Finite Group Databasebeta

← #28389630

Subgroups — #28389630

Order 14464.

336 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×D452C211yesmaximal, characteristic, complemented
2#20298975C211yesmaximal, characteristic, complemented
3#20298794C211yesmaximal, characteristic, complemented
4#20298793C211yesmaximal, characteristic, complemented
5#20298341C211yesmaximal, characteristic, complemented
6#20298327C211yesmaximal, characteristic, complemented
7D4⋊C8×C113C211yesmaximal, characteristic, complemented
8C22×D452—21no—
9C2×D4×D113—21no—
10C2×D904—21no—
11C2×D904—22no—
12C2×#14268632—21no—
13#16813619C2211yescharacteristic
14#16813619C2211yescharacteristic, complemented
15#16813597—21no—
16#16813596—21no—
17#16813592—22no—
18C4×D452C2211yescharacteristic
19C4⋊#11744751C2211yescharacteristic, complemented
20#16813544—21no—
21#16813542—21no—
22C4×D4×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic, complemented
24C4×C8×C113C2211yescharacteristic, complemented
25C23×D113—22no—
26C2×D452—22no—
27C2×D452—21no—
28C2×D452—21no—
29C2×D452—21no—
30C2×D452—21no—
31C2×D452—21no—
32C2×D452—42no—
33C2×D452—42no—
34C2×D452D411yescharacteristic
35C2×D452D412yes—
36C2×C22⋊D113—22no—
37D4×D113—42no—
38D4×D113—42no—
39C2×C4×D113—21no—
40D904—44no—
41D904—42no—
42#14268632—42no—
43C2×#11744751—21no—
44C4⋊Dic113D411yescharacteristic
45#14268624—22no—
46#14268624—21no—
47C2×D4×C113D411yescharacteristic
48C22×C4×C113—21no—
49C2×C8×C113—21no—
50C2×C8×C113—21no—
51C4⋊C4×C113D411yescharacteristic
52C22⋊C4×C113—21no—
53C42×C113C2311yescharacteristic
54C23×C113—21no—
55C22×D113—21no—
56C22×D113—22no—
57C22×D113—44no—
58C22×D113—44no—
59C22×D113—41no—
60C22×D113—82no—
61D4×C113—21no—
62D4×C113D812yescomplemented
63C2×C4×C113—21no—
64C2×C4×C113—41no—
65C2×C4×C113—41no—
66C2×C4×C113C2×D411yescharacteristic
67C2×C4×C113C2×D411yescharacteristic
68C2×C4×C113C2×D411yescharacteristic
69C22⋊D113—44no—
70C2×Dic113—21no—
71D452—21no—
72D452—42no—
73D452—42no—
74D452—44no—
75D452—41no—
76D452—41no—
77D452—41no—
78D452—41no—
79D452—41no—
80D452—41no—
81D452—41no—
82D452—41no—
83D452D812yescomplemented
84C4×D113—41no—
85C4×D113—41no—
86C8×C113—22no—
87C8×C113—41no—
88#11744751—41no—
89C22×C113—22no—
90C22×C113—41no—
91C22×C113—41no—
92C22×C113#12011yescharacteristic
93C2×D113—22no—
94C2×D113—41no—
95C2×D113—41no—
96C2×D113—42no—
97C2×D113—42no—
98C2×D113—42no—
99C2×D113—88no—
100C2×D113—81no—
101C2×D113—81no—
102C2×D113—81no—
103C4×C113—21no—
104C4×C113—41no—
105C4×C113C2×D811yescharacteristic
106C4×C113C2×D811yescharacteristic
107C4×C113AGL(1,ℤ/8)11yescharacteristic
108C4×C113AGL(1,ℤ/8)11yescharacteristic
109Dic113—41no—
110C2×C113—42no—
111C2×C113#44711yescharacteristic
112C2×C113#44711yescharacteristic
113C2×C113#45311yescharacteristic
114D113—42no—
115D113—82no—
116D113—161no—
117#1619—1131nomaximal, Sylow
118C113#161911yescharacteristic, complemented, Sylow
119D42—1131no—
120#493—1131no—
121#459—1131no—
