Finite Group Databasebeta

← #49133862

Subgroups — #49133862

Order 36224.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827167C211yesmaximal, characteristic, complemented
2#31827162C211yesmaximal, characteristic, complemented
3#31826865C211yesmaximal, characteristic, complemented
4#31826788C211yesmaximal, characteristic, complemented
5#31826786C211yesmaximal, characteristic, complemented
6#31826777C211yesmaximal, characteristic, complemented
7#31826776C211yesmaximal, characteristic, complemented
8#31826767C211yesmaximal, characteristic, complemented
9#31826763C211yesmaximal, characteristic, complemented
10#31826715C211yesmaximal, characteristic, complemented
11D8×Dic283C211yesmaximal, characteristic, complemented
12#31826541C211yesmaximal, characteristic, complemented
13#31826507C211yesmaximal, characteristic, complemented
14#31826504C211yesmaximal, characteristic, complemented
15#469×C283C211yesmaximal, characteristic, complemented
16C2×#17985375C2211yescharacteristic
17#22583603—21no—
18#22583603—21no—
19#22583601C2211yescharacteristic
20#22583601C2211yescharacteristic
21#22583594—21no—
22#22583591—21no—
23#22583582—21no—
24#22583581—21no—
25#22583581C2211yescharacteristic
26#22583581C2211yescharacteristic
27D4×Dic283—21no—
28D4×Dic283C2211yescharacteristic
29D4×Dic283C2211yescharacteristic
30C4×C22⋊D283C2211yescharacteristic
31(C22⋊D283)⋊C4—21no—
32#22583569C2211yescharacteristic
33#22583568C2211yescharacteristic
34C2×C4⋊Dic283C2211yescharacteristic
35C4⋊C4×D283C2211yescharacteristic
36#22583544C2211yescharacteristic
37#22583544C2211yescharacteristic
38#22583543C2211yescharacteristic
39#22583543C2211yescharacteristic
40#22583543C2211yescharacteristic
41#22583542C2211yescharacteristic
42#22583542C2211yescharacteristic
43#22583541C2211yescharacteristic
44Dic283⋊C8C2211yescharacteristic
45#22583531C2211yescharacteristic
46#22583531C2211yescharacteristic
47#22583531C2211yescharacteristic
48#22583531C2211yescharacteristic
49C22⋊(C283⋊C8)C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52C2×D8×C283C2211yescharacteristic
53C2×M16×C283C2211yescharacteristic
54#121×C283C2211yescharacteristic
55#121×C283C2211yescharacteristic
56#106×C283C2211yescharacteristic
57#102×C283C2211yescharacteristic
58#102×C283C2211yescharacteristic
59C2×C22⋊D283—21no—
60C2×C22⋊D283—21no—
61C2×C22⋊D283D411yescharacteristic
62C22×Dic283—21no—
63C22×Dic283—21no—
64C22×Dic283—21no—
65C2×C4×D283—21no—
66C2×C4×D283C2311yescharacteristic
67#17985375—22no—
68C2×C283⋊C8C2311yescharacteristic
69C2×C283⋊C8C2311yescharacteristic
70C4⋊Dic283—21no—
71C4⋊Dic283—21no—
72C4⋊Dic283—21no—
73C4⋊Dic283C2311yescharacteristic
74C4⋊Dic283C2311yescharacteristic
75C4⋊Dic283C2311yescharacteristic
76C4⋊Dic283C2311yescharacteristic
77Dic283⋊C4—21no—
78Dic283⋊C4—21no—
79Dic283⋊C4—21no—
80Dic283⋊C4D411yescharacteristic
81C22⋊Dic283—21no—
82C22⋊Dic283—21no—
83C22⋊Dic283—21no—
84C22⋊Dic283—21no—
85C22⋊Dic283—21no—
86C22⋊Dic283D411yescharacteristic
