Finite Group Databasebeta

← #14814370

Subgroups — #14814370

Order 2816.

844 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072032C211yesmaximal, characteristic
2#13071548C211yesmaximal, characteristic, complemented
3#13070184C211yesmaximal, characteristic, complemented
4#13070054C211yesmaximal, characteristic, complemented
5#13070031C211yesmaximal, characteristic, complemented
6#13069800C211yesmaximal, characteristic, complemented
7#13069243C211yesmaximal, characteristic, complemented
8#13069043C211yesmaximal, characteristic, complemented
9#13068937C211yesmaximal, characteristic, complemented
10#13068932C211yesmaximal, characteristic, complemented
11#13068907C211yesmaximal, characteristic, complemented
12#13068812C211yesmaximal, characteristic, complemented
13#13068705C211yesmaximal, characteristic, complemented
14#13068331C211yesmaximal, characteristic, complemented
15C11×#1918C211yesmaximal, characteristic, complemented
16C22×C8×D11C2211yescharacteristic
17C2×#66948C2211yescharacteristic
18C2×#66948C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×#66945C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31#10622604—21no—
32#10622601—21no—
33#10622600C2211yescharacteristic
34#10622600C2211yescharacteristic
35#10622600C2211yescharacteristic
36C2×#66873C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39#10622553—21no—
40#10622552C2211yescharacteristic
41C4×(C2×D11)⋊C4—21no—
42#10622549C2211yescharacteristic
43#10622284—21no—
44#10622283—21no—
45#10622278—21no—
46#10622266—21no—
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D44—21no—
60C22×D44—21no—
61C22×D44D411yescharacteristic
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11C2311yescharacteristic
65C22×C4×D11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C42×C11—21no—
74C2×C42×C11C2311yescharacteristic
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4D411yescharacteristic
85C2×(C2×D11)⋊C4D411yescharacteristic
86C2×C4⋊Dic11D411yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C2×C8×D11—22no—
96C2×C8×D11—41no—
97C2×C8×D11—41no—
98#66948—22no—
99#66948—22no—
100#66948—22no—
101#66948—41no—
102#66945—22no—
103#66945—22no—
104#66945—41no—
105#66945—41no—
106C4⋊C4×D11—22no—
107C4⋊C4×D11—41no—
108C4×D44—22no—
109C4×D44—22no—
110C11×#107—22no—
111C11×#95—21no—
112C11×#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118#66885—41no—
119#66885—41no—
120(C2×D11)⋊C8—22no—
121(C2×D11)⋊C8—41no—
122(C2×D11)⋊C8—41no—
123#66873—22no—
124#66873—41no—
125#66872—41no—
126#26199—111nomaximal, Sylow
127C23×D11—21no—
128C23×D11C2×D411yescharacteristic
129C23×D11C2×D411yescharacteristic
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C2×D44—22no—
143C2×D44—22no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—41no—
151C2×D44—42no—
152C2×D44—42no—
153C2×D44—42no—
154C2×D44—81no—
155C2×D44—81no—
156C2×D44—81no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×C4×D11—81no—
170C2×C4×D11#4112yes—
171C2×C4×D11#4112yes—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—81no—
185C11×C4⋊C4#4112yes—
186C11×C4⋊C4#4112yes—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—81no—
190(C2×D11)⋊C4—22no—
191(C2×D11)⋊C4—22no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—42no—
197(C2×D11)⋊C4—42no—
198(C2×D11)⋊C4—81no—
199(C2×D11)⋊C4—81no—
200(C2×D11)⋊C4—81no—
201C4⋊Dic11—22no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208Dic11⋊C4—42no—
209C4×Dic11—42no—
210C4×Dic11—42no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C8×D11—44no—
218#2414—111no—
219#2352—111no—
220#2101—111no—
221#2077—111no—
222#2073—111no—
223#2033—111no—
224#1926—111no—
225#1918D1111yescharacteristic, complemented
226#1893—111no—
227#1875—111no—
228#1874—111no—
229#1869—111no—
230#1854—111no—
231#1824—111no—
232#1735—111no—
233C23×C11C22×D411yescharacteristic
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11#12312yes—
254C22×D11#13512yes—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
