Finite Group Databasebeta

← #28400800

Subgroups — #28400800

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#20299217C211yesmaximal, characteristic
2#20299074C211yesmaximal, characteristic, complemented
3#20298937C211yesmaximal, characteristic, complemented
4#20298921C211yesmaximal, characteristic
5#20298893C211yesmaximal, characteristic, complemented
6#20298884C211yesmaximal, characteristic, complemented
7#20298817C211yesmaximal, characteristic, complemented
8#20298752C211yesmaximal, characteristic, complemented
9#20298735C211yesmaximal, characteristic
10#20298705C211yesmaximal, characteristic, complemented
11#20298695C211yesmaximal, characteristic, complemented
12#20298690C211yesmaximal, characteristic, complemented
13SD16×Dic113C211yesmaximal, characteristic, complemented
14#20298658C211yesmaximal, characteristic, complemented
15#464×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic
17C2×#14268637C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19#16813622C2211yescharacteristic
20#16813615—21no—
21#16813608—21no—
22#16813606—21no—
23#16813599—21no—
24#16813598C2211yescharacteristic
25#16813593C2211yescharacteristic
26Q8×Dic113C2211yescharacteristic
27Q8×Dic113C2211yescharacteristic
28C4×Dic226—21no—
29C4×Dic226C2211yescharacteristic
30#16813587—21no—
31#16813587C2211yescharacteristic
32D4×Dic113C2211yescharacteristic
33#16813580—21no—
34#16813580C2211yescharacteristic
35#16813579—21no—
36#16813579C2211yescharacteristic
37#16813555C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813554C2211yescharacteristic
40#16813554C2211yescharacteristic
41C4⋊#11744751C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813546C2211yescharacteristic
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
59C2×Dic226—21no—
60C2×Dic226—21no—
61C2×Dic226C2311yescharacteristic
62Q8×D113—22no—
63Q8×D113—22no—
64C2×C22⋊D113—21no—
65C22×Dic113—21no—
66C2×C4×D113—21no—
67C2×C4×D113C2311yescharacteristic
68#14268637—22no—
69#14268635—22no—
70C2×#11744751C2311yescharacteristic
71C2×#11744751C2311yescharacteristic
72C4⋊Dic113—21no—
73C4⋊Dic113—21no—
74C4⋊Dic113—21no—
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77C4⋊Dic113C2311yescharacteristic
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626D411yescharacteristic
82#14268626D411yescharacteristic
83C22⋊Dic113—21no—
84C22⋊Dic113—21no—
85#14268624—21no—
86#14268624—21no—
87#14268624D411yescharacteristic
88#14268624D411yescharacteristic
89C4×Dic113—21no—
90C4×Dic113—21no—
91C4×Dic113—21no—
92C4×Dic113—21no—
93C4×Dic113—21no—
94C4×Dic113C2311yescharacteristic
95C2×Q8×C113C2311yescharacteristic
96C2×Q8×C113C2311yescharacteristic
97C2×D4×C113C2311yescharacteristic
98Q16×C113—22no—
99SD16×C113—22no—
100C2×C8×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C4⋊C4×C113—21no—
103C4⋊C4×C113C2311yescharacteristic
104C22⋊C4×C113—21no—
105C22⋊C4×C113—21no—
106C42×C113—21no—
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C22×D113C2×D411yescharacteristic
110Q8×C113—21no—
111Q8×C113—21no—
112Q8×C113—21no—
113Q8×C113#4112yes—
114D4×C113—21no—
115D4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113C2×D411yescharacteristic
120C2×C4×C113C2×D411yescharacteristic
121C2×C4×C113C2411yescharacteristic
122C22⋊D113—81no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113—21no—
127C2×Dic113—81no—
128C2×Dic113C2×D411yescharacteristic
129C2×Dic113C2×D411yescharacteristic
130C2×Dic113C2×D411yescharacteristic
131C4×D113—24no—
132C4×D113—21no—
133C4×D113—21no—
134Dic226—24no—
135Dic226—21no—
136Dic226—81no—
137Dic226#4112yes—
138C8×C113—21no—
139C8×C113—21no—
140#11744751—21no—
141#11744751—21no—
142C22×C113—41no—
143C22×C113—41no—
144C22×C113—41no—
145C22×C113C22×D411yescharacteristic
146C2×D113—21no—
147C2×D113—21no—
148C2×D113—21no—
149C4×C113—22no—
150C4×C113—21no—
