Finite Group Databasebeta

← #28403322

Subgroups — #28403322

Order 14464.

358 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#20299334C211yesmaximal, characteristic, complemented
2#20299304C211yesmaximal, characteristic, complemented
3#20298956C211yesmaximal, characteristic, complemented
4#20298951C211yesmaximal, characteristic, complemented
5#20298902C211yesmaximal, characteristic, complemented
6#20298896C211yesmaximal, characteristic, complemented
7#20298876C211yesmaximal, characteristic, complemented
8#20298812C211yesmaximal, characteristic, complemented
9#20298812C211yesmaximal, characteristic, complemented
10#20298790C211yesmaximal, characteristic
11#20298726C211yesmaximal, characteristic, complemented
12#20298707C211yesmaximal, characteristic, complemented
13#20298700C211yesmaximal, characteristic, complemented
14#20298678C211yesmaximal, characteristic, complemented
15#490×C113C211yesmaximal, characteristic, complemented
16C2×#14268636C2211yescharacteristic
17C2×#14268632C2211yescharacteristic
18C2×#14268632C2211yescharacteristic
19#16813621C2211yescharacteristic
20#16813613C2211yescharacteristic
21#16813609—21no—
22#16813609C2211yescharacteristic
23#16813609C2211yescharacteristic
24#16813603—21no—
25#16813603—21no—
26#16813602—21no—
27#16813600—21no—
28#16813600—21no—
29C4×Dic226C2211yescharacteristic
30C4×Dic226C2211yescharacteristic
31C4×D452C2211yescharacteristic
32D4×Dic113—21no—
33D4×Dic113C2211yescharacteristic
34D4×Dic113C2211yescharacteristic
35#16813584C2211yescharacteristic
36#16813584C2211yescharacteristic
37C4⋊C4×D113—21no—
38#16813556C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813553C2211yescharacteristic
41C4⋊#11744751C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813551C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813544C2211yescharacteristic
48#16813543C2211yescharacteristic
49#16813543C2211yescharacteristic
50#16813532C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52#127×C113C2211yescharacteristic
53#125×C113C2211yescharacteristic
54#102×C113C2211yescharacteristic
55#102×C113C2211yescharacteristic
56#102×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#97×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226D411yescharacteristic
61C2×Dic226C2311yescharacteristic
62C2×D452C2311yescharacteristic
63C22×Dic113—21no—
64C22×Dic113—21no—
65C2×C4×D113—21no—
66C2×C4×D113—21no—
67C2×C4×D113—21no—
68#14268636—22no—
69#14268632—22no—
70#14268632—22no—
71C2×#11744751C2311yescharacteristic
72C2×#11744751C2311yescharacteristic
73C4⋊Dic113—21no—
74C4⋊Dic113D411yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626D411yescharacteristic
81#14268626D411yescharacteristic
82C22⋊Dic113—21no—
83C22⋊Dic113—21no—
84C22⋊Dic113—21no—
85C22⋊Dic113—21no—
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91C4×Dic113—21no—
92C4×Dic113C2311yescharacteristic
93C4×Dic113C2311yescharacteristic
94C2×D4×C113—21no—
95C2×D4×C113—21no—
96C2×D4×C113C2311yescharacteristic
97C2×D4×C113C2311yescharacteristic
98C2×C8×C113C2311yescharacteristic
99C2×C8×C113C2311yescharacteristic
100C4⋊C4×C113—21no—
101C4⋊C4×C113—21no—
102C4⋊C4×C113C2311yescharacteristic
103C4⋊C4×C113C2311yescharacteristic
104C42×C113C2311yescharacteristic
105C23×C113—21no—
106C23×C113—21no—
107C22×D113—21no—
108D4×C113—21no—
109D4×C113—21no—
110D4×C113—21no—
111D4×C113—21no—
112D4×C113—42no—
113D4×C113—81no—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113C2×D411yescharacteristic
117C2×C4×C113C2×D411yescharacteristic
118C2×C4×C113C2411yescharacteristic
119C2×Dic113—21no—
120C2×Dic113—21no—
121C2×Dic113—21no—
122C2×Dic113—81no—
123C2×Dic113—81no—
124C2×Dic113C2×D411yescharacteristic
125C2×Dic113C2×D411yescharacteristic
126C2×Dic113C2×D411yescharacteristic
127C2×Dic113C2×D411yescharacteristic
128D452—21no—
129D452#4112yes—
130C4×D113—42no—
131C4×D113—81no—
132C4×D113—81no—
133Dic226—21no—
134Dic226—21no—
135Dic226—41no—
136Dic226—81no—
137C8×C113—21no—
138C8×C113—21no—
139#11744751—21no—
140#11744751—21no—
141C22×C113—41no—
142C22×C113—41no—
143C22×C113—41no—
144C22×C113—41no—
145C22×C113—41no—
146C22×C113—41no—
147C22×C113C22×D411yescharacteristic
148C2×D113—22no—
149C2×D113—41no—
150C2×D113—41no—
151C4×C113—21no—
152C4×C113—21no—
153C4×C113—41no—
154C4×C113—41no—
155C4×C113C2×#4111yescharacteristic
