Finite Group Databasebeta

← #28403173

Subgroups — #28403173

Order 14464.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299300C211yesmaximal, characteristic, complemented
2#20299292C211yesmaximal, characteristic, complemented
3#20298999C211yesmaximal, characteristic, complemented
4#20298925C211yesmaximal, characteristic, complemented
5#20298912C211yesmaximal, characteristic, complemented
6#20298910C211yesmaximal, characteristic, complemented
7#20298897C211yesmaximal, characteristic, complemented
8#20298896C211yesmaximal, characteristic, complemented
9#20298850C211yesmaximal, characteristic, complemented
10#20298849C211yesmaximal, characteristic, complemented
11#20298678C211yesmaximal, characteristic, complemented
12#20298673C211yesmaximal, characteristic, complemented
13#20298641C211yesmaximal, characteristic, complemented
14#20298637C211yesmaximal, characteristic, complemented
15#482×C113C211yesmaximal, characteristic, complemented
16C2×#14268632C2211yescharacteristic
17C2×#14268631C2211yescharacteristic
18C2×#14268630C2211yescharacteristic
19#16813616—21no—
20#16813615—21no—
21#16813613C2211yescharacteristic
22#16813613C2211yescharacteristic
23#16813606—21no—
24#16813604—21no—
25#16813597C2211yescharacteristic
26#16813596C2211yescharacteristic
27#16813595—21no—
28#16813594—21no—
29#16813593C2211yescharacteristic
30C4×D452—21no—
31D4×Dic113—21no—
32D4×Dic113C2211yescharacteristic
33#16813584C2211yescharacteristic
34C4×C22⋊D113C2211yescharacteristic
35#16813580C2211yescharacteristic
36C2×C4⋊Dic113C2211yescharacteristic
37C4⋊C4×D113C2211yescharacteristic
38#16813556C2211yescharacteristic
39#16813556C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813555C2211yescharacteristic
42#16813553C2211yescharacteristic
43#16813553C2211yescharacteristic
44#16813553C2211yescharacteristic
45#16813551C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813544C2211yescharacteristic
48#16813543C2211yescharacteristic
49#16813542C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52#121×C113C2211yescharacteristic
53#117×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56#102×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59C2×D452—21no—
60C2×D452C2311yescharacteristic
61C2×C22⋊D113—21no—
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#14268632—22no—
70#14268631—22no—
71#14268630—22no—
72C2×#11744751C2311yescharacteristic
73C2×#11744751C2311yescharacteristic
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#14268626D411yescharacteristic
84C22⋊Dic113—21no—
85C22⋊Dic113—21no—
86C22⋊Dic113D411yescharacteristic
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624D411yescharacteristic
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×D113—21no—
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—41no—
120C22⋊D113—81no—
121C22⋊D113—81no—
122C2×Dic113—21no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—81no—
126C2×Dic113—81no—
127C2×Dic113C2×D411yescharacteristic
128C2×Dic113C2×D411yescharacteristic
129C2×Dic113C2×D411yescharacteristic
130D452—21no—
131D452—21no—
132D452—42no—
133C4×D113—21no—
134C4×D113—21no—
135C4×D113—81no—
136C4×D113—81no—
137C8×C113—21no—
138C8×C113—21no—
139#11744751—21no—
140#11744751#4112yes—
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×D113—21no—
151C2×D113—41no—
152C2×D113—41no—
153C2×D113—41no—
154C4×C113—21no—
155C4×C113—41no—
156C4×C113—41no—
157C4×C113—41no—
158C4×C113C2×#4111yescharacteristic
159C4×C1132−1+411yescharacteristic
160Dic113—21no—
161Dic113—21no—
162Dic113—21no—
163Dic113—41no—
164Dic113—41no—
165Dic113—41no—
166C2×C113—41no—
167C2×C113—81no—
168C2×C113#54711yescharacteristic
169C2×C113#57511yescharacteristic
170C2×C113#57611yescharacteristic
171D113—41no—
172D113—81no—
