Finite Group Databasebeta

← #28402480

Subgroups — #28402480

Order 14464.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299300C211yesmaximal, characteristic, complemented
2#20299259C211yesmaximal, characteristic, complemented
3#20298954C211yesmaximal, characteristic, complemented
4#20298937C211yesmaximal, characteristic, complemented
5#20298917C211yesmaximal, characteristic, complemented
6#20298903C211yesmaximal, characteristic, complemented
7#20298832C211yesmaximal, characteristic, complemented
8#20298824C211yesmaximal, characteristic, complemented
9#20298815C211yesmaximal, characteristic, complemented
10#20298742C211yesmaximal, characteristic, complemented
11SD16×Dic113C211yesmaximal, characteristic, complemented
12#20298661C211yesmaximal, characteristic, complemented
13#20298593C211yesmaximal, characteristic, complemented
14C2×#16813546C211yesmaximal, characteristic, complemented
15#448×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268632C2211yescharacteristic
18C22×#11744751C2211yescharacteristic
19C2×C8×D113C2211yescharacteristic
20#16813615—21no—
21#16813613C2211yescharacteristic
22#16813611—21no—
23#16813611C2211yescharacteristic
24#16813606—21no—
25#16813598—21no—
26#16813598C2211yescharacteristic
27#16813596—21no—
28#16813596C2211yescharacteristic
29#16813594—21no—
30#16813593C2211yescharacteristic
31Q8×Dic113C2211yescharacteristic
32D4×Dic113—21no—
33D4×Dic113C2211yescharacteristic
34C4×C22⋊D113—21no—
35C4×C22⋊D113C2211yescharacteristic
36#16813580C2211yescharacteristic
37C2×C4⋊Dic113C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813554C2211yescharacteristic
40#16813554C2211yescharacteristic
41#16813551C2211yescharacteristic
42#16813546C2211yescharacteristic
43#16813546C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813544C2211yescharacteristic
48#16813543C2211yescharacteristic
49#16813542C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C22×Q8×C113C2211yescharacteristic
53C2×SD16×C113C2211yescharacteristic
54C2×SD16×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59#14268648—22no—
60#14268648—41no—
61C2×D452—21no—
62C2×D452C2311yescharacteristic
63C2×C22⋊D113—21no—
64C2×C22⋊D113—21no—
65C2×C22⋊D113D411yescharacteristic
66C22×Dic113—21no—
67C22×Dic113—21no—
68C2×C4×D113—21no—
69C2×C4×D113C2311yescharacteristic
70#14268632—41no—
71C2×#11744751—41no—
72C2×#11744751C2311yescharacteristic
73C2×#11744751C2311yescharacteristic
74C8×D113—41no—
75C4⋊Dic113—21no—
76C4⋊Dic113—21no—
77C4⋊Dic113—21no—
78C4⋊Dic113C2311yescharacteristic
79C4⋊Dic113C2311yescharacteristic
80C4⋊Dic113C2311yescharacteristic
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#14268624—21no—
92#14268624D411yescharacteristic
93C4×Dic113—21no—
94C4×Dic113—21no—
95C4×Dic113C2311yescharacteristic
96C2×Q8×C113—21no—
97C2×Q8×C113—22no—
98C2×Q8×C113—41no—
99C2×Q8×C113C2311yescharacteristic
100C2×Q8×C113C2311yescharacteristic
101C2×D4×C113—21no—
102C2×D4×C113C2311yescharacteristic
103C22×C4×C113—21no—
