Finite Group Databasebeta

← #28399022

Subgroups — #28399022

Order 14464.

774 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D113C211yesmaximal, characteristic
2C2×#16813630C211yesmaximal, characteristic, complemented
3C2×#16813628C211yesmaximal, characteristic, complemented
4#20298565C211yesmaximal, characteristic, complemented
5#20298563C212yesmaximal, complemented
6#20298563C212yesmaximal, complemented
7#20298561C211yesmaximal, characteristic, complemented
8#20298560C212yesmaximal, complemented
9C2×#16813534C211yesmaximal, characteristic, complemented
10C22⋊C8×D113C212yesmaximal, complemented
11#408×C113C211yesmaximal, characteristic, complemented
12C2×#14268648C411yescharacteristic
13C2×#14268647C2212yes—
14C2×#14268647C2211yescharacteristic
15C2×#14268646C411yescharacteristic
16C2×#14268646C412yes—
17#41×D113—24no—
18#41×D113—24no—
19C2×Q8×D113C411yescharacteristic
20C2×D4×D113C412yes—
21C2×D4×D113C411yescharacteristic
22C22×C4×D113C2212yes—
23C22×C4×D113C2211yescharacteristic
24#16813630—24no—
25#16813628—24no—
26C2×#14268631C2211yescharacteristic, complemented
27C2×#14268630C2212yescomplemented
28C2×#14268630C2212yescomplemented
29C22×#11744751C2211yescharacteristic, complemented
30C2×C8×D113C2212yescomplemented
31C2×C8×D113C2212yescomplemented
32C22⋊#11744751C2212yescomplemented
33C22⋊#11744751C2212yescomplemented
34#16813534C2211yescharacteristic
35#16813534C2212yes—
36#16813534C2211yescharacteristic
37#16813534C2211yescharacteristic, complemented
38#16813534C2211yescharacteristic, complemented
39#16813534C2212yescomplemented
40C2×#41×C113C2211yescharacteristic
41C2×M16×C113C2211yescharacteristic, complemented
42C22×C8×C113C2211yescharacteristic, complemented
43C22⋊C8×C113C2212yescomplemented
44C22⋊C8×C113C2212yescomplemented
45C23×D113C2×C411yescharacteristic
46C23×D113C2×C412yes—
47#14268648—24no—
48#14268647—24no—
49#14268647—24no—
50#14268647D414yes—
51#14268647D414yes—
52#14268646—28no—
53#14268646—24no—
54C2×Dic226C2×C412yes—
55C2×Dic226C2×C411yescharacteristic
56Q8×D113—24no—
57C2×D452C2×C412yes—
58C2×D452C2×C411yescharacteristic
59C2×C22⋊D113C2×C412yes—
60C2×C22⋊D113C2×C412yes—
61C2×C22⋊D113C2×C412yes—
62D4×D113—28no—
63D4×D113—24no—
64C22×Dic113C2×C411yescharacteristic
65C22×Dic113C2×C412yes—
66C2×C4×D113—22no—
67C2×C4×D113—22no—
68C2×C4×D113—24no—
69C2×C4×D113—24no—
70C2×C4×D113C2×C411yescharacteristic
71C2×C4×D113C2×C412yes—
72C2×C4×D113C2×C412yes—
73C2×C4×D113C2×C411yescharacteristic
74C2×C4×D113C2311yescharacteristic
75C2×C4×D113C2311yescharacteristic
76C2×C4×D113C2312yes—
77#14268631—22no—
78#14268630—24no—
79#14268630—24no—
80C2×#11744751—22no—
81C2×#11744751C2311yescharacteristic
82C2×#11744751C2312yes—
83C2×#11744751C2311yescharacteristic
84C8×D113—24no—
85C8×D113—24no—
86#41×C113—22no—
87#41×C113—22no—
88C2×Q8×C113C2×C411yescharacteristic
89C2×D4×C113C2×C412yes—
90C2×D4×C113C2×C411yescharacteristic
91C22×C4×C113C2312yes—
92C22×C4×C113C2311yescharacteristic
93M16×C113—22no—
94C2×C8×C113—22no—
95C2×C8×C113C2311yescharacteristic
96C2×C8×C113C2312yes—
97C2×C8×C113C2311yescharacteristic
98C23×C113C22×C412yes—
99C23×C113C22×C411yescharacteristic
100C22×D113—22no—
101C22×D113—24no—
102C22×D113—24no—
103C22×D113—22no—
