Finite Group Databasebeta

← #28393894

Subgroups — #28393894

Order 14464.

1056 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 159 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×#14268648C211yesmaximal, characteristic, complemented
2C2×#16813592C212yesmaximal, complemented
3C2×C22⋊C4×D113C211yesmaximal, characteristic, complemented
4#20298509C211yesmaximal, characteristic, complemented
5#20298508C211yesmaximal, characteristic, complemented
6#20298507C211yesmaximal, characteristic, complemented
7#20298476C212yesmaximal, complemented
8#20298476C212yesmaximal, complemented
9#20298474C212yesmaximal, complemented
10#20298460C211yesmaximal, characteristic, complemented
11#393×C113C211yesmaximal, characteristic, complemented
12C24×D113C2211yescharacteristic
13C2×#14268648—28no—
14C2×#14268648—24no—
15C22×D452C2212yes—
16C22×D452C2212yes—
17C22×D452C2211yescharacteristic, complemented
18C22×C22⋊D113C2212yes—
19C22×C4×D113C2211yescharacteristic
20C22×C4×D113C2211yescharacteristic
21C22×C4×D113C2212yescomplemented
22#16813592—28no—
23C2×C22⋊Dic113C2211yescharacteristic
24C2×#14268624C2211yescharacteristic
25C2×#14268624C2212yes—
26C2×#14268624C2211yescharacteristic
27C2×#14268624C2212yes—
28C2×#14268624C2212yescomplemented
29C2×#14268624C2212yescomplemented
30C22⋊C4×D113—24no—
31#16813529C2211yescharacteristic, complemented
32#16813529C2212yescomplemented
33#16813529C2212yescomplemented
34C22×Q8×C113C2211yescharacteristic, complemented
35C2×C22⋊C4×C113C2211yescharacteristic
36C2×C22⋊C4×C113C2212yes—
37#95×C113C2211yescharacteristic, complemented
38#95×C113C2212yescomplemented
39C23×D113—22no—
40C23×D113—22no—
41C23×D113—22no—
42C23×D113—24no—
43C23×D113—42no—
44C23×D113C2312yes—
45C23×D113C2311yescharacteristic
46C23×D113C2311yescharacteristic
47#14268648—232no—
48C2×D452—24no—
49C2×D452—24no—
50C2×D452—24no—
51C2×D452—22no—
52C2×D452—24no—
53C2×D452—24no—
54C2×D452—42no—
55C2×D452D418yescomplemented
56C2×C22⋊D113—24no—
57C2×C22⋊D113—24no—
58C2×C22⋊D113—42no—
59C22×Dic113C2312yes—
60C22×Dic113C2311yescharacteristic
61C22×Dic113C2311yescharacteristic
62C2×C4×D113—24no—
63C2×C4×D113—24no—
64C2×C4×D113—24no—
65C2×C4×D113—24no—
66C2×C4×D113—22no—
67C2×C4×D113—42no—
68C2×C4×D113D414yescomplemented
69C22⋊Dic113—22no—
70#14268624—24no—
71#14268624—22no—
72#14268624—24no—
73#14268624—22no—
74#14268624—42no—
75#14268624—42no—
76C24×C113C2311yescharacteristic
77C2×Q8×C113—24no—
78C2×Q8×C113—22no—
79C22×C4×C113C2311yescharacteristic
80C22×C4×C113C2312yes—
81C22×C4×C113C2311yescharacteristic
82C22×C4×C113C2312yes—
83C22⋊C4×C113—22no—
84C22⋊C4×C113—24no—
85C23×C113—21no—
86C23×C113—22no—
87C23×C113—21no—
88C23×C113—22no—
89C23×C113#4112yescomplemented
90C23×C113C2411yescharacteristic
91C22×D113—21no—
92C22×D113—21no—
93C22×D113—22no—
94C22×D113—28no—
95C22×D113—21no—
96C22×D113—22no—
97C22×D113—22no—
98C22×D113—22no—
99C22×D113—22no—
100C22×D113—22no—
101C22×D113—21no—
102C22×D113—22no—
103C22×D113—22no—
104C22×D113—22no—
105C22×D113—48no—
106C22×D113—48no—
107C22×D113—44no—
