Finite Group Databasebeta

← #49131554

Subgroups — #49131554

Order 36224.

382 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827071C211yesmaximal, characteristic
2#31826941C211yesmaximal, characteristic, complemented
3#31826792C211yesmaximal, characteristic, complemented
4#31826791C211yesmaximal, characteristic, complemented
5#31826769C211yesmaximal, characteristic, complemented
6#31826666C211yesmaximal, characteristic, complemented
7#31826665C211yesmaximal, characteristic, complemented
8#31826605C211yesmaximal, characteristic, complemented
9#31826605C211yesmaximal, characteristic, complemented
10#31826568C211yesmaximal, characteristic, complemented
11#31826564C211yesmaximal, characteristic, complemented
12#31826552C211yesmaximal, characteristic, complemented
13#31826550C211yesmaximal, characteristic, complemented
14#31826525C211yesmaximal, characteristic, complemented
15#479×C283C211yesmaximal, characteristic, complemented
16C2×Q8×D283C2211yescharacteristic
17C2×#17985381C2211yescharacteristic
18C2×#17985381C2211yescharacteristic
19C2×#17985379C2211yescharacteristic
20C2×#17985379C2211yescharacteristic
21#22583607C2211yescharacteristic
22#22583595—21no—
23#22583595—21no—
24#22583585—21no—
25#22583585—21no—
26#22583585C2211yescharacteristic
27#22583585C2211yescharacteristic
28Q8×Dic283C2211yescharacteristic
29C4×Dic566—21no—
30C4×Dic566C2211yescharacteristic
31#22583575—21no—
32#22583575C2211yescharacteristic
33#22583572C2211yescharacteristic
34#22583572C2211yescharacteristic
35#22583568—21no—
36#22583568C2211yescharacteristic
37#22583567—21no—
38#22583567C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583541C2211yescharacteristic
41C4⋊(C283⋊C8)C2211yescharacteristic
42#22583533C2211yescharacteristic
43#22583533C2211yescharacteristic
44#22583532C2211yescharacteristic
45#22583532C2211yescharacteristic
46#22583530C2211yescharacteristic
47#22583530C2211yescharacteristic
48(C2×D283)⋊C8C2211yescharacteristic
49(C2×D283)⋊C8C2211yescharacteristic
50#22583520C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52#125×C283C2211yescharacteristic
53C4×Q8×C283C2211yescharacteristic
54#107×C283C2211yescharacteristic
55#106×C283C2211yescharacteristic
56C4⋊C8×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#103×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×Dic566C2311yescharacteristic
61Q8×D283—22no—
62Q8×D283—22no—
63C2×D1132—21no—
64C2×D1132—21no—
65C2×D1132—21no—
66C2×D1132—21no—
67C2×D1132C2311yescharacteristic
68C2×D1132C2311yescharacteristic
69C2×C4×D283—21no—
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72C2×C4×D283C2311yescharacteristic
73#17985381—22no—
74#17985381—22no—
75#17985379—22no—
76#17985379—22no—
77C2×C283⋊C8C2311yescharacteristic
78C2×C283⋊C8C2311yescharacteristic
79C4⋊Dic283—21no—
80C4⋊Dic283C2311yescharacteristic
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4D411yescharacteristic
84Dic283⋊C4D411yescharacteristic
85(C2×D283)⋊C4—21no—
86(C2×D283)⋊C4—21no—
