Finite Group Databasebeta

← #14771043

Subgroups — #14771043

Order 2816.

934 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622838C211yesmaximal, characteristic
2#13071507C211yesmaximal, characteristic
3#13069309C211yesmaximal, characteristic, complemented
4#13069295C211yesmaximal, characteristic, complemented
5#13069254C211yesmaximal, characteristic, complemented
6#13069247C211yesmaximal, characteristic, complemented
7#13068884C211yesmaximal, characteristic, complemented
8#13068870C211yesmaximal, characteristic, complemented
9#13068708C211yesmaximal, characteristic
10#13068647C211yesmaximal, characteristic
11#13068551C211yesmaximal, characteristic
12#13068446C211yesmaximal, characteristic, complemented
13C4×#66899C211yesmaximal, characteristic, complemented
14#13068400C211yesmaximal, characteristic
15Q8×C11×C22⋊C4C211yesmaximal, characteristic
16C23×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C11×#391—21no—
22C11×#391—21no—
23C11×#391C2211yescharacteristic
24C11×#391C2211yescharacteristic
25C11×#380—21no—
26C11×#380C2211yescharacteristic
27C4×C11×C22⋊C4—21no—
28C4×C11×C22⋊C4C2211yescharacteristic
29#10622838C418yescomplemented
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38#10622825C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42#10622558—21no—
43#10622558—21no—
44C4×C4⋊Dic11C2211yescharacteristic
45C4×C4⋊Dic11C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622541C2211yescharacteristic
48C2×#66867C2211yescharacteristic
49C2×C4×C11⋊C8C2211yescharacteristic
50#10622264—21no—
51#10622262—21no—
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×Q8×C11—21no—
61C22×Q8×C11—22no—
62C22×Q8×C11—22no—
63C22×Q8×C11—22no—
64C22×Q8×C11—41no—
65C22×Q8×C11—41no—
66C22×Q8×C11C2×C414yes—
67C22×Q8×C11C2311yescharacteristic
68C22×Q8×C11C2311yescharacteristic
69C23×C4×C11—21no—
70C23×C4×C11C2311yescharacteristic
71C4×Q8×C11—22no—
72C4×Q8×C11—22no—
73C4×Q8×C11—41no—
74C4×Q8×C11—41no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C42×C11—21no—
83C2×C42×C11—21no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88#66979—22no—
89#66979C2×C414yes—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×#4318—41no—
100C2×#4318—41no—
101C2×#4318C2×C414yes—
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C11×#95—21no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95D411yescharacteristic
112C11×#95D411yescharacteristic
113#66899—22no—
114#66899—22no—
115#66899—41no—
116#66899—41no—
117#66899C2×C414yes—
118#66899C2×C414yes—
119#66899C2×C414yes—
120#66899C2×C414yes—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C22⋊(C11⋊C8)—22no—
127#66872—41no—
128#66871—41no—
129#66867—41no—
130C4×C11⋊C8—41no—
131#22581—111nomaximal, Sylow
132C24×C11C2×D411yescharacteristic
133C2×Q8×C11—24no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—28no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—42no—
144C2×Q8×C11—42no—
145C2×Q8×C11—44no—
146C2×Q8×C11—44no—
147C2×Q8×C11—44no—
148C2×Q8×C11C22×C412yes—
149C2×Q8×C11C22×C412yes—
150C2×Q8×C11#4112yes—
151C2×Q8×C11#4112yes—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—24no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—42no—
162C22×C4×C11—42no—
163C22×C4×C11C22×C412yes—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11#4112yes—
170C22×C4×C11C2411yescharacteristic
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—42no—
180C11×C4⋊C4—42no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—41no—
183C11×C22⋊C4—42no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—42no—
189C42×C11—42no—
190C22⋊Dic11—24no—
191C22⋊Dic11—81no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11C22×C412yes—
199C4⋊Dic11C22×C412yes—
200Dic11⋊C4—42no—
201Dic11⋊C4—42no—
