Finite Group Databasebeta

← #28403087

Subgroups — #28403087

Order 14464.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299312C211yesmaximal, characteristic
2#20299287C211yesmaximal, characteristic, complemented
3#20299006C211yesmaximal, characteristic, complemented
4#20298941C211yesmaximal, characteristic, complemented
5#20298940C211yesmaximal, characteristic, complemented
6#20298915C211yesmaximal, characteristic, complemented
7#20298896C211yesmaximal, characteristic, complemented
8#20298882C211yesmaximal, characteristic, complemented
9#20298843C211yesmaximal, characteristic, complemented
10#20298825C211yesmaximal, characteristic, complemented
11#20298695C211yesmaximal, characteristic, complemented
12#20298666C211yesmaximal, characteristic, complemented
13#20298637C211yesmaximal, characteristic, complemented
14#20298634C211yesmaximal, characteristic, complemented
15#482×C113C211yesmaximal, characteristic, complemented
16C2×#14268635C2211yescharacteristic
17C2×#14268630C2211yescharacteristic
18C22×#11744751C2211yescharacteristic
19#16813621C2211yescharacteristic
20#16813615—21no—
21#16813614—21no—
22#16813613C2211yescharacteristic
23#16813609—21no—
24#16813608—21no—
25#16813604—21no—
26#16813602C2211yescharacteristic
27#16813601C2211yescharacteristic
28#16813594—21no—
29#16813593C2211yescharacteristic
30#16813587C2211yescharacteristic
31D4×Dic113C2211yescharacteristic
32C4×C22⋊D113C2211yescharacteristic
33#16813581C2211yescharacteristic
34#16813580C2211yescharacteristic
35#16813579—21no—
36#16813578—21no—
37C4⋊C4×D113C2211yescharacteristic
38#16813556C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813554C2211yescharacteristic
42#16813553C2211yescharacteristic
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
59C2×Dic226—21no—
60C2×Dic226C2311yescharacteristic
61C2×C22⋊D113—21no—
62C2×C22⋊D113D411yescharacteristic
63C22×Dic113—21no—
64C2×C4×D113—21no—
65C2×C4×D113C2311yescharacteristic
66#14268635—22no—
67#14268630—22no—
68C2×#11744751—22no—
69C2×#11744751C2311yescharacteristic
70C2×#11744751C2311yescharacteristic
71C4⋊Dic113—21no—
72C4⋊Dic113—21no—
73C4⋊Dic113C2311yescharacteristic
74C4⋊Dic113C2311yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76#14268626—21no—
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626D411yescharacteristic
82C22⋊Dic113—21no—
83C22⋊Dic113—21no—
84C22⋊Dic113—21no—
85C22⋊Dic113—21no—
86C22⋊Dic113D411yescharacteristic
87#14268624—21no—
88#14268624—21no—
89#14268624D411yescharacteristic
90C4×Dic113—21no—
91C4×Dic113—21no—
92C4×Dic113—21no—
93C4×Dic113C2311yescharacteristic
94C2×D4×C113—21no—
95C2×D4×C113C2311yescharacteristic
96C22×C4×C113C2311yescharacteristic
97C2×C8×C113C2311yescharacteristic
98C2×C8×C113C2311yescharacteristic
99C4⋊C4×C113C2311yescharacteristic
100C4⋊C4×C113C2311yescharacteristic
101C4⋊C4×C113C2311yescharacteristic
102C22⋊C4×C113—21no—
103C22⋊C4×C113—21no—
104C42×C113—21no—
105C23×C113—21no—
106C23×C113C2×D411yescharacteristic
107C22×D113C2×D411yescharacteristic
108D4×C113—21no—
109D4×C113—21no—
110D4×C113—81no—
111C2×C4×C113—21no—
112C2×C4×C113—21no—
113C2×C4×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113C2×D411yescharacteristic
117C2×C4×C113C2411yescharacteristic
118C22⋊D113—41no—
119C22⋊D113—81no—
120C2×Dic113—21no—
121C2×Dic113—21no—
122C2×Dic113—21no—
123C2×Dic113—21no—
124C2×Dic113—42no—
125C2×Dic113C2×D411yescharacteristic
126C2×Dic113C2×D411yescharacteristic
127C2×Dic113C2×D411yescharacteristic
128C4×D113—21no—
129C4×D113—21no—
130C4×D113—42no—
131Dic226—21no—
132Dic226—21no—
133Dic226—81no—
134C8×C113—21no—
135C8×C113—21no—
136#11744751—21no—
137#11744751#4112yes—
138C22×C113—21no—
139C22×C113—21no—
140C22×C113—21no—
141C22×C113—41no—
142C22×C113—41no—
143C22×C113—41no—
144C22×C113C22×D411yescharacteristic
145C2×D113—21no—
146C2×D113—21no—
147C2×D113—21no—
148C4×C113—21no—
149C4×C113—41no—
150C4×C113—41no—
151C4×C113—41no—
152C4×C113C2×#4111yescharacteristic
153C4×C1132−1+411yescharacteristic
154Dic113—21no—
155Dic113—21no—
156Dic113—21no—
157Dic113—41no—
158Dic113—41no—
159Dic113—41no—
160Dic113—41no—
161C2×C113—41no—
162C2×C113—81no—
