Finite Group Databasebeta

← #49122263

Subgroups — #49122263

Order 36224.

444 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#17985379C211yesmaximal, characteristic, complemented
2C2×#22583586C211yesmaximal, characteristic, complemented
3C2×#22583585C211yesmaximal, characteristic
4C2×#22583532C211yesmaximal, characteristic, complemented
5C2×(C2×D283)⋊C8C211yesmaximal, characteristic, complemented
6#31826227C211yesmaximal, characteristic, complemented
7C2×#103×C283C211yesmaximal, characteristic, complemented
8C22×D1132—21no—
9C22×D1132C2211yescharacteristic
10C22×C4×D283C2211yescharacteristic
11C2×#17985379—22no—
12C2×#17985379—22no—
13C2×#17985379—22no—
14C22×C283⋊C8C2211yescharacteristic
15#22583586—22no—
16#22583586—22no—
17#22583585—22no—
18#22583585—22no—
19C2×C4⋊Dic283C2211yescharacteristic
20C2×Dic283⋊C4—21no—
21C2×(C2×D283)⋊C4—21no—
22C2×(C2×D283)⋊C4—21no—
23#22583532—22no—
24(C2×D283)⋊C8—22no—
25C22×Q8×C283C2211yescharacteristic
26C22×C8×C283C2211yescharacteristic
27C2×C4⋊C4×C283C2211yescharacteristic
28#103×C283—22no—
29C23×D283—21no—
30C23×D283D411yescharacteristic
31C2×D1132—24no—
32C2×D1132—21no—
33C2×D1132—21no—
34C2×D1132—21no—
35C2×D1132—21no—
36C2×D1132—21no—
37C2×D1132—42no—
38C2×D1132—42no—
39C2×D1132D412yes—
40C22×Dic283—21no—
41C22×Dic283D411yescharacteristic
42C2×C4×D283—21no—
43C2×C4×D283—21no—
44C2×C4×D283—21no—
45C2×C4×D283—21no—
46C2×C4×D283—21no—
47C2×C4×D283—21no—
48#17985379—28no—
49C2×C283⋊C8—21no—
50C2×C283⋊C8—21no—
51C2×C283⋊C8D412yescomplemented
52C4⋊Dic283—21no—
53C4⋊Dic283D412yescomplemented
54Dic283⋊C4—24no—
55(C2×D283)⋊C4—24no—
56(C2×D283)⋊C4—24no—
57C2×Q8×C283—21no—
58C2×Q8×C283—21no—
59C2×Q8×C283—21no—
60C2×Q8×C283—21no—
61C2×Q8×C283—21no—
62C2×Q8×C283D412yescomplemented
63C22×C4×C283—21no—
64C22×C4×C283—21no—
65C22×C4×C283C2311yescharacteristic
66C2×C8×C283—21no—
67C2×C8×C283—21no—
68C2×C8×C283—21no—
69C4⋊C4×C283—21no—
70C4⋊C4×C283D412yes—
71C22×D283—21no—
72C22×D283—21no—
73C22×D283—21no—
74C22×D283—21no—
75C22×D283—21no—
76C22×D283—21no—
77C22×D283—22no—
78C22×D283—41no—
79C22×D283—41no—
80C22×D283—41no—
81C22×D283—41no—
82C22×D283—41no—
83C22×D283—41no—
84C22×D283SD1612yescomplemented
85D1132—22no—
86D1132—22no—
87D1132—48no—
88D1132—41no—
89D1132—41no—
90C2×Dic283—21no—
91C2×Dic283—22no—
92C2×Dic283—21no—
93C2×Dic283—21no—
94C2×Dic283—41no—
95C2×Dic283—41no—
96C4×D283—41no—
97C4×D283—41no—
98C4×D283—41no—
99C4×D283—41no—
100C283⋊C8—22no—
101C23×C283C2×D411yescharacteristic
102Q8×C283—22no—
103Q8×C283—22no—
104Q8×C283—41no—
105Q8×C283—41no—
106C2×C4×C283—22no—
107C2×C4×C283—22no—
108C2×C4×C283—41no—
109C2×C4×C283—41no—
