Finite Group Databasebeta

← #14816645

Subgroups — #14816645

Order 2816.

860 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622679C211yesmaximal, characteristic, complemented
2C2×#10622577C211yesmaximal, characteristic, complemented
3#13071652C211yesmaximal, characteristic
4#13070140C211yesmaximal, characteristic, complemented
5#13070118C211yesmaximal, characteristic, complemented
6#13069987C211yesmaximal, characteristic, complemented
7#13069951C211yesmaximal, characteristic, complemented
8#13069382C211yesmaximal, characteristic, complemented
9#13069184C211yesmaximal, characteristic, complemented
10#13069052C211yesmaximal, characteristic
11#13068933C211yesmaximal, characteristic
12#13068862C211yesmaximal, characteristic, complemented
13#13068813C211yesmaximal, characteristic, complemented
14#13068801C211yesmaximal, characteristic, complemented
15C11×#2442C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×#66983C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C11×#400—21no—
23C11×#398—21no—
24C11×#389C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#385—21no—
27C11×#382C2211yescharacteristic
28C11×#380—21no—
29C11×#380C2211yescharacteristic
30C4×C11×C22⋊C4C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32#10622679—24no—
33C2×#66873C2211yescharacteristic
34C2×#66873C2211yescharacteristic
35C2×#66873C2211yescharacteristic
36C2×#66873C2211yescharacteristic
37#10622577—24no—
38C2×#66872C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622570—21no—
45#10622569—21no—
46#10622552C2211yescharacteristic
47C4×C4⋊Dic11C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622282—21no—
52#10622279—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C11×#125—22no—
67C11×#125—41no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—41no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11—21no—
85#66983—22no—
86#66983Q814yes—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91#66979—22no—
92#66979—41no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×#4318—22no—
100C2×#4318—22no—
101C2×#4318—22no—
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C4×D44—22no—
107C4×D44—41no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95D411yescharacteristic
114C11×#95D411yescharacteristic
115C11⋊#95—21no—
116C11⋊#95—21no—
117C22⋊(C11⋊C8)—22no—
118#66873—22no—
119#66873—22no—
120#66873—22no—
121#66873—41no—
122#66872—22no—
123#66872—22no—
124#66872—22no—
125#66871—22no—
126#66871—41no—
127#66871D414yescomplemented
128C4⋊(C11⋊C8)—22no—
129C4⋊(C11⋊C8)—22no—
130#26363—111nomaximal, Sylow
131C24×C11C2×D411yescharacteristic
132C23×D11—21no—
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×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11—81no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×Q812yes—
150C22×C4×C11#4112yes—
151C22×C4×C11C2411yescharacteristic
152C2×C22⋊D11—24no—
153C2×C22⋊D11—81no—
154C2×C22⋊D11—81no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44C2×Q812yes—
164C2×C4×D11—42no—
165C2×C4×D11—42no—
166C2×C4×D11—81no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—42no—
175C11×C4⋊C4—42no—
176C11×C4⋊C4—42no—
177C11×C4⋊C4—81no—
178C11×C4⋊C4—81no—
179C11×C4⋊C4C2×D412yes—
180C11×C22⋊C4—41no—
181C11×C22⋊C4—41no—
182C11×C22⋊C4—42no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C22⋊Dic11—42no—
188(C2×D11)⋊C4—24no—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—81no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11C2×D412yes—
197C4⋊Dic11C2×Q812yes—
198Dic11⋊C4—81no—
199C4×Dic11—42no—
200C4×Dic11—81no—
201#4318—28no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
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⋊C8C2×D412yes—
213C2×C11⋊C8#4112yes—
214C2×#478—111no—
215C2×#428—111no—
216#2442D1111yescharacteristic, complemented
