Finite Group Databasebeta

← #49132701

Subgroups — #49132701

Order 36224.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827075C211yesmaximal, characteristic, complemented
2#31827068C211yesmaximal, characteristic
3#31826775C211yesmaximal, characteristic, complemented
4#31826770C211yesmaximal, characteristic, complemented
5#31826767C211yesmaximal, characteristic, complemented
6#31826764C211yesmaximal, characteristic, complemented
7#31826713C211yesmaximal, characteristic, complemented
8#31826709C211yesmaximal, characteristic, complemented
9#31826694C211yesmaximal, characteristic, complemented
10#31826669C211yesmaximal, characteristic, complemented
11#31826668C211yesmaximal, characteristic, complemented
12#31826664C211yesmaximal, characteristic, complemented
13#31826663C211yesmaximal, characteristic, complemented
14#31826491C211yesmaximal, characteristic, complemented
15#465×C283C211yesmaximal, characteristic, complemented
16C2×#17985381C2211yescharacteristic
17C2×#17985380C2211yescharacteristic
18C2×#17985379C2211yescharacteristic
19C2×#17985376C2211yescharacteristic
20#22583608C2211yescharacteristic
21#22583606C2211yescharacteristic
22#22583603—21no—
23#22583603—21no—
24#22583601—21no—
25#22583601C2211yescharacteristic
26#22583601C2211yescharacteristic
27#22583600—21no—
28#22583594—21no—
29#22583592—21no—
30#22583589C2211yescharacteristic
31#22583584C2211yescharacteristic
32#22583582—21no—
33#22583581—21no—
34Q8×Dic283C2211yescharacteristic
35#22583575C2211yescharacteristic
36D4×Dic283C2211yescharacteristic
37#22583572C2211yescharacteristic
38#22583569C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583543C2211yescharacteristic
41#22583542C2211yescharacteristic
42Dic283⋊C8C2211yescharacteristic
43Dic283⋊C8C2211yescharacteristic
44Dic283⋊C8C2211yescharacteristic
45Dic283⋊C8C2211yescharacteristic
46#22583535C2211yescharacteristic
47#22583534C2211yescharacteristic
48#22583533C2211yescharacteristic
49#22583532C2211yescharacteristic
50#22583531C2211yescharacteristic
51#22583530C2211yescharacteristic
52C2×SD16×C283C2211yescharacteristic
53C22×C8×C283C2211yescharacteristic
54C22⋊Q8×C283C2211yescharacteristic
55#121×C283C2211yescharacteristic
56#106×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#102×C283C2211yescharacteristic
59C2×Dic566C2311yescharacteristic
60C2×D1132C2311yescharacteristic
61C2×C22⋊D283—21no—
62C2×C22⋊D283—21no—
63C2×C22⋊D283—21no—
64C22×Dic283—21no—
65C2×C4×D283—21no—
66#17985381—41no—
67#17985380—41no—
68#17985379—41no—
69#17985376—41no—
70C2×C283⋊C8C2311yescharacteristic
71C2×C283⋊C8C2311yescharacteristic
72C4⋊Dic283—21no—
73C4⋊Dic283—21no—
74C4⋊Dic283—21no—
75C4⋊Dic283D411yescharacteristic
76C4⋊Dic283D411yescharacteristic
77C4⋊Dic283C2311yescharacteristic
78C4⋊Dic283C2311yescharacteristic
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85C22⋊Dic283—21no—
86C22⋊Dic283—21no—
87C22⋊Dic283D411yescharacteristic
88C22⋊Dic283D411yescharacteristic