202C4×Dic11—24no—
203C4×Dic11—81no—
204C4×Dic11—81no—
205#4318—44no—
206C2×C11⋊C8—21no—
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⋊C8C22×C412yes—
217C2×C11⋊C8C22×C412yes—
218C2×#419—111no—
219#2347—111no—
220Q8×C22⋊C4D1111yescharacteristic
221#1935—111no—
222#1933—111no—
223#1928—111no—
224#1927—111no—
225#1865—111no—
226#1863—111no—
227#1825—111no—
228#1809—111no—
229#1787—111no—
230#1763—111no—
231C4×#103—111no—
232#1753—111no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11C4×D412yes—
240C23×C11C22×D411yescharacteristic
241Q8×C11—22no—
242Q8×C11—22no—
243Q8×C11—22no—
244Q8×C11—22no—
245Q8×C11—22no—
246Q8×C11—48no—
247Q8×C11—41no—
248Q8×C11—41no—
249Q8×C11#11714yes—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
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—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—48no—
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—41no—
280C2×C4×C11C4×D412yes—
281C2×C4×C11#13712yes—
282C2×C4×C11C23×C411yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11H(5,𝔽2)11yescharacteristic
287C2×C4×C11H(5,𝔽2)11yescharacteristic
288C2×Dic11—22no—
289C2×Dic11—22no—
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—
300C11⋊C8—22no—
301C11⋊C8—22no—
302C11⋊C8—41no—
303C11⋊C8—41no—
304C23×Q8C2×D1111yescharacteristic
305C22×M16—111no—
306C2×C4×Q8C2×D1111yescharacteristic
307C2×C4×Q8C2×D1111yescharacteristic
308C2×#117—111no—
309C2×#107—111no—
310C2×#106—111no—
311#419—118no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#103—111no—
318C2×#103—111no—
319C2×#103—111no—
320C2×C22⋊C8—111no—
321C2×#97—111no—
322C2×C4×C8—111no—
323#391—21no—
324#391—21no—
325#391C2×D1111yescharacteristic
326#391C2×D1111yescharacteristic
327#389—111no—
328#389—111no—
329#388—221no—
330#388—221no—
331#383—221no—
332#380—21no—
333#380—111no—
334#380C2×D1111yescharacteristic
335C4×C4⋊C4—111no—
336C4×C4⋊C4—111no—
337C4×C4⋊C4—221no—
338C4×C22⋊C4—21no—
339C4×C22⋊C4C2×D1111yescharacteristic
340#340—111no—
341#340—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#340—111no—
346#336—111no—
347#336—111no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11C2×C4×D411yescharacteristic
356C22×C11#54611yescharacteristic
357C22×C11#54611yescharacteristic
358C22×C11C2×#13711yescharacteristic
359C22×C11#57511yescharacteristic
360C22×C11#57711yescharacteristic
361C22×C11#57811yescharacteristic
362C4×C11—22no—
363C4×C11—24no—
364C4×C11—22no—
365C4×C11—41no—
366C4×C11—42no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11—81no—
370C4×C11—81no—
371C4×C11C2×#11711yescharacteristic
372C4×C11#51811yescharacteristic
373C4×C11#55111yescharacteristic
374C4×C11#55111yescharacteristic
375Dic11—42no—
376Dic11—42no—
377Dic11—81no—
378Dic11—81no—
379C22×Q8—22no—
380C22×Q8—21no—
381C22×Q8—22no—
382C22×Q8—22no—
383C22×Q8—41no—
384C22×Q8—41no—
385C22×Q8C4×D1114yes—
386C22×Q8C22×D1111yescharacteristic
387C22×Q8C22×D1111yescharacteristic
388C23×C4—21no—
389C23×C4C22×D1111yescharacteristic
390C2×M16—114no—
391C2×M16—441no—
392C2×M16—441no—
393C22×C8—111no—
394C22×C8—111no—
395C22×C8—111no—
396C22×C8—111no—
397C4×Q8—22no—
398C4×Q8—22no—
399C4×Q8—41no—
400C4×Q8—41no—
401#117—114no—
402#117—222no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C4⋊C4C22×D1111yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4C22⋊D1111yescharacteristic
417C2×C22⋊C4C22⋊D1111yescharacteristic
418C2×C42—21no—
419C2×C42—21no—
420C2×C42—221no—
421C2×C42—221no—
422C2×C42—221no—
423C2×C42C22×D1111yescharacteristic
424C2×C42C22×D1111yescharacteristic
425#107—441no—
426#106—441no—
427#103—114no—
428#103—114no—
429#103—114no—
430#103—114no—
431#103—222no—
432#103—222no—
433#103—441no—
434#103—441no—
435C22⋊C8—222no—
436#97—441no—
