Finite Group Databasebeta

← #15772604

Subgroups — #15772604

Order 3328.

426 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 83 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#13120179C211yesmaximal, characteristic
2#13113177C211yesmaximal, characteristic
3#13112785C212yesmaximal, complemented
4#13112783C212yesmaximal, complemented
5C13×#1459C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C22×#6101C411yescharacteristic
8C2×C13×C22⋊C8—21no—
9#11718881C411yescharacteristic
10#11718881C411yescharacteristic
11#11718873C411yescharacteristic
12#11718871—21no—
13#11718645—21no—
14#11718609—21no—
15#11718607C2211yescharacteristic
16#11718607C2211yescharacteristic
17#11718594—21no—
18#11718587—21no—
19C13×#324—21no—
20C13×#323C2212yes—
21#11718117—21no—
22#11718117C2212yes—
23C22×D4×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×Dic13C2×C411yescharacteristic
27C23×Dic13C2×C411yescharacteristic
28C22×C8×C13—41no—
29C4×D4×C13—41no—
30C4×D4×C13—41no—
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C22⋊C4D411yescharacteristic
33C2×C13×C22⋊C4C2311yescharacteristic
34C2×C42×C13D411yescharacteristic
35C2×C22⋊Dic13—21no—
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13C2×C411yescharacteristic
38C2×C22⋊Dic13C2×C411yescharacteristic
39C2×C4⋊Dic13—21no—
40C2×#6101—21no—
41C2×#6101—21no—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×#6101—41no—
45C2×#6101—41no—
46C13×C22⋊C8—22no—
47C13×C22⋊C8—41no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53C22⋊#1055—22no—
54C4⋊#1055—41no—
55#88043—41no—
56#11578—131nomaximal, Sylow
57C24×C13C22⋊C411yescharacteristic
58C24×C13C22×C411yescharacteristic
59C2×D4×C13—22no—
60C2×D4×C13—22no—
61C2×D4×C13—41no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—81no—
67C22×C4×C13—81no—
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—42no—
78C22×Dic13—41no—
79C22×Dic13—41no—
80C22×Dic13—81no—
81C2×C8×C13—42no—
82C2×C8×C13—82no—
83C13×C4⋊C4—41no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—41no—
86C42×C13—21no—
87C42×C13—21no—
88C22⋊Dic13—22no—
89C22⋊Dic13—22no—
90C22⋊Dic13—42no—
91C22⋊Dic13—81no—
92C4⋊Dic13—81no—
93#6101—42no—
94#6101—42no—
95#6101—41no—
96#6101—41no—
97#6101—81no—
98C2×#1055—42no—
99#2579—131no—
100#1466—131no—
101#1459D1311yescharacteristic
102#1326—132no—
103#1326—132no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13#10112yes—
113C23×C13C2×C22⋊C411yescharacteristic
114C23×C13#13112yes—
115D4×C13—44no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—41no—
123C2×C4×C13—42no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—81no—
128C2×C4×C13—81no—
129C2×C4×C13—81no—
130C2×C4×C13#9911yescharacteristic
131C2×C4×C13#9911yescharacteristic
132C2×Dic13—22no—
133C2×Dic13—41no—
134C2×Dic13—42no—
135C2×Dic13—41no—
136C2×Dic13—42no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—82no—
147C8×C13—82no—
148#1055—82no—
149C2×C4×D4C2×D1311yescharacteristic
150C22×C4⋊C4—131no—
151#432—261no—
152C2×C22⋊C8—21no—
153#398—261no—
154#396—261no—
155#387—261no—
156#386—131no—
157#386—131no—
158#385—131no—
159#385—131no—
160#385—261no—
161#380—131no—
162#324—21no—
163#323—132no—
164#323—261no—
165#323C2×D1312yes—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—22no—
169C22×C13—22no—
170C22×C13—42no—
171C22×C13—42no—
172C22×C13—42no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—81no—
178C22×C13#40811yescharacteristic
179C22×C13C2×#9911yescharacteristic
