Finite Group Databasebeta

← #28401668

Subgroups — #28401668

Order 14464.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299219C211yesmaximal, characteristic, complemented
2#20298985C211yesmaximal, characteristic, complemented
3#20298980C211yesmaximal, characteristic, complemented
4#20298957C211yesmaximal, characteristic, complemented
5#20298944C211yesmaximal, characteristic, complemented
6#20298817C211yesmaximal, characteristic, complemented
7#20298810C211yesmaximal, characteristic, complemented
8#20298795C211yesmaximal, characteristic, complemented
9#20298790C211yesmaximal, characteristic, complemented
10#20298760C211yesmaximal, characteristic, complemented
11#20298749C211yesmaximal, characteristic, complemented
12#20298743C211yesmaximal, characteristic, complemented
13#20298732C211yesmaximal, characteristic, complemented
14#20298659C211yesmaximal, characteristic, complemented
15#535×C113C211yesmaximal, characteristic, complemented
16C2×#14268637C2211yescharacteristic, complemented
17C2×#14268635C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19C2×#14268635C2211yescharacteristic, complemented
20C2×#14268634C2211yescharacteristic, complemented
21C2×#14268632C2211yescharacteristic
22C2×#14268632C2211yescharacteristic
23C2×#14268632C2211yescharacteristic, complemented
24#16813622C2211yescharacteristic, complemented
25#16813617—21no—
26#16813610C2211yescharacteristic, complemented
27#16813608—21no—
28#16813604—21no—
29#16813601C2211yescharacteristic
30#16813600—21no—
31#16813596C2211yescharacteristic
32C4×Dic226C2211yescharacteristic, complemented
33C4×D452C2211yescharacteristic, complemented
34C4⋊#11744751C2211yescharacteristic, complemented
35C4⋊#11744751C2211yescharacteristic, complemented
36#16813546C2211yescharacteristic, complemented
37#16813546C2211yescharacteristic, complemented
38#16813543C2211yescharacteristic
39#16813543C2211yescharacteristic
40#16813543C2211yescharacteristic
41#16813543C2211yescharacteristic
42#16813543C2211yescharacteristic, complemented
43#16813543C2211yescharacteristic, complemented
44C22⋊#11744751C2211yescharacteristic
45C22⋊#11744751C2211yescharacteristic
46#16813533C2211yescharacteristic, complemented
47C4×#11744751C2211yescharacteristic, complemented
48C2×#41×C113C2211yescharacteristic
49C22×D4×C113C2211yescharacteristic
50#127×C113C2211yescharacteristic
51#127×C113C2211yescharacteristic
52#124×C113C2211yescharacteristic
53#124×C113C2211yescharacteristic
54#121×C113—21no—
55#121×C113—21no—
56#120×C113—21no—
57#120×C113—21no—
58#117×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226C2311yescharacteristic
61C2×D452C2311yescharacteristic
62C2×C22⋊D113—21no—
63C2×C4×D113—21no—
64#14268637—41no—
65#14268635—41no—
66#14268635—41no—
67#14268635—41no—
68#14268634—41no—
69#14268632—41no—
70#14268632—41no—
71#14268632—41no—
72C2×#11744751C2311yescharacteristic
73C2×#11744751C2311yescharacteristic
74C2×#11744751C2311yescharacteristic
75C2×#11744751C2311yescharacteristic
76C4⋊Dic113—21no—
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79#14268626—21no—
80#14268626—21no—
81C22⋊Dic113—21no—
82#14268624—21no—
83#14268624—21no—
84#14268624—21no—
85#14268624—21no—
86C4×Dic113—21no—
87C24×C113—21no—
88#41×C113—41no—
89#41×C113—41no—
90C2×Q8×C113C2311yescharacteristic
91C2×D4×C113—21no—
92C2×D4×C113—21no—
93C2×D4×C113—21no—
94C2×D4×C113—21no—
95C2×D4×C113—21no—
96C2×D4×C113—21no—
97C2×D4×C113—41no—
98C2×D4×C113—41no—
