Finite Group Databasebeta

← #49131524

Subgroups — #49131524

Order 36224.

384 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#31827088C211yesmaximal, characteristic, complemented
2#31826948C211yesmaximal, characteristic, complemented
3#31826798C211yesmaximal, characteristic, complemented
4#31826779C211yesmaximal, characteristic, complemented
5#31826758C211yesmaximal, characteristic, complemented
6#31826743C211yesmaximal, characteristic, complemented
7#31826689C211yesmaximal, characteristic, complemented
8#31826682C211yesmaximal, characteristic, complemented
9#31826610C211yesmaximal, characteristic
10#31826568C211yesmaximal, characteristic, complemented
11#31826566C211yesmaximal, characteristic, complemented
12Q16×Dic283C211yesmaximal, characteristic, complemented
13#31826545C211yesmaximal, characteristic, complemented
14#31826523C211yesmaximal, characteristic, complemented
15#452×C283C211yesmaximal, characteristic, complemented
16C2×#17985379C2211yescharacteristic
17C2×#17985377C2211yescharacteristic
18#22583609C2211yescharacteristic
19#22583605—21no—
20#22583599C2211yescharacteristic
21#22583596—21no—
22#22583592—21no—
23#22583590—21no—
24#22583584C2211yescharacteristic
25Q8×Dic283C2211yescharacteristic
26Q8×Dic283C2211yescharacteristic
27Q8×Dic283C2211yescharacteristic
28D4×Dic283—21no—
29D4×Dic283—21no—
30D4×Dic283C2211yescharacteristic
31D4×Dic283C2211yescharacteristic
32#22583572C2211yescharacteristic
33#22583569—21no—
34#22583569C2211yescharacteristic
35C2×C4⋊Dic283—21no—
36C2×C4⋊Dic283C2211yescharacteristic
37#22583544C2211yescharacteristic
38#22583544C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583543C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43#22583534C2211yescharacteristic
44#22583534C2211yescharacteristic
45#22583534C2211yescharacteristic
46#22583532C2211yescharacteristic
47#22583532C2211yescharacteristic
48#22583531C2211yescharacteristic
49C22⋊(C283⋊C8)C2211yescharacteristic
50#22583520C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52C2×#41×C283C2211yescharacteristic
53C2×Q16×C283C2211yescharacteristic
54C2×SD16×C283C2211yescharacteristic
55C22⋊Q8×C283C2211yescharacteristic
56#103×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58C22⋊C8×C283C2211yescharacteristic
59C2×Dic566—21no—
60C2×D1132C2311yescharacteristic
61C2×C22⋊D283—21no—
62C22×Dic283—21no—
63C22×Dic283—21no—
64C22×Dic283—21no—
65C2×C4×D283—21no—
66#17985379—22no—
67#17985377—22no—
68C2×C283⋊C8C2311yescharacteristic
69C2×C283⋊C8C2311yescharacteristic
70C4⋊Dic283—21no—
71C4⋊Dic283—21no—
72C4⋊Dic283—21no—
73C4⋊Dic283—21no—
74C4⋊Dic283D411yescharacteristic
75C4⋊Dic283D411yescharacteristic
76C4⋊Dic283C2311yescharacteristic
77C4⋊Dic283C2311yescharacteristic
78C4⋊Dic283C2311yescharacteristic
79Dic283⋊C4—21no—
80C22⋊Dic283—21no—
81C22⋊Dic283—21no—
82C22⋊Dic283D411yescharacteristic
83C22⋊Dic283D411yescharacteristic
84(C2×D283)⋊C4—21no—
85(C2×D283)⋊C4—21no—
86(C2×D283)⋊C4—21no—
87(C2×D283)⋊C4—21no—
88C4×Dic283—21no—
