Finite Group Databasebeta

← #14810935

Subgroups — #14810935

Order 2816.

946 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622635C211yesmaximal, characteristic, complemented
2C22×#66899C211yesmaximal, characteristic
3#13072340C211yesmaximal, characteristic
4#13070164C211yesmaximal, characteristic, complemented
5#13070011C211yesmaximal, characteristic, complemented
6#13069997C211yesmaximal, characteristic, complemented
7#13069767C211yesmaximal, characteristic, complemented
8#13068884C211yesmaximal, characteristic, complemented
9#13068870C211yesmaximal, characteristic, complemented
10#13068803C211yesmaximal, characteristic
11#13068796C211yesmaximal, characteristic
12#13068639C211yesmaximal, characteristic
13#13068631C211yesmaximal, characteristic, complemented
14#13068551C211yesmaximal, characteristic
15Q8×C11×C22⋊C4C211yesmaximal, characteristic
16C23×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21C2×#66923C2211yescharacteristic
22C11×#391—21no—
23C11×#391—21no—
24C11×#391C2211yescharacteristic
25C11×#391C2211yescharacteristic
26C11×#380—21no—
27C11×#380C2211yescharacteristic
28C4×C11×C22⋊C4—21no—
29C4×C11×C22⋊C4C2211yescharacteristic
30C2×#66899—24no—
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39#10622825C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41#10622635—24no—
42C2×#66872C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622559—21no—
47#10622555—21no—
48#10622549C2211yescharacteristic
49#10622541C2211yescharacteristic
50#10622541C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53#10622273—21no—
54#10622270—21no—
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×Q8×C11—22no—
63C22×Q8×C11—22no—
64C22×Q8×C11—22no—
65C22×Q8×C11—41no—
66C22×Q8×C11—41no—
67C22×Q8×C11Q814yes—
68C22×Q8×C11C2311yescharacteristic
69C22×Q8×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11C2311yescharacteristic
72C23×Dic11—21no—
73C4×Q8×C11—22no—
74C4×Q8×C11—22no—
75C4×Q8×C11—41no—
76C4×Q8×C11—41no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C11×C22⋊C4D411yescharacteristic
84C2×C42×C11—21no—
85C2×C42×C11—21no—
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C22⋊Dic11—21no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—41no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C22×C11⋊C8—22no—
101C22×C11⋊C8—22no—
102C22×C11⋊C8—41no—
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107#66923—22no—
108#66923—41no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95D411yescharacteristic
115C11×#95D411yescharacteristic
116#66899—22no—
117#66899—22no—
118#66899—22no—
119#66899—22no—
120#66899—22no—
121#66899—41no—
122#66899—41no—
123#66899D414yes—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C22⋊(C11⋊C8)—22no—
130#66872—22no—
131#66872—41no—
132#66871—22no—
133#66871—41no—
134C4⋊(C11⋊C8)—22no—
135C4⋊(C11⋊C8)—41no—
136#25957—111nomaximal, Sylow
137C24×C11C2×D411yescharacteristic
138C2×Q8×C11—24no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—28no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—42no—
149C2×Q8×C11—42no—
150C2×Q8×C11—44no—
151C2×Q8×C11—44no—
152C2×Q8×C11—44no—
153C2×Q8×C11C2×D412yes—
154C2×Q8×C11C2×Q812yes—
155C2×Q8×C11C2×Q812yes—
156C2×Q8×C11#4112yes—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—24no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—42no—
167C22×C4×C11—42no—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×Q812yes—
174C22×C4×C11#4112yes—
175C22×C4×C11C2411yescharacteristic
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—42no—
181C22×Dic11—42no—
182C22×Dic11—81no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—42no—
188C11×C4⋊C4—42no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—42no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—42no—
197C42×C11—42no—
198C22⋊Dic11—42no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—42no—
207C4⋊Dic11C2×D412yes—
208Dic11⋊C4—42no—
209Dic11⋊C4—42no—
210Dic11⋊C4—81no—
