Finite Group Databasebeta

← #49124422

Subgroups — #49124422

Order 36224.

464 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583586C211yesmaximal, characteristic
2#31826372C211yesmaximal, characteristic, complemented
3#31826362C211yesmaximal, characteristic, complemented
4#31826360C211yesmaximal, characteristic, complemented
5#31826357C211yesmaximal, characteristic
6#31826356C211yesmaximal, characteristic
7#31826355C211yesmaximal, characteristic
8#31826354C211yesmaximal, characteristic
9#31826350C211yesmaximal, characteristic, complemented
10#31826349C211yesmaximal, characteristic, complemented
11#31826348C211yesmaximal, characteristic, complemented
12#31826347C211yesmaximal, characteristic, complemented
13#31826327C211yesmaximal, characteristic
14#31826324C211yesmaximal, characteristic
15#391×C283C211yesmaximal, characteristic, complemented
16C22×C4×D283C2211yescharacteristic
17#22583586C418yescomplemented
18C2×C4⋊Dic283C2211yescharacteristic
19C2×C4⋊Dic283C2211yescharacteristic
20C2×Dic283⋊C4C2211yescharacteristic
21C2×Dic283⋊C4C2211yescharacteristic
22C2×Dic283⋊C4C2211yescharacteristic
23C2×Dic283⋊C4C2211yescharacteristic
24C2×Dic283⋊C4C2211yescharacteristic
25C2×Dic283⋊C4C2211yescharacteristic
26C2×(C2×D283)⋊C4C2211yescharacteristic
27C2×(C2×D283)⋊C4C2211yescharacteristic
28C2×(C2×D283)⋊C4C2211yescharacteristic
29C2×(C2×D283)⋊C4C2211yescharacteristic
30C2×(C2×D283)⋊C4C2211yescharacteristic
31C2×(C2×D283)⋊C4C2211yescharacteristic
32C2×C4×Dic283C2211yescharacteristic
33C2×C4×Dic283C2211yescharacteristic
34C2×C4×Dic283C2211yescharacteristic
35C283⋊#95C2211yescharacteristic
36C283⋊#95C2211yescharacteristic
37C283⋊#95C2211yescharacteristic
38C283⋊#95C2211yescharacteristic
39C283⋊#95C2211yescharacteristic
40C283⋊#95C2211yescharacteristic
41C283⋊#95C2211yescharacteristic
42C283⋊#95C2211yescharacteristic
43C283⋊#95C2211yescharacteristic
44C283⋊#95C2211yescharacteristic
45C22×Q8×C283C2211yescharacteristic
46C2×C4⋊C4×C283C2211yescharacteristic
47C2×C42×C283C2211yescharacteristic
48#95×C283C2211yescharacteristic
49#95×C283C2211yescharacteristic
50#95×C283C2211yescharacteristic
51#95×C283C2211yescharacteristic
52C23×D283C2311yescharacteristic
53C22×Dic283C2311yescharacteristic
54C22×Dic283C2311yescharacteristic
55C22×Dic283C2311yescharacteristic
56C22×Dic283C2311yescharacteristic
57C22×Dic283C2311yescharacteristic
58C22×Dic283C2311yescharacteristic
59C22×Dic283C2311yescharacteristic
60C2×C4×D283—41no—
61C2×C4×D283—41no—
62C2×C4×D283C2×C414yes—
63C4⋊Dic283—41no—
64C4⋊Dic283C2×C414yes—
65Dic283⋊C4—41no—
66Dic283⋊C4—41no—
67Dic283⋊C4—41no—
68Dic283⋊C4—41no—
69Dic283⋊C4C2×C414yes—
70Dic283⋊C4C2×C414yes—
71(C2×D283)⋊C4—41no—
72(C2×D283)⋊C4—41no—
73(C2×D283)⋊C4—41no—
74(C2×D283)⋊C4—41no—
75(C2×D283)⋊C4C2×C414yes—
76(C2×D283)⋊C4C2×C414yes—
77C4×Dic283—41no—
78C4×Dic283—41no—
79C4×Dic283—41no—
80C2×Q8×C283—41no—
81C2×Q8×C283—41no—
82C2×Q8×C283C2×C414yes—
83C22×C4×C283C2311yescharacteristic
