Finite Group Databasebeta

← #13118513

Subgroups — #13118513

Order 1664.

528 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×#88151C211yesmaximal, characteristic
2C2×#88146C211yesmaximal, characteristic
3C13×#398C211yesmaximal, characteristic, complemented
4#11718650C211yesmaximal, characteristic
5#11718648C211yesmaximal, characteristic
6#11718647C211yesmaximal, characteristic, complemented
7#11718646C211yesmaximal, characteristic, complemented
8#11718642C211yesmaximal, characteristic, complemented
9#11718639C211yesmaximal, characteristic, complemented
10#11718329C211yesmaximal, characteristic
11#11718325C211yesmaximal, characteristic
12D13×#95C211yesmaximal, characteristic
13#11718322C211yesmaximal, characteristic, complemented
14#11718317C211yesmaximal, characteristic, complemented
15#11718307C211yesmaximal, characteristic, complemented
16C22×C4×D13C2211yescharacteristic
17C22×C4×D13C2211yescharacteristic
18C22×C4×D13C2211yescharacteristic
19C22×Dic26C2211yescharacteristic
20C2×C13×C4⋊C4C2211yescharacteristic
21C2×C13×C4⋊C4C2211yescharacteristic
22C2×C13×C4⋊C4C2211yescharacteristic
23C2×C13×C4⋊C4C2211yescharacteristic
24C2×#6103C2211yescharacteristic
25C2×#6103C2211yescharacteristic
26C2×#6103C2211yescharacteristic
27C2×#6103C2211yescharacteristic
28C2×C4⋊Dic13C2211yescharacteristic
29C2×C4⋊Dic13C2211yescharacteristic
30C2×C4⋊Dic13C2211yescharacteristic
31C2×C4⋊Dic13C2211yescharacteristic
32C2×C4⋊Dic13C2211yescharacteristic
33C2×#6101C2211yescharacteristic
34C2×#6101C2211yescharacteristic
35C2×C4×Dic13C2211yescharacteristic
36C2×C4×Dic13C2211yescharacteristic
37#88151—24no—
38#88146—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
53C23×D13C2311yescharacteristic
54C22×C4×C13C2311yescharacteristic
55C22×C4×C13C2311yescharacteristic
56C22×C4×C13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×Dic13C2311yescharacteristic
62C22×Dic13C2311yescharacteristic
63C22×Dic13C2311yescharacteristic
64C22×Dic13C2311yescharacteristic
65C22×Dic13C2311yescharacteristic
66C22×Dic13C2311yescharacteristic
67C22×Dic13C2311yescharacteristic
68C2×C4×D13—22no—
69C2×C4×D13—22no—
70C2×C4×D13—22no—
71C2×C4×D13—22no—
72C2×C4×D13—22no—
73C2×C4×D13—22no—
74C2×C4×D13—41no—
75C2×C4×D13—41no—
76C2×C4×D13Q814yescomplemented
77C2×Dic26—22no—
78C2×Dic26—22no—
79C2×Dic26—41no—
80C13×C4⋊C4—22no—
81C13×C4⋊C4—22no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4—22no—
84#6103—22no—
85#6103—22no—
86#6103—22no—
87#6103D414yes—
88C4⋊Dic13—22no—
89C4⋊Dic13—22no—
90C4⋊Dic13—22no—
91C4⋊Dic13—41no—
92C4⋊Dic13—41no—
93#6101—22no—
94#6101—41no—
95C4×Dic13—22no—
96C4×Dic13—22no—
97#2438—131nomaximal, Sylow
98C23×C13C2411yescharacteristic
99C22×D13—21no—
100C22×D13—21no—
101C22×D13—21no—
102C22×D13—21no—
103C22×D13C2×D412yes—
104C22×D13C2×Q812yes—
105C22×D13#4112yes—
106C2×C4×C13—21no—
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×C13C2×Q812yes—
125C2×C4×C13#4112yes—
126C2×C4×C13#4112yes—
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—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13C2×D412yes—
147C2×Dic13C2×Q812yes—
148C4×D13—28no—
149C4×D13—44no—
150C4×D13—44no—
151Dic26—44no—
152C2×C22⋊Q8—131no—
153C2×#117—131no—
154#400—131no—
155#398—131no—
156#398D1311yescharacteristic, complemented
157#395—131no—
158#391—131no—
159#389—131no—
160#387—131no—
161#387—131no—
162#385—131no—
163#385—131no—
164#381—131no—
165#380—131no—
166C2×#95—131no—
167C22×C13C22×D411yescharacteristic
168C22×C13C22×Q811yescharacteristic
169C22×C13C2×#4111yescharacteristic
170C22×C13C2×#4111yescharacteristic
171C22×C13C2×#4111yescharacteristic
172C22×C13H(5,𝔽2)11yescharacteristic
173C22×C132−1+411yescharacteristic
174C2×D13—22no—
175C2×D13—22no—
176C2×D13—22no—
177C2×D13—22no—
178C2×D13—22no—
179C2×D13—22no—
