Finite Group Databasebeta

← #28402739

Subgroups — #28402739

Order 14464.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×Dic226C211yesmaximal, characteristic, complemented
2#20298968C211yesmaximal, characteristic, complemented
3#20298939C211yesmaximal, characteristic, complemented
4#20298933C211yesmaximal, characteristic, complemented
5#20298902C211yesmaximal, characteristic, complemented
6#20298842C211yesmaximal, characteristic, complemented
7#20298825C211yesmaximal, characteristic, complemented
8#20298803C211yesmaximal, characteristic, complemented
9#20298736C211yesmaximal, characteristic, complemented
10#20298736C211yesmaximal, characteristic, complemented
11#20298698C211yesmaximal, characteristic, complemented
12#20298670C211yesmaximal, characteristic, complemented
13#20298606C211yesmaximal, characteristic, complemented
14C2×#16813545C211yesmaximal, characteristic, complemented
15#553×C113C211yesmaximal, characteristic
16C22×Dic226C2211yescharacteristic
17C22×Dic226C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19C2×#14268635C2211yescharacteristic
20C2×#14268635C2211yescharacteristic
21C2×#14268631C2211yescharacteristic
22C22×#11744751C2211yescharacteristic
23#16813622C2211yescharacteristic
24#16813621—21no—
25#16813601C2211yescharacteristic
26#16813601C2211yescharacteristic
27#16813599—21no—
28#16813599—21no—
29C4×Dic226C2211yescharacteristic
30D4×Dic113—21no—
31#16813555C2211yescharacteristic
32#16813555C2211yescharacteristic
33#16813553C2211yescharacteristic
34C4⋊#11744751C2211yescharacteristic
35#16813545C2211yescharacteristic
36#16813545C2211yescharacteristic
37#16813545C2211yescharacteristic
38#16813545C2211yescharacteristic
39#16813545C2211yescharacteristic
40#16813545C2211yescharacteristic
41#16813545C2211yescharacteristic
42#16813545C2211yescharacteristic
43#16813545C2211yescharacteristic
44#16813543C2211yescharacteristic
45C22⋊#11744751C2211yescharacteristic
46C22⋊#11744751C2211yescharacteristic
47#16813533C2211yescharacteristic
48#126×C113—21no—
49#125×C113C2211yescharacteristic
50#123×C113—21no—
51#121×C113—21no—
52#121×C113C2211yescharacteristic
53#121×C113C2211yescharacteristic
54C4×D4×C113—21no—
55C4×D4×C113C2211yescharacteristic
56C4×D4×C113C2211yescharacteristic
57#117×C113C2211yescharacteristic
58C2×C4⋊C4×C113C2211yescharacteristic
59C2×Dic226—22no—
60C2×Dic226—22no—
61C2×Dic226—21no—
62C2×Dic226—21no—
63C2×Dic226—41no—
64C2×Dic226—41no—
65C2×Dic226C2311yescharacteristic
66C2×Dic226C2311yescharacteristic
67C2×Dic226C2311yescharacteristic
68C22×Dic113—21no—
69C22×Dic113—21no—
70#14268635—22no—
71#14268635—41no—
72#14268635—41no—
73#14268631—41no—
74C2×#11744751—41no—
75C2×#11744751C2311yescharacteristic
76C2×#11744751C2311yescharacteristic
77C2×#11744751C2311yescharacteristic
78C2×#11744751C2311yescharacteristic
79C4⋊Dic113—21no—
80C4⋊Dic113—21no—
81C4⋊Dic113C2311yescharacteristic
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85C22⋊Dic113—21no—
86C22⋊Dic113—21no—
87C4×Dic113—21no—
88C2×D4×C113—21no—
89C2×D4×C113—21no—
