Finite Group Databasebeta

← #14660601

Subgroups — #14660601

Order 2816.

1370 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4325C211yesmaximal, characteristic
2C2×#10622838C211yesmaximal, characteristic, complemented
3C2×#10622744C211yesmaximal, characteristic
4C22×#66887C211yesmaximal, characteristic
5C2×#10622196C211yesmaximal, characteristic, complemented
6#13068314C211yesmaximal, characteristic, complemented
7C22×C11×#101C211yesmaximal, characteristic, complemented
8C23×Q8×C11C2211yescharacteristic
9C23×D44C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×#4325—22no—
13C22×#4325—22no—
14C22×#4325—22no—
15C22×#4325—22no—
16C22×#4325—22no—
17C22×#4325—22no—
18C22×#4325C414yescomplemented
19C2×#66979C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22C2×C11×#101—22no—
23C2×C11×#101—22no—
24C2×C11×#101—22no—
25#10622838—22no—
26#10622838—22no—
27C2×#66899—22no—
28#10622744—22no—
29#10622744—22no—
30C2×#66887—22no—
31C2×#66887—22no—
32C2×#66887—22no—
33C2×#66885—22no—
34#10622196—22no—
35#10622188—22no—
36C24×D11—21no—
37C22×Q8×C11—21no—
38C22×Q8×C11—21no—
39C22×Q8×C11—21no—
40C22×Q8×C11—21no—
41C22×Q8×C11—21no—
42C22×Q8×C11—21no—
43C22×Q8×C11—21no—
44C22×Q8×C11—21no—
45C22×Q8×C11—21no—
46C22×Q8×C11—21no—
47C22×Q8×C11—21no—
48C22×Q8×C11C2×C412yes—
49C22×Q8×C11D412yes—
50C22×Q8×C11D412yes—
51C23×C4×C11—21no—
52C23×C4×C11C2311yescharacteristic
53C22×D44—21no—
54C22×D44—21no—
55C22×D44—21no—
56C22×D44—21no—
57C22×D44—21no—
58C22×D44—21no—
59C22×D44—21no—
60C22×D44—21no—
61C22×D44—21no—
62C22×D44—21no—
63C22×D44—21no—
64C22×D44C2×C412yes—
65C22×D44D412yes—
66C22×D44D412yes—
67C2×C11×M16—21no—
68C2×C11×M16—21no—
69C2×C11×M16—21no—
70C2×C11×M16—21no—
71C2×C11×M16—21no—
72C2×C11×M16—21no—
73C2×C11×M16—21no—
74C2×C11×M16—21no—
75C2×C11×M16—21no—
76C2×C11×M16—21no—
77C2×C11×M16D412yes—
78C2×C11×M16D412yes—
79C22×C8×C11—21no—
80C22×C8×C11—21no—
81C2×C22⋊Dic11—21no—
82C2×#4325—28no—
83C2×#4325—28no—
84C2×#4325—28no—
85C2×#4325—28no—
86C2×#4325—28no—
87C2×#4325—28no—
88C2×#4325—28no—
89#66979—21no—
90#66979—21no—
91#66979—21no—
92#66979—21no—
93C2×C4⋊Dic11D412yes—
94C2×C4×Dic11—21no—
95C2×#4318—21no—
96C2×#4318—21no—
97C2×#4318—21no—
98C2×#4318—21no—
99C2×#4318—21no—
100C2×#4318D412yes—
101C22×C11⋊C8—21no—
102C22×C11⋊C8—21no—
103C22×C11⋊C8—21no—
104C22×C11⋊C8—21no—
105C22×C11⋊C8—21no—
106C22×C11⋊C8C2×C412yes—
107C22×C11⋊C8D412yes—
108C22×C11⋊C8D412yes—
109C11×#101—28no—
110#66899—28no—
111#66887—28no—
112#66885—28no—
113#11028—111nomaximal, Sylow
114C24×C11#4111yescharacteristic
115C23×D11—22no—
116C23×D11—22no—
117C23×D11—22no—
118C23×D11—41no—
119C23×D11—41no—
120C23×D11—41no—
121C23×D11—41no—
122C23×D11—84no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11—22no—
133C2×Q8×C11—22no—
134C2×Q8×C11—22no—
135C2×Q8×C11—22no—
136C2×Q8×C11—22no—
137C2×Q8×C11—22no—
138C2×Q8×C11—41no—
139C2×Q8×C11—41no—
140C2×Q8×C11—41no—
141C2×Q8×C11—41no—
142C2×Q8×C11—41no—
143C2×Q8×C11—41no—
144C2×Q8×C11—41no—
145C2×Q8×C11—41no—
