Finite Group Databasebeta

← #49133880

Subgroups — #49133880

Order 36224.

354 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827179C211yesmaximal, characteristic
2#31827170C211yesmaximal, characteristic, complemented
3#31826869C211yesmaximal, characteristic, complemented
4#31826808C211yesmaximal, characteristic, complemented
5#31826807C211yesmaximal, characteristic, complemented
6#31826777C211yesmaximal, characteristic, complemented
7#31826759C211yesmaximal, characteristic, complemented
8#31826753C211yesmaximal, characteristic, complemented
9#31826710C211yesmaximal, characteristic, complemented
10#31826709C211yesmaximal, characteristic, complemented
11#31826556C211yesmaximal, characteristic, complemented
12#31826540C211yesmaximal, characteristic, complemented
13#31826506C211yesmaximal, characteristic, complemented
14#31826505C211yesmaximal, characteristic, complemented
15#480×C283C211yesmaximal, characteristic, complemented
16C2×#17985380C2211yescharacteristic
17C2×#17985376C2211yescharacteristic
18C2×#17985375C2211yescharacteristic
19#22583609C2211yescharacteristic
20#22583609C2211yescharacteristic
21#22583600—21no—
22#22583597—21no—
23#22583596—21no—
24#22583590C2211yescharacteristic
25#22583589—21no—
26#22583589C2211yescharacteristic
27#22583588—21no—
28#22583582—21no—
29#22583581C2211yescharacteristic
30#22583575C2211yescharacteristic
31D4×Dic283C2211yescharacteristic
32C4×C22⋊D283—21no—
33C4×C22⋊D283C2211yescharacteristic
34#22583569C2211yescharacteristic
35#22583568C2211yescharacteristic
36#22583566—21no—
37C4⋊C4×D283C2211yescharacteristic
38#22583544C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583543C2211yescharacteristic
41#22583543C2211yescharacteristic
42#22583542C2211yescharacteristic
43#22583541C2211yescharacteristic
44#22583541C2211yescharacteristic
45Dic283⋊C8C2211yescharacteristic
46#22583535C2211yescharacteristic
47#22583535C2211yescharacteristic
48#22583533C2211yescharacteristic
49#22583531C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52#121×C283C2211yescharacteristic
53C2×C4⋊C4×C283C2211yescharacteristic
54#107×C283C2211yescharacteristic
55#107×C283C2211yescharacteristic
56#102×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58C22⋊C8×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566—21no—
61C2×Dic566C2311yescharacteristic
62C2×C22⋊D283—21no—
63C2×C22⋊D283D411yescharacteristic
64C22×Dic283—21no—
65C2×C4×D283—21no—
66C2×C4×D283C2311yescharacteristic
67#17985380—22no—
68#17985376—22no—
69#17985375—22no—
70C2×C283⋊C8C2311yescharacteristic
71C2×C283⋊C8C2311yescharacteristic
72C4⋊Dic283—21no—
73C4⋊Dic283C2311yescharacteristic
74C4⋊Dic283C2311yescharacteristic
75C4⋊Dic283C2311yescharacteristic
76Dic283⋊C4—21no—
77Dic283⋊C4—21no—
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4D411yescharacteristic
82C22⋊Dic283—21no—
83C22⋊Dic283—21no—
84C22⋊Dic283—21no—
85C22⋊Dic283—21no—
86C22⋊Dic283D411yescharacteristic
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4D411yescharacteristic
90C4×Dic283—21no—
91C4×Dic283—21no—
92C4×Dic283—21no—
93C4×Dic283C2311yescharacteristic
94C2×D4×C283—21no—
95C2×D4×C283C2311yescharacteristic
96C22×C4×C283—21no—
97C22×C4×C283C2311yescharacteristic
98C2×C8×C283C2311yescharacteristic
99C2×C8×C283C2311yescharacteristic
100C4⋊C4×C283—21no—
101C4⋊C4×C283C2311yescharacteristic
102C4⋊C4×C283C2311yescharacteristic
103C4⋊C4×C283C2311yescharacteristic
104C22⋊C4×C283—21no—
105C22×D283C2×D411yescharacteristic
106Dic566—21no—
107Dic566—21no—
108Dic566—81no—
109Dic566—81no—
110C22⋊D283—22no—
111C22⋊D283—81no—
112C2×Dic283—21no—
113C2×Dic283—21no—
114C2×Dic283—21no—
115C2×Dic283—21no—
116C2×Dic283—42no—
117C2×Dic283C2×D411yescharacteristic
118C2×Dic283C2×D411yescharacteristic
119C2×Dic283C2×D411yescharacteristic
120C4×D283—21no—
121C4×D283—21no—
122C4×D283—81no—
123C283⋊C8—21no—
124C283⋊C8#4112yes—
125C23×C283—21no—
126C23×C283C2×D411yescharacteristic
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×C283C2411yescharacteristic
138C8×C283—21no—
139C8×C283—21no—
140C22×C283—21no—
141C22×C283—21no—
142C22×C283—21no—
143C22×C283—41no—
144C22×C283—41no—
145C22×C283—41no—
146C22×C283C22×D411yescharacteristic
147C2×D283—21no—
148C2×D283—21no—
149C2×D283—21no—
150C4×C283—21no—
151C4×C283—41no—
152C4×C283—41no—
153C4×C283—41no—
