Finite Group Databasebeta

← #16786891

Subgroups — #16786891

Order 3328.

460 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 98 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#13130076C211yesmaximal, characteristic
2#13130072C211yesmaximal, characteristic
3#13129780C212yesmaximal, complemented
4#13129762C212yesmaximal, complemented
5#13117508C211yesmaximal, characteristic
6C2×C13×#123C411yescharacteristic
7C2×D4×Dic13C2211yescharacteristic
8C22×C4⋊Dic13C411yescharacteristic
9C2×C22⋊#1057—21no—
10#11719119—21no—
11#11718881C411yescharacteristic
12#11718872C2211yescharacteristic
13#11718646—21no—
14#11718642—21no—
15#11718612—21no—
16#11718611—21no—
17#11718611C2211yescharacteristic
18C22⋊C4×Dic13C411yescharacteristic
19#11718305—21no—
20#11718305C2212yes—
21#11718305C2212yes—
22#11718285—21no—
23C22×D4×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×Dic13C2×C411yescharacteristic
26C23×Dic13C2×C411yescharacteristic
27C23×Dic13D411yescharacteristic
28C22×#1057—41no—
29C13×#123—22no—
30C13×#123C814yescomplemented
31C2×C13×C4⋊C4—21no—
32C2×C13×C22⋊C4—21no—
33C2×C13×C22⋊C4C2×C411yescharacteristic
34C2×C22⋊Dic13—21no—
35C2×C22⋊Dic13C2×C411yescharacteristic
36C2×C22⋊Dic13D411yescharacteristic
37C2×C22⋊Dic13C2311yescharacteristic
38D4×Dic13—41no—
39D4×Dic13—41no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13—21no—
42C2×C4⋊Dic13—21no—
43C2×C4⋊Dic13—41no—
44C2×C4⋊Dic13—41no—
45C2×C4⋊Dic13D411yescharacteristic
46C2×C4×Dic13—21no—
47C2×C4×Dic13D411yescharacteristic
48C22⋊#1057—22no—
49C22⋊#1057—22no—
50C22⋊#1057—41no—
51C4⋊#1057—41no—
52C4×#1057—41no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#11474—131nomaximal, Sylow
59C24×C13C22⋊C411yescharacteristic
60C24×C13C22×C411yescharacteristic
61C2×D4×C13—41no—
62C2×D4×C13—41no—
63C2×D4×C13C2×C812yes—
64C2×D4×C13M1612yes—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—41no—
69C22×C4×C13—41no—
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C2×C812yescomplemented
72C22×Dic13—21no—
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—21no—
78C22×Dic13—41no—
79C22×Dic13—81no—
80C22×Dic13—81no—
81C22×Dic13—81no—
82C22×Dic13C22⋊C411yescharacteristic
83C22×Dic13C22⋊C411yescharacteristic
84C22×Dic13C2×D411yescharacteristic
85C22×Dic13C2×D411yescharacteristic
86C2×#1057—42no—
87C2×#1057—42no—
88C2×#1057—82no—
89C13×C4⋊C4—24no—
90C13×C22⋊C4—24no—
91C13×C22⋊C4—21no—
92C13×C22⋊C4C2×C812yescomplemented
93C22⋊Dic13—41no—
94C22⋊Dic13—41no—
95C22⋊Dic13—41no—
96C22⋊Dic13—81no—
97C4⋊Dic13—41no—
98C4⋊Dic13—42no—
99C4⋊Dic13—41no—
100C4⋊Dic13—41no—
101C4⋊Dic13—81no—
102C4×Dic13—21no—
103C4×Dic13—21no—
104C4×Dic13—81no—
105#2322—131no—
106#1460—131no—
107#1459—131no—
108#1326—132no—
109#1317—132no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13C22⋊C812yes—
119C23×C13C2×C22⋊C411yescharacteristic
120C23×C13C22×C811yescharacteristic
121C23×C13C2×M1611yescharacteristic
122D4×C13—42no—
123D4×C13—42no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—22no—
127C2×C4×C13—22no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—42no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—42no—
134C2×C4×C13C22⋊C812yes—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—41no—
139C2×Dic13—42no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—81no—
150C2×Dic13—81no—
151C2×Dic13—81no—
152C2×Dic13—82no—
153C2×Dic13#9911yescharacteristic
154C2×Dic13#9911yescharacteristic
155#1057—82no—
156#1057—82no—
157C2×#123#26111yescharacteristic
158C2×C4×D4—131no—
159C22×C4⋊C4—131no—
160#431—261no—
161C2×C22⋊C8—261no—
162#389—261no—
163#388—261no—
164#387—261no—
165#386—131no—
166#385—131no—
167#385—261no—
168#381—131no—
169C4×C22⋊C4—131no—
170#324—261no—
171#323—132no—
172#323—132no—
173#323—261no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—22no—
179C22×C13—42no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—42no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13—41no—
