Finite Group Databasebeta

← #15773973

Subgroups — #15773973

Order 3328.

476 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 107 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#13114832C211yesmaximal, characteristic, complemented
2#13113160C211yesmaximal, characteristic, complemented
3#13112839C214yesmaximal, complemented
4C13×#2548C211yesmaximal, characteristic
5C2×C13×#127C411yescharacteristic
6C2×C13×#124—21no—
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#394C412yes—
9C13×#394C2212yes—
10C13×#390—21no—
11C13×#390—21no—
12C13×#390—21no—
13C4×C13×C4⋊C4C411yescharacteristic
14C2×#88076—21no—
15#11718586—21no—
16#11718585—21no—
17#11718122C2212yes—
18#11718120—21no—
19#11718120C2212yes—
20C22×Q8×C13D411yescharacteristic
21C22×D4×C13—21no—
22C22×D4×C13—21no—
23C22×D4×C13C2×C412yes—
24C13×#127—41no—
25C13×#127—41no—
26C13×#124—42no—
27C13×#124—42no—
28C4×Q8×C13—41no—
29C4×Q8×C13—41no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4C2311yescharacteristic
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—22no—
38C2×C42×C13—21no—
39C2×C42×C13C2×C411yescharacteristic
40C2×C42×C13D411yescharacteristic
41C2×C42×C13D411yescharacteristic
42C2×#6099—22no—
43C13×#95C2×C412yes—
44#88076—42no—
45C22⋊#1055—22no—
46C4⋊#1055—41no—
47C4⋊#1055—41no—
48C4⋊#1055—41no—
49C4×#1055—41no—
50#11882—131nomaximal, Sylow
51C24×C13—22no—
52C2×Q8×C13—41no—
53C2×Q8×C13—41no—
54C2×Q8×C13D812yes—
55C2×Q8×C13SD1612yes—
56C2×D4×C13—42no—
57C2×D4×C13—42no—
58C2×D4×C13—42no—
59C2×D4×C13—42no—
60C2×D4×C13—42no—
61C2×D4×C13—41no—
62C2×D4×C13—41no—
63C2×D4×C13—42no—
64C2×D4×C13—82no—
65C22×C4×C13—22no—
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22×C411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C13×C4⋊C4—41no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—42no—
77C13×C22⋊C4—44no—
78C13×C22⋊C4—42no—
79C13×C22⋊C4—42no—
80C13×C22⋊C4—82no—
81C13×C22⋊C4—82no—
82C42×C13—21no—
83C42×C13—21no—
84C42×C13—21no—
85C42×C13—21no—
86C42×C13—21no—
87C42×C13—21no—
88C42×C13—42no—
89#6099—42no—
90#6099—42no—
91C2×#1055—42no—
92C2×#1055—42no—
93#2548D1311yescharacteristic
94#1801—131no—
95#1461—131no—
96#1345—134no—
97C23×C13—42no—
98C23×C13—42no—
99C23×C13—42no—
100C23×C13—42no—
101C23×C13—42no—
102C23×C13—42no—
103C23×C13—42no—
104C23×C13C2×C22⋊C411yescharacteristic
105Q8×C13—42no—
106Q8×C13—42no—
107D4×C13—82no—
108D4×C13—84no—
109D4×C13—84no—
110D4×C13—82no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—22no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13#9911yescharacteristic
128C2×C4×C13#9911yescharacteristic
129C2×C4×C13#10212yes—
130C2×C4×C13#10212yes—
131C2×C4×C13C2×D811yescharacteristic
132C2×C4×C13C2×SD1611yescharacteristic
133#1055—82no—
134#1055—82no—
135C2×#127Dic1311yescharacteristic
136C2×#124—21no—
137C2×C4×Q8C2×D1311yescharacteristic
138#431—261no—
139#423—261no—
140C2×#101—261no—
141#394Dic1312yes—
142#394C2×D1312yes—
143#390—21no—
144#390—21no—
145#390—21no—
146C4×C4⋊C4Dic1311yescharacteristic
147#343—132no—
148#324—132no—
149#324—261no—
150C22×C13—21no—
151C22×C13—21no—
152C22×C13—82no—
153C22×C13—82no—
154C22×C13—82no—
155C22×C13—82no—
156C22×C13—82no—
157C22×C13—82no—
158C22×C13—82no—
159C22×C13C2×#9911yescharacteristic
160C22×C13C2×#10211yescharacteristic
161C22×C13#42111yescharacteristic
