Finite Group Databasebeta

← #49133325

Subgroups — #49133325

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#31827183C211yesmaximal, characteristic, complemented
2#31827125C211yesmaximal, characteristic
3#31826826C211yesmaximal, characteristic, complemented
4#31826791C211yesmaximal, characteristic, complemented
5#31826759C211yesmaximal, characteristic, complemented
6#31826712C211yesmaximal, characteristic, complemented
7#31826704C211yesmaximal, characteristic, complemented
8#31826690C211yesmaximal, characteristic, complemented
9#31826629C211yesmaximal, characteristic, complemented
10#31826622C211yesmaximal, characteristic, complemented
11#31826571C211yesmaximal, characteristic, complemented
12#31826533C211yesmaximal, characteristic, complemented
13#31826472C211yesmaximal, characteristic, complemented
14#31826459C211yesmaximal, characteristic, complemented
15#485×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C2×Q8×D283C2211yescharacteristic
18C2×Dic1132C2211yescharacteristic
19C2×#17985382C2211yescharacteristic
20C2×#17985381C2211yescharacteristic
21C2×#17985375C2211yescharacteristic
22C22×C283⋊C8C2211yescharacteristic
23#22583609C2211yescharacteristic
24#22583604—21no—
25#22583603—21no—
26#22583599C2211yescharacteristic
27#22583596—21no—
28#22583596—21no—
29#22583590C2211yescharacteristic
30#22583589C2211yescharacteristic
31#22583588—21no—
32#22583585C2211yescharacteristic
33#22583583—21no—
34C4×Dic566—21no—
35#22583575C2211yescharacteristic
36#22583575C2211yescharacteristic
37#22583572—21no—
38C4×C22⋊D283C2211yescharacteristic
39#22583568C2211yescharacteristic
40#22583543C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42#22583535C2211yescharacteristic
43#22583534C2211yescharacteristic
44#22583533C2211yescharacteristic
45#22583533C2211yescharacteristic
46#22583533C2211yescharacteristic
47#22583532C2211yescharacteristic
48#22583530C2211yescharacteristic
49#22583530C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51#22583520C2211yescharacteristic
52C22⋊Q8×C283C2211yescharacteristic
53#117×C283C2211yescharacteristic
54#107×C283C2211yescharacteristic
55#106×C283C2211yescharacteristic
56#103×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58C22⋊C8×C283C2211yescharacteristic
59#17985392—22no—
60#17985392—41no—
61C2×Dic566—21no—
62C2×Dic566—21no—
63C2×Dic566C2311yescharacteristic
64C2×Dic566C2311yescharacteristic
65Q8×D283—22no—
66Q8×D283—41no—
67C2×D1132—21no—
68C2×D1132C2311yescharacteristic
69C2×C22⋊D283—21no—
70C2×C22⋊D283D411yescharacteristic
71C2×C4×D283—21no—
72C2×C4×D283—21no—
73C2×C4×D283C2311yescharacteristic
74Dic1132—22no—
75#17985382—41no—
76#17985381—41no—
77#17985375—41no—
78C2×C283⋊C8—41no—
79C2×C283⋊C8C2311yescharacteristic
80C2×C283⋊C8C2311yescharacteristic
81C4⋊Dic283—21no—
82C4⋊Dic283C2311yescharacteristic
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87Dic283⋊C4D411yescharacteristic
88C22⋊Dic283—21no—
89C22⋊Dic283D411yescharacteristic
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4D411yescharacteristic
96C4×Dic283—21no—
97C4×Dic283—21no—
98C4×Dic283—21no—
99C4×Dic283C2311yescharacteristic
100C2×Q8×C283C2311yescharacteristic
101C22×C4×C283C2311yescharacteristic
102C2×C8×C283C2311yescharacteristic
103C2×C8×C283C2311yescharacteristic
104C4⋊C4×C283—21no—
105C4⋊C4×C283C2311yescharacteristic
106C4⋊C4×C283C2311yescharacteristic
107C4⋊C4×C283C2311yescharacteristic
108C22⋊C4×C283—21no—
109C22⋊C4×C283—21no—
110C42×C283—21no—
111C22×D283—21no—
112C22×D283C2×D411yescharacteristic
113Dic566—21no—
114Dic566—21no—
115Dic566—21no—
116Dic566—42no—
117Dic566—42no—
118Dic566#4112yes—
119D1132—21no—
120D1132—21no—
121D1132—42no—
122C22⋊D283—41no—
123C22⋊D283—42no—
124C2×Dic283—21no—
125C2×Dic283—21no—
126C2×Dic283—21no—
127C2×Dic283C2×D411yescharacteristic
128C2×Dic283C2×D411yescharacteristic
129C2×Dic283C2×D411yescharacteristic
130C4×D283—21no—
131C4×D283—21no—
132C4×D283—42no—
133C4×D283—42no—
134C283⋊C8—21no—
135C283⋊C8—21no—
136C23×C283C2×D411yescharacteristic
137Q8×C283—21no—
138Q8×C283—21no—
139C2×C4×C283—21no—
140C2×C4×C283—21no—
141C2×C4×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283C2×D411yescharacteristic
146C2×C4×C283C2411yescharacteristic
147C8×C283—21no—
148C8×C283—21no—
