Finite Group Databasebeta

← #49131225

Subgroups — #49131225

Order 36224.

386 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827038C211yesmaximal, characteristic
2#31826945C211yesmaximal, characteristic
3#31826808C211yesmaximal, characteristic, complemented
4#31826806C211yesmaximal, characteristic, complemented
5#31826805C211yesmaximal, characteristic, complemented
6#31826801C211yesmaximal, characteristic, complemented
7#31826799C211yesmaximal, characteristic, complemented
8#31826797C211yesmaximal, characteristic, complemented
9#31826793C211yesmaximal, characteristic, complemented
10#31826504C211yesmaximal, characteristic, complemented
11#31826502C211yesmaximal, characteristic, complemented
12#31826472C211yesmaximal, characteristic, complemented
13#103×D283C211yesmaximal, characteristic, complemented
14#31826430C211yesmaximal, characteristic
15#485×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C2×Q8×D283C2211yescharacteristic
18C2×#17985375C2211yescharacteristic
19C2×C8×D283C2211yescharacteristic
20#22583609—21no—
21#22583596—21no—
22#22583595—21no—
23#22583592—21no—
24#22583590C2211yescharacteristic
25#22583589C2211yescharacteristic
26#22583586C2211yescharacteristic
27C4×Dic566—21no—
28C4×D1132—21no—
29(C22⋊D283)⋊C4—21no—
30(C22⋊D283)⋊C4—21no—
31#22583568C2211yescharacteristic
32#22583568C2211yescharacteristic
33#22583568C2211yescharacteristic
34C2×C4⋊Dic283C2211yescharacteristic
35C4⋊C4×D283C2211yescharacteristic
36C4⋊C4×D283C2211yescharacteristic
37#22583544C2211yescharacteristic
38#22583544C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583541C2211yescharacteristic
41#22583541C2211yescharacteristic
42#22583541C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583535C2211yescharacteristic
45#22583534C2211yescharacteristic
46#22583534C2211yescharacteristic
47#22583533C2211yescharacteristic
48#22583533C2211yescharacteristic
49C22⋊(C283⋊C8)C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51(C2×D283)⋊C8C2211yescharacteristic
52C22⋊Q8×C283C2211yescharacteristic
53#117×C283C2211yescharacteristic
54#107×C283C2211yescharacteristic
55#106×C283C2211yescharacteristic
56#103×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58C22⋊C8×C283C2211yescharacteristic
59#17985392—22no—
60#17985392—22no—
61C2×Dic566—21no—
62C2×Dic566D411yescharacteristic
63C2×Dic566C2311yescharacteristic
64Q8×D283—22no—
65Q8×D283—22no—
66C2×D1132D411yescharacteristic
67C2×C22⋊D283D411yescharacteristic
68C2×C22⋊D283D411yescharacteristic
69C22×Dic283—21no—
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72C2×C4×D283—21no—
73C2×C4×D283C2311yescharacteristic
74C2×C4×D283C2311yescharacteristic
75#17985375—22no—
76C2×C283⋊C8C2311yescharacteristic
77C2×C283⋊C8C2311yescharacteristic
78C8×D283—22no—
79C4⋊Dic283—21no—
80C4⋊Dic283—21no—
81C4⋊Dic283C2311yescharacteristic
82C4⋊Dic283C2311yescharacteristic
83C4⋊Dic283C2311yescharacteristic
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88C22⋊Dic283—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94C4×Dic283—21no—
95C4×Dic283—21no—
96C4×Dic283—21no—
97C2×Q8×C283C2311yescharacteristic
98C22×C4×C283C2311yescharacteristic
99C2×C8×C283C2311yescharacteristic
100C2×C8×C283C2311yescharacteristic
101C4⋊C4×C283—21no—
102C4⋊C4×C283C2311yescharacteristic
103C4⋊C4×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C22⋊C4×C283—21no—
106C22⋊C4×C283—21no—
107C42×C283—21no—
108C22×D283C2×D411yescharacteristic
109C22×D283C2×D411yescharacteristic
110Dic566—22no—
111Dic566—21no—
112Dic566—21no—
113Dic566—42no—
114D1132—22no—
115C22⋊D283—22no—
116C22⋊D283—22no—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283—21no—
120C2×Dic283—21no—
121C2×Dic283—81no—
122C2×Dic283C2×D411yescharacteristic
123C2×Dic283C2×D411yescharacteristic
124C4×D283—21no—
125C4×D283—21no—
126C4×D283—42no—
127C4×D283—81no—
128C4×D283—81no—
129C4×D283#4112yes—
130C4×D283#4112yes—
131C283⋊C8—21no—
132C283⋊C8—21no—
133C23×C283C2×D411yescharacteristic
134Q8×C283—21no—
135Q8×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283C2×D411yescharacteristic
143C2×C4×C283C2411yescharacteristic
144C8×C283—21no—
145C8×C283—21no—
146C22×C283—21no—
147C22×C283—21no—
148C22×C283—21no—
149C22×C283C22×D411yescharacteristic
150C2×D283—21no—
151C2×D283—21no—
152C2×D283—21no—
153C2×D283—21no—
154C2×D283—21no—
155C2×D283#12312yes—
156C4×C283—21no—
157C4×C283—41no—
158C4×C283—41no—
159C4×C283—41no—
160C4×C283—41no—
