Finite Group Databasebeta

← #49131815

Subgroups — #49131815

Order 36224.

412 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827017C211yesmaximal, characteristic, complemented
2#31827010C211yesmaximal, characteristic
3#31826862C211yesmaximal, characteristic, complemented
4#31826836C211yesmaximal, characteristic, complemented
5#31826814C211yesmaximal, characteristic, complemented
6#31826810C211yesmaximal, characteristic, complemented
7#31826696C211yesmaximal, characteristic, complemented
8#31826694C211yesmaximal, characteristic, complemented
9#31826692C211yesmaximal, characteristic, complemented
10#31826556C211yesmaximal, characteristic, complemented
11SD16×Dic283C211yesmaximal, characteristic, complemented
12#31826552C211yesmaximal, characteristic, complemented
13#31826550C211yesmaximal, characteristic, complemented
14C2×C8×Dic283C211yesmaximal, characteristic, complemented
15#465×C283C211yesmaximal, characteristic, complemented
16C2×#17985391—21no—
17C2×#17985381C2211yescharacteristic
18C2×#17985380C2211yescharacteristic
19C2×#17985379C2211yescharacteristic
20C22×C283⋊C8C2211yescharacteristic
21#22583609C2211yescharacteristic
22#22583609C2211yescharacteristic
23#22583608C2211yescharacteristic
24#22583606C2211yescharacteristic
25#22583600—21no—
26#22583596—21no—
27#22583589C2211yescharacteristic
28#22583587—21no—
29#22583584C2211yescharacteristic
30#22583582—21no—
31Q8×Dic283C2211yescharacteristic
32#22583575—21no—
33#22583575C2211yescharacteristic
34D4×Dic283C2211yescharacteristic
35#22583572C2211yescharacteristic
36(C22⋊D283)⋊C4—21no—
37#22583566—21no—
38C2×C4×Dic283C2211yescharacteristic
39#22583542C2211yescharacteristic
40#22583541C2211yescharacteristic
41#22583541C2211yescharacteristic
42#22583535C2211yescharacteristic
43#22583534C2211yescharacteristic
44#22583533C2211yescharacteristic
45#22583532C2211yescharacteristic
46#22583531C2211yescharacteristic
47#22583530C2211yescharacteristic
48C8×Dic283C2211yescharacteristic
49C8×Dic283C2211yescharacteristic
50C8×Dic283C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52C2×SD16×C283C2211yescharacteristic
53C22×C8×C283C2211yescharacteristic
54C22⋊Q8×C283C2211yescharacteristic
55#121×C283C2211yescharacteristic
56#106×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58#102×C283C2211yescharacteristic
59#17985391—44no—
60C2×Dic566—21no—
61C2×Dic566—21no—
62C2×Dic566C2311yescharacteristic
63C2×D1132C2311yescharacteristic
64C2×C22⋊D283—21no—
65C2×C22⋊D283—21no—
66C2×C22⋊D283—21no—
67C22×Dic283—21no—
68C22×Dic283D411yescharacteristic
69C22×Dic283D411yescharacteristic
70C2×C4×D283—21no—
71#17985381—22no—
72#17985380—22no—
73#17985379—22no—
74C2×C283⋊C8—22no—
75C2×C283⋊C8C2311yescharacteristic
76C2×C283⋊C8C2311yescharacteristic
77C4⋊Dic283—21no—
78C4⋊Dic283C2311yescharacteristic
79C4⋊Dic283C2311yescharacteristic
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86C22⋊Dic283—21no—
87C22⋊Dic283—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90C4×Dic283—21no—
91C4×Dic283—21no—
92C4×Dic283D411yescharacteristic
93C4×Dic283D411yescharacteristic
94C4×Dic283C2311yescharacteristic
