Finite Group Databasebeta

← #46819273

Subgroups — #46819273

Order 34432.

418 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31770499C211yesmaximal, characteristic
2#31770499C211yesmaximal, characteristic
3#31770498C211yesmaximal, characteristic
4#31770498C211yesmaximal, characteristic
5#31770493C211yesmaximal, characteristic
6#31770493C211yesmaximal, characteristic
7#31770492C211yesmaximal, characteristic, complemented
8#31770491C211yesmaximal, characteristic, complemented
9#31770490C211yesmaximal, characteristic, complemented
10#31770489C211yesmaximal, characteristic, complemented
11#31770488C211yesmaximal, characteristic, complemented
12#31770487C211yesmaximal, characteristic, complemented
13#31770486C211yesmaximal, characteristic, complemented
14C42×Dic269C211yesmaximal, characteristic, complemented
15#388×C269C211yesmaximal, characteristic
16C2×C4⋊Dic269C2211yescharacteristic
17C2×C4⋊Dic269C2211yescharacteristic
18C2×#16864381C2211yescharacteristic
19C2×#16864381C2211yescharacteristic
20C2×#16864381C2211yescharacteristic
21C2×#16864381C2211yescharacteristic
22C2×C22⋊Dic269C2211yescharacteristic
23C2×C22⋊Dic269C2211yescharacteristic
24C2×C22⋊Dic269C2211yescharacteristic
25C2×C22⋊Dic269C2211yescharacteristic
26C2×C4×Dic269C2211yescharacteristic
27C2×C4×Dic269C2211yescharacteristic
28C2×C4×Dic269C2211yescharacteristic
29C2×C4×Dic269C2211yescharacteristic
30C2×C4×Dic269C2211yescharacteristic
31C2×C4×Dic269C2211yescharacteristic
32#22575360C2211yescharacteristic
33#22575360C2211yescharacteristic
34#22575360C2211yescharacteristic
35#22575360C2211yescharacteristic
36#22575360C2211yescharacteristic
37#22575360C2211yescharacteristic
38#22575360C2211yescharacteristic
39#22575360C2211yescharacteristic
40#22575360C2211yescharacteristic
41#22575360C2211yescharacteristic
42#22575360C2211yescharacteristic
43#22575360C2211yescharacteristic
44C2×C4⋊C4×C269C2211yescharacteristic
45C2×C22⋊C4×C269C2211yescharacteristic
46C2×C22⋊C4×C269C2211yescharacteristic
47C2×C22⋊C4×C269C2211yescharacteristic
48C2×C42×C269C2211yescharacteristic
49#95×C269C2211yescharacteristic
50#95×C269C2211yescharacteristic
51C22×Dic269C2311yescharacteristic
52C22×Dic269C2311yescharacteristic
53C22×Dic269C2311yescharacteristic
54C22×Dic269C2311yescharacteristic
55C22×Dic269C2311yescharacteristic
56C22×Dic269C2311yescharacteristic
57C22×Dic269C2311yescharacteristic
58C22×Dic269C2311yescharacteristic
59C4⋊Dic269—22no—
60C4⋊Dic269—22no—
61#16864381—22no—
62#16864381—22no—
63#16864381—22no—
64#16864381—22no—
65C22⋊Dic269—22no—
66C22⋊Dic269—22no—
67C22⋊Dic269—22no—
68C22⋊Dic269—22no—
69C4×Dic269—22no—
70C4×Dic269—22no—
71C4×Dic269—22no—
72C4×Dic269—22no—
73C4×Dic269—22no—
74C4×Dic269—22no—
75C24×C269C2311yescharacteristic
76C22×C4×C269C2311yescharacteristic
77C22×C4×C269C2311yescharacteristic
78C22×C4×C269C2311yescharacteristic
79C22×C4×C269C2311yescharacteristic
80C22×C4×C269C2311yescharacteristic
