Finite Group Databasebeta

← #14802082

Subgroups — #14802082

Order 2816.

884 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622657C211yesmaximal, characteristic, complemented
2#13073109C211yesmaximal, characteristic
3#13071625C211yesmaximal, characteristic, complemented
4#13070101C211yesmaximal, characteristic, complemented
5#13070037C211yesmaximal, characteristic, complemented
6#13070000C211yesmaximal, characteristic, complemented
7#13069929C211yesmaximal, characteristic, complemented
8#13069385C211yesmaximal, characteristic, complemented
9#13069239C211yesmaximal, characteristic, complemented
10#13068973C211yesmaximal, characteristic, complemented
11#13068934C211yesmaximal, characteristic
12#13068794C211yesmaximal, characteristic, complemented
13#13068629C211yesmaximal, characteristic, complemented
14C2×#10622189C211yesmaximal, characteristic, complemented
15C2×C11×#465C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C11×#465—24no—
24C2×C11×#106C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27#10622843C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30#10622834C2211yescharacteristic
31#10622834C2211yescharacteristic
32#10622833—21no—
33#10622833—21no—
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C4×C22⋊Dic11C2211yescharacteristic
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40#10622657—24no—
41#10622598—21no—
42#10622598C2211yescharacteristic
43#10622594—21no—
44#10622590C2211yescharacteristic
45#10622590C2211yescharacteristic
46C4⋊C4×Dic11C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49#10622566—21no—
50#10622566—21no—
51#10622563—21no—
52C22⋊C4×Dic11—21no—
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×Dic11—21no—
66C23×Dic11—21no—
67C2×C11×SD16—22no—
68C2×C11×SD16—22no—
69C2×C11×SD16—41no—
70C22×C8×C11—22no—
71C22×C8×C11—22no—
72C22×C8×C11—41no—
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8D414yes—
77C11×#121—22no—
78C11×#121—22no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11D411yescharacteristic
89C2×C22⋊Dic11D411yescharacteristic
90Q8×Dic11—22no—
91Q8×Dic11—41no—
92C2×C4⋊Dic11—22no—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11—22no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—41no—
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11C2311yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C11×#106—22no—
111C11×#103—22no—
112C11×#102—22no—
113#66899—22no—
114#66899—22no—
115#66896—22no—
116#66896—41no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95D411yescharacteristic
126C11⋊#95D411yescharacteristic
127C22⋊(C11⋊C8)—22no—
128Dic11⋊C8—22no—
129Dic11⋊C8—41no—
130#66871—22no—
131#66871—22no—
132#25210—111nomaximal, Sylow
133C24×C11—21no—
134C24×C11C2×D411yescharacteristic
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11C2×D412yes—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—42no—
148C2×D4×C11—42no—
149C2×D4×C11—42no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D412yes—
159C22×C4×C11#4112yes—
160C22×C4×C11C2411yescharacteristic
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—42no—
166C22×Dic11—42no—
167C22×Dic11—42no—
168C22×Dic11—81no—
169C22×Dic11—81no—
170C22×Dic11—81no—
171C22×Dic11C2×D411yescharacteristic
172C22×Dic11C2×D411yescharacteristic
173C22×Dic11C2×D411yescharacteristic
174C22×Dic11C2×D411yescharacteristic
175C11×SD16—44no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—44no—
182C2×C8×C11#4112yes—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4C2×D412yes—
188C11×C22⋊C4—24no—
189C11×C22⋊C4—42no—
190C22⋊Dic11—22no—
191C22⋊Dic11—22no—
192C22⋊Dic11—81no—
193C22⋊Dic11—81no—
194C22⋊Dic11—81no—
195C22⋊Dic11—81no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—42no—
204C4⋊Dic11—42no—
205C4⋊Dic11—42no—
206C4⋊Dic11—81no—
207C4⋊Dic11#4112yes—
208C4×Dic11—21no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C4×Dic11—21no—