104C22×D113—42no—
105C22×D113—41no—
106C22×D113C22×C411yescharacteristic
107C22×D113C22×C412yes—
108C22×D113C22×C411yescharacteristic
109Q8×C113—22no—
110D4×C113—24no—
111D4×C113—22no—
112C2×C4×C113—22no—
113C2×C4×C113—22no—
114C2×C4×C113C22×C412yes—
115C2×C4×C113C22×C411yescharacteristic
116C2×C4×C113C2×D412yes—
117C2×C4×C113C2×D412yes—
118C2×C4×C113C2411yescharacteristic
119C22⋊D113—24no—
120C22⋊D113—24no—
121C22⋊D113C22⋊C418yes—
122C2×Dic113—22no—
123C2×Dic113—24no—
124C2×Dic113C22×C411yescharacteristic
125C2×Dic113C22×C411yescharacteristic
126C2×Dic113C22×C412yes—
127D452—24no—
128D452C22⋊C414yes—
129C4×D113—24no—
130C4×D113—22no—
131C4×D113—22no—
132C4×D113—21no—
133C4×D113—21no—
134C4×D113—21no—
135C4×D113—21no—
136C4×D113—24no—
137C4×D113C2×D414yes—
138C4×D113C2×D414yes—
139Dic226—24no—
140Dic226C22⋊C414yes—
141C8×C113—21no—
142C8×C113—21no—
143C8×C113—22no—
144#11744751—21no—
145#11744751—22no—
146#11744751—21no—
147C22×C113—21no—
148C22×C113—21no—
149C22×C113—22no—
150C22×C113—22no—
151C22×C113—22no—
152C22×C113C2×C22⋊C412yes—
153C22×C113C23×C411yescharacteristic
154C2×D113—21no—
155C2×D113—22no—
156C2×D113—21no—
157C2×D113—22no—
158C2×D113—21no—
159C2×D113—21no—
160C2×D113—21no—
161C2×D113—48no—
162C2×D113—44no—
163C2×D113C2×C22⋊C414yes—
164C2×D113#13112yescomplemented
165C4×C113—22no—
166C4×C113C2×C22⋊C412yes—
167C4×C113C22×D411yescharacteristic
168C4×C113C22×D411yescharacteristic
169Dic113—21no—
170Dic113—21no—
171Dic113C2×C22⋊C414yes—
172C2×C113—22no—
173C2×C113—42no—
174C2×C113C22×C22⋊C411yescharacteristic
175C2×C113C2×#13111yescharacteristic
176C2×C113#56811yescharacteristic
177D113—22no—
178D113—24no—
179D113—41no—
180#2880—1131nomaximal, Sylow
181C113#288011yescharacteristic, complemented, Sylow
182C22×#41—1131no—
183C2×#131—1131no—
184C2×#131—1131no—
185#408—1131no—
186#408—1132no—
187#408—1132no—
188#408D11311yescharacteristic, complemented
189#407—1131no—
190#407—1132no—
191C2×C22⋊C8—1131no—
192C2×C22⋊C8—1132no—
193C2×#41—1131no—
194C2×#41—1132no—
195C2×#41—1131no—
196C2×#41—1131no—
197C2×#41—1132no—
198C2×#41—2264no—
199C2×#41—2264no—
200C2×#41C2×D11311yescharacteristic
201C22×Q8—1131no—
202C22×D4—1132no—
203C22×D4—1131no—
204C23×C4—1132no—
205C23×C4—1131no—
206#131—2264no—
207#131—2264no—
208C2×M16—1131no—
209C2×M16—1132no—
210C2×M16—1132no—
211C2×M16C2×D11311yescharacteristic, complemented
212C22×C8—1131no—
213C22×C8—1132no—
214C22×C8—1132no—
215C22×C8C2×D11311yescharacteristic, complemented
216C22⋊C8—1132no—
217C22⋊C8—1132no—
218C22⋊C8—1131no—
219C22⋊C8—1132no—
220C22⋊C8—1131no—
221C22⋊C8—1131no—
222C22⋊C8—1131no—
223C22⋊C8—1132no—
224C22⋊C8C2×D11312yescomplemented
225C22⋊C8C2×D11312yescomplemented
226C24—1132no—
227C24—1131no—
228#41—22no—
229#41—22no—
230#41—1134no—
231#41—1134no—
232#41—2264no—
233#41—2264no—
234#41—2268no—
235#41—2264no—
236#41—2264no—
237C2×Q8—1131no—
238C2×Q8—1132no—
239C2×Q8—2264no—
240C2×Q8C4×D11311yescharacteristic
241C2×D4—1132no—
242C2×D4—1132no—
243C2×D4—1132no—
244C2×D4—1131no—
245C2×D4—1132no—
246C2×D4—2268no—
247C2×D4—2264no—
248C2×D4C4×D11312yes—
249C2×D4C4×D11311yescharacteristic
250C22×C4—1132no—
251C22×C4—1132no—
252C22×C4—1131no—
253C22×C4—1132no—
254C22×C4—1131no—
255C22×C4—1132no—