146C2×Q8×C11—41no—
147C2×Q8×C11—41no—
148C2×Q8×C11—41no—
149C2×Q8×C11—41no—
150C2×Q8×C11C22⋊C414yes—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—41no—
155C22×C4×C11—41no—
156C22×C4×C11—41no—
157C22×C4×C11—41no—
158C22×C4×C11C22×C411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11#4111yescharacteristic
170C22×C4×C11#4111yescharacteristic
171C22×C4×C11#4111yescharacteristic
172C22×Dic11—22no—
173C2×D44—22no—
174C2×D44—22no—
175C2×D44—22no—
176C2×D44—22no—
177C2×D44—22no—
178C2×D44—22no—
179C2×D44—22no—
180C2×D44—22no—
181C2×D44—22no—
182C2×D44—22no—
183C2×D44—22no—
184C2×D44—22no—
185C2×D44—22no—
186C2×D44—22no—
187C2×D44—22no—
188C2×D44—41no—
189C2×D44—41no—
190C2×D44—41no—
191C2×D44—41no—
192C2×D44—41no—
193C2×D44—41no—
194C2×D44—41no—
195C2×D44—41no—
196C2×D44—41no—
197C2×D44—41no—
198C2×D44—41no—
199C2×D44—41no—
200C2×D44C22⋊C414yes—
201C11×M16—22no—
202C11×M16—22no—
203C11×M16—22no—
204C11×M16—22no—
205C11×M16—41no—
206C11×M16—41no—
207C11×M16—41no—
208C11×M16—41no—
209C2×C8×C11—22no—
210C2×C8×C11—22no—
211C2×C8×C11—41no—
212C2×C8×C11—41no—
213C2×C8×C11—41no—
214C2×C8×C11—41no—
215C22⋊Dic11—41no—
216C22⋊Dic11—41no—
217#4325—232no—
218C4⋊Dic11—22no—
219C4⋊Dic11—22no—
220C4×Dic11—41no—
221C4×Dic11—41no—
222#4318—22no—
223#4318—22no—
224#4318—41no—
225#4318—41no—
226C2×C11⋊C8—22no—
227C2×C11⋊C8—22no—
228C2×C11⋊C8—22no—
229C2×C11⋊C8—22no—
230C2×C11⋊C8—22no—
231C2×C11⋊C8—22no—
232C2×C11⋊C8—22no—
233C2×C11⋊C8—41no—
234C2×C11⋊C8—41no—
235C2×C11⋊C8C22⋊C414yes—
236C23×SD16—111no—
237C2×#419—111no—
238C2×#418—111no—
239C22×#101D1111yescharacteristic, complemented
240C22×#100—111no—
241C2×#341—111no—
242#1729—111no—
243C23×C11—24no—
244C23×C11C4×D411yescharacteristic
245C23×C11#12111yescharacteristic
246C23×C11#12111yescharacteristic
247C23×C11#12111yescharacteristic
248C23×C11#12311yescharacteristic
249C23×C11#12311yescharacteristic
250C23×C11#12411yescharacteristic
251C22×D11—24no—
252C22×D11—42no—
253C22×D11—42no—
254C22×D11—42no—
255C22×D11—42no—
256C22×D11—42no—
257C22×D11—42no—
258C22×D11—84no—
259C22×D11—84no—
260C22×D11—84no—
261C22×D11—84no—
262C22×D11—84no—
263C22×D11—84no—
264C22×D11—84no—
265Q8×C11—24no—
266Q8×C11—24no—
267Q8×C11—42no—
268Q8×C11—42no—
269Q8×C11—42no—
270Q8×C11—42no—
271Q8×C11—42no—
272Q8×C11—42no—
273C2×C4×C11—24no—
274C2×C4×C11—42no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—42no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C2×C4×C11C2×C22⋊C411yescharacteristic
281C2×C4×C11C2×C22⋊C411yescharacteristic
282C2×C4×C11C2×C22⋊C411yescharacteristic
283C2×C4×C11C4×D411yescharacteristic
284C2×C4×C11C4×D411yescharacteristic
285C2×C4×C11C4×D411yescharacteristic
286C2×C4×C11#12011yescharacteristic
287C2×C4×C11#12011yescharacteristic
288C2×C4×C11#12011yescharacteristic
289C2×C4×C11#12011yescharacteristic
290C2×C4×C11#12011yescharacteristic
291C2×C4×C11#12011yescharacteristic
292C2×C4×C11#12011yescharacteristic
293C2×C4×C11#12011yescharacteristic
294C2×C4×C11#12111yescharacteristic
