Finite Group Databasebeta

← #49133241

Subgroups — #49133241

Order 36224.

394 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827162C211yesmaximal, characteristic, complemented
2#31827114C211yesmaximal, characteristic, complemented
3#31826832C211yesmaximal, characteristic, complemented
4#31826807C211yesmaximal, characteristic, complemented
5#31826794C211yesmaximal, characteristic, complemented
6#31826763C211yesmaximal, characteristic, complemented
7#31826708C211yesmaximal, characteristic, complemented
8#31826692C211yesmaximal, characteristic, complemented
9#31826668C211yesmaximal, characteristic, complemented
10#31826607C211yesmaximal, characteristic, complemented
11#31826577C211yesmaximal, characteristic, complemented
12#31826533C211yesmaximal, characteristic, complemented
13#31826463C211yesmaximal, characteristic, complemented
14#31826461C211yesmaximal, characteristic, complemented
15#449×C283C211yesmaximal, characteristic, complemented
16C2×#17985391C2211yescharacteristic
17C2×#17985380C2211yescharacteristic
18C2×#17985375C2211yescharacteristic
19C22×C283⋊C8C2211yescharacteristic
20#22583608C2211yescharacteristic
21#22583603—21no—
22#22583601C2211yescharacteristic
23#22583593—21no—
24#22583591—21no—
25#22583591—21no—
26#22583589C2211yescharacteristic
27#22583586C2211yescharacteristic
28#22583582—21no—
29#22583581—21no—
30#22583581C2211yescharacteristic
31D4×Dic283C2211yescharacteristic
32D4×Dic283C2211yescharacteristic
33C4×C22⋊D283C2211yescharacteristic
34(C22⋊D283)⋊C4—21no—
35#22583569C2211yescharacteristic
36C2×Dic283⋊C4—21no—
37C4⋊C4×D283C2211yescharacteristic
38#22583544C2211yescharacteristic
39#22583542C2211yescharacteristic
40#22583541C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42#22583535C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583534C2211yescharacteristic
45#22583534C2211yescharacteristic
46#22583533C2211yescharacteristic
47#22583531C2211yescharacteristic
48#22583531C2211yescharacteristic
49#22583531C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51#22583520C2211yescharacteristic
52C2×#41×C283C2211yescharacteristic
53C2×SD16×C283C2211yescharacteristic
54C2×D8×C283C2211yescharacteristic
55#121×C283C2211yescharacteristic
56#103×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58C22⋊C8×C283C2211yescharacteristic
59#17985391—22no—
60#17985391—41no—
61C2×Dic566C2311yescharacteristic
62C2×C22⋊D283—21no—
63C2×C22⋊D283—21no—
64C2×C22⋊D283D411yescharacteristic
65C22×Dic283—21no—
66C22×Dic283—21no—
67C22×Dic283—21no—
68C2×C4×D283—21no—
69C2×C4×D283C2311yescharacteristic
70#17985380—41no—
71#17985375—41no—
72C2×C283⋊C8—41no—
73C2×C283⋊C8C2311yescharacteristic
74C2×C283⋊C8C2311yescharacteristic
75C4⋊Dic283—21no—
76C4⋊Dic283C2311yescharacteristic
77C4⋊Dic283C2311yescharacteristic
78C4⋊Dic283C2311yescharacteristic
79Dic283⋊C4—21no—
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4—21no—
84Dic283⋊C4—21no—
85Dic283⋊C4D411yescharacteristic
86C22⋊Dic283—21no—
87C22⋊Dic283—21no—
88C22⋊Dic283—21no—
89C22⋊Dic283—21no—
90C22⋊Dic283—21no—
91C22⋊Dic283D411yescharacteristic
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4D411yescharacteristic
