Finite Group Databasebeta

← #49133369

Subgroups — #49133369

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#31827176C211yesmaximal, characteristic, complemented
2#31827127C211yesmaximal, characteristic
3#31826827C211yesmaximal, characteristic, complemented
4#31826797C211yesmaximal, characteristic, complemented
5#31826785C211yesmaximal, characteristic, complemented
6#31826724C211yesmaximal, characteristic, complemented
7#31826695C211yesmaximal, characteristic, complemented
8#31826688C211yesmaximal, characteristic, complemented
9#31826630C211yesmaximal, characteristic, complemented
10#31826622C211yesmaximal, characteristic, complemented
11#31826570C211yesmaximal, characteristic, complemented
12#31826535C211yesmaximal, characteristic, complemented
13#31826465C211yesmaximal, characteristic, complemented
14#103×D283C211yesmaximal, characteristic, complemented
15#475×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×Q8×D283C2211yescharacteristic
18C2×Dic1132C2211yescharacteristic
19C2×#17985382C2211yescharacteristic
20C2×#17985381C2211yescharacteristic
21C2×#17985375C2211yescharacteristic
22C2×C8×D283C2211yescharacteristic
23#22583601—21no—
24#22583598—21no—
25#22583598C2211yescharacteristic
26#22583590—21no—
27#22583590C2211yescharacteristic
28#22583590C2211yescharacteristic
29#22583590C2211yescharacteristic
30#22583586—21no—
31#22583586—21no—
32#22583585—21no—
33#22583585C2211yescharacteristic
34C4×Dic566C2211yescharacteristic
35C4×D1132—21no—
36C4×D1132C2211yescharacteristic
37#22583572—21no—
38C4⋊C4×D283C2211yescharacteristic
39C4⋊C4×D283C2211yescharacteristic
40#22583541C2211yescharacteristic
41#22583535C2211yescharacteristic
42#22583534C2211yescharacteristic
43#22583533C2211yescharacteristic
44#22583533C2211yescharacteristic
45#22583533C2211yescharacteristic
46#22583532C2211yescharacteristic
47#22583530C2211yescharacteristic
48#22583530C2211yescharacteristic
49(C2×D283)⋊C8C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51#22583521C2211yescharacteristic
52C4⋊Q8×C283C2211yescharacteristic
53C4×Q8×C283C2211yescharacteristic
54#106×C283C2211yescharacteristic
55#106×C283C2211yescharacteristic
56C4⋊C8×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#103×C283C2211yescharacteristic
59#17985393—22no—
60#17985393—41no—
61C2×Dic566—21no—
62C2×Dic566C2311yescharacteristic
63C2×Dic566C2311yescharacteristic
64Q8×D283—22no—
65Q8×D283—41no—
66C2×D1132—21no—
67C2×D1132—21no—
68C2×D1132D411yescharacteristic
69C2×D1132C2311yescharacteristic
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72C2×C4×D283—21no—
73C2×C4×D283—21no—
74C2×C4×D283C2311yescharacteristic
75C2×C4×D283C2311yescharacteristic
76Dic1132—41no—
77#17985382—22no—
78#17985381—41no—
79#17985375—41no—
80C2×C283⋊C8C2311yescharacteristic
81C2×C283⋊C8C2311yescharacteristic
82C8×D283—41no—
83C4⋊Dic283—21no—
84C4⋊Dic283—21no—
85C4⋊Dic283—21no—
86C4⋊Dic283D411yescharacteristic
87C4⋊Dic283C2311yescharacteristic
