Finite Group Databasebeta

← #14771100

Subgroups — #14771100

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×#10622617C211yesmaximal, characteristic
2#13071501C211yesmaximal, characteristic
3#13071448C211yesmaximal, characteristic
4#13069307C211yesmaximal, characteristic, complemented
5#13069293C211yesmaximal, characteristic, complemented
6#13069255C211yesmaximal, characteristic, complemented
7#13069248C211yesmaximal, characteristic, complemented
8#13068885C211yesmaximal, characteristic, complemented
9#13068871C211yesmaximal, characteristic, complemented
10#13068647C211yesmaximal, characteristic
11#13068552C211yesmaximal, characteristic
12#13068445C211yesmaximal, characteristic, complemented
13#13068435C211yesmaximal, characteristic, complemented
14#13068402C211yesmaximal, characteristic
15C11×#1825C211yesmaximal, characteristic
16C23×Dic22C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19C2×#66940C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C11×#380C2211yescharacteristic
23#10622825C2211yescharacteristic
24C4×C22⋊Dic11C2211yescharacteristic
25C2×#66880C2211yescharacteristic
26C2×#66880C2211yescharacteristic
27C2×#66880C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×#66879C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31#10622617C418yescomplemented
32#10622598C2211yescharacteristic
33#10622598C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36#10622587C2211yescharacteristic
37#10622587C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622564—21no—
45#10622564—21no—
46#10622555—21no—
47C22⋊C4×Dic11—21no—
48#10622549—21no—
49#10622545—21no—
50#10622259—21no—
51#10622259—21no—
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×Dic11—21no—
62C22×Dic22—22no—
63C22×Dic22—22no—
64C22×Dic22—21no—
65C22×Dic22—22no—
66C22×Dic22—41no—
67C22×Dic22—41no—
68C22×Dic22C2×C414yes—
69C22×Dic22C2311yescharacteristic
70C22×Dic22C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×#117—22no—
74C11×#117C2×C414yes—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C42×C11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11D411yescharacteristic
84C2×C22⋊Dic11D411yescharacteristic
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11C2311yescharacteristic
96C2×C4×Dic11C2311yescharacteristic
97C2×#4318—41no—
98C2×#4318—41no—
99C2×#4318C2×C414yes—
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102#66940—22no—
103#66940—22no—
104#66940—41no—
105#66940—41no—
106C11×C22⋊C8—22no—
107C11×#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95D411yescharacteristic
118C11⋊#95D411yescharacteristic
119#66880—22no—
120#66880—22no—
121#66880—41no—
122#66880—41no—
123#66879—41no—
124C8×Dic11—41no—
125#66874C2×C414yes—
126#66874C2×C414yes—
127#66874C2×C414yes—
128#66874C2×C414yes—
129#66872—41no—
130#66871—41no—
131#22585—111nomaximal, Sylow
132C24×C11C2×D411yescharacteristic
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×C11C22×C412yes—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11#4112yes—
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—24no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—42no—
151C22×Dic11—42no—
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C2×Dic22—28no—
157C2×Dic22—24no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—44no—
167C2×Dic22—44no—
168C2×Dic22—44no—
169C2×Dic22—42no—
170C2×Dic22—42no—
171C2×Dic22C22×C412yes—
172C2×Dic22C22×C412yes—
173C2×Dic22#4112yes—
174C2×Dic22#4112yes—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4C22×C412yes—
188C11×C4⋊C4C22×C412yes—
189C11×C22⋊C4—24no—
190C11×C22⋊C4—42no—
