Finite Group Databasebeta

← #14826934

Subgroups — #14826934

Order 2816.

848 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073191C211yesmaximal, characteristic, complemented
2#13070149C211yesmaximal, characteristic, complemented
3#13069933C211yesmaximal, characteristic, complemented
4#13069847C211yesmaximal, characteristic
5#13069704C211yesmaximal, characteristic
6#13069469C211yesmaximal, characteristic, complemented
7#13069250C211yesmaximal, characteristic, complemented
8#13069240C211yesmaximal, characteristic, complemented
9#13069201C211yesmaximal, characteristic, complemented
10#13069175C211yesmaximal, characteristic, complemented
11#13068950C211yesmaximal, characteristic, complemented
12#13068950C211yesmaximal, characteristic, complemented
13#13068616C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, characteristic, complemented
15C11×#2366C211yesmaximal, characteristic
16C2×C11×#127C2211yescharacteristic
17C2×C4×D4×C11—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C22×#4324C2211yescharacteristic
22C11×#390—21no—
23C11×#390C2211yescharacteristic
24C11×#390C2211yescharacteristic
25C11×#386—21no—
26C11×#386—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35#10622599—21no—
36#10622594—21no—
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41#10622548C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43#10622542C2211yescharacteristic
44#10622542C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622541C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622273—21no—
50#10622267—21no—
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C22×Dic22C2311yescharacteristic
66C11×#127—22no—
67C11×#127—22no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11—41no—
71C4×D4×C11—41no—
72C4×D4×C11—44no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C42×C11—21no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×#4324—22no—
88C2×#4324—22no—
89C2×#4324—22no—
90C2×#4324—41no—
91C2×#4324—41no—
92C2×#4324—41no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C11×#95—21no—
105C11×#95D411yescharacteristic
106C11×#95D411yescharacteristic
107#66896—22no—
108#66896—22no—
109#66896—22no—
110#66896—41no—
111#66896—41no—
112#66896—41no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121#66874—22no—
122#66874—41no—
123#66872—22no—
124#66872—41no—
125C4⋊(C11⋊C8)—41no—
126C4×C11⋊C8—41no—
127#27064—111nomaximal, Sylow
128C24×C11—21no—
129C24×C11—21no—
130C2×D4×C11—24no—
131C2×D4×C11—24no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—42no—
143C2×D4×C11—42no—
144C2×D4×C11—81no—
145C2×D4×C11—81no—
146C2×D4×C11#4112yes—
147C2×D4×C11#4112yes—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11—81no—
155C22×C4×C11—81no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2411yescharacteristic
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—41no—
177C11×C4⋊C4SD1614yescomplemented
178C11×C4⋊C4#4112yes—
179C11×C22⋊C4—42no—
180C11×C22⋊C4—42no—
181C11×C22⋊C4—42no—
182C11×C22⋊C4—42no—
183C11×C22⋊C4—81no—
184C11×C22⋊C4—81no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—42no—
192#4324—44no—
193#4324—44no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—42no—
201C4⋊Dic11—81no—
202Dic11⋊C4—81no—
203C4×Dic11—81no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8#4112yes—
216#2511—111no—
217#2366D1111yescharacteristic
218#2094—111no—
219#2055—111no—
220#2041—111no—
221#2014—111no—
222#1968—111no—
223#1927—111no—
224#1926—111no—
225#1920—111no—
226#1916—111no—
227#1877—111no—
228#1877—111no—
229#1802—111no—
230C4×#102—111no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11C22×D411yescharacteristic