156C4×C1132−1+411yescharacteristic
157Dic113—21no—
158Dic113—21no—
159Dic113—21no—
160Dic113—21no—
161Dic113—41no—
162Dic113—41no—
163Dic113—41no—
164C2×C113—81no—
165C2×C113—81no—
166C2×C113#54811yescharacteristic
167C2×C113#57511yescharacteristic
168C2×C113#57611yescharacteristic
169D113—42no—
170#3370—1131nomaximal, Sylow
171C113#337011yescharacteristic, complemented, Sylow
172#559—1131no—
173#554—1131no—
174#490D11311yescharacteristic, complemented
175#489—1131no—
176#488—1131no—
177#479—1131no—
178#478—1131no—
179#474—1131no—
180#463—1131no—
181#463—1131no—
182#459—1131no—
183#446—1131no—
184#442—1131no—
185#440—1131no—
186C4×D8—1131no—
187C2×SD16—1131no—
188C2×D8—1131no—
189C2×D8—1131no—
190C4⋊Q8—1131no—
191#127C2×D11311yescharacteristic
192#125—1131no—
193#125C2×D11311yescharacteristic
194#124—1131no—
195#124—1131no—
196#124—2261no—
197#123—2261no—
198#123—2261no—
199C22⋊Q8—2261no—
200C22⋊Q8—2261no—
201C22⋊Q8—2261no—
202C4×Q8—1131no—
203C4×Q8—1131no—
204C4×D4—1131no—
205C4×D4—1131no—
206C4×D4—1131no—
207C4×D4—1131no—
208C4×D4—1131no—
209C4×D4—2261no—
210C2×C4⋊C4—2261no—
211#107—1131no—
212#107—1131no—
213#106—1131no—
214C4⋊C8—1131no—
215C4⋊C8—1131no—
216C4⋊C8—1131no—
217#103—1131no—
218#103—1131no—
219#103—1131no—
220#102—1131no—
221#102—1131no—
222#102—1131no—
223#102C2×D11311yescharacteristic
224#102C2×D11311yescharacteristic
225#102C2×D11311yescharacteristic
226#102C2×D11311yescharacteristic
227#97—1131no—
228#97C2×D11311yescharacteristic
229C4×C8—1131no—
230C2×Q8—1131no—
231C2×Q8—1131no—
232C2×Q8—2261no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—1131no—
236C2×D4C22×D11311yescharacteristic
237C2×D4C22×D11311yescharacteristic
238C22×C4—2261no—
239C22×C4—2261no—
240C22×C4—2261no—
241C22×C4—2261no—
242C22×C4—2261no—
243SD16—2262no—
244D8—2262no—
245D8—2262no—
246C2×C8—1131no—
247C2×C8—1131no—
248C2×C8C22×D11311yescharacteristic
249C2×C8C22×D11311yescharacteristic
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—1131no—
253C4⋊C4—1131no—
254C4⋊C4—1131no—
255C4⋊C4—1131no—
256C4⋊C4—1131no—
257C4⋊C4—2261no—
258C4⋊C4—2261no—
259C4⋊C4—2261no—
260C4⋊C4—2261no—
261C4⋊C4C22×D11311yescharacteristic
262C4⋊C4C22×D11311yescharacteristic
263C22⋊C4—2261no—
264C22⋊C4—2261no—
265C22⋊C4—2261no—
266C22⋊C4—2261no—
267C22⋊C4—2261no—
268C22⋊C4—2261no—
269C22⋊C4—2261no—
270C22⋊C4—2261no—
271C22⋊C4—2261no—
272C42—1131no—
273C42—1131no—
274C42—2261no—
275C42C22×D11311yescharacteristic
276C23—21no—
277C23—21no—
278C23—2261no—
279Q8—9041no—
280Q8—4521no—
281Q8—2261no—
282Q8—2261no—
283D4—21no—
284D4—21no—
285D4—21no—
286D4—21no—
287D4—42no—
288D4—81no—
289D4—1132no—
290D4—2261no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—1131no—
294C2×C4—1131no—
295C2×C4—1131no—
296C2×C4—1131no—
297C2×C4—9041no—
298C2×C4—9041no—
299C2×C4—9041no—
300C2×C4—9041no—
301C2×C4—4522no—
302C2×C4—2261no—
303C2×C4—2261no—
304C2×C4—2261no—
305C2×C4D4×D11311yescharacteristic
306C2×C4D4×D11311yescharacteristic
307C2×C4C23×D11311yescharacteristic
308C8—21no—
309C8—21no—
310C8—2261no—
311C8—2261no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—4521no—
319C22—4521no—
320C22—2262no—
321C22C2×D4×D11311yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—4521no—
327C4—4521no—
328C4—4521no—
329C4—2261no—
330C4—2261no—
331C4—2261no—
332C4—2261no—
333C4#41×D11311yescharacteristic
334C4#1681366911yescharacteristic
335C2—81no—
336C2—81no—
337C2—4522no—
338C2#2029925611yescharacteristic
339C2#2029939411yescharacteristic
340C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#490×C113C2
socleC22×C113C22×D4
prime radical#20298790C2
hypercenter#490D113
hypocenterC113#3370
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #20299334C2semidirect
2. #20299304C2semidirect
3. #20298956C2semidirect
4. #20298951C2semidirect
5. #20298902C2semidirect
6. #20298896C2semidirect
7. #20298876C2semidirect
8. #20298812C2semidirect
9. #20298812C2semidirect
11. #20298726C2semidirect
12. #20298707C2semidirect
13. #20298700C2semidirect
14. #20298678C2semidirect
15. #490×C113C2semidirect
171. C113#3370semidirect
174. #490D113semidirect

Maximal subgroups

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

subgroupindex
#202993342
#202993042
#202989562
#202989512
#202989022
#202988962
#202988762
#202988122
#202987902
#202987262
#202987072
#202987002
#202986782
#490×C1132
#3370113