Finite Group Databasebeta

← #49133147

Subgroups — #49133147

Order 36224.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827153C211yesmaximal, characteristic, complemented
2#31827123C211yesmaximal, characteristic
3#31826805C211yesmaximal, characteristic, complemented
4#31826777C211yesmaximal, characteristic, complemented
5#31826769C211yesmaximal, characteristic, complemented
6#31826705C211yesmaximal, characteristic, complemented
7#31826693C211yesmaximal, characteristic, complemented
8#31826684C211yesmaximal, characteristic, complemented
9#31826628C211yesmaximal, characteristic, complemented
10#31826622C211yesmaximal, characteristic, complemented
11C4×Dic1132C211yesmaximal, characteristic, complemented
12C8×D1132C211yesmaximal, characteristic, complemented
13#31826458C211yesmaximal, characteristic, complemented
14#103×D283C211yesmaximal, characteristic, complemented
15#488×C283C211yesmaximal, characteristic, complemented
16C2×#17985391C2211yescharacteristic
17C2×Q8×D283C2211yescharacteristic
18C2×Dic1132C2211yescharacteristic
19C2×#17985382C2211yescharacteristic
20C2×#17985380C2211yescharacteristic
21C2×C8×D283C2211yescharacteristic
22C2×C8×D283C2211yescharacteristic
23#22583605—21no—
24#22583601—21no—
25#22583596—21no—
26#22583595—21no—
27#22583590C2211yescharacteristic
28#22583590C2211yescharacteristic
29#22583587—21no—
30#22583586C2211yescharacteristic
31#22583583—21no—
32#22583581C2211yescharacteristic
33C4×Dic566C2211yescharacteristic
34C4×Dic566C2211yescharacteristic
35C4×D1132C2211yescharacteristic
36(C22⋊D283)⋊C4—21no—
37#22583568—21no—
38#22583568C2211yescharacteristic
39C4⋊C4×D283C2211yescharacteristic
40#22583544C2211yescharacteristic
41#22583543C2211yescharacteristic
42#22583541C2211yescharacteristic
43C4⋊(C283⋊C8)C2211yescharacteristic
44#22583535C2211yescharacteristic
45#22583535C2211yescharacteristic
46#22583534C2211yescharacteristic
47#22583533C2211yescharacteristic
48#22583533C2211yescharacteristic
49#22583531C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51(C2×D283)⋊C8C2211yescharacteristic
52#125×C283C2211yescharacteristic
53#124×C283C2211yescharacteristic
54#103×C283C2211yescharacteristic
55#103×C283C2211yescharacteristic
56#102×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58C4×C8×C283C2211yescharacteristic
59#17985391—22no—
60#17985391—41no—
61C2×Dic566—21no—
62C2×Dic566C2311yescharacteristic
63C2×Dic566C2311yescharacteristic
64Q8×D283—22no—
65Q8×D283—41no—
66C2×D1132D411yescharacteristic
67C2×C22⋊D283—21no—
68C2×C22⋊D283—21no—
69C22×Dic283—21no—
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72C2×C4×D283C2311yescharacteristic
73C2×C4×D283C2311yescharacteristic
74Dic1132—22no—
75#17985382—41no—
76#17985380—41no—
77C2×C283⋊C8C2311yescharacteristic
78C2×C283⋊C8C2311yescharacteristic
79C8×D283—41no—
80C8×D283—41no—
81C4⋊Dic283—21no—
82C4⋊Dic283—21no—
83C4⋊Dic283D411yescharacteristic
84C4⋊Dic283C2311yescharacteristic
85C4⋊Dic283C2311yescharacteristic
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88Dic283⋊C4—21no—
89Dic283⋊C4—21no—