94C4×Dic283—21no—
95C4×Dic283C2311yescharacteristic
96#41×C283—22no—
97#41×C283—41no—
98C2×Q8×C283C2311yescharacteristic
99C2×D4×C283—21no—
100C2×D4×C283—21no—
101C2×D4×C283C2311yescharacteristic
102C2×D4×C283C2311yescharacteristic
103C22×C4×C283—21no—
104C22×C4×C283C2311yescharacteristic
105SD16×C283—41no—
106D8×C283—22no—
107C2×C8×C283C2311yescharacteristic
108C2×C8×C283C2311yescharacteristic
109C4⋊C4×C283C2311yescharacteristic
110C22⋊C4×C283—21no—
111C22×D283C2×D411yescharacteristic
112Dic566—21no—
113Dic566—21no—
114C22⋊D283—41no—
115C22⋊D283—42no—
116C22⋊D283—42no—
117C2×Dic283—21no—
118C2×Dic283—21no—
119C2×Dic283—21no—
120C2×Dic283—21no—
121C2×Dic283—42no—
122C2×Dic283—42no—
123C2×Dic283—81no—
124C2×Dic283C2×D411yescharacteristic
125C2×Dic283C2×D411yescharacteristic
126C2×Dic283C2×D411yescharacteristic
127C4×D283—21no—
128C4×D283—21no—
129C4×D283—81no—
130C283⋊C8—21no—
131C283⋊C8—21no—
132C23×C283—21no—
133C23×C283—21no—
134C23×C283C2×D411yescharacteristic
135Q8×C283—21no—
136Q8×C283—21no—
137D4×C283—21no—
138D4×C283—21no—
139D4×C283—21no—
140D4×C283—42no—
141D4×C283—81no—
142D4×C283#4112yes—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—21no—
146C2×C4×C283—21no—
147C2×C4×C283—42no—
148C2×C4×C283C2×D411yescharacteristic
149C2×C4×C283C2411yescharacteristic
150C8×C283—21no—
151C8×C283—21no—
152C22×C283—21no—
153C22×C283—22no—
154C22×C283—21no—
155C22×C283—21no—
156C22×C283—41no—
157C22×C283—41no—
158C22×C283—41no—
159C22×C283—41no—
160C22×C283—41no—
161C22×C283C22×D411yescharacteristic
162C2×D283—21no—
163C2×D283—21no—
164C2×D283—21no—
165C4×C283—21no—
166C4×C283—41no—
167C4×C283—41no—
168C4×C283C2×#4111yescharacteristic
169C4×C283H(5,𝔽2)11yescharacteristic
170Dic283—21no—
171Dic283—21no—
172Dic283—21no—
173Dic283—41no—
174Dic283—41no—
175Dic283—41no—
176Dic283—41no—
177C2×C283—41no—
178C2×C283—42no—
179C2×C283—81no—
180C2×C283#54611yescharacteristic
181C2×C283#57511yescharacteristic
182C2×C283#57711yescharacteristic
183D283—41no—
184C283#330711yescharacteristic, complemented, Sylow
185#3307—2831nomaximal, Sylow
186#553—2831no—
187#547—2831no—
188#491—2831no—
189#485—2831no—
190#483—2831no—
191#478—2831no—
192#468—2831no—
193#465—2831no—
194#461—2831no—
195#449—2831no—
196#449D28311yescharacteristic, complemented
197#442—2831no—
198#435—2831no—
199#417—2831no—
200#416—2831no—
201C2×#41—2831no—
202C2×#41C2×D28311yescharacteristic
203C2×SD16—2831no—
204C2×SD16C2×D28311yescharacteristic
205C2×D8C2×D28311yescharacteristic
206C2×M16—2831no—
207C22×C8—2831no—
208C4⋊Q8—2831no—
209#126—5661no—
210#125—2831no—
211#123—5661no—
212#123—5661no—
213#123—5661no—
214C22⋊Q8—2831no—
215C22⋊Q8—2831no—
216#121—2831no—
217#121—5661no—
218#121—5661no—
219#121C2×D28311yescharacteristic
220C4×D4—2831no—
221C4×D4—2831no—
222C4×D4—2831no—
223C4×D4—5661no—
224#117—2831no—
225C2×C4⋊C4—2831no—
226C2×C4⋊C4—5661no—
227#107—2831no—
228#106—2831no—
229#106—2831no—
230C4⋊C8—2831no—
231#103—2831no—
232#103—2831no—
233#103—2831no—
234#103—2831no—
235#103—2831no—
236#103C2×D28311yescharacteristic
237#102—2831no—
238#102—2831no—
239#102—2831no—
