Finite Group Databasebeta

← #14803263

Subgroups — #14803263

Order 2816.

828 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×#10622680C211yesmaximal, characteristic
2#13073615C211yesmaximal, characteristic
3#13071716C211yesmaximal, characteristic, complemented
4#13069999C211yesmaximal, characteristic, complemented
5#13069985C211yesmaximal, characteristic, complemented
6#13069854C211yesmaximal, characteristic, complemented
7#13069854C211yesmaximal, characteristic, complemented
8#13069545C211yesmaximal, characteristic, complemented
9#13069545C211yesmaximal, characteristic, complemented
10#13069542C211yesmaximal, characteristic
11#13069337C211yesmaximal, characteristic, complemented
12#13069242C211yesmaximal, characteristic, complemented
13#13069235C211yesmaximal, characteristic, complemented
14#13068446C211yesmaximal, characteristic, complemented
15C2×C11×#479C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×#67000C2211yescharacteristic
19C2×#67000C2211yescharacteristic
20C2×#66927C2211yescharacteristic
21C11×#479—24no—
22C2×C11×#107C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35#10622680—24no—
36#10622604—21no—
37#10622604—21no—
38#10622601C2211yescharacteristic
39#10622601C2211yescharacteristic
40#10622598—21no—
41#10622598C2211yescharacteristic
42#10622598C2211yescharacteristic
43#10622594—21no—
44#10622594—21no—
45C4⋊C4×Dic11—21no—
46C4⋊C4×Dic11C2211yescharacteristic
47C4⋊C4×Dic11C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66873C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51C2×#66873C2211yescharacteristic
52#10622552—21no—
53#10622552—21no—
54C4×C4⋊Dic11C2211yescharacteristic
55C4×C4⋊Dic11C2211yescharacteristic
56C2×#66867C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D44—21no—
63C22×D44—21no—
64C22×D44C2311yescharacteristic
65C22×D44C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×#125—22no—
69C11×#125D414yes—
70C4×Q8×C11—22no—
71C4×Q8×C11—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80#67000—22no—
81#67000—22no—
82#67000—41no—
83#67000—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×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11D411yescharacteristic
95C2×C4⋊Dic11D411yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11C2311yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105#66927—22no—
106#66927—22no—
107C11×#107—22no—
108C11×#106—22no—
109C11×C4⋊C8—22no—
110C11×#103—22no—
111C11×#103—22no—
112#66899—22no—
113#66899—22no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95D411yescharacteristic
120C11⋊#95D411yescharacteristic
121#66885—22no—
122#66885—22no—
123#66885—41no—
124#66885—41no—
125Dic11⋊C8—41no—
126Dic11⋊C8—41no—
127#66873—22no—
128#66873—22no—
129#66873—22no—
130#66873—22no—
131#66867—22no—
132#25291—111nomaximal, Sylow
133C23×D11—21no—
134C23×D11—21no—
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×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—42no—
167C2×D44—42no—
168C2×D44—42no—
169C2×D44—42no—
170C2×D44—81no—
171C2×D44—81no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C11×C4⋊C4—24no—
179C11×C4⋊C4—24no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4C2×D412yes—
186C11×C4⋊C4C2×D412yes—
187C42×C11—42no—
188C42×C11C2×D412yes—
189C42×C11#4112yes—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—81no—
195(C2×D11)⋊C4—81no—
196(C2×D11)⋊C4—81no—
197(C2×D11)⋊C4—81no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—41no—
202C4⋊Dic11—41no—
203C4⋊Dic11—42no—
204C4⋊Dic11—81no—
205C4⋊Dic11#4112yes—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—21no—
210C4×Dic11—42no—
211C4×Dic11—81no—
212C4×Dic11—81no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×#490—111no—
220C2×#479D1111yescharacteristic, complemented
221#2548—111no—
222#2370—111no—
223#2067—111no—
224#2065—111no—
