Finite Group Databasebeta

← #14776069

Subgroups — #14776069

Order 2816.

958 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622798C211yesmaximal, characteristic
2C2×Q16×Dic11C211yesmaximal, characteristic, complemented
3C2×C4×#4325C211yesmaximal, characteristic
4#13071692C211yesmaximal, characteristic
5#13071534C211yesmaximal, characteristic, complemented
6#13069424C211yesmaximal, characteristic
7#13069387C211yesmaximal, characteristic, complemented
8#13069297C211yesmaximal, characteristic
9#13069295C211yesmaximal, characteristic, complemented
10#13068969C211yesmaximal, characteristic
11#13068882C211yesmaximal, characteristic, complemented
12#13068866C211yesmaximal, characteristic
13#13068477C211yesmaximal, characteristic, complemented
14#103×Dic11C211yesmaximal, characteristic, complemented
15C11×#1878C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×#67000C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C22×#4325C2211yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C11×#391C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30#10622798C418yescomplemented
31Q16×Dic11—24no—
32C2×#66885C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38C4×#4325—24no—
39#10622601C2211yescharacteristic
40#10622590—21no—
41#10622590C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43#10622586—21no—
44#10622586C2211yescharacteristic
45C2×#66873C2211yescharacteristic
46C2×#66872C2211yescharacteristic
47C4×Dic11⋊C4—21no—
48C4×Dic11⋊C4C2211yescharacteristic
49#10622541—21no—
50#10622541C2211yescharacteristic
51C2×C4×C11⋊C8C2211yescharacteristic
52#10622283—21no—
53#10622282—21no—
54#10622281—21no—
55#10622279—21no—
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C2×C11×Q16—22no—
67C2×C11×Q16—22no—
68C2×C11×Q16C2×C414yescomplemented
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C4×Q8×C11—22no—
72C4×Q8×C11—41no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78#67000—22no—
79#67000C2×C414yes—
80Q8×Dic11—22no—
81Q8×Dic11—22no—
82Q8×Dic11—22no—
83Q8×Dic11—41no—
84Q8×Dic11—41no—
85Q8×Dic11C2×C414yescomplemented
86C2×#4325—22no—
87C2×#4325—22no—
88C2×#4325C2×C414yes—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4D411yescharacteristic
103C2×Dic11⋊C4D411yescharacteristic
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11—21no—
108C2×C4×Dic11C2311yescharacteristic
109C2×C4×Dic11C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C4×D44—22no—
113C4×D44—41no—
114C11×#103—22no—
115C11×#103—41no—
116C11×#95—21no—
117C11×#95—21no—
118#66899—22no—
119#66899C2×C414yescomplemented
120#66899D414yes—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95D411yescharacteristic
127C11⋊#95D411yescharacteristic
128#66885—41no—
129#66885C2×C414yes—
130#66882—22no—
131Dic11⋊C8C2×C414yescomplemented
132C8×Dic11—22no—
133C8×Dic11—22no—
134#66873—22no—
135#66872—22no—
136C4×C11⋊C8—22no—
137#23000—111nomaximal, Sylow
138C23×D11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11C22×C412yes—
148C2×Q8×C11C22×C412yes—
149C2×Q8×C11C2×D412yes—
150C2×Q8×C11#4112yes—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2411yescharacteristic
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44—21no—
170C2×D44C22×C412yes—
171C2×C4×D11—42no—
172C2×C4×D11—42no—
173C2×C4×D11—81no—
174C11×Q16—28no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11C22×C412yes—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—42no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—42no—
189#4325—28no—
190(C2×D11)⋊C4—24no—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—81no—
195C4⋊Dic11—24no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—42no—
201C4⋊Dic11—42no—
202C4⋊Dic11C22×C412yes—
203C4⋊Dic11C2×D412yes—
204Dic11⋊C4—22no—
205Dic11⋊C4—22no—
206Dic11⋊C4—42no—
207Dic11⋊C4—42no—
208C4×Dic11—24no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C4×Dic11—42no—
212C4×Dic11—42no—
213C4×Dic11—81no—
214C4×Dic11C22×C412yes—
