Finite Group Databasebeta

← #28400743

Subgroups — #28400743

Order 14464.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299130C211yesmaximal, characteristic
2C4×Q8×D113C211yesmaximal, characteristic, complemented
3#20298935C211yesmaximal, characteristic, complemented
4#20298915C211yesmaximal, characteristic
5#20298904C211yesmaximal, characteristic, complemented
6#20298903C211yesmaximal, characteristic, complemented
7#20298819C211yesmaximal, characteristic, complemented
8#20298818C211yesmaximal, characteristic, complemented
9#20298755C211yesmaximal, characteristic, complemented
10#20298735C211yesmaximal, characteristic
11#20298706C211yesmaximal, characteristic, complemented
12#20298703C211yesmaximal, characteristic, complemented
13#20298698C211yesmaximal, characteristic, complemented
14#20298653C211yesmaximal, characteristic, complemented
15#440×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic
17C2×Dic452C2211yescharacteristic
18C2×#14268637C2211yescharacteristic
19C2×#14268635C2211yescharacteristic
20#16813615—21no—
21#16813613C2211yescharacteristic
22#16813609C2211yescharacteristic
23#16813604—21no—
24#16813602C2211yescharacteristic
25#16813593C2211yescharacteristic
26Q8×Dic113C2211yescharacteristic
27C4×Dic226—21no—
28C4×Dic226C2211yescharacteristic
29C4×Dic226C2211yescharacteristic
30#16813587—21no—
31#16813587C2211yescharacteristic
32C4×C22⋊D113—21no—
33#16813581—21no—
34C4⋊C4×D113—21no—
35C4⋊C4×D113C2211yescharacteristic
36C42×D113—21no—
37C42×D113C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813554C2211yescharacteristic
40#16813553C2211yescharacteristic
41#16813551C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813543C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813533C2211yescharacteristic
52C2×SD16×C113C2211yescharacteristic
53C4×Q8×C113C2211yescharacteristic
54C4×D4×C113C2211yescharacteristic
55#107×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#97×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226C2311yescharacteristic
61C2×Dic226C2311yescharacteristic
62Q8×D113—22no—
63Q8×D113—22no—
64C2×C22⋊D113—21no—
65C2×C4×D113—21no—
66C2×C4×D113—21no—
67C2×C4×D113D411yescharacteristic
68C2×C4×D113D411yescharacteristic
69C2×C4×D113C2311yescharacteristic
70Dic452—22no—
71#14268637—22no—
72#14268635—22no—
73C2×#11744751C2311yescharacteristic
74C2×#11744751C2311yescharacteristic
75C4⋊Dic113—21no—
76C4⋊Dic113—21no—
77C4⋊Dic113—21no—
78C4⋊Dic113C2311yescharacteristic
79C4⋊Dic113C2311yescharacteristic
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85C22⋊Dic113—21no—
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88#14268624—21no—
89C4×Dic113—21no—
90C4×Dic113—21no—
91C4×Dic113—21no—
92C4×Dic113—21no—
93C4×Dic113D411yescharacteristic
94C4×Dic113D411yescharacteristic
95C4×Dic113C2311yescharacteristic
96C2×Q8×C113C2311yescharacteristic
97C2×D4×C113C2311yescharacteristic
98C22×C4×C113—21no—
99SD16×C113—22no—
100C2×C8×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C4⋊C4×C113—21no—
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C22⋊C4×C113—21no—
106C42×C113—21no—
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C22×D113C2×D411yescharacteristic
110Q8×C113—21no—
111Q8×C113#4112yes—
112D4×C113—21no—
113D4×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—42no—
118C2×C4×C113C2×D411yescharacteristic
119C2×C4×C113C2×D411yescharacteristic
120C2×C4×C113C2411yescharacteristic
121C22⋊D113—42no—
122C2×Dic113—21no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113C2×D411yescharacteristic
127C2×Dic113C2×D411yescharacteristic
128C2×Dic113C2×D411yescharacteristic
129C4×D113—24no—
130C4×D113—22no—
131C4×D113—21no—
132C4×D113—21no—
133C4×D113—41no—
134C4×D113—42no—
135Dic226—24no—
136Dic226—21no—
137Dic226—21no—
138Dic226—21no—
139Dic226#4112yes—
140C8×C113—21no—
141C8×C113—21no—
142#11744751—21no—
143#11744751—21no—
144C22×C113—41no—
145C22×C113—41no—
146C22×C113—41no—
147C22×C113C22×D411yescharacteristic
148C2×D113—21no—
149C2×D113—21no—
150C2×D113#13712yes—
151C4×C113—22no—
152C4×C113—21no—
153C4×C113—21no—
154C4×C113—41no—
155C4×C113—41no—
156C4×C113C2×#4111yescharacteristic
157C4×C113C2×#4111yescharacteristic
158Dic113—21no—
159Dic113—22no—
160Dic113—21no—
161Dic113—21no—