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4D411yescharacteristic
89C4×Dic283—21no—
90C4×Dic283—21no—
91C4×Dic283C2311yescharacteristic
92C2×D4×C283—21no—
93C2×D4×C283—21no—
94C2×D4×C283C2311yescharacteristic
95C2×D4×C283C2311yescharacteristic
96C22×C4×C283C2311yescharacteristic
97D8×C283—22no—
98M16×C283—22no—
99C2×C8×C283C2311yescharacteristic
100C2×C8×C283C2311yescharacteristic
101C4⋊C4×C283C2311yescharacteristic
102C4⋊C4×C283C2311yescharacteristic
103C22⋊C4×C283—21no—
104C22⋊C4×C283—21no—
105C22×D283C2×D411yescharacteristic
106C22⋊D283—41no—
107C22⋊D283—42no—
108C22⋊D283—81no—
109C2×Dic283—21no—
110C2×Dic283—21no—
111C2×Dic283—21no—
112C2×Dic283—21no—
113C2×Dic283—81no—
114C2×Dic283—81no—
115C2×Dic283—81no—
116C2×Dic283C2×D411yescharacteristic
117C2×Dic283C2×D411yescharacteristic
118C2×Dic283C2×D411yescharacteristic
119C4×D283—21no—
120C4×D283—21no—
121C4×D283—81no—
122C283⋊C8—21no—
123C283⋊C8—21no—
124C23×C283—21no—
125C23×C283—21no—
126C23×C283C2×D411yescharacteristic
127D4×C283—21no—
128D4×C283—21no—
129D4×C283—21no—
130D4×C283—21no—
131D4×C283—42no—
132D4×C283—81no—
133C2×C4×C283—21no—
134C2×C4×C283—21no—
135C2×C4×C283—21no—
136C2×C4×C283—21no—
137C2×C4×C283C2×D411yescharacteristic
138C2×C4×C283C2411yescharacteristic
139C8×C283—21no—
140C8×C283#4112yes—
141C22×C283—21no—
142C22×C283—21no—
143C22×C283—21no—
144C22×C283—41no—
145C22×C283—41no—
146C22×C283—41no—
147C22×C283—41no—
148C22×C283—41no—
149C22×C283—41no—
150C22×C283C22×D411yescharacteristic
151C2×D283—21no—
152C2×D283—21no—
153C2×D283—21no—
154C4×C283—21no—
155C4×C283—41no—
156C4×C283—41no—
157C4×C283C2×#4111yescharacteristic
158C4×C2832−1+411yescharacteristic
159Dic283—21no—
160Dic283—21no—
161Dic283—21no—
162Dic283—41no—
163Dic283—41no—
164Dic283—41no—
165Dic283—41no—
166C2×C283—41no—
167C2×C283—81no—
168C2×C283—81no—
169C2×C283#54711yescharacteristic
170C2×C283#57511yescharacteristic
171C2×C283#57611yescharacteristic
172D283—41no—
173C283#335511yescharacteristic, complemented, Sylow
174#3355—2831nomaximal, Sylow
175#553—2831no—
176#553—2831no—
177#499—2831no—
178#482—2831no—
179#482—2831no—
180#480—2831no—
181#480—2831no—
182#478—2831no—
183#478—2831no—
184#469—2831no—
185#469D28311yescharacteristic, complemented
186C4×D8—2831no—
187#436—2831no—
188#428—2831no—
189#428—2831no—
190C2×D8C2×D28311yescharacteristic
191C2×M16—2831no—
192C2×M16C2×D28311yescharacteristic
193#126—5661no—
194#126—5661no—
195#125—2831no—
196#125—2831no—
197#123—5661no—
198#123—5661no—
199#121—2831no—
200#121—2831no—
201#121—5661no—
202#121—5661no—
203#121C2×D28311yescharacteristic
204#121C2×D28311yescharacteristic
205C4×D4—2831no—
206C4×D4—2831no—
207C4×D4—2831no—
208C4×D4—5661no—
209C4×D4—5661no—
210#117—2831no—
211#117—2831no—
212C2×C4⋊C4—2831no—
213C2×C4⋊C4—2831no—
214#107—2831no—
215#107—2831no—
216#107—2831no—
217#107—2831no—
218#107—2831no—
219#106—2831no—
220#106—2831no—
221#106—2831no—
222#106C2×D28311yescharacteristic
223C4⋊C8—2831no—
224#102—2831no—
225#102—2831no—
226#102—2831no—
