Finite Group Databasebeta

← #28393883

Subgroups — #28393883

Order 14464.

1564 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 1564 conjugacy classes of subgroups — too many to draw. Only its 181 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×D4×D113C212yesmaximal, complemented
2C2×#16813592C212yesmaximal, complemented
3C2×#16813590C212yesmaximal, complemented
4#20298507C211yesmaximal, characteristic, complemented
5#20298506C212yesmaximal, complemented
6#20298476C212yesmaximal, complemented
7#20298474C212yesmaximal, complemented
8#20298453C211yesmaximal, characteristic, complemented
9#392×C113C211yesmaximal, characteristic, complemented
10C24×D113C2211yescharacteristic
11C24×D113C2212yescomplemented
12C22×D452C2212yes—
13C22×D452C2211yescharacteristic, complemented
14C22×C22⋊D113C2212yes—
15C22×C22⋊D113C2212yescomplemented
16C22×C22⋊D113C2212yescomplemented
17C2×D4×D113—28no—
18C2×D4×D113—28no—
19C2×D4×D113—28no—
20C22×C4×D113C2212yescomplemented
21#16813592—28no—
22#16813590—28no—
23C2×C22⋊Dic113C2212yescomplemented
24C2×C22⋊Dic113C2211yescharacteristic, complemented
25C2×#14268624C2212yescomplemented
26C2×#14268624C2212yescomplemented
27C2×#14268624C2212yescomplemented
28C2×#14268624C2212yescomplemented
29#16813529C2212yescomplemented
30#16813529C2211yescharacteristic, complemented
31C22×D4×C113C2212yescomplemented
32C22×D4×C113C2211yescharacteristic, complemented
33C2×C22⋊C4×C113C2212yescomplemented
34C2×C22⋊C4×C113C2211yescharacteristic, complemented
35#95×C113C2211yescharacteristic, complemented
36C23×D113—24no—
37C23×D113—24no—
38C23×D113—24no—
39C23×D113—24no—
40C23×D113—24no—
41C23×D113—24no—
42C23×D113—24no—
43C23×D113—41no—
44C23×D113—41no—
45C23×D113—42no—
46C23×D113—42no—
47C23×D113D414yescomplemented
48C23×D113C2312yes—
49C23×D113C2312yes—
50C2×D452—24no—
51C2×D452—24no—
52C2×D452—24no—
53C2×D452—41no—
54C2×D452D418yescomplemented
55C2×C22⋊D113—24no—
56C2×C22⋊D113—24no—
57C2×C22⋊D113—24no—
58C2×C22⋊D113—24no—
59C2×C22⋊D113—24no—
60C2×C22⋊D113—24no—
61C2×C22⋊D113—24no—
62C2×C22⋊D113—42no—
63C2×C22⋊D113D418yescomplemented
64D4×D113—264no—
65C22×Dic113C2312yes—
66C22×Dic113C2312yes—
67C2×C4×D113—24no—
68C2×C4×D113—24no—
69C2×C4×D113—24no—
70C22⋊Dic113—24no—
71C22⋊Dic113—41no—
72#14268624—24no—
73#14268624—24no—
74#14268624—24no—
75#14268624—24no—
76C24×C113C2311yescharacteristic
77C24×C113C2312yes—
78C2×D4×C113—24no—
79C2×D4×C113—24no—
80C2×D4×C113—24no—
81C2×D4×C113—24no—
82C2×D4×C113—41no—
83C22×C4×C113C2311yescharacteristic
84C22×C4×C113C2311yescharacteristic
85C22×C4×C113C2312yes—
86C22⋊C4×C113—24no—
87C22⋊C4×C113—41no—
88C23×C113—22no—
89C23×C113—22no—
90C23×C113—22no—
91C23×C113—22no—
92C23×C113—22no—
93C23×C113—22no—
94C23×C113—21no—
95C23×C113—22no—
96C23×C113—21no—
97C23×C113—22no—
98C23×C113C2×D412yes—
99C23×C113C2×D414yescomplemented
100C23×C113C2411yescharacteristic
101C22×D113—22no—
102C22×D113—22no—
103C22×D113—22no—
104C22×D113—22no—
105C22×D113—216no—
106C22×D113—22no—
107C22×D113—22no—
108C22×D113—22no—
109C22×D113—22no—
110C22×D113—22no—
111C22×D113—22no—
112C22×D113—216no—
113C22×D113—44no—
114C22×D113—44no—
115C22×D113—48no—
116C22×D113—44no—
117C22×D113—48no—
118C22×D113—48no—
119C22×D113—48no—
120C22×D113—48no—
121C22×D113—48no—
122C22×D113—48no—
123C22×D113C2×D414yes—
