Finite Group Databasebeta

← #49131475

Subgroups — #49131475

Order 36224.

372 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#31827077C211yesmaximal, characteristic, complemented
2#31826800C211yesmaximal, characteristic, complemented
3#31826795C211yesmaximal, characteristic, complemented
4#31826772C211yesmaximal, characteristic, complemented
5#31826765C211yesmaximal, characteristic, complemented
6#31826675C211yesmaximal, characteristic, complemented
7#31826670C211yesmaximal, characteristic, complemented
8#31826627C211yesmaximal, characteristic
9#31826627C211yesmaximal, characteristic
10#31826570C211yesmaximal, characteristic, complemented
11#31826565C211yesmaximal, characteristic, complemented
12C4×#17985382C211yesmaximal, characteristic, complemented
13C4×#17985380C211yesmaximal, characteristic, complemented
14#31826526C211yesmaximal, characteristic, complemented
15#520×C283C211yesmaximal, characteristic
16C2×#17985382C2211yescharacteristic
17C2×#17985382C2211yescharacteristic
18C2×#17985380C2211yescharacteristic
19C2×#17985380C2211yescharacteristic
20#22583610C2211yescharacteristic
21#22583603—21no—
22#22583603—21no—
23#22583602C2211yescharacteristic
24#22583600—21no—
25#22583600—21no—
26#22583589C2211yescharacteristic
27#22583589C2211yescharacteristic
28C4×Dic566C2211yescharacteristic
29C4×Dic566C2211yescharacteristic
30#22583543C2211yescharacteristic
31#22583543C2211yescharacteristic
32#22583541C2211yescharacteristic
33#22583541C2211yescharacteristic
34C4⋊(C283⋊C8)C2211yescharacteristic
35C4⋊(C283⋊C8)C2211yescharacteristic
36#22583534C2211yescharacteristic
37#22583534C2211yescharacteristic
38#22583533C2211yescharacteristic
39#22583533C2211yescharacteristic
40#22583533C2211yescharacteristic
41#22583533C2211yescharacteristic
42#22583531C2211yescharacteristic
43#22583531C2211yescharacteristic
44C22⋊(C283⋊C8)C2211yescharacteristic
45C22⋊(C283⋊C8)C2211yescharacteristic
46#22583521C2211yescharacteristic
47C4×C283⋊C8C2211yescharacteristic
48C2×#41×C283C2211yescharacteristic
49C4×Q8×C283C2211yescharacteristic
50C4×Q8×C283C2211yescharacteristic
51C4×D4×C283—21no—
52C4×D4×C283—21no—
53C4×D4×C283C2211yescharacteristic
54C4×D4×C283C2211yescharacteristic
55#117×C283—21no—
56#117×C283C2211yescharacteristic
57C2×C4⋊C4×C283—21no—
58C2×C4⋊C4×C283C2211yescharacteristic
59C2×Dic566C2311yescharacteristic
60C2×Dic566C2311yescharacteristic
61#17985382—22no—
62#17985382—22no—
63#17985380—22no—
64#17985380—22no—
65C2×C283⋊C8C2311yescharacteristic
66C2×C283⋊C8C2311yescharacteristic
67C2×C283⋊C8C2311yescharacteristic
68C2×C283⋊C8C2311yescharacteristic
69C4⋊Dic283—21no—
70C4⋊Dic283—21no—
71C4⋊Dic283C2311yescharacteristic
72C4⋊Dic283C2311yescharacteristic
73Dic283⋊C4—21no—
74Dic283⋊C4—21no—
75Dic283⋊C4—21no—
76Dic283⋊C4—21no—
77Dic283⋊C4—21no—
78Dic283⋊C4—21no—
79C22⋊Dic283—21no—
80C22⋊Dic283—21no—
81C4×Dic283—21no—
82C4×Dic283—21no—
83#41×C283—22no—
84#41×C283—22no—
85C2×Q8×C283C2311yescharacteristic
86C2×D4×C283—21no—
87C2×D4×C283C2311yescharacteristic
88C22×C4×C283—21no—
89C22×C4×C283—21no—
90C22×C4×C283—21no—
91C22×C4×C283—21no—
92C22×C4×C283C2311yescharacteristic
93C4⋊C4×C283—21no—
94C4⋊C4×C283—21no—
95C4⋊C4×C283—21no—
96C4⋊C4×C283D411yescharacteristic
97C4⋊C4×C283D411yescharacteristic
98C4⋊C4×C283C2311yescharacteristic
99C4⋊C4×C283C2311yescharacteristic
100C22⋊C4×C283—21no—
101C22⋊C4×C283—21no—
102C22⋊C4×C283D411yescharacteristic
103C22⋊C4×C283D411yescharacteristic
104C42×C283—21no—
105C42×C283—21no—
106C42×C283C2311yescharacteristic
107C42×C283C2311yescharacteristic
108Dic566—21no—
109Dic566—21no—
110Dic566—21no—
111Dic566—21no—
112C2×Dic283—21no—
113C2×Dic283—21no—
114C2×Dic283—21no—
115C2×Dic283—21no—
116C283⋊C8—21no—
117C283⋊C8—21no—
118C283⋊C8—21no—
119C283⋊C8—21no—
120C23×C283—21no—
121C23×C283C2×D411yescharacteristic
122Q8×C283—21no—
123Q8×C283#4112yes—
124D4×C283—24no—
125D4×C283—21no—
126D4×C283#4112yes—
127C2×C4×C283—24no—
128C2×C4×C283—21no—
129C2×C4×C283—21no—
130C2×C4×C283—21no—
131C2×C4×C283—21no—
