Finite Group Databasebeta

← #49133374

Subgroups — #49133374

Order 36224.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827172C211yesmaximal, characteristic, complemented
2#31827124C211yesmaximal, characteristic
3#31826825C211yesmaximal, characteristic, complemented
4#31826796C211yesmaximal, characteristic, complemented
5#31826784C211yesmaximal, characteristic, complemented
6#31826751C211yesmaximal, characteristic, complemented
7#31826723C211yesmaximal, characteristic, complemented
8#31826694C211yesmaximal, characteristic, complemented
9#31826688C211yesmaximal, characteristic, complemented
10#31826629C211yesmaximal, characteristic, complemented
11#31826623C211yesmaximal, characteristic, complemented
12#31826573C211yesmaximal, characteristic, complemented
13#31826467C211yesmaximal, characteristic, complemented
14C2×#22583535C211yesmaximal, characteristic, complemented
15#435×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C22×Dic566C2211yescharacteristic
18C2×Dic1132C2211yescharacteristic
19C2×Dic1132C2211yescharacteristic
20C2×#17985381C2211yescharacteristic
21#22583610C2211yescharacteristic
22#22583601—21no—
23#22583598C2211yescharacteristic
24#22583596—21no—
25#22583589C2211yescharacteristic
26#22583589C2211yescharacteristic
27#22583589C2211yescharacteristic
28#22583588—21no—
29#22583587—21no—
30#22583587—21no—
31#22583584C2211yescharacteristic
32#22583582—21no—
33C4×Dic566C2211yescharacteristic
34C4×Dic566C2211yescharacteristic
35D4×Dic283—21no—
36(C22⋊D283)⋊C4—21no—
37C2×C4⋊Dic283C2211yescharacteristic
38C2×C4⋊Dic283C2211yescharacteristic
39#22583542C2211yescharacteristic
40#22583542C2211yescharacteristic
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—
72C22×Dic283—21no—
73C22×Dic283—21no—
74C2×C4×D283—21no—
75Dic1132—22no—
76Dic1132—41no—
77#17985381—41no—
78C4⋊Dic283—21no—
79C4⋊Dic283—21no—
80C4⋊Dic283—21no—
81C4⋊Dic283C2311yescharacteristic
82C4⋊Dic283C2311yescharacteristic
83C4⋊Dic283C2311yescharacteristic
84C4⋊Dic283C2311yescharacteristic
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88Dic283⋊C4—21no—
89Dic283⋊C4—21no—
90C22⋊Dic283—21no—
91C22⋊Dic283—21no—
92C22⋊Dic283—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4—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—81no—
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—
132C2×Dic283—81no—
133C2×Dic283—81no—
134C4×D283—42no—
135C23×C283C2×D411yescharacteristic
136C23×C283C2×D411yescharacteristic
137D4×C283—22no—
138C2×C4×C283—21no—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283C2×D411yescharacteristic
143C2×C4×C283C2×D411yescharacteristic
144C2×C4×C283C2×D411yescharacteristic
145C2×C4×C283C2×D411yescharacteristic
146C2×C4×C283C2411yescharacteristic
147C8×C283—21no—
148C8×C283—21no—
149C8×C283—21no—
150C8×C283—21no—
151C22×C283—21no—
152C22×C283—21no—
153C22×C283—21no—
154C22×C283—21no—
155C22×C283—21no—
156C22×C283#13712yes—
157C22×C283C22×D411yescharacteristic
158C2×D283—41no—
159C2×D283—41no—
160C2×D283—41no—
161C4×C283—21no—
162C4×C283—21no—
163C4×C283—21no—
164C4×C283—21no—
165C4×C283C2×#4111yescharacteristic
166C4×C283H(5,𝔽2)11yescharacteristic
167Dic283—22no—
168Dic283—41no—
169Dic283—41no—
170Dic283—41no—
171Dic283—41no—
172Dic283—41no—
173Dic283—41no—
174C2×C283—22no—
175C2×C283—41no—
176C2×C283#54611yescharacteristic
177C2×C283C2×#13711yescharacteristic
178C2×C283#57711yescharacteristic
179D283—81no—
180C283#331611yescharacteristic, complemented, Sylow
181#3316—2831nomaximal, Sylow
182#554—2831no—
183#548—2831no—
184#489—2831no—
185#483—2831no—
186#481—2831no—
187#475—2831no—
188#470—2831no—
189#465—2831no—
190#464—2831no—
191#452—2831no—
192#451—2831no—
193#441—2831no—
194#435D28311yescharacteristic, complemented
195#417—2831no—
196C2×#103—2831no—
197C2×#41—2831no—
198C22×Q8—2831no—
199C2×Q16—2831no—
200C2×Q16—2831no—
201C2×SD16—2831no—
202C2×M16C2×D28311yescharacteristic
203C22×C8C2×D28311yescharacteristic
