Finite Group Databasebeta

← #49133167

Subgroups — #49133167

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#31827167C211yesmaximal, characteristic, complemented
2#31827126C211yesmaximal, characteristic, complemented
3#31826821C211yesmaximal, characteristic, complemented
4#31826804C211yesmaximal, characteristic, complemented
5#31826784C211yesmaximal, characteristic, complemented
6#31826770C211yesmaximal, characteristic, complemented
7#31826699C211yesmaximal, characteristic, complemented
8#31826691C211yesmaximal, characteristic, complemented
9#31826682C211yesmaximal, characteristic, complemented
10#31826609C211yesmaximal, characteristic, complemented
11SD16×Dic283C211yesmaximal, characteristic, complemented
12(C22⋊D283)⋊C8C211yesmaximal, characteristic, complemented
13#31826460C211yesmaximal, characteristic, complemented
14C2×#22583534C211yesmaximal, characteristic, complemented
15#448×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×#17985377C2211yescharacteristic
18C22×C283⋊C8C2211yescharacteristic
19C2×C8×D283C2211yescharacteristic
20#22583603—21no—
21#22583601C2211yescharacteristic
22#22583599—21no—
23#22583599C2211yescharacteristic
24#22583594—21no—
25#22583586—21no—
26#22583586C2211yescharacteristic
27#22583584—21no—
28#22583584C2211yescharacteristic
29#22583582—21no—
30#22583581C2211yescharacteristic
31Q8×Dic283C2211yescharacteristic
32D4×Dic283—21no—
33D4×Dic283C2211yescharacteristic
34C4×C22⋊D283—21no—
35C4×C22⋊D283C2211yescharacteristic
36#22583568C2211yescharacteristic
37C2×C4⋊Dic283C2211yescharacteristic
38#22583543C2211yescharacteristic
39#22583542C2211yescharacteristic
40#22583542C2211yescharacteristic
41Dic283⋊C8C2211yescharacteristic
42#22583534C2211yescharacteristic
43#22583534C2211yescharacteristic
44#22583534C2211yescharacteristic
45#22583534C2211yescharacteristic
46#22583532C2211yescharacteristic
47#22583532C2211yescharacteristic
48#22583531C2211yescharacteristic
49#22583530C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic
51C8×Dic283C2211yescharacteristic
52C22×Q8×C283C2211yescharacteristic
53C2×SD16×C283C2211yescharacteristic
54C2×SD16×C283C2211yescharacteristic
55#121×C283C2211yescharacteristic
56#103×C283C2211yescharacteristic
57#103×C283C2211yescharacteristic
58C22⋊C8×C283C2211yescharacteristic
59#17985393—22no—
60#17985393—41no—
61C2×D1132—21no—
62C2×D1132C2311yescharacteristic
63C2×C22⋊D283—21no—
64C2×C22⋊D283—21no—
65C2×C22⋊D283D411yescharacteristic
66C22×Dic283—21no—
67C22×Dic283—21no—
68C2×C4×D283—21no—
69C2×C4×D283C2311yescharacteristic
70#17985377—41no—
71C2×C283⋊C8—41no—
72C2×C283⋊C8C2311yescharacteristic
73C2×C283⋊C8C2311yescharacteristic
74C8×D283—41no—
75C4⋊Dic283—21no—
76C4⋊Dic283—21no—
77C4⋊Dic283—21no—
78C4⋊Dic283C2311yescharacteristic
79C4⋊Dic283C2311yescharacteristic
80C4⋊Dic283C2311yescharacteristic
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83Dic283⋊C4D411yescharacteristic
84C22⋊Dic283—21no—
85C22⋊Dic283—21no—
86C22⋊Dic283D411yescharacteristic
87(C2×D283)⋊C4—21no—
88(C2×D283)⋊C4—21no—
89(C2×D283)⋊C4—21no—
90(C2×D283)⋊C4—21no—
91(C2×D283)⋊C4—21no—
92(C2×D283)⋊C4D411yescharacteristic
93C4×Dic283—21no—
94C4×Dic283—21no—
95C4×Dic283C2311yescharacteristic
96C2×Q8×C283—21no—
97C2×Q8×C283—22no—
98C2×Q8×C283—41no—
99C2×Q8×C283C2311yescharacteristic
100C2×Q8×C283C2311yescharacteristic
101C2×D4×C283—21no—
102C2×D4×C283C2311yescharacteristic
103C22×C4×C283—21no—
104C22×C4×C283C2311yescharacteristic
105SD16×C283—22no—
