Finite Group Databasebeta

← #28393765

Subgroups — #28393765

Order 14464.

456 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813617C211yesmaximal, characteristic
2#20298494C211yesmaximal, characteristic, complemented
3#20298493C211yesmaximal, characteristic, complemented
4#20298489C211yesmaximal, characteristic
5#20298488C211yesmaximal, characteristic
6#20298487C211yesmaximal, characteristic
7#20298484C211yesmaximal, characteristic, complemented
8#20298483C211yesmaximal, characteristic, complemented
9#20298482C211yesmaximal, characteristic, complemented
10#20298472C211yesmaximal, characteristic
11#20298469C211yesmaximal, characteristic
12#20298469C211yesmaximal, characteristic
13#20298467C211yesmaximal, characteristic, complemented
14#20298465C211yesmaximal, characteristic, complemented
15#389×C113C211yesmaximal, characteristic, complemented
16C22×C4×D113C2211yescharacteristic
17#16813617C418yescomplemented
18C2×C4⋊Dic113C2211yescharacteristic
19C2×C4⋊Dic113C2211yescharacteristic
20C2×#14268626C2211yescharacteristic
21C2×#14268626C2211yescharacteristic
22C2×#14268626C2211yescharacteristic
23C2×#14268626C2211yescharacteristic
24C2×#14268626C2211yescharacteristic
25C2×#14268626C2211yescharacteristic
26C2×#14268624C2211yescharacteristic
27C2×#14268624C2211yescharacteristic
28C2×#14268624C2211yescharacteristic
29C2×#14268624C2211yescharacteristic
30C2×#14268624C2211yescharacteristic
31C2×#14268624C2211yescharacteristic
32C2×C4×Dic113C2211yescharacteristic
33C2×C4×Dic113C2211yescharacteristic
34C2×C4×Dic113C2211yescharacteristic
35#16813529C2211yescharacteristic
36#16813529C2211yescharacteristic
37#16813529C2211yescharacteristic
38#16813529C2211yescharacteristic
39#16813529C2211yescharacteristic
40#16813529C2211yescharacteristic
41#16813529C2211yescharacteristic
42#16813529C2211yescharacteristic
43#16813529C2211yescharacteristic
44#16813529C2211yescharacteristic
45C2×C4⋊C4×C113C2211yescharacteristic
46C2×C4⋊C4×C113C2211yescharacteristic
47C2×C4⋊C4×C113C2211yescharacteristic
48C2×C4⋊C4×C113C2211yescharacteristic
49C2×C42×C113C2211yescharacteristic
50#95×C113C2211yescharacteristic
51#95×C113C2211yescharacteristic
52C23×D113C2311yescharacteristic
53C22×Dic113C2311yescharacteristic
54C22×Dic113C2311yescharacteristic
55C22×Dic113C2311yescharacteristic
56C22×Dic113C2311yescharacteristic
57C22×Dic113C2311yescharacteristic
58C22×Dic113C2311yescharacteristic
59C22×Dic113C2311yescharacteristic
60C2×C4×D113—41no—
61C2×C4×D113—41no—
62C2×C4×D113—41no—
63C4⋊Dic113—41no—
64C4⋊Dic113C2×C414yescomplemented
65#14268626—41no—
66#14268626—41no—
67#14268626—41no—
68#14268626—41no—
69#14268626—41no—
70#14268626C2×C414yescomplemented
71#14268624—41no—
72#14268624—41no—
73#14268624—41no—
74#14268624C2×C414yes—
75#14268624C2×C414yes—
76#14268624C2×C414yes—
77C4×Dic113—41no—
78C4×Dic113—41no—
79C4×Dic113C2×C414yescomplemented
80C22×C4×C113C2311yescharacteristic
81C22×C4×C113C2311yescharacteristic
82C22×C4×C113C2311yescharacteristic
83C22×C4×C113C2311yescharacteristic
84C22×C4×C113C2311yescharacteristic