211Dic11⋊C4—81no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—44no—
224C2×C11⋊C8C2×D412yes—
225C2×#479—111no—
226C22×#103—111no—
227#2442—111no—
228Q8×C22⋊C4D1111yescharacteristic
229#2097—111no—
230#2068—111no—
231#2066—111no—
232#2026—111no—
233#1865—111no—
234#1863—111no—
235#1852—111no—
236#1850—111no—
237#1807—111no—
238#1805—111no—
239#1787—111no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11C22⋊Q812yes—
245C23×C11#13512yes—
246C23×C11#13712yes—
247C23×C11C22×D411yescharacteristic
248Q8×C11—22no—
249Q8×C11—22no—
250Q8×C11—22no—
251Q8×C11—22no—
252Q8×C11—22no—
253Q8×C11—48no—
254Q8×C11—41no—
255Q8×C11—41no—
256Q8×C11C22⋊Q814yes—
257C2×C4×C11—22no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—21no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—48no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11C22⋊Q812yes—
289C2×C4×C11C22×D411yescharacteristic
290C2×C4×C11C22×Q811yescharacteristic
291C2×C4×C11C2×#4111yescharacteristic
292C2×C4×C11C2×#4111yescharacteristic
293C2×C4×C11H(5,𝔽2)11yescharacteristic
294C2×C4×C11H(5,𝔽2)11yescharacteristic
295C2×Dic11—22no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—84no—
308C11⋊C8—22no—
309C11⋊C8—41no—
310C11⋊C8—41no—
311C11⋊C8—41no—
312C23×Q8C2×D1111yescharacteristic
313C23×C8—111no—
314C2×#125—111no—
315C2×C4×Q8C2×D1111yescharacteristic
316C2×C4×Q8C2×D1111yescharacteristic
317C22×C4⋊C4—111no—
318#479—224no—
319C2×#107—111no—
320C2×#107—111no—
321C2×#106—111no—
322C2×#106—111no—
323C2×C4⋊C8—111no—
324C2×C4⋊C8—111no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#103—111no—
328C2×#103—111no—
329C2×#103—111no—
330C2×#103—111no—
331C2×#103—111no—
332C2×#103—111no—
333C2×#103—224no—
334C2×C22⋊C8—111no—
335#400—221no—
336#398—221no—
337#391—21no—
338#391—21no—
339#391C2×D1111yescharacteristic
340#391C2×D1111yescharacteristic
341#389—111no—
342#389—111no—
343#385—221no—
344#382—111no—
345#380—21no—
346#380—111no—
347#380—221no—
348#380C2×D1111yescharacteristic
349C4×C22⋊C4—21no—
350C4×C22⋊C4C2×D1111yescharacteristic
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#336—111no—
356#336—111no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—22no—
363C22×C11#47914yescomplemented
364C22×C11C2×C22⋊Q811yescharacteristic
365C22×C11D4211yescharacteristic
366C22×C11#54611yescharacteristic
367C22×C11C2×#13511yescharacteristic
368C22×C11C2×#13711yescharacteristic
369C22×C11#57711yescharacteristic
370C22×C11#57811yescharacteristic
371C4×C11—22no—
372C4×C11—24no—
373C4×C11—42no—
374C4×C11—41no—
375C4×C11—41no—
376C4×C11—41no—
377C4×C11—41no—
378C4×C11—81no—
379C4×C11—81no—
380C4×C11C2×C22⋊Q811yescharacteristic
381C4×C11#54311yescharacteristic
382C4×C11#54611yescharacteristic
383C4×C11#55111yescharacteristic
384Dic11—42no—
385Dic11—81no—
386Dic11—81no—
387Dic11—81no—
388C22×Q8—22no—
389C22×Q8—21no—
390C22×Q8—22no—
391C22×Q8—22no—
392C22×Q8—41no—
393C22×Q8—41no—
394C22×Q8Dic2214yes—
395C22×Q8C22×D1111yescharacteristic
396C22×Q8C22×D1111yescharacteristic
397C23×C4—21no—
398C23×C4—221no—
399C23×C4C22×D1111yescharacteristic
400C22×C8—111no—
401C22×C8—111no—
402C22×C8—111no—
403C22×C8—111no—
404C22×C8—222no—
405C22×C8—222no—
406C22×C8—441no—
407#125—222no—
408#125—441no—
409C4×Q8—22no—
410C4×Q8—22no—
411C4×Q8—41no—
412C4×Q8—41no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—222no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—441no—
426C2×C4⋊C4C22×D1111yescharacteristic
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4C22⋊D1111yescharacteristic
431C2×C22⋊C4C22⋊D1111yescharacteristic
432C2×C42—21no—
433C2×C42—21no—
434C2×C42C22×D1111yescharacteristic
435C2×C42C22×D1111yescharacteristic
436#107—222no—
437#107—441no—
438#106—222no—
439#106—441no—
440C4⋊C8—222no—
441C4⋊C8—441no—
442#103—114no—
443#103—222no—
444#103—222no—
445#103—222no—
446#103—222no—
447#103—222no—
448#103—441no—
449#103—441no—
450C22⋊C8—222no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95C22⋊D1111yescharacteristic
