Finite Group Databasebeta

← #28399824

Subgroups — #28399824

Order 14464.

806 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 153 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×#14268647C211yesmaximal, characteristic, complemented
2C2×#16813648C212yesmaximal, complemented
3#20298741C214yesmaximal, complemented
4#20298736C212yesmaximal, complemented
5#20298731C212yesmaximal, complemented
6#20298597C212yesmaximal, complemented
7#20298562C211yesmaximal, characteristic, complemented
8C2×#121×C113C211yesmaximal, characteristic, complemented
9C2×#14268647—28no—
10C2×#14268647—21no—
11C2×#14268647—21no—
12C2×#14268647C2212yes—
13C2×#14268647C2212yescomplemented
14C22×Dic226C2211yescharacteristic, complemented
15C22×D452C2211yescharacteristic, complemented
16C22×C22⋊D113—21no—
17C22×C4×D113—21no—
18#16813648—28no—
19C2×#14268635C2214yescomplemented
20C2×#14268632C2214yescomplemented
21C2×#14268631C2212yescomplemented
22#16813545C2214yescomplemented
23#16813542C2214yescomplemented
24C22⋊#11744751C2212yescomplemented
25C22⋊#11744751C2212yescomplemented
26C22×D4×C113—21no—
27C22×D4×C113C2211yescharacteristic, complemented
28C23×C4×C113C2211yescharacteristic
29#121×C113—21no—
30#121×C113—21no—
31#121×C113C2212yes—
32#121×C113C2212yescomplemented
33C2×C4⋊C4×C113C2211yescharacteristic, complemented
34C2×C22⋊C4×C113—21no—
35C23×D113—21no—
36#14268647—28no—
37#14268647—28no—
38#14268647—24no—
39#14268647—24no—
40#14268647—24no—
41#14268647D418yescomplemented
42C2×Dic226—21no—
43C2×Dic226—24no—
44C2×Dic226C2312yes—
45C2×D452—21no—
46C2×D452—24no—
47C2×D452C2312yes—
48C2×C22⋊D113—28no—
49C2×C22⋊D113—22no—
50C2×C22⋊D113—22no—
51C22×Dic113—21no—
52C2×C4×D113—28no—
53C2×C4×D113—22no—
54C2×C4×D113—22no—
55#14268635—28no—
56#14268632—28no—
57#14268631—24no—
58C2×#11744751C2314yes—
59C24×C113—21no—
60C24×C113D411yescharacteristic
61C2×D4×C113—22no—
62C2×D4×C113—22no—
63C2×D4×C113—24no—
64C2×D4×C113—21no—
65C2×D4×C113—44no—
66C2×D4×C113C2312yes—
67C22×C4×C113—24no—
68C22×C4×C113—21no—
69C22×C4×C113D411yescharacteristic
70C22×C4×C113D411yescharacteristic
71C22×C4×C113D411yescharacteristic
72C22×C4×C113C2311yescharacteristic
73C22×C4×C113C2311yescharacteristic
74C22×C4×C113C2311yescharacteristic
75C4⋊C4×C113—21no—
76C4⋊C4×C113C2312yes—
77C22⋊C4×C113—22no—
78C22⋊C4×C113—22no—
79C23×C113—22no—
80C23×C113—22no—
81C23×C113—22no—
82C23×C113—41no—
83C23×C113—42no—
84C23×C113—42no—
85C23×C113—42no—
86C23×C113C2×D411yescharacteristic
87C23×C113C2×D411yescharacteristic
88C23×C113C2×D411yescharacteristic
89C22×D113—24no—
90C22×D113—22no—
91C22×D113—42no—
92C22×D113—42no—
93D4×C113—24no—
94D4×C113—44no—
95D4×C113—44no—
96D4×C113—42no—
97C2×C4×C113—22no—
98C2×C4×C113—22no—
