Finite Group Databasebeta

← #49133943

Subgroups — #49133943

Order 36224.

336 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827192C211yesmaximal, characteristic, complemented
2#31827184C211yesmaximal, characteristic
3#31826818C211yesmaximal, characteristic
4#31826814C211yesmaximal, characteristic, complemented
5#31826774C211yesmaximal, characteristic, complemented
6#31826769C211yesmaximal, characteristic, complemented
7#31826743C211yesmaximal, characteristic
8#31826686C211yesmaximal, characteristic
9#31826684C211yesmaximal, characteristic
10#31826674C211yesmaximal, characteristic, complemented
11C8×Dic566C211yesmaximal, characteristic, complemented
12C4×Dic1132C211yesmaximal, characteristic, complemented
13#31826557C211yesmaximal, characteristic, complemented
14#31826556C211yesmaximal, characteristic
15#488×C283C211yesmaximal, characteristic
16C2×Dic1132C2211yescharacteristic
17C2×#17985382C2211yescharacteristic
18C2×#17985380C2211yescharacteristic
19#22583609—21no—
20#22583609C2211yescharacteristic
21#22583608C2211yescharacteristic
22#22583603—21no—
23#22583603—21no—
24#22583601C2211yescharacteristic
25#22583600—21no—
26#22583600—21no—
27#22583597C2211yescharacteristic
28#22583587—21no—
29Q8×Dic283C2211yescharacteristic
30C4×Dic566C2211yescharacteristic
31C4×Dic566C2211yescharacteristic
32C4×Dic566C2211yescharacteristic
33#22583575—21no—
34#22583575C2211yescharacteristic
35#22583575C2211yescharacteristic
36D4×Dic283C2211yescharacteristic
37#22583566—21no—
38#22583544C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583541C2211yescharacteristic
41C4⋊(C283⋊C8)C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43Dic283⋊C8C2211yescharacteristic
44#22583535C2211yescharacteristic
45#22583535C2211yescharacteristic
46#22583534C2211yescharacteristic
47#22583533C2211yescharacteristic
48#22583533C2211yescharacteristic
49#22583531C2211yescharacteristic
50C8×Dic283C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52#125×C283C2211yescharacteristic
53#124×C283C2211yescharacteristic
54#103×C283C2211yescharacteristic
55#103×C283C2211yescharacteristic
56#102×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58C4×C8×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566D411yescharacteristic
61C2×Dic566C2311yescharacteristic
62C2×Dic566C2311yescharacteristic
63C22×Dic283—21no—
64Dic1132—22no—
65#17985382—22no—
66#17985380—22no—
67C2×C283⋊C8C2311yescharacteristic
68C2×C283⋊C8C2311yescharacteristic
69C4⋊Dic283—21no—
70C4⋊Dic283—21no—
71C4⋊Dic283D411yescharacteristic
72C4⋊Dic283C2311yescharacteristic
73C4⋊Dic283C2311yescharacteristic
74Dic283⋊C4—21no—
75Dic283⋊C4—21no—
76Dic283⋊C4—21no—
77Dic283⋊C4—21no—
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4D411yescharacteristic
83Dic283⋊C4D411yescharacteristic
84C22⋊Dic283—21no—
85C22⋊Dic283—21no—
86C22⋊Dic283—21no—
87C4×Dic283—21no—
88C4×Dic283—21no—
89C4×Dic283—21no—
90C4×Dic283—21no—
91C4×Dic283—21no—
92C4×Dic283C2311yescharacteristic
93C4×Dic283C2311yescharacteristic
94C2×Q8×C283C2311yescharacteristic
95C2×D4×C283C2311yescharacteristic
96C2×C8×C283C2311yescharacteristic
97C2×C8×C283C2311yescharacteristic
98C4⋊C4×C283—21no—
99C4⋊C4×C283—21no—
100C4⋊C4×C283C2311yescharacteristic
101C4⋊C4×C283C2311yescharacteristic
102C22⋊C4×C283—21no—
103C22⋊C4×C283—21no—
104C42×C283C2311yescharacteristic
105Dic566—21no—
106Dic566—22no—
107Dic566—21no—
108Dic566—21no—
109Dic566—42no—
110Dic566#4112yes—
111C2×Dic283—21no—
112C2×Dic283—21no—
113C2×Dic283—21no—
114C2×Dic283—21no—
115C2×Dic283—42no—
116C2×Dic283C2×D411yescharacteristic
117C2×Dic283C2×D411yescharacteristic
118C2×Dic283C2×D411yescharacteristic
119C2×Dic283C2×D411yescharacteristic
120C283⋊C8—21no—
121C283⋊C8—21no—
122C23×C283—21no—
123Q8×C283—21no—
124Q8×C283—21no—
125D4×C283—21no—
126D4×C283—21no—
127C2×C4×C283—21no—
128C2×C4×C283—21no—
129C2×C4×C283—21no—
130C2×C4×C283C2×D411yescharacteristic
131C2×C4×C283C2×D411yescharacteristic
132C2×C4×C283C2411yescharacteristic
133C8×C283—21no—
134C8×C283—21no—
135C22×C283—41no—
136C22×C283—41no—
137C22×C283—41no—
138C22×C283C22×D411yescharacteristic
139C4×C283—21no—
