Finite Group Databasebeta

← #49131484

Subgroups — #49131484

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#31826942C211yesmaximal, characteristic, complemented
2#31826803C211yesmaximal, characteristic, complemented
3#31826786C211yesmaximal, characteristic
4#31826757C211yesmaximal, characteristic, complemented
5#31826747C211yesmaximal, characteristic, complemented
6#31826684C211yesmaximal, characteristic, complemented
7#31826684C211yesmaximal, characteristic, complemented
8#31826620C211yesmaximal, characteristic, complemented
9#31826603C211yesmaximal, characteristic
10#31826570C211yesmaximal, characteristic, complemented
11#31826565C211yesmaximal, characteristic, complemented
12C4×#17985382C211yesmaximal, characteristic, complemented
13C4×#17985380C211yesmaximal, characteristic, complemented
14#31826526C211yesmaximal, characteristic, complemented
15#542×C283C211yesmaximal, characteristic
16C22×Dic566C2211yescharacteristic
17C2×#17985382C2211yescharacteristic
18C2×#17985382C2211yescharacteristic
19C2×#17985380C2211yescharacteristic
20C2×#17985380C2211yescharacteristic
21C4×Dic566C2211yescharacteristic
22C4×Dic566C2211yescharacteristic
23C4×Dic566C2211yescharacteristic
24C4×Dic566C2211yescharacteristic
25#22583575—21no—
26#22583575—21no—
27#22583569C2211yescharacteristic
28#22583566—21no—
29#22583566—21no—
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
48C4⋊Q8×C283C2211yescharacteristic
49#126×C283—21no—
50#124×C283—21no—
51#124×C283C2211yescharacteristic
52#123×C283—21no—
53C22⋊Q8×C283—21no—
54C22⋊Q8×C283C2211yescharacteristic
55#121×C283C2211yescharacteristic
56C4×Q8×C283C2211yescharacteristic
57C4×D4×C283C2211yescharacteristic
58#117×C283C2211yescharacteristic
59C2×Dic566—22no—
60C2×Dic566—22no—
61C2×Dic566—21no—
62C2×Dic566C2311yescharacteristic
63C2×Dic566C2311yescharacteristic
64C22×Dic283—21no—
65#17985382—22no—
66#17985382—22no—
67#17985380—22no—
68#17985380—22no—
69C2×C283⋊C8C2311yescharacteristic
70C2×C283⋊C8C2311yescharacteristic
71C2×C283⋊C8C2311yescharacteristic
72C2×C283⋊C8C2311yescharacteristic
73C4⋊Dic283C2311yescharacteristic
74C4⋊Dic283C2311yescharacteristic
75Dic283⋊C4—21no—
76Dic283⋊C4—21no—
77Dic283⋊C4—21no—
78Dic283⋊C4—21no—
79C22⋊Dic283—21no—
80C4×Dic283—21no—
81C4×Dic283—21no—
82C4×Dic283—21no—
83C4×Dic283—21no—
84C4×Dic283—21no—
85C2×Q8×C283—21no—
86C2×Q8×C283C2311yescharacteristic
87C2×D4×C283—21no—
88C2×D4×C283C2311yescharacteristic
89C22×C4×C283—21no—
90C22×C4×C283C2311yescharacteristic
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×C283—21no—
100C22⋊C4×C283—21no—
101C22⋊C4×C283—21no—
102C22⋊C4×C283—21no—
103C22⋊C4×C283D411yescharacteristic
104C22⋊C4×C283D411yescharacteristic
105C42×C283—21no—
106C42×C283C2311yescharacteristic
107C42×C283C2311yescharacteristic
108Dic566—24no—
109Dic566—21no—
110Dic566—21no—
111Dic566#4112yes—
112Dic566#4112yes—
113C2×Dic283—24no—
114C2×Dic283—21no—
115C2×Dic283—21no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C283⋊C8—21no—
119C283⋊C8—21no—
120C283⋊C8—21no—
121C283⋊C8—21no—
122C23×C283—21no—
123C23×C283C2×D411yescharacteristic
124Q8×C283—21no—
125Q8×C283—21no—
126Q8×C283—81no—
127D4×C283—21no—
128D4×C283—21no—
129D4×C283—81no—
130C2×C4×C283—21no—
131C2×C4×C283—21no—
132C2×C4×C283—21no—
133C2×C4×C283—21no—
134C2×C4×C283—21no—
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—21no—
144C22×C283—21no—
