Finite Group Databasebeta

← #28402746

Subgroups — #28402746

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
1#20299292C211yesmaximal, characteristic
2Q8×C22⋊D113C211yesmaximal, characteristic, complemented
3#20298965C211yesmaximal, characteristic, complemented
4#20298939C211yesmaximal, characteristic, complemented
5#20298932C211yesmaximal, characteristic, complemented
6#20298907C211yesmaximal, characteristic, complemented
7#20298844C211yesmaximal, characteristic, complemented
8#20298830C211yesmaximal, characteristic, complemented
9#20298802C211yesmaximal, characteristic, complemented
10#20298738C211yesmaximal, characteristic, complemented
11#20298737C211yesmaximal, characteristic, complemented
12#20298701C211yesmaximal, characteristic, complemented
13#20298667C211yesmaximal, characteristic, complemented
14#103×D113C211yesmaximal, characteristic, complemented
15#419×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic
17C2×#14268636C2211yescharacteristic
18C2×#14268634C2211yescharacteristic
19C2×#14268634C2211yescharacteristic
20C2×C8×D113C2211yescharacteristic
21#16813620—21no—
22#16813620C2211yescharacteristic
23#16813616—21no—
24#16813613C2211yescharacteristic
25#16813604—21no—
26#16813601—21no—
27#16813601C2211yescharacteristic
28#16813598—21no—
29#16813598C2211yescharacteristic
30#16813597C2211yescharacteristic
31#16813596C2211yescharacteristic
32#16813595—21no—
33Q8×Dic113C2211yescharacteristic
34C4×D452—21no—
35#16813584C2211yescharacteristic
36C4×C22⋊D113—21no—
37C4×C22⋊D113C2211yescharacteristic
38C4⋊C4×D113C2211yescharacteristic
39#16813556C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813553C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813544C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813532C2211yescharacteristic
52C22×Q8×C113C2211yescharacteristic
53C2×M16×C113C2211yescharacteristic
54#117×C113C2211yescharacteristic
55#103×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226C2311yescharacteristic
61Q8×D113—22no—
62Q8×D113—41no—
63C2×D452—21no—
64C2×D452C2311yescharacteristic
65C2×C22⋊D113—21no—
66C2×C22⋊D113D411yescharacteristic
67C2×C4×D113—21no—
68C2×C4×D113—21no—
69C2×C4×D113—21no—
70C2×C4×D113C2311yescharacteristic
71#14268636—41no—
72#14268634—22no—
73#14268634—41no—
74C2×#11744751C2311yescharacteristic
75C2×#11744751C2311yescharacteristic
76C8×D113—41no—
77C4⋊Dic113—21no—
78C4⋊Dic113—21no—
79C4⋊Dic113C2311yescharacteristic
80C4⋊Dic113C2311yescharacteristic
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626D411yescharacteristic
88C22⋊Dic113—21no—
89C22⋊Dic113D411yescharacteristic
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624D411yescharacteristic
95C4×Dic113—21no—
96C4×Dic113C2311yescharacteristic
97C2×Q8×C113—21no—
98C2×Q8×C113—22no—
99C2×Q8×C113—41no—
100C2×Q8×C113C2311yescharacteristic
101C2×Q8×C113C2311yescharacteristic
102C22×C4×C113—21no—
103C22×C4×C113C2311yescharacteristic
104M16×C113—41no—
105C2×C8×C113C2311yescharacteristic
106C2×C8×C113C2311yescharacteristic
107C4⋊C4×C113C2311yescharacteristic
108C4⋊C4×C113C2311yescharacteristic
109C22⋊C4×C113—21no—
110C42×C113—21no—
111C23×C113C2×D411yescharacteristic
112C22×D113—21no—
113C22×D113C2×D411yescharacteristic
114Q8×C113—21no—
115Q8×C113—21no—
116Q8×C113—21no—
117Q8×C113—42no—
118Q8×C113#4112yes—
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—42no—
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2411yescharacteristic
128C22⋊D113—22no—
129C22⋊D113—81no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113C2×D411yescharacteristic
134C2×Dic113C2×D411yescharacteristic
135C2×Dic113C2×D411yescharacteristic
136D452—21no—
137D452—21no—
138D452—42no—
139C4×D113—21no—
140C4×D113—21no—
141C4×D113—42no—
142C4×D113—81no—
143C4×D113—81no—
144Dic226—21no—
145Dic226—21no—
146Dic226—42no—
147C8×C113—21no—
148C8×C113—21no—
149#11744751—21no—
150#11744751—21no—
151C22×C113—21no—
152C22×C113—21no—
153C22×C113—21no—
154C22×C113C22×D411yescharacteristic
155C2×D113—21no—
156C2×D113—21no—
157C2×D113—41no—
158C2×D113—41no—
159C2×D113—41no—
160C2×D113#13712yes—
161C4×C113—22no—
162C4×C113—21no—
163C4×C113—41no—
164C4×C113—41no—
165C4×C113—41no—