99C2×D4×C113C2311yescharacteristic
100C2×D4×C113C2311yescharacteristic
101C2×D4×C113C2311yescharacteristic
102C22×C4×C113—21no—
103C22×C4×C113C2311yescharacteristic
104C4⋊C4×C113D411yescharacteristic
105C4⋊C4×C113D411yescharacteristic
106C22⋊C4×C113—21no—
107C22⋊C4×C113—21no—
108C22⋊C4×C113—21no—
109C22⋊C4×C113—21no—
110C22⋊C4×C113D411yescharacteristic
111C22⋊C4×C113D411yescharacteristic
112C42×C113C2311yescharacteristic
113C42×C113C2311yescharacteristic
114C23×C113—21no—
115C23×C113—21no—
116C23×C113—21no—
117C23×C113—42no—
118C23×C113—81no—
119C23×C113—81no—
120C23×C113C2×D411yescharacteristic
121C22×D113—21no—
122Q8×C113—21no—
123Q8×C113—21no—
124D4×C113—21no—
125D4×C113—21no—
126D4×C113—21no—
127D4×C113—21no—
128D4×C113—21no—
129D4×C113—21no—
130D4×C113—42no—
131D4×C113—42no—
132D4×C113—81no—
133D4×C113—81no—
134D4×C113—81no—
135D4×C113—81no—
136C2×C4×C113—21no—
137C2×C4×C113—21no—
138C2×C4×C113—21no—
139C2×C4×C113—42no—
140C2×C4×C113C2×D411yescharacteristic
141C2×C4×C113C2×D411yescharacteristic
142C2×C4×C113C2×D411yescharacteristic
143C2×C4×C113C2×D411yescharacteristic
144C2×C4×C113C2×D411yescharacteristic
145C2×C4×C113C2411yescharacteristic
146C22⋊D113—81no—
147C2×Dic113—21no—
148C2×Dic113—21no—
149C2×Dic113—21no—
150D452—21no—
151D452—21no—
152C4×D113—81no—
153Dic226—21no—
154Dic226—21no—
155Dic226—81no—
156#11744751—21no—
157#11744751—21no—
158#11744751—21no—
159#11744751—21no—
160C22×C113—21no—
161C22×C113—21no—
162C22×C113—21no—
163C22×C113—41no—
164C22×C113—41no—
165C22×C113—41no—
166C22×C113—41no—
167C22×C113—41no—
168C22×C113—41no—
169C22×C113—41no—
170C22×C113—41no—
171C22×C113—41no—
172C22×C113—84no—
173C22×C113C22×D411yescharacteristic
174C2×D113—41no—
175C2×D113—41no—
176C2×D113—41no—
177C4×C113—21no—
178C4×C113—21no—
179C4×C113—21no—
180C4×C113—21no—
181C4×C113—21no—
182C4×C113—41no—
183C4×C113H(5,𝔽2)11yescharacteristic
184C4×C113H(5,𝔽2)11yescharacteristic
185Dic113—41no—
186Dic113—41no—
187Dic113—41no—
188C2×C113—41no—
189C2×C113—81no—
190C2×C113—81no—
191C2×C113—81no—
192C2×C113#53511yescharacteristic
193C2×C113#57611yescharacteristic
194C2×C113#57711yescharacteristic
195D113—81no—
196#3224—1131nomaximal, Sylow
197C113#322411yescharacteristic, complemented, Sylow
198#542—1131no—
199#535D11311yescharacteristic, complemented
200#496—1131no—
201#495—1131no—
202#489—1131no—
203#486—1131no—
204#464—1131no—
205#463—1131no—
206#460—1131no—
207#459—1131no—
208#452—1131no—
209#450—1131no—
210#449—1131no—
211#447—1131no—
212#433—1131no—
213C2×#41C2×D11311yescharacteristic
214C22×D4C2×D11311yescharacteristic
215C2×Q16—1131no—
216C2×SD16—1131no—
217C2×SD16—1131no—
218C2×SD16—1131no—
219C2×SD16—1131no—
220C2×D8—1131no—
221C2×D8—1131no—
222C2×D8—1131no—
223C4⋊Q8—1131no—
224#127C2×D11311yescharacteristic
225#127C2×D11311yescharacteristic
226#126—2261no—
227#124—1131no—
228#124—2261no—
229#124C2×D11311yescharacteristic
230#124C2×D11311yescharacteristic
231#123—2261no—
232C22⋊Q8—1131no—
233C22⋊Q8—2261no—
234#121—21no—
235#121—21no—
236#121—1131no—
237#120—21no—
238#120—21no—
239C4×Q8—1131no—
240C4×D4—1131no—
241#117C2×D11311yescharacteristic
242C4⋊C8—1131no—
243C4⋊C8—1131no—
244#103—1131no—
245#103—1131no—
246#102—1131no—
247#102—1131no—
248#102—1131no—
249#102—1131no—
250#102—1131no—
251#102—1131no—
252C22⋊C8—1131no—
253C22⋊C8—1131no—
254#97—1131no—
255C4×C8—1131no—
256C24—21no—
257#41—41no—
258#41—41no—
259C2×Q8—1131no—
260C2×Q8—2261no—