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91C4×Dic283—21no—
92C4×Dic283—21no—
93C4×Dic283C2311yescharacteristic
94C4×Dic283C2311yescharacteristic
95C2×Q8×C283C2311yescharacteristic
96C2×D4×C283—21no—
97C2×D4×C283C2311yescharacteristic
98C22×C4×C283C2311yescharacteristic
99SD16×C283—41no—
100C2×C8×C283—41no—
101C2×C8×C283C2311yescharacteristic
102C2×C8×C283C2311yescharacteristic
103C4⋊C4×C283—21no—
104C4⋊C4×C283C2311yescharacteristic
105C4⋊C4×C283C2311yescharacteristic
106C22⋊C4×C283—21no—
107C22⋊C4×C283—21no—
108C22×D283—21no—
109Dic566—21no—
110Dic566—21no—
111D1132—21no—
112D1132—21no—
113C22⋊D283—81no—
114C22⋊D283—81no—
115C22⋊D283—81no—
116C2×Dic283—21no—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283—81no—
120C2×Dic283C2×D411yescharacteristic
121C2×Dic283C2×D411yescharacteristic
122C2×Dic283C2×D411yescharacteristic
123C2×Dic283C2×D411yescharacteristic
124C4×D283—81no—
125C283⋊C8—21no—
126C283⋊C8—21no—
127C23×C283—21no—
128C23×C283C2×D411yescharacteristic
129Q8×C283—21no—
130Q8×C283—21no—
131D4×C283—21no—
132D4×C283—21no—
133D4×C283—81no—
134C2×C4×C283—21no—
135C2×C4×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283—21no—
138C2×C4×C283—21no—
139C2×C4×C283C2×D411yescharacteristic
140C2×C4×C283C2411yescharacteristic
141C8×C283—21no—
142C8×C283—21no—
143C22×C283—21no—
144C22×C283—21no—
145C22×C283—21no—
146C22×C283—41no—
147C22×C283—41no—
148C22×C283—41no—
149C22×C283C22×D411yescharacteristic
150C2×D283—41no—
151C2×D283—41no—
152C2×D283—41no—
153C4×C283—21no—
154C4×C283—41no—
155C4×C283—41no—
156C4×C283—41no—
157C4×C283H(5,𝔽2)11yescharacteristic
158C4×C2832−1+411yescharacteristic
159Dic283—21no—
160Dic283—21no—
161Dic283—21no—
162Dic283—21no—
163Dic283—41no—
164Dic283—41no—
165Dic283—41no—
166C2×C283—41no—
167C2×C283—81no—
168C2×C283#53711yescharacteristic
169C2×C283#57711yescharacteristic
170C2×C283#57711yescharacteristic
171D283—81no—
172C283#326011yescharacteristic, complemented, Sylow
173#3260—2831nomaximal, Sylow
174#541—2831no—
175#540—2831no—
176#479—2831no—
177#479—2831no—
178#478—2831no—
179#478—2831no—
180#468—2831no—
181#468—2831no—
182#465—2831no—
183#465D28311yescharacteristic, complemented
184#461—2831no—
185#461—2831no—
186#460—2831no—
187#460—2831no—
188#424—2831no—
189C2×SD16—2831no—
190C2×SD16—2831no—
191C2×SD16—2831no—
192C2×SD16C2×D28311yescharacteristic
193C2×M16—2831no—
194C22×C8C2×D28311yescharacteristic
195C4⋊Q8—2831no—
196#127—2831no—
197#126—5661no—
198#126—5661no—
199#125—2831no—
200#125—2831no—
201#125—5661no—
202#125—5661no—
203#123—5661no—
204#123—5661no—
205C22⋊Q8—2831no—
206C22⋊Q8C2×D28311yescharacteristic
207#121—2831no—
208#121—5661no—
209#121—5661no—
210#121C2×D28311yescharacteristic
211C4×Q8—2831no—
212C4×Q8—2831no—
213C4×D4—2831no—
214C4×D4—2831no—
215#117—2831no—
216#107—2831no—
217#107—2831no—
218#106—2831no—
219#106C2×D28311yescharacteristic
220C4⋊C8—2831no—
221C4⋊C8—2831no—
222C4⋊C8—2831no—
223C4⋊C8—2831no—
224#103—2831no—
225#103—2831no—
226#103—2831no—
