Finite Group Databasebeta

← #16778827

Subgroups — #16778827

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#13130764C211yesmaximal, characteristic, complemented
3#13129655C212yesmaximal, complemented
4#13129653C212yesmaximal
5#13123204C211yesmaximal, characteristic
6C2×#88152—21no—
7C13×#389C411yescharacteristic
8#11718651—21no—
9#11718649C411yescharacteristic
10#11718649C2211yescharacteristic
11#11718646C411yescharacteristic
12#11718634C2211yescharacteristic
13#11718600C411yescharacteristic
14C42×Dic13C2211yescharacteristic
15#11718331—21no—
16#11718330—21no—
17#11718290—21no—
18#11718290—21no—
19#11718290—21no—
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C22×D52C2×C411yescharacteristic
24C22×#1057—22no—
25C22×#1057—22no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C42×C13C2×C411yescharacteristic
30C2×#6103—21no—
31C2×#6103—21no—
32C2×#6103—21no—
33C2×#6103—21no—
34C2×#6103—21no—
35C2×#6103—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13C2×C411yescharacteristic
38C2×#6101—21no—
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×C4×Dic13C2311yescharacteristic
45#88152—44no—
46C13×#95—21no—
47#88071—21no—
48#88071—21no—
49#7726—131nomaximal, Sylow
50C23×D13—21no—
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22×C411yescharacteristic
56C22×Dic13—21no—
57C22×Dic13C22⋊C411yescharacteristic
58C22×Dic13C22⋊C411yescharacteristic
59C22×Dic13C2×D411yescharacteristic
60C22×Dic13C2×D411yescharacteristic
61C2×D52—22no—
62C2×D52—41no—
63C2×D52—41no—
64C2×#1057—42no—
65C2×#1057—42no—
66C2×#1057—42no—
67C2×#1057—42no—
68C2×#1057—42no—
69C2×#1057—42no—
70C13×C4⋊C4—41no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—42no—
73C42×C13—41no—
74#6103—42no—
75#6103—42no—
76#6103—42no—
77#6103—42no—
78#6103—42no—
79#6103—42no—
80C4⋊Dic13—22no—
81C4⋊Dic13—42no—
82#6101—42no—
83C4×Dic13—22no—
84C4×Dic13—22no—
85C4×Dic13—22no—
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×C13C2×C22⋊C411yescharacteristic
95C22×D13—41no—
96C22×D13—41no—
97C22×D13—41no—
98C22×D13—41no—
99C22×D13—41no—
100C22×D13—41no—
101C22×D13—41no—
102C2×C4×C13—21no—
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—41no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13#13112yes—
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—21no—
126C2×Dic13—21no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13#13512yes—
131C2×Dic13AGL(1,ℤ/8)12yes—
132D52—82no—
133#1057—82no—
134#1057—82no—
135C2×#126—261no—
136#390—131no—
137#390—131no—
138#390—131no—
139#389—131no—
140#389—131no—
141#389#26111yescharacteristic
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#40811yescharacteristic
153C22×C13#41011yescharacteristic
154C22×C13#41311yescharacteristic
155C22×C13#41611yescharacteristic
156C22×C13#41811yescharacteristic
157C22×C13#42111yescharacteristic
158C22×C13#42111yescharacteristic
159C2×D13—81no—
160C2×D13—81no—
161C2×D13—81no—
162C2×D13—81no—
163C2×D13—81no—
164C2×D13—81no—
165C2×D13—81no—
166C4×C13—22no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13—81no—
170C4×C13—81no—
171Dic13—22no—
172Dic13—22no—
173Dic13—41no—
174Dic13—41no—
175Dic13—81no—
176C22×D4—131no—
177C22×C8—262no—
178C22×C8—262no—
179#126—524no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—131no—
182C2×C4⋊C4—261no—
183C2×C4⋊C4—261no—
184C2×C4⋊C4C2×#26111yescharacteristic
185C2×C4⋊C4C2×#26111yescharacteristic
186C2×C22⋊C4—261no—
187C2×C22⋊C4—261no—
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—21no—
200#95—261no—
201#95—261no—
202C2×C13#147311yescharacteristic
203C2×C13#148211yescharacteristic
204C2×C13#149611yescharacteristic
205C2×C13#151411yescharacteristic
206C2×C13#152111yescharacteristic
207C2×C13#153511yescharacteristic
208C2×C13#155311yescharacteristic
209D13—161no—
210C24—261no—
211C2×D4—262no—
212C2×D4—521no—
213C2×D4—521no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—131no—
217C22×C4—131no—
218C22×C4—131no—
219C22×C4—131no—
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—41no—
232C4⋊C4—42no—
233C4⋊C4—262no—
234C4⋊C4—522no—
235C4⋊C4—522no—
236C22⋊C4—522no—
237C22⋊C4—522no—
238C22⋊C4—522no—
239C22⋊C4—522no—
240C22⋊C4—522no—
241C22⋊C4—522no—
242C42—41no—
243C42—262no—
244C42—262no—
245C42—262no—
246C42—521no—
247C42—521no—
248C42—521no—
249C13#772611yescharacteristic, complemented, Sylow
250C23—521no—
251C23—521no—
252C23—521no—
253C23—521no—
254C23—521no—
255C23—521no—
256C23—521no—
257C23C2×C22⋊#26111yescharacteristic
258D4—1042no—
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—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—132no—
274C2×C4—132no—
275C2×C4—261no—
276C2×C4—261no—
277C2×C4—261no—
278C2×C4—261no—
279C2×C4—261no—
280C2×C4—261no—
281C2×C4—261no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4#8824012yes—
289C8—1042no—
290C8—1042no—
291C22—1041no—
292C22—1041no—
293C22—1041no—
294C22—1041no—
295C22—1041no—
296C22—1041no—
297C22—1041no—
298C22#1171911611yescharacteristic
299C22#1171913811yescharacteristic
300C22#1171914811yescharacteristic
301C22#1171915511yescharacteristic
302C22#1171915911yescharacteristic
303C22#1171916511yescharacteristic
304C22#1171916611yescharacteristic
305C4—22no—
306C4—41no—
307C4—41no—
308C4—81no—
309C4—81no—
310C4—262no—
311C4—262no—
312C4—521no—
313C4—521no—
314C4—1041no—
315C2—2081no—
316C2#1313011911yescharacteristic
317C2#1313015011yescharacteristic
318C2#1313019711yescharacteristic
319C2#1313025511yescharacteristic
320C2#1313028011yescharacteristic
321C2#1313032311yescharacteristic
322C2#1313036011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#389C4
socleC23×C13C2×C22⋊C4
prime radicalC22×D52C2×C4
cosocleC2×C4×Dic13C23
hypercenter#389#261
hypocenterC13#7726
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
1. #13130764C2semidirect
2. #13130764C2semidirect
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
#131296552
#131296532
#131232042
#772613