Finite Group Databasebeta

← #14737317

Subgroups — #14737317

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079923C211yesmaximal, characteristic
2#13079744C211yesmaximal, characteristic, complemented
3#13077362C211yesmaximal, characteristic, complemented
4#13068188C212yesmaximal, complemented
5#13068146C212yesmaximal, complemented
6#13068064C212yesmaximal, complemented
7#13068022C212yesmaximal, complemented
8#13067368C211yesmaximal, characteristic, complemented
9C2×#10622184C211yesmaximal, characteristic, complemented
10#13067265C211yesmaximal, characteristic, complemented
11C11×#3141C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#66960—21no—
15#10623008C2211yescharacteristic
16C11×#489—22no—
17C11×#487C2212yes—
18C11×#486C2212yes—
19C11×#417—21no—
20C11×#417—21no—
21C4×C11×M16C2211yescharacteristic
22#10622742—21no—
23#10622701—21no—
24#10622700C2212yes—
25#10622697C2212yes—
26#10622697C2212yes—
27#10622692—21no—
28#10622685C2212yes—
29#10622651—22no—
30#10622628—21no—
31#10622620—21no—
32#10622581—22no—
33#10622538C2211yescharacteristic
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622319—22no—
37#10622301C2212yes—
38C8×D44C2212yes—
39#10622185C2211yescharacteristic
40#10622185C2211yescharacteristic
41#10622184C2212yes—
42#10622184C2212yes—
43#10622182C2211yescharacteristic
44#10622182C2211yescharacteristic
45#10622096C2212yes—
46#10622095C2212yes—
47C2×C11×#41—21no—
48C22×Q8×C11—21no—
49C2×#4339—21no—
50C2×C11×M16D411yescharacteristic
51C2×C11×M16D411yescharacteristic
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8C2312yes—
56C11×C4⋊Q8C2311yescharacteristic
57C11×#127C2311yescharacteristic
58C11×#124—21no—
59C11×#121—21no—
60C11×#121—21no—
61C4×D4×C11—21no—
62C4×D4×C11—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C42×C11C2311yescharacteristic
66C2×#4323—22no—
67#66983—21no—
68#66983D412yes—
69C22×C11⋊C8—21no—
70C22×C11⋊C8—21no—
71#66960—44no—
72C2×#4313—22no—
73C2×C8×D11—22no—
74#66928—21no—
75#66927D411yescharacteristic
76C4×D44—21no—
77C4×D44C2312yes—
78#66922D411yescharacteristic
79C11×#103—22no—
80C11×#103—22no—
81C11×#102—22no—
82C11×#102—22no—
83C11×#97D412yes—
84C4×C8×C11C2312yes—
85#66896—22no—
86C22⋊(C11⋊C8)—21no—
87(C2×D11)⋊C8—22no—
88(C2×D11)⋊C8—22no—
89#66873—22no—
90#66873—22no—
91#66873—22no—
92#66872—22no—
93#66872—22no—
94#66871—22no—
95C4⋊(C11⋊C8)—21no—
96C4⋊(C11⋊C8)—21no—
97C4⋊(C11⋊C8)C2311yescharacteristic
98C4⋊(C11⋊C8)C2311yescharacteristic
99C4⋊(C11⋊C8)C2312yes—
100C4⋊(C11⋊C8)C2311yescharacteristic
101C4⋊(C11⋊C8)C2311yescharacteristic
102C4×C11⋊C8—21no—
103#19236—111nomaximal, Sylow
104C11×#41—42no—
105C11×#41—42no—
106C2×Q8×C11—21no—
107C2×Q8×C11—22no—
108C2×Q8×C11—41no—
109C2×Q8×C11—82no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—41no—
114C22×C4×C11—41no—
115C22×C4×C11—41no—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11#4111yescharacteristic
119C2×C22⋊D11—22no—
120#4339—42no—
121#4339—42no—
122C2×D44—21no—
123C2×D44—21no—
124C2×D44C2×D412yes—
125C2×C4×D11—22no—
126C2×Dic22—21no—
127C11×M16—22no—
128C11×M16—22no—
129C2×C8×C11C2×D412yes—
130C2×C8×C11C2×D412yes—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—41no—
136C11×C4⋊C4—41no—
137C11×C22⋊C4—41no—
138C11×C22⋊C4—41no—
139C42×C11C2×D411yescharacteristic
140C42×C11C2×D411yescharacteristic
