Finite Group Databasebeta

← #28400527

Subgroups — #28400527

Order 14464.

418 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299164C211yesmaximal, characteristic
2#20299078C211yesmaximal, characteristic, complemented
3#20298924C211yesmaximal, characteristic, complemented
4#20298922C211yesmaximal, characteristic, complemented
5#20298921C211yesmaximal, characteristic, complemented
6#20298917C211yesmaximal, characteristic, complemented
7#20298915C211yesmaximal, characteristic, complemented
8#20298913C211yesmaximal, characteristic, complemented
9#20298909C211yesmaximal, characteristic, complemented
10#20298639C211yesmaximal, characteristic, complemented
11#20298633C211yesmaximal, characteristic, complemented
12#20298601C211yesmaximal, characteristic, complemented
13#102×D113C211yesmaximal, characteristic, complemented
14#20298563C211yesmaximal, characteristic, complemented
15#482×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×D4×D113C2211yescharacteristic
18C2×#14268630C2211yescharacteristic
19C2×C8×D113C2211yescharacteristic
20#16813618—21no—
21#16813608—21no—
22#16813597C2211yescharacteristic
23#16813596C2211yescharacteristic
24#16813593C2211yescharacteristic
25#16813592—21no—
26#16813590—21no—
27C4×Dic226—21no—
28C4×D452—21no—
29#16813582—21no—
30#16813582—21no—
31#16813580C2211yescharacteristic
32#16813580C2211yescharacteristic
33#16813580C2211yescharacteristic, complemented
34C2×C4⋊Dic113C2211yescharacteristic, complemented
35C4⋊C4×D113C2211yescharacteristic
36C4⋊C4×D113C2211yescharacteristic, complemented
37#16813555C2211yescharacteristic, complemented
38#16813555C2211yescharacteristic, complemented
39#16813555C2211yescharacteristic, complemented
40#16813554C2211yescharacteristic, complemented
41#16813554C2211yescharacteristic, complemented
42#16813553C2211yescharacteristic, complemented
43#16813544C2211yescharacteristic
44#16813544C2211yescharacteristic
45#16813543C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic, complemented
50#16813534C2211yescharacteristic, complemented
51#16813534C2211yescharacteristic, complemented
52#121×C113C2211yescharacteristic
53#117×C113C2211yescharacteristic, complemented
54#107×C113C2211yescharacteristic, complemented
55#106×C113C2211yescharacteristic, complemented
56#102×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60#14268647—22no—
61#14268647—22no—
62C2×Dic226D411yescharacteristic
63C2×D452—21no—
64C2×D452D411yescharacteristic
65C2×D452C2311yescharacteristic
66C2×C22⋊D113—21no—
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69C2×C22⋊D113D411yescharacteristic
70C2×C22⋊D113D411yescharacteristic
71D4×D113—22no—
72D4×D113—22no—
73C22×Dic113—21no—
74C2×C4×D113—21no—
75C2×C4×D113—21no—
76C2×C4×D113C2311yescharacteristic
77C2×C4×D113C2311yescharacteristic
78#14268630—22no—
79C2×#11744751C2311yescharacteristic
80C2×#11744751C2311yescharacteristic
81C8×D113—22no—
82C4⋊Dic113—21no—
83C4⋊Dic113C2311yescharacteristic
84C4⋊Dic113C2311yescharacteristic
85C4⋊Dic113C2311yescharacteristic
86#14268626—21no—
87#14268626—21no—
88C22⋊Dic113—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94C4×Dic113—21no—
95C4×Dic113—21no—
96C4×Dic113—21no—
97C2×D4×C113—21no—
98C2×D4×C113C2311yescharacteristic
99C22×C4×C113C2311yescharacteristic