256C22×C4—1131no—
257C22×C4—1131no—
258C22×C4—1131no—
259C22×C4—2264no—
260C22×C4—2264no—
261C22×C4—2262no—
262C22×C4—2262no—
263C22×C4C22×D11312yes—
264C22×C4C22×D11311yescharacteristic
265M16—22no—
266M16—2264no—
267M16—2264no—
268M16—2262no—
269C2×C8—22no—
270C2×C8—1131no—
271C2×C8—1132no—
272C2×C8—1131no—
273C2×C8—2264no—
274C2×C8—2264no—
275C2×C8—2262no—
276C2×C8C22×D11311yescharacteristic
277C2×C8C22×D11312yes—
278C2×C8C22×D11311yescharacteristic
279C23—1131no—
280C23—1132no—
281C23—1131no—
282C23—4521no—
283C23—4522no—
284C23—2264no—
285C23—2262no—
286C23—2264no—
287C23—2262no—
288C23C2×C4×D11312yes—
289C23C2×C4×D11311yescharacteristic
290Q8—22no—
291Q8—1134no—
292Q8—2264no—
293D4—24no—
294D4—22no—
295D4—1138no—
296D4—1134no—
297D4—2264no—
298D4—2264no—
299D4—2264no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—1132no—
303C2×C4—1134no—
304C2×C4—1134no—
305C2×C4—1131no—
306C2×C4—1131no—
307C2×C4—2264no—
308C2×C4—2264no—
309C2×C4—2264no—
310C2×C4—2262no—
311C2×C4—2262no—
312C2×C4—2262no—
313C2×C4—2261no—
314C2×C4—2261no—
315C2×C4—2261no—
316C2×C4—2261no—
317C2×C4C2×C4×D11312yes—
318C2×C4C2×C4×D11311yescharacteristic
319C2×C4D4×D11312yes—
320C2×C4D4×D11312yes—
321C2×C4C23×D11311yescharacteristic
322C8—21no—
323C8—21no—
324C8—22no—
325C8—2261no—
326C8—2262no—
327C8—2261no—
328C22—21no—
329C22—21no—
330C22—22no—
331C22—22no—
332C22—22no—
333C22—1134no—
334C22—1132no—
335C22—4524no—
336C22—4528no—
337C22—2261no—
338C22—2261no—
339C22—2261no—
340C22—2261no—
341C22—2262no—
342C22—2261no—
343C22—2262no—
344C22C22⋊C4×D11312yes—
345C22C22×C4×D11311yescharacteristic
346C4—22no—
347C4—1134no—
348C4—2261no—
349C4—2261no—
350C4C22⋊C4×D11312yes—
351C4C2×D4×D11311yescharacteristic
352C4C2×D4×D11311yescharacteristic
353C2—22no—
354C2—42no—
355C2—4521no—
356C2—2262no—
357C2—2264no—
358C2C2×C22⋊C4×D11311yescharacteristic
359C2#131×D11311yescharacteristic
360C2#2029936311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D113
commutator, socleC22×C113C23×C4
Fitting#408×C113C2
prime radicalC2×#41×D113C2
cosocleC2×C4×C113C24
hypercenter#408D113
hypocenterC113#2880
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
2. C2×#16813630C2semidirect
3. C2×#16813628C2semidirect
4. #20298565C2semidirect
5. #20298563C2semidirect
6. #20298563C2semidirect
7. #20298561C2semidirect
8. #20298560C2semidirect
9. C2×#16813534C2semidirect
10. C22⋊C8×D113C2semidirect
11. #408×C113C2semidirect
26. C2×#14268631C22semidirect
27. C2×#14268630C22semidirect
28. C2×#14268630C22semidirect
29. C22×#11744751C22semidirect
30. C2×C8×D113C22semidirect
31. C2×C8×D113C22semidirect
32. C22⋊#11744751C22semidirect
33. C22⋊#11744751C22semidirect
37. #16813534C22semidirect
38. #16813534C22semidirect
39. #16813534C22semidirect
41. C2×M16×C113C22semidirect
42. C22×C8×C113C22semidirect
43. C22⋊C8×C113C22semidirect
44. C22⋊C8×C113C22semidirect
164. C2×D113#131semidirect
181. C113#2880semidirect
188. #408D113semidirect
211. C2×M16C2×D113semidirect
215. C22×C8C2×D113semidirect
224. C22⋊C8C2×D113semidirect
225. C22⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D1132
C2×#168136302
C2×#168136282
#202985652
#202985632
#202985612
#202985602
C2×#168135342
C22⋊C8×D1132
#408×C1132
#2880113