124C22×D113C2×D414yes—
125C22×D113C2×D414yes—
126C22×D113C2×D414yescomplemented
127D4×C113—216no—
128D4×C113—44no—
129C2×C4×C113—22no—
130C2×C4×C113—22no—
131C2×C4×C113—22no—
132C2×C4×C113—22no—
133C2×C4×C113—21no—
134C2×C4×C113—21no—
135C2×C4×C113C2×D414yescomplemented
136C22⋊D113—216no—
137C22⋊D113—216no—
138C22⋊D113—48no—
139C2×Dic113—22no—
140C2×Dic113—22no—
141C2×Dic113—22no—
142C2×Dic113—22no—
143C2×Dic113—22no—
144C2×Dic113C2×D414yescomplemented
145D452—216no—
146D452—44no—
147C4×D113—216no—
148C22×C113—24no—
149C22×C113—24no—
150C22×C113—22no—
151C22×C113—24no—
152C22×C113—24no—
153C22×C113—42no—
154C22×C113—42no—
155C22×C113—41no—
156C22×C113—42no—
157C22×C113—42no—
158C22×C113—42no—
159C22×C113—41no—
160C22×C113C22×D411yescharacteristic
161C22×C113C22×D412yes—
162C22×C113C22×D412yes—
163C22×C113H(5,𝔽2)11yescharacteristic
164C22×C113H(5,𝔽2)11yescharacteristic
165C2×D113—24no—
166C2×D113—24no—
167C2×D113—24no—
168C2×D113—24no—
169C2×D113—24no—
170C2×D113—24no—
171C2×D113—24no—
172C2×D113—24no—
173C2×D113—24no—
174C2×D113—416no—
175C2×D113—432no—
176C2×D113—42no—
177C2×D113—42no—
178C2×D113—42no—
179C2×D113—42no—
180C2×D113#12018yescomplemented
181C4×C113—24no—
182C4×C113—41no—
183C4×C113—41no—
184Dic113—24no—
185Dic113—42no—
186C2×C113—42no—
187C2×C113—44no—
188C2×C113C2×#12012yes—
189C2×C113#53411yescharacteristic
190C2×C113D4211yescharacteristic
191C2×C113D4212yes—
192C2×C113D4211yescharacteristic
193D113—28no—
194D113—44no—
195#2403—1131nomaximal, Sylow
196C113#240311yescharacteristic, complemented, Sylow
197C23×D4—1132no—
198C2×#120—1132no—
199C2×#120—1132no—
200#392—1132no—
201#392—1131no—
202#392D11311yescharacteristic, complemented
203#386—1132no—
204#386—1132no—
205#379—1131no—
206C25—1131no—
207C25—1132no—
208C22×D4—1132no—
209C22×D4—1132no—
210C22×D4—1132no—
211C22×D4—1132no—
212C22×D4—1131no—
213C22×D4—2268no—
214C22×D4—2268no—
215C22×D4—2268no—
216C22×D4C2×D11312yescomplemented
217C22×D4C2×D11311yescharacteristic, complemented
218C23×C4—1132no—
219#120—2268no—
220#120—2268no—
221C2×C22⋊C4—1131no—
222C2×C22⋊C4—1132no—
223C2×C22⋊C4—1132no—
224C2×C22⋊C4—1132no—
225C2×C22⋊C4—1132no—
226C2×C22⋊C4—1132no—
227C2×C22⋊C4C2×D11312yescomplemented
228C2×C22⋊C4C2×D11311yescharacteristic, complemented
229#95—1131no—
230#95—1132no—
231#95C2×D11311yescharacteristic, complemented
232C24—1132no—
233C24—1134no—
234C24—1132no—
235C24—4521no—
236C24—4522no—
237C24—4521no—
238C24—4522no—
239C24—2264no—
240C24—2264no—
241C24—2264no—
242C24—2264no—
243C24—2264no—
244C24—2264no—
245C24—2264no—
246C24C22×D11311yescharacteristic
247C24C22×D11312yes—
248C2×D4—24no—
249C2×D4—24no—
250C2×D4—24no—
251C2×D4—24no—
252C2×D4—41no—
253C2×D4—1138no—
254C2×D4—1138no—
255C2×D4—4521no—
256C2×D4—4522no—
257C2×D4—2264no—
258C2×D4—2264no—
259C2×D4—2264no—
260C2×D4—2264no—
261C2×D4—22664no—
262C2×D4—2264no—
263C2×D4—2264no—
264C2×D4—2264no—
265C2×D4—2264no—
266C2×D4—2264no—
267C2×D4—2264no—
268C22×C4—1132no—
269C22×C4—1132no—
270C22×C4—2264no—
271C22×C4—2264no—
272C22×C4—2264no—
273C22×C4C22×D11311yescharacteristic
274C22×C4C22×D11311yescharacteristic
275C22×C4C22×D11312yes—
276C22⋊C4—24no—
277C22⋊C4—41no—
278C22⋊C4—4521no—
279C22⋊C4—2264no—
280C22⋊C4—2264no—
281C22⋊C4—2264no—
282C22⋊C4—2264no—
283C22⋊C4—2264no—
284C23—22no—
285C23—22no—
