Finite Group Databasebeta

← #14739169

Subgroups — #14739169

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#13079541C211yesmaximal, characteristic, complemented
2#13078071C211yesmaximal, characteristic
3#13077727C211yesmaximal, characteristic, complemented
4#13068044C212yesmaximal, complemented
5#13068037C212yesmaximal, complemented
6#13067966C212yesmaximal, complemented
7#13067959C212yesmaximal, complemented
8#13067388C211yesmaximal, characteristic, complemented
9#13067294C211yesmaximal, characteristic, complemented
10C2×#10622185C211yesmaximal, characteristic, complemented
11C11×#3079C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C4×C11×#41C2211yescharacteristic
14C2×#67003—21no—
15#10623008C2211yescharacteristic
16C11×#477—21no—
17C11×#476—21no—
18C11×#475C2212yes—
19C11×#474C2212yes—
20C11×#428—21no—
21C11×#423C2211yescharacteristic
22C11×#417—21no—
23#10622840—22no—
24#10622698C2212yes—
25#10622696—21no—
26#10622696—21no—
27#10622694C2212yes—
28#10622644C2211yescharacteristic
29#10622641—21no—
30#10622640C2211yescharacteristic
31Q8×C11⋊C8C2212yes—
32#10622632C2211yescharacteristic
33#10622629—21no—
34#10622628C2211yescharacteristic
35D4×C11⋊C8—22no—
36D4×C11⋊C8C2212yes—
37#10622615—21no—
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#10622118C2212yes—
48#10622118C2212yes—
49C2×C11×#41D411yescharacteristic
50C22×Q8×C11—21no—
51C2×#4339—21no—
52C2×C11×M16—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8C2312yes—
57C4×Q8×C11D411yescharacteristic
58C4×Q8×C11C2311yescharacteristic
59C4×D4×C11—21no—
60C4×D4×C11—21no—
61C4×D4×C11D411yescharacteristic
62C4×D4×C11C2311yescharacteristic
63C11×#117—21no—
64C11×#117D411yescharacteristic
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C42×C11—21no—
68C2×C42×C11C2311yescharacteristic
69#67003—44no—
70C2×#4326—21no—
71C2×#4325—21no—
72C2×#4325—22no—
73C2×#4325—22no—
74C2×#4324—21no—
75C2×#4323—21no—
76#66983—21no—
77#66983—21no—
78C22×C11⋊C8—21no—
79C22×C11⋊C8—21no—
80C22×C11⋊C8—22no—
81#66928—21no—
82#66927C2311yescharacteristic
83C4×D44—21no—
84C4×D44—21no—
85#66922C2311yescharacteristic
86C11×#107—22no—
87C11×#106—22no—
88C11×C4⋊C8—21no—
89C11×C4⋊C8C2312yes—
90C11×#103—22no—
91C11×#102—22no—
92#66899—22no—
93#66899—22no—
94C22⋊(C11⋊C8)—22no—
95C22⋊(C11⋊C8)D412yes—
96#66874—21no—
97#66874—21no—
98#66873—21no—
99#66873—21no—
100C4⋊(C11⋊C8)—21no—
101C4⋊(C11⋊C8)—21no—
102C4⋊(C11⋊C8)—22no—
103C4⋊(C11⋊C8)D411yescharacteristic
104C4⋊(C11⋊C8)D411yescharacteristic
105C4⋊(C11⋊C8)C2312yes—
106C4⋊(C11⋊C8)C2311yescharacteristic
107C4⋊(C11⋊C8)C2311yescharacteristic
108C4×C11⋊C8—22no—
109C4×C11⋊C8C2312yes—
110#19408—111nomaximal, Sylow
111C11×#41—22no—
112C11×#41SD1614yescomplemented
113C2×Q8×C11—22no—
114C2×Q8×C11—41no—
115C2×Q8×C11—81no—
116C2×Q8×C11—81no—
117C2×Q8×C11C2×D411yescharacteristic
118C2×D4×C11—21no—
119C2×D4×C11C2×D411yescharacteristic
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—41no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11#4111yescharacteristic
127C2×C22⋊D11—41no—
128#4339—42no—
129#4339—42no—
130C2×D44—21no—
131C2×D44—21no—
132C2×D44—21no—
133C2×C4×D11—41no—
134C2×Dic22—21no—
135C11×M16—42no—
136C2×C8×C11—22no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—41no—
142C11×C4⋊C4—41no—
143C11×C4⋊C4C2×D411yescharacteristic
