Finite Group Databasebeta

← #15755812

Subgroups — #15755812

Order 3328.

550 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×#11718386C211yesmaximal, characteristic
2#13114859C212yesmaximal, complemented
3#13114821C212yesmaximal
4#13112704C211yesmaximal, characteristic, complemented
5C13×#1289C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊D13C2211yescharacteristic
7C23×#1055C2211yescharacteristic
8C22×C8×D13C411yescharacteristic, complemented
9C2×C13×C22⋊C8C2211yescharacteristic
10C13×#380C2212yes—
11#11718873C2212yes—
12C2×#88060C411yescharacteristic, complemented
13C2×#88054C411yescharacteristic, complemented
14C2×C8×Dic13C411yescharacteristic, complemented
15C2×#88048—22no—
16C2×#88046—22no—
17#11718386—22no—
18#11718386—22no—
19#11718121—22no—
20#11718119—22no—
21C23×C4×C13C2311yescharacteristic
22C22×C22⋊D13D411yescharacteristic
23C22×C4×D13C2×C411yescharacteristic
24C22×C8×C13C2×C411yescharacteristic
25C22×C8×C13C2×C411yescharacteristic
26C2×C13×C4⋊C4—22no—
27C2×C13×C22⋊C4—22no—
28C2×C22⋊Dic13—22no—
29C2×C22⋊Dic13D411yescharacteristic
30C4×C22⋊D13—22no—
31C4×C22⋊D13—22no—
32C2×#6103Q811yescharacteristic
33C2×C4⋊Dic13—22no—
34C2×#6101Q811yescharacteristic
35C2×C4×Dic13C2×C411yescharacteristic
36C22×#1055—42no—
37C22×#1055C2×C411yescharacteristic
38C22×#1055C2×C411yescharacteristic
39C22×#1055D412yes—
40C22×#1055D412yes—
41C2×C8×D13—21no—
42C2×C8×D13—21no—
43C2×C8×D13—42no—
44C13×C22⋊C8—22no—
45C13×#95—22no—
46#88071—22no—
47#88060—22no—
48#88054—22no—
49C8×Dic13—21no—
50C8×Dic13—21no—
51#88048—44no—
52#88046—44no—
53#8608—131nomaximal, Sylow
54C24×C13C2×D411yescharacteristic
55C23×D13C4⋊C411yescharacteristic
56C22×C4×C13—41no—
57C22×C4×C13—41no—
58C22×C4×C13—42no—
59C22×C4×C13C22×C411yescharacteristic
60C22×C4×C13C2×D412yes—
61C22×C4×C13C2×Q811yescharacteristic
62C22×C4×C13#4112yes—
63C2×C22⋊D13—22no—
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66C2×C22⋊D13SD1614yes—
67C22×Dic13—42no—
68C22×Dic13C4⋊C411yescharacteristic
69C22×Dic13C4⋊C411yescharacteristic
70C22×Dic13C4⋊C411yescharacteristic
71C2×C4×D13—21no—
72C2×C4×D13—21no—
73C2×C4×D13—41no—
74C2×C4×D13—41no—
75C2×C8×C13—21no—
76C2×C8×C13—21no—
77C2×C8×C13—41no—
78C2×C8×C13—41no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—42no—
81C13×C22⋊C4—42no—
82C13×C22⋊C4—42no—
83C22⋊Dic13—22no—
84C22⋊Dic13—42no—
85C22⋊Dic13—42no—
86#6103—22no—
87C4⋊Dic13—42no—
88C4⋊Dic13—42no—
89#6101—22no—
90C4×Dic13—21no—
91C4×Dic13—21no—
92C2×#1055—22no—
93C2×#1055—24no—
94C2×#1055—41no—
95C2×#1055—42no—
96C2×#1055C22⋊C411yescharacteristic
97C2×#1055C22⋊C412yes—
98C2×#1055C22⋊C411yescharacteristic
99C8×D13—42no—
100C8×D13—42no—
101C2×C8×D4—131no—
102#1807—132no—
103#1799—132no—
104#1289—131no—
