Finite Group Databasebeta

← #28400804

Subgroups — #28400804

Order 14464.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299221C211yesmaximal, characteristic
2#20299076C211yesmaximal, characteristic, complemented
3#20298936C211yesmaximal, characteristic, complemented
4#20298923C211yesmaximal, characteristic
5#20298891C211yesmaximal, characteristic, complemented
6#20298881C211yesmaximal, characteristic, complemented
7#20298822C211yesmaximal, characteristic, complemented
8#20298822C211yesmaximal, characteristic, complemented
9#20298737C211yesmaximal, characteristic
10#20298705C211yesmaximal, characteristic, complemented
11#20298701C211yesmaximal, characteristic, complemented
12Q16×Dic113C211yesmaximal, characteristic, complemented
13#20298683C211yesmaximal, characteristic, complemented
14#20298656C211yesmaximal, characteristic, complemented
15#451×C113C211yesmaximal, characteristic, complemented
16C2×#14268634C2211yescharacteristic
17C2×#14268634C2211yescharacteristic
18#16813621C2211yescharacteristic
19#16813617—21no—
20#16813611C2211yescharacteristic
21#16813608—21no—
22#16813604—21no—
23#16813602—21no—
24#16813596C2211yescharacteristic
25Q8×Dic113—21no—
26Q8×Dic113—21no—
27Q8×Dic113C2211yescharacteristic
28Q8×Dic113C2211yescharacteristic
29Q8×Dic113C2211yescharacteristic
30Q8×Dic113C2211yescharacteristic
31Q8×Dic113C2211yescharacteristic
32#16813584C2211yescharacteristic
33#16813581—21no—
34#16813581—21no—
35#16813581C2211yescharacteristic
36#16813581C2211yescharacteristic
37#16813556C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813554C2211yescharacteristic
40#16813553C2211yescharacteristic
41#16813551C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813546C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813546C2211yescharacteristic
47#16813544C2211yescharacteristic
48#16813544C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813532C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C22×Q8×C113C2211yescharacteristic
53C2×Q16×C113C2211yescharacteristic
54C2×Q16×C113C2211yescharacteristic
55C22⋊Q8×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×D452C2311yescharacteristic
61C2×C22⋊D113—21no—
62C2×C4×D113—21no—
63#14268634—22no—
64#14268634—22no—
65C2×#11744751C2311yescharacteristic
66C2×#11744751C2311yescharacteristic
67C4⋊Dic113—21no—
68C4⋊Dic113—21no—
69C4⋊Dic113—21no—
70C4⋊Dic113—21no—
71C4⋊Dic113—21no—
72C4⋊Dic113D411yescharacteristic
73C4⋊Dic113D411yescharacteristic
74C4⋊Dic113C2311yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77#14268626—21no—
78C22⋊Dic113—21no—
79C22⋊Dic113D411yescharacteristic
80C22⋊Dic113D411yescharacteristic
81#14268624—21no—
82#14268624—21no—
83#14268624—21no—
84#14268624—21no—
85C4×Dic113—21no—
86C4×Dic113—21no—
87C4×Dic113—21no—
88C4×Dic113—21no—
89C4×Dic113—21no—
90C4×Dic113—21no—
91C4×Dic113C2311yescharacteristic
92C4×Dic113C2311yescharacteristic
93C2×Q8×C113—22no—
94C2×Q8×C113—22no—
95C2×Q8×C113—21no—
96C2×Q8×C113C2311yescharacteristic
97C2×Q8×C113C2311yescharacteristic
98C2×Q8×C113C2311yescharacteristic
99C22×C4×C113—21no—
100C22×C4×C113C2311yescharacteristic
101Q16×C113—22no—
102Q16×C113—22no—
103C2×C8×C113C2311yescharacteristic
104C2×C8×C113C2311yescharacteristic
105C4⋊C4×C113—21no—
106C4⋊C4×C113C2311yescharacteristic
107C22⋊C4×C113—21no—
108C23×C113C2×D411yescharacteristic
109C22×D113—21no—
110Q8×C113—24no—
111Q8×C113—21no—
112Q8×C113—21no—
113Q8×C113—21no—
114Q8×C113—21no—
115Q8×C113#4112yes—
116Q8×C113#4112yes—
117C2×C4×C113—24no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2411yescharacteristic
126C22⋊D113—81no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113—21no—
130C2×Dic113C2×D411yescharacteristic
131C2×Dic113C2×D411yescharacteristic
132C2×Dic113C2×D411yescharacteristic
133C2×Dic113C2×D411yescharacteristic
134D452—21no—
135D452—21no—
136C4×D113—81no—
137Dic226—81no—
138C8×C113—21no—
139C8×C113—21no—
140#11744751—21no—
141#11744751—21no—
142C22×C113—21no—
143C22×C113—21no—
144C22×C113—21no—
145C22×C113C22×D411yescharacteristic
146C2×D113—41no—
147C2×D113—41no—
148C2×D113—41no—
149C4×C113—22no—
150C4×C113—22no—
151C4×C113—21no—
152C4×C113—41no—
153C4×C113—41no—
154C4×C113C2×#4111yescharacteristic
155C4×C113C2×#4111yescharacteristic
