Finite Group Databasebeta

← #14803314

Subgroups — #14803314

Order 2816.

848 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×#10622443C211yesmaximal, characteristic, complemented
2#13074105C211yesmaximal, characteristic, complemented
3#13073970C211yesmaximal, characteristic, complemented
4#13070009C211yesmaximal, characteristic, complemented
5#13069988C211yesmaximal, characteristic, complemented
6#13069929C211yesmaximal, characteristic, complemented
7#13069924C211yesmaximal, characteristic
8#13069483C211yesmaximal, characteristic
9#13069472C211yesmaximal, characteristic, complemented
10#13069428C211yesmaximal, characteristic, complemented
11#13069386C211yesmaximal, characteristic, complemented
12#13069296C211yesmaximal, characteristic, complemented
13#13069289C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, characteristic, complemented
15C2×C11×#463C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C11×#463—24no—
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25#10622843C2211yescharacteristic
26#10622843C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29#10622834C2211yescharacteristic
30#10622834C2211yescharacteristic
31#10622834C2211yescharacteristic
32#10622834C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37#10622823—21no—
38#10622823—21no—
39C2×#66882C2211yescharacteristic
40C2×#66881C2211yescharacteristic
41C2×Dic11⋊C8C2211yescharacteristic
42C2×Dic11⋊C8C2211yescharacteristic
43C2×C8×Dic11C2211yescharacteristic
44C2×C8×Dic11C2211yescharacteristic
45#10622586C2211yescharacteristic
46#10622586C2211yescharacteristic
47#10622566—21no—
48#10622562—21no—
49#10622560—21no—
50#10622560—21no—
51#10622558—21no—
52#10622558—21no—
53#10622549C2211yescharacteristic
54C4×C4⋊Dic11C2211yescharacteristic
55C2×C4×C11⋊C8C2211yescharacteristic
56#10622443—24no—
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C22×Dic22D411yescharacteristic
66C2×C11×SD16—22no—
67C2×C11×SD16—22no—
68C2×C11×SD16—41no—
69C2×C11×D8—22no—
70C2×C11×D8—22no—
71C2×C11×D8—41no—
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C11×#124—22no—
75C11×#124—22no—
76C4×D4×C11—22no—
77C4×D4×C11—22no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C42×C11C2311yescharacteristic
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90C2×C22⋊Dic11—21no—
91C2×C4⋊Dic11D411yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4D411yescharacteristic
99C2×Dic11⋊C4D411yescharacteristic
100C2×C4×Dic11—21no—
101C2×C4×Dic11C2311yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C4×Dic22—22no—
106C4×Dic22—22no—
107C11×C4⋊C8D414yes—
108C11×#103—22no—
109C11×#102—22no—
110#66899—22no—
111#66899—41no—
112#66896—22no—
113#66896—22no—
114#66896—22no—
115#66896—41no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125#66882—41no—
126#66881—41no—
127Dic11⋊C8—22no—
128Dic11⋊C8—22no—
129C8×Dic11—22no—
130C8×Dic11—22no—
131C4×C11⋊C8—22no—
132#25296—111nomaximal, Sylow
133C24×C11—21no—
134C24×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11#4112yes—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—42no—
156C22×C4×C11—81no—
157C22×C4×C11—81no—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2411yescharacteristic
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169C2×Dic22—22no—
170C2×Dic22—22no—
171C2×Dic22—22no—
172C11×SD16—44no—
173C11×D8—44no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11C2×D412yes—
179C2×C8×C11C2×D412yes—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C22⋊C4—42no—
183C11×C22⋊C4—42no—
184C11×C22⋊C4—42no—
185C42×C11C2×D412yes—
186C42×C11#4112yes—
187C22⋊Dic11—42no—
188C22⋊Dic11—42no—
189C22⋊Dic11—42no—
190C22⋊Dic11—42no—
191C22⋊Dic11—81no—
192C22⋊Dic11—81no—
193C22⋊Dic11—81no—
194C22⋊Dic11—81no—
195C4⋊Dic11—22no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204Dic11⋊C4—22no—
205Dic11⋊C4—22no—