462#95C22⋊D1111yescharacteristic
463C2×C11—24no—
464C2×C11#243711yescharacteristic
465C2×C11C2×#47911yescharacteristic
466C2×C11#308211yescharacteristic
467C2×C11#327011yescharacteristic
468C2×C11#328211yescharacteristic
469C2×C11#330011yescharacteristic
470C2×C11#332011yescharacteristic
471C24C2×C22⋊D1111yescharacteristic
472C2×Q8—24no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—28no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8C2×Dic2212yes—
488C2×Q8C2×Dic2212yes—
489C2×Q8D4×D1112yes—
490C2×Q8#434112yes—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—24no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—442no—
507C22×C4—442no—
508C22×C4—881no—
509C22×C4C2×Dic2212yes—
510C22×C4#433912yes—
511C22×C4C2×C22⋊D1111yescharacteristic
512C22×C4C2×C22⋊D1111yescharacteristic
513C22×C4C2×C22⋊D1111yescharacteristic
514C22×C4C2×C22⋊D1111yescharacteristic
515C22×C4C2×C22⋊D1111yescharacteristic
516C22×C4C23×D1111yescharacteristic
517C2×C8—112no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—221no—
528C2×C8—221no—
529C2×C8—444no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4—112no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—221no—
543C4⋊C4—221no—
544C4⋊C4—442no—
545C4⋊C4—442no—
546C4⋊C4—442no—
547C4⋊C4—881no—
548C4⋊C4—881no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—42no—
552C22⋊C4—442no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—42no—
558C42—42no—
559C11#2595711yescharacteristic, complemented, Sylow
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23#6697712yes—
565C23#6699512yes—
566C23#6700312yes—
567C23C22×C22⋊D1111yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—22no—
571Q8—22no—
572Q8—22no—
573Q8—48no—
574Q8—41no—
575Q8—41no—
576Q8#6693114yes—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—48no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—222no—
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×C4—441no—
619C2×C4—441no—
620C2×C4—884no—
621C2×C4#6697712yes—
622C2×C4C22×Dic2211yescharacteristic
623C2×C4C2×#433911yescharacteristic
624C2×C4C2×D4×D1111yescharacteristic
625C2×C4C2×#434111yescharacteristic
626C2×C4#6703711yescharacteristic
627C2×C4#6703711yescharacteristic
628C8—222no—
629C8—441no—
630C8—441no—
631C8—441no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22#1062263514yescomplemented
639C22C2×#6697711yescharacteristic
640C22D4×C22⋊D1111yescharacteristic
641C22#1062333711yescharacteristic
642C22C2×#6699511yescharacteristic
643C22C2×#6700311yescharacteristic
644C22#1062336811yescharacteristic
645C22#1062336911yescharacteristic
646C4—22no—
647C4—24no—
648C4—41no—
649C4—41no—
650C4—42no—
651C4—41no—
652C4—41no—
653C4—81no—
654C4—81no—
655C4—442no—
656C4—881no—
657C4—881no—
658C4—881no—
659C4C2×#6693111yescharacteristic
660C4#1062301411yescharacteristic
661C4#1062302111yescharacteristic
662C4#1062302611yescharacteristic
663C2—24no—
664C2#1307227711yescharacteristic
665C2C2×#1062263511yescharacteristic
666C2#1307845811yescharacteristic
667C2#1308018711yescharacteristic
668C2#1308032411yescharacteristic
669C2#1308050311yescharacteristic
670C2#1308078711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingQ8×C11×C22⋊C4C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterQ8×C22⋊C4D11
hypocenterC11#25957
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622635C2semidirect
4. #13070164C2semidirect
5. #13070011C2semidirect
6. #13069997C2semidirect
7. #13069767C2semidirect
8. #13068884C2semidirect
9. #13068870C2semidirect
13. #13068631C2semidirect
363. C22×C11#479semidirect
559. C11#25957semidirect
638. C22#10622635semidirect

Maximal subgroups

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

subgroupindex
C2×#106226352
C22×#668992
#130723402
#130701642
#130700112
#130699972
#130697672
#130688842
#130688702
#130688032
#130687962
#130686392
#130686312
#130685512
Q8×C11×C22⋊C42
#2595711