Finite Group Databasebeta

← #14731379

Subgroups — #14731379

Order 2816.

936 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079928C211yesmaximal, characteristic, complemented
2#13079191C211yesmaximal, characteristic
3#13078088C211yesmaximal, characteristic, complemented
4#13067858C212yesmaximal, complemented
5#13067802C212yesmaximal, complemented
6#13067712C212yesmaximal, complemented
7#13067675C212yesmaximal, complemented
8#13067293C211yesmaximal, characteristic, complemented
9#13067071C211yesmaximal, characteristic, complemented
10C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
11C11×#3507C211yesmaximal, characteristic, complemented
12C11×#559C2212yes—
13C11×#557C2212yes—
14C11×#556—21no—
15C11×#556—22no—
16C11×#554—21no—
17C11×#552—22no—
18C11×#539—22no—
19C11×#536—21no—
20C11×#533C2211yescharacteristic
21C11×#532C2211yescharacteristic
22C11×#529—22no—
23C11×#520—21no—
24C2×C4×Q8×C11C2211yescharacteristic
25C2×#66995—21no—
26#10623008C2211yescharacteristic
27#10622701C2211yescharacteristic
28#10622697—21no—
29#10622696—21no—
30#10622691C2211yescharacteristic
31#10622686C2211yescharacteristic
32#10622683C2211yescharacteristic
33#10622661—22no—
34#10622651—22no—
35#10622644C2212yes—
36#10622641—22no—
37#10622640C2212yes—
38#10622640C2212yes—
39#10622633C2212yes—
40C4×#4323—22no—
41#10622579—21no—
42#10622537C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622185C2212yes—
46#10622182C2212yes—
47Q8⋊(C11⋊C8)C2212yes—
48Q8⋊(C11⋊C8)C2212yes—
49Q8⋊(C11⋊C8)C2212yes—
50Q8⋊(C11⋊C8)C2212yes—
51C2×C11×#41—21no—
52C22×Q8×C11D411yescharacteristic
53C2×#4339—21no—
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8D411yescharacteristic
56C11×C4⋊Q8D411yescharacteristic
57C11×C4⋊Q8C2311yescharacteristic
58C11×#127C2311yescharacteristic
59C11×#126—24no—
60C11×#126—24no—
61C11×#125—22no—
62C11×#125—24no—
63C11×#125—21no—
64C11×#124—22no—
65C11×#124—22no—
66C11×#124—21no—
67C11×#123—24no—
68C11×#123—24no—
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8—24no—
72C11×C22⋊Q8—21no—
73C11×C22⋊Q8D412yes—
74C11×#121—21no—
75C11×#121D412yes—
76C4×Q8×C11—22no—
77C4×Q8×C11—22no—
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11—21no—
81C4×Q8×C11D412yes—
82C4×Q8×C11C2312yes—
83C4×Q8×C11C2312yes—
84C4×D4×C11—24no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11—21no—
88C4×D4×C11D412yes—
89C11×#117—22no—
90C11×#117—24no—
91C11×#117—21no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C42×C11—21no—
96C2×C42×C11C2311yescharacteristic
97C2×#4326—22no—
98#66995—44no—
99C2×#4325—22no—
100C2×#4325—22no—
101C2×#4323—22no—
102#66983—21no—
103#66983—21no—
104C2×#4318—21no—
105C22×C11⋊C8—21no—
106C22×C11⋊C8—21no—
107#66928—21no—
108#66927C2311yescharacteristic
109C4×D44—21no—
110C4×D44—21no—
111#66922C2311yescharacteristic
112#66899—22no—
113#66896—22no—
114#66874—22no—
115#66873—22no—
116#66873—22no—
117#66873—22no—
118#66872—22no—
119#66871—22no—
120C4⋊(C11⋊C8)—21no—
121C4⋊(C11⋊C8)—21no—
122C4⋊(C11⋊C8)C2312yes—
123C4⋊(C11⋊C8)C2312yes—
124C4×C11⋊C8—21no—
125C4×C11⋊C8C2311yescharacteristic
126C4×C11⋊C8C2311yescharacteristic
127#18666—111nomaximal, Sylow
128C11×#41—42no—
129C11×#41—42no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—22no—
134C2×Q8×C11—22no—
135C2×Q8×C11C2×D412yes—
136C2×Q8×C11C2×D412yes—
137C2×D4×C11—22no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11C2×D412yes—
141C22×C4×C11—21no—
142C22×C4×C11—24no—
143C22×C4×C11—21no—
144C22×C4×C11—22no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C2×C22⋊D11—41no—
149#4339—42no—
150#4339—42no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×C4×D11—41no—
155C2×Dic22—21no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4C2×D412yes—
169C11×C4⋊C4C2×D412yes—
170C11×C4⋊C4C2×D412yes—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C42×C11—24no—
