Finite Group Databasebeta

← #28403177

Subgroups — #28403177

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#20299301C211yesmaximal, characteristic, complemented
2#20299298C211yesmaximal, characteristic, complemented
3#20298997C211yesmaximal, characteristic, complemented
4#20298924C211yesmaximal, characteristic, complemented
5#20298921C211yesmaximal, characteristic, complemented
6#20298913C211yesmaximal, characteristic, complemented
7#20298910C211yesmaximal, characteristic, complemented
8#20298899C211yesmaximal, characteristic, complemented
9#20298850C211yesmaximal, characteristic, complemented
10#20298850C211yesmaximal, characteristic, complemented
11C4×#14268632C211yesmaximal, characteristic, complemented
12#20298675C211yesmaximal, characteristic, complemented
13#20298639C211yesmaximal, characteristic, complemented
14#20298637C211yesmaximal, characteristic, complemented
15#478×C113C211yesmaximal, characteristic, complemented
16C2×#14268632C2211yescharacteristic
17C2×#14268630C2211yescharacteristic
18C2×#14268630C2211yescharacteristic
19#16813617—21no—
20#16813615—21no—
21#16813614C2211yescharacteristic
22#16813607—21no—
23#16813605—21no—
24#16813597—21no—
25#16813597C2211yescharacteristic
26#16813597C2211yescharacteristic
27#16813595—21no—
28#16813593C2211yescharacteristic
29#16813593C2211yescharacteristic
30C4×D452C2211yescharacteristic
31C4×D452C2211yescharacteristic
32#16813584—21no—
33C4×C22⋊D113—21no—
34#16813580C2211yescharacteristic
35#16813580C2211yescharacteristic
36C4⋊C4×D113C2211yescharacteristic
37C4⋊C4×D113C2211yescharacteristic
38#16813556C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813555C2211yescharacteristic
42#16813554C2211yescharacteristic
43#16813553C2211yescharacteristic
44#16813553C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813542C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813534C2211yescharacteristic
51C4×#11744751C2211yescharacteristic
52#125×C113C2211yescharacteristic
53C4×D4×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59C2×D452—21no—
60C2×D452—21no—
61C2×D452D411yescharacteristic
62C2×D452C2311yescharacteristic
63C2×C22⋊D113—21no—
64C2×C22⋊D113—21no—
65C2×C4×D113—21no—
66C2×C4×D113—21no—
67C2×C4×D113—21no—
68C2×C4×D113C2311yescharacteristic
69C2×C4×D113C2311yescharacteristic
70#14268632—22no—
71#14268630—22no—
72#14268630—22no—
73C2×#11744751C2311yescharacteristic
74C2×#11744751C2311yescharacteristic
75C4⋊Dic113D411yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83C22⋊Dic113—21no—
84C22⋊Dic113—21no—
85#14268624—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624D411yescharacteristic
91#14268624D411yescharacteristic
92C4×Dic113—21no—
93C4×Dic113—21no—
94C2×D4×C113C2311yescharacteristic
95C22×C4×C113—21no—
96C2×C8×C113C2311yescharacteristic
97C2×C8×C113C2311yescharacteristic
98C4⋊C4×C113—21no—
99C4⋊C4×C113—21no—
100C4⋊C4×C113C2311yescharacteristic
101C4⋊C4×C113C2311yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C22⋊C4×C113—21no—
104C42×C113C2311yescharacteristic
105C23×C113—21no—
106C22×D113—21no—
107C22×D113C2×D411yescharacteristic
108C22×D113C2×D411yescharacteristic
109D4×C113—21no—
110D4×C113—21no—
111C2×C4×C113—21no—
112C2×C4×C113—21no—
113C2×C4×C113—21no—
114C2×C4×C113—81no—
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×Dic113C2×D411yescharacteristic
124C2×Dic113C2×D411yescharacteristic
125D452—21no—
126D452—21no—
127D452—41no—
128D452—42no—
129D452—81no—
130C4×D113—21no—
131C4×D113—21no—
132C4×D113—21no—
133C4×D113—21no—
134C4×D113—81no—
135C4×D113—81no—
136C4×D113—81no—
137C8×C113—21no—
138C8×C113—21no—
139#11744751—21no—
140#11744751#4112yes—
141C22×C113—41no—
142C22×C113—41no—
143C22×C113—41no—
144C22×C113C22×D411yescharacteristic
145C2×D113—21no—
146C2×D113—21no—
147C2×D113—21no—
148C2×D113—21no—
149C2×D113—21no—
150C2×D113—21no—
151C2×D113—41no—
152C2×D113—41no—
153C2×D113—41no—
154C4×C113—21no—
