Finite Group Databasebeta

← #451×D283 #49130452

Subgroups — #451×D283 #49130452

Order 36224.

740 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 740 conjugacy classes of subgroups — too many to draw. Only its 155 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×Q8×D283C211yesmaximal, characteristic
2C2×Q16×D283C212yesmaximal, complemented
3C22⋊Q8×D283C211yesmaximal, characteristic
4#31826623C211yesmaximal, characteristic, complemented
5#31826622C212yesmaximal, complemented
6#31826621C211yesmaximal, characteristic, complemented
7#31826620C211yesmaximal, characteristic, complemented
8#31826619C212yesmaximal, complemented
9#103×D283C212yesmaximal, complemented
10C22⋊C8×D283C211yesmaximal, characteristic
11#451×C283C211yesmaximal, characteristic, complemented
12C22×Dic566—21no—
13C22×Dic566C2211yescharacteristic
14C2×Q8×D283—28no—
15C2×Q8×D283—21no—
16C2×Q8×D283—21no—
17C2×Q8×D283C2211yescharacteristic
18C2×Q8×D283C2212yes—
19C2×Q8×D283C2212yes—
20C22×C4×D283—21no—
21C22×C4×D283C2211yescharacteristic
22C2×Dic1132C2212yescomplemented
23C2×#17985382C2212yescomplemented
24C2×#17985382C2212yescomplemented
25Q16×D283—28no—
26C2×C8×D283C2212yes—
27#22583590C2211yescharacteristic
28#22583589C2211yescharacteristic
29#22583588—21no—
30#22583587—21no—
31#22583586C2211yescharacteristic
32C4⋊C4×D283—21no—
33C4⋊C4×D283C2211yescharacteristic
34C22⋊C4×D283—21no—
35#22583535C2212yescomplemented
36#22583534C2212yescomplemented
37#22583533C2212yescomplemented
38C22⋊(C283⋊C8)C2211yescharacteristic
39(C2×D283)⋊C8C2212yes—
40C22×Q8×C283C2211yescharacteristic
41C2×Q16×C283C2212yescomplemented
42C22⋊Q8×C283C2211yescharacteristic
43#103×C283C2212yescomplemented
44C22⋊C8×C283C2211yescharacteristic
45C23×D283D411yescharacteristic
46C2×Dic566—28no—
47C2×Dic566—24no—
48C2×Dic566—22no—
49C2×Dic566—22no—
50C2×Dic566—21no—
51C2×Dic566—21no—
52C2×Dic566C2311yescharacteristic
53C2×Dic566C2312yes—
54Q8×D283—28no—
55Q8×D283—28no—
56Q8×D283—24no—
57Q8×D283—24no—
58Q8×D283—24no—
59Q8×D283—24no—
60Q8×D283D418yes—
61C22×Dic283—21no—
62C22×Dic283D411yescharacteristic
63C2×C4×D283—28no—
64C2×C4×D283—22no—
65C2×C4×D283—22no—
66C2×C4×D283—24no—
67C2×C4×D283—21no—
68C2×C4×D283—21no—
69C2×C4×D283D411yescharacteristic
70C2×C4×D283D411yescharacteristic
71C2×C4×D283C2311yescharacteristic
72C2×C4×D283C2311yescharacteristic
73Dic1132—24no—
74#17985382—24no—
75#17985382—24no—
76C2×C283⋊C8C2312yes—
77C8×D283—24no—
78C4⋊Dic283—21no—
79C4⋊Dic283C2311yescharacteristic
80Dic283⋊C4—21no—
81Dic283⋊C4—21no—
82Dic283⋊C4—21no—
83C22⋊Dic283—21no—
84(C2×D283)⋊C4—21no—
85(C2×D283)⋊C4—21no—
86C2×Q8×C283—24no—
87C2×Q8×C283—21no—
88C2×Q8×C283C2311yescharacteristic
89C2×Q8×C283C2312yes—
90C22×C4×C283—21no—
91C22×C4×C283C2311yescharacteristic
92Q16×C283—24no—
93C2×C8×C283C2312yes—
94C4⋊C4×C283—21no—
95C4⋊C4×C283C2311yescharacteristic
