Finite Group Databasebeta

← #14802022

Subgroups — #14802022

Order 2816.

858 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622657C211yesmaximal, characteristic
2#13073095C211yesmaximal, characteristic
3#13071625C211yesmaximal, characteristic
4#13070090C211yesmaximal, characteristic, complemented
5#13070027C211yesmaximal, characteristic, complemented
6#13070007C211yesmaximal, characteristic, complemented
7#13069936C211yesmaximal, characteristic, complemented
8#13069371C211yesmaximal, characteristic, complemented
9#13069260C211yesmaximal, characteristic, complemented
10#13068959C211yesmaximal, characteristic, complemented
11#13068924C211yesmaximal, characteristic
12#13068794C211yesmaximal, characteristic
13#13068619C211yesmaximal, characteristic, complemented
14C2×#10622189C211yesmaximal, characteristic
15C2×C11×#467C211yesmaximal, characteristic
16C22×C11×Q16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C11×#467—24no—
24C2×C11×#107C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27#10622843C2211yescharacteristic
28#10622843C2211yescharacteristic
29#10622843C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C4×C22⋊Dic11C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38#10622657—24no—
39#10622598—21no—
40#10622598C2211yescharacteristic
41#10622596—21no—
42#10622596—21no—
43#10622594—21no—
44#10622589C2211yescharacteristic
45#10622589C2211yescharacteristic
46C4⋊C4×Dic11C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49#10622563—21no—
50#10622559—21no—
51#10622559—21no—
52C22⋊C4×Dic11—21no—
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11—21no—
65C23×Dic11—21no—
66C2×C11×Q16—22no—
67C2×C11×Q16—22no—
68C2×C11×Q16—41no—
69C22×C8×C11—22no—
70C22×C8×C11—22no—
71C22×C8×C11—41no—
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8D414yes—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C22⋊Dic11D411yescharacteristic
85C2×C22⋊Dic11D411yescharacteristic
86Q8×Dic11—22no—
87Q8×Dic11—41no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—41no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11C2311yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C11×#107—22no—
111C11×#103—22no—
112C11×#103—22no—
113#66899—22no—
114#66899—22no—
115#66899—22no—
116#66899—41no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95D411yescharacteristic
126C11⋊#95D411yescharacteristic
127C22⋊(C11⋊C8)—22no—
128Dic11⋊C8—22no—
129Dic11⋊C8—41no—
130#66871—22no—
131#66871—22no—
132#25206—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C2×Q8×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×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11C2×D412yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D412yes—
156C22×C4×C11#4112yes—
157C22×C4×C11C2411yescharacteristic
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—42no—
163C22×Dic11—42no—
164C22×Dic11—42no—
165C22×Dic11—81no—
166C22×Dic11—81no—
167C22×Dic11—81no—
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D411yescharacteristic
170C22×Dic11C2×D411yescharacteristic
171C22×Dic11C2×D411yescharacteristic
172C11×Q16—44no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—44no—
179C2×C8×C11#4112yes—
180C11×C4⋊C4—24no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4C2×D412yes—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—42no—
188C22⋊Dic11—22no—
189C22⋊Dic11Q1614yescomplemented
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—42no—
198C4⋊Dic11—42no—
199C4⋊Dic11—42no—
200C4⋊Dic11—81no—
201C4⋊Dic11#4112yes—
202Dic11⋊C4—81no—
203Dic11⋊C4—81no—
204Dic11⋊C4—81no—
205Dic11⋊C4—81no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—21no—
210C4×Dic11—42no—