155C4×C113—21no—
156C4×C113—41no—
157C4×C113—41no—
158C4×C113—41no—
159C4×C113C2×#4111yescharacteristic
160C4×C1132−1+411yescharacteristic
161Dic113—21no—
162Dic113—21no—
163Dic113—41no—
164Dic113—41no—
165Dic113—41no—
166C2×C113—81no—
167C2×C113#54711yescharacteristic
168C2×C113#57511yescharacteristic
169C2×C113#57611yescharacteristic
170D113—41no—
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#482—1131no—
180#480—1131no—
181#480—1131no—
182#478—1131no—
183#478D11311yescharacteristic, complemented
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#125C2×D11311yescharacteristic
197#123—2261no—
198#123—2261no—
199#121—1131no—
200#121—1131no—
201#121—1131no—
202#121—1131no—
203#121—2261no—
204#121—2261no—
205C4×D4—1131no—
206C4×D4—1131no—
207C4×D4—2261no—
208C4×D4—2261no—
209C4×D4C2×D11311yescharacteristic
210#117—1131no—
211#117—1131no—
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⋊C8C2×D11311yescharacteristic
224#102—1131no—
225#102—1131no—
226#102—1131no—
227#102—1131no—
228#102C2×D11311yescharacteristic
229#102C2×D11311yescharacteristic
230C22⋊C8—1131no—
231C22⋊C8—1131no—
232C4×C8—1131no—
233C2×D4—1131no—
234C2×D4—1131no—
235C2×D4—2261no—
236C2×D4—2261no—
237C2×D4—2261no—
238C2×D4—2261no—
239C2×D4C22×D11311yescharacteristic
240C22×C4—21no—
241C22×C4—1131no—
242C22×C4—1131no—
243C22×C4—2261no—
244C22×C4—2261no—
245C22×C4—2261no—
246D8—2262no—
247M16—2262no—
248M16—2262no—
249C2×C8—1131no—
250C2×C8—1131no—
251C2×C8C22×D11311yescharacteristic
252C2×C8C22×D11311yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—1131no—
256C4⋊C4—1131no—
257C4⋊C4—1131no—
258C4⋊C4—1131no—
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—1131no—
268C22⋊C4—1131no—
269C22⋊C4—2261no—
270C22⋊C4—2261no—
271C22⋊C4—2261no—
272C22⋊C4—2261no—
273C22⋊C4—2261no—
274C22⋊C4—2261no—
275C22⋊C4—2261no—
276C42—2261no—
277C42—2261no—
278C42C22×D11311yescharacteristic
279C23—21no—
280C23—1131no—
281C23—1131no—
282C23—2261no—
283D4—21no—
284D4—21no—
285D4—9041no—
286D4—9041no—
287D4—4521no—
288D4—4522no—
289D4—4522no—
290D4—2261no—
291D4—2261no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—81no—
296C2×C4—1131no—
297C2×C4—1131no—
298C2×C4—9041no—
299C2×C4—9041no—
300C2×C4—9041no—
301C2×C4—2261no—
302C2×C4—2261no—
303C2×C4—2261no—
304C2×C4—2261no—
305C2×C4—2261no—
306C2×C4—2261no—
307C2×C4—2261no—
308C2×C4D4×D11311yescharacteristic
309C2×C4D4×D11311yescharacteristic
310C2×C4C23×D11311yescharacteristic
311C8—21no—
312C8—21no—
313C8—1132no—
314C8—2261no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—4521no—
319C22—4521no—
320C22—4521no—
321C22—2261no—
322C22—2261no—
323C22—2261no—
324C22—2261no—
325C22—2261no—
326C22—2261no—
327C22C2×D4×D11311yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—4521no—
334C4—4521no—
335C4—4521no—
336C4—2261no—
337C4—2261no—
338C4#41×D11311yescharacteristic
339C4#1681367011yescharacteristic
340C2—81no—
341C2—9041no—
342C2—4521no—
343C2—4521no—
344C2#2029925011yescharacteristic
345C2#2029939511yescharacteristic
346C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#478×C113C2
socleC22×C113C22×D4
hypercenter#478D113
hypocenterC113#3355
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #20299301C2semidirect
2. #20299298C2semidirect
3. #20298997C2semidirect
4. #20298924C2semidirect
5. #20298921C2semidirect
6. #20298913C2semidirect
7. #20298910C2semidirect
8. #20298899C2semidirect
9. #20298850C2semidirect
10. #20298850C2semidirect
11. C4×#14268632C2semidirect
12. #20298675C2semidirect
13. #20298639C2semidirect
14. #20298637C2semidirect
15. #478×C113C2semidirect
174. C113#3355semidirect
183. #478D113semidirect

Maximal subgroups

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

subgroupindex
#202993012
#202992982
#202989972
#202989242
#202989212
#202989132
#202989102
#202988992
#202988502
C4×#142686322
#202986752
#202986392
#202986372
#478×C1132
#3355113