Finite Group Databasebeta

← #28401437

Subgroups — #28401437

Order 14464.

442 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299165C211yesmaximal, characteristic, complemented
2#20299164C211yesmaximal, characteristic, complemented
3#20298923C211yesmaximal, characteristic, complemented
4#20298921C211yesmaximal, characteristic, complemented
5#20298920C211yesmaximal, characteristic, complemented
6#20298919C211yesmaximal, characteristic, complemented
7#20298850C211yesmaximal, characteristic, complemented
8#20298848C211yesmaximal, characteristic, complemented
9#20298833C211yesmaximal, characteristic, complemented
10#20298831C211yesmaximal, characteristic, complemented
11#20298732C211yesmaximal, characteristic, complemented
12#20298730C211yesmaximal, characteristic, complemented
13#20298730C211yesmaximal, characteristic, complemented
14#20298563C211yesmaximal, characteristic, complemented
15#447×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×D4×D113C2211yescharacteristic, complemented
18C2×#14268632C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20C2×#14268630C2211yescharacteristic, complemented
21C2×C8×D113C2211yescharacteristic, complemented
22#16813618—21no—
23#16813618—21no—
24#16813609—21no—
25#16813608—21no—
26#16813597C2211yescharacteristic, complemented
27#16813596C2211yescharacteristic
28#16813593C2211yescharacteristic
29#16813593C2211yescharacteristic
30#16813593C2211yescharacteristic, complemented
31#16813593C2211yescharacteristic, complemented
32#16813593C2211yescharacteristic, complemented
33#16813592—21no—
34#16813591—21no—
35#16813591—21no—
36#16813590—21no—
37#16813581C2211yescharacteristic, complemented
38#16813580C2211yescharacteristic, complemented
39#16813556C2211yescharacteristic, complemented
40#16813555C2211yescharacteristic, complemented
41#16813554C2211yescharacteristic, complemented
42#16813553C2211yescharacteristic, complemented
43#16813544C2211yescharacteristic, complemented
44#16813544C2211yescharacteristic, complemented
45#16813543C2211yescharacteristic, complemented
46#16813543C2211yescharacteristic, complemented
47#16813543C2211yescharacteristic, complemented
48#16813543C2211yescharacteristic, complemented
49C22⋊#11744751C2211yescharacteristic, complemented
50#16813534C2211yescharacteristic, complemented
51#16813534C2211yescharacteristic, complemented
52C22×D4×C113C2211yescharacteristic, complemented
53C2×D8×C113C2211yescharacteristic
54C2×D8×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic
56#102×C113C2211yescharacteristic, complemented
57#102×C113C2211yescharacteristic, complemented
58C22⋊C8×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60#14268647—41no—
61#14268647—41no—
62C2×Dic226D411yescharacteristic
63C2×D452—21no—
64C2×D452D411yescharacteristic
65C2×D452C2311yescharacteristic
66C2×C22⋊D113—21no—
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72C2×C22⋊D113—21no—
73C2×C22⋊D113D411yescharacteristic
74C2×C22⋊D113D411yescharacteristic
75D4×D113—41no—
76D4×D113—41no—
77C2×C4×D113C2311yescharacteristic
78C2×C4×D113C2311yescharacteristic
79#14268632—41no—
80#14268632—41no—
81#14268630—41no—
82C2×#11744751C2311yescharacteristic
83C2×#11744751C2311yescharacteristic
84C8×D113—41no—
85C4⋊Dic113C2311yescharacteristic
86C4⋊Dic113C2311yescharacteristic
87C4⋊Dic113C2311yescharacteristic
88C22⋊Dic113—21no—
89C22⋊Dic113—21no—
90C22⋊Dic113—21no—
91C22⋊Dic113—21no—
92C22⋊Dic113—21no—
93C22⋊Dic113—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97C4×Dic113—21no—
98C4×Dic113—21no—
99C24×C113—21no—
100C2×D4×C113—21no—
101C2×D4×C113—21no—
102C2×D4×C113—41no—
103C2×D4×C113—41no—
104C2×D4×C113C2311yescharacteristic
105C2×D4×C113C2311yescharacteristic
106C2×D4×C113C2311yescharacteristic