108C22×D113—44no—
109C22×D113C2×D414yes—
110C22×D113C2×D414yes—
111C22×D113C2×D412yes—
112C22×D113#4112yescomplemented
113Q8×C113—28no—
114C2×C4×C113—22no—
115C2×C4×C113—22no—
116C2×C4×C113—22no—
117C2×C4×C113—21no—
118C2×C4×C113—22no—
119C2×C4×C113—22no—
120C2×C4×C113—22no—
121C2×C4×C113—22no—
122C2×C4×C113C2×D414yes—
123C2×C4×C113C2×D412yes—
124C22⋊D113—48no—
125C2×Dic113—22no—
126C2×Dic113—22no—
127C2×Dic113—21no—
128C2×Dic113—22no—
129C2×Dic113—22no—
130C2×Dic113—22no—
131C2×Dic113C2×D412yes—
132D452—28no—
133D452—216no—
134D452—48no—
135C4×D113—216no—
136C4×D113—28no—
137C4×D113—44no—
138C22×C113—22no—
139C22×C113—24no—
140C22×C113—41no—
141C22×C113—41no—
142C22×C113—42no—
143C22×C113C22×D411yescharacteristic
144C22×C113C22×D412yes—
145C22×C113C2×#4111yescharacteristic
146C22×C113C2×#4111yescharacteristic
147C22×C113H(5,𝔽2)12yes—
148C2×D113—22no—
149C2×D113—22no—
150C2×D113—24no—
151C2×D113—24no—
152C2×D113—24no—
153C2×D113—22no—
154C2×D113—24no—
155C2×D113—24no—
156C2×D113—24no—
157C2×D113—416no—
158C2×D113—41no—
159C2×D113—42no—
160C2×D113—42no—
161C2×D113—41no—
162C2×D113—42no—
163C2×D113—42no—
164C2×D113—42no—
165C2×D113#12014yes—
166C4×C113—24no—
167C4×C113—22no—
168C4×C113—41no—
169C4×C113—42no—
170Dic113—22no—
171Dic113—41no—
172Dic113—42no—
173C2×C113—42no—
174C2×C113C2×#12011yescharacteristic
175C2×C113#52511yescharacteristic
176C2×C113#53511yescharacteristic
177C2×C113#54612yes—
178C2×C113#54612yes—
179D113—24no—
180D113—44no—
181D113—42no—
182#2404—1131nomaximal, Sylow
183C113#240411yescharacteristic, complemented, Sylow
184C22×#41—1131no—
185C2×#120—1132no—
186C22×C22⋊C4—1131no—
187#393—1131no—
188#393D11311yescharacteristic, complemented
189#392—1131no—
190#392—1131no—
191#386—1132no—
192#386—1132no—
193#386—1132no—
194#381—1131no—
195C25—1131no—
196C2×#41—2264no—
197C2×#41—2268no—
198C22×Q8C2×D11311yescharacteristic, complemented
199C22×D4—1132no—
200C22×D4—1132no—
201C22×D4—1132no—
202C22×D4—1131no—
203C23×C4—1131no—
204C23×C4—1131no—
205C23×C4—1132no—
206#120—2268no—
207C2×C22⋊C4—1132no—
208C2×C22⋊C4—1132no—
209C2×C22⋊C4—1131no—
210C2×C22⋊C4—1131no—
211C2×C22⋊C4—1131no—
212C2×C22⋊C4—1132no—
213C2×C22⋊C4—1132no—
214C2×C22⋊C4—2264no—
215C2×C22⋊C4C2×D11311yescharacteristic
216C2×C22⋊C4C2×D11312yes—
217#95—1132no—
218#95—1131no—
219#95—1132no—
220#95C2×D11311yescharacteristic, complemented
221#95C2×D11312yescomplemented
222C24—1131no—
223C24—1131no—
224C24—1132no—
225C24—4522no—
226C24—2264no—
227C24—2262no—
228C24—2262no—
229C24—2262no—
230C24C22×D11311yescharacteristic
231#41—22632no—
232C2×Q8—22no—
233C2×Q8—24no—
234C2×D4—1138no—
235C2×D4—4522no—
236C2×D4—4522no—
237C2×D4—2264no—
238C2×D4—2264no—
239C2×D4—2264no—
240C2×D4—2264no—
241C2×D4—2264no—
242C2×D4—2264no—
243C2×D4—2264no—
244C2×D4—2262no—
245C22×C4—1131no—
246C22×C4—1134no—
247C22×C4—1132no—
248C22×C4—1131no—
249C22×C4—4522no—
250C22×C4—2264no—
251C22×C4—2262no—
252C22×C4—2264no—
253C22×C4—2264no—
254C22×C4—2264no—
255C22×C4C22×D11312yes—
256C22×C4C22×D11311yescharacteristic