90C2×D4×C113D411yescharacteristic
91C2×D4×C113C2311yescharacteristic
92C22×C4×C113—21no—
93C22×C4×C113—21no—
94C22×C4×C113C2311yescharacteristic
95C22×C4×C113C2311yescharacteristic
96C4⋊C4×C113—21no—
97C4⋊C4×C113—21no—
98C4⋊C4×C113—21no—
99C4⋊C4×C113D411yescharacteristic
100C4⋊C4×C113C2311yescharacteristic
101C4⋊C4×C113C2311yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C22⋊C4×C113—21no—
104C22⋊C4×C113—21no—
105C22⋊C4×C113—21no—
106C22⋊C4×C113—21no—
107C22⋊C4×C113D411yescharacteristic
108C22⋊C4×C113D411yescharacteristic
109C42×C113—21no—
110C42×C113C2311yescharacteristic
111C23×C113—21no—
112C23×C113C2×D411yescharacteristic
113C23×C113C2×D411yescharacteristic
114D4×C113—22no—
115D4×C113—21no—
116D4×C113—21no—
117D4×C113—42no—
118D4×C113—81no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—81no—
127C2×C4×C113—81no—
128C2×C4×C113C2×D411yescharacteristic
129C2×C4×C113C2×D411yescharacteristic
130C2×C4×C113C2×D411yescharacteristic
131C2×C4×C113C2×D411yescharacteristic
132C2×C4×C113C2411yescharacteristic
133C2×Dic113—21no—
134C2×Dic113—21no—
135C2×Dic113—21no—
136C2×Dic113—21no—
137C2×Dic113—42no—
138C2×Dic113—42no—
139Dic226—21no—
140Dic226—21no—
141Dic226—21no—
142Dic226—21no—
143Dic226—21no—
144Dic226—42no—
145Dic226—42no—
146Dic226#4112yes—
147#11744751—21no—
148#11744751—21no—
149#11744751—21no—
150#11744751—21no—
151C22×C113—21no—
152C22×C113—21no—
153C22×C113—21no—
154C22×C113—21no—
155C22×C113—21no—
156C22×C113—41no—
157C22×C113—41no—
158C22×C113—41no—
159C22×C113#13712yes—
160C22×C113C22×D411yescharacteristic
161C4×C113—21no—
162C4×C113—21no—
163C4×C113—21no—
164C4×C113—21no—
165C4×C113—41no—
166C4×C113—41no—
167C4×C113—41no—
168C4×C113C2×#4111yescharacteristic
169C4×C113H(5,𝔽2)11yescharacteristic
170Dic113—22no—
171Dic113—41no—
172Dic113—41no—
173Dic113—41no—
174C2×C113—22no—
175C2×C113—41no—
176C2×C113—81no—
177C2×C113#54611yescharacteristic
178C2×C113C2×#13711yescharacteristic
179C2×C113#57711yescharacteristic
180#3320—1131nomaximal, Sylow
181C113#332011yescharacteristic, complemented, Sylow
182#553D11311yescharacteristic
183D4×Q8—1131no—
184#491—1131no—
185#485—1131no—
186#484—1131no—
187#479—1131no—
188#468—1131no—
189#465—1131no—
190#461—1131no—
191#448—1131no—
192#448—1131no—
193#440—1131no—
194#435—1131no—
195#419—1131no—
196C2×#103—1131no—
197C22×Q8—1131no—
198C22×Q8—1131no—
199C2×SD16—1131no—
200C2×SD16—1131no—
201C2×SD16—1131no—
202C2×M16—1131no—
203C22×C8—1131no—
204C4⋊Q8—1131no—
205C4⋊Q8—2261no—
206#126—21no—
207#125C2×D11311yescharacteristic
208#123—21no—
209C22⋊Q8—1131no—
210C22⋊Q8—1131no—
211C22⋊Q8—2261no—
212C22⋊Q8—2261no—
213#121—21no—
214#121C2×D11311yescharacteristic
215#121C2×D11311yescharacteristic
216C4×Q8—1131no—
217C4×D4—21no—
218C4×D4—2261no—
219C4×D4C2×D11311yescharacteristic
220C4×D4C2×D11311yescharacteristic
221#117C2×D11311yescharacteristic
222C2×C4⋊C4C2×D11311yescharacteristic
223#107—1131no—
224#107—1131no—
225#106—1131no—
226C4⋊C8—1131no—
227#103—1131no—
228#103—1131no—
229#103—1131no—
230#103—1131no—
231#103—1131no—
232#103—1131no—
