Finite Group Databasebeta

← #14813703

Subgroups — #14813703

Order 2816.

854 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×#10622734C211yesmaximal, characteristic, complemented
3#13072067C211yesmaximal, characteristic
4#13071565C211yesmaximal, characteristic
5#13070158C211yesmaximal, characteristic, complemented
6#13070094C211yesmaximal, characteristic, complemented
7#13070049C211yesmaximal, characteristic, complemented
8#13069813C211yesmaximal, characteristic, complemented
9#13069258C211yesmaximal, characteristic, complemented
10#13069209C211yesmaximal, characteristic, complemented
11#13069049C211yesmaximal, characteristic, complemented
12#13068926C211yesmaximal, characteristic, complemented
13#13068817C211yesmaximal, characteristic, complemented
14#13068811C211yesmaximal, characteristic, complemented
15C11×#1870C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C2×#66977C2211yescharacteristic
22C2×#66977C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26#10622834—21no—
27#10622833—21no—
28#10622825C2211yescharacteristic
29#10622825C2211yescharacteristic
30#10622825C2211yescharacteristic
31#10622734—24no—
32C2×#66882C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×#66881C2211yescharacteristic
36C2×#66881C2211yescharacteristic
37C2×#66881C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39C2×#66880C2211yescharacteristic
40C2×#66880C2211yescharacteristic
41C2×#66880C2211yescharacteristic
42#10622597—21no—
43C4⋊C4×Dic11—21no—
44#10622564—21no—
45#10622564—21no—
46#10622561—21no—
47#10622555—21no—
48#10622548C2211yescharacteristic
49C4×C4⋊Dic11C2211yescharacteristic
50#10622542C2211yescharacteristic
51#10622541C2211yescharacteristic
52#10622336—24no—
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C22×D4×C11D411yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11—21no—
65C22×Dic22C2311yescharacteristic
66C2×C11×M16—22no—
67C2×C11×M16—22no—
68C2×C11×M16—22no—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C22⋊C4D411yescharacteristic
77C2×C11×C22⋊C4D411yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86#66979—22no—
87#66979—22no—
88#66979—41no—
89#66979—41no—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—41no—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102#66977—22no—
103#66977—22no—
104#66977—22no—
105#66977—41no—
106C2×Dic11⋊C4—21no—
107C2×Dic11⋊C4—21no—
108C2×Dic11⋊C4—21no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11—21no—
112C11×C22⋊C8—22no—
113C11×C22⋊C8—22no—
114C11×C22⋊C8—22no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122#66882—22no—
123#66882D414yescomplemented
124#66881—22no—
125#66881—22no—
126#66881—22no—
127#66881—41no—
128#66880—22no—
129#66880—22no—
130#66880—22no—
131#66880—41no—
132#26155—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C24×C11C2×D411yescharacteristic
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—41no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11#4112yes—
153C22×C4×C11#4112yes—
154C22×C4×C11C2411yescharacteristic
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—42no—
164C22×Dic11—42no—
165C22×Dic11—81no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C11×M16—28no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11C2×D412yes—
184C2×C8×C11#4112yes—
185C11×C4⋊C4—22no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C42×C11—21no—
189C42×C11—21no—
190C22⋊Dic11—42no—
191C22⋊Dic11—42no—
192C22⋊Dic11—42no—
193C22⋊Dic11—42no—
194C22⋊Dic11—81no—
195C22⋊Dic11—81no—
196C22⋊Dic11—81no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—42no—
210C4⋊Dic11—42no—
211C4⋊Dic11—81no—
212C4⋊Dic11C2×D412yes—
213C4⋊Dic11C2×D412yes—
214Dic11⋊C4—42no—
215Dic11⋊C4—42no—
216Dic11⋊C4—81no—
