Finite Group Databasebeta

← #49133329

Subgroups — #49133329

Order 36224.

380 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#31827185C211yesmaximal, characteristic, complemented
2#31827124C211yesmaximal, characteristic
3#31826825C211yesmaximal, characteristic, complemented
4#31826807C211yesmaximal, characteristic, complemented
5#31826790C211yesmaximal, characteristic, complemented
6#31826761C211yesmaximal, characteristic, complemented
7#31826711C211yesmaximal, characteristic, complemented
8#31826706C211yesmaximal, characteristic, complemented
9#31826688C211yesmaximal, characteristic, complemented
10#31826629C211yesmaximal, characteristic, complemented
11#31826623C211yesmaximal, characteristic, complemented
12#31826573C211yesmaximal, characteristic, complemented
13#31826475C211yesmaximal, characteristic, complemented
14#31826462C211yesmaximal, characteristic, complemented
15#435×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C22×Dic566C2211yescharacteristic
18C2×Dic1132C2211yescharacteristic
19C2×Dic1132C2211yescharacteristic
20C2×#17985381C2211yescharacteristic
21#22583610C2211yescharacteristic
22#22583603—21no—
23#22583603—21no—
24#22583598C2211yescharacteristic
25#22583597—21no—
26#22583596—21no—
27#22583589C2211yescharacteristic
28#22583589C2211yescharacteristic
29#22583589C2211yescharacteristic
30#22583588—21no—
31#22583584C2211yescharacteristic
32#22583582—21no—
33C4×Dic566C2211yescharacteristic
34C4×Dic566C2211yescharacteristic
35#22583575—21no—
36(C22⋊D283)⋊C4—21no—
37#22583569C2211yescharacteristic
38#22583569C2211yescharacteristic
39#22583544C2211yescharacteristic
40#22583544C2211yescharacteristic
41#22583542C2211yescharacteristic
42#22583535C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583535C2211yescharacteristic
45#22583535C2211yescharacteristic
46#22583535C2211yescharacteristic
47#22583535C2211yescharacteristic
48#22583535C2211yescharacteristic
49#22583532C2211yescharacteristic
50#22583532C2211yescharacteristic
51#22583532C2211yescharacteristic
52C2×M16×C283C2211yescharacteristic
53C22×C8×C283C2211yescharacteristic
54C4×D4×C283C2211yescharacteristic
55C4⋊C8×C283C2211yescharacteristic
56C22⋊C8×C283C2211yescharacteristic
57C22⋊C8×C283C2211yescharacteristic
58#97×C283C2211yescharacteristic
59#17985392—22no—
60#17985392—41no—
61C2×Dic566—22no—
62C2×Dic566—21no—
63C2×Dic566—21no—
64C2×Dic566—41no—
65C2×Dic566C2311yescharacteristic
66C2×Dic566C2311yescharacteristic
67C2×Dic566C2311yescharacteristic
68C2×D1132C2311yescharacteristic
69C2×C22⋊D283—21no—
70C2×C22⋊D283—21no—
71C22×Dic283—21no—
72C2×C4×D283—21no—
73Dic1132—22no—
74Dic1132—41no—
75#17985381—41no—
76C4⋊Dic283—21no—
77C4⋊Dic283C2311yescharacteristic
78C4⋊Dic283C2311yescharacteristic
79C4⋊Dic283C2311yescharacteristic
80C4⋊Dic283C2311yescharacteristic
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86C22⋊Dic283—21no—
87C22⋊Dic283—21no—
88C22⋊Dic283—21no—
89C22⋊Dic283—21no—
90C22⋊Dic283—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—
97C4×Dic283—21no—