246D4×C11—22no—
247D4×C11—22no—
248D4×C11—22no—
249D4×C11—22no—
250D4×C11—48no—
251D4×C11—41no—
252D4×C11—41no—
253D4×C11—41no—
254D4×C11—41no—
255D4×C11—84no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—22no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—84no—
278C2×C4×C11—84no—
279C2×C4×C11C2×SD1612yes—
280C2×C4×C11C2×SD1612yes—
281C2×C4×C11C2×SD1612yes—
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11H(5,𝔽2)11yescharacteristic
287C2×C4×C11H(5,𝔽2)11yescharacteristic
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300Dic22—41no—
301Dic22—41no—
302Dic22—41no—
303Dic22—41no—
304C11⋊C8—22no—
305C11⋊C8—41no—
306C11⋊C8—41no—
307C11⋊C8—41no—
308C22×SD16—111no—
309C22×SD16—111no—
310C2×#127C2×D1111yescharacteristic
311C2×C4×D4—21no—
312C2×C4×D4C2×D1111yescharacteristic
313C2×C4×D4C2×D1111yescharacteristic
314C2×#106—111no—
315C2×#106—111no—
316C2×C4⋊C8—111no—
317C2×#103—111no—
318C2×#103—111no—
319C2×#102—111no—
320C2×#102—111no—
321C2×#102—111no—
322C2×#102—111no—
323C2×#102—111no—
324C2×#102—111no—
325C2×C4×C8—111no—
326#400—221no—
327#400—221no—
328#391—111no—
329#391—111no—
330#391—111no—
331#390—21no—
332#390C2×D1111yescharacteristic
333#390C2×D1111yescharacteristic
334#389—111no—
335#387—221no—
336#387—221no—
337#386—21no—
338#386—21no—
339#384—111no—
340C4×C4⋊C4—111no—
341C4×C4⋊C4C2×D1111yescharacteristic
342C4×C4⋊C4C2×D1111yescharacteristic
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#336—111no—
348#336—111no—
349#336—111no—
350#336—111no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—42no—
356C22×C11—42no—
357C22×C11—81no—
358C22×C11—81no—
359C22×C11—81no—
360C22×C11—81no—
361C22×C11—81no—
362C22×C11—81no—
363C22×C11—81no—
364C22×C11—81no—
365C22×C11#52511yescharacteristic
366C22×C11#54611yescharacteristic
367C22×C11#55011yescharacteristic
368C22×C11C22×SD1611yescharacteristic
369C22×C11#57511yescharacteristic
370C22×C11#57611yescharacteristic
371C22×C11#57711yescharacteristic
372C4×C11—22no—
373C4×C11—22no—
374C4×C11—22no—
375C4×C11—41no—
376C4×C11—42no—
377C4×C11—41no—
378C4×C11—41no—
379C4×C11—81no—
380C4×C11#52911yescharacteristic
381C4×C11#53811yescharacteristic
382C4×C11#55111yescharacteristic
383C4×C11#55311yescharacteristic
384Dic11—81no—
385Dic11—81no—
386Dic11—81no—
387Dic11—81no—
388C22×Q8—111no—
389C22×D4—21no—
390C22×D4—21no—
391C22×D4C22×D1111yescharacteristic
392C22×D4C22×D1111yescharacteristic
393C23×C4—21no—
394C23×C4—21no—
395C2×SD16—222no—
396C2×SD16—222no—
397C2×SD16—222no—
398C2×SD16—441no—
399C2×SD16—441no—
400C2×SD16—441no—
401C22×C8—111no—
402C22×C8—111no—
403C22×C8—111no—
404C22×C8—111no—
405#127—22no—
406#127—22no—
407C4×D4—22no—
408C4×D4—22no—
409C4×D4—41no—
410C4×D4—41no—
411C4×D4—44no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4C22⋊D1111yescharacteristic
419C2×C4⋊C4C22⋊D1111yescharacteristic
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C42—21no—
429C2×C42—221no—
430C2×C42C22×D1111yescharacteristic
431C2×C42C22×D1111yescharacteristic
432C2×C42C22×D1111yescharacteristic
433#106—222no—
434#106—441no—
435C4⋊C8—441no—
436#103—222no—
437#103—441no—
438#102—222no—
439#102—222no—
440#102—222no—
441#102—441no—
442#102—441no—
443#102—441no—
444C4×C8—441no—
445#95—21no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95C22⋊D1111yescharacteristic
455#95C22⋊D1111yescharacteristic
456C2×C11—82no—
457C2×C11—82no—
458C2×C11#246711yescharacteristic
459C2×C11#310111yescharacteristic
460C2×C11#311811yescharacteristic
461C2×C11#329511yescharacteristic
462C2×C11#331711yescharacteristic
463C2×C11#339211yescharacteristic
464C2×C11#340311yescharacteristic