215C4×Dic11#4112yes—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8C22×C412yes—
221C2×C11⋊C8C2×D412yes—
222C2×#464—111no—
223C2×C4×Q16—111no—
224C2×C4×SD16—111no—
225#2367—111no—
226#2351—111no—
227#1958—111no—
228#1949—111no—
229#1934—111no—
230#1933—111no—
231#1880—111no—
232#1878D1111yescharacteristic, complemented
233#1865—111no—
234#1862—111no—
235C8×C4⋊C4—111no—
236C4×#103—111no—
237C23×C11C22×D411yescharacteristic
238C22×D11—22no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245Q8×C11—22no—
246Q8×C11—22no—
247Q8×C11—22no—
248Q8×C11—22no—
249Q8×C11—22no—
250Q8×C11—41no—
251Q8×C11—41no—
252Q8×C11C4×D414yes—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
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#13512yes—
271C2×C4×C11C23×C411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
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—22no—
284C2×Dic11—21no—
285C2×Dic11—22no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11C4×D412yes—
296C2×Dic11C4×D412yes—
297C2×Dic11#13512yes—
298D44—22no—
299D44—22no—
300D44—41no—
301D44—41no—
302C4×D11—84no—
303C8×C11—22no—
304C8×C11—41no—
305C11⋊C8—22no—
306C11⋊C8—22no—
307C22×Q16C2×D1111yescharacteristic
308C22×SD16—111no—
309C2×#124—111no—
310C2×C4×Q8—111no—
311C2×C4×Q8—111no—
312C2×C4×Q8—111no—
313C2×C4×Q8C2×D1111yescharacteristic
314C2×C4×D4—111no—
315#464—118no—
316C4×Q16—224no—
317C4×SD16—224no—
318C2×#107—111no—
319C2×#106—111no—
320C2×C4⋊C8—111no—
321C2×#103—111no—
322C2×#103—111no—
323C2×#103—111no—
324C2×#103C2×D1111yescharacteristic
325C2×#103C2×D1111yescharacteristic
326C2×#102—111no—
327C2×#102—111no—
328C2×#102—111no—
329C2×C4×C8—111no—
330C2×C4×C8—111no—
331C2×C4×C8—111no—
332#391C2×D1111yescharacteristic
333#390—111no—
334#389—111no—
335#389—111no—
336#389—221no—
337#389—221no—
338#388—221no—
339#388—221no—
340#385—221no—
341#382—111no—
342#382—221no—
343C4×C4⋊C4—111no—
344C4×C4⋊C4—111no—
345C4×C4⋊C4—221no—
346C4×C22⋊C4—221no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340C2×D1111yescharacteristic
351#336—111no—
352#336C2×D1111yescharacteristic
353C22×C11C2×C4×D411yescharacteristic
354C22×C11D4211yescharacteristic
355C22×C11#54811yescharacteristic
356C22×C11C2×#13511yescharacteristic
357C22×C11C2×#13511yescharacteristic
358C22×C11#57711yescharacteristic
359C22×C11#57811yescharacteristic
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—42no—
363C2×D11—81no—
364C2×D11—81no—
365C2×D11—81no—
366C2×D11—81no—
367C4×C11—24no—
368C4×C11—22no—
369C4×C11—42no—
370C4×C11—41no—
371C4×C11—81no—
372C4×C11—81no—
373C4×C11C2×C4×D411yescharacteristic
374C4×C11#52011yescharacteristic
375C4×C11#54711yescharacteristic
376C4×C11#55311yescharacteristic
377Dic11—22no—
378Dic11—22no—
379Dic11—22no—
380Dic11—42no—
381Dic11—42no—
382Dic11—41no—
383Dic11—81no—
384C22×Q8C22×D1111yescharacteristic
385C22×Q8C22×D1111yescharacteristic
386C22×D4—111no—
387C23×C4—221no—
388C2×Q16—22no—
389C2×Q16—22no—
390C2×Q16C4×D1114yescomplemented
391C2×SD16—114no—
392C2×SD16—222no—
393C2×SD16—222no—
394C22×C8—111no—
395C22×C8—111no—
396C22×C8C22×D1111yescharacteristic
397C22×C8C22×D1111yescharacteristic
398#124—114no—
399#124—222no—
400C4×Q8—22no—
401C4×Q8—41no—
402C4×Q8—114no—
403C4×Q8—222no—
404C4×Q8—222no—
405C4×Q8—222no—
406C4×Q8—441no—
407C4×Q8—441no—
408C4×D4—222no—
409C4×D4—441no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C42—21no—
429C2×C42—111no—
430C2×C42—111no—
431C2×C42—221no—
432C2×C42—221no—
433C2×C42—221no—
434C2×C42—221no—
435C2×C42C22×D1111yescharacteristic
436#107—222no—
437#106—222no—
438C4⋊C8—114no—
439#103—22no—
440#103—41no—
441#103—114no—
442#103—114no—
443#103—222no—
444#102—114no—
445#102—222no—
446#102—441no—
447C4×C8—222no—
448C4×C8—222no—
449C4×C8—222no—
450#95—21no—
451#95—21no—
452#95—111no—
453#95—111no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459C2×C11#236111yescharacteristic
460C2×C11C4×#13511yescharacteristic
461C2×C11#294711yescharacteristic
462C2×C11#328211yescharacteristic