85C22×C4×C113C2311yescharacteristic
86C22×C4×C113C2311yescharacteristic
87C4⋊C4×C113—41no—
88C4⋊C4×C113—41no—
89C4⋊C4×C113—41no—
90C4⋊C4×C113C2×C414yescomplemented
91C42×C113—41no—
92C23×C113C2411yescharacteristic
93C22×D113—21no—
94C22×D113—21no—
95C22×D113—21no—
96C22×D113—21no—
97C22×D113—21no—
98C22×D113—21no—
99C22×D113C22×C412yes—
100C2×C4×C113—21no—
101C2×C4×C113—21no—
102C2×C4×C113—21no—
103C2×C4×C113—21no—
104C2×C4×C113—21no—
105C2×C4×C113—21no—
106C2×C4×C113—21no—
107C2×C4×C113—21no—
108C2×C4×C113—21no—
109C2×C4×C113—21no—
110C2×C4×C113—21no—
111C2×C4×C113—21no—
112C2×C4×C113—21no—
113C2×C4×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113C22×C412yes—
119C2×C4×C113C22×C412yes—
120C2×C4×C113C22×C412yes—
121C2×Dic113—21no—
122C2×Dic113—21no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113—21no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113—21no—
135C2×Dic113—21no—
136C2×Dic113—21no—
137C2×Dic113—21no—
138C2×Dic113—21no—
139C2×Dic113C22×C412yes—
140C2×Dic113C22×C412yes—
141C2×Dic113C22×C412yes—
142C4×D113—44no—
143C22×C113C23×C411yescharacteristic
144C22×C113H(5,𝔽2)11yescharacteristic
145C22×C113H(5,𝔽2)11yescharacteristic
146C22×C113H(5,𝔽2)11yescharacteristic
147C22×C1132−1+411yescharacteristic
148C22×C1132−1+411yescharacteristic
149C22×C1132−1+411yescharacteristic
150C2×D113—22no—
151C2×D113—22no—
152C2×D113—22no—
153C2×D113—41no—
154C2×D113—41no—
155C2×D113—41no—
156C2×D113—41no—
157C4×C113—22no—
158C4×C113—22no—
159C4×C113—22no—
160C4×C113—41no—
161C4×C113—41no—
162C4×C113—41no—
163C4×C113—41no—
164Dic113—22no—
165Dic113—22no—
166Dic113—22no—
167Dic113—41no—
168Dic113—41no—
169Dic113—41no—
170Dic113—41no—
171C2×C113#52011yescharacteristic
172C2×C113#52011yescharacteristic
173C2×C113#52011yescharacteristic
174C2×C113#56011yescharacteristic
175C2×C113#56311yescharacteristic
176C2×C113#56311yescharacteristic
177C2×C113#56311yescharacteristic
178D113—42no—
179#2383—1131nomaximal, Sylow
180C113#238311yescharacteristic, complemented, Sylow
181C2×#126—1131no—
182#389—1131no—
183#389—1131no—
184#389D11311yescharacteristic, complemented
185#388—1131no—
186#388—1131no—
187#388—1131no—
188#387—1131no—
189#387—1131no—
190#387—1131no—
191#385—1131no—
192#385—1131no—
193#385—1131no—
194#384—1131no—
195#383—1131no—
196C23×C4—1131no—
197#126—1138no—
198C2×C4⋊C4—1131no—
199C2×C4⋊C4—1131no—
200C2×C4⋊C4—1131no—
201C2×C4⋊C4—1131no—
202C2×C4⋊C4—1131no—
203C2×C4⋊C4—1131no—
204C2×C4⋊C4—1131no—
205C2×C4⋊C4—1131no—
206C2×C4⋊C4C2×D11311yescharacteristic
207C2×C4⋊C4C2×D11311yescharacteristic
208C2×C4⋊C4C2×D11311yescharacteristic
209C2×C4⋊C4C2×D11311yescharacteristic
210C2×C22⋊C4—1131no—
211C2×C22⋊C4—1131no—
212C2×C22⋊C4—1131no—
213C2×C22⋊C4—1131no—
214C2×C22⋊C4—1131no—
215C2×C22⋊C4—1131no—
216C2×C42—1131no—
217C2×C42—1131no—
218C2×C42—1131no—
219C2×C42C2×D11311yescharacteristic
220#95—1131no—
221#95—1131no—
222#95—1131no—
223#95—1131no—
224#95—1131no—
225#95—1131no—
226#95—1131no—
227#95—1131no—
228#95—1131no—
229#95—1131no—
230#95C2×D11311yescharacteristic
