Finite Group Databasebeta

← #28402731

Subgroups — #28402731

Order 14464.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299311C211yesmaximal, characteristic, complemented
2#20299242C211yesmaximal, characteristic, complemented
3#20298956C211yesmaximal, characteristic, complemented
4#20298939C211yesmaximal, characteristic, complemented
5#20298920C211yesmaximal, characteristic, complemented
6#20298876C211yesmaximal, characteristic, complemented
7#20298844C211yesmaximal, characteristic, complemented
8#20298833C211yesmaximal, characteristic, complemented
9#20298812C211yesmaximal, characteristic, complemented
10#20298744C211yesmaximal, characteristic, complemented
11#20298732C211yesmaximal, characteristic, complemented
12#20298707C211yesmaximal, characteristic, complemented
13#20298667C211yesmaximal, characteristic, complemented
14#20298591C211yesmaximal, characteristic, complemented
15#418×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C2×#14268636C2211yescharacteristic, complemented
18C2×#14268632C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20C2×C8×D113C2211yescharacteristic, complemented
21#16813621C2211yescharacteristic, complemented
22#16813610—21no—
23#16813609C2211yescharacteristic
24#16813608—21no—
25#16813603—21no—
26#16813601C2211yescharacteristic
27#16813597C2211yescharacteristic, complemented
28#16813596C2211yescharacteristic
29#16813595—21no—
30#16813594—21no—
31#16813593C2211yescharacteristic
32#16813591—21no—
33D4×Dic113C2211yescharacteristic
34#16813584C2211yescharacteristic, complemented
35C4×C22⋊D113C2211yescharacteristic
36#16813580C2211yescharacteristic, complemented
37#16813579—21no—
38C2×C22⋊Dic113—21no—
39#16813556C2211yescharacteristic, complemented
40#16813555C2211yescharacteristic, complemented
41#16813553C2211yescharacteristic, complemented
42#16813551C2211yescharacteristic, complemented
43#16813547C2211yescharacteristic, complemented
44#16813545C2211yescharacteristic, complemented
45#16813545C2211yescharacteristic, complemented
46#16813544C2211yescharacteristic, complemented
47#16813543C2211yescharacteristic
48#16813543C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic, complemented
51#16813532C2211yescharacteristic, complemented
52C22×D4×C113C2211yescharacteristic
53C2×M16×C113C2211yescharacteristic
54#117×C113C2211yescharacteristic
55#102×C113C2211yescharacteristic
56#102×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59#14268646—22no—
60#14268646—41no—
61C2×Dic226—21no—
62C2×Dic226C2311yescharacteristic
63C2×D452—21no—
64C2×D452C2311yescharacteristic
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67C2×C22⋊D113—21no—
68C2×C22⋊D113D411yescharacteristic
69C22×Dic113—21no—
70C22×Dic113—21no—
71C2×C4×D113—21no—
72C2×C4×D113C2311yescharacteristic
73#14268636—41no—
74#14268632—22no—
75#14268632—41no—
76C2×#11744751C2311yescharacteristic
77C2×#11744751C2311yescharacteristic
78C8×D113—41no—
79C4⋊Dic113C2311yescharacteristic
80C4⋊Dic113C2311yescharacteristic
81#14268626—21no—
82#14268626—21no—
83#14268626D411yescharacteristic
84C22⋊Dic113—21no—
85C22⋊Dic113—21no—
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113D411yescharacteristic
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624D411yescharacteristic
95C4×Dic113—21no—
96C4×Dic113C2311yescharacteristic
97C24×C113—21no—
98C2×D4×C113—22no—
