Finite Group Databasebeta

← #49133166

Subgroups — #49133166

Order 36224.

398 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#31827159C211yesmaximal, characteristic, complemented
2#31827125C211yesmaximal, characteristic, complemented
3#31826821C211yesmaximal, characteristic, complemented
4#31826785C211yesmaximal, characteristic, complemented
5#31826771C211yesmaximal, characteristic, complemented
6#31826702C211yesmaximal, characteristic, complemented
7#31826696C211yesmaximal, characteristic, complemented
8#31826683C211yesmaximal, characteristic, complemented
9#31826612C211yesmaximal, characteristic, complemented
10#31826605C211yesmaximal, characteristic, complemented
11#31826552C211yesmaximal, characteristic, complemented
12(C22⋊D283)⋊C8C211yesmaximal, characteristic, complemented
13#31826459C211yesmaximal, characteristic, complemented
14#103×D283C211yesmaximal, characteristic, complemented
15#485×C283C211yesmaximal, characteristic, complemented
16C2×#17985392C2211yescharacteristic
17C2×Q8×D283C2211yescharacteristic
18C2×#17985381C2211yescharacteristic
19C2×#17985379C2211yescharacteristic
20C2×D2264C2211yescharacteristic
21C22×C283⋊C8C2211yescharacteristic
22C2×C8×D283C2211yescharacteristic
23#22583604—21no—
24#22583601C2211yescharacteristic
25#22583599C2211yescharacteristic
26#22583596—21no—
27#22583592—21no—
28#22583588—21no—
29#22583585C2211yescharacteristic
30#22583585C2211yescharacteristic
31#22583584C2211yescharacteristic
32#22583583—21no—
33#22583583—21no—
34#22583575C2211yescharacteristic
35C4×D1132—21no—
36#22583572—21no—
37#22583572C2211yescharacteristic
38C4×C22⋊D283C2211yescharacteristic
39C4⋊C4×D283C2211yescharacteristic
40#22583541C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42#22583535C2211yescharacteristic
43#22583534C2211yescharacteristic
44#22583533C2211yescharacteristic
45#22583533C2211yescharacteristic
46#22583532C2211yescharacteristic
47#22583530C2211yescharacteristic
48#22583530C2211yescharacteristic
49#22583530C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
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×Dic566C2311yescharacteristic
63Q8×D283—22no—
64Q8×D283—41no—
65C2×D1132—21no—
66C2×D1132—21no—
67C2×D1132C2311yescharacteristic
68C2×D1132C2311yescharacteristic
69C2×C22⋊D283—21no—
70C2×C22⋊D283—21no—
71C2×C22⋊D283D411yescharacteristic
72C2×C4×D283—21no—
73C2×C4×D283—21no—
74C2×C4×D283—21no—
75C2×C4×D283—21no—
76C2×C4×D283C2311yescharacteristic
77#17985381—22no—
78#17985379—41no—
79D2264—41no—
80C2×C283⋊C8—41no—
81C2×C283⋊C8C2311yescharacteristic
82C2×C283⋊C8C2311yescharacteristic
83C8×D283—41no—
84C4⋊Dic283—21no—
85C4⋊Dic283C2311yescharacteristic
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88Dic283⋊C4—21no—
89Dic283⋊C4D411yescharacteristic
90C22⋊Dic283D411yescharacteristic
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4—21no—
96(C2×D283)⋊C4—21no—
97(C2×D283)⋊C4D411yescharacteristic
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×D283—21no—
113C22×D283C2×D411yescharacteristic
114Dic566—21no—
115Dic566—42no—
116Dic566#4112yes—
117D1132—21no—
118D1132—21no—
119D1132—21no—
120D1132—21no—
121D1132—42no—
122D1132—42no—
123C22⋊D283—22no—
124C22⋊D283—42no—
125C22⋊D283—81no—
126C2×Dic283—21no—
127C2×Dic283—21no—
128C2×Dic283C2×D411yescharacteristic
129C2×Dic283C2×D411yescharacteristic
130C2×Dic283C2×D411yescharacteristic
131C4×D283—21no—
132C4×D283—21no—
133C4×D283—42no—
134C4×D283—42no—
135C4×D283—81no—
136C4×D283—81no—
137C283⋊C8—21no—
138C283⋊C8—21no—
139C23×C283C2×D411yescharacteristic
140Q8×C283—21no—
141Q8×C283—21no—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—21no—
146C2×C4×C283—21no—
147C2×C4×C283—21no—
148C2×C4×C283C2×D411yescharacteristic
149C2×C4×C283C2411yescharacteristic
150C8×C283—21no—
151C8×C283—21no—
152C22×C283—21no—
153C22×C283—21no—
154C22×C283—21no—
155C22×C283C22×D411yescharacteristic
156C2×D283—21no—
157C2×D283—21no—
158C2×D283—41no—
159C2×D283—41no—
160C2×D283—41no—
161C2×D283—41no—
162C2×D283—41no—
163C2×D283—41no—
164C2×D283#13512yes—
165C4×C283—21no—
166C4×C283—41no—
167C4×C283—41no—
168C4×C283—41no—
169C4×C283—41no—
170C4×C283C2×#4111yescharacteristic
171C4×C283H(5,𝔽2)11yescharacteristic
172Dic283—21no—
173Dic283—22no—
174Dic283—21no—
