Finite Group Databasebeta

← #14770843

Subgroups — #14770843

Order 2816.

994 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622417C211yesmaximal, characteristic
2#13071497C211yesmaximal, characteristic, complemented
3#13071445C211yesmaximal, characteristic
4#13069309C211yesmaximal, characteristic, complemented
5#13069303C211yesmaximal, characteristic, complemented
6#13069259C211yesmaximal, characteristic, complemented
7#13068866C211yesmaximal, characteristic, complemented
8#13068860C211yesmaximal, characteristic, complemented
9#13068709C211yesmaximal, characteristic, complemented
10#13068642C211yesmaximal, characteristic, complemented
11#13068555C211yesmaximal, characteristic
12#13068444C211yesmaximal, characteristic, complemented
13#13068440C211yesmaximal, characteristic, complemented
14#13068391C211yesmaximal, characteristic, complemented
15C11×#1928C211yesmaximal, characteristic, complemented
16C22×#4343C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18C2×#66946C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C11×#391C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26#10622843C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66879C2211yescharacteristic
34#10622600C2211yescharacteristic
35#10622600C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622586C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40#10622553—21no—
41C4×(C2×D11)⋊C4C2211yescharacteristic
42#10622545—21no—
43#10622541C2211yescharacteristic
44C2×#66867C2211yescharacteristic
45#10622417C418yescomplemented
46#10622282—21no—
47#10622278—21no—
48#10622278—21no—
49#10622277—21no—
50D11×#95—21no—
51#10622263—21no—
52C11×#340C2211yescharacteristic
53C11×#336C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C2×#4343—22no—
62C2×#4343—22no—
63C2×#4343—22no—
64C2×#4343—41no—
65C2×#4343—41no—
66C2×#4343C2×C414yes—
67C22×D44—21no—
68C22×D44C2311yescharacteristic
69C22×C4×D11—21no—
70C22×C4×D11—21no—
71C22×C4×D11—21no—
72C22×C4×D11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4D411yescharacteristic
86C2×(C2×D11)⋊C4D411yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C2×C8×D11—41no—
98C2×C8×D11—41no—
99C2×C8×D11C2×C414yescomplemented
100#66946—22no—
101#66946—41no—
102#66945—22no—
103#66945C2×C414yescomplemented
104C4×D44—22no—
105C4×D44—41no—
106C11×#107—41no—
107C11×#103—41no—
108C11×#103C2×C414yescomplemented
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112#66899—41no—
113#66899C2×C414yescomplemented
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95D411yescharacteristic
122C11⋊#95D411yescharacteristic
123#66885—22no—
124#66885C2×C414yes—
125(C2×D11)⋊C8—22no—
126#66882—41no—
127#66879—41no—
128#66873—22no—
129#66873C2×C414yes—
130#66867—41no—
131#22564—111nomaximal, Sylow
132C23×D11—21no—
133C23×D11C2×D411yescharacteristic
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11C22×C412yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153#4343—28no—
154#4343—44no—
155#4343—44no—
156#4343—44no—
157C2×D44—24no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—42no—
162C2×D44—42no—
163C2×D44C22×C412yes—
164C2×D44#4112yes—
165C2×D44#4112yes—
166C2×C4×D11—24no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—42no—
172C2×C4×D11—42no—
173C2×C4×D11—42no—
174C2×C4×D11—42no—
175C2×C4×D11—42no—
176C2×C4×D11—42no—
177C2×C4×D11—81no—
178C2×C4×D11—81no—
179C2×C4×D11C22×C412yes—
180C2×C4×D11#4112yes—
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—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4C22×C412yes—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—42no—
196(C2×D11)⋊C4—24no—
197(C2×D11)⋊C4—41no—
198(C2×D11)⋊C4—41no—
199(C2×D11)⋊C4—42no—
200(C2×D11)⋊C4—42no—
201(C2×D11)⋊C4—81no—
202(C2×D11)⋊C4—81no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11C22×C412yes—
209Dic11⋊C4—81no—
210Dic11⋊C4—81no—
211C4×Dic11—24no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—42no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8C22×C412yes—
221C8×D11—44no—
222C2×#416—111no—
223#2346—111no—
224#2339—111no—
225#1935—111no—
226#1935—111no—
227#1928—111no—
228#1928D1111yescharacteristic, complemented
229#1862—111no—
230#1862—111no—