212C4×Dic11—42no—
213C4×Dic11—81no—
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×#484—111no—
221C2×#465D1111yescharacteristic
222#2504—111no—
223#2360—111no—
224#2085—111no—
225#2074—111no—
226#2067—111no—
227#2055—111no—
228#1949—111no—
229#1925—111no—
230#1880—111no—
231#1874—111no—
232#1850—111no—
233#1805—111no—
234C2×#340—111no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11#12112yes—
247C23×C11#13512yes—
248C23×C11#13712yes—
249C23×C11C22×D411yescharacteristic
250Q8×C11—22no—
251Q8×C11—22no—
252Q8×C11—41no—
253Q8×C11—41no—
254D4×C11—41no—
255D4×C11—41no—
256D4×C11—41no—
257D4×C11—41no—
258D4×C11—84no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11#12112yes—
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11H(5,𝔽2)11yescharacteristic
280C2×C4×C112−1+411yescharacteristic
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—22no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—41no—
295C2×Dic11—41no—
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—84no—
306C2×Dic11—84no—
307C8×C11—22no—
308C8×C11—41no—
309C11⋊C8—41no—
310C11⋊C8—41no—
311C22×SD16C2×D1111yescharacteristic
312C23×C8C2×D1111yescharacteristic
313C2×C22⋊Q8C2×D1111yescharacteristic
314C2×#121C2×D1111yescharacteristic
315C2×C4×Q8—111no—
316C22×C4⋊C4—111no—
317C22×C4⋊C4—111no—
318#484—224no—
319#465—24no—
320C2×#107—111no—
321C2×#107—111no—
322C2×#106C2×D1111yescharacteristic
323C2×C4⋊C8—111no—
324C2×C4⋊C8—111no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#103C2×D1111yescharacteristic
328C2×#102—111no—
329C2×#102—111no—
330C2×#102C2×D1111yescharacteristic
331C2×C22⋊C8—111no—
332#397—221no—
333#397—221no—
334#391—111no—
335#390—111no—
336#390—111no—
337#389—111no—
338#389—221no—
339#387—221no—
340#386—221no—
341#386—221no—
342#385—221no—
343#382—111no—
344#382—111no—
345C4×C4⋊C4—111no—
346C4×C22⋊C4—111no—
347C4×C22⋊C4—221no—
348#340—111no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#336—111no—
355#336—111no—
356C22×C11—22no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—81no—
363C22×C11—81no—
364C22×C11—81no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11#46414yes—
370C22×C11C2×#12111yescharacteristic
371C22×C11#54611yescharacteristic
372C22×C11#54711yescharacteristic
373C22×C11C2×#13511yescharacteristic
374C22×C11C2×#13711yescharacteristic
375C22×C11#57611yescharacteristic
376C22×C11#57711yescharacteristic
377C4×C11—22no—
378C4×C11—42no—
379C4×C11—42no—
380C4×C11—81no—
381C4×C11#52911yescharacteristic
382C4×C11#53911yescharacteristic
383C4×C11#54611yescharacteristic
384C4×C11#54711yescharacteristic
385Dic11—41no—
386Dic11—41no—
387Dic11—41no—
388Dic11—42no—
389Dic11—41no—
390Dic11—81no—
391Dic11—81no—
392Dic11—81no—
393C22×Q8C22×D1111yescharacteristic
394C22×D4—21no—
395C22×D4C22×D1111yescharacteristic
396C23×C4—221no—
397C23×C4—221no—
398C23×C4C22×D1111yescharacteristic
399C2×SD16—22no—
400C2×SD16—22no—
401C2×SD16—41no—
402C22×C8—22no—
403C22×C8—22no—
404C22×C8—41no—
405C22×C8—111no—
406C22×C8—111no—
407C22×C8C22×D1111yescharacteristic
408C22×C8C22×D1111yescharacteristic
409C22⋊Q8—22no—
410C22⋊Q8C22⋊D1114yes—
411#121—22no—
412#121—22no—
413C4×Q8—222no—
414C4×Q8—441no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—222no—
421C2×C4⋊C4—222no—
422C2×C4⋊C4—222no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—441no—
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C4⋊C4C22×D1111yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—111no—
433C2×C22⋊C4—111no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C42—111no—
439C2×C42—111no—
440C2×C42—221no—
441C2×C42—221no—
442#107—222no—
443#107—222no—
444#106—22no—
445C4⋊C8—222no—
446C4⋊C8—441no—
447#103—22no—
448#103—222no—
449#103—222no—
450#102—22no—
451#102—222no—
452#102—441no—
453C22⋊C8—222no—
454#95—111no—
455#95—111no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462#95—221no—
