Finite Group Databasebeta

← #14803195

Subgroups — #14803195

Order 2816.

794 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622668C211yesmaximal, characteristic
2C2×#10622633C211yesmaximal, characteristic, complemented
3#13071705C211yesmaximal, characteristic, complemented
4#13069997C211yesmaximal, characteristic, complemented
5#13069990C211yesmaximal, characteristic
6#13069859C211yesmaximal, characteristic, complemented
7#13069852C211yesmaximal, characteristic
8#13069549C211yesmaximal, characteristic
9#13069549C211yesmaximal, characteristic
10#13069540C211yesmaximal, characteristic, complemented
11#13069340C211yesmaximal, characteristic, complemented
12#13069247C211yesmaximal, characteristic, complemented
13#13069240C211yesmaximal, characteristic
14#13068446C211yesmaximal, characteristic, complemented
15C11×#2545C211yesmaximal, characteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#124C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C11×#396—21no—
22C11×#396—21no—
23C11×#391C2211yescharacteristic
24C11×#390C2211yescharacteristic
25C11×#388—21no—
26C11×#388—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40#10622668—24no—
41#10622633—24no—
42C4⋊C4×Dic11—21no—
43#10622586—21no—
44C2×#66872C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C4×C4⋊Dic11C2211yescharacteristic
47C4×C4⋊Dic11C2211yescharacteristic
48C4×C4⋊Dic11C2211yescharacteristic
49#10622541C2211yescharacteristic
50#10622541C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×#66867C2211yescharacteristic
55#10622259—21no—
56#10622259—21no—
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C22×Dic22—21no—
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8—41no—
67C11×#124—22no—
68C11×#124—22no—
69C11×#124—22no—
70C11×#124—41no—
71C4×Q8×C11—22no—
72C4×Q8×C11—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C42×C11—21no—
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103#66922—22no—
104#66922D414yes—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95D411yescharacteristic
108C11×#95D411yescharacteristic
109#66899—22no—
110#66899—22no—
111#66899—22no—
112#66899—22no—
113#66899—22no—
114#66899—22no—
115#66899—22no—
116#66899—41no—
117#66896—22no—
118#66896—22no—
119#66896—22no—
120#66896—41no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126#66872—22no—
127#66872—22no—
128C4⋊(C11⋊C8)—22no—
129C4⋊(C11⋊C8)—41no—
130C4⋊(C11⋊C8)—41no—
131#66867—22no—
132#25287—111nomaximal, Sylow
133C24×C11—21no—
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×C11#4112yes—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2411yescharacteristic
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C2×Dic22—24no—
167C2×Dic22—81no—
168C2×Dic22—81no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—41no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4—42no—
175C11×C4⋊C4—42no—
176C11×C22⋊C4—42no—
177C11×C22⋊C4—42no—
178C11×C22⋊C4—42no—
179C11×C22⋊C4—42no—
180C11×C22⋊C4—42no—
181C11×C22⋊C4—42no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—42no—
187C42×C11C2×D412yes—
188C42×C11#4112yes—
189C4⋊Dic11—24no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11C2×D412yes—
196C4⋊Dic11C2×D412yes—
197C4⋊Dic11#4112yes—
198Dic11⋊C4—81no—
199Dic11⋊C4—81no—
200C4×Dic11—42no—
201C4×Dic11—81no—
202C4×Dic11—81no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×#489—111no—
216C2×#475—111no—
217#2545D1111yescharacteristic
218#2369—111no—
219#2066—111no—
220#2065—111no—
221#2043—111no—
222#2042—111no—
223#1983—111no—
