Finite Group Databasebeta

← #49133161

Subgroups — #49133161

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#31827163C211yesmaximal, characteristic, complemented
2#31827121C211yesmaximal, characteristic, complemented
3#31826818C211yesmaximal, characteristic, complemented
4#31826809C211yesmaximal, characteristic, complemented
5#31826775C211yesmaximal, characteristic, complemented
6#31826699C211yesmaximal, characteristic, complemented
7#31826695C211yesmaximal, characteristic, complemented
8#31826679C211yesmaximal, characteristic, complemented
9#31826611C211yesmaximal, characteristic, complemented
10#31826606C211yesmaximal, characteristic, complemented
11#31826552C211yesmaximal, characteristic, complemented
12(C22⋊D283)⋊C8C211yesmaximal, characteristic, complemented
13#31826458C211yesmaximal, characteristic, complemented
14C2×#22583533C211yesmaximal, characteristic, complemented
15#481×C283C211yesmaximal, characteristic, complemented
16C2×#17985391C2211yescharacteristic
17C22×Dic566C2211yescharacteristic
18C2×#17985381C2211yescharacteristic
19C2×#17985381C2211yescharacteristic
20C2×#17985377C2211yescharacteristic
21C22×C283⋊C8C2211yescharacteristic
22C2×C8×D283C2211yescharacteristic
23#22583605—21no—
24#22583601C2211yescharacteristic
25#22583597C2211yescharacteristic
26#22583596—21no—
27#22583595—21no—
28#22583590C2211yescharacteristic
29#22583587—21no—
30#22583585C2211yescharacteristic
31#22583584—21no—
32#22583584C2211yescharacteristic
33#22583582—21no—
34#22583575C2211yescharacteristic
35D4×Dic283—21no—
36#22583572C2211yescharacteristic
37C4×C22⋊D283—21no—
38C4×C22⋊D283C2211yescharacteristic
39#22583568C2211yescharacteristic
40#22583543C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42#22583535C2211yescharacteristic
43#22583535C2211yescharacteristic
44#22583533C2211yescharacteristic
45#22583533C2211yescharacteristic
46#22583533C2211yescharacteristic
47#22583533C2211yescharacteristic
48#22583531C2211yescharacteristic
49#22583530C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
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—22no—
62C2×Dic566—21no—
63C2×Dic566—41no—
64C2×Dic566C2311yescharacteristic
65C2×Dic566C2311yescharacteristic
66C2×D1132—21no—
67C2×D1132C2311yescharacteristic
68C2×C22⋊D283—21no—
69C2×C22⋊D283—21no—
70C2×C22⋊D283D411yescharacteristic
71C22×Dic283—21no—
72C22×Dic283—21no—
73C2×C4×D283—21no—
74C2×C4×D283C2311yescharacteristic
75#17985381—22no—
76#17985381—41no—
77#17985377—41no—
78C2×C283⋊C8—41no—
79C2×C283⋊C8C2311yescharacteristic
80C2×C283⋊C8C2311yescharacteristic
81C8×D283—41no—
82C4⋊Dic283—21no—
83C4⋊Dic283—21no—
84C4⋊Dic283C2311yescharacteristic
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87Dic283⋊C4D411yescharacteristic
88C22⋊Dic283—21no—
89C22⋊Dic283—21no—
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)⋊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×D283—21no—
112C22×D283C2×D411yescharacteristic
113Dic566—21no—
114Dic566—21no—
115Dic566—21no—
116Dic566—42no—
117Dic566#4112yes—
118D1132—21no—
119D1132—21no—
120D1132—81no—
121C22⋊D283—22no—
122C22⋊D283—42no—
123C22⋊D283—42no—
124C2×Dic283—21no—
125C2×Dic283—21no—
126C2×Dic283—21no—
127C2×Dic283—42no—
128C2×Dic283—42no—
129C2×Dic283C2×D411yescharacteristic
130C2×Dic283C2×D411yescharacteristic
131C2×Dic283C2×D411yescharacteristic
132C4×D283—21no—
133C4×D283—21no—
134C4×D283—81no—
135C283⋊C8—21no—
136C283⋊C8—21no—
137C23×C283—21no—
138C23×C283C2×D411yescharacteristic
139D4×C283—21no—
140D4×C283—21no—
141D4×C283—42no—
142C2×C4×C283—21no—
143C2×C4×C283—21no—
144C2×C4×C283—21no—
145C2×C4×C283—21no—
146C2×C4×C283—21no—
147C2×C4×C283—81no—
148C2×C4×C283C2×D411yescharacteristic
149C2×C4×C283C2411yescharacteristic
150C8×C283—21no—
151C8×C283—21no—
152C22×C283—21no—
153C22×C283—21no—
154C22×C283—41no—
155C22×C283—41no—
156C22×C283—41no—
157C22×C283#13512yes—
158C22×C283C22×D411yescharacteristic
159C2×D283—21no—
160C2×D283—21no—
161C2×D283—21no—