105#1289D1311yescharacteristic, complemented
106C23×C13—41no—
107C23×C13—41no—
108C23×C13C2×C4⋊C411yescharacteristic
109C23×C13#12112yes—
110C23×C13C2×SD1612yes—
111C23×C13#13511yescharacteristic
112C23×C13#13511yescharacteristic
113C22×D13—21no—
114C22×D13—21no—
115C22×D13—41no—
116C22×D13—41no—
117C22×D13#10612yescomplemented
118C2×C4×C13—22no—
119C2×C4×C13—21no—
120C2×C4×C13—22no—
121C2×C4×C13—21no—
122C2×C4×C13—41no—
123C2×C4×C13—42no—
124C2×C4×C13—82no—
125C2×C4×C13—82no—
126C2×C4×C13—82no—
127C2×C4×C13C2×C22⋊C411yescharacteristic
128C2×C4×C13#11711yescharacteristic
129C2×C4×C13C22⋊Q812yes—
130C22⋊D13—24no—
131C22⋊D13—24no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—82no—
139C2×Dic13—82no—
140C2×Dic13—82no—
141C2×Dic13#10612yescomplemented
142C4×D13—42no—
143C4×D13—41no—
144C4×D13—41no—
145C8×C13—41no—
146C8×C13—41no—
147#1055—21no—
148#1055—22no—
149#1055#9912yescomplemented
150C23×C8—131no—
151C23×C8—131no—
152C2×C4×D4—131no—
153C8×D4—262no—
154C8×D4—262no—
155C2×#106—262no—
156C2×C4⋊C8—131no—
157C2×#99—262no—
158C2×C22⋊C8—131no—
159C2×C22⋊C8C2×D1311yescharacteristic
160C2×C4×C8—131no—
161#380—132no—
162#380C2×D1312yes—
163#342—262no—
164#340—262no—
165C22×C13—21no—
166C22×C13—22no—
167C22×C13—21no—
168C22×C13—22no—
169C22×C13—42no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13#38011yescharacteristic
173C22×C13C2×#10611yescharacteristic
174C22×C13#42711yescharacteristic
175C22×C13#46512yes—
176C22×C13#46512yes—
177C2×D13—22no—
178C2×D13—42no—
179C2×D13—41no—
180C2×D13—41no—
181C2×D13—42no—
182C4×C13—21no—
183C4×C13—22no—
184C4×C13—162no—
185C4×C13C2×#9911yescharacteristic
186C4×C13#41011yescharacteristic
187Dic13—22no—
188Dic13—41no—
189Dic13—41no—
190Dic13—162no—
191C22×D4—131no—
192C23×C4—131no—
193C23×C4C22×D1311yescharacteristic
194C22×C8—131no—
195C22×C8—132no—
196C22×C8—131no—
197C22×C8—132no—
198C22×C8—261no—
199C22×C8—261no—
200C22×C8—522no—
201C22×C8—522no—
202C22×C8C4×D1311yescharacteristic
203C22×C8C4×D1311yescharacteristic
204C4×D4—262no—
205C4×D4—262no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—131no—
208C2×C4⋊C4—262no—
209C2×C22⋊C4—22no—
210C2×C22⋊C4—131no—
211C2×C22⋊C4—131no—
212C2×C22⋊C4—262no—
213C2×C42—131no—
214#106—524no—
215C4⋊C8—262no—
216#99—524no—
217C22⋊C8—22no—
218C22⋊C8—262no—
219C4×C8—261no—
220C4×C8—261no—
221#95—22no—
222#95—262no—
223C2×C13—22no—
224C2×C13—22no—
225C2×C13—21no—
226C2×C13—21no—
227C2×C13#179911yescharacteristic
228C2×C13#180711yescharacteristic
229C2×C13#181211yescharacteristic
230D13—42no—
231C24—131no—
232C24D4×D1311yescharacteristic
233C2×D4—134no—
234C2×D4—262no—
235C2×D4—261no—
236C2×D4—261no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—42no—
240C22×C4—131no—
241C22×C4—131no—
