Finite Group Databasebeta

← #14775791

Subgroups — #14775791

Order 2816.

850 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622700C211yesmaximal, characteristic
2#13071527C211yesmaximal, characteristic
3#13069590C211yesmaximal, characteristic, complemented
4#13069384C211yesmaximal, characteristic, complemented
5#13069351C211yesmaximal, characteristic, complemented
6#13069346C211yesmaximal, characteristic, complemented
7#13069208C211yesmaximal, characteristic, complemented
8#13069187C211yesmaximal, characteristic, complemented
9#13068876C211yesmaximal, characteristic
10#13068862C211yesmaximal, characteristic
11#13068491C211yesmaximal, characteristic, complemented
12#13068444C211yesmaximal, characteristic
13#13068444C211yesmaximal, characteristic
14C4×#66873C211yesmaximal, characteristic
15C11×#2369C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C2×C4×D44C2211yescharacteristic
20C11×#391—21no—
21C11×#391—21no—
22C11×#389—21no—
23C11×#389C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C4×C11×C4⋊C4—21no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C4×C11×C4⋊C4C2211yescharacteristic
30#10622700C418yescomplemented
31#10622602—21no—
32#10622602—21no—
33C2×#66873C2211yescharacteristic
34C2×#66873C2211yescharacteristic
35C2×#66873C2211yescharacteristic
36C2×#66873C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622549C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622541C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45C2×#66867C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47C2×C4×C11⋊C8C2211yescharacteristic
48#10622280—21no—
49D11×#95—21no—
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×Q8×C11—21no—
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8C2×C414yescomplemented
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C42×C11—21no—
77C2×C42×C11—21no—
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C4×D44—22no—
95C4×D44—22no—
96C4×D44—22no—
97C4×D44—41no—
98C4×D44—41no—
99C4×D44C2×C414yes—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95—21no—
105C11×#95D411yescharacteristic
106C11×#95D411yescharacteristic
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111#66873—22no—
112#66873C2×C414yes—
113#66873C2×C414yes—
114#66873Q814yescomplemented
115#66872—41no—
116#66871—41no—
117#66871C2×C414yescomplemented
118#66871C2×C414yescomplemented
119C4⋊(C11⋊C8)C2×C414yescomplemented
120#66867—22no—
121#66867—41no—
122C4×C11⋊C8—41no—
123#22979—111nomaximal, Sylow
124C23×D11—21no—
125C2×Q8×C11—24no—
126C2×Q8×C11—81no—
127C2×Q8×C11—81no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44C22×C412yes—
146C2×D44C2×Q812yes—
147C2×D44#4112yes—
148C2×C4×D11—24no—
149C2×C4×D11—42no—
150C2×C4×D11—42no—
151C2×C4×D11—42no—
152C2×C4×D11—42no—
153C2×C4×D11—81no—
154C2×C4×D11—81no—
155C2×C4×D11—81no—
156C2×C4×D11—81no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—41no—
165C11×C4⋊C4—81no—
166C11×C4⋊C4—81no—
167C11×C4⋊C4C22×C412yes—
168C11×C4⋊C4C22×C412yes—
169C11×C4⋊C4C2×Q812yes—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—42no—
175C42×C11—81no—
176C42×C11—81no—
177C42×C11C22×C412yes—
178C42×C11#4112yes—
179(C2×D11)⋊C4—24no—
180(C2×D11)⋊C4—42no—
181(C2×D11)⋊C4—42no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11C22×C412yes—
188Dic11⋊C4—81no—
189Dic11⋊C4—81no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8C22×C412yes—
200C2×C11⋊C8C22×C412yes—
201C2×C11⋊C8C2×Q812yes—
202C2×#474—111no—
203#2369D1111yescharacteristic, complemented
204#2349—111no—
205#1993—111no—
206#1949—111no—
207#1943—111no—
208#1942—111no—
209#1921—111no—
210#1918—111no—
211#1864—111no—
212#1862—111no—
213#1771—111no—
214#1762—111no—
215#1762—111no—
216C4×#102—111no—
