Finite Group Databasebeta

← #49131234

Subgroups — #49131234

Order 36224.

398 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827044C211yesmaximal, characteristic
2#31826946C211yesmaximal, characteristic, complemented
3#31826808C211yesmaximal, characteristic, complemented
4#31826807C211yesmaximal, characteristic, complemented
5#31826802C211yesmaximal, characteristic, complemented
6#31826800C211yesmaximal, characteristic, complemented
7#31826788C211yesmaximal, characteristic, complemented
8#31826786C211yesmaximal, characteristic, complemented
9#31826777C211yesmaximal, characteristic, complemented
10#31826506C211yesmaximal, characteristic, complemented
11#107×D283C211yesmaximal, characteristic, complemented
12#31826463C211yesmaximal, characteristic, complemented
13#31826458C211yesmaximal, characteristic, complemented
14#31826430C211yesmaximal, characteristic, complemented
15#480×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C2×#17985391C2211yescharacteristic
18C2×#17985375C2211yescharacteristic
19C2×C8×D283C2211yescharacteristic
20#22583590C2211yescharacteristic
21#22583589C2211yescharacteristic
22#22583587—21no—
23#22583583—21no—
24#22583582—21no—
25#22583581—21no—
26#22583581C2211yescharacteristic
27#22583575—21no—
28#22583572—21no—
29C4×C22⋊D283—21no—
30C4×C22⋊D283—21no—
31#22583569C2211yescharacteristic
32#22583568C2211yescharacteristic
33#22583568C2211yescharacteristic
34C4⋊C4×D283C2211yescharacteristic
35C4⋊C4×D283C2211yescharacteristic
36C4⋊C4×D283C2211yescharacteristic
37#22583544C2211yescharacteristic
38#22583543C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583543C2211yescharacteristic
41#22583542C2211yescharacteristic
42#22583541C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583535C2211yescharacteristic
45#22583533C2211yescharacteristic
46#22583533C2211yescharacteristic
47#22583531C2211yescharacteristic
48#22583531C2211yescharacteristic
49C22⋊(C283⋊C8)C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51(C2×D283)⋊C8C2211yescharacteristic
52#121×C283C2211yescharacteristic
53C2×C4⋊C4×C283C2211yescharacteristic
54#107×C283C2211yescharacteristic
55#107×C283C2211yescharacteristic
56#102×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58C22⋊C8×C283C2211yescharacteristic
59#17985392—22no—
60#17985392—22no—
61#17985391—22no—
62#17985391—22no—
63C2×Dic566D411yescharacteristic
64C2×Dic566C2311yescharacteristic
65C2×D1132D411yescharacteristic
66C2×C22⋊D283—21no—
67C2×C22⋊D283—21no—
68C2×C22⋊D283D411yescharacteristic
69C2×C22⋊D283D411yescharacteristic
70C22×Dic283—21no—
71C2×C4×D283—21no—
72C2×C4×D283—21no—
73C2×C4×D283—21no—
74C2×C4×D283C2311yescharacteristic
75C2×C4×D283C2311yescharacteristic
76#17985375—22no—
77C2×C283⋊C8C2311yescharacteristic
78C2×C283⋊C8C2311yescharacteristic
79C8×D283—22no—
80C4⋊Dic283—21no—
81C4⋊Dic283C2311yescharacteristic
82C4⋊Dic283C2311yescharacteristic
83C4⋊Dic283C2311yescharacteristic
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88C22⋊Dic283—21no—
89C22⋊Dic283—21no—