187C22×C13—81no—
188C22×C13C2×C22⋊C811yescharacteristic
189C22×C13C2×#9911yescharacteristic
190C22×C13#41311yescharacteristic
191C4×C13—22no—
192C4×C13—42no—
193C4×C13—42no—
194Dic13—21no—
195Dic13—21no—
196Dic13—41no—
197Dic13—41no—
198Dic13—41no—
199Dic13—81no—
200Dic13—81no—
201C22×D4C2×#26111yescharacteristic
202C23×C4—131no—
203C23×C4—131no—
204C23×C4—131no—
205C23×C4C2×#26111yescharacteristic
206C22×C8—521no—
207#123—22no—
208#123#105714yescomplemented
209C4×D4—521no—
210C4×D4—521no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—131no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4—261no—
215C2×C4⋊C4—261no—
216C2×C4⋊C4—521no—
217C2×C4⋊C4—521no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—131no—
220C2×C22⋊C4—131no—
221C2×C22⋊C4—131no—
222C2×C22⋊C4—261no—
223C2×C22⋊C4C2×#26111yescharacteristic
224C2×C42—131no—
225C2×C42—261no—
226C4⋊C8—521no—
227C22⋊C8—262no—
228C22⋊C8—262no—
229C22⋊C8—521no—
230C4×C8—521no—
231#95—261no—
232#95—261no—
233#95—261no—
234#95—261no—
235#95—261no—
236C2×C13—21no—
237C2×C13—21no—
238C2×C13—41no—
239C2×C13—41no—
240C2×C13—42no—
241C2×C13#145911yescharacteristic
242C2×C13#212111yescharacteristic
243C2×C13#212311yescharacteristic
244C24C22⋊#26111yescharacteristic
245C24C22×#26111yescharacteristic
246C2×D4—41no—
247C2×D4—41no—
248C2×D4C2×#105712yes—
249C2×D4#612212yes—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—131no—
256C22×C4—131no—
257C22×C4—131no—
258C22×C4—131no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4—261no—
262C22×C4—261no—
263C22×C4—261no—
264C22×C4—261no—
265C22×C4—521no—
266C22×C4—1041no—
267C22×C4—1041no—
268C22×C4—1041no—
269C22×C4C2×#105712yescomplemented
270C22×C4C22⋊#26111yescharacteristic
271C2×C8—522no—
272C2×C8—522no—
273C2×C8—1042no—
274C4⋊C4—24no—
275C4⋊C4—521no—
276C4⋊C4—521no—
277C4⋊C4—521no—
278C4⋊C4—522no—
279C4⋊C4—1041no—
280C22⋊C4—24no—
281C22⋊C4—21no—
282C22⋊C4—521no—
283C22⋊C4—521no—
284C22⋊C4—521no—
285C22⋊C4—1041no—
286C22⋊C4C2×#105712yescomplemented
287C42—261no—
288C42—261no—
289C42—1041no—
290C13#1147411yescharacteristic, complemented, Sylow
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23C22⋊#105712yes—
300C23C22×#105711yescharacteristic
301C23C2×#612211yescharacteristic
302C23C2×C22⋊#26111yescharacteristic
303D4—42no—
304D4—42no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—131no—
316C2×C4—131no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—521no—
321C2×C4—522no—
322C2×C4—521no—
323C2×C4—521no—
324C2×C4—521no—
325C2×C4—521no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—1041no—
332C2×C4—1041no—
333C2×C4—1041no—
334C2×C4—1042no—
335C2×C4C22⋊#105712yes—
336C8—1042no—
337C8—1042no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—22no—
343C22—42no—
344C22—41no—
345C22—41no—
346C22—42no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—81no—
352C22D13⋊#9911yescharacteristic
353C22#1171914811yescharacteristic
354C22C2×C22⋊#105711yescharacteristic
355C4—22no—
356C4—42no—
357C4—42no—
358C4—261no—
359C4—261no—
360C4—521no—
361C4—521no—
362C4—521no—
363C4—1041no—
364C4—1041no—
365C2—21no—
366C2—21no—
367C2—41no—
368C2—41no—
369C2—42no—
370C2#1313007211yescharacteristic
371C2#1313109411yescharacteristic
372C2#1313109911yescharacteristic
subgroupG/H
centerC22D13⋊#99
commutatorC23×C13C22×C8
FrattiniC24C22×#261
FittingC2×C13×#123C4
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC2×C22⋊Dic13C23
hypercenterC2×#123#261
hypocenterC13#11474
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
3. #13129780C2semidirect
4. #13129762C2semidirect
30. C13×#123C8semidirect
71. C22×C4×C13C2×C8semidirect
92. C13×C22⋊C4C2×C8semidirect
208. #123#1057semidirect
269. C22×C4C2×#1057semidirect
286. C22⋊C4C2×#1057semidirect
290. C13#11474semidirect

Maximal subgroups

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

subgroupindex
#131300762
#131300722
#131297802
#131297622
#131175082
#1147413