Finite Group Databasebeta

← #14739265

Subgroups — #14739265

Order 2816.

694 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079737C211yesmaximal, characteristic, complemented
2#13078071C211yesmaximal, characteristic
3#13077727C211yesmaximal, characteristic, complemented
4#13068062C212yesmaximal, complemented
5#13068055C212yesmaximal, complemented
6#13068008C212yesmaximal, complemented
7#13068003C212yesmaximal, complemented
8#13067392C211yesmaximal, characteristic, complemented
9#13067294C211yesmaximal, characteristic, complemented
10C2×#10622185C211yesmaximal, characteristic, complemented
11C11×#3039C211yesmaximal, characteristic, complemented
12C2×C11×#137—21no—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C4×C11×#41C2211yescharacteristic
15C2×#67003—21no—
16#10623008C2211yescharacteristic
17C11×#462—21no—
18C11×#462C2212yes—
19C11×#461—21no—
20C11×#461C2212yes—
21C11×#423C2211yescharacteristic
22C11×#419—21no—
23#10622701C2212yes—
24#10622700—21no—
25#10622700—21no—
26#10622691C2212yes—
27#10622644C2211yescharacteristic
28#10622641—21no—
29#10622640C2211yescharacteristic
30Q8×C11⋊C8C2212yes—
31#10622632C2211yescharacteristic
32#10622629—21no—
33#10622628C2211yescharacteristic
34D4×C11⋊C8—22no—
35D4×C11⋊C8C2212yes—
36#10622615—21no—
37#10622580—22no—
38#10622538—21no—
39#10622538C2211yescharacteristic
40C2×C4⋊(C11⋊C8)—21no—
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43#10622185C2212yes—
44#10622185C2212yes—
45#10622123C2212yes—
46#10622120C2212yes—
47#10622117C2212yes—
48#10622117C2212yes—
49C2×C11×#41D411yescharacteristic
50C22×Q8×C11—21no—
51C2×#4339—21no—
52C11×#137—44no—
53C2×C11×Q16—22no—
54C2×C11×SD16—22no—
55C2×C11×M16—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8—21no—
58C11×C4⋊Q8—21no—
59C11×C4⋊Q8C2312yes—
60C4×Q8×C11D411yescharacteristic
61C4×Q8×C11C2311yescharacteristic
62C4×D4×C11—21no—
63C4×D4×C11—21no—
64C4×D4×C11D411yescharacteristic
65C4×D4×C11C2311yescharacteristic
66C11×#117—21no—
67C11×#117D411yescharacteristic
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72#67003—44no—
73C2×#4326—21no—
74C2×#4325—21no—
75C2×#4324—21no—
76C2×#4323—21no—
77#66983—21no—
78#66983—21no—
79C22×C11⋊C8—21no—
80C22×C11⋊C8—21no—
81C22×C11⋊C8—22no—
82#66928—21no—
83#66927C2311yescharacteristic
84C4×D44—21no—
85C4×D44—21no—
86#66922C2311yescharacteristic
87C11×C4⋊C8—21no—
88C11×C4⋊C8C2312yes—
89C11×#103—22no—
90C11×#103—22no—
91C22⋊(C11⋊C8)—22no—
92C22⋊(C11⋊C8)D412yes—
93#66874—21no—
94#66874—21no—
95#66873—21no—
96#66873—21no—
97#66873—22no—
98#66873—22no—
99#66871—22no—
100#66871—22no—
101C4⋊(C11⋊C8)—21no—
102C4⋊(C11⋊C8)—21no—
103C4⋊(C11⋊C8)—22no—
104C4⋊(C11⋊C8)D411yescharacteristic
105C4⋊(C11⋊C8)D411yescharacteristic
106C4⋊(C11⋊C8)C2312yes—
107C4⋊(C11⋊C8)C2311yescharacteristic
108C4⋊(C11⋊C8)C2311yescharacteristic
109C4×C11⋊C8—22no—
110C4×C11⋊C8C2312yes—
111#19416—111nomaximal, Sylow
112C11×#41—22no—
113C11×#41D814yes—
114C2×Q8×C11—22no—
115C2×Q8×C11—41no—
116C2×Q8×C11—42no—
117C2×Q8×C11—42no—
118C2×Q8×C11C2×D411yescharacteristic
119C2×D4×C11—21no—
120C2×D4×C11C2×D411yescharacteristic
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—41no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11#4111yescharacteristic
128C2×C22⋊D11—41no—
129#4339—42no—
130#4339—42no—
131C2×D44—21no—
132C2×D44—21no—
133C2×D44—21no—
134C2×C4×D11—41no—
135C2×Dic22—21no—
136C11×Q16—44no—
137C11×SD16—44no—
138C11×M16—42no—
139C2×C8×C11—22no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—41no—
145C11×C4⋊C4—41no—
146C11×C4⋊C4C2×D411yescharacteristic
147C11×C4⋊C4C2×D411yescharacteristic
148C11×C22⋊C4—21no—