89C4×Dic283—21no—
90C4×Dic283—21no—
91C4×Dic283C2311yescharacteristic
92C4×Dic283C2311yescharacteristic
93#41×C283—22no—
94#41×C283—22no—
95C2×Q8×C283C2311yescharacteristic
96C2×Q8×C283C2311yescharacteristic
97C2×D4×C283—21no—
98C2×D4×C283C2311yescharacteristic
99C22×C4×C283—21no—
100C22×C4×C283C2311yescharacteristic
101Q16×C283—22no—
102SD16×C283—22no—
103C2×C8×C283C2311yescharacteristic
104C2×C8×C283C2311yescharacteristic
105C4⋊C4×C283—21no—
106C4⋊C4×C283C2311yescharacteristic
107C22⋊C4×C283—21no—
108C22×D283—21no—
109Dic566—81no—
110D1132—21no—
111D1132—21no—
112C22⋊D283—81no—
113C2×Dic283—21no—
114C2×Dic283—21no—
115C2×Dic283—21no—
116C2×Dic283—81no—
117C2×Dic283—81no—
118C2×Dic283—81no—
119C2×Dic283C2×D411yescharacteristic
120C2×Dic283C2×D411yescharacteristic
121C2×Dic283C2×D411yescharacteristic
122C2×Dic283C2×D411yescharacteristic
123C4×D283—81no—
124C283⋊C8—21no—
125C283⋊C8—21no—
126C23×C283—21no—
127C23×C283C2×D411yescharacteristic
128Q8×C283—21no—
129Q8×C283—21no—
130Q8×C283—21no—
131Q8×C283#4112yes—
132D4×C283—24no—
133D4×C283—21no—
134D4×C283#4112yes—
135C2×C4×C283—24no—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283C2×D411yescharacteristic
142C2×C4×C283C2411yescharacteristic
143C8×C283—21no—
144C8×C283—21no—
145C22×C283—21no—
146C22×C283—22no—
147C22×C283—21no—
148C22×C283—21no—
149C22×C283—41no—
150C22×C283—41no—
151C22×C283C22×D411yescharacteristic
152C2×D283—41no—
153C2×D283—41no—
154C2×D283—41no—
155C4×C283—21no—
156C4×C283—22no—
157C4×C283—41no—
158C4×C283—41no—
159C4×C283C2×#4111yescharacteristic
160C4×C283C2×#4111yescharacteristic
161Dic283—21no—
162Dic283—21no—
163Dic283—21no—
164Dic283—21no—
165Dic283—41no—
166Dic283—41no—
167Dic283—41no—
168C2×C283—41no—
169C2×C283—42no—
170C2×C283#52511yescharacteristic
171C2×C283#57611yescharacteristic
172C2×C283#57811yescharacteristic
173D283—81no—
174C283#312411yescharacteristic, complemented, Sylow
175#3124—2831nomaximal, Sylow
176#542—2831no—
177#520—2831no—
178#484—2831no—
179#480—2831no—
180#477—2831no—
181#474—2831no—
182#464—2831no—
183#463—2831no—
184#452D28311yescharacteristic, complemented
185#449—2831no—
186#440—2831no—
187#440—2831no—
188C4×Q16—2831no—
189C4×D8—2831no—
190#433—2831no—
191C2×#41C2×D28311yescharacteristic
192C2×Q16C2×D28311yescharacteristic
193C2×SD16—2831no—
194C2×SD16C2×D28311yescharacteristic
195C2×D8—2831no—
196C4⋊Q8—2831no—
197#126—5661no—
198#124—2831no—
199#124—5661no—
200#123—5661no—
201C22⋊Q8—5661no—
202C22⋊Q8C2×D28311yescharacteristic
203#121—2831no—
204C4×Q8—2831no—
205C4×Q8—2831no—
206C4×Q8—2831no—
207C4×D4—2831no—
208C4×D4—2831no—
209C4×D4—2831no—
210C4×D4—5661no—
211C4×D4—5661no—
212#117—2831no—
213#117—5661no—
214C2×C4⋊C4—2831no—
215C2×C4⋊C4—5661no—
216#107—2831no—
217#107—2831no—
218#107—2831no—
219#107—2831no—
220C4⋊C8—2831no—
221C4⋊C8—2831no—
222#103—2831no—
223#103—2831no—
224#103—2831no—
225#103C2×D28311yescharacteristic
226#102—2831no—
227#102—2831no—
228#102—2831no—
229#102C2×D28311yescharacteristic
