Finite Group Databasebeta

← #28402769

Subgroups — #28402769

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#20299244C211yesmaximal, characteristic, complemented
2#20298955C211yesmaximal, characteristic, complemented
3#20298939C211yesmaximal, characteristic, complemented
4#20298911C211yesmaximal, characteristic, complemented
5#20298895C211yesmaximal, characteristic, complemented
6#20298849C211yesmaximal, characteristic, complemented
7#20298842C211yesmaximal, characteristic, complemented
8#20298813C211yesmaximal, characteristic, complemented
9#20298741C211yesmaximal, characteristic, complemented
10#20298731C211yesmaximal, characteristic, complemented
11C4×#14268632C211yesmaximal, characteristic, complemented
12#20298676C211yesmaximal, characteristic, complemented
13#20298602C211yesmaximal, characteristic, complemented
14#20298597C211yesmaximal, characteristic, complemented
15#553×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C22×D452C2211yescharacteristic
18C2×#14268635C2211yescharacteristic, complemented
19C2×#14268632C2211yescharacteristic
20C2×#14268632C2211yescharacteristic
21C2×#14268631C2211yescharacteristic
22C2×#14268631C2211yescharacteristic, complemented
23#16813610C2211yescharacteristic
24#16813607—21no—
25#16813601C2211yescharacteristic
26#16813596C2211yescharacteristic
27#16813595—21no—
28#16813590—21no—
29C4×D452C2211yescharacteristic
30C22⋊C4×D113—21no—
31#16813555C2211yescharacteristic, complemented
32#16813555C2211yescharacteristic, complemented
33#16813553C2211yescharacteristic, complemented
34C4⋊#11744751C2211yescharacteristic, complemented
35#16813545C2211yescharacteristic, complemented
36#16813545C2211yescharacteristic, complemented
37#16813545C2211yescharacteristic, complemented
38#16813543C2211yescharacteristic, complemented
39#16813542C2211yescharacteristic
40#16813542C2211yescharacteristic
41#16813542C2211yescharacteristic
42#16813542C2211yescharacteristic
43#16813542C2211yescharacteristic
44#16813542C2211yescharacteristic
45C22⋊#11744751C2211yescharacteristic
46C22⋊#11744751C2211yescharacteristic, complemented
47C4×#11744751C2211yescharacteristic, complemented
48#126×C113—21no—
49#125×C113C2211yescharacteristic, complemented
50#123×C113—21no—
51#121×C113—21no—
52#121×C113C2211yescharacteristic
53#121×C113C2211yescharacteristic, complemented
54C4×D4×C113—21no—
55C4×D4×C113C2211yescharacteristic
56C4×D4×C113C2211yescharacteristic, complemented
57#117×C113C2211yescharacteristic
58C2×C4⋊C4×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60#14268647—22no—
61#14268647—41no—
62C2×Dic226C2311yescharacteristic
63C2×D452—22no—
64C2×D452—21no—
65C2×D452—41no—
66C2×D452C2311yescharacteristic
67C2×D452C2311yescharacteristic
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70C2×C4×D113—21no—
71C2×C4×D113—21no—
72#14268635—41no—
73#14268632—22no—
74#14268632—41no—
75#14268631—41no—
76#14268631—41no—
77C2×#11744751C2311yescharacteristic
78C2×#11744751C2311yescharacteristic
79C2×#11744751C2311yescharacteristic
80C2×#11744751C2311yescharacteristic
81C4⋊Dic113C2311yescharacteristic
82#14268626—21no—
83C22⋊Dic113—21no—
84#14268624—21no—
85#14268624—21no—
86#14268624—21no—
87#14268624—21no—
88C2×D4×C113—21no—
89C2×D4×C113—21no—
90C2×D4×C113D411yescharacteristic
91C2×D4×C113C2311yescharacteristic
92C22×C4×C113—21no—
93C22×C4×C113—21no—
94C22×C4×C113C2311yescharacteristic
