Finite Group Databasebeta

← #28402461

Subgroups — #28402461

Order 14464.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299288C211yesmaximal, characteristic, complemented
2#20298952C211yesmaximal, characteristic, complemented
3#20298936C211yesmaximal, characteristic, complemented
4#20298909C211yesmaximal, characteristic, complemented
5#20298905C211yesmaximal, characteristic, complemented
6#20298837C211yesmaximal, characteristic, complemented
7#20298825C211yesmaximal, characteristic, complemented
8#20298817C211yesmaximal, characteristic, complemented
9#20298760C211yesmaximal, characteristic, complemented
10#20298754C211yesmaximal, characteristic, complemented
11C4×#14268637C211yesmaximal, characteristic, complemented
12D4×#11744751C211yesmaximal, characteristic, complemented
13#20298594C211yesmaximal, characteristic, complemented
14C2×#16813546C211yesmaximal, characteristic, complemented
15#548×C113C211yesmaximal, characteristic
16C2×#14268637C2211yescharacteristic
17C2×#14268637C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19C22×#11744751C2211yescharacteristic
20C22×#11744751C2211yescharacteristic
21#16813615—21no—
22#16813614C2211yescharacteristic
23#16813612—21no—
24#16813603—21no—
25#16813601C2211yescharacteristic
26#16813601C2211yescharacteristic
27C4×Dic226C2211yescharacteristic
28#16813581C2211yescharacteristic
29#16813578—21no—
30C2×C4⋊Dic113C2211yescharacteristic
31#16813555C2211yescharacteristic
32#16813555C2211yescharacteristic
33#16813553C2211yescharacteristic
34C4⋊#11744751C2211yescharacteristic
35#16813546C2211yescharacteristic
36#16813546C2211yescharacteristic
37#16813546C2211yescharacteristic
38#16813546C2211yescharacteristic
39#16813546C2211yescharacteristic
40#16813546C2211yescharacteristic
41#16813545C2211yescharacteristic
42#16813543C2211yescharacteristic
43#16813543C2211yescharacteristic
44#16813543C2211yescharacteristic
45C22⋊#11744751C2211yescharacteristic
46C22⋊#11744751C2211yescharacteristic
47C4×#11744751C2211yescharacteristic
48C2×#41×C113C2211yescharacteristic
49C22×Q8×C113C2211yescharacteristic
50#124×C113—21no—
51#124×C113C2211yescharacteristic
52C22⋊Q8×C113—21no—
53C22⋊Q8×C113C2211yescharacteristic
54#121×C113—21no—
55#121×C113C2211yescharacteristic
56C4×Q8×C113C2211yescharacteristic
57C4×D4×C113—21no—
58C4×D4×C113C2211yescharacteristic
59C2×Dic226C2311yescharacteristic
60C22×Dic113—21no—
61#14268637—22no—
62#14268637—41no—
63#14268635—41no—
64C2×#11744751—41no—
65C2×#11744751—41no—
66C2×#11744751C2311yescharacteristic
67C2×#11744751C2311yescharacteristic
68C2×#11744751C2311yescharacteristic
69C2×#11744751C2311yescharacteristic
70C4⋊Dic113—21no—
71C4⋊Dic113C2311yescharacteristic
72C4⋊Dic113C2311yescharacteristic
73C4⋊Dic113C2311yescharacteristic
74#14268626—21no—
75#14268626—21no—
76#14268626—21no—
77#14268626—21no—
78#14268626—21no—
79C22⋊Dic113—21no—
80C22⋊Dic113—21no—
81C22⋊Dic113—21no—
82C4×Dic113—21no—
83C4×Dic113—21no—
84#41×C113—22no—
85#41×C113—41no—
86C2×Q8×C113—21no—
87C2×Q8×C113—22no—
88C2×Q8×C113—41no—