242C22×C4—131no—
243C22×C4—261no—
244C22×C4—261no—
245C22×C4—521no—
246C22×C4—521no—
247C22×C4—522no—
248C22×C4C2×C4×D1311yescharacteristic
249C22×C4#612712yes—
250C22×C4D4×D1312yes—
251C22×C4Q8×D1311yescharacteristic
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—131no—
257C2×C8—131no—
258C2×C8—132no—
259C2×C8—264no—
260C2×C8—262no—
261C2×C8—522no—
262C2×C8—522no—
263C2×C8—521no—
264C2×C8—522no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—262no—
268C4⋊C4—522no—
269C4⋊C4—522no—
270C22⋊C4—42no—
271C22⋊C4—42no—
272C22⋊C4—262no—
273C22⋊C4—262no—
274C22⋊C4—522no—
275C22⋊C4—522no—
276C42—261no—
277C42—261no—
278C13#860811yescharacteristic, complemented, Sylow
279C23—41no—
280C23—41no—
281C23—132no—
282C23—261no—
283C23—261no—
284C23—521no—
285C23—521no—
286C23#8813812yes—
287C23C4⋊C4×D1311yescharacteristic
288C23#8816611yescharacteristic
289C23SD16×D1312yes—
290C23#8817311yescharacteristic
291D4—264no—
292D4—264no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—82no—
300C2×C4—82no—
301C2×C4—82no—
302C2×C4—132no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—522no—
308C2×C4—521no—
309C2×C4—521no—
310C2×C4—521no—
311C2×C4—521no—
312C2×C4—1042no—
313C2×C4—1042no—
314C2×C4—1042no—
315C2×C4#8812611yescharacteristic
316C2×C4C22⋊C4×D1311yescharacteristic
317C2×C4#8815012yes—
318C8—41no—
319C8—41no—
320C8—132no—
321C8—262no—
322C8—261no—
323C22—22no—
324C22—21no—
325C22—22no—
326C22—21no—
327C22—41no—
328C22—42no—
329C22—41no—
330C22—262no—
331C22—522no—
332C22—522no—
333C22—521no—
334C22—521no—
335C22#1171832811yescharacteristic
336C22#1171843912yes—
337C22#1171846812yes—
338C22D13×#10611yescharacteristic
339C22#1171854111yescharacteristic
340C4—21no—
341C4—22no—
342C4—162no—
343C4—262no—
344C4—521no—
345C4—521no—
346C4—2082no—
347C4#1171840111yescharacteristic
348C4D13×#9911yescharacteristic
349C2—22no—
350C2—22no—
351C2—21no—
352C2—21no—
353C2—522no—
354C2#1311482311yescharacteristic
355C2#1311486011yescharacteristic
356C2#1311488111yescharacteristic
subgroupG/H
centerC22#11718328
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1289C2
socleC22×C13#380
prime radicalC22×C22⋊D13D4
cosocleC23×C4×C13C23
hypercenter#1289D13
hypocenterC13#8608
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
2. #13114859C2semidirect
4. #13112704C2semidirect
5. C13×#1289C2semidirect
8. C22×C8×D13C4semidirect
12. C2×#88060C4semidirect
13. C2×#88054C4semidirect
14. C2×C8×Dic13C4semidirect
105. #1289D13semidirect
117. C22×D13#106semidirect
141. C2×Dic13#106semidirect
149. #1055#99semidirect
278. C13#8608semidirect

Maximal subgroups

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

subgroupindex
C2×#117183862
#131148592
#131148212
#131127042
C13×#12892
#860813