Finite Group Databasebeta

← #13119203

Subgroups — #13119203

Order 1664.

508 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88198C211yesmaximal, characteristic, complemented
2C2×#88132C211yesmaximal, characteristic
3C13×#393C211yesmaximal, characteristic
4#11718891C211yesmaximal, characteristic, complemented
5#11718608C211yesmaximal, characteristic
6#11718606C211yesmaximal, characteristic
7#11718605C211yesmaximal, characteristic
8#11718603C211yesmaximal, characteristic
9C22⋊C4×Dic13C211yesmaximal, characteristic
10#11718320C211yesmaximal, characteristic, complemented
11#11718319C211yesmaximal, characteristic, complemented
12#11718310C211yesmaximal, characteristic, complemented
13#11718307C211yesmaximal, characteristic, complemented
14#11718307C211yesmaximal, characteristic, complemented
15#11718307C211yesmaximal, characteristic, complemented
16C22×Q8×C13C2211yescharacteristic
17C23×Dic13C2211yescharacteristic
18C22×Dic26C2211yescharacteristic
19C22×Dic26C2211yescharacteristic
20C2×C13×C22⋊C4C2211yescharacteristic
21C2×C13×C22⋊C4C2211yescharacteristic
22C2×C13×C22⋊C4C2211yescharacteristic
23C2×C22⋊Dic13C2211yescharacteristic
24C2×C22⋊Dic13C2211yescharacteristic
25C2×C22⋊Dic13C2211yescharacteristic
26#88198—24no—
27C2×C4⋊Dic13C2211yescharacteristic
28C2×#6101C2211yescharacteristic
29C2×#6101C2211yescharacteristic
30C2×#6101C2211yescharacteristic
31C2×#6101C2211yescharacteristic
32C2×#6101C2211yescharacteristic
33C2×#6101C2211yescharacteristic
34C2×C4×Dic13C2211yescharacteristic
35C2×C4×Dic13C2211yescharacteristic
36C2×C4×Dic13C2211yescharacteristic
37C2×C4×Dic13C2211yescharacteristic
38#88132—24no—
39C13×#95C2211yescharacteristic
40C13×#95C2211yescharacteristic
41C13×#95C2211yescharacteristic
42#88071C2211yescharacteristic
43#88071C2211yescharacteristic
44#88071C2211yescharacteristic
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53C24×C13C2311yescharacteristic
54C2×Q8×C13—22no—
55C2×Q8×C13—22no—
56C2×Q8×C13—41no—
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C22×Dic13—22no—
64C22×Dic13—22no—
65C22×Dic13—22no—
66C22×Dic13C2311yescharacteristic
67C22×Dic13C2311yescharacteristic
68C22×Dic13C2311yescharacteristic
69C22×Dic13C2311yescharacteristic
70C22×Dic13C2311yescharacteristic
71C22×Dic13C2311yescharacteristic
72C22×Dic13C2311yescharacteristic
73C22×Dic13C2311yescharacteristic
74C2×Dic26—22no—
75C2×Dic26—22no—
76C2×Dic26—22no—
77C2×Dic26—22no—
78C2×Dic26—22no—
79C2×Dic26—41no—
80C13×C22⋊C4—22no—
81C13×C22⋊C4—22no—
82C13×C22⋊C4—41no—
83C22⋊Dic13—22no—
84C22⋊Dic13—41no—
85C22⋊Dic13Q814yescomplemented
86C4⋊Dic13—22no—
87#6101—22no—
88#6101—22no—
89#6101—22no—
90#6101—22no—
91#6101—22no—
92#6101D414yes—
93C4×Dic13—22no—
94C4×Dic13—22no—
95C4×Dic13—41no—
96C4×Dic13—41no—
97#2492—131nomaximal, Sylow
98C23×C13—21no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13C2×Q812yes—
105C23×C13C2411yescharacteristic
106Q8×C13—44no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13C2×D412yes—
124C2×C4×C13#4112yes—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—44no—
144C2×Dic13C2×D412yes—
145C2×Dic13C2×D412yes—
146C2×Dic13C2×Q812yes—
147C2×Dic13C2×Q812yes—
148C2×Dic13#4112yes—
149C2×Dic13#4112yes—
150Dic26—44no—
151Dic26—44no—
152C2×C4⋊Q8—131no—
153C2×C22⋊Q8—131no—
154#400—131no—
155#400—131no—
156#393—131no—
157#393D1311yescharacteristic
158#391—131no—
159#391—131no—
160#391—131no—
161#391—131no—
162#388—131no—
163#388—131no—
164#380—131no—
165C4×C4⋊C4—131no—
166C4×C22⋊C4—131no—
167C22×C13—22no—
168C22×C13—22no—
169C22×C13—22no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13C22×D411yescharacteristic
175C22×C13C22×Q811yescharacteristic
176C22×C13C2×#4111yescharacteristic
177C22×C13C2×#4111yescharacteristic
178C22×C13C2×#4111yescharacteristic
179C22×C13H(5,𝔽2)11yescharacteristic
180C22×C132−1+411yescharacteristic
181C4×C13—22no—
182C4×C13—22no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13—41no—
186C4×C13—41no—
187Dic13—22no—
