Finite Group Databasebeta

← #49130867

Subgroups — #49130867

Order 36224.

500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C2×#22583630C211yesmaximal, characteristic, complemented
2C22×#17985376C211yesmaximal, characteristic, complemented
3#31826976C211yesmaximal, characteristic, complemented
4#31826721C212yesmaximal, complemented
5#31826716C212yesmaximal, complemented
6#31826713C212yesmaximal, complemented
7#31826709C212yesmaximal, complemented
8#31826501C211yesmaximal, characteristic, complemented
9#31826461C211yesmaximal, characteristic, complemented
10#31826459C211yesmaximal, characteristic, complemented
11#525×C283C211yesmaximal, characteristic, complemented
12C2×#17985392C2211yescharacteristic
13#22583630—24no—
14C2×#17985382C2211yescharacteristic, complemented
15C2×#17985380C2211yescharacteristic, complemented
16C2×#17985379C2211yescharacteristic, complemented
17C2×#17985377C2211yescharacteristic, complemented
18C2×#17985376—24no—
19C2×#17985376C2212yes—
20C2×#17985376C2212yes—
21C22×C283⋊C8C2211yescharacteristic
22C22×C283⋊C8C2211yescharacteristic
23#22583593—21no—
24#22583589C2212yes—
25#22583584C2212yes—
26#22583579—21no—
27C4×C22⋊D283—22no—
28#22583569C2211yescharacteristic
29#22583543C2212yescomplemented
30#22583541C2212yescomplemented
31#22583534C2212yescomplemented
32#22583533C2212yescomplemented
33#22583531C2212yescomplemented
34#22583530C2212yescomplemented
35C2×#41×C283C2211yescharacteristic
36C23×C4×C283C2211yescharacteristic
37#123×C283—21no—
38C22⋊Q8×C283C2212yes—
39#121×C283C2212yes—
40#120×C283—21no—
41C4×D4×C283—22no—
42#117×C283C2211yescharacteristic
43#17985392—22no—
44#17985392—22no—
45C2×Dic566C2311yescharacteristic
46C2×D1132C2311yescharacteristic
47C2×C22⋊D283—22no—
48C2×C22⋊D283—21no—
49C2×C4×D283—21no—
50#17985382—22no—
51#17985380—22no—
52#17985379—22no—
53#17985377—22no—
54#17985376—24no—
55#17985376—24no—
56C2×C283⋊C8—22no—
57C2×C283⋊C8D414yescomplemented
58C2×C283⋊C8C2312yes—
59C2×C283⋊C8C2311yescharacteristic
60C2×C283⋊C8C2311yescharacteristic
61C4⋊Dic283C2312yes—
62Dic283⋊C4—22no—
63C22⋊Dic283—21no—
64C22⋊Dic283—22no—
65(C2×D283)⋊C4—22no—
66C4×Dic283—21no—
67C24×C283D411yescharacteristic
68#41×C283—22no—
69#41×C283—22no—
70C2×Q8×C283C2311yescharacteristic
71C2×D4×C283—22no—
72C2×D4×C283—21no—
73C2×D4×C283C2311yescharacteristic
74C22×C4×C283—22no—
75C22×C4×C283—22no—
76C22×C4×C283—21no—
77C22×C4×C283D412yes—
78C22×C4×C283D411yescharacteristic
79C22×C4×C283C2312yes—
80C22×C4×C283C2311yescharacteristic
81C4⋊C4×C283—22no—
82C4⋊C4×C283C2312yes—
83C22⋊C4×C283—21no—
84C22⋊C4×C283—22no—
85C22⋊C4×C283—22no—
86C42×C283—21no—
87C22×D283—21no—
88Dic566—21no—
89Dic566—21no—
90D1132—21no—
91D1132—21no—
92C22⋊D283—44no—
93C22⋊D283—42no—
94C2×Dic283—22no—
95C2×Dic283—21no—
96C4×D283—42no—
97C283⋊C8—22no—
98C283⋊C8C2×D412yes—
99C283⋊C8C2×D412yes—
100C23×C283—22no—
101C23×C283—21no—
102C23×C283—42no—
103C23×C283C2×D412yes—
104C23×C283C2×D411yescharacteristic
105Q8×C283—21no—
106Q8×C283—21no—
107D4×C283—21no—
108D4×C283—21no—
109D4×C283—44no—
110D4×C283—42no—
111C2×C4×C283—22no—
112C2×C4×C283—24no—
113C2×C4×C283—22no—
114C2×C4×C283—22no—
115C2×C4×C283—22no—
116C2×C4×C283—21no—
117C2×C4×C283—42no—
118C2×C4×C283C2×D412yes—
119C2×C4×C283C2×D412yes—
120C2×C4×C283C2×D411yescharacteristic
121C2×C4×C283#4112yes—
122C2×C4×C283C2411yescharacteristic
123C22×C283—22no—
124C22×C283—22no—
125C22×C283—22no—
126C22×C283—22no—
127C22×C283—44no—
128C22×C283—41no—
129C22×C283—42no—
130C22×C283#12112yes—
131C22×C283C22×D411yescharacteristic
132C2×D283—41no—
133C2×D283—42no—
134C4×C283—22no—
135C4×C283—41no—
136C4×C283—42no—
137C4×C283#12112yes—
138C4×C283C22×D411yescharacteristic
139C4×C283C2×#4111yescharacteristic
140Dic283—41no—
141Dic283—42no—
142C2×C283—22no—
143C2×C283—42no—
144C2×C283—81no—
145C2×C283C2×#12111yescharacteristic
