Finite Group Databasebeta

← #14823207

Subgroups — #14823207

Order 2816.

848 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622336C211yesmaximal, characteristic, complemented
2C2×#10622374C211yesmaximal, characteristic, complemented
3#13072986C211yesmaximal, characteristic, complemented
4#13071658C211yesmaximal, characteristic
5#13070006C211yesmaximal, characteristic, complemented
6#13069943C211yesmaximal, characteristic, complemented
7#13069619C211yesmaximal, characteristic
8#13069498C211yesmaximal, characteristic, complemented
9#13069248C211yesmaximal, characteristic, complemented
10#13069238C211yesmaximal, characteristic, complemented
11#13069232C211yesmaximal, characteristic, complemented
12#13068948C211yesmaximal, characteristic, complemented
13#13068813C211yesmaximal, characteristic, complemented
14#13068515C211yesmaximal, characteristic, complemented
15C11×#2033C211yesmaximal, characteristic
16C2×C11×#121C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C22×#4324C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C2×#66977C2211yescharacteristic
21C2×#66941C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C11×#380C2211yescharacteristic
27#10622834—21no—
28#10622834C2211yescharacteristic
29#10622833—21no—
30C2×#66896C2211yescharacteristic
31C4×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66879C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39#10622598C2211yescharacteristic
40C4⋊C4×Dic11C2211yescharacteristic
41C4⋊C4×Dic11C2211yescharacteristic
42#10622587C2211yescharacteristic
43#10622587C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47#10622564—21no—
48#10622560—21no—
49#10622557—21no—
50C22⋊C4×Dic11—21no—
51#10622374—24no—
52#10622336—24no—
53#10622271—21no—
54#10622259—21no—
55C11×#340C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11—21no—
65C22×Dic22—21no—
66C22×Dic22C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×#121—22no—
70C11×#121—22no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11D411yescharacteristic
82C2×C22⋊Dic11D411yescharacteristic
83D4×Dic11—22no—
84D4×Dic11—41no—
85C2×#4324—22no—
86C2×#4324—22no—
87C2×#4324—41no—
88#66979—22no—
89#66979—41no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94#66977—22no—
95#66977—41no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11C2311yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105#66941—22no—
106#66941—41no—
107C11×#107—22no—
108C11×#102—22no—
109C11×#102—22no—
110C11×C22⋊C8—22no—
111C11×#95—21no—
112#66896—22no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95D411yescharacteristic
121C11⋊#95D411yescharacteristic
122C22⋊(C11⋊C8)—22no—
123#66882—22no—
124#66881D414yescomplemented
125#66880—22no—
126#66880—22no—
127#66879—22no—
128Dic11⋊C8—22no—
129#66874—22no—
130#66872—22no—
131#66871—41no—
132#26814—111nomaximal, Sylow
133C24×C11—21no—
134C24×C11C2×D411yescharacteristic
135C2×D4×C11—24no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—81no—
142C2×D4×C11—81no—
143C2×D4×C11#4112yes—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—42no—
160C22×Dic11—42no—
161C22×Dic11—81no—
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—42no—
173C2×Dic22—42no—
174C2×Dic22—81no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11C2×D412yes—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4#4112yes—
187C11×C22⋊C4—24no—
188C11×C22⋊C4—81no—
189C22⋊Dic11—22no—
190C22⋊Dic11—41no—
191C22⋊Dic11—42no—
192C22⋊Dic11—42no—
193C22⋊Dic11—42no—
194C22⋊Dic11—42no—
195C22⋊Dic11—81no—
196#4324—44no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—81no—
202C4⋊Dic11C2×D412yes—
203C4⋊Dic11C2×D412yes—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—21no—
210C4×Dic11—42no—
211C4×Dic11—81no—
212C4×Dic11—81no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8#4112yes—