233#103—1131no—
234#103—1131no—
235#103—1131no—
236#102—1131no—
237C22⋊C8—1131no—
238C22⋊C8—1131no—
239#97—1131no—
240C2×Q8—1131no—
241C2×Q8—1131no—
242C2×Q8—1131no—
243C2×Q8—4521no—
244C2×Q8—4521no—
245C2×Q8—2262no—
246C2×Q8—2262no—
247C2×Q8—2261no—
248C2×Q8—2261no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4C22⋊D11311yescharacteristic
252C2×D4C22×D11311yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—2261no—
256C22×C4—2261no—
257C22×C4C22×D11311yescharacteristic
258C22×C4C22×D11311yescharacteristic
259SD16—4521no—
260SD16—4521no—
261SD16—2262no—
262M16—4521no—
263C2×C8—1131no—
264C2×C8—1131no—
265C2×C8—1131no—
266C2×C8—1131no—
267C2×C8—4521no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—1131no—
272C4⋊C4—2261no—
273C4⋊C4—2261no—
274C4⋊C4—2261no—
275C4⋊C4—2261no—
276C4⋊C4—2261no—
277C4⋊C4C22⋊D11311yescharacteristic
278C4⋊C4C22×D11311yescharacteristic
279C4⋊C4C22×D11311yescharacteristic
280C4⋊C4C22×D11311yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—2261no—
286C22⋊C4—2261no—
287C22⋊C4C22⋊D11311yescharacteristic
288C22⋊C4C22⋊D11311yescharacteristic
289C42—21no—
290C42—2261no—
291C42C22×D11311yescharacteristic
292C23—21no—
293C23C2×C22⋊D11311yescharacteristic
294C23C2×C22⋊D11311yescharacteristic
295Q8—1132no—
296Q8—4522no—
297Q8—4522no—
298Q8—2261no—
299Q8—2261no—
300Q8—2261no—
301Q8—2261no—
302Q8—2261no—
303D4—22no—
304D4—21no—
305D4—21no—
306D4—42no—
307D4—81no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—4522no—
318C2×C4—4522no—
319C2×C4—2261no—
320C2×C4—2261no—
321C2×C4—2261no—
322C2×C4—2261no—
323C2×C4C2×C22⋊D11311yescharacteristic
324C2×C4C2×C22⋊D11311yescharacteristic
325C2×C4C2×C22⋊D11311yescharacteristic
326C2×C4C2×C22⋊D11311yescharacteristic
327C2×C4C23×D11311yescharacteristic
328C8—2261no—
329C8—2261no—
330C8—2261no—
331C8—2261no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22#1681365212yes—
341C22C22×C22⋊D11311yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—4521no—
350C4—4521no—
351C4—4521no—
352C4—2262no—
353C4#41×D11311yescharacteristic
354C4#1681366811yescharacteristic
355C2—22no—
356C2—41no—
357C2—81no—
358C2#2029923611yescharacteristic
359C2C2×#1681365211yescharacteristic
360C2#2029940911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting, prime radical#553×C113C2
socleC22×C113C22×D4
hypercenter#553D113
hypocenterC113#3320
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. D4×Dic226C2semidirect
2. #20298968C2semidirect
3. #20298939C2semidirect
4. #20298933C2semidirect
5. #20298902C2semidirect
6. #20298842C2semidirect
7. #20298825C2semidirect
8. #20298803C2semidirect
9. #20298736C2semidirect
10. #20298736C2semidirect
11. #20298698C2semidirect
12. #20298670C2semidirect
13. #20298606C2semidirect
14. C2×#16813545C2semidirect
181. C113#3320semidirect

Maximal subgroups

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

subgroupindex
D4×Dic2262
#202989682
#202989392
#202989332
#202989022
#202988422
#202988252
#202988032
#202987362
#202986982
#202986702
#202986062
C2×#168135452
#553×C1132
#3320113