206Dic11⋊C4—81no—
207Dic11⋊C4—81no—
208C4×Dic11—21no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C4×Dic11—21no—
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#4112yes—
219C2×#463D1111yescharacteristic
220C2×C8×Q8—111no—
221#2592—111no—
222#2580—111no—
223#2068—111no—
224#2065—111no—
225#2055—111no—
226#2054—111no—
227#1970—111no—
228#1968—111no—
229#1958—111no—
230#1949—111no—
231#1934—111no—
232#1933—111no—
233C4×#102—111no—
234C23×C11—22no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11C22×D411yescharacteristic
249Q8×C11—41no—
250Q8×C11—41no—
251Q8×C11—41no—
252Q8×C11—41no—
253D4×C11—22no—
254D4×C11—22no—
255D4×C11—41no—
256D4×C11—41no—
257D4×C11—41no—
258D4×C11—41no—
259D4×C11—41no—
260D4×C11—41no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
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—84no—
272C2×C4×C11#12112yes—
273C2×C4×C11#12112yes—
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×C4×C112−1+411yescharacteristic
280C2×Dic11—21no—
281C2×Dic11—21no—
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—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11#13512yes—
303C2×Dic11#13512yes—
304Dic22—28no—
305C8×C11—22no—
306C8×C11—22no—
307C11⋊C8—22no—
308C11⋊C8—41no—
309C22×SD16C2×D1111yescharacteristic
310C22×D8C2×D1111yescharacteristic
311C2×#124C2×D1111yescharacteristic
312C2×C4×Q8—111no—
313C2×C4×D4C2×D1111yescharacteristic
314#463—24no—
315C8×Q8—224no—
316C2×#107—111no—
317C2×#106—111no—
318C2×C4⋊C8—111no—
319C2×C4⋊C8—111no—
320C2×C4⋊C8C2×D1111yescharacteristic
321C2×#103—111no—
322C2×#103—111no—
323C2×#103C2×D1111yescharacteristic
324C2×#102—111no—
325C2×#102—111no—
326C2×#102—111no—
327C2×#102—111no—
328C2×#102C2×D1111yescharacteristic
329C2×C4×C8—111no—
330C2×C4×C8—111no—
331C2×C4×C8—111no—
332#399—221no—
333#397—221no—
334#393—221no—
335#393—221no—
336#391—111no—
337#391—111no—
338#390—111no—
339#390—111no—
340#390—111no—
341#390—111no—
342#389—111no—
343#389—111no—
344#388—221no—
345#388—221no—
346#385—221no—
347#385—221no—
348#382—111no—
349C4×C4⋊C4—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354C22×C11—42no—
355C22×C11—42no—
356C22×C11—42no—
357C22×C11—81no—
358C22×C11—81no—
359C22×C11—81no—
360C22×C11—81no—
361C22×C11—81no—
362C22×C11—81no—
363C22×C11—81no—
364C22×C11—81no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11C2×#12111yescharacteristic
369C22×C11#54811yescharacteristic
370C22×C11#55011yescharacteristic
371C22×C11C2×#13511yescharacteristic
372C22×C11C2×#13511yescharacteristic
373C22×C11#57611yescharacteristic
374C22×C11#57711yescharacteristic
375C4×C11—22no—
376C4×C11—22no—
377C4×C11—81no—
378C4×C11—81no—
379C4×C11#52911yescharacteristic
380C4×C11#54211yescharacteristic
381C4×C11#54611yescharacteristic
382C4×C11#54811yescharacteristic
383Dic11—22no—
384Dic11—22no—
385Dic11—41no—
386Dic11—41no—
387Dic11—81no—
388Dic11—81no—
389Dic11—81no—
390Dic11—81no—
391C22×Q8—111no—
392C22×Q8C22×D1111yescharacteristic
393C22×D4C22×D1111yescharacteristic
394C22×D4C22×D1111yescharacteristic
395C23×C4—21no—
396C2×SD16—22no—
397C2×SD16—22no—
398C2×SD16—41no—
399C2×D8—22no—
400C2×D8—22no—
401C2×D8—41no—
402C22×C8—111no—
403C22×C8—111no—
404C22×C8C22×D1111yescharacteristic
405C22×C8C22×D1111yescharacteristic
406#124—22no—
407#124—22no—
408C4×Q8—222no—
409C4×Q8—222no—
410C4×D4—22no—
411C4×D4—22no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C42—111no—
434C2×C42—111no—
435C2×C42—221no—
436C2×C42C22×D1111yescharacteristic
437#107—441no—
438#106—441no—
439C4⋊C8—222no—
440C4⋊C8—222no—
441C4⋊C8C22⋊D1114yes—
442#103—22no—
443#103—222no—
444#103—441no—
445#102—22no—
446#102—222no—
447#102—222no—
448#102—222no—
449#102—441no—
450C4×C8—222no—
451C4×C8—222no—
452C4×C8—222no—
453#95—221no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462C2×C11—82no—
463C2×C11—161no—
