Finite Group Databasebeta

← #28403639

Subgroups — #28403639

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#20299330C211yesmaximal, characteristic, complemented
2#20299322C211yesmaximal, characteristic, complemented
3#20298984C211yesmaximal, characteristic
4#20298983C211yesmaximal, characteristic, complemented
5#20298822C211yesmaximal, characteristic, complemented
6#20298822C211yesmaximal, characteristic, complemented
7#20298815C211yesmaximal, characteristic, complemented
8#20298810C211yesmaximal, characteristic, complemented
9#20298800C211yesmaximal, characteristic, complemented
10#20298796C211yesmaximal, characteristic, complemented
11#20298726C211yesmaximal, characteristic, complemented
12#20298711C211yesmaximal, characteristic, complemented
13#20298705C211yesmaximal, characteristic, complemented
14SD16×Dic113C211yesmaximal, characteristic, complemented
15#497×C113C211yesmaximal, characteristic, complemented
16C2×#14268634C2211yescharacteristic
17C2×#14268634C2211yescharacteristic
18C2×#14268634C2211yescharacteristic
19C2×D904C2211yescharacteristic
20C2×#14268632C2211yescharacteristic
21#16813618C2211yescharacteristic
22#16813617—21no—
23#16813617—21no—
24#16813611C2211yescharacteristic
25#16813611C2211yescharacteristic
26#16813611C2211yescharacteristic
27#16813608—21no—
28#16813606—21no—
29#16813604—21no—
30#16813602—21no—
31Q8×Dic113C2211yescharacteristic
32Q8×Dic113C2211yescharacteristic
33Q8×Dic113C2211yescharacteristic
34C4×Dic226C2211yescharacteristic
35C4×D452C2211yescharacteristic
36C4×D452C2211yescharacteristic
37D4×Dic113C2211yescharacteristic
38#16813582—21no—
39#16813580—21no—
40#16813554C2211yescharacteristic
41C4⋊#11744751C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813551C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813546C2211yescharacteristic
47#16813544C2211yescharacteristic
48#16813544C2211yescharacteristic
49#16813543C2211yescharacteristic
50#16813532C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×Q16×C113C2211yescharacteristic
53C2×Q16×C113C2211yescharacteristic
54C2×SD16×C113C2211yescharacteristic
55C2×SD16×C113C2211yescharacteristic
56C4⋊Q8×C113C2211yescharacteristic
57#124×C113C2211yescharacteristic
58#97×C113C2211yescharacteristic
59C2×Dic226D411yescharacteristic
60C2×D452C2311yescharacteristic
61C2×D452C2311yescharacteristic
62C2×C22⋊D113—21no—
63C2×C22⋊D113—21no—
64C22×Dic113—21no—
65C2×C4×D113—21no—
66C2×C4×D113—21no—
67#14268634—41no—
68#14268634—41no—
69#14268634—41no—
70D904—22no—
71#14268632—41no—
72C2×#11744751C2311yescharacteristic
73C2×#11744751C2311yescharacteristic
74C4⋊Dic113—21no—
75C4⋊Dic113—21no—
76C4⋊Dic113—21no—
77C4⋊Dic113D411yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79C4⋊Dic113C2311yescharacteristic
80#14268626D411yescharacteristic
81#14268626D411yescharacteristic
82C22⋊Dic113—21no—
83#14268624—21no—
84#14268624—21no—
85#14268624—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91C4×Dic113—21no—
92C4×Dic113—21no—
93C4×Dic113—21no—
94C4×Dic113C2311yescharacteristic
95C4×Dic113C2311yescharacteristic
96C2×Q8×C113C2311yescharacteristic
97C2×Q8×C113C2311yescharacteristic
98C2×Q8×C113C2311yescharacteristic
99C2×D4×C113C2311yescharacteristic
100Q16×C113—22no—
101Q16×C113—41no—
102SD16×C113—22no—
103SD16×C113—41no—
104C2×C8×C113C2311yescharacteristic
105C2×C8×C113C2311yescharacteristic
106C4⋊C4×C113—21no—
107C4⋊C4×C113—21no—
108C22⋊C4×C113—21no—
109C22⋊C4×C113—21no—
110C42×C113C2311yescharacteristic
111C23×C113—21no—
112C22×D113—21no—
113C22×D113—21no—
114Q8×C113—21no—
115Q8×C113—21no—
116Q8×C113—21no—
117Q8×C113—21no—
118Q8×C113—21no—
119Q8×C113—21no—
120D4×C113—21no—
121D4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2411yescharacteristic
128C22⋊D113—42no—
129C22⋊D113—81no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—81no—
133C2×Dic113C2×D411yescharacteristic