227#102—2831no—
228#102C2×D28311yescharacteristic
229#102C2×D28311yescharacteristic
230C22⋊C8—2831no—
231C22⋊C8—2831no—
232C4×C8—2831no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—2831no—
236C2×D4—5661no—
237C2×D4—5661no—
238C2×D4C22×D28311yescharacteristic
239C2×D4C22×D28311yescharacteristic
240C22×C4—2831no—
241C22×C4—5661no—
242C22×C4—5661no—
243C22×C4—5661no—
244C22×C4—5661no—
245C22×C4C22×D28311yescharacteristic
246D8—22no—
247M16—22no—
248M16—5662no—
249C2×C8—2831no—
250C2×C8—2831no—
251C2×C8C22×D28311yescharacteristic
252C2×C8C22×D28311yescharacteristic
253C4⋊C4—2831no—
254C4⋊C4—2831no—
255C4⋊C4—2831no—
256C4⋊C4—2831no—
257C4⋊C4—2831no—
258C4⋊C4—5661no—
259C4⋊C4—5661no—
260C4⋊C4—5661no—
261C4⋊C4—5661no—
262C4⋊C4—5661no—
263C4⋊C4—5661no—
264C4⋊C4C22×D28311yescharacteristic
265C4⋊C4C22×D28311yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—2831no—
269C22⋊C4—2831no—
270C22⋊C4—5661no—
271C22⋊C4—5661no—
272C22⋊C4—5661no—
273C22⋊C4—5661no—
274C22⋊C4—5661no—
275C22⋊C4—5661no—
276C42—2831no—
277C42—5661no—
278C42—5661no—
279C23—21no—
280C23—21no—
281C23—2831no—
282C23D4×D28311yescharacteristic
283D4—21no—
284D4—21no—
285D4—21no—
286D4—21no—
287D4—42no—
288D4—81no—
289D4—11321no—
290D4—11322no—
291D4—22641no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—2831no—
297C2×C4—2831no—
298C2×C4—2831no—
299C2×C4—5661no—
300C2×C4—5661no—
301C2×C4—5661no—
302C2×C4—5661no—
303C2×C4—5661no—
304C2×C4—5661no—
305C2×C4—22641no—
306C2×C4—22641no—
307C2×C4—22641no—
308C2×C4—22641no—
309C2×C4D4×D28311yescharacteristic
310C2×C4C23×D28311yescharacteristic
311C8—21no—
312C8—5661no—
313C8—5661no—
314C8#1798539112yes—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—5661no—
325C22—5661no—
326C22—5661no—
327C22C2×D4×D28311yescharacteristic
328C4—21no—
329C4—41no—
330C4—41no—
331C4—5661no—
332C4—5661no—
333C4—5661no—
334C4—11321no—
335C4—11321no—
336C4—11321no—
337C4—11321no—
338C4C2×#1798539111yescharacteristic
339C4#2258365711yescharacteristic
340C2—41no—
341C2—81no—
342C2—81no—
343C2—11321no—
344C2#3182711511yescharacteristic
345C2#3182726111yescharacteristic
346C2#3182726911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#469×C283C2
socleC22×C283C22×D4
hypercenter#469D283
hypocenterC283#3355
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #31827167C2semidirect
2. #31827162C2semidirect
3. #31826865C2semidirect
4. #31826788C2semidirect
5. #31826786C2semidirect
6. #31826777C2semidirect
7. #31826776C2semidirect
8. #31826767C2semidirect
9. #31826763C2semidirect
10. #31826715C2semidirect
11. D8×Dic283C2semidirect
12. #31826541C2semidirect
13. #31826507C2semidirect
14. #31826504C2semidirect
15. #469×C283C2semidirect
173. C283#3355semidirect
185. #469D283semidirect

Maximal subgroups

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

subgroupindex
#318271672
#318271622
#318268652
#318267882
#318267862
#318267772
#318267762
#318267672
#318267632
#318267152
D8×Dic2832
#318265412
#318265072
#318265042
#469×C2832
#3355283