Finite Group Databasebeta

← #49131613

Subgroups — #49131613

Order 36224.

404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#31827096C211yesmaximal, characteristic, complemented
2#31827032C211yesmaximal, characteristic
3#31826828C212yesmaximal, complemented
4#31826823C212yesmaximal, complemented
5#31826818C212yesmaximal, complemented
6#31826810C212yesmaximal, complemented
7#31826470C211yesmaximal, characteristic, complemented
8#31826464C211yesmaximal, characteristic, complemented
9#31826462C211yesmaximal, characteristic, complemented
10#31826420C211yesmaximal, characteristic, complemented
11C2×#102×C283C211yesmaximal, characteristic, complemented
12C2×#17985392C2211yescharacteristic
13C2×#17985376C2211yescharacteristic
14#22583609—21no—
15#22583609C2212yescomplemented
16#22583606C2212yes—
17#22583601—21no—
18#22583601C2212yescomplemented
19#22583597C2212yes—
20#22583589—22no—
21#22583581—21no—
22#22583581—21no—
23#22583579—22no—
24#22583569C2211yescharacteristic
25#22583569C2211yescharacteristic
26#22583535C2211yescharacteristic, complemented
27#22583535C2211yescharacteristic, complemented
28#22583533C2212yescomplemented
29#22583532C2211yescharacteristic, complemented
30#22583532C2211yescharacteristic, complemented
31#22583531C2212yes—
32#22583531C2212yes—
33#22583530C2212yescomplemented
34#22583520C2212yescomplemented
35C8×Dic283C2212yescomplemented
36C22×D4×C283C2211yescharacteristic
37C22×C8×C283C2211yescharacteristic
38C2×C4⋊C4×C283C2211yescharacteristic
39#102×C283C2212yes—
40#102×C283C2212yes—
41#17985392—22no—
42#17985392—22no—
43C2×Dic566—22no—
44C2×Dic566C2311yescharacteristic
45C2×D1132C2311yescharacteristic
46C2×C22⋊D283—22no—
47C2×C22⋊D283—22no—
48C2×C22⋊D283—21no—
49C2×C4×D283—21no—
50#17985376—22no—
51C2×C283⋊C8C2312yes—
52C4⋊Dic283—22no—
53C4⋊Dic283D411yescharacteristic
54C4⋊Dic283D411yescharacteristic
55C4⋊Dic283C2311yescharacteristic
56C4⋊Dic283C2311yescharacteristic
57Dic283⋊C4—22no—
58Dic283⋊C4—22no—
59C22⋊Dic283—22no—
60C22⋊Dic283—22no—
61C22⋊Dic283—21no—
62C22⋊Dic283D412yes—
63C4×Dic283—21no—
64C4×Dic283C2312yes—
65C24×C283—21no—
66C2×D4×C283—21no—
67C2×D4×C283—22no—
68C2×D4×C283—22no—
69C2×D4×C283C2312yes—
70C22×C4×C283—21no—
71C22×C4×C283C2311yescharacteristic
72C2×C8×C283—22no—
73C2×C8×C283C2311yescharacteristic
74C2×C8×C283C2311yescharacteristic
75C4⋊C4×C283—21no—
76C4⋊C4×C283C2312yes—
77C22×D283—21no—
78Dic566—21no—
79Dic566—21no—
80Dic566—82no—
81D1132—21no—
82D1132—21no—
83C22⋊D283—42no—
84C22⋊D283—82no—
85C22⋊D283—82no—
86C2×Dic283—21no—
87C2×Dic283—21no—
88C2×Dic283—21no—
89C2×Dic283C2×D412yes—
90C2×Dic283C2×D412yes—
91C4×D283—42no—
92C283⋊C8—22no—
93C23×C283—22no—
94C23×C283—42no—
95C23×C283—81no—
96C23×C283—81no—
97C23×C283C2×D411yescharacteristic
98D4×C283—22no—
99D4×C283—22no—
100D4×C283—42no—
101C2×C4×C283—22no—
102C2×C4×C283—81no—
103C2×C4×C283C2×D411yescharacteristic
104C2×C4×C283#4112yes—
105C2×C4×C283#4112yes—
106C2×C4×C283C2411yescharacteristic
107C8×C283—21no—
108C8×C283—21no—
109C22×C283—21no—
110C22×C283—21no—
111C22×C283—42no—
112C22×C283—42no—
113C22×C283—42no—
114C22×C283—84no—
115C22×C283#12412yes—
116C22×C283C22×D411yescharacteristic
117C2×D283—41no—
118C2×D283—41no—
119C2×D283—41no—
120C4×C283—42no—
121C4×C283#12412yes—
122C4×C283C2×#4111yescharacteristic
123C4×C283C2×#4111yescharacteristic
124Dic283—22no—
125Dic283—22no—
126Dic283—41no—
127Dic283—41no—
128Dic283—41no—
129C2×C283—22no—
130C2×C283—82no—
131C2×C283C2×#12411yescharacteristic
132C2×C283#57611yescharacteristic
133C2×C283#57711yescharacteristic
134D283—81no—