217C23×C11C22×D411yescharacteristic
218C22×D11—22no—
219C22×D11—22no—
220C22×D11—22no—
221C22×D11—41no—
222C22×D11—41no—
223C22×D11—41no—
224C22×D11—41no—
225Q8×C11—84no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11C4×D412yes—
254C2×C4×C11C4×D412yes—
255C2×C4×C11#13712yes—
256C2×C4×C11C23×C411yescharacteristic
257C2×C4×C11C22×Q811yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11H(5,𝔽2)11yescharacteristic
261C2×C4×C112−1+411yescharacteristic
262C2×Dic11—22no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271D44—22no—
272D44—22no—
273D44—22no—
274D44C4×Q814yes—
275C4×D11—84no—
276C4×D11—84no—
277C4×D11—84no—
278C11⋊C8—22no—
279C11⋊C8—22no—
280C11⋊C8—22no—
281C11⋊C8—41no—
282C2×C4⋊Q8C2×D1111yescharacteristic
283C2×C4×D4—111no—
284C2×C4×D4—111no—
285C2×C4×D4—111no—
286#474—118no—
287C2×#107—111no—
288C2×#107—111no—
289C2×#107—111no—
290C2×#106—111no—
291C2×C4⋊C8—111no—
292C2×#102—111no—
293C2×#102—111no—
294C2×#102—111no—
295C2×#102—111no—
296C2×#97—111no—
297C2×#97—111no—
298C2×C4×C8—111no—
299#391—21no—
300#391—21no—
301#389—21no—
302#389—111no—
303#389—111no—
304#389C2×D1111yescharacteristic
305#389C2×D1111yescharacteristic
306#385—221no—
307#385—221no—
308#382—111no—
309#380—221no—
310C4×C4⋊C4—21no—
311C4×C4⋊C4C2×D1111yescharacteristic
312C4×C4⋊C4C2×D1111yescharacteristic
313C4×C4⋊C4C2×D1111yescharacteristic
314C4×C4⋊C4C2×D1111yescharacteristic
315C2×#95—221no—
316#340—111no—
317#340—111no—
318#340—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#336—111no—
325#336—111no—
326C22×C11C2×C4×D411yescharacteristic
327C22×C11#54611yescharacteristic
328C22×C11D4×Q811yescharacteristic
329C22×C11C2×#13711yescharacteristic
330C22×C11#57511yescharacteristic
331C22×C11#57611yescharacteristic
332C22×C11#57611yescharacteristic
333C2×D11—24no—
334C2×D11—42no—
335C2×D11—42no—
336C2×D11—42no—
337C2×D11—42no—
338C2×D11—42no—
339C2×D11—42no—
340C4×C11—22no—
341C4×C11—22no—
342C4×C11—22no—
343C4×C11—42no—
344C4×C11—42no—
345C4×C11—42no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11—81no—
350C4×C11C2×C4×Q811yescharacteristic
351C4×C11#52011yescharacteristic
352C4×C11#55211yescharacteristic
353C4×C11#55411yescharacteristic
354Dic11—42no—
355Dic11—81no—
356Dic11—81no—
357C22×Q8—21no—
358C22×D4—111no—
359C23×C4—221no—
360C23×C4—221no—
361C23×C4—221no—
362C22×C8—111no—
363C22×C8—111no—
364C22×C8—111no—
365C22×C8—111no—
366C4⋊Q8—22no—
367C4⋊Q8C4×D1114yescomplemented
368C4×D4—114no—
369C4×D4—222no—
370C4×D4—222no—
371C4×D4—222no—
372C4×D4—441no—
373C4×D4—441no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4C22⋊D1111yescharacteristic
383C2×C4⋊C4C22⋊D1111yescharacteristic
384C2×C4⋊C4C22×D1111yescharacteristic
385C2×C4⋊C4C22×D1111yescharacteristic
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C22⋊C4—221no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42C22×D1111yescharacteristic
395C2×C42C22×D1111yescharacteristic
396C2×C42C22×D1111yescharacteristic
397#107—114no—
398#107—114no—
399#107—441no—
400#106—441no—
401C4⋊C8—114no—
402#102—114no—
403#102—114no—
404#102—114no—
405#102—222no—
406#97—222no—
407#97—441no—
408C4×C8—441no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—221no—
415#95—221no—
416#95—221no—
417#95—221no—
418#95C22⋊D1111yescharacteristic
419#95C22⋊D1111yescharacteristic
420C2×C11#236011yescharacteristic
421C2×C11C4×#13711yescharacteristic
422C2×C11#294811yescharacteristic
423C2×C11#331411yescharacteristic
424C2×C11#331911yescharacteristic
425C2×C11#338511yescharacteristic
426C2×C11#338911yescharacteristic
427D11—44no—
428C24—221no—
429C2×Q8—24no—
430C2×Q8—81no—
431C2×Q8—81no—
432C2×D4—112no—
433C2×D4—112no—
434C2×D4—112no—
435C2×D4—221no—
436C2×D4—221no—