144C11×C4⋊C4C2×D411yescharacteristic
145C11×C22⋊C4—21no—
146C11×C22⋊C4—21no—
147C11×C22⋊C4—21no—
148C42×C11—21no—
149C42×C11—21no—
150C42×C11—21no—
151C42×C11C2×D411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C42×C11#4111yescharacteristic
154C42×C11C2411yescharacteristic
155#4326—42no—
156#4325—42no—
157#4325—82no—
158#4325—82no—
159#4324—42no—
160#4323—42no—
161(C2×D11)⋊C4—41no—
162(C2×D11)⋊C4—41no—
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—42no—
169C2×C11⋊C8—81no—
170C2×C11⋊C8—82no—
171C2×C11⋊C8C2×D412yes—
172C2×C11⋊C8C2×D412yes—
173#3206—111no—
174#3079D1111yescharacteristic, complemented
175#3035—111no—
176#2988—111no—
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×C11—42no—
189Q8×C11—42no—
190Q8×C11—82no—
191Q8×C11C2×SD1612yes—
192D4×C11—24no—
193D4×C11—21no—
194D4×C11C2×SD1612yes—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—24no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11—81no—
206C2×C4×C11—82no—
207C2×C4×C11#12111yescharacteristic
208C2×C4×C11#12111yescharacteristic
209C2×C4×C11#12111yescharacteristic
210C2×C4×C11C2×SD1612yes—
211C2×C4×C11#13512yes—
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C22⋊D11—82no—
216C2×Dic11—41no—
217D44—41no—
218D44—41no—
219D44—41no—
220D44—41no—
221D44—81no—
222C4×D11—82no—
223Dic22—41no—
224Dic22—41no—
225C8×C11—42no—
226C11⋊C8—22no—
227C11⋊C8—22no—
228C11⋊C8—41no—
229C11⋊C8—41no—
230C11⋊C8—42no—
231C2×#135—221no—
232#532—111no—
233C2×C4⋊Q8C2×D1111yescharacteristic
234C4×#41C2×D1111yescharacteristic
235#492—112no—
236#487—112no—
237#477—21no—
238#476—21no—
239#475C2×D1112yes—
240#474C2×D1112yes—
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×Q8—112no—
251C8×D4—112no—
252C8×D4—222no—
253#431—111no—
254#431—221no—
255#428—21no—
256#423C2×D1111yescharacteristic
257C2×C4⋊C8—111no—
258C2×C4⋊C8—111no—
259C2×C4⋊C8—221no—
260#417—21no—
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—82no—
285C4×C11#46512yes—
286C4×C11C22×SD1611yescharacteristic
287C4×C11C2×#13511yescharacteristic
288C4×C11#57611yescharacteristic
289C4×C11#57711yescharacteristic
290Dic11—81no—
291C2×#41—221no—
292C2×#41C22⋊D1111yescharacteristic
293C22×Q8—21no—
294#135—444no—
295C2×Q16—221no—
296C2×SD16—222no—
297C2×SD16—222no—
298C2×SD16—221no—
299C2×SD16—221no—
300C2×D8—221no—
301C2×M16—21no—
302C22×C8—222no—
303C22×C8—221no—
304C22×C8—221no—
305C4⋊Q8—21no—
306C4⋊Q8—21no—
307C4⋊Q8—21no—
308C4⋊Q8—111no—
309C4⋊Q8C22×D1112yes—
310#127—111no—
311#124—221no—
312#121—221no—
313#121—221no—
314C4×Q8C22⋊D1111yescharacteristic
315C4×Q8C22×D1111yescharacteristic
316C4×D4—21no—
317C4×D4—21no—
318C4×D4—221no—
319C4×D4—221no—
320C4×D4C22⋊D1111yescharacteristic
321C4×D4C22×D1111yescharacteristic
322#117—21no—
323#117C22⋊D1111yescharacteristic
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C42—21no—
327C2×C42C22×D1111yescharacteristic
328#107—22no—
329#106—22no—
330C4⋊C8—21no—
331C4⋊C8—111no—
332C4⋊C8—111no—
333C4⋊C8—112no—
334C4⋊C8—111no—
335C4⋊C8—111no—
336C4⋊C8—222no—
337C4⋊C8—221no—
338C4⋊C8—221no—
339C4⋊C8C22×D1112yes—
340#103—22no—
341#103—222no—
342#103—222no—
343#103—221no—
344#103—221no—
345#102—22no—
346#102—221no—
347#102—221no—
348C22⋊C8—112no—
349C22⋊C8—222no—
350C4×C8—112no—
351C4×C8—222no—
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#432514yescomplemented
