Finite Group Databasebeta

← #49124475

Subgroups — #49124475

Order 36224.

944 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 944 conjugacy classes of subgroups — too many to draw. Only its 163 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×#17985391C211yesmaximal, characteristic, complemented
2C2×#22583572C211yesmaximal, characteristic, complemented
3C2×(C22⋊D283)⋊C4C212yesmaximal, complemented
4#31826385C211yesmaximal, characteristic, complemented
5#31826380C212yesmaximal, complemented
6#31826378C211yesmaximal, characteristic, complemented
7#31826374C212yesmaximal, complemented
8#31826373C211yesmaximal, characteristic, complemented
9C22⋊C4×Dic283C212yesmaximal, complemented
10#31826312C211yesmaximal, characteristic, complemented
11#394×C283C211yesmaximal, characteristic, complemented
12C2×#17985391—28no—
13C2×#17985391—24no—
14C22×Dic566C2211yescharacteristic
15C22×D1132C2211yescharacteristic
16C22×C22⋊D283C2212yes—
17C22×C22⋊D283C2212yes—
18C23×Dic283C2212yes—
19C22×C4×D283C2211yescharacteristic
20C22×C4×D283C2211yescharacteristic
21#22583572—24no—
22(C22⋊D283)⋊C4—28no—
23C2×Dic283⋊C4C2212yes—
24C2×C22⋊Dic283C2212yes—
25C2×(C2×D283)⋊C4C2212yes—
26C2×(C2×D283)⋊C4C2211yescharacteristic
27C2×(C2×D283)⋊C4C2212yes—
28C2×(C2×D283)⋊C4C2211yescharacteristic
29C2×C4×Dic283C2212yes—
30C2×C4×Dic283C2211yescharacteristic
31C283⋊#95C2211yescharacteristic
32C283⋊#95C2212yes—
33C283⋊#95C2212yes—
34C22×D4×C283C2211yescharacteristic
35C2×C4⋊C4×C283C2211yescharacteristic
36C2×C22⋊C4×C283C2212yes—
37C2×C22⋊C4×C283C2212yes—
38#95×C283C2211yescharacteristic
39C23×D283C2311yescharacteristic
40C23×D283C2311yescharacteristic
41#17985391—232no—
42C2×Dic566—24no—
43C2×Dic566—22no—
44C2×D1132—22no—
45C2×D1132—22no—
46C2×D1132—22no—
47C2×C22⋊D283—24no—
48C2×C22⋊D283—24no—
49C2×C22⋊D283—24no—
50C2×C22⋊D283—24no—
51C2×C22⋊D283—24no—
52C2×C22⋊D283—24no—
53C22×Dic283—24no—
54C22×Dic283—24no—
55C22×Dic283D418yescomplemented
56C22×Dic283C2311yescharacteristic
57C22×Dic283C2312yes—
58C22×Dic283C2312yes—
59C22×Dic283C2311yescharacteristic
60C2×C4×D283—24no—
61C2×C4×D283—24no—
62C2×C4×D283—22no—
63C2×C4×D283D414yescomplemented
64Dic283⋊C4—24no—
65C22⋊Dic283—24no—
66(C2×D283)⋊C4—22no—
67(C2×D283)⋊C4—24no—
68(C2×D283)⋊C4—24no—
69(C2×D283)⋊C4—22no—
70C4×Dic283—24no—
71C4×Dic283—22no—
72C24×C283C2312yes—
73C2×D4×C283—24no—
74C2×D4×C283—22no—
75C22×C4×C283C2312yes—
76C22×C4×C283C2311yescharacteristic
77C22×C4×C283C2311yescharacteristic
78C22×C4×C283C2311yescharacteristic
79C4⋊C4×C283—22no—
80C22⋊C4×C283—24no—
81C22⋊C4×C283—24no—
82C22×D283—22no—
83C22×D283—21no—
84C22×D283—22no—
85C22×D283—22no—
86C22×D283—22no—
87C22×D283—21no—
88C22×D283—21no—
89C22×D283—21no—
90C22×D283C2×D412yes—
91C22×D283#4112yescomplemented
92Dic566—28no—