224#1983—111no—
225#1981—111no—
226#1940—111no—
227#1927—111no—
228#1926—111no—
229#1763—111no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11C22×D411yescharacteristic
238Q8×C11—22no—
239Q8×C11—22no—
240Q8×C11—41no—
241Q8×C11—41no—
242Q8×C11—41no—
243Q8×C11—41no—
244Q8×C11—41no—
245Q8×C11—41no—
246D4×C11—41no—
247D4×C11—41no—
248D4×C11—41no—
249D4×C11—41no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
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×C11#12112yes—
275C2×C4×C11#12112yes—
276C2×C4×C11#13712yes—
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11H(5,𝔽2)11yescharacteristic
282C2×C4×C112−1+411yescharacteristic
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—22no—
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—
295Dic22—84no—
296C11⋊C8—41no—
297C11⋊C8—41no—
298C11⋊C8—41no—
299C11⋊C8—41no—
300C2×C4⋊Q8—111no—
301C2×C4⋊Q8C2×D1111yescharacteristic
302C2×#124C2×D1111yescharacteristic
303C2×#124C2×D1111yescharacteristic
304C2×C4×Q8C2×D1111yescharacteristic
305#489—224no—
306#475—224no—
307C2×#106—111no—
308C2×#106—111no—
309C2×C4⋊C8—111no—
310C2×C4⋊C8—111no—
311C2×C4⋊C8—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#103—111no—
318C2×#103—111no—
319C2×#103—111no—
320C2×#102—111no—
321C2×#102—111no—
322C2×#102—111no—
323C2×#102—111no—
324C2×#97—111no—
325#396—21no—
326#396—21no—
327#391—221no—
328#391—221no—
329#391C2×D1111yescharacteristic
330#390C2×D1111yescharacteristic
331#389—111no—
332#389—111no—
333#389—221no—
334#388—21no—
335#388—21no—
336C4×C4⋊C4—111no—
337C4×C4⋊C4—111no—
338C4×C4⋊C4—111no—
339C4×C4⋊C4—221no—
340C4×C4⋊C4C2×D1111yescharacteristic
341#340—111no—
342#340—111no—
343#336—111no—
344#336—111no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11—81no—
351C22×C11—81no—
352C22×C11C2×#12111yescharacteristic
353C22×C11#54611yescharacteristic
354C22×C11#54811yescharacteristic
355C22×C11C2×#13711yescharacteristic
356C22×C11#57511yescharacteristic
357C22×C11#57711yescharacteristic
358C22×C11#57711yescharacteristic
359C4×C11—22no—
360C4×C11—22no—
361C4×C11—22no—
362C4×C11—42no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—81no—
367C4×C11—81no—
368C4×C11#52911yescharacteristic
369C4×C11#54211yescharacteristic
370C4×C11#54811yescharacteristic
371C4×C11#55011yescharacteristic
372Dic11—42no—
373Dic11—42no—
374Dic11—42no—
375Dic11—81no—
376C22×Q8—221no—
377C22×Q8C22×D1111yescharacteristic
378C22×Q8C22×D1111yescharacteristic
379C22×D4C22×D1111yescharacteristic
380C22×C8—111no—
381C22×C8—111no—
382C22×C8—111no—
383C22×C8—111no—
384C4⋊Q8—22no—
385C4⋊Q8—41no—
386C4⋊Q8—114no—
387C4⋊Q8—222no—
388#124—22no—
389#124—22no—
390#124—22no—
391#124—41no—
392C4×Q8—22no—
393C4×Q8—22no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4C22⋊D1111yescharacteristic
405C2×C4⋊C4C22⋊D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C42—21no—
414C2×C42—221no—
415C2×C42—221no—
416C2×C42—221no—
417C2×C42C22×D1111yescharacteristic
418C2×C42C22×D1111yescharacteristic
419C2×C42C22×D1111yescharacteristic
420#106—222no—
421#106—222no—
422C4⋊C8—222no—
423C4⋊C8—441no—
424C4⋊C8—441no—
425#103—222no—
426#103—222no—
427#103—222no—
428#103—222no—
429#103—222no—
430#103—222no—
431#103—222no—
432#103—441no—
433#102—222no—
434#102—222no—
435#102—222no—
436#102—441no—
437#97—222no—
438#95—21no—
439#95—21no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95C22⋊D1111yescharacteristic
446#95C22⋊D1111yescharacteristic
447C2×C11—161no—
448C2×C11#242611yescharacteristic
449C2×C11#303711yescharacteristic
