Finite Group Databasebeta

← #49131490

Subgroups — #49131490

Order 36224.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827086C211yesmaximal, characteristic
2#31826806C211yesmaximal, characteristic, complemented
3#31826789C211yesmaximal, characteristic
4#31826760C211yesmaximal, characteristic, complemented
5#31826750C211yesmaximal, characteristic, complemented
6#31826687C211yesmaximal, characteristic, complemented
7#31826687C211yesmaximal, characteristic, complemented
8#31826621C211yesmaximal, characteristic, complemented
9#31826604C211yesmaximal, characteristic
10#31826570C211yesmaximal, characteristic, complemented
11#31826563C211yesmaximal, characteristic, complemented
12C4×#17985382C211yesmaximal, characteristic, complemented
13C4×#17985379C211yesmaximal, characteristic, complemented
14#31826526C211yesmaximal, characteristic, complemented
15#519×C283C211yesmaximal, characteristic, complemented
16C2×#17985382C2211yescharacteristic
17C2×#17985382C2211yescharacteristic
18C2×#17985379C2211yescharacteristic
19C2×#17985379C2211yescharacteristic
20#22583610C2211yescharacteristic
21#22583605—21no—
22#22583598C2211yescharacteristic
23#22583596—21no—
24#22583592—21no—
25#22583589C2211yescharacteristic
26#22583588—21no—
27#22583584C2211yescharacteristic
28C4×Dic566C2211yescharacteristic
29C4×D1132C2211yescharacteristic
30#22583543C2211yescharacteristic
31#22583543C2211yescharacteristic
32#22583541C2211yescharacteristic
33#22583541C2211yescharacteristic
34C4⋊(C283⋊C8)C2211yescharacteristic
35C4⋊(C283⋊C8)C2211yescharacteristic
36#22583534C2211yescharacteristic
37#22583534C2211yescharacteristic
38#22583534C2211yescharacteristic
39#22583534C2211yescharacteristic
40#22583533C2211yescharacteristic
41#22583533C2211yescharacteristic
42#22583530C2211yescharacteristic
43#22583530C2211yescharacteristic
44C22⋊(C283⋊C8)C2211yescharacteristic
45C22⋊(C283⋊C8)C2211yescharacteristic
46#22583521C2211yescharacteristic
47C4×C283⋊C8C2211yescharacteristic
48C22×Q8×C283C2211yescharacteristic
49C4×Q8×C283—21no—
50C4×Q8×C283—21no—
51C4×Q8×C283C2211yescharacteristic
52C4×Q8×C283C2211yescharacteristic
53C4×Q8×C283C2211yescharacteristic
54C4×Q8×C283C2211yescharacteristic
55#117×C283—21no—
56#117×C283—21no—
57#117×C283C2211yescharacteristic
58#117×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566C2311yescharacteristic
61C2×D1132C2311yescharacteristic
62C2×C22⋊D283—21no—
63C2×C4×D283—21no—
64#17985382—22no—
65#17985382—22no—
66#17985379—22no—
67#17985379—22no—
68C2×C283⋊C8C2311yescharacteristic
69C2×C283⋊C8C2311yescharacteristic
70C2×C283⋊C8C2311yescharacteristic
71C2×C283⋊C8C2311yescharacteristic
72C4⋊Dic283—21no—
73C4⋊Dic283C2311yescharacteristic
74C4⋊Dic283C2311yescharacteristic
75Dic283⋊C4—21no—
76Dic283⋊C4—21no—
77C22⋊Dic283—21no—
78(C2×D283)⋊C4—21no—
79(C2×D283)⋊C4—21no—
80(C2×D283)⋊C4—21no—
81(C2×D283)⋊C4—21no—
82C4×Dic283—21no—
83C2×Q8×C283—22no—
84C2×Q8×C283—22no—
85C2×Q8×C283—21no—
86C2×Q8×C283C2311yescharacteristic