93D1132—28no—
94C22⋊D283—216no—
95C22⋊D283—216no—
96C2×Dic283—22no—
97C2×Dic283—22no—
98C2×Dic283—22no—
99C2×Dic283—22no—
100C2×Dic283—216no—
101C2×Dic283—21no—
102C2×Dic283—22no—
103C2×Dic283C2×D414yes—
104C2×Dic283C2×D414yes—
105C2×Dic283C2×D412yes—
106C2×Dic283#4114yescomplemented
107C4×D283—28no—
108C4×D283—44no—
109C23×C283—22no—
110C23×C283—22no—
111C23×C283—22no—
112C23×C283—22no—
113C23×C283—22no—
114C23×C283—22no—
115C23×C283C2×D414yes—
116C23×C283C2411yescharacteristic
117D4×C283—28no—
118C2×C4×C283—21no—
119C2×C4×C283—22no—
120C2×C4×C283—21no—
121C2×C4×C283—22no—
122C2×C4×C283—22no—
123C2×C4×C283—21no—
124C2×C4×C283—22no—
125C2×C4×C283—22no—
126C2×C4×C283C2×D412yes—
127C2×C4×C283#4112yescomplemented
128C22×C283—24no—
129C22×C283—24no—
130C22×C283—24no—
131C22×C283—42no—
132C22×C283—42no—
133C22×C283—42no—
134C22×C283—42no—
135C22×C283C22×D412yes—
136C22×C283C22×D411yescharacteristic
137C22×C283C2×#4111yescharacteristic
138C22×C283C2×#4112yes—
139C22×C283C2×#4111yescharacteristic
140C2×D283—22no—
141C2×D283—24no—
142C2×D283—22no—
143C2×D283—22no—
144C2×D283—22no—
145C2×D283—41no—
146C2×D283—42no—
147C2×D283—42no—
148C2×D283—42no—
149C2×D283—41no—
150C4×C283—22no—
151C4×C283—22no—
152C4×C283—41no—
153C4×C283—42no—
154Dic283—24no—
155Dic283—24no—
156Dic283—41no—
157Dic283#12014yes—
158C2×C283—44no—
159C2×C283C2×#12011yescharacteristic
160C2×C283#52512yes—
161C2×C283#52511yescharacteristic
162C2×C283#53212yes—
163C2×C283#53211yescharacteristic
164D283—42no—
165D283—42no—
166C283#238811yescharacteristic, complemented, Sylow
167#2388—2831nomaximal, Sylow
168C22×#41—2831no—
169C2×C4×D4—2831no—
170C2×C4×D4—2832no—
171#395—2831no—
172#394—2832no—
173#394D28311yescharacteristic, complemented
174#393—2831no—
175#392—2831no—
176#392—2832no—
177C4×C22⋊C4—2832no—
178C4×C22⋊C4—2831no—
179C2×#41—5668no—
180C2×#41—5664no—
181C22×Q8—2831no—
182C22×D4—2832no—
183C22×D4—2832no—
184C22×D4—2831no—
185C22×D4C2×D28311yescharacteristic
186C23×C4—2832no—
187C23×C4—2831no—
188C23×C4—2831no—
189C4×D4—5668no—
190C4×D4—5664no—
191C2×C4⋊C4—2832no—
192C2×C4⋊C4C2×D28311yescharacteristic
193C2×C22⋊C4—2832no—
194C2×C22⋊C4—2832no—
195C2×C22⋊C4—2831no—
196C2×C22⋊C4—2831no—
197C2×C22⋊C4—2832no—
198C2×C22⋊C4C2×D28312yes—
199C2×C22⋊C4C2×D28312yes—
200C2×C42—2832no—
201C2×C42—2831no—
202#95—2831no—
203#95—2832no—
204#95—2832no—
205#95C2×D28311yescharacteristic
206C24—2831no—
207C24—2831no—
208C24C22×D28312yes—
209#41—56632no—
210C2×Q8—5664no—
211C2×Q8—5662no—
212C2×D4—24no—
213C2×D4—22no—
214C2×D4—5662no—
215C2×D4—5662no—
216C2×D4—5664no—
217C2×D4—5664no—
218C2×D4—5664no—
219C2×D4—5664no—
220C2×D4—5664no—
221C2×D4—5664no—
222C2×D4—5662no—
223C22×C4—2831no—
224C22×C4—2838no—
225C22×C4—2832no—
226C22×C4—2832no—
227C22×C4—2834no—
