Finite Group Databasebeta

← #14823236

Subgroups — #14823236

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622479C211yesmaximal, characteristic, complemented
2#13072971C211yesmaximal, characteristic, complemented
3#13071650C211yesmaximal, characteristic, complemented
4#13070003C211yesmaximal, characteristic, complemented
5#13069951C211yesmaximal, characteristic, complemented
6#13069797C211yesmaximal, characteristic, complemented
7#13069613C211yesmaximal, characteristic
8#13069489C211yesmaximal, characteristic, complemented
9#13069239C211yesmaximal, characteristic, complemented
10#13069235C211yesmaximal, characteristic, complemented
11#13069228C211yesmaximal, characteristic, complemented
12#13068964C211yesmaximal, characteristic, complemented
13#13068812C211yesmaximal, characteristic, complemented
14#13068516C211yesmaximal, characteristic, complemented
15C2×C11×#478C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×#66991C2211yescharacteristic
19C22×#4323C2211yescharacteristic
20C2×#66948C2211yescharacteristic
21C2×#66945C2211yescharacteristic
22C11×#478—24no—
23C2×C11×#107C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28#10622834C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30#10622826—21no—
31C4×C22⋊Dic11—21no—
32C2×#66885C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×#66882C2211yescharacteristic
37C2×#66879C2211yescharacteristic
38#10622606—21no—
39#10622604—21no—
40#10622603—21no—
41#10622601—21no—
42#10622601C2211yescharacteristic
43#10622600C2211yescharacteristic
44C4⋊C4×Dic11C2211yescharacteristic
45C4⋊C4×Dic11C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49#10622570—21no—
50#10622557—21no—
51#10622552C2211yescharacteristic
52C4×(C2×D11)⋊C4C2211yescharacteristic
53#10622541C2211yescharacteristic
54#10622479—24no—
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C22×C22⋊D11—21no—
64C22×D44—21no—
65C22×D44C2311yescharacteristic
66C22×C4×D11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×#125—22no—
70C11×#125—41no—
71C4×D4×C11—22no—
72C4×D4×C11—41no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C42×C11C2311yescharacteristic
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83#66991—22no—
84#66991—22no—
85C2×#4323—22no—
86C2×#4323—22no—
87C2×#4323—41no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4D411yescharacteristic
96C2×(C2×D11)⋊C4D411yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×Dic11⋊C4—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107#66948—22no—
108#66948—41no—
109#66945—22no—
110#66945—41no—
111C11×#107—22no—
112C11×#106D414yescomplemented
113C11×C4⋊C8—22no—
114C11×#102—22no—
115C11×#102—22no—
116#66896—22no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95D411yescharacteristic
122C11⋊#95D411yescharacteristic
123#66885—22no—
124#66885—22no—
125(C2×D11)⋊C8—22no—
126(C2×D11)⋊C8—22no—
127#66882—22no—
128#66879—22no—
129#66873—22no—
130#66872—41no—
131#66871—22no—
132#26815—111nomaximal, Sylow
133C24×C11—21no—
134C23×D11—21no—
135C23×D11C2×D411yescharacteristic
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11#4112yes—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11—81no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C2×C22⋊D11—24no—
152C2×C22⋊D11—81no—
