Finite Group Databasebeta

← #28403040

Subgroups — #28403040

Order 14464.

388 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#20299296C211yesmaximal, characteristic, complemented
2#20299249C211yesmaximal, characteristic, complemented
3#20299005C211yesmaximal, characteristic, complemented
4#20298924C211yesmaximal, characteristic, complemented
5#20298918C211yesmaximal, characteristic, complemented
6#20298916C211yesmaximal, characteristic, complemented
7#20298911C211yesmaximal, characteristic, complemented
8#20298897C211yesmaximal, characteristic, complemented
9#20298887C211yesmaximal, characteristic, complemented
10#20298852C211yesmaximal, characteristic, complemented
11#20298834C211yesmaximal, characteristic, complemented
12#20298709C211yesmaximal, characteristic, complemented
13#20298669C211yesmaximal, characteristic, complemented
14#20298637C211yesmaximal, characteristic, complemented
15C2×#106×C113C211yesmaximal, characteristic, complemented
16C2×#14268647—21no—
17C2×D904C2211yescharacteristic
18C2×#14268630C2211yescharacteristic
19#16813621C2211yescharacteristic
20#16813617—21no—
21#16813613C2211yescharacteristic
22#16813607—21no—
23#16813607—21no—
24#16813605—21no—
25#16813600—21no—
26#16813597C2211yescharacteristic
27#16813597C2211yescharacteristic
28#16813596—21no—
29#16813596C2211yescharacteristic
30#16813596C2211yescharacteristic
31#16813584C2211yescharacteristic
32#16813584C2211yescharacteristic
33C4×C22⋊D113—21no—
34C4×C22⋊D113C2211yescharacteristic
35#16813580C2211yescharacteristic
36C4⋊C4×D113C2211yescharacteristic
37#16813556C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813553C2211yescharacteristic
41#16813553C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813544C2211yescharacteristic
44#16813544C2211yescharacteristic
45#16813542C2211yescharacteristic
46#16813542C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813532C2211yescharacteristic
52C22×C8×C113C2211yescharacteristic
53C2×C4⋊C4×C113C2211yescharacteristic
54C2×C4⋊C4×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56#106×C113C2211yescharacteristic
57#106×C113C2211yescharacteristic
58#106×C113C2211yescharacteristic
59#14268647—44no—
60C2×Dic226—21no—
61C2×D452—21no—
62C2×D452—21no—
63C2×D452C2311yescharacteristic
64C2×D452C2311yescharacteristic
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67C2×C22⋊D113D411yescharacteristic
68C2×C4×D113—21no—
69C2×C4×D113—21no—
70C2×C4×D113—21no—
71C2×C4×D113C2311yescharacteristic
72D904—22no—
73#14268630—22no—
74C2×#11744751C2311yescharacteristic
75C2×#11744751C2311yescharacteristic
76C4⋊Dic113—21no—
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626D411yescharacteristic
83C22⋊Dic113D411yescharacteristic
84#14268624—21no—
85#14268624—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624D411yescharacteristic
92C4×Dic113—21no—
93C4×Dic113C2311yescharacteristic
94C22×C4×C113—21no—
95C22×C4×C113—21no—
96C22×C4×C113C2311yescharacteristic
97C2×C8×C113—22no—
98C2×C8×C113C2311yescharacteristic
99C2×C8×C113C2311yescharacteristic
100C4⋊C4×C113—21no—
101C4⋊C4×C113—21no—
102C4⋊C4×C113C2311yescharacteristic
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C4⋊C4×C113C2311yescharacteristic
106C23×C113C2×D411yescharacteristic
107C22×D113—21no—
108C22×D113—21no—
109C22×D113C2×D411yescharacteristic
110C2×C4×C113—21no—
111C2×C4×C113—21no—
112C2×C4×C113—21no—
113C2×C4×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—42no—
117C2×C4×C113—81no—
118C2×C4×C113C2×D411yescharacteristic
119C2×C4×C113C2411yescharacteristic
120C22⋊D113—22no—
121C22⋊D113—42no—
122C22⋊D113—42no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113C2×D411yescharacteristic
126C2×Dic113C2×D411yescharacteristic
127C2×Dic113C2×D411yescharacteristic
128D452—21no—
129D452—21no—
130D452—21no—
131D452—21no—
132D452—42no—
133D452—81no—
134C4×D113—21no—
135C4×D113—21no—
136C4×D113—42no—
137C4×D113—42no—
138C4×D113—81no—
139Dic226—42no—
140C8×C113—21no—
141C8×C113#4112yescomplemented
142#11744751—21no—
143#11744751—21no—
144C22×C113—21no—
145C22×C113—21no—
146C22×C113AGL(1,ℤ/8)12yes—
147C22×C113C22×D411yescharacteristic
148C2×D113—21no—
149C2×D113—21no—
150C2×D113—21no—
151C2×D113—41no—
152C2×D113—41no—
153C2×D113—41no—
154C2×D113—41no—
155C2×D113—41no—
156C2×D113—41no—
157C4×C113—21no—
158C4×C113—41no—
159C4×C113—41no—
160C4×C113—41no—