81C22×C4×C269C2311yescharacteristic
82C4⋊C4×C269—22no—
83C22⋊C4×C269—22no—
84C22⋊C4×C269—22no—
85C22⋊C4×C269—22no—
86C42×C269—22no—
87C2×Dic269—21no—
88C2×Dic269—21no—
89C2×Dic269—21no—
90C2×Dic269—21no—
91C2×Dic269—21no—
92C2×Dic269—21no—
93C2×Dic269—21no—
94C2×Dic269—21no—
95C2×Dic269—21no—
96C2×Dic269—21no—
97C2×Dic269—21no—
98C2×Dic269—21no—
99C2×Dic269—21no—
100C2×Dic269—21no—
101C2×Dic269—21no—
102C2×Dic269—21no—
103C2×Dic269—21no—
104C2×Dic269—21no—
105C2×Dic269—21no—
106C2×Dic269—21no—
107C2×Dic269#4112yes—
108C2×Dic269#4112yes—
109C2×Dic269#4112yes—
110C2×Dic269#4112yes—
111C23×C269—21no—
112C23×C269—21no—
113C23×C269—21no—
114C23×C269—21no—
115C23×C269—21no—
116C23×C269—21no—
117C23×C269—21no—
118C23×C269C2411yescharacteristic
119C2×C4×C269—21no—
120C2×C4×C269—21no—
121C2×C4×C269—21no—
122C2×C4×C269—21no—
123C2×C4×C269—21no—
124C2×C4×C269—21no—
125C2×C4×C269—21no—
126C2×C4×C269—21no—
127C2×C4×C269—21no—
128C2×C4×C269—21no—
129C2×C4×C269—21no—
130C2×C4×C269—21no—
131C2×C4×C269—21no—
132C2×C4×C269—21no—
133C2×C4×C269—21no—
134C2×C4×C269#4112yes—
135C2×C4×C269#4112yes—
136C2×C4×C269#4112yes—
137C22×C269—41no—
138C22×C269—41no—
139C22×C269—41no—
140C22×C269—41no—
141C22×C269—41no—
142C22×C269—41no—
143C22×C269—41no—
144C22×C269C2×#4111yescharacteristic
145C22×C269C2×#4111yescharacteristic
146C22×C269C2×#4111yescharacteristic
147C22×C269C2×#4111yescharacteristic
148C22×C269C2×#4111yescharacteristic
149C22×C269C2×#4111yescharacteristic
150C22×C269C2×#4111yescharacteristic
151C4×C269—22no—
152C4×C269—22no—
153C4×C269—22no—
154C4×C269—41no—
155C4×C269—41no—
156C4×C269—41no—
157Dic269—22no—
158Dic269—22no—
159Dic269—22no—
160Dic269—22no—
161Dic269—41no—
162Dic269—41no—
163Dic269—41no—
164Dic269—41no—
165C2×C269—81no—
166C2×C269#52911yescharacteristic
167C2×C269#52911yescharacteristic
168C2×C269#52911yescharacteristic
169C2×C269#52911yescharacteristic
170C2×C269#52911yescharacteristic
171C2×C269#52911yescharacteristic
172C2×C269#52911yescharacteristic
173C269#286511yescharacteristic, complemented, Sylow
174#2865—2691nomaximal, Sylow
175#388—2691no—
176#388—2691no—
177#388—2691no—
178#388—2691no—
179#388—2691no—
180#388—2691no—
181#388D26911yescharacteristic
182#387—2691no—
183#387—2691no—
184#387—2691no—
185#387—2691no—
186#387—2691no—
187#387—2691no—
188#387—2691no—
189C43—2691no—
190C2×C4⋊C4—2691no—
191C2×C4⋊C4—2691no—
192C2×C4⋊C4—2691no—
193C2×C4⋊C4—2691no—
194C2×C4⋊C4—2691no—
195C2×C4⋊C4—2691no—
196C2×C4⋊C4C2×D26911yescharacteristic
197C2×C22⋊C4—2691no—
198C2×C22⋊C4—2691no—
199C2×C22⋊C4—2691no—
200C2×C22⋊C4—2691no—
201C2×C22⋊C4C2×D26911yescharacteristic
202C2×C22⋊C4C2×D26911yescharacteristic
203C2×C22⋊C4C2×D26911yescharacteristic
204C2×C42—2691no—
205C2×C42—2691no—
206C2×C42—2691no—
207C2×C42—2691no—
208C2×C42—2691no—
209C2×C42—2691no—
210C2×C42C2×D26911yescharacteristic
211#95—2691no—
212#95—2691no—
213#95—2691no—
214#95—2691no—
215#95—2691no—
216#95—2691no—
