Finite Group Databasebeta

← #49133370

Subgroups — #49133370

Order 36224.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827170C211yesmaximal, characteristic, complemented
2#31827121C211yesmaximal, characteristic
3#31826823C211yesmaximal, characteristic, complemented
4#31826797C211yesmaximal, characteristic, complemented
5#31826749C211yesmaximal, characteristic, complemented
6#31826724C211yesmaximal, characteristic, complemented
7#31826692C211yesmaximal, characteristic, complemented
8#31826686C211yesmaximal, characteristic, complemented
9#31826628C211yesmaximal, characteristic, complemented
10#31826623C211yesmaximal, characteristic, complemented
11#31826571C211yesmaximal, characteristic, complemented
12#31826533C211yesmaximal, characteristic, complemented
13#31826463C211yesmaximal, characteristic, complemented
14C2×#22583533C211yesmaximal, characteristic, complemented
15#481×C283C211yesmaximal, characteristic, complemented
16C2×#17985391C2211yescharacteristic
17C22×Dic566C2211yescharacteristic
18C2×Dic1132C2211yescharacteristic
19C2×Dic1132C2211yescharacteristic
20C2×#17985380C2211yescharacteristic
21C2×#17985375C2211yescharacteristic
22C22×C283⋊C8C2211yescharacteristic
23#22583609C2211yescharacteristic
24#22583600—21no—
25#22583597C2211yescharacteristic
26#22583596—21no—
27#22583590C2211yescharacteristic
28#22583590C2211yescharacteristic
29#22583589—21no—
30#22583589C2211yescharacteristic
31#22583588—21no—
32#22583587—21no—
33#22583582—21no—
34#22583575C2211yescharacteristic
35#22583575C2211yescharacteristic
36D4×Dic283—21no—
37C4×C22⋊D283—21no—
38C4×C22⋊D283C2211yescharacteristic
39C4⋊C4×D283C2211yescharacteristic
40#22583541C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42#22583535C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583533C2211yescharacteristic
45#22583533C2211yescharacteristic
46#22583533C2211yescharacteristic
47#22583533C2211yescharacteristic
48#22583533C2211yescharacteristic
49#22583531C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51#22583520C2211yescharacteristic
52#121×C283C2211yescharacteristic
53C2×C4⋊C4×C283C2211yescharacteristic
54#106×C283C2211yescharacteristic
55#106×C283C2211yescharacteristic
56#102×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58C22⋊C8×C283C2211yescharacteristic
59#17985391—22no—
60#17985391—41no—
61C2×Dic566—21no—
62C2×Dic566—22no—
63C2×Dic566—21no—
64C2×Dic566—41no—
65C2×Dic566C2311yescharacteristic
66C2×Dic566C2311yescharacteristic
67C2×Dic566C2311yescharacteristic
68C2×C22⋊D283—21no—
69C2×C22⋊D283D411yescharacteristic
70C22×Dic283—21no—
71C22×Dic283—21no—
72C2×C4×D283—21no—
73C2×C4×D283C2311yescharacteristic
74Dic1132—22no—
75Dic1132—41no—
76#17985380—41no—
77#17985375—41no—
78C2×C283⋊C8—41no—
79C2×C283⋊C8C2311yescharacteristic
80C2×C283⋊C8C2311yescharacteristic
81C4⋊Dic283—21no—
82C4⋊Dic283—21no—
83C4⋊Dic283C2311yescharacteristic
84Dic283⋊C4—21no—
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88Dic283⋊C4—21no—
89Dic283⋊C4D411yescharacteristic
90C22⋊Dic283—21no—
91C22⋊Dic283—21no—
92C22⋊Dic283—21no—
93C22⋊Dic283D411yescharacteristic
