Finite Group Databasebeta

← #49131102

Subgroups — #49131102

Order 36224.

362 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827095C211yesmaximal, characteristic
2#31826941C211yesmaximal, characteristic
3#31826774C211yesmaximal, characteristic, complemented
4#31826771C211yesmaximal, characteristic, complemented
5#31826769C211yesmaximal, characteristic, complemented
6#31826761C211yesmaximal, characteristic, complemented
7#31826758C211yesmaximal, characteristic, complemented
8#31826750C211yesmaximal, characteristic, complemented
9#31826749C211yesmaximal, characteristic, complemented
10#31826504C211yesmaximal, characteristic
11#31826502C211yesmaximal, characteristic
12#31826490C211yesmaximal, characteristic
13#31826472C211yesmaximal, characteristic
14#103×D283C211yesmaximal, characteristic
15#479×C283C211yesmaximal, characteristic, complemented
16C2×Q8×D283C2211yescharacteristic
17C2×#17985375C2211yescharacteristic
18C2×C8×D283C2211yescharacteristic
19#22583610C2211yescharacteristic
20#22583609—21no—
21#22583609C2211yescharacteristic
22#22583601C2211yescharacteristic
23#22583600—21no—
24#22583590—21no—
25#22583588—21no—
26Q8×Dic283C2211yescharacteristic
27C4×Dic566—21no—
28C4×Dic566C2211yescharacteristic
29#22583575—21no—
30#22583575C2211yescharacteristic
31#22583568—21no—
32#22583568C2211yescharacteristic
33#22583568C2211yescharacteristic
34#22583567—21no—
35#22583567C2211yescharacteristic
36C4⋊C4×D283C2211yescharacteristic
37#22583544C2211yescharacteristic
38#22583544C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583541C2211yescharacteristic
41#22583541C2211yescharacteristic
42#22583541C2211yescharacteristic
43C4⋊(C283⋊C8)C2211yescharacteristic
44Dic283⋊C8C2211yescharacteristic
45Dic283⋊C8C2211yescharacteristic
46#22583535C2211yescharacteristic
47#22583535C2211yescharacteristic
48#22583534C2211yescharacteristic
49#22583534C2211yescharacteristic
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×Dic566—21no—
60C2×Dic566—21no—
61C2×Dic566—21no—
62C2×Dic566C2311yescharacteristic
63Q8×D283—22no—
64Q8×D283Q814yescomplemented
65C2×C4×D283—21no—
66C2×C4×D283—21no—
67C2×C4×D283C2311yescharacteristic
68#17985375—22no—
69C2×C283⋊C8C2311yescharacteristic
70C2×C283⋊C8C2311yescharacteristic
71C8×D283—22no—
72C4⋊Dic283—21no—
73C4⋊Dic283—21no—
74C4⋊Dic283—21no—
75C4⋊Dic283C2311yescharacteristic
76C4⋊Dic283C2311yescharacteristic
77C4⋊Dic283C2311yescharacteristic
78Dic283⋊C4—21no—
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)⋊C4D411yescharacteristic
88(C2×D283)⋊C4D411yescharacteristic
89C4×Dic283—21no—
90C4×Dic283—21no—
91C4×Dic283—21no—
92C4×Dic283—21no—
93C4×Dic283—21no—
94C4×Dic283C2311yescharacteristic
95C2×Q8×C283C2311yescharacteristic
96C2×C8×C283C2311yescharacteristic
97C2×C8×C283C2311yescharacteristic
98C4⋊C4×C283—21no—
99C4⋊C4×C283—21no—
100C4⋊C4×C283—21no—
101C4⋊C4×C283C2311yescharacteristic
102C4⋊C4×C283C2311yescharacteristic
103C4⋊C4×C283C2311yescharacteristic
104C42×C283—21no—
105C42×C283C2311yescharacteristic
106C22×D283C2×D411yescharacteristic
107Dic566—21no—
108Dic566—24no—
109Dic566—81no—
110Dic566—81no—
111Dic566C2×Q812yes—
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—81no—
121C4×D283C2×Q812yes—
122C4×D283#4112yes—
123C283⋊C8—21no—
124C283⋊C8—21no—
125Q8×C283—21no—
126Q8×C283C2×Q812yes—
127C2×C4×C283—21no—
128C2×C4×C283—21no—
129C2×C4×C283—21no—
130C2×C4×C283—21no—
131C2×C4×C283C2×D411yescharacteristic
132C2×C4×C283C2×D411yescharacteristic
133C2×C4×C283C2411yescharacteristic
134C8×C283—21no—
135C8×C283—21no—
136C22×C283C22×D411yescharacteristic
137C2×D283—21no—
138C2×D283—21no—
139C2×D283C22⋊Q812yes—
140C4×C283—22no—
141C4×C283—21no—
142C4×C283—21no—
143C4×C283—41no—
144C4×C283—41no—
145C4×C283—41no—
146C4×C283C22×Q811yescharacteristic
147C4×C283C2×#4111yescharacteristic
