Finite Group Databasebeta

← #14803253

Subgroups — #14803253

Order 2816.

828 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622680C211yesmaximal, characteristic
2C2×#10622676C211yesmaximal, characteristic, complemented
3#13073618C211yesmaximal, characteristic
4#13070001C211yesmaximal, characteristic, complemented
5#13069987C211yesmaximal, characteristic, complemented
6#13069857C211yesmaximal, characteristic, complemented
7#13069857C211yesmaximal, characteristic, complemented
8#13069548C211yesmaximal, characteristic, complemented
9#13069548C211yesmaximal, characteristic, complemented
10#13069543C211yesmaximal, characteristic
11#13069340C211yesmaximal, characteristic, complemented
12#13069243C211yesmaximal, characteristic, complemented
13#13069236C211yesmaximal, characteristic, complemented
14#13068449C211yesmaximal, characteristic, complemented
15C11×#2370C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C2×#66928C2211yescharacteristic
18C2×#66928C2211yescharacteristic
19C2×#66927C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C11×#389—21no—
22C11×#389C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C11×#387—21no—
25C11×#387—21no—
26C4×C11×C4⋊C4—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C4×C11×C4⋊C4C2211yescharacteristic
30C4×C11×C4⋊C4C2211yescharacteristic
31#10622680—24no—
32#10622676—24no—
33#10622601—21no—
34#10622601—21no—
35C2×#66874C2211yescharacteristic
36C2×#66874C2211yescharacteristic
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45C2×#66873C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49#10622552C2211yescharacteristic
50#10622552C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×#66867C2211yescharacteristic
55#10622285—21no—
56#10622285—21no—
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D44—21no—
62C22×D44—21no—
63C22×D44C2311yescharacteristic
64C22×D44C2311yescharacteristic
65C22×Dic22C2311yescharacteristic
66C11×#125—22no—
67C11×#125D414yes—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C42×C11—21no—
79C2×C42×C11—21no—
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×C4×Dic11—21no—
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99#66928—22no—
100#66928—22no—
101#66928—41no—
102#66928—41no—
103#66927—22no—
104#66927—22no—
105C4×Dic22—22no—
106C4×Dic22—22no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95D411yescharacteristic
113C11×#95D411yescharacteristic
114#66874—22no—
115#66874—22no—
116#66874—22no—
117#66874—22no—
118#66873—22no—
119#66873—22no—
120#66873—22no—
121#66873—22no—
122#66873—22no—
123#66873—22no—
124#66873—41no—
125#66873—41no—
126#66872—22no—
127#66871—22no—
128C4⋊(C11⋊C8)—22no—
129C4⋊(C11⋊C8)—41no—
130C4⋊(C11⋊C8)—41no—
131#66867—22no—
132#25291—111nomaximal, Sylow
133C23×D11—21no—
134C23×D11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—21no—
147C22×Dic11—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—42no—
161C2×D44—42no—
162C2×D44—42no—
163C2×D44—42no—
164C2×D44—81no—
165C2×D44—81no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22#4112yes—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—41no—
180C11×C4⋊C4—41no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4—81no—
183C11×C4⋊C4C2×D412yes—
184C11×C4⋊C4C2×D412yes—
185C11×C4⋊C4#4112yes—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—42no—
191C42×C11—81no—
192C42×C11—81no—
193C42×C11C2×D412yes—
194C42×C11#4112yes—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—42no—
197(C2×D11)⋊C4—42no—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4—81no—
200(C2×D11)⋊C4—81no—
201(C2×D11)⋊C4—81no—
202(C2×D11)⋊C4—81no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205Dic11⋊C4—42no—
206C4×Dic11—42no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×#490—111no—
220C2×#479—111no—
221#2548—111no—
222#2370D1111yescharacteristic, complemented
223#2067—111no—
224#2065—111no—
225#2042—111no—
