Finite Group Databasebeta

← #28401428

Subgroups — #28401428

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#20299176C211yesmaximal, characteristic, complemented
2#20299162C211yesmaximal, characteristic, complemented
3#20298940C211yesmaximal, characteristic, complemented
4#20298923C211yesmaximal, characteristic, complemented
5#20298917C211yesmaximal, characteristic, complemented
6#20298912C211yesmaximal, characteristic, complemented
7#20298851C211yesmaximal, characteristic, complemented
8#20298844C211yesmaximal, characteristic, complemented
9#20298834C211yesmaximal, characteristic, complemented
10#20298827C211yesmaximal, characteristic, complemented
11#20298751C211yesmaximal, characteristic, complemented
12#20298745C211yesmaximal, characteristic, complemented
13#20298745C211yesmaximal, characteristic, complemented
14#20298734C211yesmaximal, characteristic, complemented
15#408×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic, complemented
17C22×D452C2211yescharacteristic
18C2×#14268636C2211yescharacteristic
19C2×#14268636C2211yescharacteristic
20C2×D904C2211yescharacteristic
21C2×D904C2211yescharacteristic
22#16813618—21no—
23#16813611—21no—
24#16813601C2211yescharacteristic
25#16813601C2211yescharacteristic, complemented
26#16813598—21no—
27#16813596C2211yescharacteristic
28#16813596C2211yescharacteristic
29#16813596C2211yescharacteristic
30#16813596C2211yescharacteristic
31#16813596C2211yescharacteristic
32#16813596C2211yescharacteristic, complemented
33#16813594—21no—
34#16813594—21no—
35#16813593—21no—
36#16813590—21no—
37#16813590—21no—
38#16813581C2211yescharacteristic
39C2×C4⋊Dic113C2211yescharacteristic, complemented
40#16813556C2211yescharacteristic, complemented
41#16813556C2211yescharacteristic, complemented
42#16813554C2211yescharacteristic, complemented
43#16813554C2211yescharacteristic, complemented
44#16813547C2211yescharacteristic, complemented
45#16813547C2211yescharacteristic, complemented
46#16813544C2211yescharacteristic
47#16813544C2211yescharacteristic
48#16813544C2211yescharacteristic
49#16813544C2211yescharacteristic
50#16813544C2211yescharacteristic, complemented
51#16813544C2211yescharacteristic, complemented
52C2×#41×C113C2211yescharacteristic
53C2×M16×C113C2211yescharacteristic, complemented
54C22×C8×C113C2211yescharacteristic, complemented
55C22⋊C8×C113C2211yescharacteristic
56C22⋊C8×C113C2211yescharacteristic
57C22⋊C8×C113C2211yescharacteristic, complemented
58C22⋊C8×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60#14268647—41no—
61#14268647—41no—
62C2×Dic226C2311yescharacteristic
63C2×D452—21no—
64C2×D452—41no—
65C2×D452—41no—
66C2×D452C2311yescharacteristic
67C2×D452C2311yescharacteristic
68C2×D452C2311yescharacteristic
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72C2×C22⋊D113—21no—
73C2×C22⋊D113—21no—
74C2×C22⋊D113—21no—
75C2×C22⋊D113—21no—
76C22×Dic113—21no—
77C2×C4×D113—21no—
78#14268636—41no—
79#14268636—41no—
80D904—41no—
81D904—41no—
82C4⋊Dic113—21no—
83C4⋊Dic113C2311yescharacteristic
84C4⋊Dic113C2311yescharacteristic
85C4⋊Dic113C2311yescharacteristic
86C4⋊Dic113C2311yescharacteristic
87#14268626—21no—
88#14268626—21no—
89C22⋊Dic113—21no—
90C22⋊Dic113—21no—
91C22⋊Dic113—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97#14268624—21no—
98C4×Dic113—21no—
99#41×C113—41no—
100#41×C113—41no—
101C2×Q8×C113D411yescharacteristic
102C2×D4×C113D411yescharacteristic
103C2×D4×C113D411yescharacteristic