230C22⋊C8—2831no—
231C22⋊C8C2×D28311yescharacteristic
232#97—2831no—
233C4×C8—2831no—
234#41—22no—
235#41—22no—
236C2×Q8—5661no—
237C2×Q8C22×D28311yescharacteristic
238C2×Q8C22×D28311yescharacteristic
239C2×D4—21no—
240C2×D4—2831no—
241C2×D4—5661no—
242C2×D4C22×D28311yescharacteristic
243C22×C4—21no—
244C22×C4—5661no—
245C22×C4—5661no—
246C22×C4—5661no—
247C22×C4—5661no—
248C22×C4C22×D28311yescharacteristic
249Q16—22no—
250SD16—22no—
251SD16—5662no—
252D8—5662no—
253C2×C8—2831no—
254C2×C8—2831no—
255C2×C8C22×D28311yescharacteristic
256C2×C8C22×D28311yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—2831no—
259C4⋊C4—2831no—
260C4⋊C4—2831no—
261C4⋊C4—2831no—
262C4⋊C4—2831no—
263C4⋊C4—5661no—
264C4⋊C4—5661no—
265C4⋊C4—5661no—
266C4⋊C4—5661no—
267C4⋊C4—5661no—
268C4⋊C4C22×D28311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—2831no—
271C22⋊C4—2831no—
272C22⋊C4—5661no—
273C22⋊C4—5661no—
274C22⋊C4—5661no—
275C22⋊C4—5661no—
276C22⋊C4—5661no—
277C22⋊C4—5661no—
278C42—2831no—
279C42—2831no—
280C42—5661no—
281C42—5661no—
282C42—5661no—
283C23—21no—
284C23—5661no—
285C23D4×D28311yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—22641no—
290Q8#1798539112yes—
291D4—24no—
292D4—21no—
293D4—5661no—
294D4—5661no—
295D4—22641no—
296D4#1798539112yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—2831no—
304C2×C4—2831no—
305C2×C4—2831no—
306C2×C4—2831no—
307C2×C4—5661no—
308C2×C4—5661no—
309C2×C4—5661no—
310C2×C4—22641no—
311C2×C4—22641no—
312C2×C4—22641no—
313C2×C4—22641no—
314C2×C4D4×D28311yescharacteristic
315C2×C4C23×D28311yescharacteristic
316C8—21no—
317C8—21no—
318C8—5661no—
319C8—5661no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—11321no—
327C22—11321no—
328C22—11321no—
329C22C2×D4×D28311yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—41no—
334C4—5661no—
335C4—5661no—
336C4—5661no—
337C4—5661no—
338C4—11321no—
339C4—11321no—
340C4—11321no—
341C4C2×#1798539111yescharacteristic
342C4C2×#1798539111yescharacteristic
343C2—41no—
344C2—42no—
345C2—22641no—
346C2#3182697111yescharacteristic
347C2#3182726711yescharacteristic
348C2#3182728111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#452×C283C2
socleC22×C283C22×D4
prime radical#31826610C2
hypercenter#452D283
hypocenterC283#3124
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #31827088C2semidirect
2. #31826948C2semidirect
3. #31826798C2semidirect
4. #31826779C2semidirect
5. #31826758C2semidirect
6. #31826743C2semidirect
7. #31826689C2semidirect
8. #31826682C2semidirect
10. #31826568C2semidirect
11. #31826566C2semidirect
12. Q16×Dic283C2semidirect
13. #31826545C2semidirect
14. #31826523C2semidirect
15. #452×C283C2semidirect
174. C283#3124semidirect
184. #452D283semidirect

Maximal subgroups

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

subgroupindex
#318270882
#318269482
#318267982
#318267792
#318267582
#318267432
#318266892
#318266822
#318266102
#318265682
#318265662
Q16×Dic2832
#318265452
#318265232
#452×C2832
#3124283