Finite Group Databasebeta

← #15766686

Subgroups — #15766686

Order 3328.

398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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#13124629C211yesmaximal, characteristic
2#13114847C211yesmaximal, characteristic
3#13113610C211yesmaximal, characteristic, complemented
4#13113400C211yesmaximal, characteristic, complemented
5#13113156C211yesmaximal, characteristic
6#13112695C211yesmaximal, characteristic, complemented
7C13×#1542C211yesmaximal, characteristic, complemented
8C13×#533C2211yescharacteristic
9C2×C4×D52C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×#88061—21no—
13#11718748—21no—
14#11718745—21no—
15#11718727—22no—
16#11718662—21no—
17#11718656—21no—
18#11718597C2211yescharacteristic
19#11718586C2211yescharacteristic
20#11718585C2211yescharacteristic
21C13×#333—21no—
22C13×#332—21no—
23#11718143—21no—
24#11718130—22no—
25#11718071—22no—
26#11718060—22no—
27C22×D52D411yescharacteristic
28C22×C4×D13—21no—
29C22×C8×C13—21no—
30C13×C4⋊Q8D411yescharacteristic
31C13×C4⋊Q8D411yescharacteristic
32C13×#125—21no—
33C13×C22⋊Q8—21no—
34C13×C22⋊Q8—21no—
35C4×Q8×C13—21no—
36C4×Q8×C13—21no—
37C13×#117—21no—
38C2×C42×C13C2311yescharacteristic
39C2×#6103—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13D411yescharacteristic
42C2×#6099—21no—
43C4×D52—21no—
44C4×D52—21no—
45C4×D52—21no—
46C4×D52—21no—
47C13×C4⋊C8—21no—
48C13×C4⋊C8—21no—
49C13×C4⋊C8—21no—
50C13×C22⋊C8—21no—
51C4×C8×C13—21no—
52#88071—21no—
53#88071—21no—
54C22⋊#1055D412yes—
55#88061—42no—
56#88049—22no—
57#88049—22no—
58#88048—22no—
59#88047—22no—
60C4⋊#1055—21no—
61C4⋊#1055—21no—
62C4⋊#1055D412yes—
63C4×#1055—21no—
64#10469—131nomaximal, Sylow
65C23×D13—21no—
66C2×Q8×C13—21no—
67C2×Q8×C13—21no—
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13#4111yescharacteristic
71C22×Dic13—21no—
72C22×Dic13—41no—
73C2×D52—21no—
74C2×D52—21no—
75C2×D52—21no—
76C2×D52—21no—
77C2×D52—21no—
78C2×D52Q1612yes—
79C2×C4×D13—41no—
80C2×C4×D13—41no—
81C2×C4×D13—82no—
82C2×C8×C13—41no—
83C2×C8×C13—41no—
84C2×C8×C13—41no—
85C2×C8×C13—41no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C22⋊C4—41no—
93C42×C13—41no—
94C42×C13C2×D411yescharacteristic
95C42×C13C2×D411yescharacteristic
96C42×C13#4111yescharacteristic
97C42×C13#4111yescharacteristic
98#6103—41no—
99#6103—41no—
100C4⋊Dic13—21no—
101C4⋊Dic13—21no—
102C4⋊Dic13—41no—
103C4⋊Dic13—41no—
104#6099—41no—
105#6099—41no—
106C2×#1055—22no—
107C2×#1055—22no—
108#3077—131no—
109#1804—131no—
110#1571—131no—
111#1542D1311yescharacteristic, complemented
112#1518—131no—
113#1460—131no—
114#1286—131no—
115C23×C13#12111yescharacteristic
116C22×D13—22no—
117C22×D13—41no—
118C22×D13—41no—
119C22×D13—81no—
120C22×D13—81no—
121Q8×C13—81no—
122Q8×C13—81no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13#12011yescharacteristic
128C2×C4×C13#12111yescharacteristic
129C2×C4×C13#12111yescharacteristic
130C2×C4×C13#12311yescharacteristic
131C2×C4×C13#12311yescharacteristic
132C2×C4×C13#12411yescharacteristic
133C2×C4×C13C2×Q1611yescharacteristic
134C2×C4×C13#13511yescharacteristic
135C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C13#13711yescharacteristic
137C2×Dic13—41no—
138C2×Dic13—81no—
139C2×Dic13—81no—
140C2×Dic13—81no—
141C2×Dic13—81no—
142D52—22no—
143D52—22no—
144D52—41no—
145D52—41no—
146C4×D13—82no—
147C4×D13—82no—
148C8×C13—81no—
149C8×C13—81no—
150#1055—42no—
151#1055—42no—
152#533C2×D1311yescharacteristic
153C2×C4×D4—131no—
154#478—262no—
155#476—261no—
156#474—261no—
157#431—131no—
158#431C2×D1311yescharacteristic
159#428—261no—
160#423—131no—
161C2×C4⋊C8C2×D1311yescharacteristic
162#418—261no—
163C2×#102—261no—
164#382—131no—
165#340—261no—
166#335—262no—
167#333—21no—
168#332—21no—
169#328—262no—
170#323—262no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13#39411yescharacteristic