286C23—22no—
287C23—22no—
288C23—22no—
289C23—22no—
290C23—21no—
291C23—22no—
292C23—21no—
293C23—22no—
294C23—1134no—
295C23—1134no—
296C23—1134no—
297C23—1134no—
298C23—4528no—
299C23—4528no—
300C23—4524no—
301C23—4528no—
302C23—4528no—
303C23—4524no—
304C23—4528no—
305C23—4528no—
306C23—4528no—
307C23—4524no—
308C23—22616no—
309C23—22616no—
310C23—2262no—
311C23—2262no—
312C23—2262no—
313C23—2262no—
314C23—2262no—
315C23—2262no—
316C23—2262no—
317C23—2262no—
318C23—2262no—
319C23—2262no—
320C23D4×D11312yes—
321C23D4×D11314yescomplemented
322C23C23×D11311yescharacteristic
323D4—216no—
324D4—44no—
325D4—4524no—
326D4—4528no—
327D4—22616no—
328D4—22616no—
329D4—22616no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—1134no—
337C2×C4—22616no—
338C2×C4—2262no—
339C2×C4—2262no—
340C2×C4—2262no—
341C2×C4—2262no—
342C2×C4—2262no—
343C2×C4D4×D11314yescomplemented
344C22—24no—
345C22—24no—
346C22—22no—
347C22—24no—
348C22—24no—
349C22—42no—
350C22—42no—
351C22—41no—
352C22—42no—
353C22—42no—
354C22—42no—
355C22—41no—
356C22—1138no—
357C22—45232no—
358C22—45216no—
359C22—4522no—
360C22—4522no—
361C22—4522no—
362C22—4522no—
363C22—2264no—
364C22—2264no—
365C22—2264no—
366C22—2264no—
367C22—2264no—
368C22—2264no—
369C22—2264no—
370C22—2264no—
371C22—2264no—
372C22C2×D4×D11311yescharacteristic
373C22C2×D4×D11312yes—
374C22C2×D4×D11312yes—
375C22#1681366711yescharacteristic
376C22#1681366811yescharacteristic
377C4—24no—
378C4—41no—
379C4—41no—
380C4—4522no—
381C4—2264no—
382C2—42no—
383C2—44no—
384C2—4524no—
385C2—2268no—
386C2#120×D11312yes—
387C2#2029915611yescharacteristic
388C2#2029923011yescharacteristic
389C2#2029923212yes—
390C2#2029923311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutator, socle, cosocleC23×C113C24
Fitting#392×C113C2
hypercenter#392D113
hypocenterC113#2403
LCSG ▷ C23×C113 ▷ C113
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×D4×D113C2semidirect
2. C2×#16813592C2semidirect
3. C2×#16813590C2semidirect
4. #20298507C2semidirect
5. #20298506C2semidirect
6. #20298476C2semidirect
7. #20298474C2semidirect
8. #20298453C2semidirect
9. #392×C113C2semidirect
11. C24×D113C22semidirect
13. C22×D452C22semidirect
15. C22×C22⋊D113C22semidirect
16. C22×C22⋊D113C22semidirect
20. C22×C4×D113C22semidirect
23. C2×C22⋊Dic113C22semidirect
24. C2×C22⋊Dic113C22semidirect
25. C2×#14268624C22semidirect
26. C2×#14268624C22semidirect
27. C2×#14268624C22semidirect
28. C2×#14268624C22semidirect
29. #16813529C22semidirect
30. #16813529C22semidirect
31. C22×D4×C113C22semidirect
32. C22×D4×C113C22semidirect
33. C2×C22⋊C4×C113C22semidirect
34. C2×C22⋊C4×C113C22semidirect
35. #95×C113C22semidirect
47. C23×D113D4semidirect
54. C2×D452D4semidirect
63. C2×C22⋊D113D4semidirect
99. C23×C113C2×D4semidirect
126. C22×D113C2×D4semidirect
135. C2×C4×C113C2×D4semidirect
144. C2×Dic113C2×D4semidirect
180. C2×D113#120semidirect
196. C113#2403semidirect
202. #392D113semidirect
216. C22×D4C2×D113semidirect
217. C22×D4C2×D113semidirect
227. C2×C22⋊C4C2×D113semidirect
228. C2×C22⋊C4C2×D113semidirect
231. #95C2×D113semidirect
321. C23D4×D113semidirect
343. C2×C4D4×D113semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D1132
C2×#168135922
C2×#168135902
#202985072
#202985062
#202984762
#202984742
#202984532
#392×C1132
#2403113