Finite Group Databasebeta

← #14804122

Subgroups — #14804122

Order 2816.

840 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622633C211yesmaximal, characteristic, complemented
2C2×#10622319C211yesmaximal, characteristic
3#13073785C211yesmaximal, characteristic
4#13073521C211yesmaximal, characteristic
5#13070055C211yesmaximal, characteristic, complemented
6#13070054C211yesmaximal, characteristic, complemented
7#13069817C211yesmaximal, characteristic, complemented
8#13069810C211yesmaximal, characteristic, complemented
9#13069589C211yesmaximal, characteristic, complemented
10#13069384C211yesmaximal, characteristic, complemented
11#13069046C211yesmaximal, characteristic, complemented
12#13069036C211yesmaximal, characteristic, complemented
13#13068648C211yesmaximal, characteristic, complemented
14#13068640C211yesmaximal, characteristic, complemented
15C11×#1763C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C2×#66999C2211yescharacteristic
19C22×#4313C2211yescharacteristic
20C22×C8×D11C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#97C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31#10622633—24no—
32#10622604—21no—
33#10622600C2211yescharacteristic
34#10622600C2211yescharacteristic
35#10622600C2211yescharacteristic
36#10622600C2211yescharacteristic
37#10622600C2211yescharacteristic
38#10622600C2211yescharacteristic
39#10622596—21no—
40C2×#66872C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622553—21no—
45#10622553—21no—
46#10622552—21no—
47#10622549—21no—
48#10622549C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622319—24no—
51#10622286—21no—
52#10622286—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D44D411yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×C4×D11C2311yescharacteristic
65C22×Dic22—21no—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C4×Q8×C11—22no—
69C4×Q8×C11—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C42×C11—21no—
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77#66999—22no—
78#66999—22no—
79#66999—41no—
80#66999—41no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4D411yescharacteristic
90C2×(C2×D11)⋊C4D411yescharacteristic
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11D411yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C2×#4313—22no—
102C2×#4313—22no—
103C2×#4313—41no—
104C2×C8×D11—22no—
105C2×C8×D11—22no—
106C2×C8×D11—41no—
107C4×D44—22no—
108C4×D44—22no—
109#66922—22no—
110#66922—22no—
111C11×#103—22no—
112C11×#103—22no—
113C11×#97—22no—
114C11×#95—21no—
115#66899—22no—
116#66899—22no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125(C2×D11)⋊C8—22no—
126(C2×D11)⋊C8—22no—
127#66872—22no—
128#66872—22no—
129#66872—41no—
130#66871—41no—
131C4⋊(C11⋊C8)D414yes—
132#25356—111nomaximal, Sylow
133C23×D11C2×D411yescharacteristic
134C23×D11C2×D411yescharacteristic
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11#4112yes—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C2×D44—22no—
155C2×D44—22no—
156C2×D44—41no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×Dic22—42no—
170C2×Dic22—81no—
171C2×Dic22—81no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11#4112yes—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—42no—
185C42×C11—42no—
186C42×C11—42no—
187C42×C11C2×D412yes—
188C42×C11#4112yes—
189(C2×D11)⋊C4—22no—
190(C2×D11)⋊C4—22no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—81no—
196(C2×D11)⋊C4—81no—
197(C2×D11)⋊C4—81no—
198(C2×D11)⋊C4—81no—
199C4⋊Dic11—22no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—42no—
209Dic11⋊C4—42no—
210Dic11⋊C4—42no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8C2×D412yes—
216C2×C11⋊C8C2×D412yes—
217#4313—44no—
218C8×D11—44no—
219C2×#475—111no—
220C2×#435—111no—
221#2563—111no—
222#2536—111no—
