Finite Group Databasebeta

← #49130869

Subgroups — #49130869

Order 36224.

500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 133 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×#17985375C211yesmaximal, characteristic, complemented
3#31826977C211yesmaximal, characteristic, complemented
4#31826972C211yesmaximal, characteristic, complemented
5#31826722C212yesmaximal, complemented
6#31826717C212yesmaximal, complemented
7#31826714C212yesmaximal, complemented
8#31826710C212yesmaximal, complemented
9#31826501C211yesmaximal, characteristic, complemented
10#31826462C211yesmaximal, characteristic, complemented
11#416×C283C211yesmaximal, characteristic, complemented
12C2×#17985392C2211yescharacteristic
13C22×C4×D283C2211yescharacteristic
14#22583630—24no—
15C2×#17985382C2211yescharacteristic, complemented
16C2×#17985380C2211yescharacteristic, complemented
17C2×#17985379C2211yescharacteristic, complemented
18C2×#17985377C2211yescharacteristic, complemented
19C2×#17985375—24no—
20C2×#17985375C2212yes—
21C2×#17985375C2212yes—
22C22×C283⋊C8C2211yescharacteristic
23#22583594—21no—
24#22583591—21no—
25#22583590C2212yes—
26#22583586C2212yes—
27#22583585C2212yes—
28#22583581C2212yes—
29#22583580—21no—
30#22583578—21no—
31C4×D1132—22no—
32C4×C22⋊D283—22no—
33#22583569C2211yescharacteristic
34#22583543C2212yescomplemented
35#22583541C2212yescomplemented
36#22583535C2212yescomplemented
37#22583532C2212yescomplemented
38C2×#41×C283C2211yescharacteristic
39C22×C8×C283C2211yescharacteristic
40#117×C283C2211yescharacteristic
41#103×C283C2212yescomplemented
42#102×C283C2212yescomplemented
43C23×D283D411yescharacteristic
44#17985392—22no—
45#17985392—22no—
46C2×Dic566C2311yescharacteristic
47C2×D1132—22no—
48C2×D1132C2311yescharacteristic
49C2×C22⋊D283—22no—
50C2×C22⋊D283—21no—
51C22×Dic283D411yescharacteristic
52C2×C4×D283—22no—
53C2×C4×D283—21no—
54C2×C4×D283—22no—
55C2×C4×D283D412yes—
56C2×C4×D283C2312yes—
57#17985382—22no—
58#17985380—22no—
59#17985379—22no—
60#17985377—22no—
61#17985375—24no—
62#17985375—24no—
63C2×C283⋊C8D414yescomplemented
64C2×C283⋊C8C2311yescharacteristic
65C2×C283⋊C8C2311yescharacteristic
66C4⋊Dic283—22no—
67C4⋊Dic283C2312yes—
68Dic283⋊C4—22no—
69C22⋊Dic283—22no—
70C22⋊Dic283—21no—
71(C2×D283)⋊C4—22no—
72(C2×D283)⋊C4—22no—
73(C2×D283)⋊C4—22no—
74C4×Dic283—21no—
75#41×C283—22no—
76#41×C283—22no—
77C2×Q8×C283C2311yescharacteristic
78C2×D4×C283—21no—
79C2×D4×C283C2311yescharacteristic
80C22×C4×C283—21no—
81C22×C4×C283C2311yescharacteristic
82C2×C8×C283—22no—
83C2×C8×C283C2312yes—
84C4⋊C4×C283C2312yes—
85C22⋊C4×C283—21no—
86C42×C283—21no—
87C22×D283—22no—
88C22×D283—21no—
89C22×D283—42no—
90C22×D283C2×D412yes—
91Dic566—21no—
92Dic566—21no—
93D1132—21no—
94D1132—21no—
95D1132—44no—
96C22⋊D283—44no—
97C22⋊D283—42no—
98C2×Dic283—22no—
99C2×Dic283—22no—
100C2×Dic283—21no—
101C2×Dic283C2×D412yes—
102C4×D283—24no—
103C4×D283—22no—
104C4×D283—22no—
105C4×D283—42no—
106C283⋊C8C2×D412yes—
107C283⋊C8C2×D412yes—
108C23×C283—21no—
109C23×C283C2×D411yescharacteristic
110Q8×C283—21no—
111Q8×C283—21no—
112D4×C283—21no—
113D4×C283—21no—
114D4×C283—42no—
115C2×C4×C283—22no—
116C2×C4×C283—21no—
117C2×C4×C283—42no—
118C2×C4×C283C2×D412yes—
119C2×C4×C283C2×D411yescharacteristic
120C2×C4×C283#4112yes—
121C2×C4×C283C2411yescharacteristic
122C8×C283—22no—
123C22×C283—22no—
124C22×C283—41no—
125C22×C283—42no—
126C22×C283#12112yes—
127C22×C283C22×D411yescharacteristic
128C2×D283—22no—
129C2×D283—22no—
130C2×D283—22no—
131C2×D283—44no—
132C2×D283—41no—
133C2×D283—42no—
134C4×C283—41no—
135C4×C283—42no—
136C4×C283#12112yes—
137C4×C283C22×D411yescharacteristic
138C4×C283C2×#4111yescharacteristic
139Dic283—22no—
140Dic283—41no—
141Dic283—42no—
142C2×C283—22no—
143C2×C283—81no—
144C2×C283C2×#12111yescharacteristic
