Finite Group Databasebeta

← #49133925

Subgroups — #49133925

Order 36224.

362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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#31827201C211yesmaximal, characteristic, complemented
2#31827172C211yesmaximal, characteristic, complemented
3#31826818C212yesmaximal, complemented
4#31826811C211yesmaximal, characteristic, complemented
5#31826763C212yesmaximal, complemented
6#31826761C211yesmaximal, characteristic, complemented
7#31826678C212yesmaximal, complemented
8#31826589C211yesmaximal, characteristic, complemented
9C4×#17985380C211yesmaximal, characteristic, complemented
10D8×Dic283C212yesmaximal, complemented
11#459×C283C211yesmaximal, characteristic
12C2×#17985380C2211yescharacteristic
13#22583610C2211yescharacteristic
14#22583601C2212yes—
15#22583597—21no—
16#22583597C2212yes—
17#22583591—22no—
18#22583589—21no—
19#22583587—22no—
20C4×Dic566C2211yescharacteristic
21C4×Dic566C2211yescharacteristic
22D4×Dic283—21no—
23D4×Dic283C2212yes—
24D4×Dic283C2212yes—
25C2×C4⋊Dic283—21no—
26#22583544C2212yes—
27#22583541C2211yescharacteristic
28Dic283⋊C8C2212yes—
29#22583535C2212yes—
30#22583533C2211yescharacteristic
31#22583531C2212yes—
32#22583531C2211yescharacteristic
33#22583531C2212yes—
34C4×C283⋊C8C2211yescharacteristic
35C8×Dic283C2212yes—
36C2×D8×C283C2212yes—
37#127×C283C2211yescharacteristic
38C4×D4×C283C2211yescharacteristic
39C4⋊C8×C283C2211yescharacteristic
40#102×C283C2212yes—
41C2×Dic566—21no—
42C2×Dic566D411yescharacteristic
43C2×Dic566C2311yescharacteristic
44C22×Dic283—22no—
45C22×Dic283—22no—
46#17985380—22no—
47C2×C283⋊C8C2311yescharacteristic
48C2×C283⋊C8C2311yescharacteristic
49C4⋊Dic283—22no—
50C4⋊Dic283—21no—
51C4⋊Dic283D411yescharacteristic
52C4⋊Dic283C2311yescharacteristic
53C4⋊Dic283C2312yes—
54Dic283⋊C4—22no—
55Dic283⋊C4—21no—
56Dic283⋊C4D412yes—
57C22⋊Dic283—22no—
58C22⋊Dic283—22no—
59C22⋊Dic283—22no—
60C22⋊Dic283—22no—
61C4×Dic283—21no—
62C4×Dic283C2312yes—
63C2×D4×C283—21no—
64C2×D4×C283—21no—
65C2×D4×C283C2312yes—
66C2×D4×C283C2311yescharacteristic
67C22×C4×C283—21no—
68D8×C283—24no—
69C2×C8×C283C2312yes—
70C4⋊C4×C283C2311yescharacteristic
71C22⋊C4×C283—21no—
72C42×C283C2311yescharacteristic
73Dic566—22no—
74Dic566—21no—
75Dic566—21no—
76Dic566—81no—
77C2×Dic283—21no—
78C2×Dic283—21no—
79C2×Dic283—22no—
80C2×Dic283—82no—
81C2×Dic283—82no—
82C2×Dic283C2×D412yes—
83C2×Dic283C2×D412yes—
84C283⋊C8—21no—
85C283⋊C8—21no—
86C23×C283—21no—
87C23×C283—22no—
88D4×C283—22no—
89D4×C283—21no—
90D4×C283—22no—
91D4×C283—42no—
92D4×C283—81no—
93D4×C283#4112yes—
94C2×C4×C283—21no—
95C2×C4×C283—42no—
96C2×C4×C283C2×D411yescharacteristic
97C2×C4×C283C2×D411yescharacteristic
98C2×C4×C283C2411yescharacteristic
99C8×C283—22no—
100C22×C283—22no—
101C22×C283—41no—
102C22×C283—41no—
103C22×C283—42no—
104C22×C283—42no—
105C22×C283—42no—
106C22×C283C22×D411yescharacteristic
107C4×C283—21no—
108C4×C283—41no—
109C4×C283#13512yes—
110C4×C283C2×#4111yescharacteristic
111C4×C2832−1+411yescharacteristic
112Dic283—22no—
113Dic283—22no—
114Dic283—41no—
115Dic283—41no—
116Dic283—42no—
117C2×C283—42no—
118C2×C283—82no—