110C2×C4×C283—41no—
111C2×C4×C283—41no—
112C2×C4×C283C2×D411yescharacteristic
113C2×C4×C283C2×D411yescharacteristic
114C2×C4×C283C2×D411yescharacteristic
115C2×C4×C283C2×D411yescharacteristic
116C2×C4×C283C2×D411yescharacteristic
117C2×C4×C283#4111yescharacteristic
118C8×C283—41no—
119C22×C283#12011yescharacteristic
120C22×C283#12011yescharacteristic
121C22×C283#12111yescharacteristic
122C22×C283C2×SD1611yescharacteristic
123C22×C283#13511yescharacteristic
124C22×C283AGL(1,ℤ/8)11yescharacteristic
125C22×C283#13711yescharacteristic
126C2×D283—22no—
127C2×D283—22no—
128C2×D283—22no—
129C2×D283—41no—
130C2×D283—41no—
131C2×D283—41no—
132C2×D283—41no—
133C2×D283—42no—
134C2×D283—42no—
135C2×D283—42no—
136C2×D283—81no—
137C2×D283—81no—
138C2×D283—81no—
139C2×D283—81no—
140C4×C283—42no—
141C4×C283—42no—
142C4×C283#12011yescharacteristic
143C4×C283#12111yescharacteristic
144C4×C283#12111yescharacteristic
145C4×C283#12711yescharacteristic
146Dic283—41no—
147Dic283—42no—
148C2×C283#39211yescharacteristic
149C2×C283#44811yescharacteristic
150C2×C283#44911yescharacteristic
151C2×C283#45011yescharacteristic
152C2×C283#45211yescharacteristic
153C2×C283#46511yescharacteristic
154C2×C283#46811yescharacteristic
155D283—42no—
156D283—82no—
157C283#200011yescharacteristic, complemented, Sylow
158#2000—2831nomaximal, Sylow
159C22×SD16—2831no—
160C2×C22⋊Q8—2831no—
161C2×#121—2831no—
162C2×#103D28311yescharacteristic, complemented
163C2×#102—2831no—
164C2×C22⋊C8—2831no—
165#340—2831no—
166C22×Q8C2×D28311yescharacteristic
167C22×D4—2831no—
168C22×D4—5661no—
169C23×C4—2831no—
170C2×SD16—5662no—
171C2×SD16—5662no—
172C2×SD16—5662no—
173C22×C8—2831no—
174C22×C8C2×D28311yescharacteristic
175C22⋊Q8—5662no—
176C22⋊Q8—5662no—
177#121—5662no—
178#121—5662no—
179C2×C4⋊C4—2831no—
180C2×C4⋊C4—5661no—
181C2×C4⋊C4C2×D28311yescharacteristic
182C2×C22⋊C4—5661no—
183C2×C22⋊C4—5661no—
184#103—22no—
185#102—5662no—
186C22⋊C8—5662no—
187C24—2831no—
188C24—5661no—
189C2×Q8—21no—
190C2×Q8—21no—
191C2×Q8—21no—
192C2×Q8—21no—
193C2×Q8—21no—
194C2×Q8D113212yescomplemented
195C2×D4—2832no—
196C2×D4—5664no—
197C2×D4—5661no—
198C2×D4—5661no—
199C2×D4—5661no—
200C2×D4—5661no—
201C2×D4—5661no—
202C2×D4—11322no—
203C2×D4—11322no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—2831no—
207C22×C4—5661no—
208C22×C4—5661no—
209C22×C4—5661no—
210C22×C4—5661no—
211C22×C4—5661no—
212C22×C4—5661no—
213C22×C4—5661no—
214C22×C4C22×D28311yescharacteristic
215SD16—5668no—
216C2×C8—21no—
217C2×C8—21no—
218C2×C8—21no—
219C2×C8—2832no—
220C2×C8—5661no—
221C2×C8—5661no—
222C4⋊C4—21no—
223C4⋊C4—2832no—
224C4⋊C4—5664no—
225C4⋊C4—5661no—
