Finite Group Databasebeta

← #14730538

Subgroups — #14730538

Order 2816.

894 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080007C211yesmaximal, characteristic, complemented
2#13079158C211yesmaximal, characteristic, complemented
3#13078687C211yesmaximal, characteristic
4#13067893C212yesmaximal, complemented
5#13067879C212yesmaximal, complemented
6#13067865C212yesmaximal, complemented
7#13067858C212yesmaximal, complemented
8#13067288C211yesmaximal, characteristic, complemented
9#13067055C211yesmaximal, characteristic
10#13067037C211yesmaximal, characteristic, complemented
11C11×#3503C211yesmaximal, characteristic
12Q82×C11—21no—
13C11×#557C2212yes—
14C11×#554—21no—
15C11×#554—22no—
16D4×Q8×C11—22no—
17D4×Q8×C11C2212yes—
18C11×#544—22no—
19C11×#544—21no—
20C11×#533—21no—
21C11×#533C2211yescharacteristic
22C2×C11×C4⋊Q8—21no—
23C2×C11×C4⋊Q8C2211yescharacteristic
24C11×#520—21no—
25C4×C11×#41C2211yescharacteristic
26#10623001C2211yescharacteristic
27#10622852—21no—
28#10622707—21no—
29#10622703—21no—
30#10622693—22no—
31#10622692C2212yes—
32#10622691C2212yes—
33#10622665—22no—
34#10622644C2212yes—
35#10622644C2211yescharacteristic
36C4×#4326—21no—
37#10622633C2211yescharacteristic
38#10622633C2212yes—
39#10622632C2211yescharacteristic
40C4×#4324—21no—
41#10622620C2211yescharacteristic
42#10622609—21no—
43#10622577—22no—
44#10622538C2211yescharacteristic
45#10622537C2211yescharacteristic
46C4×#4318C2211yescharacteristic
47#10622185C2212yes—
48#10622185C2212yes—
49Q8⋊(C11⋊C8)C2212yes—
50Q8⋊(C11⋊C8)C2212yes—
51Q8⋊(C11⋊C8)C2212yes—
52D4⋊(C11⋊C8)C2212yes—
53C2×C11×#41D411yescharacteristic
54C22×Q8×C11—22no—
55C22×Q8×C11—21no—
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8—24no—
59C11×C4⋊Q8—22no—
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8—21no—
63C11×C4⋊Q8D411yescharacteristic
64C11×C4⋊Q8D412yes—
65C11×C4⋊Q8D411yescharacteristic
66C11×C4⋊Q8C2312yes—
67C11×#125—22no—
68C11×#125—24no—
69C11×#125—22no—
70C11×#125—21no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—24no—
73C11×C22⋊Q8—24no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8—24no—
77C11×C22⋊Q8D412yes—
78C4×Q8×C11—22no—
79C4×Q8×C11—22no—
80C4×Q8×C11—22no—
81C4×Q8×C11—21no—
82C4×Q8×C11D411yescharacteristic
83C4×Q8×C11C2311yescharacteristic
84C4×Q8×C11C2312yes—
85C4×D4×C11—24no—
86C4×D4×C11—22no—
87C4×D4×C11—21no—
88C4×D4×C11—21no—
89C4×D4×C11D411yescharacteristic
90C4×D4×C11C2311yescharacteristic
91C11×#117—22no—
92C11×#117—21no—
93C11×#117—21no—
94C11×#117D411yescharacteristic
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4D412yes—
99C2×C42×C11—21no—
100C2×C42×C11C2311yescharacteristic
101C2×#4326—21no—
102C2×#4326—22no—
103C2×#4324—21no—
104#66979—21no—
105#66977—21no—
106#66977—21no—
107C2×#4318—21no—
108C2×#4318—21no—
109#66923—21no—
110#66922C2311yescharacteristic
111#66922C2311yescharacteristic