295C2×C4×C11#12111yescharacteristic
296C2×C4×C11#12111yescharacteristic
297C2×C4×C11#12111yescharacteristic
298C2×C4×C11#12111yescharacteristic
299C2×C4×C11#12111yescharacteristic
300C2×C4×C11#12111yescharacteristic
301C2×C4×C11#12111yescharacteristic
302C2×C4×C11#12111yescharacteristic
303C2×C4×C11#12311yescharacteristic
304C2×C4×C11#12311yescharacteristic
305C2×C4×C11#12411yescharacteristic
306C2×C4×C11#12711yescharacteristic
307C2×C4×C11#12711yescharacteristic
308C2×Dic11—42no—
309C2×Dic11—44no—
310D44—24no—
311D44—24no—
312D44—42no—
313D44—42no—
314D44—42no—
315D44—42no—
316D44—42no—
317D44—42no—
318C8×C11—42no—
319C8×C11—42no—
320C11⋊C8—24no—
321C11⋊C8—42no—
322C23×Q8C2×D1111yescharacteristic
323C23×D4—111no—
324C22×SD16—114no—
325C22×SD16—222no—
326C22×SD16—222no—
327C22×SD16—222no—
328C22×SD16—222no—
329C22×SD16—222no—
330C22×SD16—222no—
331C22×M16—111no—
332C22×M16C2×D1111yescharacteristic
333C22×M16C2×D1111yescharacteristic
334C23×C8—111no—
335C2×#117—111no—
336#419—222no—
337#419—222no—
338#418—222no—
339#418—222no—
340C2×#103—222no—
341C2×#102—222no—
342C2×#101—22no—
343C2×#101—22no—
344C2×#101—22no—
345C2×#100—222no—
346C2×#100—222no—
347C2×#100—222no—
348#341—222no—
349#336—222no—
350C22×C11—22no—
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11—22no—
355C22×C11—22no—
356C22×C11#38611yescharacteristic
357C22×C11#38611yescharacteristic
358C22×C11#39011yescharacteristic
359C22×C11#39211yescharacteristic
360C22×C11#39411yescharacteristic
361C22×C11#39411yescharacteristic
362C22×C11#39411yescharacteristic
363C22×C11#47114yes—
364C2×D11—44no—
365C2×D11—84no—
366C2×D11—84no—
367C2×D11—84no—
368C2×D11—84no—
369C2×D11—84no—
370C2×D11—84no—
371C2×D11—84no—
372C4×C11—44no—
373C4×C11#37911yescharacteristic
374C4×C11#38611yescharacteristic
375C4×C11#38611yescharacteristic
376C4×C11#39011yescharacteristic
377C4×C11#39211yescharacteristic
378C4×C11#39211yescharacteristic
379C4×C11#39211yescharacteristic
380C4×C11#39411yescharacteristic
381Dic11—82no—
382C25—221no—
383C22×Q8—21no—
384C22×Q8—21no—
385C22×Q8—21no—
386C22×Q8—21no—
387C22×Q8—21no—
388C22×Q8—21no—
389C22×Q8—21no—
390C22×Q8—21no—
391C22×Q8—21no—
392C22×Q8—21no—
393C22×Q8—21no—
394C22×Q8C4×D1112yes—
395C22×Q8D4412yes—
396C22×Q8C22⋊D1112yes—
397C22×D4—112no—
398C22×D4—112no—
399C22×D4—112no—
400C22×D4—221no—
401C22×D4—221no—
402C22×D4—221no—
403C22×D4—221no—
404C22×D4—221no—
405C22×D4—221no—
406C22×D4—221no—
407C22×D4—221no—
408C22×D4—221no—
409C22×D4—221no—
410C22×D4—221no—
411C23×C4—21no—
412C23×C4C22×D1111yescharacteristic
413C2×SD16—228no—
414C2×SD16—228no—
415C2×SD16—228no—
416C2×SD16—228no—
417C2×SD16—228no—
418C2×SD16—228no—
419C2×SD16—228no—
420C2×M16—21no—
421C2×M16—21no—
422C2×M16—21no—
423C2×M16—21no—
424C2×M16—21no—
425C2×M16—21no—
426C2×M16—21no—
427C2×M16—21no—
428C2×M16—21no—
429C2×M16—21no—
430C2×M16—112no—
431C2×M16—221no—
432C2×M16—221no—
433C2×M16—221no—
434C2×M16—221no—
435C2×M16—221no—
436C2×M16C22⋊D1112yes—
437C2×M16C22⋊D1112yes—
438C22×C8—21no—
