Finite Group Databasebeta

← #28401654

Subgroups — #28401654

Order 14464.

364 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#20299206C211yesmaximal, characteristic, complemented
2#20299168C211yesmaximal, characteristic
3#20298989C211yesmaximal, characteristic, complemented
4#20298976C211yesmaximal, characteristic, complemented
5#20298965C211yesmaximal, characteristic, complemented
6#20298951C211yesmaximal, characteristic, complemented
7#20298817C211yesmaximal, characteristic, complemented
8#20298809C211yesmaximal, characteristic, complemented
9#20298808C211yesmaximal, characteristic, complemented
10#20298761C211yesmaximal, characteristic
11#20298757C211yesmaximal, characteristic
12#20298755C211yesmaximal, characteristic, complemented
13#20298752C211yesmaximal, characteristic, complemented
14#20298658C211yesmaximal, characteristic, complemented
15#464×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18C2×Dic452C2211yescharacteristic
19C2×Dic452C2211yescharacteristic
20C2×#14268637C2211yescharacteristic
21C2×#14268637C2211yescharacteristic
22C2×#14268637C2211yescharacteristic
23C2×#14268635C2211yescharacteristic
24#16813622C2211yescharacteristic
25#16813620C2211yescharacteristic
26#16813620C2211yescharacteristic
27#16813617—21no—
28#16813616—21no—
29#16813614—21no—
30#16813613C2211yescharacteristic
31#16813612—21no—
32#16813609C2211yescharacteristic
33#16813604—21no—
34#16813604—21no—
35#16813602C2211yescharacteristic
36#16813599—21no—
37#16813599—21no—
38#16813598C2211yescharacteristic
39C4×Dic226C2211yescharacteristic
40#16813579C2211yescharacteristic
41C4⋊#11744751C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813534C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813532C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×Q16×C113C2211yescharacteristic
53C2×SD16×C113C2211yescharacteristic
54#124×C113C2211yescharacteristic
55C4×Q8×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59#14268646—41no—
60#14268646—41no—
61C2×Dic226—21no—
62C2×Dic226C2311yescharacteristic
63C2×Dic226C2311yescharacteristic
64C2×Dic226C2311yescharacteristic
65Q8×D113—41no—
66Q8×D113—41no—
67C2×C22⋊D113—21no—
68C22×Dic113—21no—
69C2×C4×D113—21no—
70C2×C4×D113C2311yescharacteristic
71Dic452—41no—
72Dic452—41no—
73#14268637—41no—
74#14268637—41no—
75#14268637—41no—
76#14268635—41no—
77C2×#11744751C2311yescharacteristic
78C2×#11744751C2311yescharacteristic
79C4⋊Dic113—21no—
80C4⋊Dic113—21no—
81C4⋊Dic113—21no—
82C4⋊Dic113—21no—
83C4⋊Dic113C2311yescharacteristic
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88#14268626—21no—
89#14268626—21no—
90#14268626—21no—
91#14268626D411yescharacteristic
92#14268626D411yescharacteristic
93C22⋊Dic113—21no—
94C22⋊Dic113—21no—
95#14268624—21no—
96#14268624—21no—
97#14268624D411yescharacteristic
98#14268624D411yescharacteristic
99C4×Dic113—21no—
100C4×Dic113C2311yescharacteristic
101C2×Q8×C113C2311yescharacteristic
102C2×Q8×C113C2311yescharacteristic
103C2×D4×C113C2311yescharacteristic
104Q16×C113—41no—
105SD16×C113—41no—
106C2×C8×C113C2311yescharacteristic
107C2×C8×C113C2311yescharacteristic
108C4⋊C4×C113—21no—
109C4⋊C4×C113C2311yescharacteristic
110C22⋊C4×C113—21no—
111C22⋊C4×C113—21no—
112C42×C113—21no—
113C42×C113C2311yescharacteristic
114C23×C113—21no—
115C22×D113C2×D411yescharacteristic
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—
129C2×Dic113—21no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—42no—
134C2×Dic113C2×D411yescharacteristic
135C2×Dic113C2×D411yescharacteristic
136C2×Dic113C2×D411yescharacteristic
137C4×D113—21no—
138C4×D113—21no—
139C4×D113—42no—
140Dic226—21no—
141Dic226—21no—
142Dic226—21no—
143Dic226—21no—
144Dic226—21no—
145Dic226—21no—
146Dic226—42no—
147C8×C113—21no—
148C8×C113—21no—
149#11744751—21no—
150#11744751—21no—
151C22×C113—41no—
152C22×C113—41no—
153C22×C113—41no—
154C22×C113C22×D411yescharacteristic
155C2×D113—21no—
156C2×D113—21no—
157C2×D113—21no—
158C4×C113—21no—
159C4×C113—21no—
160C4×C113—41no—
161C4×C113—41no—
162C4×C113—41no—
163C4×C113H(5,𝔽2)11yescharacteristic
164C4×C113H(5,𝔽2)11yescharacteristic
165Dic113—21no—
166Dic113—21no—
167Dic113—21no—
168Dic113—41no—
169Dic113—41no—
170Dic113—41no—
171Dic113—41no—
172C2×C113—81no—