84C22×C4×C283C2311yescharacteristic
85C22×C4×C283C2311yescharacteristic
86C22×C4×C283C2311yescharacteristic
87C22×C4×C283C2311yescharacteristic
88C22×C4×C283C2311yescharacteristic
89C22×C4×C283C2311yescharacteristic
90C4⋊C4×C283—41no—
91C42×C283—41no—
92C22×D283—21no—
93C22×D283—21no—
94C22×D283—21no—
95C22×D283—21no—
96C22×D283—21no—
97C22×D283—21no—
98C22×D283C22×C412yes—
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—21no—
112C2×Dic283—21no—
113C2×Dic283—21no—
114C2×Dic283—21no—
115C2×Dic283—21no—
116C2×Dic283—21no—
117C2×Dic283C22×C412yes—
118C2×Dic283C22×C412yes—
119C2×Dic283C22×C412yes—
120C4×D283—44no—
121C23×C283C2411yescharacteristic
122Q8×C283—44no—
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—21no—
135C2×C4×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283C22×C412yes—
142C2×C4×C283C22×C412yes—
143C2×C4×C283C22×C412yes—
144C22×C283C23×C411yescharacteristic
145C22×C283H(5,𝔽2)11yescharacteristic
146C22×C283H(5,𝔽2)11yescharacteristic
147C22×C283H(5,𝔽2)11yescharacteristic
148C22×C2832−1+411yescharacteristic
149C22×C2832−1+411yescharacteristic
150C22×C2832−1+411yescharacteristic
151C2×D283—22no—
152C2×D283—22no—
153C2×D283—22no—
154C2×D283—41no—
155C2×D283—41no—
156C2×D283—41no—
157C2×D283—41no—
158C4×C283—22no—
159C4×C283—22no—
160C4×C283—22no—
161C4×C283—41no—
162C4×C283—41no—
163C4×C283—41no—
164C4×C283—41no—
165Dic283—22no—
166Dic283—22no—
167Dic283—22no—
168Dic283—41no—
169Dic283—41no—
170Dic283—41no—
171Dic283—41no—
172C2×C283#51811yescharacteristic
173C2×C283#51911yescharacteristic
174C2×C283#52011yescharacteristic
175C2×C283#56211yescharacteristic
176C2×C283#56211yescharacteristic
177C2×C283#56311yescharacteristic
178C2×C283#56311yescharacteristic
179D283—42no—
180C283#237811yescharacteristic, complemented, Sylow
181#2378—2831nomaximal, Sylow
182C2×C22⋊Q8—2831no—
183#391—2831no—
184#391D28311yescharacteristic, complemented
185#389—2831no—
186#389—2831no—
187#388—2831no—
188#388—2831no—
189#388—2831no—
190#388—2831no—
191#387—2831no—
192#387—2831no—
193#387—2831no—
194#387—2831no—
195#381—2831no—
196#380—2831no—
197C22×Q8C2×D28311yescharacteristic
198C23×C4—2831no—
199C22⋊Q8—2838no—
200C2×C4⋊C4—2831no—
201C2×C4⋊C4—2831no—
202C2×C4⋊C4—2831no—
203C2×C4⋊C4—2831no—
204C2×C4⋊C4—2831no—
205C2×C4⋊C4—2831no—
206C2×C4⋊C4—2831no—
207C2×C4⋊C4—2831no—
208C2×C4⋊C4C2×D28311yescharacteristic
209C2×C22⋊C4—2831no—
210C2×C22⋊C4—2831no—
211C2×C22⋊C4—2831no—
212C2×C22⋊C4—2831no—
213C2×C22⋊C4—2831no—
214C2×C22⋊C4—2831no—
215C2×C42—2831no—
216C2×C42—2831no—
217C2×C42—2831no—
218C2×C42C2×D28311yescharacteristic
219#95—2831no—
220#95—2831no—
221#95—2831no—
222#95—2831no—
223#95—2831no—
224#95—2831no—
225#95—2831no—
226#95—2831no—
227#95—2831no—
228#95—2831no—
229#95C2×D28311yescharacteristic
230#95C2×D28311yescharacteristic
231#95C2×D28311yescharacteristic
232#95C2×D28311yescharacteristic
233C24—2831no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8C4×D28314yes—
