Finite Group Databasebeta

← #13117860

Subgroups — #13117860

Order 1664.

576 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88141C211yesmaximal, characteristic, complemented
2C2×#88132C211yesmaximal, characteristic
3C2×#88131C211yesmaximal, characteristic
4C13×#388C211yesmaximal, characteristic
5#11718639C211yesmaximal, characteristic, complemented
6#11718612C211yesmaximal, characteristic
7#11718605C211yesmaximal, characteristic
8#11718605C211yesmaximal, characteristic
9C22⋊C4×Dic13C211yesmaximal, characteristic
10C4×C4⋊Dic13C211yesmaximal, characteristic, complemented
11C4×#6101C211yesmaximal, characteristic, complemented
12#11718315C211yesmaximal, characteristic, complemented
13#11718310C211yesmaximal, 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×C42×C13C2211yescharacteristic
23C2×C22⋊Dic13C2211yescharacteristic
24C2×C22⋊Dic13C2211yescharacteristic
25C2×C22⋊Dic13C2211yescharacteristic
26C2×C4⋊Dic13C2211yescharacteristic
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
38C2×C4×Dic13C2211yescharacteristic
39C2×C4×Dic13C2211yescharacteristic
40C2×C4×Dic13C2211yescharacteristic
41#88141—24no—
42#88132C418yescomplemented
43#88131—24no—
44C13×#95C2211yescharacteristic
45C13×#95C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53#88071C2211yescharacteristic
54C24×C13C2311yescharacteristic
55C22×C4×C13C2311yescharacteristic
56C22×C4×C13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×Dic13—22no—
62C22×Dic13—22no—
63C22×Dic13C2×C414yes—
64C22×Dic13C2311yescharacteristic
65C22×Dic13C2311yescharacteristic
66C22×Dic13C2311yescharacteristic
67C22×Dic13C2311yescharacteristic
68C22×Dic13C2311yescharacteristic
69C22×Dic13C2311yescharacteristic
70C22×Dic13C2311yescharacteristic
71C22×Dic13C2311yescharacteristic
72C2×Dic26—22no—
73C2×Dic26—22no—
74C2×Dic26C2×C414yes—
75C13×C4⋊C4—22no—
76C13×C22⋊C4—22no—
77C13×C22⋊C4—22no—
78C13×C22⋊C4C2×C414yes—
79C42×C13—22no—
80C22⋊Dic13—22no—
81C22⋊Dic13—22no—
82C22⋊Dic13C2×C414yes—
83C4⋊Dic13—22no—
84C4⋊Dic13C2×C414yes—
85#6101—22no—
86#6101—22no—
87#6101—22no—
88#6101C2×C414yes—
89#6101C2×C414yes—
90#6101D414yes—
91C4×Dic13—22no—
92C4×Dic13—22no—
93C4×Dic13—22no—
94C4×Dic13—22no—
95C4×Dic13—22no—
96C4×Dic13—22no—
97C4×Dic13—22no—
98#2362—131nomaximal, Sylow
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13C22×C412yes—
106C23×C13C2411yescharacteristic
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×C13C22×C412yes—
122C2×C4×C13C22×C412yes—
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—28no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13C22×C412yes—
143C2×Dic13C22×C412yes—
144C2×Dic13C22×C412yes—
145C2×Dic13C22×C412yes—
146C2×Dic13C2×D412yes—
147C2×Dic13C2×D412yes—
148C2×Dic13#4112yes—
149C2×Dic13#4112yes—
150Dic26—28no—
151C2×C22⋊Q8—131no—
152C2×C4×Q8—131no—
153C2×#117—131no—
154#391—131no—
155#389—131no—
156#388—131no—
157#388—131no—
158#388—131no—
159#388D1311yescharacteristic
160#387—131no—
161#387—131no—
162C4×C4⋊C4—131no—
163C4×C4⋊C4—131no—
164C4×C4⋊C4—131no—
165C4×C22⋊C4—131no—
166C22×C13—22no—
167C22×C13—22no—
168C22×C13—22no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13—41no—
173C22×C13C23×C411yescharacteristic
174C22×C13C22×D411yescharacteristic
175C22×C13C2×#4111yescharacteristic
176C22×C13C2×#4111yescharacteristic
177C22×C13C2×#4111yescharacteristic
178C22×C132−1+411yescharacteristic
179C22×C132−1+411yescharacteristic
180C4×C13—22no—
181C4×C13—22no—
182C4×C13—22no—
183C4×C13—22no—
184C4×C13—41no—
185C4×C13—41no—
186Dic13—22no—
187Dic13—22no—
188Dic13—22no—
189Dic13—22no—
190Dic13—22no—
