Finite Group Databasebeta

← #28402380

Subgroups — #28402380

Order 14464.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299248C211yesmaximal, characteristic, complemented
2D4×C22⋊D113C211yesmaximal, characteristic, complemented
3#20298943C211yesmaximal, characteristic, complemented
4#20298912C211yesmaximal, characteristic, complemented
5#20298910C211yesmaximal, characteristic, complemented
6#20298876C211yesmaximal, characteristic, complemented
7#20298832C211yesmaximal, characteristic, complemented
8#20298831C211yesmaximal, characteristic, complemented
9#20298791C211yesmaximal, characteristic, complemented
10#20298730C211yesmaximal, characteristic, complemented
11D8×Dic113C211yesmaximal, characteristic, complemented
12#20298661C211yesmaximal, characteristic, complemented
13C2×#16813543C211yesmaximal, characteristic, complemented
14#102×D113C211yesmaximal, characteristic, complemented
15#447×C113C211yesmaximal, characteristic, complemented
16C2×#14268646—21no—
17C22×C22⋊D113—21no—
18C2×D4×D113C2211yescharacteristic
19C2×#14268632C2211yescharacteristic, complemented
20C22×#11744751C2211yescharacteristic, complemented
21C2×C8×D113C2211yescharacteristic, complemented
22#16813621C2211yescharacteristic, complemented
23#16813618C2211yescharacteristic
24#16813604—21no—
25#16813603—21no—
26#16813599—21no—
27#16813596C2211yescharacteristic
28#16813594—21no—
29#16813593C2211yescharacteristic
30#16813593C2211yescharacteristic, complemented
31#16813591—21no—
32#16813590—21no—
33D4×Dic113C2211yescharacteristic
34D4×Dic113C2211yescharacteristic, complemented
35C4×C22⋊D113C2211yescharacteristic
36C2×C4⋊Dic113C2211yescharacteristic, complemented
37C4⋊C4×D113C2211yescharacteristic, complemented
38#16813556C2211yescharacteristic, complemented
39#16813556C2211yescharacteristic, complemented
40#16813555C2211yescharacteristic, complemented
41#16813551C2211yescharacteristic, complemented
42#16813544C2211yescharacteristic, complemented
43#16813544C2211yescharacteristic, complemented
44#16813543C2211yescharacteristic
45#16813543C2211yescharacteristic
46#16813543C2211yescharacteristic, complemented
47#16813543C2211yescharacteristic, complemented
48#16813543C2211yescharacteristic, complemented
49#16813542C2211yescharacteristic, complemented
50#16813534C2211yescharacteristic, complemented
51C8×Dic113C2211yescharacteristic, complemented
52C22×D4×C113C2211yescharacteristic
53C2×D8×C113C2211yescharacteristic
54C2×D8×C113C2211yescharacteristic, complemented
55#121×C113C2211yescharacteristic, complemented
56#102×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic, complemented
58C22⋊C8×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60#14268646—44no—
61C2×Dic226—21no—
62C2×D452C2311yescharacteristic
63C2×C22⋊D113—21no—
64C2×C22⋊D113—21no—
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69C2×C22⋊D113—44no—
70C2×C22⋊D113D411yescharacteristic
71D4×D113—22no—
72D4×D113—41no—
73C22×Dic113—21no—
74C22×Dic113—21no—
75C22×Dic113—21no—
76C2×C4×D113—21no—
77C2×C4×D113C2311yescharacteristic
78#14268632—41no—
79C2×#11744751—41no—
80C2×#11744751C2311yescharacteristic
81C2×#11744751C2311yescharacteristic
82C8×D113—41no—
83C4⋊Dic113—21no—
84C4⋊Dic113C2311yescharacteristic
85C4⋊Dic113C2311yescharacteristic
86C4⋊Dic113C2311yescharacteristic
87#14268626—21no—
88#14268626—21no—
89#14268626D411yescharacteristic
90C22⋊Dic113—21no—
91C22⋊Dic113—21no—
92C22⋊Dic113—21no—
93C22⋊Dic113—21no—
94C22⋊Dic113D411yescharacteristic
95#14268624—21no—
96#14268624D411yescharacteristic
97C4×Dic113C2311yescharacteristic
98C24×C113—21no—
99C2×D4×C113—22no—
100C2×D4×C113—21no—
101C2×D4×C113—21no—
102C2×D4×C113—41no—
103C2×D4×C113C2311yescharacteristic
104C2×D4×C113C2311yescharacteristic
105C2×D4×C113C2311yescharacteristic