134C2×Dic113C2×D411yescharacteristic
135C2×Dic113C2×D411yescharacteristic
136C2×Dic113C2×D411yescharacteristic
137D452—21no—
138D452—21no—
139D452—21no—
140D452—21no—
141C4×D113—42no—
142C4×D113—81no—
143Dic226—41no—
144C8×C113—21no—
145C8×C113#4112yes—
146#11744751—21no—
147#11744751—21no—
148C22×C113—41no—
149C22×C113—41no—
150C22×C113—41no—
151C22×C113C22×D411yescharacteristic
152C2×D113—41no—
153C2×D113—41no—
154C2×D113—41no—
155C2×D113—41no—
156C2×D113—41no—
157C2×D113—41no—
158C4×C113—21no—
159C4×C113—21no—
160C4×C113—41no—
161C4×C113—41no—
162C4×C113—41no—
163C4×C113C2×#4111yescharacteristic
164C4×C113H(5,𝔽2)11yescharacteristic
165Dic113—21no—
166Dic113—21no—
167Dic113—21no—
168Dic113—21no—
169Dic113—41no—
170Dic113—41no—
171C2×C113—81no—
172C2×C113#55011yescharacteristic
173C2×C113#57511yescharacteristic
174C2×C113#57711yescharacteristic
175D113—81no—
176D113—81no—
177#3401—1131nomaximal, Sylow
178C113#340111yescharacteristic, complemented, Sylow
179#559—1131no—
180#556—1131no—
181#497D11311yescharacteristic, complemented
182#496—1131no—
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×Q16C2×D11311yescharacteristic
195C2×Q16C2×D11311yescharacteristic
196C2×SD16—1131no—
197C2×SD16—1131no—
198C2×SD16—1131no—
199C2×SD16C2×D11311yescharacteristic
200C2×SD16C2×D11311yescharacteristic
201C2×D8—1131no—
202C2×D8—1131no—
203C4⋊Q8C2×D11311yescharacteristic
204#127—1131no—
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×Q8C22×D11311yescharacteristic
239C2×Q8C22×D11311yescharacteristic
240C2×Q8C22×D11311yescharacteristic
241C2×D4—1131no—
242C2×D4—1131no—
243C2×D4—2261no—
244C2×D4—2261no—
245C2×D4C22×D11311yescharacteristic
246C22×C4—2261no—
247C22×C4—2261no—
248C22×C4—2261no—
249Q16—22no—
250Q16—41no—
251SD16—22no—
252SD16—41no—
253SD16—4521no—
254SD16—4521no—
255SD16—4521no—
256D8—4521no—
257D8—2262no—
258C2×C8—1131no—
259C2×C8—1131no—
260C2×C8C22×D11311yescharacteristic
261C2×C8C22×D11311yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—1131no—
265C4⋊C4—1131no—
266C4⋊C4—1131no—
267C4⋊C4—1131no—
268C4⋊C4—1131no—
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—2261no—
291C23—2261no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—4521no—
299D4—21no—
300D4—21no—
301D4—9041no—
302D4—4522no—
303D4—2261no—
304D4—2261no—
305D4—2261no—
306D4—2261no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—1131no—
311C2×C4—1131no—
312C2×C4—1131no—
313C2×C4—1131no—
314C2×C4—9041no—
315C2×C4—9041no—
316C2×C4—4522no—
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—4521no—
330C22—4521no—
331C22—4521no—
332C22—4521no—
333C22—4521no—
334C22—4521no—
335C22C2×D4×D11311yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—4521no—
342C4—4521no—
343C4—2261no—
344C4—2261no—
345C4—2261no—
346C4—2261no—
347C4C2×#1426864611yescharacteristic
348C4#1681366711yescharacteristic
349C2—81no—
350C2—9041no—
351C2—9041no—
352C2#2029926811yescharacteristic
353C2#2029939711yescharacteristic
354C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#497×C113C2
socleC22×C113C22×D4
prime radical#20298984C2
hypercenter#497D113
hypocenterC113#3401
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #20299330C2semidirect
2. #20299322C2semidirect
4. #20298983C2semidirect
5. #20298822C2semidirect
6. #20298822C2semidirect
7. #20298815C2semidirect
8. #20298810C2semidirect
9. #20298800C2semidirect
10. #20298796C2semidirect
11. #20298726C2semidirect
12. #20298711C2semidirect
13. #20298705C2semidirect
14. SD16×Dic113C2semidirect
15. #497×C113C2semidirect
178. C113#3401semidirect
181. #497D113semidirect

Maximal subgroups

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

subgroupindex
#202993302
#202993222
#202989842
#202989832
#202988222
#202988152
#202988102
#202988002
#202987962
#202987262
#202987112
#202987052
SD16×Dic1132
#497×C1132
#3401113