Finite Group Databasebeta

← #14804058

Subgroups — #14804058

Order 2816.

860 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622449C211yesmaximal, characteristic
2#13073612C211yesmaximal, characteristic
3#13073521C211yesmaximal, characteristic
4#13070045C211yesmaximal, characteristic, complemented
5#13070040C211yesmaximal, characteristic, complemented
6#13069818C211yesmaximal, characteristic, complemented
7#13069811C211yesmaximal, characteristic, complemented
8#13069590C211yesmaximal, characteristic, complemented
9#13069386C211yesmaximal, characteristic, complemented
10#13069046C211yesmaximal, characteristic, complemented
11#13069036C211yesmaximal, characteristic, complemented
12#13068650C211yesmaximal, characteristic, complemented
13#13068642C211yesmaximal, characteristic, complemented
14#13068446C211yesmaximal, characteristic, complemented
15C2×C11×#477C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×#67000—21no—
19C2×#66999C2211yescharacteristic
20C2×#66999C2211yescharacteristic
21C22×#4313C2211yescharacteristic
22C22×C8×D11C2211yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C11×#477—24no—
25C2×C11×#107C2211yescharacteristic
26C2×C11×#107C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30#10622843—21no—
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×#66882C2211yescharacteristic
36C2×#66881C2211yescharacteristic
37#10622606—21no—
38#10622606—21no—
39#10622604—21no—
40#10622600C2211yescharacteristic
41#10622600C2211yescharacteristic
42#10622600C2211yescharacteristic
43#10622600C2211yescharacteristic
44#10622600C2211yescharacteristic
45#10622600C2211yescharacteristic
46#10622596—21no—
47#10622553—21no—
48#10622553—21no—
49#10622549C2211yescharacteristic
50C4×C4⋊Dic11C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52#10622449—24no—
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×Q8×C11C2311yescharacteristic
63C22×D44D411yescharacteristic
64C22×C4×D11C2311yescharacteristic
65C22×C4×D11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8—22no—
70C4×Q8×C11—22no—
71C4×Q8×C11—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79#67000—44no—
80#66999—22no—
81#66999—22no—
82#66999—41no—
83#66999—41no—
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)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4D411yescharacteristic
93C2×(C2×D11)⋊C4D411yescharacteristic
94C2×C4⋊Dic11D411yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×C4×Dic11—21no—
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C2×#4313—22no—
105C2×#4313—22no—
106C2×#4313—41no—
107C2×C8×D11—22no—
108C2×C8×D11—22no—
109C2×C8×D11—41no—
110C4×D44—22no—
111C4×D44—22no—
112C11×#107—22no—
113C11×#107—22no—
114C11×C4⋊C8D414yes—
115C11×#103—22no—
116C11×#103—22no—
117#66899—22no—
118#66899—22no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128(C2×D11)⋊C8—22no—
129(C2×D11)⋊C8—22no—
130#66882—41no—
131#66881—41no—
132#66867—22no—
133#25352—111nomaximal, Sylow
134C23×D11C2×D411yescharacteristic
135C23×D11C2×D411yescharacteristic
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—42no—
142C2×Q8×C11—42no—
143C2×Q8×C11—42no—
144C2×Q8×C11#4112yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C2×D44—22no—
159C2×D44—22no—
160C2×D44—41no—
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×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—21no—
172C2×C4×D11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11C2×D412yes—
178C2×C8×C11C2×D412yes—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—42no—
186C11×C4⋊C4—42no—
187C42×C11—42no—
188C42×C11C2×D412yes—
189C42×C11#4112yes—
190(C2×D11)⋊C4—22no—
191(C2×D11)⋊C4—22no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—42no—
197(C2×D11)⋊C4—42no—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4—42no—
200C4⋊Dic11—22no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209Dic11⋊C4—42no—
210Dic11⋊C4—42no—