226C4⋊C4C22⋊D28312yes—
227C22⋊C4—5664no—
228C22⋊C4—5664no—
229C23—2832no—
230C23—5661no—
231C23—5661no—
232C23—5661no—
233C23—5661no—
234C23—5661no—
235C23—5661no—
236C23—5662no—
237C23—11321no—
238C23—11321no—
239C23—11321no—
240C23—11321no—
241C23—11321no—
242C23—11321no—
243C23D4×D28311yescharacteristic
244Q8—22no—
245Q8—22no—
246Q8—41no—
247Q8—41no—
248D4—5662no—
249D4—5662no—
250D4—11328no—
251D4—11321no—
252D4—11321no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—5661no—
260C2×C4—5662no—
261C2×C4—5661no—
262C2×C4—5661no—
263C2×C4—11321no—
264C2×C4—11321no—
265C2×C4—11321no—
266C2×C4—11321no—
267C2×C4—11321no—
268C2×C4—11321no—
269C2×C4D4×D28311yescharacteristic
270C2×C4D4×D28311yescharacteristic
271C2×C4D4×D28311yescharacteristic
272C2×C4C2×C22⋊D28311yescharacteristic
273C2×C4C2×D113211yescharacteristic
274C2×C4#1798539211yescharacteristic
275C8—41no—
276C8—5662no—
277C22—5662no—
278C22—5662no—
279C22—5662no—
280C22—11321no—
281C22—11321no—
282C22—11321no—
283C22—11321no—
284C22—11322no—
285C22—11322no—
286C22—11322no—
287C22—22641no—
288C22—22641no—
289C22—22641no—
290C22—22641no—
291C22#2258357811yescharacteristic
292C22#2258358011yescharacteristic
293C22#2258358311yescharacteristic
294C22SD16×D28311yescharacteristic
295C22#2258363311yescharacteristic
296C22#2258363711yescharacteristic
297C22#2258364211yescharacteristic
298C4—42no—
299C4—42no—
300C4—11322no—
301C4—11321no—
302C4#2258358011yescharacteristic
303C4#2258358311yescharacteristic
304C4#2258358411yescharacteristic
305C4#2258360611yescharacteristic
306C2—11322no—
307C2—22642no—
308C2#3182637411yescharacteristic
309C2#3182660511yescharacteristic
310C2#3182661311yescharacteristic
311C2#3182661411yescharacteristic
312C2#3182662611yescharacteristic
313C2#3182669711yescharacteristic
314C2#3182671411yescharacteristic
subgroupG/H
centerC23D4×D283
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
FittingC2×#103×C283C2
socleC23×C283C2×D4
prime radicalC2×#22583585C2
hypercenterC2×#103D283
hypocenterC283#2000
LCSG ▷ C22×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C22×#17985379C2semidirect
2. C2×#22583586C2semidirect
4. C2×#22583532C2semidirect
5. C2×(C2×D283)⋊C8C2semidirect
6. #31826227C2semidirect
7. C2×#103×C283C2semidirect
51. C2×C283⋊C8D4semidirect
53. C4⋊Dic283D4semidirect
62. C2×Q8×C283D4semidirect
84. C22×D283SD16semidirect
157. C283#2000semidirect
162. C2×#103D283semidirect
194. C2×Q8D1132semidirect

Maximal subgroups

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

subgroupindex
C22×#179853792
C2×#225835862
C2×#225835852
C2×#225835322
C2×(C2×D283)⋊C82
#318262272
C2×#103×C2832
#2000283