188Dic13—22no—
189Dic13—22no—
190Dic13—41no—
191Dic13—41no—
192Dic13—41no—
193Dic13—41no—
194Dic13#12414yes—
195C22×Q8—131no—
196C22×Q8—131no—
197C22×Q8C2×D1311yescharacteristic
198C23×C4—131no—
199C4⋊Q8—264no—
200C22⋊Q8—264no—
201C2×C4⋊C4—131no—
202C2×C4⋊C4—131no—
203C2×C4⋊C4—131no—
204C2×C4⋊C4—131no—
205C2×C4⋊C4—131no—
206C2×C4⋊C4—131no—
207C2×C4⋊C4—131no—
208C2×C22⋊C4—131no—
209C2×C22⋊C4—131no—
210C2×C22⋊C4—131no—
211C2×C22⋊C4C2×D1311yescharacteristic
212C2×C22⋊C4C2×D1311yescharacteristic
213C2×C22⋊C4C2×D1311yescharacteristic
214C2×C42—131no—
215C2×C42—131no—
216C2×C42—131no—
217C2×C42—131no—
218#95—131no—
219#95—131no—
220#95—131no—
221#95—131no—
222#95—131no—
223#95—131no—
224#95—131no—
225#95—131no—
226#95—131no—
227#95—131no—
228#95—131no—
229#95C2×D1311yescharacteristic
230#95C2×D1311yescharacteristic
231#95C2×D1311yescharacteristic
232C2×C13—42no—
233C2×C13C2×#12411yescharacteristic
234C2×C13#53311yescharacteristic
235C2×C13#54211yescharacteristic
236C2×C13#54611yescharacteristic
237C2×C13D4×Q811yescharacteristic
238C2×C13#55411yescharacteristic
239C2×C13#55611yescharacteristic
240C24C22×D1311yescharacteristic
241C2×Q8—22no—
242C2×Q8—22no—
243C2×Q8—41no—
244C2×Q8—262no—
245C2×Q8—262no—
246C2×Q8—262no—
247C2×Q8—262no—
248C2×Q8—262no—
249C2×Q8—521no—
250C22×C4—131no—
251C22×C4—131no—
252C22×C4—131no—
253C22×C4—131no—
254C22×C4—131no—
255C22×C4—131no—
256C22×C4—131no—
257C22×C4—131no—
258C22×C4—262no—
259C22×C4—262no—
260C22×C4—262no—
261C22×C4C22×D1311yescharacteristic
262C22×C4C22×D1311yescharacteristic
263C22×C4C22×D1311yescharacteristic
264C22×C4C22×D1311yescharacteristic
265C22×C4C22×D1311yescharacteristic
266C22×C4C22×D1311yescharacteristic
267C4⋊C4—134no—
268C4⋊C4—262no—
269C4⋊C4—262no—
270C4⋊C4—262no—
271C4⋊C4—262no—
272C4⋊C4—262no—
273C4⋊C4—262no—
274C22⋊C4—22no—
275C22⋊C4—22no—
276C22⋊C4—41no—
277C22⋊C4—134no—
278C22⋊C4—262no—
279C22⋊C4—521no—
280C42—262no—
281C42—262no—
282C42—521no—
283C42—521no—
284C13#249211yescharacteristic, complemented, Sylow
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23Q8×D1312yes—
292C23C23×D1311yescharacteristic
293Q8—44no—
294Q8—524no—
295Q8—524no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—132no—
313C2×C4—132no—
314C2×C4—132no—
315C2×C4—132no—
316C2×C4—132no—
317C2×C4—132no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—261no—
323C2×C4—261no—
324C2×C4—261no—
325C2×C4—261no—
326C2×C4—261no—
327C2×C4—261no—
328C2×C4—261no—
329C2×C4—261no—
330C2×C4—261no—
331C2×C4—261no—
332C2×C4—261no—
333C2×C4—261no—
334C2×C4—261no—
335C2×C4—261no—
336C2×C4—524no—
337C2×C4D4×D1312yes—
338C2×C4#612912yes—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22C2×D4×D1311yescharacteristic
347C22C2×#612911yescharacteristic
348C22#8825111yescharacteristic
349C22C2×Q8×D1311yescharacteristic
350C22#41×D1311yescharacteristic
351C22#41×D1311yescharacteristic
352C22#8825711yescharacteristic
353C4—22no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—134no—
360C4—262no—
361C4—262no—
362C4—262no—
363C4—521no—
364C4—521no—
365C4—521no—
366C4—521no—
367C2—42no—
368C2#1171929611yescharacteristic
369C2#1171932711yescharacteristic
370C2#1171933711yescharacteristic
371C2#1171934111yescharacteristic
372C2#1171937411yescharacteristic
373C2#1171937611yescharacteristic
374C2D13×#12411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#393C2
prime radicalC24×C13C23
hypercenter#393D13
hypocenterC13#2492
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#88198C2semidirect
4. #11718891C2semidirect
10. #11718320C2semidirect
11. #11718319C2semidirect
12. #11718310C2semidirect
13. #11718307C2semidirect
14. #11718307C2semidirect
15. #11718307C2semidirect
85. C22⋊Dic13Q8semidirect
284. C13#2492semidirect

Maximal subgroups

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

subgroupindex
C2×#881982
C2×#881322
C13×#3932
#117188912
#117186082
#117186062
#117186052
#117186032
C22⋊C4×Dic132
#117183202
#117183192
#117183102
#117183072
#249213