Finite Group Databasebeta

← #44408122

Subgroups — #44408122

Order 29056.

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#28408926C211yesmaximal, characteristic
2#28408926C211yesmaximal, characteristic
3#28408925C211yesmaximal, characteristic
4#28408925C211yesmaximal, characteristic
5#28408920C211yesmaximal, characteristic
6#28408920C211yesmaximal, characteristic
7#28408919C211yesmaximal, characteristic, complemented
8#28408918C211yesmaximal, characteristic, complemented
9#28408917C211yesmaximal, characteristic, complemented
10#28408916C211yesmaximal, characteristic, complemented
11#28408915C211yesmaximal, characteristic, complemented
12#28408914C211yesmaximal, characteristic, complemented
13#28408913C211yesmaximal, characteristic, complemented
14C42×Dic227C211yesmaximal, characteristic, complemented
15#388×C227C211yesmaximal, characteristic
16C2×C4⋊Dic227C2211yescharacteristic
17C2×C4⋊Dic227C2211yescharacteristic
18C2×Dic227⋊C4C2211yescharacteristic
19C2×Dic227⋊C4C2211yescharacteristic
20C2×Dic227⋊C4C2211yescharacteristic
21C2×Dic227⋊C4C2211yescharacteristic
22C2×C22⋊Dic227C2211yescharacteristic
23C2×C22⋊Dic227C2211yescharacteristic
24C2×C22⋊Dic227C2211yescharacteristic
25C2×C22⋊Dic227C2211yescharacteristic
26C2×C4×Dic227C2211yescharacteristic
27C2×C4×Dic227C2211yescharacteristic
28C2×C4×Dic227C2211yescharacteristic
29C2×C4×Dic227C2211yescharacteristic
30C2×C4×Dic227C2211yescharacteristic
31C2×C4×Dic227C2211yescharacteristic
32C227⋊#95C2211yescharacteristic
33C227⋊#95C2211yescharacteristic
34C227⋊#95C2211yescharacteristic
35C227⋊#95C2211yescharacteristic
36C227⋊#95C2211yescharacteristic
37C227⋊#95C2211yescharacteristic
38C227⋊#95C2211yescharacteristic
39C227⋊#95C2211yescharacteristic
40C227⋊#95C2211yescharacteristic
41C227⋊#95C2211yescharacteristic
42C227⋊#95C2211yescharacteristic
43C227⋊#95C2211yescharacteristic
44C2×C4⋊C4×C227C2211yescharacteristic
45C2×C22⋊C4×C227C2211yescharacteristic
46C2×C22⋊C4×C227C2211yescharacteristic
47C2×C22⋊C4×C227C2211yescharacteristic
48C2×C42×C227C2211yescharacteristic
49#95×C227C2211yescharacteristic
50#95×C227C2211yescharacteristic
51C22×Dic227C2311yescharacteristic
52C22×Dic227C2311yescharacteristic
53C22×Dic227C2311yescharacteristic
54C22×Dic227C2311yescharacteristic
55C22×Dic227C2311yescharacteristic
56C22×Dic227C2311yescharacteristic
57C22×Dic227C2311yescharacteristic
58C22×Dic227C2311yescharacteristic
59C4⋊Dic227—22no—
60C4⋊Dic227—22no—
61Dic227⋊C4—22no—
62Dic227⋊C4—22no—
63Dic227⋊C4—22no—
64Dic227⋊C4—22no—
65C22⋊Dic227—22no—
66C22⋊Dic227—22no—
67C22⋊Dic227—22no—
68C22⋊Dic227—22no—
69C4×Dic227—22no—
70C4×Dic227—22no—
71C4×Dic227—22no—
72C4×Dic227—22no—
73C4×Dic227—22no—
74C4×Dic227—22no—
75C24×C227C2311yescharacteristic
76C22×C4×C227C2311yescharacteristic
77C22×C4×C227C2311yescharacteristic
78C22×C4×C227C2311yescharacteristic
79C22×C4×C227C2311yescharacteristic
80C22×C4×C227C2311yescharacteristic
81C22×C4×C227C2311yescharacteristic