178C42×C11—22no—
179C42×C11—22no—
180C42×C11—22no—
181C42×C11C2×D411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11C2×D411yescharacteristic
184C42×C11C2411yescharacteristic
185#4326—44no—
186#4325—44no—
187#4325—82no—
188#4323—44no—
189(C2×D11)⋊C4—41no—
190(C2×D11)⋊C4—41no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193#4318—42no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—42no—
199C2×C11⋊C8—81no—
200#3507D1111yescharacteristic, complemented
201#3246—111no—
202#3169—111no—
203#3037—111no—
204#1648—112no—
205#1640—112no—
206#1626—112no—
207#1620—112no—
208#1547—111no—
209#1493—111no—
210C2×Q8⋊C8—111no—
211C23×C11—22no—
212C23×C11#12011yescharacteristic
213C22×D11—41no—
214Q8×C11—22no—
215Q8×C11—22no—
216Q8×C11—22no—
217Q8×C11—22no—
218Q8×C11—41no—
219Q8×C11—41no—
220Q8×C11—42no—
221Q8×C11—81no—
222D4×C11—42no—
223D4×C11—44no—
224D4×C11—41no—
225D4×C11—41no—
226D4×C11—41no—
227D4×C11—41no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—41no—
236C2×C4×C11—42no—
237C2×C4×C11—44no—
238C2×C4×C11—81no—
239C2×C4×C11—84no—
240C2×C4×C11#12011yescharacteristic
241C2×C4×C11#12011yescharacteristic
242C2×C4×C11#12011yescharacteristic
243C2×C4×C11#13512yes—
244C2×C4×C11AGL(1,ℤ/8)12yes—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C22⋊D11—82no—
249C2×Dic11—41no—
250D44—42no—
251D44—41no—
252D44—41no—
253D44—41no—
254D44—41no—
255C4×D11—82no—
256Dic22—41no—
257Dic22—41no—
258C11⋊C8—22no—
259C11⋊C8—41no—
260C11⋊C8—42no—
261C11⋊C8—42no—
262C2×#137—221no—
263#559C2×D1112yes—
264#557C2×D1112yes—
265#556—21no—
266#556—22no—
267#554—21no—
268#552—22no—
269#539—22no—
270#536—21no—
271#533C2×D1111yescharacteristic
272#532—111no—
273#532C2×D1111yescharacteristic
274#529—22no—
275#520—21no—
276C2×C4×Q8C2×D1111yescharacteristic
277#500—111no—
278#493—111no—
279#486—111no—
280#486—111no—
281#476—221no—
282#475—112no—
283#466—222no—
284#465—222no—
285#464—222no—
286#462—112no—
287#461—221no—
288#460—112no—
289#460—112no—
290C4×D8—222no—
291#423—111no—
292C2×C4⋊C8—111no—
293#417—221no—
294C2×C4×C8—111no—
295#332—112no—
296#331—112no—
297Q8⋊C8—112no—
298Q8⋊C8—112no—
299Q8⋊C8—112no—
300Q8⋊C8—112no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11#44912yes—
307C22×C11C2×#12011yescharacteristic
308C2×D11—81no—
309C2×D11—81no—
310C2×D11—81no—
311C4×C11—21no—
312C4×C11—21no—
313C4×C11—21no—
314C4×C11—42no—
315C4×C11—42no—
316C4×C11—42no—
317C4×C11—42no—
318C4×C11—42no—
319C4×C11#44912yes—
320C4×C11C2×#13511yescharacteristic
321C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
322C4×C11#57711yescharacteristic
323C4×C11#57811yescharacteristic
324Dic11—81no—
325C2×#41—21no—
326C2×#41—221no—
327C22×Q8C22⋊D1111yescharacteristic
328#137—444no—
329C2×Q16—222no—
330C2×SD16—222no—
331C2×SD16—222no—
332C2×D8—222no—
333C2×M16—221no—
334C22×C8—221no—
335C22×C8—221no—
336C4⋊Q8—22no—
337C4⋊Q8—111no—
338C4⋊Q8C22⋊D1111yescharacteristic
339C4⋊Q8C22⋊D1111yescharacteristic
340C4⋊Q8C22×D1111yescharacteristic
341#127—111no—
342#127C22×D1111yescharacteristic
343#126—24no—
344#126—24no—
345#125—22no—
346#125—24no—
347#125—21no—
348#124—22no—
349#124—22no—
350#124—21no—
351#124—221no—
352#123—24no—
353#123—24no—
354C22⋊Q8—22no—
355C22⋊Q8—22no—
356C22⋊Q8—24no—
357C22⋊Q8—21no—
358C22⋊Q8C22⋊D1112yes—
359#121—21no—
360#121—221no—
361#121—221no—
362#121C22⋊D1112yes—
363C4×Q8—22no—
364C4×Q8—22no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8C22⋊D1112yes—
369C4×Q8C22×D1112yes—
370C4×Q8C22×D1112yes—
371C4×D4—24no—
372C4×D4—22no—
373C4×D4—22no—
374C4×D4—21no—
375C4×D4—221no—
376C4×D4—221no—
377C4×D4C22⋊D1112yes—
378#117—22no—
379#117—24no—
380#117—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4C22⋊D1111yescharacteristic
384C2×C42—21no—
385C2×C42C22×D1111yescharacteristic