106C22×C4×C113C2311yescharacteristic
107D8×C113—22no—
108D8×C113—41no—
109C2×C8×C113C2311yescharacteristic
110C2×C8×C113C2311yescharacteristic
111C4⋊C4×C113C2311yescharacteristic
112C22⋊C4×C113—21no—
113C23×C113—21no—
114C23×C113—21no—
115C23×C113—21no—
116C23×C113—42no—
117C23×C113—42no—
118C23×C113—81no—
119C23×C113C2×D411yescharacteristic
120C22×D113—21no—
121C22×D113—42no—
122C22×D113—42no—
123C22×D113—81no—
124C22×D113C2×D411yescharacteristic
125D4×C113—21no—
126D4×C113—21no—
127D4×C113—21no—
128D4×C113—21no—
129D4×C113—21no—
130D4×C113—42no—
131D4×C113—42no—
132D4×C113#4112yescomplemented
133C2×C4×C113—21no—
134C2×C4×C113—21no—
135C2×C4×C113—21no—
136C2×C4×C113C2×D411yescharacteristic
137C2×C4×C113C2411yescharacteristic
138C22⋊D113—42no—
139C22⋊D113—42no—
140C22⋊D113—42no—
141C22⋊D113—42no—
142C22⋊D113—42no—
143C22⋊D113—81no—
144C22⋊D113D814yescomplemented
145C2×Dic113—21no—
146C2×Dic113—21no—
147C2×Dic113—21no—
148C2×Dic113—42no—
149C2×Dic113—42no—
150C2×Dic113—42no—
151C2×Dic113C2×D411yescharacteristic
152C2×Dic113C2×D411yescharacteristic
153C2×Dic113C2×D411yescharacteristic
154D452—21no—
155D452—21no—
156C4×D113—21no—
157C4×D113—21no—
158C4×D113—42no—
159Dic226—42no—
160C8×C113—21no—
161C8×C113—21no—
162#11744751—21no—
163#11744751—21no—
164C22×C113—21no—
165C22×C113—21no—
166C22×C113—22no—
167C22×C113—41no—
168C22×C113—41no—
169C22×C113—41no—
170C22×C113—41no—
171C22×C113—41no—
172C22×C113—41no—
173C22×C113—41no—
174C22×C113—41no—
175C22×C113—84no—
176C22×C113C2×D812yes—
177C22×C113C22×D411yescharacteristic
178C2×D113—21no—
179C2×D113—21no—
180C2×D113—41no—
181C2×D113—41no—
182C2×D113—41no—
183C2×D113—84no—
184C2×D113C2×D812yes—
185C4×C113—21no—
186C4×C113—41no—
187C4×C113C2×#4111yescharacteristic
188C4×C113H(5,𝔽2)11yescharacteristic
189Dic113—21no—
190Dic113—21no—
191Dic113—41no—
192Dic113—41no—
193Dic113—41no—
194Dic113C2×D812yes—
195C2×C113—22no—
196C2×C113—42no—
197C2×C113—81no—
198C2×C113—81no—
199C2×C113#54611yescharacteristic
200C2×C113C22×D811yescharacteristic
201C2×C113#57711yescharacteristic
202D113—22no—
203D113—81no—
204#3294—1131nomaximal, Sylow
205C113#329411yescharacteristic, complemented, Sylow
206#547—1131no—
207D42—1131no—
208#486—1131no—
209#480—1131no—
210#480—1131no—
211#474—1131no—
212#466—1131no—
213#466—1131no—
214#459—1131no—
215#447—1131no—
216#447D11311yescharacteristic, complemented
217C4×D8—1131no—
218C8×D4—1131no—
219C2×#102—1131no—
220C2×#102—1131no—
221C2×#41—2261no—
222C22×D4—1131no—
223C22×D4—2261no—
224C22×D4C2×D11311yescharacteristic
225C2×D8—1131no—
226C2×D8C2×D11311yescharacteristic
227C2×D8C2×D11311yescharacteristic, complemented
228C22×C8—1131no—
229C22×C8—1131no—
230C4⋊Q8—1131no—
231#127—1131no—
232#123—2261no—
233#123—2261no—
234C22⋊Q8—2261no—
235#121—1131no—
236#121—1131no—
237#121—1131no—
238#121—2261no—
239#121C2×D11311yescharacteristic, complemented
240#120—2261no—
241#120—2261no—
242C4×D4—1131no—
243C4×D4—1131no—
244C4×D4—1131no—
245C2×C4⋊C4—1131no—
246C2×C4⋊C4—1131no—
247#107—1131no—
248#107—1131no—
249#107—1131no—
250C4⋊C8—1131no—
251#102—1131no—
252#102—1131no—
253#102—1131no—
254#102—1131no—
255#102—1131no—
256#102—1131no—
257#102—1131no—
258#102—1131no—
259#102C2×D11311yescharacteristic
260#102C2×D11311yescharacteristic, complemented
261C22⋊C8—1131no—
262C22⋊C8C2×D11311yescharacteristic, complemented
263C4×C8—1131no—
264C24—21no—
265C24—2261no—
266#41—4524no—
267C2×Q8—2261no—
268C2×D4—22no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—1131no—
273C2×D4—1131no—
274C2×D4—4524no—
275C2×D4—4521no—
276C2×D4—2261no—
277C2×D4—2261no—
278C2×D4—2261no—
279C2×D4—2261no—
280C2×D4—2261no—
281C2×D4—2261no—
282C2×D4—2262no—
283C2×D4C22×D11311yescharacteristic
284C2×D4C22×D11311yescharacteristic
285C2×D4C22×D11311yescharacteristic