82C4⋊C4×C227—22no—
83C22⋊C4×C227—22no—
84C22⋊C4×C227—22no—
85C22⋊C4×C227—22no—
86C42×C227—22no—
87C2×Dic227—21no—
88C2×Dic227—21no—
89C2×Dic227—21no—
90C2×Dic227—21no—
91C2×Dic227—21no—
92C2×Dic227—21no—
93C2×Dic227—21no—
94C2×Dic227—21no—
95C2×Dic227—21no—
96C2×Dic227—21no—
97C2×Dic227—21no—
98C2×Dic227—21no—
99C2×Dic227—21no—
100C2×Dic227—21no—
101C2×Dic227—21no—
102C2×Dic227—21no—
103C2×Dic227—21no—
104C2×Dic227—21no—
105C2×Dic227—21no—
106C2×Dic227—21no—
107C2×Dic227#4112yes—
108C2×Dic227#4112yes—
109C2×Dic227#4112yes—
110C2×Dic227#4112yes—
111C23×C227—21no—
112C23×C227—21no—
113C23×C227—21no—
114C23×C227—21no—
115C23×C227—21no—
116C23×C227—21no—
117C23×C227—21no—
118C23×C227C2411yescharacteristic
119C2×C4×C227—21no—
120C2×C4×C227—21no—
121C2×C4×C227—21no—
122C2×C4×C227—21no—
123C2×C4×C227—21no—
124C2×C4×C227—21no—
125C2×C4×C227—21no—
126C2×C4×C227—21no—
127C2×C4×C227—21no—
128C2×C4×C227—21no—
129C2×C4×C227—21no—
130C2×C4×C227—21no—
131C2×C4×C227—21no—
132C2×C4×C227—21no—
133C2×C4×C227—21no—
134C2×C4×C227#4112yes—
135C2×C4×C227#4112yes—
136C2×C4×C227#4112yes—
137C22×C227—41no—
138C22×C227—41no—
139C22×C227—41no—
140C22×C227—41no—
141C22×C227—41no—
142C22×C227—41no—
143C22×C227—41no—
144C22×C227C2×#4111yescharacteristic
145C22×C227C2×#4111yescharacteristic
146C22×C227C2×#4111yescharacteristic
147C22×C227C2×#4111yescharacteristic
148C22×C227C2×#4111yescharacteristic
149C22×C227C2×#4111yescharacteristic
150C22×C227C2×#4111yescharacteristic
151C4×C227—22no—
152C4×C227—22no—
153C4×C227—22no—
154C4×C227—41no—
155C4×C227—41no—
156C4×C227—41no—
157Dic227—22no—
158Dic227—22no—
159Dic227—22no—
160Dic227—22no—
161Dic227—41no—
162Dic227—41no—
163Dic227—41no—
164Dic227—41no—
165C2×C227—81no—
166C2×C227#52911yescharacteristic
167C2×C227#52911yescharacteristic
168C2×C227#52911yescharacteristic
169C2×C227#52911yescharacteristic
170C2×C227#52911yescharacteristic
171C2×C227#52911yescharacteristic
172C2×C227#52911yescharacteristic
173C227#286511yescharacteristic, complemented, Sylow
174#2865—2271nomaximal, Sylow
175#388—2271no—
176#388—2271no—
177#388—2271no—
178#388—2271no—
179#388—2271no—
180#388—2271no—
181#388D22711yescharacteristic
182#387—2271no—
183#387—2271no—
184#387—2271no—
185#387—2271no—
186#387—2271no—
187#387—2271no—
188#387—2271no—
189C43—2271no—
190C2×C4⋊C4—2271no—
191C2×C4⋊C4—2271no—
192C2×C4⋊C4—2271no—
193C2×C4⋊C4—2271no—
194C2×C4⋊C4—2271no—
195C2×C4⋊C4—2271no—
196C2×C4⋊C4C2×D22711yescharacteristic
197C2×C22⋊C4—2271no—
198C2×C22⋊C4—2271no—
199C2×C22⋊C4—2271no—
200C2×C22⋊C4—2271no—
201C2×C22⋊C4C2×D22711yescharacteristic
202C2×C22⋊C4C2×D22711yescharacteristic
203C2×C22⋊C4C2×D22711yescharacteristic
204C2×C42—2271no—
205C2×C42—2271no—
206C2×C42—2271no—
207C2×C42—2271no—
208C2×C42—2271no—
209C2×C42—2271no—
210C2×C42C2×D22711yescharacteristic
211#95—2271no—
212#95—2271no—
213#95—2271no—
214#95—2271no—
215#95—2271no—
216#95—2271no—
217#95—2271no—
