Finite Group Databasebeta

← #49131559

Subgroups — #49131559

Order 36224.

358 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827076C211yesmaximal, characteristic
2#31826941C211yesmaximal, characteristic
3#31826805C211yesmaximal, characteristic
4#31826804C211yesmaximal, characteristic
5#31826773C211yesmaximal, characteristic, complemented
6#31826772C211yesmaximal, characteristic, complemented
7#31826672C211yesmaximal, characteristic, complemented
8#31826619C211yesmaximal, characteristic
9#31826619C211yesmaximal, characteristic
10#31826572C211yesmaximal, characteristic, complemented
11#31826569C211yesmaximal, characteristic, complemented
12Q16×Dic283C211yesmaximal, characteristic, complemented
13#31826557C211yesmaximal, characteristic, complemented
14#31826525C211yesmaximal, characteristic
15#462×C283C211yesmaximal, characteristic, complemented
16C2×Q8×D283C2211yescharacteristic
17C2×#17985382C2211yescharacteristic
18C2×#17985382C2211yescharacteristic
19#22583605—21no—
20#22583605—21no—
21#22583602C2211yescharacteristic
22#22583600—21no—
23#22583600—21no—
24#22583586C2211yescharacteristic
25#22583586C2211yescharacteristic
26Q8×Dic283C2211yescharacteristic
27Q8×Dic283C2211yescharacteristic
28Q8×Dic283C2211yescharacteristic
29C4×Dic566—21no—
30C4×Dic566C2211yescharacteristic
31#22583575—21no—
32#22583575C2211yescharacteristic
33#22583568—21no—
34#22583568C2211yescharacteristic
35#22583567—21no—
36#22583567C2211yescharacteristic
37#22583544C2211yescharacteristic
38#22583543C2211yescharacteristic
39#22583542C2211yescharacteristic
40#22583541C2211yescharacteristic
41C4⋊(C283⋊C8)C2211yescharacteristic
42#22583535C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583534C2211yescharacteristic
45#22583534C2211yescharacteristic
46#22583534C2211yescharacteristic
47#22583534C2211yescharacteristic
48(C2×D283)⋊C8C2211yescharacteristic
49(C2×D283)⋊C8C2211yescharacteristic
50#22583520C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52C2×Q16×C283C2211yescharacteristic
53C2×Q16×C283C2211yescharacteristic
54C4⋊Q8×C283C2211yescharacteristic
55C4×Q8×C283C2211yescharacteristic
56C4⋊C8×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#103×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566C2311yescharacteristic
61Q8×D283—22no—
62Q8×D283—22no—
63C2×C4×D283—21no—
64C2×C4×D283C2311yescharacteristic
65#17985382—22no—
66#17985382—22no—
67C2×C283⋊C8C2311yescharacteristic
68C2×C283⋊C8C2311yescharacteristic
69C4⋊Dic283—21no—
70C4⋊Dic283—21no—
71C4⋊Dic283—21no—
72C4⋊Dic283C2311yescharacteristic
73C4⋊Dic283C2311yescharacteristic
74C4⋊Dic283C2311yescharacteristic
75Dic283⋊C4—21no—
76Dic283⋊C4—21no—
77Dic283⋊C4—21no—
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4D411yescharacteristic
82Dic283⋊C4D411yescharacteristic
83(C2×D283)⋊C4—21no—
84(C2×D283)⋊C4—21no—
85(C2×D283)⋊C4—21no—
86(C2×D283)⋊C4D411yescharacteristic
87(C2×D283)⋊C4D411yescharacteristic
88C4×Dic283—21no—
89C4×Dic283—21no—
90C4×Dic283—21no—
91C4×Dic283—21no—
92C4×Dic283—21no—
93C4×Dic283—21no—
94C4×Dic283C2311yescharacteristic
95C2×Q8×C283C2311yescharacteristic
96C2×Q8×C283C2311yescharacteristic
97C2×Q8×C283C2311yescharacteristic
98Q16×C283—22no—
99Q16×C283—22no—
100C2×C8×C283C2311yescharacteristic
101C2×C8×C283C2311yescharacteristic
102C4⋊C4×C283—21no—
103C4⋊C4×C283—21no—
104C4⋊C4×C283—21no—
105C4⋊C4×C283C2311yescharacteristic
106C42×C283—21no—
107C42×C283C2311yescharacteristic
108C22×D283C2×D411yescharacteristic
109Dic566—24no—
110Dic566—21no—
111Dic566#4112yes—
112C2×Dic283—21no—
113C2×Dic283—21no—
114C2×Dic283—21no—
115C2×Dic283—21no—
116C2×Dic283C2×D411yescharacteristic
117C2×Dic283C2×D411yescharacteristic
118C2×Dic283C2×D411yescharacteristic
119C4×D283—24no—
120C4×D283—21no—
121C4×D283—21no—
122C283⋊C8—21no—
123C283⋊C8—21no—
124Q8×C283—21no—
125Q8×C283—21no—
126Q8×C283—21no—
127Q8×C283—21no—
128Q8×C283—21no—
129Q8×C283#4112yes—
130C2×C4×C283—21no—
131C2×C4×C283—21no—
132C2×C4×C283—21no—
133C2×C4×C283—21no—
134C2×C4×C283C2×D411yescharacteristic
135C2×C4×C283C2×D411yescharacteristic
136C2×C4×C283C2411yescharacteristic
137C8×C283—21no—
138C8×C283—21no—
139C22×C283C22×D411yescharacteristic
140C2×D283—21no—
141C2×D283—21no—
142C2×D283—21no—