217#95—2691no—
218#95—2691no—
219#95—2691no—
220#95—2691no—
221#95—2691no—
222#95—2691no—
223#95C2×D26911yescharacteristic
224#95C2×D26911yescharacteristic
225C24C22×D26911yescharacteristic
226C22×C4—2691no—
227C22×C4—2691no—
228C22×C4—2691no—
229C22×C4—2691no—
230C22×C4—2691no—
231C22×C4—2691no—
232C22×C4—2691no—
233C22×C4—2691no—
234C22×C4C22×D26911yescharacteristic
235C22×C4C22×D26911yescharacteristic
236C22×C4C22×D26911yescharacteristic
237C22×C4C22×D26911yescharacteristic
238C22×C4C22×D26911yescharacteristic
239C22×C4C22×D26911yescharacteristic
240C4⋊C4—22no—
241C4⋊C4—5382no—
242C4⋊C4—5382no—
243C4⋊C4—5382no—
244C4⋊C4—5382no—
245C4⋊C4—5382no—
246C4⋊C4—5382no—
247C22⋊C4—22no—
248C22⋊C4—22no—
249C22⋊C4—22no—
250C22⋊C4—5382no—
251C22⋊C4—5382no—
252C22⋊C4—5382no—
253C22⋊C4—5382no—
254C42—22no—
255C42—5382no—
256C42—5382no—
257C42—5382no—
258C42—5382no—
259C42—5382no—
260C42—5382no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23C23×D26911yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—2692no—
285C2×C4—2692no—
286C2×C4—2692no—
287C2×C4—2692no—
288C2×C4—5381no—
289C2×C4—5381no—
290C2×C4—5381no—
291C2×C4—5381no—
292C2×C4—5381no—
293C2×C4—5381no—
294C2×C4—5381no—
295C2×C4—5381no—
296C2×C4—5381no—
297C2×C4—5381no—
298C2×C4—5381no—
299C2×C4—5381no—
300C2×C4—5381no—
301C2×C4—5381no—
302C2×C4—5381no—
303C2×C4—5381no—
304C2×C4—5381no—
305C2×C4—5381no—
306C2×C4—5381no—
307C2×C4—5381no—
308C2×C4#1686440112yes—
309C2×C4#1686440112yes—
310C2×C4#1686440212yes—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22#41×D26911yescharacteristic
319C22#41×D26911yescharacteristic
320C22#41×D26911yescharacteristic
321C22#41×D26911yescharacteristic
322C22C2×#1686440111yescharacteristic
323C22C2×#1686440111yescharacteristic
324C22C2×#1686440211yescharacteristic
325C4—22no—
326C4—22no—
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—5382no—
332C4—5382no—
333C4—5382no—
334C4—5382no—
335C4—10761no—
336C4—10761no—
337C4—10761no—
338C4—10761no—
339C2—81no—
340C2#3177113211yescharacteristic
341C2#3177113311yescharacteristic
342C2#3177113411yescharacteristic
343C2#3177113511yescharacteristic
344C2#3177113611yescharacteristic
345C2#3177113711yescharacteristic
346C2#3177113811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D269
commutator, socle, cosocleC23×C269C24
Fitting#388×C269C2
prime radicalC24×C269C23
hypercenter#388D269
hypocenterC269#2865
LCSG ▷ C23×C269 ▷ C269
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
7. #31770492C2semidirect
8. #31770491C2semidirect
9. #31770490C2semidirect
10. #31770489C2semidirect
11. #31770488C2semidirect
12. #31770487C2semidirect
13. #31770486C2semidirect
14. C42×Dic269C2semidirect
173. C269#2865semidirect

Maximal subgroups

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

subgroupindex
#317704992
#317704982
#317704932
#317704922
#317704912
#317704902
#317704892
#317704882
#317704872
#317704862
C42×Dic2692
#388×C2692
#2865269