225#2042—111no—
226#2042—111no—
227#1983—111no—
228#1983—111no—
229#1982—111no—
230#1940—111no—
231#1926—111no—
232#1925—111no—
233#1763—111no—
234C23×C11C22×D411yescharacteristic
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
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—22no—
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#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—22no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295D44—41no—
296D44—41no—
297D44—41no—
298D44—41no—
299D44—41no—
300D44—41no—
301D44—41no—
302D44—41no—
303D44—84no—
304D44—84no—
305C8×C11—41no—
306C8×C11—41no—
307C11⋊C8—41no—
308C11⋊C8—41no—
309C2×#127—111no—
310C2×#125C2×D1111yescharacteristic
311C2×#124—111no—
312C2×#124—111no—
313C2×C4×Q8C2×D1111yescharacteristic
314#490—224no—
315#479—24no—
316C2×#107C2×D1111yescharacteristic
317C2×#106C2×D1111yescharacteristic
318C2×C4⋊C8—111no—
319C2×C4⋊C8—111no—
320C2×C4⋊C8C2×D1111yescharacteristic
321C2×#103—111no—
322C2×#103—111no—
323C2×#103C2×D1111yescharacteristic
324C2×#103C2×D1111yescharacteristic
325C2×#102—111no—
326C2×#102—111no—
327C2×#102—111no—
328C2×#102—111no—
329C2×#102—111no—
330C2×#102—111no—
331C2×#102—111no—
332C2×#102—111no—
333C2×#97—111no—
334#394—221no—
335#394—221no—
336#390—111no—
337#390—111no—
338#390—221no—
339#390—221no—
340#389—111no—
341#389—111no—
342#389—221no—
343#387—221no—
344#387—221no—
345C4×C4⋊C4—111no—
346C4×C4⋊C4—111no—
347C4×C4⋊C4—111no—
348C4×C4⋊C4—111no—
349C4×C4⋊C4—221no—
350#340—111no—
351#340—111no—
352#336—111no—
353#336—111no—
354C22×C11C2×#12111yescharacteristic
355C22×C11#54611yescharacteristic
356C22×C11#54811yescharacteristic
357C22×C11#57511yescharacteristic
358C22×C11#57511yescharacteristic
359C22×C11#57611yescharacteristic
360C22×C11#57711yescharacteristic
361C2×D11—81no—
362C2×D11—81no—
363C2×D11—81no—
364C2×D11—81no—
365C2×D11—81no—
366C2×D11—81no—
367C2×D11—81no—
368C2×D11—81no—
369C2×D11—81no—
370C2×D11—81no—
371C2×D11—81no—
372C2×D11—81no—
373C2×D11—81no—
374C2×D11—81no—
375C4×C11—22no—
376C4×C11—22no—
377C4×C11—42no—
378C4×C11—42no—
379C4×C11—42no—
380C4×C11—81no—
381C4×C11#52911yescharacteristic
382C4×C11#54211yescharacteristic
383C4×C11#54811yescharacteristic
384C4×C11#55011yescharacteristic
385Dic11—42no—
386Dic11—41no—
387Dic11—41no—
388Dic11—41no—
389Dic11—41no—
390Dic11—81no—
391C22×Q8C22×D1111yescharacteristic
392C22×D4—111no—
393C22×D4—111no—
394C22×D4—221no—
395C22×D4—221no—
396C22×C8—111no—
397C22×C8—111no—
398C22×C8C22×D1111yescharacteristic
399C22×C8C22×D1111yescharacteristic
400#127—222no—
401#127—222no—
402#125—22no—
403#125C22⋊D1114yes—
404#124—222no—
405#124—222no—
406#124—441no—
407#124—441no—
408C4×Q8—22no—
409C4×Q8—22no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C42—21no—
431C2×C42—111no—
432C2×C42—111no—
433C2×C42—221no—
434C2×C42—221no—
435C2×C42—221no—
436C2×C42C22×D1111yescharacteristic
437#107—22no—
438#106—22no—
439C4⋊C8—22no—
440C4⋊C8—441no—
441C4⋊C8—441no—
442#103—22no—
443#103—22no—
444#103—222no—
445#103—222no—
446#102—222no—
447#102—222no—
448#102—222no—
449#102—222no—
450#102—222no—
451#102—222no—
452#102—441no—
453#102—441no—
454#97—222no—
455#95—111no—
456#95—111no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462C2×C11#242611yescharacteristic
463C2×C11#304011yescharacteristic
464C2×C11#304511yescharacteristic
465C2×C11#330911yescharacteristic
466C2×C11#331711yescharacteristic
467C2×C11#337011yescharacteristic
468C2×C11#337111yescharacteristic
469D11—161no—
470D11—161no—
471C24—221no—
472C24—221no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8#434312yes—
479C2×D4—221no—
480C2×D4—221no—
481C2×D4—221no—
482C2×D4—221no—
483C2×D4—221no—
484C2×D4—221no—
485C2×D4—221no—
486C2×D4—221no—
487C2×D4—221no—
488C2×D4—221no—
489C2×D4—221no—
490C2×D4—221no—
