Finite Group Databasebeta

← #28400863

Subgroups — #28400863

Order 14464.

382 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299202C211yesmaximal, characteristic
2#20299074C211yesmaximal, characteristic, complemented
3#20298921C211yesmaximal, characteristic, complemented
4#20298920C211yesmaximal, characteristic, complemented
5#20298906C211yesmaximal, characteristic, complemented
6#20298905C211yesmaximal, characteristic, complemented
7#20298795C211yesmaximal, characteristic, complemented
8#20298735C211yesmaximal, characteristic, complemented
9#20298735C211yesmaximal, characteristic, complemented
10#20298699C211yesmaximal, characteristic, complemented
11#20298695C211yesmaximal, characteristic, complemented
12#20298689C211yesmaximal, characteristic, complemented
13SD16×Dic113C211yesmaximal, characteristic, complemented
14#20298658C211yesmaximal, characteristic, complemented
15#460×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic
17C2×#14268635C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19#16813614C2211yescharacteristic
20#16813603—21no—
21#16813603—21no—
22#16813594—21no—
23#16813594—21no—
24#16813593C2211yescharacteristic
25#16813593C2211yescharacteristic
26Q8×Dic113C2211yescharacteristic
27C4×Dic226—21no—
28C4×Dic226C2211yescharacteristic
29#16813587—21no—
30#16813587C2211yescharacteristic
31D4×Dic113C2211yescharacteristic
32D4×Dic113C2211yescharacteristic
33#16813580—21no—
34#16813580C2211yescharacteristic
35#16813579—21no—
36#16813579C2211yescharacteristic
37#16813556C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813554C2211yescharacteristic
40#16813553C2211yescharacteristic
41C4⋊#11744751C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813534C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813532C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×SD16×C113C2211yescharacteristic
53C2×SD16×C113C2211yescharacteristic
54#127×C113C2211yescharacteristic
55C4×Q8×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226C2311yescharacteristic
61Q8×D113—22no—
62Q8×D113—22no—
63C2×C22⋊D113—21no—
64C2×C22⋊D113—21no—
65C22×Dic113—21no—
66C22×Dic113—21no—
67C2×C4×D113—21no—
68C2×C4×D113C2311yescharacteristic
69#14268635—22no—
70#14268635—22no—
71C2×#11744751C2311yescharacteristic
72C2×#11744751C2311yescharacteristic
73C4⋊Dic113—21no—
74C4⋊Dic113C2311yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626D411yescharacteristic
82#14268626D411yescharacteristic
83C22⋊Dic113—21no—
84C22⋊Dic113—21no—
85C22⋊Dic113—21no—
86C22⋊Dic113—21no—
87#14268624—21no—
88#14268624D411yescharacteristic
89#14268624D411yescharacteristic
90C4×Dic113—21no—
91C4×Dic113—21no—
92C4×Dic113—21no—
93C4×Dic113—21no—
94C4×Dic113C2311yescharacteristic
95C2×Q8×C113C2311yescharacteristic
96C2×D4×C113—21no—
97C2×D4×C113—21no—
98C2×D4×C113C2311yescharacteristic
99C2×D4×C113C2311yescharacteristic
100SD16×C113—22no—
101SD16×C113—22no—
102C2×C8×C113C2311yescharacteristic
103C2×C8×C113C2311yescharacteristic
104C4⋊C4×C113—21no—
105C4⋊C4×C113C2311yescharacteristic
106C42×C113—21no—
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C23×C113—21no—
110C22×D113C2×D411yescharacteristic
111Q8×C113—21no—
112Q8×C113#4112yes—
113D4×C113—21no—
114D4×C113—21no—
115D4×C113—21no—
116D4×C113—21no—
117D4×C113—81no—
118D4×C113—81no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113C2×D411yescharacteristic
122C2×C4×C113C2×D411yescharacteristic
123C2×C4×C113C2411yescharacteristic
124C22⋊D113—81no—
125C22⋊D113—81no—
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113—21no—
130C2×Dic113—81no—
131C2×Dic113—81no—
132C2×Dic113C2×D411yescharacteristic
133C2×Dic113C2×D411yescharacteristic
134C2×Dic113C2×D411yescharacteristic
135C4×D113—24no—
136C4×D113—21no—
137C4×D113—21no—
138Dic226—24no—
139Dic226—21no—
140Dic226#4112yes—
141C8×C113—21no—
142C8×C113—21no—
143#11744751—21no—
144#11744751—21no—
145C22×C113—41no—
146C22×C113—41no—
147C22×C113—41no—
148C22×C113—41no—
149C22×C113—41no—
150C22×C113—41no—
151C22×C113C22×D411yescharacteristic
152C2×D113—21no—
153C2×D113—21no—
154C2×D113—21no—
155C4×C113—22no—
156C4×C113—21no—
157C4×C113—21no—
158C4×C113—41no—
159C4×C113C2×#4111yescharacteristic
160C4×C113C2×#4111yescharacteristic
161Dic113—21no—
162Dic113—22no—
163Dic113—21no—
164Dic113—21no—
165Dic113—41no—
166Dic113—41no—