99C2×C4×C113—22no—
100C2×C4×C113—22no—
101C2×C4×C113—22no—
102C2×C4×C113—22no—
103C2×C4×C113—42no—
104C2×C4×C113C2×D414yes—
105C2×C4×C113C2×D411yescharacteristic
106C2×C4×C113C2×D411yescharacteristic
107C2×C4×C113C2×D411yescharacteristic
108C2×C4×C113C2411yescharacteristic
109C22⋊D113—28no—
110C22⋊D113—28no—
111C2×Dic113—24no—
112C2×Dic113—22no—
113D452—24no—
114D452—22no—
115D452C2×D414yescomplemented
116C4×D113—28no—
117C4×D113—28no—
118Dic226—24no—
119Dic226—22no—
120Dic226C2×D414yescomplemented
121#11744751—24no—
122C22×C113—21no—
123C22×C113—21no—
124C22×C113—21no—
125C22×C113—21no—
126C22×C113—21no—
127C22×C113—21no—
128C22×C113—21no—
129C22×C113—44no—
130C22×C113—42no—
131C22×C113—42no—
132C22×C113—42no—
133C22×C113—84no—
134C22×C113#12012yes—
135C22×C113AGL(1,ℤ/8)12yescomplemented
136C22×C113C22×D411yescharacteristic
137C2×D113—24no—
138C2×D113—48no—
139C2×D113—42no—
140C2×D113—42no—
141C4×C113—21no—
142C4×C113—21no—
143C4×C113—42no—
144C4×C113#12012yes—
145C4×C113C22×D412yes—
146Dic113—24no—
147C2×C113—22no—
148C2×C113—22no—
149C2×C113—41no—
150C2×C113—82no—
151C2×C113C2×#12011yescharacteristic
152C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
153C2×C113#57511yescharacteristic
154D113—44no—
155#3006—1131nomaximal, Sylow
156C113#300611yescharacteristic, complemented, Sylow
157C22×#41—1131no—
158C2×AGL(1,ℤ/8)—1132no—
159C2×#121D11311yescharacteristic, complemented
160#449—1134no—
161#448—1132no—
162#447—1132no—
163#417—1132no—
164#407—1131no—
165C2×#41—1132no—
166C2×#41—1132no—
167C2×#41—2268no—
168C2×#41—2261no—
169C2×#41—2261no—
170C22×Q8—1131no—
171C22×D4—21no—
172C22×D4—1131no—
173C22×D4—2261no—
174C22×D4C2×D11311yescharacteristic, complemented
175C23×C4—2261no—
176C23×C4C2×D11311yescharacteristic
177AGL(1,ℤ/8)—2268no—
178C2×SD16—1134no—
179C2×D8—1134no—
180C2×M16—1132no—
181#121—21no—
182#121—21no—
183#121C2×D11312yes—
184#121C2×D11312yescomplemented
185C2×C4⋊C4C2×D11311yescharacteristic, complemented
186C2×C22⋊C4—21no—
187#103—1134no—
188#102—1134no—
189C22⋊C8—1132no—
190C22⋊C8—1132no—
191C24—21no—
192C24—2261no—
193C24C22⋊D11311yescharacteristic
194#41—1138no—
195#41—2264no—
196#41—2264no—
197#41—2268no—
198#41—2268no—
199#41—2264no—
200C2×Q8—1132no—
201C2×Q8—2264no—
202C2×Q8—2261no—
203C2×D4—22no—
204C2×D4—22no—
205C2×D4—24no—
206C2×D4—21no—
207C2×D4—44no—
208C2×D4—1132no—
209C2×D4—2264no—
210C2×D4—2268no—
211C2×D4—2262no—
212C2×D4—2262no—
213C2×D4—2261no—
214C2×D4C22×D11312yes—
215C22×C4—24no—
216C22×C4—21no—
217C22×C4—2268no—
218C22×C4—2261no—
219C22×C4—2262no—
220C22×C4—2262no—
221C22×C4C22⋊D11311yescharacteristic
222C22×C4C22⋊D11311yescharacteristic
223C22×C4C22⋊D11311yescharacteristic
224C22×C4C22×D11311yescharacteristic
