Finite Group Databasebeta

← #14736247

Subgroups — #14736247

Order 2816.

664 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079195C211yesmaximal, characteristic, complemented
2#13078676C212yesmaximal, complemented
3#13068032C212yesmaximal, complemented
4#13068025C212yesmaximal, complemented
5#13068020C211yesmaximal, characteristic, complemented
6#13068015C211yesmaximal, characteristic, complemented
7#13067976C211yesmaximal, characteristic, complemented
8#13067971C211yesmaximal, characteristic, complemented
9#13067364C211yesmaximal, characteristic, complemented
10#13067276C212yesmaximal, complemented
11C8×C11×#41C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13#10623008C2212yes—
14C8×Q8×C11C2211yescharacteristic
15C8×Q8×C11C2211yescharacteristic
16C8×D4×C11—21no—
17C8×D4×C11—21no—
18C8×D4×C11C2211yescharacteristic
19C8×D4×C11C2211yescharacteristic
20C11×#431—21no—
21C11×#431C2211yescharacteristic
22C2×C4×C8×C11—21no—
23C2×C4×C8×C11C2211yescharacteristic
24#10622851—22no—
25#10622728—21no—
26#10622728—21no—
27#10622640C2212yes—
28C4×#4325—22no—
29#10622634C2212yes—
30#10622628C2212yes—
31C4×#4323—22no—
32#10622621C2212yes—
33#10622616—22no—
34#10622538C2212yes—
35#10622308C2211yescharacteristic
36#10622307C2212yes—
37C4×D88—21no—
38C4×D88—21no—
39#10622295C2211yescharacteristic
40#10622123C2212yes—
41#10622123C2212yes—
42#10622119C2212yes—
43#10622119C2212yes—
44#10622096C2211yescharacteristic
45#10622096C2211yescharacteristic
46#10622095C2212yes—
47C2×C11×#41D411yescharacteristic
48C2×#4339—22no—
49C22×C8×C11—21no—
50C22×C8×C11—21no—
51C22×C8×C11D411yescharacteristic
52C22×C8×C11D411yescharacteristic
53C4×Q8×C11D411yescharacteristic
54C4×Q8×C11C2311yescharacteristic
55C4×D4×C11—21no—
56C4×D4×C11—21no—
57C4×D4×C11D411yescharacteristic
58C4×D4×C11C2311yescharacteristic
59C11×#117—21no—
60C11×#117D411yescharacteristic
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63C2×#4325—22no—
64C2×#4323—22no—
65#66983—22no—
66#66983—22no—
67C2×D88—21no—
68C2×D88—21no—
69#66928—22no—
70#66927C2312yes—
71C4×D44—22no—
72C4×D44—22no—
73#66922C2312yes—
74C11×C4⋊C8—21no—
75C11×C4⋊C8—21no—
76C11×C4⋊C8C2311yescharacteristic
77C11×C4⋊C8C2311yescharacteristic
78C11×C22⋊C8—21no—
79C11×C22⋊C8—21no—
80C11×C22⋊C8—21no—
81C4×C8×C11—21no—
82C4×C8×C11—21no—
83C4×C8×C11—21no—
84C4×C8×C11D411yescharacteristic
85C4×C8×C11D411yescharacteristic
86C4×C8×C11C2311yescharacteristic
87C4×C8×C11C2311yescharacteristic
88#66899—22no—
89#66896—22no—
90C22⋊(C11⋊C8)—22no—
91#66885—22no—
92#66885—22no—
93#66882—21no—
94#66882—21no—
95#66873—22no—
96#66873—22no—
97#66872—22no—
98#66871—22no—
99C4⋊(C11⋊C8)C2312yes—
100C4⋊(C11⋊C8)C2312yes—
101C4×C11⋊C8—22no—
102#19128—111nomaximal, Sylow
103C11×#41—22no—
104C11×#41—22no—
105C2×Q8×C11C2×D411yescharacteristic
106C2×D4×C11—21no—
107C2×D4×C11C2×D411yescharacteristic
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11#4111yescharacteristic
114C2×C22⋊D11—42no—
115#4339—84no—
116C2×D44—22no—
117C2×D44—22no—
118C2×D44—22no—
119C2×C4×D11—42no—
120C2×Dic22—22no—
121C2×C8×C11—22no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—41no—
125C2×C8×C11—42no—
126C2×C8×C11—42no—
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11C2×D411yescharacteristic
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4C2×D411yescharacteristic
134C11×C4⋊C4C2×D411yescharacteristic
135C11×C22⋊C4—21no—
136C11×C22⋊C4—21no—
137C11×C22⋊C4—21no—
138C42×C11—21no—