223#2077—111no—
224#2077—111no—
225#2036—111no—
226#2035—111no—
227#1993—111no—
228#1949—111no—
229#1894—111no—
230#1892—111no—
231#1809—111no—
232#1807—111no—
233#1763D1111yescharacteristic, complemented
234C23×C11C22×D411yescharacteristic
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11#13712yes—
249Q8×C11—22no—
250Q8×C11—22no—
251Q8×C11—41no—
252Q8×C11—41no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—22no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
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#12112yes—
270C2×C4×C11#12112yes—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11H(5,𝔽2)11yescharacteristic
276C2×C4×C112−1+411yescharacteristic
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—41no—
284C2×Dic11—41no—
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—
295D44—44no—
296C4×D11—41no—
297C4×D11—41no—
298C4×D11—41no—
299C4×D11—41no—
300C4×D11—41no—
301C4×D11—41no—
302C4×D11—41no—
303C4×D11—41no—
304Dic22—84no—
305C8×C11—22no—
306C8×C11—41no—
307C11⋊C8—22no—
308C11⋊C8—22no—
309C22×M16—111no—
310C23×C8—111no—
311C2×C4⋊Q8—111no—
312C2×C22⋊Q8—111no—
313C2×C22⋊Q8—111no—
314C2×C4×Q8C2×D1111yescharacteristic
315C2×C4×D4—111no—
316#475—224no—
317#435—224no—
318C2×#107—111no—
319C2×#106—111no—
320C2×#106—111no—
321C2×#106—111no—
322C2×C4⋊C8—111no—
323C2×#103—111no—
324C2×#103—111no—
325C2×#103C2×D1111yescharacteristic
326C2×#103C2×D1111yescharacteristic
327C2×C22⋊C8—111no—
328C2×C22⋊C8—111no—
329C2×#97C2×D1111yescharacteristic
330#398—221no—
331#394—221no—
332#393—221no—
333#393—221no—
334#390—221no—
335#388—221no—
336#388—221no—
337#382—111no—
338#382—221no—
339#380—111no—
340#380—111no—
341#380—111no—
342#380—111no—
343#380—111no—
344#380—111no—
345C4×C4⋊C4C2×D1111yescharacteristic
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340C2×D1111yescharacteristic
353#340C2×D1111yescharacteristic
354C22×C11C2×#12111yescharacteristic
355C22×C11#54611yescharacteristic
356C22×C11#54711yescharacteristic
357C22×C11C2×#13711yescharacteristic
358C22×C11#57511yescharacteristic
359C22×C11#57711yescharacteristic
360C22×C11#57711yescharacteristic
361C2×D11—22no—
362C2×D11—22no—
363C2×D11—22no—
364C2×D11—41no—
365C2×D11—41no—
366C2×D11—41no—
367C2×D11—41no—
368C2×D11—41no—
369C2×D11—41no—
370C2×D11—41no—
371C2×D11—41no—
372C2×D11—41no—
373C2×D11—41no—
374C2×D11—41no—
375C4×C11—22no—
376C4×C11—22no—
377C4×C11—42no—
378C4×C11—81no—
379C4×C11—81no—
380C4×C11—81no—
381C4×C11#52911yescharacteristic
382C4×C11#54211yescharacteristic
383C4×C11#54611yescharacteristic
384C4×C11#54811yescharacteristic
385Dic11—41no—
386Dic11—41no—
387Dic11—81no—
388Dic11—81no—
389Dic11—81no—
390Dic11—81no—
391C22×Q8—221no—
392C22×Q8C22×D1111yescharacteristic
393C22×D4—111no—
394C23×C4—111no—
395C23×C4—111no—
396C2×M16—222no—
397C2×M16—222no—
398C2×M16—441no—
399C22×C8—111no—
400C22×C8—111no—
401C22×C8—222no—
402C22×C8—222no—
403C22×C8—441no—
404C22×C8C22×D1111yescharacteristic
405C22×C8C22×D1111yescharacteristic
406C4⋊Q8—222no—
407C4⋊Q8—222no—
408C22⋊Q8—222no—
409C22⋊Q8—222no—
410C22⋊Q8—441no—
411C22⋊Q8—441no—
412C4×Q8—22no—
413C4×Q8—22no—
414C4×D4—222no—
415C4×D4—222no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4C22×D1111yescharacteristic
426C2×C4⋊C4C22×D1111yescharacteristic
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C22⋊C4—111no—
429C2×C22⋊C4—111no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C42—21no—
439C2×C42—21no—
440C2×C42C22×D1111yescharacteristic
441#107—441no—
442#106—222no—
443#106—222no—
444#106—441no—
445C4⋊C8—114no—
446#103—22no—
447#103—22no—
448#103—222no—
449#103—222no—
450C22⋊C8—222no—
451C22⋊C8—222no—
452#97—22no—
453#95—21no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462C2×C11#242711yescharacteristic