154C4×C283C2×#4111yescharacteristic
155C4×C2832−1+411yescharacteristic
156Dic283—21no—
157Dic283—21no—
158Dic283—41no—
159Dic283—41no—
160Dic283—41no—
161Dic283—41no—
162Dic283#13712yes—
163C2×C283—41no—
164C2×C283—81no—
165C2×C283#54711yescharacteristic
166C2×C283C2×#13711yescharacteristic
167C2×C283#57611yescharacteristic
168D283—41no—
169C283#335711yescharacteristic, complemented, Sylow
170#3357—2831nomaximal, Sylow
171#555—2831no—
172#554—2831no—
173#500—2831no—
174#485—2831no—
175#485—2831no—
176#480—2831no—
177#480D28311yescharacteristic, complemented
178#477—2831no—
179#476—2831no—
180#468—2831no—
181#468—2831no—
182C4×SD16—2831no—
183#436—2831no—
184#428—2831no—
185#428—2831no—
186C2×SD16—2831no—
187C2×M16—2831no—
188C2×M16—2831no—
189C4⋊Q8—2831no—
190C4⋊Q8—2831no—
191#125—5661no—
192#124—5661no—
193#124—5661no—
194C22⋊Q8—2831no—
195C22⋊Q8—2831no—
196C22⋊Q8—5661no—
197C22⋊Q8—5661no—
198#121—2831no—
199#121—5661no—
200#121C2×D28311yescharacteristic
201C4×Q8—2831no—
202C4×D4—2831no—
203C4×D4—2831no—
204C4×D4—5661no—
205#117—2831no—
206#117—2831no—
207#117—5661no—
208C2×C4⋊C4—2831no—
209C2×C4⋊C4C2×D28311yescharacteristic
210#107—2831no—
211#107—2831no—
212#107—2831no—
213#107—2831no—
214#107C2×D28311yescharacteristic
215#107C2×D28311yescharacteristic
216#106—2831no—
217#106—2831no—
218#106—2831no—
219C4⋊C8—2831no—
220#103—2831no—
221#103—2831no—
222#103—2831no—
223#102—2831no—
224#102C2×D28311yescharacteristic
225#102C2×D28311yescharacteristic
226C22⋊C8—2831no—
227C22⋊C8C2×D28311yescharacteristic
228C4×C8—2831no—
229C2×Q8—2831no—
230C2×Q8—5661no—
231C2×Q8—5661no—
232C2×D4—21no—
233C2×D4—2831no—
234C2×D4—5661no—
235C2×D4C22×D28311yescharacteristic
236C22×C4—21no—
237C22×C4—2831no—
238C22×C4—5661no—
239C22×C4—5661no—
240C22×C4C22×D28311yescharacteristic
241SD16—5662no—
242M16—5662no—
243M16—5662no—
244C2×C8—2831no—
245C2×C8—2831no—
246C2×C8C22×D28311yescharacteristic
247C2×C8C22×D28311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—2831no—
250C4⋊C4—2831no—
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⋊C4C22×D28311yescharacteristic
260C4⋊C4C22×D28311yescharacteristic
261C4⋊C4C22×D28311yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—2831no—
264C22⋊C4—2831no—
265C22⋊C4—5661no—
266C22⋊C4—5661no—
267C22⋊C4—5661no—
268C22⋊C4—5661no—
269C22⋊C4—5661no—
270C22⋊C4—5661no—
271C42—2831no—
272C42—5661no—
273C42—5661no—
274C42—5661no—
275C23—21no—
276C23—2831no—
277C23D4×D28311yescharacteristic
278Q8—5661no—
279Q8—5661no—
280Q8—22641no—
281Q8—22641no—
282D4—21no—
283D4—21no—
284D4—81no—
285D4—5662no—
286D4—22641no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—81no—
293C2×C4—2831no—
294C2×C4—2831no—
295C2×C4—2831no—
296C2×C4—5661no—
297C2×C4—5661no—
298C2×C4—5661no—
299C2×C4—5661no—
300C2×C4—5661no—
301C2×C4—5661no—
302C2×C4—11322no—
303C2×C4—22641no—
304C2×C4D4×D28311yescharacteristic
305C2×C4C23×D28311yescharacteristic
306C8—21no—
307C8—21no—
308C8—2832no—
309C8—5661no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—5661no—
317C22—5661no—
318C22—5661no—
319C22C2×D4×D28311yescharacteristic
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—2832no—
325C4—5661no—
326C4—5661no—
327C4—11321no—
328C4—11321no—
329C4—11321no—
330C4—11321no—
331C4#41×D28311yescharacteristic
332C4#2258365711yescharacteristic
333C2—41no—
334C2—81no—
335C2—11321no—
336C2#3182711311yescharacteristic
337C2#137×D28311yescharacteristic
338C2#3182726611yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#480×C283C2
socleC22×C283C22×D4
prime radical#31827179C2
hypercenter#480D283
hypocenterC283#3357
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. #31827170C2semidirect
3. #31826869C2semidirect
4. #31826808C2semidirect
5. #31826807C2semidirect
6. #31826777C2semidirect
7. #31826759C2semidirect
8. #31826753C2semidirect
9. #31826710C2semidirect
10. #31826709C2semidirect
11. #31826556C2semidirect
12. #31826540C2semidirect
13. #31826506C2semidirect
14. #31826505C2semidirect
15. #480×C283C2semidirect
169. C283#3357semidirect
177. #480D283semidirect

Maximal subgroups

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

subgroupindex
#318271792
#318271702
#318268692
#318268082
#318268072
#318267772
#318267592
#318267532
#318267102
#318267092
#318265562
#318265402
#318265062
#318265052
#480×C2832
#3357283