Finite Group Databasebeta

← #49124452

Subgroups — #49124452

Order 36224.

456 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583605C211yesmaximal, characteristic
2#31826361C211yesmaximal, characteristic, complemented
3#31826360C211yesmaximal, characteristic, complemented
4#31826356C211yesmaximal, characteristic
5#31826355C211yesmaximal, characteristic
6#31826354C211yesmaximal, characteristic
7#31826351C211yesmaximal, characteristic, complemented
8#31826350C211yesmaximal, characteristic, complemented
9#31826349C211yesmaximal, characteristic, complemented
10#31826339C211yesmaximal, characteristic
11#31826336C211yesmaximal, characteristic
12#31826336C211yesmaximal, characteristic
13#31826334C211yesmaximal, characteristic, complemented
14#31826332C211yesmaximal, characteristic, complemented
15#389×C283C211yesmaximal, characteristic, complemented
16C22×C4×D283C2211yescharacteristic
17#22583605C418yescomplemented
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
45C2×C4⋊C4×C283C2211yescharacteristic
46C2×C4⋊C4×C283C2211yescharacteristic
47C2×C4⋊C4×C283C2211yescharacteristic
48C2×C4⋊C4×C283C2211yescharacteristic
49C2×C42×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×D283—41no—
63C4⋊Dic283—41no—
64C4⋊Dic283C2×C414yescomplemented
65Dic283⋊C4—41no—
66Dic283⋊C4—41no—
67Dic283⋊C4—41no—
68Dic283⋊C4—41no—
69Dic283⋊C4—41no—
70Dic283⋊C4C2×C414yescomplemented
71(C2×D283)⋊C4—41no—
72(C2×D283)⋊C4—41no—
73(C2×D283)⋊C4—41no—
74(C2×D283)⋊C4C2×C414yes—
75(C2×D283)⋊C4C2×C414yes—
76(C2×D283)⋊C4C2×C414yes—
77C4×Dic283—41no—
78C4×Dic283—41no—
79C4×Dic283C2×C414yescomplemented
80C22×C4×C283C2311yescharacteristic
81C22×C4×C283C2311yescharacteristic
82C22×C4×C283C2311yescharacteristic
83C22×C4×C283C2311yescharacteristic
84C22×C4×C283C2311yescharacteristic
85C22×C4×C283C2311yescharacteristic
86C22×C4×C283C2311yescharacteristic
87C4⋊C4×C283—41no—
88C4⋊C4×C283—41no—
89C4⋊C4×C283—41no—
90C4⋊C4×C283C2×C414yescomplemented
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
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—21no—
135C2×C4×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283—21no—
140C2×C4×C283C22×C412yes—
141C2×C4×C283C22×C412yes—
142C2×C4×C283C22×C412yes—
143C22×C283C23×C411yescharacteristic
144C22×C283H(5,𝔽2)11yescharacteristic
145C22×C283H(5,𝔽2)11yescharacteristic
146C22×C283H(5,𝔽2)11yescharacteristic
147C22×C2832−1+411yescharacteristic
148C22×C2832−1+411yescharacteristic
149C22×C2832−1+411yescharacteristic
150C2×D283—22no—
151C2×D283—22no—
152C2×D283—22no—
153C2×D283—41no—
154C2×D283—41no—
155C2×D283—41no—
156C2×D283—41no—
157C4×C283—22no—
158C4×C283—22no—
159C4×C283—22no—
160C4×C283—41no—
161C4×C283—41no—
162C4×C283—41no—
163C4×C283—41no—
164Dic283—22no—
165Dic283—22no—
166Dic283—22no—
167Dic283—41no—
168Dic283—41no—
169Dic283—41no—
170Dic283—41no—
171C2×C283#52011yescharacteristic
172C2×C283#52011yescharacteristic
173C2×C283#52011yescharacteristic
174C2×C283#56011yescharacteristic
175C2×C283#56311yescharacteristic
176C2×C283#56311yescharacteristic
177C2×C283#56311yescharacteristic
178D283—42no—
179C283#238311yescharacteristic, complemented, Sylow
180#2383—2831nomaximal, Sylow
181C2×#126—2831no—
182#389—2831no—
183#389—2831no—
184#389D28311yescharacteristic, complemented
185#388—2831no—
186#388—2831no—
187#388—2831no—
188#387—2831no—
189#387—2831no—
190#387—2831no—
191#385—2831no—
192#385—2831no—
193#385—2831no—
194#384—2831no—
195#383—2831no—
196C23×C4—2831no—