151C4×C113—21no—
152C4×C113—41no—
153C4×C113—41no—
154C4×C113C2×#4111yescharacteristic
155C4×C113C2×#4111yescharacteristic
156Dic113—21no—
157Dic113—22no—
158Dic113—21no—
159Dic113—21no—
160Dic113—41no—
161Dic113—41no—
162Dic113—41no—
163C2×C113—81no—
164C2×C113#52511yescharacteristic
165C2×C113#57711yescharacteristic
166C2×C113#57811yescharacteristic
167D113—41no—
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#464D11311yescharacteristic, complemented
178#451—1131no—
179#448—1131no—
180#441—1131no—
181#440—1131no—
182C4×Q16—1131no—
183C4×SD16—1131no—
184#433—1131no—
185C22×Q8—1131no—
186C2×Q16—1131no—
187C2×Q16C2×D11311yescharacteristic
188C2×SD16—1131no—
189C2×SD16C2×D11311yescharacteristic
190C4⋊Q8—1131no—
191#126—2261no—
192#124—2261no—
193#124C2×D11311yescharacteristic
194#123—2261no—
195C22⋊Q8—1131no—
196C22⋊Q8—2261no—
197#121—1131no—
198C4×Q8—1131no—
199C4×Q8—1131no—
200C4×Q8—1131no—
201C4×Q8—1131no—
202C4×Q8—2261no—
203C4×Q8—2261no—
204C4×Q8C2×D11311yescharacteristic
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⋊C8C2×D11311yescharacteristic
216#103—1131no—
217#103—1131no—
218#103—1131no—
219#103—1131no—
220#103—1131no—
221#103C2×D11311yescharacteristic
222#102—1131no—
223#102C2×D11311yescharacteristic
224C22⋊C8—1131no—
225C22⋊C8—1131no—
226#97—1131no—
227C4×C8—1131no—
228C2×Q8—1131no—
229C2×Q8—2261no—
230C2×Q8—2262no—
231C2×Q8—2262no—
232C2×Q8—2261no—
233C2×Q8C22×D11311yescharacteristic
234C2×Q8C22×D11311yescharacteristic
235C2×D4—2261no—
236C2×D4C22×D11311yescharacteristic
237C22×C4—1131no—
238C22×C4—2261no—
239C22×C4—2261no—
240Q16—22no—
241Q16—2262no—
242SD16—22no—
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—21no—
263C22⋊C4—1131no—
264C22⋊C4—1131no—
265C22⋊C4—2261no—
266C22⋊C4—2261no—
267C22⋊C4—2261no—
268C22⋊C4—2261no—
269C42—21no—
270C42—1131no—
271C42—2261no—
272C42—2261no—
273C42—2261no—
274C42—2261no—
275C42—2261no—
276C42C22×D11311yescharacteristic
277C23—21no—
278C23—1131no—
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—1132no—
283Q8—9041no—
284Q8—2264no—
285Q8—2261no—
286Q8#1426864612yes—
287D4—21no—
288D4—21no—
289D4—9041no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—1131no—
294C2×C4—1131no—
295C2×C4—1131no—
296C2×C4—9041no—
297C2×C4—2264no—
298C2×C4—2261no—
299C2×C4—2261no—
300C2×C4—2261no—
301C2×C4—2261no—
302C2×C4—2261no—
303C2×C4—2261no—
304C2×C4D4×D11311yescharacteristic
305C2×C4D4×D11311yescharacteristic
306C2×C4C23×D11311yescharacteristic
307C8—21no—
308C8—21no—
309C8—2261no—
310C8—2261no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—2261no—
315C22—2261no—
316C22—2261no—
317C22C2×D4×D11311yescharacteristic
318C4—22no—
319C4—21no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—4521no—
324C4—4521no—
325C4—4521no—
326C4—2261no—
327C4—2262no—
328C4—2261no—
329C4—2261no—
330C4#41×D11311yescharacteristic
331C4C2×#1426864611yescharacteristic
332C2—81no—
333C2—4521no—
334C2#2029910811yescharacteristic
335C2#2029940511yescharacteristic
336C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#464×C113C2
socleC22×C113C22×D4
prime radical#16813593C22
hypercenter#464D113
hypocenterC113#3121
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
2. #20299074C2semidirect
3. #20298937C2semidirect
5. #20298893C2semidirect
6. #20298884C2semidirect
7. #20298817C2semidirect
8. #20298752C2semidirect
10. #20298705C2semidirect
11. #20298695C2semidirect
12. #20298690C2semidirect
13. SD16×Dic113C2semidirect
14. #20298658C2semidirect
15. #464×C113C2semidirect
169. C113#3121semidirect
177. #464D113semidirect

Maximal subgroups

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

subgroupindex
#202992172
#202990742
#202989372
#202989212
#202988932
#202988842
#202988172
#202987522
#202987352
#202987052
#202986952
#202986902
SD16×Dic1132
#202986582
#464×C1132
#3121113