145C22×C283—41no—
146C22×C283—41no—
147C22×C283—41no—
148C22×C283C22×D411yescharacteristic
149C4×C283—21no—
150C4×C283—21no—
151C4×C283—21no—
152C4×C283—21no—
153C4×C283—21no—
154C4×C283—41no—
155C4×C283—41no—
156C4×C283—41no—
157C4×C283C2×#4111yescharacteristic
158C4×C283C2×#4111yescharacteristic
159Dic283—22no—
160Dic283—22no—
161Dic283—41no—
162Dic283—41no—
163C2×C283—41no—
164C2×C283—81no—
165C2×C283#52511yescharacteristic
166C2×C283#57711yescharacteristic
167C2×C283#57811yescharacteristic
168C283#312111yescharacteristic, complemented, Sylow
169#3121—2831nomaximal, Sylow
170#542D28311yescharacteristic
171#519—2831no—
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×Q8—2831no—
186C2×Q16—2831no—
187C2×Q16—2831no—
188C2×SD16—2831no—
189C2×SD16—2831no—
190C4⋊Q8C2×D28311yescharacteristic
191#126—21no—
192#124—21no—
193#124C2×D28311yescharacteristic
194#123—21no—
195C22⋊Q8—21no—
196C22⋊Q8C2×D28311yescharacteristic
197#121C2×D28311yescharacteristic
198C4×Q8—2831no—
199C4×Q8—2831no—
200C4×Q8—2831no—
201C4×Q8—2831no—
202C4×Q8—5661no—
203C4×Q8—5661no—
204C4×Q8C2×D28311yescharacteristic
205C4×D4C2×D28311yescharacteristic
206#117—2831no—
207#117—5661no—
208#117—5661no—
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—21no—
229C2×Q8—2831no—
230C2×Q8—2831no—
231C2×Q8—5662no—
232C2×Q8—5662no—
233C2×Q8—5661no—
234C2×Q8C22×D28311yescharacteristic
235C2×D4—21no—
236C2×D4C22×D28311yescharacteristic
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—2831no—
252C4⋊C4—2831no—
253C4⋊C4—5661no—
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—21no—
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—5661no—
267C22⋊C4C22⋊D28311yescharacteristic
268C22⋊C4C22⋊D28311yescharacteristic
269C42—21no—
270C42—5661no—
271C42—5661no—
272C42—5661no—
273C42—5661no—
274C42—5661no—
275C42C22×D28311yescharacteristic
276C42C22×D28311yescharacteristic
277C23—21no—
278C23C2×C22⋊D28311yescharacteristic
279Q8—21no—
280Q8—21no—
281Q8—81no—
282Q8—2832no—
283Q8—2832no—
284Q8—5664no—
285Q8—5661no—
286Q8—5661no—
287D4—21no—
288D4—21no—
289D4—81no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—81no—
296C2×C4—5664no—
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—21no—
313C22—21no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22C22×C22⋊D28311yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—5662no—
327C4—5662no—
328C4—11321no—
329C4—11321no—
330C4#41×D28311yescharacteristic
331C4#41×D28311yescharacteristic
332C2—41no—
333C2—81no—
334C2#3182697211yescharacteristic
335C2#3182727611yescharacteristic
336C2#3182728011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#542×C283C2
socleC22×C283C22×D4
prime radical#121×C283C22
hypercenter#542D283
hypocenterC283#3121
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #31826942C2semidirect
2. #31826803C2semidirect
4. #31826757C2semidirect
5. #31826747C2semidirect
6. #31826684C2semidirect
7. #31826684C2semidirect
8. #31826620C2semidirect
10. #31826570C2semidirect
11. #31826565C2semidirect
12. C4×#17985382C2semidirect
13. C4×#17985380C2semidirect
14. #31826526C2semidirect
168. C283#3121semidirect

Maximal subgroups

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

subgroupindex
#318269422
#318268032
#318267862
#318267572
#318267472
#318266842
#318266202
#318266032
#318265702
#318265652
C4×#179853822
C4×#179853802
#318265262
#542×C2832
#3121283