99C2×D4×C113—21no—
100C2×D4×C113—41no—
101C2×D4×C113C2311yescharacteristic
102C2×D4×C113C2311yescharacteristic
103C22×C4×C113C2311yescharacteristic
104M16×C113—41no—
105C2×C8×C113C2311yescharacteristic
106C2×C8×C113C2311yescharacteristic
107C4⋊C4×C113C2311yescharacteristic
108C4⋊C4×C113C2311yescharacteristic
109C22⋊C4×C113—21no—
110C42×C113—21no—
111C23×C113—21no—
112C23×C113—21no—
113C23×C113—42no—
114C23×C113—42no—
115C23×C113—81no—
116C23×C113C2×D411yescharacteristic
117C22×D113—21no—
118C22×D113C2×D411yescharacteristic
119D4×C113—21no—
120D4×C113—21no—
121D4×C113—21no—
122D4×C113—42no—
123D4×C113#4112yes—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113C2×D411yescharacteristic
129C2×C4×C113C2411yescharacteristic
130C22⋊D113—41no—
131C22⋊D113—42no—
132C22⋊D113—81no—
133C22⋊D113—81no—
134C2×Dic113—21no—
135C2×Dic113—21no—
136C2×Dic113—21no—
137C2×Dic113—42no—
138C2×Dic113—81no—
139C2×Dic113C2×D411yescharacteristic
140C2×Dic113C2×D411yescharacteristic
141C2×Dic113C2×D411yescharacteristic
142D452—21no—
143D452—21no—
144D452—81no—
145C4×D113—21no—
146C4×D113—21no—
147C4×D113—42no—
148Dic226—21no—
149Dic226—21no—
150Dic226—81no—
151C8×C113—21no—
152C8×C113—21no—
153#11744751—21no—
154#11744751—21no—
155C22×C113—22no—
156C22×C113—21no—
157C22×C113—21no—
158C22×C113—21no—
159C22×C113—41no—
160C22×C113—41no—
161C22×C113—41no—
162C22×C113—41no—
163C22×C113—41no—
164C22×C113—84no—
165C22×C113C22×D411yescharacteristic
166C2×D113—21no—
167C2×D113—21no—
168C2×D113—21no—
169C2×D113—41no—
170C2×D113—41no—
171C2×D113—41no—
172C4×C113—21no—
173C4×C113—41no—
174C4×C113—41no—
175C4×C113C2×#4111yescharacteristic
176C4×C113H(5,𝔽2)11yescharacteristic
177Dic113—21no—
178Dic113—21no—
179Dic113—21no—
180Dic113—41no—
181Dic113—41no—
182Dic113—41no—
183C2×C113—41no—
184C2×C113—42no—
185C2×C113—81no—
186C2×C113#54611yescharacteristic
187C2×C113#57511yescharacteristic
188C2×C113#57611yescharacteristic
189D113—41no—
190D113—81no—
191#3319—1131nomaximal, Sylow
192C113#331911yescharacteristic, complemented, Sylow
193#555—1131no—
194#546—1131no—
195#489—1131no—
196#485—1131no—
197#482—1131no—
198#474—1131no—
199#468—1131no—
200#466—1131no—
201#463—1131no—
202#449—1131no—
203#447—1131no—
204#442—1131no—
205#435—1131no—
206#418D11311yescharacteristic, complemented
207#416—1131no—
208C2×#41—1131no—
209C22×D4C2×D11311yescharacteristic
210C2×SD16—1131no—
211C2×D8—1131no—
212C2×D8—1131no—
213C2×M16C2×D11311yescharacteristic
214C22×C8—1131no—
215C4⋊Q8—1131no—
216#124—1131no—
217#124—2261no—
218#124—2261no—
219#123—2261no—
220C22⋊Q8—1131no—
221#121—1131no—
222#121—1131no—
223#121—1131no—
224#121—2261no—
225#121—2261no—
226#120—2261no—
227C4×D4—1131no—
228C4×D4—1131no—
229C4×D4—1131no—
230#117—1131no—
231#117—2261no—
232#117C2×D11311yescharacteristic
233C2×C22⋊C4—2261no—
234#107—1131no—
235#107—1131no—
236#106—1131no—
237C4⋊C8—1131no—
238#103—1131no—
239#103—1131no—
240#103—1131no—
241#102—1131no—
242#102—1131no—
243#102—1131no—
244#102C2×D11311yescharacteristic
245#102C2×D11311yescharacteristic
246#102C2×D11311yescharacteristic
247#102C2×D11311yescharacteristic
248C22⋊C8—1131no—
249C22⋊C8—1131no—
250#97—1131no—
251C24—21no—
252#41—4521no—
253#41—2262no—
254C2×Q8—1131no—
255C2×Q8—2261no—
256C2×D4—22no—
257C2×D4—21no—
258C2×D4—41no—
259C2×D4—1131no—
260C2×D4—1131no—
261C2×D4—2261no—
262C2×D4—2261no—
