Finite Group Databasebeta

← #15772207

Subgroups — #15772207

Order 3328.

440 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 103 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#13117543C211yesmaximal, characteristic
2#13113160C211yesmaximal, characteristic, complemented
3#13112781C212yesmaximal, complemented
4#13112767C212yesmaximal
5C13×#1461C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C13C2211yescharacteristic
7C2×#88201C411yescharacteristic
8C2×C4×D52C411yescharacteristic
9C13×#431—21no—
10#11718891C411yescharacteristic
11#11718650—21no—
12#11718650—21no—
13#11718649C2211yescharacteristic
14#11718637C2211yescharacteristic
15#11718601—21no—
16#11718601—21no—
17#11718593C411yescharacteristic
18#11718586—21no—
19C13×#324—21no—
20C13×#324C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C22×D52C2×C411yescharacteristic
25C22×C4×D13—21no—
26C4×Q8×C13—41no—
27C4×Q8×C13—41no—
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C13×C4⋊C4C2311yescharacteristic
31C2×C42×C13C2×C411yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C42×C13D411yescharacteristic
34#88201—22no—
35#88201C814yescomplemented
36C2×#6103—21no—
37C2×#6103—21no—
38C2×#6103—21no—
39C2×#6103—21no—
40C2×#6103—21no—
41C2×C4⋊Dic13C2×C411yescharacteristic
42C2×#6101—21no—
43C2×#6101—21no—
44C2×C4×Dic13C2×C411yescharacteristic
45C2×C4×Dic13C2×C411yescharacteristic
46C4×D52—41no—
47C4×D52—41no—
48C13×C4⋊C8—41no—
49C13×C22⋊C8—22no—
50C4×C8×C13—41no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55C22⋊#1055—22no—
56C4⋊#1055—41no—
57C4×#1055—41no—
58#11480—131nomaximal, Sylow
59C23×D13—21no—
60C2×Q8×C13—41no—
61C2×Q8×C13—41no—
62C2×Q8×C13C2×C812yes—
63C2×Q8×C13M1612yes—
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22×C411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×Dic13—21no—
72C22×Dic13—21no—
73C22×Dic13—21no—
74C2×D52—21no—
75C2×D52—41no—
76C2×D52—41no—
77C2×D52C2×C812yes—
78C2×C4×D13—42no—
79C2×C4×D13—81no—
80C2×C4×D13—81no—
81C2×C8×C13—42no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C42×C13—21no—
86C42×C13—21no—
87C42×C13—21no—
88C42×C13—21no—
89C42×C13—21no—
90C42×C13—21no—
91#6103—24no—
92#6103—24no—
93#6103—41no—
94#6103—41no—
95#6103—81no—
96#6103—81no—
97C4⋊Dic13—41no—
98#6101—81no—
99#6101—81no—
100C4×Dic13—21no—
101C4×Dic13—41no—
102C4×Dic13C2×C812yes—
103C2×#1055—42no—
104#2326—131no—
105#1461—131no—
106#1461D1311yescharacteristic, complemented
107#1325—132no—
108#1318—132no—
109C23×C13C2×C22⋊C411yescharacteristic
110C22×D13—22no—
111C22×D13—41no—
112C22×D13—41no—
113C22×D13—41no—
114C22×D13—41no—
115C22×D13—41no—
116C22×D13—41no—
117Q8×C13—42no—
118Q8×C13—42no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13C22⋊C812yes—
133C2×C4×C13C22⋊C812yes—
134C2×C4×C13#9911yescharacteristic
135C2×C4×C13#9911yescharacteristic
136C2×C4×C13C22×C811yescharacteristic
137C2×C4×C13C2×M1611yescharacteristic
138C2×Dic13—22no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147D52—42no—
148D52—42no—
149C4×D13—84no—
150C8×C13—82no—
151#1055—82no—
152C2×#124—131no—
153C2×C4×Q8C2×D1311yescharacteristic
154C2×C4×D4—131no—
155#431—21no—
156#431—261no—
157#391—131no—
158#390—131no—
159#388—261no—
160#388—261no—
161#385—261no—
162#385—261no—
163#384—131no—
164#376—131no—
165#324—21no—
166#324—132no—
167#324—261no—
168#324C2×D1312yes—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13C2×C22⋊C811yescharacteristic
172C22×C13C2×#9911yescharacteristic
173C22×C13#41311yescharacteristic
174C2×D13—42no—
175C2×D13—42no—
176C2×D13—42no—
177C2×D13—81no—
178C2×D13—81no—
179C2×D13—81no—