231#1825—111no—
232#1808—111no—
233#1788—111no—
234#1762—111no—
235#1762—111no—
236#1752—111no—
237C23×C11C22×D411yescharacteristic
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251C22×D11C4×D412yes—
252Q8×C11—22no—
253Q8×C11—22no—
254Q8×C11—41no—
255Q8×C11—41no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
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—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11C23×C411yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×C4×C11H(5,𝔽2)11yescharacteristic
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—22no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11C4×D412yes—
298D44—22no—
299D44—22no—
300D44—22no—
301D44—48no—
302D44#11714yes—
303C4×D11—22no—
304C4×D11—22no—
305C4×D11—22no—
306C4×D11—22no—
307C4×D11—48no—
308C4×D11—84no—
309C4×D11—84no—
310C8×C11—22no—
311C8×C11—41no—
312C11⋊C8—22no—
313C11⋊C8—41no—
314C22×#41—111no—
315C23×C8—111no—
316C2×C4×D4—111no—
317C2×C4×D4—111no—
318C2×#117—111no—
319C2×#107—111no—
320C2×#107C2×D1111yescharacteristic
321#416—118no—
322C2×#103—111no—
323C2×#103—111no—
324C2×#103C2×D1111yescharacteristic
325C2×#103C2×D1111yescharacteristic
326C2×#102—111no—
327C2×#102—111no—
328C2×#102—111no—
329C2×#102—111no—
330C2×C22⋊C8—111no—
331C2×#97—111no—
332C2×#97—111no—
333#391—111no—
334#391C2×D1111yescharacteristic
335#389—111no—
336#389—111no—
337#388—221no—
338#388—221no—
339#386—221no—
340#386—221no—
341#382—221no—
342#381—221no—
343#380—111no—
344#380—111no—
345C4×C4⋊C4—111no—
346C4×C4⋊C4C2×D1111yescharacteristic
347C4×C22⋊C4—111no—
348#376—221no—
349C2×#95—221no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#340C2×D1111yescharacteristic
356#336—111no—
357#336C2×D1111yescharacteristic
358C22×C11C2×C4×D411yescharacteristic
359C22×C11#54611yescharacteristic
360C22×C11#54611yescharacteristic
361C22×C11#57511yescharacteristic
362C22×C11#57511yescharacteristic
363C22×C11#57611yescharacteristic
364C22×C11#57811yescharacteristic
365C2×D11—24no—
366C2×D11—22no—
367C2×D11—22no—
368C2×D11—22no—
369C2×D11—42no—
370C2×D11—42no—
371C2×D11—41no—
372C2×D11—41no—
373C2×D11—42no—
374C2×D11—42no—
375C2×D11—41no—
376C2×D11—41no—
377C2×D11—42no—
378C2×D11—42no—
379C4×C11—42no—
380C4×C11—42no—
381C4×C11—41no—
382C4×C11—41no—
383C4×C11—81no—
384C4×C11—81no—
385C4×C11C2×#11711yescharacteristic
386C4×C11#51811yescharacteristic
387C4×C11#55111yescharacteristic
388C4×C11#55111yescharacteristic
389Dic11—22no—
390Dic11—42no—
391Dic11—41no—
392Dic11—41no—
393Dic11—81no—
394Dic11—81no—
395C2×#41—114no—
396C2×#41—222no—
397C2×#41—222no—
398C2×#41—222no—
399C2×#41—441no—
400C2×#41—441no—
401C22×Q8C22×D1111yescharacteristic
402C22×D4—111no—
403C22×D4—221no—
404C23×C4—111no—
405C23×C4—221no—
406C23×C4—221no—
407C23×C4—221no—
408C22×C8—111no—
409C22×C8—114no—
410C22×C8—111no—
411C22×C8—441no—
412C22×C8—441no—
413C22×C8C22×D1111yescharacteristic
414C22×C8C22×D1111yescharacteristic
415C4×D4—222no—
416C4×D4—222no—
417C4×D4—441no—
418C4×D4—441no—
419#117—114no—
420#117—222no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4C22×D1111yescharacteristic
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C22⋊C4—111no—
430C2×C22⋊C4—111no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C42—21no—
437C2×C42—111no—
438C2×C42—221no—
439C2×C42—221no—
440C2×C42C22×D1111yescharacteristic
441#107—41no—
442#107—441no—
443#103—41no—
444#103—114no—
445#103—441no—
446#103C4×D1114yescomplemented
447#102—114no—
448#102—114no—
449#102—222no—
450#102—222no—
451C22⋊C8—222no—
452#97—441no—
453#97—441no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—111no—
458#95—111no—
459#95—221no—
460#95—221no—
461#95—221no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95—221no—
466C2×C11#234211yescharacteristic
467C2×C11#294311yescharacteristic
468C2×C11#295111yescharacteristic
469C2×C11#331511yescharacteristic
470C2×C11#331511yescharacteristic
471C2×C11#331911yescharacteristic
472C2×C11#331911yescharacteristic
473D11—42no—
474D11—44no—
475C24—111no—
476C24—221no—
477#41—228no—
478#41—444no—
479#41—444no—
480#41—444no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8C2×C4×D1112yes—