240#102C2×D28311yescharacteristic
241C22⋊C8—2831no—
242C22⋊C8C2×D28311yescharacteristic
243#97—2831no—
244#41—22no—
245#41—41no—
246#41—5662no—
247#41—11321no—
248C2×Q8—2831no—
249C2×Q8C22×D28311yescharacteristic
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—2831no—
253C2×D4—5661no—
254C2×D4—5661no—
255C2×D4C22×D28311yescharacteristic
256C2×D4C22×D28311yescharacteristic
257C22×C4—21no—
258C22×C4—2831no—
259C22×C4—5661no—
260C22×C4—5661no—
261C22×C4—5661no—
262C22×C4—5661no—
263C22×C4C22×D28311yescharacteristic
264SD16—41no—
265SD16—11321no—
266D8—22no—
267M16—11321no—
268C2×C8—2831no—
269C2×C8—2831no—
270C2×C8—11321no—
271C2×C8C22×D28311yescharacteristic
272C2×C8C22×D28311yescharacteristic
273C4⋊C4—2831no—
274C4⋊C4—2831no—
275C4⋊C4—2831no—
276C4⋊C4—2831no—
277C4⋊C4—5661no—
278C4⋊C4—5661no—
279C4⋊C4—5661no—
280C4⋊C4—5661no—
281C4⋊C4—5661no—
282C4⋊C4—5661no—
283C4⋊C4—5661no—
284C4⋊C4C22×D28311yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—2831no—
287C22⋊C4—2831no—
288C22⋊C4—5661no—
289C22⋊C4—5661no—
290C22⋊C4—5661no—
291C22⋊C4—5661no—
292C22⋊C4—5661no—
293C22⋊C4—5661no—
294C42—2831no—
295C42—5661no—
296C23—21no—
297C23—21no—
298C23—2831no—
299C23D4×D28311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—5661no—
303Q8—5661no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—81no—
309D4—11321no—
310D4—11322no—
311D4—11322no—
312D4#1798539112yes—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—42no—
318C2×C4—2831no—
319C2×C4—2831no—
320C2×C4—2831no—
321C2×C4—5661no—
322C2×C4—5661no—
323C2×C4—5661no—
324C2×C4—5661no—
325C2×C4—5661no—
326C2×C4—5661no—
327C2×C4—11322no—
328C2×C4—11322no—
329C2×C4—22641no—
330C2×C4—22641no—
331C2×C4D4×D28311yescharacteristic
332C2×C4C23×D28311yescharacteristic
333C8—21no—
334C8—21no—
335C8—5661no—
336C8—5661no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—5661no—
347C22—5661no—
348C22—5661no—
349C22C2×D4×D28311yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—5661no—
354C4—5661no—
355C4—5661no—
356C4—11321no—
357C4—11321no—
358C4—11321no—
359C4—11321no—
360C4C2×#1798539111yescharacteristic
361C4#2258365511yescharacteristic
362C2—41no—
363C2—42no—
364C2—81no—
365C2—11321no—
366C2#3182710211yescharacteristic
367C2#3182726211yescharacteristic
368C2#3182727511yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#449×C283C2
socleC22×C283C22×D4
hypercenter#449D283
hypocenterC283#3307
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #31827162C2semidirect
2. #31827114C2semidirect
3. #31826832C2semidirect
4. #31826807C2semidirect
5. #31826794C2semidirect
6. #31826763C2semidirect
7. #31826708C2semidirect
8. #31826692C2semidirect
9. #31826668C2semidirect
10. #31826607C2semidirect
11. #31826577C2semidirect
12. #31826533C2semidirect
13. #31826463C2semidirect
14. #31826461C2semidirect
15. #449×C283C2semidirect
184. C283#3307semidirect
196. #449D283semidirect

Maximal subgroups

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

subgroupindex
#318271622
#318271142
#318268322
#318268072
#318267942
#318267632
#318267082
#318266922
#318266682
#318266072
#318265772
#318265332
#318264632
#318264612
#449×C2832
#3307283