Finite Group Databasebeta

← #13118332

Subgroups — #13118332

Order 1664.

484 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88141C211yesmaximal, characteristic, complemented
2C2×#88132C211yesmaximal, characteristic
3C13×#397C211yesmaximal, characteristic
4#11718643C211yesmaximal, characteristic, complemented
5#11718613C211yesmaximal, characteristic
6#11718612C211yesmaximal, characteristic
7#11718605C211yesmaximal, characteristic
8#11718603C211yesmaximal, characteristic
9C22⋊C4×Dic13C211yesmaximal, characteristic
10#11718321C211yesmaximal, characteristic, complemented
11#11718316C211yesmaximal, characteristic, complemented
12#11718314C211yesmaximal, characteristic, complemented
13#11718311C211yesmaximal, characteristic, complemented
14#11718308C211yesmaximal, characteristic, complemented
15#11718307C211yesmaximal, characteristic, complemented
16C23×Dic13C2211yescharacteristic
17C22×Dic26C2211yescharacteristic
18C2×C13×C4⋊C4C2211yescharacteristic
19C2×C13×C22⋊C4C2211yescharacteristic
20C2×C13×C22⋊C4C2211yescharacteristic
21C2×C13×C22⋊C4C2211yescharacteristic
22C2×C22⋊Dic13C2211yescharacteristic
23C2×C22⋊Dic13C2211yescharacteristic
24C2×C22⋊Dic13C2211yescharacteristic
25C2×C4⋊Dic13C2211yescharacteristic
26C2×C4⋊Dic13C2211yescharacteristic
27C2×#6101C2211yescharacteristic
28C2×#6101C2211yescharacteristic
29C2×#6101C2211yescharacteristic
30C2×#6101C2211yescharacteristic
31C2×#6101C2211yescharacteristic
32C2×#6101C2211yescharacteristic
33C2×C4×Dic13C2211yescharacteristic
34C2×C4×Dic13C2211yescharacteristic
35C2×C4×Dic13C2211yescharacteristic
36C2×C4×Dic13C2211yescharacteristic
37#88141—24no—
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
54C22×C4×C13C2311yescharacteristic
55C22×C4×C13C2311yescharacteristic
56C22×C4×C13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×Dic13—22no—
61C22×Dic13—22no—
62C22×Dic13—22no—
63C22×Dic13C2311yescharacteristic
64C22×Dic13C2311yescharacteristic
65C22×Dic13C2311yescharacteristic
66C22×Dic13C2311yescharacteristic
67C22×Dic13C2311yescharacteristic
68C22×Dic13C2311yescharacteristic
69C22×Dic13C2311yescharacteristic
70C22×Dic13C2311yescharacteristic
71C2×Dic26—22no—
72C2×Dic26—22no—
73C2×Dic26D414yes—
74C13×C4⋊C4—22no—
75C13×C22⋊C4—22no—
76C13×C22⋊C4—22no—
77C13×C22⋊C4—22no—
78C22⋊Dic13—22no—
79C22⋊Dic13—22no—
80C22⋊Dic13—22no—
81C4⋊Dic13—22no—
82C4⋊Dic13—22no—
83#6101—22no—
84#6101—22no—
85#6101—22no—
86#6101—22no—
87#6101—22no—
88#6101—22no—
89C4×Dic13—22no—
90C4×Dic13—22no—
91C4×Dic13—22no—
92C4×Dic13—22no—
93#2421—131nomaximal, Sylow
94C23×C13—21no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13—21no—
100C23×C13#4112yes—
101C23×C13C2411yescharacteristic
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
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×C13C2×D412yes—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
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—44no—
140C2×Dic13C2×D412yes—
141C2×Dic13C2×D412yes—
142C2×Dic13#4112yes—
143C2×Dic13#4112yes—
144C2×Dic13#4112yes—
145Dic26—28no—
146C2×C22⋊Q8—131no—
147C2×C4×Q8—131no—
148#400—131no—
149#400—131no—
150#397—131no—
151#397D1311yescharacteristic
152#391—131no—
153#389—131no—
154#388—131no—
155#388—131no—
156#387—131no—
157#387—131no—
158#382—131no—
159#380—131no—
160C4×C22⋊C4—131no—
161C22×C13—22no—
162C22×C13—22no—
163C22×C13—22no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13—41no—
168C22×C13C22×D411yescharacteristic
169C22×C13C2×#4111yescharacteristic
170C22×C13C2×#4111yescharacteristic
171C22×C13C2×#4111yescharacteristic
172C22×C13C2×#4111yescharacteristic
173C22×C132−1+411yescharacteristic
174C22×C132−1+411yescharacteristic
175C4×C13—22no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13—41no—
180C4×C13—41no—
181Dic13—22no—
182Dic13—22no—
