Finite Group Databasebeta

← #49130243

Subgroups — #49130243

Order 36224.

362 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31826997C211yesmaximal, characteristic
2#31826594C211yesmaximal, characteristic, complemented
3#31826593C211yesmaximal, characteristic, complemented
4#31826541C211yesmaximal, characteristic, complemented
5#31826540C211yesmaximal, characteristic, complemented
6#31826537C211yesmaximal, characteristic, complemented
7#31826536C211yesmaximal, characteristic, complemented
8#31826533C211yesmaximal, characteristic, complemented
9#31826523C211yesmaximal, characteristic, complemented
10#31826523C211yesmaximal, characteristic, complemented
11#31826521C211yesmaximal, characteristic, complemented
12#31826423C211yesmaximal, characteristic, complemented
13#31826420C211yesmaximal, characteristic, complemented
14#31826417C211yesmaximal, characteristic, complemented
15#435×C283C211yesmaximal, characteristic, complemented
16C2×#17985376C2211yescharacteristic
17C2×#17985375C2211yescharacteristic
18C2×#17985375C2211yescharacteristic
19C22×C283⋊C8C2211yescharacteristic
20#22583603C411yescharacteristic
21#22583603C411yescharacteristic
22#22583601C411yescharacteristic
23#22583597C411yescharacteristic
24#22583592C411yescharacteristic
25#22583592C411yescharacteristic
26#22583590C411yescharacteristic
27#22583581C411yescharacteristic
28C4×Dic566C2211yescharacteristic
29C4×C22⋊D283C2211yescharacteristic
30C4×C22⋊D283C2211yescharacteristic
31#22583569C2211yescharacteristic
32#22583569C2211yescharacteristic
33C42×D283C2211yescharacteristic
34C4⋊(C283⋊C8)C2211yescharacteristic
35Dic283⋊C8C2211yescharacteristic
36Dic283⋊C8C2211yescharacteristic
37Dic283⋊C8C2211yescharacteristic
38Dic283⋊C8C2211yescharacteristic
39C22⋊(C283⋊C8)C2211yescharacteristic
40C22⋊(C283⋊C8)C2211yescharacteristic
41(C2×D283)⋊C8C2211yescharacteristic
42(C2×D283)⋊C8C2211yescharacteristic
43#22583521C2211yescharacteristic
44#22583520C2211yescharacteristic
45#22583520C2211yescharacteristic
46#22583520C2211yescharacteristic
47#22583520C2211yescharacteristic
48C8×Dic283C2211yescharacteristic
49C8×Dic283C2211yescharacteristic
50C8×Dic283C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52C2×M16×C283C2211yescharacteristic
53C22×C8×C283C2211yescharacteristic
54C4×D4×C283C2211yescharacteristic
55C4⋊C8×C283C2211yescharacteristic
56C22⋊C8×C283C2211yescharacteristic
57C22⋊C8×C283C2211yescharacteristic
58#97×C283C2211yescharacteristic
59C2×Dic566C2×C411yescharacteristic
60C2×C22⋊D283C2×C411yescharacteristic
61C2×C22⋊D283C2×C411yescharacteristic
62C2×C4×D283C2×C411yescharacteristic
63C2×C4×D283C2×C411yescharacteristic
64C2×C4×D283C2311yescharacteristic
65#17985376—22no—
66#17985375—22no—
67#17985375—22no—
68C2×C283⋊C8—22no—
69C2×C283⋊C8C2311yescharacteristic
70C2×C283⋊C8C2311yescharacteristic
71C2×C283⋊C8C2311yescharacteristic
72C2×C283⋊C8C2311yescharacteristic
73C4⋊Dic283C2×C411yescharacteristic
74C4⋊Dic283C2×C411yescharacteristic
75C4⋊Dic283C2×C411yescharacteristic
76C4⋊Dic283C2×C411yescharacteristic
77C4⋊Dic283C2×C411yescharacteristic
78Dic283⋊C4C2×C411yescharacteristic
79Dic283⋊C4C2×C411yescharacteristic
80Dic283⋊C4C2×C411yescharacteristic
81Dic283⋊C4C2×C411yescharacteristic
82C22⋊Dic283C2×C411yescharacteristic
83C22⋊Dic283C2×C411yescharacteristic
84C22⋊Dic283C2×C411yescharacteristic