217#2363—111no—
218#2092—111no—
219#2088—111no—
220#2065—111no—
221#2059—111no—
222#1949—111no—
223#1918—111no—
224#1895—111no—
225#1874—111no—
226#1862—111no—
227#1854—111no—
228#1851—111no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11C22⋊Q812yes—
236C23×C11C22×D411yescharacteristic
237C22×D11—22no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
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×C11—41no—
274C2×C4×C11—84no—
275C2×C4×C11C22⋊Q812yes—
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C22×Q811yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11H(5,𝔽2)11yescharacteristic
281C2×C4×C112−1+411yescharacteristic
282C22⋊D11—84no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292D44—22no—
293D44—22no—
294D44—41no—
295D44—41no—
296C4×D11—84no—
297C11⋊C8—22no—
298C11⋊C8—22no—
299C11⋊C8—41no—
300C11⋊C8—41no—
301C22×M16—111no—
302C2×#125C2×D1111yescharacteristic
303C2×#121—111no—
304C2×C4×D4—111no—
305C2×#117—111no—
306C22×C4⋊C4C2×D1111yescharacteristic
307#478—224no—
308#428—224no—
309C2×#107—111no—
310C2×#107—111no—
311C2×#107—111no—
312C2×#106—111no—
313C2×#106—111no—
314C2×#106—111no—
315C2×C4⋊C8—111no—
316C2×C4⋊C8—111no—
317C2×#102—111no—
318C2×#102—111no—
319C2×#102—111no—
320C2×#102—111no—
321C2×C22⋊C8—111no—
322#400—21no—
323#398—21no—
324#390—111no—
325#390—221no—
326#389—111no—
327#389C2×D1111yescharacteristic
328#389C2×D1111yescharacteristic
329#388—221no—
330#386—221no—
331#385—21no—
332#382C2×D1111yescharacteristic
333#380—21no—
334#380C2×D1111yescharacteristic
335C4×C4⋊C4—111no—
336C4×C22⋊C4—221no—
337C4×C22⋊C4C2×D1111yescharacteristic
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#340—111no—
344#336—111no—
345#336—111no—
346C22×C11—22no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11C2×C22⋊Q811yescharacteristic
354C22×C11D4211yescharacteristic
355C22×C11#54711yescharacteristic
356C22×C11#57511yescharacteristic
357C22×C11#57511yescharacteristic
358C22×C11#57611yescharacteristic
359C22×C11#57711yescharacteristic
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—42no—
363C2×D11—81no—
364C2×D11—81no—
365C2×D11—81no—
366C2×D11—81no—
367C4×C11—22no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11—41no—
372C4×C11—42no—
373C4×C11—81no—
374C4×C11—81no—
375C4×C11—81no—
376C4×C11#52511yescharacteristic
377C4×C11#53911yescharacteristic
378C4×C11D4×Q811yescharacteristic
379C4×C11#55411yescharacteristic
380Dic11—42no—
381Dic11—42no—
382Dic11—81no—
383C22×D4—111no—
384C22×D4—221no—
385C23×C4—21no—
386C23×C4—221no—
387C23×C4C22×D1111yescharacteristic
388C2×M16—222no—
389C2×M16—222no—
390C2×M16—222no—
391C22×C8—111no—
392C22×C8—111no—
393C22×C8—111no—
394C22×C8—111no—
395#125—22no—
396#125—41no—
397#121—114no—
398#121—222no—
399C4×D4—222no—
400C4×D4—441no—
401#117—222no—
402#117—441no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—41no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4C22⋊D1111yescharacteristic
425C2×C22⋊C4C22⋊D1111yescharacteristic
426C2×C42—221no—
427C2×C42—221no—
428C2×C42C22×D1111yescharacteristic
429C2×C42C22×D1111yescharacteristic
430#107—114no—
431#107—222no—
432#107—441no—
433#106—222no—
434#106—222no—
435#106—222no—
436C4⋊C8—222no—
437C4⋊C8—222no—
438#102—222no—
439#102—222no—
440#102—222no—
441#102—441no—
442C22⋊C8—222no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—221no—
449#95—221no—
450#95C22⋊D1111yescharacteristic
451#95C22⋊D1111yescharacteristic
452C2×C11—42no—
453C2×C11#244911yescharacteristic
454C2×C11#308011yescharacteristic
455C2×C11#308111yescharacteristic
456C2×C11#327111yescharacteristic
457C2×C11#327311yescharacteristic
458C2×C11#334811yescharacteristic
459C2×C11#335511yescharacteristic
460D11—82no—
461C24—221no—
462C24C2×C22⋊D1111yescharacteristic
463C2×D4—112no—
464C2×D4—224no—
465C2×D4—221no—