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4—21no—
96(C2×D283)⋊C4D411yescharacteristic
97C4×Dic283—21no—
98C4×Dic283—21no—
99C4×Dic283C2311yescharacteristic
100C2×D4×C283—21no—
101C2×D4×C283C2311yescharacteristic
102C22×C4×C283—21no—
103C22×C4×C283C2311yescharacteristic
104C2×C8×C283C2311yescharacteristic
105C2×C8×C283C2311yescharacteristic
106C4⋊C4×C283—21no—
107C4⋊C4×C283C2311yescharacteristic
108C4⋊C4×C283C2311yescharacteristic
109C4⋊C4×C283C2311yescharacteristic
110C22⋊C4×C283—21no—
111C22×D283C2×D411yescharacteristic
112Dic566—21no—
113Dic566—21no—
114Dic566—21no—
115Dic566—21no—
116Dic566—21no—
117Dic566—42no—
118Dic566—81no—
119Dic566#4112yes—
120C22⋊D283—22no—
121C22⋊D283—42no—
122C2×Dic283—21no—
123C2×Dic283—21no—
124C2×Dic283—21no—
125C2×Dic283—21no—
126C2×Dic283—42no—
127C2×Dic283—42no—
128C2×Dic283C2×D411yescharacteristic
129C2×Dic283C2×D411yescharacteristic
130C2×Dic283C2×D411yescharacteristic
131C4×D283—21no—
132C4×D283—21no—
133C4×D283—81no—
134C283⋊C8—21no—
135C283⋊C8—21no—
136C23×C283—21no—
137C23×C283C2×D411yescharacteristic
138D4×C283—21no—
139D4×C283—21no—
140D4×C283—42no—
141C2×C4×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—21no—
146C2×C4×C283—81no—
147C2×C4×C283C2×D411yescharacteristic
148C2×C4×C283C2411yescharacteristic
149C8×C283—21no—
150C8×C283—21no—
151C22×C283—21no—
152C22×C283—21no—
153C22×C283—41no—
154C22×C283—41no—
155C22×C283—41no—
156C22×C283#13712yes—
157C22×C283C22×D411yescharacteristic
158C2×D283—21no—
159C2×D283—21no—
160C2×D283—21no—
161C4×C283—21no—
162C4×C283—41no—
163C4×C283—41no—
164C4×C283—41no—
165C4×C283C2×#4111yescharacteristic
166C4×C283H(5,𝔽2)11yescharacteristic
167Dic283—21no—
168Dic283—22no—
169Dic283—21no—
170Dic283—21no—
171Dic283—41no—
172Dic283—41no—
173Dic283—41no—
174C2×C283—22no—
175C2×C283—81no—
176C2×C283#54611yescharacteristic
177C2×C283C2×#13711yescharacteristic
178C2×C283#57711yescharacteristic
179D283—41no—
180C283#331611yescharacteristic, complemented, Sylow
181#3316—2831nomaximal, Sylow
182#554—2831no—
183#548—2831no—
184#489—2831no—
185#483—2831no—
186#481D28311yescharacteristic, complemented
187#475—2831no—
188#470—2831no—
189#465—2831no—
190#464—2831no—
191#452—2831no—
192#451—2831no—
193#441—2831no—
194#435—2831no—
195#417—2831no—
196C2×#103—2831no—
197C2×#41—2831no—
198C22×Q8—2831no—
199C2×Q16—2831no—
200C2×Q16—2831no—
201C2×SD16—2831no—
202C2×M16—2831no—
203C22×C8—2831no—
204C4⋊Q8—2831no—
205#125—5661no—
206#124—2831no—
207#124—5661no—
208C22⋊Q8—2831no—
209C22⋊Q8—2831no—
210C22⋊Q8—2831no—
211C22⋊Q8—5661no—
212C22⋊Q8—5661no—
213C22⋊Q8—5661no—
214#121—5661no—
215#121C2×D28311yescharacteristic
216C4×Q8—2831no—
217C4×Q8—2831no—
218C4×D4—2831no—
219C4×D4—5661no—
220C4×D4—5661no—
221C2×C4⋊C4—2831no—
222C2×C4⋊C4C2×D28311yescharacteristic
223#106—2831no—
224#106C2×D28311yescharacteristic
225#106C2×D28311yescharacteristic
226C4⋊C8—2831no—
227#103—2831no—
228#103—2831no—
229#103—2831no—
230#103—2831no—
231#103—2831no—
232#103—2831no—
233#103—2831no—
234#102—2831no—
235#102C2×D28311yescharacteristic
236#102C2×D28311yescharacteristic