90C22⋊Dic283—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94C4×Dic283—21no—
95C4×Dic283—21no—
96C4×Dic283—21no—
97C2×D4×C283—21no—
98C2×D4×C283C2311yescharacteristic
99C22×C4×C283—21no—
100C22×C4×C283C2311yescharacteristic
101C2×C8×C283C2311yescharacteristic
102C2×C8×C283C2311yescharacteristic
103C4⋊C4×C283—21no—
104C4⋊C4×C283C2311yescharacteristic
105C4⋊C4×C283C2311yescharacteristic
106C4⋊C4×C283C2311yescharacteristic
107C22⋊C4×C283—21no—
108C22×D283C2×D411yescharacteristic
109C22×D283C2×D411yescharacteristic
110Dic566—22no—
111Dic566—21no—
112Dic566—21no—
113D1132—22no—
114C22⋊D283—22no—
115C22⋊D283—22no—
116C22⋊D283—42no—
117C22⋊D283—81no—
118C2×Dic283—21no—
119C2×Dic283—21no—
120C2×Dic283—21no—
121C2×Dic283—21no—
122C2×Dic283—42no—
123C2×Dic283C2×D411yescharacteristic
124C2×Dic283C2×D411yescharacteristic
125C4×D283—21no—
126C4×D283—21no—
127C4×D283—81no—
128C4×D283—81no—
129C4×D283—81no—
130C4×D283#4112yes—
131C4×D283#4112yes—
132C283⋊C8—21no—
133C283⋊C8—21no—
134C23×C283—21no—
135C23×C283C2×D411yescharacteristic
136D4×C283—21no—
137D4×C283—21no—
138D4×C283—81no—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283—81no—
145C2×C4×C283C2×D411yescharacteristic
146C2×C4×C283C2411yescharacteristic
147C8×C283—21no—
148C8×C283—21no—
149C22×C283—21no—
150C22×C283—21no—
151C22×C283—21no—
152C22×C283—41no—
153C22×C283—41no—
154C22×C283—41no—
155C22×C283C22×D411yescharacteristic
156C2×D283—21no—
157C2×D283—21no—
158C2×D283—21no—
159C2×D283—21no—
160C2×D283—21no—
161C2×D283#12312yes—
162C4×C283—21no—
163C4×C283—41no—
164C4×C283—41no—
165C4×C283—41no—
166C4×C283C2×#4111yescharacteristic
167C4×C283C2×#4111yescharacteristic
168Dic283—21no—
169Dic283—41no—
170Dic283—41no—
171Dic283—41no—
172Dic283—41no—
173Dic283#12312yes—
174C2×C283—41no—
175C2×C283—81no—
176C2×C283C2×#12311yescharacteristic
177C2×C283#57611yescharacteristic
178C2×C283#57811yescharacteristic
179D283—22no—
180D283—41no—
181C283#309811yescharacteristic, complemented, Sylow
182#3098—2831nomaximal, Sylow
183#537—2831no—
184#520—2831no—
185#485—2831no—
186#485—2831no—
187#484—2831no—
188#484—2831no—
189#482—2831no—
190#482—2831no—
191#480—2831no—
192#480D28311yescharacteristic, complemented
193#428—2831no—
194C2×#107—2831no—
195#417—2831no—
196#416—2831no—
197#408—2831no—
198C2×#41—2831no—
199C2×#41—2831no—
200C2×M16—2831no—
201C22×C8—2831no—
202C22⋊Q8—2831no—
203C22⋊Q8—2831no—
204C22⋊Q8—5661no—
205#121—2831no—
206#121—5661no—
207#121—5661no—
208#121—5661no—
209#121C2×D28311yescharacteristic
210C4×Q8—5661no—
211C4×D4—5661no—
212C4×D4—5661no—
213C4×D4—5661no—
214#117—2831no—
215#117—2831no—
216#117—2831no—
217C2×C4⋊C4—2831no—
218C2×C4⋊C4—2831no—
219C2×C4⋊C4—2831no—
220C2×C4⋊C4C2×D28311yescharacteristic
221#107—2831no—
222#107—2831no—
223#107—2831no—
224#107—2831no—
225#107C2×D28311yescharacteristic
226#107C2×D28311yescharacteristic
227#106—2831no—
228#106—2831no—
229#103—2831no—
230#103—2831no—
231#103—2831no—
232#103—2831no—
233#102—2831no—
234#102—2831no—
235#102C2×D28311yescharacteristic
