Finite Group Databasebeta

← #49133331

Subgroups — #49133331

Order 36224.

380 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827186C211yesmaximal, characteristic, complemented
2#31827122C211yesmaximal, characteristic
3#31826823C211yesmaximal, characteristic, complemented
4#31826807C211yesmaximal, characteristic, complemented
5#31826788C211yesmaximal, characteristic, complemented
6#31826758C211yesmaximal, characteristic, complemented
7#31826708C211yesmaximal, characteristic, complemented
8#31826704C211yesmaximal, characteristic, complemented
9#31826685C211yesmaximal, characteristic, complemented
10#31826619C211yesmaximal, characteristic, complemented
11#31826572C211yesmaximal, characteristic, complemented
12#31826533C211yesmaximal, characteristic, complemented
13#31826472C211yesmaximal, characteristic, complemented
14#31826461C211yesmaximal, characteristic, complemented
15#452×C283C211yesmaximal, characteristic, complemented
16C2×Q8×D283C2211yescharacteristic
17C2×#17985382C2211yescharacteristic
18C2×#17985375C2211yescharacteristic
19C22×C283⋊C8C2211yescharacteristic
20#22583609C2211yescharacteristic
21#22583605—21no—
22#22583603—21no—
23#22583597—21no—
24#22583597C2211yescharacteristic
25#22583596—21no—
26#22583589—21no—
27#22583589C2211yescharacteristic
28#22583586C2211yescharacteristic
29#22583581—21no—
30#22583581C2211yescharacteristic
31Q8×Dic283C2211yescharacteristic
32Q8×Dic283C2211yescharacteristic
33#22583575—21no—
34C4×C22⋊D283—21no—
35C4×C22⋊D283C2211yescharacteristic
36#22583569C2211yescharacteristic
37#22583568C2211yescharacteristic
38#22583544C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583542C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42#22583535C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583534C2211yescharacteristic
45#22583534C2211yescharacteristic
46#22583534C2211yescharacteristic
47#22583533C2211yescharacteristic
48#22583531C2211yescharacteristic
49#22583531C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51#22583520C2211yescharacteristic
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×Dic566—21no—
61C2×Dic566C2311yescharacteristic
62Q8×D283—22no—
63Q8×D283—41no—
64C2×C22⋊D283—21no—
65C2×C22⋊D283D411yescharacteristic
66C2×C4×D283—21no—
67C2×C4×D283C2311yescharacteristic
68#17985382—41no—
69#17985375—41no—
70C2×C283⋊C8—41no—
71C2×C283⋊C8C2311yescharacteristic
72C2×C283⋊C8C2311yescharacteristic
73C4⋊Dic283—21no—
74C4⋊Dic283—21no—
75C4⋊Dic283C2311yescharacteristic
76C4⋊Dic283C2311yescharacteristic
77C4⋊Dic283C2311yescharacteristic
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4D411yescharacteristic
82C22⋊Dic283—21no—
83C22⋊Dic283—21no—
84C22⋊Dic283—21no—
85C22⋊Dic283—21no—
86C22⋊Dic283—21no—
87C22⋊Dic283D411yescharacteristic
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4D411yescharacteristic
91C4×Dic283—21no—
92C4×Dic283—21no—
93C4×Dic283—21no—
94C4×Dic283—21no—
95C4×Dic283C2311yescharacteristic
96#41×C283—22no—
97#41×C283—41no—
98C2×Q8×C283C2311yescharacteristic
99C2×Q8×C283C2311yescharacteristic
100C2×D4×C283—21no—
101C2×D4×C283C2311yescharacteristic
102C22×C4×C283—21no—
103C22×C4×C283C2311yescharacteristic
104Q16×C283—22no—
105SD16×C283—41no—
106C2×C8×C283C2311yescharacteristic
107C2×C8×C283C2311yescharacteristic
108C4⋊C4×C283—21no—
109C4⋊C4×C283C2311yescharacteristic
110C22⋊C4×C283—21no—
111C22×D283C2×D411yescharacteristic
112Dic566—21no—
113Dic566—21no—
114Dic566—42no—
115Dic566—42no—
116C22⋊D283—41no—
117C22⋊D283—42no—
118C2×Dic283—21no—
119C2×Dic283—21no—
120C2×Dic283—21no—
121C2×Dic283—21no—
122C2×Dic283C2×D411yescharacteristic
123C2×Dic283C2×D411yescharacteristic
124C2×Dic283C2×D411yescharacteristic
125C4×D283—21no—
126C4×D283—21no—
127C4×D283—42no—
128C283⋊C8—21no—
129C283⋊C8—21no—
130C23×C283—21no—
131C23×C283C2×D411yescharacteristic
132Q8×C283—21no—
133Q8×C283—21no—
134Q8×C283—21no—
135Q8×C283#4112yes—
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×C283—42no—
145C2×C4×C283C2×D411yescharacteristic
146C2×C4×C283C2411yescharacteristic
147C8×C283—21no—
148C8×C283—21no—
149C22×C283—21no—
150C22×C283—21no—
151C22×C283—21no—
152C22×C283—41no—
153C22×C283—41no—
154C22×C283—41no—
155C22×C283C22×D411yescharacteristic
156C2×D283—21no—
157C2×D283—21no—
158C2×D283—21no—
159C4×C283—21no—
160C4×C283—22no—
161C4×C283—41no—
162C4×C283—41no—
163C4×C283C2×#4111yescharacteristic
164C4×C283H(5,𝔽2)11yescharacteristic
