Finite Group Databasebeta

← #28401424

Subgroups — #28401424

Order 14464.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299177C211yesmaximal, characteristic, complemented
2#20299167C211yesmaximal, characteristic, complemented
3#20298939C211yesmaximal, characteristic, complemented
4#20298918C211yesmaximal, characteristic, complemented
5#20298913C211yesmaximal, characteristic, complemented
6#20298850C211yesmaximal, characteristic, complemented
7#20298845C211yesmaximal, characteristic, complemented
8#20298833C211yesmaximal, characteristic, complemented
9#20298828C211yesmaximal, characteristic, complemented
10#20298751C211yesmaximal, characteristic, complemented
11#20298744C211yesmaximal, characteristic, complemented
12#20298744C211yesmaximal, characteristic, complemented
13#20298731C211yesmaximal, characteristic, complemented
14#20298563C211yesmaximal, characteristic, complemented
15#482×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×#14268646C2211yescharacteristic, complemented
18C22×D452C2211yescharacteristic
19C2×#14268636C2211yescharacteristic
20C2×#14268636C2211yescharacteristic
21C2×#14268632C2211yescharacteristic
22C2×#14268632C2211yescharacteristic
23C2×#14268630C2211yescharacteristic, complemented
24C2×C8×D113C2211yescharacteristic, complemented
25#16813619—21no—
26#16813610—21no—
27#16813602C2211yescharacteristic, complemented
28#16813601C2211yescharacteristic
29#16813599—21no—
30#16813597C2211yescharacteristic
31#16813597C2211yescharacteristic
32#16813597C2211yescharacteristic
33#16813597C2211yescharacteristic
34#16813595—21no—
35#16813594—21no—
36#16813593—21no—
37#16813593C2211yescharacteristic, complemented
38#16813592—21no—
39#16813592—21no—
40C4⋊C4×D113C2211yescharacteristic, complemented
41#16813555C2211yescharacteristic, complemented
42#16813553C2211yescharacteristic, complemented
43#16813545C2211yescharacteristic, complemented
44#16813545C2211yescharacteristic, complemented
45#16813544C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic, complemented
51#16813534C2211yescharacteristic, complemented
52#121×C113C2211yescharacteristic
53#117×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic, complemented
55#106×C113C2211yescharacteristic, complemented
56#102×C113C2211yescharacteristic, complemented
57#102×C113C2211yescharacteristic, complemented
58C22⋊C8×C113C2211yescharacteristic
59C23×D113—21no—
60#14268647—41no—
61#14268647—41no—
62#14268646—41no—
63#14268646—41no—
64C2×Dic226D411yescharacteristic
65C2×Dic226C2311yescharacteristic
66C2×D452—21no—
67C2×D452—21no—
68C2×D452—21no—
69C2×D452—21no—
70C2×D452—21no—
71C2×D452—41no—
72C2×D452—41no—
73C2×D452D411yescharacteristic
74C2×D452C2311yescharacteristic
75C2×D452C2311yescharacteristic
76C2×C22⋊D113—21no—
77C2×C22⋊D113—21no—
78C2×C22⋊D113D411yescharacteristic
79C2×C22⋊D113D411yescharacteristic
80C22×Dic113—21no—
81C2×C4×D113—21no—
82C2×C4×D113C2311yescharacteristic
83C2×C4×D113C2311yescharacteristic
84#14268636—41no—
85#14268636—41no—
86#14268632—41no—
87#14268632—41no—
88#14268630—41no—
89C2×#11744751C2311yescharacteristic
90C2×#11744751C2311yescharacteristic
91C8×D113—41no—
92C4⋊Dic113—21no—
93C4⋊Dic113C2311yescharacteristic
94#14268626—21no—
95#14268626—21no—
96C22⋊Dic113—21no—
97C22⋊Dic113—21no—
98#14268624—21no—
99#14268624—21no—
100#14268624—21no—
101#14268624—21no—
102#14268624—21no—
103C2×D4×C113—21no—
104C2×D4×C113C2311yescharacteristic
105C22×C4×C113C2311yescharacteristic
106C2×C8×C113C2311yescharacteristic