153C2×C22⋊D11—81no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—42no—
167C2×D44—42no—
168C2×D44—81no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—21no—
172C2×C4×D11—21no—
173C2×C4×D11—21no—
174C2×C4×D11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11C2×D412yes—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—42no—
186C11×C4⋊C4—42no—
187C11×C4⋊C4C2×D412yes—
188C11×C4⋊C4C2×D412yes—
189C11×C22⋊C4—42no—
190C42×C11—21no—
191C42×C11—21no—
192C22⋊Dic11—24no—
193C22⋊Dic11—42no—
194C22⋊Dic11—81no—
195#4323—44no—
196(C2×D11)⋊C4—41no—
197(C2×D11)⋊C4—41no—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4—42no—
200(C2×D11)⋊C4—42no—
201(C2×D11)⋊C4—81no—
202(C2×D11)⋊C4—81no—
203(C2×D11)⋊C4—81no—
204(C2×D11)⋊C4—81no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11#4112yes—
211Dic11⋊C4—81no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—42no—
215C4×Dic11—81no—
216C4×Dic11—81no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8#4112yes—
223C2×#482—111no—
224C2×#478D1111yescharacteristic, complemented
225#2490—111no—
226#2363—111no—
227#2067—111no—
228#2059—111no—
229#2033—111no—
230#1999—111no—
231#1972—111no—
232#1925—111no—
233#1925—111no—
234#1924—111no—
235#1879—111no—
236#1854—111no—
237#1776—111no—
238C23×C11—22no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11C22×D411yescharacteristic
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—21no—
250C22×D11—21no—
251C22×D11—21no—
252C22×D11—21no—
253C22×D11—41no—
254C22×D11—41no—
255C22×D11—41no—
256C22×D11—41no—
257C22×D11—41no—
258C22×D11—41no—
259C22×D11—41no—
260D4×C11—22no—
261D4×C11—22no—
262D4×C11—41no—
263D4×C11—41no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—84no—
280C2×C4×C11C22×D411yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11H(5,𝔽2)11yescharacteristic
285C2×C4×C112−1+411yescharacteristic
286C22⋊D11—84no—
287C2×Dic11—22no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305D44—41no—
306D44—41no—
307D44—41no—
308D44—41no—
309D44—84no—
310C4×D11—41no—
311C4×D11—41no—
312C4×D11—41no—
313C4×D11—41no—
314C8×C11—22no—
315C8×C11—41no—
316C11⋊C8—22no—
317C11⋊C8—41no—
318C22×D8—111no—
319C2×#125C2×D1111yescharacteristic
320C2×#121—111no—
321C2×#121—111no—
322C2×C4×D4C2×D1111yescharacteristic
323C2×#117—111no—
324#482—224no—
325#478—24no—
326C2×#107—111no—
327C2×#107—111no—
328C2×#107C2×D1111yescharacteristic
329C2×#106—111no—
330C2×#106C2×D1111yescharacteristic
331C2×C4⋊C8C2×D1111yescharacteristic
332C2×#102—111no—
333C2×#102—111no—
334C2×#102—111no—
335C2×#102—111no—
336C2×#102C2×D1111yescharacteristic
337C2×#102C2×D1111yescharacteristic
338C2×C22⋊C8—111no—
339C2×C22⋊C8—111no—
340C2×#97—111no—
341#397—221no—
342#394—221no—
343#390—111no—
344#390—111no—
345#390—111no—
346#390—221no—
347#390—221no—
348#389—111no—
349#388—221no—
350#388—221no—
351#386—221no—
352#380—111no—
353C4×C4⋊C4—111no—
354C4×C4⋊C4—111no—
355C4×C22⋊C4—111no—
356C4×C22⋊C4—221no—
357#340—111no—
358#340—111no—
359#340—111no—
360#340—111no—
361#336—111no—
362#336—111no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—42no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11—81no—
370C22×C11#52511yescharacteristic
371C22×C11D4211yescharacteristic
372C22×C11#54711yescharacteristic
373C22×C11#57511yescharacteristic
374C22×C11#57511yescharacteristic
