⋊#26111yescharacteristic
290C8—21no—
291C8—21no—
292C8—41no—
293C8—132no—
294C8—261no—
295C8—521no—
296C22—22no—
297C22—41no—
298C22—41no—
299C22—132no—
300C22—261no—
301C22—261no—
302C22—262no—
303C22—528no—
304C22—521no—
305C22—521no—
306C22D13⋊(C22⋊C8)11yescharacteristic
307C4—21no—
308C4—41no—
309C4—132no—
310C4—261no—
311C4—261no—
312C4—521no—
313C4C2×D13⋊C1611yescharacteristic
314C4D13⋊M3211yescharacteristic
315C4#1171913811yescharacteristic
316C4#1171916611yescharacteristic
317C2—42no—
318C2—262no—
319C2—522no—
320C2#1313013611yescharacteristic
321C2D13⋊(C22⋊C16)11yescharacteristic
322C2#1313107911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC4×C13C22×C16
FrattiniC42C22×#261
FittingC8×D4×C13C4
socleC22×C13C2×C22⋊C8
prime radicalC2×D4×D13C8
cosocleC4×#1055C23
hypercenterC8×D4#261
hypocenterC13#11629
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #13131196C2semidirect
2. #13131195C2semidirect
3. #13129787C2semidirect
4. D4⋊#6092C2semidirect
21. C4⋊#6092C22semidirect
22. C4×#6092C22semidirect
62. D4×D13C16semidirect
258. C13#11629semidirect

Maximal subgroups

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

subgroupindex
#131311962
#131311952
#131297872
D4⋊#60922
C8×D4×D132
#1162913