Finite Group Databasebeta

← #16778826

Subgroups — #16778826

Order 3328.

400 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 84 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#13130764C211yesmaximal, characteristic, complemented
2#13130763C211yesmaximal, characteristic, complemented
3#13129655C212yesmaximal, complemented
4#13129652C212yesmaximal
5#13123200C211yesmaximal, characteristic
6C2×#88133—21no—
7C13×#390C411yescharacteristic
8#11718882C411yescharacteristic
9#11718882C2211yescharacteristic
10#11718646C411yescharacteristic
11#11718634C2211yescharacteristic
12#11718612—21no—
13#11718606—21no—
14#11718605—21no—
15C42×Dic13C2211yescharacteristic
16#11718589C411yescharacteristic
17#11718290—21no—
18#11718290—21no—
19#11718290—21no—
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C22×D4×C13C2×C411yescharacteristic
24C22×#1057—22no—
25C22×#1057—22no—
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C13×C22⋊C4—21no—
28C2×C13×C22⋊C4—21no—
29C2×C42×C13C2×C411yescharacteristic
30C2×C22⋊Dic13—21no—
31C2×C22⋊Dic13—21no—
32C2×C22⋊Dic13—21no—
33C2×C22⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×#6101—21no—
38C2×#6101—21no—
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×C4×Dic13C2311yescharacteristic
45#88133—44no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#7726—131nomaximal, Sylow
50C24×C13—21no—
51C2×D4×C13—22no—
52C2×D4×C13—41no—
53C2×D4×C13—41no—
54C22×C4×C13—21no—
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22×C411yescharacteristic
58C22×Dic13—21no—
59C22×Dic13—21no—
60C22×Dic13C22⋊C411yescharacteristic
61C22×Dic13C22⋊C411yescharacteristic
62C22×Dic13C2×D411yescharacteristic
63C22×Dic13C2×D411yescharacteristic
64C2×#1057—42no—
65C2×#1057—42no—
66C2×#1057—42no—
67C2×#1057—42no—
68C2×#1057—42no—
69C2×#1057—42no—
70C13×C4⋊C4—41no—
71C13×C22⋊C4—42no—
72C13×C22⋊C4—42no—
73C42×C13—22no—
74C22⋊Dic13—42no—
75C22⋊Dic13—42no—
76C22⋊Dic13—42no—
77C22⋊Dic13—42no—
78C4⋊Dic13—22no—
79C4⋊Dic13—42no—
80C4⋊Dic13—41no—
81#6101—42no—
82#6101—42no—
83C4×Dic13—22no—
84C4×Dic13—22no—
85C4×Dic13—41no—
86C4×Dic13—41no—
87C4×Dic13—41no—
88C4×Dic13—41no—
89#2860—131no—
90#1839—131no—
91#1839—131no—
92#1271—132no—
93#1270—132no—
94C23×C13—41no—
95C23×C13—41no—
96C23×C13—41no—
97C23×C13—41no—
98C23×C13—41no—
99C23×C13—41no—
100C23×C13—41no—
101C23×C13C2×C22⋊C411yescharacteristic
102D4×C13—82no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13#13112yes—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13#13512yes—
132C2×Dic13AGL(1,ℤ/8)12yes—
133#1057—82no—
134#1057—82no—
135C2×#126—261no—
136#390—131no—
137#390—131no—
138#390#26111yescharacteristic
139#389—131no—
140#389—131no—
141#389—131no—
142#388—261no—
143#388—261no—
144#388—261no—
145C43—131no—
146#336—132no—
147#336—132no—
148#336—261no—
149#336—261no—
150#336—261no—
151#336—261no—
152C22×C13—81no—
153C22×C13—81no—
154C22×C13—81no—
155C22×C13—81no—
156C22×C13—81no—
157C22×C13—81no—
158C22×C13—81no—
159C22×C13#40811yescharacteristic
160C22×C13#41011yescharacteristic
161C22×C13#41311yescharacteristic
162C22×C13#41611yescharacteristic
163C22×C13#41811yescharacteristic
164C22×C13#42111yescharacteristic
165C22×C13#42111yescharacteristic
166C4×C13—22no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13—81no—
170Dic13—22no—