491C2×D4—442no—
492C2×D4—442no—
493C2×D4—442no—
494C2×D4—442no—
495C2×D4—881no—
496C2×D4—881no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—111no—
502C22×C4—111no—
503C22×C4—111no—
504C22×C4—111no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4D4×D1111yescharacteristic
508C22×C4D4×D1111yescharacteristic
509C22×C4C23×D1111yescharacteristic
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C4⋊C4—24no—
523C4⋊C4—24no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—42no—
529C4⋊C4—112no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—441no—
534C4⋊C4—441no—
535C4⋊C4—442no—
536C4⋊C4—881no—
537C4⋊C4C2×C22⋊D1112yes—
538C4⋊C4C2×C22⋊D1112yes—
539C22⋊C4—442no—
540C22⋊C4—442no—
541C22⋊C4—442no—
542C22⋊C4—442no—
543C22⋊C4—881no—
544C22⋊C4—881no—
545C22⋊C4—881no—
546C22⋊C4—881no—
547C42—42no—
548C42—221no—
549C42—221no—
550C42—221no—
551C42—221no—
552C42—442no—
553C42—881no—
554C42—881no—
555C42#434112yes—
556C42C2×C22⋊D1112yes—
557C11#2529111yescharacteristic, complemented, Sylow
558C23—441no—
559C23—441no—
560C23—441no—
561C23—441no—
562C23—441no—
563C23—441no—
564C23—441no—
565C23—441no—
566C23—441no—
567C23—441no—
568C23—441no—
569C23—441no—
570C23—441no—
571C23—441no—
572C23C2×D4×D1111yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—41no—
576Q8—41no—
577D4—441no—
578D4—441no—
579D4—441no—
580D4—441no—
581D4—441no—
582D4—441no—
583D4—441no—
584D4—441no—
585D4—884no—
586D4—884no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—221no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—221no—
610C2×C4—221no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—221no—
614C2×C4—221no—
615C2×C4—222no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4#6699212yes—
622C2×C4#6699212yes—
623C2×C4C2×#434111yescharacteristic
624C2×C4C2×#434311yescharacteristic
625C2×C4#6704011yescharacteristic
626C2×C4#41×D1111yescharacteristic
627C2×C4#6704211yescharacteristic
628C2×C4C22×C22⋊D1111yescharacteristic
629C8—41no—
630C8—41no—
631C8—441no—
632C8—441no—
633C22—881no—
634C22—881no—
635C22—881no—
636C22—881no—
637C22—881no—
638C22—881no—
639C22—881no—
640C22—881no—
641C22—881no—
642C22—881no—
643C22—881no—
644C22—881no—
645C22—881no—
646C22—881no—
647C22#1062316111yescharacteristic
648C22#1062316411yescharacteristic
649C22#1062330011yescharacteristic
650C22#1062330111yescharacteristic
651C22#1062330811yescharacteristic
652C22#1062330811yescharacteristic
653C22C2×#6699211yescharacteristic
654C4—22no—
655C4—22no—
656C4—42no—
657C4—42no—
658C4—42no—
659C4—81no—
660C4—442no—
661C4—441no—
662C4—441no—
663C4—441no—
664C4—441no—
665C4—881no—
666C4#1062315511yescharacteristic
667C4#1062317411yescharacteristic
668C4#1062334811yescharacteristic
669C4#1062336511yescharacteristic
670C2—1761no—
671C2—1761no—
672C2#1307218411yescharacteristic
673C2#1307811211yescharacteristic
674C2#1307815311yescharacteristic
675C2#1308061911yescharacteristic
676C2#1308073911yescharacteristic
677C2#1308137211yescharacteristic
678C2#1308138711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#479C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenterC2×#479D11
hypocenterC11#25291
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
3. #13071716C2semidirect
4. #13069999C2semidirect
5. #13069985C2semidirect
6. #13069854C2semidirect
7. #13069854C2semidirect
8. #13069545C2semidirect
9. #13069545C2semidirect
11. #13069337C2semidirect
12. #13069242C2semidirect
13. #13069235C2semidirect
14. #13068446C2semidirect
15. C2×C11×#479C2semidirect
220. C2×#479D11semidirect
557. C11#25291semidirect

Maximal subgroups

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

subgroupindex
C2×#106226802
#130736152
#130717162
#130699992
#130699852
#130698542
#130695452
#130695422
#130693372
#130692422
#130692352
#130684462
C2×C11×#4792
#2529111