139C42×C11—21no—
140C42×C11—21no—
141C42×C11C2×D411yescharacteristic
142C42×C11C2×D411yescharacteristic
143C42×C11#4111yescharacteristic
144C42×C11C2411yescharacteristic
145#4325—44no—
146#4323—44no—
147(C2×D11)⋊C4—42no—
148(C2×D11)⋊C4—42no—
149C4⋊Dic11—22no—
150C4⋊Dic11—22no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—22no—
153D88—42no—
154D88—42no—
155#3169—111no—
156#3106—112no—
157C8×#41D1111yescharacteristic, complemented
158#1678—112no—
159#1677—112no—
160#1676—111no—
161#1675—111no—
162#1668—111no—
163#1667—111no—
164#1564—111no—
165#1543—112no—
166C23×C11—21no—
167C23×C11#12111yescharacteristic
168C22×D11—42no—
169Q8×C11—21no—
170Q8×C11#13512yes—
171D4×C11—24no—
172D4×C11—21no—
173D4×C11#13512yes—
174C2×C4×C11—24no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—22no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—42no—
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11#12111yescharacteristic
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C22×D411yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C22⋊D11—84no—
193C2×Dic11—42no—
194D44—42no—
195D44—42no—
196D44—42no—
197D44—42no—
198D44—82no—
199C4×D11—84no—
200Dic22—82no—
201C8×C11—21no—
202C8×C11—21no—
203C8×C11—21no—
204C8×C11—41no—
205C8×C11—41no—
206C8×C11#13512yes—
207C11⋊C8—42no—
208C11⋊C8—42no—
209#532—112no—
210C4×#41C2×D1111yescharacteristic
211#500—111no—
212#493—111no—
213#486—112no—
214#482—222no—
215#477—112no—
216#476—112no—
217#466—221no—
218#466—221no—
219#460—112no—
220#459—112no—
221#449—222no—
222C8×Q8C2×D1111yescharacteristic
223C8×Q8C2×D1111yescharacteristic
224C4×SD16—222no—
225C4×D8—222no—
226C4×D8—221no—
227C4×D8—221no—
228C8×D4—21no—
229C8×D4—21no—
230C8×D4C2×D1111yescharacteristic
231C8×D4C2×D1111yescharacteristic
232#431—21no—
233#431—112no—
234#431C2×D1111yescharacteristic
235C2×C4×C8—21no—
236C2×C4×C8C2×D1111yescharacteristic
237#335—111no—
238#335—111no—
239#334—112no—
240#333—112no—
241#333—112no—
242#331—112no—
243#331—112no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—22no—
247C22×C11—21no—
248C22×C11—41no—
249C22×C11—41no—
250C22×C11C2×#12111yescharacteristic
251C2×D11—82no—
252C2×D11—82no—
253C2×D11—82no—
254C4×C11—21no—
255C4×C11—21no—
256C4×C11—22no—
257C4×C11—21no—
258C4×C11—41no—
259C4×C11—41no—
260C4×C11#47212yes—
261C4×C11C2×#13511yescharacteristic
262C4×C11C2×#13511yescharacteristic
263C4×C11C2×#13511yescharacteristic
264C4×C11#57511yescharacteristic
265Dic11—82no—
266C2×#41—222no—
267C2×#41D4411yescharacteristic
268C2×SD16—222no—
269C2×D8—222no—
270C2×D8—221no—
271C2×D8—221no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8C22⋊D1111yescharacteristic
275C22×C8C22⋊D1111yescharacteristic
276C4⋊Q8—112no—
277#127—112no—
278#124—222no—
279#121—222no—
280#121—222no—
281C4×Q8D4411yescharacteristic
282C4×Q8C22×D1111yescharacteristic
283C4×D4—21no—
284C4×D4—21no—
285C4×D4—222no—
286C4×D4—222no—
287C4×D4D4411yescharacteristic
288C4×D4C22×D1111yescharacteristic
289#117—21no—
290#117D4411yescharacteristic
291C2×C42—21no—
292C2×C42C22×D1111yescharacteristic
293#107—221no—
294#107—221no—
295#107—222no—
296#106—222no—
297C4⋊C8—21no—
298C4⋊C8—21no—
299C4⋊C8—112no—
300C4⋊C8—112no—
301C4⋊C8C22×D1111yescharacteristic
302C4⋊C8C22×D1111yescharacteristic
303#103—222no—
304#102—222no—
305#102—222no—
306#102—222no—
307#102—222no—
308#102—222no—
309C22⋊C8—21no—
310C22⋊C8—21no—
311C22⋊C8—21no—
312C22⋊C8—222no—
313C4×C8—21no—
314C4×C8—21no—
315C4×C8—21no—