95C22×C4×C113C2311yescharacteristic
96C4⋊C4×C113—21no—
97C4⋊C4×C113—21no—
98C4⋊C4×C113—21no—
99C4⋊C4×C113D411yescharacteristic
100C4⋊C4×C113C2311yescharacteristic
101C4⋊C4×C113C2311yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C22⋊C4×C113—21no—
104C22⋊C4×C113—21no—
105C22⋊C4×C113—21no—
106C22⋊C4×C113—21no—
107C22⋊C4×C113D411yescharacteristic
108C22⋊C4×C113D411yescharacteristic
109C42×C113—21no—
110C42×C113C2311yescharacteristic
111C23×C113—21no—
112C23×C113C2×D411yescharacteristic
113C23×C113C2×D411yescharacteristic
114C22×D113—21no—
115C22×D113—21no—
116C22×D113—42no—
117C22×D113—42no—
118C22×D113—81no—
119D4×C113—21no—
120D4×C113—21no—
121D4×C113—41no—
122D4×C113—42no—
123D4×C113—81no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113—81no—
132C2×C4×C113—81no—
133C2×C4×C113C2×D411yescharacteristic
134C2×C4×C113C2×D411yescharacteristic
135C2×C4×C113C2×D411yescharacteristic
136C2×C4×C113C2×D411yescharacteristic
137C2×C4×C113C2411yescharacteristic
138C22⋊D113—42no—
139C22⋊D113—81no—
140C2×Dic113—21no—
141C2×Dic113—21no—
142D452—21no—
143D452—21no—
144D452—21no—
145D452—42no—
146D452#4112yes—
147C4×D113—42no—
148C4×D113—81no—
149Dic226—21no—
150Dic226—21no—
151#11744751—21no—
152#11744751—21no—
153#11744751—21no—
154#11744751—21no—
155C22×C113—21no—
156C22×C113—21no—
157C22×C113—21no—
158C22×C113—21no—
159C22×C113—21no—
160C22×C113—21no—
161C22×C113—41no—
162C22×C113—41no—
163C22×C113—41no—
164C22×C113C22×D411yescharacteristic
165C2×D113—22no—
166C2×D113—41no—
167C2×D113—41no—
168C2×D113—41no—
169C2×D113—41no—
170C2×D113—41no—
171C2×D113—84no—
172C4×C113—21no—
173C4×C113—21no—
174C4×C113—21no—
175C4×C113—21no—
176C4×C113—41no—
177C4×C113—41no—
178C4×C113—41no—
179C4×C113C2×#4111yescharacteristic
180C4×C113H(5,𝔽2)11yescharacteristic
181Dic113—41no—
182Dic113—41no—
183C2×C113—41no—
184C2×C113—41no—
185C2×C113—81no—
186C2×C113#54611yescharacteristic
187C2×C113#57511yescharacteristic
188C2×C113#57611yescharacteristic
189D113—42no—
190D113—81no—
191#3322—1131nomaximal, Sylow
192C113#332211yescharacteristic, complemented, Sylow
193#553D11311yescharacteristic, complemented
194#546—1131no—
195#488—1131no—
196#485—1131no—
197#480—1131no—
198#478—1131no—
199#469—1131no—
200#468—1131no—
201#463—1131no—
202#449—1131no—
203#447—1131no—
204C4×D8—1131no—
205#436—1131no—
206#418—1131no—
207#417—1131no—
208C2×#41—1131no—
209C22×D4—1131no—
210C2×SD16—1131no—
211C2×D8—1131no—
212C2×D8—1131no—
213C2×M16—1131no—
214C2×M16—1131no—
215#126—21no—
216#125C2×D11311yescharacteristic, complemented
217#124—1131no—
218#123—21no—
219#123—2261no—
220C22⋊Q8—1131no—
221#121—21no—
222#121—1131no—
223#121—2261no—
224#121C2×D11311yescharacteristic
225#121C2×D11311yescharacteristic, complemented
226#120—2261no—
227C4×D4—21no—
228C4×D4—1131no—
229C4×D4C2×D11311yescharacteristic
230C4×D4C2×D11311yescharacteristic, complemented
231#117C2×D11311yescharacteristic
232C2×C4⋊C4C2×D11311yescharacteristic, complemented
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#102—1131no—
245#102—1131no—
246#102—1131no—
247#102—1131no—
248C22⋊C8—1131no—
249C22⋊C8—1131no—
250C4×C8—1131no—
251C24—2261no—
252#41—4521no—
253#41—2262no—
254C2×Q8—1131no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—1131no—
258C2×D4—1131no—
259C2×D4—4521no—
260C2×D4—2262no—
261C2×D4—2261no—
262C2×D4—2261no—
263C2×D4—2261no—