211C4×Dic11—42no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8#4112yes—
218#4313—44no—
219C8×D11—44no—
220C2×#477D1111yescharacteristic, complemented
221C2×#435—111no—
222#2547—111no—
223#2536—111no—
224#2076—111no—
225#2075—111no—
226#2036—111no—
227#2035—111no—
228#1993—111no—
229#1949—111no—
230#1894—111no—
231#1892—111no—
232#1809—111no—
233#1808—111no—
234#1763—111no—
235C23×C11C22×D411yescharacteristic
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—21no—
249C22×D11AGL(1,ℤ/8)12yes—
250Q8×C11—22no—
251Q8×C11—22no—
252Q8×C11—41no—
253Q8×C11—41no—
254Q8×C11—84no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
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—41no—
270C2×C4×C11—41no—
271C2×C4×C11#12112yes—
272C2×C4×C11#12112yes—
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11H(5,𝔽2)11yescharacteristic
278C2×C4×C112−1+411yescharacteristic
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
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—41no—
297D44—44no—
298C4×D11—41no—
299C4×D11—41no—
300C4×D11—41no—
301C4×D11—41no—
302C4×D11—41no—
303C4×D11—41no—
304C4×D11—41no—
305C4×D11—41no—
306C8×C11—22no—
307C8×C11—22no—
308C11⋊C8—22no—
309C11⋊C8—41no—
310C22×M16—111no—
311C23×C8—111no—
312C2×C4⋊Q8C2×D1111yescharacteristic
313C2×#124—221no—
314C2×C22⋊Q8—111no—
315C2×C22⋊Q8—111no—
316C2×C4×Q8C2×D1111yescharacteristic
317C2×C4×D4—111no—
318#477—24no—
319#435—224no—
320C2×#107—111no—
321C2×#107C2×D1111yescharacteristic
322C2×#107C2×D1111yescharacteristic
323C2×#106—111no—
324C2×C4⋊C8C2×D1111yescharacteristic
325C2×#103—111no—
326C2×#103—111no—
327C2×#103C2×D1111yescharacteristic
328C2×#103C2×D1111yescharacteristic
329C2×C22⋊C8—111no—
330C2×C22⋊C8—111no—
331C2×#97—111no—
332#398—221no—
333#397—221no—
334#397—221no—
335#394—221no—
336#391—221no—
337#388—221no—
338#388—221no—
339#382—111no—
340#380—111no—
341#380—111no—
342#380—111no—
343#380—111no—
344#380—111no—
345#380—111no—
346C4×C4⋊C4—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355C22×C11C2×#12111yescharacteristic
356C22×C11#54611yescharacteristic
357C22×C11#54711yescharacteristic
358C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
359C22×C11#57511yescharacteristic
360C22×C11#57811yescharacteristic
361C22×C11#57811yescharacteristic
362C2×D11—22no—
363C2×D11—22no—
364C2×D11—22no—
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—
375C2×D11—41no—
376C4×C11—22no—
377C4×C11—22no—
378C4×C11—42no—
379C4×C11—81no—
380C4×C11—81no—
381C4×C11—81no—
382C4×C11#52911yescharacteristic
383C4×C11#54211yescharacteristic
384C4×C11#54611yescharacteristic
385C4×C11#54811yescharacteristic
386Dic11—41no—
387Dic11—41no—
388Dic11—81no—
389Dic11—81no—
390Dic11—81no—
391Dic11—81no—
392C22×Q8—21no—
393C22×Q8C22×D1111yescharacteristic
394C22×D4—111no—
395C23×C4—111no—
396C23×C4—111no—
397C2×M16—222no—
398C2×M16—222no—
399C2×M16—441no—
400C22×C8—111no—
401C22×C8—111no—
402C22×C8—222no—
403C22×C8—222no—
404C22×C8—441no—
405C22×C8C22×D1111yescharacteristic
406C22×C8C22×D1111yescharacteristic
407C4⋊Q8—22no—
408C4⋊Q8—22no—
409#124—444no—
410C22⋊Q8—222no—
411C22⋊Q8—222no—
412C22⋊Q8—441no—
413C22⋊Q8—441no—
414C4×Q8—22no—
415C4×Q8—22no—
416C4×D4—222no—
417C4×D4—222no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C4⋊C4C22×D1111yescharacteristic
430C2×C22⋊C4—111no—
431C2×C22⋊C4—111no—
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×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C42—21no—
441C2×C42—221no—
442C2×C42C22×D1111yescharacteristic
443#107—22no—
444#107—22no—
445#107—441no—
446#106—441no—
447C4⋊C8C22⋊D1114yes—
448#103—22no—
449#103—22no—
450#103—222no—
451#103—222no—
452C22⋊C8—222no—
453C22⋊C8—222no—
454#97—222no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462#95—221no—
463#95—221no—
464C2×C11#242711yescharacteristic
465C2×C11#305511yescharacteristic
466C2×C11#305911yescharacteristic
467C2×C11#330811yescharacteristic
468C2×C11#331311yescharacteristic