89C2×Q8×C113C2311yescharacteristic
90C2×Q8×C113C2311yescharacteristic
91C2×D4×C113—21no—
92C2×D4×C113—21no—
93C2×D4×C113D411yescharacteristic
94C2×D4×C113C2311yescharacteristic
95C22×C4×C113—21no—
96C22×C4×C113—21no—
97C22×C4×C113C2311yescharacteristic
98C22×C4×C113C2311yescharacteristic
99C4⋊C4×C113—21no—
100C4⋊C4×C113—21no—
101C4⋊C4×C113D411yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C22⋊C4×C113—21no—
104C22⋊C4×C113—21no—
105C22⋊C4×C113—21no—
106C22⋊C4×C113—21no—
107C22⋊C4×C113D411yescharacteristic
108C22⋊C4×C113D411yescharacteristic
109C42×C113—21no—
110C42×C113C2311yescharacteristic
111C23×C113—21no—
112C23×C113C2×D411yescharacteristic
113C23×C113C2×D411yescharacteristic
114Q8×C113—21no—
115Q8×C113—21no—
116Q8×C113—21no—
117Q8×C113—42no—
118Q8×C113#4112yes—
119D4×C113—22no—
120D4×C113—21no—
121D4×C113—21no—
122D4×C113—42no—
123D4×C113—42no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113—42no—
132C2×C4×C113—42no—
133C2×C4×C113C2×D411yescharacteristic
134C2×C4×C113C2×D411yescharacteristic
135C2×C4×C113C2×D411yescharacteristic
136C2×C4×C113C2×D411yescharacteristic
137C2×C4×C113C2411yescharacteristic
138C2×Dic113—21no—
139C2×Dic113—21no—
140C2×Dic113—21no—
141C2×Dic113—21no—
142C2×Dic113—42no—
143Dic226—21no—
144Dic226—21no—
145#11744751—21no—
146#11744751—21no—
147#11744751—21no—
148#11744751—21no—
149C22×C113—21no—
150C22×C113—21no—
151C22×C113—21no—
152C22×C113—21no—
153C22×C113—21no—
154C22×C113—41no—
155C22×C113—41no—
156C22×C113—41no—
157C22×C113#13512yes—
158C22×C113C22×D411yescharacteristic
159C4×C113—21no—
160C4×C113—21no—
161C4×C113—22no—
162C4×C113—21no—
163C4×C113—21no—
164C4×C113—41no—
165C4×C113—41no—
166C4×C113C2×#4111yescharacteristic
167C4×C113H(5,𝔽2)11yescharacteristic
168Dic113—41no—
169Dic113—41no—
170Dic113—41no—
171Dic113—41no—
172C2×C113—22no—
173C2×C113—41no—
174C2×C113—81no—
175C2×C113#54611yescharacteristic
176C2×C113C2×#13511yescharacteristic
177C2×C113#57811yescharacteristic
178#3300—1131nomaximal, Sylow
179C113#330011yescharacteristic, complemented, Sylow
180#552—1131no—
181#548D11311yescharacteristic
182#488—1131no—
183#485—1131no—
184#480—1131no—
185#479—1131no—
186#467—1131no—
187#465—1131no—
188#464—1131no—
189#452—1131no—
190#451—1131no—
191C4×Q16—1131no—
192C8×D4—1131no—
193#416—1131no—
194C2×#103—1131no—
195C2×#41C2×D11311yescharacteristic
196C22×Q8C2×D11311yescharacteristic
197C2×Q16—1131no—
198C2×Q16—1131no—
199C2×SD16—1131no—
200C22×C8—1131no—
201C22×C8—1131no—
202#126—2261no—
203#125—1131no—
204#125—2261no—
205#124—21no—
206#124C2×D11311yescharacteristic
207#123—2261no—
208C22⋊Q8—21no—
209C22⋊Q8—1131no—
210C22⋊Q8—1131no—
211C22⋊Q8C2×D11311yescharacteristic
212#121—21no—
213#121C2×D11311yescharacteristic
214C4×Q8—1131no—
215C4×Q8C2×D11311yescharacteristic
216C4×D4—21no—
217C4×D4C2×D11311yescharacteristic
218#117—1131no—
219#117—2261no—
220C2×C4⋊C4—1131no—
221#107—1131no—
222#107—1131no—
223#106—1131no—
224C4⋊C8—1131no—
225#103—1131no—
226#103—1131no—
227#103—1131no—
228#103—1131no—
229#103—1131no—
230#103—1131no—