156Dic113—21no—
157Dic113—21no—
158Dic113—21no—
159Dic113—21no—
160Dic113—41no—
161Dic113—41no—
162Dic113—41no—
163C2×C113—41no—
164C2×C113#52511yescharacteristic
165C2×C113#57711yescharacteristic
166C2×C113#57811yescharacteristic
167D113—81no—
168#3121—1131nomaximal, Sylow
169C113#312111yescharacteristic, complemented, Sylow
170#542—1131no—
171#519—1131no—
172#485—1131no—
173#482—1131no—
174#477—1131no—
175#475—1131no—
176#464—1131no—
177#464—1131no—
178#451D11311yescharacteristic, complemented
179#448—1131no—
180#441—1131no—
181#440—1131no—
182C4×Q16—1131no—
183C4×SD16—1131no—
184#433—1131no—
185C22×Q8C2×D11311yescharacteristic
186C2×Q16C2×D11311yescharacteristic
187C2×Q16C2×D11311yescharacteristic
188C2×SD16—1131no—
189C2×SD16—1131no—
190C4⋊Q8—1131no—
191#126—2261no—
192#124—1131no—
193#124—2261no—
194#123—2261no—
195C22⋊Q8—2261no—
196C22⋊Q8C2×D11311yescharacteristic
197#121—1131no—
198C4×Q8—1131no—
199C4×Q8—1131no—
200C4×Q8—1131no—
201C4×Q8—1131no—
202C4×Q8—1131no—
203C4×Q8—2261no—
204C4×Q8—2261no—
205C4×D4—1131no—
206#117—1131no—
207#117—1131no—
208#117—2261no—
209#117—2261no—
210#107—1131no—
211#107—1131no—
212#106—1131no—
213#106—1131no—
214C4⋊C8—1131no—
215C4⋊C8—1131no—
216#103—1131no—
217#103—1131no—
218#103—1131no—
219#103—1131no—
220#103C2×D11311yescharacteristic
221#103C2×D11311yescharacteristic
222#102—1131no—
223#102—1131no—
224C22⋊C8—1131no—
225C22⋊C8C2×D11311yescharacteristic
226#97—1131no—
227C4×C8—1131no—
228C2×Q8—22no—
229C2×Q8—22no—
230C2×Q8—21no—
231C2×Q8—2261no—
232C2×Q8C22×D11311yescharacteristic
233C2×Q8C22×D11311yescharacteristic
234C2×Q8C22×D11311yescharacteristic
235C2×D4—1131no—
236C2×D4—2261no—
237C22×C4—21no—
238C22×C4—2261no—
239C22×C4C22×D11311yescharacteristic
240Q16—22no—
241Q16—22no—
242SD16—2262no—
243SD16—2262no—
244C2×C8—1131no—
245C2×C8—1131no—
246C2×C8C22×D11311yescharacteristic
247C2×C8C22×D11311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—1131no—
250C4⋊C4—1131no—
251C4⋊C4—1131no—
252C4⋊C4—1131no—
253C4⋊C4—1131no—
254C4⋊C4—2261no—
255C4⋊C4—2261no—
256C4⋊C4—2261no—
257C4⋊C4—2261no—
258C4⋊C4—2261no—
259C4⋊C4—2261no—
260C4⋊C4C22×D11311yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—1131no—
263C22⋊C4—1131no—
264C22⋊C4—2261no—
265C22⋊C4—2261no—
266C22⋊C4—2261no—
267C22⋊C4—2261no—
268C22⋊C4—2261no—
269C42—1131no—
270C42—1131no—
271C42—2261no—
272C42—2261no—
273C42—2261no—
274C42—2261no—
275C42—2261no—
276C42—2261no—
277C23—2261no—
278C23D4×D11311yescharacteristic
279Q8—24no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—9041no—
285Q8#1426864612yes—
286Q8#1426864612yes—
287D4—9041no—
288D4—2261no—
289D4—2261no—
290C2×C4—24no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—1131no—
298C2×C4—1131no—
299C2×C4—1131no—
300C2×C4—1131no—
301C2×C4—9041no—
302C2×C4—2261no—
303C2×C4—2261no—
304C2×C4—2261no—
305C2×C4D4×D11311yescharacteristic
306C2×C4C23×D11311yescharacteristic
307C8—21no—
308C8—21no—
309C8—2261no—
310C8—2261no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—4521no—
315C22—4521no—
316C22—4521no—
317C22C2×D4×D11311yescharacteristic
318C4—22no—
319C4—22no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—4521no—
324C4—4521no—
325C4—4521no—
326C4—2261no—
327C4—2261no—
328C4—2261no—
329C4—2261no—
330C4C2×#1426864611yescharacteristic
331C4C2×#1426864611yescharacteristic
332C2—41no—
333C2—9041no—
334C2#2029910411yescharacteristic
335C2#2029940711yescharacteristic
336C2#2029941111yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#451×C113C2
socleC22×C113C22×D4
prime radical#16813596C22
hypercenter#451D113
hypocenterC113#3121
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. #20299076C2semidirect
3. #20298936C2semidirect
5. #20298891C2semidirect
6. #20298881C2semidirect
7. #20298822C2semidirect
8. #20298822C2semidirect
10. #20298705C2semidirect
11. #20298701C2semidirect
12. Q16×Dic113C2semidirect
13. #20298683C2semidirect
14. #20298656C2semidirect
15. #451×C113C2semidirect
169. C113#3121semidirect
178. #451D113semidirect

Maximal subgroups

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

subgroupindex
#202992212
#202990762
#202989362
#202989232
#202988912
#202988812
#202988222
#202987372
#202987052
#202987012
Q16×Dic1132
#202986832
#202986562
#451×C1132
#3121113