Finite Group Databasebeta

← #15772505

Subgroups — #15772505

Order 3328.

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

normal subgroups only

This group has 414 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#13113166C211yesmaximal, characteristic
2C2×#11718120C211yesmaximal, characteristic
3#13112782C212yesmaximal, complemented
4#13112770C212yesmaximal, complemented
5C13×#2502C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C411yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C13×#398—21no—
9C13×#398—21no—
10C13×#391C411yescharacteristic
11C13×#391C2211yescharacteristic
12C13×#385—21no—
13C13×#385—21no—
14C13×#384C411yescharacteristic
15C13×#384C2211yescharacteristic
16C4×C13×C22⋊C4C411yescharacteristic
17#11718868—21no—
18C2×C22⋊#1055—21no—
19#11718120—21no—
20#11718120—21no—
21#11718120C2212yes—
22#11718120C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C13×C22⋊Q8—41no—
28C13×C22⋊Q8—41no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—41no—
35C2×C13×C4⋊C4—41no—
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C4⋊C4D411yescharacteristic
39C2×C13×C4⋊C4D411yescharacteristic
40C2×C13×C4⋊C4C2311yescharacteristic
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C42×C13C2×C411yescharacteristic
44C2×C42×C13C2×C411yescharacteristic
45C2×#6099—41no—
46C22×#1055—41no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C22⋊#1055—22no—
53C22⋊#1055—22no—
54C22⋊#1055—41no—
55C22⋊#1055—41no—
56#11555—131nomaximal, Sylow
57C24×C13C22⋊C411yescharacteristic
58C2×Q8×C13—22no—
59C2×Q8×C13—41no—
60C2×Q8×C13—41no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—22no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—41no—
73C22×C4×C13—81no—
74C22×C4×C13—81no—
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22×C411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—42no—
87C13×C4⋊C4—81no—
88C13×C4⋊C4—81no—
89C13×C4⋊C4—81no—
90C13×C4⋊C4—81no—
91C13×C22⋊C4—24no—
92C13×C22⋊C4—41no—
93C13×C22⋊C4—41no—
94C42×C13—22no—
95C42×C13—41no—
96#6099—82no—
97C2×#1055—42no—
98C2×#1055—42no—
99C2×#1055—82no—
100#2502D1311yescharacteristic
101#1463—131no—
102C2×#324—131no—
103#1325—132no—
104#1319—132no—
105C23×C13—22no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—41no—
109C23×C13#9911yescharacteristic
110C23×C13#9911yescharacteristic
111C23×C13C2×C22⋊C411yescharacteristic
112Q8×C13—82no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—22no—
116C2×C4×C13—22no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—81no—
143C2×C4×C13—81no—
144C2×C4×C13#13112yes—
145#1055—82no—
146#1055—82no—
147C2×C22⋊Q8Dic1311yescharacteristic
148C22×C4⋊C4C2×D1311yescharacteristic
149#407—261no—
150C2×C22⋊C8—261no—
151#398—21no—
152#398—21no—
153#391Dic1311yescharacteristic
154#391C2×D1311yescharacteristic
155#385—21no—
156#385—21no—
157#384Dic1311yescharacteristic
158#384C2×D1311yescharacteristic
159C4×C22⋊C4Dic1311yescharacteristic
160#324—132no—
161#324—132no—
162#324—261no—
163#324—261no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—42no—
172C22×C13—42no—
173C22×C13#35612yes—
174C22×C13#40811yescharacteristic
175C22×C13C2×#9911yescharacteristic
176C22×C13#41311yescharacteristic
177C4×C13—22no—
178C4×C13—42no—
179C4×C13—42no—
180C4×C13—41no—
181C4×C13—41no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13—81no—
186C4×C13—81no—
187C22×Q8C2×Dic1311yescharacteristic
188C23×C4C2×Dic1311yescharacteristic
189C23×C4C22⋊D1311yescharacteristic
190C23×C4C22⋊D1311yescharacteristic
191C2×M16—521no—
192C22×C8—521no—
193C22⋊Q8—41no—
194C22⋊Q8—41no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—41no—
201C2×C4⋊C4—41no—
202C2×C4⋊C4C2×Dic1311yescharacteristic
203C2×C4⋊C4C2×Dic1311yescharacteristic
204C2×C4⋊C4C22⋊D1311yescharacteristic
205C2×C4⋊C4C22⋊D1311yescharacteristic
206C2×C4⋊C4C22×D1311yescharacteristic
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C42C2×Dic1311yescharacteristic
210C2×C42C2×Dic1311yescharacteristic
211C22⋊C8—262no—
212C22⋊C8—262no—
213C22⋊C8—521no—
214C22⋊C8—521no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220C2×C13—21no—
221C2×C13—21no—
222C2×C13—22no—
223C2×C13—41no—
224C2×C13#146811yescharacteristic
225C2×C13#212711yescharacteristic
226C2×C13C2×#35611yescharacteristic
227C24C22⋊Dic1311yescharacteristic
228C2×Q8—22no—
229C2×Q8—41no—
230C2×Q8—41no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—22no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—41no—
243C22×C4—81no—
244C22×C4—81no—
245C22×C4C22⋊Dic1311yescharacteristic
246C22×C4C22⋊Dic1311yescharacteristic
247C22×C4C22⋊Dic1311yescharacteristic
248C22×C4C22×Dic1311yescharacteristic
249C22×C4C2×C22⋊D1311yescharacteristic
250C22×C4C2×C22⋊D1311yescharacteristic
251M16—1042no—
252C2×C8—522no—
253C2×C8—522no—
254C2×C8—1042no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—42no—
261C4⋊C4—81no—
262C4⋊C4—81no—
263C4⋊C4—81no—
264C4⋊C4—81no—
265C22⋊C4—24no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C42—22no—
269C42—41no—
270C13#1155511yescharacteristic, complemented, Sylow
271C23—21no—
272C23—21no—
273C23—22no—
274C23—41no—
275C23#8807411yescharacteristic
276C23#8807411yescharacteristic
277C23C2×C22⋊Dic1311yescharacteristic
278Q8—82no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4#8820212yes—
311C8—1042no—
312C8—1042no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—42no—
321C22—42no—
322C22#1171814012yes—
323C22C2×#8807411yescharacteristic
324C22#1171889511yescharacteristic
325C22#1171889811yescharacteristic
326C4—22no—
327C4—42no—
328C4—42no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—81no—
335C4—81no—
336C2—21no—
337C2—21no—
338C2—22no—
339C2—41no—
340C2#1311318411yescharacteristic
341C2#1311650511yescharacteristic
342C2C2×#1171814011yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2502C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2502D13
hypocenterC13#11555
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2502

Complements

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

NH ≅ G/Ntype
3. #13112782C2semidirect
4. #13112770C2semidirect
270. C13#11555semidirect

Maximal subgroups

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

subgroupindex
#131131662
C2×#117181202
#131127822
#131127702
C13×#25022
#1155513