Finite Group Databasebeta

← #14796421

Subgroups — #14796421

Order 2816.

838 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622488C211yesmaximal, characteristic, complemented
2C2×#10622371C211yesmaximal, characteristic
3#13073787C211yesmaximal, characteristic
4#13071530C211yesmaximal, characteristic, complemented
5#13070100C211yesmaximal, characteristic, complemented
6#13070097C211yesmaximal, characteristic, complemented
7#13070000C211yesmaximal, characteristic
8#13069575C211yesmaximal, characteristic, complemented
9#13069331C211yesmaximal, characteristic, complemented
10#13068974C211yesmaximal, characteristic
11#13068968C211yesmaximal, characteristic
12#13068632C211yesmaximal, characteristic, complemented
13#13068630C211yesmaximal, characteristic, complemented
14#13068614C211yesmaximal, characteristic
15C11×#2067C211yesmaximal, characteristic
16C2×D4×Dic11C2211yescharacteristic
17C22×#4324C2211yescharacteristic
18C2×#66941C2211yescharacteristic
19C2×#66940C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C11×#389C2211yescharacteristic
28#10622834C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×C8×Dic11C2211yescharacteristic
35#10622598C2211yescharacteristic
36#10622590C2211yescharacteristic
37#10622589—21no—
38#10622589C2211yescharacteristic
39#10622585—21no—
40C2×#66874C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43#10622560—21no—
44#10622560—21no—
45#10622555—21no—
46#10622555—21no—
47#10622549C2211yescharacteristic
48C4×Dic11⋊C4C2211yescharacteristic
49#10622488—24no—
50#10622371—24no—
51#10622262—21no—
52#10622260—21no—
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C22×Dic22—21no—
64C22×Dic22C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77D4×Dic11—22no—
78D4×Dic11—22no—
79C2×#4324—22no—
80C2×#4324—22no—
81C2×#4324Q814yescomplemented
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4D411yescharacteristic
93C2×Dic11⋊C4D411yescharacteristic
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66941—22no—
102#66941—22no—
103#66940—22no—
104#66940—22no—
105#66940—41no—
106#66940D414yes—
107C4×Dic22—22no—
108C4×Dic22—41no—
109C11×#107—22no—
110C11×C4⋊C8—41no—
111C11×#102—22no—
112C11×#102—41no—
113C11×#95—21no—
114#66896—41no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95D411yescharacteristic
121C11⋊#95D411yescharacteristic
122#66880—22no—
123#66880—22no—
124Dic11⋊C8—22no—
125Dic11⋊C8—41no—
126C8×Dic11—22no—
127#66874—22no—
128#66872—22no—
129#66871—22no—
130#24814—111nomaximal, Sylow
131C24×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11C2×Q812yes—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—42no—
149C22×Dic11—42no—
150C22×Dic11—42no—
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—42no—
159C2×Dic22—81no—
160C2×Dic22—81no—
161C2×Dic22C2×D412yes—
162C2×Dic22C2×Q812yes—
163C2×Dic22#4112yes—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—81no—
176C11×C4⋊C4C2×D412yes—
177C11×C22⋊C4—81no—
178C11×C22⋊C4—81no—
179C42×C11—21no—
180C42×C11—21no—
181C22⋊Dic11—42no—
182C22⋊Dic11—81no—
183C22⋊Dic11—81no—
184#4324—28no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—81no—
192Dic11⋊C4—24no—
193Dic11⋊C4—22no—
194Dic11⋊C4—22no—
195Dic11⋊C4—42no—
196Dic11⋊C4—42no—
197Dic11⋊C4—42no—
198Dic11⋊C4—42no—
199Dic11⋊C4—81no—
200C4×Dic11—24no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—42no—
204C4×Dic11—42no—
205C4×Dic11C2×D412yes—
206C4×Dic11#4112yes—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8C2×Q812yes—
