Finite Group Databasebeta

← #28400249

Subgroups — #28400249

Order 14464.

504 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813649C211yesmaximal, characteristic, complemented
2C2×#16813630C211yesmaximal, characteristic, complemented
3#20299178C211yesmaximal, characteristic, complemented
4#20299164C211yesmaximal, characteristic, complemented
5#20298851C211yesmaximal, characteristic, complemented
6#20298850C211yesmaximal, characteristic, complemented
7#20298847C211yesmaximal, characteristic, complemented
8#20298835C211yesmaximal, characteristic, complemented
9#20298832C211yesmaximal, characteristic, complemented
10#20298829C211yesmaximal, characteristic, complemented
11#20298824C211yesmaximal, characteristic, complemented
12#20298639C211yesmaximal, characteristic, complemented
13#20298593C211yesmaximal, characteristic, complemented
14#102×D113C211yesmaximal, characteristic, complemented
15#468×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268647C2211yescharacteristic
18C2×D4×D113C2211yescharacteristic
19#16813649—24no—
20C2×#14268634C2211yescharacteristic
21C2×D904C2211yescharacteristic
22C2×#14268632C2211yescharacteristic
23#16813630—24no—
24C2×#14268630C2211yescharacteristic
25C2×#14268630C2211yescharacteristic, complemented
26C22×#11744751C2211yescharacteristic, complemented
27C2×C8×D113C2211yescharacteristic
28C2×C8×D113C2211yescharacteristic, complemented
29#16813618—21no—
30#16813608—21no—
31#16813600—21no—
32#16813598C2211yescharacteristic, complemented
33#16813597—21no—
34#16813597C2211yescharacteristic
35#16813597C2211yescharacteristic, complemented
36#16813596C2211yescharacteristic
37#16813596C2211yescharacteristic, complemented
38#16813595—21no—
39#16813595—21no—
40#16813593C2211yescharacteristic
41#16813592—21no—
42#16813590—21no—
43#16813580C2211yescharacteristic
44C4⋊C4×D113C2211yescharacteristic
45#16813555C2211yescharacteristic, complemented
46#16813554C2211yescharacteristic, complemented
47#16813553C2211yescharacteristic, complemented
48#16813546C2211yescharacteristic, complemented
49#16813544C2211yescharacteristic
50#16813544C2211yescharacteristic, complemented
51#16813543C2211yescharacteristic
52#16813542C2211yescharacteristic
53#16813542C2211yescharacteristic, complemented
54C2×SD16×C113C2211yescharacteristic
55C2×M16×C113C2211yescharacteristic, complemented
56C22⋊Q8×C113C2211yescharacteristic, complemented
57#121×C113C2211yescharacteristic
58#107×C113C2211yescharacteristic, complemented
59#103×C113C2211yescharacteristic, complemented
60#102×C113C2211yescharacteristic
61C23×D113—21no—
62#14268648—22no—
63#14268648—22no—
64#14268647—22no—
65#14268647—22no—
66C2×Dic226D411yescharacteristic
67C2×D452—21no—
68C2×D452—21no—
69C2×D452—21no—
70C2×D452D411yescharacteristic
71C2×D452C2311yescharacteristic
72C2×D452C2311yescharacteristic
73C2×C22⋊D113—21no—
74C2×C22⋊D113—21no—
75C2×C22⋊D113—21no—
76C2×C22⋊D113—21no—
77C2×C22⋊D113D411yescharacteristic
78C2×C22⋊D113D411yescharacteristic
79D4×D113—22no—
80D4×D113—22no—
81C2×C4×D113—21no—
82C2×C4×D113—21no—
83C2×C4×D113C2311yescharacteristic
84C2×C4×D113C2311yescharacteristic
85#14268634—22no—
86D904—22no—
87#14268632—22no—
88#14268630—22no—
89#14268630D414yescomplemented
90C2×#11744751—22no—
91C2×#11744751C2311yescharacteristic
92C2×#11744751C2311yescharacteristic
93C8×D113—22no—
94C8×D113—22no—
95C4⋊Dic113C2311yescharacteristic
96C4⋊Dic113C2311yescharacteristic
97#14268626—21no—
98#14268626—21no—
99C22⋊Dic113—21no—
100#14268624—21no—
101#14268624—21no—
102#14268624—21no—
103#14268624—21no—
104#14268624—21no—
105#14268624—21no—
106C4×Dic113—21no—
107C2×Q8×C113C2311yescharacteristic
108C2×D4×C113—21no—
