Finite Group Databasebeta

← #14814618

Subgroups — #14814618

Order 2816.

840 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072045C211yesmaximal, characteristic
2D4×C4⋊Dic11C211yesmaximal, characteristic
3#13070180C211yesmaximal, characteristic, complemented
4#13070039C211yesmaximal, characteristic, complemented
5#13070026C211yesmaximal, characteristic, complemented
6#13069813C211yesmaximal, characteristic, complemented
7#13069258C211yesmaximal, characteristic, complemented
8#13069195C211yesmaximal, characteristic, complemented
9#13069049C211yesmaximal, characteristic, complemented
10#13068921C211yesmaximal, characteristic, complemented
11#13068921C211yesmaximal, characteristic, complemented
12#13068817C211yesmaximal, characteristic, complemented
13#13068703C211yesmaximal, characteristic, complemented
14#13068336C211yesmaximal, characteristic, complemented
15C11×#1870C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×D4×Dic11—21no—
19C2×#66979C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C2×#66977C2211yescharacteristic
23C2×#66977C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622835—21no—
28#10622825C2211yescharacteristic
29#10622825C2211yescharacteristic
30#10622825C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37#10622598—21no—
38#10622585—21no—
39#10622565—21no—
40#10622563—21no—
41#10622563—21no—
42#10622558—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—
64C22×Dic22C2311yescharacteristic
65C2×C11×M16—22no—
66C2×C11×M16—41no—
67C2×C11×M16—41no—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C22⋊C4D411yescharacteristic
76C2×C11×C22⋊C4D411yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84D4×Dic11—44no—
85#66979—22no—
86#66979—41no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—22no—
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⋊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—
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#66882—41no—
122#66881—22no—
123#66880—22no—
124#66880—41no—
125#66880—41no—
126#66880—41no—
127#26216—111nomaximal, Sylow
128C24×C11C2×D411yescharacteristic
129C24×C11C2×D411yescharacteristic
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
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—81no—
163C22×Dic11—81no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C11×M16—44no—
171C2×C8×C11—21no—
172C2×C8×C11—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—
183C11×C4⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C42×C11—21no—
187C42×C11—21no—
188C22⋊Dic11—42no—
189C22⋊Dic11—42no—
190C22⋊Dic11—42no—
191C22⋊Dic11—42no—
192C22⋊Dic11—42no—
193C22⋊Dic11—42no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
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—42no—
207C4⋊Dic11—42no—
208C4⋊Dic11—42no—
209C4⋊Dic11—81no—
210C4⋊Dic11#4112yes—
211C4⋊Dic11#4112yes—
212Dic11⋊C4—42no—
213Dic11⋊C4—42no—
214Dic11⋊C4—42no—
215C4×Dic11—42no—
216C4×Dic11—42no—
217#2415—111no—
218D4×C4⋊C4—111no—
219#2100—111no—
220#2075—111no—
221#2072—111no—
222#2035—111no—
223#1928—111no—
224#1919—111no—
225#1894—111no—
226#1872—111no—
227#1872—111no—
228#1870D1111yescharacteristic
229#1854—111no—
230#1823—111no—
231#1736—111no—
232C23×C11—21no—
233C23×C11—21no—
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×C11AGL(1,ℤ/8)12yes—
246C23×C11C22×D411yescharacteristic
247D4×C11—28no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11#12312yes—
267C2×C4×C11#13712yes—
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11H(5,𝔽2)11yescharacteristic
273C2×C4×C11H(5,𝔽2)11yescharacteristic
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—41no—
277C2×Dic11—41no—
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—84no—
299C2×Dic11—84no—
300Dic22—41no—
301Dic22—41no—
302Dic22—41no—
303Dic22—41no—
304C8×C11—41no—
305C8×C11—41no—
306C8×C11—41no—
307C8×C11—41no—
308C22×M16C2×D1111yescharacteristic
309C2×C22⋊Q8—111no—
310C2×C22⋊Q8—111no—
311C2×C4×D4—221no—
312C2×C4×D4C2×D1111yescharacteristic
313C2×#117—111no—
314C22×C4⋊C4—111no—
315C22×C4⋊C4—111no—
316C2×#107—111no—
317C2×#106—111no—
318C2×#103—111no—
319C2×#103—111no—
320C2×#103—111no—
321C2×#103—111no—
322C2×C22⋊C8C2×D1111yescharacteristic
323C2×C22⋊C8C2×D1111yescharacteristic
324C2×C22⋊C8C2×D1111yescharacteristic
325#397—221no—
326#394—221no—
327#391—111no—
328#389—111no—
329#389—221no—
330#389—221no—
331#388—221no—
332#385—221no—
333#385—221no—
334#384—111no—
335#380—111no—
336#380—111no—
337#380—111no—
338C4×C4⋊C4—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#336C2×D1111yescharacteristic
350#336C2×D1111yescharacteristic
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—22no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11C2×#12311yescharacteristic
366C22×C11#54611yescharacteristic
367C22×C11#54611yescharacteristic
368C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
369C22×C11C2×#13711yescharacteristic
370C22×C11#57711yescharacteristic
371C22×C11#57811yescharacteristic
372C4×C11—22no—
373C4×C11—22no—
