Finite Group Databasebeta

← #28390926

Subgroups — #28390926

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×#14268635C211yesmaximal, characteristic
2C2×#16813587C211yesmaximal, characteristic, complemented
3C2×#16813547C211yesmaximal, characteristic, complemented
4#20298501C211yesmaximal, characteristic
5#20298360C211yesmaximal, characteristic, complemented
6#20298352C211yesmaximal, characteristic, complemented
7C2×#102×C113C211yesmaximal, characteristic
8C22×Dic226C2211yescharacteristic
9C2×#14268635—22no—
10C2×#14268635—22no—
11C2×#14268635C414yescomplemented
12C22×#11744751C2211yescharacteristic
13#16813587—22no—
14#16813587—22no—
15C2×C4⋊Dic113C2211yescharacteristic
16C2×#14268626—21no—
17C2×C22⋊Dic113—21no—
18C2×C22⋊Dic113—21no—
19C2×C4×Dic113—21no—
20C2×C4×Dic113C2211yescharacteristic
21#16813547—22no—
22C22×D4×C113C2211yescharacteristic
23C22×C8×C113C2211yescharacteristic
24C2×C4⋊C4×C113C2211yescharacteristic
25#102×C113—22no—
26C2×Dic226—21no—
27C2×Dic226—21no—
28C2×Dic226—21no—
29C2×Dic226C2×C412yes—
30C2×Dic226D412yes—
31C2×Dic226D412yes—
32C22×Dic113—21no—
33C22×Dic113—21no—
34C22×Dic113D411yescharacteristic
35C22×Dic113D411yescharacteristic
36#14268635—28no—
37C2×#11744751—21no—
38C2×#11744751—21no—
39C2×#11744751C2×C412yes—
40C4⋊Dic113—21no—
41C4⋊Dic113—21no—
42#14268626—24no—
43C22⋊Dic113—42no—
44C22⋊Dic113—42no—
45C4×Dic113—24no—
46C4×Dic113—21no—
47C4×Dic113—21no—
48C24×C113—21no—
49C2×D4×C113—21no—
50C2×D4×C113—21no—
51C2×D4×C113—21no—
52C2×D4×C113—21no—
53C2×D4×C113—21no—
54C2×D4×C113C2×C412yes—
55C22×C4×C113—21no—
56C22×C4×C113C2311yescharacteristic
57C2×C8×C113—21no—
58C2×C8×C113—21no—
59C2×C8×C113—21no—
60C4⋊C4×C113—21no—
61C4⋊C4×C113D412yes—
62C23×C113—22no—
63C23×C113—41no—
64C23×C113—41no—
65C23×C113—41no—
66C23×C113—41no—
67C23×C113—41no—
68C23×C113—41no—
69C23×C113C2×D411yescharacteristic
70D4×C113—22no—
71D4×C113—22no—
72D4×C113—41no—
73D4×C113—41no—
74C2×C4×C113—22no—
75C2×C4×C113—41no—
76C2×C4×C113—41no—
77C2×C4×C113C22×C411yescharacteristic
78C2×C4×C113C2×D411yescharacteristic
79C2×C4×C113C2×D411yescharacteristic
80C2×C4×C113C2×D411yescharacteristic
81C2×C4×C113#4111yescharacteristic
82C2×C4×C113#4111yescharacteristic
83C2×Dic113—22no—
84C2×Dic113—21no—
85C2×Dic113—22no—
86C2×Dic113—22no—
87C2×Dic113—21no—
88C2×Dic113—21no—
89C2×Dic113—21no—
90C2×Dic113—21no—
91C2×Dic113—41no—
92C2×Dic113—41no—
93C2×Dic113—41no—
94C2×Dic113SD1612yescomplemented
95Dic226—22no—
96Dic226—22no—
97Dic226—22no—
98Dic226C22⋊C414yescomplemented
99C8×C113—41no—
100#11744751—22no—
101C22×C113—42no—
102C22×C113—42no—
103C22×C113—42no—
104C22×C113—81no—
105C22×C113—81no—
106C22×C113—81no—
107C22×C113—81no—
108C22×C113C4×D411yescharacteristic
109C22×C113#12011yescharacteristic
110C22×C113#12111yescharacteristic
111C22×C113C2×SD1611yescharacteristic
112C22×C113#13511yescharacteristic
113C22×C113AGL(1,ℤ/8)11yescharacteristic
114C22×C113#13711yescharacteristic
115C4×C113—42no—
116C4×C113C2×C22⋊C411yescharacteristic
117C4×C113C4×D411yescharacteristic
118C4×C113#12111yescharacteristic
119C4×C113#12311yescharacteristic
120Dic113—24no—
121Dic113—22no—
122Dic113—41no—
123Dic113—81no—
124C2×C113—82no—
125C2×C113#38611yescharacteristic
126C2×C113C4×SD1611yescharacteristic
127C2×C113#44011yescharacteristic
128C2×C113#44811yescharacteristic
