Finite Group Databasebeta

← #28393456

Subgroups — #28393456

Order 14464.

504 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×#16813578C211yesmaximal, characteristic
2#20298495C211yesmaximal, characteristic, complemented
3#20298493C211yesmaximal, characteristic, complemented
4#20298492C211yesmaximal, characteristic
5#20298491C211yesmaximal, characteristic
6#20298486C211yesmaximal, characteristic
7#20298463C211yesmaximal, characteristic, complemented
8#20298462C211yesmaximal, characteristic, complemented
9#20298456C211yesmaximal, characteristic
10C4×#14268626C211yesmaximal, characteristic, complemented
11#20298449C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic113C211yesmaximal, characteristic
13#20298444C211yesmaximal, characteristic, complemented
14#20298443C211yesmaximal, characteristic, complemented
15#388×C113C211yesmaximal, characteristic
16C23×Dic113C2211yescharacteristic
17#16813578C418yescomplemented
18C2×C4⋊Dic113C2211yescharacteristic
19C2×#14268626C2211yescharacteristic
20C2×#14268626C2211yescharacteristic
21C2×#14268626C2211yescharacteristic
22C2×#14268626C2211yescharacteristic
23C2×#14268626C2211yescharacteristic
24C2×#14268626C2211yescharacteristic
25C2×C22⋊Dic113C2211yescharacteristic
26C2×C22⋊Dic113C2211yescharacteristic
27C2×C22⋊Dic113C2211yescharacteristic
28C2×C4×Dic113C2211yescharacteristic
29C2×C4×Dic113C2211yescharacteristic
30C2×C4×Dic113C2211yescharacteristic
31C2×C4×Dic113C2211yescharacteristic
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×C22⋊C4×C113C2211yescharacteristic
47C2×C22⋊C4×C113C2211yescharacteristic
48C2×C22⋊C4×C113C2211yescharacteristic
49C2×C42×C113C2211yescharacteristic
50#95×C113C2211yescharacteristic
51#95×C113C2211yescharacteristic
52C22×Dic113—22no—
53C22×Dic113—22no—
54C22×Dic113C2×C414yes—
55C22×Dic113C2311yescharacteristic
56C22×Dic113C2311yescharacteristic
57C22×Dic113C2311yescharacteristic
58C22×Dic113C2311yescharacteristic
59C22×Dic113C2311yescharacteristic
60C22×Dic113C2311yescharacteristic
61C22×Dic113C2311yescharacteristic
62C22×Dic113C2311yescharacteristic
63C4⋊Dic113—41no—
64#14268626—22no—
65#14268626—22no—
66#14268626—41no—
67#14268626—41no—
68#14268626C2×C414yes—
69#14268626C2×C414yes—
70C22⋊Dic113—22no—
71C22⋊Dic113—41no—
72C22⋊Dic113C2×C414yes—
73C4×Dic113—22no—
74C4×Dic113—22no—
75C4×Dic113—22no—
76C4×Dic113—22no—
77C4×Dic113—22no—
78C4×Dic113C2×C414yes—
79C4×Dic113C2×C414yes—
80C24×C113C2311yescharacteristic
81C22×C4×C113C2311yescharacteristic
82C22×C4×C113C2311yescharacteristic
83C22×C4×C113C2311yescharacteristic
84C22×C4×C113C2311yescharacteristic
85C22×C4×C113C2311yescharacteristic
86C22×C4×C113C2311yescharacteristic
87C4⋊C4×C113—41no—
88C22⋊C4×C113—22no—
89C22⋊C4×C113—41no—
90C22⋊C4×C113C2×C414yes—
91C42×C113—22no—
92C23×C113—21no—
93C23×C113—21no—
94C23×C113—21no—
95C23×C113—21no—
96C23×C113—21no—
97C23×C113—21no—
98C23×C113C22×C412yes—
99C23×C113C2411yescharacteristic
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×C113C22×C412yes—
116C2×C4×C113C22×C412yes—
117C2×C4×C113#4112yes—
118C2×Dic113—21no—
119C2×Dic113—21no—
120C2×Dic113—21no—
121C2×Dic113—21no—
122C2×Dic113—21no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113—28no—
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×Dic113C22×C412yes—
137C2×Dic113C22×C412yes—
138C2×Dic113C22×C412yes—
139C2×Dic113C22×C412yes—
140C2×Dic113#4112yes—
141C2×Dic113#4112yes—
142C2×Dic113#4112yes—
143C22×C113—22no—
144C22×C113—22no—
145C22×C113—22no—
146C22×C113—41no—
147C22×C113—41no—
148C22×C113—41no—
149C22×C113—41no—
150C22×C113C23×C411yescharacteristic
151C22×C113C2×#4111yescharacteristic
152C22×C113C2×#4111yescharacteristic
153C22×C113C2×#4111yescharacteristic
154C22×C113C2×#4111yescharacteristic
155C22×C113H(5,𝔽2)11yescharacteristic
156C22×C1132−1+411yescharacteristic
157C4×C113—22no—
