Finite Group Databasebeta

← #14739165

Subgroups — #14739165

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079543C211yesmaximal, characteristic, complemented
2#13078431C211yesmaximal, characteristic, complemented
3#13078071C211yesmaximal, characteristic
4#13068046C212yesmaximal, complemented
5#13068039C212yesmaximal, complemented
6#13067964C212yesmaximal, complemented
7#13067957C212yesmaximal, complemented
8#13067387C211yesmaximal, characteristic, complemented
9#13067291C211yesmaximal, characteristic, complemented
10C2×#10622120C211yesmaximal, characteristic, complemented
11C11×#2988C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13C2×#67003—21no—
14#10623008C2211yescharacteristic
15C2×#66922C2211yescharacteristic
16C8×Q8×C11C2212yes—
17C8×D4×C11—22no—
18C8×D4×C11C2212yes—
19C11×#431—21no—
20C11×#431C2211yescharacteristic
21C2×C11×C4⋊C8—21no—
22C2×C11×C4⋊C8C2211yescharacteristic
23#10622845—21no—
24#10622644C2211yescharacteristic
25#10622641—21no—
26#10622640C2211yescharacteristic
27#10622634—21no—
28#10622633C2212yes—
29#10622632C2211yescharacteristic
30#10622629—21no—
31#10622628C2211yescharacteristic
32#10622621—21no—
33#10622620C2212yes—
34#10622615—21no—
35#10622608—21no—
36#10622537C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622454—21no—
39#10622454—21no—
40#10622351—22no—
41#10622306C2212yes—
42#10622294C2212yes—
43#10622124C2212yes—
44#10622123C2212yes—
45#10622120C2212yes—
46#10622120C2212yes—
47#10622095C2212yes—
48#10622095C2212yes—
49C2×C11×#41D411yescharacteristic
50C2×#4339—21no—
51C22×Dic22—21no—
52C22×C8×C11—21no—
53C22×C8×C11—22no—
54C4×Q8×C11D411yescharacteristic
55C4×Q8×C11C2311yescharacteristic
56C4×D4×C11—21no—
57C4×D4×C11—21no—
58C4×D4×C11D411yescharacteristic
59C4×D4×C11C2311yescharacteristic
60C11×#117—21no—
61C11×#117D411yescharacteristic
62C2×C42×C11—21no—
63C2×C42×C11C2311yescharacteristic
64#67003—44no—
65C2×#4326—21no—
66C2×#4325—21no—
67C2×#4324—21no—
68C2×#4323—21no—
69#66983—21no—
70#66983—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×#4318—21no—
74C22×C11⋊C8—21no—
75C2×#4314—22no—
76C2×#4314—22no—
77#66928—21no—
78#66927C2311yescharacteristic
79C4×D44—21no—
80C4×D44—21no—
81#66922—21no—
82#66922—21no—
83#66922—21no—
84#66922C2312yes—
85#66922C2311yescharacteristic
86C11×C4⋊C8—22no—
87C11×C4⋊C8—21no—
88C11×C4⋊C8D411yescharacteristic
89C11×C4⋊C8D411yescharacteristic
90C11×C4⋊C8C2312yes—
91C11×C22⋊C8—22no—
92C11×C22⋊C8D412yes—
93C4×C8×C11—22no—
94C4×C8×C11C2312yes—
95#66899—22no—
96#66896—22no—
97#66880—22no—
98#66880—22no—
99#66874—21no—
100#66874—21no—
101#66873—21no—
102#66873—21no—
103#66872—22no—
104#66871—22no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)C2311yescharacteristic
108C4⋊(C11⋊C8)C2311yescharacteristic
109C4⋊(C11⋊C8)C2312yes—
110#19408—111nomaximal, Sylow
111C11×#41—22no—
112C11×#41SD1614yescomplemented
113C2×Q8×C11C2×D411yescharacteristic
114C2×D4×C11—21no—
115C2×D4×C11C2×D411yescharacteristic
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11#4111yescharacteristic
122C2×C22⋊D11—41no—
123C22×Dic11—41no—
124#4339—42no—
125#4339—42no—
126C2×D44—21no—
127C2×D44—21no—
128C2×D44—21no—
129C2×C4×D11—41no—
130C2×Dic22—21no—
131C2×Dic22—22no—
132C2×Dic22—41no—
133C2×Dic22—81no—
134C2×Dic22—81no—
135C2×C8×C11—22no—
136C2×C8×C11—81no—
137C2×C8×C11—82no—
138C2×C8×C11C2×D412yes—
139C2×C8×C11C2×D412yes—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4C2×D411yescharacteristic
143C11×C4⋊C4C2×D411yescharacteristic
144C11×C22⋊C4—21no—
145C11×C22⋊C4—21no—
146C11×C22⋊C4—21no—
147C42×C11—21no—
148C42×C11—21no—
149C42×C11—21no—
150C42×C11C2×D411yescharacteristic
151C42×C11C2×D411yescharacteristic