104C22×C4×C113C2311yescharacteristic
105SD16×C113—22no—
106SD16×C113—41no—
107C2×C8×C113C2311yescharacteristic
108C2×C8×C113C2311yescharacteristic
109C4⋊C4×C113C2311yescharacteristic
110C22⋊C4×C113—21no—
111C23×C113—21no—
112C23×C113C2×D411yescharacteristic
113C22×D113—21no—
114C22×D113C2×D411yescharacteristic
115Q8×C113—21no—
116Q8×C113—21no—
117Q8×C113—21no—
118Q8×C113—42no—
119Q8×C113#4112yes—
120D4×C113—21no—
121D4×C113—21no—
122D4×C113—42no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113—42no—
129C2×C4×C113C2×D411yescharacteristic
130C2×C4×C113C2411yescharacteristic
131C22⋊D113—22no—
132C22⋊D113—42no—
133C22⋊D113—81no—
134C2×Dic113—21no—
135C2×Dic113—21no—
136C2×Dic113—21no—
137C2×Dic113—81no—
138C2×Dic113—81no—
139C2×Dic113C2×D411yescharacteristic
140C2×Dic113C2×D411yescharacteristic
141C2×Dic113C2×D411yescharacteristic
142D452—21no—
143D452—21no—
144D452—42no—
145C4×D113—21no—
146C4×D113—21no—
147C4×D113—42no—
148C8×C113—21no—
149C8×C113—21no—
150#11744751—21no—
151#11744751—21no—
152C22×C113—21no—
153C22×C113—21no—
154C22×C113—41no—
155C22×C113—41no—
156C22×C113—41no—
157C22×C113#13512yes—
158C22×C113C22×D411yescharacteristic
159C2×D113—21no—
160C2×D113—21no—
161C2×D113—21no—
162C2×D113—41no—
163C2×D113—41no—
164C2×D113—41no—
165C4×C113—22no—
166C4×C113—21no—
167C4×C113—41no—
168C4×C113—41no—
169C4×C113C2×#4111yescharacteristic
170C4×C113H(5,𝔽2)11yescharacteristic
171Dic113—21no—
172Dic113—21no—
173Dic113—21no—
174Dic113—41no—
175Dic113—41no—
176Dic113—41no—
177C2×C113—22no—
178C2×C113—81no—
179C2×C113#54611yescharacteristic
180C2×C113C2×#13511yescharacteristic
181C2×C113#57711yescharacteristic
182D113—41no—
183D113—81no—
184#3301—1131nomaximal, Sylow
185C113#330111yescharacteristic, complemented, Sylow
186#553—1131no—
187#548—1131no—
188#488—1131no—
189#485—1131no—
190#481—1131no—
191#479—1131no—
192#466—1131no—
193#465—1131no—
194#463—1131no—
195#449—1131no—
196#448D11311yescharacteristic, complemented
197C4×SD16—1131no—
198C8×D4—1131no—
199#416—1131no—
200C2×#103—1131no—
201C2×#41—1131no—
202C22×Q8C2×D11311yescharacteristic
203C2×SD16C2×D11311yescharacteristic
204C2×SD16C2×D11311yescharacteristic
205C2×D8—1131no—
206C22×C8—1131no—
207C22×C8—1131no—
208#126—2261no—
209#125—1131no—
210#124—1131no—
211#124—2261no—
212#123—2261no—
213C22⋊Q8—1131no—
214C22⋊Q8—2261no—
215#121—1131no—
216#121—1131no—
217#121—2261no—
218#121—2261no—
219#121C2×D11311yescharacteristic
220C4×Q8—1131no—
221C4×D4—1131no—
222C4×D4—1131no—
223C4×D4—2261no—
224C4×D4—2261no—
225#117—1131no—
226C2×C4⋊C4—1131no—
227#107—1131no—
228#106—1131no—
229#106—1131no—
230C4⋊C8—1131no—
231#103—1131no—
232#103—1131no—
233#103—1131no—
234#103—1131no—
235#103C2×D11311yescharacteristic
236#103C2×D11311yescharacteristic
237#102—1131no—
238#102—1131no—
239#102—1131no—
240#102—1131no—
241C22⋊C8—1131no—
242C22⋊C8C2×D11311yescharacteristic
243C4×C8—1131no—
244#41—4521no—
245#41—2262no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8C22×D11311yescharacteristic
