Finite Group Databasebeta

← #28402084

Subgroups — #28402084

Order 14464.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813651C211yesmaximal, characteristic, complemented
2Q8×C22⋊D113C211yesmaximal, characteristic, complemented
3#20299242C211yesmaximal, characteristic
4#20298989C211yesmaximal, characteristic, complemented
5#20298841C211yesmaximal, characteristic, complemented
6#20298839C211yesmaximal, characteristic, complemented
7#20298818C211yesmaximal, characteristic, complemented
8#20298801C211yesmaximal, characteristic, complemented
9#20298757C211yesmaximal, characteristic, complemented
10#20298754C211yesmaximal, characteristic, complemented
11#20298749C211yesmaximal, characteristic, complemented
12#20298735C211yesmaximal, characteristic, complemented
13#20298699C211yesmaximal, characteristic, complemented
14#20298669C211yesmaximal, characteristic, complemented
15C22×SD16×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic, complemented
18#16813651—24no—
19C2×Dic452C2211yescharacteristic, complemented
20C2×#14268637C2211yescharacteristic, complemented
21C2×#14268637C2211yescharacteristic, complemented
22C2×#14268635C2211yescharacteristic
23C2×#14268635C2211yescharacteristic
24C2×#14268630C2211yescharacteristic, complemented
25#16813620—21no—
26#16813620C2211yescharacteristic, complemented
27#16813609C2211yescharacteristic
28#16813603—21no—
29#16813601—21no—
30#16813601C2211yescharacteristic
31#16813601C2211yescharacteristic
32#16813598—21no—
33#16813598C2211yescharacteristic, complemented
34#16813594—21no—
35#16813593C2211yescharacteristic
36#16813591—21no—
37Q8×Dic113C2211yescharacteristic, complemented
38D4×Dic113C2211yescharacteristic
39C4×C22⋊D113—21no—
40C4×C22⋊D113C2211yescharacteristic
41C2×C22⋊Dic113—21no—
42#16813556C2211yescharacteristic, complemented
43#16813551C2211yescharacteristic, complemented
44#16813547C2211yescharacteristic, complemented
45#16813547C2211yescharacteristic, complemented
46#16813546C2211yescharacteristic, complemented
47#16813546C2211yescharacteristic, complemented
48#16813543C2211yescharacteristic
49#16813543C2211yescharacteristic
50C22⋊#11744751C2211yescharacteristic
51#16813534C2211yescharacteristic, complemented
52#16813532C2211yescharacteristic, complemented
53C22×Q8×C113C2211yescharacteristic
54C22×D4×C113C2211yescharacteristic
55C2×SD16×C113—24no—
56C2×SD16×C113C2211yescharacteristic
57C2×SD16×C113C2211yescharacteristic
58C2×SD16×C113C2211yescharacteristic
59C2×SD16×C113C2211yescharacteristic
60C22×C8×C113C2211yescharacteristic
61#14268646—22no—
62#14268646—41no—
63C2×Dic226—21no—
64C2×Dic226C2311yescharacteristic
65C2×Dic226C2311yescharacteristic
66Q8×D113—22no—
67Q8×D113—41no—
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70C2×C22⋊D113D411yescharacteristic
71C22×Dic113—21no—
72C22×Dic113—21no—
73C2×C4×D113—21no—
74C2×C4×D113C2311yescharacteristic
75Dic452—22no—
76#14268637—22no—
77#14268637—41no—
78#14268635—22no—
79#14268635—41no—
80#14268630—22no—
81C2×#11744751C2311yescharacteristic
82C2×#11744751C2311yescharacteristic
83C4⋊Dic113—21no—
84C4⋊Dic113C2311yescharacteristic
85C4⋊Dic113C2311yescharacteristic
86#14268626—21no—
87#14268626—21no—
88#14268626—21no—
89#14268626—21no—
90#14268626—21no—
91#14268626D411yescharacteristic
92C22⋊Dic113—21no—
93C22⋊Dic113—21no—
94C22⋊Dic113—21no—
95C22⋊Dic113—21no—
96C22⋊Dic113—21no—
97C22⋊Dic113—21no—
98C22⋊Dic113D411yescharacteristic
99#14268624—21no—
100#14268624D411yescharacteristic
101C4×Dic113—21no—
102C4×Dic113C2311yescharacteristic
103C24×C113—21no—
104C2×Q8×C113—21no—
105C2×Q8×C113—22no—
106C2×Q8×C113—41no—
107C2×Q8×C113C2311yescharacteristic
