Finite Group Databasebeta

← #49132714

Subgroups — #49132714

Order 36224.

322 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827078C211yesmaximal, characteristic
2#31827073C211yesmaximal, characteristic
3#31826775C211yesmaximal, characteristic, complemented
4#31826771C211yesmaximal, characteristic, complemented
5#31826769C211yesmaximal, characteristic, complemented
6#31826724C211yesmaximal, characteristic
7#31826722C211yesmaximal, characteristic
8#31826707C211yesmaximal, characteristic
9#31826705C211yesmaximal, characteristic
10#31826676C211yesmaximal, characteristic, complemented
11#31826675C211yesmaximal, characteristic, complemented
12#31826674C211yesmaximal, characteristic, complemented
13#31826674C211yesmaximal, characteristic, complemented
14#31826490C211yesmaximal, characteristic
15#479×C283C211yesmaximal, characteristic, complemented
16C2×Dic1132C2211yescharacteristic
17C2×Dic1132C2211yescharacteristic
18C2×#17985382C2211yescharacteristic
19C2×#17985382C2211yescharacteristic
20C2×#17985375C2211yescharacteristic
21C2×C8×D283C2211yescharacteristic
22#22583610C2211yescharacteristic
23#22583608C2211yescharacteristic
24#22583605—21no—
25#22583605—21no—
26#22583605—21no—
27#22583604—21no—
28#22583602—21no—
29#22583601—21no—
30#22583601—21no—
31#22583601C2211yescharacteristic
32#22583600—21no—
33#22583590C2211yescharacteristic
34#22583590C2211yescharacteristic
35#22583590C2211yescharacteristic
36#22583586C2211yescharacteristic
37C4×Dic566C2211yescharacteristic
38#22583575C2211yescharacteristic
39#22583575C2211yescharacteristic
40#22583567C2211yescharacteristic
41#22583543C2211yescharacteristic
42#22583541C2211yescharacteristic
43C4⋊(C283⋊C8)C2211yescharacteristic
44Dic283⋊C8C2211yescharacteristic
45Dic283⋊C8C2211yescharacteristic
46#22583535C2211yescharacteristic
47#22583535C2211yescharacteristic
48#22583533C2211yescharacteristic
49#22583533C2211yescharacteristic
50#22583533C2211yescharacteristic
51#22583533C2211yescharacteristic
52#125×C283C2211yescharacteristic
53C4×Q8×C283C2211yescharacteristic
54#107×C283C2211yescharacteristic
55#106×C283C2211yescharacteristic
56C4⋊C8×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#103×C283C2211yescharacteristic
59C2×Dic566C2311yescharacteristic
60C2×Dic566C2311yescharacteristic
61C2×Dic566C2311yescharacteristic
62C2×C4×D283C2311yescharacteristic
63Dic1132—41no—
64Dic1132—41no—
65#17985382—41no—
66#17985382—41no—
67#17985375—41no—
68C2×C283⋊C8C2311yescharacteristic
69C2×C283⋊C8C2311yescharacteristic
70C8×D283—41no—
71C4⋊Dic283—21no—
72C4⋊Dic283—21no—
73C4⋊Dic283—21no—
74C4⋊Dic283—21no—
75C4⋊Dic283—21no—
76C4⋊Dic283—21no—
77C4⋊Dic283C2311yescharacteristic
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4D411yescharacteristic
86Dic283⋊C4D411yescharacteristic
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4D411yescharacteristic
92(C2×D283)⋊C4D411yescharacteristic
93C4×Dic283—21no—
94C4×Dic283—21no—
95C4×Dic283—21no—
96C4×Dic283C2311yescharacteristic
97C2×Q8×C283C2311yescharacteristic
98C2×C8×C283C2311yescharacteristic
99C2×C8×C283C2311yescharacteristic
100C4⋊C4×C283—21no—
101C4⋊C4×C283—21no—
102C4⋊C4×C283—21no—
103C4⋊C4×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C4⋊C4×C283C2311yescharacteristic
106C42×C283—21no—
107C42×C283C2311yescharacteristic
108C22×D283C2×D411yescharacteristic
109Dic566—21no—
110Dic566—21no—
111Dic566—21no—
112Dic566—21no—
113Dic566—21no—
114Dic566—21no—
115C2×Dic283—21no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283C2×D411yescharacteristic
120C2×Dic283C2×D411yescharacteristic
121C2×Dic283C2×D411yescharacteristic
122C4×D283—21no—
123C4×D283—21no—
124C283⋊C8—21no—
125C283⋊C8—21no—
126Q8×C283—21no—
127Q8×C283—21no—
128C2×C4×C283—21no—
129C2×C4×C283—21no—
130C2×C4×C283—21no—
131C2×C4×C283—21no—
132C2×C4×C283C2×D411yescharacteristic
133C2×C4×C283C2×D411yescharacteristic
134C2×C4×C283C2411yescharacteristic
135C8×C283—21no—
136C8×C283—21no—
137C22×C283C22×D411yescharacteristic
138C2×D283—21no—
139C2×D283—21no—
140C2×D283—21no—
141C4×C283—21no—