141C42×C11#4111yescharacteristic
142C42×C11C2411yescharacteristic
143#4323—82no—
144(C2×D11)⋊C4—22no—
145(C2×D11)⋊C4—22no—
146C4⋊Dic11—21no—
147C4⋊Dic11C2×D412yes—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—42no—
154C2×C11⋊C8—81no—
155#4313—44no—
156C8×D11—44no—
157#3245—111no—
158#3227—111no—
159#3141D1111yescharacteristic, complemented
160#2935—111no—
161#1703—112no—
162#1697—112no—
163#1683—112no—
164#1677—112no—
165#1565—111no—
166C2×#333—111no—
167#1540—111no—
168C23×C11—41no—
169C23×C11#12111yescharacteristic
170C22×D11—22no—
171Q8×C11—41no—
172Q8×C11—41no—
173Q8×C11—82no—
174Q8×C11—82no—
175D4×C11—41no—
176D4×C11—41no—
177D4×C11—41no—
178D4×C11—41no—
179D4×C11—81no—
180D4×C11—82no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—42no—
186C2×C4×C11—82no—
187C2×C4×C11—82no—
188C2×C4×C11#12111yescharacteristic
189C2×C4×C11#12111yescharacteristic
190C2×C4×C11#12111yescharacteristic
191C2×C4×C11#13512yes—
192C2×C4×C11AGL(1,ℤ/8)12yes—
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C22⋊D11—44no—
197C2×Dic11—22no—
198D44—22no—
199D44—22no—
200D44—42no—
201D44—81no—
202C4×D11—42no—
203C4×D11—42no—
204Dic22—42no—
205C8×C11—22no—
206C8×C11—22no—
207C11⋊C8—41no—
208C11⋊C8—41no—
209C11⋊C8—41no—
210C11⋊C8—42no—
211C11⋊C8—41no—
212C2×#131—221no—
213#532—111no—
214#532C2×D1111yescharacteristic
215C2×C4⋊Q8C2×D1111yescharacteristic
216#498—221no—
217#489—22no—
218#487C2×D1112yes—
219#486—221no—
220#486C2×D1112yes—
221#481—222no—
222#476—112no—
223#476—112no—
224#474—112no—
225#474—221no—
226#466—222no—
227#459—112no—
228#459—221no—
229#436—112no—
230#435—222no—
231C8×D4—112no—
232#431—111no—
233C2×C4⋊C8—111no—
234C2×C4⋊C8—111no—
235#417—21no—
236#417—21no—
237#408—221no—
238C4×M16C2×D1111yescharacteristic
239#335—112no—
240#334—112no—
241#333—112no—
242#333—112no—
243#332—111no—
244#332—111no—
245#331—111no—
246#331—111no—
247C22×C11—21no—
248C22×C11—21no—
249C22×C11—81no—
250C22×C11—81no—
251C22×C11—81no—
252C22×C11#46312yes—
253C22×C11C2×#12111yescharacteristic
254C2×D11—42no—
255C2×D11—42no—
256C2×D11—42no—
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—81no—
261C4×C11—82no—
262C4×C11#46312yes—
263C4×C11C2×#13511yescharacteristic
264C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
265C4×C11#57711yescharacteristic
266C4×C11#57811yescharacteristic
267Dic11—42no—
268C2×#41—21no—
269C2×#41—221no—
270C22×Q8—21no—
271C2×D8—222no—
272#131—444no—
273C2×M16—222no—
274C2×M16C22⋊D1111yescharacteristic
275C2×M16C22⋊D1111yescharacteristic
276C22×C8—221no—
277C22×C8—221no—
278C22×C8—222no—
279C4⋊Q8—21no—
280C4⋊Q8—21no—
281C4⋊Q8—21no—
282C4⋊Q8—111no—
283C4⋊Q8C22×D1112yes—
284C4⋊Q8C22×D1111yescharacteristic
285#127—111no—
286#127C22×D1111yescharacteristic
287#124—21no—
288#124—221no—
289#121—21no—
290#121—21no—
291#121—112no—
292#121—221no—
293C4×D4—21no—
294C4×D4—21no—
295C4×D4—112no—
296C4×D4—221no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C42C22×D1111yescharacteristic
300#107—222no—
301#106—222no—
302#106—222no—
303C4⋊C8—111no—
304C4⋊C8—111no—
305C4⋊C8—111no—
306C4⋊C8—111no—
307C4⋊C8—112no—
308C4⋊C8—221no—
309C4⋊C8—221no—
310#103—22no—
311#103—22no—
312#102—22no—
313#102—22no—
314#102—222no—
315#102—222no—
316#102—222no—
317#102—222no—
318C22⋊C8—221no—
319C22⋊C8—222no—
320C22⋊C8—222no—
321#97C22⋊D1112yes—