100C2×C8×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C22⋊C4×C113—21no—
106C22⋊C4×C113—21no—
107C42×C113—21no—
108C23×C113—21no—
109C23×C113C2×D411yescharacteristic
110C22×D113—21no—
111C22×D113—42no—
112C22×D113—81no—
113C22×D113—81no—
114C22×D113C2×D411yescharacteristic
115C22×D113C2×D411yescharacteristic
116D4×C113—21no—
117D4×C113—21no—
118D4×C113—81no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2411yescharacteristic
126C22⋊D113—22no—
127C22⋊D113—22no—
128C22⋊D113—42no—
129C22⋊D113—81no—
130C22⋊D113—81no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113—81no—
135C2×Dic113C2×D411yescharacteristic
136C2×Dic113C2×D411yescharacteristic
137D452—22no—
138D452—21no—
139D452—21no—
140D452—81no—
141C4×D113—21no—
142C4×D113—21no—
143C4×D113—81no—
144C4×D113—81no—
145C4×D113#4112yes—
146C4×D113#4112yes—
147Dic226—22no—
148C8×C113—21no—
149C8×C113—21no—
150#11744751—21no—
151#11744751—21no—
152C22×C113—21no—
153C22×C113—21no—
154C22×C113—21no—
155C22×C113—41no—
156C22×C113—41no—
157C22×C113—41no—
158C22×C113C22×D411yescharacteristic
159C2×D113—21no—
160C2×D113—21no—
161C2×D113—21no—
162C2×D113—21no—
163C2×D113—21no—
164C2×D113—41no—
165C2×D113—41no—
166C2×D113—41no—
167C2×D113—84no—
168C2×D113#12312yes—
169C4×C113—21no—
170C4×C113—41no—
171C4×C113—41no—
172C4×C113—41no—
173C4×C113C2×#4111yescharacteristic
174C4×C113C2×#4111yescharacteristic
175Dic113—21no—
176Dic113—41no—
177Dic113—41no—
178Dic113—41no—
179Dic113#12312yes—
180C2×C113—41no—
181C2×C113—81no—
182C2×C113C2×#12311yescharacteristic
183C2×C113#57611yescharacteristic
184C2×C113#57711yescharacteristic
185D113—22no—
186D113—41no—
187D113—81no—
188#3096—1131nomaximal, Sylow
189C113#309611yescharacteristic, complemented, Sylow
190#535—1131no—
191#520—1131no—
192#482—1131no—
193#482—1131no—
194#482—1131no—
195#482D11311yescharacteristic, complemented
196#481—1131no—
197#481—1131no—
198#480—1131no—
199#480—1131no—
200#428—1131no—
201#427—1131no—
202#418—1131no—
203C2×#102—1131no—
204#408—1131no—
205C2×#41—1131no—
206C22×D4—1131no—
207C2×M16—1131no—
208C22×C8—1131no—
209#127—2261no—
210#124—2261no—
211#121—1131no—
212#121—1131no—
213#121—1131no—
214#121C2×D11311yescharacteristic
215#120—2261no—
216#120—2261no—
217C4×Q8—2261no—
218C4×D4—2261no—
219C4×D4—2261no—
220C4×D4—2261no—
221#117—1131no—
222#117—1131no—
223#117—1131no—
224#117C2×D11311yescharacteristic, complemented
225C2×C4⋊C4—1131no—
226C2×C4⋊C4—1131no—
227C2×C4⋊C4—1131no—
228#107—1131no—
229#107—1131no—
230#107—1131no—
231#107C2×D11311yescharacteristic, complemented
232#106—1131no—
233#106—1131no—
234#106—1131no—
235#106C2×D11311yescharacteristic, complemented
236#102—1131no—
237#102—1131no—
238#102—1131no—
239#102—1131no—
240#102—1131no—
241#102—1131no—
242#102C2×D11311yescharacteristic
243#102C2×D11311yescharacteristic
244C22⋊C8—1131no—
245C22⋊C8—1131no—
246C22⋊C8—1131no—
247C22⋊C8C2×D11311yescharacteristic, complemented
248C24—2261no—
249#41—2262no—
250#41—2262no—
251C2×Q8—1131no—
252C2×D4—21no—
253C2×D4—1131no—
254C2×D4—1131no—
255C2×D4—1131no—
256C2×D4—1131no—
257C2×D4—2261no—
258C2×D4—2262no—
259C2×D4—2262no—
260C2×D4—2261no—
261C2×D4—2261no—
262C2×D4—2261no—
263C2×D4C22×D11311yescharacteristic
264C22×C4—1131no—
265C22×C4—1131no—