152C42×C11#4111yescharacteristic
153C42×C11C2411yescharacteristic
154#4326—42no—
155#4325—42no—
156#4324—42no—
157#4323—42no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—41no—
160C4⋊Dic11—22no—
161C4⋊Dic11—21no—
162C4⋊Dic11—22no—
163C4⋊Dic11—21no—
164C4⋊Dic11—41no—
165C4⋊Dic11—41no—
166#4318—42no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—42no—
171#4314—82no—
172#4314—82no—
173#3206—111no—
174#3079—111no—
175#3035—111no—
176#2988D1111yescharacteristic, complemented
177#1680—112no—
178#1679—112no—
179#1666—112no—
180#1665—112no—
181#1570—111no—
182#1547—111no—
183C2×#332—111no—
184C23×C11—21no—
185C23×C11#12111yescharacteristic
186C22×D11—41no—
187Q8×C11—21no—
188Q8×C11C2×SD1612yes—
189D4×C11—24no—
190D4×C11—21no—
191D4×C11C2×SD1612yes—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—24no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—81no—
202C2×C4×C11#12111yescharacteristic
203C2×C4×C11#12111yescharacteristic
204C2×C4×C11#12111yescharacteristic
205C2×C4×C11C2×SD1612yes—
206C2×C4×C11#13512yes—
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C22⋊D11—82no—
211C2×Dic11—42no—
212C2×Dic11—41no—
213C2×Dic11—82no—
214D44—41no—
215D44—41no—
216D44—41no—
217D44—41no—
218D44—81no—
219C4×D11—82no—
220Dic22—41no—
221Dic22—41no—
222Dic22—42no—
223Dic22—42no—
224Dic22—82no—
225C8×C11—22no—
226C8×C11—22no—
227C8×C11—42no—
228C11⋊C8—41no—
229C11⋊C8—41no—
230C11⋊C8—42no—
231C2×#135—221no—
232#532—111no—
233C2×C4⋊Q8—111no—
234C4×#41C2×D1111yescharacteristic
235#492—112no—
236#487—112no—
237#477—221no—
238#476—221no—
239#475—112no—
240#474—112no—
241#464—221no—
242#463—221no—
243#462—111no—
244#461—111no—
245#461—221no—
246#461—221no—
247#460—111no—
248#459—111no—
249#448—222no—
250C8×Q8C2×D1112yes—
251C8×D4—22no—
252C8×D4C2×D1112yes—
253#431—21no—
254#431C2×D1111yescharacteristic
255#428—221no—
256#423—111no—
257C2×C4⋊C8—21no—
258C2×C4⋊C8—111no—
259C2×C4⋊C8C2×D1111yescharacteristic
260#417—221no—
261#416—221no—
262#334—112no—
263#334—112no—
264#332—112no—
265#332—112no—
266#332—112no—
267#331—112no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—22no—
271C22×C11—41no—
272C22×C11—41no—
273C22×C11#46512yes—
274C22×C11C2×#12111yescharacteristic
275C2×D11—81no—
276C2×D11—81no—
277C2×D11—81no—
278C4×C11—21no—
279C4×C11—22no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—41no—
283C4×C11—41no—
284C4×C11#46512yes—
285C4×C11C22×SD1611yescharacteristic
286C4×C11C2×#13511yescharacteristic
287C4×C11#57611yescharacteristic
288C4×C11#57711yescharacteristic
289Dic11—82no—
290Dic11—81no—
291C2×#41—221no—
292C2×#41D4411yescharacteristic
293C22×Q8—221no—
294#135—444no—
295C2×Q16—221no—
296C2×SD16—221no—
297C2×SD16—221no—
298C2×SD16—222no—
299C2×SD16—222no—
300C2×D8—221no—
301C2×M16—221no—
302C22×C8—21no—
303C22×C8—22no—
304C22×C8—221no—
305C4⋊Q8—112no—
306C4⋊Q8—111no—
307C4⋊Q8—221no—
308C4⋊Q8—221no—
309C4⋊Q8—221no—
310#127—111no—
311#124—221no—
312#121—221no—
313#121—221no—
314C4×Q8D4411yescharacteristic
315C4×Q8C22×D1111yescharacteristic
316C4×D4—21no—
317C4×D4—21no—
318C4×D4—221no—
319C4×D4—221no—
320C4×D4D4411yescharacteristic
321C4×D4C22×D1111yescharacteristic
322#117—21no—
323#117D4411yescharacteristic
324C2×C4⋊C4—221no—
325C2×C4⋊C4—221no—
326C2×C42—21no—
327C2×C42C22×D1111yescharacteristic
328#107—222no—
329#106—222no—
330C4⋊C8—22no—
331C4⋊C8—21no—
332C4⋊C8—112no—
333C4⋊C8—111no—
334C4⋊C8—111no—
335C4⋊C8—221no—
336C4⋊C8—221no—
337C4⋊C8C22⋊D1111yescharacteristic
338C4⋊C8C22⋊D1111yescharacteristic
339C4⋊C8C22×D1112yes—
340#103—222no—
341#103—222no—
342#103—222no—
343#103—221no—
344#103—221no—
345#102—222no—
346#102—221no—
347#102—221no—