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—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×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11H(5,𝔽2)11yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
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#12312yes—
294D44—44no—
295D44—41no—
296D44—41no—
297D44—41no—
298D44—41no—
299D44—84no—
300D44—84no—
301C4×D11—22no—
302C4×D11—22no—
303C4×D11—22no—
304C4×D11—22no—
305C4×D11—41no—
306C4×D11—41no—
307C4×D11—41no—
308C4×D11—41no—
309C4×D11—84no—
310C8×C11—41no—
311C8×C11—41no—
312C11⋊C8—41no—
313C11⋊C8—41no—
314C23×C8—111no—
315C2×#121—111no—
316C2×#121—111no—
317C2×C4×D4—111no—
318C2×#117—111no—
319C2×#117—111no—
320C22×C4⋊C4—111no—
321C2×#107C2×D1111yescharacteristic
322C2×#106—111no—
323C2×#102—111no—
324C2×#102—111no—
325C2×#102—111no—
326C2×#102—111no—
327C2×C22⋊C8—111no—
328C2×C22⋊C8—111no—
329C2×C22⋊C8—111no—
330#394—221no—
331#392—221no—
332#390—111no—
333#390—221no—
334#389C2×D1111yescharacteristic
335#388—221no—
336#388—221no—
337#387—221no—
338#386—221no—
339#382—111no—
340#380—111no—
341#380—111no—
342#380—111no—
343C4×C4⋊C4C2×D1111yescharacteristic
344C4×C22⋊C4—221no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340C2×D1111yescharacteristic
353#340C2×D1111yescharacteristic
354#340C2×D1111yescharacteristic
355#336—111no—
356#336C2×D1111yescharacteristic
357C22×C11C2×#12311yescharacteristic
358C22×C11#54611yescharacteristic
359C22×C11#54611yescharacteristic
360C22×C11C2×#13511yescharacteristic
361C22×C11#57511yescharacteristic
362C22×C11#57611yescharacteristic
363C22×C11#57711yescharacteristic
364C2×D11—22no—
365C2×D11—22no—
366C2×D11—22no—
367C2×D11—22no—
368C2×D11—22no—
369C2×D11—22no—
370C2×D11—41no—
371C2×D11—41no—
372C2×D11—41no—
373C2×D11—41no—
374C2×D11—41no—
375C2×D11—41no—
376C2×D11—41no—
377C2×D11—41no—
378C2×D11—81no—
379C2×D11—81no—
380C2×D11—81no—
381C2×D11—81no—
382C2×D11—81no—
383C2×D11—81no—
384C2×D11—81no—
385C4×C11—41no—
386C4×C11—41no—
387C4×C11—42no—
388C4×C11—42no—
389C4×C11—81no—
390C4×C11—81no—
391C4×C11#52911yescharacteristic
392C4×C11#53811yescharacteristic
393C4×C11#55311yescharacteristic
394C4×C11#55311yescharacteristic
395Dic11—22no—
396Dic11—41no—
397Dic11—81no—
398Dic11—81no—
399Dic11—81no—
400C22×D4—111no—
401C22×D4—111no—
402C22×D4—221no—
403C22×D4—221no—
404C23×C4—111no—
405C23×C4—111no—
406C23×C4—221no—
407C22×C8—111no—
408C22×C8—111no—
409C22×C8—222no—
410C22×C8—441no—
411C22×C8—441no—
412C22×C8C22×D1111yescharacteristic
413C22×C8C22×D1111yescharacteristic
414#121—222no—
415#121—222no—
416#121—222no—
417#121—441no—
418C4×D4—222no—
419C4×D4—222no—
420#117—222no—
421#117—222no—
422#117—441no—
423#117—441no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—222no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—441no—
432C2×C4⋊C4C22×D1111yescharacteristic
433C2×C4⋊C4C22×D1111yescharacteristic
434C2×C4⋊C4C22×D1111yescharacteristic
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C22⋊C4—111no—
437C2×C22⋊C4—111no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C42—21no—
448C2×C42—221no—
449C2×C42—221no—
450C2×C42C22×D1111yescharacteristic
451#107—22no—
452#106—441no—
453#102—222no—
454#102—441no—
455#102—441no—
456#102—441no—
457C22⋊C8—222no—
458C22⋊C8—441no—
459C22⋊C8—441no—
460#95—21no—
461#95—21no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95—221no—
466#95—221no—
467C2×C11#244411yescharacteristic
468C2×C11#309111yescharacteristic
469C2×C11#309611yescharacteristic
470C2×C11#329711yescharacteristic
471C2×C11#330111yescharacteristic
472C2×C11#331711yescharacteristic
473C2×C11#331911yescharacteristic
474D11—42no—
475D11—42no—
476D11—161no—
477C24—111no—
478C24—111no—
479C24—221no—
480C2×D4—222no—
481C2×D4—222no—
482C2×D4—221no—
483C2×D4—221no—
484C2×D4—221no—
485C2×D4—221no—
486C2×D4—221no—
487C2×D4—221no—
488C2×D4—441no—
489C2×D4—442no—
490C2×D4—442no—
491C2×D4—442no—
492C2×D4—881no—