106SD16×C283—41no—
107C2×C8×C283C2311yescharacteristic
108C2×C8×C283C2311yescharacteristic
109C4⋊C4×C283C2311yescharacteristic
110C22⋊C4×C283—21no—
111C22×D283—21no—
112C22×D283C2×D411yescharacteristic
113D1132—21no—
114D1132—21no—
115D1132—42no—
116C22⋊D283—22no—
117C22⋊D283—42no—
118C22⋊D283—81no—
119C2×Dic283—21no—
120C2×Dic283—21no—
121C2×Dic283—21no—
122C2×Dic283—81no—
123C2×Dic283—81no—
124C2×Dic283C2×D411yescharacteristic
125C2×Dic283C2×D411yescharacteristic
126C2×Dic283C2×D411yescharacteristic
127C4×D283—21no—
128C4×D283—21no—
129C4×D283—42no—
130C283⋊C8—21no—
131C283⋊C8—21no—
132C23×C283—21no—
133C23×C283C2×D411yescharacteristic
134Q8×C283—21no—
135Q8×C283—21no—
136Q8×C283—21no—
137Q8×C283—42no—
138Q8×C283#4112yes—
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—42no—
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—22no—
167C4×C283—41no—
168C4×C283—41no—
169C4×C283C2×#4111yescharacteristic
170C4×C283H(5,𝔽2)11yescharacteristic
171Dic283—21no—
172Dic283—21no—
173Dic283—21no—
174Dic283—41no—
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#481—2831no—
191#479—2831no—
192#466—2831no—
193#465—2831no—
194#463—2831no—
195#449—2831no—
196#448D28311yescharacteristic, complemented
197C4×SD16—2831no—
198C8×D4—2831no—
199#416—2831no—
200C2×#103—2831no—
201C2×#41—2831no—
202C22×Q8C2×D28311yescharacteristic
203C2×SD16C2×D28311yescharacteristic
204C2×SD16C2×D28311yescharacteristic
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⋊C4—2831no—
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#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—21no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8C22×D28311yescharacteristic
250C2×Q8C22×D28311yescharacteristic
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—22no—
265SD16—41no—
266D8—11321no—
267C2×C8—2831no—
268C2×C8—2831no—
269C2×C8—11321no—
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⋊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—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8#1798539112yes—
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—42no—
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—22641no—
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—22no—
352C4—41no—
353C4—41no—
354C4—5661no—
355C4—5661no—
356C4—5661no—
357C4—11321no—
358C4—11321no—
359C4—11321no—
360C4C2×#1798539111yescharacteristic
361C4#2258365511yescharacteristic
362C2—22no—
363C2—81no—
364C2—11321no—
365C2—22641no—
366C2#3182710211yescharacteristic
367C2C2×#2258363111yescharacteristic
368C2#3182727411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#448×C283C2
socleC22×C283C22×D4
hypercenter#448D283
hypocenterC283#3301
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. #31827167C2semidirect
2. #31827126C2semidirect
3. #31826821C2semidirect
4. #31826804C2semidirect
5. #31826784C2semidirect
6. #31826770C2semidirect
7. #31826699C2semidirect
8. #31826691C2semidirect
9. #31826682C2semidirect
10. #31826609C2semidirect
11. SD16×Dic283C2semidirect
12. (C22⋊D283)⋊C8C2semidirect
13. #31826460C2semidirect
14. C2×#22583534C2semidirect
15. #448×C283C2semidirect
184. C283#3301semidirect
196. #448D283semidirect

Maximal subgroups

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

subgroupindex
#318271672
#318271262
#318268212
#318268042
#318267842
#318267702
#318266992
#318266912
#318266822
#318266092
SD16×Dic2832
(C22⋊D283)⋊C82
#318264602
C2×#225835342
#448×C2832
#3301283