Finite Group Databasebeta

← #49130915

Subgroups — #49130915

Order 36224.

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

normal subgroups only

This group has 460 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
1C22×#17985382C211yesmaximal, characteristic, complemented
2C2×#22583618C211yesmaximal, characteristic
3#31827041C211yesmaximal, characteristic
4#31827039C211yesmaximal, characteristic
5#31826722C214yesmaximal, complemented
6#31826705C214yesmaximal, complemented
7#31826501C211yesmaximal, characteristic, complemented
8#31826475C211yesmaximal, characteristic, complemented
9#419×C283C211yesmaximal, characteristic, complemented
10C2×#17985392C2211yescharacteristic
11C22×Dic566C2211yescharacteristic
12C2×#17985382—24no—
13C2×#17985382C2212yes—
14C2×#17985382C2212yes—
15#22583618—24no—
16C2×#17985375C2212yes—
17C22×C283⋊C8C2211yescharacteristic
18C2×C8×D283C2212yes—
19#22583610—21no—
20#22583608—21no—
21#22583599—21no—
22#22583598—21no—
23#22583594—22no—
24#22583593—22no—
25#22583590C2214yes—
26#22583586C2214yes—
27#22583569C2211yescharacteristic
28#22583543C2212yes—
29#22583541C2212yes—
30#22583535C2214yes—
31C22×Q8×C283C2211yescharacteristic
32C2×M16×C283C2211yescharacteristic
33#117×C283C2211yescharacteristic
34#103×C283C2214yes—
35#17985392—22no—
36#17985392—22no—
37C2×Dic566—21no—
38C2×Dic566—22no—
39C2×Dic566—22no—
40C2×Dic566D411yescharacteristic
41C2×Dic566C2312yes—
42C2×D1132D411yescharacteristic
43C2×C22⋊D283D412yes—
44C22×Dic283—21no—
45C2×C4×D283C2312yes—
46#17985382—24no—
47#17985382—24no—
48#17985375—24no—
49C2×C283⋊C8D414yes—
50C2×C283⋊C8C2311yescharacteristic
51C2×C283⋊C8C2311yescharacteristic
52C8×D283—24no—
53C4⋊Dic283—24no—
54C4⋊Dic283C2312yes—
55Dic283⋊C4—24no—
56C22⋊Dic283—21no—
57(C2×D283)⋊C4—24no—
58(C2×D283)⋊C4—24no—
59C4×Dic283—21no—
60C2×Q8×C283—21no—
61C2×Q8×C283—22no—
62C2×Q8×C283—22no—
63C2×Q8×C283C2312yes—
64C22×C4×C283—21no—
65C22×C4×C283C2311yescharacteristic
66M16×C283—22no—
67C2×C8×C283C2312yes—
68C4⋊C4×C283C2312yes—
69C22⋊C4×C283—21no—
70C42×C283—21no—
71C22×D283C2×D412yes—
72Dic566—22no—
73Dic566—22no—
74Dic566—22no—
75Dic566—42no—
76D1132—22no—
77C22⋊D283—24no—
78C2×Dic283—22no—
79C2×Dic283—22no—
80C2×Dic283—42no—
81C2×Dic283C2×D412yes—
82C4×D283—22no—
83C4×D283—22no—
84C283⋊C8C2×D412yes—
85C283⋊C8C2×D412yes—
86C23×C283C2×D411yescharacteristic
87Q8×C283—22no—
88Q8×C283—22no—
89Q8×C283—42no—
90C2×C4×C283—22no—
91C2×C4×C283—22no—
92C2×C4×C283—42no—
93C2×C4×C283C2×D411yescharacteristic
94C2×C4×C283C2×D412yes—
95C2×C4×C283#4112yes—
96C2×C4×C283C2411yescharacteristic
97C8×C283—22no—
98C22×C283—22no—
99C22×C283#12112yes—
100C22×C283C22×D411yescharacteristic
101C2×D283—22no—
102C2×D283—24no—
103C4×C283—42no—
104C4×C283—42no—
105C4×C283#12112yes—
106C4×C283C22×D411yescharacteristic
107C4×C283C2×#4111yescharacteristic
108Dic283—22no—
109Dic283—42no—
110Dic283—42no—
111C2×C283—22no—