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4D411yescharacteristic
91(C2×D283)⋊C4D411yescharacteristic
92C4×Dic283—21no—
93C4×Dic283—21no—
94C4×Dic283—21no—
95C4×Dic283—21no—
96C4×Dic283C2311yescharacteristic
97C2×Q8×C283C2311yescharacteristic
98C2×C8×C283C2311yescharacteristic
99C2×C8×C283C2311yescharacteristic
100C4⋊C4×C283—21no—
101C4⋊C4×C283—21no—
102C4⋊C4×C283—21no—
103C4⋊C4×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C4⋊C4×C283C2311yescharacteristic
106C42×C283—21no—
107C42×C283C2311yescharacteristic
108C22×D283—21no—
109C22×D283—21no—
110C22×D283C2×D411yescharacteristic
111Dic566—24no—
112Dic566—21no—
113Dic566#4112yes—
114D1132—21no—
115D1132—21no—
116D1132—21no—
117D1132—21no—
118D1132—81no—
119D1132—81no—
120D1132—81no—
121D1132—81no—
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283C2×D411yescharacteristic
125C2×Dic283C2×D411yescharacteristic
126C2×Dic283C2×D411yescharacteristic
127C4×D283—24no—
128C4×D283—21no—
129C4×D283—21no—
130C4×D283—81no—
131C4×D283—81no—
132C283⋊C8—21no—
133C283⋊C8—21no—
134Q8×C283—21no—
135Q8×C283#4112yes—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283—21no—
140C2×C4×C283C2×D411yescharacteristic
141C2×C4×C283C2×D411yescharacteristic
142C2×C4×C283C2411yescharacteristic
143C8×C283—21no—
144C8×C283—21no—
145C22×C283C22×D411yescharacteristic
146C2×D283—21no—
147C2×D283—21no—
148C2×D283—21no—
149C2×D283—41no—
150C2×D283—41no—
151C2×D283—41no—
152C2×D283—41no—
153C2×D283—41no—
154C2×D283—41no—
155C4×C283—22no—
156C4×C283—21no—
157C4×C283—21no—
158C4×C283—41no—
159C4×C283—41no—
160C4×C283—41no—
161C4×C283C2×#4111yescharacteristic
162C4×C283C2×#4111yescharacteristic
163Dic283—22no—
164Dic283—21no—
165Dic283—21no—
166Dic283—21no—
167Dic283—41no—
168C2×C283#52511yescharacteristic
169C2×C283#57711yescharacteristic
170C2×C283#57711yescharacteristic
171D283—41no—
172D283—81no—
173D283—81no—
174C283#312611yescharacteristic, complemented, Sylow
175#3126—2831nomaximal, Sylow
176#540—2831no—
177#519—2831no—
178#482—2831no—
179#482—2831no—
180#479—2831no—
181#479D28311yescharacteristic, complemented
182#460—2831no—
183#460—2831no—
184#448—2831no—
185#448—2831no—
186#440—2831no—
187#440—2831no—
188C4×SD16—2831no—
189C4×SD16—2831no—
190#433—2831no—
191C22×Q8—2831no—
192C2×SD16—2831no—
193C2×SD16—2831no—
194C2×SD16—2831no—
195C2×SD16—2831no—
196#127—2831no—
197#125C2×D28311yescharacteristic
198#123—5661no—
199#123—5661no—
200#121—2831no—
201#121—2831no—
202#121—5661no—
203#121—5661no—
204C4×Q8—2831no—
205C4×Q8—2831no—
206C4×Q8—2831no—
207C4×Q8—5661no—
208C4×Q8—5661no—
209C4×Q8C2×D28311yescharacteristic
210C4×D4—2831no—
211C4×D4—2831no—
212#117—2831no—
213#117—2831no—
214#117—5661no—
215#117—5661no—
216#107—2831no—
217#107C2×D28311yescharacteristic
218#106—2831no—
219#106C2×D28311yescharacteristic
220C4⋊C8—2831no—
221C4⋊C8C2×D28311yescharacteristic
222#103—2831no—
223#103—2831no—
224#103C2×D28311yescharacteristic
225#103C2×D28311yescharacteristic
226#102—2831no—
227#102—2831no—
228#102—2831no—
229#102—2831no—
