Finite Group Databasebeta

← #28390930

Subgroups — #28390930

Order 14464.

374 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 101 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×#14268636C211yesmaximal, characteristic
2C2×#16813587C211yesmaximal, characteristic, complemented
3C2×#16813545C211yesmaximal, characteristic, complemented
4C2×#16813542C211yesmaximal, characteristic
5#20298499C211yesmaximal, characteristic
6#20298352C211yesmaximal, characteristic, complemented
7#340×C113C211yesmaximal, characteristic, complemented
8C22×Dic226C2211yescharacteristic
9C22×D452C2211yescharacteristic
10C2×#14268636—22no—
11C2×#14268636—22no—
12C2×#14268636C414yescomplemented
13C22×#11744751C2211yescharacteristic
14#16813587—22no—
15#16813587—22no—
16C2×#14268626—21no—
17C2×#14268624—21no—
18C2×#14268624—21no—
19C2×C4×Dic113—21no—
20C2×C4×Dic113C2211yescharacteristic
21#16813545—22no—
22#16813542—22no—
23C22×C8×C113C2211yescharacteristic
24C2×C4⋊C4×C113C2211yescharacteristic
25C2×C4⋊C4×C113C2211yescharacteristic
26C23×D113—21no—
27C2×Dic226—21no—
28C2×Dic226—21no—
29C2×Dic226—21no—
30C2×Dic226C2×C412yes—
31C2×Dic226D412yes—
32C2×Dic226D412yes—
33C2×D452—21no—
34C2×D452—21no—
35C2×D452—21no—
36C2×D452—21no—
37C2×D452—21no—
38C2×D452C2×C412yes—
39C22×Dic113—21no—
40C22×Dic113D411yescharacteristic
41C22×Dic113D411yescharacteristic
42#14268636—28no—
43C2×#11744751—21no—
44C2×#11744751—21no—
45C2×#11744751—21no—
46#14268626—24no—
47#14268624—42no—
48#14268624—42no—
49C4×Dic113—24no—
50C4×Dic113—21no—
51C4×Dic113—21no—
52C22×C4×C113—21no—
53C22×C4×C113—21no—
54C22×C4×C113C2311yescharacteristic
55C2×C8×C113—21no—
56C2×C8×C113—21no—
57C2×C8×C113C2×C412yes—
58C4⋊C4×C113—21no—
59C4⋊C4×C113—21no—
60C4⋊C4×C113—21no—
61C4⋊C4×C113D412yes—
62C23×C113C2×D411yescharacteristic
63C22×D113—22no—
64C22×D113—41no—
65C22×D113—41no—
66C22×D113—41no—
67C22×D113—41no—
68C22×D113—41no—
69C22×D113—41no—
70C2×C4×C113—22no—
71C2×C4×C113—41no—
72C2×C4×C113—41no—
73C2×C4×C113—41no—
74C2×C4×C113—41no—
75C2×C4×C113—41no—
76C2×C4×C113C22×C411yescharacteristic
77C2×C4×C113C2×D411yescharacteristic
78C2×C4×C113C2×D411yescharacteristic
79C2×C4×C113C2×D411yescharacteristic
80C2×C4×C113#4111yescharacteristic
81C2×C4×C113#4111yescharacteristic
82C2×Dic113—22no—
83C2×Dic113—21no—
84C2×Dic113—22no—
85C2×Dic113—22no—
86C2×Dic113—21no—
87C2×Dic113—21no—
88C2×Dic113—21no—
89C2×Dic113—21no—
90C2×Dic113SD1612yescomplemented
91D452—22no—
92D452—22no—
93D452—41no—
94D452—41no—
95Dic226—22no—
96Dic226—22no—
97Dic226—22no—
98Dic226C22⋊C414yescomplemented
99C8×C113—22no—
100#11744751—41no—
101C22×C113C4×D411yescharacteristic
102C22×C113#12011yescharacteristic
103C22×C113#12111yescharacteristic
104C22×C113C2×SD1611yescharacteristic
105C22×C113#13511yescharacteristic
106C22×C113AGL(1,ℤ/8)11yescharacteristic
107C22×C113#13711yescharacteristic
108C2×D113—42no—
109C2×D113—42no—
110C2×D113—42no—
111C2×D113—81no—
112C2×D113—81no—
113C2×D113—81no—
114C2×D113—81no—
115C4×C113—42no—
116C4×C113—81no—
117C4×C113C2×C22⋊C411yescharacteristic
118C4×C113C4×D411yescharacteristic
119C4×C113#12111yescharacteristic
120C4×C113#12311yescharacteristic
121Dic113—24no—
122Dic113—22no—
123Dic113—41no—
124C2×C113#38611yescharacteristic
125C2×C113C4×SD1611yescharacteristic
126C2×C113#44011yescharacteristic
127C2×C113#44811yescharacteristic
128C2×C113#44911yescharacteristic
129C2×C113#46011yescharacteristic
130C2×C113#46411yescharacteristic
131D113—82no—