148Dic283—22no—
149Dic283—21no—
150Dic283—21no—
151Dic283—41no—
152Dic283—41no—
153Dic283—41no—
154Dic283C22⋊Q812yes—
155C2×C283C2×C22⋊Q811yescharacteristic
156C2×C283#57711yescharacteristic
157C2×C283#57811yescharacteristic
158D283—22no—
159C283#308211yescharacteristic, complemented, Sylow
160#3082—2831nomaximal, Sylow
161#544—2831no—
162#519—2831no—
163#479—2831no—
164#479—2831no—
165#479—2831no—
166#479D28311yescharacteristic, complemented
167#477—2831no—
168#477—2831no—
169#475—2831no—
170#475—2831no—
171#428—2831no—
172#427—2831no—
173#424—2831no—
174#419—2831no—
175C2×#103—2831no—
176C22×Q8—2831no—
177C2×M16—2831no—
178C22×C8—2831no—
179C4⋊Q8—2831no—
180C4⋊Q8—2831no—
181C4⋊Q8—5661no—
182#125—2831no—
183#125—5661no—
184#125C2×D28311yescharacteristic
185C22⋊Q8—5661no—
186C22⋊Q8—5661no—
187C4×Q8—2831no—
188C4×Q8—2831no—
189C4×Q8—2831no—
190C4×Q8—5661no—
191C4×Q8—5661no—
192C4×Q8C2×D28311yescharacteristic
193#117—2831no—
194#117—2831no—
195#117—2831no—
196#117—5661no—
197#117—5661no—
198C2×C4⋊C4—2831no—
199#107—2831no—
200#107—2831no—
201#107—2831no—
202#107C2×D28311yescharacteristic
203#106—2831no—
204#106—2831no—
205#106—2831no—
206#106C2×D28311yescharacteristic
207C4⋊C8—2831no—
208C4⋊C8—2831no—
209C4⋊C8—2831no—
210C4⋊C8C2×D28311yescharacteristic
211#103—2831no—
212#103—2831no—
213#103—2831no—
214#103—2831no—
215#103—2831no—
216#103—2831no—
217#103C2×D28311yescharacteristic
218#103C2×D28311yescharacteristic
219C2×Q8—2834no—
220C2×Q8—2831no—
221C2×Q8—5661no—
222C2×Q8—5661no—
223C2×Q8—5662no—
224C2×Q8—5661no—
225C2×Q8C22×D28311yescharacteristic
226C22×C4—2831no—
227C22×C4—5661no—
228C22×C4—5661no—
229M16—5662no—
230C2×C8—2831no—
231C2×C8—2831no—
232C2×C8—5662no—
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—2831no—
242C4⋊C4—2831no—
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⋊C4C22×D28311yescharacteristic
252C4⋊C4C22×D28311yescharacteristic
253C4⋊C4C22×D28311yescharacteristic
254C22⋊C4—2831no—
255C22⋊C4—2831no—
256C22⋊C4—5661no—
257C22⋊C4—5661no—
258C42—21no—
259C42—2831no—
260C42—5661no—
261C42—5661no—
262C42—5661no—
263C42—5661no—
264C42—5661no—
265C42C22×D28311yescharacteristic
266C23—2831no—
267Q8—21no—
268Q8—2832no—
269Q8—5664no—
270Q8—5661no—
271Q8—22641no—
272Q8—22641no—
273Q8Q8×D28312yes—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—2831no—
279C2×C4—2832no—
280C2×C4—2832no—
281C2×C4—2831no—
282C2×C4—2831no—
283C2×C4—5664no—
284C2×C4—5661no—
285C2×C4—5661no—
286C2×C4—5661no—
287C2×C4—5661no—
288C2×C4—22641no—
289C2×C4D4×D28311yescharacteristic
290C2×C4D4×D28311yescharacteristic
291C2×C4C23×D28311yescharacteristic
292C8—21no—
293C8—21no—
294C8—5661no—
295C8—5661no—
296C22—2832no—
297C22—5661no—
298C22—5661no—
299C22C2×D4×D28311yescharacteristic
300C4—22no—
301C4—21no—
302C4—21no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—2832no—
307C4—5662no—
308C4—5661no—
309C4—5661no—
310C4—11321no—
311C4—11321no—
312C4—11321no—
313C4C2×Q8×D28311yescharacteristic
314C4#41×D28311yescharacteristic
315C2—5662no—
316C2C22⋊Q8×D28311yescharacteristic
317C2#3182727411yescharacteristic
318C2#3182727911yescharacteristic
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#3082
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. #31826774C2semidirect
4. #31826771C2semidirect
5. #31826769C2semidirect
6. #31826761C2semidirect
7. #31826758C2semidirect
8. #31826750C2semidirect
9. #31826749C2semidirect
15. #479×C283C2semidirect
64. Q8×D283Q8semidirect
159. C283#3082semidirect
166. #479D283semidirect

Maximal subgroups

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

subgroupindex
#318270952
#318269412
#318267742
#318267712
#318267692
#318267612
#318267582
#318267502
#318267492
#318265042
#318265022
#318264902
#318264722
#103×D2832
#479×C2832
#3082283