316C4×C8—222no—
317C4×C8C22⋊D1111yescharacteristic
318C4×C8C22⋊D1111yescharacteristic
319C4×C8C22×D1111yescharacteristic
320C4×C8C22×D1111yescharacteristic
321C2×C11—41no—
322C2×C11—42no—
323C2×C11#303511yescharacteristic
324C2×C11#305011yescharacteristic
325C2×C11C2×#47211yescharacteristic
326D11—162no—
327#41—22no—
328#41—22no—
329#41—884no—
330C2×Q8—222no—
331C2×Q8C2×D4411yescharacteristic
332C2×D4—21no—
333C2×D4—222no—
334C2×D4—222no—
335C2×D4—222no—
336C2×D4—442no—
337C2×D4C2×D4411yescharacteristic
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—442no—
342C22×C4C2×D4411yescharacteristic
343C22×C4#433911yescharacteristic
344C22×C4C2×C22⋊D1111yescharacteristic
345SD16—444no—
346D8—442no—
347D8—444no—
348D8—442no—
349C2×C8—22no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—41no—
353C2×C8—42no—
354C2×C8—42no—
355C2×C8—222no—
356C2×C8—222no—
357C2×C8C2×C22⋊D1111yescharacteristic
358C2×C8C2×C22⋊D1111yescharacteristic
359C2×C8C2×C22⋊D1111yescharacteristic
360C2×C8C2×C22⋊D1111yescharacteristic
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—222no—
364C4⋊C4—222no—
365C4⋊C4C2×D4411yescharacteristic
366C4⋊C4C2×D4411yescharacteristic
367C22⋊C4—21no—
368C22⋊C4—21no—
369C22⋊C4—21no—
370C22⋊C4—442no—
371C22⋊C4—442no—
372C42—21no—
373C42—21no—
374C42—21no—
375C42C2×D4411yescharacteristic
376C42#433911yescharacteristic
377C42C2×C22⋊D1111yescharacteristic
378C42C23×D1111yescharacteristic
379C11#1912811yescharacteristic, complemented, Sylow
380C23—21no—
381C23—442no—
382C23#6698311yescharacteristic
383Q8—21no—
384Q8—882no—
385Q8#6695712yes—
386D4—24no—
387D4—21no—
388D4—442no—
389D4—442no—
390D4—442no—
391D4—442no—
392D4—882no—
393D4—884no—
394D4#6695712yes—
395C2×C4—24no—
396C2×C4—21no—
397C2×C4—22no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—442no—
408C2×C4—884no—
409C2×C4#6698311yescharacteristic
410C2×C4#6698311yescharacteristic
411C2×C4#6698311yescharacteristic
412C2×C4C22×D4411yescharacteristic
413C2×C4C2×#433911yescharacteristic
414C2×C4C22×C22⋊D1111yescharacteristic
415C8—21no—
416C8—21no—
417C8—21no—
418C8—41no—
419C8—41no—
420C8—442no—
421C8—442no—
422C8#6700312yes—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—22no—
427C22—41no—
428C22—41no—
429C22—882no—
430C22—882no—
431C22—882no—
432C22C2×#6698311yescharacteristic
433C4—21no—
434C4—21no—
435C4—21no—
436C4—22no—
437C4—41no—
438C4—41no—
439C4—882no—
440C4#1062275512yes—
441C4C2×#6695711yescharacteristic
442C4C2×#6695711yescharacteristic
443C4C2×#6700311yescharacteristic
444C4#1062335311yescharacteristic
445C2—41no—
446C2—42no—
447C2—1762no—
448C2#1307807111yescharacteristic
449C2#1307819711yescharacteristic
450C2C2×#1062275511yescharacteristic
subgroupG/H
centerC2×C4#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC8×C11×#41C2
socleC22×C11C2×#121
hypercenterC8×#41D11
hypocenterC11#19128
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
1. #13079195C2semidirect
2. #13078676C2semidirect
3. #13068032C2semidirect
4. #13068025C2semidirect
5. #13068020C2semidirect
6. #13068015C2semidirect
7. #13067976C2semidirect
8. #13067971C2semidirect
9. #13067364C2semidirect
10. #13067276C2semidirect
11. C8×C11×#41C2semidirect
157. C8×#41D11semidirect
379. C11#19128semidirect

Maximal subgroups

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

subgroupindex
#130791952
#130786762
#130680322
#130680252
#130680202
#130680152
#130679762
#130679712
#130673642
#130672762
C8×C11×#412
#1912811