142C4×C283—21no—
143C4×C283—41no—
144C4×C283—41no—
145C4×C283—41no—
146C4×C283—41no—
147C4×C283H(5,𝔽2)11yescharacteristic
148C4×C2832−1+411yescharacteristic
149Dic283—21no—
150Dic283—21no—
151Dic283—21no—
152Dic283—41no—
153Dic283—41no—
154Dic283—41no—
155Dic283—41no—
156C2×C283#53711yescharacteristic
157C2×C283#57811yescharacteristic
158C2×C283#57811yescharacteristic
159D283—41no—
160C283#326111yescharacteristic, complemented, Sylow
161#3261—2831nomaximal, Sylow
162#541—2831no—
163#541—2831no—
164#479—2831no—
165#479—2831no—
166#479—2831no—
167#479D28311yescharacteristic, complemented
168#470—2831no—
169#470—2831no—
170#467—2831no—
171#467—2831no—
172#462—2831no—
173#462—2831no—
174#462—2831no—
175#462—2831no—
176#424—2831no—
177C2×Q16—2831no—
178C2×Q16—2831no—
179C2×Q16—2831no—
180C2×Q16—2831no—
181C2×M16—2831no—
182C22×C8—2831no—
183C4⋊Q8—2831no—
184C4⋊Q8—2831no—
185#126—5661no—
186#126—5661no—
187#126—5661no—
188#126—5661no—
189#125—2831no—
190#125—5661no—
191#125—5661no—
192#125—5661no—
193#125—5661no—
194#125C2×D28311yescharacteristic
195C22⋊Q8—2831no—
196C22⋊Q8—2831no—
197C22⋊Q8—2831no—
198C22⋊Q8—2831no—
199C4×Q8—2831no—
200C4×Q8—2831no—
201C4×Q8—2831no—
202C4×Q8C2×D28311yescharacteristic
203#117—2831no—
204#107—2831no—
205#107C2×D28311yescharacteristic
206#106—2831no—
207#106C2×D28311yescharacteristic
208C4⋊C8—2831no—
209C4⋊C8—2831no—
210C4⋊C8—2831no—
211C4⋊C8C2×D28311yescharacteristic
212#103—2831no—
213#103—2831no—
214#103—2831no—
215#103—2831no—
216#103—2831no—
217#103—2831no—
218#103C2×D28311yescharacteristic
219#103C2×D28311yescharacteristic
220C2×Q8—2831no—
221C2×Q8—2831no—
222C2×Q8—2831no—
223C2×Q8C22×D28311yescharacteristic
224C22×C4—2831no—
225Q16—11321no—
226Q16—11321no—
227Q16—11321no—
228Q16—11321no—
229M16—11321no—
230C2×C8—2831no—
231C2×C8—2831no—
232C2×C8—11321no—
233C2×C8C22×D28311yescharacteristic
234C2×C8C22×D28311yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—2831no—
239C4⋊C4—2831no—
240C4⋊C4—2831no—
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⋊C4—5661no—
250C4⋊C4—5661no—
251C4⋊C4—5661no—
252C4⋊C4—5661no—
253C4⋊C4—5661no—
254C4⋊C4C22×D28311yescharacteristic
255C4⋊C4C22×D28311yescharacteristic
256C4⋊C4C22×D28311yescharacteristic
257C22⋊C4—2831no—
258C22⋊C4—2831no—
259C22⋊C4—5661no—
260C22⋊C4—5661no—
261C22⋊C4—5661no—
262C22⋊C4—5661no—
263C42—21no—
264C42—2831no—
265C42—5661no—
266C42—5661no—
267C42—5661no—
268C42C22×D28311yescharacteristic
269C23—2831no—
270Q8—21no—
271Q8—21no—
272Q8—5661no—
273Q8—5661no—
274Q8—5661no—
275Q8—5661no—
276Q8—5661no—
277Q8—5661no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—2831no—
283C2×C4—2831no—
284C2×C4—2831no—
285C2×C4—5661no—
286C2×C4—5661no—
287C2×C4—5661no—
288C2×C4—5661no—
289C2×C4—5661no—
290C2×C4—5661no—
291C2×C4D4×D28311yescharacteristic
292C2×C4D4×D28311yescharacteristic
293C2×C4C23×D28311yescharacteristic
294C8—21no—
295C8—21no—
296C8—5661no—
297C8—5661no—
298C22—5661no—
299C22—5661no—
300C22—5661no—
301C22C2×D4×D28311yescharacteristic
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—5661no—
309C4—5661no—
310C4—5661no—
311C4—11321no—
312C4—11321no—
313C4—11321no—
314C4—11321no—
315C4#2258365611yescharacteristic
316C4#2258365811yescharacteristic
317C2—11321no—
318C2#3182704511yescharacteristic
319C2#3182727911yescharacteristic
320C2#3182728111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#479×C283C2
socleC22×C283C22×D4
prime radicalC22×D283C2×D4
hypercenter#479D283
hypocenterC283#3261
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
3. #31826775C2semidirect
4. #31826771C2semidirect
5. #31826769C2semidirect
10. #31826676C2semidirect
11. #31826675C2semidirect
12. #31826674C2semidirect
13. #31826674C2semidirect
15. #479×C283C2semidirect
160. C283#3261semidirect
167. #479D283semidirect

Maximal subgroups

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

subgroupindex
#318270782
#318270732
#318267752
#318267712
#318267692
#318267242
#318267222
#318267072
#318267052
#318266762
#318266752
#318266742
#318264902
#479×C2832
#3261283