140C4×C283—21no—
141C4×C283—41no—
142C4×C283—41no—
143C4×C283—41no—
144C4×C283C2×#4111yescharacteristic
145C4×C2832−1+411yescharacteristic
146Dic283—22no—
147Dic283—21no—
148Dic283—21no—
149Dic283—21no—
150Dic283—41no—
151Dic283—41no—
152Dic283—41no—
153Dic283#13512yes—
154C2×C283—81no—
155C2×C283#54811yescharacteristic
156C2×C283C2×#13511yescharacteristic
157C2×C283#57811yescharacteristic
158C283#336411yescharacteristic, complemented, Sylow
159#3364—2831nomaximal, Sylow
160#557—2831no—
161#556—2831no—
162#488—2831no—
163#488D28311yescharacteristic
164#487—2831no—
165#479—2831no—
166#479—2831no—
167#474—2831no—
168#464—2831no—
169#464—2831no—
170#462—2831no—
171C8×Q8—2831no—
172C4×Q16—2831no—
173C4×Q16—2831no—
174C4×SD16—2831no—
175C2×Q16—2831no—
176C2×Q16—2831no—
177C2×SD16—2831no—
178C4⋊Q8—2831no—
179C4⋊Q8—2831no—
180C4⋊Q8—5661no—
181#126—5661no—
182#126—5661no—
183#125—2831no—
184#125—5661no—
185#125—5661no—
186#125C2×D28311yescharacteristic
187#124—2831no—
188#124C2×D28311yescharacteristic
189C22⋊Q8—5661no—
190C4×Q8—2831no—
191C4×Q8—2831no—
192C4×Q8—2831no—
193C4×Q8—2831no—
194C4×Q8—2831no—
195C4×Q8—2831no—
196C4×Q8—5661no—
197C4×D4—2831no—
198#117—5661no—
199#107—2831no—
200#107—2831no—
201#106—2831no—
202C4⋊C8—2831no—
203C4⋊C8—2831no—
204C4⋊C8—2831no—
205#103—2831no—
206#103—2831no—
207#103—2831no—
208#103—2831no—
209#103—2831no—
210#103C2×D28311yescharacteristic
211#103C2×D28311yescharacteristic
212#102—2831no—
213#102C2×D28311yescharacteristic
214#102C2×D28311yescharacteristic
215C4×C8—2831no—
216C4×C8—2831no—
217C4×C8C2×D28311yescharacteristic
218C2×Q8—2831no—
219C2×Q8—2831no—
220C2×Q8—2831no—
221C2×Q8—5661no—
222C2×Q8C22×D28311yescharacteristic
223C2×D4C22×D28311yescharacteristic
224C22×C4—5661no—
225Q16—5662no—
226Q16—5662no—
227SD16—5662no—
228C2×C8—2831no—
229C2×C8—2831no—
230C2×C8C22×D28311yescharacteristic
231C2×C8C22×D28311yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—2831no—
235C4⋊C4—2831no—
236C4⋊C4—2831no—
237C4⋊C4—2831no—
238C4⋊C4—2831no—
239C4⋊C4—5661no—
240C4⋊C4—5661no—
241C4⋊C4—5661no—
242C4⋊C4—5661no—
243C4⋊C4—5661no—
244C4⋊C4—5661no—
245C4⋊C4—5661no—
246C4⋊C4—5661no—
247C4⋊C4—5661no—
248C4⋊C4—5661no—
249C4⋊C4C22×D28311yescharacteristic
250C4⋊C4C22×D28311yescharacteristic
251C22⋊C4—21no—
252C22⋊C4—21no—
253C22⋊C4—5661no—
254C22⋊C4—5661no—
255C22⋊C4—5661no—
256C42—2831no—
257C42—2831no—
258C42—5661no—
259C42—5661no—
260C42—5661no—
261C42—5661no—
262C42—5661no—
263C42C22×D28311yescharacteristic
264C23—21no—
265Q8—21no—
266Q8—21no—
267Q8—2832no—
268Q8—5662no—
269Q8—5661no—
270Q8—5661no—
271Q8—5661no—
272Q8—11322no—
273D4—21no—
274D4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—2831no—
279C2×C4—2831no—
280C2×C4—2831no—
281C2×C4—2831no—
282C2×C4—5661no—
283C2×C4—5661no—
284C2×C4—5661no—
285C2×C4—5661no—
286C2×C4—11322no—
287C2×C4D4×D28311yescharacteristic
288C2×C4D4×D28311yescharacteristic
289C2×C4C23×D28311yescharacteristic
290C8—21no—
291C8—21no—
292C8—5661no—
293C8—5661no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22C2×D4×D28311yescharacteristic
298C4—21no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—2832no—
304C4—5661no—
305C4—5661no—
306C4—5661no—
307C4—5662no—
308C4—11321no—
309C4—11321no—
310C4—11321no—
311C4#41×D28311yescharacteristic
312C4#2258365711yescharacteristic
313C2—81no—
314C2#3182712311yescharacteristic
315C2#135×D28311yescharacteristic
316C2#3182727911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#488×C283C2
socleC22×C283C22×D4
prime radicalC2×D4×C283C23
hypercenter#488D283
hypocenterC283#3364
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #31827192C2semidirect
4. #31826814C2semidirect
5. #31826774C2semidirect
6. #31826769C2semidirect
10. #31826674C2semidirect
11. C8×Dic566C2semidirect
12. C4×Dic1132C2semidirect
13. #31826557C2semidirect
158. C283#3364semidirect

Maximal subgroups

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

subgroupindex
#318271922
#318271842
#318268182
#318268142
#318267742
#318267692
#318267432
#318266862
#318266842
#318266742
C8×Dic5662
C4×Dic11322
#318265572
#318265562
#488×C2832
#3364283