87C2×Q8×C283C2311yescharacteristic
88C22×C4×C283—21no—
89C22×C4×C283C2311yescharacteristic
90C4⋊C4×C283—21no—
91C4⋊C4×C283—21no—
92C4⋊C4×C283—21no—
93C4⋊C4×C283—21no—
94C4⋊C4×C283D411yescharacteristic
95C4⋊C4×C283D411yescharacteristic
96C4⋊C4×C283C2311yescharacteristic
97C4⋊C4×C283C2311yescharacteristic
98C22⋊C4×C283—21no—
99C22⋊C4×C283D411yescharacteristic
100C22⋊C4×C283D411yescharacteristic
101C42×C283—21no—
102C42×C283—21no—
103C42×C283—21no—
104C42×C283—21no—
105C42×C283—21no—
106C42×C283C2311yescharacteristic
107C42×C283C2311yescharacteristic
108C22×D283—21no—
109Dic566—21no—
110Dic566—21no—
111Dic566—81no—
112D1132—21no—
113D1132—21no—
114C22⋊D283—81no—
115C2×Dic283—21no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C4×D283—81no—
119C283⋊C8—21no—
120C283⋊C8—21no—
121C283⋊C8—21no—
122C283⋊C8—21no—
123C23×C283C2×D411yescharacteristic
124Q8×C283—24no—
125Q8×C283—21no—
126Q8×C283—21no—
127Q8×C283#4112yes—
128Q8×C283#4112yes—
129C2×C4×C283—24no—
130C2×C4×C283—21no—
131C2×C4×C283—21no—
132C2×C4×C283—21no—
133C2×C4×C283—21no—
134C2×C4×C283—21no—
135C2×C4×C283—21no—
136C2×C4×C283C2×D411yescharacteristic
137C2×C4×C283C2×D411yescharacteristic
138C2×C4×C283C2×D411yescharacteristic
139C2×C4×C283C2×D411yescharacteristic
140C2×C4×C283C2×D411yescharacteristic
141C2×C4×C283C2411yescharacteristic
142C22×C283—21no—
143C22×C283—21no—
144C22×C283—21no—
145C22×C283C22×D411yescharacteristic
146C2×D283—41no—
147C2×D283—41no—
148C2×D283—41no—
149C4×C283—22no—
150C4×C283—22no—
151C4×C283—21no—
152C4×C283—21no—
153C4×C283—21no—
154C4×C283—21no—
155C4×C283—21no—
156C4×C283—41no—
157C4×C283—41no—
158C4×C283C2×#4111yescharacteristic
159C4×C283C2×#4111yescharacteristic
160Dic283—41no—
161Dic283—41no—
162Dic283—41no—
163C2×C283—41no—
164C2×C283#52511yescharacteristic
165C2×C283#57711yescharacteristic
166C2×C283#57811yescharacteristic
167D283—81no—
168C283#312111yescharacteristic, complemented, Sylow
169#3121—2831nomaximal, Sylow
170#542—2831no—
171#519D28311yescharacteristic, complemented
172#485—2831no—
173#482—2831no—
174#477—2831no—
175#475—2831no—
176#464—2831no—
177#464—2831no—
178#451—2831no—
179#448—2831no—
180#441—2831no—
181#440—2831no—
182C4×Q16—2831no—
183C4×SD16—2831no—
184#433—2831no—
185C22×Q8C2×D28311yescharacteristic
186C2×Q16—2831no—
187C2×Q16—2831no—
188C2×SD16—2831no—
189C2×SD16—2831no—
190C4⋊Q8—2831no—
191#126—5661no—
192#124—2831no—
193#124—5661no—
194#123—5661no—
195C22⋊Q8—2831no—
196C22⋊Q8—5661no—
197#121—2831no—
198C4×Q8—21no—
199C4×Q8—21no—
200C4×Q8—2831no—
201C4×Q8C2×D28311yescharacteristic
202C4×Q8C2×D28311yescharacteristic
203C4×Q8C2×D28311yescharacteristic
204C4×Q8C2×D28311yescharacteristic
205C4×D4—2831no—
206#117—21no—
207#117—21no—
208#117C2×D28311yescharacteristic
209#117C2×D28311yescharacteristic
210#107—2831no—
211#107—2831no—
212#106—2831no—
213#106—2831no—
214C4⋊C8—2831no—
215C4⋊C8—2831no—
216#103—2831no—
217#103—2831no—
218#103—2831no—
219#103—2831no—
220#103—2831no—
221#103—2831no—
222#102—2831no—