171Dic13—22no—
172Dic13—41no—
173Dic13—41no—
174Dic13—81no—
175Dic13—81no—
176C22×D4C2×#26111yescharacteristic
177C22×C8—262no—
178C22×C8—262no—
179#126—524no—
180C2×C4⋊C4—131no—
181C2×C4⋊C4—131no—
182C2×C4⋊C4—261no—
183C2×C4⋊C4—261no—
184C2×C4⋊C4—261no—
185C2×C4⋊C4C2×#26111yescharacteristic
186C2×C22⋊C4—21no—
187C2×C22⋊C4—21no—
188C2×C22⋊C4—261no—
189C2×C22⋊C4—261no—
190C2×C22⋊C4—261no—
191C2×C22⋊C4—261no—
192C2×C42—131no—
193C2×C42—131no—
194C2×C42—131no—
195C2×C42—131no—
196C2×C42—131no—
197C2×C42—131no—
198C2×C42C2×#26111yescharacteristic
199#95—261no—
200#95—261no—
201#95—261no—
202C2×C13—161no—
203C2×C13#147311yescharacteristic
204C2×C13#148211yescharacteristic
205C2×C13#149611yescharacteristic
206C2×C13#151411yescharacteristic
207C2×C13#152111yescharacteristic
208C2×C13#153511yescharacteristic
209C2×C13#155311yescharacteristic
210C24—21no—
211C2×D4—22no—
212C2×D4—41no—
213C2×D4—41no—
214C22×C4—21no—
215C22×C4—131no—
216C22×C4—131no—
217C22×C4—131no—
218C22×C4—131no—
219C22×C4—261no—
220C22×C4—261no—
221C22×C4C22⋊#26111yescharacteristic
222C22×C4C22⋊#26111yescharacteristic
223C22×C4C22×#26111yescharacteristic
224C2×C8—522no—
225C2×C8—522no—
226C2×C8—522no—
227C2×C8—522no—
228C2×C8—522no—
229C2×C8—522no—
230C4⋊C4—41no—
231C4⋊C4—262no—
232C4⋊C4—521no—
233C4⋊C4—522no—
234C4⋊C4—522no—
235C4⋊C4—522no—
236C22⋊C4—42no—
237C22⋊C4—42no—
238C22⋊C4—522no—
239C22⋊C4—522no—
240C22⋊C4—522no—
241C22⋊C4—522no—
242C42—22no—
243C42—262no—
244C42—262no—
245C42—521no—
246C42—521no—
247C42—521no—
248C42—521no—
249C13#772611yescharacteristic, complemented, Sylow
250C23—41no—
251C23—41no—
252C23—41no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23—41no—
257C23C2×C22⋊#26111yescharacteristic
258D4—82no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—132no—
271C2×C4—132no—
272C2×C4—261no—
273C2×C4—261no—
274C2×C4—261no—
275C2×C4—261no—
276C2×C4—261no—
277C2×C4—261no—
278C2×C4—261no—
279C2×C4—261no—
280C2×C4—261no—
281C2×C4—261no—
282C2×C4—521no—
283C2×C4—521no—
284C2×C4—521no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4#8823812yes—
289C8—1042no—
290C8—1042no—
291C22—81no—
292C22—81no—
293C22—81no—
294C22—81no—
295C22—81no—
296C22—81no—
297C22—81no—
298C22#1171913211yescharacteristic
299C22#1171913811yescharacteristic
300C22#1171914011yescharacteristic
301C22#1171914211yescharacteristic
302C22#1171914611yescharacteristic
303C22#1171916511yescharacteristic
304C22#1171916611yescharacteristic
305C4—22no—
306C4—41no—
307C4—41no—
308C4—81no—
309C4—262no—
310C4—262no—
311C4—521no—
312C4—521no—
313C4—1041no—
314C4—1041no—
315C2—161no—
316C2#1313011811yescharacteristic
317C2#1313014711yescharacteristic
318C2#1313019511yescharacteristic
319C2#1313025611yescharacteristic
320C2#1313027711yescharacteristic
321C2#1313032011yescharacteristic
322C2#1313035911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#390C4
socleC23×C13C2×C22⋊C4
prime radicalC22×D4×C13C2×C4
cosocleC2×C4×Dic13C23
hypercenter#390#261
hypocenterC13#7726
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #13130764C2semidirect
2. #13130763C2semidirect
3. #13129655C2semidirect
249. C13#7726semidirect

Maximal subgroups

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

subgroupindex
#131307642
#131307632
#131296552
#131296522
#131232002
#772613