161C4×C283C2×#4111yescharacteristic
162C4×C283C2×#4111yescharacteristic
163Dic283—21no—
164Dic283—41no—
165Dic283—41no—
166Dic283—41no—
167Dic283—41no—
168Dic283#12312yes—
169C2×C283—41no—
170C2×C283C2×#12311yescharacteristic
171C2×C283#57711yescharacteristic
172C2×C283#57811yescharacteristic
173D283—22no—
174D283—41no—
175C283#309711yescharacteristic, complemented, Sylow
176#3097—2831nomaximal, Sylow
177#536—2831no—
178#520—2831no—
179#485—2831no—
180#485—2831no—
181#485—2831no—
182#485D28311yescharacteristic, complemented
183#484—2831no—
184#484—2831no—
185#483—2831no—
186#483—2831no—
187#428—2831no—
188#427—2831no—
189#419—2831no—
190C2×#103—2831no—
191#408—2831no—
192C2×#41—2831no—
193C22×Q8—2831no—
194C2×M16—2831no—
195C22×C8—2831no—
196C4⋊Q8—5661no—
197#124—5661no—
198#123—5661no—
199#123—5661no—
200C22⋊Q8—2831no—
201C22⋊Q8—2831no—
202C22⋊Q8—2831no—
203C22⋊Q8C2×D28311yescharacteristic
204C4×Q8—5661no—
205C4×D4—5661no—
206C4×D4—5661no—
207C4×D4—5661no—
208#117—2831no—
209#117—2831no—
210#117—2831no—
211#117C2×D28311yescharacteristic
212C2×C4⋊C4—2831no—
213C2×C4⋊C4—2831no—
214C2×C4⋊C4—2831no—
215#107—2831no—
216#107—2831no—
217#107—2831no—
218#107C2×D28311yescharacteristic
219#106—2831no—
220#106—2831no—
221#106—2831no—
222#106C2×D28311yescharacteristic
223#103—2831no—
224#103—2831no—
225#103—2831no—
226#103—2831no—
227#103—2831no—
228#103—2831no—
229#103C2×D28311yescharacteristic
230#103C2×D28311yescharacteristic
231C22⋊C8—2831no—
232C22⋊C8—2831no—
233C22⋊C8—2831no—
234C22⋊C8C2×D28311yescharacteristic
235#41—5662no—
236#41—5662no—
237C2×Q8—2831no—
238C2×Q8—2831no—
239C2×Q8—5661no—
240C2×Q8—5662no—
241C2×Q8—5662no—
242C2×Q8C22×D28311yescharacteristic
243C2×D4—2831no—
244C2×D4—2831no—
245C2×D4—2831no—
246C22×C4—2831no—
247C22×C4—2831no—
248C22×C4—5661no—
249C22×C4—5661no—
250C22×C4—5661no—
251C22×C4—5661no—
252C22×C4C22×D28311yescharacteristic
253M16—5662no—
254C2×C8—2831no—
255C2×C8—2831no—
256C2×C8—5662no—
257C2×C8C22×D28311yescharacteristic
258C2×C8C22×D28311yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—2831no—
261C4⋊C4—2831no—
262C4⋊C4—2831no—
263C4⋊C4—5661no—
264C4⋊C4—5661no—
265C4⋊C4—5661no—
266C4⋊C4—5661no—
267C4⋊C4—5661no—
268C4⋊C4—5661no—
269C4⋊C4C22×D28311yescharacteristic
270C4⋊C4C22×D28311yescharacteristic
271C4⋊C4C22×D28311yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—5661no—
275C22⋊C4—5661no—
276C22⋊C4—5661no—
277C22⋊C4—5661no—
278C22⋊C4—5661no—
279C22⋊C4—5661no—
280C42—21no—
281C42—5661no—
282C42—5661no—
283C42—5661no—
284C23—2831no—
285C23—2831no—
286C23D4×D28311yescharacteristic
287Q8—21no—
288Q8—21no—
289Q8—5662no—
290Q8—5661no—
291Q8—5661no—
292Q8—11322no—
293D4—5662no—
294D4—5662no—
295D4—5662no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—2831no—
303C2×C4—2832no—
304C2×C4—2832no—
305C2×C4—2831no—
306C2×C4—5661no—
307C2×C4—5661no—
308C2×C4—5661no—
309C2×C4—5661no—
310C2×C4—5661no—
311C2×C4—5661no—
312C2×C4—11322no—
313C2×C4—22641no—
314C2×C4—22641no—
315C2×C4—22641no—
316C2×C4D4×D28311yescharacteristic
317C2×C4C23×D28311yescharacteristic
318C8—21no—
319C8—21no—
320C8—5661no—
321C8—5661no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—2832no—
326C22—5661no—
327C22—5661no—
328C22—5661no—
329C22—5661no—
330C22—5661no—
331C22C2×D4×D28311yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—2832no—
338C4—5661no—
339C4—11321no—
340C4—11321no—
341C4—11321no—
342C4—11321no—
343C4#41×D28311yescharacteristic
344C4#41×D28311yescharacteristic
345C2—41no—
346C2—5662no—
347C2—11321no—
348C2#123×D28311yescharacteristic
349C2#3182727411yescharacteristic
350C2#3182727911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#485×C283C2
socleC22×C283C22×D4
prime radicalC2×#17985392C22
hypercenter#485D283
hypocenterC283#3097
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #31826808C2semidirect
4. #31826806C2semidirect
5. #31826805C2semidirect
6. #31826801C2semidirect
7. #31826799C2semidirect
8. #31826797C2semidirect
9. #31826793C2semidirect
10. #31826504C2semidirect
11. #31826502C2semidirect
12. #31826472C2semidirect
13. #103×D283C2semidirect
15. #485×C283C2semidirect
175. C283#3097semidirect
182. #485D283semidirect

Maximal subgroups

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

subgroupindex
#318270382
#318269452
#318268082
#318268062
#318268052
#318268012
#318267992
#318267972
#318267932
#318265042
#318265022
#318264722
#103×D2832
#318264302
#485×C2832
#3097283