108C2×Q8×C113C2311yescharacteristic
109C2×D4×C113—22no—
110C2×D4×C113—21no—
111C2×D4×C113—41no—
112C2×D4×C113C2311yescharacteristic
113C2×D4×C113C2311yescharacteristic
114C22×C4×C113—21no—
115C22×C4×C113C2311yescharacteristic
116SD16×C113—22no—
117SD16×C113—22no—
118SD16×C113—22no—
119SD16×C113D414yescomplemented
120C2×C8×C113—22no—
121C2×C8×C113C2311yescharacteristic
122C2×C8×C113C2311yescharacteristic
123C23×C113—21no—
124C23×C113—21no—
125C23×C113—42no—
126C23×C113—42no—
127C23×C113—81no—
128C23×C113C2×D411yescharacteristic
129C22×D113C2×D411yescharacteristic
130Q8×C113—21no—
131Q8×C113—21no—
132Q8×C113—21no—
133Q8×C113—42no—
134Q8×C113C2×D412yes—
135D4×C113—21no—
136D4×C113—21no—
137D4×C113—21no—
138D4×C113—42no—
139D4×C113C2×D412yes—
140C2×C4×C113—21no—
141C2×C4×C113—21no—
142C2×C4×C113—21no—
143C2×C4×C113—21no—
144C2×C4×C113—42no—
145C2×C4×C113C2×D411yescharacteristic
146C2×C4×C113C2411yescharacteristic
147C22⋊D113—22no—
148C22⋊D113—42no—
149C22⋊D113—81no—
150C2×Dic113—21no—
151C2×Dic113—21no—
152C2×Dic113—21no—
153C2×Dic113—21no—
154C2×Dic113—42no—
155C2×Dic113—81no—
156C2×Dic113C2×D411yescharacteristic
157C2×Dic113C2×D411yescharacteristic
158C2×Dic113C2×D411yescharacteristic
159C4×D113—21no—
160C4×D113—21no—
161C4×D113—42no—
162Dic226—21no—
163Dic226—21no—
164Dic226—21no—
165Dic226—21no—
166Dic226—42no—
167C8×C113—21no—
168C8×C113C2×D412yes—
169#11744751—21no—
170#11744751—21no—
171C22×C113—21no—
172C22×C113—21no—
173C22×C113—22no—
174C22×C113—41no—
175C22×C113—41no—
176C22×C113—41no—
177C22×C113—41no—
178C22×C113—41no—
179C22×C113—84no—
180C22×C113#13712yescomplemented
181C22×C113C22×D411yescharacteristic
182C2×D113—21no—
183C2×D113—21no—
184C2×D113—21no—
185C4×C113—22no—
186C4×C113—21no—
187C4×C113—41no—
188C4×C113C22×D411yescharacteristic
189C4×C113H(5,𝔽2)11yescharacteristic
190Dic113—21no—
191Dic113—21no—
192Dic113—21no—
193Dic113—41no—
194Dic113—41no—
195Dic113—41no—
196Dic113—41no—
197C2×C113—22no—
198C2×C113—42no—
199C2×C113—81no—
200C2×C113D4211yescharacteristic
201C2×C113C2×#13711yescharacteristic
202C2×C113#57711yescharacteristic
203D113—41no—
204#3266—1131nomaximal, Sylow
205C113#326611yescharacteristic, complemented, Sylow
206C2×#137—1131no—
207C22×SD16D11311yescharacteristic, complemented
208D4×Q8—1131no—
209#546—1131no—
210#497—1131no—
211#468—1131no—
212#467—1131no—
213#464—1131no—
214#461—1131no—
215#452—1131no—
216#451—1131no—
217#450—1131no—
218#448—1131no—
219#440—1131no—
220#435—1131no—
221C2×#41—1131no—
222C22×Q8—1131no—
223C22×Q8C2×D11311yescharacteristic
224C22×D4C2×D11311yescharacteristic
225#137—2264no—
226C2×Q16—1131no—
227C2×Q16—1131no—
228C2×Q16—1131no—
229C2×SD16—24no—
230C2×SD16—1131no—
231C2×SD16—1131no—
232C2×SD16C2×D11311yescharacteristic
233C2×SD16C2×D11311yescharacteristic
234C2×SD16C2×D11311yescharacteristic
235C2×SD16C2×D11311yescharacteristic
236C2×M16—1131no—
237C22×C8C2×D11311yescharacteristic
238C4⋊Q8—1131no—
239C4⋊Q8—2261no—
240#124—1131no—
241#123—2261no—
242C22⋊Q8—1131no—
243C22⋊Q8—1131no—
244C22⋊Q8—1131no—
245C22⋊Q8—2261no—
246C22⋊Q8—2261no—
247#121—1131no—
248#121—2261no—
249#120—2261no—
250C4×Q8—1131no—
251C4×D4—1131no—
252C4×D4—1131no—
253C4×D4—2261no—
254C2×C22⋊C4—2261no—
255#107—1131no—
256C4⋊C8—1131no—
257#103—1131no—
258#103—1131no—
259#103—1131no—
260#103—1131no—
261#102—1131no—
262#102—1131no—
263C22⋊C8—1131no—
264C22⋊C8—1131no—
265#97—1131no—
266C24—21no—
267#41—4521no—
268#41—2262no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—1131no—
273C2×Q8—1131no—
274C2×Q8—4521no—
275C2×Q8—2261no—
276C2×Q8—2262no—
277C2×Q8C22×D11311yescharacteristic
278C2×Q8C22×D11311yescharacteristic
279C2×D4—22no—
280C2×D4—21no—
281C2×D4—41no—