98C2×D4×C283D411yescharacteristic
99C22×C4×C283C2311yescharacteristic
100C22×C4×C283C2311yescharacteristic
101M16×C283—41no—
102C2×C8×C283—41no—
103C2×C8×C283C2311yescharacteristic
104C2×C8×C283C2311yescharacteristic
105C2×C8×C283C2311yescharacteristic
106C2×C8×C283C2311yescharacteristic
107C4⋊C4×C283D411yescharacteristic
108C22⋊C4×C283D411yescharacteristic
109C22⋊C4×C283D411yescharacteristic
110C42×C283C2311yescharacteristic
111C22×D283—21no—
112Dic566—21no—
113Dic566—21no—
114Dic566—21no—
115Dic566—21no—
116Dic566—21no—
117Dic566—42no—
118Dic566—42no—
119Dic566#4112yes—
120D1132—21no—
121D1132—21no—
122C22⋊D283—42no—
123C22⋊D283—42no—
124C2×Dic283—21no—
125C2×Dic283—21no—
126C2×Dic283—21no—
127C2×Dic283—21no—
128C2×Dic283—21no—
129C2×Dic283—21no—
130C2×Dic283—21no—
131C2×Dic283—42no—
132C4×D283—42no—
133C23×C283C2×D411yescharacteristic
134C23×C283C2×D411yescharacteristic
135D4×C283—41no—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283—21no—
140C2×C4×C283C2×D411yescharacteristic
141C2×C4×C283C2×D411yescharacteristic
142C2×C4×C283C2×D411yescharacteristic
143C2×C4×C283C2×D411yescharacteristic
144C2×C4×C283C2411yescharacteristic
145C8×C283—21no—
146C8×C283—21no—
147C8×C283—21no—
148C8×C283—21no—
149C22×C283—21no—
150C22×C283—21no—
151C22×C283—21no—
152C22×C283—21no—
153C22×C283—21no—
154C22×C283—21no—
155C22×C283C22×D411yescharacteristic
156C2×D283—41no—
157C2×D283—41no—
158C2×D283—41no—
159C4×C283—21no—
160C4×C283—21no—
161C4×C283—21no—
162C4×C283—21no—
163C4×C283C2×#4111yescharacteristic
164C4×C283H(5,𝔽2)11yescharacteristic
165Dic283—22no—
166Dic283—41no—
167Dic283—41no—
168Dic283—41no—
169Dic283—41no—
170Dic283—41no—
171Dic283—41no—
172C2×C283—41no—
173C2×C283—41no—
174C2×C283#54611yescharacteristic
175C2×C283#57511yescharacteristic
176C2×C283#57811yescharacteristic
177D283—81no—
178C283#331311yescharacteristic, complemented, Sylow
179#3313—2831nomaximal, Sylow
180#556—2831no—
181#548—2831no—
182#489—2831no—
183#485—2831no—
184#482—2831no—
185#477—2831no—
186#468—2831no—
187#467—2831no—
188#464—2831no—
189#452—2831no—
190#451—2831no—
191#441—2831no—
192#435D28311yescharacteristic, complemented
193#419—2831no—
194#416—2831no—
195C2×#41—2831no—
196C22×Q8—2831no—
197C2×Q16—2831no—
198C2×Q16—2831no—
199C2×SD16—2831no—
200C2×M16C2×D28311yescharacteristic
201C22×C8C2×D28311yescharacteristic
202C4⋊Q8—2831no—
203#126—5661no—
204#126—5661no—
205#124—2831no—
206#124—5661no—
207#124—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×Q8—5661no—
217C4×D4—5661no—
218C4×D4C2×D28311yescharacteristic
219#117—2831no—
220#117—2831no—
221#107—2831no—
222#107—2831no—
223#106—2831no—
224C4⋊C8C2×D28311yescharacteristic
225#103—2831no—
226#103—2831no—
227#103—2831no—
228#103—2831no—
229#103—2831no—
230#103—2831no—
231#103—2831no—
232#102—2831no—
233#102—2831no—
234#102—2831no—
235C22⋊C8C2×D28311yescharacteristic
236C22⋊C8C2×D28311yescharacteristic
237#97C2×D28311yescharacteristic
238#41—5662no—
239#41—11321no—
240C2×Q8—2831no—
241C2×Q8—2831no—