180C22×C13C2×#10111yescharacteristic
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13—41no—
186C4×C13—41no—
187Dic13—42no—
188Dic13—81no—
189Dic13—81no—
190Dic13—81no—
191C22×D4C4×D1311yescharacteristic
192C23×C4—131no—
193C23×C4—131no—
194C23×C4C4×D1311yescharacteristic
195C23×C4C22⋊D1311yescharacteristic
196C22×C8—41no—
197C4×D4—41no—
198C4×D4—41no—
199C2×C4⋊C4—261no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4—261no—
203C2×C4⋊C4—261no—
204C2×C4⋊C4—521no—
205C2×C4⋊C4—521no—
206C2×C4⋊C4C22⋊D1311yescharacteristic
207C2×C22⋊C4—131no—
208C2×C22⋊C4—131no—
209C2×C22⋊C4—261no—
210C2×C22⋊C4—261no—
211C2×C22⋊C4D5211yescharacteristic
212C2×C22⋊C4C22×D1311yescharacteristic
213C2×C42D5211yescharacteristic
214C4⋊C8—521no—
215C22⋊C8—22no—
216C22⋊C8—41no—
217C22⋊C8—262no—
218#97—521no—
219#95—261no—
220#95—261no—
221#95—261no—
222#95—261no—
223#95—261no—
224C2×C13—21no—
225C2×C13—21no—
226C2×C13—42no—
227C2×C13—42no—
228C2×C13#147211yescharacteristic
229C2×C13#212011yescharacteristic
230C2×C13#212111yescharacteristic
231C24#610311yescharacteristic
232C24C2×C4×D1311yescharacteristic
233C2×D4—22no—
234C2×D4—22no—
235C2×D4—41no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—81no—
241C22×C4—81no—
242C22×C4—261no—
243C22×C4—261no—
244C22×C4—261no—
245C22×C4—261no—
246C22×C4—522no—
247C22×C4—521no—
248C22×C4—521no—
249C22×C4—1041no—
250C22×C4#610311yescharacteristic
251C22×C4#610311yescharacteristic
252C22×C4#610311yescharacteristic
253C22×C4C2×D5211yescharacteristic
254C22×C4C2×C22⋊D1311yescharacteristic
255C2×C8—42no—
256C2×C8—82no—
257C2×C8—522no—
258C4⋊C4—41no—
259C4⋊C4—522no—
260C4⋊C4—522no—
261C4⋊C4—521no—
262C4⋊C4—521no—
263C4⋊C4—1041no—
264C4⋊C4—1041no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C22⋊C4—262no—
268C22⋊C4—262no—
269C22⋊C4—522no—
270C22⋊C4—1041no—
271C42—21no—
272C42—21no—
273C13#1157811yescharacteristic, complemented, Sylow
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23#8806412yes—
283C23#8815512yes—
284C23C2×#610311yescharacteristic
285D4—44no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—262no—
301C2×C4—521no—
302C2×C4—522no—
303C2×C4—521no—
304C2×C4—522no—
305C2×C4—521no—
306C2×C4—521no—
307C2×C4—521no—
308C2×C4—521no—
309C2×C4—521no—
310C2×C4—521no—
311C2×C4—521no—
312C2×C4—521no—
313C2×C4—521no—
314C2×C4—1042no—
315C2×C4#8804611yescharacteristic
316C2×C4#8804611yescharacteristic
317C8—82no—
318C8—1042no—
319C22—21no—
320C22—21no—
321C22—22no—
322C22—22no—
323C22—42no—
324C22—42no—
325C22—42no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22C2×#8804611yescharacteristic
332C22#1171877111yescharacteristic
333C22C2×#8806411yescharacteristic
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—522no—
341C4—1041no—
342C4—1041no—
343C4—1041no—
344C2—21no—
345C2—21no—
346C2—42no—
347C2—42no—
348C2#1311319911yescharacteristic
349C2#1311647811yescharacteristic
350C2#1311648011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC24×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#1459C2
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC2×C13×C22⋊C4C23
hypercenter#1459D13
hypocenterC13#11578
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #13112785C2semidirect
4. #13112783C2semidirect
273. C13#11578semidirect

Maximal subgroups

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

subgroupindex
#131201792
#131131772
#131127852
#131127832
C13×#14592
#1157813