174C22×C13#46711yescharacteristic
175C22×C13#46811yescharacteristic
176C2×D13—42no—
177C2×D13—82no—
178C2×D13—81no—
179C2×D13—81no—
180C2×D13—82no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—81no—
186C4×C13—81no—
187C4×C13#44911yescharacteristic
188C4×C13#45111yescharacteristic
189C4×C13#48411yescharacteristic
190C4×C13#48511yescharacteristic
191Dic13—81no—
192Dic13—161no—
193C22×D4—131no—
194C23×C4—261no—
195C2×M16—261no—
196C22×C8—21no—
197C4⋊Q8C22⋊D1311yescharacteristic
198C4⋊Q8C22⋊D1311yescharacteristic
199#125—21no—
200C22⋊Q8—21no—
201C22⋊Q8—21no—
202C4×Q8—21no—
203C4×Q8—21no—
204C4×D4—261no—
205C4×D4—261no—
206C4×D4—261no—
207C4×D4—261no—
208#117—21no—
209C2×C4⋊C4—131no—
210C2×C4⋊C4—261no—
211C2×C22⋊C4—261no—
212C2×C42C22×D1311yescharacteristic
213#107—262no—
214#106—262no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—132no—
219C4⋊C8—261no—
220C4⋊C8—261no—
221#102—262no—
222#102—262no—
223#102—522no—
224C22⋊C8—21no—
225C22⋊C8—132no—
226C4×C8—21no—
227C4×C8—261no—
228#95—261no—
229#95—261no—
230C2×C13—21no—
231C2×C13—21no—
232C2×C13#203611yescharacteristic
233C2×C13#204811yescharacteristic
234C2×C13#205311yescharacteristic
235D13—82no—
236C24—261no—
237C2×Q8—21no—
238C2×Q8—21no—
239C2×D4—132no—
240C2×D4—261no—
241C2×D4—261no—
242C2×D4—261no—
243C2×D4—261no—
244C2×D4—261no—
245C22×C4—261no—
246C22×C4—521no—
247C22×C4—521no—
248C22×C4—521no—
249C22×C4—1042no—
250C22×C4#612711yescharacteristic
251C22×C4D4×D1311yescharacteristic
252C22×C4D4×D1311yescharacteristic
253M16—521no—
254M16—521no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—262no—
260C2×C8—262no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—261no—
268C4⋊C4—261no—
269C4⋊C4—521no—
270C4⋊C4—521no—
271C22⋊C4—41no—
272C22⋊C4—521no—
273C22⋊C4—521no—
274C42—41no—
275C42#612711yescharacteristic
276C42D4×D1311yescharacteristic
277C42#612911yescharacteristic
278C42C2×C22⋊D1311yescharacteristic
279C13#1046911yescharacteristic, complemented, Sylow
280C23—262no—
281C23—521no—
282C23—521no—
283C23—1041no—
284C23—1041no—
285C23#8813811yescharacteristic
286Q8—81no—
287Q8—81no—
288D4—262no—
289D4—262no—
290D4—521no—
291D4—521no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—521no—
297C2×C4—1042no—
298C2×C4—1042no—
299C2×C4—1041no—
300C2×C4—1041no—
301C2×C4—1041no—
302C2×C4—1041no—
303C2×C4#8813711yescharacteristic
304C2×C4#8813811yescharacteristic
305C2×C4#8813911yescharacteristic
306C2×C4#8816811yescharacteristic
307C2×C4#8817011yescharacteristic
308C2×C4Q16×D1311yescharacteristic
309C2×C4#8817211yescharacteristic
310C2×C4#8818311yescharacteristic
311C2×C4#8819111yescharacteristic
312C2×C4#8819311yescharacteristic
313C8—81no—
314C8—81no—
315C8—522no—
316C8—522no—
317C22—21no—
318C22—21no—
319C22—522no—
320C22—1042no—
321C22—1042no—
322C22—1041no—
323C22—1041no—
324C22#1171847311yescharacteristic
325C22#1171847411yescharacteristic
326C22#1171862011yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—81no—
332C4—81no—
333C4—1041no—
334C4—2081no—
335C4#1171847011yescharacteristic
336C4#1171847611yescharacteristic
337C4#1171883311yescharacteristic
338C4#1171884711yescharacteristic
339C2—21no—
340C2—21no—
341C2—1042no—
342C2#1311603711yescharacteristic
343C2#1311610911yescharacteristic
344C2#1311614011yescharacteristic
subgroupG/H
centerC22#11718620
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1542C2
socleC22×C13#394
prime radicalC22×D52D4
hypercenter#1542D13
hypocenterC13#10469
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
3. #13113610C2semidirect
4. #13113400C2semidirect
6. #13112695C2semidirect
7. C13×#1542C2semidirect
111. #1542D13semidirect
279. C13#10469semidirect

Maximal subgroups

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

subgroupindex
#131246292
#131148472
#131136102
#131134002
#131131562
#131126952
C13×#15422
#1046913