112C4×Dic22—21no—
113C4×Dic22—21no—
114#66899—21no—
115#66899—22no—
116#66896—21no—
117C22⋊(C11⋊C8)—21no—
118#66874—21no—
119#66874—21no—
120#66874—22no—
121#66872—24no—
122#66872—21no—
123#66872—22no—
124#66871—24no—
125#66871—21no—
126C4⋊(C11⋊C8)—21no—
127C4⋊(C11⋊C8)C2312yes—
128C4⋊(C11⋊C8)C2311yescharacteristic
129C4⋊(C11⋊C8)C2311yescharacteristic
130#66867—21no—
131C4×C11⋊C8—21no—
132C4×C11⋊C8C2312yes—
133#18591—111nomaximal, Sylow
134C11×#41—22no—
135C11×#41—22no—
136C2×Q8×C11—24no—
137C2×Q8×C11—21no—
138C2×Q8×C11—22no—
139C2×Q8×C11—22no—
140C2×Q8×C11—81no—
141C2×Q8×C11—81no—
142C2×Q8×C11—82no—
143C2×Q8×C11—82no—
144C2×Q8×C11C2×D412yes—
145C2×Q8×C11C2×D411yescharacteristic
146C2×D4×C11—21no—
147C2×D4×C11C2×D411yescharacteristic
148C22×C4×C11—21no—
149C22×C4×C11—24no—
150C22×C4×C11—22no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C2×Dic22—21no—
157C2×Dic22—21no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4C2×D414yes—
173C11×C4⋊C4C2×D411yescharacteristic
174C11×C4⋊C4C2×D411yescharacteristic
175C11×C4⋊C4C2×D412yes—
176C11×C22⋊C4—24no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C42×C11—24no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—22no—
186C42×C11C2×D411yescharacteristic
187C42×C11C2×D411yescharacteristic
188C42×C11C2×D411yescharacteristic
189C42×C11C2411yescharacteristic
190C22⋊Dic11—41no—
191#4326—42no—
192#4326—82no—
193#4324—42no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198Dic11⋊C4—41no—
199Dic11⋊C4—41no—
200C4×Dic11—41no—
201#4318—24no—
202#4318—81no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—22no—
207#3503D1111yescharacteristic
208#3255—111no—
209#3165—111no—
210#3107—111no—
211#1653—112no—
212#1651—112no—
213#1649—112no—
214#1648—112no—
215#1546—111no—
216#1489—111no—
217#1485—111no—
218C23×C11—21no—
219C23×C11#12011yescharacteristic
220Q8×C11—21no—
221Q8×C11—22no—
222Q8×C11—22no—
223Q8×C11—42no—
224Q8×C11—42no—
225Q8×C11—42no—
226Q8×C11—82no—
227Q8×C11—84no—
228Q8×C11#13712yes—
229D4×C11—24no—
230D4×C11—21no—
231D4×C11#13712yes—
232C2×C4×C11—24no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—22no—
243C2×C4×C11—24no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—42no—
247C2×C4×C11—82no—
248C2×C4×C11—84no—
249C2×C4×C11#12011yescharacteristic
250C2×C4×C11#12011yescharacteristic
251C2×C4×C11#12011yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×Dic11—41no—
256C2×Dic11—41no—
257Dic22—41no—
258Dic22—41no—
259Dic22—41no—
260Dic22—41no—
261C11⋊C8—24no—
262C11⋊C8—41no—
263C11⋊C8—41no—
264C11⋊C8—42no—
265Q82—21no—
266#557C2×D1112yes—
267#554—21no—
268#554—22no—
269D4×Q8—22no—
270D4×Q8C2×D1112yes—
271#544—22no—
272#544—21no—
273#533—21no—
274#533—111no—
275#533C2×D1111yescharacteristic
276C2×C4⋊Q8—21no—
277C2×C4⋊Q8C2×D1111yescharacteristic
278#520—21no—
279C4×#41C2×D1111yescharacteristic
280#501—222no—
