Finite Group Databasebeta

← #14814378

Subgroups — #14814378

Order 2816.

874 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
1#13072067C211yesmaximal, characteristic
2D4×C4⋊Dic11C211yesmaximal, characteristic
3#13070175C211yesmaximal, characteristic, complemented
4#13070049C211yesmaximal, characteristic, complemented
5#13070026C211yesmaximal, characteristic, complemented
6#13069813C211yesmaximal, characteristic, complemented
7#13069251C211yesmaximal, characteristic, complemented
8#13069202C211yesmaximal, characteristic, complemented
9#13069039C211yesmaximal, characteristic, complemented
10#13068921C211yesmaximal, characteristic, complemented
11#13068921C211yesmaximal, characteristic, complemented
12#13068811C211yesmaximal, characteristic, complemented
13#13068703C211yesmaximal, characteristic, complemented
14C2×#10622189C211yesmaximal, characteristic, complemented
15C11×#1869C211yesmaximal, characteristic
16C23×C8×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×D4×Dic11—21no—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C2×#66977C2211yescharacteristic
23C2×#66977C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622833—21no—
28#10622825C2211yescharacteristic
29#10622825C2211yescharacteristic
30#10622825C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37#10622598—21no—
38#10622597—21no—
39#10622563—21no—
40#10622563—21no—
41#10622561—21no—
42#10622555—21no—
43#10622548C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622541C2211yescharacteristic
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49#10622189C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59C22×D4×C11D411yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C23×Dic11—21no—
64C23×Dic11—21no—
65C22×Dic22C2311yescharacteristic
66C22×C8×C11—22no—
67C22×C8×C11—41no—
68C22×C8×C11—41no—
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—
84D4×Dic11—44no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—41no—
94C2×C4⋊Dic11—41no—
95C2×C4⋊Dic11—41no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103#66977—22no—
104#66977—22no—
105#66977—22no—
106#66977—41no—
107C2×Dic11⋊C4—21no—
108C2×Dic11⋊C4—21no—
109C2×Dic11⋊C4—21no—
110C2×C4×Dic11—21no—
111C11×C22⋊C8—22no—
112C11×C22⋊C8—41no—
113C11×C22⋊C8—41no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121#66881—22no—
122#66881—41no—
123#66880—22no—
124#66880—41no—
125#66880—41no—
126#66880—41no—
127#26200—111nomaximal, Sylow
128C24×C11C2×D411yescharacteristic
129C24×C11C2×D411yescharacteristic
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11SD1614yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11#4112yes—
148C22×C4×C11#4112yes—
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—42no—
159C22×Dic11—42no—
160C22×Dic11—42no—
161C22×Dic11—42no—
162C22×Dic11—42no—
163C22×Dic11—42no—
164C22×Dic11—81no—
165C22×Dic11—81no—
166C22×Dic11—81no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
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×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—44no—
186C11×C4⋊C4—22no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C42×C11—21no—
190C42×C11—21no—
191C22⋊Dic11—42no—
192C22⋊Dic11—42no—
193C22⋊Dic11—42no—
194C22⋊Dic11—42no—
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—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—42no—
209C4⋊Dic11—42no—
210C4⋊Dic11—42no—
211C4⋊Dic11—42no—
212C4⋊Dic11—81no—
213C4⋊Dic11#4112yes—
214C4⋊Dic11#4112yes—
215Dic11⋊C4—42no—
216Dic11⋊C4—42no—
217Dic11⋊C4—81no—
218C4×Dic11—42no—
219#2417—111no—
220D4×C4⋊C4—111no—
221#2099—111no—
222#2077—111no—
223#2072—111no—
224#2035—111no—
225#1927—111no—
226#1920—111no—