261C2×Q8C22×D11311yescharacteristic
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—1131no—
271C2×D4—2261no—
272C2×D4C22×D11311yescharacteristic
273C2×D4C22×D11311yescharacteristic
274C2×D4C22×D11311yescharacteristic
275C22×C4—21no—
276C22×C4—2261no—
277C22×C4C22×D11311yescharacteristic
278Q16—4521no—
279SD16—4521no—
280SD16—4521no—
281SD16—4521no—
282SD16—4521no—
283D8—4521no—
284D8—4521no—
285D8—4521no—
286C2×C8—1131no—
287C2×C8—1131no—
288C2×C8—1131no—
289C2×C8—1131no—
290C4⋊C4—1131no—
291C4⋊C4—1131no—
292C4⋊C4—2261no—
293C4⋊C4—2261no—
294C4⋊C4—2261no—
295C4⋊C4C22⋊D11311yescharacteristic
296C4⋊C4C22⋊D11311yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—2261no—
302C22⋊C4—2261no—
303C22⋊C4—2261no—
304C22⋊C4—2261no—
305C22⋊C4—2261no—
306C22⋊C4C22⋊D11311yescharacteristic
307C22⋊C4C22⋊D11311yescharacteristic
308C42—2261no—
309C42C22×D11311yescharacteristic
310C42C22×D11311yescharacteristic
311C23—21no—
312C23—21no—
313C23—21no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—2261no—
318C23C2×C22⋊D11311yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—9041no—
322Q8—2261no—
323Q8—2261no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—42no—
332D4—81no—
333D4—81no—
334D4—81no—
335D4—81no—
336D4—9041no—
337D4—2261no—
338D4—2261no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—9041no—
344C2×C4—2261no—
345C2×C4—2261no—
346C2×C4—2261no—
347C2×C4C2×C22⋊D11311yescharacteristic
348C2×C4C2×C22⋊D11311yescharacteristic
349C2×C4C2×C22⋊D11311yescharacteristic
350C2×C4C2×C22⋊D11311yescharacteristic
351C2×C4C2×C22⋊D11311yescharacteristic
352C2×C4C23×D11311yescharacteristic
353C8—2261no—
354C8—2261no—
355C8—2261no—
356C8—2261no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—84no—
370C22—4521no—
371C22—4521no—
372C22—4521no—
373C22C22×C22⋊D11311yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—4521no—
381C4—4521no—
382C4—4521no—
383C4#1681366711yescharacteristic
384C4#1681366711yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—81no—
389C2—9041no—
390C2#2029916511yescharacteristic
391C2#2029940111yescharacteristic
392C2#2029940911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#535×C113C2
socleC22×C113C22×D4
hypercenter#535D113
hypocenterC113#3224
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #20299219C2semidirect
2. #20298985C2semidirect
3. #20298980C2semidirect
4. #20298957C2semidirect
5. #20298944C2semidirect
6. #20298817C2semidirect
7. #20298810C2semidirect
8. #20298795C2semidirect
9. #20298790C2semidirect
10. #20298760C2semidirect
11. #20298749C2semidirect
12. #20298743C2semidirect
13. #20298732C2semidirect
14. #20298659C2semidirect
15. #535×C113C2semidirect
16. C2×#14268637C22semidirect
19. C2×#14268635C22semidirect
20. C2×#14268634C22semidirect
23. C2×#14268632C22semidirect
24. #16813622C22semidirect
26. #16813610C22semidirect
32. C4×Dic226C22semidirect
33. C4×D452C22semidirect
34. C4⋊#11744751C22semidirect
35. C4⋊#11744751C22semidirect
36. #16813546C22semidirect
37. #16813546C22semidirect
42. #16813543C22semidirect
43. #16813543C22semidirect
46. #16813533C22semidirect
47. C4×#11744751C22semidirect
197. C113#3224semidirect
199. #535D113semidirect

Maximal subgroups

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

subgroupindex
#202992192
#202989852
#202989802
#202989572
#202989442
#202988172
#202988102
#202987952
#202987902
#202987602
#202987492
#202987432
#202987322
#202986592
#535×C1132
#3224113