90C22⋊Dic283—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4D411yescharacteristic
96(C2×D283)⋊C4D411yescharacteristic
97C4×Dic283—21no—
98C4×Dic283—21no—
99C4×Dic283—21no—
100C2×Q8×C283C2311yescharacteristic
101C2×D4×C283C2311yescharacteristic
102C2×C8×C283C2311yescharacteristic
103C2×C8×C283C2311yescharacteristic
104C4⋊C4×C283—21no—
105C4⋊C4×C283—21no—
106C4⋊C4×C283C2311yescharacteristic
107C4⋊C4×C283C2311yescharacteristic
108C22⋊C4×C283—21no—
109C22⋊C4×C283—21no—
110C42×C283C2311yescharacteristic
111C22×D283C2×D411yescharacteristic
112C22×D283C2×D411yescharacteristic
113Dic566—21no—
114Dic566—21no—
115Dic566—21no—
116Dic566—42no—
117Dic566#4112yes—
118D1132—22no—
119C22⋊D283—42no—
120C22⋊D283—42no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283—21no—
125C2×Dic283—42no—
126C2×Dic283C2×D411yescharacteristic
127C2×Dic283C2×D411yescharacteristic
128C4×D283—21no—
129C4×D283—21no—
130C4×D283—21no—
131C4×D283—21no—
132C4×D283—42no—
133C4×D283—42no—
134C283⋊C8—21no—
135C283⋊C8—21no—
136C23×C283—21no—
137Q8×C283—21no—
138Q8×C283—21no—
139D4×C283—21no—
140D4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283C2×D411yescharacteristic
145C2×C4×C283C2×D411yescharacteristic
146C2×C4×C283C2411yescharacteristic
147C8×C283—21no—
148C8×C283—21no—
149C22×C283—41no—
150C22×C283—41no—
151C22×C283—41no—
152C22×C283C22×D411yescharacteristic
153C2×D283—21no—
154C2×D283—21no—
155C2×D283—21no—
156C2×D283—21no—
157C2×D283—21no—
158C2×D283#13512yes—
159C4×C283—21no—
160C4×C283—21no—
161C4×C283—41no—
162C4×C283—41no—
163C4×C283—41no—
164C4×C283C2×#4111yescharacteristic
165C4×C283H(5,𝔽2)11yescharacteristic
166Dic283—21no—
167Dic283—21no—
168Dic283—22no—
169Dic283—41no—
170Dic283—41no—
171Dic283—41no—
172C2×C283—81no—
173C2×C283#54611yescharacteristic
174C2×C283C2×#13511yescharacteristic
175C2×C283#57811yescharacteristic
176D283—22no—
177D283—41no—
178C283#330011yescharacteristic, complemented, Sylow
179#3300—2831nomaximal, Sylow
180#552—2831no—
181#548—2831no—
182#488D28311yescharacteristic, complemented
183#485—2831no—
184#480—2831no—
185#479—2831no—
186#467—2831no—
187#465—2831no—
188#464—2831no—
189#452—2831no—
190#451—2831no—
191C4×Q16—2831no—
192C8×D4—2831no—
193#416—2831no—
194C2×#103—2831no—
195C2×#41—2831no—
196C22×Q8—2831no—
197C2×Q16—2831no—
198C2×Q16—2831no—
199C2×SD16—2831no—
200C22×C8—2831no—
201C22×C8—2831no—
202#126—5661no—
203#125—5661no—
204#125C2×D28311yescharacteristic
205#124—5661no—
206#124C2×D28311yescharacteristic
207#123—5661no—
208C22⋊Q8—2831no—
209C22⋊Q8—2831no—
210C22⋊Q8—2831no—
211C22⋊Q8—5661no—
212#121—2831no—
213#121—5661no—
214C4×Q8—2831no—
215C4×Q8—2831no—
216C4×D4—2831no—
217C4×D4—5661no—
218#117—2831no—
219#117—5661no—
220C2×C4⋊C4—2831no—
221#107—2831no—
222#107—2831no—
223#106—2831no—
224C4⋊C8—2831no—
225#103—2831no—
226#103—2831no—
227#103—2831no—
228#103—2831no—
229#103—2831no—
230#103C2×D28311yescharacteristic
231#103C2×D28311yescharacteristic
232#102—2831no—
233#102C2×D28311yescharacteristic
234#102C2×D28311yescharacteristic
235C22⋊C8—2831no—
236C22⋊C8—2831no—