213C2×#477—111no—
214C2×C4×SD16—111no—
215#2563—111no—
216Q8×C4⋊C4—111no—
217#2085—111no—
218#2085—111no—
219#2067—111no—
220#2067D1111yescharacteristic
221#1990—111no—
222#1939—111no—
223#1880—111no—
224#1880—111no—
225#1805—111no—
226#1805—111no—
227#1802—111no—
228C23×C11—22no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11C22×D411yescharacteristic
236D4×C11—22no—
237D4×C11—22no—
238D4×C11—41no—
239D4×C11—41no—
240C2×C4×C11—22no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×Q811yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C2×C4×C112−1+411yescharacteristic
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—84no—
282C2×Dic11#12112yes—
283C2×Dic11#12112yes—
284C2×Dic11#13512yes—
285C2×Dic11#13712yes—
286Dic22—22no—
287Dic22—22no—
288Dic22—22no—
289Dic22—84no—
290Dic22C22⋊Q814yes—
291C8×C11—41no—
292C8×C11—41no—
293C11⋊C8—22no—
294C11⋊C8—41no—
295C22×SD16—111no—
296C2×C4⋊Q8—111no—
297C2×C4×Q8—111no—
298C2×C4×Q8—111no—
299C2×C4×Q8—111no—
300C2×C4×D4—111no—
301#477—224no—
302C4×SD16—224no—
303C2×#107—111no—
304C2×#107C2×D1111yescharacteristic
305C2×#106—111no—
306C2×C4⋊C8—111no—
307C2×C4⋊C8—111no—
308C2×C4⋊C8C2×D1111yescharacteristic
309C2×#103—111no—
310C2×#103—111no—
311C2×#103—111no—
312C2×#102—111no—
313C2×#102C2×D1111yescharacteristic
314C2×#102C2×D1111yescharacteristic
315C2×C4×C8—111no—
316#393—221no—
317#393—221no—
318#390—111no—
319#390C2×D1111yescharacteristic
320#389—111no—
321#389—221no—
322#389—221no—
323#389C2×D1111yescharacteristic
324#384—111no—
325#384—221no—
326#382—111no—
327#382—111no—
328#380—221no—
329#380—221no—
330C4×C4⋊C4—111no—
331C4×C4⋊C4—221no—
332#340—111no—
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340C2×D1111yescharacteristic
338#336—111no—
339#336—111no—
340C22×C11—42no—
341C22×C11—42no—
342C22×C11—42no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11C2×#12111yescharacteristic
348C22×C11#54611yescharacteristic
349C22×C11D4×Q811yescharacteristic
350C22×C11C2×#13511yescharacteristic
351C22×C11C2×#13711yescharacteristic
352C22×C11#57611yescharacteristic
353C22×C11#57711yescharacteristic
354C4×C11—41no—
355C4×C11—42no—
356C4×C11—41no—
357C4×C11—81no—
358C4×C11—81no—
359C4×C11C2×C22⋊Q811yescharacteristic
360C4×C11#53711yescharacteristic
361C4×C11#55211yescharacteristic
362C4×C11#55411yescharacteristic
363Dic11—24no—
364Dic11—22no—
365Dic11—41no—
366Dic11—41no—
367Dic11—81no—
368Dic11—81no—
369Dic11—81no—
370Dic11#46414yes—
371C22×Q8—111no—
372C22×Q8—221no—
373C22×D4C22×D1111yescharacteristic
374C23×C4—221no—
375C2×SD16—114no—
376C2×SD16—222no—
377C2×SD16—222no—
378C22×C8—111no—
379C22×C8—111no—
380C22×C8C22×D1111yescharacteristic
381C22×C8C22×D1111yescharacteristic
382C4⋊Q8—222no—
383C4⋊Q8—222no—
384C4×Q8—114no—
385C4×Q8—222no—
386C4×Q8—222no—
387C4×Q8—222no—
388C4×Q8—441no—
389C4×Q8—441no—
390C4×D4—222no—
391C4×D4—222no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C42—111no—
414C2×C42—111no—
415C2×C42—221no—
416C2×C42—221no—
417C2×C42—221no—
418C2×C42C22×D1111yescharacteristic
419#107—22no—
420#107—222no—
421#106—222no—
422C4⋊C8—41no—
423C4⋊C8—222no—
424C4⋊C8—441no—
425#103—222no—
426#103—222no—
427#103—222no—
428#102—22no—
429#102—41no—
430#102—441no—
431C4×C8—222no—
432#95—21no—
433#95—111no—
434#95—111no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440C2×C11—82no—
441C2×C11#241711yescharacteristic
442C2×C11C2×#46411yescharacteristic
443C2×C11#304511yescharacteristic
444C2×C11#330511yescharacteristic