109C2×D4×C113C2311yescharacteristic
110C22×C4×C113C2311yescharacteristic
111SD16×C113—22no—
112M16×C113—22no—
113C2×C8×C113C2311yescharacteristic
114C2×C8×C113C2311yescharacteristic
115C4⋊C4×C113—21no—
116C4⋊C4×C113C2311yescharacteristic
117C4⋊C4×C113C2311yescharacteristic
118C22⋊C4×C113—21no—
119C22⋊C4×C113—21no—
120C23×C113—21no—
121C23×C113C2×D411yescharacteristic
122C22×D113—21no—
123C22×D113—21no—
124C22×D113—42no—
125C22×D113—81no—
126C22×D113—81no—
127C22×D113C2×D411yescharacteristic
128C22×D113C2×D411yescharacteristic
129Q8×C113—21no—
130Q8×C113—21no—
131D4×C113—21no—
132D4×C113—21no—
133D4×C113—81no—
134C2×C4×C113—21no—
135C2×C4×C113—21no—
136C2×C4×C113—21no—
137C2×C4×C113—21no—
138C2×C4×C113—21no—
139C2×C4×C113C2×D411yescharacteristic
140C2×C4×C113C2411yescharacteristic
141C22⋊D113—22no—
142C22⋊D113—22no—
143C22⋊D113—42no—
144C22⋊D113—81no—
145C22⋊D113—81no—
146C22⋊D113—81no—
147C2×Dic113—21no—
148C2×Dic113—21no—
149C2×Dic113C2×D411yescharacteristic
150C2×Dic113C2×D411yescharacteristic
151D452—22no—
152D452—21no—
153D452—21no—
154D452—21no—
155D452—21no—
156D452—42no—
157D452—81no—
158D452—81no—
159C4×D113—21no—
160C4×D113—21no—
161C4×D113—42no—
162C4×D113—81no—
163C4×D113C2×D412yes—
164C4×D113#4112yes—
165Dic226—22no—
166C8×C113—21no—
167C8×C113C2×D412yes—
168#11744751—21no—
169#11744751C2×D412yes—
170C22×C113—21no—
171C22×C113—21no—
172C22×C113—21no—
173C22×C113—41no—
174C22×C113—41no—
175C22×C113—41no—
176C22×C113C22×D411yescharacteristic
177C2×D113—21no—
178C2×D113—21no—
179C2×D113—21no—
180C2×D113—21no—
181C2×D113—21no—
182C2×D113—41no—
183C2×D113—41no—
184C2×D113—41no—
185C2×D113—41no—
186C2×D113—41no—
187C2×D113—41no—
188C2×D113—84no—
189C2×D113#12112yes—
190C4×C113—21no—
191C4×C113—41no—
192C4×C113—41no—
193C4×C113—41no—
194C4×C113C22×D411yescharacteristic
195C4×C113C2×#4111yescharacteristic
196Dic113—21no—
197Dic113—41no—
198Dic113—41no—
199Dic113#12112yes—
200C2×C113—41no—
201C2×C113—81no—
202C2×C113C2×#12111yescharacteristic
203C2×C113#57611yescharacteristic
204C2×C113#57711yescharacteristic
205D113—22no—
206D113—41no—
207D113—81no—
208D113—81no—
209#3062—1131nomaximal, Sylow
210C113#306211yescharacteristic, complemented, Sylow
211C2×AGL(1,ℤ/8)—1131no—
212C2×#131—1131no—
213#537—1131no—
214#535—1131no—
215#469—1131no—
216#469—1131no—
217#468—1131no—
218#468D11311yescharacteristic, complemented
219#466—1131no—
220#466—1131no—
221#465—1131no—
222#465—1131no—
223#428—1131no—
224#416—1131no—
225C2×#102—1131no—
226C2×#41—1131no—
227C2×#41—1131no—
228C22×D4—1131no—
229AGL(1,ℤ/8)—2264no—
230C2×SD16—1131no—
231C2×SD16C2×D11311yescharacteristic
232C2×D8—1131no—
233C2×D8—1131no—
234#131—2264no—
235C2×M16—1131no—
236C2×M16—1131no—
237C2×M16C2×D11311yescharacteristic, complemented
238C22×C8—1131no—
239C22×C8—1131no—
240C22×C8—1131no—
241#127—2261no—
242#124—2261no—
243C22⋊Q8—1131no—
244C22⋊Q8—2261no—
245C22⋊Q8C2×D11311yescharacteristic, complemented
246#121—1131no—
247#121—1131no—
248#121—1131no—
249#121—1131no—
250#121—1131no—
251#121—2261no—
252#121—2261no—
253#121—2261no—
254#121C2×D11311yescharacteristic
255#120—2261no—
256#120—2261no—
257#117—1131no—
258C2×C4⋊C4—1131no—
259#107—1131no—
260#107C2×D11311yescharacteristic, complemented
261#106—1131no—
262#106—1131no—
263#103—1131no—
264#103C2×D11311yescharacteristic, complemented
265#102—1131no—
266#102—1131no—
267#102—1131no—
268#102—1131no—
269#102—1131no—
270#102C2×D11311yescharacteristic
271C24—2261no—
272#41—2262no—
273#41—2262no—
274#41—2262no—
275#41—2262no—
276C2×Q8—1131no—
277C2×Q8C22×D11311yescharacteristic
278C2×D4—21no—
279C2×D4—1131no—
280C2×D4—1131no—
281C2×D4—1131no—
282C2×D4—1131no—
283C2×D4—1131no—
284C2×D4—2261no—