465C24—21no—
466C24—21no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×Q8—221no—
471C2×Q8—221no—
472C2×Q8—221no—
473C2×D4—24no—
474C2×D4—24no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—81no—
488C2×D4—81no—
489C2×D4#433912yes—
490C2×D4#433912yes—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—81no—
498C22×C4—81no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4C2×C22⋊D1111yescharacteristic
504C22×C4C2×C22⋊D1111yescharacteristic
505C22×C4C2×C22⋊D1111yescharacteristic
506C22×C4C2×C22⋊D1111yescharacteristic
507C22×C4C2×C22⋊D1111yescharacteristic
508C22×C4C2×C22⋊D1111yescharacteristic
509C22×C4C23×D1111yescharacteristic
510SD16—444no—
511SD16—444no—
512C2×C8—112no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—41no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—442no—
535C4⋊C4—881no—
536C4⋊C4—881no—
537C4⋊C4#432414yescomplemented
538C4⋊C4#434112yes—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—81no—
544C22⋊C4—81no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—42no—
552C42—881no—
553C11#2706411yescharacteristic, complemented, Sylow
554C23—22no—
555C23—22no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23C22×C22⋊D1111yescharacteristic
569Q8—441no—
570Q8—441no—
571Q8—441no—
572Q8—441no—
573D4—22no—
574D4—22no—
575D4—22no—
576D4—22no—
577D4—48no—
578D4—41no—
579D4—41no—
580D4—41no—
581D4—41no—
582D4—84no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—84no—
605C2×C4—84no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4C2×#432412yes—
619C2×C4C2×#432412yes—
620C2×C4C2×#432412yes—
621C2×C4C2×#433911yescharacteristic
622C2×C4C2×#433911yescharacteristic
623C2×C4C2×#434111yescharacteristic
624C2×C4#6703711yescharacteristic
625C2×C4#41×D1111yescharacteristic
626C2×C4#6704211yescharacteristic
627C8—222no—
628C8—441no—
629C8—441no—
630C8—441no—
631C22—42no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22#1062332211yescharacteristic
646C22C22×#432411yescharacteristic
647C22#1062333711yescharacteristic
648C22#1062335311yescharacteristic
649C22#1062336511yescharacteristic
650C22#1062336611yescharacteristic
651C22#1062336711yescharacteristic
652C4—22no—
653C4—22no—
654C4—22no—
655C4—41no—
656C4—42no—
657C4—41no—
658C4—41no—
659C4—81no—
660C4—881no—
661C4—881no—
662C4—881no—
663C4—881no—
664C4#1062306911yescharacteristic
665C4#1062308711yescharacteristic
666C4#1062309111yescharacteristic
667C4#1062309611yescharacteristic
668C2—82no—
669C2—82no—
670C2#1307266111yescharacteristic
671C2#1307862411yescharacteristic
672C2#1307880011yescharacteristic
673C2#1308044011yescharacteristic
674C2#1308074211yescharacteristic
675C2#1308159711yescharacteristic
676C2#1308170011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2366C2
socleC23×C11C22×D4
prime radicalC2×C11×#127C22
hypercenter#2366D11
hypocenterC11#27064
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2366

Complements

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

NH ≅ G/Ntype
1. #13073191C2semidirect
2. #13070149C2semidirect
3. #13069933C2semidirect
6. #13069469C2semidirect
7. #13069250C2semidirect
8. #13069240C2semidirect
9. #13069201C2semidirect
10. #13069175C2semidirect
11. #13068950C2semidirect
12. #13068950C2semidirect
13. #13068616C2semidirect
14. C4×#66896C2semidirect
177. C11×C4⋊C4SD16semidirect
537. C4⋊C4#4324semidirect
553. C11#27064semidirect

Maximal subgroups

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

subgroupindex
#130731912
#130701492
#130699332
#130698472
#130697042
#130694692
#130692502
#130692402
#130692012
#130691752
#130689502
#130686162
C4×#668962
C11×#23662
#2706411