143C4×C283—22no—
144C4×C283—21no—
145C4×C283—21no—
146C4×C283—41no—
147C4×C283—41no—
148C4×C283—41no—
149C4×C283C2×#4111yescharacteristic
150C4×C283C2×#4111yescharacteristic
151Dic283—22no—
152Dic283—21no—
153Dic283—21no—
154Dic283—21no—
155Dic283—41no—
156Dic283—41no—
157Dic283—41no—
158C2×C283#52511yescharacteristic
159C2×C283#57811yescharacteristic
160C2×C283#57811yescharacteristic
161D283—41no—
162C283#312711yescharacteristic, complemented, Sylow
163#3127—2831nomaximal, Sylow
164#541—2831no—
165#519—2831no—
166#485—2831no—
167#485—2831no—
168#479—2831no—
169#479—2831no—
170#462—2831no—
171#462D28311yescharacteristic, complemented
172#451—2831no—
173#451—2831no—
174#441—2831no—
175#441—2831no—
176C4×Q16—2831no—
177C4×Q16—2831no—
178#433—2831no—
179C22×Q8—2831no—
180C2×Q16—2831no—
181C2×Q16—2831no—
182C2×Q16C2×D28311yescharacteristic
183C2×Q16C2×D28311yescharacteristic
184C4⋊Q8C2×D28311yescharacteristic
185#126—5661no—
186#126—5661no—
187#125—2831no—
188#125—5661no—
189#125—5661no—
190C22⋊Q8—2831no—
191C22⋊Q8—2831no—
192C4×Q8—2831no—
193C4×Q8—2831no—
194C4×Q8—2831no—
195C4×Q8—2831no—
196C4×Q8—2831no—
197C4×Q8—5661no—
198C4×Q8—5661no—
199C4×Q8C2×D28311yescharacteristic
200#117—2831no—
201#117—2831no—
202#117—5661no—
203#117—5661no—
204#107—2831no—
205#107—2831no—
206#106—2831no—
207#106—2831no—
208C4⋊C8—2831no—
209C4⋊C8C2×D28311yescharacteristic
210#103—2831no—
211#103—2831no—
212#103—2831no—
213#103—2831no—
214#103—2831no—
215#103—2831no—
216#103C2×D28311yescharacteristic
217#103C2×D28311yescharacteristic
218C22⋊C8—2831no—
219C22⋊C8—2831no—
220#97—2831no—
221C4×C8—2831no—
222C2×Q8—2831no—
223C2×Q8—5661no—
224C2×Q8—5662no—
225C2×Q8—5662no—
226C2×Q8C22×D28311yescharacteristic
227C2×Q8C22×D28311yescharacteristic
228C2×Q8C22×D28311yescharacteristic
229C22×C4—2831no—
230C22×C4—5661no—
231Q16—22no—
232Q16—22no—
233Q16—5662no—
234Q16—5662no—
235C2×C8—2831no—
236C2×C8—2831no—
237C2×C8C22×D28311yescharacteristic
238C2×C8C22×D28311yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—2831no—
243C4⋊C4—2831no—
244C4⋊C4—2831no—
245C4⋊C4—2831no—
246C4⋊C4—2831no—
247C4⋊C4—5661no—
248C4⋊C4—5661no—
249C4⋊C4—5661no—
250C4⋊C4—5661no—
251C4⋊C4—5661no—
252C4⋊C4—5661no—
253C4⋊C4—5661no—
254C4⋊C4—5661no—
255C4⋊C4—5661no—
256C4⋊C4C22×D28311yescharacteristic
257C22⋊C4—2831no—
258C22⋊C4—2831no—
259C22⋊C4—5661no—
260C22⋊C4—5661no—
261C22⋊C4—5661no—
262C42—21no—
263C42—2831no—
264C42—5661no—
265C42—5661no—
266C42—5661no—
267C42—5661no—
268C42—5661no—
269C42—5661no—
270C42C22×D28311yescharacteristic
271C23—2831no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—21no—
276Q8—21no—
277Q8—2832no—
278Q8—5664no—
279Q8—5661no—
280Q8#1798539112yes—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—2831no—
286C2×C4—2831no—
287C2×C4—2831no—
288C2×C4—5664no—
289C2×C4—5661no—
290C2×C4—5661no—
291C2×C4—5661no—
292C2×C4—5661no—
293C2×C4—5661no—
294C2×C4—5661no—
295C2×C4D4×D28311yescharacteristic
296C2×C4D4×D28311yescharacteristic
297C2×C4C23×D28311yescharacteristic
298C8—21no—
299C8—21no—
300C8—5661no—
301C8—5661no—
302C22—5661no—
303C22—5661no—
304C22—5661no—
305C22C2×D4×D28311yescharacteristic
306C4—22no—
307C4—21no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—5661no—
313C4—5662no—
314C4—5661no—
315C4—5661no—
316C4—11321no—
317C4—11321no—
318C4—11321no—
319C4#41×D28311yescharacteristic
320C4C2×#1798539111yescharacteristic
321C2—11321no—
322C2#3182697511yescharacteristic
323C2#3182727811yescharacteristic
324C2#3182728111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#462×C283C2
socleC22×C283C22×D4
prime radicalC22×D283C2×D4
hypercenter#462D283
hypocenterC283#3127
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
5. #31826773C2semidirect
6. #31826772C2semidirect
7. #31826672C2semidirect
10. #31826572C2semidirect
11. #31826569C2semidirect
12. Q16×Dic283C2semidirect
13. #31826557C2semidirect
15. #462×C283C2semidirect
162. C283#3127semidirect
171. #462D283semidirect

Maximal subgroups

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

subgroupindex
#318270762
#318269412
#318268052
#318268042
#318267732
#318267722
#318266722
#318266192
#318265722
#318265692
Q16×Dic2832
#318265572
#318265252
#462×C2832
#3127283