437C2×D4—221no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—221no—
443C22×C4—224no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—442no—
447C22×C4—442no—
448C22×C4—442no—
449C22×C4—442no—
450C22×C4—881no—
451C22×C4—881no—
452C22×C4—881no—
453C22×C4—881no—
454C22×C4C2×C22⋊D1111yescharacteristic
455C22×C4C2×C22⋊D1111yescharacteristic
456C22×C4C2×C22⋊D1111yescharacteristic
457C22×C4C2×C22⋊D1111yescharacteristic
458C22×C4C2×C22⋊D1111yescharacteristic
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C23×D1111yescharacteristic
461C2×C8—112no—
462C2×C8—112no—
463C2×C8—112no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C4⋊C4—24no—
474C4⋊C4—22no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—41no—
481C4⋊C4—81no—
482C4⋊C4—81no—
483C4⋊C4—112no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—881no—
490C4⋊C4—881no—
491C4⋊C4C2×C4×D1112yes—
492C4⋊C4C2×C4×D1112yes—
493C4⋊C4Q8×D1112yes—
494C22⋊C4—224no—
495C22⋊C4—442no—
496C22⋊C4—442no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—42no—
502C42—81no—
503C42—81no—
504C42C2×C4×D1112yes—
505C42#433912yes—
506C11#2297911yescharacteristic, complemented, Sylow
507C23—222no—
508C23—222no—
509C23—222no—
510C23—441no—
511C23—441no—
512C23—441no—
513C23—441no—
514C23C22×C22⋊D1111yescharacteristic
515Q8—84no—
516D4—114no—
517D4—222no—
518D4—222no—
519D4—222no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—222no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—884no—
557C2×C4—884no—
558C2×C4—884no—
559C2×C4C4×C22⋊D1112yes—
560C2×C4C4×C22⋊D1112yes—
561C2×C4#6699512yes—
562C2×C4C22×C4×D1111yescharacteristic
563C2×C4C2×#433911yescharacteristic
564C2×C4C2×Q8×D1111yescharacteristic
565C2×C4#6704011yescharacteristic
566C2×C4#41×D1111yescharacteristic
567C2×C4#6704211yescharacteristic
568C8—222no—
569C8—222no—
570C8—222no—
571C8—441no—
572C22—224no—
573C22—442no—
574C22—442no—
575C22—442no—
576C22—442no—
577C22—442no—
578C22—442no—
579C22C2×C4×C22⋊D1111yescharacteristic
580C22C2×#6699511yescharacteristic
581C22Q8×C22⋊D1111yescharacteristic
582C22#1062335311yescharacteristic
583C22#1062336011yescharacteristic
584C22#1062336611yescharacteristic
585C22#1062336611yescharacteristic
586C4—22no—
587C4—22no—
588C4—22no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—42no—
593C4—42no—
594C4—42no—
595C4—81no—
596C4—442no—
597C4—881no—
598C4—881no—
599C4C4×Q8×D1111yescharacteristic
600C4#1062310511yescharacteristic
601C4#1062311011yescharacteristic
602C4#1062311211yescharacteristic
603C2—444no—
604C2#1307161711yescharacteristic
605C2C4×#6699511yescharacteristic
606C2#1307746611yescharacteristic
607C2#1308069111yescharacteristic
608C2#1308076611yescharacteristic
609C2#1308152211yescharacteristic
610C2#1308157011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2369C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#2369D11
hypocenterC11#22979
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2369

Complements

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

NH ≅ G/Ntype
3. #13069590C2semidirect
4. #13069384C2semidirect
5. #13069351C2semidirect
6. #13069346C2semidirect
7. #13069208C2semidirect
8. #13069187C2semidirect
11. #13068491C2semidirect
15. C11×#2369C2semidirect
30. #10622700C4semidirect
66. C11×C4⋊Q8C2×C4semidirect
114. #66873Q8semidirect
117. #66871C2×C4semidirect
118. #66871C2×C4semidirect
119. C4⋊(C11⋊C8)C2×C4semidirect
203. #2369D11semidirect
367. C4⋊Q8C4×D11semidirect
506. C11#22979semidirect

Maximal subgroups

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

subgroupindex
C2×#106227002
#130715272
#130695902
#130693842
#130693512
#130693462
#130692082
#130691872
#130688762
#130688622
#130684912
#130684442
C4×#668732
C11×#23692
#2297911