285C2×D4—2261no—
286C2×D4—2261no—
287C2×D4—2262no—
288C2×D4—2262no—
289C2×D4—2261no—
290C2×D4—2261no—
291C2×D4—2261no—
292C2×D4—2261no—
293C2×D4C22×D11311yescharacteristic
294C22×C4—1131no—
295C22×C4—1131no—
296C22×C4—2261no—
297C22×C4—2261no—
298C22×C4C22×D11311yescharacteristic
299SD16—22no—
300SD16—2262no—
301D8—2262no—
302D8—2262no—
303M16—22no—
304M16—1134no—
305M16—2262no—
306C2×C8—1131no—
307C2×C8—1131no—
308C2×C8—2262no—
309C2×C8—2262no—
310C2×C8—2262no—
311C2×C8C22×D11311yescharacteristic
312C2×C8C22×D11311yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—1131no—
315C4⋊C4—1131no—
316C4⋊C4—2261no—
317C4⋊C4—2261no—
318C4⋊C4C22×D11311yescharacteristic
319C4⋊C4C22×D11311yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—2261no—
323C22⋊C4—2261no—
324C22⋊C4—2261no—
325C22⋊C4—2261no—
326C22⋊C4—2261no—
327C22⋊C4—2261no—
328C22⋊C4—2261no—
329C42—2261no—
330C23—21no—
331C23—1131no—
332C23—1131no—
333C23—9041no—
334C23—9041no—
335C23—4522no—
336C23—2261no—
337C23—2261no—
338C23D4×D11311yescharacteristic
339Q8—21no—
340Q8—21no—
341Q8—2262no—
342D4—21no—
343D4—21no—
344D4—81no—
345D4—9041no—
346D4—9041no—
347D4—9041no—
348D4—9041no—
349D4—9041no—
350D4—4522no—
351D4—4522no—
352D4—2262no—
353D4—2262no—
354D4—2262no—
355D4—2261no—
356D4—2261no—
357D4—2261no—
358D4—2261no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—1131no—
365C2×C4—1132no—
366C2×C4—1132no—
367C2×C4—1131no—
368C2×C4—9041no—
369C2×C4—4522no—
370C2×C4—2261no—
371C2×C4—2261no—
372C2×C4—2261no—
373C2×C4—2261no—
374C2×C4D4×D11311yescharacteristic
375C2×C4C23×D11311yescharacteristic
376C8—21no—
377C8—1132no—
378C8—2261no—
379C8D4×D11312yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—1132no—
387C22—9044no—
388C22—4521no—
389C22—4521no—
390C22—4521no—
391C22—4521no—
392C22—4521no—
393C22—4521no—
394C22—2261no—
395C22—2261no—
396C22—2261no—
397C22—2261no—
398C22—2261no—
399C22C2×D4×D11311yescharacteristic
400C4—21no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—1132no—
405C4—4521no—
406C4—4521no—
407C4—2261no—
408C4C2×D4×D11311yescharacteristic
409C4#41×D11311yescharacteristic
410C2—41no—
411C2—81no—
412C2—9041no—
413C2—9041no—
414C2—4521no—
415C2—2262no—
416C2#121×D11311yescharacteristic
417C2#2029940211yescharacteristic
418C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#468×C113C2
socleC22×C113C22×D4
hypercenter#468D113
hypocenterC113#3062
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#16813649C2semidirect
2. C2×#16813630C2semidirect
3. #20299178C2semidirect
4. #20299164C2semidirect
5. #20298851C2semidirect
6. #20298850C2semidirect
7. #20298847C2semidirect
8. #20298835C2semidirect
9. #20298832C2semidirect
10. #20298829C2semidirect
11. #20298824C2semidirect
12. #20298639C2semidirect
13. #20298593C2semidirect
14. #102×D113C2semidirect
15. #468×C113C2semidirect
25. C2×#14268630C22semidirect
26. C22×#11744751C22semidirect
28. C2×C8×D113C22semidirect
32. #16813598C22semidirect
35. #16813597C22semidirect
37. #16813596C22semidirect
45. #16813555C22semidirect
46. #16813554C22semidirect
47. #16813553C22semidirect
48. #16813546C22semidirect
50. #16813544C22semidirect
53. #16813542C22semidirect
55. C2×M16×C113C22semidirect
56. C22⋊Q8×C113C22semidirect
58. #107×C113C22semidirect
59. #103×C113C22semidirect
89. #14268630D4semidirect
210. C113#3062semidirect
218. #468D113semidirect
237. C2×M16C2×D113semidirect
245. C22⋊Q8C2×D113semidirect
260. #107C2×D113semidirect
264. #103C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136492
C2×#168136302
#202991782
#202991642
#202988512
#202988502
#202988472
#202988352
#202988322
#202988292
#202988242
#202986392
#202985932
#102×D1132
#468×C1132
#3062113