162Dic113—41no—
163Dic113—41no—
164Dic113—41no—
165C2×C113—81no—
166C2×C113#52511yescharacteristic
167C2×C113C2×#13711yescharacteristic
168C2×C113#57511yescharacteristic
169D113—22no—
170#3117—1131nomaximal, Sylow
171C113#311711yescharacteristic, complemented, Sylow
172#529—1131no—
173C2×C4×Q8—1131no—
174#484—1131no—
175#481—1131no—
176#479—1131no—
177#479—1131no—
178#464—1131no—
179#464—1131no—
180#451—1131no—
181#448—1131no—
182#441—1131no—
183#441—1131no—
184#440—1131no—
185#440D11311yescharacteristic, complemented
186#432—1131no—
187C22×Q8—1131no—
188C2×Q16—1131no—
189C2×Q16—1131no—
190C2×SD16—1131no—
191C2×SD16C2×D11311yescharacteristic
192#126—2261no—
193#125—1131no—
194#124—1131no—
195#123—2261no—
196C22⋊Q8—1131no—
197#121—1131no—
198C4×Q8—1131no—
199C4×Q8—1131no—
200C4×Q8—1131no—
201C4×Q8—1131no—
202C4×Q8—2261no—
203C4×Q8—2261no—
204C4×Q8C2×D11311yescharacteristic
205C4×D4—2261no—
206C4×D4C2×D11311yescharacteristic
207#117—2261no—
208C2×C4⋊C4—1131no—
209C2×C4⋊C4—2261no—
210C2×C42—1131no—
211C2×C42—2261no—
212#107—1131no—
213#107C2×D11311yescharacteristic
214#106—1131no—
215#106—1131no—
216C4⋊C8—1131no—
217C4⋊C8—1131no—
218#103—1131no—
219#103—1131no—
220#103—1131no—
221#103—1131no—
222#103—1131no—
223#103C2×D11311yescharacteristic
224#102—1131no—
225#102C2×D11311yescharacteristic
226C22⋊C8—1131no—
227C22⋊C8—1131no—
228#97—1131no—
229#97C2×D11311yescharacteristic
230C2×Q8—1131no—
231C2×Q8—1131no—
232C2×Q8—2261no—
233C2×Q8—2262no—
234C2×Q8—2262no—
235C2×Q8C22×D11311yescharacteristic
236C2×D4—2261no—
237C2×D4C22×D11311yescharacteristic
238C22×C4—21no—
239C22×C4—1131no—
240C22×C4—1131no—
241C22×C4—1131no—
242C22×C4—2261no—
243C22×C4—2261no—
244Q16—2262no—
245Q16—2262no—
246SD16—22no—
247SD16—2262no—
248C2×C8—1131no—
249C2×C8—1131no—
250C2×C8C22×D11311yescharacteristic
251C2×C8C22×D11311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—1131no—
254C4⋊C4—1131no—
255C4⋊C4—2261no—
256C4⋊C4—2261no—
257C4⋊C4—2261no—
258C4⋊C4—2261no—
259C4⋊C4—2261no—
260C4⋊C4—2261no—
261C4⋊C4—2261no—
262C4⋊C4—2261no—
263C4⋊C4C22×D11311yescharacteristic
264C4⋊C4C22×D11311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—2261no—
267C22⋊C4—2261no—
268C22⋊C4—2261no—
269C22⋊C4—2261no—
270C42—21no—
271C42—1131no—
272C42—1131no—
273C42—1131no—
274C42—2261no—
275C42—2261no—
276C42—2261no—
277C42—2261no—
278C42C22×D11311yescharacteristic
279C23—21no—
280C23—1131no—
281Q8—21no—
282Q8—1132no—
283Q8—2264no—
284Q8—2261no—
285Q8—2261no—
286Q8—2261no—
287Q8#1426864712yes—
288D4—21no—
289D4—21no—
290D4—4522no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—1131no—
296C2×C4—1131no—
297C2×C4—1131no—
298C2×C4—4521no—
299C2×C4—4522no—
300C2×C4—2262no—
301C2×C4—2264no—
302C2×C4—2261no—
303C2×C4—2261no—
304C2×C4—2261no—
305C2×C4—2261no—
306C2×C4—2261no—
307C2×C4—2261no—
308C2×C4D4×D11311yescharacteristic
309C2×C4D4×D11311yescharacteristic
310C2×C4C23×D11311yescharacteristic
311C8—21no—
312C8—21no—
313C8—2261no—
314C8—2261no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—1132no—
319C22—2261no—
320C22—2261no—
321C22C2×D4×D11311yescharacteristic
322C4—22no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—4521no—
328C4—4521no—
329C4—4521no—
330C4—2261no—
331C4—2262no—
332C4—2261no—
333C4—2261no—
334C4#41×D11311yescharacteristic
335C4C2×#1426864711yescharacteristic
336C2—81no—
337C2—2262no—
338C2#2029910711yescharacteristic
339C2#137×D11311yescharacteristic
340C2#2029939411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#440×C113C2
socleC22×C113C22×D4
prime radical#16813593C22
hypercenter#440D113
hypocenterC113#3117
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D113C2semidirect
3. #20298935C2semidirect
5. #20298904C2semidirect
6. #20298903C2semidirect
7. #20298819C2semidirect
8. #20298818C2semidirect
9. #20298755C2semidirect
11. #20298706C2semidirect
12. #20298703C2semidirect
13. #20298698C2semidirect
14. #20298653C2semidirect
15. #440×C113C2semidirect
171. C113#3117semidirect
185. #440D113semidirect

Maximal subgroups

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

subgroupindex
#202991302
C4×Q8×D1132
#202989352
#202989152
#202989042
#202989032
#202988192
#202988182
#202987552
#202987352
#202987062
#202987032
#202986982
#202986532
#440×C1132
#3117113