228C22×C4—2831no—
229C22×C4—5664no—
230C22×C4—5664no—
231C22×C4—5662no—
232C22×C4—5664no—
233C22×C4—5664no—
234C22×C4C22×D28312yes—
235C22×C4C22×D28311yescharacteristic
236C22×C4C22×D28311yescharacteristic
237C22×C4C22×D28311yescharacteristic
238C4⋊C4—22no—
239C4⋊C4—5664no—
240C22⋊C4—24no—
241C22⋊C4—24no—
242C22⋊C4—5664no—
243C22⋊C4—5664no—
244C22⋊C4—5662no—
245C22⋊C4—5664no—
246C22⋊C4—5662no—
247C42—5662no—
248C42—5664no—
249C23—22no—
250C23—22no—
251C23—22no—
252C23—22no—
253C23—22no—
254C23—22no—
255C23—2832no—
256C23—2832no—
257C23—5662no—
258C23—5661no—
259C23—5662no—
260C23—5662no—
261C23—5662no—
262C23—5661no—
263C23—5661no—
264C23—5661no—
265C23D4×D28314yes—
266C23C23×D28311yescharacteristic
267Q8—5668no—
268D4—28no—
269D4—5668no—
270D4—56616no—
271D4—56616no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—2834no—
281C2×C4—2832no—
282C2×C4—2834no—
283C2×C4—2834no—
284C2×C4—5668no—
285C2×C4—56616no—
286C2×C4—5662no—
287C2×C4—5662no—
288C2×C4—5662no—
289C2×C4—5662no—
290C2×C4—5661no—
291C2×C4—5662no—
292C2×C4—11324no—
293C2×C4D4×D28312yes—
294C2×C4#1798539112yescomplemented
295C22—24no—
296C22—24no—
297C22—24no—
298C22—42no—
299C22—42no—
300C22—42no—
301C22—42no—
302C22—5662no—
303C22—5664no—
304C22—5662no—
305C22—5662no—
306C22—5662no—
307C22—11321no—
308C22—11322no—
309C22—11322no—
310C22—11322no—
311C22—11321no—
312C22C2×D4×D28312yes—
313C22C2×D4×D28311yescharacteristic
314C22#41×D28311yescharacteristic
315C22#41×D28312yes—
316C22C2×#1798539111yescharacteristic
317C4—22no—
318C4—22no—
319C4—41no—
320C4—42no—
321C4—2834no—
322C4—5664no—
323C4—5664no—
324C4—11321no—
325C2—44no—
326C2—11322no—
327C2—11322no—
328C2#120×D28311yescharacteristic
329C2#3182697312yes—
330C2#3182697511yescharacteristic
331C2#3182701012yes—
332C2#3182701411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D283
commutator, socle, cosocleC23×C283C24
Fitting#394×C283C2
hypercenter#394D283
hypocenterC283#2388
LCSG ▷ C23×C283 ▷ C283
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C22×#17985391C2semidirect
2. C2×#22583572C2semidirect
3. C2×(C22⋊D283)⋊C4C2semidirect
4. #31826385C2semidirect
5. #31826380C2semidirect
6. #31826378C2semidirect
7. #31826374C2semidirect
8. #31826373C2semidirect
9. C22⋊C4×Dic283C2semidirect
10. #31826312C2semidirect
11. #394×C283C2semidirect
55. C22×Dic283D4semidirect
63. C2×C4×D283D4semidirect
91. C22×D283#41semidirect
106. C2×Dic283#41semidirect
127. C2×C4×C283#41semidirect
166. C283#2388semidirect
173. #394D283semidirect
294. C2×C4#17985391semidirect

Maximal subgroups

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

subgroupindex
C22×#179853912
C2×#225835722
C2×(C22⋊D283)⋊C42
#318263852
#318263802
#318263782
#318263742
#318263732
C22⋊C4×Dic2832
#318263122
#394×C2832
#2388283