227#1892—111no—
228#1872—111no—
229#1872—111no—
230#1869D1111yescharacteristic
231#1853—111no—
232#1823—111no—
233C2×#340—111no—
234C23×C11—21no—
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#12312yes—
245C23×C11C2×SD1612yes—
246C23×C11C2×SD1612yes—
247C23×C11#13712yes—
248C23×C11C22×D411yescharacteristic
249D4×C11—28no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11#12312yes—
269C2×C4×C11C2×SD1612yes—
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11H(5,𝔽2)11yescharacteristic
275C2×C4×C11H(5,𝔽2)11yescharacteristic
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—41no—
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—84no—
301C2×Dic11—84no—
302C2×Dic11—84no—
303Dic22—41no—
304Dic22—41no—
305Dic22—41no—
306Dic22—41no—
307C8×C11—41no—
308C8×C11—41no—
309C8×C11—41no—
310C8×C11—41no—
311C23×C8C2×D1111yescharacteristic
312C2×C22⋊Q8—111no—
313C2×C22⋊Q8—111no—
314C2×C4×D4—221no—
315C2×C4×D4C2×D1111yescharacteristic
316C22×C4⋊C4—111no—
317C22×C4⋊C4—111no—
318C22×C4⋊C4—111no—
319C2×#106—111no—
320C2×#106—111no—
321C2×#103—111no—
322C2×#103—111no—
323C2×#103—111no—
324C2×#103—111no—
325C2×C22⋊C8C2×D1111yescharacteristic
326C2×C22⋊C8C2×D1111yescharacteristic
327C2×C22⋊C8C2×D1111yescharacteristic
328#398—221no—
329#396—221no—
330#391—111no—
331#389—111no—
332#389—221no—
333#386—221no—
334#385—221no—
335#385—221no—
336#384—111no—
337#380—111no—
338#380—111no—
339#380—111no—
340#380—221no—
341C4×C4⋊C4—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351#340—111no—
352#336C2×D1111yescharacteristic
353#336C2×D1111yescharacteristic
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—22no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—22no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11#48314yes—
368C22×C11C2×#12311yescharacteristic
369C22×C11#54611yescharacteristic
370C22×C11#54611yescharacteristic
371C22×C11C22×SD1611yescharacteristic
372C22×C11C2×#13711yescharacteristic
373C22×C11#57611yescharacteristic
374C22×C11#57811yescharacteristic
375C4×C11—22no—
376C4×C11—22no—
377C4×C11—41no—
378C4×C11—41no—
379C4×C11#52911yescharacteristic
380C4×C11#53811yescharacteristic
381C4×C11#55311yescharacteristic
382C4×C11#55311yescharacteristic
383Dic11—42no—
384Dic11—42no—
385Dic11—81no—
386Dic11—81no—
387Dic11—81no—
388Dic11—81no—
389Dic11—81no—
390Dic11—81no—
391C22×Q8—111no—
392C22×D4D4411yescharacteristic
393C23×C4—221no—
394C23×C4—221no—
395C23×C4—221no—
396C23×C4C22×D1111yescharacteristic
397C23×C4C22×D1111yescharacteristic
398C22×C8—22no—
399C22×C8—41no—
400C22×C8—41no—
401C22×C8C22×D1111yescharacteristic
402C22×C8C22×D1111yescharacteristic
403C22×C8C22×D1111yescharacteristic
404C22×C8C22×D1111yescharacteristic
405C22⋊Q8—222no—
406C22⋊Q8—222no—
407C22⋊Q8—222no—
408C22⋊Q8—441no—
409C4×D4—22no—
410C4×D4—22no—
411C4×D4—444no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—222no—
420C2×C4⋊C4—222no—
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—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—441no—
431C2×C4⋊C4—441no—
432C2×C4⋊C4—441no—
433C2×C4⋊C4D4411yescharacteristic
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4D4411yescharacteristic
440C2×C22⋊C4D4411yescharacteristic
441C2×C42—221no—
442C2×C42C22×D1111yescharacteristic
443#106—222no—
444#106—441no—
445#103—222no—
446#103—441no—
447#103—441no—
448#103—441no—
449C22⋊C8—22no—
450C22⋊C8—41no—
451C22⋊C8—41no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459C2×C11—24no—
460C2×C11—42no—
461C2×C11#244411yescharacteristic
462C2×C11C2×#48311yescharacteristic
463C2×C11#309811yescharacteristic
464C2×C11#329511yescharacteristic
465C2×C11#329811yescharacteristic