237C22×C4—2831no—
238C22×C4—2831no—
239C22×C4—2831no—
240C22×C4—2834no—
241C22×C4—2831no—
242C22×C4—2831no—
243C22×C4—2831no—
244C22×C4—2831no—
245C22×C4—11321no—
246C22×C4—11321no—
247C22×C4C22×D28311yescharacteristic
248C22×C4C22×D28311yescharacteristic
249C22×C4C22×D28311yescharacteristic
250C22×C4C22×D28311yescharacteristic
251C22×C4C22×D28311yescharacteristic
252C22×C4C22×D28311yescharacteristic
253C22×C4C22×D28311yescharacteristic
254C4⋊C4—41no—
255C4⋊C4—2834no—
256C4⋊C4—2834no—
257C4⋊C4—2834no—
258C4⋊C4—11321no—
259C4⋊C4—11321no—
260C4⋊C4—11321no—
261C4⋊C4—11321no—
262C4⋊C4—11321no—
263C22⋊C4—2834no—
264C22⋊C4—2834no—
265C22⋊C4—11321no—
266C22⋊C4—11321no—
267C22⋊C4—11321no—
268C22⋊C4—11321no—
269C42—41no—
270C42—11321no—
271C42—11321no—
272C42—11321no—
273C23—2832no—
274C23—5661no—
275C23—5661no—
276C23—5661no—
277C23—5661no—
278C23—5661no—
279C23—5661no—
280C23C23×D28311yescharacteristic
281Q8—44no—
282C2×C4—21no—
283C2×C4—21no—
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—2832no—
301C2×C4—2832no—
302C2×C4—2832no—
303C2×C4—5661no—
304C2×C4—5661no—
305C2×C4—5661no—
306C2×C4—5661no—
307C2×C4—5661no—
308C2×C4—5661no—
309C2×C4—5661no—
310C2×C4—5661no—
311C2×C4—5661no—
312C2×C4—5661no—
313C2×C4—5661no—
314C2×C4—5661no—
315C2×C4—5661no—
316C2×C4—5661no—
317C2×C4—5661no—
318C2×C4—5661no—
319C2×C4—5661no—
320C2×C4—5661no—
321C2×C4—11324no—
322C2×C4C2×C4×D28312yes—
323C2×C4C2×C4×D28312yes—
324C2×C4C2×C4×D28312yes—
325C22—5662no—
326C22—5662no—
327C22—5662no—
328C22—11321no—
329C22—11321no—
330C22—11321no—
331C22—11321no—
332C22C22×C4×D28311yescharacteristic
333C22#2258365511yescharacteristic
334C22#2258365511yescharacteristic
335C22#2258365611yescharacteristic
336C22#2258365711yescharacteristic
337C22#2258365811yescharacteristic
338C22#2258365811yescharacteristic
339C4—22no—
340C4—22no—
341C4—22no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—5662no—
347C4—5662no—
348C4—5662no—
349C4—11321no—
350C4—11321no—
351C4—11321no—
352C4—11321no—
353C2—11322no—
354C2#3182693811yescharacteristic
355C2#3182694111yescharacteristic
356C2#3182694711yescharacteristic
357C2#3182720911yescharacteristic
358C2#3182721111yescharacteristic
359C2#3182721411yescharacteristic
360C2#3182721611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
Fitting#391×C283C2
socle, cosocleC23×C283C24
prime radicalC23×D283C23
hypercenter#391D283
hypocenterC283#2378
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
2. #31826372C2semidirect
3. #31826362C2semidirect
4. #31826360C2semidirect
9. #31826350C2semidirect
10. #31826349C2semidirect
11. #31826348C2semidirect
12. #31826347C2semidirect
15. #391×C283C2semidirect
17. #22583586C4semidirect
180. C283#2378semidirect
184. #391D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225835862
#318263722
#318263622
#318263602
#318263572
#318263562
#318263552
#318263542
#318263502
#318263492
#318263482
#318263472
#318263272
#318263242
#391×C2832
#2378283