281#500—112no—
282#498—112no—
283#485—221no—
284#475—111no—
285#475—112no—
286#475—221no—
287#474—111no—
288#470—222no—
289#462—111no—
290#462—112no—
291#462—221no—
292#461—111no—
293#452—221no—
294C4×Q16—221no—
295C4×SD16—221no—
296#431—111no—
297#428—222no—
298#423—111no—
299C4×M16—111no—
300#332—112no—
301#332—112no—
302Q8⋊C8—112no—
303Q8⋊C8—112no—
304Q8⋊C8—112no—
305D4⋊C8—112no—
306C22×C11—21no—
307C22×C11—22no—
308C22×C11—21no—
309C22×C11—21no—
310C22×C11—41no—
311C22×C11—41no—
312C22×C11C2×#12011yescharacteristic
313C4×C11—21no—
314C4×C11—22no—
315C4×C11—21no—
316C4×C11—21no—
317C4×C11—41no—
318C4×C11—42no—
319C4×C11—44no—
320C4×C11—41no—
321C4×C11—42no—
322C4×C11#45612yes—
323C4×C11C2×#13711yescharacteristic
324C4×C11C2×#13711yescharacteristic
325C4×C11#57611yescharacteristic
326C4×C11#57711yescharacteristic
327Dic11—81no—
328Dic11—81no—
329C2×#41C22⋊D1111yescharacteristic
330C22×Q8—22no—
331C22×Q8—21no—
332C2×Q16—221no—
333C2×Q16—222no—
334C2×SD16—221no—
335C2×M16—221no—
336C2×M16—221no—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339C4⋊Q8—24no—
340C4⋊Q8—22no—
341C4⋊Q8—22no—
342C4⋊Q8—21no—
343C4⋊Q8—21no—
344C4⋊Q8—111no—
345C4⋊Q8—111no—
346C4⋊Q8C22⋊D1111yescharacteristic
347C4⋊Q8C22⋊D1112yes—
348C4⋊Q8C22⋊D1111yescharacteristic
349C4⋊Q8C22×D1112yes—
350#125—22no—
351#125—24no—
352#125—22no—
353#125—21no—
354#125—221no—
355C22⋊Q8—22no—
356C22⋊Q8—24no—
357C22⋊Q8—24no—
358C22⋊Q8—21no—
359C22⋊Q8—22no—
360C22⋊Q8—24no—
361C22⋊Q8—221no—
362C22⋊Q8—221no—
363C22⋊Q8C22⋊D1112yes—
364C4×Q8—22no—
365C4×Q8—22no—
366C4×Q8—22no—
367C4×Q8—21no—
368C4×Q8—221no—
369C4×Q8—221no—
370C4×Q8C22⋊D1111yescharacteristic
371C4×Q8C22×D1111yescharacteristic
372C4×Q8C22×D1112yes—
373C4×D4—24no—
374C4×D4—22no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4C22⋊D1111yescharacteristic
378C4×D4C22×D1111yescharacteristic
379#117—22no—
380#117—21no—
381#117—21no—
382#117—221no—
383#117C22⋊D1111yescharacteristic
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4C22⋊D1112yes—
388C2×C42—21no—
389C2×C42C22×D1111yescharacteristic
390#107—224no—
391#107—221no—
392#106—224no—
393#106—221no—
394#106—222no—
395C4⋊C8—112no—
396C4⋊C8—111no—
397C4⋊C8—111no—
398C4⋊C8—221no—
399#103—221no—
400#103—222no—
401#103—221no—
402#103—221no—
403#103—222no—
404#102—221no—
405C22⋊C8—221no—
406#97—221no—
407C4×C8—112no—
408C4×C8—221no—
409C2×C11—41no—
410C2×C11—42no—
411C2×C11#300411yescharacteristic
412C2×C11#301211yescharacteristic
413C2×C11C2×#45611yescharacteristic
414#41—22no—
415#41—22no—
416C2×Q8—24no—
417C2×Q8—21no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—81no—
421C2×Q8—81no—
422C2×Q8—82no—
423C2×Q8—82no—
424C2×Q8—221no—
425C2×Q8—221no—
426C2×Q8C2×C22⋊D1112yes—
427C2×Q8C2×C22⋊D1111yescharacteristic
428C2×D4—21no—
429C2×D4C2×C22⋊D1111yescharacteristic
430C22×C4—21no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4C2×C22⋊D1111yescharacteristic