463C2×C11#328511yescharacteristic
464C2×C11#336411yescharacteristic
465C2×C11#336511yescharacteristic
466D11—82no—
467C24—221no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8C2×C4×D1112yes—
477C2×Q8C2×C4×D1112yes—
478C2×Q8D4×D1112yes—
479C2×Q8#434112yes—
480C2×D4—112no—
481C2×D4—221no—
482C2×D4—221no—
483C2×D4—221no—
484C2×D4—221no—
485C2×D4—221no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—111no—
491C22×C4—111no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—442no—
498C22×C4—442no—
499C22×C4—881no—
500C22×C4D4×D1111yescharacteristic
501C22×C4D4×D1111yescharacteristic
502C22×C4C23×D1111yescharacteristic
503Q16—28no—
504SD16—228no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—112no—
511C2×C8—112no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8C2×C4×D1112yes—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—42no—
522C4⋊C4—112no—
523C4⋊C4—112no—
524C4⋊C4—222no—
525C4⋊C4—224no—
526C4⋊C4—222no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—442no—
532C4⋊C4—442no—
533C4⋊C4—442no—
534C4⋊C4—442no—
535C22⋊C4—224no—
536C22⋊C4—224no—
537C22⋊C4—442no—
538C22⋊C4—442no—
539C22⋊C4—881no—
540C42—21no—
541C42—21no—
542C42—42no—
543C42—112no—
544C42—112no—
545C42—224no—
546C42—221no—
547C42—221no—
548C42—442no—
549C42—442no—
550C42—881no—
551C11#2300011yescharacteristic, complemented, Sylow
552C23—222no—
553C23—441no—
554C23—441no—
555C23—441no—
556C23—441no—
557C23—441no—
558C23—441no—
559C23C2×D4×D1111yescharacteristic
560Q8—22no—
561Q8—22no—
562Q8—22no—
563Q8—22no—
564Q8—22no—
565Q8—41no—
566Q8—41no—
567Q8(C22⋊D11)⋊C414yes—
568D4—222no—
569D4—222no—
570D4—441no—
571D4—441no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—112no—
590C2×C4—112no—
591C2×C4—112no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—222no—
601C2×C4—221no—
602C2×C4—222no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—884no—
611C2×C4#6697212yes—
612C2×C4C22×C4×D1111yescharacteristic
613C2×C4C2×D4×D1111yescharacteristic
614C2×C4C2×#434111yescharacteristic
615C2×C4#6703711yescharacteristic
616C2×C4#41×D1111yescharacteristic
617C2×C4#6704311yescharacteristic
618C8—22no—
619C8—41no—
620C8—222no—
621C8—222no—
622C22—442no—
623C22—442no—
624C22—442no—
625C22—881no—
626C22—881no—
627C22—881no—
628C22—881no—
629C22C4×D4×D1111yescharacteristic
630C22#1062312111yescharacteristic
631C22#1062312911yescharacteristic
632C22C2×#6697211yescharacteristic
633C22D11×#13511yescharacteristic
634C22#1062330911yescharacteristic
635C22#1062331011yescharacteristic
636C4—24no—
637C4—22no—
638C4—42no—
639C4—41no—
640C4—81no—
641C4—81no—
642C4—222no—
643C4—222no—
644C4—222no—
645C4—442no—
646C4—441no—
647C4—442no—
648C4—881no—
649C4C2×(C22⋊D11)⋊C411yescharacteristic
650C4#1062307711yescharacteristic
651C4#1062313211yescharacteristic
652C4#1062318611yescharacteristic
653C2—882no—
654C2#1307162711yescharacteristic
655C2C4×#6697211yescharacteristic
656C2#1307745811yescharacteristic
657C2#1308031611yescharacteristic
658C2#1308035511yescharacteristic
659C2#1308130511yescharacteristic
660C2#1308130711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1878C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1878D11
hypocenterC11#23000
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
2. C2×Q16×Dic11C2semidirect
5. #13071534C2semidirect
7. #13069387C2semidirect
9. #13069295C2semidirect
11. #13068882C2semidirect
13. #13068477C2semidirect
14. #103×Dic11C2semidirect
15. C11×#1878C2semidirect
30. #10622798C4semidirect
68. C2×C11×Q16C2×C4semidirect
85. Q8×Dic11C2×C4semidirect
119. #66899C2×C4semidirect
131. Dic11⋊C8C2×C4semidirect
232. #1878D11semidirect
390. C2×Q16C4×D11semidirect
551. C11#23000semidirect

Maximal subgroups

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

subgroupindex
C2×#106227982
C2×Q16×Dic112
C2×C4×#43252
#130716922
#130715342
#130694242
#130693872
#130692972
#130692952
#130689692
#130688822
#130688662
#130684772
#103×Dic112
C11×#18782
#2300011