Finite Group Databasebeta

← #14760177

Subgroups — #14760177

Order 2816.

1008 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622775C211yesmaximal, characteristic
2C2×#10622370C211yesmaximal, characteristic
3C2×SD16×Dic11C211yesmaximal, characteristic
4#13071334C211yesmaximal, characteristic, complemented
5#13070977C211yesmaximal, characteristic
6#13069537C211yesmaximal, characteristic, complemented
7#13069383C211yesmaximal, characteristic, complemented
8#13069254C211yesmaximal, characteristic, complemented
9#13069251C211yesmaximal, characteristic, complemented
10#13068950C211yesmaximal, characteristic
11#13068624C211yesmaximal, characteristic
12#13068472C211yesmaximal, characteristic, complemented
13#13068448C211yesmaximal, characteristic, complemented
14#13068435C211yesmaximal, characteristic, complemented
15C11×#1877C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×#66997C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C2×D4×Dic11C2211yescharacteristic
22C22×#4324C2211yescharacteristic
23C2×#66940C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C11×#391C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C4×C22⋊Dic11—21no—
31C2×C11⋊#95—21no—
32#10622775C418yescomplemented
33SD16×Dic11—24no—
34C2×#66881C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66879C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40C2×C8×Dic11C2211yescharacteristic
41#10622590C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43C4⋊C4×Dic11C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C22⋊C4×Dic11—21no—
47C22⋊C4×Dic11—21no—
48C4×C4⋊Dic11C2211yescharacteristic
49#10622545C2211yescharacteristic
50#10622542C2211yescharacteristic
51#10622370—24no—
52#10622268—21no—
53#10622268—21no—
54#10622265—21no—
55#10622265—21no—
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C23×Dic11—21no—
66C23×Dic11—21no—
67C22×Dic22C2311yescharacteristic
68C2×C11×SD16—22no—
69C2×C11×SD16—22no—
70C2×C11×SD16C2×C414yes—
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81Q8×Dic11—22no—
82Q8×Dic11—22no—
83#66997—22no—
84#66997C2×C414yescomplemented
85D4×Dic11—22no—
86D4×Dic11—22no—
87D4×Dic11C2×C414yes—
88D4×Dic11D414yes—
89C2×#4324—22no—
90C2×#4324—22no—
91C2×#4324C2×C414yes—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11C2311yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108#66940—22no—
109#66940—22no—
110C11×#103—22no—
111C11×#102—22no—
112C11×#95—21no—
113C11×#95—21no—
114#66899—22no—
115#66899C2×C414yescomplemented
116#66896—22no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95D411yescharacteristic
125C11⋊#95D411yescharacteristic
126C11⋊#95D411yescharacteristic
127C11⋊#95D411yescharacteristic
128#66881—22no—
129#66880—22no—
130#66880C2×C414yescomplemented
131#66879—22no—
132Dic11⋊C8—22no—
133Dic11⋊C8C2×C414yescomplemented
134C8×Dic11—22no—
135#66874—22no—
136#66871—22no—
137#21514—111nomaximal, Sylow
138C24×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11C22×C412yes—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11C22×C412yes—
149C2×D4×C11C2×D412yes—
150C2×D4×C11#4112yes—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—24no—
154C22×C4×C11—21no—
155C22×C4×C11—81no—
156C22×C4×C11—81no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—81no—
167C22×Dic11—81no—
168C22×Dic11—81no—
169C22×Dic11—81no—
170C22×Dic11C2×D411yescharacteristic
171C22×Dic11C2×D411yescharacteristic
172C22×Dic11C2×D411yescharacteristic
173C22×Dic11C2×D411yescharacteristic
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C2×Dic22C22×C412yes—
180C11×SD16—28no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11C22×C412yes—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4#4112yes—
191C11×C22⋊C4—24no—
192C42×C11—21no—
193C42×C11—21no—
194C22⋊Dic11—24no—
195C22⋊Dic11—24no—
196#4324—28no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—42no—
202C4⋊Dic11C22×C412yes—
203C4⋊Dic11C2×D412yes—
204Dic11⋊C4—24no—
205Dic11⋊C4—24no—
206Dic11⋊C4—42no—
207C4×Dic11—42no—
208C4×Dic11—42no—
209C4×Dic11—81no—
210C4×Dic11—81no—
211C4×Dic11—81no—
212C4×Dic11C22×C412yes—
213C4×Dic11C2×D412yes—