236#102C2×D28311yescharacteristic
237C22⋊C8—2831no—
238C22⋊C8—2831no—
239C22⋊C8—2831no—
240C22⋊C8C2×D28311yescharacteristic
241#41—5662no—
242#41—5662no—
243#41—5662no—
244#41—5662no—
245C2×Q8—2831no—
246C2×Q8—2831no—
247C2×D4—21no—
248C2×D4—2831no—
249C2×D4—2831no—
250C2×D4—2831no—
251C2×D4—5661no—
252C2×D4—5661no—
253C2×D4C22×D28311yescharacteristic
254C22×C4—21no—
255C22×C4—2831no—
256C22×C4—2831no—
257C22×C4—5661no—
258C22×C4—5661no—
259C22×C4—5661no—
260C22×C4—5661no—
261C22×C4C22×D28311yescharacteristic
262M16—5662no—
263C2×C8—2831no—
264C2×C8—2831no—
265C2×C8—5662no—
266C2×C8C22×D28311yescharacteristic
267C2×C8C22×D28311yescharacteristic
268C4⋊C4—21no—
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⋊C4C22×D28311yescharacteristic
278C4⋊C4C22×D28311yescharacteristic
279C4⋊C4C22×D28311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C22⋊C4—5661no—
284C22⋊C4—5661no—
285C22⋊C4—5661no—
286C22⋊C4—5661no—
287C42—5661no—
288C42—5661no—
289C42—5661no—
290C23—21no—
291C23—2831no—
292C23—2831no—
293C23D4×D28311yescharacteristic
294Q8—5662no—
295Q8—5661no—
296Q8—5661no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—5662no—
301D4—5662no—
302D4—5662no—
303D4—11322no—
304D4—22641no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—2831no—
312C2×C4—2832no—
313C2×C4—2832no—
314C2×C4—2831no—
315C2×C4—5661no—
316C2×C4—5661no—
317C2×C4—5661no—
318C2×C4—5661no—
319C2×C4—5661no—
320C2×C4—5661no—
321C2×C4—11322no—
322C2×C4—22641no—
323C2×C4—22641no—
324C2×C4—22641no—
325C2×C4D4×D28311yescharacteristic
326C2×C4C23×D28311yescharacteristic
327C8—21no—
328C8—21no—
329C8—5661no—
330C8—5661no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—2832no—
338C22—5661no—
339C22—5661no—
340C22—5661no—
341C22—5661no—
342C22—5661no—
343C22C2×D4×D28311yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—2832no—
349C4—5661no—
350C4—11321no—
351C4—11321no—
352C4—11321no—
353C4—11321no—
354C4#41×D28311yescharacteristic
355C4#41×D28311yescharacteristic
356C2—41no—
357C2—81no—
358C2—5662no—
359C2—11321no—
360C2#123×D28311yescharacteristic
361C2#3182726611yescharacteristic
362C2#3182728111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#480×C283C2
socleC22×C283C22×D4
prime radical#31827044C2
hypercenter#480D283
hypocenterC283#3098
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #31826946C2semidirect
3. #31826808C2semidirect
4. #31826807C2semidirect
5. #31826802C2semidirect
6. #31826800C2semidirect
7. #31826788C2semidirect
8. #31826786C2semidirect
9. #31826777C2semidirect
10. #31826506C2semidirect
11. #107×D283C2semidirect
12. #31826463C2semidirect
13. #31826458C2semidirect
14. #31826430C2semidirect
15. #480×C283C2semidirect
181. C283#3098semidirect
192. #480D283semidirect

Maximal subgroups

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

subgroupindex
#318270442
#318269462
#318268082
#318268072
#318268022
#318268002
#318267882
#318267862
#318267772
#318265062
#107×D2832
#318264632
#318264582
#318264302
#480×C2832
#3098283