149C22×C283—21no—
150C22×C283—21no—
151C22×C283—21no—
152C22×C283C22×D411yescharacteristic
153C2×D283—21no—
154C2×D283—21no—
155C2×D283—21no—
156C2×D283—41no—
157C2×D283—41no—
158C2×D283—41no—
159C4×C283—21no—
160C4×C283—41no—
161C4×C283—41no—
162C4×C283—41no—
163C4×C283—41no—
164C4×C283C2×#4111yescharacteristic
165C4×C283H(5,𝔽2)11yescharacteristic
166Dic283—21no—
167Dic283—22no—
168Dic283—21no—
169Dic283—21no—
170Dic283—41no—
171Dic283—41no—
172C2×C283—41no—
173C2×C283#54611yescharacteristic
174C2×C283#57511yescharacteristic
175C2×C283#57811yescharacteristic
176D283—41no—
177D283—81no—
178C283#331311yescharacteristic, complemented, Sylow
179#3313—2831nomaximal, Sylow
180#556—2831no—
181#548—2831no—
182#489—2831no—
183#485D28311yescharacteristic, complemented
184#482—2831no—
185#477—2831no—
186#468—2831no—
187#467—2831no—
188#464—2831no—
189#452—2831no—
190#451—2831no—
191#441—2831no—
192#435—2831no—
193#419—2831no—
194#416—2831no—
195C2×#41—2831no—
196C22×Q8—2831no—
197C2×Q16—2831no—
198C2×Q16—2831no—
199C2×SD16—2831no—
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#117C2×D28311yescharacteristic
221#107—2831no—
222#107C2×D28311yescharacteristic
223#106C2×D28311yescharacteristic
224C4⋊C8—2831no—
225#103—2831no—
226#103—2831no—
227#103—2831no—
228#103—2831no—
229#103—2831no—
230#103C2×D28311yescharacteristic
231#103C2×D28311yescharacteristic
232#102—2831no—
233#102—2831no—
234#102—2831no—
235C22⋊C8—2831no—
236C22⋊C8C2×D28311yescharacteristic
237#97—2831no—
238#41—5662no—
239#41—11321no—
240C2×Q8—2831no—
241C2×Q8—2831no—
242C2×Q8—5661no—
243C2×Q8—5661no—
244C2×Q8—5662no—
245C2×Q8—11321no—
246C2×Q8C22×D28311yescharacteristic
247C2×D4—2831no—
248C2×D4—2831no—
249C2×D4—5661no—
250C2×D4—5661no—
251C22×C4—2831no—
252C22×C4—5661no—
253C22×C4—5661no—
254C22×C4C22×D28311yescharacteristic
255Q16—5662no—
256Q16—11321no—
257SD16—11321no—
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—5661no—
268C4⋊C4—5661no—
269C4⋊C4—5661no—
270C4⋊C4—5661no—
271C4⋊C4—5661no—
272C4⋊C4C22×D28311yescharacteristic
273C4⋊C4C22×D28311yescharacteristic
274C4⋊C4C22×D28311yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—2831no—
278C22⋊C4—2831no—
279C22⋊C4—5661no—
280C22⋊C4—5661no—
281C22⋊C4—5661no—
282C22⋊C4—5661no—
283C22⋊C4—5661no—
284C22⋊C4—5661no—
285C42—21no—
286C42—2831no—
287C42—5661no—
288C42—5661no—
289C42—5661no—
290C23—2831no—
291C23—5661no—
292C23D4×D28311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—2832no—
296Q8—5661no—
297Q8—5661no—
298Q8—5661no—
299Q8—11322no—
300Q8—11322no—
301D4—5661no—
302D4—5661no—
303D4—11322no—
304D4—11321no—
305D4—11322no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
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—11322no—
321C2×C4—11322no—
322C2×C4D4×D28311yescharacteristic
323C2×C4C23×D28311yescharacteristic
324C8—21no—
325C8—21no—
326C8—5661no—
327C8—5661no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—5661no—
332C22—5661no—
333C22—5661no—
334C22—11321no—
335C22—11321no—
336C22—11321no—
337C22C2×D4×D28311yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—5661no—
344C4—5661no—
345C4—5661no—
346C4—5662no—
347C4—11321no—
348C4—11321no—
349C4#41×D28311yescharacteristic
350C4#2258365611yescharacteristic
351C2—41no—
352C2—11321no—
353C2—22641no—
354C2#3182710711yescharacteristic
355C2#3182726211yescharacteristic
356C2#3182728111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#485×C283C2
socleC22×C283C22×D4
prime radical#31827125C2
hypercenter#485D283
hypocenterC283#3313
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #31827183C2semidirect
3. #31826826C2semidirect
4. #31826791C2semidirect
5. #31826759C2semidirect
6. #31826712C2semidirect
7. #31826704C2semidirect
8. #31826690C2semidirect
9. #31826629C2semidirect
10. #31826622C2semidirect
11. #31826571C2semidirect
12. #31826533C2semidirect
13. #31826472C2semidirect
14. #31826459C2semidirect
15. #485×C283C2semidirect
178. C283#3313semidirect
183. #485D283semidirect

Maximal subgroups

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

subgroupindex
#318271832
#318271252
#318268262
#318267912
#318267592
#318267122
#318267042
#318266902
#318266292
#318266222
#318265712
#318265332
#318264722
#318264592
#485×C2832
#3313283