146C2×C283#57512yes—
147D283—81no—
148C283#305411yescharacteristic, complemented, Sylow
149#3054—2831nomaximal, Sylow
150C2×#135—2831no—
151C22×M16—2831no—
152#525—2831no—
153#525D28311yescharacteristic, complemented
154#470—2832no—
155#469—2832no—
156#468—2832no—
157#468—2832no—
158#427—2831no—
159#416—2831no—
160#416—2831no—
161C2×#41—2831no—
162C2×#41C2×D28311yescharacteristic
163C23×C4C2×D28311yescharacteristic
164#135—5664no—
165C2×Q16—2831no—
166C2×SD16—2831no—
167C2×SD16—2831no—
168C2×D8—2831no—
169C2×M16—2832no—
170C2×M16—2832no—
171C2×M16—5664no—
172C22×C8—2831no—
173C22×C8—2831no—
174#123—21no—
175#123—5661no—
176C22⋊Q8—2832no—
177C22⋊Q8C2×D28312yes—
178#121—2832no—
179#121C2×D28312yes—
180#120—21no—
181#120—5661no—
182C4×D4—22no—
183C4×D4—5662no—
184#117—2831no—
185#117C2×D28311yescharacteristic
186#107—2832no—
187#106—2832no—
188#103—2832no—
189#103—2832no—
190#102—2832no—
191#102—2832no—
192C24C22⋊D28311yescharacteristic
193#41—22no—
194#41—22no—
195#41—5662no—
196#41—5662no—
197C2×Q8—2831no—
198C2×Q8C22×D28311yescharacteristic
199C2×D4—22no—
200C2×D4—21no—
201C2×D4—2831no—
202C2×D4—5662no—
203C2×D4—5661no—
204C2×D4C22×D28311yescharacteristic
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—5661no—
209C22×C4C22⋊D28311yescharacteristic
210C22×C4C22⋊D28312yes—
211C22×C4C22×D28312yes—
212C22×C4C22×D28311yescharacteristic
213Q16—5662no—
214SD16—5662no—
215SD16—5662no—
216D8—5662no—
217M16—5664no—
218M16—5664no—
219C2×C8—2834no—
220C2×C8—2831no—
221C2×C8—2831no—
222C2×C8—2832no—
223C2×C8—5662no—
224C4⋊C4—22no—
225C4⋊C4—2832no—
226C4⋊C4—5662no—
227C4⋊C4C22×D28312yes—
228C22⋊C4—21no—
229C22⋊C4—22no—
230C22⋊C4—22no—
231C22⋊C4—5661no—
232C22⋊C4—5662no—
233C22⋊C4—5662no—
234C42—21no—
235C42—5661no—
236C23—22no—
237C23—21no—
238C23—42no—
239C23—5661no—
240C23C2×C22⋊D28312yes—
241C23C2×C22⋊D28311yescharacteristic
242Q8—21no—
243Q8—21no—
244Q8—5661no—
245Q8—5661no—
246D4—21no—
247D4—21no—
248D4—44no—
249D4—42no—
250D4—5661no—
251D4—5661no—
252D4—11324no—
253D4—11322no—
254C2×C4—22no—
255C2×C4—24no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—42no—
261C2×C4—5662no—
262C2×C4—5661no—
263C2×C4—11322no—
264C2×C4D4×D28312yes—
265C2×C4C2×C22⋊D28312yes—
266C2×C4C2×C22⋊D28311yescharacteristic
267C2×C4#1798539112yes—
268C2×C4C23×D28311yescharacteristic
269C8—2832no—
270C8—2832no—
271C8—5662no—
272C22—22no—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—44no—
277C22—41no—
278C22—42no—
279C22—11321no—
280C22—11322no—
281C22#2258358212yes—
282C22C22×C22⋊D28311yescharacteristic
283C4—22no—
284C4—41no—
285C4—42no—
286C4—11321no—
287C4—11322no—
288C4#2258358212yes—
289C4C2×D4×D28311yescharacteristic
290C4C2×#1798539111yescharacteristic
291C2—22no—
292C2—42no—
293C2—81no—
294C2—22641no—
295C2C2×#2258358211yescharacteristic
296C2#3182726312yes—
subgroupG/H
centerC2×C4C2×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#525×C283C2
socleC22×C283C22×D4
hypercenter#525D283
hypocenterC283#3054
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×#22583630C2semidirect
2. C22×#17985376C2semidirect
3. #31826976C2semidirect
4. #31826721C2semidirect
5. #31826716C2semidirect
6. #31826713C2semidirect
7. #31826709C2semidirect
8. #31826501C2semidirect
9. #31826461C2semidirect
10. #31826459C2semidirect
11. #525×C283C2semidirect
14. C2×#17985382C22semidirect
15. C2×#17985380C22semidirect
16. C2×#17985379C22semidirect
17. C2×#17985377C22semidirect
29. #22583543C22semidirect
30. #22583541C22semidirect
31. #22583534C22semidirect
32. #22583533C22semidirect
33. #22583531C22semidirect
34. #22583530C22semidirect
57. C2×C283⋊C8D4semidirect
148. C283#3054semidirect
153. #525D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836302
C22×#179853762
#318269762
#318267212
#318267162
#318267132
#318267092
#318265012
#318264612
#318264592
#525×C2832
#3054283