463C2×C11#305611yescharacteristic
464C2×C11#305711yescharacteristic
465C2×C11#331611yescharacteristic
466C2×C11#332111yescharacteristic
467C2×C11#334411yescharacteristic
468C2×C11#334811yescharacteristic
469D11—42no—
470D11—81no—
471C24—111no—
472C24—111no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—442no—
479C2×Q8—881no—
480C2×Q8—881no—
481C2×Q8#433912yes—
482C2×D4—222no—
483C2×D4—222no—
484C2×D4—441no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4D4×D1111yescharacteristic
508C22×C4D4×D1111yescharacteristic
509C22×C4C23×D1111yescharacteristic
510M16—444no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—112no—
517C2×C8—112no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—444no—
523C2×C8#433912yes—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—42no—
531C4⋊C4—222no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—442no—
541C4⋊C4—442no—
542C4⋊C4—442no—
543C22⋊C4—222no—
544C22⋊C4—222no—
545C22⋊C4—442no—
546C22⋊C4—442no—
547C22⋊C4—442no—
548C22⋊C4—442no—
549C22⋊C4—881no—
550C22⋊C4—881no—
551C22⋊C4—881no—
552C22⋊C4—881no—
553C42—42no—
554C42—42no—
555C42#433912yes—
556C42D4×D1112yes—
557C11#2535611yescharacteristic, complemented, Sylow
558C23—112no—
559C23—221no—
560C23—221no—
561C23—221no—
562C23—221no—
563C23—221no—
564C23—221no—
565C23—221no—
566C23—221no—
567C23—221no—
568C23—221no—
569C23—221no—
570C23—221no—
571C23—221no—
572C23C2×D4×D1111yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—41no—
576Q8—41no—
577Q8—884no—
578D4—444no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
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—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4#6693712yes—
622C2×C4#6693712yes—
623C2×C4C2×#433911yescharacteristic
624C2×C4C2×#433911yescharacteristic
625C2×C4C2×#433911yescharacteristic
626C2×C4C2×D4×D1111yescharacteristic
627C2×C4#6704211yescharacteristic
628C2×C4#6704311yescharacteristic
629C8—22no—
630C8—41no—
631C8—222no—
632C8—222no—
633C22—222no—
634C22—222no—
635C22—222no—
636C22—441no—
637C22—441no—
638C22—441no—
639C22—441no—
640C22—441no—
641C22—441no—
642C22—441no—
643C22—441no—
644C22—441no—
645C22—441no—
646C22—441no—
647C22C2×#6693711yescharacteristic
648C22#1062308111yescharacteristic
649C22#1062308211yescharacteristic
650C22#1062330411yescharacteristic
651C22D11×#13711yescharacteristic
652C22#1062330911yescharacteristic
653C22#1062330911yescharacteristic
654C4—22no—
655C4—22no—
656C4—42no—
657C4—81no—
658C4—81no—
659C4—81no—
660C4—441no—
661C4—441no—
662C4—881no—
663C4—881no—
664C4—881no—
665C4—881no—
666C4#1062301011yescharacteristic
667C4#1062306511yescharacteristic
668C4#1062308111yescharacteristic
669C4#1062308311yescharacteristic
670C2—442no—
671C2—881no—
672C2#1307219311yescharacteristic
673C2#1307824911yescharacteristic
674C2#1307825811yescharacteristic
675C2#1308073211yescharacteristic
676C2#1308080711yescharacteristic
677C2#1308107611yescharacteristic
678C2#1308113611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1763C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenter#1763D11
hypocenterC11#25356
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
1. C2×#10622633C2semidirect
5. #13070055C2semidirect
6. #13070054C2semidirect
7. #13069817C2semidirect
8. #13069810C2semidirect
9. #13069589C2semidirect
10. #13069384C2semidirect
11. #13069046C2semidirect
12. #13069036C2semidirect
13. #13068648C2semidirect
14. #13068640C2semidirect
15. C11×#1763C2semidirect
233. #1763D11semidirect
557. C11#25356semidirect

Maximal subgroups

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

subgroupindex
C2×#106226332
C2×#106223192
#130737852
#130735212
#130700552
#130700542
#130698172
#130698102
#130695892
#130693842
#130690462
#130690362
#130686482
#130686402
C11×#17632
#2535611