Finite Group Databasebeta

← #49131375

Subgroups — #49131375

Order 36224.

392 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#31827000C211yesmaximal, characteristic, complemented
2C4×#17985391C211yesmaximal, characteristic, complemented
3#31826808C211yesmaximal, characteristic, complemented
4#31826791C211yesmaximal, characteristic, complemented
5#31826769C211yesmaximal, characteristic, complemented
6#31826688C211yesmaximal, characteristic, complemented
7#31826680C211yesmaximal, characteristic, complemented
8#31826628C211yesmaximal, characteristic, complemented
9#31826611C211yesmaximal, characteristic
10#31826574C211yesmaximal, characteristic, complemented
11#31826571C211yesmaximal, characteristic, complemented
12#31826564C211yesmaximal, characteristic, complemented
13#31826562C211yesmaximal, characteristic, complemented
14#31826521C211yesmaximal, characteristic, complemented
15#478×C283C211yesmaximal, characteristic, complemented
16C2×#17985391C2211yescharacteristic
17C2×Dic1132C2211yescharacteristic
18C2×#17985381C2211yescharacteristic
19C2×#17985380C2211yescharacteristic
20C2×#17985377C2211yescharacteristic
21#22583605—21no—
22#22583598C2211yescharacteristic
23#22583595—21no—
24#22583590C2211yescharacteristic
25#22583585C2211yescharacteristic
26C4×Dic566C2211yescharacteristic
27#22583575C2211yescharacteristic
28#22583575C2211yescharacteristic
29D4×Dic283C2211yescharacteristic
30#22583572—21no—
31#22583572C2211yescharacteristic
32C4×C22⋊D283—21no—
33(C22⋊D283)⋊C4—21no—
34#22583568—21no—
35#22583568C2211yescharacteristic
36#22583566—21no—
37C2×C4×Dic283—21no—
38C42×D283C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583541C2211yescharacteristic
41C4⋊(C283⋊C8)C2211yescharacteristic
42#22583535C2211yescharacteristic
43#22583533C2211yescharacteristic
44#22583533C2211yescharacteristic
45#22583533C2211yescharacteristic
46#22583532C2211yescharacteristic
47#22583530C2211yescharacteristic
48(C2×D283)⋊C8C2211yescharacteristic
49(C2×D283)⋊C8C2211yescharacteristic
50#22583520C2211yescharacteristic
51#22583520C2211yescharacteristic
52#125×C283C2211yescharacteristic
53C4×D4×C283C2211yescharacteristic
54#107×C283C2211yescharacteristic
55#106×C283C2211yescharacteristic
56C4⋊C8×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58#102×C283C2211yescharacteristic
59#17985391—22no—
60#17985391—22no—
61C2×Dic566C2311yescharacteristic
62C2×Dic566C2311yescharacteristic
63C2×D1132—21no—
64C2×D1132C2311yescharacteristic
65C2×C22⋊D283—21no—
66C22×Dic283—21no—
67C22×Dic283—21no—
68C2×C4×D283—21no—
69C2×C4×D283D411yescharacteristic
70C2×C4×D283D411yescharacteristic
71C2×C4×D283C2311yescharacteristic
72Dic1132—22no—
73#17985381—22no—
74#17985380—22no—
75#17985377—22no—
76C2×C283⋊C8C2311yescharacteristic
77C2×C283⋊C8C2311yescharacteristic
78C4⋊Dic283—21no—
79C4⋊Dic283C2311yescharacteristic
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83C22⋊Dic283—21no—
84(C2×D283)⋊C4—21no—
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—
