Finite Group Databasebeta

← #49130913

Subgroups — #49130913

Order 36224.

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

normal subgroups only

This group has 460 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
1C22×#17985382C211yesmaximal, characteristic, complemented
2C2×#22583617C211yesmaximal, characteristic
3#31827036C211yesmaximal, characteristic
4#31826721C214yesmaximal, complemented
5#31826704C214yesmaximal, complemented
6#31826501C211yesmaximal, characteristic, complemented
7#31826474C211yesmaximal, characteristic, complemented
8#31826473C211yesmaximal, characteristic, complemented
9#536×C283C211yesmaximal, characteristic
10C22×Dic566C2211yescharacteristic
11C2×#17985382—24no—
12C2×#17985382C2212yes—
13C2×#17985382C2212yes—
14#22583617—24no—
15C2×#17985376C2212yes—
16C2×#17985376C2211yescharacteristic
17C22×C283⋊C8C2212yes—
18C22×C283⋊C8C2211yescharacteristic
19#22583608—21no—
20#22583597—21no—
21#22583591—22no—
22#22583589C2214yes—
23#22583569C2211yescharacteristic
24#22583543C2212yes—
25#22583541C2212yes—
26#22583534C2214yes—
27#22583533C2214yes—
28C2×#41×C283C2211yescharacteristic
29C22×Q8×C283C2211yescharacteristic
30C4⋊Q8×C283—21no—
31#124×C283—21no—
32#123×C283—22no—
33C22⋊Q8×C283C2214yes—
34#117×C283C2211yescharacteristic
35C2×Dic566—21no—
36C2×Dic566—22no—
37C2×Dic566—22no—
38C2×Dic566C2312yes—
39C22×Dic283—21no—
40#17985382—24no—
41#17985382—24no—
42#17985376—24no—
43#17985376—22no—
44C2×C283⋊C8—24no—
45C2×C283⋊C8D414yes—
46C2×C283⋊C8C2312yes—
47C2×C283⋊C8C2311yescharacteristic
48C2×C283⋊C8C2311yescharacteristic
49C4⋊Dic283C2312yes—
50Dic283⋊C4—24no—
51C22⋊Dic283—21no—
52C22⋊Dic283—24no—
53C4×Dic283—21no—
54#41×C283—22no—
55#41×C283—22no—
56C2×Q8×C283—21no—
57C2×Q8×C283—22no—
58C2×Q8×C283—22no—
59C2×Q8×C283D411yescharacteristic
60C2×Q8×C283C2312yes—
61C2×D4×C283D412yes—
62C2×D4×C283D411yescharacteristic
63C22×C4×C283—21no—
64C22×C4×C283C2312yes—
65C22×C4×C283C2311yescharacteristic
66C4⋊C4×C283—24no—
67C4⋊C4×C283C2312yes—
68C22⋊C4×C283—21no—
69C22⋊C4×C283—24no—
70C42×C283—21no—
71Dic566—22no—
72Dic566—22no—
73Dic566—42no—
74C2×Dic283—22no—
75C2×Dic283—22no—
76C2×Dic283—42no—
77C283⋊C8—22no—
78C283⋊C8C2×D412yes—
79C283⋊C8C2×D412yes—
80C23×C283C2×D412yes—
81C23×C283C2×D411yescharacteristic
82Q8×C283—22no—
83Q8×C283—22no—
84Q8×C283—22no—
85Q8×C283—42no—
86D4×C283—24no—
87D4×C283—22no—
88C2×C4×C283—22no—
89C2×C4×C283—22no—
90C2×C4×C283—22no—
91C2×C4×C283—22no—
92C2×C4×C283—42no—
93C2×C4×C283C2×D412yes—
94C2×C4×C283C2×D412yes—
95C2×C4×C283C2×D411yescharacteristic
96C2×C4×C283#4112yes—
97C2×C4×C283C2411yescharacteristic
98C22×C283—22no—
99C22×C283—22no—
100C22×C283—24no—
101C22×C283#12112yes—
102C22×C283C22×D411yescharacteristic
103C4×C283—22no—
104C4×C283—42no—
105C4×C283—42no—
106C4×C283#12112yes—
107C4×C283C22×D411yescharacteristic
108C4×C283C2×#4111yescharacteristic
109Dic283—42no—
110Dic283—42no—
