Finite Group Databasebeta

← #28403385

Subgroups — #28403385

Order 14464.

350 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299330C211yesmaximal, characteristic
2#20299328C211yesmaximal, characteristic, complemented
3#20298959C211yesmaximal, characteristic, complemented
4#20298943C211yesmaximal, characteristic
5#20298891C211yesmaximal, characteristic, complemented
6#20298876C211yesmaximal, characteristic, complemented
7#20298875C211yesmaximal, characteristic, complemented
8#20298823C211yesmaximal, characteristic, complemented
9#20298817C211yesmaximal, characteristic, complemented
10#20298797C211yesmaximal, characteristic
11#20298726C211yesmaximal, characteristic, complemented
12#20298700C211yesmaximal, characteristic, complemented
13#20298695C211yesmaximal, characteristic, complemented
14#20298690C211yesmaximal, characteristic, complemented
15#489×C113C211yesmaximal, characteristic, complemented
16C2×#14268637C2211yescharacteristic
17C2×#14268636C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19#16813621—21no—
20#16813621C2211yescharacteristic
21#16813621C2211yescharacteristic
22#16813620—21no—
23#16813620—21no—
24#16813618C2211yescharacteristic
25#16813611C2211yescharacteristic
26#16813608—21no—
27#16813606—21no—
28#16813604—21no—
29Q8×Dic113C2211yescharacteristic
30C4×Dic226C2211yescharacteristic
31C4×Dic226C2211yescharacteristic
32#16813587—21no—
33#16813587C2211yescharacteristic
34#16813587C2211yescharacteristic
35C4×D452C2211yescharacteristic
36D4×Dic113C2211yescharacteristic
37#16813582—21no—
38#16813556C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813555C2211yescharacteristic
41C4⋊#11744751C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813551C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813542C2211yescharacteristic
49#16813542C2211yescharacteristic
50#16813532C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C4⋊Q8×C113C2211yescharacteristic
53#124×C113C2211yescharacteristic
54#103×C113C2211yescharacteristic
55#103×C113C2211yescharacteristic
56#102×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#97×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226—21no—
61C2×Dic226D411yescharacteristic
62C2×Dic226C2311yescharacteristic
63C2×D452C2311yescharacteristic
64C2×C22⋊D113—21no—
65C2×C22⋊D113—21no—
66C22×Dic113—21no—
67C2×C4×D113—21no—
68#14268637—22no—
69#14268636—22no—
70#14268635—22no—
71C2×#11744751C2311yescharacteristic
72C2×#11744751C2311yescharacteristic
73C4⋊Dic113—21no—
74C4⋊Dic113D411yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626D411yescharacteristic
83#14268626D411yescharacteristic
84C22⋊Dic113—21no—
85#14268624—21no—
86#14268624—21no—
87#14268624—21no—
88C4×Dic113—21no—
89C4×Dic113—21no—
90C4×Dic113—21no—
91C4×Dic113—21no—
92C4×Dic113C2311yescharacteristic
93C4×Dic113C2311yescharacteristic
94C2×Q8×C113—21no—
95C2×Q8×C113C2311yescharacteristic
96C2×D4×C113C2311yescharacteristic
97C2×C8×C113C2311yescharacteristic
98C2×C8×C113C2311yescharacteristic
99C4⋊C4×C113—21no—
100C4⋊C4×C113C2311yescharacteristic
101C4⋊C4×C113C2311yescharacteristic
102C22⋊C4×C113—21no—
103C22⋊C4×C113—21no—
104C42×C113C2311yescharacteristic
105C23×C113—21no—
106C22×D113—21no—
107Q8×C113—21no—
108Q8×C113—21no—
109Q8×C113—81no—
110D4×C113—21no—
111D4×C113—21no—
112C2×C4×C113—21no—
113C2×C4×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113C2×D411yescharacteristic
116C2×C4×C113C2×D411yescharacteristic
117C2×C4×C113C2411yescharacteristic
118C22⋊D113—42no—
119C22⋊D113—81no—
120C2×Dic113—21no—
121C2×Dic113—21no—
122C2×Dic113—21no—
123C2×Dic113—81no—
124C2×Dic113C2×D411yescharacteristic
125C2×Dic113C2×D411yescharacteristic
126C2×Dic113C2×D411yescharacteristic
127C2×Dic113C2×D411yescharacteristic
128D452—21no—
129D452—21no—
130C4×D113—81no—
131Dic226—21no—
132Dic226—22no—
133Dic226—81no—
134Dic226—81no—
135Dic226#4112yes—
136C8×C113—21no—
137C8×C113—21no—
138#11744751—21no—
139#11744751—21no—
140C22×C113—41no—
141C22×C113—41no—
142C22×C113—41no—
143C22×C113C22×D411yescharacteristic
144C2×D113—41no—
145C2×D113—41no—
146C2×D113—41no—
147C4×C113—21no—
148C4×C113—21no—
149C4×C113—41no—
150C4×C113—41no—
151C4×C113—41no—
152C4×C113C2×#4111yescharacteristic
153C4×C1132−1+411yescharacteristic