107C22×C4×C113C2311yescharacteristic
108D8×C113—41no—
109D8×C113—41no—
110C2×C8×C113C2311yescharacteristic
111C2×C8×C113C2311yescharacteristic
112C4⋊C4×C113C2311yescharacteristic
113C22⋊C4×C113—21no—
114C23×C113—21no—
115C23×C113—21no—
116C23×C113—21no—
117C23×C113—42no—
118C23×C113—81no—
119C23×C113—81no—
120C23×C113C2×D411yescharacteristic
121C22×D113—21no—
122C22×D113—42no—
123C22×D113—81no—
124C22×D113—81no—
125C22×D113C2×D411yescharacteristic
126C22×D113C2×D411yescharacteristic
127D4×C113—21no—
128D4×C113—21no—
129D4×C113—21no—
130D4×C113—21no—
131D4×C113—21no—
132D4×C113—21no—
133D4×C113—42no—
134D4×C113—81no—
135C2×C4×C113—21no—
136C2×C4×C113—21no—
137C2×C4×C113—21no—
138C2×C4×C113C2×D411yescharacteristic
139C2×C4×C113C2411yescharacteristic
140C22⋊D113—41no—
141C22⋊D113—41no—
142C22⋊D113—42no—
143C22⋊D113—81no—
144C22⋊D113—81no—
145C22⋊D113—81no—
146C22⋊D113—81no—
147C22⋊D113—81no—
148C22⋊D113—81no—
149C2×Dic113—21no—
150C2×Dic113—21no—
151C2×Dic113—21no—
152C2×Dic113C2×D411yescharacteristic
153C2×Dic113C2×D411yescharacteristic
154D452—21no—
155D452—21no—
156D452—41no—
157D452—81no—
158C4×D113—21no—
159C4×D113—21no—
160C4×D113—21no—
161C4×D113—21no—
162Dic226—41no—
163C8×C113—21no—
164C8×C113—21no—
165#11744751—21no—
166#11744751—21no—
167C22×C113—21no—
168C22×C113—21no—
169C22×C113—21no—
170C22×C113—41no—
171C22×C113—41no—
172C22×C113—41no—
173C22×C113—41no—
174C22×C113—41no—
175C22×C113—41no—
176C22×C113—41no—
177C22×C113—41no—
178C22×C113—41no—
179C22×C113—84no—
180C22×C113C22×D411yescharacteristic
181C2×D113—21no—
182C2×D113—21no—
183C2×D113—21no—
184C2×D113—21no—
185C2×D113—21no—
186C2×D113—21no—
187C2×D113—41no—
188C2×D113—41no—
189C2×D113—41no—
190C2×D113—84no—
191C4×C113—21no—
192C4×C113—41no—
193C4×C113H(5,𝔽2)11yescharacteristic
194C4×C113H(5,𝔽2)11yescharacteristic
195Dic113—21no—
196Dic113—21no—
197Dic113—41no—
198Dic113—41no—
199Dic113—41no—
200C2×C113—41no—
201C2×C113—81no—
202C2×C113—81no—
203C2×C113—81no—
204C2×C113#53411yescharacteristic
205C2×C113#57611yescharacteristic
206C2×C113#57611yescharacteristic
207D113—41no—
208D113—41no—
209D113—81no—
210#3199—1131nomaximal, Sylow
211C113#319911yescharacteristic, complemented, Sylow
212#535—1131no—
213#535—1131no—
214#482—1131no—
215#482—1131no—
216#482—1131no—
217#482—1131no—
218#469—1131no—
219#469—1131no—
220#466—1131no—
221#466—1131no—
222#447—1131no—
223#447—1131no—
224#447—1131no—
225#447D11311yescharacteristic, complemented
226#408—1131no—
227C2×#41—1131no—
228C22×D4—1131no—
229C22×D4C2×D11311yescharacteristic, complemented
230C2×D8—1131no—
231C2×D8—1131no—
232C2×D8C2×D11311yescharacteristic
233C2×D8C2×D11311yescharacteristic
234C2×M16—1131no—
235C22×C8—1131no—
236#127—2261no—
237#127—2261no—
238#124—2261no—
239#124—2261no—
240#121—1131no—
241#121—1131no—
242#121—1131no—
243#121—1131no—
244#121—1131no—
245#121—1131no—
246#121—1131no—
247#121C2×D11311yescharacteristic
248#120—2261no—
249#120—2261no—
250#120—2261no—
251#120—2261no—
252#117—1131no—
253#117—1131no—
254#107—1131no—
255#107—1131no—
256#106—1131no—
257#106—1131no—
258#102—1131no—
259#102—1131no—
260#102—1131no—
261#102—1131no—
262#102—1131no—
263#102—1131no—
264#102C2×D11311yescharacteristic, complemented
265#102C2×D11311yescharacteristic, complemented
266C22⋊C8—1131no—
267C22⋊C8—1131no—
268C22⋊C8—1131no—
269C22⋊C8C2×D11311yescharacteristic, complemented
270C24—21no—
271C24—2261no—
272#41—4521no—
273#41—4521no—
274C2×Q8—1131no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—1131no—
280C2×D4—1131no—
281C2×D4—1131no—
282C2×D4—1131no—
283C2×D4—4521no—
284C2×D4—4521no—
285C2×D4—2261no—
286C2×D4—2261no—
287C2×D4—2261no—
288C2×D4—2261no—
289C2×D4—2261no—
290C2×D4—2261no—
291C2×D4—2261no—