226#2042—111no—
227#1983—111no—
228#1983—111no—
229#1982—111no—
230#1940—111no—
231#1926—111no—
232#1925—111no—
233#1763—111no—
234C23×C11C22×D411yescharacteristic
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11#12112yes—
278C2×C4×C11#12112yes—
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C2×C4×C112−1+411yescharacteristic
285C2×Dic11—22no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291D44—41no—
292D44—41no—
293D44—41no—
294D44—41no—
295D44—41no—
296D44—41no—
297D44—41no—
298D44—41no—
299D44—84no—
300D44—84no—
301Dic22—22no—
302Dic22—22no—
303Dic22—41no—
304Dic22—41no—
305C11⋊C8—41no—
306C11⋊C8—41no—
307C11⋊C8—41no—
308C11⋊C8—41no—
309C2×#127—111no—
310C2×#125C2×D1111yescharacteristic
311C2×#124—111no—
312C2×#124—111no—
313C2×C4×Q8—111no—
314#490—224no—
315#479—224no—
316C2×#107—111no—
317C2×#106—111no—
318C2×C4⋊C8—111no—
319C2×C4⋊C8—111no—
320C2×C4⋊C8—111no—
321C2×#103—111no—
322C2×#103—111no—
323C2×#103—111no—
324C2×#103—111no—
325C2×#102—111no—
326C2×#102—111no—
327C2×#102—111no—
328C2×#102—111no—
329C2×#102—111no—
330C2×#102—111no—
331C2×#102—111no—
332C2×#102—111no—
333C2×#97—111no—
334#394—221no—
335#394—221no—
336#390—111no—
337#390—111no—
338#390—221no—
339#390—221no—
340#389—21no—
341#389C2×D1111yescharacteristic
342#389C2×D1111yescharacteristic
343#387—21no—
344#387—21no—
345C4×C4⋊C4—21no—
346C4×C4⋊C4C2×D1111yescharacteristic
347C4×C4⋊C4C2×D1111yescharacteristic
348C4×C4⋊C4C2×D1111yescharacteristic
349C4×C4⋊C4C2×D1111yescharacteristic
350#340—111no—
351#340—111no—
352#336—111no—
353#336—111no—
354C22×C11C2×#12111yescharacteristic
355C22×C11#54611yescharacteristic
356C22×C11#54811yescharacteristic
357C22×C11#57511yescharacteristic
358C22×C11#57511yescharacteristic
359C22×C11#57611yescharacteristic
360C22×C11#57711yescharacteristic
361C2×D11—81no—
362C2×D11—81no—
363C2×D11—81no—
364C2×D11—81no—
365C2×D11—81no—
366C2×D11—81no—
367C2×D11—81no—
368C2×D11—81no—
369C2×D11—81no—
370C2×D11—81no—
371C2×D11—81no—
372C2×D11—81no—
373C2×D11—81no—
374C2×D11—81no—
375C4×C11—22no—
376C4×C11—22no—
377C4×C11—42no—
378C4×C11—42no—
379C4×C11—42no—
380C4×C11—41no—
381C4×C11—41no—
382C4×C11—41no—
383C4×C11—41no—
384C4×C11—81no—
385C4×C11#52911yescharacteristic
386C4×C11#54211yescharacteristic
387C4×C11#54811yescharacteristic
388C4×C11#55011yescharacteristic
389Dic11—42no—
390Dic11—81no—
391C22×Q8—111no—
392C22×D4—111no—
393C22×D4—111no—
394C22×D4—221no—
395C22×D4—221no—
396C22×C8—111no—
397C22×C8—111no—
398C22×C8—111no—
399C22×C8—111no—
400#127—222no—
401#127—222no—
402#125—22no—
403#125D4414yes—
404#124—222no—
405#124—222no—
406#124—441no—
407#124—441no—
408C4×Q8—222no—
409C4×Q8—222no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4C22⋊D1111yescharacteristic
417C2×C4⋊C4C22⋊D1111yescharacteristic
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C42—21no—
431C2×C42—21no—
432C2×C42—21no—
433C2×C42—221no—
434C2×C42C22×D1111yescharacteristic
435C2×C42C22×D1111yescharacteristic
436C2×C42C22×D1111yescharacteristic
437#107—222no—
438#106—222no—
439C4⋊C8—222no—
440C4⋊C8—441no—
441C4⋊C8—441no—
442#103—222no—
443#103—222no—
444#103—222no—
445#103—222no—
446#102—222no—
447#102—222no—
448#102—222no—
449#102—222no—
450#102—222no—
451#102—222no—
452#102—441no—
453#102—441no—
454#97—222no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95C22⋊D1111yescharacteristic
461#95C22⋊D1111yescharacteristic
462C2×C11#242611yescharacteristic
463C2×C11#304011yescharacteristic
464C2×C11#304511yescharacteristic
465C2×C11#330911yescharacteristic
466C2×C11#331711yescharacteristic
467C2×C11#337011yescharacteristic
468C2×C11#337111yescharacteristic
469D11—161no—
470D11—161no—
471C24—221no—
472C24—221no—
473C2×Q8—112no—
474C2×Q8—221no—
475C2×Q8—221no—
476C2×Q8—221no—
477C2×Q8—221no—
478C2×Q8—221no—
479C2×D4—221no—
480C2×D4—221no—
481C2×D4—221no—
482C2×D4—221no—
483C2×D4—221no—