90C4×Dic283—21no—
91C4×Dic283—21no—
92C4×Dic283—21no—
93C4×Dic283—21no—
94C4×Dic283D411yescharacteristic
95C4×Dic283D411yescharacteristic
96C4×Dic283C2311yescharacteristic
97C2×D4×C283C2311yescharacteristic
98C22×C4×C283—21no—
99C2×C8×C283C2311yescharacteristic
100C2×C8×C283C2311yescharacteristic
101C4⋊C4×C283—21no—
102C4⋊C4×C283—21no—
103C4⋊C4×C283C2311yescharacteristic
104C4⋊C4×C283C2311yescharacteristic
105C4⋊C4×C283C2311yescharacteristic
106C22⋊C4×C283—21no—
107C42×C283C2311yescharacteristic
108C22×D283—21no—
109C22×D283C2×D411yescharacteristic
110Dic566—21no—
111Dic566—21no—
112Dic566—21no—
113Dic566#4112yes—
114D1132—21no—
115D1132—21no—
116D1132—42no—
117C22⋊D283—24no—
118C2×Dic283—24no—
119C2×Dic283—21no—
120C2×Dic283—21no—
121C2×Dic283—21no—
122C2×Dic283—42no—
123C2×Dic283C2×D411yescharacteristic
124C2×Dic283C2×D411yescharacteristic
125C2×Dic283C2×D411yescharacteristic
126C4×D283—21no—
127C4×D283—21no—
128C4×D283—41no—
129C4×D283—41no—
130C4×D283—42no—
131C283⋊C8—21no—
132C283⋊C8—21no—
133C23×C283—21no—
134D4×C283—21no—
135D4×C283#4112yes—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283—42no—
140C2×C4×C283C2×D411yescharacteristic
141C2×C4×C283C2×D411yescharacteristic
142C2×C4×C283C2411yescharacteristic
143C8×C283—21no—
144C8×C283—21no—
145C22×C283—22no—
146C22×C283—41no—
147C22×C283—41no—
148C22×C283C22×D411yescharacteristic
149C2×D283—21no—
150C2×D283—21no—
151C2×D283—21no—
152C2×D283—41no—
153C2×D283—41no—
154C2×D283—41no—
155C4×C283—21no—
156C4×C283—21no—
157C4×C283—41no—
158C4×C283—41no—
159C4×C283—41no—
160C4×C283C2×#4111yescharacteristic
161C4×C283C2×#4111yescharacteristic
162Dic283—21no—
163Dic283—22no—
164Dic283—21no—
165Dic283—21no—
166Dic283—41no—
167Dic283—41no—
168C2×C283—42no—
169C2×C283#52511yescharacteristic
170C2×C283#57511yescharacteristic
171C2×C283#57511yescharacteristic
172D283—41no—
173D283—81no—
174C283#311111yescharacteristic, complemented, Sylow
175#3111—2831nomaximal, Sylow
176#529—2831no—
177C4×#41—2831no—
178#485—2831no—
179#482—2831no—
180#479—2831no—
181#478D28311yescharacteristic, complemented
182#464—2831no—
183#463—2831no—
184#452—2831no—
185#449—2831no—
186#442—2831no—
187#441—2831no—
188#440—2831no—
189#440—2831no—
190#432—2831no—
191C2×#41—2831no—
192C2×Q16—2831no—
193C2×SD16—2831no—
194C2×SD16—2831no—
195C2×D8—2831no—
196#126—5661no—
197#125C2×D28311yescharacteristic
198#124—2831no—
199#123—5661no—
200C22⋊Q8—2831no—
201#121—2831no—
202C4×Q8—2831no—
203C4×Q8—2831no—
204C4×Q8—2831no—
205C4×D4—2831no—
206C4×D4—2831no—
207C4×D4—5661no—
208C4×D4—5661no—
209C4×D4—5661no—
210C4×D4C2×D28311yescharacteristic
211#117—2831no—
212#117—5661no—
213#117—5661no—
214C2×C42—2831no—
215C2×C42—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#103—2831no—
225#103—2831no—
226#102—2831no—
227#102—2831no—
228#102C2×D28311yescharacteristic
229#102C2×D28311yescharacteristic
230C22⋊C8—2831no—
231C22⋊C8—2831no—
232#97—2831no—
233#97—2831no—