437C4×C8—441no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95C22⋊D1111yescharacteristic
449#95C22⋊D1111yescharacteristic
450C2×C11—42no—
451C2×C11#234211yescharacteristic
452C2×C11C4×#13711yescharacteristic
453C2×C11#294711yescharacteristic
454C2×C11#331311yescharacteristic
455C2×C11#332011yescharacteristic
456C2×C11#332611yescharacteristic
457C2×C11#332811yescharacteristic
458C24C2×C22⋊D1111yescharacteristic
459C2×Q8—24no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—28no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8C2×C4×D1112yes—
475C2×Q8C2×C4×D1112yes—
476C2×Q8#434112yes—
477C2×Q8#434112yes—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—24no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4C2×C4×D1112yes—
494C22×C4#433912yes—
495C22×C4C2×C22⋊D1111yescharacteristic
496C22×C4C2×C22⋊D1111yescharacteristic
497C22×C4C2×C22⋊D1111yescharacteristic
498C22×C4C2×C22⋊D1111yescharacteristic
499C22×C4C2×C22⋊D1111yescharacteristic
500C22×C4C23×D1111yescharacteristic
501M16—444no—
502C2×C8—112no—
503C2×C8—112no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—42no—
519C4⋊C4—42no—
520C4⋊C4—112no—
521C4⋊C4—112no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—442no—
529C4⋊C4—442no—
530C22⋊C4—22no—
531C22⋊C4—41no—
532C22⋊C4—42no—
533C22⋊C4—224no—
534C22⋊C4—881no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—42no—
540C42—42no—
541C42—224no—
542C42—881no—
543C42—881no—
544C11#2258111yescharacteristic, complemented, Sylow
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23C4×C22⋊D1112yes—
552C23C22×C22⋊D1111yescharacteristic
553Q8—22no—
554Q8—22no—
555Q8—22no—
556Q8—22no—
557Q8—22no—
558Q8—48no—
559Q8—41no—
560Q8—41no—
561Q8#6693014yes—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—48no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—441no—
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×C4C4×C22⋊D1112yes—
605C2×C4#6699512yes—
606C2×C4C22×C4×D1111yescharacteristic
607C2×C4C2×#433911yescharacteristic
608C2×C4C2×#434111yescharacteristic
609C2×C4C2×#434111yescharacteristic
610C2×C4#6703711yescharacteristic
611C2×C4#6703711yescharacteristic
612C8—222no—
613C8—222no—
614C8—441no—
615C8—441no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22C2×C4×C22⋊D1111yescharacteristic
624C22#1062333711yescharacteristic
625C22#1062333711yescharacteristic
626C22C2×#6699511yescharacteristic
627C22#1062335311yescharacteristic
628C22#1062336811yescharacteristic
629C22#1062336911yescharacteristic
630C4—22no—
631C4—24no—
632C4—22no—
633C4—41no—
634C4—41no—
635C4—42no—
636C4—41no—
637C4—81no—
638C4—81no—
639C4—442no—
640C4—442no—
641C4—881no—
642C4—881no—
643C4C2×#6693011yescharacteristic
644C4#1062301711yescharacteristic
645C4#1062302611yescharacteristic
646C4#1062302611yescharacteristic
647C2—42no—
648C2#1307146111yescharacteristic
649C2C4×#6699511yescharacteristic
650C2#1307745911yescharacteristic
651C2#1308068211yescharacteristic
652C2#1308078711yescharacteristic
653C2#1308086911yescharacteristic
654C2#1308089911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingQ8×C11×C22⋊C4C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterQ8×C22⋊C4D11
hypocenterC11#22581
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #13069309C2semidirect
4. #13069295C2semidirect
5. #13069254C2semidirect
6. #13069247C2semidirect
7. #13068884C2semidirect
8. #13068870C2semidirect
12. #13068446C2semidirect
13. C4×#66899C2semidirect
29. #10622838C4semidirect
544. C11#22581semidirect

Maximal subgroups

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

subgroupindex
C2×#106228382
#130715072
#130693092
#130692952
#130692542
#130692472
#130688842
#130688702
#130687082
#130686472
#130685512
#130684462
C4×#668992
#130684002
Q8×C11×C22⋊C42
#2258111