266C22×C4—2261no—
267C22×C4—2261no—
268C22×C4—2261no—
269C22×C4C22×D11311yescharacteristic
270M16—2262no—
271C2×C8—1131no—
272C2×C8—1131no—
273C2×C8—2262no—
274C2×C8C22×D11311yescharacteristic
275C2×C8C22×D11311yescharacteristic
276C4⋊C4—1131no—
277C4⋊C4—1131no—
278C4⋊C4—1131no—
279C4⋊C4—2261no—
280C4⋊C4—2261no—
281C4⋊C4—2261no—
282C4⋊C4C22×D11311yescharacteristic
283C4⋊C4C22×D11311yescharacteristic
284C4⋊C4C22×D11311yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—2261no—
288C22⋊C4—2261no—
289C22⋊C4—2261no—
290C22⋊C4—2261no—
291C22⋊C4—2261no—
292C22⋊C4—2261no—
293C42—21no—
294C42—2261no—
295C42—2261no—
296C42—2261no—
297C23—21no—
298C23—1131no—
299C23—1131no—
300C23—9041no—
301C23—9041no—
302C23—4522no—
303C23—2261no—
304C23D4×D11311yescharacteristic
305Q8—2262no—
306D4—21no—
307D4—21no—
308D4—81no—
309D4—9041no—
310D4—9041no—
311D4—9041no—
312D4—4522no—
313D4—2262no—
314D4—2262no—
315D4—2262no—
316D4—2261no—
317D4—2261no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—1131no—
324C2×C4—1132no—
325C2×C4—1132no—
326C2×C4—1131no—
327C2×C4—9041no—
328C2×C4—9041no—
329C2×C4—9041no—
330C2×C4—2261no—
331C2×C4—2261no—
332C2×C4—2261no—
333C2×C4—2261no—
334C2×C4—2261no—
335C2×C4D4×D11311yescharacteristic
336C2×C4C23×D11311yescharacteristic
337C8—21no—
338C8—21no—
339C8—2261no—
340C8—2261no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—1132no—
348C22—9044no—
349C22—4521no—
350C22—4521no—
351C22—4521no—
352C22—2261no—
353C22—2261no—
354C22—2261no—
355C22—2261no—
356C22—2261no—
357C22C2×D4×D11311yescharacteristic
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—1132no—
363C4—4521no—
364C4—4521no—
365C4—4521no—
366C4—2261no—
367C4#41×D11311yescharacteristic
368C4#41×D11311yescharacteristic
369C2—41no—
370C2—81no—
371C2—9041no—
372C2—4521no—
373C2—2262no—
374C2#123×D11311yescharacteristic
375C2#2029940211yescharacteristic
376C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#482×C113C2
socleC22×C113C22×D4
prime radical#20299164C2
hypercenter#482D113
hypocenterC113#3096
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #20299078C2semidirect
3. #20298924C2semidirect
4. #20298922C2semidirect
5. #20298921C2semidirect
6. #20298917C2semidirect
7. #20298915C2semidirect
8. #20298913C2semidirect
9. #20298909C2semidirect
10. #20298639C2semidirect
11. #20298633C2semidirect
12. #20298601C2semidirect
13. #102×D113C2semidirect
14. #20298563C2semidirect
15. #482×C113C2semidirect
33. #16813580C22semidirect
34. C2×C4⋊Dic113C22semidirect
36. C4⋊C4×D113C22semidirect
37. #16813555C22semidirect
38. #16813555C22semidirect
39. #16813555C22semidirect
40. #16813554C22semidirect
41. #16813554C22semidirect
42. #16813553C22semidirect
49. C22⋊#11744751C22semidirect
50. #16813534C22semidirect
51. #16813534C22semidirect
53. #117×C113C22semidirect
54. #107×C113C22semidirect
55. #106×C113C22semidirect
58. C22⋊C8×C113C22semidirect
189. C113#3096semidirect
195. #482D113semidirect
224. #117C2×D113semidirect
231. #107C2×D113semidirect
235. #106C2×D113semidirect
247. C22⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991642
#202990782
#202989242
#202989222
#202989212
#202989172
#202989152
#202989132
#202989092
#202986392
#202986332
#202986012
#102×D1132
#202985632
#482×C1132
#3096113