Finite Group Databasebeta

← #28400729

Subgroups — #28400729

Order 14464.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299150C211yesmaximal, characteristic, complemented
2#41×Dic113C211yesmaximal, characteristic
3#20298940C211yesmaximal, characteristic, complemented
4#20298936C211yesmaximal, characteristic, complemented
5#20298891C211yesmaximal, characteristic, complemented
6#20298886C211yesmaximal, characteristic, complemented
7#20298806C211yesmaximal, characteristic, complemented
8#20298801C211yesmaximal, characteristic, complemented
9#20298760C211yesmaximal, characteristic
10#20298705C211yesmaximal, characteristic, complemented
11#20298702C211yesmaximal, characteristic, complemented
12#20298699C211yesmaximal, characteristic, complemented
13#20298695C211yesmaximal, characteristic, complemented
14#20298652C211yesmaximal, characteristic, complemented
15#452×C113C211yesmaximal, characteristic
16C2×#14268637C2211yescharacteristic
17C2×#14268635C2211yescharacteristic
18#16813621C2211yescharacteristic
19#16813620C2211yescharacteristic
20#16813612—21no—
21#16813601C2211yescharacteristic
22#16813599—21no—
23Q8×Dic113C2211yescharacteristic
24Q8×Dic113C2211yescharacteristic
25Q8×Dic113C2211yescharacteristic
26#16813587—21no—
27#16813587C2211yescharacteristic
28D4×Dic113—21no—
29D4×Dic113—21no—
30D4×Dic113C2211yescharacteristic
31D4×Dic113C2211yescharacteristic
32#16813581—21no—
33#16813581C2211yescharacteristic
34#16813578—21no—
35C2×C4×Dic113—21no—
36C2×C4×Dic113C2211yescharacteristic
37#16813556C2211yescharacteristic
38#16813555C2211yescharacteristic
39#16813554C2211yescharacteristic
40#16813553C2211yescharacteristic
41#16813551C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813546C2211yescharacteristic
47#16813546C2211yescharacteristic
48#16813543C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813532C2211yescharacteristic
51#16813532C2211yescharacteristic
52C2×#41×C113C2211yescharacteristic
53C2×Q16×C113C2211yescharacteristic
54C2×SD16×C113C2211yescharacteristic
55C22⋊Q8×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226C2311yescharacteristic
61C22×Dic113—21no—
62C22×Dic113—21no—
63C22×Dic113D411yescharacteristic
64C22×Dic113D411yescharacteristic
65#14268637—22no—
66#14268635—22no—
67C2×#11744751C2311yescharacteristic
68C2×#11744751C2311yescharacteristic
69C4⋊Dic113—21no—
70C4⋊Dic113—21no—
71C4⋊Dic113—21no—
72C4⋊Dic113C2311yescharacteristic
73C4⋊Dic113C2311yescharacteristic
74C4⋊Dic113C2311yescharacteristic
75#14268626—21no—
76#14268626—21no—
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80C22⋊Dic113—21no—
81C22⋊Dic113—21no—
82C22⋊Dic113—21no—
83C22⋊Dic113—21no—
84C4×Dic113—21no—
85C4×Dic113—21no—
86C4×Dic113—21no—
87C4×Dic113—21no—
88C4×Dic113—21no—
89C4×Dic113D411yescharacteristic
90C4×Dic113D411yescharacteristic
91C4×Dic113C2311yescharacteristic
92C4×Dic113C2311yescharacteristic
93#41×C113—22no—
94#41×C113—22no—
95C2×Q8×C113C2311yescharacteristic
96C2×Q8×C113C2311yescharacteristic
97C2×D4×C113—21no—
98C2×D4×C113C2311yescharacteristic
99C22×C4×C113—21no—
100C22×C4×C113C2311yescharacteristic
101Q16×C113—22no—
102SD16×C113—22no—
103C2×C8×C113C2311yescharacteristic
104C2×C8×C113C2311yescharacteristic
105C4⋊C4×C113—21no—
106C4⋊C4×C113C2311yescharacteristic
107C22⋊C4×C113—21no—
108C23×C113—21no—
109C23×C113C2×D411yescharacteristic
110Q8×C113—21no—
111Q8×C113—21no—
112Q8×C113—21no—
113Q8×C113#4112yes—
114D4×C113—24no—
115D4×C113—21no—
116D4×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×C113C2×D411yescharacteristic
124C2×C4×C113C2411yescharacteristic
125C2×Dic113—22no—
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113—21no—
130C2×Dic113—41no—
131C2×Dic113—42no—
132C2×Dic113—42no—
133C2×Dic113C2×D411yescharacteristic
134C2×Dic113C2×D411yescharacteristic
135C2×Dic113C2×D411yescharacteristic
136C2×Dic113C2×D411yescharacteristic
137Dic226—21no—
138Dic226—21no—
139Dic226—42no—
140C8×C113—21no—
141C8×C113—21no—
142#11744751—21no—
143#11744751—21no—
144C22×C113—21no—
145C22×C113—22no—
146C22×C113—21no—
147C22×C113—21no—
148C22×C113—41no—
149C22×C113—41no—
150C22×C113C22×D411yescharacteristic
151C4×C113—21no—
152C4×C113—22no—
153C4×C113—41no—
154C4×C113—41no—
155C4×C113C2×#4111yescharacteristic