104C2×D4×C113D411yescharacteristic
105C22×C4×C113C2311yescharacteristic
106C22×C4×C113C2311yescharacteristic
107C22×C4×C113C2311yescharacteristic
108M16×C113—41no—
109C2×C8×C113—41no—
110C2×C8×C113C2311yescharacteristic
111C2×C8×C113C2311yescharacteristic
112C2×C8×C113C2311yescharacteristic
113C2×C8×C113C2311yescharacteristic
114C23×C113C2×D411yescharacteristic
115C23×C113C2×D411yescharacteristic
116C23×C113C2×D411yescharacteristic
117C22×D113—21no—
118C22×D113—21no—
119C22×D113—21no—
120C22×D113—42no—
121C22×D113—81no—
122C22×D113—81no—
123Q8×C113—41no—
124D4×C113—41no—
125D4×C113—41no—
126D4×C113—41no—
127C2×C4×C113—21no—
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113—21no—
132C2×C4×C113—21no—
133C2×C4×C113C2×D411yescharacteristic
134C2×C4×C113C2×D411yescharacteristic
135C2×C4×C113C2×D411yescharacteristic
136C2×C4×C113C2411yescharacteristic
137C22⋊D113—42no—
138C22⋊D113—81no—
139C22⋊D113—81no—
140C22⋊D113—81no—
141C22⋊D113—81no—
142C22⋊D113—81no—
143C22⋊D113—81no—
144C2×Dic113—21no—
145C2×Dic113—21no—
146C2×Dic113—21no—
147C2×Dic113—21no—
148C2×Dic113—21no—
149C2×Dic113—81no—
150D452—21no—
151D452—21no—
152D452—21no—
153D452—21no—
154D452—21no—
155D452—21no—
156D452—42no—
157C4×D113—42no—
158Dic226—21no—
159Dic226—21no—
160C8×C113—21no—
161C8×C113—21no—
162C8×C113—21no—
163C8×C113—21no—
164C22×C113—21no—
165C22×C113—21no—
166C22×C113—21no—
167C22×C113—21no—
168C22×C113—21no—
169C22×C113—21no—
170C22×C113—21no—
171C22×C113—21no—
172C22×C113—21no—
173C22×C113C22×D411yescharacteristic
174C2×D113—41no—
175C2×D113—41no—
176C2×D113—41no—
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—21no—
186C4×C113—21no—
187C4×C113H(5,𝔽2)11yescharacteristic
188C4×C113H(5,𝔽2)11yescharacteristic
189Dic113—41no—
190Dic113—41no—
191Dic113—41no—
192Dic113—41no—
193Dic113—41no—
194C2×C113—41no—
195C2×C113—41no—
196C2×C113—41no—
197C2×C113#53411yescharacteristic
198C2×C113#57611yescharacteristic
199C2×C113#57711yescharacteristic
200D113—81no—
201D113—81no—
202D113—81no—
203#3198—1131nomaximal, Sylow
204C113#319811yescharacteristic, complemented, Sylow
205#537—1131no—
206#535—1131no—
207#485—1131no—
208#482—1131no—
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#408D11311yescharacteristic, complemented
220C2×#41—1131no—
221C2×#41C2×D11311yescharacteristic
222C22×D4—1131no—
223C2×SD16—1131no—
224C2×SD16—1131no—
225C2×D8—1131no—
226C2×D8—1131no—
227C2×M16C2×D11311yescharacteristic, complemented
228C22×C8C2×D11311yescharacteristic, complemented
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—1131no—
240#121—2261no—
241#121—2261no—
242#121—2261no—
243#120—2261no—
244#120—2261no—
245#117—1131no—
246C2×C4⋊C4—1131no—
247#107—1131no—
248#107—1131no—
249#106—1131no—
250#106—1131no—
251#103—1131no—
252#103—1131no—
253#102—1131no—
254#102—1131no—
255#102—1131no—
256#102—1131no—
257#102—1131no—
258#102—1131no—
259C22⋊C8C2×D11311yescharacteristic
260C22⋊C8C2×D11311yescharacteristic
261C22⋊C8C2×D11311yescharacteristic, complemented
262C22⋊C8C2×D11311yescharacteristic, complemented
263C24—2261no—
264#41—41no—
265#41—41no—
266#41—4521no—
267#41—4521no—
268C2×Q8—1131no—
269C2×Q8D45211yescharacteristic
270C2×D4—1131no—
271C2×D4—1131no—
272C2×D4—1131no—
273C2×D4—4521no—
274C2×D4—4521no—
275C2×D4—2261no—
276C2×D4—2261no—
277C2×D4—2261no—
278C2×D4—2261no—
279C2×D4—2261no—
280C2×D4—2261no—
281C2×D4—2261no—
282C2×D4—2261no—
283C2×D4D45211yescharacteristic