88Dic283⋊C4—21no—
89Dic283⋊C4—21no—
90Dic283⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4—21no—
96(C2×D283)⋊C4—21no—
97(C2×D283)⋊C4D411yescharacteristic
98(C2×D283)⋊C4D411yescharacteristic
99C4×Dic283—21no—
100C2×Q8×C283—21no—
101C2×Q8×C283C2311yescharacteristic
102C2×C8×C283C2311yescharacteristic
103C2×C8×C283C2311yescharacteristic
104C4⋊C4×C283—21no—
105C4⋊C4×C283—21no—
106C4⋊C4×C283C2311yescharacteristic
107C4⋊C4×C283C2311yescharacteristic
108C4⋊C4×C283C2311yescharacteristic
109C42×C283—21no—
110C42×C283C2311yescharacteristic
111C22×D283—21no—
112C22×D283C2×D411yescharacteristic
113C22×D283C2×D411yescharacteristic
114Dic566—21no—
115Dic566—21no—
116Dic566—21no—
117Dic566—21no—
118Dic566—42no—
119D1132—22no—
120D1132—21no—
121D1132—21no—
122D1132—42no—
123D1132—42no—
124C2×Dic283—21no—
125C2×Dic283—21no—
126C2×Dic283—21no—
127C2×Dic283C2×D411yescharacteristic
128C2×Dic283C2×D411yescharacteristic
129C4×D283—21no—
130C4×D283—21no—
131C4×D283—21no—
132C4×D283—21no—
133C4×D283—42no—
134C4×D283—42no—
135C4×D283—81no—
136C4×D283—81no—
137C283⋊C8—21no—
138C283⋊C8—21no—
139Q8×C283—21no—
140Q8×C283—81no—
141Q8×C283#4112yes—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—21no—
146C2×C4×C283C2×D411yescharacteristic
147C2×C4×C283C2×D411yescharacteristic
148C2×C4×C283C2411yescharacteristic
149C8×C283—21no—
150C8×C283—21no—
151C22×C283C22×D411yescharacteristic
152C2×D283—21no—
153C2×D283—21no—
154C2×D283—21no—
155C2×D283—21no—
156C2×D283—21no—
157C2×D283—41no—
158C2×D283—41no—
159C2×D283—41no—
160C2×D283#13712yes—
161C4×C283—22no—
162C4×C283—21no—
163C4×C283—21no—
164C4×C283—41no—
165C4×C283—41no—
166C4×C283—41no—
167C4×C283C2×#4111yescharacteristic
168C4×C283H(5,𝔽2)11yescharacteristic
169Dic283—21no—
170Dic283—21no—
171Dic283—41no—
172Dic283—41no—
173Dic283—41no—
174C2×C283#54611yescharacteristic
175C2×C283C2×#13711yescharacteristic
176C2×C283#57711yescharacteristic
177D283—22no—
178D283—41no—
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#475D28311yescharacteristic, complemented
188#470—2831no—
189#465—2831no—
190#464—2831no—
191#452—2831no—
192#451—2831no—
193#441—2831no—
194#435—2831no—
195#417—2831no—
196C2×#103—2831no—
197C2×#41—2831no—
198C22×Q8—2831no—
199C2×Q16—2831no—
200C2×Q16—2831no—
201C2×SD16—2831no—
202C2×M16—2831no—
203C22×C8—2831no—
204C4⋊Q8C2×D28311yescharacteristic
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×Q8C2×D28311yescharacteristic
218C4×D4—2831no—
219C4×D4—5661no—
220C4×D4—5661no—
221C2×C4⋊C4—2831no—
222C2×C4⋊C4—2831no—
223#106—2831no—
224#106C2×D28311yescharacteristic
225#106C2×D28311yescharacteristic
226C4⋊C8C2×D28311yescharacteristic
227#103—2831no—
228#103—2831no—
229#103—2831no—
230#103—2831no—
231#103—2831no—
232#103C2×D28311yescharacteristic
233#103C2×D28311yescharacteristic
234#102—2831no—
235#102—2831no—
236#102—2831no—
237C22⋊C8—2831no—
238C22⋊C8—2831no—
239#97—2831no—
240#41—5662no—
241#41—11321no—
242C2×Q8—21no—
243C2×Q8—2831no—