217C4×Dic11—42no—
218C4×Dic11—42no—
219C4×Dic11—42no—
220C2×#485—111no—
221C2×#428—111no—
222#2417—111no—
223#2354—111no—
224#2096—111no—
225#2084—111no—
226#2077—111no—
227#2035—111no—
228#1928—111no—
229#1921—111no—
230#1894—111no—
231#1873—111no—
232#1870D1111yescharacteristic
233#1854—111no—
234#1853—111no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11#12312yes—
249C23×C11C22×D411yescharacteristic
250D4×C11—44no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
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—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11#12312yes—
270C2×C4×C11#13712yes—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11H(5,𝔽2)11yescharacteristic
276C2×C4×C112−1+411yescharacteristic
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
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—
300C2×Dic11—41no—
301C2×Dic11—84no—
302Dic22—41no—
303Dic22—41no—
304Dic22—41no—
305Dic22—41no—
306C8×C11—22no—
307C8×C11—22no—
308C8×C11—41no—
309C8×C11—41no—
310C22×M16C2×D1111yescharacteristic
311C2×C22⋊Q8—111no—
312C2×C22⋊Q8—111no—
313C2×C4×D4C2×D1111yescharacteristic
314C2×#117—111no—
315C2×#117—111no—
316C22×C4⋊C4—111no—
317#485—224no—
318#428—224no—
319C2×#107—111no—
320C2×#107—111no—
321C2×#106—111no—
322C2×#106—111no—
323C2×#106—111no—
324C2×#106—111no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#103—111no—
328C2×#103—111no—
329C2×C22⋊C8C2×D1111yescharacteristic
330C2×C22⋊C8C2×D1111yescharacteristic
331C2×C22⋊C8C2×D1111yescharacteristic
332#398—221no—
333#396—221no—
334#391—111no—
335#390—221no—
336#389—111no—
337#388—221no—
338#388—221no—
339#386—221no—
340#384—111no—
341#380—111no—
342#380—111no—
343#380—111no—
344#380—221no—
345C4×C4⋊C4—111no—
346C4×C4⋊C4—221no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#336C2×D1111yescharacteristic
354#336C2×D1111yescharacteristic
355C22×C11—22no—
356C22×C11—22no—
357C22×C11—22no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11C2×#12311yescharacteristic
370C22×C11D4211yescharacteristic
371C22×C11#54711yescharacteristic
372C22×C11C2×#13711yescharacteristic
373C22×C11#57511yescharacteristic
374C22×C11#57711yescharacteristic
375C22×C11#57711yescharacteristic
376C4×C11—22no—
377C4×C11—22no—
378C4×C11—41no—
379C4×C11—41no—
380C4×C11#52511yescharacteristic
381C4×C11#53911yescharacteristic
382C4×C11#54811yescharacteristic
383C4×C11#55311yescharacteristic
384Dic11—42no—
385Dic11—42no—
386Dic11—81no—
387Dic11—81no—
388Dic11—81no—
389Dic11—81no—
390Dic11—81no—
391Dic11—81no—
392C22×Q8—111no—
393C22×D4D4411yescharacteristic
394C23×C4—221no—
395C23×C4C22×D1111yescharacteristic
396C23×C4C22×D1111yescharacteristic
397C2×M16—22no—
398C2×M16—22no—
399C2×M16—22no—
400C22×C8C22×D1111yescharacteristic
401C22×C8C22×D1111yescharacteristic
402C22×C8C22×D1111yescharacteristic
403C22×C8C22×D1111yescharacteristic
404C22⋊Q8—222no—
405C22⋊Q8—222no—
406C22⋊Q8—222no—
407C22⋊Q8—441no—
408C4×D4—22no—
409C4×D4—22no—
410#117—222no—
411#117—222no—
412#117—441no—
413#117—441no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—222no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—441no—
429C2×C4⋊C4D4411yescharacteristic
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4D4411yescharacteristic
438C2×C22⋊C4D4411yescharacteristic
439C2×C42—221no—
440C2×C42—221no—
441C2×C42—221no—
442C2×C42C22×D1111yescharacteristic
443#107—114no—
444#107—222no—
445#106—222no—
446#106—222no—
447#106—222no—
448#106—441no—
449#103—222no—
450#103—222no—
451#103—222no—
452#103—441no—
453C22⋊C8—22no—
454C22⋊C8—22no—
455C22⋊C8—22no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462#95—221no—
463C2×C11—42no—
464C2×C11—81no—
465C2×C11#244311yescharacteristic