234#41—5662no—
235#41—5662no—
236C2×Q8—2831no—
237C2×Q8—2831no—
238C2×D4—2831no—
239C2×D4—5661no—
240C2×D4—5661no—
241C2×D4C22×D28311yescharacteristic
242C22×C4—21no—
243C22×C4—2831no—
244C22×C4—2831no—
245C22×C4—2831no—
246C22×C4—5661no—
247C22×C4—5661no—
248C22×C4—5661no—
249Q16—5662no—
250SD16—5662no—
251SD16—5662no—
252D8—5662no—
253C2×C8—2831no—
254C2×C8—2831no—
255C2×C8C22×D28311yescharacteristic
256C2×C8C22×D28311yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—2831no—
260C4⋊C4—5661no—
261C4⋊C4—5661no—
262C4⋊C4—5661no—
263C4⋊C4—5661no—
264C4⋊C4C22×D28311yescharacteristic
265C4⋊C4C22×D28311yescharacteristic
266C4⋊C4C22×D28311yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—5661no—
269C22⋊C4—5661no—
270C22⋊C4—5661no—
271C22⋊C4—5661no—
272C22⋊C4—5661no—
273C22⋊C4—5661no—
274C22⋊C4—5661no—
275C42—2831no—
276C42—2831no—
277C42—2831no—
278C42—5661no—
279C42—5661no—
280C42—5661no—
281C42—5661no—
282C42C22×D28311yescharacteristic
283C23—21no—
284C23—2831no—
285C23—5661no—
286Q8—2832no—
287Q8—5661no—
288Q8—5661no—
289Q8—5661no—
290D4—21no—
291D4—5664no—
292D4—5661no—
293D4—5661no—
294D4—11322no—
295D4#1798539312yes—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—42no—
300C2×C4—2831no—
301C2×C4—2831no—
302C2×C4—2831no—
303C2×C4—5664no—
304C2×C4—5661no—
305C2×C4—5661no—
306C2×C4—5661no—
307C2×C4—5661no—
308C2×C4—5661no—
309C2×C4—11321no—
310C2×C4—11321no—
311C2×C4—11322no—
312C2×C4—11322no—
313C2×C4D4×D28311yescharacteristic
314C2×C4D4×D28311yescharacteristic
315C2×C4C23×D28311yescharacteristic
316C8—21no—
317C8—21no—
318C8—5661no—
319C8—5661no—
320C22—22no—
321C22—41no—
322C22—41no—
323C22—5661no—
324C22—5661no—
325C22—5661no—
326C22—11321no—
327C22—11321no—
328C22—11321no—
329C22C2×D4×D28311yescharacteristic
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—5661no—
336C4—5662no—
337C4—5661no—
338C4—5661no—
339C4—11321no—
340C4—11321no—
341C4#41×D28311yescharacteristic
342C4C2×#1798539311yescharacteristic
343C2—42no—
344C2—11321no—
345C2—22641no—
346C2#3182697811yescharacteristic
347C2#3182726111yescharacteristic
348C2#3182726211yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#478×C283C2
socleC22×C283C22×D4
prime radical#31826611C2
hypercenter#478D283
hypocenterC283#3111
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #31827000C2semidirect
2. C4×#17985391C2semidirect
3. #31826808C2semidirect
4. #31826791C2semidirect
5. #31826769C2semidirect
6. #31826688C2semidirect
7. #31826680C2semidirect
8. #31826628C2semidirect
10. #31826574C2semidirect
11. #31826571C2semidirect
12. #31826564C2semidirect
13. #31826562C2semidirect
14. #31826521C2semidirect
15. #478×C283C2semidirect
174. C283#3111semidirect
181. #478D283semidirect

Maximal subgroups

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

subgroupindex
#318270002
C4×#179853912
#318268082
#318267912
#318267692
#318266882
#318266802
#318266282
#318266112
#318265742
#318265712
#318265642
#318265622
#318265212
#478×C2832
#3111283