250C2×Q8C22×D11311yescharacteristic
251C2×D4—21no—
252C2×D4—1131no—
253C2×D4—1131no—
254C2×D4—2261no—
255C2×D4—2261no—
256C2×D4—2261no—
257C2×D4C22×D11311yescharacteristic
258C22×C4—21no—
259C22×C4—1131no—
260C22×C4—2261no—
261C22×C4—2261no—
262C22×C4—2261no—
263C22×C4C22×D11311yescharacteristic
264SD16—22no—
265SD16—41no—
266D8—4521no—
267C2×C8—1131no—
268C2×C8—1131no—
269C2×C8—4521no—
270C2×C8—4521no—
271C2×C8C22×D11311yescharacteristic
272C2×C8C22×D11311yescharacteristic
273C4⋊C4—1131no—
274C4⋊C4—1131no—
275C4⋊C4—1131no—
276C4⋊C4—1131no—
277C4⋊C4—2261no—
278C4⋊C4—2261no—
279C4⋊C4—2261no—
280C4⋊C4—2261no—
281C4⋊C4—2261no—
282C4⋊C4C22×D11311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—1131no—
285C22⋊C4—1131no—
286C22⋊C4—2261no—
287C22⋊C4—2261no—
288C22⋊C4—2261no—
289C22⋊C4—2261no—
290C22⋊C4—2261no—
291C22⋊C4—2261no—
292C22⋊C4—2261no—
293C42—1131no—
294C42—2261no—
295C42—2261no—
296C23—21no—
297C23—1131no—
298C23—2261no—
299C23D4×D11311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8#1426864612yes—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—9041no—
309D4—4522no—
310D4—4522no—
311D4—2262no—
312D4—2261no—
313D4—2261no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—1131no—
321C2×C4—1131no—
322C2×C4—1131no—
323C2×C4—9041no—
324C2×C4—9041no—
325C2×C4—4522no—
326C2×C4—2261no—
327C2×C4—2261no—
328C2×C4—2261no—
329C2×C4—2261no—
330C2×C4—2261no—
331C2×C4D4×D11311yescharacteristic
332C2×C4C23×D11311yescharacteristic
333C8—21no—
334C8—21no—
335C8—2261no—
336C8—2261no—
337C22—21no—
338C22—21no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—4521no—
343C22—4521no—
344C22—4521no—
345C22—2261no—
346C22—2261no—
347C22—2261no—
348C22#1681364312yes—
349C22C2×D4×D11311yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—4521no—
355C4—4521no—
356C4—4521no—
357C4—2261no—
358C4—2261no—
359C4—2261no—
360C4C2×#1426864611yescharacteristic
361C4#1681366711yescharacteristic
362C2—22no—
363C2—81no—
364C2—9041no—
365C2—4521no—
366C2#2029923511yescharacteristic
367C2C2×#1681364311yescharacteristic
368C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#448×C113C2
socleC22×C113C22×D4
hypercenter#448D113
hypocenterC113#3301
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. #20299300C2semidirect
2. #20299259C2semidirect
3. #20298954C2semidirect
4. #20298937C2semidirect
5. #20298917C2semidirect
6. #20298903C2semidirect
7. #20298832C2semidirect
8. #20298824C2semidirect
9. #20298815C2semidirect
10. #20298742C2semidirect
11. SD16×Dic113C2semidirect
12. #20298661C2semidirect
13. #20298593C2semidirect
14. C2×#16813546C2semidirect
15. #448×C113C2semidirect
185. C113#3301semidirect
196. #448D113semidirect

Maximal subgroups

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

subgroupindex
#202993002
#202992592
#202989542
#202989372
#202989172
#202989032
#202988322
#202988242
#202988152
#202987422
SD16×Dic1132
#202986612
#202985932
C2×#168135462
#448×C1132
#3301113