487C2×D4—112no—
488C2×D4—112no—
489C2×D4—112no—
490C2×D4—224no—
491C2×D4—221no—
492C2×D4—221no—
493C2×D4—221no—
494C2×D4—442no—
495C2×D4—442no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—111no—
501C22×C4—112no—
502C22×C4—112no—
503C22×C4—111no—
504C22×C4—111no—
505C22×C4—224no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—442no—
514C22×C4—442no—
515C22×C4—442no—
516C22×C4—442no—
517C22×C4—442no—
518C22×C4—442no—
519C22×C4—881no—
520C22×C4—881no—
521C22×C4D4×D1111yescharacteristic
522C22×C4D4×D1111yescharacteristic
523C22×C4C23×D1111yescharacteristic
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—112no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8—444no—
536C2×C8C2×C4×D1112yes—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—112no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—881no—
549C4⋊C4—881no—
550C4⋊C4C2×C4×D1112yes—
551C22⋊C4—224no—
552C22⋊C4—441no—
553C22⋊C4—441no—
554C22⋊C4—442no—
555C22⋊C4—442no—
556C22⋊C4—881no—
557C22⋊C4—881no—
558C42—21no—
559C42—21no—
560C42—42no—
561C42—224no—
562C42—221no—
563C42—221no—
564C42—442no—
565C11#2256411yescharacteristic, complemented, Sylow
566C23—112no—
567C23—221no—
568C23—221no—
569C23—221no—
570C23—221no—
571C23—222no—
572C23—222no—
573C23—221no—
574C23—222no—
575C23—221no—
576C23—441no—
577C23—441no—
578C23—441no—
579C23—441no—
580C23C2×D4×D1111yescharacteristic
581Q8—22no—
582Q8—22no—
583Q8—41no—
584Q8—41no—
585D4—114no—
586D4—222no—
587D4—222no—
588D4—222no—
589D4—448no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—112no—
609C2×C4—221no—
610C2×C4—221no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—222no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—222no—
620C2×C4—221no—
621C2×C4—221no—
622C2×C4—448no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—884no—
632C2×C4—884no—
633C2×C4C22×C4×D1111yescharacteristic
634C2×C4#6703711yescharacteristic
635C2×C4#41×D1111yescharacteristic
636C2×C4#41×D1111yescharacteristic
637C2×C4#41×D1111yescharacteristic
638C2×C4#6704211yescharacteristic
639C8—22no—
640C8—41no—
641C8—222no—
642C8—441no—
643C22—222no—
644C22—224no—
645C22—222no—
646C22—222no—
647C22—441no—
648C22—442no—
649C22—441no—
650C22—442no—
651C22—442no—
652C22—442no—
653C22—441no—
654C22—442no—
655C22—441no—
656C22—442no—
657C22C4×D4×D1111yescharacteristic
658C22#1062314311yescharacteristic
659C22#1062318511yescharacteristic
660C22#1062329711yescharacteristic
661C22#1062330011yescharacteristic
662C22#1062330411yescharacteristic
663C22#1062330811yescharacteristic
664C4—42no—
665C4—41no—
666C4—42no—
667C4—41no—
668C4—81no—
669C4—81no—
670C4—222no—
671C4—441no—
672C4—441no—
673C4—442no—
674C4—881no—
675C4—881no—
676C4D11×#11711yescharacteristic
677C4#1062307611yescharacteristic
678C4#1062321011yescharacteristic
679C4#1062323611yescharacteristic
680C2—442no—
681C2—444no—
682C2#1307146011yescharacteristic
683C2#1307741111yescharacteristic
684C2#1307749111yescharacteristic
685C2#1308071511yescharacteristic
686C2#1308071911yescharacteristic
687C2#1308077511yescharacteristic
688C2#1308077911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1928C2
socleC23×C11C22×D4
prime radicalC22×#4343C22
cosocleC22×C4×C11C24
hypercenter#1928D11
hypocenterC11#22564
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1928

Complements

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

NH ≅ G/Ntype
2. #13071497C2semidirect
4. #13069309C2semidirect
5. #13069303C2semidirect
6. #13069259C2semidirect
7. #13068866C2semidirect
8. #13068860C2semidirect
9. #13068709C2semidirect
10. #13068642C2semidirect
12. #13068444C2semidirect
13. #13068440C2semidirect
14. #13068391C2semidirect
15. C11×#1928C2semidirect
45. #10622417C4semidirect
99. C2×C8×D11C2×C4semidirect
103. #66945C2×C4semidirect
108. C11×#103C2×C4semidirect
113. #66899C2×C4semidirect
228. #1928D11semidirect
446. #103C4×D11semidirect
565. C11#22564semidirect

Maximal subgroups

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

subgroupindex
C2×#106224172
#130714972
#130714452
#130693092
#130693032
#130692592
#130688662
#130688602
#130687092
#130686422
#130685552
#130684442
#130684402
#130683912
C11×#19282
#2256411