211C4×Dic11—81no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×#484—111no—
219C2×#467D1111yescharacteristic
220#2502—111no—
221#2360—111no—
222#2083—111no—
223#2072—111no—
224#2068—111no—
225#2056—111no—
226#1947—111no—
227#1928—111no—
228#1878—111no—
229#1872—111no—
230#1850—111no—
231#1803—111no—
232C2×#340—111no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11#12112yes—
238C23×C11C2×Q1612yes—
239C23×C11#13712yes—
240C23×C11C22×D411yescharacteristic
241Q8×C11—22no—
242Q8×C11—22no—
243Q8×C11—41no—
244Q8×C11—41no—
245Q8×C11—41no—
246Q8×C11—41no—
247Q8×C11—41no—
248Q8×C11—41no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
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#12112yes—
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11H(5,𝔽2)11yescharacteristic
273C2×C4×C112−1+411yescharacteristic
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—22no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—41no—
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—41no—
296C2×Dic11—84no—
297C2×Dic11—84no—
298C2×Dic11C2×Q1612yes—
299C2×Dic11C2×Q1612yes—
300C8×C11—22no—
301C8×C11—41no—
302C11⋊C8—41no—
303C11⋊C8—41no—
304C22×Q16C2×D1111yescharacteristic
305C23×C8C2×D1111yescharacteristic
306C2×C22⋊Q8C2×D1111yescharacteristic
307C2×C22⋊Q8C2×D1111yescharacteristic
308C2×C4×Q8—111no—
309C22×C4⋊C4—111no—
310C22×C4⋊C4—111no—
311#484—224no—
312#467—24no—
313C2×#107—111no—
314C2×#107—111no—
315C2×#107C2×D1111yescharacteristic
316C2×C4⋊C8—111no—
317C2×C4⋊C8—111no—
318C2×#103—111no—
319C2×#103—111no—
320C2×#103—111no—
321C2×#103—111no—
322C2×#103C2×D1111yescharacteristic
323C2×#103C2×D1111yescharacteristic
324C2×C22⋊C8—111no—
325#398—221no—
326#398—221no—
327#391—111no—
328#391—111no—
329#391—111no—
330#389—111no—
331#389—221no—
332#387—221no—
333#385—221no—
334#385—221no—
335#385—221no—
336#384—111no—
337#384—111no—
338C4×C4⋊C4—111no—
339C4×C22⋊C4—111no—
340C4×C22⋊C4—221no—
341#340—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#336—111no—
348#336—111no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11—22no—
355C22×C11#46214yes—
356C22×C11C2×#12111yescharacteristic
357C22×C11#54611yescharacteristic
358C22×C11#54711yescharacteristic
359C22×C11C22×Q1611yescharacteristic
360C22×C11C2×#13711yescharacteristic
361C22×C11#57611yescharacteristic
362C22×C11#57711yescharacteristic
363C4×C11—22no—
364C4×C11—42no—
365C4×C11—42no—
366C4×C11—81no—
367C4×C11—81no—
368C4×C11#52911yescharacteristic
369C4×C11#53911yescharacteristic
370C4×C11#54611yescharacteristic
371C4×C11#54711yescharacteristic
372Dic11—22no—
373Dic11—22no—
374Dic11—41no—
375Dic11—41no—
376Dic11—42no—
377Dic11—81no—
378Dic11—81no—
379Dic11—81no—
380C22×Q8C22×D1111yescharacteristic
381C22×Q8C22×D1111yescharacteristic
382C23×C4—221no—
383C23×C4—221no—
384C23×C4C22×D1111yescharacteristic
385C2×Q16—22no—
386C2×Q16—22no—
387C2×Q16—41no—
388C22×C8—22no—
389C22×C8—22no—
390C22×C8—41no—
391C22×C8—111no—
392C22×C8—111no—
393C22×C8C22×D1111yescharacteristic
394C22×C8C22×D1111yescharacteristic
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398C22⋊Q8C22⋊D1114yes—
399C4×Q8—222no—
400C4×Q8—441no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—222no—
408C2×C4⋊C4—222no—
409C2×C4⋊C4—222no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—441no—
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—111no—
424C2×C22⋊C4—111no—
425C2×C42—111no—
426C2×C42—111no—
427C2×C42—221no—
428C2×C42—221no—
429#107—22no—
430#107—222no—
431#107—222no—
432C4⋊C8—222no—
433C4⋊C8—441no—
434#103—22no—
435#103—22no—
436#103—222no—
437#103—222no—
438#103—222no—
439#103—441no—
440C22⋊C8—222no—
441#95—111no—