219C2×#485—111no—
220C2×#476—111no—
221#2492—111no—
222#2363—111no—
223#2068—111no—
224#2057—111no—
225#2033D1111yescharacteristic
226#2000—111no—
227#1973—111no—
228#1927—111no—
229#1925—111no—
230#1924—111no—
231#1877—111no—
232#1854—111no—
233#1776—111no—
234C23×C11—22no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11C22×D411yescharacteristic
249D4×C11—22no—
250D4×C11—22no—
251D4×C11—41no—
252D4×C11—41no—
253D4×C11—84no—
254C2×C4×C11—21no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11H(5,𝔽2)11yescharacteristic
275C2×C4×C112−1+411yescharacteristic
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
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—84no—
300C2×Dic11#13712yes—
301Dic22—41no—
302Dic22—41no—
303Dic22—41no—
304Dic22—41no—
305Dic22—84no—
306C8×C11—22no—
307C8×C11—41no—
308C11⋊C8—22no—
309C11⋊C8—41no—
310C22×SD16—111no—
311C2×C4⋊Q8—111no—
312C2×C22⋊Q8—111no—
313C2×#121C2×D1111yescharacteristic
314C2×C4×D4—111no—
315C2×#117—111no—
316#485—224no—
317#476—224no—
318C2×#107—111no—
319C2×#107—111no—
320C2×#107C2×D1111yescharacteristic
321C2×#106—111no—
322C2×#106—111no—
323C2×C4⋊C8—111no—
324C2×#103—111no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#102—111no—
328C2×#102C2×D1111yescharacteristic
329C2×#102C2×D1111yescharacteristic
330C2×C22⋊C8—111no—
331C2×C22⋊C8C2×D1111yescharacteristic
332C2×#97—111no—
333#400—221no—
334#393—221no—
335#391—111no—
336#391—111no—
337#391—221no—
338#390—111no—
339#390—221no—
340#389—111no—
341#388—221no—
342#388—221no—
343#386—221no—
344#380C2×D1111yescharacteristic
345C4×C4⋊C4—111no—
346C4×C4⋊C4—111no—
347C4×C22⋊C4—111no—
348C4×C22⋊C4—221no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340C2×D1111yescharacteristic
353#336—111no—
354#336—111no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—42no—
359C22×C11—41no—
360C22×C11—42no—
361C22×C11—41no—
362C22×C11—42no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11#52511yescharacteristic
370C22×C11D4211yescharacteristic
371C22×C11#54711yescharacteristic
372C22×C11C2×#13711yescharacteristic
373C22×C11#57511yescharacteristic
374C22×C11#57611yescharacteristic
375C22×C11#57711yescharacteristic
376C4×C11—42no—
377C4×C11—41no—
378C4×C11—81no—
379C4×C11—81no—
380C4×C11#53211yescharacteristic
381C4×C11#54211yescharacteristic
382C4×C11#54811yescharacteristic
383C4×C11#55111yescharacteristic
384Dic11—22no—
385Dic11—41no—
386Dic11—41no—
387Dic11—42no—
388Dic11—41no—
389Dic11—42no—
390Dic11—81no—
391Dic11—81no—
392C22×Q8—111no—
393C22×Q8—221no—
394C22×D4—21no—
395C22×D4C22×D1111yescharacteristic
396C23×C4—221no—
397C23×C4C22×D1111yescharacteristic
398C2×SD16—222no—
399C2×SD16—222no—
400C2×SD16—441no—
401C22×C8—111no—
402C22×C8—111no—
403C22×C8C22×D1111yescharacteristic
404C22×C8C22×D1111yescharacteristic
405C4⋊Q8—222no—
406C4⋊Q8—441no—
407C22⋊Q8—222no—
408C22⋊Q8—441no—
409#121—22no—
410#121—22no—
411C4×D4—222no—
412C4×D4—441no—
413#117—222no—
414#117—441no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C4⋊C4C22×D1111yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—111no—
427C2×C22⋊C4—111no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C42—111no—
434C2×C42—111no—
435C2×C42—221no—
436C2×C42—221no—
437C2×C42—221no—
438#107—22no—
439#107—222no—
440#107—441no—
441#106—114no—
442#106—222no—
443C4⋊C8—222no—
444#103—222no—
445#103—222no—
446#103—222no—
447#102—22no—
448#102—22no—
449#102—222no—
450C22⋊C8—22no—
451C22⋊C8—222no—
452#97—222no—
453#95—21no—
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—
463C2×C11—81no—
464C2×C11—82no—
465C2×C11#246111yescharacteristic
466C2×C11#311611yescharacteristic
467C2×C11#311811yescharacteristic
468C2×C11#326611yescharacteristic
469C2×C11#326811yescharacteristic
470C2×C11#335011yescharacteristic
471C2×C11#335711yescharacteristic