464C2×C11#242611yescharacteristic
465C2×C11#305011yescharacteristic
466C2×C11#306211yescharacteristic
467C2×C11#336011yescharacteristic
468C2×C11#336111yescharacteristic
469C2×C11#339411yescharacteristic
470C2×C11#339611yescharacteristic
471C24—21no—
472C24—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—222no—
480C2×Q8—222no—
481C2×Q8—222no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4#434112yes—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—42no—
497C22×C4—81no—
498C22×C4—81no—
499C22×C4—111no—
500C22×C4—111no—
501C22×C4—111no—
502C22×C4—111no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4D4×D1111yescharacteristic
508C22×C4D4×D1111yescharacteristic
509C22×C4C23×D1111yescharacteristic
510SD16—44no—
511D8—44no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—112no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8C2×C22⋊D1112yes—
523C2×C8C2×C22⋊D1112yes—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—222no—
527C4⋊C4—222no—
528C4⋊C4—222no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—881no—
538C4⋊C4—881no—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—442no—
543C22⋊C4—442no—
544C22⋊C4—442no—
545C22⋊C4—442no—
546C22⋊C4—881no—
547C22⋊C4—881no—
548C22⋊C4—881no—
549C22⋊C4—881no—
550C42—221no—
551C42—221no—
552C42—221no—
553C42—221no—
554C42—881no—
555C42#434112yes—
556C42C2×C22⋊D1112yes—
557C11#2529611yescharacteristic, complemented, Sylow
558C23—22no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23C2×D4×D1111yescharacteristic
573Q8—41no—
574Q8—41no—
575Q8—41no—
576Q8—41no—
577Q8—228no—
578D4—22no—
579D4—22no—
580D4—41no—
581D4—41no—
582D4—41no—
583D4—41no—
584D4—41no—
585D4—41no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—84no—
597C2×C4—112no—
598C2×C4—112no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—221no—
607C2×C4—221no—
608C2×C4—221no—
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#6699112yes—
622C2×C4#6699112yes—
623C2×C4C2×#434111yescharacteristic
624C2×C4C2×#434111yescharacteristic
625C2×C4#6703711yescharacteristic
626C2×C4#41×D1111yescharacteristic
627C2×C4#6704311yescharacteristic
628C2×C4C22×C22⋊D1111yescharacteristic
629C8—22no—
630C8—22no—
631C8—222no—
632C8—441no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22#1062312911yescharacteristic
648C22#1062313011yescharacteristic
649C22D11×#13511yescharacteristic
650C22D11×#13511yescharacteristic
651C22#1062330511yescharacteristic
652C22#1062330611yescharacteristic
653C22C2×#6699111yescharacteristic
654C4—22no—
655C4—22no—
656C4—81no—
657C4—81no—
658C4—222no—
659C4—222no—
660C4—441no—
661C4—441no—
662C4—881no—
663C4—881no—
664C4—881no—
665C4—881no—
666C4#1062313111yescharacteristic
667C4#1062313411yescharacteristic
668C4#1062333711yescharacteristic
669C4#1062336211yescharacteristic
670C2—82no—
671C2—161no—
672C2#1307217811yescharacteristic
673C2#1307819311yescharacteristic
674C2#1307829011yescharacteristic
675C2#1308126011yescharacteristic
676C2#1308127111yescharacteristic
677C2#1308161511yescharacteristic
678C2#1308162311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#463C2
socleC23×C11C22×D4
prime radicalC22×C11×D8C22
hypercenterC2×#463D11
hypocenterC11#25296
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#10622443C2semidirect
2. #13074105C2semidirect
3. #13073970C2semidirect
4. #13070009C2semidirect
5. #13069988C2semidirect
6. #13069929C2semidirect
9. #13069472C2semidirect
10. #13069428C2semidirect
11. #13069386C2semidirect
12. #13069296C2semidirect
13. #13069289C2semidirect
14. C4×#66896C2semidirect
557. C11#25296semidirect

Maximal subgroups

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

subgroupindex
C2×#106224432
#130741052
#130739702
#130700092
#130699882
#130699292
#130699242
#130694832
#130694722
#130694282
#130693862
#130692962
#130692892
C4×#668962
C2×C11×#4632
#2529611