145C2×C283#57512yes—
146D283—42no—
147D283—81no—
148C283#305411yescharacteristic, complemented, Sylow
149#3054—2831nomaximal, Sylow
150C2×#135—2831no—
151C22×M16—2831no—
152#525—2831no—
153#525—2831no—
154#470—2832no—
155#469—2832no—
156#468—2832no—
157#468—2832no—
158#427—2831no—
159#416—2831no—
160#416D28311yescharacteristic, complemented
161C2×#41—2831no—
162C2×#41C2×D28311yescharacteristic
163C23×C4—2831no—
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×C8C2×D28311yescharacteristic
174#123—5661no—
175#123—5661no—
176C22⋊Q8—2832no—
177C22⋊Q8—2832no—
178#121—2832no—
179#121—2832no—
180#120—5661no—
181#120—5661no—
182C4×D4—5662no—
183C4×D4—5662no—
184#117—2831no—
185#117C2×D28311yescharacteristic
186#107—2832no—
187#106—2832no—
188#103—2832no—
189#103C2×D28312yescomplemented
190#102—2832no—
191#102C2×D28312yescomplemented
192C24—2831no—
193#41—22no—
194#41—22no—
195#41—5662no—
196#41—5662no—
197C2×Q8—2831no—
198C2×Q8C22×D28311yescharacteristic
199C2×D4—21no—
200C2×D4—2831no—
201C2×D4—5662no—
202C2×D4—5662no—
203C2×D4—5661no—
204C2×D4C22×D28311yescharacteristic
205C22×C4—21no—
206C22×C4—2831no—
207C22×C4—2832no—
208C22×C4—2832no—
209C22×C4—5662no—
210C22×C4—5662no—
211C22×C4—5661no—
212C22×C4C22×D28311yescharacteristic
213Q16—5662no—
214SD16—5662no—
215SD16—5662no—
216D8—5662no—
217M16—5664no—
218M16—5664no—
219C2×C8—22no—
220C2×C8—2834no—
221C2×C8—2831no—
222C2×C8—2831no—
223C2×C8C22×D28312yes—
224C4⋊C4—2832no—
225C4⋊C4—5662no—
226C4⋊C4—5662no—
227C4⋊C4C22×D28312yes—
228C22⋊C4—21no—
229C22⋊C4—5662no—
230C22⋊C4—5662no—
231C22⋊C4—5662no—
232C22⋊C4—5662no—
233C22⋊C4—5661no—
234C42—21no—
235C42—5661no—
236C23—21no—
237C23—2832no—
238C23—5662no—
239C23—5661no—
240C23—11322no—
241C23D4×D28311yescharacteristic
242Q8—21no—
243Q8—21no—
244Q8—5661no—
245Q8—5661no—
246D4—21no—
247D4—21no—
248D4—42no—
249D4—5661no—
250D4—5661no—
251D4—11324no—
252D4—11324no—
253D4—11322no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—2832no—
258C2×C4—5662no—
259C2×C4—5664no—
260C2×C4—5662no—
261C2×C4—5662no—
262C2×C4—5662no—
263C2×C4—5661no—
264C2×C4—11322no—
265C2×C4D4×D28312yes—
266C2×C4D4×D28311yescharacteristic
267C2×C4#1798539212yes—
268C2×C4C23×D28311yescharacteristic
269C8—22no—
270C8—2832no—
271C8—2832no—
272C22—22no—
273C22—41no—
274C22—42no—
275C22—5662no—
276C22—5662no—
277C22—5662no—
278C22—11324no—
279C22—11321no—
280C22—11322no—
281C22#2258358312yes—
282C22C2×D4×D28311yescharacteristic
283C4—41no—
284C4—42no—
285C4—5662no—
286C4—11321no—
287C4—11322no—
288C4#2258358312yes—
289C4C2×D4×D28311yescharacteristic
290C4C2×#1798539211yescharacteristic
291C2—22no—
292C2—81no—
293C2—11322no—
294C2—22641no—
295C2C2×#2258358311yescharacteristic
296C2#3182726212yes—
subgroupG/H
centerC2×C4D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#416×C283C2
socleC22×C283C22×D4
hypercenter#416D283
hypocenterC283#3054
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C2×#22583630C2semidirect
2. C22×#17985375C2semidirect
3. #31826977C2semidirect
4. #31826972C2semidirect
5. #31826722C2semidirect
6. #31826717C2semidirect
7. #31826714C2semidirect
8. #31826710C2semidirect
9. #31826501C2semidirect
10. #31826462C2semidirect
11. #416×C283C2semidirect
15. C2×#17985382C22semidirect
16. C2×#17985380C22semidirect
17. C2×#17985379C22semidirect
18. C2×#17985377C22semidirect
34. #22583543C22semidirect
35. #22583541C22semidirect
36. #22583535C22semidirect
37. #22583532C22semidirect
41. #103×C283C22semidirect
42. #102×C283C22semidirect
63. C2×C283⋊C8D4semidirect
148. C283#3054semidirect
160. #416D283semidirect
189. #103C2×D283semidirect
191. #102C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836302
C22×#179853752
#318269772
#318269722
#318267222
#318267172
#318267142
#318267102
#318265012
#318264622
#416×C2832
#3054283