362C2×Q8—22no—
363C2×Q8—41no—
364C2×Q8—81no—
365C2×Q8—81no—
366C2×Q8—221no—
367C2×Q8C2×C22⋊D1111yescharacteristic
368C2×D4—21no—
369C2×D4—221no—
370C2×D4—221no—
371C2×D4—221no—
372C2×D4—441no—
373C2×D4C2×C22⋊D1111yescharacteristic
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—41no—
378C22×C4—441no—
379C22×C4D4×D1111yescharacteristic
380C22×C4#434111yescharacteristic
381C22×C4C2×C22⋊D1111yescharacteristic
382Q16—442no—
383SD16—442no—
384SD16—442no—
385SD16—882no—
386SD16—882no—
387D8—442no—
388M16—42no—
389C2×C8—22no—
390C2×C8—112no—
391C2×C8—112no—
392C2×C8—222no—
393C2×C8—221no—
394C2×C8—221no—
395C2×C8—442no—
396C2×C8—882no—
397C2×C8—881no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C4⋊C4—221no—
405C4⋊C4—221no—
406C4⋊C4C2×C22⋊D1111yescharacteristic
407C4⋊C4C2×C22⋊D1111yescharacteristic
408C22⋊C4—21no—
409C22⋊C4—21no—
410C22⋊C4—21no—
411C22⋊C4—441no—
412C22⋊C4—441no—
413C42—21no—
414C42—21no—
415C42—21no—
416C42D4×D1111yescharacteristic
417C42#434111yescharacteristic
418C42C2×C22⋊D1111yescharacteristic
419C42C23×D1111yescharacteristic
420C11#1940811yescharacteristic, complemented, Sylow
421C23—21no—
422C23—441no—
423C23#6699211yescharacteristic
424Q8—21no—
425Q8—42no—
426Q8—42no—
427Q8—82no—
428Q8—441no—
429Q8—441no—
430Q8C2×#432512yes—
431D4—24no—
432D4—21no—
433D4—441no—
434D4—441no—
435D4—441no—
436D4—441no—
437D4—881no—
438D4—882no—
439D4C2×#432512yes—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—24no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—81no—
451C2×C4—82no—
452C2×C4—441no—
453C2×C4—882no—
454C2×C4#6699211yescharacteristic
455C2×C4#6699211yescharacteristic
456C2×C4#6699211yescharacteristic
457C2×C4C2×#432512yes—
458C2×C4#6700312yes—
459C2×C4C2×D4×D1111yescharacteristic
460C2×C4C2×#434111yescharacteristic
461C2×C4C22×C22⋊D1111yescharacteristic
462C8—42no—
463C8—222no—
464C8—222no—
465C8—442no—
466C8—441no—
467C8—441no—
468C22—21no—
469C22—21no—
470C22—22no—
471C22—41no—
472C22—41no—
473C22—881no—
474C22—881no—
475C22—881no—
476C22#1062266112yes—
477C22C2×#6699211yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—22no—
482C4—41no—
483C4—41no—
484C4—82no—
485C4—881no—
486C4#1062266112yes—
487C4#1062330511yescharacteristic
488C4#1062330611yescharacteristic
489C4C22×#432511yescharacteristic
490C4C2×#6700311yescharacteristic
491C2—22no—
492C2—42no—
493C2—1761no—
494C2#1307815911yescharacteristic
495C2C2×#1062266111yescharacteristic
496C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3079C2
socleC22×C11C2×#121
prime radical#13078071C2
hypercenter#3079D11
hypocenterC11#19408
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3079

Complements

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

NH ≅ G/Ntype
1. #13079541C2semidirect
3. #13077727C2semidirect
4. #13068044C2semidirect
5. #13068037C2semidirect
6. #13067966C2semidirect
7. #13067959C2semidirect
8. #13067388C2semidirect
9. #13067294C2semidirect
10. C2×#10622185C2semidirect
11. C11×#3079C2semidirect
112. C11×#41SD16semidirect
174. #3079D11semidirect
361. #41#4325semidirect
420. C11#19408semidirect

Maximal subgroups

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

subgroupindex
#130795412
#130780712
#130777272
#130680442
#130680372
#130679662
#130679592
#130673882
#130672942
C2×#106221852
C11×#30792
#1940811