466C2×C11#331211yescharacteristic
467C2×C11#331411yescharacteristic
468C24C2×D4411yescharacteristic
469C24C2×D4411yescharacteristic
470C2×Q8—221no—
471C2×Q8—221no—
472C2×Q8—221no—
473C2×Q8—221no—
474C2×Q8—221no—
475C2×Q8—221no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4#431414yes—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—442no—
498C22×C4—442no—
499C22×C4—442no—
500C22×C4—442no—
501C22×C4—442no—
502C22×C4—442no—
503C22×C4—881no—
504C22×C4—881no—
505C22×C4—881no—
506C22×C4C2×D4411yescharacteristic
507C22×C4C2×D4411yescharacteristic
508C22×C4C2×D4411yescharacteristic
509C22×C4C2×D4411yescharacteristic
510C22×C4#434112yes—
511C22×C4#434112yes—
512C22×C4C23×D1111yescharacteristic
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×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—44no—
526C4⋊C4—22no—
527C4⋊C4—112no—
528C4⋊C4—112no—
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—221no—
540C4⋊C4—221no—
541C4⋊C4—442no—
542C4⋊C4—442no—
543C4⋊C4—442no—
544C4⋊C4—442no—
545C4⋊C4—442no—
546C4⋊C4—442no—
547C4⋊C4—881no—
548C4⋊C4—881no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—442no—
552C22⋊C4—442no—
553C22⋊C4—442no—
554C22⋊C4—442no—
555C22⋊C4—881no—
556C42—21no—
557C42—21no—
558C42—442no—
559C11#2620011yescharacteristic, complemented, Sylow
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23#6693912yes—
571C23C2×#431412yes—
572C23C2×#431412yes—
573C23#6696212yes—
574C23C22×D4411yescharacteristic
575Q8—441no—
576Q8—441no—
577Q8—441no—
578Q8—441no—
579D4—28no—
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—884no—
624C2×C4—884no—
625C2×C4#6693912yes—
626C2×C4C2×#431412yes—
627C2×C4C2×#434111yescharacteristic
628C2×C4C2×#434111yescharacteristic
629C2×C4#6703711yescharacteristic
630C2×C4#6703711yescharacteristic
631C2×C4#41×D1111yescharacteristic
632C2×C4#41×D1111yescharacteristic
633C8—41no—
634C8—41no—
635C8—41no—
636C8—41no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22#1062233414yes—
651C22C2×#6693911yescharacteristic
652C22#1062308511yescharacteristic
653C22#1062308511yescharacteristic
654C22C22×#431411yescharacteristic
655C22C2×#6696211yescharacteristic
656C22#1062328311yescharacteristic
657C22#1062328411yescharacteristic
658C4—22no—
659C4—22no—
660C4—41no—
661C4—41no—
662C4—442no—
663C4—442no—
664C4—881no—
665C4—881no—
666C4—881no—
667C4—881no—
668C4—881no—
669C4—881no—
670C4#1062312411yescharacteristic
671C4#1062313211yescharacteristic
672C4#1062313211yescharacteristic
673C4#1062318011yescharacteristic
674C2—24no—
675C2—42no—
676C2#1307236411yescharacteristic
677C2C2×#1062233411yescharacteristic
678C2#1307859611yescharacteristic
679C2#1308044111yescharacteristic
680C2#1308048211yescharacteristic
681C2#1308066911yescharacteristic
682C2#1308069911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1869C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#1869D11
hypocenterC11#26200
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1869

Complements

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

NH ≅ G/Ntype
3. #13070175C2semidirect
4. #13070049C2semidirect
5. #13070026C2semidirect
6. #13069813C2semidirect
7. #13069251C2semidirect
8. #13069202C2semidirect
9. #13069039C2semidirect
10. #13068921C2semidirect
11. #13068921C2semidirect
12. #13068811C2semidirect
13. #13068703C2semidirect
14. C2×#10622189C2semidirect
559. C11#26200semidirect

Maximal subgroups

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

subgroupindex
#130720672
D4×C4⋊Dic112
#130701752
#130700492
#130700262
#130698132
#130692512
#130692022
#130690392
#130689212
#130688112
#130687032
C2×#106221892
C11×#18692
#2620011