263C2×D4—2261no—
264C2×D4—2261no—
265C2×D4C22×D11311yescharacteristic
266C2×D4C22×D11311yescharacteristic
267C22×C4—1131no—
268C22×C4—2261no—
269C22×C4—2261no—
270C22×C4—2261no—
271C22×C4C22×D11311yescharacteristic
272SD16—4521no—
273D8—4521no—
274D8—2262no—
275M16—41no—
276C2×C8—1131no—
277C2×C8—1131no—
278C2×C8—4521no—
279C2×C8C22×D11311yescharacteristic
280C2×C8C22×D11311yescharacteristic
281C4⋊C4—1131no—
282C4⋊C4—1131no—
283C4⋊C4—1131no—
284C4⋊C4—2261no—
285C4⋊C4—2261no—
286C4⋊C4C22×D11311yescharacteristic
287C4⋊C4C22×D11311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—1131no—
290C22⋊C4—1131no—
291C22⋊C4—2261no—
292C22⋊C4—2261no—
293C22⋊C4—2261no—
294C22⋊C4—2261no—
295C22⋊C4—2261no—
296C22⋊C4—2261no—
297C22⋊C4—2261no—
298C22⋊C4—2261no—
299C22⋊C4—2261no—
300C42—21no—
301C42—1131no—
302C42—2261no—
303C23—21no—
304C23—21no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—1131no—
309C23—2261no—
310C23D4×D11311yescharacteristic
311Q8—9041no—
312Q8—2261no—
313Q8—2261no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—42no—
318D4—9041no—
319D4—9041no—
320D4—9041no—
321D4—4522no—
322D4—4521no—
323D4—2261no—
324D4—2261no—
325D4#1426864712yes—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—1131no—
331C2×C4—1131no—
332C2×C4—1131no—
333C2×C4—9041no—
334C2×C4—4522no—
335C2×C4—4522no—
336C2×C4—2261no—
337C2×C4—2261no—
338C2×C4—2261no—
339C2×C4—2261no—
340C2×C4—2261no—
341C2×C4D4×D11311yescharacteristic
342C2×C4C23×D11311yescharacteristic
343C8—21no—
344C8—21no—
345C8—2261no—
346C8—2261no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—84no—
357C22—4521no—
358C22—4521no—
359C22—4521no—
360C22—2261no—
361C22—2261no—
362C22—2261no—
363C22C2×D4×D11311yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—4521no—
368C4—4521no—
369C4—4521no—
370C4—2261no—
371C4—2261no—
372C4—2261no—
373C4C2×#1426864711yescharacteristic
374C4#1681366711yescharacteristic
375C2—41no—
376C2—42no—
377C2—81no—
378C2—9041no—
379C2—4521no—
380C2#2029923811yescharacteristic
381C2#2029939411yescharacteristic
382C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#418×C113C2
socleC22×C113C22×D4
hypercenter#418D113
hypocenterC113#3319
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #20299311C2semidirect
2. #20299242C2semidirect
3. #20298956C2semidirect
4. #20298939C2semidirect
5. #20298920C2semidirect
6. #20298876C2semidirect
7. #20298844C2semidirect
8. #20298833C2semidirect
9. #20298812C2semidirect
10. #20298744C2semidirect
11. #20298732C2semidirect
12. #20298707C2semidirect
13. #20298667C2semidirect
14. #20298591C2semidirect
15. #418×C113C2semidirect
17. C2×#14268636C22semidirect
20. C2×C8×D113C22semidirect
21. #16813621C22semidirect
27. #16813597C22semidirect
34. #16813584C22semidirect
36. #16813580C22semidirect
39. #16813556C22semidirect
40. #16813555C22semidirect
41. #16813553C22semidirect
42. #16813551C22semidirect
43. #16813547C22semidirect
44. #16813545C22semidirect
45. #16813545C22semidirect
46. #16813544C22semidirect
50. #16813534C22semidirect
51. #16813532C22semidirect
192. C113#3319semidirect
206. #418D113semidirect

Maximal subgroups

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

subgroupindex
#202993112
#202992422
#202989562
#202989392
#202989202
#202988762
#202988442
#202988332
#202988122
#202987442
#202987322
#202987072
#202986672
#202985912
#418×C1132
#3319113