173#3355—1131nomaximal, Sylow
174C113#335511yescharacteristic, complemented, Sylow
175#553—1131no—
176#553—1131no—
177#499—1131no—
178#482—1131no—
179#482D11311yescharacteristic, complemented
180#480—1131no—
181#480—1131no—
182#478—1131no—
183#478—1131no—
184#469—1131no—
185#469—1131no—
186C4×D8—1131no—
187#436—1131no—
188#428—1131no—
189#428—1131no—
190C2×D8—1131no—
191C2×M16—1131no—
192C2×M16—1131no—
193#126—2261no—
194#126—2261no—
195#125—1131no—
196#125—1131no—
197#123—2261no—
198#123—2261no—
199#121—1131no—
200#121—1131no—
201#121—1131no—
202#121—2261no—
203#121—2261no—
204#121C2×D11311yescharacteristic
205C4×D4—1131no—
206C4×D4—1131no—
207C4×D4—1131no—
208C4×D4—2261no—
209C4×D4—2261no—
210#117—1131no—
211#117C2×D11311yescharacteristic
212C2×C4⋊C4—1131no—
213C2×C4⋊C4—1131no—
214#107—1131no—
215#107—1131no—
216#107—1131no—
217#107—1131no—
218#107C2×D11311yescharacteristic
219#106—1131no—
220#106—1131no—
221#106—1131no—
222#106C2×D11311yescharacteristic
223C4⋊C8—1131no—
224#102—1131no—
225#102—1131no—
226#102—1131no—
227#102—1131no—
228#102C2×D11311yescharacteristic
229#102C2×D11311yescharacteristic
230C22⋊C8—1131no—
231C22⋊C8C2×D11311yescharacteristic
232C4×C8—1131no—
233C2×D4—21no—
234C2×D4—1131no—
235C2×D4—1131no—
236C2×D4—2261no—
237C2×D4—2261no—
238C2×D4—2261no—
239C2×D4C22×D11311yescharacteristic
240C22×C4—1131no—
241C22×C4—2261no—
242C22×C4—2261no—
243C22×C4—2261no—
244C22×C4—2261no—
245C22×C4C22×D11311yescharacteristic
246D8—2262no—
247M16—2262no—
248M16—2262no—
249C2×C8—1131no—
250C2×C8—1131no—
251C2×C8C22×D11311yescharacteristic
252C2×C8C22×D11311yescharacteristic
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⋊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—
274C22⋊C4—2261no—
275C22⋊C4—2261no—
276C42—21no—
277C42—1131no—
278C42—2261no—
279C23—21no—
280C23—1131no—
281C23—2261no—
282C23D4×D11311yescharacteristic
283D4—21no—
284D4—21no—
285D4—42no—
286D4—9041no—
287D4—9041no—
288D4—4522no—
289D4—4521no—
290D4—2261no—
291D4—2261no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—1131no—
298C2×C4—1131no—
299C2×C4—1131no—
300C2×C4—9041no—
301C2×C4—9041no—
302C2×C4—9041no—
303C2×C4—9041no—
304C2×C4—2261no—
305C2×C4—2261no—
306C2×C4—2261no—
307C2×C4—2261no—
308C2×C4—2261no—
309C2×C4D4×D11311yescharacteristic
310C2×C4C23×D11311yescharacteristic
311C8—21no—
312C8—21no—
313C8—1132no—
314C8—2261no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—4521no—
322C22—4521no—
323C22—4521no—
324C22—2261no—
325C22—2261no—
326C22—2261no—
327C22C2×D4×D11311yescharacteristic
328C4—21no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—4521no—
333C4—4521no—
334C4—4521no—
335C4—2261no—
336C4—2261no—
337C4—2261no—
338C4#41×D11311yescharacteristic
339C4#1681366911yescharacteristic
340C2—41no—
341C2—81no—
342C2—9041no—
343C2—4521no—
344C2#2029924611yescharacteristic
345C2#2029939411yescharacteristic
346C2#2029940011yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#482×C113C2
socleC22×C113C22×D4
hypercenter#482D113
hypocenterC113#3355
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. #20299300C2semidirect
2. #20299292C2semidirect
3. #20298999C2semidirect
4. #20298925C2semidirect
5. #20298912C2semidirect
6. #20298910C2semidirect
7. #20298897C2semidirect
8. #20298896C2semidirect
9. #20298850C2semidirect
10. #20298849C2semidirect
11. #20298678C2semidirect
12. #20298673C2semidirect
13. #20298641C2semidirect
14. #20298637C2semidirect
15. #482×C113C2semidirect
174. C113#3355semidirect
179. #482D113semidirect

Maximal subgroups

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

subgroupindex
#202993002
#202992922
#202989992
#202989252
#202989122
#202989102
#202988972
#202988962
#202988502
#202988492
#202986782
#202986732
#202986412
#202986372
#482×C1132
#3355113