85C22⋊Dic283C2×C411yescharacteristic
86C22⋊Dic283C2×C411yescharacteristic
87C22⋊Dic283C2×C411yescharacteristic
88(C2×D283)⋊C4C2×C411yescharacteristic
89(C2×D283)⋊C4C2×C411yescharacteristic
90C4×Dic283C2×C411yescharacteristic
91C4×Dic283C2×C411yescharacteristic
92C4×Dic283C2311yescharacteristic
93C4×Dic283C2311yescharacteristic
94C4×Dic283C2311yescharacteristic
95C2×D4×C283C2×C411yescharacteristic
96C22×C4×C283C2311yescharacteristic
97C22×C4×C283C2311yescharacteristic
98M16×C283—22no—
99C2×C8×C283—22no—
100C2×C8×C283C2311yescharacteristic
101C2×C8×C283C2311yescharacteristic
102C2×C8×C283C2311yescharacteristic
103C2×C8×C283C2311yescharacteristic
104C4⋊C4×C283C2×C411yescharacteristic
105C22⋊C4×C283C2×C411yescharacteristic
106C22⋊C4×C283C2×C411yescharacteristic
107C42×C283C2311yescharacteristic
108C22×D283C22×C411yescharacteristic
109Dic566—41no—
110C22⋊D283—41no—
111C22⋊D283—41no—
112C2×Dic283C22×C411yescharacteristic
113C2×Dic283C22×C411yescharacteristic
114C2×Dic283C22×C411yescharacteristic
115C2×Dic283C22×C411yescharacteristic
116C2×Dic283C22×C411yescharacteristic
117C2×Dic283C22×C411yescharacteristic
118C2×Dic283C22×C411yescharacteristic
119C4×D283—21no—
120C4×D283—21no—
121C4×D283—41no—
122C4×D283—41no—
123C283⋊C8—21no—
124C283⋊C8—21no—
125C283⋊C8—21no—
126C283⋊C8#4112yes—
127C23×C283C22×C411yescharacteristic
128C23×C283C22×C411yescharacteristic
129D4×C283—41no—
130C2×C4×C283—21no—
131C2×C4×C283—21no—
132C2×C4×C283—21no—
133C2×C4×C283—21no—
134C2×C4×C283C22×C411yescharacteristic
135C2×C4×C283C22×C411yescharacteristic
136C2×C4×C283C22×C411yescharacteristic
137C2×C4×C283C22×C411yescharacteristic
138C2×C4×C283C2411yescharacteristic
139C8×C283—21no—
140C8×C283—21no—
141C8×C283—21no—
142C8×C283#4112yes—
143C22×C283—21no—
144C22×C283—21no—
145C22×C283—21no—
146C22×C283—21no—
147C22×C283—21no—
148C22×C283—21no—
149C22×C283C23×C411yescharacteristic
150C2×D283—21no—
151C2×D283—21no—
152C2×D283—21no—
153C4×C283—21no—
154C4×C283—21no—
155C4×C283—21no—
156C4×C283—21no—
157C4×C283C2×#4111yescharacteristic
158C4×C283C2×#4111yescharacteristic
159Dic283—21no—
160Dic283—21no—
161Dic283—21no—
162Dic283—21no—
163Dic283—21no—
164Dic283—21no—
165Dic283—21no—
166C2×C283—41no—
167C2×C283—41no—
168C2×C283C4×#4111yescharacteristic
169C2×C283#56811yescharacteristic
170C2×C283#56811yescharacteristic
171D283—41no—
172C283#296711yescharacteristic, complemented, Sylow
173#2967—2831nomaximal, Sylow
174#529—2831no—
175#446—2831no—
176#446—2831no—
177#436—2831no—
178#436—2831no—
179#435—2831no—
180#435—2831no—
181#435—2831no—
182#435D28311yescharacteristic, complemented
183#433—2831no—
184#433—2831no—
185#432—2831no—
186#405—2831no—
187#405—2831no—
188C4×M16—2831no—
189C2×M16—2831no—
190C2×M16—2831no—
191C2×M16—2831no—
192C2×M16C2×D28311yescharacteristic
193C22×C8—2831no—
194C22×C8C2×D28311yescharacteristic
195#126—2831no—
196#126—2831no—
197#125—2831no—
198#124—2831no—
199#123—2831no—
200#123—2831no—
201C22⋊Q8—2831no—
202#121—2831no—
203C4×Q8—2831no—
204C4×D4—2831no—
205C4×D4—2831no—
206C4×D4C2×D28311yescharacteristic
207#117—2831no—
208#117—2831no—
209C2×C42—2831no—
210C4⋊C8—2831no—
211C4⋊C8—2831no—
212C4⋊C8—2831no—
213C4⋊C8—2831no—
214C4⋊C8—2831no—
215C4⋊C8C2×D28311yescharacteristic
216C22⋊C8—2831no—
217C22⋊C8—2831no—
218C22⋊C8—2831no—
219C22⋊C8—2831no—