161C4×C113—41no—
162C4×C113C2×#4111yescharacteristic
163C4×C1132−1+411yescharacteristic
164Dic113—21no—
165Dic113—21no—
166Dic113—21no—
167Dic113—41no—
168Dic113—41no—
169C2×C113—22no—
170C2×C113#54711yescharacteristic
171C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
172C2×C113#57711yescharacteristic
173D113—41no—
174D113—81no—
175D113—81no—
176#3345—1131nomaximal, Sylow
177C113#334511yescharacteristic, complemented, Sylow
178#553—1131no—
179#547—1131no—
180#501—1131no—
181#482—1131no—
182#481—1131no—
183#481—1131no—
184#480—1131no—
185#478—1131no—
186#476—1131no—
187#469—1131no—
188#466—1131no—
189#442—1131no—
190#435—1131no—
191#428—1131no—
192C2×#106D11311yescharacteristic, complemented
193C2×#41—2261no—
194C2×D8—1131no—
195C2×M16—1131no—
196C22×C8C2×D11311yescharacteristic
197C4⋊Q8—1131no—
198#126—2261no—
199#125—1131no—
200#123—2261no—
201#123—2261no—
202#123—2261no—
203C22⋊Q8—2261no—
204#121—1131no—
205#121—1131no—
206#121—1131no—
207#121—1131no—
208#121—2261no—
209C4×D4—1131no—
210C4×D4—1131no—
211C4×D4—1131no—
212C4×D4—2261no—
213#117—1131no—
214C2×C4⋊C4—1131no—
215C2×C4⋊C4C2×D11311yescharacteristic
216C2×C4⋊C4C2×D11311yescharacteristic
217#107—1131no—
218#107—1131no—
219#107—1131no—
220#106—1131no—
221#106—1131no—
222#106C2×D11311yescharacteristic
223#106C2×D11311yescharacteristic
224#106C2×D11311yescharacteristic
225#106C2×D11311yescharacteristic
226C4⋊C8—1131no—
227#102—1131no—
228#102—1131no—
229#102—1131no—
230#102—1131no—
231#102—1131no—
232#102—1131no—
233C22⋊C8—1131no—
234C22⋊C8—1131no—
235#97—1131no—
236#41—4524no—
237C2×Q8—2261no—
238C2×D4—1131no—
239C2×D4—1131no—
240C2×D4—1131no—
241C2×D4—2261no—
242C2×D4—2261no—
243C2×D4—2261no—
244C2×D4—2261no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—1131no—
248C22×C4—2261no—
249C22×C4—2261no—
250C22×C4—2261no—
251C22×C4C22×D11311yescharacteristic
252D8—2262no—
253M16—2262no—
254C2×C8—22no—
255C2×C8—1131no—
256C2×C8—1131no—
257C2×C8C22×D11311yescharacteristic
258C2×C8C22×D11311yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—21no—
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
270C4⋊C4C22×D11311yescharacteristic
271C4⋊C4C22×D11311yescharacteristic
272C22⋊C4—1131no—
273C22⋊C4—1131no—
274C22⋊C4—2261no—
275C22⋊C4—2261no—
276C22⋊C4—2261no—
277C22⋊C4—2261no—
278C22⋊C4—2261no—
279C22⋊C4—2261no—
280C22⋊C4—2261no—
281C42—1131no—
282C42—2261no—
283C23—1131no—
284C23—2261no—
285C23—2261no—
286C23D4×D11311yescharacteristic
287Q8—4522no—
288D4—9041no—
289D4—4522no—
290D4—4522no—
291D4—4522no—
292D4—2262no—
293D4—2261no—
294D4—2261no—
295D4—2261no—
296D4—2261no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—42no—
304C2×C4—81no—
305C2×C4—1131no—
306C2×C4—1131no—
307C2×C4—1131no—
308C2×C4—9041no—
309C2×C4—4522no—
310C2×C4—4522no—
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#1426864712yescomplemented
321C22—21no—
322C22—21no—
323C22—4521no—
324C22—4521no—
325C22—4521no—
326C22—4521no—
327C22—4521no—
328C22—4521no—
329C22—2261no—
330C22—2261no—
331C22—2261no—
332C22#1681364912yes—
333C22C2×D4×D11311yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—4521no—
340C4—4521no—
341C4—2261no—
342C4—2261no—
343C4—2261no—
344C4C2×#1426864711yescharacteristic
345C4#1681367011yescharacteristic
346C2—22no—
347C2—9041no—
348C2—9041no—
349C2—4521no—
350C2#2029924911yescharacteristic
351C2C2×#1681364911yescharacteristic
352C2#2029940411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#106×C113C2
socleC22×C113C22×D4
hypercenterC2×#106D113
hypocenterC113#3345
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
1. #20299296C2semidirect
2. #20299249C2semidirect
3. #20299005C2semidirect
4. #20298924C2semidirect
5. #20298918C2semidirect
6. #20298916C2semidirect
7. #20298911C2semidirect
8. #20298897C2semidirect
9. #20298887C2semidirect
10. #20298852C2semidirect
11. #20298834C2semidirect
12. #20298709C2semidirect
13. #20298669C2semidirect
14. #20298637C2semidirect
15. C2×#106×C113C2semidirect
141. C8×C113#41semidirect
177. C113#3345semidirect
192. C2×#106D113semidirect
320. C8#14268647semidirect

Maximal subgroups

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

subgroupindex
#202992962
#202992492
#202990052
#202989242
#202989182
#202989162
#202989112
#202988972
#202988872
#202988522
#202988342
#202987092
#202986692
#202986372
C2×#106×C1132
#3345113