154Dic113—22no—
155Dic113—21no—
156Dic113—21no—
157Dic113—21no—
158Dic113—41no—
159Dic113—41no—
160Dic113#13712yes—
161C2×C113—81no—
162C2×C113#54811yescharacteristic
163C2×C113C2×#13711yescharacteristic
164C2×C113#57611yescharacteristic
165D113—81no—
166#3375—1131nomaximal, Sylow
167C113#337511yescharacteristic, complemented, Sylow
168#559—1131no—
169Q82—1131no—
170#489—1131no—
171#489D11311yescharacteristic, complemented
172#486—1131no—
173#477—1131no—
174#474—1131no—
175#474—1131no—
176#464—1131no—
177#464—1131no—
178#460—1131no—
179#446—1131no—
180#440—1131no—
181#440—1131no—
182C4×Q16—1131no—
183C2×Q16—1131no—
184C2×SD16—1131no—
185C2×SD16—1131no—
186C4⋊Q8—1131no—
187C4⋊Q8—1131no—
188C4⋊Q8—2261no—
189C4⋊Q8—2261no—
190C4⋊Q8—2261no—
191C4⋊Q8C2×D11311yescharacteristic
192#127—1131no—
193#124—1131no—
194#124—2261no—
195#124C2×D11311yescharacteristic
196#123—2261no—
197#123—2261no—
198C4×Q8—1131no—
199C4×Q8—1131no—
200C4×Q8—1131no—
201C4×Q8—1131no—
202C4×Q8—1131no—
203C4×Q8—2261no—
204C4×D4—1131no—
205C4×D4—1131no—
206C4×D4—2261no—
207#107—1131no—
208#107—1131no—
209#107—1131no—
210C4⋊C8—1131no—
211C4⋊C8—1131no—
212C4⋊C8—1131no—
213#103—1131no—
214#103—1131no—
215#103C2×D11311yescharacteristic
216#103C2×D11311yescharacteristic
217#102—1131no—
218#102—1131no—
219#102—1131no—
220#102—1131no—
221#102C2×D11311yescharacteristic
222#102C2×D11311yescharacteristic
223#97—1131no—
224#97C2×D11311yescharacteristic
225C4×C8—1131no—
226C2×Q8—21no—
227C2×Q8—1131no—
228C2×Q8—1131no—
229C2×Q8—2261no—
230C2×Q8—2261no—
231C2×Q8C22×D11311yescharacteristic
232C2×D4—1131no—
233C2×D4—2261no—
234C2×D4—2261no—
235C2×D4C22×D11311yescharacteristic
236C22×C4—2261no—
237C22×C4—2261no—
238Q16—2262no—
239SD16—2262no—
240SD16—2262no—
241C2×C8—1131no—
242C2×C8—1131no—
243C2×C8C22×D11311yescharacteristic
244C2×C8C22×D11311yescharacteristic
245C4⋊C4—21no—
246C4⋊C4—1131no—
247C4⋊C4—1131no—
248C4⋊C4—1131no—
249C4⋊C4—1131no—
250C4⋊C4—1131no—
251C4⋊C4—2261no—
252C4⋊C4—2261no—
253C4⋊C4—2261no—
254C4⋊C4—2261no—
255C4⋊C4—2261no—
256C4⋊C4—2261no—
257C4⋊C4C22×D11311yescharacteristic
258C4⋊C4C22×D11311yescharacteristic
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—2261no—
262C22⋊C4—2261no—
263C22⋊C4—2261no—
264C22⋊C4—2261no—
265C42—1131no—
266C42—1131no—
267C42—2261no—
268C42—2261no—
269C42—2261no—
270C42—2261no—
271C42C22×D11311yescharacteristic
272C23—21no—
273C23—2261no—
274Q8—21no—
275Q8—21no—
276Q8—81no—
277Q8—1132no—
278Q8—9041no—
279Q8—9041no—
280Q8—2262no—
281Q8—2261no—
282D4—21no—
283D4—21no—
284D4—9041no—
285D4—4522no—
286D4—2261no—
287D4—2261no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—1131no—
292C2×C4—1131no—
293C2×C4—1131no—
294C2×C4—1131no—
295C2×C4—9041no—
296C2×C4—9041no—
297C2×C4—2261no—
298C2×C4—2261no—
299C2×C4—2261no—
300C2×C4D4×D11311yescharacteristic
301C2×C4D4×D11311yescharacteristic
302C2×C4C23×D11311yescharacteristic
303C8—21no—
304C8—21no—
305C8—2261no—
306C8—2261no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—4521no—
311C22—4521no—
312C22—4521no—
313C22C2×D4×D11311yescharacteristic
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—1132no—
320C4—4521no—
321C4—4521no—
322C4—2261no—
323C4—2261no—
324C4—2261no—
325C4—2262no—
326C4#41×D11311yescharacteristic
327C4#1681366911yescharacteristic
328C2—81no—
329C2—9041no—
330C2#2029925611yescharacteristic
331C2#137×D11311yescharacteristic
332C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#489×C113C2
socleC22×C113C22×D4
prime radical#16813618C22
hypercenter#489D113
hypocenterC113#3375
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. #20299328C2semidirect
3. #20298959C2semidirect
5. #20298891C2semidirect
6. #20298876C2semidirect
7. #20298875C2semidirect
8. #20298823C2semidirect
9. #20298817C2semidirect
11. #20298726C2semidirect
12. #20298700C2semidirect
13. #20298695C2semidirect
14. #20298690C2semidirect
15. #489×C113C2semidirect
167. C113#3375semidirect
171. #489D113semidirect

Maximal subgroups

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

subgroupindex
#202993302
#202993282
#202989592
#202989432
#202988912
#202988762
#202988752
#202988232
#202988172
#202987972
#202987262
#202987002
#202986952
#202986902
#489×C1132
#3375113