231#95C2×D11311yescharacteristic
232C24—1131no—
233C22×C4—1131no—
234C22×C4—1131no—
235C22×C4—1131no—
236C22×C4—1131no—
237C22×C4—1131no—
238C22×C4—1131no—
239C22×C4—1131no—
240C22×C4—4521no—
241C22×C4—4521no—
242C22×C4—4521no—
243C22×C4C22×D11311yescharacteristic
244C22×C4C22×D11311yescharacteristic
245C22×C4C22×D11311yescharacteristic
246C22×C4C22×D11311yescharacteristic
247C22×C4C22×D11311yescharacteristic
248C22×C4C22×D11311yescharacteristic
249C22×C4C22×D11311yescharacteristic
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—1134no—
254C4⋊C4—1134no—
255C4⋊C4—4521no—
256C4⋊C4—4521no—
257C4⋊C4—4521no—
258C4⋊C4—4521no—
259C4⋊C4—4521no—
260C4⋊C4—4521no—
261C4⋊C4C4×D11314yescomplemented
262C22⋊C4—1134no—
263C22⋊C4—1134no—
264C22⋊C4—1134no—
265C22⋊C4—4521no—
266C22⋊C4—4521no—
267C22⋊C4—4521no—
268C42—41no—
269C42—1134no—
270C42—4521no—
271C42—4521no—
272C23—1132no—
273C23—2261no—
274C23—2261no—
275C23—2261no—
276C23—2261no—
277C23—2261no—
278C23—2261no—
279C23C23×D11311yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—1132no—
299C2×C4—1132no—
300C2×C4—1132no—
301C2×C4—4524no—
302C2×C4—2261no—
303C2×C4—2261no—
304C2×C4—2261no—
305C2×C4—2261no—
306C2×C4—2261no—
307C2×C4—2261no—
308C2×C4—2261no—
309C2×C4—2261no—
310C2×C4—2261no—
311C2×C4—2261no—
312C2×C4—2261no—
313C2×C4—2261no—
314C2×C4—2261no—
315C2×C4—2261no—
316C2×C4—2261no—
317C2×C4—2261no—
318C2×C4—2261no—
319C2×C4—2261no—
320C2×C4C2×C4×D11312yes—
321C2×C4C2×C4×D11312yes—
322C2×C4C2×C4×D11312yes—
323C22—4521no—
324C22—4521no—
325C22—4521no—
326C22—4521no—
327C22—2262no—
328C22—2262no—
329C22—2262no—
330C22C22×C4×D11311yescharacteristic
331C22#1681366711yescharacteristic
332C22#1681366711yescharacteristic
333C22#1681366811yescharacteristic
334C22#1681366911yescharacteristic
335C22#1681367011yescharacteristic
336C22#1681367011yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—4521no—
345C4—4521no—
346C4—4521no—
347C4—4521no—
348C4—2262no—
349C4—2262no—
350C4—2262no—
351C2—4522no—
352C2#2029907711yescharacteristic
353C2#2029907911yescharacteristic
354C2#2029908011yescharacteristic
355C2#2029933611yescharacteristic
356C2#2029934711yescharacteristic
357C2#2029934911yescharacteristic
358C2#2029935211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
Fitting#389×C113C2
socle, cosocleC23×C113C24
prime radicalC23×D113C23
hypercenter#389D113
hypocenterC113#2383
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
2. #20298494C2semidirect
3. #20298493C2semidirect
7. #20298484C2semidirect
8. #20298483C2semidirect
9. #20298482C2semidirect
13. #20298467C2semidirect
14. #20298465C2semidirect
15. #389×C113C2semidirect
17. #16813617C4semidirect
64. C4⋊Dic113C2×C4semidirect
70. #14268626C2×C4semidirect
79. C4×Dic113C2×C4semidirect
90. C4⋊C4×C113C2×C4semidirect
180. C113#2383semidirect
184. #389D113semidirect
261. C4⋊C4C4×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136172
#202984942
#202984932
#202984892
#202984882
#202984872
#202984842
#202984832
#202984822
#202984722
#202984692
#202984672
#202984652
#389×C1132
#2383113