218#95—2271no—
219#95—2271no—
220#95—2271no—
221#95—2271no—
222#95—2271no—
223#95C2×D22711yescharacteristic
224#95C2×D22711yescharacteristic
225C24C22×D22711yescharacteristic
226C22×C4—2271no—
227C22×C4—2271no—
228C22×C4—2271no—
229C22×C4—2271no—
230C22×C4—2271no—
231C22×C4—2271no—
232C22×C4—2271no—
233C22×C4—2271no—
234C22×C4C22×D22711yescharacteristic
235C22×C4C22×D22711yescharacteristic
236C22×C4C22×D22711yescharacteristic
237C22×C4C22×D22711yescharacteristic
238C22×C4C22×D22711yescharacteristic
239C22×C4C22×D22711yescharacteristic
240C4⋊C4—22no—
241C4⋊C4—4542no—
242C4⋊C4—4542no—
243C4⋊C4—4542no—
244C4⋊C4—4542no—
245C4⋊C4—4542no—
246C4⋊C4—4542no—
247C22⋊C4—22no—
248C22⋊C4—22no—
249C22⋊C4—22no—
250C22⋊C4—4542no—
251C22⋊C4—4542no—
252C22⋊C4—4542no—
253C22⋊C4—4542no—
254C42—22no—
255C42—4542no—
256C42—4542no—
257C42—4542no—
258C42—4542no—
259C42—4542no—
260C42—4542no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23C23×D22711yescharacteristic
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—4541no—
285C2×C4—4541no—
286C2×C4—4541no—
287C2×C4—4541no—
288C2×C4—4541no—
289C2×C4—4541no—
290C2×C4—4541no—
291C2×C4—4541no—
292C2×C4—4541no—
293C2×C4—4541no—
294C2×C4—4541no—
295C2×C4—4541no—
296C2×C4—4541no—
297C2×C4—4541no—
298C2×C4—4541no—
299C2×C4—4541no—
300C2×C4—4541no—
301C2×C4—4541no—
302C2×C4—4541no—
303C2×C4—4541no—
304C2×C4—2272no—
305C2×C4—2272no—
306C2×C4—2272no—
307C2×C4—2272no—
308C2×C4#1681388312yes—
309C2×C4#1681388312yes—
310C2×C4#1681388412yes—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22#41×D22711yescharacteristic
319C22#41×D22711yescharacteristic
320C22#41×D22711yescharacteristic
321C22#41×D22711yescharacteristic
322C22C2×#1681388311yescharacteristic
323C22C2×#1681388311yescharacteristic
324C22C2×#1681388411yescharacteristic
325C4—22no—
326C4—22no—
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—9081no—
332C4—9081no—
333C4—9081no—
334C4—9081no—
335C4—4542no—
336C4—4542no—
337C4—4542no—
338C4—4542no—
339C2—81no—
340C2#2840955911yescharacteristic
341C2#2840956011yescharacteristic
342C2#2840956111yescharacteristic
343C2#2840956211yescharacteristic
344C2#2840956311yescharacteristic
345C2#2840956411yescharacteristic
346C2#2840956511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D227
commutator, socle, cosocleC23×C227C24
Fitting#388×C227C2
prime radicalC24×C227C23
hypercenter#388D227
hypocenterC227#2865
LCSG ▷ C23×C227 ▷ C227
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
7. #28408919C2semidirect
8. #28408918C2semidirect
9. #28408917C2semidirect
10. #28408916C2semidirect
11. #28408915C2semidirect
12. #28408914C2semidirect
13. #28408913C2semidirect
14. C42×Dic227C2semidirect
173. C227#2865semidirect

Maximal subgroups

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

subgroupindex
#284089262
#284089252
#284089202
#284089192
#284089182
#284089172
#284089162
#284089152
#284089142
#284089132
C42×Dic2272
#388×C2272
#2865227