Finite Group Databasebeta

← #14823603

Subgroups — #14823603

Order 2816.

814 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622668C211yesmaximal, characteristic
2C2×#10622631C211yesmaximal, characteristic
3#13072455C211yesmaximal, characteristic, complemented
4#13070011C211yesmaximal, characteristic, complemented
5#13069944C211yesmaximal, characteristic, complemented
6#13069933C211yesmaximal, characteristic
7#13069710C211yesmaximal, characteristic
8#13069476C211yesmaximal, characteristic, complemented
9#13069309C211yesmaximal, characteristic, complemented
10#13069305C211yesmaximal, characteristic, complemented
11#13069302C211yesmaximal, characteristic
12#13068960C211yesmaximal, characteristic, complemented
13#13068863C211yesmaximal, characteristic
14#13068485C211yesmaximal, characteristic, complemented
15C11×#2447C211yesmaximal, characteristic
16C2×C11×#124C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C22×#4326C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C11×#397—21no—
23C11×#397—21no—
24C11×#391C2211yescharacteristic
25C11×#391C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C11×#385—21no—
29C11×#381—21no—
30C4×C11×C4⋊C4C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37#10622668—24no—
38#10622631—24no—
39#10622594—21no—
40#10622592—21no—
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622542C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×#66867C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622270—21no—
54#10622259—21no—
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C22×Dic22—21no—
65C22×Dic22C2311yescharacteristic
66C11×#124—22no—
67C11×#124—41no—
68C4×D4×C11—22no—
69C4×D4×C11—41no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×#4326—22no—
84C2×#4326—22no—
85C2×#4326—41no—
86C2×#4324—22no—
87C2×#4324—22no—
88C2×#4324—22no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66922—22no—
102#66922—41no—
103C4×Dic22—22no—
104C4×Dic22—41no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95D411yescharacteristic
111C11×#95D411yescharacteristic
112#66899—22no—
113#66899—22no—
114#66899—22no—
115#66896—22no—
116#66896—22no—
117#66896D414yes—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124#66874—22no—
125#66874—22no—
126#66871—22no—
127#66871—41no—
128C4⋊(C11⋊C8)—22no—
129#66867—22no—
130#66867—22no—
131C4×C11⋊C8—22no—
132#26840—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×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11C2×D412yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11—81no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2411yescharacteristic
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—42no—
169C2×Dic22—42no—
170C2×Dic22—81no—
171C2×Dic22#4112yes—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—41no—
178C11×C4⋊C4—81no—
179C11×C22⋊C4—42no—
180C11×C22⋊C4—42no—
181C11×C22⋊C4—42no—
182C11×C22⋊C4—42no—
183C11×C22⋊C4—81no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190#4326—44no—
191#4324—28no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—42no—
198C4⋊Dic11C2×D412yes—
199Dic11⋊C4—42no—
200Dic11⋊C4—81no—
201Dic11⋊C4—81no—
202C4×Dic11—42no—
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⋊C8C2×D412yes—
213C2×C11⋊C8#4112yes—
214C2×C11⋊C8#4112yes—
215C2×#489—111no—
216C2×#440—111no—
217#2451—111no—
218#2447D1111yescharacteristic
219#2068—111no—
220#2057—111no—
221#2055—111no—
222#2015—111no—
223#1969—111no—
224#1935—111no—
225#1935—111no—
226#1934—111no—
227#1878—111no—
228#1862—111no—
229#1770—111no—
230C23×C11—22no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11C22×D411yescharacteristic
238Q8×C11—41no—
239Q8×C11—41no—
240Q8×C11—41no—
241Q8×C11—41no—
242D4×C11—22no—
243D4×C11—22no—
244D4×C11—41no—
245D4×C11—41no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
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—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
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—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—84no—
273C2×C4×C11#13712yes—
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—22no—
281C2×Dic11—22no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292Dic22—22no—
293Dic22—22no—
294Dic22—41no—
295Dic22—41no—
296Dic22—84no—
297C11⋊C8—22no—
298C11⋊C8—22no—
299C11⋊C8—22no—
300C11⋊C8—41no—
301C22×Q16—111no—
302C22×SD16—111no—
303C2×C4⋊Q8—111no—
304C2×#124C2×D1111yescharacteristic
305C2×C4×Q8—111no—
306C2×C4×D4C2×D1111yescharacteristic
307#489—224no—
308#440—224no—
309C2×#107—111no—
310C2×#107—111no—
311C2×C4⋊C8—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#102—111no—
318C2×#102—111no—
319C2×#102—111no—
320C2×#97—111no—
321C2×#97—111no—
322C2×C4×C8—111no—
323#398—221no—
324#397—21no—
325#397—21no—
326#395—221no—
327#391—111no—
328#391—111no—
329#391—221no—
330#391C2×D1111yescharacteristic
331#391C2×D1111yescharacteristic
332#390C2×D1111yescharacteristic
333#389—111no—
334#389—111no—
335#389C2×D1111yescharacteristic
336#387—221no—
337#385—21no—
338#381—21no—
339C4×C4⋊C4C2×D1111yescharacteristic
340#340—111no—
341#340—111no—
342#340—111no—
343#340—111no—
344#336—111no—
345#336—111no—
346C22×C11—42no—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11—81no—
350C22×C11—81no—
351C22×C11—81no—
352C22×C11—81no—
353C22×C11#53211yescharacteristic
354C22×C11D4211yescharacteristic