282C2×D4—1131no—
283C2×D4—2261no—
284C2×D4—2261no—
285C2×D4C22×D11311yescharacteristic
286C2×D4C22×D11311yescharacteristic
287C22×C4—21no—
288C22×C4—1131no—
289C22×C4—2261no—
290C22×C4—2261no—
291C22×C4—2261no—
292C22×C4C22×D11311yescharacteristic
293Q16—4521no—
294Q16—2262no—
295Q16—2262no—
296SD16—22no—
297SD16—22no—
298SD16—22no—
299SD16—4521no—
300SD16—2262no—
301SD16C22⋊D11314yescomplemented
302M16—2262no—
303C2×C8—22no—
304C2×C8—1131no—
305C2×C8—1131no—
306C2×C8C22×D11311yescharacteristic
307C2×C8C22×D11311yescharacteristic
308C4⋊C4—1131no—
309C4⋊C4—1131no—
310C4⋊C4—1131no—
311C4⋊C4—2261no—
312C4⋊C4—2261no—
313C4⋊C4—2261no—
314C4⋊C4—2261no—
315C4⋊C4—2261no—
316C4⋊C4—2261no—
317C22⋊C4—1131no—
318C22⋊C4—1131no—
319C22⋊C4—2261no—
320C22⋊C4—2261no—
321C22⋊C4—2261no—
322C22⋊C4—2261no—
323C22⋊C4—2261no—
324C22⋊C4—2261no—
325C22⋊C4—2261no—
326C42—1131no—
327C42—2261no—
328C23—21no—
329C23—21no—
330C23—42no—
331C23—42no—
332C23—81no—
333C23—1131no—
334C23D4×D11311yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—42no—
339Q8—4522no—
340Q8—2261no—
341Q8—2261no—
342Q8—2261no—
343Q8—2261no—
344Q8C2×C22⋊D11312yes—
345D4—21no—
346D4—21no—
347D4—21no—
348D4—42no—
349D4—9041no—
350D4—4522no—
351D4—2262no—
352D4C2×C22⋊D11312yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—42no—
358C2×C4—1131no—
359C2×C4—1131no—
360C2×C4—1131no—
361C2×C4—9041no—
362C2×C4—4522no—
363C2×C4—4522no—
364C2×C4—2261no—
365C2×C4—2261no—
366C2×C4—2261no—
367C2×C4—2261no—
368C2×C4—2261no—
369C2×C4—2261no—
370C2×C4D4×D11311yescharacteristic
371C2×C4C23×D11311yescharacteristic
372C8—21no—
373C8—2261no—
374C8—2261no—
375C8C2×C22⋊D11312yes—
376C22—21no—
377C22—21no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—84no—
385C22—2261no—
386C22—2261no—
387C22—2261no—
388C22#1681365112yescomplemented
389C22C2×D4×D11311yescharacteristic
390C4—21no—
391C4—22no—
392C4—41no—
393C4—4521no—
394C4—4521no—
395C4—4521no—
396C4—4521no—
397C4—2261no—
398C4—2261no—
399C4—2261no—
400C4C22×C22⋊D11311yescharacteristic
401C4#1681366711yescharacteristic
402C2—22no—
403C2—42no—
404C2—81no—
405C2—4521no—
406C2D4×C22⋊D11311yescharacteristic
407C2C2×#1681365111yescharacteristic
408C2#2029940411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC22×SD16×C113C2
socleC22×C113C22×D4
prime radical#20299242C2
hypercenterC22×SD16D113
hypocenterC113#3266
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#16813651C2semidirect
2. Q8×C22⋊D113C2semidirect
4. #20298989C2semidirect
5. #20298841C2semidirect
6. #20298839C2semidirect
7. #20298818C2semidirect
8. #20298801C2semidirect
9. #20298757C2semidirect
10. #20298754C2semidirect
11. #20298749C2semidirect
12. #20298735C2semidirect
13. #20298699C2semidirect
14. #20298669C2semidirect
15. C22×SD16×C113C2semidirect
17. C2×Q8×D113C22semidirect
19. C2×Dic452C22semidirect
20. C2×#14268637C22semidirect
21. C2×#14268637C22semidirect
24. C2×#14268630C22semidirect
26. #16813620C22semidirect
33. #16813598C22semidirect
37. Q8×Dic113C22semidirect
42. #16813556C22semidirect
43. #16813551C22semidirect
44. #16813547C22semidirect
45. #16813547C22semidirect
46. #16813546C22semidirect
47. #16813546C22semidirect
51. #16813534C22semidirect
52. #16813532C22semidirect
119. SD16×C113D4semidirect
180. C22×C113#137semidirect
205. C113#3266semidirect
207. C22×SD16D113semidirect
301. SD16C22⋊D113semidirect
388. C22#16813651semidirect

Maximal subgroups

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

subgroupindex
C2×#168136512
Q8×C22⋊D1132
#202992422
#202989892
#202988412
#202988392
#202988182
#202988012
#202987572
#202987542
#202987492
#202987352
#202986992
#202986692
C22×SD16×C1132
#3266113