191C42×C11—24no—
192C22⋊Dic11—22no—
193C22⋊Dic11—41no—
194C22⋊Dic11—81no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—81no—
200C4⋊Dic11—81no—
201Dic11⋊C4—42no—
202Dic11⋊C4—42no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—42no—
208C4×Dic11—42no—
209C4×Dic11—42no—
210C4×Dic11—42no—
211#4318—44no—
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#2346—111no—
220Q8×C22⋊C4—111no—
221#1935—111no—
222#1933—111no—
223#1928—111no—
224#1927—111no—
225#1865—111no—
226#1863—111no—
227#1825D1111yescharacteristic
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
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11C4×D412yes—
260C2×C4×C11C23×C411yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11H(5,𝔽2)11yescharacteristic
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C2×Dic11—22no—
267C2×Dic11—21no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—21no—
271C2×Dic11—22no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—48no—
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#13712yes—
291Dic22—22no—
292Dic22—22no—
293Dic22—22no—
294Dic22—22no—
295Dic22—22no—
296Dic22—48no—
297Dic22—41no—
298Dic22—41no—
299Dic22#11714yes—
300C8×C11—41no—
301C8×C11—41no—
302C11⋊C8—22no—
303C11⋊C8—22no—
304C23×Q8—111no—
305C22×M16—111no—
306C2×C4×Q8—111no—
307C2×C4×Q8—111no—
308C2×#117C2×D1111yescharacteristic
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⋊C8C2×D1111yescharacteristic
321C2×#97—111no—
322C2×C4×C8—111no—
323#391—111no—
324#391—111no—
325#391—221no—
326#391—221no—
327#389—111no—
328#389—111no—
329#388—221no—
330#388—221no—
331#382—221no—
332#380—111no—
333#380—221no—
334#380C2×D1111yescharacteristic
335C4×C4⋊C4—111no—
336C4×C4⋊C4—111no—
337C4×C22⋊C4—111no—
338C4×C22⋊C4—221no—
339#376—221no—
340#340—111no—
341#340—111no—
342#340C2×D1111yescharacteristic
343#340C2×D1111yescharacteristic
344#340C2×D1111yescharacteristic
345#340C2×D1111yescharacteristic
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—42no—
364C4×C11—42no—
365C4×C11—81no—
366C4×C11—81no—
367C4×C11C2×#11711yescharacteristic
368C4×C11#51811yescharacteristic
369C4×C11#55111yescharacteristic
370C4×C11#55111yescharacteristic
371Dic11—24no—
372Dic11—22no—
373Dic11—41no—
374Dic11—42no—
375Dic11—41no—
376Dic11—41no—
377Dic11—81no—
378Dic11—81no—
379C22×Q8—114no—
380C22×Q8—111no—
381C22×Q8—111no—
382C22×Q8—222no—
383C22×Q8—222no—
384C22×Q8—221no—
385C22×Q8—222no—
386C22×Q8—441no—
387C22×Q8—441no—
388C23×C4—221no—
389C23×C4C22×D1111yescharacteristic
390C2×M16—114no—
391C2×M16—441no—
392C2×M16—441no—
393C22×C8—111no—
394C22×C8—111no—
395C22×C8C22×D1111yescharacteristic
396C22×C8C22×D1111yescharacteristic
397C4×Q8—222no—
398C4×Q8—222no—
399C4×Q8—441no—
400C4×Q8—441no—
401#117—22no—
402#117C4×D1114yes—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C4⋊C4C22×D1111yescharacteristic
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C4⋊C4C22×D1111yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—111no—
416C2×C22⋊C4—111no—
417C2×C22⋊C4—221no—
418C2×C42—21no—
419C2×C42—111no—
420C2×C42—111no—
421C2×C42—221no—
422C2×C42—221no—
423C2×C42—221no—
424C2×C42—221no—
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—22no—
436#97—441no—
437C4×C8—441no—
438#95—21no—
439#95—111no—
440#95—111no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450C2×C11—42no—
451C2×C11#234211yescharacteristic
452C2×C11C4×#13711yescharacteristic
453C2×C11#294711yescharacteristic
454C2×C11#331211yescharacteristic
455C2×C11#332111yescharacteristic
456C2×C11#332711yescharacteristic
457C2×C11#332911yescharacteristic
