Finite Group Databasebeta

← #49129651

Subgroups — #49129651

Order 36224.

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#31826357C211yesmaximal, characteristic
2#31826357C211yesmaximal, characteristic
3#31826356C211yesmaximal, characteristic
4#31826355C211yesmaximal, characteristic
5#31826355C211yesmaximal, characteristic
6#31826354C211yesmaximal, characteristic
7#31826354C211yesmaximal, characteristic
8#31826352C211yesmaximal, characteristic, complemented
9#31826351C211yesmaximal, characteristic, complemented
10#31826350C211yesmaximal, characteristic, complemented
11#31826348C211yesmaximal, characteristic, complemented
12#31826347C211yesmaximal, characteristic, complemented
13#31826346C211yesmaximal, characteristic, complemented
14C42×Dic283C211yesmaximal, characteristic, complemented
15#387×C283C211yesmaximal, characteristic, complemented
16C2×C4⋊Dic283C2211yescharacteristic
17C2×C4⋊Dic283C2211yescharacteristic
18C2×Dic283⋊C4C2211yescharacteristic
19C2×Dic283⋊C4C2211yescharacteristic
20C2×Dic283⋊C4C2211yescharacteristic
21C2×(C2×D283)⋊C4C2211yescharacteristic
22C2×(C2×D283)⋊C4C2211yescharacteristic
23C2×(C2×D283)⋊C4C2211yescharacteristic
24C2×(C2×D283)⋊C4C2211yescharacteristic
25C2×(C2×D283)⋊C4C2211yescharacteristic
26C2×(C2×D283)⋊C4C2211yescharacteristic
27C2×(C2×D283)⋊C4C2211yescharacteristic
28C2×C4×Dic283C2211yescharacteristic
29C2×C4×Dic283C2211yescharacteristic
30C2×C4×Dic283C2211yescharacteristic
31C2×C4×Dic283C2211yescharacteristic
32C2×C4×Dic283C2211yescharacteristic
33C2×C4×Dic283C2211yescharacteristic
34C283⋊#95C2211yescharacteristic
35C283⋊#95C2211yescharacteristic
36C283⋊#95C2211yescharacteristic
37C283⋊#95C2211yescharacteristic
38C283⋊#95C2211yescharacteristic
39C283⋊#95C2211yescharacteristic
40C283⋊#95C2211yescharacteristic
41C283⋊#95C2211yescharacteristic
42C283⋊#95C2211yescharacteristic
43C283⋊#95C2211yescharacteristic
44C2×C4⋊C4×C283C2211yescharacteristic
45C2×C4⋊C4×C283C2211yescharacteristic
46C2×C42×C283C2211yescharacteristic
47#95×C283C2211yescharacteristic
48#95×C283C2211yescharacteristic
49#95×C283C2211yescharacteristic
50#95×C283C2211yescharacteristic
51C23×D283C2311yescharacteristic
52C22×Dic283C2311yescharacteristic
53C22×Dic283C2311yescharacteristic
54C22×Dic283C2311yescharacteristic
55C22×Dic283C2311yescharacteristic
56C22×Dic283C2311yescharacteristic
57C22×Dic283C2311yescharacteristic
58C22×Dic283C2311yescharacteristic
59C4⋊Dic283—22no—
60C4⋊Dic283—22no—
61Dic283⋊C4—22no—
62Dic283⋊C4—22no—
63Dic283⋊C4—22no—
64(C2×D283)⋊C4—22no—
65(C2×D283)⋊C4—22no—
66(C2×D283)⋊C4—22no—
67(C2×D283)⋊C4—22no—
68(C2×D283)⋊C4—22no—
69(C2×D283)⋊C4—22no—
70(C2×D283)⋊C4—22no—
71C4×Dic283—22no—
72C4×Dic283—22no—
73C4×Dic283—22no—
74C4×Dic283—22no—
75C4×Dic283—22no—
76C4×Dic283—22no—
77C22×C4×C283C2311yescharacteristic
78C22×C4×C283C2311yescharacteristic
79C22×C4×C283C2311yescharacteristic
80C22×C4×C283C2311yescharacteristic
81C22×C4×C283C2311yescharacteristic
82C22×C4×C283C2311yescharacteristic