264C2×D4C22⋊D11311yescharacteristic
265C2×D4C22×D11311yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—2261no—
269C22×C4—2261no—
270C22×C4C22×D11311yescharacteristic
271C22×C4C22×D11311yescharacteristic
272SD16—4521no—
273D8—4521no—
274D8—2262no—
275M16—4521no—
276M16—4521no—
277C2×C8—1131no—
278C2×C8—1131no—
279C2×C8—1131no—
280C2×C8—1131no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—1131no—
285C4⋊C4—2261no—
286C4⋊C4C22⋊D11311yescharacteristic
287C4⋊C4C22×D11311yescharacteristic
288C4⋊C4C22×D11311yescharacteristic
289C4⋊C4C22×D11311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—2261no—
295C22⋊C4—2261no—
296C22⋊C4—2261no—
297C22⋊C4—2261no—
298C22⋊C4—2261no—
299C22⋊C4C22⋊D11311yescharacteristic
300C22⋊C4C22⋊D11311yescharacteristic
301C42—21no—
302C42C22×D11311yescharacteristic
303C23—21no—
304C23—9041no—
305C23—4522no—
306C23—4522no—
307C23—2261no—
308C23—2261no—
309C23C2×C22⋊D11311yescharacteristic
310C23C2×C22⋊D11311yescharacteristic
311Q8—2261no—
312Q8—2261no—
313D4—21no—
314D4—21no—
315D4—41no—
316D4—42no—
317D4—81no—
318D4—1132no—
319D4—9041no—
320D4—4522no—
321D4—4522no—
322D4—2261no—
323D4—2261no—
324D4—2261no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—9041no—
335C2×C4—4522no—
336C2×C4—2261no—
337C2×C4—2261no—
338C2×C4C2×C22⋊D11311yescharacteristic
339C2×C4C2×C22⋊D11311yescharacteristic
340C2×C4C2×C22⋊D11311yescharacteristic
341C2×C4C2×C22⋊D11311yescharacteristic
342C2×C4C23×D11311yescharacteristic
343C8—2261no—
344C8—2261no—
345C8—2261no—
346C8—2261no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—9044no—
357C22—4521no—
358C22—4521no—
359C22—4521no—
360C22—4521no—
361C22—4521no—
362C22—2262no—
363C22C22×C22⋊D11311yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—4521no—
372C4—4521no—
373C4#41×D11311yescharacteristic
374C4#1681366811yescharacteristic
375C2—41no—
376C2—41no—
377C2—81no—
378C2—9041no—
379C2—4522no—
380C2#2029923611yescharacteristic
381C2#2029939611yescharacteristic
382C2#2029940111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#553×C113C2
socleC22×C113C22×D4
hypercenter#553D113
hypocenterC113#3322
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #20299244C2semidirect
2. #20298955C2semidirect
3. #20298939C2semidirect
4. #20298911C2semidirect
5. #20298895C2semidirect
6. #20298849C2semidirect
7. #20298842C2semidirect
8. #20298813C2semidirect
9. #20298741C2semidirect
10. #20298731C2semidirect
11. C4×#14268632C2semidirect
12. #20298676C2semidirect
13. #20298602C2semidirect
14. #20298597C2semidirect
15. #553×C113C2semidirect
18. C2×#14268635C22semidirect
22. C2×#14268631C22semidirect
31. #16813555C22semidirect
32. #16813555C22semidirect
33. #16813553C22semidirect
34. C4⋊#11744751C22semidirect
35. #16813545C22semidirect
36. #16813545C22semidirect
37. #16813545C22semidirect
38. #16813543C22semidirect
46. C22⋊#11744751C22semidirect
47. C4×#11744751C22semidirect
49. #125×C113C22semidirect
53. #121×C113C22semidirect
56. C4×D4×C113C22semidirect
58. C2×C4⋊C4×C113C22semidirect
192. C113#3322semidirect
193. #553D113semidirect
216. #125C2×D113semidirect
225. #121C2×D113semidirect
230. C4×D4C2×D113semidirect
232. C2×C4⋊C4C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992442
#202989552
#202989392
#202989112
#202988952
#202988492
#202988422
#202988132
#202987412
#202987312
C4×#142686322
#202986762
#202986022
#202985972
#553×C1132
#3322113