237C22⋊C8—2831no—
238C22⋊C8C2×D28311yescharacteristic
239#97—2831no—
240#41—5662no—
241#41—11321no—
242C2×Q8—2831no—
243C2×Q8—2831no—
244C2×Q8—2831no—
245C2×Q8—5661no—
246C2×Q8—5662no—
247C2×Q8—5661no—
248C2×Q8—11321no—
249C2×D4—21no—
250C2×D4—2831no—
251C2×D4—5661no—
252C2×D4C22×D28311yescharacteristic
253C22×C4—21no—
254C22×C4—2831no—
255C22×C4—5661no—
256C22×C4—5661no—
257C22×C4—5661no—
258C22×C4C22×D28311yescharacteristic
259Q16—5662no—
260Q16—11321no—
261SD16—11321no—
262M16—11321no—
263C2×C8—2831no—
264C2×C8—2831no—
265C2×C8—11321no—
266C2×C8C22×D28311yescharacteristic
267C2×C8C22×D28311yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—2831no—
270C4⋊C4—2831no—
271C4⋊C4—5661no—
272C4⋊C4—5661no—
273C4⋊C4—5661no—
274C4⋊C4—5661no—
275C4⋊C4—5661no—
276C4⋊C4—5661no—
277C4⋊C4—5661no—
278C4⋊C4C22×D28311yescharacteristic
279C4⋊C4C22×D28311yescharacteristic
280C4⋊C4C22×D28311yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—2831no—
283C22⋊C4—2831no—
284C22⋊C4—5661no—
285C22⋊C4—5661no—
286C22⋊C4—5661no—
287C22⋊C4—5661no—
288C22⋊C4—5661no—
289C42—2831no—
290C42—5661no—
291C42—5661no—
292C23—21no—
293C23—2831no—
294C23D4×D28311yescharacteristic
295Q8—2832no—
296Q8—5661no—
297Q8—5661no—
298Q8—5661no—
299Q8—5661no—
300Q8—5661no—
301Q8—11322no—
302Q8—22641no—
303D4—21no—
304D4—21no—
305D4—42no—
306D4—5662no—
307D4—11322no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—81no—
314C2×C4—2831no—
315C2×C4—2831no—
316C2×C4—2831no—
317C2×C4—5661no—
318C2×C4—5661no—
319C2×C4—5661no—
320C2×C4—5661no—
321C2×C4—5661no—
322C2×C4—5661no—
323C2×C4—11322no—
324C2×C4—11322no—
325C2×C4—22641no—
326C2×C4D4×D28311yescharacteristic
327C2×C4C23×D28311yescharacteristic
328C8—21no—
329C8—21no—
330C8—5661no—
331C8—5661no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—5661no—
338C22—5661no—
339C22—5661no—
340C22#2258363912yes—
341C22C2×D4×D28311yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—5661no—
347C4—5661no—
348C4—5661no—
349C4—5662no—
350C4—11321no—
351C4—11321no—
352C4—11321no—
353C4#41×D28311yescharacteristic
354C4#2258365611yescharacteristic
355C2—22no—
356C2—81no—
357C2—11321no—
358C2#3182710711yescharacteristic
359C2C2×#2258363911yescharacteristic
360C2#3182727511yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#481×C283C2
socleC22×C283C22×D4
prime radical#31827121C2
hypercenter#481D283
hypocenterC283#3316
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #31827170C2semidirect
3. #31826823C2semidirect
4. #31826797C2semidirect
5. #31826749C2semidirect
6. #31826724C2semidirect
7. #31826692C2semidirect
8. #31826686C2semidirect
9. #31826628C2semidirect
10. #31826623C2semidirect
11. #31826571C2semidirect
12. #31826533C2semidirect
13. #31826463C2semidirect
14. C2×#22583533C2semidirect
15. #481×C283C2semidirect
180. C283#3316semidirect
186. #481D283semidirect

Maximal subgroups

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

subgroupindex
#318271702
#318271212
#318268232
#318267972
#318267492
#318267242
#318266922
#318266862
#318266282
#318266232
#318265712
#318265332
#318264632
C2×#225835332
#481×C2832
#3316283