119C2×C283#54811yescharacteristic
120C2×C283C2×#13511yescharacteristic
121C2×C283#57611yescharacteristic
122C283#336111yescharacteristic, complemented, Sylow
123#3361—2831nomaximal, Sylow
124#559—2831no—
125#554—2831no—
126#488—2832no—
127#486—2831no—
128#478—2832no—
129#477—2831no—
130#463—2832no—
131#459D28311yescharacteristic
132C8×Q8—2831no—
133C4×SD16—2831no—
134C4×D8—2832no—
135C2×SD16—2831no—
136C2×D8C2×D28312yes—
137C4⋊Q8—2831no—
138#127C2×D28311yescharacteristic
139#125—2832no—
140#124—2832no—
141#124—5661no—
142#123—5662no—
143C22⋊Q8—5662no—
144C22⋊Q8—5661no—
145C4×Q8—2831no—
146C4×Q8—2831no—
147C4×D4—2832no—
148C4×D4—2832no—
149C4×D4—5661no—
150C4×D4C2×D28311yescharacteristic
151C2×C4⋊C4—5661no—
152#107—2832no—
153#106—2831no—
154C4⋊C8—2832no—
155C4⋊C8C2×D28311yescharacteristic
156#103—2832no—
157#103—2831no—
158#102—2831no—
159#102—2832no—
160#102—2832no—
161#102C2×D28312yes—
162C4×C8—2832no—
163C4×C8—2831no—
164C2×Q8—2831no—
165C2×Q8—2831no—
166C2×Q8—5661no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4C22×D28312yes—
170C2×D4C22×D28311yescharacteristic
171C22×C4—21no—
172C22×C4—5662no—
173C22×C4—5662no—
174SD16—5662no—
175D8—24no—
176C2×C8—2831no—
177C2×C8—2831no—
178C2×C8C22×D28312yes—
179C4⋊C4—2832no—
180C4⋊C4—2831no—
181C4⋊C4—2832no—
182C4⋊C4—2831no—
183C4⋊C4—5662no—
184C4⋊C4—5662no—
185C4⋊C4—5661no—
186C4⋊C4—5661no—
187C4⋊C4C22×D28311yescharacteristic
188C22⋊C4—21no—
189C22⋊C4—5662no—
190C22⋊C4—5662no—
191C22⋊C4—5662no—
192C22⋊C4—5662no—
193C42—2832no—
194C42—5661no—
195C42C22×D28311yescharacteristic
196C23—21no—
197C23—22no—
198Q8—5662no—
199Q8—5661no—
200Q8—5661no—
201Q8—22641no—
202D4—22no—
203D4—21no—
204D4—22no—
205D4—42no—
206D4—81no—
207D4#1798539112yes—
208C2×C4—21no—
209C2×C4—42no—
210C2×C4—2832no—
211C2×C4—2832no—
212C2×C4—5661no—
213C2×C4—5661no—
214C2×C4—5662no—
215C2×C4—22642no—
216C2×C4—22642no—
217C2×C4D4×D28311yescharacteristic
218C2×C4D4×D28311yescharacteristic
219C2×C4C23×D28311yescharacteristic
220C8—22no—
221C8—5661no—
222C8—5661no—
223C22—22no—
224C22—41no—
225C22—41no—
226C22—42no—
227C22—42no—
228C22—42no—
229C22C2×D4×D28311yescharacteristic
230C4—21no—
231C4—41no—
232C4—5662no—
233C4—5662no—
234C4—11321no—
235C4—11322no—
236C4—11321no—
237C4#2258362912yes—
238C4C2×#1798539111yescharacteristic
239C4#2258365711yescharacteristic
240C2—42no—
241C2—82no—
242C2#3182712111yescharacteristic
243C2C2×#2258362911yescharacteristic
244C2#3182726911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting, prime radical#459×C283C2
socleC22×C283C22×D4
hypercenter#459D283
hypocenterC283#3361
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #31827201C2semidirect
2. #31827172C2semidirect
3. #31826818C2semidirect
4. #31826811C2semidirect
5. #31826763C2semidirect
6. #31826761C2semidirect
7. #31826678C2semidirect
8. #31826589C2semidirect
9. C4×#17985380C2semidirect
10. D8×Dic283C2semidirect
122. C283#3361semidirect

Maximal subgroups

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

subgroupindex
#318272012
#318271722
#318268182
#318268112
#318267632
#318267612
#318266782
#318265892
C4×#179853802
D8×Dic2832
#459×C2832
#3361283