156C4×C113C2×#4111yescharacteristic
157Dic113—21no—
158Dic113—21no—
159Dic113—21no—
160Dic113—41no—
161Dic113—41no—
162Dic113—41no—
163Dic113—41no—
164Dic113#13712yes—
165C2×C113—41no—
166C2×C113—42no—
167C2×C113#52511yescharacteristic
168C2×C113C2×#13711yescharacteristic
169C2×C113#57511yescharacteristic
170#3116—1131nomaximal, Sylow
171C113#311611yescharacteristic, complemented, Sylow
172#533—1131no—
173C4×#41—1131no—
174#485—1131no—
175#485—1131no—
176#477—1131no—
177#476—1131no—
178#462—1131no—
179#461—1131no—
180#452—1131no—
181#452D11311yescharacteristic
182#441—1131no—
183#441—1131no—
184#440—1131no—
185#440—1131no—
186#432—1131no—
187C2×#41C2×D11311yescharacteristic
188C2×Q16—1131no—
189C2×Q16C2×D11311yescharacteristic
190C2×SD16—1131no—
191C2×SD16C2×D11311yescharacteristic
192C4⋊Q8—1131no—
193C4⋊Q8—1131no—
194#125—2261no—
195C22⋊Q8—1131no—
196C22⋊Q8—2261no—
197C22⋊Q8C2×D11311yescharacteristic
198C4×Q8—1131no—
199C4×Q8—1131no—
200C4×Q8—1131no—
201C4×Q8—1131no—
202C4×Q8—2261no—
203C4×D4—1131no—
204C4×D4—1131no—
205C4×D4—2261no—
206C4×D4—2261no—
207#117—1131no—
208#117—2261no—
209#117—2261no—
210C2×C42—1131no—
211C2×C42—2261no—
212#107—1131no—
213#107—1131no—
214#106—1131no—
215#106—1131no—
216C4⋊C8—1131no—
217C4⋊C8—1131no—
218#103—1131no—
219#103—1131no—
220#103—1131no—
221#103—1131no—
222#103—1131no—
223#103C2×D11311yescharacteristic
224#102—1131no—
225#102C2×D11311yescharacteristic
226C22⋊C8—1131no—
227C22⋊C8C2×D11311yescharacteristic
228#97—1131no—
229#97—1131no—
230#41—22no—
231#41—22no—
232C2×Q8—1131no—
233C2×Q8—2261no—
234C2×Q8C22×D11311yescharacteristic
235C2×Q8C22×D11311yescharacteristic
236C2×D4—21no—
237C2×D4C22×D11311yescharacteristic
238C22×C4—21no—
239C22×C4—1131no—
240C22×C4—1131no—
241C22×C4—2261no—
242C22×C4—2261no—
243C22×C4C22×D11311yescharacteristic
244Q16—22no—
245Q16—2262no—
246SD16—22no—
247SD16—2262no—
248C2×C8—1131no—
249C2×C8—1131no—
250C2×C8C22×D11311yescharacteristic
251C2×C8C22×D11311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—1131no—
254C4⋊C4—1131no—
255C4⋊C4—1131no—
256C4⋊C4—2261no—
257C4⋊C4—2261no—
258C4⋊C4—2261no—
259C4⋊C4—2261no—
260C4⋊C4—2261no—
261C4⋊C4—2261no—
262C4⋊C4—2261no—
263C4⋊C4—2261no—
264C4⋊C4C22×D11311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—2261no—
267C22⋊C4—2261no—
268C22⋊C4—2261no—
269C22⋊C4—2261no—
270C42—1131no—
271C42—1131no—
272C42—1131no—
273C42—1131no—
274C42—2261no—
275C42—2261no—
276C42—2261no—
277C42—2261no—
278C42—2261no—
279C23—21no—
280C23D4×D11311yescharacteristic
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—4522no—
285Q8—2261no—
286Q8—2261no—
287Q8#1426864612yes—
288D4—24no—
289D4—21no—
290D4#1426864612yes—
291C2×C4—24no—
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—4522no—
302C2×C4—4522no—
303C2×C4—4521no—
304C2×C4—2262no—
305C2×C4—2261no—
306C2×C4—2261no—
307C2×C4—2261no—
308C2×C4—2261no—
309C2×C4D4×D11311yescharacteristic
310C2×C4C23×D11311yescharacteristic
311C8—21no—
312C8—21no—
313C8—2261no—
314C8—2261no—
315C22—21no—
316C22—22no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22C2×D4×D11311yescharacteristic
322C4—21no—
323C4—22no—
324C4—41no—
325C4—41no—
326C4—1132no—
327C4—4521no—
328C4—4521no—
329C4—4521no—
330C4—4521no—
331C4—2261no—
332C4—2261no—
333C4—2261no—
334C4C2×#1426864611yescharacteristic
335C4C2×#1426864611yescharacteristic
336C2—41no—
337C2—42no—
338C2#2029910411yescharacteristic
339C2#137×D11311yescharacteristic
340C2#2029939511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#452×C113C2
socleC22×C113C22×D4
prime radicalC2×#41×C113C22
hypercenter#452D113
hypocenterC113#3116
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #20299150C2semidirect
3. #20298940C2semidirect
4. #20298936C2semidirect
5. #20298891C2semidirect
6. #20298886C2semidirect
7. #20298806C2semidirect
8. #20298801C2semidirect
10. #20298705C2semidirect
11. #20298702C2semidirect
12. #20298699C2semidirect
13. #20298695C2semidirect
14. #20298652C2semidirect
171. C113#3116semidirect

Maximal subgroups

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

subgroupindex
#202991502
#41×Dic1132
#202989402
#202989362
#202988912
#202988862
#202988062
#202988012
#202987602
#202987052
#202987022
#202986992
#202986952
#202986522
#452×C1132
#3116113