180C2×D13—81no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—22no—
186C4×C13—22no—
187C4×C13—41no—
188C4×C13—41no—
189C4×C13—41no—
190Dic13—42no—
191Dic13—81no—
192Dic13—81no—
193C22×Q8C4×D1311yescharacteristic
194C22×D4—131no—
195C23×C4—261no—
196#124—134no—
197#124—262no—
198C4×Q8—41no—
199C4×Q8—41no—
200C4×D4—521no—
201C4×D4—521no—
202C2×C4⋊C4—131no—
203C2×C4⋊C4—261no—
204C2×C4⋊C4—261no—
205C2×C4⋊C4D5211yescharacteristic
206C2×C4⋊C4C22⋊D1311yescharacteristic
207C2×C4⋊C4C22×D1311yescharacteristic
208C2×C22⋊C4—261no—
209C2×C22⋊C4—261no—
210C2×C22⋊C4—261no—
211C2×C22⋊C4—261no—
212C2×C22⋊C4—261no—
213C2×C42—131no—
214C2×C42—131no—
215C2×C42C4×D1311yescharacteristic
216C2×C42D5211yescharacteristic
217C2×C42C22⋊D1311yescharacteristic
218C4⋊C8—41no—
219C4⋊C8—521no—
220C22⋊C8—22no—
221C22⋊C8—262no—
222C4×C8—41no—
223C4×C8—521no—
224#95—261no—
225#95—261no—
226#95—261no—
227#95—261no—
228C2×C13—21no—
229C2×C13—21no—
230C2×C13#145911yescharacteristic
231C2×C13#212811yescharacteristic
232C2×C13#213311yescharacteristic
233D13—82no—
234C24—261no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8C8×D1312yes—
238C2×Q8#609412yes—
239C2×D4—132no—
240C2×D4—261no—
241C2×D4—521no—
242C2×D4—521no—
243C22×C4—261no—
244C22×C4—261no—
245C22×C4—261no—
246C22×C4—522no—
247C22×C4—1041no—
248C22×C4—1041no—
249C22×C4#610311yescharacteristic
250C22×C4#610311yescharacteristic
251C22×C4#610311yescharacteristic
252C22×C4#610311yescharacteristic
253C22×C4C2×C4×D1311yescharacteristic
254C22×C4C2×D5211yescharacteristic
255C22×C4C2×C22⋊D1311yescharacteristic
256C2×C8—42no—
257C2×C8—522no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—521no—
262C4⋊C4—1041no—
263C4⋊C4—1041no—
264C22⋊C4—264no—
265C22⋊C4—264no—
266C22⋊C4—521no—
267C22⋊C4—521no—
268C22⋊C4—1041no—
269C22⋊C4—1041no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42—21no—
275C42—21no—
276C42—132no—
277C42—261no—
278C42—521no—
279C13#1148011yescharacteristic, complemented, Sylow
280C23—262no—
281C23—521no—
282C23—521no—
283C23—521no—
284C23—521no—
285C23—521no—
286C23—521no—
287C23C2×#610311yescharacteristic
288Q8—42no—
289Q8—42no—
290D4—522no—
291D4—522no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—262no—
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—1044no—
315C2×C4#8804611yescharacteristic
316C2×C4#8804611yescharacteristic
317C2×C4#8806012yes—
318C2×C4#8806012yes—
319C2×C4C2×C8×D1311yescharacteristic
320C2×C4C2×#609411yescharacteristic
321C8—82no—
322C8—1042no—
323C22—21no—
324C22—21no—
325C22—522no—
326C22—522no—
327C22—522no—
328C22—1041no—
329C22—1041no—
330C22—1041no—
331C22—1041no—
332C22C2×#8804611yescharacteristic
333C22C2×#8806011yescharacteristic
334C22#1171879311yescharacteristic
335C4—21no—
336C4—21no—
337C4—22no—
338C4—22no—
339C4—21no—
340C4—21no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—522no—
345C4—1041no—
346C4—1041no—
347C2—21no—
348C2—21no—
349C2—1042no—
350C2#1311315211yescharacteristic
351C2#1311650711yescharacteristic
352C2#1311652311yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC2×C4×C13C22×C8
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1461C2
socleC22×C13C2×#99
prime radicalC22×D52C2×C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1461D13
hypocenterC13#11480
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
2. #13113160C2semidirect
3. #13112781C2semidirect
5. C13×#1461C2semidirect
35. #88201C8semidirect
106. #1461D13semidirect
279. C13#11480semidirect

Maximal subgroups

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

subgroupindex
#131175432
#131131602
#131127812
#131127672
C13×#14612
#1148013