442#95—111no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451C2×C11—24no—
452C2×C11#242511yescharacteristic
453C2×C11C2×#46211yescharacteristic
454C2×C11#304511yescharacteristic
455C2×C11#329911yescharacteristic
456C2×C11#331411yescharacteristic
457C2×C11#333811yescharacteristic
458C2×C11#334411yescharacteristic
459C24D4×D1111yescharacteristic
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8C2×C22⋊D1112yes—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—442no—
489C22×C4—442no—
490C22×C4—442no—
491C22×C4—881no—
492C22×C4—881no—
493C22×C4—881no—
494C22×C4D4×D1111yescharacteristic
495C22×C4#434112yes—
496C22×C4C2×C22⋊D1112yes—
497C22×C4C23×D1111yescharacteristic
498Q16—44no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—44no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8#434112yes—
512C4⋊C4—24no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—42no—
517C4⋊C4—112no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—442no—
526C4⋊C4—442no—
527C4⋊C4—442no—
528C4⋊C4—881no—
529C4⋊C4—881no—
530C4⋊C4—881no—
531C4⋊C4—881no—
532C4⋊C4—881no—
533C4⋊C4C2×C22⋊D1112yes—
534C22⋊C4—24no—
535C22⋊C4—42no—
536C22⋊C4—114no—
537C22⋊C4—222no—
538C42—221no—
539C42—221no—
540C42—221no—
541C42—221no—
542C42—442no—
543C42—881no—
544C11#2520611yescharacteristic, complemented, Sylow
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23Q16×D1112yes—
550C23#6697112yes—
551C23#6699212yes—
552C23C2×D4×D1111yescharacteristic
553Q8—22no—
554Q8—22no—
555Q8—41no—
556Q8—41no—
557Q8—41no—
558Q8—41no—
559Q8—41no—
560Q8—41no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—112no—
580C2×C4—112no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—222no—
591C2×C4—221no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—884no—
604C2×C4—884no—
605C2×C4#6699212yes—
606C2×C4C2×#434111yescharacteristic
607C2×C4C2×#434111yescharacteristic
608C2×C4#6703711yescharacteristic
609C2×C4#41×D1111yescharacteristic
610C2×C4#6704311yescharacteristic
611C2×C4C22×C22⋊D1111yescharacteristic
612C8—22no—
613C8—41no—
614C8—441no—
615C8—441no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22#1062279514yes—
623C22#1062314111yescharacteristic
624C22#1062314211yescharacteristic
625C22C2×Q16×D1111yescharacteristic
626C22C2×#6697111yescharacteristic
627C22#1062330011yescharacteristic
628C22#1062330111yescharacteristic
629C22C2×#6699211yescharacteristic
630C4—22no—
631C4—42no—
632C4—42no—
633C4—81no—
634C4—81no—
635C4—222no—
636C4—222no—
637C4—441no—
638C4—442no—
639C4—441no—
640C4—881no—
641C4—881no—
642C4—881no—
643C4#1062313111yescharacteristic
644C4#1062313311yescharacteristic
645C4#1062333711yescharacteristic
646C4#1062335511yescharacteristic
647C2—24no—
648C2#1307217311yescharacteristic
649C2C2×#1062279511yescharacteristic
650C2#1307815311yescharacteristic
651C2#1308048711yescharacteristic
652C2#1308070311yescharacteristic
653C2#1308100511yescharacteristic
654C2#1308107711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#467C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC2×#467D11
hypocenterC11#25206
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
4. #13070090C2semidirect
5. #13070027C2semidirect
6. #13070007C2semidirect
7. #13069936C2semidirect
8. #13069371C2semidirect
9. #13069260C2semidirect
10. #13068959C2semidirect
13. #13068619C2semidirect
189. C22⋊Dic11Q16semidirect
544. C11#25206semidirect

Maximal subgroups

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

subgroupindex
C2×#106226572
#130730952
#130716252
#130700902
#130700272
#130700072
#130699362
#130693712
#130692602
#130689592
#130689242
#130687942
#130686192
C2×#106221892
C2×C11×#4672
#2520611