163C2×C113#54711yescharacteristic
164C2×C113#57511yescharacteristic
165C2×C113#57711yescharacteristic
166D113—41no—
167#3348—1131nomaximal, Sylow
168C113#334811yescharacteristic, complemented, Sylow
169#555—1131no—
170#552—1131no—
171#501—1131no—
172#485—1131no—
173#485—1131no—
174#482D11311yescharacteristic, complemented
175#481—1131no—
176#478—1131no—
177#475—1131no—
178#468—1131no—
179#465—1131no—
180#440—1131no—
181#435—1131no—
182#428—1131no—
183#427—1131no—
184C2×SD16—1131no—
185C2×M16—1131no—
186C22×C8—1131no—
187C4⋊Q8—1131no—
188#126—2261no—
189#125—1131no—
190#125—2261no—
191#124—2261no—
192#124—2261no—
193#123—2261no—
194C22⋊Q8—1131no—
195C22⋊Q8—1131no—
196#121—1131no—
197#121—2261no—
198#121C2×D11311yescharacteristic
199C4×Q8—1131no—
200C4×D4—1131no—
201C4×D4—1131no—
202#117—1131no—
203#117—1131no—
204#117—2261no—
205#117—2261no—
206#117C2×D11311yescharacteristic
207C2×C4⋊C4—1131no—
208#107—1131no—
209#107—1131no—
210#107—1131no—
211#107C2×D11311yescharacteristic
212#106—1131no—
213#106—1131no—
214#106—1131no—
215#106—1131no—
216#106C2×D11311yescharacteristic
217C4⋊C8—1131no—
218#103—1131no—
219#103—1131no—
220#103—1131no—
221#102—1131no—
222#102C2×D11311yescharacteristic
223#102C2×D11311yescharacteristic
224C22⋊C8—1131no—
225C22⋊C8C2×D11311yescharacteristic
226#97—1131no—
227C2×Q8—1131no—
228C2×Q8—2261no—
229C2×D4—21no—
230C2×D4—1131no—
231C2×D4—2261no—
232C2×D4C22×D11311yescharacteristic
233C22×C4—1131no—
234C22×C4—2261no—
235C22×C4—2261no—
236C22×C4C22×D11311yescharacteristic
237SD16—2262no—
238M16—2262no—
239C2×C8—1131no—
240C2×C8—1131no—
241C2×C8—2262no—
242C2×C8C22×D11311yescharacteristic
243C2×C8C22×D11311yescharacteristic
244C4⋊C4—1131no—
245C4⋊C4—1131no—
246C4⋊C4—1131no—
247C4⋊C4—1131no—
248C4⋊C4—2261no—
249C4⋊C4—2261no—
250C4⋊C4—2261no—
251C4⋊C4—2261no—
252C4⋊C4—2261no—
253C4⋊C4—2261no—
254C4⋊C4—2261no—
255C4⋊C4C22×D11311yescharacteristic
256C4⋊C4C22×D11311yescharacteristic
257C4⋊C4C22×D11311yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—1131no—
261C22⋊C4—1131no—
262C22⋊C4—2261no—
263C22⋊C4—2261no—
264C22⋊C4—2261no—
265C22⋊C4—2261no—
266C22⋊C4—2261no—
267C22⋊C4—2261no—
268C42—21no—
269C42—1131no—
270C42—2261no—
271C42—2261no—
272C42—2261no—
273C23—21no—
274C23—1131no—
275C23D4×D11311yescharacteristic
276Q8—9041no—
277Q8—2261no—
278Q8—2261no—
279D4—21no—
280D4—21no—
281D4—81no—
282D4—9041no—
283D4—4521no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—1131no—
290C2×C4—1131no—
291C2×C4—1131no—
292C2×C4—4522no—
293C2×C4—4522no—
294C2×C4—2261no—
295C2×C4—2261no—
296C2×C4—2261no—
297C2×C4—2261no—
298C2×C4—2261no—
299C2×C4—2261no—
300C2×C4D4×D11311yescharacteristic
301C2×C4C23×D11311yescharacteristic
302C8—21no—
303C8—21no—
304C8—1132no—
305C8—2261no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—41no—
310C22—41no—
311C22—41no—
312C22—2261no—
313C22—2261no—
314C22—2261no—
315C22C2×D4×D11311yescharacteristic
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—4521no—
321C4—4521no—
322C4—4521no—
323C4—4521no—
324C4—2261no—
325C4—2261no—
326C4—2261no—
327C4#41×D11311yescharacteristic
328C4#1681366911yescharacteristic
329C2—41no—
330C2—81no—
331C2—4521no—
332C2#2029924611yescharacteristic
333C2#2029939511yescharacteristic
334C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#482×C113C2
socleC22×C113C22×D4
prime radical#20299312C2
hypercenter#482D113
hypocenterC113#3348
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
2. #20299287C2semidirect
3. #20299006C2semidirect
4. #20298941C2semidirect
5. #20298940C2semidirect
6. #20298915C2semidirect
7. #20298896C2semidirect
8. #20298882C2semidirect
9. #20298843C2semidirect
10. #20298825C2semidirect
11. #20298695C2semidirect
12. #20298666C2semidirect
13. #20298637C2semidirect
14. #20298634C2semidirect
15. #482×C113C2semidirect
168. C113#3348semidirect
174. #482D113semidirect

Maximal subgroups

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

subgroupindex
#202993122
#202992872
#202990062
#202989412
#202989402
#202989152
#202988962
#202988822
#202988432
#202988252
#202986952
#202986662
#202986372
#202986342
#482×C1132
#3348113