166C4×C113C2×#4111yescharacteristic
167C4×C113H(5,𝔽2)11yescharacteristic
168Dic113—21no—
169Dic113—21no—
170Dic113—21no—
171Dic113—41no—
172Dic113—41no—
173Dic113—41no—
174C2×C113—41no—
175C2×C113#54611yescharacteristic
176C2×C113C2×#13711yescharacteristic
177C2×C113#57711yescharacteristic
178D113—22no—
179D113—81no—
180#3320—1131nomaximal, Sylow
181C113#332011yescharacteristic, complemented, Sylow
182#553—1131no—
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#419D11311yescharacteristic, complemented
196C2×#103—1131no—
197C22×Q8—1131no—
198C22×Q8C2×D11311yescharacteristic
199C2×SD16—1131no—
200C2×SD16—1131no—
201C2×SD16—1131no—
202C2×M16C2×D11311yescharacteristic
203C22×C8—1131no—
204C4⋊Q8—1131no—
205C4⋊Q8—2261no—
206#126—2261no—
207#125—1131no—
208#123—2261no—
209C22⋊Q8—1131no—
210C22⋊Q8—1131no—
211C22⋊Q8—2261no—
212C22⋊Q8—2261no—
213#121—1131no—
214#121—1131no—
215#121—2261no—
216C4×Q8—1131no—
217C4×D4—1131no—
218C4×D4—1131no—
219C4×D4—2261no—
220C4×D4—2261no—
221#117C2×D11311yescharacteristic
222C2×C4⋊C4—1131no—
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#103C2×D11311yescharacteristic
233#103C2×D11311yescharacteristic
234#103C2×D11311yescharacteristic
235#103C2×D11311yescharacteristic
236#102—1131no—
237C22⋊C8—1131no—
238C22⋊C8—1131no—
239#97—1131no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—1131no—
244C2×Q8—4521no—
245C2×Q8—2261no—
246C2×Q8—2262no—
247C2×Q8C22×D11311yescharacteristic
248C2×Q8C22×D11311yescharacteristic
249C2×D4—1131no—
250C2×D4—1131no—
251C2×D4—2261no—
252C2×D4—2261no—
253C22×C4—21no—
254C22×C4—1131no—
255C22×C4—2261no—
256C22×C4—2261no—
257C22×C4—2261no—
258C22×C4C22×D11311yescharacteristic
259SD16—4521no—
260SD16—4521no—
261SD16—2262no—
262M16—41no—
263C2×C8—1131no—
264C2×C8—1131no—
265C2×C8—4521no—
266C2×C8C22×D11311yescharacteristic
267C2×C8C22×D11311yescharacteristic
268C4⋊C4—1131no—
269C4⋊C4—1131no—
270C4⋊C4—1131no—
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
280C4⋊C4C22×D11311yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—1131no—
283C22⋊C4—1131no—
284C22⋊C4—2261no—
285C22⋊C4—2261no—
286C22⋊C4—2261no—
287C22⋊C4—2261no—
288C22⋊C4—2261no—
289C42—21no—
290C42—1131no—
291C42—2261no—
292C23—1131no—
293C23—2261no—
294C23D4×D11311yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—42no—
299Q8—4522no—
300Q8—2261no—
301Q8—2261no—
302Q8#1426864712yes—
303D4—9041no—
304D4—4522no—
305D4—2262no—
306D4—2261no—
307D4—2261no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—1131no—
316C2×C4—1131no—
317C2×C4—1131no—
318C2×C4—9041no—
319C2×C4—9041no—
320C2×C4—4522no—
321C2×C4—2261no—
322C2×C4—2261no—
323C2×C4—2261no—
324C2×C4—2261no—
325C2×C4—2261no—
326C2×C4D4×D11311yescharacteristic
327C2×C4C23×D11311yescharacteristic
328C8—21no—
329C8—21no—
330C8—2261no—
331C8—2261no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—1132no—
336C22—4521no—
337C22—4521no—
338C22—4521no—
339C22—2261no—
340C22—2261no—
341C22C2×D4×D11311yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—4521no—
348C4—4521no—
349C4—4521no—
350C4—2261no—
351C4—2261no—
352C4—2261no—
353C4C2×#1426864711yescharacteristic
354C4#1681366711yescharacteristic
355C2—41no—
356C2—9041no—
357C2—2262no—
358C2#2029923811yescharacteristic
359C2#137×D11311yescharacteristic
360C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#419×C113C2
socleC22×C113C22×D4
prime radical#20299292C2
hypercenter#419D113
hypocenterC113#3320
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
2. Q8×C22⋊D113C2semidirect
3. #20298965C2semidirect
4. #20298939C2semidirect
5. #20298932C2semidirect
6. #20298907C2semidirect
7. #20298844C2semidirect
8. #20298830C2semidirect
9. #20298802C2semidirect
10. #20298738C2semidirect
11. #20298737C2semidirect
12. #20298701C2semidirect
13. #20298667C2semidirect
14. #103×D113C2semidirect
15. #419×C113C2semidirect
181. C113#3320semidirect
195. #419D113semidirect

Maximal subgroups

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

subgroupindex
#202992922
Q8×C22⋊D1132
#202989652
#202989392
#202989322
#202989072
#202988442
#202988302
#202988022
#202987382
#202987372
#202987012
#202986672
#103×D1132
#419×C1132
#3320113