445C2×C11#332911yescharacteristic
446C2×C11#338111yescharacteristic
447C2×C11#338511yescharacteristic
448C24—21no—
449C2×Q8—112no—
450C2×Q8—112no—
451C2×Q8—112no—
452C2×Q8—221no—
453C2×Q8—221no—
454C2×Q8—221no—
455C2×Q8—442no—
456C2×Q8—881no—
457C2×Q8—881no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4Q8×D1112yes—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—111no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—442no—
476C22×C4—442no—
477C22×C4—442no—
478C22×C4D4×D1111yescharacteristic
479C22×C4D4×D1111yescharacteristic
480C22×C4C23×D1111yescharacteristic
481SD16—228no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—112no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—81no—
500C4⋊C4—222no—
501C4⋊C4—222no—
502C4⋊C4—224no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—442no—
510C4⋊C4—442no—
511C4⋊C4—442no—
512C4⋊C4—442no—
513C4⋊C4—881no—
514C4⋊C4—881no—
515C4⋊C4D4×D1112yes—
516C22⋊C4—81no—
517C22⋊C4—81no—
518C22⋊C4—442no—
519C22⋊C4—881no—
520C22⋊C4—881no—
521C42—21no—
522C42—21no—
523C42—112no—
524C42—112no—
525C42—224no—
526C42—221no—
527C42—221no—
528C42—442no—
529C42—442no—
530C11#2481411yescharacteristic, complemented, Sylow
531C23—22no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23C2×D4×D1111yescharacteristic
539Q8—114no—
540Q8—222no—
541Q8—222no—
542Q8—222no—
543Q8—884no—
544D4—22no—
545D4—22no—
546D4—41no—
547D4—41no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—112no—
564C2×C4—112no—
565C2×C4—112no—
566C2×C4—112no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—884no—
588C2×C4C2×D4×D1111yescharacteristic
589C2×C4#6703711yescharacteristic
590C2×C4C2×Q8×D1111yescharacteristic
591C2×C4#41×D1111yescharacteristic
592C2×C4#41×D1111yescharacteristic
593C2×C4#6704311yescharacteristic
594C8—41no—
595C8—41no—
596C8—222no—
597C8—441no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22D11×#12111yescharacteristic
606C22#1062314111yescharacteristic
607C22#1062316311yescharacteristic
608C22#1062328811yescharacteristic
609C22D11×#13511yescharacteristic
610C22#1062330611yescharacteristic
611C22D11×#13711yescharacteristic
612C4—41no—
613C4—42no—
614C4—41no—
615C4—81no—
616C4—81no—
617C4—114no—
618C4—222no—
619C4—224no—
620C4—441no—
621C4—441no—
622C4—881no—
623C4—881no—
624C4—881no—
625C4#1062313911yescharacteristic
626C4D11×C22⋊Q811yescharacteristic
627C4#1062316711yescharacteristic
628C4#1062323911yescharacteristic
629C2—82no—
630C2#1307206011yescharacteristic
631C2D11×#46411yescharacteristic
632C2#1307815011yescharacteristic
633C2#1308056111yescharacteristic
634C2#1308090511yescharacteristic
635C2#1308148611yescharacteristic
636C2#1308152111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2067C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2067D11
hypocenterC11#24814
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2067

Complements

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

NH ≅ G/Ntype
1. C2×#10622488C2semidirect
4. #13071530C2semidirect
5. #13070100C2semidirect
6. #13070097C2semidirect
8. #13069575C2semidirect
9. #13069331C2semidirect
12. #13068632C2semidirect
13. #13068630C2semidirect
81. C2×#4324Q8semidirect
530. C11#24814semidirect

Maximal subgroups

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

subgroupindex
C2×#106224882
C2×#106223712
#130737872
#130715302
#130701002
#130700972
#130700002
#130695752
#130693312
#130689742
#130689682
#130686322
#130686302
#130686142
C11×#20672
#2481411