83C22×C4×C283C2311yescharacteristic
84C4⋊C4×C283—22no—
85C4⋊C4×C283—22no—
86C42×C283—22no—
87C22×D283—21no—
88C22×D283—21no—
89C22×D283—21no—
90C22×D283—21no—
91C22×D283—21no—
92C22×D283—21no—
93C22×D283—21no—
94C2×Dic283—21no—
95C2×Dic283—21no—
96C2×Dic283—21no—
97C2×Dic283—21no—
98C2×Dic283—21no—
99C2×Dic283—21no—
100C2×Dic283—21no—
101C2×Dic283—21no—
102C2×Dic283—21no—
103C2×Dic283—21no—
104C2×Dic283—21no—
105C2×Dic283—21no—
106C2×Dic283—21no—
107C2×Dic283—21no—
108C2×Dic283—21no—
109C2×Dic283—21no—
110C2×Dic283—21no—
111C2×Dic283#4112yes—
112C2×Dic283#4112yes—
113C2×Dic283#4112yes—
114C2×Dic283#4112yes—
115C23×C283C2411yescharacteristic
116C2×C4×C283—21no—
117C2×C4×C283—21no—
118C2×C4×C283—21no—
119C2×C4×C283—21no—
120C2×C4×C283—21no—
121C2×C4×C283—21no—
122C2×C4×C283—21no—
123C2×C4×C283—21no—
124C2×C4×C283—21no—
125C2×C4×C283—21no—
126C2×C4×C283—21no—
127C2×C4×C283—21no—
128C2×C4×C283—21no—
129C2×C4×C283—21no—
130C2×C4×C283—21no—
131C2×C4×C283—21no—
132C2×C4×C283—21no—
133C2×C4×C283—21no—
134C2×C4×C283#4112yes—
135C2×C4×C283#4112yes—
136C2×C4×C283#4112yes—
137C22×C283C2×#4111yescharacteristic
138C22×C283C2×#4111yescharacteristic
139C22×C283C2×#4111yescharacteristic
140C22×C283C2×#4111yescharacteristic
141C22×C283C2×#4111yescharacteristic
142C22×C283C2×#4111yescharacteristic
143C22×C283C2×#4111yescharacteristic
144C2×D283—41no—
145C2×D283—41no—
146C2×D283—41no—
147C2×D283—41no—
148C2×D283—41no—
149C2×D283—41no—
150C2×D283—41no—
151C4×C283—22no—
152C4×C283—22no—
153C4×C283—22no—
154C4×C283—41no—
155C4×C283—41no—
156C4×C283—41no—
157C4×C283—41no—
158Dic283—22no—
159Dic283—22no—
160Dic283—22no—
161Dic283—22no—
162Dic283—41no—
163Dic283—41no—
164Dic283—41no—
165C2×C283#52911yescharacteristic
166C2×C283#52911yescharacteristic
167C2×C283#52911yescharacteristic
168C2×C283#52911yescharacteristic
169C2×C283#52911yescharacteristic
170C2×C283#52911yescharacteristic
171C2×C283#52911yescharacteristic
172D283—81no—
173C283#286511yescharacteristic, complemented, Sylow
174#2865—2831nomaximal, Sylow
175#388—2831no—
176#388—2831no—
177#388—2831no—
178#388—2831no—
179#388—2831no—
180#388—2831no—
181#388—2831no—
182#387—2831no—
183#387—2831no—
184#387—2831no—
185#387—2831no—
186#387—2831no—
187#387—2831no—
188#387D28311yescharacteristic, complemented
189C43—2831no—
190C2×C4⋊C4—2831no—
191C2×C4⋊C4—2831no—
192C2×C4⋊C4—2831no—
193C2×C4⋊C4—2831no—
194C2×C4⋊C4—2831no—
195C2×C4⋊C4C2×D28311yescharacteristic
196C2×C4⋊C4C2×D28311yescharacteristic
197C2×C22⋊C4—2831no—
198C2×C22⋊C4—2831no—
199C2×C22⋊C4—2831no—
200C2×C22⋊C4—2831no—
201C2×C22⋊C4—2831no—
202C2×C22⋊C4—2831no—
203C2×C22⋊C4—2831no—
204C2×C42—2831no—
205C2×C42—2831no—
206C2×C42—2831no—
207C2×C42—2831no—
208C2×C42—2831no—
209C2×C42—2831no—
210C2×C42C2×D28311yescharacteristic
211#95—2831no—
212#95—2831no—
213#95—2831no—
214#95—2831no—
215#95—2831no—
216#95—2831no—
217#95—2831no—
218#95—2831no—
219#95—2831no—
220#95—2831no—
221#95C2×D28311yescharacteristic
222#95C2×D28311yescharacteristic
223#95C2×D28311yescharacteristic