214C4×Dic11#4112yes—
215C4×Dic11#4112yes—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8C22×C412yes—
222C2×#461—111no—
223C2×#440—111no—
224C2×C4×SD16—111no—
225#2327—111no—
226#2275—111no—
227#1981—111no—
228#1949—111no—
229#1928—111no—
230#1927—111no—
231#1877—111no—
232#1877D1111yescharacteristic
233#1804—111no—
234#1768—111no—
235#1763—111no—
236C4×#103—111no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—22no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11C22×D411yescharacteristic
245Q8×C11—22no—
246Q8×C11—22no—
247Q8×C11—41no—
248Q8×C11—41no—
249D4×C11—22no—
250D4×C11—22no—
251D4×C11—22no—
252D4×C11C4×D414yes—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
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—84no—
269C2×C4×C11C23×C411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—22no—
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—84no—
296C2×Dic11—84no—
297C2×Dic11C4×D412yes—
298C2×Dic11C4×D412yes—
299C2×Dic11#12112yes—
300C2×Dic11#12112yes—
301Dic22—22no—
302Dic22—22no—
303Dic22—41no—
304Dic22—41no—
305C8×C11—22no—
306C8×C11—41no—
307C11⋊C8—22no—
308C11⋊C8—41no—
309C22×SD16—111no—
310C22×SD16C2×D1111yescharacteristic
311C2×C4⋊Q8—111no—
312C2×C4×Q8—111no—
313C2×C4×Q8—111no—
314C2×C4×D4—111no—
315C2×C4×D4—111no—
316C2×C4×D4C2×D1111yescharacteristic
317#461—118no—
318#440—224no—
319C4×SD16—224no—
320C2×#107—111no—
321C2×#106—111no—
322C2×C4⋊C8—111no—
323C2×C4⋊C8—111no—
324C2×#103—111no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#103—111no—
328C2×#103—111no—
329C2×#103C2×D1111yescharacteristic
330C2×#102—111no—
331C2×#102C2×D1111yescharacteristic
332C2×#97—111no—
333C2×C4×C8—111no—
334#391—111no—
335#391C2×D1111yescharacteristic
336#387—221no—
337#387—221no—
338#387—221no—
339#387—221no—
340#382—111no—
341C4×C4⋊C4—111no—
342C4×C4⋊C4—111no—
343C4×C4⋊C4—111no—
344C4×C22⋊C4—221no—
345C4×C22⋊C4—221no—
346C4×C22⋊C4—221no—
347#376—111no—
348C2×#95—221no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340C2×D1111yescharacteristic
353#336—111no—
354#336C2×D1111yescharacteristic
355C22×C11—24no—
356C22×C11—42no—
357C22×C11—42no—
358C22×C11—42no—
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—42no—
362C22×C11C2×C4×D411yescharacteristic
363C22×C11C2×#12111yescharacteristic
364C22×C11#52511yescharacteristic
365C22×C11#57711yescharacteristic
366C22×C11#57711yescharacteristic
367C22×C11#57711yescharacteristic
368C22×C11#57811yescharacteristic
369C4×C11—41no—
370C4×C11—41no—
371C4×C11—42no—
372C4×C11—42no—
373C4×C11—81no—
374C4×C11C2×C4×D411yescharacteristic
375C4×C11C4×#4111yescharacteristic
376C4×C11#52911yescharacteristic
377C4×C11#53211yescharacteristic
378Dic11—22no—
379Dic11—22no—
380Dic11—22no—
381Dic11—22no—
382Dic11—42no—
383Dic11—42no—
384Dic11—42no—
385Dic11—81no—
386C22×Q8—111no—
387C22×Q8C22×D1111yescharacteristic
388C22×D4C22×D1111yescharacteristic
389C23×C4—21no—
390C23×C4—221no—
391C23×C4—221no—
392C2×SD16—22no—
393C2×SD16—22no—
394C2×SD16—114no—
395C2×SD16—222no—
396C2×SD16—222no—
397C2×SD16C4×D1114yes—
398C22×C8—111no—
399C22×C8—111no—
400C22×C8C22×D1111yescharacteristic
401C22×C8C22×D1111yescharacteristic
402C4⋊Q8—114no—
403C4⋊Q8—222no—
404C4×Q8—222no—
405C4×Q8—222no—
406C4×Q8—222no—
407C4×Q8—222no—
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—114no—
411C4×D4—114no—
412C4×D4—222no—
413C4×D4—222no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
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—21no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C42—111no—
427C2×C42—111no—
428C2×C42—221no—
429C2×C42—221no—
430C2×C42—221no—
431C2×C42—221no—
432C2×C42—221no—
433C2×C42C22×D1111yescharacteristic
434#107—222no—
435#106—222no—
436C4⋊C8—114no—
437C4⋊C8—222no—
438#103—22no—
439#103—114no—
440#103—114no—
441#103—222no—
442#103—222no—
443#103—222no—
444#102—22no—
445#102—222no—
446#97—222no—
447C4×C8—222no—
448#95—21no—
449#95—21no—
450#95—111no—
451#95—111no—
452#95—111no—
453#95—111no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461C2×C11—44no—
462C2×C11C4×#12111yescharacteristic
463C2×C11#294711yescharacteristic