96C22⋊C4×C283—21no—
97C22×D283—22no—
98C22×D283—22no—
99C22×D283Q1614yescomplemented
100C22×D283C2×D411yescharacteristic
101C22×D283C2×D411yescharacteristic
102Dic566—24no—
103Dic566—28no—
104Dic566—22no—
105Dic566—28no—
106Dic566—22no—
107Dic566—42no—
108Dic566C2×D414yes—
109C2×Dic283—24no—
110C2×Dic283—22no—
111C2×Dic283—22no—
112C2×Dic283—21no—
113C2×Dic283—21no—
114C2×Dic283C2×D411yescharacteristic
115C2×Dic283C2×D411yescharacteristic
116C4×D283—28no—
117C4×D283—28no—
118C4×D283—22no—
119C4×D283—22no—
120C4×D283—22no—
121C4×D283—42no—
122C4×D283—42no—
123C4×D283C2×D414yes—
124C283⋊C8—22no—
125C23×C283C2×D411yescharacteristic
126Q8×C283—24no—
127Q8×C283—22no—
128Q8×C283—22no—
129Q8×C283C2×D414yes—
130C2×C4×C283—24no—
131C2×C4×C283—22no—
132C2×C4×C283—22no—
133C2×C4×C283—21no—
134C2×C4×C283—21no—
135C2×C4×C283C2×D411yescharacteristic
136C2×C4×C283C2411yescharacteristic
137C8×C283—22no—
138C22×C283—21no—
139C22×C283—21no—
140C22×C283C2×Q1612yescomplemented
141C22×C283C22×D411yescharacteristic
142C2×D283—21no—
143C2×D283—21no—
144C2×D283—28no—
145C2×D283#12012yes—
146C2×D283C2×Q1612yes—
147C2×D283C2×Q1612yescomplemented
148C2×D283#13712yes—
149C4×C283—24no—
150C4×C283—21no—
151C4×C283—41no—
152C4×C283—41no—
153C4×C283C22×D412yes—
154Dic283—24no—
155Dic283—21no—
156Dic283—41no—
157Dic283—41no—
158Dic283#12012yes—
159C2×C283—22no—
160C2×C283C2×#12011yescharacteristic
161C2×C283C22×Q1611yescharacteristic
162C2×C283C2×#13711yescharacteristic
163D283—22no—
164D283#45114yesdirect product factor
165C283C2×#45111yescharacteristic, complemented, Sylow
166C2×#451—2831nomaximal, Sylow
167C23×Q8—2831no—
168C22×Q16—2832no—
169C2×C22⋊Q8—2831no—
170#451—2831no—
171#451—2832no—
172#451—2831no—
173#451—2832no—
174#451—2831no—
175#451D28311yescharacteristic, direct product factor
176C2×#103—2832no—
177C2×C22⋊C8—2831no—
178C22×Q8—2832no—
179C22×Q8—2831no—
180C22×Q8—2832no—
181C22×Q8—2831no—
182C22×Q8—5661no—
183C22×Q8—5661no—
184C22×Q8—5661no—
185C22×Q8—5668no—
186C22×Q8C2×D28311yescharacteristic
187C23×C4—2831no—
188C23×C4—5661no—
189C2×Q16—2832no—
190C2×Q16—2832no—
191C2×Q16—2832no—
192C2×Q16—5668no—
193C2×Q16C2×D28312yescomplemented
194C22×C8—2832no—
195C22⋊Q8—2831no—
196C22⋊Q8—2831no—
197C22⋊Q8—2831no—
198C22⋊Q8—5661no—
199C22⋊Q8—5661no—
200C22⋊Q8C2×D28311yescharacteristic
201C2×C4⋊C4—2831no—
202C2×C4⋊C4—5661no—
203C2×C22⋊C4—5661no—
204#103—2832no—
205#103—2832no—
206#103—2832no—
207#103C2×D28312yescomplemented
208C22⋊C8—2831no—
209C22⋊C8—2832no—
210C22⋊C8C2×D28311yescharacteristic
211C24—2831no—
212C2×Q8—24no—
213C2×Q8—21no—
214C2×Q8—2838no—
215C2×Q8—2832no—
216C2×Q8—2831no—
217C2×Q8—5662no—
218C2×Q8—5662no—
219C2×Q8—5661no—
220C2×Q8—5664no—
221C2×Q8—5668no—
222C2×Q8—5664no—
223C2×Q8—5664no—
224C2×Q8—5664no—
225C2×Q8—5668no—
226C2×Q8—5668no—
227C2×Q8—5664no—
228C2×Q8—5661no—
229C2×Q8C22×D28311yescharacteristic
