Finite Group Databasebeta

← #49131563

Subgroups — #49131563

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#31827078C211yesmaximal, characteristic
2#31826941C211yesmaximal, characteristic
3#31826809C211yesmaximal, characteristic
4#31826808C211yesmaximal, characteristic
5#31826769C211yesmaximal, characteristic, complemented
6#31826676C211yesmaximal, characteristic, complemented
7#31826675C211yesmaximal, characteristic, complemented
8#31826622C211yesmaximal, characteristic
9#31826622C211yesmaximal, characteristic
10#31826571C211yesmaximal, characteristic, complemented
11#31826569C211yesmaximal, characteristic, complemented
12#31826559C211yesmaximal, characteristic, complemented
13#31826557C211yesmaximal, characteristic, complemented
14#31826525C211yesmaximal, characteristic
15#479×C283C211yesmaximal, characteristic, complemented
16C2×Q8×D283C2211yescharacteristic
17C2×Dic1132C2211yescharacteristic
18C2×Dic1132C2211yescharacteristic
19C2×#17985382C2211yescharacteristic
20C2×#17985382C2211yescharacteristic
21#22583610C2211yescharacteristic
22#22583605—21no—
23#22583605—21no—
24#22583601—21no—
25#22583601—21no—
26#22583590C2211yescharacteristic
27#22583590C2211yescharacteristic
28Q8×Dic283C2211yescharacteristic
29C4×Dic566—21no—
30C4×Dic566C2211yescharacteristic
31#22583575—21no—
32#22583575C2211yescharacteristic
33#22583575C2211yescharacteristic
34#22583575C2211yescharacteristic
35#22583568—21no—
36#22583568C2211yescharacteristic
37#22583567—21no—
38#22583567C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583541C2211yescharacteristic
41C4⋊(C283⋊C8)C2211yescharacteristic
42#22583535C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583533C2211yescharacteristic
45#22583533C2211yescharacteristic
46#22583533C2211yescharacteristic
47#22583533C2211yescharacteristic
48(C2×D283)⋊C8C2211yescharacteristic
49(C2×D283)⋊C8C2211yescharacteristic
50#22583520C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52#125×C283C2211yescharacteristic
53C4×Q8×C283C2211yescharacteristic
54#107×C283C2211yescharacteristic
55#106×C283C2211yescharacteristic
56C4⋊C8×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#103×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566C2311yescharacteristic
61C2×Dic566C2311yescharacteristic
62C2×Dic566C2311yescharacteristic
63Q8×D283—22no—
64Q8×D283—22no—
65C2×C4×D283—21no—
66C2×C4×D283C2311yescharacteristic
67Dic1132—22no—
68Dic1132—22no—
69#17985382—22no—
70#17985382—22no—
71C2×C283⋊C8C2311yescharacteristic
72C2×C283⋊C8C2311yescharacteristic
73C4⋊Dic283—21no—
74C4⋊Dic283—21no—
75C4⋊Dic283—21no—
76C4⋊Dic283—21no—
77C4⋊Dic283—21no—
78C4⋊Dic283C2311yescharacteristic
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4D411yescharacteristic
84Dic283⋊C4D411yescharacteristic
85(C2×D283)⋊C4—21no—
86(C2×D283)⋊C4—21no—
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4D411yescharacteristic
89(C2×D283)⋊C4D411yescharacteristic
90C4×Dic283—21no—
91C4×Dic283—21no—
92C4×Dic283—21no—
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—24no—
110Dic566—21no—
111Dic566—21no—
112Dic566—21no—
113Dic566—21no—
114Dic566—21no—
115Dic566#4112yes—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283—21no—
120C2×Dic283C2×D411yescharacteristic
121C2×Dic283C2×D411yescharacteristic
122C2×Dic283C2×D411yescharacteristic
123C4×D283—24no—
124C4×D283—21no—
125C4×D283—21no—
126C283⋊C8—21no—
127C283⋊C8—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#479D28311yescharacteristic, complemented
170#462—2831no—
171#462—2831no—
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×Q16—2831no—
183C2×Q16—2831no—
184C4⋊Q8—2831no—
185#126—5661no—
186#126—5661no—
187#125—5661no—
188#125—5661no—
189#125C2×D28311yescharacteristic
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#107C2×D28311yescharacteristic
206#106—2831no—
207#106C2×D28311yescharacteristic
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—2831no—
224C2×Q8—2831no—
225C2×Q8—5661no—
226C2×Q8—5662no—
227C2×Q8—5662no—
228C2×Q8C22×D28311yescharacteristic
229C22×C4—2831no—
230C22×C4—5661no—
231Q16—5662no—
232Q16—5662no—
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—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—
262C42—21no—
263C42—2831no—
264C42—5661no—
265C42—5661no—
266C42—5661no—
267C42—5661no—
268C42—5661no—
269C42—5661no—
270C42C22×D28311yescharacteristic
271C23—2831no—
272Q8—21no—
273Q8—2832no—
274Q8—5664no—
275Q8—5661no—
276Q8—5661no—
277Q8—5661no—
278Q8—5661no—
279Q8—5661no—
280Q8#1798539312yes—
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×#1798539311yescharacteristic
321C2—11321no—
322C2#3182697811yescharacteristic
323C2#3182727911yescharacteristic
324C2#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#3127
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
5. #31826769C2semidirect
6. #31826676C2semidirect
7. #31826675C2semidirect
10. #31826571C2semidirect
11. #31826569C2semidirect
12. #31826559C2semidirect
13. #31826557C2semidirect
15. #479×C283C2semidirect
162. C283#3127semidirect
169. #479D283semidirect

Maximal subgroups

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

subgroupindex
#318270782
#318269412
#318268092
#318268082
#318267692
#318266762
#318266752
#318266222
#318265712
#318265692
#318265592
#318265572
#318265252
#479×C2832
#3127283