292C2×D4—2261no—
293C2×D4C22×D11311yescharacteristic
294C2×D4C22×D11311yescharacteristic
295C2×D4C22×D11311yescharacteristic
296C22×C4—1131no—
297C22×C4—1131no—
298C22×C4C22×D11311yescharacteristic
299D8—41no—
300D8—41no—
301D8—4521no—
302D8—4521no—
303M16—4521no—
304C2×C8—1131no—
305C2×C8—1131no—
306C2×C8—4521no—
307C2×C8C22×D11311yescharacteristic
308C2×C8C22×D11311yescharacteristic
309C4⋊C4—1131no—
310C4⋊C4—1131no—
311C4⋊C4—1131no—
312C4⋊C4C22×D11311yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—2261no—
315C22⋊C4—2261no—
316C22⋊C4—2261no—
317C22⋊C4—2261no—
318C22⋊C4—2261no—
319C22⋊C4—2261no—
320C22⋊C4—2261no—
321C22⋊C4—2261no—
322C22⋊C4—2261no—
323C42—2261no—
324C42—2261no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—42no—
329C23—81no—
330C23—81no—
331C23—1131no—
332C23—1131no—
333C23—9041no—
334C23—9041no—
335C23—4522no—
336C23—2261no—
337C23D4×D11311yescharacteristic
338Q8—4521no—
339D4—21no—
340D4—21no—
341D4—21no—
342D4—21no—
343D4—21no—
344D4—21no—
345D4—42no—
346D4—81no—
347D4—9041no—
348D4—9041no—
349D4—9041no—
350D4—9041no—
351D4—9041no—
352D4—9041no—
353D4—9041no—
354D4—4521no—
355D4—4521no—
356D4—4521no—
357D4—4522no—
358D4—2261no—
359D4—2261no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—1131no—
364C2×C4—1131no—
365C2×C4—2261no—
366C2×C4—2261no—
367C2×C4—2261no—
368C2×C4—2261no—
369C2×C4—2261no—
370C2×C4—2261no—
371C2×C4—2261no—
372C2×C4D4×D11311yescharacteristic
373C2×C4C23×D11311yescharacteristic
374C8—21no—
375C8—21no—
376C8—2261no—
377C8—2261no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—84no—
391C22—9044no—
392C22—4521no—
393C22—4521no—
394C22—4521no—
395C22—2261no—
396C22—2261no—
397C22—2261no—
398C22—2261no—
399C22—2261no—
400C22—2261no—
401C22C2×D4×D11311yescharacteristic
402C4—21no—
403C4—41no—
404C4—4521no—
405C4—4521no—
406C4—4521no—
407C4—2261no—
408C4—2261no—
409C4#1681366711yescharacteristic
410C4#1681366711yescharacteristic
411C2—41no—
412C2—81no—
413C2—81no—
414C2—81no—
415C2—9041no—
416C2—4521no—
417C2—4521no—
418C2#2029915811yescharacteristic
419C2#2029939911yescharacteristic
420C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#447×C113C2
socleC22×C113C22×D4
hypercenter#447D113
hypocenterC113#3199
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #20299165C2semidirect
2. #20299164C2semidirect
3. #20298923C2semidirect
4. #20298921C2semidirect
5. #20298920C2semidirect
6. #20298919C2semidirect
7. #20298850C2semidirect
8. #20298848C2semidirect
9. #20298833C2semidirect
10. #20298831C2semidirect
11. #20298732C2semidirect
12. #20298730C2semidirect
13. #20298730C2semidirect
14. #20298563C2semidirect
15. #447×C113C2semidirect
17. C2×D4×D113C22semidirect
20. C2×#14268630C22semidirect
21. C2×C8×D113C22semidirect
26. #16813597C22semidirect
30. #16813593C22semidirect
31. #16813593C22semidirect
32. #16813593C22semidirect
37. #16813581C22semidirect
38. #16813580C22semidirect
39. #16813556C22semidirect
40. #16813555C22semidirect
41. #16813554C22semidirect
42. #16813553C22semidirect
43. #16813544C22semidirect
44. #16813544C22semidirect
45. #16813543C22semidirect
46. #16813543C22semidirect
47. #16813543C22semidirect
48. #16813543C22semidirect
49. C22⋊#11744751C22semidirect
50. #16813534C22semidirect
51. #16813534C22semidirect
52. C22×D4×C113C22semidirect
56. #102×C113C22semidirect
57. #102×C113C22semidirect
58. C22⋊C8×C113C22semidirect
211. C113#3199semidirect
225. #447D113semidirect
229. C22×D4C2×D113semidirect
264. #102C2×D113semidirect
265. #102C2×D113semidirect
269. C22⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991652
#202991642
#202989232
#202989212
#202989202
#202989192
#202988502
#202988482
#202988332
#202988312
#202987322
#202987302
#202985632
#447×C1132
#3199113