223#102—2831no—
224C22⋊C8—2831no—
225C22⋊C8—2831no—
226#97—2831no—
227C4×C8—2831no—
228C2×Q8—22no—
229C2×Q8—22no—
230C2×Q8—21no—
231C2×Q8—2831no—
232C2×Q8—5661no—
233C2×Q8C22×D28311yescharacteristic
234C2×Q8C22×D28311yescharacteristic
235C2×D4—2831no—
236C2×D4—5661no—
237C22×C4—21no—
238C22×C4—5661no—
239C22×C4C22×D28311yescharacteristic
240Q16—5662no—
241Q16—5662no—
242SD16—5662no—
243SD16—5662no—
244C2×C8—2831no—
245C2×C8—2831no—
246C2×C8—2831no—
247C2×C8—2831no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—2831no—
253C4⋊C4—2831no—
254C4⋊C4—5661no—
255C4⋊C4—5661no—
256C4⋊C4—5661no—
257C4⋊C4C22⋊D28311yescharacteristic
258C4⋊C4C22⋊D28311yescharacteristic
259C4⋊C4C22×D28311yescharacteristic
260C4⋊C4C22×D28311yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—5661no—
263C22⋊C4—5661no—
264C22⋊C4—5661no—
265C22⋊C4—5661no—
266C22⋊C4—5661no—
267C22⋊C4C22⋊D28311yescharacteristic
268C22⋊C4C22⋊D28311yescharacteristic
269C42—21no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42—5661no—
275C42C22×D28311yescharacteristic
276C42C22×D28311yescharacteristic
277C23—5661no—
278C23C2×C22⋊D28311yescharacteristic
279Q8—24no—
280Q8—21no—
281Q8—21no—
282Q8—5661no—
283Q8—5661no—
284Q8—22641no—
285Q8#1798539212yes—
286Q8#1798539212yes—
287D4—5661no—
288D4—5661no—
289D4—22641no—
290C2×C4—24no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—5661no—
298C2×C4—5661no—
299C2×C4—5661no—
300C2×C4—22641no—
301C2×C4C2×C22⋊D28311yescharacteristic
302C2×C4C2×C22⋊D28311yescharacteristic
303C2×C4C2×C22⋊D28311yescharacteristic
304C2×C4C2×C22⋊D28311yescharacteristic
305C2×C4C2×C22⋊D28311yescharacteristic
306C2×C4C23×D28311yescharacteristic
307C8—5661no—
308C8—5661no—
309C8—5661no—
310C8—5661no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—11321no—
315C22—11321no—
316C22—11321no—
317C22C22×C22⋊D28311yescharacteristic
318C4—22no—
319C4—22no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—11321no—
328C4—11321no—
329C4—11321no—
330C4C2×#1798539211yescharacteristic
331C4C2×#1798539211yescharacteristic
332C2—41no—
333C2—22641no—
334C2#3182697611yescharacteristic
335C2#3182727311yescharacteristic
336C2#3182728011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#519×C283C2
socleC22×C283C22×D4
prime radical#22583584C22
hypercenter#519D283
hypocenterC283#3121
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
2. #31826806C2semidirect
4. #31826760C2semidirect
5. #31826750C2semidirect
6. #31826687C2semidirect
7. #31826687C2semidirect
8. #31826621C2semidirect
10. #31826570C2semidirect
11. #31826563C2semidirect
12. C4×#17985382C2semidirect
13. C4×#17985379C2semidirect
14. #31826526C2semidirect
15. #519×C283C2semidirect
168. C283#3121semidirect
171. #519D283semidirect

Maximal subgroups

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

subgroupindex
#318270862
#318268062
#318267892
#318267602
#318267502
#318266872
#318266212
#318266042
#318265702
#318265632
C4×#179853822
C4×#179853792
#318265262
#519×C2832
#3121283