230C22⋊C8—2831no—
231C22⋊C8—2831no—
232#97—2831no—
233C4×C8—2831no—
234C2×Q8—2831no—
235C2×Q8—5661no—
236C2×Q8—5662no—
237C2×Q8—5662no—
238C2×Q8C22×D28311yescharacteristic
239C2×D4—2831no—
240C2×D4—2831no—
241C2×D4—5661no—
242C2×D4—5661no—
243C2×D4—5661no—
244C2×D4—5661no—
245C22×C4—2831no—
246C22×C4—5661no—
247C22×C4—5661no—
248C22×C4—5661no—
249SD16—5662no—
250SD16—5662no—
251SD16—5662no—
252SD16—5662no—
253C2×C8—2831no—
254C2×C8—2831no—
255C2×C8C22×D28311yescharacteristic
256C2×C8C22×D28311yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—2831no—
261C4⋊C4—2831no—
262C4⋊C4—2831no—
263C4⋊C4—5661no—
264C4⋊C4—5661no—
265C4⋊C4—5661no—
266C4⋊C4C22×D28311yescharacteristic
267C4⋊C4C22×D28311yescharacteristic
268C4⋊C4C22×D28311yescharacteristic
269C22⋊C4—2831no—
270C22⋊C4—2831no—
271C22⋊C4—5661no—
272C22⋊C4—5661no—
273C22⋊C4—5661no—
274C22⋊C4—5661no—
275C22⋊C4—5661no—
276C42—21no—
277C42—2831no—
278C42—5661no—
279C42—5661no—
280C42—5661no—
281C42—5661no—
282C42C22×D28311yescharacteristic
283C23—2831no—
284C23—5661no—
285C23—5661no—
286Q8—21no—
287Q8—2832no—
288Q8—5664no—
289Q8—5661no—
290Q8#1798539312yes—
291D4—5661no—
292D4—5661no—
293D4—5661no—
294D4—5661no—
295D4—22641no—
296D4—22641no—
297D4—22641no—
298D4—22641no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—2831no—
304C2×C4—2831no—
305C2×C4—2831no—
306C2×C4—5664no—
307C2×C4—5661no—
308C2×C4—5661no—
309C2×C4—5661no—
310C2×C4—5661no—
311C2×C4—22641no—
312C2×C4—22641no—
313C2×C4D4×D28311yescharacteristic
314C2×C4D4×D28311yescharacteristic
315C2×C4C23×D28311yescharacteristic
316C8—21no—
317C8—21no—
318C8—5661no—
319C8—5661no—
320C22—5661no—
321C22—5661no—
322C22—5661no—
323C22—11321no—
324C22—11321no—
325C22—11321no—
326C22—11321no—
327C22—11321no—
328C22—11321no—
329C22C2×D4×D28311yescharacteristic
330C4—22no—
331C4—21no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—5661no—
337C4—5662no—
338C4—5661no—
339C4—5661no—
340C4—11321no—
341C4#41×D28311yescharacteristic
342C4C2×#1798539311yescharacteristic
343C2—11321no—
344C2—22641no—
345C2—22641no—
346C2#3182697811yescharacteristic
347C2#3182727211yescharacteristic
348C2#3182727411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#479×C283C2
socleC22×C283C22×D4
prime radical#31827071C2
hypercenter#479D283
hypocenterC283#3126
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
2. #31826941C2semidirect
3. #31826792C2semidirect
4. #31826791C2semidirect
5. #31826769C2semidirect
6. #31826666C2semidirect
7. #31826665C2semidirect
8. #31826605C2semidirect
9. #31826605C2semidirect
10. #31826568C2semidirect
11. #31826564C2semidirect
12. #31826552C2semidirect
13. #31826550C2semidirect
14. #31826525C2semidirect
15. #479×C283C2semidirect
174. C283#3126semidirect
181. #479D283semidirect

Maximal subgroups

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

subgroupindex
#318270712
#318269412
#318267922
#318267912
#318267692
#318266662
#318266652
#318266052
#318265682
#318265642
#318265522
#318265502
#318265252
#479×C2832
#3126283