257C22×C4C22×D11311yescharacteristic
258C22×C4C22×D11312yes—
259C22⋊C4—22no—
260C22⋊C4—24no—
261C22⋊C4—4522no—
262C22⋊C4—4522no—
263C22⋊C4—2262no—
264C22⋊C4—2264no—
265C22⋊C4—2262no—
266C22⋊C4—2262no—
267C22⋊C4—2264no—
268C23—21no—
269C23—22no—
270C23—21no—
271C23—22no—
272C23—1134no—
273C23—1132no—
274C23—1134no—
275C23—1132no—
276C23—4528no—
277C23—4524no—
278C23—4524no—
279C23—4528no—
280C23—2268no—
281C23—2261no—
282C23—2262no—
283C23—2262no—
284C23—2262no—
285C23—2262no—
286C23—2262no—
287C23—2261no—
288C23—2262no—
289C23—2262no—
290C23—2262no—
291C23—2261no—
292C23—2261no—
293C23—2262no—
294C23#1426864812yescomplemented
295C23C23×D11311yescharacteristic
296Q8—28no—
297D4—4528no—
298D4—4528no—
299D4—22616no—
300D4—2268no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—1132no—
310C2×C4—4524no—
311C2×C4—2268no—
312C2×C4—22616no—
313C2×C4—2261no—
314C2×C4—2262no—
315C2×C4—2262no—
316C2×C4—2262no—
317C2×C4—2262no—
318C2×C4—2262no—
319C2×C4D4×D11312yes—
320C2×C4D4×D11314yes—
321C22—22no—
322C22—24no—
323C22—41no—
324C22—41no—
325C22—42no—
326C22—1134no—
327C22—45216no—
328C22—4521no—
329C22—4522no—
330C22—4521no—
331C22—4522no—
332C22—4522no—
333C22—4522no—
334C22—4522no—
335C22—2264no—
336C22—2262no—
337C22—2264no—
338C22—2264no—
339C22—2264no—
340C22—2262no—
341C22—2262no—
342C22—2264no—
343C22—2264no—
344C22C2×D4×D11311yescharacteristic
345C22C2×D4×D11312yes—
346C22#41×D11311yescharacteristic
347C22C2×#1426864811yescharacteristic
348C22#1681366812yes—
349C4—22no—
350C4—24no—
351C4—41no—
352C4—42no—
353C4—4521no—
354C4—4522no—
355C4—2262no—
356C2—42no—
357C2—4522no—
358C2—4524no—
359C2—2264no—
360C2#120×D11311yescharacteristic
361C2#2029911111yescharacteristic
362C2#2029916611yescharacteristic
363C2#2029923912yes—
364C2#2029924112yes—
subgroupG/H
center, FrattiniC23C23×D113
commutator, socle, cosocleC23×C113C24
Fitting#393×C113C2
hypercenter#393D113
hypocenterC113#2404
LCSG ▷ C23×C113 ▷ C113
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C22×#14268648C2semidirect
2. C2×#16813592C2semidirect
3. C2×C22⋊C4×D113C2semidirect
4. #20298509C2semidirect
5. #20298508C2semidirect
6. #20298507C2semidirect
7. #20298476C2semidirect
8. #20298476C2semidirect
9. #20298474C2semidirect
10. #20298460C2semidirect
11. #393×C113C2semidirect
17. C22×D452C22semidirect
21. C22×C4×D113C22semidirect
28. C2×#14268624C22semidirect
29. C2×#14268624C22semidirect
31. #16813529C22semidirect
32. #16813529C22semidirect
33. #16813529C22semidirect
34. C22×Q8×C113C22semidirect
37. #95×C113C22semidirect
38. #95×C113C22semidirect
55. C2×D452D4semidirect
68. C2×C4×D113D4semidirect
89. C23×C113#41semidirect
112. C22×D113#41semidirect
183. C113#2404semidirect
188. #393D113semidirect
198. C22×Q8C2×D113semidirect
220. #95C2×D113semidirect
221. #95C2×D113semidirect
294. C23#14268648semidirect

Maximal subgroups

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

subgroupindex
C22×#142686482
C2×#168135922
C2×C22⋊C4×D1132
#202985092
#202985082
#202985072
#202984762
#202984742
#202984602
#393×C1132
#2404113