466C2×D4—221no—
467C2×D4—221no—
468C2×D4—221no—
469C2×D4—221no—
470C2×D4—881no—
471C2×D4—881no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—81no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—442no—
487C22×C4—442no—
488C22×C4—881no—
489C22×C4Q8×D1112yes—
490C22×C4#434312yes—
491C22×C4C2×C22⋊D1111yescharacteristic
492C22×C4C2×C22⋊D1111yescharacteristic
493C22×C4C2×C22⋊D1111yescharacteristic
494C22×C4C2×C22⋊D1111yescharacteristic
495C22×C4C2×C22⋊D1111yescharacteristic
496C22×C4C23×D1111yescharacteristic
497M16—228no—
498C2×C8—112no—
499C2×C8—112no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—42no—
518C4⋊C4—42no—
519C4⋊C4—42no—
520C4⋊C4—81no—
521C4⋊C4—81no—
522C4⋊C4—112no—
523C4⋊C4—112no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—881no—
529C4⋊C4D4×D1112yes—
530C22⋊C4—41no—
531C22⋊C4—41no—
532C22⋊C4—42no—
533C22⋊C4—224no—
534C22⋊C4—442no—
535C22⋊C4—442no—
536C22⋊C4—442no—
537C22⋊C4—881no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—442no—
543C42—881no—
544C11#2636311yescharacteristic, complemented, Sylow
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—222no—
552C23—441no—
553C23—441no—
554C23—441no—
555C23—441no—
556C23—441no—
557C23—441no—
558C23#6699912yes—
559C23C22×C22⋊D1111yescharacteristic
560D4—222no—
561D4—222no—
562D4—441no—
563D4—441no—
564D4—884no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
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—21no—
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—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—84no—
596C2×C4—222no—
597C2×C4—222no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—884no—
606C2×C4#6699912yes—
607C2×C4C2×D4×D1111yescharacteristic
608C2×C4#6703711yescharacteristic
609C2×C4C2×Q8×D1111yescharacteristic
610C2×C4C2×#434311yescharacteristic
611C2×C4#41×D1111yescharacteristic
612C2×C4#6704311yescharacteristic
613C8—222no—
614C8—222no—
615C8—441no—
616C8—441no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—442no—
625C22—442no—
626C22—442no—
627C22—881no—
628C22—881no—
629C22—881no—
630C22—881no—
631C22D4×C22⋊D1111yescharacteristic
632C22C2×#6699911yescharacteristic
633C22#1062335311yescharacteristic
634C22#1062335311yescharacteristic
635C22#1062335511yescharacteristic
636C22#1062336611yescharacteristic
637C22#1062336811yescharacteristic
638C4—22no—
639C4—41no—
640C4—41no—
641C4—41no—
642C4—41no—
643C4—42no—
644C4—81no—
645C4—81no—
646C4—81no—
647C4—442no—
648C4—442no—
649C4—881no—
650C4#1062315811yescharacteristic
651C4#1062316311yescharacteristic
652C4#1062316711yescharacteristic
653C4#1062317611yescharacteristic
654C2—42no—
655C2—882no—
656C2#1307242111yescharacteristic
657C2#1307843411yescharacteristic
658C2#1307844111yescharacteristic
659C2#1308020211yescharacteristic
660C2#1308022311yescharacteristic
661C2#1308112511yescharacteristic
662C2#1308121611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2442C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#2442D11
hypocenterC11#26363
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2442

Complements

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

NH ≅ G/Ntype
1. C2×#10622679C2semidirect
2. C2×#10622577C2semidirect
4. #13070140C2semidirect
5. #13070118C2semidirect
6. #13069987C2semidirect
7. #13069951C2semidirect
8. #13069382C2semidirect
9. #13069184C2semidirect
12. #13068862C2semidirect
13. #13068813C2semidirect
14. #13068801C2semidirect
15. C11×#2442C2semidirect
127. #66871D4semidirect
216. #2442D11semidirect
544. C11#26363semidirect

Maximal subgroups

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

subgroupindex
C2×#106226792
C2×#106225772
#130716522
#130701402
#130701182
#130699872
#130699512
#130693822
#130691842
#130690522
#130689332
#130688622
#130688132
#130688012
C11×#24422
#2636311