111C2×C283—22no—
112C2×C283—42no—
113C2×C283C2×#12111yescharacteristic
114C2×C283#57812yes—
115C283#305911yescharacteristic, complemented, Sylow
116#3059—2831nomaximal, Sylow
117C22×Q16—2831no—
118C2×#131—2831no—
119#536—2831no—
120#536D28311yescharacteristic
121#470—2834no—
122#467—2834no—
123#427—2831no—
124#419—2831no—
125#419—2831no—
126C2×#41C2×D28311yescharacteristic
127C22×Q8—2831no—
128C22×Q8C2×D28311yescharacteristic
129C2×Q16—2832no—
130C2×Q16—2832no—
131C2×Q16—5664no—
132#131—5664no—
133C2×M16—2831no—
134C2×M16—2832no—
135C22×C8—2831no—
136C22×C8—2832no—
137C4⋊Q8—21no—
138C4⋊Q8—5661no—
139#124—21no—
140#124—5661no—
141#123—22no—
142#123—5662no—
143C22⋊Q8—2834no—
144C22⋊Q8C2×D28314yes—
145#117—2831no—
146#117C2×D28311yescharacteristic
147#107—2832no—
148#106—2832no—
149#103—2834no—
150#103—2834no—
151#41—22no—
152#41—22no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—2832no—
157C2×Q8—5661no—
158C2×Q8—5662no—
159C2×Q8—5662no—
160C2×Q8C22⋊D28311yescharacteristic
161C2×Q8C22×D28312yes—
162C2×D4C22⋊D28312yes—
163C2×D4C22⋊D28311yescharacteristic
164C22×C4—21no—
165C22×C4—5661no—
166C22×C4C22×D28312yes—
167C22×C4C22×D28311yescharacteristic
168Q16—5664no—
169Q16—5664no—
170M16—5664no—
171M16—5662no—
172C2×C8—2834no—
173C2×C8—2831no—
174C2×C8—2831no—
175C2×C8—2832no—
176C2×C8—5664no—
177C4⋊C4—24no—
178C4⋊C4—2832no—
179C4⋊C4—5664no—
180C4⋊C4C22×D28312yes—
181C22⋊C4—21no—
182C22⋊C4—24no—
183C22⋊C4—5661no—
184C22⋊C4—5664no—
185C42—21no—
186C42—5661no—
187C23C2×C22⋊D28312yes—
188C23C2×C22⋊D28311yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—22no—
192Q8—42no—
193Q8—5662no—
194Q8—5662no—
195Q8—11322no—
196D4—24no—
197D4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—5662no—
204C2×C4—5662no—
205C2×C4—11322no—
206C2×C4D4×D28312yes—
207C2×C4C2×C22⋊D28312yes—
208C2×C4C2×C22⋊D28311yescharacteristic
209C2×C4#1798539112yes—
210C2×C4C23×D28311yescharacteristic
211C8—2832no—
212C8—2832no—
213C8—5662no—
214C22—22no—
215C22—22no—
216C22—24no—
217C22#2258358212yes—
218C22C22×C22⋊D28311yescharacteristic
219C4—22no—
220C4—42no—
221C4—42no—
222C4—11322no—
223C4—11322no—
224C4#2258358212yes—
225C4C2×D4×D28311yescharacteristic
226C4C2×#1798539111yescharacteristic
227C2—22no—
228C2—42no—
229C2C2×#2258358211yescharacteristic
230C2#3182728012yes—
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#536×C283C2
socleC22×C283C22×D4
prime radicalC2×#41×C283C22
hypercenter#536D283
hypocenterC283#3059
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C22×#17985382C2semidirect
4. #31826721C2semidirect
5. #31826704C2semidirect
6. #31826501C2semidirect
7. #31826474C2semidirect
8. #31826473C2semidirect
115. C283#3059semidirect

Maximal subgroups

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

subgroupindex
C22×#179853822
C2×#225836172
#318270362
#318267212
#318267042
#318265012
#318264742
#318264732
#536×C2832
#3059283