95C4×Dic283C2311yescharacteristic
96C2×Q8×C283C2311yescharacteristic
97C2×D4×C283—21no—
98C2×D4×C283C2311yescharacteristic
99C22×C4×C283C2311yescharacteristic
100SD16×C283—22no—
101C2×C8×C283—22no—
102C2×C8×C283C2311yescharacteristic
103C2×C8×C283C2311yescharacteristic
104C4⋊C4×C283—21no—
105C4⋊C4×C283C2311yescharacteristic
106C4⋊C4×C283C2311yescharacteristic
107C22⋊C4×C283—21no—
108C22⋊C4×C283—21no—
109C22×D283—21no—
110Dic566—21no—
111Dic566—21no—
112Dic566—42no—
113Dic566—42no—
114D1132—21no—
115D1132—21no—
116C22⋊D283—42no—
117C22⋊D283—42no—
118C22⋊D283—42no—
119C2×Dic283—22no—
120C2×Dic283—21no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283—42no—
124C2×Dic283SD1614yescomplemented
125C2×Dic283C2×D411yescharacteristic
126C2×Dic283C2×D411yescharacteristic
127C2×Dic283C2×D411yescharacteristic
128C2×Dic283C2×D411yescharacteristic
129C4×D283—42no—
130C283⋊C8—21no—
131C283⋊C8#4112yescomplemented
132C23×C283—21no—
133C23×C283C2×D411yescharacteristic
134Q8×C283—21no—
135Q8×C283—21no—
136D4×C283—21no—
137D4×C283—21no—
138D4×C283—42no—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283C2×D411yescharacteristic
145C2×C4×C283C2411yescharacteristic
146C8×C283—21no—
147C8×C283#4112yescomplemented
148C22×C283—21no—
149C22×C283—21no—
150C22×C283—41no—
151C22×C283—41no—
152C22×C283—41no—
153C22×C283C2×SD1612yes—
154C22×C283C22×D411yescharacteristic
155C2×D283—41no—
156C2×D283—41no—
157C2×D283—41no—
158C4×C283—21no—
159C4×C283—41no—
160C4×C283—41no—
161C4×C283—41no—
162C4×C283C2×#4111yescharacteristic
163C4×C283C2×#4111yescharacteristic
164Dic283—21no—
165Dic283—41no—
166Dic283—41no—
167Dic283—41no—
168Dic283C2×SD1612yes—
169Dic283C2×SD1612yes—
170Dic283#13512yes—
171C2×C283—22no—
172C2×C283—81no—
173C2×C283#53211yescharacteristic
174C2×C283C22×SD1611yescharacteristic
175C2×C283C2×#13511yescharacteristic
176D283—81no—
177C283#316711yescharacteristic, complemented, Sylow
178#3167—2831nomaximal, Sylow
179#533—2831no—
180#532—2831no—
181#498—2831no—
182#492—2831no—
183#487—2831no—
184#486—2831no—
185#465—2831no—
186#465—2831no—
187#465—2831no—
188#465D28311yescharacteristic, complemented
189C4×SD16—2831no—
190C4×SD16—2831no—
191C4×SD16—2831no—
192C4×SD16—2831no—
193C2×C4×C8—2831no—
194C2×#41—5661no—
195C2×SD16—2831no—
196C2×SD16—2831no—
197C2×SD16—2831no—
198C2×SD16C2×D28311yescharacteristic
199C22×C8—2831no—
200C22×C8C2×D28311yescharacteristic
201C4⋊Q8—2831no—
202C4⋊Q8—2831no—
203C4⋊Q8—2831no—
204#127—2831no—
205#125—5661no—
206#124—5661no—
207C22⋊Q8—2831no—
208C22⋊Q8—5661no—
209C22⋊Q8C2×D28311yescharacteristic
210#121—2831no—
211#121—5661no—
212#121C2×D28311yescharacteristic
213C4×Q8—2831no—
214C4×Q8—2831no—
215C4×Q8—5661no—
216C4×D4—2831no—
217C4×D4—2831no—
218C4×D4—5661no—
219#117—5661no—
220C2×C42—2831no—
221#106—2831no—
222#106—2831no—
223#106—2831no—
224#106C2×D28311yescharacteristic
225#103—2831no—
226#103—2831no—
227#103—2831no—
228#103C2×D28311yescharacteristic
229#102—2831no—
230#102—2831no—
231#102—2831no—
232#102C2×D28311yescharacteristic
233C4×C8—2831no—
234C4×C8—2831no—
235C4×C8—2831no—
236C4×C8—2831no—