439C22×C8—21no—
440C22×C8—112no—
441C22×C8—112no—
442C22×C8—112no—
443C22×C8—221no—
444C22×C8—221no—
445C22×C8—221no—
446C22×C8—221no—
447C22×C8—221no—
448#117—221no—
449#117—221no—
450#117—221no—
451#117—221no—
452C2×C4⋊C4—112no—
453C2×C22⋊C4—221no—
454C2×C42—221no—
455#103—228no—
456#102—228no—
457#101—28no—
458#100—228no—
459C2×C11—21no—
460C2×C11—21no—
461C2×C11—21no—
462C2×C11—21no—
463C2×C11#143811yescharacteristic
464C2×C11#197712yes—
465C2×C11#201912yes—
466C2×C11#204612yes—
467D11—84no—
468C24—222no—
469C24—222no—
470C24—222no—
471C24—441no—
472C24—441no—
473C24—441no—
474C24—441no—
475C24—884no—
476C24#433911yescharacteristic
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—22no—
487C2×Q8—22no—
488C2×Q8—22no—
489C2×Q8—22no—
490C2×Q8—22no—
491C2×Q8—22no—
492C2×Q8—41no—
493C2×Q8—41no—
494C2×Q8—41no—
495C2×Q8—41no—
496C2×Q8—41no—
497C2×Q8—41no—
498C2×Q8—41no—
499C2×Q8—41no—
500C2×Q8—41no—
501C2×Q8—41no—
502C2×Q8—41no—
503C2×Q8—41no—
504C2×Q8(C2×D11)⋊C414yes—
505C2×D4—114no—
506C2×D4—222no—
507C2×D4—222no—
508C2×D4—222no—
509C2×D4—222no—
510C2×D4—222no—
511C2×D4—222no—
512C2×D4—222no—
513C2×D4—222no—
514C2×D4—222no—
515C2×D4—222no—
516C2×D4—222no—
517C2×D4—222no—
518C2×D4—222no—
519C2×D4—222no—
520C2×D4—222no—
521C2×D4—441no—
522C2×D4—441no—
523C2×D4—441no—
524C2×D4—441no—
525C2×D4—441no—
526C2×D4—441no—
527C2×D4—441no—
528C2×D4—441no—
529C2×D4—441no—
530C2×D4—441no—
531C2×D4—441no—
532C2×D4—441no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—222no—
541C22×C4C2×C4×D1111yescharacteristic
542C22×C4C2×D4411yescharacteristic
543C22×C4#433911yescharacteristic
544C22×C4D4×D1111yescharacteristic
545C22×C4D4×D1111yescharacteristic
546C22×C4D4×D1111yescharacteristic
547C22×C4D4×D1111yescharacteristic
548C22×C4D4×D1111yescharacteristic
549C22×C4D4×D1111yescharacteristic
550C22×C4#434111yescharacteristic
551C22×C4#434111yescharacteristic
552C22×C4C2×C22⋊D1111yescharacteristic
553C22×C4C2×C22⋊D1111yescharacteristic
554C22×C4C2×C22⋊D1111yescharacteristic
555SD16—2232no—
556M16—22no—
557M16—22no—
558M16—22no—
559M16—22no—
560M16—41no—
561M16—41no—
562M16—41no—
563M16—41no—
564M16—222no—
565M16—222no—
566M16—441no—
567M16—441no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—41no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—41no—
574C2×C8—114no—
575C2×C8—222no—
576C2×C8—222no—
577C2×C8—222no—
578C2×C8—222no—
579C2×C8—222no—
580C2×C8—222no—
581C2×C8—222no—
582C2×C8—441no—
583C2×C8—441no—
584C4⋊C4—222no—
585C4⋊C4—222no—
586C22⋊C4—441no—
587C22⋊C4—441no—
588C42—441no—
589C42—441no—
590C11#1102811yescharacteristic, complemented, Sylow
591C23—24no—
592C23—224no—
593C23—442no—
594C23—442no—
595C23—442no—
596C23—442no—
597C23—442no—
598C23—442no—
599C23—884no—
600C23—884no—
601C23—884no—
602C23—884no—
603C23—884no—
604C23—884no—
605C23—884no—
606C23#6693611yescharacteristic
607C23#6693711yescharacteristic
608C23#6693711yescharacteristic
609C23#6693811yescharacteristic
610C23C4×C22⋊D1111yescharacteristic
