Finite Group Databasebeta

← #28400228

Subgroups — #28400228

Order 14464.

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×#14268637C211yesmaximal, characteristic, complemented
2C2×#16813630C211yesmaximal, characteristic
3#20299174C211yesmaximal, characteristic
4#20299172C211yesmaximal, characteristic
5#20298855C214yesmaximal, complemented
6#20298838C214yesmaximal, complemented
7#20298634C211yesmaximal, characteristic, complemented
8#20298608C211yesmaximal, characteristic, complemented
9#419×C113C211yesmaximal, characteristic, complemented
10C2×#14268647C2211yescharacteristic
11C22×Dic226C2211yescharacteristic
12C2×#14268637—24no—
13C2×#14268637C2212yes—
14C2×#14268637C2212yes—
15#16813630—24no—
16C2×#14268630C2212yes—
17C22×#11744751C2211yescharacteristic
18C2×C8×D113C2212yes—
19#16813622—21no—
20#16813620—21no—
21#16813611—21no—
22#16813610—21no—
23#16813606—22no—
24#16813605—22no—
25#16813602C2214yes—
26#16813598C2214yes—
27#16813581C2211yescharacteristic
28#16813555C2212yes—
29#16813553C2212yes—
30#16813547C2214yes—
31C22×Q8×C113C2211yescharacteristic
32C2×M16×C113C2211yescharacteristic
33#117×C113C2211yescharacteristic
34#103×C113C2214yes—
35#14268647—22no—
36#14268647—22no—
37C2×Dic226—22no—
38C2×Dic226—22no—
39C2×Dic226—21no—
40C2×Dic226D411yescharacteristic
41C2×Dic226C2312yes—
42C2×D452D411yescharacteristic
43C2×C22⋊D113D412yes—
44C22×Dic113—21no—
45C2×C4×D113C2312yes—
46#14268637—24no—
47#14268637—24no—
48#14268630—24no—
49C2×#11744751D414yes—
50C2×#11744751C2311yescharacteristic
51C2×#11744751C2311yescharacteristic
52C8×D113—24no—
53C4⋊Dic113—24no—
54C4⋊Dic113C2312yes—
55#14268626—24no—
56C22⋊Dic113—21no—
57#14268624—24no—
58#14268624—24no—
59C4×Dic113—21no—
60C2×Q8×C113—21no—
61C2×Q8×C113—22no—
62C2×Q8×C113—22no—
63C2×Q8×C113C2312yes—
64C22×C4×C113—21no—
65C22×C4×C113C2311yescharacteristic
66M16×C113—22no—
67C2×C8×C113C2312yes—
68C4⋊C4×C113C2312yes—
69C22⋊C4×C113—21no—
70C42×C113—21no—
71C23×C113C2×D411yescharacteristic
72C22×D113C2×D412yes—
73Q8×C113—22no—
74Q8×C113—22no—
75Q8×C113—42no—
76C2×C4×C113—22no—
77C2×C4×C113—22no—
78C2×C4×C113—42no—
79C2×C4×C113C2×D411yescharacteristic
80C2×C4×C113C2×D412yes—
81C2×C4×C113#4112yes—
82C2×C4×C113C2411yescharacteristic
83C22⋊D113—24no—
84C2×Dic113—22no—
85C2×Dic113—22no—
86C2×Dic113—42no—
87C2×Dic113C2×D412yes—
88D452—22no—
89C4×D113—22no—
90C4×D113—22no—
91Dic226—22no—
92Dic226—22no—
93Dic226—22no—
94Dic226—42no—
95C8×C113—22no—
96#11744751C2×D412yes—
97#11744751C2×D412yes—
98C22×C113—22no—
99C22×C113#12112yes—
100C22×C113C22×D411yescharacteristic
101C2×D113—22no—
102C2×D113—24no—
103C4×C113—42no—
104C4×C113—42no—
105C4×C113#12112yes—
106C4×C113C22×D411yescharacteristic
107C4×C113C2×#4111yescharacteristic
108Dic113—22no—
109Dic113—42no—
110Dic113—42no—
111C2×C113—22no—
112C2×C113C2×#12111yescharacteristic
113C2×C113#57812yes—
