Finite Group Databasebeta

← #28403164

Subgroups — #28403164

Order 14464.

386 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299312C211yesmaximal, characteristic, complemented
2#20299248C211yesmaximal, characteristic, complemented
3#20298995C211yesmaximal, characteristic, complemented
4#20298920C211yesmaximal, characteristic, complemented
5#20298919C211yesmaximal, characteristic, complemented
6#20298915C211yesmaximal, characteristic, complemented
7#20298914C211yesmaximal, characteristic, complemented
8#20298886C211yesmaximal, characteristic, complemented
9#20298876C211yesmaximal, characteristic, complemented
10#20298848C211yesmaximal, characteristic, complemented
11D8×Dic113C211yesmaximal, characteristic, complemented
12#20298674C211yesmaximal, characteristic, complemented
13#20298640C211yesmaximal, characteristic, complemented
14#20298637C211yesmaximal, characteristic, complemented
15#469×C113C211yesmaximal, characteristic, complemented
16C2×#14268646—21no—
17C2×#14268630C2211yescharacteristic
18#16813621C2211yescharacteristic
19#16813621C2211yescharacteristic
20#16813609—21no—
21#16813608—21no—
22#16813604—21no—
23#16813603—21no—
24#16813599—21no—
25#16813594—21no—
26#16813593C2211yescharacteristic
27#16813593C2211yescharacteristic
28D4×Dic113C2211yescharacteristic
29D4×Dic113C2211yescharacteristic
30C4×C22⋊D113C2211yescharacteristic
31#16813581C2211yescharacteristic
32#16813580C2211yescharacteristic
33#16813578—21no—
34C2×C4⋊Dic113C2211yescharacteristic
35C4⋊C4×D113C2211yescharacteristic
36#16813556C2211yescharacteristic
37#16813556C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813554C2211yescharacteristic
40#16813554C2211yescharacteristic
41#16813553C2211yescharacteristic
42#16813553C2211yescharacteristic
43#16813553C2211yescharacteristic
44#16813551C2211yescharacteristic
45#16813543C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813543C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×D8×C113C2211yescharacteristic
53C2×M16×C113C2211yescharacteristic
54#121×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic
56#106×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59#14268646—44no—
60C2×Dic226—21no—
61C2×Dic226—21no—
62C2×C22⋊D113—21no—
63C2×C22⋊D113—21no—
64C2×C22⋊D113D411yescharacteristic
65C22×Dic113—21no—
66C22×Dic113—21no—
67C22×Dic113—21no—
68C2×C4×D113—21no—
69C2×C4×D113C2311yescharacteristic
70#14268630—22no—
71C2×#11744751C2311yescharacteristic
72C2×#11744751C2311yescharacteristic
73C4⋊Dic113—21no—
74C4⋊Dic113C2311yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77C4⋊Dic113C2311yescharacteristic
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626D411yescharacteristic
82C22⋊Dic113—21no—
83C22⋊Dic113—21no—
84C22⋊Dic113—21no—
85C22⋊Dic113—21no—
86C22⋊Dic113—21no—
87C22⋊Dic113D411yescharacteristic
88#14268624—21no—
89#14268624D411yescharacteristic
90C4×Dic113—21no—
91C4×Dic113—21no—
92C4×Dic113C2311yescharacteristic
93C2×D4×C113—21no—
94C2×D4×C113—21no—
95C2×D4×C113C2311yescharacteristic
96C2×D4×C113C2311yescharacteristic
97C22×C4×C113C2311yescharacteristic
98D8×C113—22no—
99M16×C113—22no—
100C2×C8×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C4⋊C4×C113C2311yescharacteristic
104C22⋊C4×C113—21no—
105C22⋊C4×C113—21no—
106C23×C113—21no—
107C23×C113—21no—
108C23×C113C2×D411yescharacteristic
109C22×D113C2×D411yescharacteristic
110D4×C113—21no—
111D4×C113—21no—
112D4×C113—21no—
113D4×C113—21no—
114D4×C113—42no—
115D4×C113—81no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113C2×D411yescharacteristic
121C2×C4×C113C2411yescharacteristic
122C22⋊D113—22no—
123C22⋊D113—42no—
124C22⋊D113—81no—
125C2×Dic113—21no—
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113—42no—
130C2×Dic113—42no—
131C2×Dic113—42no—
132C2×Dic113C2×D411yescharacteristic
133C2×Dic113C2×D411yescharacteristic
134C2×Dic113C2×D411yescharacteristic
135C4×D113—21no—
136C4×D113—21no—
137C4×D113—42no—
138Dic226—42no—
139Dic226—81no—
140C8×C113—21no—
141C8×C113#4112yescomplemented
142#11744751—21no—
143#11744751—21no—
144C22×C113—21no—
145C22×C113—21no—
146C22×C113—21no—
147C22×C113—41no—
148C22×C113—41no—
149C22×C113—41no—
150C22×C113—41no—
151C22×C113—41no—
152C22×C113—41no—
153C22×C113C22×D411yescharacteristic
154C2×D113—21no—
155C2×D113—21no—
156C2×D113—21no—
157C4×C113—21no—
158C4×C113—41no—
159C4×C113—41no—
160C4×C113C2×#4111yescharacteristic
161C4×C1132−1+411yescharacteristic
162Dic113—21no—
163Dic113—21no—
