Finite Group Databasebeta

← #28403635

Subgroups — #28403635

Order 14464.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299334C211yesmaximal, characteristic, complemented
2#20299317C211yesmaximal, characteristic, complemented
3#20298989C211yesmaximal, characteristic, complemented
4#20298981C211yesmaximal, characteristic, complemented
5#20298818C211yesmaximal, characteristic, complemented
6#20298817C211yesmaximal, characteristic, complemented
7#20298811C211yesmaximal, characteristic, complemented
8#20298811C211yesmaximal, characteristic, complemented
9#20298801C211yesmaximal, characteristic, complemented
10#20298795C211yesmaximal, characteristic, complemented
11#20298726C211yesmaximal, characteristic, complemented
12#20298710C211yesmaximal, characteristic, complemented
13#20298706C211yesmaximal, characteristic, complemented
14SD16×Dic113C211yesmaximal, characteristic, complemented
15#496×C113C211yesmaximal, characteristic
16C2×Dic452C2211yescharacteristic
17C2×#14268637C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19C2×#14268635C2211yescharacteristic
20C2×#14268635C2211yescharacteristic
21#16813620C2211yescharacteristic
22#16813615—21no—
23#16813615—21no—
24#16813609—21no—
25#16813609C2211yescharacteristic
26#16813609C2211yescharacteristic
27#16813609C2211yescharacteristic
28#16813603—21no—
29#16813603—21no—
30#16813599—21no—
31Q8×Dic113C2211yescharacteristic
32C4×Dic226C2211yescharacteristic
33C4×Dic226C2211yescharacteristic
34C4×Dic226C2211yescharacteristic
35D4×Dic113—21no—
36D4×Dic113C2211yescharacteristic
37D4×Dic113C2211yescharacteristic
38D4×Dic113C2211yescharacteristic
39#16813578—21no—
40#16813554C2211yescharacteristic
41C4⋊#11744751C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813551C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813547C2211yescharacteristic
46#16813546C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813543C2211yescharacteristic
49#16813543C2211yescharacteristic
50#16813532C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×SD16×C113C2211yescharacteristic
53C2×SD16×C113C2211yescharacteristic
54C2×D8×C113C2211yescharacteristic
55C2×D8×C113C2211yescharacteristic
56#127×C113C2211yescharacteristic
57#124×C113C2211yescharacteristic
58#97×C113C2211yescharacteristic
59C2×Dic226D411yescharacteristic
60C2×Dic226C2311yescharacteristic
61C2×Dic226C2311yescharacteristic
62C22×Dic113—21no—
63C22×Dic113—21no—
64C22×Dic113—21no—
65Dic452—22no—
66#14268637—41no—
67#14268635—41no—
68#14268635—41no—
69#14268635—41no—
70C2×#11744751C2311yescharacteristic
71C2×#11744751C2311yescharacteristic
72C4⋊Dic113—21no—
73C4⋊Dic113D411yescharacteristic
74C4⋊Dic113C2311yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76#14268626—21no—
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626D411yescharacteristic
81#14268626D411yescharacteristic
82C22⋊Dic113—21no—
83C22⋊Dic113—21no—
84C22⋊Dic113—21no—
85C22⋊Dic113—21no—
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113—21no—
90C22⋊Dic113—21no—
91C4×Dic113—21no—
92C4×Dic113—21no—
93C4×Dic113—21no—
94C4×Dic113C2311yescharacteristic
95C4×Dic113C2311yescharacteristic
96C2×Q8×C113C2311yescharacteristic
97C2×D4×C113—21no—
98C2×D4×C113—21no—
99C2×D4×C113C2311yescharacteristic
100C2×D4×C113C2311yescharacteristic
101C2×D4×C113C2311yescharacteristic
102SD16×C113—22no—
103SD16×C113—41no—
104D8×C113—22no—
105D8×C113—41no—
106C2×C8×C113C2311yescharacteristic
107C2×C8×C113C2311yescharacteristic
108C22⋊C4×C113—21no—
109C22⋊C4×C113—21no—
110C42×C113C2311yescharacteristic
111C23×C113—21no—
112C23×C113—21no—
113C23×C113—21no—
114Q8×C113—21no—
115Q8×C113—21no—
116D4×C113—21no—
117D4×C113—21no—
118D4×C113—21no—
119D4×C113—21no—
120D4×C113—21no—
121D4×C113—21no—
122D4×C113—42no—
123D4×C113—81no—
124C2×C4×C113—21no—
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2411yescharacteristic
128C2×Dic113—21no—
129C2×Dic113—21no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—42no—
133C2×Dic113—81no—
134C2×Dic113—81no—
135C2×Dic113C2×D411yescharacteristic
136C2×Dic113C2×D411yescharacteristic
137C2×Dic113C2×D411yescharacteristic
138C2×Dic113C2×D411yescharacteristic
139Dic226—21no—
140Dic226—21no—
141Dic226—21no—
142Dic226—21no—
143Dic226—41no—
144C8×C113—21no—
145C8×C113#4112yes—
146#11744751—21no—
147#11744751—21no—
148C22×C113—41no—
149C22×C113—41no—
150C22×C113—41no—
151C22×C113—41no—
152C22×C113—41no—
153C22×C113—41no—
154C22×C113—41no—
155C22×C113—41no—
156C22×C113—41no—