122#459—1131no—
123#331—1131no—
124D4⋊C8—1131no—
125D4⋊C8D11311yescharacteristic, complemented
126C22×D4—2261no—
127C22×D4—2261no—
128C2×D8—2261no—
129C2×D8—2262no—
130C2×D8—2261no—
131#127—1131no—
132#127—1131no—
133#121—2261no—
134#121—2261no—
135#120—2262no—
136C4×D4—1131no—
137C4×D4C2×D11311yescharacteristic
138C4⋊C8—1131no—
139C4⋊C8C2×D11311yescharacteristic, complemented
140#102—2261no—
141#102—2261no—
142C4×C8C2×D11311yescharacteristic, complemented
143C24—2262no—
144C2×D4—1131no—
145C2×D4—1132no—
146C2×D4—4522no—
147C2×D4—4522no—
148C2×D4—4522no—
149C2×D4—4522no—
150C2×D4—2262no—
151C2×D4—2262no—
152C2×D4—2261no—
153C2×D4—2261no—
154C2×D4—2261no—
155C2×D4—2261no—
156C2×D4—2261no—
157C2×D4D45211yescharacteristic
158C22×C4—21no—
159C22×C4—2261no—
160D8—4524no—
161D8—4522no—
162D8—4522no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—2261no—
166C4⋊C4—1131no—
167C4⋊C4D45211yescharacteristic
168C22⋊C4—21no—
169C22⋊C4—2262no—
170C22⋊C4—2261no—
171C42C22×D11311yescharacteristic
172C23—21no—
173C23—9042no—
174C23—4524no—
175C23—4524no—
176C23—4521no—
177C23—2262no—
178C23—2261no—
179D4—21no—
180D4—1132no—
181D4—4522no—
182D4—4522no—
183D4—4524no—
184D4—4524no—
185D4—4521no—
186D4—4521no—
187D4—4521no—
188D4—4521no—
189D4—4521no—
190D4—4521no—
191D4—4521no—
192D4—4521no—
193D4—2261no—
194D4D90412yescomplemented
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—4521no—
199C2×C4—4521no—
200C2×C4—2261no—
201C2×C4D4×D11311yescharacteristic
202C2×C4D4×D11311yescharacteristic
203C2×C4C2×D45211yescharacteristic
204C8—22no—
205C8—41no—
206C8—4521no—
207C22—22no—
208C22—41no—
209C22—41no—
210C22—9048no—
211C22—9041no—
212C22—9041no—
213C22—9041no—
214C22—4522no—
215C22—4522no—
216C22—4522no—
217C22—4521no—
218C22—4521no—
219C22—2262no—
220C22#1681359211yescharacteristic
221C4—21no—
222C4—41no—
223C4—4521no—
224C4D8×D11311yescharacteristic
225C4C2×D90411yescharacteristic
226C4#1681364911yescharacteristic
227C4#1681365011yescharacteristic
228C2—42no—
229C2—18081no—
230C2—9042no—
231C2—4522no—
232C2#2029873311yescharacteristic
233C2#2029873411yescharacteristic
234C2#2029876711yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
FittingD4⋊C8×C113C2
socleC22×C113#120
hypercenterD4⋊C8D113
hypocenterC113#1619
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. D4×D452C2semidirect
2. #20298975C2semidirect
3. #20298794C2semidirect
4. #20298793C2semidirect
5. #20298341C2semidirect
6. #20298327C2semidirect
7. D4⋊C8×C113C2semidirect
14. #16813619C22semidirect
19. C4⋊#11744751C22semidirect
23. C4⋊C8×C113C22semidirect
24. C4×C8×C113C22semidirect
62. D4×C113D8semidirect
83. D452D8semidirect
118. C113#1619semidirect
125. D4⋊C8D113semidirect
139. C4⋊C8C2×D113semidirect
142. C4×C8C2×D113semidirect
194. D4D904semidirect

Maximal subgroups

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

subgroupindex
D4×D4522
#202989752
#202987942
#202987932
#202983412
#202983272
D4⋊C8×C1132
#1619113