162C4×C13—21no—
163C4×C13—21no—
164C4×C13—22no—
165C4×C13—22no—
166C4×C13—21no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—82no—
171C4×C13#35512yes—
172C22×Q8C22⋊D1311yescharacteristic
173C22×D4—21no—
174C22×D4—21no—
175C22×D4C2×Dic1312yes—
176C2×M16—262no—
177#127—41no—
178#127—41no—
179#124—42no—
180#124—42no—
181C4×Q8—41no—
182C4×Q8—41no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4C2×Dic1311yescharacteristic
185C2×C4⋊C4C22⋊D1311yescharacteristic
186C2×C4⋊C4C22×D1311yescharacteristic
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4—22no—
191C2×C42—21no—
192C2×C42C2×Dic1311yescharacteristic
193C2×C42C22⋊D1311yescharacteristic
194C2×C42C22⋊D1311yescharacteristic
195C4⋊C8—521no—
196C4⋊C8—521no—
197C4⋊C8—521no—
198#101—522no—
199C22⋊C8—262no—
200C4×C8—521no—
201#95C2×Dic1312yes—
202C2×C13—21no—
203C2×C13—21no—
204C2×C13—162no—
205C2×C13#151911yescharacteristic
206C2×C13#212211yescharacteristic
207C2×C13C2×#35511yescharacteristic
208C24—22no—
209C2×Q8—41no—
210C2×Q8—41no—
211C2×Q8#610412yes—
212C2×Q8#610512yes—
213C2×D4—42no—
214C2×D4—42no—
215C2×D4—42no—
216C2×D4—42no—
217C2×D4—42no—
218C2×D4—42no—
219C2×D4—41no—
220C2×D4—41no—
221C2×D4—82no—
222C22×C4—22no—
223C22×C4C22⋊Dic1311yescharacteristic
224C22×C4C22⋊Dic1311yescharacteristic
225C22×C4C22⋊Dic1311yescharacteristic
226C22×C4C22⋊Dic1311yescharacteristic
227C22×C4C22×Dic1311yescharacteristic
228C22×C4C2×C22⋊D1311yescharacteristic
229C22×C4C2×C22⋊D1311yescharacteristic
230M16—522no—
231M16—522no—
232C2×C8—522no—
233C2×C8—522no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—42no—
238C22⋊C4—44no—
239C22⋊C4—42no—
240C22⋊C4—42no—
241C22⋊C4—82no—
242C22⋊C4—82no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—21no—
249C42—42no—
250C13#1188211yescharacteristic, complemented, Sylow
251C23—42no—
252C23—42no—
253C23—42no—
254C23—42no—
255C23—42no—
256C23—42no—
257C23—42no—
258C23C2×C22⋊Dic1311yescharacteristic
259Q8—42no—
260Q8—42no—
261D4—84no—
262D4—82no—
263D4—84no—
264D4—82no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4#8807212yes—
282C2×C4#8807212yes—
283C2×C4#8807411yescharacteristic
284C2×C4#8807411yescharacteristic
285C2×C4C2×#610411yescharacteristic
286C2×C4C2×#610511yescharacteristic
287C8—1042no—
288C8—1042no—
289C22—21no—
290C22—21no—
291C22—82no—
292C22—82no—
293C22—82no—
294C22—82no—
295C22—82no—
296C22—82no—
297C22—82no—
298C22C2×#8807211yescharacteristic
299C22C2×#8807411yescharacteristic
300C22#1171889711yescharacteristic
301C4—21no—
302C4—22no—
303C4—22no—
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—82no—
310C4#1171813412yes—
311C2—21no—
312C2—21no—
313C2—162no—
314C2#1311340411yescharacteristic
315C2#1311648611yescharacteristic
316C2C2×#1171813411yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2548C2
socleC22×C13C2×#99
prime radicalC2×C13×#127C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2548D13
hypocenterC13#11882
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2548

Complements

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

NH ≅ G/Ntype
1. #13114832C2semidirect
2. #13113160C2semidirect
3. #13112839C2semidirect
250. C13#11882semidirect

Maximal subgroups

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

subgroupindex
#131148322
#131131602
#131128392
C13×#25482
#1188213