286C22×C4—1131no—
287C22×C4—2261no—
288C22×C4—2261no—
289C22×C4—2261no—
290C22×C4—2261no—
291C22×C4C22×D11311yescharacteristic
292D8—22no—
293D8—41no—
294D8—4521no—
295C2×C8—1131no—
296C2×C8—1131no—
297C2×C8—4521no—
298C2×C8—4521no—
299C2×C8C22×D11311yescharacteristic
300C2×C8C22×D11311yescharacteristic
301C4⋊C4—1131no—
302C4⋊C4—1131no—
303C4⋊C4—1131no—
304C4⋊C4—1131no—
305C4⋊C4—2261no—
306C4⋊C4—2261no—
307C4⋊C4—2261no—
308C4⋊C4C22×D11311yescharacteristic
309C22⋊C4—21no—
310C22⋊C4—1131no—
311C22⋊C4—1131no—
312C22⋊C4—2261no—
313C22⋊C4—2261no—
314C22⋊C4—2261no—
315C22⋊C4—2261no—
316C22⋊C4—2261no—
317C42—1131no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—42no—
322C23—42no—
323C23—81no—
324C23—1131no—
325C23—9041no—
326C23—4522no—
327C23—4522no—
328C23—2261no—
329C23D4×D11311yescharacteristic
330Q8—4522no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—42no—
337D4—42no—
338D4—1134no—
339D4—9041no—
340D4—4522no—
341D4—4522no—
342D4—4522no—
343D4—4522no—
344D4—4522no—
345D4—2261no—
346D4—2261no—
347D4#1426864612yescomplemented
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—1131no—
352C2×C4—1131no—
353C2×C4—1131no—
354C2×C4—4522no—
355C2×C4—4522no—
356C2×C4—4522no—
357C2×C4—4522no—
358C2×C4—2261no—
359C2×C4—2261no—
360C2×C4—2261no—
361C2×C4—2261no—
362C2×C4—2261no—
363C2×C4D4×D11311yescharacteristic
364C2×C4C23×D11311yescharacteristic
365C8—21no—
366C8—21no—
367C8—2261no—
368C8—2261no—
369C22—21no—
370C22—21no—
371C22—22no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—84no—
381C22—1132no—
382C22—9044no—
383C22—4521no—
384C22—4521no—
385C22—4521no—
386C22—2261no—
387C22—2261no—
388C22D8×D11312yes—
389C22C2×D4×D11311yescharacteristic
390C4—21no—
391C4—41no—
392C4—1132no—
393C4—4521no—
394C4—4521no—
395C4—4521no—
396C4—2261no—
397C4—2261no—
398C4C2×#1426864611yescharacteristic
399C4#1681366711yescharacteristic
400C2—22no—
401C2—42no—
402C2—81no—
403C2—81no—
404C2—9041no—
405C2—2262no—
406C2#2029923511yescharacteristic
407C2C2×D8×D11311yescharacteristic
408C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#447×C113C2
socleC22×C113C22×D4
hypercenter#447D113
hypocenterC113#3294
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #20299248C2semidirect
2. D4×C22⋊D113C2semidirect
3. #20298943C2semidirect
4. #20298912C2semidirect
5. #20298910C2semidirect
6. #20298876C2semidirect
7. #20298832C2semidirect
8. #20298831C2semidirect
9. #20298791C2semidirect
10. #20298730C2semidirect
11. D8×Dic113C2semidirect
12. #20298661C2semidirect
13. C2×#16813543C2semidirect
14. #102×D113C2semidirect
15. #447×C113C2semidirect
19. C2×#14268632C22semidirect
20. C22×#11744751C22semidirect
21. C2×C8×D113C22semidirect
22. #16813621C22semidirect
30. #16813593C22semidirect
34. D4×Dic113C22semidirect
36. C2×C4⋊Dic113C22semidirect
37. C4⋊C4×D113C22semidirect
38. #16813556C22semidirect
39. #16813556C22semidirect
40. #16813555C22semidirect
41. #16813551C22semidirect
42. #16813544C22semidirect
43. #16813544C22semidirect
46. #16813543C22semidirect
47. #16813543C22semidirect
48. #16813543C22semidirect
49. #16813542C22semidirect
50. #16813534C22semidirect
51. C8×Dic113C22semidirect
54. C2×D8×C113C22semidirect
55. #121×C113C22semidirect
57. #102×C113C22semidirect
58. C22⋊C8×C113C22semidirect
132. D4×C113#41semidirect
144. C22⋊D113D8semidirect
205. C113#3294semidirect
216. #447D113semidirect
227. C2×D8C2×D113semidirect
239. #121C2×D113semidirect
260. #102C2×D113semidirect
262. C22⋊C8C2×D113semidirect
347. D4#14268646semidirect

Maximal subgroups

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

subgroupindex
#202992482
D4×C22⋊D1132
#202989432
#202989122
#202989102
#202988762
#202988322
#202988312
#202987912
#202987302
D8×Dic1132
#202986612
C2×#168135432
#102×D1132
#447×C1132
#3294113