112C2×C283C2×#12111yescharacteristic
113C2×C283#57812yes—
114D283—42no—
115C283#305911yescharacteristic, complemented, Sylow
116#3059—2831nomaximal, Sylow
117C22×Q16—2831no—
118C2×#131—2831no—
119#536—2831no—
120#536—2831no—
121#470—2834no—
122#467—2834no—
123#427—2831no—
124#419—2831no—
125#419D28311yescharacteristic, complemented
126C2×#41—2831no—
127C22×Q8—2831no—
128C22×Q8C2×D28311yescharacteristic
129C2×Q16—2832no—
130C2×Q16—2832no—
131C2×Q16—5664no—
132#131—5664no—
133C2×M16—2832no—
134C2×M16C2×D28311yescharacteristic
135C22×C8—2831no—
136C22×C8—2832no—
137C4⋊Q8—5661no—
138C4⋊Q8—5661no—
139#124—5661no—
140#124—5661no—
141#123—5662no—
142#123—5662no—
143C22⋊Q8—2834no—
144C22⋊Q8—2834no—
145#117—2831no—
146#117C2×D28311yescharacteristic
147#107—2832no—
148#106—2832no—
149#103—2834no—
150#103C2×D28314yes—
151#41—5662no—
152#41—5662no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—2831no—
157C2×Q8—2832no—
158C2×Q8—5661no—
159C2×Q8—5662no—
160C2×Q8—5662no—
161C2×Q8C22×D28312yes—
162C2×D4—2832no—
163C2×D4—2831no—
164C22×C4—21no—
165C22×C4—2832no—
166C22×C4—5661no—
167C22×C4C22×D28311yescharacteristic
168Q16—5664no—
169Q16—5664no—
170M16—22no—
171M16—5664no—
172C2×C8—2834no—
173C2×C8—2831no—
174C2×C8—2831no—
175C2×C8—5664no—
176C2×C8C22×D28312yes—
177C4⋊C4—2832no—
178C4⋊C4—5664no—
179C4⋊C4—5664no—
180C4⋊C4C22×D28312yes—
181C22⋊C4—21no—
182C22⋊C4—5664no—
183C22⋊C4—5664no—
184C22⋊C4—5661no—
185C42—21no—
186C42—5661no—
187C23—2832no—
188C23D4×D28311yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—42no—
192Q8—5662no—
193Q8—5662no—
194Q8—5662no—
195Q8—11322no—
196D4—5664no—
197D4—5662no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—42no—
201C2×C4—2832no—
202C2×C4—5662no—
203C2×C4—5662no—
204C2×C4—5662no—
205C2×C4—5662no—
206C2×C4—11322no—
207C2×C4D4×D28311yescharacteristic
208C2×C4D4×D28312yes—
209C2×C4#1798539212yes—
210C2×C4C23×D28311yescharacteristic
211C8—22no—
212C8—2832no—
213C8—2832no—
214C22—22no—
215C22—5662no—
216C22—5664no—
217C22#2258358312yes—
218C22C2×D4×D28311yescharacteristic
219C4—42no—
220C4—42no—
221C4—5662no—
222C4—11322no—
223C4—11322no—
224C4#2258358312yes—
225C4C2×D4×D28311yescharacteristic
226C4C2×#1798539211yescharacteristic
227C2—22no—
228C2—11322no—
229C2C2×#2258358311yescharacteristic
230C2#3182728112yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#419×C283C2
socleC22×C283C22×D4
prime radicalC2×#17985392C22
hypercenter#419D283
hypocenterC283#3059
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. C22×#17985382C2semidirect
5. #31826722C2semidirect
6. #31826705C2semidirect
7. #31826501C2semidirect
8. #31826475C2semidirect
9. #419×C283C2semidirect
115. C283#3059semidirect
125. #419D283semidirect

Maximal subgroups

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

subgroupindex
C22×#179853822
C2×#225836182
#318270412
#318270392
#318267222
#318267052
#318265012
#318264752
#419×C2832
#3059283