114D113—42no—
115#3059—1131nomaximal, Sylow
116C113#305911yescharacteristic, complemented, Sylow
117C22×Q16—1131no—
118C2×#131—1131no—
119#536—1131no—
120#536—1131no—
121#470—1134no—
122#467—1134no—
123#427—1131no—
124#419—1131no—
125#419D11311yescharacteristic, complemented
126C2×#41—1131no—
127C22×Q8—1131no—
128C22×Q8C2×D11311yescharacteristic
129C2×Q16—1132no—
130C2×Q16—1132no—
131C2×Q16—2264no—
132#131—2264no—
133C2×M16—1132no—
134C2×M16C2×D11311yescharacteristic
135C22×C8—1131no—
136C22×C8—1132no—
137C4⋊Q8—2261no—
138C4⋊Q8—2261no—
139#124—2261no—
140#124—2261no—
141#123—2262no—
142#123—2262no—
143C22⋊Q8—1134no—
144C22⋊Q8—1134no—
145#117—1131no—
146#117C2×D11311yescharacteristic
147#107—1132no—
148#106—1132no—
149#103—1134no—
150#103C2×D11314yes—
151#41—2262no—
152#41—2262no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—1131no—
157C2×Q8—1132no—
158C2×Q8—2262no—
159C2×Q8—2262no—
160C2×Q8—2261no—
161C2×Q8C22×D11312yes—
162C2×D4—1132no—
163C2×D4—1131no—
164C22×C4—21no—
165C22×C4—1132no—
166C22×C4—2261no—
167C22×C4C22×D11311yescharacteristic
168Q16—2264no—
169Q16—2264no—
170M16—22no—
171M16—2264no—
172C2×C8—1134no—
173C2×C8—1131no—
174C2×C8—1131no—
175C2×C8—2264no—
176C2×C8C22×D11312yes—
177C4⋊C4—1132no—
178C4⋊C4—2264no—
179C4⋊C4—2264no—
180C4⋊C4C22×D11312yes—
181C22⋊C4—21no—
182C22⋊C4—2264no—
183C22⋊C4—2264no—
184C22⋊C4—2261no—
185C42—21no—
186C42—2261no—
187C23—1132no—
188C23D4×D11311yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—42no—
192Q8—4522no—
193Q8—2262no—
194Q8—2262no—
195Q8—2262no—
196D4—2264no—
197D4—2262no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—42no—
201C2×C4—1132no—
202C2×C4—4522no—
203C2×C4—2262no—
204C2×C4—2262no—
205C2×C4—2262no—
206C2×C4—2262no—
207C2×C4D4×D11311yescharacteristic
208C2×C4D4×D11312yes—
209C2×C4#1426864712yes—
210C2×C4C23×D11311yescharacteristic
211C8—22no—
212C8—1132no—
213C8—1132no—
214C22—22no—
215C22—2262no—
216C22—2264no—
217C22#1681359512yes—
218C22C2×D4×D11311yescharacteristic
219C4—42no—
220C4—42no—
221C4—4522no—
222C4—4522no—
223C4—2262no—
224C4#1681359512yes—
225C4C2×D4×D11311yescharacteristic
226C4C2×#1426864711yescharacteristic
227C2—22no—
228C2—4522no—
229C2C2×#1681359511yescharacteristic
230C2#2029941412yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#419×C113C2
socleC22×C113C22×D4
prime radicalC2×#14268647C22
hypercenter#419D113
hypocenterC113#3059
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. C22×#14268637C2semidirect
5. #20298855C2semidirect
6. #20298838C2semidirect
7. #20298634C2semidirect
8. #20298608C2semidirect
9. #419×C113C2semidirect
116. C113#3059semidirect
125. #419D113semidirect

Maximal subgroups

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

subgroupindex
C22×#142686372
C2×#168136302
#202991742
#202991722
#202988552
#202988382
#202986342
#202986082
#419×C1132
#3059113