284C2×D4D45211yescharacteristic
285C2×D4D45211yescharacteristic
286C22×C4—2261no—
287C22×C4—2261no—
288C22×C4C22×D11311yescharacteristic
289C22×C4C22×D11311yescharacteristic
290C22×C4C22×D11311yescharacteristic
291SD16—4521no—
292SD16—4521no—
293D8—4521no—
294D8—4521no—
295M16—41no—
296C2×C8—41no—
297C2×C8C22×D11311yescharacteristic
298C2×C8C22×D11311yescharacteristic
299C2×C8C22×D11311yescharacteristic
300C2×C8C22×D11311yescharacteristic
301C4⋊C4—1131no—
302C4⋊C4—1131no—
303C4⋊C4—1131no—
304C4⋊C4—1131no—
305C4⋊C4—2261no—
306C4⋊C4—2261no—
307C4⋊C4—2261no—
308C22⋊C4—2261no—
309C22⋊C4—2261no—
310C22⋊C4—2261no—
311C22⋊C4—2261no—
312C22⋊C4—2261no—
313C22⋊C4—2261no—
314C22⋊C4—2261no—
315C22⋊C4—2261no—
316C22⋊C4—2261no—
317C42—2261no—
318C23—9041no—
319C23—9041no—
320C23—4522no—
321C23—2261no—
322C23—2261no—
323C23—2261no—
324C23C2×D45211yescharacteristic
325C23C2×D45211yescharacteristic
326C23C2×D45211yescharacteristic
327Q8—41no—
328Q8—2261no—
329Q8—2261no—
330D4—41no—
331D4—41no—
332D4—41no—
333D4—9041no—
334D4—9041no—
335D4—9041no—
336D4—9041no—
337D4—9041no—
338D4—9041no—
339D4—4522no—
340D4—4522no—
341D4—2261no—
342D4—2261no—
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—21no—
353C2×C4—9041no—
354C2×C4—4522no—
355C2×C4—2261no—
356C2×C4—2261no—
357C2×C4—2261no—
358C2×C4—2261no—
359C2×C4—2261no—
360C2×C4C2×D45211yescharacteristic
361C2×C4C2×D45211yescharacteristic
362C2×C4C2×D45211yescharacteristic
363C2×C4C23×D11311yescharacteristic
364C8—21no—
365C8—21no—
366C8—21no—
367C8—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—9044no—
378C22—4521no—
379C22—4521no—
380C22—4521no—
381C22—4521no—
382C22—4521no—
383C22—4521no—
384C22—4521no—
385C22—4521no—
386C22—4521no—
387C22C22×D45211yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—4521no—
392C4—4521no—
393C4—4521no—
394C4—4521no—
395C4—4521no—
396C4#1681366711yescharacteristic
397C4#1681366711yescharacteristic
398C2—41no—
399C2—41no—
400C2—41no—
401C2—9041no—
402C2—9041no—
403C2—9041no—
404C2#2029916011yescharacteristic
405C2#2029940311yescharacteristic
406C2#2029941011yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#408×C113C2
socleC22×C113C22×D4
hypercenter#408D113
hypocenterC113#3198
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #20299176C2semidirect
2. #20299162C2semidirect
3. #20298940C2semidirect
4. #20298923C2semidirect
5. #20298917C2semidirect
6. #20298912C2semidirect
7. #20298851C2semidirect
8. #20298844C2semidirect
9. #20298834C2semidirect
10. #20298827C2semidirect
11. #20298751C2semidirect
12. #20298745C2semidirect
13. #20298745C2semidirect
14. #20298734C2semidirect
15. #408×C113C2semidirect
16. C2×#14268647C22semidirect
25. #16813601C22semidirect
32. #16813596C22semidirect
39. C2×C4⋊Dic113C22semidirect
40. #16813556C22semidirect
41. #16813556C22semidirect
42. #16813554C22semidirect
43. #16813554C22semidirect
44. #16813547C22semidirect
45. #16813547C22semidirect
50. #16813544C22semidirect
51. #16813544C22semidirect
53. C2×M16×C113C22semidirect
54. C22×C8×C113C22semidirect
57. C22⋊C8×C113C22semidirect
58. C22⋊C8×C113C22semidirect
204. C113#3198semidirect
219. #408D113semidirect
227. C2×M16C2×D113semidirect
228. C22×C8C2×D113semidirect
261. C22⋊C8C2×D113semidirect
262. C22⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991762
#202991622
#202989402
#202989232
#202989172
#202989122
#202988512
#202988442
#202988342
#202988272
#202987512
#202987452
#202987342
#408×C1132
#3198113