374C4×C11—41no—
375C4×C11—41no—
376C4×C11#52911yescharacteristic
377C4×C11#53811yescharacteristic
378C4×C11#55311yescharacteristic
379C4×C11#55311yescharacteristic
380Dic11—42no—
381Dic11—42no—
382Dic11—81no—
383Dic11—81no—
384Dic11—81no—
385Dic11—81no—
386Dic11—81no—
387Dic11—81no—
388C22×Q8—111no—
389C22×D4D4411yescharacteristic
390C23×C4—221no—
391C23×C4—221no—
392C23×C4C22×D1111yescharacteristic
393C23×C4C22×D1111yescharacteristic
394C2×M16—22no—
395C2×M16—41no—
396C2×M16—41no—
397C22×C8C22×D1111yescharacteristic
398C22×C8C22×D1111yescharacteristic
399C22×C8C22×D1111yescharacteristic
400C22×C8C22×D1111yescharacteristic
401C22⋊Q8—222no—
402C22⋊Q8—222no—
403C22⋊Q8—222no—
404C22⋊Q8—441no—
405C4×D4—22no—
406C4×D4—22no—
407C4×D4—444no—
408#117—222no—
409#117—441no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—222no—
418C2×C4⋊C4—222no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—441no—
427C2×C4⋊C4—441no—
428C2×C4⋊C4D4411yescharacteristic
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4D4411yescharacteristic
436C2×C22⋊C4D4411yescharacteristic
437C2×C42—221no—
438C2×C42—221no—
439C2×C42C22×D1111yescharacteristic
440#107—441no—
441#106—222no—
442#103—222no—
443#103—441no—
444#103—441no—
445#103—441no—
446C22⋊C8—22no—
447C22⋊C8—41no—
448C22⋊C8—41no—
449#95—221no—
450#95—221no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95—221no—
456C2×C11—42no—
457C2×C11—42no—
458C2×C11#244411yescharacteristic
459C2×C11#309211yescharacteristic
460C2×C11#309711yescharacteristic
461C2×C11#330811yescharacteristic
462C2×C11#331011yescharacteristic
463C2×C11#332811yescharacteristic
464C2×C11#333111yescharacteristic
465C24C2×D4411yescharacteristic
466C24C2×D4411yescharacteristic
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×Q8—221no—
471C2×Q8—221no—
472C2×Q8—221no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—442no—
495C22×C4—442no—
496C22×C4—442no—
497C22×C4—442no—
498C22×C4—881no—
499C22×C4—881no—
500C22×C4C2×D4411yescharacteristic
501C22×C4C2×D4411yescharacteristic
502C22×C4C2×D4411yescharacteristic
503C22×C4C2×D4411yescharacteristic
504C22×C4#434112yes—
505C22×C4#434112yes—
506C22×C4C23×D1111yescharacteristic
507M16—44no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C4⋊C4—22no—
521C4⋊C4—112no—
522C4⋊C4—112no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
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—442no—
536C4⋊C4—442no—
537C4⋊C4—442no—
538C4⋊C4—442no—
539C4⋊C4—442no—
540C4⋊C4—442no—
541C4⋊C4—881no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—442no—
545C22⋊C4—442no—
546C22⋊C4—442no—
547C22⋊C4—442no—
548C22⋊C4—442no—
549C22⋊C4—442no—
550C42—21no—
551C42—21no—
552C42—442no—
553C42—442no—
554C11#2621611yescharacteristic, complemented, Sylow
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23#6693912yes—
568C23#6696112yes—
569C23C22×D4411yescharacteristic
570Q8—441no—
571Q8—441no—
572Q8—441no—
573Q8—441no—
574D4—28no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
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—884no—
618C2×C4—884no—
619C2×C4#6693912yes—
620C2×C4#6696212yes—
621C2×C4C2×#434111yescharacteristic
622C2×C4C2×#434111yescharacteristic
623C2×C4#6703711yescharacteristic
624C2×C4#6703711yescharacteristic
625C2×C4#41×D1111yescharacteristic
626C2×C4#41×D1111yescharacteristic
627C8—41no—
628C8—41no—
629C8—41no—
630C8—41no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22C2×#6693911yescharacteristic
646C22#1062308511yescharacteristic
647C22#1062308511yescharacteristic
648C22C2×#6696111yescharacteristic
649C22C2×#6696211yescharacteristic
650C22#1062328211yescharacteristic
651C22#1062328411yescharacteristic
652C4—22no—
653C4—22no—
654C4—41no—
655C4—41no—
656C4—442no—
657C4—442no—
658C4—881no—
659C4—881no—
660C4—881no—
661C4—881no—
662C4—881no—
663C4—881no—
664C4#1062312411yescharacteristic
665C4#1062313211yescharacteristic
666C4#1062313211yescharacteristic
667C4#1062318011yescharacteristic
668C2—42no—
669C2—42no—
670C2#1307236411yescharacteristic
671C2#1307854111yescharacteristic
672C2#1307858611yescharacteristic
673C2#1308060911yescharacteristic
674C2#1308063911yescharacteristic
675C2#1308090011yescharacteristic
676C2#1308093311yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1870C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#1870D11
hypocenterC11#26216
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
3. #13070180C2semidirect
4. #13070039C2semidirect
5. #13070026C2semidirect
6. #13069813C2semidirect
7. #13069258C2semidirect
8. #13069195C2semidirect
9. #13069049C2semidirect
10. #13068921C2semidirect
11. #13068921C2semidirect
12. #13068817C2semidirect
13. #13068703C2semidirect
14. #13068336C2semidirect
554. C11#26216semidirect

Maximal subgroups

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

subgroupindex
#130720452
D4×C4⋊Dic112
#130701802
#130700392
#130700262
#130698132
#130692582
#130691952
#130690492
#130689212
#130688172
#130687032
#130683362
C11×#18702
#2621611