204C4⋊Q8—2831no—
205#125—5661no—
206#124—2831no—
207#124—5661no—
208C22⋊Q8—2831no—
209C22⋊Q8—2831no—
210C22⋊Q8—2831no—
211C22⋊Q8—5661no—
212C22⋊Q8—5661no—
213C22⋊Q8—5661no—
214#121—2831no—
215#121—5661no—
216C4×Q8—2831no—
217C4×Q8—2831no—
218C4×D4—5661no—
219C4×D4—5661no—
220C4×D4C2×D28311yescharacteristic
221C2×C4⋊C4—2831no—
222C2×C4⋊C4—2831no—
223#106—2831no—
224#106—2831no—
225#106—2831no—
226C4⋊C8C2×D28311yescharacteristic
227#103—2831no—
228#103—2831no—
229#103—2831no—
230#103—2831no—
231#103—2831no—
232#103—2831no—
233#103—2831no—
234#102—2831no—
235#102—2831no—
236#102—2831no—
237C22⋊C8C2×D28311yescharacteristic
238C22⋊C8C2×D28311yescharacteristic
239#97C2×D28311yescharacteristic
240#41—5662no—
241#41—11321no—
242C2×Q8—2831no—
243C2×Q8—2831no—
244C2×Q8—2831no—
245C2×Q8—5662no—
246C2×Q8—5661no—
247C2×Q8—5661no—
248C2×Q8—11321no—
249C2×D4—2831no—
250C2×D4—5661no—
251C2×D4—5661no—
252C2×D4D113211yescharacteristic
253C22×C4—5661no—
254C22×C4—5661no—
255C22×C4—5661no—
256C22×C4—5661no—
257C22×C4C22×D28311yescharacteristic
258C22×C4C22×D28311yescharacteristic
259Q16—5662no—
260Q16—11321no—
261SD16—11321no—
262M16—41no—
263C2×C8—41no—
264C2×C8C22×D28311yescharacteristic
265C2×C8C22×D28311yescharacteristic
266C2×C8C22×D28311yescharacteristic
267C2×C8C22×D28311yescharacteristic
268C4⋊C4—2831no—
269C4⋊C4—2831no—
270C4⋊C4—2831no—
271C4⋊C4—2831no—
272C4⋊C4—5661no—
273C4⋊C4—5661no—
274C4⋊C4—5661no—
275C4⋊C4—5661no—
276C4⋊C4—5661no—
277C4⋊C4—5661no—
278C4⋊C4—5661no—
279C4⋊C4—5661no—
280C4⋊C4D113211yescharacteristic
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C22⋊C4—5661no—
284C22⋊C4—5661no—
285C22⋊C4—5661no—
286C22⋊C4—5661no—
287C22⋊C4D113211yescharacteristic
288C22⋊C4D113211yescharacteristic
289C42—5661no—
290C42—5661no—
291C42C22×D28311yescharacteristic
292C23—5661no—
293C23C2×D113211yescharacteristic
294C23C2×D113211yescharacteristic
295Q8—2832no—
296Q8—5661no—
297Q8—5661no—
298Q8—5661no—
299Q8—5661no—
300Q8—5661no—
301Q8—11322no—
302Q8—22641no—
303D4—22no—
304D4—5661no—
305D4—5661no—
306D4—11322no—
307D4—11322no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—5661no—
313C2×C4—5661no—
314C2×C4—5661no—
315C2×C4—5661no—
316C2×C4—5661no—
317C2×C4—5661no—
318C2×C4—5661no—
319C2×C4—11322no—
320C2×C4—11322no—
321C2×C4—22641no—
322C2×C4—22641no—
323C2×C4C2×D113211yescharacteristic
324C2×C4C2×D113211yescharacteristic
325C2×C4C2×D113211yescharacteristic
326C2×C4C2×D113211yescharacteristic
327C2×C4C23×D28311yescharacteristic
328C8—21no—
329C8—21no—
330C8—21no—
331C8—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—11321no—
338C22—11321no—
339C22—11321no—
340C22#2258364312yes—
341C22C22×D113211yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—5662no—
347C4—11321no—
348C4—11321no—
349C4—11321no—
350C4—11321no—
351C4—11321no—
352C4—11321no—
353C4#41×D28311yescharacteristic
354C4#2258365511yescharacteristic
355C2—22no—
356C2—41no—
357C2—22641no—
358C2#3182711011yescharacteristic
359C2C2×#2258364311yescharacteristic
360C2#3182727711yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#435×C283C2
socleC22×C283C22×D4
prime radical#31827124C2
hypercenter#435D283
hypocenterC283#3316
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. #31827172C2semidirect
3. #31826825C2semidirect
4. #31826796C2semidirect
5. #31826784C2semidirect
6. #31826751C2semidirect
7. #31826723C2semidirect
8. #31826694C2semidirect
9. #31826688C2semidirect
10. #31826629C2semidirect
11. #31826623C2semidirect
12. #31826573C2semidirect
13. #31826467C2semidirect
14. C2×#22583535C2semidirect
15. #435×C283C2semidirect
180. C283#3316semidirect
194. #435D283semidirect

Maximal subgroups

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

subgroupindex
#318271722
#318271242
#318268252
#318267962
#318267842
#318267512
#318267232
#318266942
#318266882
#318266292
#318266232
#318265732
#318264672
C2×#225835352
#435×C2832
#3316283