355C22×C11#54811yescharacteristic
356C22×C11C2×#13711yescharacteristic
357C22×C11#57511yescharacteristic
358C22×C11#57611yescharacteristic
359C22×C11#57811yescharacteristic
360C4×C11—22no—
361C4×C11—41no—
362C4×C11—41no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—81no—
367C4×C11—81no—
368C4×C11—81no—
369C4×C11#52511yescharacteristic
370C4×C11#54211yescharacteristic
371C4×C11#54711yescharacteristic
372C4×C11#55111yescharacteristic
373Dic11—42no—
374Dic11—42no—
375Dic11—81no—
376Dic11—81no—
377C22×Q8—111no—
378C22×Q8—221no—
379C22×Q8C22×D1111yescharacteristic
380C22×D4C22×D1111yescharacteristic
381C23×C4—21no—
382C2×Q16—222no—
383C2×Q16—222no—
384C2×Q16—441no—
385C2×SD16—222no—
386C2×SD16—222no—
387C2×SD16—222no—
388C22×C8—111no—
389C22×C8—111no—
390C22×C8—111no—
391C22×C8—111no—
392C4⋊Q8—222no—
393C4⋊Q8—441no—
394#124—22no—
395#124—41no—
396C4×Q8—222no—
397C4×Q8—441no—
398C4×D4—22no—
399C4×D4—41no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4C22⋊D1111yescharacteristic
409C2×C4⋊C4C22⋊D1111yescharacteristic
410C2×C4⋊C4C22×D1111yescharacteristic
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C42—221no—
418C2×C42C22×D1111yescharacteristic
419C2×C42C22×D1111yescharacteristic
420C2×C42C22×D1111yescharacteristic
421#107—222no—
422#107—441no—
423C4⋊C8—222no—
424#103—222no—
425#103—222no—
426#103—222no—
427#103—222no—
428#103—222no—
429#102—114no—
430#102—222no—
431#102—222no—
432#97—222no—
433#97—222no—
434C4×C8—222no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95C22⋊D1111yescharacteristic
447#95C22⋊D1111yescharacteristic
448C2×C11—82no—
449C2×C11#246111yescharacteristic
450C2×C11#317511yescharacteristic
451C2×C11#318111yescharacteristic
452C2×C11#327311yescharacteristic
453C2×C11#327611yescharacteristic
454C2×C11#337511yescharacteristic
455C2×C11#337711yescharacteristic
456C24—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—112no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—442no—
470C2×Q8—442no—
471C2×Q8—881no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4D4×D1112yes—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—81no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4C2×C22⋊D1111yescharacteristic
489C22×C4C2×C22⋊D1111yescharacteristic
490C22×C4C2×C22⋊D1111yescharacteristic
491C22×C4C2×C22⋊D1111yescharacteristic
492C22×C4C2×C22⋊D1111yescharacteristic
493C22×C4C2×C22⋊D1111yescharacteristic
494C22×C4C23×D1111yescharacteristic
495Q16—444no—
496SD16—228no—
497C2×C8—112no—
498C2×C8—112no—
499C2×C8—112no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C4⋊C4—22no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—41no—
515C4⋊C4—81no—
516C4⋊C4—112no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—442no—
523C4⋊C4—442no—
524C4⋊C4—881no—
525C4⋊C4—881no—
526C22⋊C4—42no—
527C22⋊C4—42no—
528C22⋊C4—42no—
529C22⋊C4—42no—
530C22⋊C4—81no—
531C42—21no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—442no—
538C11#2684011yescharacteristic, complemented, Sylow
539C23—22no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23C22×C22⋊D1111yescharacteristic
547Q8—41no—
548Q8—41no—
549Q8—41no—
550Q8—41no—
551Q8—222no—
552Q8—222no—
553Q8—441no—
554Q8—441no—
555Q8—884no—
556D4—22no—
557D4—22no—
558D4—41no—
559D4—41no—
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—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—84no—
587C2×C4—222no—
588C2×C4—222no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4#6700412yes—
600C2×C4C2×D4×D1111yescharacteristic
601C2×C4#6703711yescharacteristic
602C2×C4#41×D1111yescharacteristic
603C2×C4#41×D1111yescharacteristic
604C2×C4#41×D1111yescharacteristic
605C2×C4#6704311yescharacteristic
606C8—222no—
607C8—222no—
608C8—222no—
609C8—441no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22D4×C22⋊D1111yescharacteristic
618C22#1062335311yescharacteristic
619C22C2×#6700411yescharacteristic
620C22#1062336211yescharacteristic
621C22#1062336311yescharacteristic
622C22#1062336611yescharacteristic
623C22#1062336911yescharacteristic
624C4—22no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—41no—
630C4—81no—
631C4—81no—
632C4—81no—
633C4—442no—
634C4—442no—
635C4—881no—
636C4—881no—
637C4#1062318611yescharacteristic
638C4#1062318711yescharacteristic
639C4#1062319011yescharacteristic
640C4#1062319311yescharacteristic
641C2—82no—
642C2#1307258211yescharacteristic
643C2#1307924911yescharacteristic
644C2#1307932611yescharacteristic
645C2#1308022311yescharacteristic
646C2#1308025811yescharacteristic
647C2#1308142611yescharacteristic
648C2#1308145211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2447C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2447D11
hypocenterC11#26840
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2447

Complements

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

NH ≅ G/Ntype
3. #13072455C2semidirect
4. #13070011C2semidirect
5. #13069944C2semidirect
8. #13069476C2semidirect
9. #13069309C2semidirect
10. #13069305C2semidirect
12. #13068960C2semidirect
14. #13068485C2semidirect
538. C11#26840semidirect

Maximal subgroups

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

subgroupindex
C2×#106226682
C2×#106226312
#130724552
#130700112
#130699442
#130699332
#130697102
#130694762
#130693092
#130693052
#130693022
#130689602
#130688632
#130684852
C11×#24472
#2684011