237C4×C8C2×D28311yescharacteristic
238#41—5662no—
239#41—11321no—
240C2×Q8—2831no—
241C2×Q8—2831no—
242C2×Q8—5661no—
243C2×Q8—5662no—
244C2×Q8—11321no—
245C2×Q8C22×D28311yescharacteristic
246C2×D4—2831no—
247C2×D4—5661no—
248C2×D4—5661no—
249C2×D4C22×D28311yescharacteristic
250C22×C4—2831no—
251C22×C4—2831no—
252C22×C4—5661no—
253C22×C4—5661no—
254C22×C4—5661no—
255Q16—5662no—
256Q16—11321no—
257SD16—11321no—
258C2×C8—2831no—
259C2×C8—2831no—
260C2×C8—11321no—
261C2×C8—11321no—
262C2×C8C22×D28311yescharacteristic
263C2×C8C22×D28311yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—2831no—
267C4⋊C4—2831no—
268C4⋊C4—2831no—
269C4⋊C4—5661no—
270C4⋊C4—5661no—
271C4⋊C4—5661no—
272C4⋊C4—5661no—
273C4⋊C4—5661no—
274C4⋊C4—5661no—
275C4⋊C4C22×D28311yescharacteristic
276C4⋊C4C22×D28311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—2831no—
280C22⋊C4—2831no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C22⋊C4—5661no—
284C22⋊C4—5661no—
285C22⋊C4—5661no—
286C42—5661no—
287C42—5661no—
288C42—5661no—
289C42C22×D28311yescharacteristic
290C23—21no—
291C23—2831no—
292C23—2831no—
293Q8—21no—
294Q8—21no—
295Q8—2832no—
296Q8—5661no—
297Q8—5661no—
298Q8—5661no—
299Q8—11322no—
300D4—21no—
301D4—21no—
302D4—5662no—
303D4—11322no—
304D4—11322no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—2831no—
309C2×C4—2831no—
310C2×C4—5661no—
311C2×C4—5661no—
312C2×C4—5661no—
313C2×C4—5661no—
314C2×C4—5661no—
315C2×C4—5661no—
316C2×C4—5661no—
317C2×C4—5661no—
318C2×C4—11322no—
319C2×C4—11322no—
320C2×C4—11322no—
321C2×C4D4×D28311yescharacteristic
322C2×C4D4×D28311yescharacteristic
323C2×C4C23×D28311yescharacteristic
324C8—21no—
325C8—21no—
326C8—5661no—
327C8—5661no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—2832no—
332C22—5661no—
333C22—5661no—
334C22—5661no—
335C22—5661no—
336C22—5661no—
337C22C2×D4×D28311yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—5661no—
344C4—5661no—
345C4—5662no—
346C4—11321no—
347C4—11321no—
348C4—11321no—
349C4#41×D28311yescharacteristic
350C4#2258365611yescharacteristic
351C2—81no—
352C2—5662no—
353C2—11321no—
354C2#3182710811yescharacteristic
355C2#135×D28311yescharacteristic
356C2#3182727911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#488×C283C2
socleC22×C283C22×D4
prime radical#31827123C2
hypercenter#488D283
hypocenterC283#3300
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #31827153C2semidirect
3. #31826805C2semidirect
4. #31826777C2semidirect
5. #31826769C2semidirect
6. #31826705C2semidirect
7. #31826693C2semidirect
8. #31826684C2semidirect
9. #31826628C2semidirect
10. #31826622C2semidirect
11. C4×Dic1132C2semidirect
12. C8×D1132C2semidirect
13. #31826458C2semidirect
14. #103×D283C2semidirect
15. #488×C283C2semidirect
178. C283#3300semidirect
182. #488D283semidirect

Maximal subgroups

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

subgroupindex
#318271532
#318271232
#318268052
#318267772
#318267692
#318267052
#318266932
#318266842
#318266282
#318266222
C4×Dic11322
C8×D11322
#318264582
#103×D2832
#488×C2832
#3300283