164Dic113—41no—
165Dic113—41no—
166Dic113—41no—
167Dic113—41no—
168Dic113AGL(1,ℤ/8)12yes—
169C2×C113—41no—
170C2×C113—81no—
171C2×C113—81no—
172C2×C113#54711yescharacteristic
173C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
174C2×C113#57711yescharacteristic
175D113—41no—
176#3354—1131nomaximal, Sylow
177C113#335411yescharacteristic, complemented, Sylow
178#555—1131no—
179#547—1131no—
180#498—1131no—
181#482—1131no—
182#482—1131no—
183#481—1131no—
184#481—1131no—
185#476—1131no—
186#474—1131no—
187#469—1131no—
188#469D11311yescharacteristic, complemented
189C4×D8—1131no—
190#436—1131no—
191#428—1131no—
192#428—1131no—
193C2×#41—2261no—
194C2×D8C2×D11311yescharacteristic
195C2×M16—1131no—
196C2×M16C2×D11311yescharacteristic
197C4⋊Q8—1131no—
198C4⋊Q8—1131no—
199#124—2261no—
200#124—2261no—
201#123—2261no—
202#123—2261no—
203C22⋊Q8—2261no—
204#121—1131no—
205#121—1131no—
206#121—2261no—
207#121C2×D11311yescharacteristic
208#121C2×D11311yescharacteristic
209C4×D4—1131no—
210C4×D4—1131no—
211C4×D4—1131no—
212#117—1131no—
213#117—1131no—
214#117—2261no—
215C2×C4⋊C4—1131no—
216C2×C4⋊C4—1131no—
217#107—1131no—
218#107—1131no—
219#107—1131no—
220#106—1131no—
221#106—1131no—
222#106—1131no—
223#106—1131no—
224#106—1131no—
225#106C2×D11311yescharacteristic
226C4⋊C8—1131no—
227#102—1131no—
228#102—1131no—
229#102—1131no—
230#102—1131no—
231#102C2×D11311yescharacteristic
232#102C2×D11311yescharacteristic
233C22⋊C8—1131no—
234C22⋊C8—1131no—
235C4×C8—1131no—
236#41—4524no—
237C2×Q8—2261no—
238C2×Q8—2261no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—1131no—
242C2×D4—2261no—
243C2×D4—2261no—
244C2×D4C22×D11311yescharacteristic
245C2×D4C22×D11311yescharacteristic
246C22×C4—1131no—
247C22×C4—2261no—
248C22×C4—2261no—
249C22×C4—2261no—
250C22×C4—2261no—
251C22×C4C22×D11311yescharacteristic
252D8—22no—
253M16—22no—
254M16—2262no—
255C2×C8—1131no—
256C2×C8—1131no—
257C2×C8C22×D11311yescharacteristic
258C2×C8C22×D11311yescharacteristic
259C4⋊C4—1131no—
260C4⋊C4—1131no—
261C4⋊C4—1131no—
262C4⋊C4—1131no—
263C4⋊C4—1131no—
264C4⋊C4—2261no—
265C4⋊C4—2261no—
266C4⋊C4—2261no—
267C4⋊C4—2261no—
268C4⋊C4C22×D11311yescharacteristic
269C4⋊C4C22×D11311yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—1131no—
273C22⋊C4—1131no—
274C22⋊C4—2261no—
275C22⋊C4—2261no—
276C22⋊C4—2261no—
277C22⋊C4—2261no—
278C22⋊C4—2261no—
279C22⋊C4—2261no—
280C42—1131no—
281C42—2261no—
282C42—2261no—
283C23—21no—
284C23—21no—
285C23—1131no—
286C23D4×D11311yescharacteristic
287Q8—9041no—
288Q8—4522no—
289D4—21no—
290D4—21no—
291D4—21no—
292D4—21no—
293D4—42no—
294D4—81no—
295D4—9041no—
296D4—4522no—
297D4—2262no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—1131no—
303C2×C4—1131no—
304C2×C4—1131no—
305C2×C4—4522no—
306C2×C4—4522no—
307C2×C4—4522no—
308C2×C4—4522no—
309C2×C4—2261no—
310C2×C4—2261no—
311C2×C4—2261no—
312C2×C4—2261no—
313C2×C4—2261no—
314C2×C4—2261no—
315C2×C4D4×D11311yescharacteristic
316C2×C4C23×D11311yescharacteristic
317C8—21no—
318C8—2261no—
319C8—2261no—
320C8#1426864612yescomplemented
321C22—21no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—2261no—
331C22—2261no—
332C22—2261no—
333C22C2×D4×D11311yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—1132no—
338C4—4521no—
339C4—4521no—
340C4—4521no—
341C4—4521no—
342C4—2261no—
343C4—2261no—
344C4C2×#1426864611yescharacteristic
345C4#1681366911yescharacteristic
346C2—41no—
347C2—81no—
348C2—81no—
349C2—4521no—
350C2#2029924811yescharacteristic
351C2AGL(1,ℤ/8)×D11311yescharacteristic
352C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#469×C113C2
socleC22×C113C22×D4
hypercenter#469D113
hypocenterC113#3354
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #20299312C2semidirect
2. #20299248C2semidirect
3. #20298995C2semidirect
4. #20298920C2semidirect
5. #20298919C2semidirect
6. #20298915C2semidirect
7. #20298914C2semidirect
8. #20298886C2semidirect
9. #20298876C2semidirect
10. #20298848C2semidirect
11. D8×Dic113C2semidirect
12. #20298674C2semidirect
13. #20298640C2semidirect
14. #20298637C2semidirect
15. #469×C113C2semidirect
141. C8×C113#41semidirect
177. C113#3354semidirect
188. #469D113semidirect
320. C8#14268646semidirect

Maximal subgroups

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

subgroupindex
#202993122
#202992482
#202989952
#202989202
#202989192
#202989152
#202989142
#202988862
#202988762
#202988482
D8×Dic1132
#202986742
#202986402
#202986372
#469×C1132
#3354113