Finite Group Databasebeta

← #28403007

Subgroups — #28403007

Order 14464.

376 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#20299287C211yesmaximal, characteristic, complemented
2#20299248C211yesmaximal, characteristic
3#20299005C211yesmaximal, characteristic, complemented
4#20298934C211yesmaximal, characteristic, complemented
5#20298930C211yesmaximal, characteristic, complemented
6#20298910C211yesmaximal, characteristic, complemented
7#20298896C211yesmaximal, characteristic, complemented
8#20298892C211yesmaximal, characteristic, complemented
9#20298842C211yesmaximal, characteristic, complemented
10#20298826C211yesmaximal, characteristic, complemented
11#20298695C211yesmaximal, characteristic, complemented
12#20298672C211yesmaximal, characteristic, complemented
13#20298641C211yesmaximal, characteristic, complemented
14#107×D113C211yesmaximal, characteristic, complemented
15#482×C113C211yesmaximal, characteristic, complemented
16C2×#14268646—21no—
17C2×#14268635C2211yescharacteristic
18C2×#14268631C2211yescharacteristic
19C2×C8×D113C2211yescharacteristic
20#16813621C2211yescharacteristic
21#16813615—21no—
22#16813614—21no—
23#16813613C2211yescharacteristic
24#16813604—21no—
25#16813604—21no—
26#16813603—21no—
27#16813602C2211yescharacteristic
28#16813601C2211yescharacteristic
29#16813599—21no—
30#16813593C2211yescharacteristic
31#16813587C2211yescharacteristic
32D4×Dic113C2211yescharacteristic
33C4×C22⋊D113C2211yescharacteristic
34#16813579—21no—
35C2×C4⋊Dic113C2211yescharacteristic
36C4⋊C4×D113C2211yescharacteristic
37C4⋊C4×D113C2211yescharacteristic
38#16813556C2211yescharacteristic
39#16813556C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813555C2211yescharacteristic
42#16813555C2211yescharacteristic
43#16813553C2211yescharacteristic
44#16813553C2211yescharacteristic
45#16813551C2211yescharacteristic
46#16813547C2211yescharacteristic
47#16813547C2211yescharacteristic
48#16813545C2211yescharacteristic
49#16813543C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813532C2211yescharacteristic
52#121×C113C2211yescharacteristic
53#117×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56#102×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59#14268646—44no—
60C2×Dic226—21no—
61C2×Dic226C2311yescharacteristic
62C2×C22⋊D113—21no—
63C2×C22⋊D113D411yescharacteristic
64C22×Dic113—21no—
65C22×Dic113—21no—
66C2×C4×D113—21no—
67C2×C4×D113—21no—
68C2×C4×D113C2311yescharacteristic
69#14268635—22no—
70#14268631—22no—
71C2×#11744751C2311yescharacteristic
72C2×#11744751C2311yescharacteristic
73C8×D113—22no—
74C4⋊Dic113—21no—
75C4⋊Dic113—21no—
76C4⋊Dic113—21no—
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79C4⋊Dic113C2311yescharacteristic
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86#14268626D411yescharacteristic
87C22⋊Dic113—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113—21no—
90C22⋊Dic113D411yescharacteristic
91#14268624—21no—
92#14268624D411yescharacteristic
93C4×Dic113—21no—
94C4×Dic113C2311yescharacteristic
95C2×D4×C113—21no—
96C2×D4×C113C2311yescharacteristic
97C22×C4×C113C2311yescharacteristic
98C2×C8×C113C2311yescharacteristic
99C2×C8×C113C2311yescharacteristic
100C4⋊C4×C113C2311yescharacteristic
101C4⋊C4×C113C2311yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C22⋊C4×C113—21no—
104C22⋊C4×C113—21no—
105C42×C113—21no—
106C23×C113—21no—
107C23×C113C2×D411yescharacteristic
108C22×D113C2×D411yescharacteristic
109D4×C113—21no—
110D4×C113—21no—
111D4×C113—42no—
112C2×C4×C113—21no—
113C2×C4×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113C2×D411yescharacteristic
118C2×C4×C113C2411yescharacteristic
119C22⋊D113—22no—
120C22⋊D113—42no—
121C2×Dic113—21no—
122C2×Dic113—21no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—42no—
126C2×Dic113—42no—
127C2×Dic113C2×D411yescharacteristic
128C2×Dic113C2×D411yescharacteristic
129C2×Dic113C2×D411yescharacteristic
130C4×D113—21no—
131C4×D113—21no—
132C4×D113—42no—
133C4×D113—42no—
134Dic226—21no—
135Dic226—21no—
136Dic226—42no—
137C8×C113—21no—
138C8×C113—21no—
139#11744751—21no—
140#11744751#4112yescomplemented
141C22×C113—21no—
142C22×C113—21no—
143C22×C113—21no—
144C22×C113—41no—
145C22×C113—41no—
146C22×C113—41no—
147C22×C113C22×D411yescharacteristic
148C2×D113—21no—
149C2×D113—21no—
150C2×D113AGL(1,ℤ/8)12yes—
151C4×C113—21no—