224#95C2×D28311yescharacteristic
225C24—2831no—
226C22×C4—2831no—
227C22×C4—2831no—
228C22×C4—2831no—
229C22×C4—2831no—
230C22×C4—2831no—
231C22×C4—2831no—
232C22×C4—2831no—
233C22×C4C22×D28311yescharacteristic
234C22×C4C22×D28311yescharacteristic
235C22×C4C22×D28311yescharacteristic
236C22×C4C22×D28311yescharacteristic
237C22×C4C22×D28311yescharacteristic
238C22×C4C22×D28311yescharacteristic
239C22×C4C22×D28311yescharacteristic
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—5662no—
243C4⋊C4—5662no—
244C4⋊C4—5662no—
245C4⋊C4—5662no—
246C4⋊C4—5662no—
247C22⋊C4—5662no—
248C22⋊C4—5662no—
249C22⋊C4—5662no—
250C22⋊C4—5662no—
251C22⋊C4—5662no—
252C22⋊C4—5662no—
253C22⋊C4—5662no—
254C42—22no—
255C42—5662no—
256C42—5662no—
257C42—5662no—
258C42—5662no—
259C42—5662no—
260C42—5662no—
261C23—5661no—
262C23—5661no—
263C23—5661no—
264C23—5661no—
265C23—5661no—
266C23—5661no—
267C23—5661no—
268C23C23×D28311yescharacteristic
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—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—2832no—
288C2×C4—2832no—
289C2×C4—2832no—
290C2×C4—2832no—
291C2×C4—5661no—
292C2×C4—5661no—
293C2×C4—5661no—
294C2×C4—5661no—
295C2×C4—5661no—
296C2×C4—5661no—
297C2×C4—5661no—
298C2×C4—5661no—
299C2×C4—5661no—
300C2×C4—5661no—
301C2×C4—5661no—
302C2×C4—5661no—
303C2×C4—5661no—
304C2×C4—5661no—
305C2×C4—5661no—
306C2×C4—5661no—
307C2×C4—5661no—
308C2×C4#1798539112yes—
309C2×C4#1798539212yes—
310C2×C4#1798539312yes—
311C22—11321no—
312C22—11321no—
313C22—11321no—
314C22—11321no—
315C22—11321no—
316C22—11321no—
317C22—11321no—
318C22#41×D28311yescharacteristic
319C22#41×D28311yescharacteristic
320C22#41×D28311yescharacteristic
321C22#41×D28311yescharacteristic
322C22C2×#1798539111yescharacteristic
323C22C2×#1798539211yescharacteristic
324C22C2×#1798539311yescharacteristic
325C4—22no—
326C4—22no—
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—5662no—
333C4—5662no—
334C4—5662no—
335C4—5662no—
336C4—11321no—
337C4—11321no—
338C4—11321no—
339C2—22641no—
340C2#3182699211yescharacteristic
341C2#3182699311yescharacteristic
342C2#3182699511yescharacteristic
343C2#3182699811yescharacteristic
344C2#3182700011yescharacteristic
345C2#3182700111yescharacteristic
346C2#3182700211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutator, socle, cosocleC23×C283C24
Fitting#387×C283C2
prime radicalC23×D283C23
hypercenter#387D283
hypocenterC283#2865
LCSG ▷ C23×C283 ▷ C283
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
8. #31826352C2semidirect
9. #31826351C2semidirect
10. #31826350C2semidirect
11. #31826348C2semidirect
12. #31826347C2semidirect
13. #31826346C2semidirect
14. C42×Dic283C2semidirect
15. #387×C283C2semidirect
173. C283#2865semidirect
188. #387D283semidirect

Maximal subgroups

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

subgroupindex
#318263572
#318263562
#318263552
#318263542
#318263522
#318263512
#318263502
#318263482
#318263472
#318263462
C42×Dic2832
#387×C2832
#2865283