450C2×C11#304211yescharacteristic
451C2×C11#331611yescharacteristic
452C2×C11#332111yescharacteristic
453C2×C11#336911yescharacteristic
454C2×C11#337611yescharacteristic
455C24—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—224no—
468C2×Q8—881no—
469C2×Q8—881no—
470C2×Q8#434112yes—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4C2×C22⋊D1111yescharacteristic
485C22×C4C2×C22⋊D1111yescharacteristic
486C22×C4C2×C22⋊D1111yescharacteristic
487C22×C4C2×C22⋊D1111yescharacteristic
488C22×C4C2×C22⋊D1111yescharacteristic
489C22×C4C2×C22⋊D1111yescharacteristic
490C22×C4C23×D1111yescharacteristic
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C4⋊C4—22no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—41no—
507C4⋊C4—42no—
508C4⋊C4—42no—
509C4⋊C4—42no—
510C4⋊C4—112no—
511C4⋊C4—112no—
512C4⋊C4—112no—
513C4⋊C4—224no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—881no—
520C4⋊C4—881no—
521C22⋊C4—42no—
522C22⋊C4—42no—
523C22⋊C4—42no—
524C22⋊C4—42no—
525C22⋊C4—42no—
526C22⋊C4—42no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—42no—
532C42—442no—
533C42—881no—
534C42—881no—
535C42D4×D1112yes—
536C42#434112yes—
537C11#2528711yescharacteristic, complemented, Sylow
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23C22×C22⋊D1111yescharacteristic
546Q8—22no—
547Q8—22no—
548Q8—41no—
549Q8—41no—
550Q8—41no—
551Q8—41no—
552Q8—41no—
553Q8—41no—
554Q8—884no—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—41no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—222no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4#6699112yes—
596C2×C4#6699112yes—
597C2×C4#6700412yes—
598C2×C4C2×D4×D1111yescharacteristic
599C2×C4C2×#434111yescharacteristic
600C2×C4C2×#434111yescharacteristic
601C2×C4#6703711yescharacteristic
602C2×C4#41×D1111yescharacteristic
603C2×C4#6704311yescharacteristic
604C8—441no—
605C8—441no—
606C8—441no—
607C8—441no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22C2×#6699111yescharacteristic
616C22#1062333711yescharacteristic
617C22#1062335311yescharacteristic
618C22C2×#6700411yescharacteristic
619C22#1062336211yescharacteristic
620C22#1062336811yescharacteristic
621C22#1062336811yescharacteristic
622C4—22no—
623C4—22no—
624C4—22no—
625C4—42no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—81no—
630C4—81no—
631C4—442no—
632C4—442no—
633C4—442no—
634C4—881no—
635C4#1062312911yescharacteristic
636C4#1062313011yescharacteristic
637C4#1062313111yescharacteristic
638C4#1062313411yescharacteristic
639C2—161no—
640C2#1307217811yescharacteristic
641C2#1307808411yescharacteristic
642C2#1307812411yescharacteristic
643C2#1308072711yescharacteristic
644C2#1308080211yescharacteristic
645C2#1308135211yescharacteristic
646C2#1308143711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2545C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2545D11
hypocenterC11#25287
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2545

Complements

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

NH ≅ G/Ntype
2. C2×#10622633C2semidirect
3. #13071705C2semidirect
4. #13069997C2semidirect
6. #13069859C2semidirect
10. #13069540C2semidirect
11. #13069340C2semidirect
12. #13069247C2semidirect
14. #13068446C2semidirect
537. C11#25287semidirect

Maximal subgroups

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

subgroupindex
C2×#106226682
C2×#106226332
#130717052
#130699972
#130699902
#130698592
#130698522
#130695492
#130695402
#130693402
#130692472
#130692402
#130684462
C11×#25452
#2528711