152C4×C113—41no—
153C4×C113—41no—
154C4×C113—41no—
155C4×C113C2×#4111yescharacteristic
156C4×C1132−1+411yescharacteristic
157Dic113—21no—
158Dic113—21no—
159Dic113—21no—
160Dic113—41no—
161Dic113—41no—
162Dic113—41no—
163Dic113—41no—
164C2×C113—41no—
165C2×C113—81no—
166C2×C113#54711yescharacteristic
167C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
168C2×C113#57811yescharacteristic
169D113—22no—
170#3343—1131nomaximal, Sylow
171C113#334311yescharacteristic, complemented, Sylow
172#552—1131no—
173#547—1131no—
174#501—1131no—
175#484—1131no—
176#483—1131no—
177#482D11311yescharacteristic, complemented
178#480—1131no—
179#478—1131no—
180#477—1131no—
181#468—1131no—
182#465—1131no—
183#440—1131no—
184#435—1131no—
185#428—1131no—
186C2×#107—1131no—
187C2×#41—2261no—
188C2×SD16—1131no—
189C2×M16—1131no—
190C22×C8—1131no—
191C4⋊Q8—1131no—
192#126—2261no—
193#125—1131no—
194#125—2261no—
195#123—2261no—
196#123—2261no—
197#123—2261no—
198C22⋊Q8—1131no—
199C22⋊Q8—1131no—
200C22⋊Q8—2261no—
201#121—1131no—
202#121C2×D11311yescharacteristic
203C4×Q8—1131no—
204C4×D4—1131no—
205C4×D4—1131no—
206#117—2261no—
207#117C2×D11311yescharacteristic
208C2×C4⋊C4—1131no—
209C2×C4⋊C4—1131no—
210C2×C4⋊C4—1131no—
211#107—1131no—
212#107—1131no—
213#107—1131no—
214#107—1131no—
215#107—1131no—
216#107C2×D11311yescharacteristic
217#106—1131no—
218#106—1131no—
219#106C2×D11311yescharacteristic
220C4⋊C8—1131no—
221#103—1131no—
222#103—1131no—
223#103—1131no—
224#102—1131no—
225#102C2×D11311yescharacteristic
226#102C2×D11311yescharacteristic
227C22⋊C8—1131no—
228C22⋊C8C2×D11311yescharacteristic
229#97—1131no—
230#41—4524no—
231C2×Q8—1131no—
232C2×Q8—2261no—
233C2×D4—21no—
234C2×D4—1131no—
235C2×D4—2261no—
236C2×D4C22×D11311yescharacteristic
237C22×C4—1131no—
238C22×C4—2261no—
239C22×C4—2261no—
240C22×C4—2261no—
241C22×C4—2261no—
242C22×C4C22×D11311yescharacteristic
243SD16—2262no—
244M16—2262no—
245C2×C8—1131no—
246C2×C8—1131no—
247C2×C8—2262no—
248C2×C8C22×D11311yescharacteristic
249C2×C8C22×D11311yescharacteristic
250C4⋊C4—1131no—
251C4⋊C4—1131no—
252C4⋊C4—1131no—
253C4⋊C4—1131no—
254C4⋊C4—2261no—
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
265C4⋊C4C22×D11311yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—1131no—
269C22⋊C4—1131no—
270C22⋊C4—2261no—
271C22⋊C4—2261no—
272C22⋊C4—2261no—
273C22⋊C4—2261no—
274C42—21no—
275C42—1131no—
276C42—2261no—
277C23—21no—
278C23—1131no—
279C23D4×D11311yescharacteristic
280Q8—4522no—
281Q8—2261no—
282Q8—2261no—
283D4—21no—
284D4—21no—
285D4—42no—
286D4—4522no—
287D4—2262no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—1131no—
294C2×C4—1131no—
295C2×C4—1131no—
296C2×C4—4522no—
297C2×C4—4522no—
298C2×C4—4522no—
299C2×C4—4522no—
300C2×C4—2261no—
301C2×C4—2261no—
302C2×C4—2261no—
303C2×C4—2261no—
304C2×C4—2261no—
305C2×C4—2261no—
306C2×C4D4×D11311yescharacteristic
307C2×C4C23×D11311yescharacteristic
308C8—21no—
309C8—21no—
310C8—1132no—
311C8—2261no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—1132no—
319C22—2261no—
320C22—2261no—
321C22C2×D4×D11311yescharacteristic
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—4521no—
327C4—4521no—
328C4—4521no—
329C4—4521no—
330C4—2261no—
331C4—2261no—
332C4—2261no—
333C4#41×D11311yescharacteristic
334C4#1681366911yescharacteristic
335C2—41no—
336C2—81no—
337C2—2262no—
338C2#2029924611yescharacteristic
339C2AGL(1,ℤ/8)×D11311yescharacteristic
340C2#2029941211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#482×C113C2
socleC22×C113C22×D4
prime radical#20299248C2
hypercenter#482D113
hypocenterC113#3343
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
1. #20299287C2semidirect
3. #20299005C2semidirect
4. #20298934C2semidirect
5. #20298930C2semidirect
6. #20298910C2semidirect
7. #20298896C2semidirect
8. #20298892C2semidirect
9. #20298842C2semidirect
10. #20298826C2semidirect
11. #20298695C2semidirect
12. #20298672C2semidirect
13. #20298641C2semidirect
14. #107×D113C2semidirect
15. #482×C113C2semidirect
140. #11744751#41semidirect
171. C113#3343semidirect
177. #482D113semidirect

Maximal subgroups

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

subgroupindex
#202992872
#202992482
#202990052
#202989342
#202989302
#202989102
#202988962
#202988922
#202988422
#202988262
#202986952
#202986722
#202986412
#107×D1132
#482×C1132
#3343113