162C2×D283—41no—
163C2×D283—41no—
164C2×D283—41no—
165C4×C283—21no—
166C4×C283—41no—
167C4×C283—41no—
168C4×C283—41no—
169C4×C283C2×#4111yescharacteristic
170C4×C283H(5,𝔽2)11yescharacteristic
171Dic283—21no—
172Dic283—22no—
173Dic283—21no—
174Dic283—21no—
175Dic283—41no—
176Dic283—41no—
177C2×C283—22no—
178C2×C283—81no—
179C2×C283#54611yescharacteristic
180C2×C283C2×#13511yescharacteristic
181C2×C283#57711yescharacteristic
182D283—41no—
183D283—81no—
184C283#330111yescharacteristic, complemented, Sylow
185#3301—2831nomaximal, Sylow
186#553—2831no—
187#548—2831no—
188#488—2831no—
189#485—2831no—
190#481D28311yescharacteristic, complemented
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—2831no—
214C22⋊Q8—5661no—
215#121—2831no—
216#121—2831no—
217#121—5661no—
218#121—5661no—
219#121C2×D28311yescharacteristic
220C4×Q8—2831no—
221C4×D4—2831no—
222C4×D4—2831no—
223C4×D4—5661no—
224C4×D4—5661no—
225#117—2831no—
226C2×C4⋊C4C2×D28311yescharacteristic
227#107—2831no—
228#106C2×D28311yescharacteristic
229#106C2×D28311yescharacteristic
230C4⋊C8—2831no—
231#103—2831no—
232#103—2831no—
233#103—2831no—
234#103—2831no—
235#103—2831no—
236#103—2831no—
237#102—2831no—
238#102—2831no—
239#102C2×D28311yescharacteristic
240#102C2×D28311yescharacteristic
241C22⋊C8—2831no—
242C22⋊C8C2×D28311yescharacteristic
243C4×C8—2831no—
244#41—5662no—
245#41—11321no—
246C2×Q8—2831no—
247C2×Q8—2831no—
248C2×Q8—5662no—
249C2×Q8—5661no—
250C2×Q8—11321no—
251C2×D4—21no—
252C2×D4—2831no—
253C2×D4—2831no—
254C2×D4—5661no—
255C2×D4—5661no—
256C2×D4—5661no—
257C2×D4C22×D28311yescharacteristic
258C22×C4—21no—
259C22×C4—2831no—
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—2831no—
285C22⋊C4—2831no—
286C22⋊C4—5661no—
287C22⋊C4—5661no—
288C22⋊C4—5661no—
289C22⋊C4—5661no—
290C22⋊C4—5661no—
291C22⋊C4—5661no—
292C22⋊C4—5661no—
293C42—2831no—
294C42—5661no—
295C42—5661no—
296C23—21no—
297C23—2831no—
298C23—5661no—
299C23D4×D28311yescharacteristic
300Q8—2832no—
301Q8—5661no—
302Q8—5661no—
303Q8—5661no—
304Q8—11322no—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—5662no—
309D4—5661no—
310D4—5661no—
311D4—11322no—
312D4—11322no—
313D4—22641no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—2831no—
321C2×C4—2831no—
322C2×C4—2831no—
323C2×C4—5661no—
324C2×C4—5661no—
325C2×C4—5661no—
326C2×C4—5661no—
327C2×C4—5661no—
328C2×C4—11322no—
329C2×C4—11322no—
330C2×C4—22641no—
331C2×C4D4×D28311yescharacteristic
332C2×C4C23×D28311yescharacteristic
333C8—21no—
334C8—21no—
335C8—5661no—
336C8—5661no—
337C22—21no—
338C22—21no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—5661no—
343C22—5661no—
344C22—5661no—
345C22—11321no—
346C22—11321no—
347C22—11321no—
348C22#2258363112yes—
349C22C2×D4×D28311yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—5661no—
355C4—5661no—
356C4—5661no—
357C4—5662no—
358C4—11321no—
359C4—11321no—
360C4#41×D28311yescharacteristic
361C4#2258365611yescharacteristic
362C2—22no—
363C2—81no—
364C2—11321no—
365C2—22641no—
366C2#3182710711yescharacteristic
367C2C2×#2258363111yescharacteristic
368C2#3182727511yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#481×C283C2
socleC22×C283C22×D4
hypercenter#481D283
hypocenterC283#3301
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. #31827163C2semidirect
2. #31827121C2semidirect
3. #31826818C2semidirect
4. #31826809C2semidirect
5. #31826775C2semidirect
6. #31826699C2semidirect
7. #31826695C2semidirect
8. #31826679C2semidirect
9. #31826611C2semidirect
10. #31826606C2semidirect
11. #31826552C2semidirect
12. (C22⋊D283)⋊C8C2semidirect
13. #31826458C2semidirect
14. C2×#22583533C2semidirect
15. #481×C283C2semidirect
184. C283#3301semidirect
190. #481D283semidirect

Maximal subgroups

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

subgroupindex
#318271632
#318271212
#318268182
#318268092
#318267752
#318266992
#318266952
#318266792
#318266112
#318266062
#318265522
(C22⋊D283)⋊C82
#318264582
C2×#225835332
#481×C2832
#3301283