436C22×C4C2×C22⋊D1111yescharacteristic
437C22×C4C2×C22⋊D1111yescharacteristic
438Q16—442no—
439Q16—882no—
440SD16—442no—
441M16—224no—
442M16—881no—
443C2×C8—222no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—222no—
447C4⋊C4—24no—
448C4⋊C4—24no—
449C4⋊C4—24no—
450C4⋊C4—24no—
451C4⋊C4—21no—
452C4⋊C4—22no—
453C4⋊C4—21no—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—21no—
460C4⋊C4—22no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—441no—
466C4⋊C4—441no—
467C4⋊C4C2×C22⋊D1111yescharacteristic
468C4⋊C4C2×C22⋊D1112yes—
469C4⋊C4C2×C22⋊D1111yescharacteristic
470C4⋊C4C2×C22⋊D1114yes—
471C22⋊C4—24no—
472C22⋊C4—22no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—441no—
477C42—24no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—22no—
482C42—441no—
483C42C2×C22⋊D1111yescharacteristic
484C42C2×C22⋊D1111yescharacteristic
485C42C2×C22⋊D1111yescharacteristic
486C42C23×D1111yescharacteristic
487C11#1859111yescharacteristic, complemented, Sylow
488C23—21no—
489C23#6700611yescharacteristic
490Q8—21no—
491Q8—22no—
492Q8—22no—
493Q8—42no—
494Q8—42no—
495Q8—42no—
496Q8—82no—
497Q8—84no—
498Q8—441no—
499Q8—441no—
500Q8—441no—
501Q8—441no—
502Q8#6699512yes—
503D4—24no—
504D4—21no—
505D4#6699512yes—
506C2×C4—24no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—82no—
522C2×C4—84no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4#6700611yescharacteristic
526C2×C4#6700611yescharacteristic
527C2×C4#6700611yescharacteristic
528C2×C4C22×C22⋊D1111yescharacteristic
529C2×C4C22×C22⋊D1111yescharacteristic
530C2×C4C22×C22⋊D1111yescharacteristic
531C8—224no—
532C8—441no—
533C8—441no—
534C8—442no—
535C22—21no—
536C22—22no—
537C22—21no—
538C22—21no—
539C22—41no—
540C22—41no—
541C22C2×#6700611yescharacteristic
542C4—21no—
543C4—22no—
544C4—21no—
545C4—21no—
546C4—41no—
547C4—42no—
548C4—44no—
549C4—41no—
550C4—42no—
551C4—881no—
552C4—881no—
553C4#1062285912yes—
554C4C2×#6699511yescharacteristic
555C4C2×#6699511yescharacteristic
556C4#1062336611yescharacteristic
557C4#1062336711yescharacteristic
558C2—41no—
559C2—42no—
560C2#1307785011yescharacteristic
561C2#1307792011yescharacteristic
562C2C2×#1062285911yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3503C2
socleC22×C11C2×#120
prime radicalC2×C11×#41D4
hypercenter#3503D11
hypocenterC11#18591
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. #13080007C2semidirect
2. #13079158C2semidirect
4. #13067893C2semidirect
5. #13067879C2semidirect
6. #13067865C2semidirect
7. #13067858C2semidirect
8. #13067288C2semidirect
10. #13067037C2semidirect
487. C11#18591semidirect

Maximal subgroups

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

subgroupindex
#130800072
#130791582
#130786872
#130678932
#130678792
#130678652
#130678582
#130672882
#130670552
#130670372
C11×#35032
#1859111