157C22×C113C22×D411yescharacteristic
158C4×C113—21no—
159C4×C113—21no—
160C4×C113—41no—
161C4×C113C2×#4111yescharacteristic
162C4×C113H(5,𝔽2)11yescharacteristic
163Dic113—21no—
164Dic113—21no—
165Dic113—21no—
166Dic113—21no—
167Dic113—41no—
168Dic113—41no—
169Dic113—41no—
170Dic113—41no—
171C2×C113—81no—
172C2×C113—81no—
173C2×C113—81no—
174C2×C113#55011yescharacteristic
175C2×C113#57511yescharacteristic
176C2×C113#57711yescharacteristic
177#3401—1131nomaximal, Sylow
178C113#340111yescharacteristic, complemented, Sylow
179#559—1131no—
180#556—1131no—
181#497—1131no—
182#496D11311yescharacteristic
183#495—1131no—
184#464—1131no—
185#464—1131no—
186#463—1131no—
187#463—1131no—
188#461—1131no—
189#460—1131no—
190#446—1131no—
191#442—1131no—
192#441—1131no—
193C4×SD16—1131no—
194C2×Q16—1131no—
195C2×Q16—1131no—
196C2×SD16—1131no—
197C2×SD16—1131no—
198C2×SD16—1131no—
199C2×SD16C2×D11311yescharacteristic
200C2×SD16C2×D11311yescharacteristic
201C2×D8C2×D11311yescharacteristic
202C2×D8C2×D11311yescharacteristic
203C4⋊Q8—1131no—
204#127C2×D11311yescharacteristic
205#126—2261no—
206#126—2261no—
207#124—1131no—
208#124—1131no—
209#124—1131no—
210#124—2261no—
211#124C2×D11311yescharacteristic
212#123—2261no—
213#123—2261no—
214C22⋊Q8—2261no—
215C4×Q8—1131no—
216C4×Q8—1131no—
217C4×Q8—1131no—
218C4×Q8—1131no—
219C4×D4—1131no—
220C4×D4—1131no—
221C4×D4—1131no—
222C4×D4—2261no—
223#117—2261no—
224#106—1131no—
225C4⋊C8—1131no—
226C4⋊C8—1131no—
227C4⋊C8—1131no—
228#103—1131no—
229#103—1131no—
230#103—1131no—
231#102—1131no—
232#102—1131no—
233#102—1131no—
234#97—1131no—
235#97C2×D11311yescharacteristic
236C4×C8—1131no—
237C2×Q8—1131no—
238C2×Q8—1131no—
239C2×Q8—1131no—
240C2×Q8C22×D11311yescharacteristic
241C2×D4—21no—
242C2×D4—21no—
243C2×D4C22×D11311yescharacteristic
244C2×D4C22×D11311yescharacteristic
245C2×D4C22×D11311yescharacteristic
246C22×C4—2261no—
247C22×C4—2261no—
248C22×C4—2261no—
249Q16—4521no—
250Q16—2262no—
251SD16—22no—
252SD16—41no—
253SD16—4521no—
254SD16—4521no—
255SD16—4521no—
256D8—22no—
257D8—41no—
258C2×C8—1131no—
259C2×C8—1131no—
260C2×C8C22×D11311yescharacteristic
261C2×C8C22×D11311yescharacteristic
262C4⋊C4—1131no—
263C4⋊C4—1131no—
264C4⋊C4—1131no—
265C4⋊C4—1131no—
266C4⋊C4—1131no—
267C4⋊C4—2261no—
268C4⋊C4—2261no—
269C4⋊C4—2261no—
270C4⋊C4—2261no—
271C4⋊C4—2261no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—2261no—
275C22⋊C4—2261no—
276C22⋊C4—2261no—
277C22⋊C4—2261no—
278C22⋊C4—2261no—
279C22⋊C4—2261no—
280C22⋊C4—2261no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C42—1131no—
284C42—1131no—
285C42—2261no—
286C42—2261no—
287C42—2261no—
288C42C22×D11311yescharacteristic
289C23—21no—
290C23—21no—
291C23—21no—
292Q8—21no—
293Q8—21no—
294Q8—4521no—
295Q8—2261no—
296Q8—2261no—
297Q8—2261no—
298Q8—2261no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—21no—
305D4—42no—
306D4—81no—
307C2×C4—21no—
308C2×C4—1131no—
309C2×C4—1131no—
310C2×C4—1131no—
311C2×C4—1131no—
312C2×C4—9041no—
313C2×C4—9041no—
314C2×C4—4522no—
315C2×C4—2261no—
316C2×C4—2261no—
317C2×C4—2261no—
318C2×C4—2261no—
319C2×C4D4×D11311yescharacteristic
320C2×C4D4×D11311yescharacteristic
321C2×C4C23×D11311yescharacteristic
322C8—21no—
323C8—2261no—
324C8—2261no—
325C8#1426864612yes—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22C2×D4×D11311yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—4521no—
340C4—4521no—
341C4—4521no—
342C4—4521no—
343C4—2261no—
344C4—2261no—
345C4—2261no—
346C4—2261no—
347C4C2×#1426864611yescharacteristic
348C4#1681366711yescharacteristic
349C2—81no—
350C2—81no—
351C2—81no—
352C2#2029926811yescharacteristic
353C2#2029939411yescharacteristic
354C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting, prime radical#496×C113C2
socleC22×C113C22×D4
hypercenter#496D113
hypocenterC113#3401
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #20299334C2semidirect
2. #20299317C2semidirect
3. #20298989C2semidirect
4. #20298981C2semidirect
5. #20298818C2semidirect
6. #20298817C2semidirect
7. #20298811C2semidirect
8. #20298811C2semidirect
9. #20298801C2semidirect
10. #20298795C2semidirect
11. #20298726C2semidirect
12. #20298710C2semidirect
13. #20298706C2semidirect
14. SD16×Dic113C2semidirect
178. C113#3401semidirect

Maximal subgroups

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

subgroupindex
#202993342
#202993172
#202989892
#202989812
#202988182
#202988172
#202988112
#202988012
#202987952
#202987262
#202987102
#202987062
SD16×Dic1132
#496×C1132
#3401113