469C2×C11#334311yescharacteristic
470C2×C11#334911yescharacteristic
471D11—42no—
472D11—81no—
473C24—111no—
474C24—111no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—42no—
481C2×Q8—42no—
482C2×Q8—42no—
483C2×Q8#434312yes—
484C2×D4—222no—
485C2×D4—222no—
486C2×D4—441no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—111no—
492C22×C4—111no—
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×C4—221no—
508C22×C4—221no—
509C22×C4D4×D1111yescharacteristic
510C22×C4D4×D1111yescharacteristic
511C22×C4C23×D1111yescharacteristic
512M16—444no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—112no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—444no—
524C2×C8C2×C22⋊D1112yes—
525C2×C8C2×C22⋊D1112yes—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—42no—
533C4⋊C4—42no—
534C4⋊C4—222no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—221no—
543C4⋊C4—442no—
544C4⋊C4—442no—
545C22⋊C4—222no—
546C22⋊C4—222no—
547C22⋊C4—442no—
548C22⋊C4—442no—
549C22⋊C4—442no—
550C22⋊C4—442no—
551C22⋊C4—442no—
552C22⋊C4—442no—
553C22⋊C4—442no—
554C22⋊C4—442no—
555C42—42no—
556C42—442no—
557C42#434112yes—
558C42C2×C22⋊D1112yes—
559C11#2535211yescharacteristic, complemented, Sylow
560C23—112no—
561C23—221no—
562C23—221no—
563C23—221no—
564C23—221no—
565C23—221no—
566C23—221no—
567C23—221no—
568C23—221no—
569C23—221no—
570C23—221no—
571C23—221no—
572C23—221no—
573C23—221no—
574C23C2×D4×D1111yescharacteristic
575Q8—22no—
576Q8—22no—
577Q8—41no—
578Q8—41no—
579Q8—84no—
580D4—444no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
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—41no—
596C2×C4—41no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—221no—
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—441no—
622C2×C4—441no—
623C2×C4#6699112yes—
624C2×C4#6699112yes—
625C2×C4C2×#434111yescharacteristic
626C2×C4C2×#434311yescharacteristic
627C2×C4#6704011yescharacteristic
628C2×C4#41×D1111yescharacteristic
629C2×C4#6704211yescharacteristic
630C2×C4C22×C22⋊D1111yescharacteristic
631C8—22no—
632C8—22no—
633C8—222no—
634C8—441no—
635C22—222no—
636C22—222no—
637C22—222no—
638C22—441no—
639C22—441no—
640C22—441no—
641C22—441no—
642C22—441no—
643C22—441no—
644C22—441no—
645C22—441no—
646C22—441no—
647C22—441no—
648C22—441no—
649C22#1062316111yescharacteristic
650C22#1062316211yescharacteristic
651C22#1062329711yescharacteristic
652C22#1062329711yescharacteristic
653C22D11×AGL(1,ℤ/8)11yescharacteristic
654C22#1062330411yescharacteristic
655C22C2×#6699111yescharacteristic
656C4—22no—
657C4—22no—
658C4—42no—
659C4—81no—
660C4—81no—
661C4—81no—
662C4—441no—
663C4—441no—
664C4—881no—
665C4—881no—
666C4—881no—
667C4—881no—
668C4#1062315511yescharacteristic
669C4#1062317411yescharacteristic
670C4#1062334811yescharacteristic
671C4#1062336011yescharacteristic
672C2—442no—
673C2—881no—
674C2#1307218911yescharacteristic
675C2#1307822911yescharacteristic
676C2#1307826711yescharacteristic
677C2#1308060411yescharacteristic
678C2#1308067911yescharacteristic
679C2#1308105311yescharacteristic
680C2#1308114311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#477C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenterC2×#477D11
hypocenterC11#25352
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
4. #13070045C2semidirect
5. #13070040C2semidirect
6. #13069818C2semidirect
7. #13069811C2semidirect
8. #13069590C2semidirect
9. #13069386C2semidirect
10. #13069046C2semidirect
11. #13069036C2semidirect
12. #13068650C2semidirect
13. #13068642C2semidirect
14. #13068446C2semidirect
15. C2×C11×#477C2semidirect
220. C2×#477D11semidirect
559. C11#25352semidirect

Maximal subgroups

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

subgroupindex
C2×#106224492
#130736122
#130735212
#130700452
#130700402
#130698182
#130698112
#130695902
#130693862
#130690462
#130690362
#130686502
#130686422
#130684462
C2×C11×#4772
#2535211