132#1880—1131nomaximal, Sylow
133C113#188011yescharacteristic, complemented, Sylow
134C22×SD16—1131no—
135C2×C4×Q8—1131no—
136C2×#103—1131no—
137C2×#102—1131no—
138#390—1131no—
139#340D11311yescharacteristic, complemented
140#336—1131no—
141C22×Q8—1131no—
142C22×D4—1131no—
143C2×SD16—1134no—
144C2×SD16—2262no—
145C2×SD16—2262no—
146C22×C8—1131no—
147C22×C8C2×D11311yescharacteristic
148C4×Q8—2262no—
149C4×Q8—2262no—
150C2×C4⋊C4—2261no—
151C2×C4⋊C4C2×D11311yescharacteristic
152C2×C4⋊C4C2×D11311yescharacteristic
153C2×C22⋊C4—2261no—
154C2×C22⋊C4—2261no—
155C2×C42—1131no—
156C2×C42—2261no—
157#103—2262no—
158#102—2262no—
159C24—2261no—
160C2×Q8—1132no—
161C2×Q8—1132no—
162C2×Q8—1132no—
163C2×Q8—2261no—
164C2×Q8—2261no—
165C2×Q8—2261no—
166C2×D4—1132no—
167C2×D4—2261no—
168C2×D4—2261no—
169C2×D4—2261no—
170C2×D4—2261no—
171C2×D4—2261no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—1131no—
175C22×C4—1131no—
176C22×C4—2261no—
177C22×C4C22×D11311yescharacteristic
178SD16—2268no—
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—2261no—
182C2×C8—2261no—
183C2×C8—2261no—
184C2×C8C4×D11312yes—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—2264no—
189C4⋊C4D45212yes—
190C22⋊C4—4522no—
191C22⋊C4—4522no—
192C42—2264no—
193C42—2261no—
194C42—2261no—
195C23—4521no—
196C23—4521no—
197C23—4521no—
198C23—4521no—
199C23—4521no—
200C23—4521no—
201C23—2262no—
202C23D4×D11311yescharacteristic
203Q8—1134no—
204Q8—2262no—
205Q8—2262no—
206Q8—2262no—
207D4—4521no—
208D4—4521no—
209D4—2262no—
210D4—2262no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—1132no—
218C2×C4—2261no—
219C2×C4—2261no—
220C2×C4—2261no—
221C2×C4—2262no—
222C2×C4—2261no—
223C2×C4—2262no—
224C2×C4—2262no—
225C2×C4—2261no—
226C2×C4C2×C4×D11311yescharacteristic
227C2×C4D4×D11311yescharacteristic
228C2×C4D4×D11311yescharacteristic
229C2×C4C2×D45211yescharacteristic
230C2×C4#1426864711yescharacteristic
231C2×C4#1426864811yescharacteristic
232C8—22no—
233C8—4521no—
234C22—9041no—
235C22—9041no—
236C22—9041no—
237C22—9041no—
238C22—4522no—
239C22—4522no—
240C22—4522no—
241C22#1681358411yescharacteristic
242C22#1681359211yescharacteristic
243C22#1681359511yescharacteristic
244C22SD16×D11311yescharacteristic
245C22#1681364311yescharacteristic
246C22#1681364611yescharacteristic
247C22#1681365411yescharacteristic
248C4—42no—
249C4—81no—
250C4—4521no—
251C4—2264no—
252C4—2262no—
253C4C22⋊C4×D11311yescharacteristic
254C4C4×D45211yescharacteristic
255C4#1681359711yescharacteristic
256C4#1681360711yescharacteristic
257C2—9042no—
258C2#2029847611yescharacteristic
259C2#2029868511yescharacteristic
260C2#2029869711yescharacteristic
261C2#2029873811yescharacteristic
262C2#2029874411yescharacteristic
263C2#2029879711yescharacteristic
264C2#2029882311yescharacteristic
subgroupG/H
centerC23D4×D113
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#340×C113C2
socleC23×C113C2×D4
prime radicalC22×D452C22
cosocleC22×C4×C113C23
hypercenter#340D113
hypocenterC113#1880
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×#16813587C2semidirect
3. C2×#16813545C2semidirect
6. #20298352C2semidirect
7. #340×C113C2semidirect
12. C2×#14268636C4semidirect
90. C2×Dic113SD16semidirect
98. Dic226C22⋊C4semidirect
133. C113#1880semidirect
139. #340D113semidirect

Maximal subgroups

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

subgroupindex
C22×#142686362
C2×#168135872
C2×#168135452
C2×#168135422
#202984992
#202983522
#340×C1132
#1880113