149C11×C22⋊C4—21no—
150C11×C22⋊C4—21no—
151C42×C11—21no—
152C42×C11—21no—
153C42×C11—21no—
154C42×C11C2×D411yescharacteristic
155C42×C11C2×D411yescharacteristic
156C42×C11#4111yescharacteristic
157C42×C11C2411yescharacteristic
158#4326—42no—
159#4325—42no—
160#4324—42no—
161#4323—42no—
162(C2×D11)⋊C4—41no—
163(C2×D11)⋊C4—41no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—42no—
170C2×C11⋊C8—81no—
171C2×C11⋊C8—82no—
172C2×C11⋊C8C2×D412yes—
173C2×C11⋊C8C2×D412yes—
174#3226—111no—
175#3039D1111yescharacteristic, complemented
176#3035—111no—
177#2988—111no—
178#1682—112no—
179#1681—112no—
180#1674—112no—
181#1673—112no—
182#1571—111no—
183#1547—111no—
184C2×#332—111no—
185C23×C11—21no—
186C23×C11#12111yescharacteristic
187C22×D11—41no—
188Q8×C11—21no—
189Q8×C11—42no—
190Q8×C11—42no—
191Q8×C11—82no—
192Q8×C11C2×D812yes—
193D4×C11—24no—
194D4×C11—21no—
195D4×C11C2×D812yes—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—24no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—81no—
207C2×C4×C11—82no—
208C2×C4×C11#12111yescharacteristic
209C2×C4×C11#12111yescharacteristic
210C2×C4×C11#12111yescharacteristic
211C2×C4×C11C2×D812yes—
212C2×C4×C11#13512yes—
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C22⋊D11—82no—
217C2×Dic11—41no—
218D44—41no—
219D44—41no—
220D44—41no—
221D44—41no—
222D44—81no—
223C4×D11—82no—
224Dic22—41no—
225Dic22—41no—
226C8×C11—42no—
227C11⋊C8—22no—
228C11⋊C8—22no—
229C11⋊C8—41no—
230C11⋊C8—41no—
231C11⋊C8—42no—
232C2×#137—21no—
233C2×#135—221no—
234#532—111no—
235C2×C4⋊Q8C2×D1111yescharacteristic
236C4×#41C2×D1111yescharacteristic
237#500—112no—
238#486—112no—
239#480—222no—
240#474—221no—
241#474—221no—
242#464—221no—
243#463—221no—
244#462—21no—
245#462—111no—
246#462C2×D1112yes—
247#461—21no—
248#461—111no—
249#461C2×D1112yes—
250#460—111no—
251#459—111no—
252C8×Q8—112no—
253C8×D4—112no—
254C8×D4—222no—
255#431—111no—
256#431—221no—
257#423C2×D1111yescharacteristic
258C2×C4⋊C8—111no—
259C2×C4⋊C8—111no—
260C2×C4⋊C8—221no—
261#419—21no—
262#416—221no—
263#335—112no—
264#335—112no—
265#332—112no—
266#332—112no—
267#332—112no—
268#331—112no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—22no—
272C22×C11—41no—
273C22×C11—41no—
274C22×C11#46612yes—
275C22×C11C2×#12111yescharacteristic
276C2×D11—81no—
277C2×D11—81no—
278C2×D11—81no—
279C4×C11—21no—
280C4×C11—22no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—41no—
284C4×C11—41no—
285C4×C11—82no—
286C4×C11#46612yes—
287C4×C11C22×D811yescharacteristic
288C4×C11C2×#13511yescharacteristic
289C4×C11#57711yescharacteristic
290C4×C11#57811yescharacteristic
291Dic11—81no—
292C2×#41—221no—
293C2×#41C22⋊D1111yescharacteristic
294C22×Q8—21no—
295#137—44no—
296#135—444no—
297C2×Q16—22no—
298C2×Q16—221no—
299C2×SD16—22no—
300C2×SD16—221no—
301C2×SD16—221no—
302C2×D8—221no—
303C2×M16—21no—
304C22×C8—222no—
305C22×C8—221no—
306C22×C8—221no—
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8—111no—
311C4⋊Q8C22×D1112yes—
312#127—111no—
313#124—221no—
314#121—221no—
315#121—221no—
316C4×Q8C22⋊D1111yescharacteristic
317C4×Q8C22×D1111yescharacteristic
318C4×D4—21no—
319C4×D4—21no—
320C4×D4—221no—
321C4×D4—221no—
322C4×D4C22⋊D1111yescharacteristic
323C4×D4C22×D1111yescharacteristic
324#117—21no—
325#117C22⋊D1111yescharacteristic
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C42—21no—
329C2×C42C22×D1111yescharacteristic
330#107—222no—
331#107—222no—
332C4⋊C8—21no—
333C4⋊C8—111no—
334C4⋊C8—111no—
335C4⋊C8—112no—
336C4⋊C8—111no—
337C4⋊C8—111no—
338C4⋊C8—222no—
339C4⋊C8—221no—
340C4⋊C8—221no—
341C4⋊C8C22×D1112yes—
342#103—22no—
343#103—22no—
