Finite Group Databasebeta

← #14816643

Subgroups — #14816643

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×#10622622C211yesmaximal, characteristic, complemented
2C2×#10622608C211yesmaximal, characteristic, complemented
3#13072340C211yesmaximal, characteristic, complemented
4#13070137C211yesmaximal, characteristic, complemented
5#13070117C211yesmaximal, characteristic, complemented
6#13069990C211yesmaximal, characteristic, complemented
7#13069954C211yesmaximal, characteristic, complemented
8#13069384C211yesmaximal, characteristic, complemented
9#13069187C211yesmaximal, characteristic, complemented
10#13069055C211yesmaximal, characteristic
11#13068934C211yesmaximal, characteristic
12#13068863C211yesmaximal, characteristic, complemented
13#13068815C211yesmaximal, characteristic, complemented
14#13068801C211yesmaximal, characteristic, complemented
15C11×#2363C211yesmaximal, characteristic
16C2×C11×#121C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C2×#66923C2211yescharacteristic
22C11×#390—21no—
23C11×#390C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C11×#388—21no—
26C11×#386—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C22⋊C4—21no—
29C4×C11×C22⋊C4C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34#10622825C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36#10622622—24no—
37#10622608—24no—
38C2×#66872C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622559—21no—
45#10622555—21no—
46#10622549C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622273—21no—
52#10622270—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11C2311yescharacteristic
65C23×Dic11—21no—
66C11×#121—22no—
67C11×#121Q814yes—
68C4×D4×C11—22no—
69C4×D4×C11—41no—
70C11×#117—22no—
71C11×#117—41no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C42×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C22⋊Dic11—21no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—41no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×#4318—22no—
100C2×#4318—22no—
101C2×#4318—22no—
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106#66923—22no—
107#66923—41no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95D411yescharacteristic
111C11×#95D411yescharacteristic
112#66896—22no—
113#66896—22no—
114#66896—22no—
115#66896—41no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C22⋊(C11⋊C8)—22no—
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×C11—21no—
132C24×C11C2×D411yescharacteristic
133C2×D4×C11—24no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—81no—
140C2×D4×C11—81no—
141C2×D4×C11C2×Q812yes—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11—81no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×Q812yes—
158C22×C4×C11#4112yes—
159C22×C4×C11C2411yescharacteristic
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—42no—
165C22×Dic11—42no—
166C22×Dic11—81no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—81no—
172C11×C4⋊C4C2×D412yes—
173C11×C4⋊C4C2×Q812yes—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—41no—
176C11×C22⋊C4—41no—
177C11×C22⋊C4—42no—
178C11×C22⋊C4—42no—
179C11×C22⋊C4—42no—
180C11×C22⋊C4—81no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—42no—
186C42×C11—81no—
187C22⋊Dic11—42no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—42no—
196C4⋊Dic11C2×D412yes—
197Dic11⋊C4—42no—
198Dic11⋊C4—42no—
199Dic11⋊C4—81no—
200Dic11⋊C4—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#2442—111no—
217#2363D1111yescharacteristic
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×C11—22no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11C22⋊Q812yes—
243C23×C11C22×D411yescharacteristic
244D4×C11—22no—
245D4×C11—22no—
246D4×C11—41no—
247D4×C11—41no—
248D4×C11—84no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—21no—
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—21no—
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—84no—
277C2×C4×C11C22⋊Q812yes—
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C22×Q811yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11H(5,𝔽2)11yescharacteristic
283C2×C4×C112−1+411yescharacteristic
284C2×Dic11—22no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—84no—
297C11⋊C8—22no—
298C11⋊C8—22no—
299C11⋊C8—41no—
300C11⋊C8—41no—
301C22×M16—111no—
302C2×#125—111no—
303C2×#121C2×D1111yescharacteristic
304C2×C4×D4C2×D1111yescharacteristic
305C2×#117C2×D1111yescharacteristic
306C22×C4⋊C4—111no—
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—221no—
323#398—221no—
324#390—21no—
325#390C2×D1111yescharacteristic
326#389—111no—
327#389—111no—
328#389C2×D1111yescharacteristic
329#388—21no—
330#386—21no—
331#385—221no—
332#382—111no—
333#380—111no—
334#380—221no—
335C4×C4⋊C4C2×D1111yescharacteristic
336C4×C22⋊C4—21no—
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×C11—42no—
354C22×C11—42no—
355C22×C11—42no—
356C22×C11—81no—
357C22×C11—81no—