227#103C2×D28311yescharacteristic
228#102—2831no—
229#102—2831no—
230#102—2831no—
231#102C2×D28311yescharacteristic
232C2×Q8—2831no—
233C2×Q8C22×D28311yescharacteristic
234C2×D4—21no—
235C2×D4—2831no—
236C2×D4—5661no—
237C2×D4—5661no—
238C2×D4—5661no—
239C2×D4C22×D28311yescharacteristic
240C22×C4—5661no—
241C22×C4—5661no—
242C22×C4C22×D28311yescharacteristic
243SD16—41no—
244SD16—11321no—
245SD16—11321no—
246SD16—11321no—
247M16—11321no—
248C2×C8—41no—
249C2×C8—2831no—
250C2×C8—2831no—
251C2×C8C22×D28311yescharacteristic
252C2×C8C22×D28311yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—2831no—
255C4⋊C4—2831no—
256C4⋊C4—2831no—
257C4⋊C4—2831no—
258C4⋊C4—5661no—
259C4⋊C4—5661no—
260C4⋊C4—5661no—
261C4⋊C4—5661no—
262C4⋊C4—5661no—
263C4⋊C4—5661no—
264C4⋊C4—5661no—
265C4⋊C4—5661no—
266C4⋊C4—5661no—
267C4⋊C4C22×D28311yescharacteristic
268C4⋊C4C22×D28311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—2831no—
272C22⋊C4—2831no—
273C22⋊C4—5661no—
274C22⋊C4—5661no—
275C22⋊C4—5661no—
276C22⋊C4—5661no—
277C42—2831no—
278C42—2831no—
279C42—5661no—
280C42—5661no—
281C23—21no—
282C23—5661no—
283C23D4×D28311yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—5661no—
287Q8—5661no—
288D4—21no—
289D4—21no—
290D4—81no—
291D4—5661no—
292D4—5661no—
293D4—22641no—
294D4—22641no—
295D4—22641no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—2831no—
302C2×C4—2831no—
303C2×C4—2831no—
304C2×C4—2831no—
305C2×C4—5661no—
306C2×C4—5661no—
307C2×C4—5661no—
308C2×C4—22641no—
309C2×C4—22641no—
310C2×C4D4×D28311yescharacteristic
311C2×C4C23×D28311yescharacteristic
312C8—21no—
313C8—21no—
314C8—5661no—
315C8—5661no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—11321no—
323C22—11321no—
324C22—11321no—
325C22C2×D4×D28311yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—5661no—
331C4—5661no—
332C4—5661no—
333C4—5661no—
334C4—11321no—
335C4—11321no—
336C4—11321no—
337C4#2258365511yescharacteristic
338C4#2258365711yescharacteristic
339C2—41no—
340C2—81no—
341C2—22641no—
342C2#3182704211yescharacteristic
343C2#3182727111yescharacteristic
344C2#3182727211yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#465×C283C2
socleC22×C283C22×D4
prime radical#31827068C2
hypercenter#465D283
hypocenterC283#3260
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #31827075C2semidirect
3. #31826775C2semidirect
4. #31826770C2semidirect
5. #31826767C2semidirect
6. #31826764C2semidirect
7. #31826713C2semidirect
8. #31826709C2semidirect
9. #31826694C2semidirect
10. #31826669C2semidirect
11. #31826668C2semidirect
12. #31826664C2semidirect
13. #31826663C2semidirect
14. #31826491C2semidirect
15. #465×C283C2semidirect
172. C283#3260semidirect
183. #465D283semidirect

Maximal subgroups

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

subgroupindex
#318270752
#318270682
#318267752
#318267702
#318267672
#318267642
#318267132
#318267092
#318266942
#318266692
#318266682
#318266642
#318266632
#318264912
#465×C2832
#3260283