231#103—1131no—
232#102—1131no—
233#102—1131no—
234#102—1131no—
235C22⋊C8—1131no—
236C22⋊C8—1131no—
237C4×C8—1131no—
238#41—22no—
239#41—41no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—1131no—
244C2×Q8C22×D11311yescharacteristic
245C2×Q8C22×D11311yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4C22⋊D11311yescharacteristic
249C2×D4C22×D11311yescharacteristic
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—2261no—
253C22×C4C22×D11311yescharacteristic
254C22×C4C22×D11311yescharacteristic
255Q16—4521no—
256Q16—2262no—
257SD16—4521no—
258C2×C8—1131no—
259C2×C8—1131no—
260C2×C8—1131no—
261C2×C8—1131no—
262C2×C8—4521no—
263C2×C8—4521no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—1131no—
267C4⋊C4—1131no—
268C4⋊C4—1131no—
269C4⋊C4—2261no—
270C4⋊C4—2261no—
271C4⋊C4—2261no—
272C4⋊C4—2261no—
273C4⋊C4—2261no—
274C4⋊C4—2261no—
275C4⋊C4C22⋊D11311yescharacteristic
276C4⋊C4C22×D11311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C22⋊C4—2261no—
284C22⋊C4C22⋊D11311yescharacteristic
285C22⋊C4C22⋊D11311yescharacteristic
286C42—21no—
287C42—2261no—
288C42—2261no—
289C42C22×D11311yescharacteristic
290C23—21no—
291C23C2×C22⋊D11311yescharacteristic
292C23C2×C22⋊D11311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—42no—
297Q8—2261no—
298Q8—2261no—
299Q8#1426864612yes—
300D4—22no—
301D4—21no—
302D4—21no—
303D4—42no—
304D4—42no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—4522no—
315C2×C4—2261no—
316C2×C4—2261no—
317C2×C4—2261no—
318C2×C4—2261no—
319C2×C4C2×C22⋊D11311yescharacteristic
320C2×C4C2×C22⋊D11311yescharacteristic
321C2×C4C2×C22⋊D11311yescharacteristic
322C2×C4C2×C22⋊D11311yescharacteristic
323C2×C4C23×D11311yescharacteristic
324C8—2261no—
325C8—2261no—
326C8—2261no—
327C8—2261no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22#1681364212yes—
337C22C22×C22⋊D11311yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—22no—
343C4—41no—
344C4—41no—
345C4—4521no—
346C4—4521no—
347C4—4521no—
348C4—4521no—
349C4C2×#1426864611yescharacteristic
350C4#1681366711yescharacteristic
351C2—22no—
352C2—41no—
353C2—81no—
354C2#2029924211yescharacteristic
355C2C2×#1681364211yescharacteristic
356C2#2029941311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting, prime radical#548×C113C2
socleC22×C113C22×D4
hypercenter#548D113
hypocenterC113#3300
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #20299288C2semidirect
2. #20298952C2semidirect
3. #20298936C2semidirect
4. #20298909C2semidirect
5. #20298905C2semidirect
6. #20298837C2semidirect
7. #20298825C2semidirect
8. #20298817C2semidirect
9. #20298760C2semidirect
10. #20298754C2semidirect
11. C4×#14268637C2semidirect
12. D4×#11744751C2semidirect
13. #20298594C2semidirect
14. C2×#16813546C2semidirect
179. C113#3300semidirect

Maximal subgroups

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

subgroupindex
#202992882
#202989522
#202989362
#202989092
#202989052
#202988372
#202988252
#202988172
#202987602
#202987542
C4×#142686372
D4×#117447512
#202985942
C2×#168135462
#548×C1132
#3300113