107C2×C8×C113C2311yescharacteristic
108C4⋊C4×C113C2311yescharacteristic
109C4⋊C4×C113C2311yescharacteristic
110C4⋊C4×C113C2311yescharacteristic
111C22⋊C4×C113—21no—
112C22⋊C4×C113—21no—
113C42×C113—21no—
114C23×C113—21no—
115C23×C113C2×D411yescharacteristic
116C22×D113—21no—
117C22×D113—21no—
118C22×D113—42no—
119C22×D113—81no—
120C22×D113—81no—
121C22×D113C2×D411yescharacteristic
122C22×D113C2×D411yescharacteristic
123D4×C113—21no—
124D4×C113—21no—
125D4×C113—81no—
126C2×C4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113C2×D411yescharacteristic
132C2×C4×C113C2411yescharacteristic
133C22⋊D113—41no—
134C22⋊D113—41no—
135C22⋊D113—42no—
136C22⋊D113—81no—
137C2×Dic113—21no—
138C2×Dic113—21no—
139C2×Dic113—42no—
140C2×Dic113C2×D411yescharacteristic
141C2×Dic113C2×D411yescharacteristic
142D452—21no—
143D452—21no—
144D452—21no—
145D452—21no—
146D452—41no—
147D452—42no—
148D452—81no—
149D452—81no—
150D452—81no—
151D452—81no—
152C4×D113—21no—
153C4×D113—21no—
154C4×D113—21no—
155C4×D113—21no—
156C4×D113—81no—
157Dic226—21no—
158Dic226—21no—
159Dic226—41no—
160C8×C113—21no—
161C8×C113—21no—
162#11744751—21no—
163#11744751—21no—
164C22×C113—21no—
165C22×C113—21no—
166C22×C113—21no—
167C22×C113—41no—
168C22×C113—41no—
169C22×C113—41no—
170C22×C113C22×D411yescharacteristic
171C2×D113—21no—
172C2×D113—21no—
173C2×D113—21no—
174C2×D113—21no—
175C2×D113—21no—
176C2×D113—21no—
177C2×D113—41no—
178C2×D113—41no—
179C2×D113—41no—
180C2×D113—41no—
181C2×D113—41no—
182C2×D113—41no—
183C2×D113—84no—
184C4×C113—21no—
185C4×C113—41no—
186C4×C113—41no—
187C4×C113—41no—
188C4×C113H(5,𝔽2)11yescharacteristic
189C4×C113H(5,𝔽2)11yescharacteristic
190Dic113—21no—
191Dic113—21no—
192Dic113—41no—
193Dic113—41no—
194C2×C113—41no—
195C2×C113—81no—
196C2×C113#53411yescharacteristic
197C2×C113#57611yescharacteristic
198C2×C113#57711yescharacteristic
199D113—41no—
200D113—41no—
201D113—81no—
202D113—81no—
203#3198—1131nomaximal, Sylow
204C113#319811yescharacteristic, complemented, Sylow
205#537—1131no—
206#535—1131no—
207#485—1131no—
208#482D11311yescharacteristic, complemented
209#481—1131no—
210#480—1131no—
211#469—1131no—
212#468—1131no—
213#466—1131no—
214#465—1131no—
215#450—1131no—
216#449—1131no—
217#449—1131no—
218#447—1131no—
219#408—1131no—
220C2×#41—1131no—
221C2×#41—1131no—
222C22×D4—1131no—
223C2×SD16—1131no—
224C2×SD16—1131no—
225C2×D8—1131no—
226C2×D8—1131no—
227C2×M16—1131no—
228C22×C8—1131no—
229#127—2261no—
230#124—2261no—
231C22⋊Q8—1131no—
232C22⋊Q8—1131no—
233C22⋊Q8—2261no—
234#121—1131no—
235#121—1131no—
236#121—1131no—
237#121—1131no—
238#121—1131no—
239#121—2261no—
240#121—2261no—
241#121—2261no—
242#121C2×D11311yescharacteristic
243#120—2261no—
244#120—2261no—
245#117C2×D11311yescharacteristic
246C2×C4⋊C4—1131no—
247#107—1131no—
248#107C2×D11311yescharacteristic, complemented
249#106—1131no—
250#106C2×D11311yescharacteristic, complemented
251#103—1131no—
252#103—1131no—
253#102—1131no—
254#102—1131no—
255#102—1131no—
256#102—1131no—
257#102C2×D11311yescharacteristic, complemented
258#102C2×D11311yescharacteristic, complemented
259C22⋊C8—1131no—
260C22⋊C8—1131no—
261C22⋊C8—1131no—
262C22⋊C8C2×D11311yescharacteristic
263C24—2261no—
264#41—4521no—
265#41—4521no—
266#41—4521no—
267#41—4521no—
268C2×Q8—1131no—
269C2×Q8—1131no—
270C2×D4—21no—
271C2×D4—1131no—
272C2×D4—1131no—
273C2×D4—1131no—
274C2×D4—1131no—
275C2×D4—1131no—
276C2×D4—4521no—
277C2×D4—4521no—
278C2×D4—2261no—
279C2×D4—2261no—