135C283#313611yescharacteristic, complemented, Sylow
136#3136—2831nomaximal, Sylow
137#544—2831no—
138#535—2831no—
139#490—2832no—
140#489—2832no—
141#488—2832no—
142#486—2832no—
143#418—2831no—
144#417—2831no—
145#416—2831no—
146C2×#102D28311yescharacteristic, complemented
147#405—2831no—
148C2×#41—2831no—
149C22×D4C2×D28311yescharacteristic
150C2×M16—2831no—
151C22×C8C2×D28311yescharacteristic
152C4⋊Q8—2832no—
153C4⋊Q8—5661no—
154#127—2832no—
155#125—2832no—
156#125—5661no—
157#124—2832no—
158C22⋊Q8—5662no—
159#121—5661no—
160#121—5661no—
161#120—5662no—
162#117—2831no—
163#117—2831no—
164C2×C4⋊C4C2×D28311yescharacteristic
165#103—2831no—
166#103—2831no—
167#103—2832no—
168#102—2832no—
169#102—2832no—
170#102—2831no—
171#102—2831no—
172#102—2832no—
173#102C2×D28312yes—
174#102C2×D28312yes—
175#97—2832no—
176C4×C8—2832no—
177C24—21no—
178#41—5662no—
179#41—5662no—
180C2×Q8—2831no—
181C2×Q8—5662no—
182C2×D4—21no—
183C2×D4—22no—
184C2×D4—22no—
185C2×D4—2831no—
186C2×D4—5662no—
187C2×D4—5662no—
188C2×D4—5661no—
189C2×D4C22×D28312yes—
190C22×C4—21no—
191C22×C4—5661no—
192C22×C4C22×D28311yescharacteristic
193M16—5662no—
194C2×C8—22no—
195C2×C8—2832no—
196C2×C8C22×D28311yescharacteristic
197C2×C8C22×D28311yescharacteristic
198C4⋊C4—21no—
199C4⋊C4—2831no—
200C4⋊C4—2831no—
201C4⋊C4—2831no—
202C4⋊C4—2831no—
203C4⋊C4—5662no—
204C4⋊C4—5662no—
205C4⋊C4—5662no—
206C4⋊C4C22×D28312yes—
207C22⋊C4—2832no—
208C22⋊C4—5662no—
209C22⋊C4—5662no—
210C22⋊C4—5661no—
211C42—2832no—
212C42—5661no—
213C23—22no—
214C23—42no—
215C23—81no—
216C23—81no—
217C23—5661no—
218C23D4×D28311yescharacteristic
219Q8—5661no—
220Q8—5661no—
221Q8—22642no—
222D4—22no—
223D4—22no—
224D4—42no—
225D4—5661no—
226D4—5661no—
227D4—11322no—
228D4—22642no—
229D4—22642no—
230C2×C4—22no—
231C2×C4—81no—
232C2×C4—2832no—
233C2×C4—2832no—
234C2×C4—5661no—
235C2×C4—5661no—
236C2×C4—5661no—
237C2×C4—11322no—
238C2×C4D4×D28311yescharacteristic
239C2×C4#1798539112yes—
240C2×C4#1798539212yes—
241C2×C4C23×D28311yescharacteristic
242C8—21no—
243C8—21no—
244C8—5662no—
245C22—21no—
246C22—21no—
247C22—42no—
248C22—42no—
249C22—42no—
250C22—84no—
251C22—11321no—
252C22—11321no—
253C22—11321no—
254C22#2258359612yes—
255C22C2×D4×D28311yescharacteristic
256C4—42no—
257C4—5662no—
258C4—5662no—
259C4—11321no—
260C4—11321no—
261C4—11321no—
262C4#2258359612yes—
263C4C2×#1798539111yescharacteristic
264C4C2×#1798539211yescharacteristic
265C2—22no—
266C2—82no—
267C2—22641no—
268C2C2×#2258359611yescharacteristic
269C2#3182726611yescharacteristic
270C2#3182727111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#102×C283C2
socleC22×C283C22×D4
prime radical#31827032C2
hypercenterC2×#102D283
hypocenterC283#3136
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #31827096C2semidirect
3. #31826828C2semidirect
4. #31826823C2semidirect
5. #31826818C2semidirect
6. #31826810C2semidirect
7. #31826470C2semidirect
8. #31826464C2semidirect
9. #31826462C2semidirect
10. #31826420C2semidirect
11. C2×#102×C283C2semidirect
15. #22583609C22semidirect
18. #22583601C22semidirect
26. #22583535C22semidirect
27. #22583535C22semidirect
28. #22583533C22semidirect
29. #22583532C22semidirect
30. #22583532C22semidirect
33. #22583530C22semidirect
34. #22583520C22semidirect
35. C8×Dic283C22semidirect
135. C283#3136semidirect
146. C2×#102D283semidirect

Maximal subgroups

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

subgroupindex
#318270962
#318270322
#318268282
#318268232
#318268182
#318268102
#318264702
#318264642
#318264622
#318264202
C2×#102×C2832
#3136283