129C2×C113#44911yescharacteristic
130C2×C113#46011yescharacteristic
131C2×C113#46411yescharacteristic
132#1880—1131nomaximal, Sylow
133C113#188011yescharacteristic, complemented, Sylow
134C22×SD16—1131no—
135C2×C4×Q8—1131no—
136C2×#103—1131no—
137C2×#102D11311yescharacteristic
138#390—1131no—
139#340—1131no—
140#336—1131no—
141C22×Q8—1131no—
142C22×D4C2×D11311yescharacteristic
143C2×SD16—1134no—
144C2×SD16—2262no—
145C2×SD16—2262no—
146C22×C8—1131no—
147C22×C8C2×D11311yescharacteristic
148C4×Q8—2262no—
149C4×Q8—2262no—
150C2×C4⋊C4—1131no—
151C2×C4⋊C4—2261no—
152C2×C4⋊C4C2×D11311yescharacteristic
153C2×C22⋊C4—2261no—
154C2×C22⋊C4—2261no—
155C2×C42—1131no—
156C2×C42—2261no—
157#103—2262no—
158#102—22no—
159C24—21no—
160C2×Q8—1132no—
161C2×Q8—1132no—
162C2×Q8—1132no—
163C2×Q8—2261no—
164C2×Q8—2261no—
165C2×Q8—2261no—
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4—21no—
171C2×D4C4×D11312yes—
172C22×C4—21no—
173C22×C4—1131no—
174C22×C4—1131no—
175C22×C4—2261no—
176C22×C4—2261no—
177C22×C4C22×D11311yescharacteristic
178SD16—2268no—
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—1132no—
183C2×C8—2261no—
184C2×C8—2261no—
185C4⋊C4—21no—
186C4⋊C4—2264no—
187C4⋊C4—2261no—
188C4⋊C4—2261no—
189C4⋊C4C22⋊D11312yes—
190C22⋊C4—4522no—
191C22⋊C4—4522no—
192C42—2264no—
193C42—2261no—
194C42—2261no—
195C23—22no—
196C23—41no—
197C23—41no—
198C23—41no—
199C23—41no—
200C23—41no—
201C23—41no—
202C23D4×D11311yescharacteristic
203Q8—1134no—
204Q8—2262no—
205Q8—2262no—
206Q8—2262no—
207D4—22no—
208D4—22no—
209D4—41no—
210D4—41no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—1132no—
215C2×C4—4521no—
216C2×C4—4521no—
217C2×C4—4521no—
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×C22⋊D11311yescharacteristic
230C2×C4#1426864611yescharacteristic
231C2×C4#1426864711yescharacteristic
232C8—41no—
233C8—2262no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—81no—
238C22—81no—
239C22—81no—
240C22—81no—
241C22#1681358211yescharacteristic
242C22#1681359011yescharacteristic
243C22#1681359511yescharacteristic
244C22SD16×D11311yescharacteristic
245C22#1681364111yescharacteristic
246C22#1681364611yescharacteristic
247C22#1681365111yescharacteristic
248C4—42no—
249C4—9041no—
250C4—4521no—
251C4—2264no—
252C4—2262no—
253C4C22⋊C4×D11311yescharacteristic
254C4C4×C22⋊D11311yescharacteristic
255C4#1681359311yescharacteristic
256C4#1681360411yescharacteristic
257C2—82no—
258C2#2029847411yescharacteristic
259C2#2029868911yescharacteristic
260C2#2029869511yescharacteristic
261C2#2029873511yescharacteristic
262C2#2029874011yescharacteristic
263C2#2029879711yescharacteristic
264C2#2029881911yescharacteristic
subgroupG/H
centerC23D4×D113
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
FittingC2×#102×C113C2
socleC23×C113C2×D4
prime radicalC22×D4×C113C22
cosocleC22×C4×C113C23
hypercenterC2×#102D113
hypocenterC113#1880
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×#16813587C2semidirect
3. C2×#16813547C2semidirect
5. #20298360C2semidirect
6. #20298352C2semidirect
11. C2×#14268635C4semidirect
94. C2×Dic113SD16semidirect
98. Dic226C22⋊C4semidirect
133. C113#1880semidirect

Maximal subgroups

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

subgroupindex
C22×#142686352
C2×#168135872
C2×#168135472
#202985012
#202983602
#202983522
C2×#102×C1132
#1880113