280C2×D4—2261no—
281C2×D4—2261no—
282C2×D4—2261no—
283C2×D4—2261no—
284C2×D4—2261no—
285C2×D4C22×D11311yescharacteristic
286C22×C4—1131no—
287C22×C4—1131no—
288C22×C4—2261no—
289C22×C4—2261no—
290C22×C4C22×D11311yescharacteristic
291SD16—4521no—
292SD16—4521no—
293D8—4521no—
294D8—4521no—
295M16—4521no—
296C2×C8—1131no—
297C2×C8—1131no—
298C2×C8—4521no—
299C2×C8C22×D11311yescharacteristic
300C2×C8C22×D11311yescharacteristic
301C4⋊C4—1131no—
302C4⋊C4—2261no—
303C4⋊C4—2261no—
304C4⋊C4—2261no—
305C4⋊C4C22×D11311yescharacteristic
306C4⋊C4C22×D11311yescharacteristic
307C4⋊C4C22×D11311yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—2261no—
311C22⋊C4—2261no—
312C22⋊C4—2261no—
313C22⋊C4—2261no—
314C22⋊C4—2261no—
315C22⋊C4—2261no—
316C22⋊C4—2261no—
317C42—21no—
318C23—21no—
319C23—1131no—
320C23—1131no—
321C23—9041no—
322C23—9041no—
323C23—4522no—
324C23—2261no—
325C23—2261no—
326C23D4×D11311yescharacteristic
327Q8—4521no—
328Q8—2261no—
329Q8—2261no—
330D4—21no—
331D4—21no—
332D4—81no—
333D4—9041no—
334D4—9041no—
335D4—9041no—
336D4—9041no—
337D4—9041no—
338D4—4522no—
339D4—4521no—
340D4—4522no—
341D4—4521no—
342D4—4521no—
343D4—2261no—
344D4—2261no—
345D4—2261no—
346D4—2261no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—1131no—
353C2×C4—1131no—
354C2×C4—9041no—
355C2×C4—4522no—
356C2×C4—2261no—
357C2×C4—2261no—
358C2×C4—2261no—
359C2×C4—2261no—
360C2×C4—2261no—
361C2×C4—2261no—
362C2×C4D4×D11311yescharacteristic
363C2×C4C23×D11311yescharacteristic
364C8—21no—
365C8—21no—
366C8—2261no—
367C8—2261no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—9044no—
375C22—4521no—
376C22—4521no—
377C22—4521no—
378C22—4521no—
379C22—4521no—
380C22—4521no—
381C22—2261no—
382C22—2261no—
383C22—2261no—
384C22—2261no—
385C22—2261no—
386C22—2261no—
387C22C2×D4×D11311yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—4521no—
393C4—4521no—
394C4—2261no—
395C4—2261no—
396C4#1681366811yescharacteristic
397C4#1681366811yescharacteristic
398C2—41no—
399C2—81no—
400C2—9041no—
401C2—9041no—
402C2—4521no—
403C2—4521no—
404C2#2029915911yescharacteristic
405C2#2029940211yescharacteristic
406C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#482×C113C2
socleC22×C113C22×D4
hypercenter#482D113
hypocenterC113#3198
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #20299177C2semidirect
2. #20299167C2semidirect
3. #20298939C2semidirect
4. #20298918C2semidirect
5. #20298913C2semidirect
6. #20298850C2semidirect
7. #20298845C2semidirect
8. #20298833C2semidirect
9. #20298828C2semidirect
10. #20298751C2semidirect
11. #20298744C2semidirect
12. #20298744C2semidirect
13. #20298731C2semidirect
14. #20298563C2semidirect
15. #482×C113C2semidirect
17. C2×#14268646C22semidirect
23. C2×#14268630C22semidirect
24. C2×C8×D113C22semidirect
27. #16813602C22semidirect
37. #16813593C22semidirect
40. C4⋊C4×D113C22semidirect
41. #16813555C22semidirect
42. #16813553C22semidirect
43. #16813545C22semidirect
44. #16813545C22semidirect
50. #16813534C22semidirect
51. #16813534C22semidirect
54. #107×C113C22semidirect
55. #106×C113C22semidirect
56. #102×C113C22semidirect
57. #102×C113C22semidirect
204. C113#3198semidirect
208. #482D113semidirect
248. #107C2×D113semidirect
250. #106C2×D113semidirect
257. #102C2×D113semidirect
258. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991772
#202991672
#202989392
#202989182
#202989132
#202988502
#202988452
#202988332
#202988282
#202987512
#202987442
#202987312
#202985632
#482×C1132
#3198113