173C2×C113#53511yescharacteristic
174C2×C113#57811yescharacteristic
175C2×C113#57811yescharacteristic
176D113—41no—
177#3223—1131nomaximal, Sylow
178C113#322311yescharacteristic, complemented, Sylow
179#541—1131no—
180#536—1131no—
181#497—1131no—
182#494—1131no—
183#491—1131no—
184#488—1131no—
185#464—1131no—
186#464D11311yescharacteristic, complemented
187#462—1131no—
188#462—1131no—
189#452—1131no—
190#452—1131no—
191#451—1131no—
192#451—1131no—
193#433—1131no—
194C2×#41—1131no—
195C22×Q8—1131no—
196C2×Q16—1131no—
197C2×Q16—1131no—
198C2×Q16—1131no—
199C2×Q16—1131no—
200C2×Q16—1131no—
201C2×Q16C2×D11311yescharacteristic
202C2×SD16—1131no—
203C2×SD16C2×D11311yescharacteristic
204C4⋊Q8—1131no—
205C4⋊Q8—1131no—
206C4⋊Q8—1131no—
207#126—2261no—
208#126—2261no—
209#125—1131no—
210#125—2261no—
211#125—2261no—
212#124—1131no—
213#124C2×D11311yescharacteristic
214#123—2261no—
215#123—2261no—
216C22⋊Q8—1131no—
217C22⋊Q8—1131no—
218C22⋊Q8—2261no—
219C22⋊Q8—2261no—
220C4×Q8—1131no—
221C4×Q8C2×D11311yescharacteristic
222#117—1131no—
223C4⋊C8—1131no—
224C4⋊C8C2×D11311yescharacteristic
225#103—1131no—
226#103—1131no—
227#103—1131no—
228#103—1131no—
229#103—1131no—
230#103C2×D11311yescharacteristic
231#102—1131no—
232#102C2×D11311yescharacteristic
233C22⋊C8—1131no—
234C22⋊C8—1131no—
235#97—1131no—
236C4×C8—1131no—
237#41—4521no—
238#41—4521no—
239C2×Q8—1131no—
240C2×Q8—1131no—
241C2×Q8—1131no—
242C2×Q8—4521no—
243C2×Q8—4521no—
244C2×Q8—2261no—
245C2×Q8C22×D11311yescharacteristic
246C2×Q8C22×D11311yescharacteristic
247C2×D4—2261no—
248C2×D4C22×D11311yescharacteristic
249C22×C4—1131no—
250C22×C4—2261no—
251C22×C4—2261no—
252Q16—41no—
253Q16—4521no—
254Q16—4521no—
255Q16—4521no—
256Q16—4521no—
257Q16—4521no—
258SD16—41no—
259SD16—4521no—
260C2×C8—1131no—
261C2×C8—1131no—
262C2×C8C22×D11311yescharacteristic
263C2×C8C22×D11311yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—1131no—
266C4⋊C4—1131no—
267C4⋊C4—1131no—
268C4⋊C4—2261no—
269C4⋊C4—2261no—
270C4⋊C4—2261no—
271C4⋊C4—2261no—
272C4⋊C4—2261no—
273C4⋊C4—2261no—
274C4⋊C4—2261no—
275C4⋊C4—2261no—
276C4⋊C4—2261no—
277C4⋊C4—2261no—
278C4⋊C4—2261no—
279C4⋊C4C22×D11311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—1131no—
283C22⋊C4—1131no—
284C22⋊C4—2261no—
285C22⋊C4—2261no—
286C22⋊C4—2261no—
287C22⋊C4—2261no—
288C42—21no—
289C42—1131no—
290C42—2261no—
291C42C22×D11311yescharacteristic
292C23—21no—
293C23—1131no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—4522no—
299Q8—2261no—
300Q8—2261no—
301Q8—2261no—
302Q8—2261no—
303Q8—2261no—
304Q8—2261no—
305D4—21no—
306D4—21no—
307D4—4522no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—1131no—
312C2×C4—1131no—
313C2×C4—1131no—
314C2×C4—4522no—
315C2×C4—4522no—
316C2×C4—2261no—
317C2×C4—2261no—
318C2×C4—2261no—
319C2×C4—2261no—
320C2×C4—2261no—
321C2×C4—2261no—
322C2×C4D4×D11311yescharacteristic
323C2×C4D4×D11311yescharacteristic
324C2×C4C23×D11311yescharacteristic
325C8—21no—
326C8—21no—
327C8—2261no—
328C8—2261no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—2261no—
333C22—2261no—
334C22—2261no—
335C22C2×D4×D11311yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—4521no—
342C4—4521no—
343C4—4521no—
344C4—4521no—
345C4—2261no—
346C4—2261no—
347C4—2261no—
348C4#1681366711yescharacteristic
349C4#1681366811yescharacteristic
350C2—81no—
351C2—4521no—
352C2#2029916411yescharacteristic
353C2#2029941211yescharacteristic
354C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#464×C113C2
socleC22×C113C22×D4
prime radicalC2×#14268646C22
hypercenter#464D113
hypocenterC113#3223
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #20299206C2semidirect
3. #20298989C2semidirect
4. #20298976C2semidirect
5. #20298965C2semidirect
6. #20298951C2semidirect
7. #20298817C2semidirect
8. #20298809C2semidirect
9. #20298808C2semidirect
12. #20298755C2semidirect
13. #20298752C2semidirect
14. #20298658C2semidirect
15. #464×C113C2semidirect
178. C113#3223semidirect
186. #464D113semidirect

Maximal subgroups

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

subgroupindex
#202992062
#202991682
#202989892
#202989762
#202989652
#202989512
#202988172
#202988092
#202988082
#202987612
#202987572
#202987552
#202987522
#202986582
#464×C1132
#3223113