464C2×C11#294911yescharacteristic
465C2×C11#304211yescharacteristic
466C2×C11#304611yescharacteristic
467C2×C11#312011yescharacteristic
468C2×C11#312311yescharacteristic
469C24—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—112no—
476C2×Q8—221no—
477C2×Q8—221no—
478C2×Q8—221no—
479C2×Q8—221no—
480C2×Q8—221no—
481C2×Q8C2×C4×D1112yes—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4C2×C4×D1112yes—
486C2×D4D4×D1112yes—
487C2×D4#434112yes—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—24no—
491C22×C4—21no—
492C22×C4—81no—
493C22×C4—81no—
494C22×C4—111no—
495C22×C4—111no—
496C22×C4—111no—
497C22×C4—111no—
498C22×C4—224no—
499C22×C4—224no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—881no—
505C22×C4—881no—
506C22×C4—881no—
507C22×C4—881no—
508C22×C4D4×D1111yescharacteristic
509C22×C4D4×D1111yescharacteristic
510C22×C4C23×D1111yescharacteristic
511SD16—28no—
512SD16—228no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—112no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8C2×C4×D1112yes—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—112no—
529C4⋊C4—112no—
530C4⋊C4—224no—
531C4⋊C4—224no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—442no—
537C4⋊C4—442no—
538C4⋊C4#434112yes—
539C22⋊C4—24no—
540C22⋊C4—224no—
541C22⋊C4—224no—
542C42—21no—
543C42—21no—
544C42—112no—
545C42—112no—
546C42—112no—
547C42—112no—
548C42—442no—
549C42—442no—
550C42—881no—
551C42—881no—
552C42—881no—
553C11#2151411yescharacteristic, complemented, Sylow
554C23—22no—
555C23—22no—
556C23—22no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23C2×D4×D1111yescharacteristic
562Q8—22no—
563Q8—22no—
564Q8—41no—
565Q8—41no—
566Q8—222no—
567Q8—222no—
568Q8—441no—
569Q8—441no—
570D4—22no—
571D4—22no—
572D4—22no—
573D4(C22⋊D11)⋊C414yes—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—84no—
590C2×C4—112no—
591C2×C4—112no—
592C2×C4—112no—
593C2×C4—112no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—222no—
603C2×C4—222no—
604C2×C4—222no—
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—884no—
615C2×C4—884no—
616C2×C4C22×C4×D1111yescharacteristic
617C2×C4C2×D4×D1111yescharacteristic
618C2×C4C2×#434111yescharacteristic
619C2×C4C2×#434111yescharacteristic
620C2×C4#41×D1111yescharacteristic
621C2×C4#41×D1111yescharacteristic
622C8—22no—
623C8—41no—
624C8—222no—
625C8—441no—
626C22—24no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22C4×D4×D1111yescharacteristic
634C22#1062311711yescharacteristic
635C22D11×#12111yescharacteristic
636C22#1062329311yescharacteristic
637C22#1062330111yescharacteristic
638C22#1062330611yescharacteristic
639C22#1062331011yescharacteristic
640C4—42no—
641C4—41no—
642C4—41no—
643C4—42no—
644C4—81no—
645C4—222no—
646C4—222no—
647C4—222no—
648C4—222no—
649C4—442no—
650C4—442no—
651C4—442no—
652C4—881no—
653C4C2×(C22⋊D11)⋊C411yescharacteristic
654C4C4×#434111yescharacteristic
655C4#1062312711yescharacteristic
656C4#1062318011yescharacteristic
657C2—44no—
658C2#1307112611yescharacteristic
659C2#1307745611yescharacteristic
660C2#1307747011yescharacteristic
661C2#1307812611yescharacteristic
662C2#1307816111yescharacteristic
663C2#1307882311yescharacteristic
664C2#1307886211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1877C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#1877D11
hypocenterC11#21514
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1877

Complements

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

NH ≅ G/Ntype
4. #13071334C2semidirect
6. #13069537C2semidirect
7. #13069383C2semidirect
8. #13069254C2semidirect
9. #13069251C2semidirect
12. #13068472C2semidirect
13. #13068448C2semidirect
14. #13068435C2semidirect
32. #10622775C4semidirect
84. #66997C2×C4semidirect
115. #66899C2×C4semidirect
130. #66880C2×C4semidirect
133. Dic11⋊C8C2×C4semidirect
553. C11#21514semidirect

Maximal subgroups

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

subgroupindex
C2×#106227752
C2×#106223702
C2×SD16×Dic112
#130713342
#130709772
#130695372
#130693832
#130692542
#130692512
#130689502
#130686242
#130684722
#130684482
#130684352
C11×#18772
#2151411