472C24—21no—
473C24D4×D1111yescharacteristic
474C2×Q8—221no—
475C2×Q8—221no—
476C2×Q8—221no—
477C2×Q8—221no—
478C2×Q8—221no—
479C2×Q8—221no—
480C2×Q8—442no—
481C2×Q8—442no—
482C2×Q8—881no—
483C2×D4—24no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—81no—
490C2×D4—81no—
491C2×D4#434112yes—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—111no—
502C22×C4—111no—
503C22×C4—111no—
504C22×C4—111no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—442no—
510C22×C4—442no—
511C22×C4—881no—
512C22×C4D4×D1111yescharacteristic
513C22×C4C23×D1111yescharacteristic
514SD16—444no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—112no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8D4×D1112yes—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—112no—
533C4⋊C4—112no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—442no—
539C4⋊C4—442no—
540C4⋊C4—881no—
541C4⋊C4#434112yes—
542C22⋊C4—24no—
543C22⋊C4—81no—
544C22⋊C4—222no—
545C22⋊C4—441no—
546C22⋊C4—442no—
547C22⋊C4—442no—
548C22⋊C4—442no—
549C22⋊C4—442no—
550C22⋊C4—881no—
551C42—221no—
552C42—221no—
553C42—221no—
554C42—221no—
555C42—442no—
556C42—881no—
557C42—881no—
558C11#2681411yescharacteristic, complemented, Sylow
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—22no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23C2×D4×D1111yescharacteristic
574Q8—441no—
575Q8—441no—
576Q8—441no—
577Q8—441no—
578Q8—884no—
579D4—22no—
580D4—22no—
581D4—41no—
582D4—41no—
583D4—84no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—112no—
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—222no—
612C2×C4—221no—
613C2×C4—221no—
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×C4C2×D4×D1111yescharacteristic
626C2×C4C2×#434111yescharacteristic
627C2×C4C2×#434111yescharacteristic
628C2×C4#41×D1111yescharacteristic
629C2×C4#6704211yescharacteristic
630C2×C4#6704311yescharacteristic
631C8—22no—
632C8—41no—
633C8—222no—
634C8—441no—
635C22—41no—
636C22—42no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—42no—
643C22—41no—
644C22—42no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22#1062311711yescharacteristic
650C22#1062314011yescharacteristic
651C22#1062318611yescharacteristic
652C22#1062328811yescharacteristic
653C22#1062329911yescharacteristic
654C22#1062330611yescharacteristic
655C22D11×#13711yescharacteristic
656C4—42no—
657C4—41no—
658C4—81no—
659C4—81no—
660C4—222no—
661C4—442no—
662C4—441no—
663C4—441no—
664C4—442no—
665C4—441no—
666C4—881no—
667C4—881no—
668C4#1062312711yescharacteristic
669C4#1062312911yescharacteristic
670C4#1062318911yescharacteristic
671C4#1062321311yescharacteristic
672C2—81no—
673C2—82no—
674C2#1307257611yescharacteristic
675C2#1307877111yescharacteristic
676C2#1307879311yescharacteristic
677C2#1308013311yescharacteristic
678C2#1308015311yescharacteristic
679C2#1308116511yescharacteristic
680C2#1308123511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2033C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#2033D11
hypocenterC11#26814
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2033

Complements

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

NH ≅ G/Ntype
1. C2×#10622336C2semidirect
2. C2×#10622374C2semidirect
3. #13072986C2semidirect
5. #13070006C2semidirect
6. #13069943C2semidirect
8. #13069498C2semidirect
9. #13069248C2semidirect
10. #13069238C2semidirect
11. #13069232C2semidirect
12. #13068948C2semidirect
13. #13068813C2semidirect
14. #13068515C2semidirect
124. #66881D4semidirect
558. C11#26814semidirect

Maximal subgroups

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

subgroupindex
C2×#106223362
C2×#106223742
#130729862
#130716582
#130700062
#130699432
#130696192
#130694982
#130692482
#130692382
#130692322
#130689482
#130688132
#130685152
C11×#20332
#2681411