175Dic283—21no—
176Dic283—41no—
177C2×C283—41no—
178C2×C283#54611yescharacteristic
179C2×C283C2×#13511yescharacteristic
180C2×C283#57711yescharacteristic
181D283—22no—
182D283—81no—
183D283—81no—
184C283#330111yescharacteristic, complemented, Sylow
185#3301—2831nomaximal, Sylow
186#553—2831no—
187#548—2831no—
188#488—2831no—
189#485D28311yescharacteristic, complemented
190#481—2831no—
191#479—2831no—
192#466—2831no—
193#465—2831no—
194#463—2831no—
195#449—2831no—
196#448—2831no—
197C4×SD16—2831no—
198C8×D4—2831no—
199#416—2831no—
200C2×#103—2831no—
201C2×#41—2831no—
202C22×Q8—2831no—
203C2×SD16—2831no—
204C2×SD16—2831no—
205C2×D8—2831no—
206C22×C8—2831no—
207C22×C8—2831no—
208#126—5661no—
209#125—2831no—
210#124—2831no—
211#124—5661no—
212#123—5661no—
213C22⋊Q8—5661no—
214C22⋊Q8C2×D28311yescharacteristic
215#121—2831no—
216#121—2831no—
217#121—2831no—
218#121—5661no—
219#121—5661no—
220C4×Q8—2831no—
221C4×D4—2831no—
222C4×D4—2831no—
223C4×D4—5661no—
224C4×D4—5661no—
225#117C2×D28311yescharacteristic
226C2×C4⋊C4—2831no—
227#107C2×D28311yescharacteristic
228#106—2831no—
229#106C2×D28311yescharacteristic
230C4⋊C8—2831no—
231#103—2831no—
232#103—2831no—
233#103—2831no—
234#103—2831no—
235#103C2×D28311yescharacteristic
236#103C2×D28311yescharacteristic
237#102—2831no—
238#102—2831no—
239#102—2831no—
240#102—2831no—
241C22⋊C8—2831no—
242C22⋊C8C2×D28311yescharacteristic
243C4×C8—2831no—
244#41—5662no—
245#41—11321no—
246C2×Q8—2831no—
247C2×Q8—5661no—
248C2×Q8—5662no—
249C2×Q8—11321no—
250C2×Q8C22×D28311yescharacteristic
251C2×D4—2831no—
252C2×D4—2831no—
253C2×D4—2831no—
254C2×D4—5661no—
255C2×D4—5661no—
256C2×D4—5661no—
257C2×D4—5661no—
258C22×C4—2831no—
259C22×C4—5661no—
260C22×C4—5661no—
261C22×C4—5661no—
262C22×C4—5661no—
263C22×C4C22×D28311yescharacteristic
264SD16—5662no—
265SD16—11321no—
266D8—11321no—
267C2×C8—2831no—
268C2×C8—2831no—
269C2×C8—11321no—
270C2×C8—11321no—
271C2×C8C22×D28311yescharacteristic
272C2×C8C22×D28311yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—2831no—
275C4⋊C4—2831no—
276C4⋊C4—5661no—
277C4⋊C4—5661no—
278C4⋊C4—5661no—
279C4⋊C4—5661no—
280C4⋊C4C22×D28311yescharacteristic
281C4⋊C4C22×D28311yescharacteristic
282C4⋊C4C22×D28311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—2831no—
286C22⋊C4—2831no—
287C22⋊C4—5661no—
288C22⋊C4—5661no—
289C22⋊C4—5661no—
290C22⋊C4—5661no—
291C22⋊C4—5661no—
292C22⋊C4—5661no—
293C42—21no—
294C42—2831no—
295C42—5661no—
296C23—2831no—
297C23—5661no—
298C23—5661no—
299C23D4×D28311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—2832no—
303Q8—5661no—
304Q8—11322no—
305D4—5662no—
306D4—5661no—
307D4—5661no—
308D4—5661no—
309D4—5661no—
310D4—11322no—
311D4—11322no—
312D4—11322no—
313D4—22641no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—2831no—
321C2×C4—2831no—
322C2×C4—2831no—
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—2832no—
341C22—5661no—
342C22—5661no—
343C22—11321no—
344C22—11321no—
345C22—11321no—
346C22—11321no—
347C22—11321no—
348C22—11321no—
349C22C2×D4×D28311yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—5661no—
356C4—5661no—
357C4—5661no—
358C4—5662no—
359C4—11321no—
360C4#41×D28311yescharacteristic
361C4#2258365611yescharacteristic
362C2—41no—
363C2—5662no—
364C2—22641no—
365C2—22641no—
366C2#3182710711yescharacteristic
367C2#135×D28311yescharacteristic
368C2#3182727411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#485×C283C2
socleC22×C283C22×D4
hypercenter#485D283
hypocenterC283#3301
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. #31827159C2semidirect
2. #31827125C2semidirect
3. #31826821C2semidirect
4. #31826785C2semidirect
5. #31826771C2semidirect
6. #31826702C2semidirect
7. #31826696C2semidirect
8. #31826683C2semidirect
9. #31826612C2semidirect
10. #31826605C2semidirect
11. #31826552C2semidirect
12. (C22⋊D283)⋊C8C2semidirect
13. #31826459C2semidirect
14. #103×D283C2semidirect
15. #485×C283C2semidirect
184. C283#3301semidirect
189. #485D283semidirect

Maximal subgroups

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

subgroupindex
#318271592
#318271252
#318268212
#318267852
#318267712
#318267022
#318266962
#318266832
#318266122
#318266052
#318265522
(C22⋊D283)⋊C82
#318264592
#103×D2832
#485×C2832
#3301283