322C4×C8—221no—
323C4×C8C22×D1112yes—
324C2×C11—22no—
325C2×C11—161no—
326C2×C11C2×#46311yescharacteristic
327C2×C11#306311yescharacteristic
328C2×C11#306811yescharacteristic
329D11—82no—
330#41—42no—
331#41—42no—
332#41—442no—
333#41—442no—
334C2×Q8—22no—
335C2×Q8—21no—
336C2×Q8—41no—
337C2×Q8—82no—
338C2×Q8—221no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—41no—
343C2×D4—112no—
344C2×D4—222no—
345C2×D4—221no—
346C2×D4—221no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—222no—
350C22×C4D4×D1111yescharacteristic
351C22×C4#434111yescharacteristic
352C22×C4C2×C22⋊D1111yescharacteristic
353D8—882no—
354M16—22no—
355M16—22no—
356M16—444no—
357C2×C8—221no—
358C2×C8—221no—
359C2×C8—222no—
360C2×C8—221no—
361C2×C8—221no—
362C2×C8—444no—
363C2×C8—442no—
364C2×C8—881no—
365C2×C8C2×C22⋊D1112yes—
366C2×C8C2×C22⋊D1112yes—
367C4⋊C4—22no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—22no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—112no—
374C4⋊C4—221no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—222no—
378C22⋊C4—222no—
379C42D4×D1111yescharacteristic
380C42#434111yescharacteristic
381C42C2×C22⋊D1111yescharacteristic
382C42C23×D1111yescharacteristic
383C11#1923611yescharacteristic, complemented, Sylow
384C23—41no—
385C23—222no—
386C23#6699111yescharacteristic
387Q8—41no—
388Q8—41no—
389Q8—82no—
390Q8—82no—
391Q8—442no—
392D4—41no—
393D4—41no—
394D4—41no—
395D4—41no—
396D4—81no—
397D4—82no—
398D4—222no—
399D4—222no—
400D4—444no—
401D4—442no—
402D4—881no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—82no—
409C2×C4—82no—
410C2×C4—222no—
411C2×C4—442no—
412C2×C4—442no—
413C2×C4#6699111yescharacteristic
414C2×C4#6699111yescharacteristic
415C2×C4#6699111yescharacteristic
416C2×C4#6700212yes—
417C2×C4#6700312yes—
418C2×C4C2×D4×D1111yescharacteristic
419C2×C4C2×#434111yescharacteristic
420C2×C4C22×C22⋊D1111yescharacteristic
421C8—22no—
422C8—22no—
423C8—442no—
424C8—441no—
425C8—441no—
426C8—441no—
427C8—441no—
428C22—21no—
429C22—21no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—442no—
434C22—442no—
435C22—442no—
436C22#1062267012yes—
437C22C2×#6699111yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—81no—
442C4—82no—
443C4—442no—
444C4#1062267012yes—
445C4#1062330911yescharacteristic
446C4#1062331011yescharacteristic
447C4C2×#6700211yescharacteristic
448C4C2×#6700311yescharacteristic
449C2—22no—
450C2—161no—
451C2—882no—
452C2C2×#1062267011yescharacteristic
453C2#1307830111yescharacteristic
454C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3141C2
socleC22×C11C2×#121
prime radical#13079923C2
hypercenter#3141D11
hypocenterC11#19236
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3141

Complements

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

NH ≅ G/Ntype
2. #13079744C2semidirect
3. #13077362C2semidirect
4. #13068188C2semidirect
5. #13068146C2semidirect
6. #13068064C2semidirect
7. #13068022C2semidirect
8. #13067368C2semidirect
9. C2×#10622184C2semidirect
10. #13067265C2semidirect
11. C11×#3141C2semidirect
159. #3141D11semidirect
383. C11#19236semidirect

Maximal subgroups

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

subgroupindex
#130799232
#130797442
#130773622
#130681882
#130681462
#130680642
#130680222
#130673682
C2×#106221842
#130672652
C11×#31412
#1923611