191Dic13—41no—
192Dic13—41no—
193Dic13C4×D414yes—
194C22×Q8—131no—
195C23×C4—131no—
196C22⋊Q8—138no—
197C4×Q8—264no—
198#117—264no—
199C2×C4⋊C4—131no—
200C2×C4⋊C4—131no—
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⋊C4C2×D1311yescharacteristic
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—
218C2×C42—131no—
219C2×C42—131no—
220C2×C42—131no—
221C2×C42C2×D1311yescharacteristic
222#95—131no—
223#95—131no—
224#95—131no—
225#95—131no—
226#95—131no—
227#95—131no—
228#95—131no—
229#95—131no—
230#95C2×D1311yescharacteristic
231#95C2×D1311yescharacteristic
232C2×C13—42no—
233C2×C13C2×C4×D411yescharacteristic
234C2×C13C4×#4111yescharacteristic
235C2×C13#51911yescharacteristic
236C2×C13#54711yescharacteristic
237C2×C13#54811yescharacteristic
238C2×C13#55211yescharacteristic
239C2×C13#55611yescharacteristic
240C24C22×D1311yescharacteristic
241C2×Q8—134no—
242C2×Q8—262no—
243C2×Q8—262no—
244C22×C4—131no—
245C22×C4—134no—
246C22×C4—131no—
247C22×C4—131no—
248C22×C4—131no—
249C22×C4—131no—
250C22×C4—131no—
251C22×C4—131no—
252C22×C4—131no—
253C22×C4—262no—
254C22×C4—262no—
255C22×C4C22×D1311yescharacteristic
256C22×C4C22×D1311yescharacteristic
257C22×C4C22×D1311yescharacteristic
258C22×C4C22×D1311yescharacteristic
259C22×C4C22×D1311yescharacteristic
260C22×C4C22×D1311yescharacteristic
261C4⋊C4—22no—
262C4⋊C4—134no—
263C4⋊C4—134no—
264C4⋊C4—134no—
265C4⋊C4—134no—
266C4⋊C4—262no—
267C4⋊C4—262no—
268C4⋊C4—262no—
269C4⋊C4—262no—
270C22⋊C4—22no—
271C22⋊C4—22no—
272C22⋊C4—134no—
273C22⋊C4—262no—
274C22⋊C4—262no—
275C22⋊C4C4×D1314yes—
276C42—22no—
277C42—262no—
278C42—262no—
279C42—262no—
280C42—262no—
281C42—262no—
282C42—262no—
283C42—262no—
284C13#236211yescharacteristic, complemented, Sylow
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23C2×C4×D1312yes—
292C23C23×D1311yescharacteristic
293Q8—268no—
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—132no—
309C2×C4—132no—
310C2×C4—132no—
311C2×C4—132no—
312C2×C4—132no—
313C2×C4—132no—
314C2×C4—132no—
315C2×C4—132no—
316C2×C4—268no—
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×C4C2×C4×D1312yes—
334C2×C4C2×C4×D1312yes—
335C2×C4D4×D1312yes—
336C2×C4#612912yes—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22C22×C4×D1311yescharacteristic
345C22C2×D4×D1311yescharacteristic
346C22C2×#612911yescharacteristic
347C22#41×D1311yescharacteristic
348C22#41×D1311yescharacteristic
349C22#8825711yescharacteristic
350C22#8825711yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—134no—
358C4—262no—
359C4—262no—
360C4—262no—
361C4—262no—
362C4—262no—
363C4—521no—
364C4—521no—
365C2—42no—
366C2#1171922111yescharacteristic
367C2C4×#612911yescharacteristic
368C2C4×D4×D1311yescharacteristic
369C2#1171931611yescharacteristic
370C2#1171935511yescharacteristic
371C2#1171938211yescharacteristic
372C2#1171940711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutatorC22×C13C23×C4
FittingC13×#388C2
socle, cosocleC23×C13C24
prime radicalC24×C13C23
hypercenter#388D13
hypocenterC13#2362
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#88141C2semidirect
5. #11718639C2semidirect
10. C4×C4⋊Dic13C2semidirect
11. C4×#6101C2semidirect
12. #11718315C2semidirect
13. #11718310C2semidirect
14. #11718308C2semidirect
15. #11718307C2semidirect
42. #88132C4semidirect
284. C13#2362semidirect

Maximal subgroups

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

subgroupindex
C2×#881412
C2×#881322
C2×#881312
C13×#3882
#117186392
#117186122
#117186052
C22⋊C4×Dic132
C4×C4⋊Dic132
C4×#61012
#117183152
#117183102
#117183082
#117183072
#236213