132C2×C4×C283—21no—
133C2×C4×C283—81no—
134C2×C4×C283—81no—
135C2×C4×C283—81no—
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—22no—
144C22×C283—21no—
145C22×C283—21no—
146C22×C283—41no—
147C22×C283—41no—
148C22×C283C22×D411yescharacteristic
149C4×C283—21no—
150C4×C283—22no—
151C4×C283—21no—
152C4×C283—21no—
153C4×C283—21no—
154C4×C283—21no—
155C4×C283—41no—
156C4×C283—41no—
157C4×C283C2×#4111yescharacteristic
158C4×C283C2×#4111yescharacteristic
159Dic283—41no—
160Dic283—41no—
161Dic283—41no—
162Dic283—41no—
163C2×C283—41no—
164C2×C283—42no—
165C2×C283#52511yescharacteristic
166C2×C283#57711yescharacteristic
167C2×C283#57811yescharacteristic
168C283#312011yescharacteristic, complemented, Sylow
169#3120—2831nomaximal, Sylow
170#541—2831no—
171#520D28311yescharacteristic
172#484—2831no—
173#483—2831no—
174#479—2831no—
175#478—2831no—
176#462—2831no—
177#461—2831no—
178#452—2831no—
179#452—2831no—
180#441—2831no—
181#440—2831no—
182C4×Q16—2831no—
183C4×SD16—2831no—
184#433—2831no—
185C2×#41C2×D28311yescharacteristic
186C2×Q16—2831no—
187C2×Q16—2831no—
188C2×SD16—2831no—
189C2×SD16—2831no—
190C4⋊Q8—2831no—
191#126—5661no—
192#126—5661no—
193#125—2831no—
194#125—5661no—
195#125—5661no—
196C22⋊Q8—2831no—
197C22⋊Q8—2831no—
198C4×Q8—2831no—
199C4×Q8—2831no—
200C4×Q8C2×D28311yescharacteristic
201C4×Q8C2×D28311yescharacteristic
202C4×D4—21no—
203C4×D4—21no—
204C4×D4C2×D28311yescharacteristic
205C4×D4C2×D28311yescharacteristic
206#117—21no—
207#117C2×D28311yescharacteristic
208C2×C4⋊C4—21no—
209C2×C4⋊C4C2×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—
228#41—22no—
229#41—22no—
230C2×Q8—2831no—
231C2×Q8—2831no—
232C2×Q8C22×D28311yescharacteristic
233C2×D4—21no—
234C2×D4C22×D28311yescharacteristic
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
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—2831no—
252C4⋊C4—2831no—
253C4⋊C4—5661no—
254C4⋊C4—5661no—
255C4⋊C4—5661no—
256C4⋊C4—5661no—
257C4⋊C4—5661no—
258C4⋊C4—5661no—
259C4⋊C4—5661no—
260C4⋊C4—5661no—
261C4⋊C4C22⋊D28311yescharacteristic
262C4⋊C4C22⋊D28311yescharacteristic
263C4⋊C4C22×D28311yescharacteristic
264C4⋊C4C22×D28311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—5661no—
268C22⋊C4—5661no—
269C22⋊C4C22⋊D28311yescharacteristic
270C22⋊C4C22⋊D28311yescharacteristic
271C42—21no—
272C42—21no—
273C42—5661no—
274C42—5661no—
275C42C22×D28311yescharacteristic
276C42C22×D28311yescharacteristic
277C23—21no—
278C23C2×C22⋊D28311yescharacteristic
279Q8—21no—
280Q8—5661no—
281Q8—5661no—
282Q8—5661no—
283Q8—5661no—
284Q8#1798539212yes—
285D4—24no—
286D4—21no—
287D4#1798539212yes—
288C2×C4—24no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—5661no—
298C2×C4—5661no—
299C2×C4—5661no—
300C2×C4—5661no—
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—22no—
313C22—21no—
314C22—21no—
315C22—41no—
316C22—41no—
317C22C22×C22⋊D28311yescharacteristic
318C4—21no—
319C4—22no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—11321no—
327C4—11321no—
328C4—11321no—
329C4—11321no—
330C4C2×#1798539211yescharacteristic
331C4C2×#1798539211yescharacteristic
332C2—41no—
333C2—42no—
334C2#3182697611yescharacteristic
335C2#3182727611yescharacteristic
336C2#3182728011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#520×C283C2
socleC22×C283C22×D4
prime radicalC2×#41×C283C22
hypercenter#520D283
hypocenterC283#3120
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #31827077C2semidirect
2. #31826800C2semidirect
3. #31826795C2semidirect
4. #31826772C2semidirect
5. #31826765C2semidirect
6. #31826675C2semidirect
7. #31826670C2semidirect
10. #31826570C2semidirect
11. #31826565C2semidirect
12. C4×#17985382C2semidirect
13. C4×#17985380C2semidirect
14. #31826526C2semidirect
168. C283#3120semidirect

Maximal subgroups

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

subgroupindex
#318270772
#318268002
#318267952
#318267722
#318267652
#318266752
#318266702
#318266272
#318265702
#318265652
C4×#179853822
C4×#179853802
#318265262
#520×C2832
#3120283