242C2×Q8—2831no—
243C2×Q8—5662no—
244C2×Q8—5661no—
245C2×Q8—5661no—
246C2×Q8—11321no—
247C2×D4—2831no—
248C2×D4—5661no—
249C2×D4—5661no—
250C2×D4D113211yescharacteristic
251C22×C4—5661no—
252C22×C4—5661no—
253C22×C4C22×D28311yescharacteristic
254C22×C4C22×D28311yescharacteristic
255Q16—5662no—
256Q16—11321no—
257SD16—11321no—
258M16—41no—
259C2×C8—41no—
260C2×C8C22×D28311yescharacteristic
261C2×C8C22×D28311yescharacteristic
262C2×C8C22×D28311yescharacteristic
263C2×C8C22×D28311yescharacteristic
264C4⋊C4—2831no—
265C4⋊C4—2831no—
266C4⋊C4—2831no—
267C4⋊C4—2831no—
268C4⋊C4—5661no—
269C4⋊C4—5661no—
270C4⋊C4—5661no—
271C4⋊C4—5661no—
272C4⋊C4—5661no—
273C4⋊C4—5661no—
274C4⋊C4D113211yescharacteristic
275C22⋊C4—5661no—
276C22⋊C4—5661no—
277C22⋊C4—5661no—
278C22⋊C4—5661no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C22⋊C4D113211yescharacteristic
284C22⋊C4D113211yescharacteristic
285C42—5661no—
286C42—5661no—
287C42—5661no—
288C42—5661no—
289C42C22×D28311yescharacteristic
290C23—5661no—
291C23C2×D113211yescharacteristic
292C23C2×D113211yescharacteristic
293Q8—2832no—
294Q8—5661no—
295Q8—5661no—
296Q8—5661no—
297Q8—5661no—
298Q8—5661no—
299Q8—11322no—
300Q8—11322no—
301D4—41no—
302D4—5661no—
303D4—5661no—
304D4—11322no—
305D4—11322no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—5661no—
311C2×C4—5661no—
312C2×C4—5661no—
313C2×C4—5661no—
314C2×C4—5661no—
315C2×C4—5661no—
316C2×C4—5661no—
317C2×C4—11322no—
318C2×C4—11322no—
319C2×C4C2×D113211yescharacteristic
320C2×C4C2×D113211yescharacteristic
321C2×C4C2×D113211yescharacteristic
322C2×C4C2×D113211yescharacteristic
323C2×C4C23×D28311yescharacteristic
324C8—21no—
325C8—21no—
326C8—21no—
327C8—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—11321no—
335C22—11321no—
336C22—11321no—
337C22C22×D113211yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—5662no—
343C4—11321no—
344C4—11321no—
345C4—11321no—
346C4—11321no—
347C4—11321no—
348C4—11321no—
349C4#41×D28311yescharacteristic
350C4#2258365511yescharacteristic
351C2—41no—
352C2—41no—
353C2—22641no—
354C2#3182711011yescharacteristic
355C2#3182726511yescharacteristic
356C2#3182728211yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#435×C283C2
socleC22×C283C22×D4
prime radical#31827124C2
hypercenter#435D283
hypocenterC283#3313
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #31827185C2semidirect
3. #31826825C2semidirect
4. #31826807C2semidirect
5. #31826790C2semidirect
6. #31826761C2semidirect
7. #31826711C2semidirect
8. #31826706C2semidirect
9. #31826688C2semidirect
10. #31826629C2semidirect
11. #31826623C2semidirect
12. #31826573C2semidirect
13. #31826475C2semidirect
14. #31826462C2semidirect
15. #435×C283C2semidirect
178. C283#3313semidirect
192. #435D283semidirect

Maximal subgroups

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

subgroupindex
#318271852
#318271242
#318268252
#318268072
#318267902
#318267612
#318267112
#318267062
#318266882
#318266292
#318266232
#318265732
#318264752
#318264622
#435×C2832
#3313283