158C4×C113—22no—
159C4×C113—22no—
160C4×C113—41no—
161C4×C113—41no—
162C4×C113—41no—
163Dic113—22no—
164Dic113—22no—
165Dic113—22no—
166Dic113—22no—
167Dic113—41no—
168Dic113—41no—
169Dic113—41no—
170Dic113#11714yes—
171C2×C113—42no—
172C2×C113C2×#11711yescharacteristic
173C2×C113C4×#4111yescharacteristic
174C2×C113#52011yescharacteristic
175C2×C113#55211yescharacteristic
176C2×C113#55211yescharacteristic
177C2×C113#55511yescharacteristic
178C2×C113#55511yescharacteristic
179#2346—1131nomaximal, Sylow
180C113#234611yescharacteristic, complemented, Sylow
181C2×#117—1131no—
182#389—1131no—
183#389—1131no—
184#388—1131no—
185#388—1131no—
186#388—1131no—
187#388D11311yescharacteristic
188#382—1131no—
189#382—1131no—
190#380—1131no—
191C4×C4⋊C4—1131no—
192C4×C4⋊C4—1131no—
193C4×C22⋊C4—1131no—
194#376—1131no—
195#376—1131no—
196C23×C4—1131no—
197#117—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⋊C4C2×D11311yescharacteristic
206C2×C22⋊C4—1131no—
207C2×C22⋊C4—1131no—
208C2×C22⋊C4—1131no—
209C2×C22⋊C4C2×D11311yescharacteristic
210C2×C22⋊C4C2×D11311yescharacteristic
211C2×C22⋊C4C2×D11311yescharacteristic
212C2×C42—1131no—
213C2×C42—1131no—
214C2×C42—1131no—
215C2×C42—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
232C24C22×D11311yescharacteristic
233C22×C4—1131no—
234C22×C4—1134no—
235C22×C4—1131no—
236C22×C4—1131no—
237C22×C4—1131no—
238C22×C4—1131no—
239C22×C4—1131no—
240C22×C4—1131no—
241C22×C4—1131no—
242C22×C4—2262no—
243C22×C4—2262no—
244C22×C4C22×D11311yescharacteristic
245C22×C4C22×D11311yescharacteristic
246C22×C4C22×D11311yescharacteristic
247C22×C4C22×D11311yescharacteristic
248C22×C4C22×D11311yescharacteristic
249C22×C4C22×D11311yescharacteristic
250C4⋊C4—41no—
251C4⋊C4—1134no—
252C4⋊C4—1134no—
253C4⋊C4—4521no—
254C4⋊C4—4521no—
255C4⋊C4—4521no—
256C4⋊C4—2262no—
257C4⋊C4—2262no—
258C22⋊C4—22no—
259C22⋊C4—41no—
260C22⋊C4—1134no—
261C22⋊C4—4521no—
262C22⋊C4—2262no—
263C22⋊C4C4×D11314yes—
264C42—22no—
265C42—1134no—
266C42—1134no—
267C42—2262no—
268C42—2262no—
269C42—2262no—
270C42—2262no—
271C42—2262no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23C2×C4×D11312yes—
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—1132no—
296C2×C4—1132no—
297C2×C4—1132no—
298C2×C4—1132no—
299C2×C4—1132no—
300C2×C4—1132no—
301C2×C4—1132no—
302C2×C4—2268no—
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×C4#1426864612yes—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22C22×C4×D11311yescharacteristic
331C22#41×D11311yescharacteristic
332C22#41×D11311yescharacteristic
333C22#41×D11311yescharacteristic
334C22C2×#1426864611yescharacteristic
335C22#1681366711yescharacteristic
336C22#1681366911yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—1134no—
344C4—4521no—
345C4—4521no—
346C4—4521no—
347C4—2262no—
348C4—2262no—
349C4—2262no—
350C4—2262no—
351C2—42no—
352C2#117×D11311yescharacteristic
353C2C4×#1426864611yescharacteristic
354C2#2029907711yescharacteristic
355C2#2029928411yescharacteristic
356C2#2029928511yescharacteristic
357C2#2029931011yescharacteristic
358C2#2029931211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
Fitting#388×C113C2
socle, cosocleC23×C113C24
prime radicalC24×C113C23
hypercenter#388D113
hypocenterC113#2346
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #20298495C2semidirect
3. #20298493C2semidirect
7. #20298463C2semidirect
8. #20298462C2semidirect
10. C4×#14268626C2semidirect
11. #20298449C2semidirect
13. #20298444C2semidirect
14. #20298443C2semidirect
17. #16813578C4semidirect
180. C113#2346semidirect

Maximal subgroups

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

subgroupindex
C2×#168135782
#202984952
#202984932
#202984922
#202984912
#202984862
#202984632
#202984622
#202984562
C4×#142686262
#202984492
C22⋊C4×Dic1132
#202984442
#202984432
#388×C1132
#2346113