180C2×D13C22⋊Q814yes—
181C4×C13—22no—
182C4×C13—22no—
183C4×C13—22no—
184C4×C13—22no—
185C4×C13—41no—
186C4×C13—41no—
187C4×C13—41no—
188Dic13—22no—
189Dic13—22no—
190Dic13—41no—
191Dic13—41no—
192Dic13—41no—
193Dic13—41no—
194Dic13—41no—
195C22×Q8—131no—
196C23×C4—131no—
197C23×C4—131no—
198C23×C4—131no—
199C22⋊Q8—264no—
200#117—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×C4⋊C4C2×D1311yescharacteristic
209C2×C4⋊C4C2×D1311yescharacteristic
210C2×C4⋊C4C2×D1311yescharacteristic
211C2×C4⋊C4C2×D1311yescharacteristic
212C2×C22⋊C4—131no—
213C2×C22⋊C4—131no—
214C2×C22⋊C4—131no—
215C2×C22⋊C4—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×C13C2×C22⋊Q811yescharacteristic
233C2×C13#53311yescharacteristic
234C2×C13#54411yescharacteristic
235C2×C13#54611yescharacteristic
236C2×C13#54711yescharacteristic
237C2×C13#55111yescharacteristic
238C2×C13#55211yescharacteristic
239D13—24no—
240C24—131no—
241C2×Q8—262no—
242C2×Q8—262no—
243C2×Q8—521no—
244C22×C4—131no—
245C22×C4—131no—
246C22×C4—134no—
247C22×C4—131no—
248C22×C4—131no—
249C22×C4—131no—
250C22×C4—131no—
251C22×C4—131no—
252C22×C4—262no—
253C22×C4—262no—
254C22×C4—262no—
255C22×C4—262no—
256C22×C4—262no—
257C22×C4—262no—
258C22×C4—521no—
259C22×C4—521no—
260C22×C4C22×D1311yescharacteristic
261C22×C4C22×D1311yescharacteristic
262C22×C4C22×D1311yescharacteristic
263C22×C4C22×D1311yescharacteristic
264C22×C4C22×D1311yescharacteristic
265C22×C4C22×D1311yescharacteristic
266C22×C4C22×D1311yescharacteristic
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—262no—
272C4⋊C4—262no—
273C4⋊C4—262no—
274C4⋊C4—262no—
275C4⋊C4—521no—
276C4⋊C4—521no—
277C4⋊C4—521no—
278C22⋊C4—134no—
279C22⋊C4—262no—
280C22⋊C4—262no—
281C22⋊C4—262no—
282C42—262no—
283C42—262no—
284C13#243811yescharacteristic, complemented, Sylow
285C23—132no—
286C23—132no—
287C23—132no—
288C23—261no—
289C23—261no—
290C23—261no—
291C23—261no—
292C23C23×D1311yescharacteristic
293Q8—524no—
294C2×C4—21no—
295C2×C4—21no—
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—132no—
312C2×C4—132no—
313C2×C4—268no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—261no—
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—524no—
334C2×C4—524no—
335C2×C4D4×D1312yes—
336C2×C4#612912yes—
337C2×C4Q8×D1312yes—
338C2×C4#613112yes—
339C22—134no—
340C22—262no—
341C22—262no—
342C22—262no—
343C22—262no—
344C22—262no—
345C22—262no—
346C22C2×D4×D1311yescharacteristic
347C22C2×#612911yescharacteristic
348C22C2×Q8×D1311yescharacteristic
349C22C2×#613111yescharacteristic
350C22#41×D1311yescharacteristic
351C22#8825611yescharacteristic
352C22#8825711yescharacteristic
353C4—22no—
354C4—22no—
355C4—22no—
356C4—22no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—262no—
361C4—262no—
362C4—521no—
363C4—521no—
364C4—521no—
365C4—521no—
366C4—521no—
367C2—264no—
368C2#1171931611yescharacteristic
369C2D13×C22⋊Q811yescharacteristic
370C2#1171933511yescharacteristic
371C2#1171936311yescharacteristic
372C2#1171939411yescharacteristic
373C2#1171939911yescharacteristic
374C2#1171943311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#398C2
prime radicalC23×D13C23
hypercenter#398D13
hypocenterC13#2438
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
3. C13×#398C2semidirect
6. #11718647C2semidirect
7. #11718646C2semidirect
8. #11718642C2semidirect
9. #11718639C2semidirect
13. #11718322C2semidirect
14. #11718317C2semidirect
15. #11718307C2semidirect
76. C2×C4×D13Q8semidirect
156. #398D13semidirect
284. C13#2438semidirect

Maximal subgroups

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

subgroupindex
C2×#881512
C2×#881462
C13×#3982
#117186502
#117186482
#117186472
#117186462
#117186422
#117186392
#117183292
#117183252
D13×#952
#117183222
#117183172
#117183072
#243813