237#41—11324no—
238C2×Q8—2831no—
239C2×Q8—5661no—
240C2×Q8—5661no—
241C2×Q8C22×D28311yescharacteristic
242C2×D4—21no—
243C2×D4—2831no—
244C2×D4—5661no—
245C2×D4—5661no—
246C2×D4—5661no—
247C2×D4C22×D28311yescharacteristic
248C22×C4—2831no—
249C22×C4—2831no—
250C22×C4—5661no—
251C22×C4—5661no—
252C22×C4C22×D28311yescharacteristic
253SD16—22no—
254SD16—5662no—
255SD16—5662no—
256SD16—5662no—
257C2×C8—22no—
258C2×C8—2831no—
259C2×C8—2831no—
260C2×C8—5662no—
261C2×C8C22×D28311yescharacteristic
262C2×C8C22×D28311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—2831no—
265C4⋊C4—2831no—
266C4⋊C4—5661no—
267C4⋊C4—5661no—
268C4⋊C4—5661no—
269C4⋊C4—5661no—
270C4⋊C4—5661no—
271C4⋊C4—5661no—
272C4⋊C4—5661no—
273C4⋊C4C22×D28311yescharacteristic
274C4⋊C4C22×D28311yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—5661no—
278C22⋊C4—5661no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C42—2831no—
282C42—2831no—
283C42—2831no—
284C42—2831no—
285C42—5661no—
286C42—5661no—
287C23—21no—
288C23—5661no—
289C23D4×D28311yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—5661no—
293Q8—5661no—
294Q8—11322no—
295Q8—11322no—
296D4—21no—
297D4—21no—
298D4—42no—
299D4—5661no—
300D4—5661no—
301D4—11322no—
302D4—11322no—
303D4—11322no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—2834no—
310C2×C4—2831no—
311C2×C4—2831no—
312C2×C4—2831no—
313C2×C4—2831no—
314C2×C4—5662no—
315C2×C4—5661no—
316C2×C4—5661no—
317C2×C4—5661no—
318C2×C4—11322no—
319C2×C4—11322no—
320C2×C4D4×D28311yescharacteristic
321C2×C4C23×D28311yescharacteristic
322C8—21no—
323C8—2832no—
324C8—5661no—
325C8#1798539112yescomplemented
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—11321no—
332C22—11321no—
333C22—11321no—
334C22SD16×D28312yes—
335C22C2×D4×D28311yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—2832no—
341C4—2832no—
342C4—2832no—
343C4—5661no—
344C4—11321no—
345C4—11321no—
346C4—11321no—
347C4#41×D28311yescharacteristic
348C4C2×#1798539111yescharacteristic
349C2—22no—
350C2—81no—
351C2—22641no—
352C2#3182701011yescharacteristic
353C2C2×SD16×D28311yescharacteristic
354C2#135×D28311yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#465×C283C2
socleC22×C283C22×D4
prime radical#31827010C2
hypercenter#465D283
hypocenterC283#3167
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. #31827017C2semidirect
3. #31826862C2semidirect
4. #31826836C2semidirect
5. #31826814C2semidirect
6. #31826810C2semidirect
7. #31826696C2semidirect
8. #31826694C2semidirect
9. #31826692C2semidirect
10. #31826556C2semidirect
11. SD16×Dic283C2semidirect
12. #31826552C2semidirect
13. #31826550C2semidirect
14. C2×C8×Dic283C2semidirect
15. #465×C283C2semidirect
124. C2×Dic283SD16semidirect
131. C283⋊C8#41semidirect
147. C8×C283#41semidirect
177. C283#3167semidirect
188. #465D283semidirect
325. C8#17985391semidirect

Maximal subgroups

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

subgroupindex
#318270172
#318270102
#318268622
#318268362
#318268142
#318268102
#318266962
#318266942
#318266922
#318265562
SD16×Dic2832
#318265522
#318265502
C2×C8×Dic2832
#465×C2832
#3167283