244C2×Q8—2831no—
245C2×Q8—5661no—
246C2×Q8—5662no—
247C2×Q8—11321no—
248C2×Q8C22×D28311yescharacteristic
249C2×D4—2831no—
250C2×D4—2831no—
251C2×D4—5661no—
252C2×D4—5661no—
253C22×C4—2831no—
254C22×C4—2831no—
255C22×C4—5661no—
256C22×C4—5661no—
257C22×C4—5661no—
258C22×C4—5661no—
259Q16—5662no—
260Q16—11321no—
261SD16—11321no—
262M16—11321no—
263C2×C8—2831no—
264C2×C8—2831no—
265C2×C8—11321no—
266C2×C8C22×D28311yescharacteristic
267C2×C8C22×D28311yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—21no—
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⋊C4C22×D28311yescharacteristic
279C4⋊C4C22×D28311yescharacteristic
280C4⋊C4C22×D28311yescharacteristic
281C22⋊C4—2831no—
282C22⋊C4—2831no—
283C22⋊C4—5661no—
284C22⋊C4—5661no—
285C22⋊C4—5661no—
286C22⋊C4—5661no—
287C22⋊C4—5661no—
288C22⋊C4—5661no—
289C42—21no—
290C42—5661no—
291C42C22×D28311yescharacteristic
292C23—2831no—
293C23—2831no—
294C23—5661no—
295Q8—21no—
296Q8—81no—
297Q8—5661no—
298Q8—5661no—
299Q8—5661no—
300Q8—5661no—
301Q8—11322no—
302Q8#1798539312yes—
303D4—5662no—
304D4—5661no—
305D4—5661no—
306D4—11322no—
307D4—11322no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—2831no—
313C2×C4—2831no—
314C2×C4—5661no—
315C2×C4—5661no—
316C2×C4—5661no—
317C2×C4—5661no—
318C2×C4—5661no—
319C2×C4—5661no—
320C2×C4—5661no—
321C2×C4—11322no—
322C2×C4—11322no—
323C2×C4—22641no—
324C2×C4—22641no—
325C2×C4D4×D28311yescharacteristic
326C2×C4D4×D28311yescharacteristic
327C2×C4C23×D28311yescharacteristic
328C8—21no—
329C8—21no—
330C8—5661no—
331C8—5661no—
332C22—2832no—
333C22—5661no—
334C22—5661no—
335C22—5661no—
336C22—5661no—
337C22—5661no—
338C22—11321no—
339C22—11321no—
340C22—11321no—
341C22C2×D4×D28311yescharacteristic
342C4—21no—
343C4—21no—
344C4—22no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—5661no—
349C4—5661no—
350C4—11321no—
351C4—11321no—
352C4—11321no—
353C4C2×#1798539311yescharacteristic
354C4#2258365611yescharacteristic
355C2—5662no—
356C2—11321no—
357C2—22641no—
358C2#3182710611yescharacteristic
359C2#137×D28311yescharacteristic
360C2#3182727111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#475×C283C2
socleC22×C283C22×D4
prime radical#31827127C2
hypercenter#475D283
hypocenterC283#3316
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #31827176C2semidirect
3. #31826827C2semidirect
4. #31826797C2semidirect
5. #31826785C2semidirect
6. #31826724C2semidirect
7. #31826695C2semidirect
8. #31826688C2semidirect
9. #31826630C2semidirect
10. #31826622C2semidirect
11. #31826570C2semidirect
12. #31826535C2semidirect
13. #31826465C2semidirect
14. #103×D283C2semidirect
15. #475×C283C2semidirect
180. C283#3316semidirect
187. #475D283semidirect

Maximal subgroups

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

subgroupindex
#318271762
#318271272
#318268272
#318267972
#318267852
#318267242
#318266952
#318266882
#318266302
#318266222
#318265702
#318265352
#318264652
#103×D2832
#475×C2832
#3316283