375C22×C11#57611yescharacteristic
376C22×C11#57611yescharacteristic
377C2×D11—41no—
378C2×D11—41no—
379C2×D11—41no—
380C2×D11—41no—
381C2×D11—41no—
382C2×D11—41no—
383C2×D11—41no—
384C2×D11—81no—
385C2×D11—81no—
386C2×D11—81no—
387C2×D11—81no—
388C2×D11—81no—
389C2×D11—81no—
390C2×D11—81no—
391C4×C11—41no—
392C4×C11—41no—
393C4×C11—42no—
394C4×C11—42no—
395C4×C11—81no—
396C4×C11#53211yescharacteristic
397C4×C11#54211yescharacteristic
398C4×C11#54811yescharacteristic
399C4×C11#55111yescharacteristic
400Dic11—41no—
401Dic11—41no—
402Dic11—42no—
403Dic11—41no—
404Dic11—81no—
405Dic11—81no—
406C22×D4—111no—
407C22×D4—221no—
408C22×D4—221no—
409C22×D4C22×D1111yescharacteristic
410C23×C4—21no—
411C23×C4—111no—
412C2×D8—222no—
413C2×D8—222no—
414C2×D8—441no—
415C22×C8—111no—
416C22×C8—111no—
417C22×C8C22×D1111yescharacteristic
418C22×C8C22×D1111yescharacteristic
419#125—22no—
420#125—41no—
421#121—222no—
422#121—222no—
423#121—222no—
424#121—441no—
425C4×D4—22no—
426C4×D4—41no—
427#117—222no—
428#117—441no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—111no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—111no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C4⋊C4C22×D1111yescharacteristic
438C2×C22⋊C4—21no—
439C2×C22⋊C4—111no—
440C2×C22⋊C4—111no—
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×C22⋊C4—221no—
448C2×C22⋊C4—221no—
449C2×C22⋊C4—221no—
450C2×C22⋊C4—221no—
451C2×C42—111no—
452C2×C42—221no—
453C2×C42—221no—
454C2×C42—221no—
455C2×C42C22×D1111yescharacteristic
456#107—22no—
457#107—222no—
458#107—222no—
459#106—441no—
460#106C22⋊D1114yescomplemented
461C4⋊C8—22no—
462#102—22no—
463#102—22no—
464#102—222no—
465#102—222no—
466#102—222no—
467#102—222no—
468C22⋊C8—222no—
469C22⋊C8—222no—
470#97—222no—
471#95—111no—
472#95—111no—
473#95—221no—
474#95—221no—
475#95—221no—
476#95—221no—
477C2×C11—82no—
478C2×C11#246111yescharacteristic
479C2×C11#311111yescharacteristic
480C2×C11#312211yescharacteristic
481C2×C11#326811yescharacteristic
482C2×C11#326811yescharacteristic
483C2×C11#334711yescharacteristic
484C2×C11#335511yescharacteristic
485D11—81no—
486D11—161no—
487C24—21no—
488C24—111no—
489C24—221no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—224no—
496C2×D4—221no—
497C2×D4—221no—
498C2×D4—221no—
499C2×D4—221no—
500C2×D4—221no—
501C2×D4—221no—
502C2×D4—442no—
503C2×D4—442no—
504C2×D4—881no—
505C2×D4—881no—
506C2×D4—881no—
507C2×D4#434312yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—81no—
514C22×C4—111no—
515C22×C4—111no—
516C22×C4—111no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4—221no—
524C22×C4—221no—
525C22×C4—221no—
526C22×C4D4×D1111yescharacteristic
527C22×C4D4×D1111yescharacteristic
528C22×C4C23×D1111yescharacteristic
529D8—444no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—112no—
536C2×C8—221no—
537C2×C8—221no—
538C2×C8—221no—
539C2×C8—221no—
540C2×C8—221no—
541C2×C8C2×C22⋊D1112yes—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—112no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—881no—
555C4⋊C4C2×C22⋊D1112yes—
556C4⋊C4C2×C22⋊D1112yes—
557C22⋊C4—42no—
558C22⋊C4—224no—
559C22⋊C4—441no—
560C22⋊C4—441no—
561C22⋊C4—442no—
562C22⋊C4—442no—
563C22⋊C4—442no—
564C22⋊C4—442no—
565C22⋊C4—881no—
566C22⋊C4—881no—
567C22⋊C4—881no—