484C2×D4—221no—
485C2×D4—221no—
486C2×D4—221no—
487C2×D4—221no—
488C2×D4—221no—
489C2×D4—221no—
490C2×D4—221no—
491C2×D4—442no—
492C2×D4—442no—
493C2×D4—442no—
494C2×D4—442no—
495C2×D4—881no—
496C2×D4—881no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4C2×C22⋊D1111yescharacteristic
504C22×C4C2×C22⋊D1111yescharacteristic
505C22×C4C2×C22⋊D1111yescharacteristic
506C22×C4C2×C22⋊D1111yescharacteristic
507C22×C4C2×C22⋊D1111yescharacteristic
508C22×C4C2×C22⋊D1111yescharacteristic
509C22×C4C23×D1111yescharacteristic
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C4⋊C4—24no—
523C4⋊C4—24no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—42no—
532C4⋊C4—81no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—442no—
536C4⋊C4C2×D4412yes—
537C4⋊C4C2×D4412yes—
538C4⋊C4#434312yes—
539C22⋊C4—442no—
540C22⋊C4—442no—
541C22⋊C4—442no—
542C22⋊C4—442no—
543C22⋊C4—881no—
544C22⋊C4—881no—
545C22⋊C4—881no—
546C22⋊C4—881no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—42no—
552C42—81no—
553C42—81no—
554C42—442no—
555C42C2×D4412yes—
556C42#433912yes—
557C11#2529111yescharacteristic, complemented, Sylow
558C23—441no—
559C23—441no—
560C23—441no—
561C23—441no—
562C23—441no—
563C23—441no—
564C23—441no—
565C23—441no—
566C23—441no—
567C23—441no—
568C23—441no—
569C23—441no—
570C23—441no—
571C23—441no—
572C23C22×C22⋊D1111yescharacteristic
573Q8—222no—
574Q8—222no—
575Q8—441no—
576Q8—441no—
577D4—441no—
578D4—441no—
579D4—441no—
580D4—441no—
581D4—441no—
582D4—441no—
583D4—441no—
584D4—441no—
585D4—884no—
586D4—884no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
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—222no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4#6698312yes—
622C2×C4#6698312yes—
623C2×C4C22×D4411yescharacteristic
624C2×C4C2×#433911yescharacteristic
625C2×C4C2×#434311yescharacteristic
626C2×C4#6704011yescharacteristic
627C2×C4#41×D1111yescharacteristic
628C2×C4#6704211yescharacteristic
629C8—441no—
630C8—441no—
631C8—441no—
632C8—441no—
633C22—881no—
634C22—881no—
635C22—881no—
636C22—881no—
637C22—881no—
638C22—881no—
639C22—881no—
640C22—881no—
641C22—881no—
642C22—881no—
643C22—881no—
644C22—881no—
645C22—881no—
646C22—881no—
647C22C2×#6698311yescharacteristic
648C22#1062334811yescharacteristic
649C22#1062335311yescharacteristic
650C22#1062335311yescharacteristic
651C22#1062336011yescharacteristic
652C22#1062336611yescharacteristic
653C22#1062336811yescharacteristic
654C4—22no—
655C4—22no—
656C4—42no—
657C4—41no—
658C4—41no—
659C4—42no—
660C4—42no—
661C4—41no—
662C4—41no—
663C4—81no—
664C4—442no—
665C4—881no—
666C4#1062310711yescharacteristic
667C4#1062310811yescharacteristic
668C4#1062311111yescharacteristic
669C4#1062311311yescharacteristic
670C2—1761no—
671C2—1761no—
672C2#1307217611yescharacteristic
673C2#1307811011yescharacteristic
674C2#1307815511yescharacteristic
675C2#1308061611yescharacteristic
676C2#1308073611yescharacteristic
677C2#1308136911yescharacteristic
678C2#1308138411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2370C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenter#2370D11
hypocenterC11#25291
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2370

Complements

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

NH ≅ G/Ntype
2. C2×#10622676C2semidirect
4. #13070001C2semidirect
5. #13069987C2semidirect
6. #13069857C2semidirect
7. #13069857C2semidirect
8. #13069548C2semidirect
9. #13069548C2semidirect
11. #13069340C2semidirect
12. #13069243C2semidirect
13. #13069236C2semidirect
14. #13068449C2semidirect
15. C11×#2370C2semidirect
222. #2370D11semidirect
557. C11#25291semidirect

Maximal subgroups

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

subgroupindex
C2×#106226802
C2×#106226762
#130736182
#130700012
#130699872
#130698572
#130695482
#130695432
#130693402
#130692432
#130692362
#130684492
C11×#23702
#2529111