463#95—221no—
464C2×C11—24no—
465C2×C11—161no—
466C2×C11#242511yescharacteristic
467C2×C11C2×#46411yescharacteristic
468C2×C11#304511yescharacteristic
469C2×C11#329711yescharacteristic
470C2×C11#332011yescharacteristic
471C2×C11#333711yescharacteristic
472C2×C11#334611yescharacteristic
473C24—21no—
474C24D4×D1111yescharacteristic
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8C2×C22⋊D1112yes—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4—42no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—111no—
498C22×C4—111no—
499C22×C4—111no—
500C22×C4—111no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—442no—
506C22×C4—442no—
507C22×C4—442no—
508C22×C4—881no—
509C22×C4—881no—
510C22×C4—881no—
511C22×C4D4×D1111yescharacteristic
512C22×C4#434112yes—
513C22×C4C2×C22⋊D1112yes—
514C22×C4C23×D1111yescharacteristic
515SD16—44no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—44no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—221no—
528C2×C8#434112yes—
529C4⋊C4—24no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—112no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—442no—
542C4⋊C4—442no—
543C4⋊C4—442no—
544C4⋊C4—881no—
545C4⋊C4C2×C22⋊D1112yes—
546C22⋊C4—24no—
547C22⋊C4—42no—
548C22⋊C4—222no—
549C22⋊C4—222no—
550C22⋊C4—881no—
551C22⋊C4—881no—
552C22⋊C4—881no—
553C22⋊C4—881no—
554C42—221no—
555C42—221no—
556C42—221no—
557C42—221no—
558C42—442no—
559C42—881no—
560C11#2521011yescharacteristic, complemented, Sylow
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23#6696812yes—
573C23#6696912yes—
574C23#6699212yes—
575C23C2×D4×D1111yescharacteristic
576Q8—22no—
577Q8—22no—
578Q8—41no—
579Q8—41no—
580D4—41no—
581D4—41no—
582D4—41no—
583D4—41no—
584D4—84no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—221no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—221no—
610C2×C4—222no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—884no—
625C2×C4—884no—
626C2×C4#6699212yes—
627C2×C4C2×#434111yescharacteristic
628C2×C4C2×#434111yescharacteristic
629C2×C4#6703711yescharacteristic
630C2×C4#41×D1111yescharacteristic
631C2×C4#6704311yescharacteristic
632C2×C4C22×C22⋊D1111yescharacteristic
633C8—22no—
634C8—41no—
635C8—441no—
636C8—441no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22#1062277914yes—
651C22#1062314111yescharacteristic
652C22#1062314211yescharacteristic
653C22C2×#6696811yescharacteristic
654C22C2×#6696911yescharacteristic
655C22#1062330011yescharacteristic
656C22#1062330111yescharacteristic
657C22C2×#6699211yescharacteristic
658C4—22no—
659C4—42no—
660C4—42no—
661C4—81no—
662C4—441no—
663C4—441no—
664C4—442no—
665C4—441no—
666C4—441no—
667C4—881no—
668C4—881no—
669C4—881no—
670C4#1062313111yescharacteristic
671C4#1062313311yescharacteristic
672C4#1062333711yescharacteristic
673C4#1062335511yescharacteristic
674C2—24no—
675C2—161no—
676C2#1307217311yescharacteristic
677C2C2×#1062277911yescharacteristic
678C2#1307815311yescharacteristic
679C2#1308047211yescharacteristic
680C2#1308079311yescharacteristic
681C2#1308100111yescharacteristic
682C2#1308110711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#465C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenterC2×#465D11
hypocenterC11#25210
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#10622657C2semidirect
3. #13071625C2semidirect
4. #13070101C2semidirect
5. #13070037C2semidirect
6. #13070000C2semidirect
7. #13069929C2semidirect
8. #13069385C2semidirect
9. #13069239C2semidirect
10. #13068973C2semidirect
12. #13068794C2semidirect
13. #13068629C2semidirect
14. C2×#10622189C2semidirect
560. C11#25210semidirect

Maximal subgroups

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

subgroupindex
C2×#106226572
#130731092
#130716252
#130701012
#130700372
#130700002
#130699292
#130693852
#130692392
#130689732
#130689342
#130687942
#130686292
C2×#106221892
C2×C11×#4652
#2521011