358C22×C11—81no—
359C22×C11—81no—
360C22×C11C2×C22⋊Q811yescharacteristic
361C22×C11D4211yescharacteristic
362C22×C11#54711yescharacteristic
363C22×C11#57511yescharacteristic
364C22×C11#57511yescharacteristic
365C22×C11#57611yescharacteristic
366C22×C11#57711yescharacteristic
367C4×C11—22no—
368C4×C11—42no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11—41no—
372C4×C11—41no—
373C4×C11—42no—
374C4×C11—81no—
375C4×C11#52511yescharacteristic
376C4×C11#53911yescharacteristic
377C4×C11D4×Q811yescharacteristic
378C4×C11#55411yescharacteristic
379Dic11—42no—
380Dic11—81no—
381Dic11—81no—
382Dic11—81no—
383C22×D4—21no—
384C22×D4C22×D1111yescharacteristic
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—222no—
396#125—441no—
397#121—22no—
398#121Dic2214yes—
399C4×D4—22no—
400C4×D4—41no—
401#117—22no—
402#117—41no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—222no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—441no—
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4C22⋊D1111yescharacteristic
425C2×C22⋊C4C22⋊D1111yescharacteristic
426C2×C42—21no—
427C2×C42—21no—
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—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95C22⋊D1111yescharacteristic
451#95C22⋊D1111yescharacteristic
452C2×C11—42no—
453C2×C11—82no—
454C2×C11#244911yescharacteristic
455C2×C11#308011yescharacteristic
456C2×C11#308111yescharacteristic
457C2×C11#327111yescharacteristic
458C2×C11#327311yescharacteristic
459C2×C11#334811yescharacteristic
460C2×C11#335511yescharacteristic
461C24—21no—
462C24C2×C22⋊D1111yescharacteristic
463C2×D4—24no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—81no—
470C2×D4—81no—
471C2×D4C2×Dic2212yes—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—81no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—442no—
487C22×C4—442no—
488C22×C4—881no—
489C22×C4C2×Dic2212yes—
490C22×C4#433912yes—
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—81no—
515C4⋊C4—112no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—442no—
524C4⋊C4—442no—
525C4⋊C4—442no—
526C4⋊C4—881no—
527C4⋊C4—881no—
528C4⋊C4C2×Dic2212yes—
529C4⋊C4D4×D1112yes—
530C22⋊C4—24no—
531C22⋊C4—41no—
532C22⋊C4—41no—
533C22⋊C4—42no—
534C22⋊C4—42no—
535C22⋊C4—42no—
536C22⋊C4—81no—
537C22⋊C4—442no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—42no—
543C42—81no—
544C11#2636311yescharacteristic, complemented, Sylow
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—22no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23#6697712yes—
559C23C22×C22⋊D1111yescharacteristic
560D4—22no—
561D4—22no—
562D4—41no—
563D4—41no—
564D4—84no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
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—21no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—84no—
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×C4—441no—
605C2×C4—884no—
606C2×C4#6697712yes—
607C2×C4C22×Dic2211yescharacteristic
608C2×C4C2×#433911yescharacteristic
609C2×C4C2×D4×D1111yescharacteristic
610C2×C4#6703711yescharacteristic
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—42no—
625C22—42no—
626C22—42no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22C2×#6697711yescharacteristic
632C22D4×C22⋊D1111yescharacteristic
633C22#1062335311yescharacteristic
634C22#1062335311yescharacteristic
635C22#1062335511yescharacteristic
636C22#1062336611yescharacteristic
637C22#1062336711yescharacteristic
638C4—22no—
639C4—41no—
640C4—41no—
641C4—41no—
642C4—41no—
643C4—42no—
644C4—42no—
645C4—81no—
646C4—442no—
647C4—881no—
648C4—881no—
649C4—881no—
650C4D4×Dic2211yescharacteristic
651C4#1062307011yescharacteristic
652C4#1062307811yescharacteristic
653C4#1062309511yescharacteristic
654C2—42no—
655C2—82no—
656C2#1307241911yescharacteristic
657C2#1307843811yescharacteristic
658C2#1307844711yescharacteristic
659C2#1308019711yescharacteristic
660C2#1308022311yescharacteristic
661C2#1308113111yescharacteristic
662C2#1308121611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2363C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#2363D11
hypocenterC11#26363
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2363

Complements

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

NH ≅ G/Ntype
1. C2×#10622622C2semidirect
2. C2×#10622608C2semidirect
3. #13072340C2semidirect
4. #13070137C2semidirect
5. #13070117C2semidirect
6. #13069990C2semidirect
7. #13069954C2semidirect
8. #13069384C2semidirect
9. #13069187C2semidirect
12. #13068863C2semidirect
13. #13068815C2semidirect
14. #13068801C2semidirect
127. #66871D4semidirect
544. C11#26363semidirect

Maximal subgroups

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

subgroupindex
C2×#106226222
C2×#106226082
#130723402
#130701372
#130701172
#130699902
#130699542
#130693842
#130691872
#130690552
#130689342
#130688632
#130688152
#130688012
C11×#23632
#2636311