165Dic283—21no—
166Dic283—21no—
167Dic283—21no—
168Dic283—41no—
169Dic283—41no—
170Dic283—41no—
171Dic283—41no—
172C2×C283—41no—
173C2×C283—81no—
174C2×C283#54611yescharacteristic
175C2×C283#57511yescharacteristic
176C2×C283#57811yescharacteristic
177D283—41no—
178C283#331311yescharacteristic, complemented, Sylow
179#3313—2831nomaximal, Sylow
180#556—2831no—
181#548—2831no—
182#489—2831no—
183#485—2831no—
184#482—2831no—
185#477—2831no—
186#468—2831no—
187#467—2831no—
188#464—2831no—
189#452D28311yescharacteristic, complemented
190#451—2831no—
191#441—2831no—
192#435—2831no—
193#419—2831no—
194#416—2831no—
195C2×#41C2×D28311yescharacteristic
196C22×Q8—2831no—
197C2×Q16—2831no—
198C2×Q16C2×D28311yescharacteristic
199C2×SD16C2×D28311yescharacteristic
200C2×M16—2831no—
201C22×C8—2831no—
202C4⋊Q8—2831no—
203#126—5661no—
204#126—5661no—
205#124—2831no—
206#124—5661no—
207#124—5661no—
208C22⋊Q8—2831no—
209C22⋊Q8—2831no—
210C22⋊Q8—5661no—
211C22⋊Q8C2×D28311yescharacteristic
212#121—2831no—
213#121—5661no—
214C4×Q8—2831no—
215C4×Q8—2831no—
216C4×Q8—5661no—
217C4×D4—2831no—
218C4×D4—5661no—
219#117—2831no—
220#117—2831no—
221#107—2831no—
222#107—2831no—
223#106—2831no—
224C4⋊C8—2831no—
225#103—2831no—
226#103—2831no—
227#103—2831no—
228#103—2831no—
229#103—2831no—
230#103—2831no—
231#103C2×D28311yescharacteristic
232#102—2831no—
233#102—2831no—
234#102C2×D28311yescharacteristic
235C22⋊C8—2831no—
236C22⋊C8C2×D28311yescharacteristic
237#97—2831no—
238#41—22no—
239#41—41no—
240C2×Q8—2831no—
241C2×Q8—5661no—
242C2×Q8—5661no—
243C2×Q8—5662no—
244C2×Q8—11321no—
245C2×Q8C22×D28311yescharacteristic
246C2×Q8C22×D28311yescharacteristic
247C2×D4—21no—
248C2×D4—2831no—
249C2×D4—5661no—
250C2×D4C22×D28311yescharacteristic
251C22×C4—21no—
252C22×C4—2831no—
253C22×C4—5661no—
254C22×C4C22×D28311yescharacteristic
255Q16—22no—
256Q16—11321no—
257SD16—41no—
258M16—11321no—
259C2×C8—2831no—
260C2×C8—2831no—
261C2×C8—11321no—
262C2×C8C22×D28311yescharacteristic
263C2×C8C22×D28311yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—2831no—
266C4⋊C4—2831no—
267C4⋊C4—2831no—
268C4⋊C4—2831no—
269C4⋊C4—5661no—
270C4⋊C4—5661no—
271C4⋊C4—5661no—
272C4⋊C4—5661no—
273C4⋊C4—5661no—
274C4⋊C4C22×D28311yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—2831no—
277C22⋊C4—2831no—
278C22⋊C4—5661no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C22⋊C4—5661no—
284C22⋊C4—5661no—
285C42—2831no—
286C42—5661no—
287C42—5661no—
288C42—5661no—
289C42—5661no—
290C23—21no—
291C23—2831no—
292C23D4×D28311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—5661no—
297Q8—5661no—
298Q8—11322no—
299Q8—11322no—
300Q8#1798539112yes—
301D4—21no—
302D4—21no—
303D4—42no—
304D4—11321no—
305D4—11322no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—2831no—
313C2×C4—2831no—
314C2×C4—2831no—
315C2×C4—5661no—
316C2×C4—5661no—
317C2×C4—5661no—
318C2×C4—5661no—
319C2×C4—5661no—
320C2×C4—5661no—
321C2×C4—11322no—
322C2×C4D4×D28311yescharacteristic
323C2×C4C23×D28311yescharacteristic
324C8—21no—
325C8—21no—
326C8—5661no—
327C8—5661no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—5661no—
335C22—5661no—
336C22—5661no—
337C22C2×D4×D28311yescharacteristic
338C4—21no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—5661no—
343C4—5661no—
344C4—5661no—
345C4—11321no—
346C4—11321no—
347C4—11321no—
348C4—11321no—
349C4C2×#1798539111yescharacteristic
350C4#2258365511yescharacteristic
351C2—41no—
352C2—81no—
353C2—11321no—
354C2#3182710211yescharacteristic
355C2#3182726211yescharacteristic
356C2#3182728111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#452×C283C2
socleC22×C283C22×D4
prime radical#31827122C2
hypercenter#452D283
hypocenterC283#3313
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. #31827186C2semidirect
3. #31826823C2semidirect
4. #31826807C2semidirect
5. #31826788C2semidirect
6. #31826758C2semidirect
7. #31826708C2semidirect
8. #31826704C2semidirect
9. #31826685C2semidirect
10. #31826619C2semidirect
11. #31826572C2semidirect
12. #31826533C2semidirect
13. #31826472C2semidirect
14. #31826461C2semidirect
15. #452×C283C2semidirect
178. C283#3313semidirect
189. #452D283semidirect

Maximal subgroups

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

subgroupindex
#318271862
#318271222
#318268232
#318268072
#318267882
#318267582
#318267082
#318267042
#318266852
#318266192
#318265722
#318265332
#318264722
#318264612
#452×C2832
#3313283