348C22⋊C8—22no—
349C22⋊C8C22⋊D1112yes—
350C4×C8—22no—
351C4×C8C22×D1112yes—
352C2×C11—22no—
353C2×C11—42no—
354C2×C11#304511yescharacteristic
355C2×C11C2×#46511yescharacteristic
356C2×C11#306911yescharacteristic
357D11—161no—
358#41—22no—
359#41—442no—
360#41—442no—
361#41#431414yescomplemented
362C2×Q8—221no—
363C2×Q8—222no—
364C2×Q8—441no—
365C2×Q8—881no—
366C2×Q8—881no—
367C2×Q8C2×D4411yescharacteristic
368C2×D4—21no—
369C2×D4—221no—
370C2×D4—221no—
371C2×D4—221no—
372C2×D4—441no—
373C2×D4C2×D4411yescharacteristic
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—441no—
378C22×C4—441no—
379C22×C4C2×D4411yescharacteristic
380C22×C4#433911yescharacteristic
381C22×C4C2×C22⋊D1111yescharacteristic
382Q16—442no—
383SD16—442no—
384SD16—442no—
385SD16—882no—
386SD16—882no—
387D8—442no—
388M16—442no—
389C2×C8—22no—
390C2×C8—82no—
391C2×C8—81no—
392C2×C8—222no—
393C2×C8—221no—
394C2×C8—221no—
395C2×C8—442no—
396C2×C8C2×C22⋊D1112yes—
397C2×C8C2×C22⋊D1112yes—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—222no—
401C4⋊C4—222no—
402C4⋊C4—221no—
403C4⋊C4—221no—
404C4⋊C4—441no—
405C4⋊C4—441no—
406C4⋊C4C2×D4411yescharacteristic
407C4⋊C4C2×D4411yescharacteristic
408C22⋊C4—21no—
409C22⋊C4—21no—
410C22⋊C4—21no—
411C22⋊C4—441no—
412C22⋊C4—441no—
413C42—21no—
414C42—21no—
415C42—21no—
416C42C2×D4411yescharacteristic
417C42#433911yescharacteristic
418C42C2×C22⋊D1111yescharacteristic
419C42C23×D1111yescharacteristic
420C11#1940811yescharacteristic, complemented, Sylow
421C23—21no—
422C23—441no—
423C23#6698311yescharacteristic
424Q8—21no—
425Q8—441no—
426Q8—441no—
427Q8—442no—
428Q8—442no—
429Q8—882no—
430Q8C2×#431412yes—
431D4—24no—
432D4—21no—
433D4—441no—
434D4—441no—
435D4—441no—
436D4—441no—
437D4—881no—
438D4—882no—
439D4C2×#431412yes—
440C2×C4—21no—
441C2×C4—24no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—81no—
450C2×C4—441no—
451C2×C4—442no—
452C2×C4—882no—
453C2×C4—882no—
454C2×C4C2×#431412yes—
455C2×C4#6695712yes—
456C2×C4#6698311yescharacteristic
457C2×C4#6698311yescharacteristic
458C2×C4#6698311yescharacteristic
459C2×C4C22×D4411yescharacteristic
460C2×C4C2×#433911yescharacteristic
461C2×C4C22×C22⋊D1111yescharacteristic
462C8—22no—
463C8—22no—
464C8—42no—
465C8—441no—
466C8—441no—
467C8—442no—
468C22—21no—
469C22—21no—
470C22—22no—
471C22—41no—
472C22—41no—
473C22—881no—
474C22—881no—
475C22—881no—
476C22#1062272712yes—
477C22C2×#6698311yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—22no—
482C4—41no—
483C4—41no—
484C4—882no—
485C4—881no—
486C4#1062272712yes—
487C4C22×#431411yescharacteristic
488C4C2×#6695711yescharacteristic
489C4#1062336611yescharacteristic
490C4#1062336811yescharacteristic
491C2—22no—
492C2—42no—
493C2—1761no—
494C2#1307815511yescharacteristic
495C2C2×#1062272711yescharacteristic
496C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2988C2
socleC22×C11C2×#121
prime radical#13078071C2
hypercenter#2988D11
hypocenterC11#19408
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2988

Complements

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

NH ≅ G/Ntype
1. #13079543C2semidirect
2. #13078431C2semidirect
4. #13068046C2semidirect
5. #13068039C2semidirect
6. #13067964C2semidirect
7. #13067957C2semidirect
8. #13067387C2semidirect
9. #13067291C2semidirect
10. C2×#10622120C2semidirect
11. C11×#2988C2semidirect
112. C11×#41SD16semidirect
176. #2988D11semidirect
361. #41#4314semidirect
420. C11#19408semidirect

Maximal subgroups

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

subgroupindex
#130795432
#130784312
#130780712
#130680462
#130680392
#130679642
#130679572
#130673872
#130672912
C2×#106221202
C11×#29882
#1940811