568C22⋊C4—881no—
569C22⋊C4—881no—
570C42—21no—
571C42—21no—
572C42—221no—
573C42—221no—
574C42—442no—
575C42—881no—
576C42—881no—
577C11#2681511yescharacteristic, complemented, Sylow
578C23—22no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—221no—
586C23—221no—
587C23—221no—
588C23—221no—
589C23—221no—
590C23—221no—
591C23—221no—
592C23—441no—
593C23—441no—
594C23—441no—
595C23—441no—
596C23—441no—
597C23—441no—
598C23—441no—
599C23C2×D4×D1111yescharacteristic
600D4—22no—
601D4—22no—
602D4—41no—
603D4—41no—
604D4—441no—
605D4—441no—
606D4—441no—
607D4—441no—
608D4—884no—
609D4—884no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—84no—
626C2×C4—221no—
627C2×C4—221no—
628C2×C4—221no—
629C2×C4—221no—
630C2×C4—221no—
631C2×C4—221no—
632C2×C4—222no—
633C2×C4—221no—
634C2×C4—221no—
635C2×C4—221no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—441no—
640C2×C4—441no—
641C2×C4—441no—
642C2×C4—441no—
643C2×C4—441no—
644C2×C4—441no—
645C2×C4—441no—
646C2×C4—441no—
647C2×C4—441no—
648C2×C4#6703711yescharacteristic
649C2×C4C2×#434311yescharacteristic
650C2×C4#6704011yescharacteristic
651C2×C4#41×D1111yescharacteristic
652C2×C4#41×D1111yescharacteristic
653C2×C4C22×C22⋊D1111yescharacteristic
654C8—22no—
655C8—41no—
656C8—222no—
657C8—441no—
658C22—42no—
659C22—42no—
660C22—42no—
661C22—81no—
662C22—81no—
663C22—81no—
664C22—81no—
665C22—441no—
666C22—441no—
667C22—441no—
668C22—441no—
669C22—441no—
670C22—441no—
671C22—441no—
672C22—881no—
673C22—881no—
674C22—881no—
675C22—881no—
676C22—881no—
677C22—881no—
678C22—881no—
679C22#1062315811yescharacteristic
680C22#1062316211yescharacteristic
681C22#1062329911yescharacteristic
682C22#1062330011yescharacteristic
683C22#1062330411yescharacteristic
684C22#1062330511yescharacteristic
685C22D4×C22⋊D1111yescharacteristic
686C4—41no—
687C4—42no—
688C4—41no—
689C4—42no—
690C4—81no—
691C4—441no—
692C4—442no—
693C4—441no—
694C4—441no—
695C4—881no—
696C4—881no—
697C4#1062316811yescharacteristic
698C4#1062317111yescharacteristic
699C4#1062334811yescharacteristic
700C4#1062336311yescharacteristic
701C2—82no—
702C2—881no—
703C2—1761no—
704C2#1307259011yescharacteristic
705C2#1307873011yescharacteristic
706C2#1307886111yescharacteristic
707C2#1308015011yescharacteristic
708C2#1308015611yescharacteristic
709C2#1308111311yescharacteristic
710C2#1308121911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#478C2
socleC23×C11C22×D4
prime radical#13069613C2
hypercenterC2×#478D11
hypocenterC11#26815
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#10622479C2semidirect
2. #13072971C2semidirect
3. #13071650C2semidirect
4. #13070003C2semidirect
5. #13069951C2semidirect
6. #13069797C2semidirect
8. #13069489C2semidirect
9. #13069239C2semidirect
10. #13069235C2semidirect
11. #13069228C2semidirect
12. #13068964C2semidirect
13. #13068812C2semidirect
14. #13068516C2semidirect
15. C2×C11×#478C2semidirect
112. C11×#106D4semidirect
224. C2×#478D11semidirect
460. #106C22⋊D11semidirect
577. C11#26815semidirect

Maximal subgroups

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

subgroupindex
C2×#106224792
#130729712
#130716502
#130700032
#130699512
#130697972
#130696132
#130694892
#130692392
#130692352
#130692282
#130689642
#130688122
#130685162
C2×C11×#4782
#2681511