344#103—221no—
345#103—221no—
346#102—222no—
347#102—222no—
348#102—221no—
349#102—221no—
350C22⋊C8—112no—
351C22⋊C8—222no—
352C4×C8—112no—
353C4×C8—222no—
354C2×C11—22no—
355C2×C11—42no—
356C2×C11#304611yescharacteristic
357C2×C11C2×#46611yescharacteristic
358C2×C11#306911yescharacteristic
359D11—161no—
360#41—22no—
361#41—442no—
362#41—442no—
363#41#432314yes—
364C2×Q8—22no—
365C2×Q8—41no—
366C2×Q8—42no—
367C2×Q8—42no—
368C2×Q8—221no—
369C2×Q8C2×C22⋊D1111yescharacteristic
370C2×D4—21no—
371C2×D4—221no—
372C2×D4—221no—
373C2×D4—221no—
374C2×D4—441no—
375C2×D4C2×C22⋊D1111yescharacteristic
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—41no—
380C22×C4—441no—
381C22×C4D4×D1111yescharacteristic
382C22×C4#434111yescharacteristic
383C22×C4C2×C22⋊D1111yescharacteristic
384Q16—44no—
385Q16—442no—
386SD16—44no—
387SD16—442no—
388SD16—442no—
389D8—442no—
390M16—42no—
391C2×C8—22no—
392C2×C8—112no—
393C2×C8—112no—
394C2×C8—222no—
395C2×C8—221no—
396C2×C8—221no—
397C2×C8—442no—
398C2×C8—882no—
399C2×C8—881no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4—221no—
407C4⋊C4—221no—
408C4⋊C4C2×C22⋊D1111yescharacteristic
409C4⋊C4C2×C22⋊D1111yescharacteristic
410C22⋊C4—21no—
411C22⋊C4—21no—
412C22⋊C4—21no—
413C22⋊C4—441no—
414C22⋊C4—441no—
415C42—21no—
416C42—21no—
417C42—21no—
418C42D4×D1111yescharacteristic
419C42#434111yescharacteristic
420C42C2×C22⋊D1111yescharacteristic
421C42C23×D1111yescharacteristic
422C11#1941611yescharacteristic, complemented, Sylow
423C23—21no—
424C23—441no—
425C23#6699211yescharacteristic
426Q8—21no—
427Q8—42no—
428Q8—42no—
429Q8—82no—
430Q8—441no—
431Q8—441no—
432Q8C2×#432312yes—
433D4—24no—
434D4—21no—
435D4—441no—
436D4—441no—
437D4—441no—
438D4—441no—
439D4—881no—
440D4—882no—
441D4C2×#432312yes—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—24no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—81no—
453C2×C4—82no—
454C2×C4—441no—
455C2×C4—882no—
456C2×C4C2×#432312yes—
457C2×C4#6699211yescharacteristic
458C2×C4#6699211yescharacteristic
459C2×C4#6699211yescharacteristic
460C2×C4#6700312yes—
461C2×C4C2×D4×D1111yescharacteristic
462C2×C4C2×#434111yescharacteristic
463C2×C4C22×C22⋊D1111yescharacteristic
464C8—42no—
465C8—222no—
466C8—222no—
467C8—442no—
468C8—441no—
469C8—441no—
470C22—21no—
471C22—21no—
472C22—22no—
473C22—41no—
474C22—41no—
475C22—881no—
476C22—881no—
477C22—881no—
478C22#1062265112yes—
479C22C2×#6699211yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—22no—
484C4—41no—
485C4—41no—
486C4—82no—
487C4—881no—
488C4#1062265112yes—
489C4#1062330911yescharacteristic
490C4#1062331011yescharacteristic
491C4C22×#432311yescharacteristic
492C4C2×#6700311yescharacteristic
493C2—22no—
494C2—42no—
495C2—1761no—
496C2#1307817011yescharacteristic
497C2C2×#1062265111yescharacteristic
498C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3039C2
socleC22×C11C2×#121
prime radical#13078071C2
hypercenter#3039D11
hypocenterC11#19416
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3039

Complements

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

NH ≅ G/Ntype
1. #13079737C2semidirect
3. #13077727C2semidirect
4. #13068062C2semidirect
5. #13068055C2semidirect
6. #13068008C2semidirect
7. #13068003C2semidirect
8. #13067392C2semidirect
9. #13067294C2semidirect
10. C2×#10622185C2semidirect
11. C11×#3039C2semidirect
175. #3039D11semidirect
422. C11#19416semidirect

Maximal subgroups

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

subgroupindex
#130797372
#130780712
#130777272
#130680622
#130680552
#130680082
#130680032
#130673922
#130672942
C2×#106221852
C11×#30392
#1941611