225C22×C4C22×D11311yescharacteristic
226C22×C4C22×D11311yescharacteristic
227SD16—2268no—
228D8—2268no—
229M16—2264no—
230C2×C8—1134no—
231C4⋊C4—21no—
232C4⋊C4C22×D11312yes—
233C22⋊C4—22no—
234C22⋊C4—22no—
235C23—22no—
236C23—22no—
237C23—22no—
238C23—41no—
239C23—42no—
240C23—42no—
241C23—42no—
242C23—4522no—
243C23—4522no—
244C23—2264no—
245C23—2262no—
246C23C2×C22⋊D11311yescharacteristic
247C23C2×C22⋊D11311yescharacteristic
248C23C2×C22⋊D11311yescharacteristic
249Q8—1134no—
250Q8—2264no—
251Q8—2262no—
252D4—24no—
253D4—44no—
254D4—44no—
255D4—42no—
256D4—1134no—
257D4—2264no—
258D4—2268no—
259D4—2268no—
260D4—2262no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—42no—
268C2×C4—2268no—
269C2×C4—2264no—
270C2×C4—2262no—
271C2×C4—2268no—
272C2×C4D4×D11314yes—
273C2×C4C2×C22⋊D11311yescharacteristic
274C2×C4C2×C22⋊D11311yescharacteristic
275C2×C4C2×C22⋊D11311yescharacteristic
276C2×C4C23×D11311yescharacteristic
277C8—2264no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—44no—
286C22—42no—
287C22—42no—
288C22—42no—
289C22—84no—
290C22—4528no—
291C22—4522no—
292C22—4522no—
293C22—2264no—
294C22#1681359012yes—
295C22#1681364812yescomplemented
296C22C22×C22⋊D11311yescharacteristic
297C4—21no—
298C4—21no—
299C4—42no—
300C4—2264no—
301C4#1681359012yes—
302C4C2×D4×D11312yes—
303C2—22no—
304C2—22no—
305C2—41no—
306C2—82no—
307C2—4524no—
308C2C2×#1681359011yescharacteristic
309C2C2×#1681364811yescharacteristic
310C2#2029939611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#121×C113C2
socleC22×C113C22×D4
hypercenterC2×#121D113
hypocenterC113#3006
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×#14268647C2semidirect
2. C2×#16813648C2semidirect
3. #20298741C2semidirect
4. #20298736C2semidirect
5. #20298731C2semidirect
6. #20298597C2semidirect
7. #20298562C2semidirect
8. C2×#121×C113C2semidirect
13. C2×#14268647C22semidirect
14. C22×Dic226C22semidirect
15. C22×D452C22semidirect
19. C2×#14268635C22semidirect
20. C2×#14268632C22semidirect
21. C2×#14268631C22semidirect
22. #16813545C22semidirect
23. #16813542C22semidirect
24. C22⋊#11744751C22semidirect
25. C22⋊#11744751C22semidirect
27. C22×D4×C113C22semidirect
32. #121×C113C22semidirect
33. C2×C4⋊C4×C113C22semidirect
41. #14268647D4semidirect
115. D452C2×D4semidirect
120. Dic226C2×D4semidirect
135. C22×C113AGL(1,ℤ/8)semidirect
156. C113#3006semidirect
159. C2×#121D113semidirect
174. C22×D4C2×D113semidirect
184. #121C2×D113semidirect
185. C2×C4⋊C4C2×D113semidirect
295. C22#16813648semidirect

Maximal subgroups

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

subgroupindex
C22×#142686472
C2×#168136482
#202987412
#202987362
#202987312
#202985972
#202985622
C2×#121×C1132
#3006113