167Dic113—41no—
168C2×C113—81no—
169C2×C113—81no—
170C2×C113#52511yescharacteristic
171C2×C113#57711yescharacteristic
172C2×C113#57711yescharacteristic
173D113—41no—
174#3126—1131nomaximal, Sylow
175C113#312611yescharacteristic, complemented, Sylow
176#540—1131no—
177#519—1131no—
178#482—1131no—
179#482—1131no—
180#479—1131no—
181#479—1131no—
182#460—1131no—
183#460D11311yescharacteristic, complemented
184#448—1131no—
185#448—1131no—
186#440—1131no—
187#440—1131no—
188C4×SD16—1131no—
189C4×SD16—1131no—
190#433—1131no—
191C22×Q8—1131no—
192C2×SD16—1131no—
193C2×SD16—1131no—
194C2×SD16C2×D11311yescharacteristic
195C2×SD16C2×D11311yescharacteristic
196#127C2×D11311yescharacteristic
197#125—1131no—
198#123—2261no—
199#123—2261no—
200#121—1131no—
201#121—1131no—
202#121—2261no—
203#121—2261no—
204C4×Q8—1131no—
205C4×Q8—1131no—
206C4×Q8—1131no—
207C4×Q8—2261no—
208C4×Q8—2261no—
209C4×Q8C2×D11311yescharacteristic
210C4×D4—1131no—
211C4×D4—1131no—
212#117—1131no—
213#117—1131no—
214#117—2261no—
215#117—2261no—
216#107—1131no—
217#107—1131no—
218#106—1131no—
219#106—1131no—
220C4⋊C8—1131no—
221C4⋊C8C2×D11311yescharacteristic
222#103—1131no—
223#103—1131no—
224#103—1131no—
225#103—1131no—
226#102—1131no—
227#102—1131no—
228#102C2×D11311yescharacteristic
229#102C2×D11311yescharacteristic
230C22⋊C8—1131no—
231C22⋊C8—1131no—
232#97—1131no—
233C4×C8—1131no—
234C2×Q8—1131no—
235C2×Q8—2261no—
236C2×Q8—2262no—
237C2×Q8—2262no—
238C2×Q8C22×D11311yescharacteristic
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—2261no—
242C2×D4—2261no—
243C2×D4C22×D11311yescharacteristic
244C2×D4C22×D11311yescharacteristic
245C22×C4—1131no—
246C22×C4—2261no—
247C22×C4—2261no—
248C22×C4—2261no—
249SD16—22no—
250SD16—22no—
251SD16—2262no—
252SD16—2262no—
253C2×C8—1131no—
254C2×C8—1131no—
255C2×C8C22×D11311yescharacteristic
256C2×C8C22×D11311yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—1131no—
259C4⋊C4—1131no—
260C4⋊C4—1131no—
261C4⋊C4—1131no—
262C4⋊C4—1131no—
263C4⋊C4—2261no—
264C4⋊C4—2261no—
265C4⋊C4—2261no—
266C4⋊C4—2261no—
267C4⋊C4—2261no—
268C4⋊C4C22×D11311yescharacteristic
269C22⋊C4—1131no—
270C22⋊C4—1131no—
271C22⋊C4—2261no—
272C22⋊C4—2261no—
273C22⋊C4—2261no—
274C22⋊C4—2261no—
275C22⋊C4—2261no—
276C42—21no—
277C42—1131no—
278C42—2261no—
279C42—2261no—
280C42—2261no—
281C42—2261no—
282C42C22×D11311yescharacteristic
283C23—21no—
284C23—21no—
285C23—1131no—
286Q8—21no—
287Q8—1132no—
288Q8—2264no—
289Q8—2261no—
290Q8#1426864612yes—
291D4—21no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—81no—
296D4—81no—
297D4—9041no—
298D4—9041no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—1131no—
302C2×C4—1131no—
303C2×C4—1131no—
304C2×C4—9041no—
305C2×C4—9041no—
306C2×C4—2264no—
307C2×C4—2261no—
308C2×C4—2261no—
309C2×C4—2261no—
310C2×C4—2261no—
311C2×C4—2261no—
312C2×C4—2261no—
313C2×C4D4×D11311yescharacteristic
314C2×C4D4×D11311yescharacteristic
315C2×C4C23×D11311yescharacteristic
316C8—21no—
317C8—21no—
318C8—2261no—
319C8—2261no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—2261no—
327C22—2261no—
328C22—2261no—
329C22C2×D4×D11311yescharacteristic
330C4—22no—
331C4—21no—
332C4—21no—
333C4—41no—
334C4—4521no—
335C4—4521no—
336C4—4521no—
337C4—2261no—
338C4—2262no—
339C4—2261no—
340C4—2261no—
341C4#41×D11311yescharacteristic
342C4C2×#1426864611yescharacteristic
343C2—81no—
344C2—81no—
345C2—4521no—
346C2#2029910811yescharacteristic
347C2#2029940411yescharacteristic
348C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#460×C113C2
socleC22×C113C22×D4
prime radical#20299202C2
hypercenter#460D113
hypocenterC113#3126
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
2. #20299074C2semidirect
3. #20298921C2semidirect
4. #20298920C2semidirect
5. #20298906C2semidirect
6. #20298905C2semidirect
7. #20298795C2semidirect
8. #20298735C2semidirect
9. #20298735C2semidirect
10. #20298699C2semidirect
11. #20298695C2semidirect
12. #20298689C2semidirect
13. SD16×Dic113C2semidirect
14. #20298658C2semidirect
15. #460×C113C2semidirect
175. C113#3126semidirect
183. #460D113semidirect

Maximal subgroups

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

subgroupindex
#202992022
#202990742
#202989212
#202989202
#202989062
#202989052
#202987952
#202987352
#202986992
#202986952
#202986892
SD16×Dic1132
#202986582
#460×C1132
#3126113