466C2×C11#309511yescharacteristic
467C2×C11#309911yescharacteristic
468C2×C11#326711yescharacteristic
469C2×C11#327811yescharacteristic
470C2×C11#334811yescharacteristic
471C2×C11#335611yescharacteristic
472C24C2×D4411yescharacteristic
473C24C2×D4411yescharacteristic
474C2×Q8—221no—
475C2×Q8—221no—
476C2×Q8—221no—
477C2×Q8—221no—
478C2×Q8—221no—
479C2×Q8—221no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—41no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—442no—
502C22×C4—442no—
503C22×C4—881no—
504C22×C4C2×D4411yescharacteristic
505C22×C4C2×D4411yescharacteristic
506C22×C4C2×D4411yescharacteristic
507C22×C4C2×D4411yescharacteristic
508C22×C4#434112yes—
509C22×C4#434112yes—
510C22×C4C23×D1111yescharacteristic
511M16—28no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8D4×D1112yes—
523C2×C8#434112yes—
524C4⋊C4—22no—
525C4⋊C4—112no—
526C4⋊C4—112no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—442no—
540C4⋊C4—442no—
541C4⋊C4—442no—
542C4⋊C4—442no—
543C4⋊C4—881no—
544C4⋊C4—881no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—442no—
548C22⋊C4—442no—
549C22⋊C4—442no—
550C22⋊C4—442no—
551C22⋊C4—881no—
552C22⋊C4—881no—
553C22⋊C4—881no—
554C42—21no—
555C42—21no—
556C42—442no—
557C42—442no—
558C42—442no—
559C11#2615511yescharacteristic, complemented, Sylow
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23#6693912yes—
574C23C22×D4411yescharacteristic
575Q8—441no—
576Q8—441no—
577Q8—441no—
578Q8—441no—
579D4—44no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
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×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—884no—
623C2×C4#6693912yes—
624C2×C4#6696212yes—
625C2×C4C2×D4×D1111yescharacteristic
626C2×C4C2×#434111yescharacteristic
627C2×C4C2×#434111yescharacteristic
628C2×C4C2×#434111yescharacteristic
629C2×C4#6704211yescharacteristic
630C2×C4#6704311yescharacteristic
631C8—22no—
632C8—22no—
633C8—41no—
634C8—41no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22C2×#6693911yescharacteristic
650C22D4×D4411yescharacteristic
651C22#1062308611yescharacteristic
652C22C2×#6696211yescharacteristic
653C22#1062327911yescharacteristic
654C22#1062328211yescharacteristic
655C22#1062328211yescharacteristic
656C4—22no—
657C4—22no—
658C4—41no—
659C4—41no—
660C4—442no—
661C4—442no—
662C4—881no—
663C4—881no—
664C4—881no—
665C4—881no—
666C4—881no—
667C4—881no—
668C4#1062311711yescharacteristic
669C4#1062312911yescharacteristic
670C4#1062314911yescharacteristic
671C4#1062319611yescharacteristic
672C2—42no—
673C2—81no—
674C2#1307234911yescharacteristic
675C2#1307856511yescharacteristic
676C2#1307860711yescharacteristic
677C2#1308014611yescharacteristic
678C2#1308028411yescharacteristic
679C2#1308113311yescharacteristic
680C2#1308123211yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1870C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#1870D11
hypocenterC11#26155
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1870

Complements

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

NH ≅ G/Ntype
1. C2×#10622336C2semidirect
2. C2×#10622734C2semidirect
5. #13070158C2semidirect
6. #13070094C2semidirect
7. #13070049C2semidirect
8. #13069813C2semidirect
9. #13069258C2semidirect
10. #13069209C2semidirect
11. #13069049C2semidirect
12. #13068926C2semidirect
13. #13068817C2semidirect
14. #13068811C2semidirect
123. #66882D4semidirect
559. C11#26155semidirect

Maximal subgroups

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

subgroupindex
C2×#106223362
C2×#106227342
#130720672
#130715652
#130701582
#130700942
#130700492
#130698132
#130692582
#130692092
#130690492
#130689262
#130688172
#130688112
C11×#18702
#2615511