220C22⋊C8C2×D28311yescharacteristic
221C22⋊C8C2×D28311yescharacteristic
222#97—2831no—
223#97—2831no—
224#97—2831no—
225#97—2831no—
226#97—2831no—
227#97C2×D28311yescharacteristic
228C4×C8—2831no—
229C4×C8—2831no—
230C4×C8—2831no—
231C4×C8—2831no—
232C2×Q8—2831no—
233C2×D4—2831no—
234C2×D4—2831no—
235C2×D4C4×D28311yescharacteristic
236C22×C4—2831no—
237C22×C4—2831no—
238C22×C4—2831no—
239C22×C4C22×D28311yescharacteristic
240C22×C4C22×D28311yescharacteristic
241M16—22no—
242M16—5662no—
243M16—5662no—
244M16—5662no—
245C2×C8—22no—
246C2×C8—2831no—
247C2×C8—2831no—
248C2×C8—2831no—
249C2×C8—2831no—
250C2×C8—5662no—
251C2×C8C22×D28311yescharacteristic
252C2×C8C22×D28311yescharacteristic
253C2×C8C22×D28311yescharacteristic
254C2×C8C22×D28311yescharacteristic
255C4⋊C4—2831no—
256C4⋊C4—2831no—
257C4⋊C4—2831no—
258C4⋊C4—2831no—
259C4⋊C4—2831no—
260C4⋊C4—2831no—
261C4⋊C4—2831no—
262C4⋊C4—2831no—
263C4⋊C4—2831no—
264C4⋊C4C4×D28311yescharacteristic
265C22⋊C4—2831no—
266C22⋊C4—2831no—
267C22⋊C4—2831no—
268C22⋊C4—2831no—
269C22⋊C4—2831no—
270C22⋊C4—2831no—
271C22⋊C4—2831no—
272C22⋊C4—2831no—
273C22⋊C4C4×D28311yescharacteristic
274C22⋊C4C4×D28311yescharacteristic
275C42—2831no—
276C42—2831no—
277C42—2831no—
278C42—2831no—
279C42—2831no—
280C42C22×D28311yescharacteristic
281C23—2831no—
282C23C2×C4×D28311yescharacteristic
283C23C2×C4×D28311yescharacteristic
284Q8—11321no—
285D4—41no—
286D4—11321no—
287D4—11321no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—2831no—
293C2×C4—2831no—
294C2×C4—2831no—
295C2×C4—2831no—
296C2×C4—2831no—
297C2×C4—2831no—
298C2×C4—2831no—
299C2×C4—5661no—
300C2×C4—5661no—
301C2×C4—11321no—
302C2×C4—11321no—
303C2×C4C2×C4×D28311yescharacteristic
304C2×C4C2×C4×D28311yescharacteristic
305C2×C4C2×C4×D28311yescharacteristic
306C2×C4C2×C4×D28311yescharacteristic
307C2×C4C23×D28311yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8—2832no—
312C8—5661no—
313C8—5661no—
314C8—5661no—
315C8#1798539112yes—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—5661no—
323C22—5661no—
324C22—5661no—
325C22C22×C4×D28311yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—5661no—
331C4—5661no—
332C4—5661no—
333C4—5661no—
334C4—5661no—
335C4—5661no—
336C4—5661no—
337C4#41×D28311yescharacteristic
338C4C2×#1798539111yescharacteristic
339C2—41no—
340C2—41no—
341C2—11321no—
342C2C4×#1798539111yescharacteristic
343C2#3182723011yescharacteristic
344C2#3182723111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D283
commutator, socleC22×C283C23×C4
Fitting#435×C283C2
prime radical#22583581C4
cosocleC2×C4×C283C24
hypercenter#435D283
hypocenterC283#2967
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #31826594C2semidirect
3. #31826593C2semidirect
4. #31826541C2semidirect
5. #31826540C2semidirect
6. #31826537C2semidirect
7. #31826536C2semidirect
8. #31826533C2semidirect
9. #31826523C2semidirect
10. #31826523C2semidirect
11. #31826521C2semidirect
12. #31826423C2semidirect
13. #31826420C2semidirect
14. #31826417C2semidirect
15. #435×C283C2semidirect
172. C283#2967semidirect
182. #435D283semidirect

Maximal subgroups

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

subgroupindex
#318269972
#318265942
#318265932
#318265412
#318265402
#318265372
#318265362
#318265332
#318265232
#318265212
#318264232
#318264202
#318264172
#435×C2832
#2967283