183Dic13—41no—
184Dic13—41no—
185Dic13—41no—
186Dic13—41no—
187Dic13—41no—
188Dic13#12314yes—
189C22×Q8—131no—
190C23×C4—131no—
191C22⋊Q8—264no—
192C4×Q8—264no—
193C2×C4⋊C4—131no—
194C2×C4⋊C4—131no—
195C2×C4⋊C4—131no—
196C2×C4⋊C4—131no—
197C2×C4⋊C4—131no—
198C2×C4⋊C4—131no—
199C2×C4⋊C4—131no—
200C2×C4⋊C4—131no—
201C2×C4⋊C4C2×D1311yescharacteristic
202C2×C22⋊C4—131no—
203C2×C22⋊C4—131no—
204C2×C22⋊C4—131no—
205C2×C22⋊C4C2×D1311yescharacteristic
206C2×C22⋊C4C2×D1311yescharacteristic
207C2×C22⋊C4C2×D1311yescharacteristic
208C2×C42—131no—
209C2×C42—131no—
210C2×C42—131no—
211C2×C42—131no—
212#95—131no—
213#95—131no—
214#95—131no—
215#95—131no—
216#95—131no—
217#95—131no—
218#95—131no—
219#95—131no—
220#95—131no—
221#95—131no—
222#95—131no—
223#95C2×D1311yescharacteristic
224#95C2×D1311yescharacteristic
225#95C2×D1311yescharacteristic
226C2×C13—42no—
227C2×C13C2×#12311yescharacteristic
228C2×C13#52911yescharacteristic
229C2×C13#54111yescharacteristic
230C2×C13#54811yescharacteristic
231C2×C13#54811yescharacteristic
232C2×C13#55211yescharacteristic
233C2×C13#55611yescharacteristic
234C24C22×D1311yescharacteristic
235C2×Q8—134no—
236C2×Q8—262no—
237C2×Q8—262no—
238C22×C4—131no—
239C22×C4—131no—
240C22×C4—131no—
241C22×C4—131no—
242C22×C4—131no—
243C22×C4—131no—
244C22×C4—131no—
245C22×C4—131no—
246C22×C4—262no—
247C22×C4—262no—
248C22×C4—262no—
249C22×C4C22×D1311yescharacteristic
250C22×C4C22×D1311yescharacteristic
251C22×C4C22×D1311yescharacteristic
252C22×C4C22×D1311yescharacteristic
253C22×C4C22×D1311yescharacteristic
254C22×C4C22×D1311yescharacteristic
255C4⋊C4—22no—
256C4⋊C4—262no—
257C4⋊C4—262no—
258C4⋊C4—262no—
259C4⋊C4—262no—
260C4⋊C4—262no—
261C4⋊C4—262no—
262C4⋊C4—262no—
263C4⋊C4—262no—
264C22⋊C4—22no—
265C22⋊C4—22no—
266C22⋊C4—22no—
267C22⋊C4—262no—
268C22⋊C4—262no—
269C22⋊C4—262no—
270C42—262no—
271C42—262no—
272C42—262no—
273C42—262no—
274C13#242111yescharacteristic, complemented, Sylow
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23#612912yes—
282C23C23×D1311yescharacteristic
283Q8—268no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
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—132no—
302C2×C4—132no—
303C2×C4—132no—
304C2×C4—132no—
305C2×C4—132no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—261no—
311C2×C4—261no—
312C2×C4—261no—
313C2×C4—261no—
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—524no—
326C2×C4D4×D1312yes—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22C2×D4×D1311yescharacteristic
335C22C2×#612911yescharacteristic
336C22#41×D1311yescharacteristic
337C22#41×D1311yescharacteristic
338C22#41×D1311yescharacteristic
339C22#8825711yescharacteristic
340C22#8825711yescharacteristic
341C4—22no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—134no—
348C4—262no—
349C4—262no—
350C4—521no—
351C4—521no—
352C4—521no—
353C4—521no—
354C4—521no—
355C2—42no—
356C2#1171930311yescharacteristic
357C2#1171935411yescharacteristic
358C2#1171935511yescharacteristic
359C2D13×#12311yescharacteristic
360C2#1171938211yescharacteristic
361C2#1171940611yescharacteristic
362C2#1171940711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#397C2
prime radicalC24×C13C23
hypercenter#397D13
hypocenterC13#2421
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#88141C2semidirect
4. #11718643C2semidirect
10. #11718321C2semidirect
11. #11718316C2semidirect
12. #11718314C2semidirect
13. #11718311C2semidirect
14. #11718308C2semidirect
15. #11718307C2semidirect
274. C13#2421semidirect

Maximal subgroups

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

subgroupindex
C2×#881412
C2×#881322
C13×#3972
#117186432
#117186132
#117186122
#117186052
#117186032
C22⋊C4×Dic132
#117183212
#117183162
#117183142
#117183112
#117183082
#117183072
#242113