197#126—2838no—
198C2×C4⋊C4—2831no—
199C2×C4⋊C4—2831no—
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⋊C4C2×D28311yescharacteristic
207C2×C4⋊C4C2×D28311yescharacteristic
208C2×C4⋊C4C2×D28311yescharacteristic
209C2×C4⋊C4C2×D28311yescharacteristic
210C2×C22⋊C4—2831no—
211C2×C22⋊C4—2831no—
212C2×C22⋊C4—2831no—
213C2×C22⋊C4—2831no—
214C2×C22⋊C4—2831no—
215C2×C22⋊C4—2831no—
216C2×C42—2831no—
217C2×C42—2831no—
218C2×C42—2831no—
219C2×C42C2×D28311yescharacteristic
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#95—2831no—
230#95C2×D28311yescharacteristic
231#95C2×D28311yescharacteristic
232C24—2831no—
233C22×C4—2831no—
234C22×C4—2831no—
235C22×C4—2831no—
236C22×C4—2831no—
237C22×C4—2831no—
238C22×C4—2831no—
239C22×C4—2831no—
240C22×C4—11321no—
241C22×C4—11321no—
242C22×C4—11321no—
243C22×C4C22×D28311yescharacteristic
244C22×C4C22×D28311yescharacteristic
245C22×C4C22×D28311yescharacteristic
246C22×C4C22×D28311yescharacteristic
247C22×C4C22×D28311yescharacteristic
248C22×C4C22×D28311yescharacteristic
249C22×C4C22×D28311yescharacteristic
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—2834no—
254C4⋊C4—2834no—
255C4⋊C4—11321no—
256C4⋊C4—11321no—
257C4⋊C4—11321no—
258C4⋊C4—11321no—
259C4⋊C4—11321no—
260C4⋊C4—11321no—
261C4⋊C4C4×D28314yescomplemented
262C22⋊C4—2834no—
263C22⋊C4—2834no—
264C22⋊C4—2834no—
265C22⋊C4—11321no—
266C22⋊C4—11321no—
267C22⋊C4—11321no—
268C42—41no—
269C42—2834no—
270C42—11321no—
271C42—11321no—
272C23—2832no—
273C23—5661no—
274C23—5661no—
275C23—5661no—
276C23—5661no—
277C23—5661no—
278C23—5661no—
279C23C23×D28311yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
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—2832no—
299C2×C4—2832no—
300C2×C4—2832no—
301C2×C4—5661no—
302C2×C4—5661no—
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—11324no—
320C2×C4C2×C4×D28312yes—
321C2×C4C2×C4×D28312yes—
322C2×C4C2×C4×D28312yes—
323C22—5662no—
324C22—5662no—
325C22—5662no—
326C22—11321no—
327C22—11321no—
328C22—11321no—
329C22—11321no—
330C22C22×C4×D28311yescharacteristic
331C22#2258365511yescharacteristic
332C22#2258365511yescharacteristic
333C22#2258365611yescharacteristic
334C22#2258365711yescharacteristic
335C22#2258365811yescharacteristic
336C22#2258365811yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—5662no—
345C4—5662no—
346C4—5662no—
347C4—11321no—
348C4—11321no—
349C4—11321no—
350C4—11321no—
351C2—11322no—
352C2#3182694411yescharacteristic
353C2#3182694611yescharacteristic
354C2#3182694711yescharacteristic
355C2#3182720311yescharacteristic
356C2#3182721411yescharacteristic
357C2#3182721611yescharacteristic
358C2#3182721911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
Fitting#389×C283C2
socle, cosocleC23×C283C24
prime radicalC23×D283C23
hypercenter#389D283
hypocenterC283#2383
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
2. #31826361C2semidirect
3. #31826360C2semidirect
7. #31826351C2semidirect
8. #31826350C2semidirect
9. #31826349C2semidirect
13. #31826334C2semidirect
14. #31826332C2semidirect
15. #389×C283C2semidirect
17. #22583605C4semidirect
64. C4⋊Dic283C2×C4semidirect
70. Dic283⋊C4C2×C4semidirect
79. C4×Dic283C2×C4semidirect
90. C4⋊C4×C283C2×C4semidirect
179. C283#2383semidirect
184. #389D283semidirect
261. C4⋊C4C4×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836052
#318263612
#318263602
#318263562
#318263552
#318263542
#318263512
#318263502
#318263492
#318263392
#318263362
#318263342
#318263322
#389×C2832
#2383283