493C2×D4—881no—
494C2×D4—881no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—111no—
500C22×C4—112no—
501C22×C4—112no—
502C22×C4—111no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—442no—
517C22×C4—442no—
518C22×C4—881no—
519C22×C4D4×D1111yescharacteristic
520C22×C4D4×D1111yescharacteristic
521C22×C4C23×D1111yescharacteristic
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—221no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8—444no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—81no—
542C4⋊C4—222no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—442no—
550C4⋊C4#433912yes—
551C4⋊C4#434312yes—
552C22⋊C4—222no—
553C22⋊C4—222no—
554C22⋊C4—442no—
555C22⋊C4—442no—
556C22⋊C4—442no—
557C22⋊C4—442no—
558C22⋊C4—442no—
559C22⋊C4—442no—
560C22⋊C4—881no—
561C22⋊C4—881no—
562C22⋊C4—881no—
563C42—21no—
564C42—21no—
565C42—81no—
566C42—442no—
567C42—442no—
568C11#2619911yescharacteristic, complemented, Sylow
569C23—112no—
570C23—112no—
571C23—221no—
572C23—221no—
573C23—221no—
574C23—221no—
575C23—221no—
576C23—221no—
577C23—221no—
578C23—221no—
579C23—221no—
580C23—221no—
581C23—221no—
582C23—221no—
583C23—441no—
584C23—441no—
585C23—441no—
586C23—441no—
587C23—441no—
588C23—441no—
589C23—441no—
590C23C2×D4×D1111yescharacteristic
591D4—444no—
592D4—441no—
593D4—441no—
594D4—441no—
595D4—441no—
596D4—884no—
597D4—884no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—112no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—222no—
620C2×C4—222no—
621C2×C4—222no—
622C2×C4—222no—
623C2×C4—221no—
624C2×C4—221no—
625C2×C4—221no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—884no—
640C2×C4C2×#433911yescharacteristic
641C2×C4C2×#434311yescharacteristic
642C2×C4#41×D1111yescharacteristic
643C2×C4#41×D1111yescharacteristic
644C2×C4#6704211yescharacteristic
645C2×C4#6704211yescharacteristic
646C8—41no—
647C8—41no—
648C8—441no—
649C8—441no—
650C22—222no—
651C22—222no—
652C22—222no—
653C22—222no—
654C22—222no—
655C22—222no—
656C22—441no—
657C22—441no—
658C22—441no—
659C22—441no—
660C22—441no—
661C22—441no—
662C22—441no—
663C22—441no—
664C22—881no—
665C22—881no—
666C22—881no—
667C22—881no—
668C22—881no—
669C22—881no—
670C22—881no—
671C22#1062308111yescharacteristic
672C22#1062316111yescharacteristic
673C22D11×#12311yescharacteristic
674C22#1062328811yescharacteristic
675C22D11×#13511yescharacteristic
676C22#1062330811yescharacteristic
677C22#1062330911yescharacteristic
678C4—41no—
679C4—41no—
680C4—42no—
681C4—42no—
682C4—81no—
683C4—81no—
684C4—222no—
685C4—441no—
686C4—881no—
687C4—881no—
688C4—881no—
689C4#1062306111yescharacteristic
690C4#1062311111yescharacteristic
691C4#1062322611yescharacteristic
692C4#1062323511yescharacteristic
693C2—442no—
694C2—442no—
695C2—1761no—
696C2#1307237111yescharacteristic
697C2#1307853411yescharacteristic
698C2#1307856711yescharacteristic
699C2#1308047111yescharacteristic
700C2#1308051511yescharacteristic
701C2#1308074711yescharacteristic
702C2#1308076911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1918C2
socleC23×C11C22×D4
prime radical#13072032C2
hypercenter#1918D11
hypocenterC11#26199
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1918

Complements

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

NH ≅ G/Ntype
2. #13071548C2semidirect
3. #13070184C2semidirect
4. #13070054C2semidirect
5. #13070031C2semidirect
6. #13069800C2semidirect
7. #13069243C2semidirect
8. #13069043C2semidirect
9. #13068937C2semidirect
10. #13068932C2semidirect
11. #13068907C2semidirect
12. #13068812C2semidirect
13. #13068705C2semidirect
14. #13068331C2semidirect
15. C11×#1918C2semidirect
225. #1918D11semidirect
568. C11#26199semidirect

Maximal subgroups

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

subgroupindex
#130720322
#130715482
#130701842
#130700542
#130700312
#130698002
#130692432
#130690432
#130689372
#130689322
#130689072
#130688122
#130687052
#130683312
C11×#19182
#2619911