230C2×Q8C22×D28312yes—
231C22×C4—21no—
232C22×C4—2831no—
233C22×C4—2831no—
234C22×C4—2831no—
235C22×C4—2831no—
236C22×C4—2831no—
237C22×C4—5664no—
238C22×C4—5662no—
239C22×C4—5662no—
240C22×C4—5668no—
241C22×C4—5661no—
242C22×C4—5661no—
243C22×C4—5661no—
244C22×C4C22×D28311yescharacteristic
245Q16—24no—
246Q16—5664no—
247Q16—5664no—
248Q16—5664no—
249C2×C8—2832no—
250C2×C8—5664no—
251C2×C8C22×D28312yes—
252C4⋊C4—21no—
253C4⋊C4—2831no—
254C4⋊C4—5661no—
255C4⋊C4—5661no—
256C4⋊C4—5661no—
257C4⋊C4—5661no—
258C4⋊C4C22×D28311yescharacteristic
259C22⋊C4—21no—
260C22⋊C4—5661no—
261C22⋊C4—5661no—
262C22⋊C4—5661no—
263C23—2831no—
264C23—2834no—
265C23—2831no—
266C23—5662no—
267C23—5662no—
268C23D4×D28311yescharacteristic
269Q8—24no—
270Q8—22no—
271Q8—22no—
272Q8—2834no—
273Q8—5668no—
274Q8—5668no—
275Q8—5664no—
276Q8—5662no—
277Q8—5662no—
278Q8—11322no—
279Q8D4×D28314yes—
280C2×C4—24no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—2831no—
286C2×C4—2834no—
287C2×C4—2831no—
288C2×C4—5662no—
289C2×C4—5662no—
290C2×C4—5668no—
291C2×C4—5668no—
292C2×C4—5662no—
293C2×C4—5664no—
294C2×C4—5662no—
295C2×C4—5662no—
296C2×C4—5661no—
297C2×C4—5661no—
298C2×C4—11322no—
299C2×C4—11322no—
300C2×C4D4×D28311yescharacteristic
301C2×C4C23×D28311yescharacteristic
302C8—22no—
303C8—5662no—
304C22—21no—
305C22—21no—
306C22—2832no—
307C22—2832no—
308C22—2832no—
309C22—2832no—
310C22—5668no—
311C22—5661no—
312C22—5661no—
313C22Q16×D28312yescomplemented
314C22C2×D4×D28311yescharacteristic
315C4—24no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—2832no—
320C4—5661no—
321C4—5664no—
322C4—11321no—
323C4—11321no—
324C4C2×D4×D28312yes—
325C2—22no—
326C2—2834no—
327C2—5662no—
328C2#120×D28311yescharacteristic
329C2C2×Q16×D28311yescharacteristic
330C2#137×D28311yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#451×C283C2
socleC22×C283C22×D4
prime radicalC23×D283D4
hypercenter#451D283
hypocenterC283C2×#451
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. C2×Q16×D283C2semidirect
4. #31826623C2semidirect
5. #31826622C2semidirect
6. #31826621C2semidirect
7. #31826620C2semidirect
8. #31826619C2semidirect
9. #103×D283C2semidirect
11. #451×C283C2semidirect
22. C2×Dic1132C22semidirect
23. C2×#17985382C22semidirect
24. C2×#17985382C22semidirect
35. #22583535C22semidirect
36. #22583534C22semidirect
37. #22583533C22semidirect
41. C2×Q16×C283C22semidirect
43. #103×C283C22semidirect
99. C22×D283Q16semidirect
140. C22×C283C2×Q16semidirect
147. C2×D283C2×Q16semidirect
164. D283#451direct (N × H)
165. C283C2×#451semidirect
175. #451D283direct (N × H)
193. C2×Q16C2×D283semidirect
207. #103C2×D283semidirect
313. C22Q16×D283semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×D2832
C2×Q16×D2832
C22⋊Q8×D2832
#318266232
#318266222
#318266212
#318266202
#318266192
#103×D2832
C22⋊C8×D2832
#451×C2832
C2×#451283