386#107—222no—
387#106—222no—
388C4⋊C8—112no—
389C4⋊C8—112no—
390C4⋊C8—221no—
391C4⋊C8—221no—
392#103—222no—
393#103—222no—
394#102—222no—
395#102—222no—
396#102—222no—
397#102—222no—
398C4×C8—111no—
399C4×C8—111no—
400C4×C8—221no—
401C2×C11—22no—
402C2×C11—82no—
403C2×C11C2×#44911yescharacteristic
404C2×C11#301311yescharacteristic
405C2×C11#301811yescharacteristic
406D11—161no—
407#41—42no—
408#41—42no—
409#41—442no—
410#41—442no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—221no—
417C2×Q8C2×C22⋊D1112yes—
418C2×Q8C2×C22⋊D1112yes—
419C2×D4—22no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—221no—
423C2×D4—221no—
424C2×D4—221no—
425C2×D4—441no—
426C2×D4C2×C22⋊D1112yes—
427C22×C4—21no—
428C22×C4—24no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—441no—
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C2×C22⋊D1111yescharacteristic
435Q16—444no—
436SD16—444no—
437SD16—882no—
438D8—444no—
439M16—442no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—442no—
445C2×C8—881no—
446C4⋊C4—24no—
447C4⋊C4—24no—
448C4⋊C4—24no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—21no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—22no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4C2×C22⋊D1112yes—
461C4⋊C4C2×C22⋊D1112yes—
462C4⋊C4C2×C22⋊D1112yes—
463C22⋊C4—24no—
464C22⋊C4—24no—
465C22⋊C4—24no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—441no—
470C22⋊C4—441no—
471C42—24no—
472C42—22no—
473C42—22no—
474C42—22no—
475C42C2×C22⋊D1111yescharacteristic
476C42C2×C22⋊D1111yescharacteristic
477C42C2×C22⋊D1111yescharacteristic
478C42C23×D1111yescharacteristic
479C11#1866611yescharacteristic, complemented, Sylow
480C23—22no—
481C23—441no—
482C23#6700611yescharacteristic
483Q8—22no—
484Q8—22no—
485Q8—22no—
486Q8—22no—
487Q8—41no—
488Q8—41no—
489Q8—42no—
490Q8—81no—
491Q8—441no—
492Q8—441no—
493D4—42no—
494D4—44no—
495D4—41no—
496D4—41no—
497D4—41no—
498D4—41no—
499D4—442no—
500D4—441no—
501D4—441no—
502D4—441no—
503D4—441no—
504D4—882no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—44no—
515C2×C4—81no—
516C2×C4—84no—
517C2×C4—441no—
518C2×C4—882no—
519C2×C4#6700212yes—
520C2×C4#6700312yes—
521C2×C4#6700611yescharacteristic
522C2×C4#6700611yescharacteristic
523C2×C4#6700611yescharacteristic
524C2×C4C22×C22⋊D1111yescharacteristic
525C2×C4C22×C22⋊D1111yescharacteristic
526C2×C4C22×C22⋊D1111yescharacteristic
527C8—222no—
528C8—441no—
529C8—442no—
530C8—442no—
531C22—21no—
532C22—21no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—881no—
537C22—881no—
538C22—881no—
539C22#1062285112yes—
540C22C2×#6700611yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—42no—
545C4—42no—
546C4—42no—
547C4—42no—
548C4—42no—
549C4—881no—
550C4#1062285112yes—
551C4C2×#6700211yescharacteristic
552C4C2×#6700311yescharacteristic
553C4#1062336811yescharacteristic
554C4#1062336911yescharacteristic
555C2—22no—
556C2—82no—
557C2—1761no—
558C2C2×#1062285111yescharacteristic
559C2#1307793111yescharacteristic
560C2#1307796511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3507C2
socleC22×C11C2×#120
prime radical#13079191C2
hypercenter#3507D11
hypocenterC11#18666
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3507

Complements

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

NH ≅ G/Ntype
1. #13079928C2semidirect
3. #13078088C2semidirect
4. #13067858C2semidirect
5. #13067802C2semidirect
6. #13067712C2semidirect
7. #13067675C2semidirect
8. #13067293C2semidirect
9. #13067071C2semidirect
10. C2×Q8⋊(C11⋊C8)C2semidirect
11. C11×#3507C2semidirect
200. #3507D11semidirect
479. C11#18666semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130791912
#130780882
#130678582
#130678022
#130677122
#130676752
#130672932
#130670712
C2×Q8⋊(C11⋊C8)2
C11×#35072
#1866611