611C23#6698211yescharacteristic
612C23#6698311yescharacteristic
613Q8—24no—
614Q8—24no—
615Q8—42no—
616Q8—42no—
617Q8—42no—
618Q8—42no—
619Q8—42no—
620Q8—42no—
621D4—224no—
622D4—224no—
623D4—442no—
624D4—442no—
625D4—442no—
626D4—442no—
627D4—442no—
628D4—442no—
629C2×C4—24no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—442no—
637C2×C4—444no—
638C2×C4C22⋊C4×D1111yescharacteristic
639C2×C4C22⋊C4×D1111yescharacteristic
640C2×C4(C22⋊D11)⋊C411yescharacteristic
641C2×C4(C22⋊D11)⋊C411yescharacteristic
642C2×C4#6693511yescharacteristic
643C2×C4#6693511yescharacteristic
644C2×C4#6693511yescharacteristic
645C2×C4#6693611yescharacteristic
646C2×C4#6693711yescharacteristic
647C2×C4#6693711yescharacteristic
648C2×C4#6693811yescharacteristic
649C2×C4#6693911yescharacteristic
650C2×C4C2×(C2×D11)⋊C411yescharacteristic
651C2×C4C4×C22⋊D1111yescharacteristic
652C2×C4#6698311yescharacteristic
653C2×C4#6699011yescharacteristic
654C2×C4#6699011yescharacteristic
655C2×C4#6699011yescharacteristic
656C2×C4#6699011yescharacteristic
657C2×C4#6699111yescharacteristic
658C2×C4#6699111yescharacteristic
659C2×C4#6699211yescharacteristic
660C2×C4#6699211yescharacteristic
661C2×C4#6699211yescharacteristic
662C2×C4#6699211yescharacteristic
663C2×C4#6699311yescharacteristic
664C2×C4#6699311yescharacteristic
665C2×C4#6700611yescharacteristic
666C8—42no—
667C8—42no—
668C8—224no—
669C8—442no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—444no—
677C22—884no—
678C22—884no—
679C22—884no—
680C22—884no—
681C22—884no—
682C22—884no—
683C22—884no—
684C22#1062236714yes—
685C22#1062256911yescharacteristic
686C22#1062257011yescharacteristic
687C22#1062257211yescharacteristic
688C22#1062257211yescharacteristic
689C22#1062257311yescharacteristic
690C22#1062257411yescharacteristic
691C22#1062282611yescharacteristic
692C4—44no—
693C4—882no—
694C4#1062256811yescharacteristic
695C4#1062256911yescharacteristic
696C4#1062257011yescharacteristic
697C4#1062257111yescharacteristic
698C4#1062257311yescharacteristic
699C4#1062257411yescharacteristic
700C4#1062283611yescharacteristic
701C4#1062283611yescharacteristic
702C2—21no—
703C2—21no—
704C2—21no—
705C2—21no—
706C2—884no—
707C2#1306685511yescharacteristic
708C2#1306952012yes—
709C2#1306972912yes—
710C2#1306987512yes—
subgroupG/H
centerC23#66937
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC22×C11×#101C2
socleC23×C11#121
prime radicalC23×D44C22
cosocleC23×C4×C11C23
hypercenterC22×#101D11
hypocenterC11#11028
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#101

Complements

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

NH ≅ G/Ntype
2. C2×#10622838C2semidirect
5. C2×#10622196C2semidirect
6. #13068314C2semidirect
7. C22×C11×#101C2semidirect
18. C22×#4325C4semidirect
239. C22×#101D11semidirect
590. C11#11028semidirect

Maximal subgroups

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

subgroupindex
C23×#43252
C2×#106228382
C2×#106227442
C22×#668872
C2×#106221962
#130683142
C22×C11×#1012
#1102811