458C24D4×D1111yescharacteristic
459C2×Q8—112no—
460C2×Q8—112no—
461C2×Q8—112no—
462C2×Q8—112no—
463C2×Q8—228no—
464C2×Q8—224no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×Q8—221no—
471C2×Q8—221no—
472C2×Q8—221no—
473C2×Q8—442no—
474C2×Q8—442no—
475C2×Q8—444no—
476C2×Q8—444no—
477C2×Q8—444no—
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—111no—
487C22×C4—111no—
488C22×C4—111no—
489C22×C4—111no—
490C22×C4—221no—
491C22×C4—224no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—442no—
496C22×C4—442no—
497C22×C4C2×C4×D1112yes—
498C22×C4D4×D1111yescharacteristic
499C22×C4#434112yes—
500C22×C4C23×D1111yescharacteristic
501M16—444no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—112no—
509C2×C8—112no—
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—21no—
519C4⋊C4—21no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—442no—
525C4⋊C4—442no—
526C4⋊C4—881no—
527C4⋊C4—881no—
528C4⋊C4C2×C4×D1112yes—
529C4⋊C4C2×C4×D1112yes—
530C22⋊C4—24no—
531C22⋊C4—42no—
532C22⋊C4—222no—
533C22⋊C4—441no—
534C22⋊C4—881no—
535C42—24no—
536C42—221no—
537C42—221no—
538C42—221no—
539C42—221no—
540C42—442no—
541C42—442no—
542C42—442no—
543C42—442no—
544C11#2258511yescharacteristic, complemented, Sylow
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23(C22⋊D11)⋊C412yes—
552C23C2×D4×D1111yescharacteristic
553Q8—114no—
554Q8—222no—
555Q8—222no—
556Q8—222no—
557Q8—222no—
558Q8—222no—
559Q8—448no—
560Q8—441no—
561Q8—441no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—112no—
581C2×C4—222no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—448no—
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(C22⋊D11)⋊C412yes—
606C2×C4C22×C4×D1111yescharacteristic
607C2×C4C2×#434111yescharacteristic
608C2×C4#41×D1111yescharacteristic
609C2×C4#41×D1111yescharacteristic
610C2×C4#6704211yescharacteristic
611C2×C4#6704211yescharacteristic
612C8—41no—
613C8—41no—
614C8—222no—
615C8—222no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22C2×(C22⋊D11)⋊C411yescharacteristic
624C22#1062318511yescharacteristic
625C22#1062318511yescharacteristic
626C22#1062330111yescharacteristic
627C22#1062330211yescharacteristic
628C22#1062330411yescharacteristic
629C22D11×#13711yescharacteristic
630C4—22no—
631C4—42no—
632C4—42no—
633C4—81no—
634C4—81no—
635C4—222no—
636C4—224no—
637C4—441no—
638C4—441no—
639C4—442no—
640C4—441no—
641C4—881no—
642C4—881no—
643C4D11×#11711yescharacteristic
644C4#1062305211yescharacteristic
645C4#1062318911yescharacteristic
646C4#1062318911yescharacteristic
647C2—42no—
648C2#1307145811yescharacteristic
649C2#1307744011yescharacteristic
650C2#1307746211yescharacteristic
651C2#1308067011yescharacteristic
652C2#1308080511yescharacteristic
653C2#1308088211yescharacteristic
654C2#1308090811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1825C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1825D11
hypocenterC11#22585
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1825

Complements

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

NH ≅ G/Ntype
4. #13069307C2semidirect
5. #13069293C2semidirect
6. #13069255C2semidirect
7. #13069248C2semidirect
8. #13068885C2semidirect
9. #13068871C2semidirect
12. #13068445C2semidirect
13. #13068435C2semidirect
31. #10622617C4semidirect
544. C11#22585semidirect

Maximal subgroups

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

subgroupindex
C2×#106226172
#130715012
#130714482
#130693072
#130692932
#130692552
#130692482
#130688852
#130688712
#130686472
#130685522
#130684452
#130684352
#130684022
C11×#18252
#2258511