Finite Group Databasebeta

← #14823551

Subgroups — #14823551

Order 2816.

842 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×#10622706C211yesmaximal, characteristic, complemented
2C2×#10622631C211yesmaximal, characteristic
3#13072392C211yesmaximal, characteristic, complemented
4#13070008C211yesmaximal, characteristic, complemented
5#13069941C211yesmaximal, characteristic, complemented
6#13069933C211yesmaximal, characteristic
7#13069698C211yesmaximal, characteristic
8#13069496C211yesmaximal, characteristic
9#13069305C211yesmaximal, characteristic, complemented
10#13069305C211yesmaximal, characteristic, complemented
11#13069302C211yesmaximal, characteristic
12#13068950C211yesmaximal, characteristic
13#13068869C211yesmaximal, characteristic, complemented
14#13068491C211yesmaximal, characteristic, complemented
15C11×#2452C211yesmaximal, characteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×C22⋊Q8—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C11×#396—21no—
24C11×#393—21no—
25C11×#390C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C11×#389C2211yescharacteristic
29C11×#385—21no—
30C4×C11×C4⋊C4C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33#10622706—24no—
34#10622631—24no—
35#10622597—21no—
36#10622594—21no—
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622542C2211yescharacteristic
47#10622542C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×#66867C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622273—21no—
54#10622268—21no—
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C22×Dic22C2311yescharacteristic
65C22×Dic22C2311yescharacteristic
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8—41no—
68C11×C22⋊Q8—44no—
69C4×D4×C11—22no—
70C4×D4×C11—41no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
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×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×#4324—22no—
88C2×#4324—22no—
89C2×#4324—22no—
90C2×#4324—22no—
91C2×#4324—22no—
92C2×#4324—41no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104#66922—22no—
105#66922—41no—
106C4×Dic22—22no—
107C4×Dic22—41no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95D411yescharacteristic
111C11×#95D411yescharacteristic
112#66896—22no—
113#66896—22no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121#66874—22no—
122#66874—22no—
123#66874—22no—
124#66874—22no—
125#66874—22no—
126#66874D414yes—
127#66871—22no—
128#66871—41no—
129C4⋊(C11⋊C8)—22no—
130#66867—22no—
131#66867—22no—
132C4×C11⋊C8—22no—
133#26836—111nomaximal, Sylow
134C24×C11—21no—
135C2×Q8×C11—42no—
136C2×Q8×C11—42no—
137C2×Q8×C11—81no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11#4112yes—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—81no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22C2×D412yes—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—42no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4—42no—
183C11×C4⋊C4C2×D412yes—
184C11×C22⋊C4—42no—
185C11×C22⋊C4—42no—
186C11×C22⋊C4—42no—
187C11×C22⋊C4—42no—
188C11×C22⋊C4—81no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195#4324—28no—
196#4324—44no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—42no—
202C4⋊Dic11—42no—
203Dic11⋊C4—42no—
204Dic11⋊C4—42no—
205C4×Dic11—42no—
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×C11⋊C8C2×D412yes—
216C2×C11⋊C8#4112yes—
217C2×C11⋊C8#4112yes—
218C2×#487—111no—
219C2×#440—111no—
220#2452D1111yescharacteristic
221#2446—111no—
222#2068—111no—
223#2057—111no—
224#2055—111no—
225#2013—111no—
226#1973—111no—
227#1935—111no—
228#1935—111no—
229#1934—111no—
230#1877—111no—
231#1863—111no—
232#1771—111no—
233C23×C11—22no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11C22×D411yescharacteristic
241Q8×C11—84no—
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—22no—
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—84no—
272C2×C4×C11AGL(1,ℤ/8)12yes—
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—41no—
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—41no—
297Dic22—41no—
298Dic22—41no—
299Dic22—41no—
300C11⋊C8—22no—
301C11⋊C8—22no—
302C11⋊C8—22no—
303C11⋊C8—41no—
304C22×SD16—111no—
305C22×SD16—111no—
306C2×C4⋊Q8—111no—
307C2×C4⋊Q8C2×D1111yescharacteristic
308C2×C22⋊Q8—21no—
309C2×C4×Q8—111no—
310C2×C4×D4C2×D1111yescharacteristic
311#487—224no—
312#440—224no—
313C2×#107—111no—
314C2×#107—111no—
315C2×C4⋊C8—111no—
316C2×#103—111no—
317C2×#103—111no—
318C2×#103—111no—
319C2×#103—111no—
320C2×#103—111no—
321C2×#103—111no—
322C2×#102—111no—
323C2×#102—111no—
324C2×#97—111no—
325C2×#97—111no—
326C2×C4×C8—111no—
327#400—221no—
328#398—221no—
329#396—21no—
330#393—21no—
331#391—111no—
332#391—111no—
333#391—111no—
334#390C2×D1111yescharacteristic
335#390C2×D1111yescharacteristic
336#389—111no—
337#389C2×D1111yescharacteristic
338#389C2×D1111yescharacteristic
339#387—221no—
340#387—221no—
341#385—21no—
342C4×C4⋊C4C2×D1111yescharacteristic
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#336—111no—
348#336—111no—
349C22×C11—42no—
350C22×C11—42no—
351C22×C11—42no—
352C22×C11—81no—
353C22×C11—81no—
354C22×C11—81no—
355C22×C11—81no—
356C22×C11#53211yescharacteristic
357C22×C11D4211yescharacteristic
358C22×C11#54811yescharacteristic
359C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
360C22×C11C2×#13711yescharacteristic
361C22×C11#57711yescharacteristic
362C22×C11#57811yescharacteristic
363C4×C11—22no—
364C4×C11—22no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11—41no—
368C4×C11—42no—
369C4×C11—41no—
370C4×C11—81no—
371C4×C11—81no—
372C4×C11#52511yescharacteristic
373C4×C11#54211yescharacteristic
374C4×C11#54711yescharacteristic
375C4×C11#55111yescharacteristic
376Dic11—42no—
377Dic11—81no—
378Dic11—81no—
379Dic11—81no—
380C22×Q8—21no—
381C22×Q8—111no—
382C22×Q8—111no—
383C22×D4C22×D1111yescharacteristic
384C23×C4—21no—
385C2×SD16—222no—
386C2×SD16—222no—
387C2×SD16—222no—
388C2×SD16—222no—
389C2×SD16—222no—
390C2×SD16—441no—
391C22×C8—111no—
392C22×C8—111no—
393C22×C8—111no—
394C22×C8—111no—
395C4⋊Q8—22no—
396C4⋊Q8—41no—
397C4⋊Q8—222no—
398C4⋊Q8—441no—
399C22⋊Q8—44no—
400C4×Q8—222no—
401C4×Q8—441no—
402C4×D4—22no—
403C4×D4—41no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4C22⋊D1111yescharacteristic
414C2×C4⋊C4C22⋊D1111yescharacteristic
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C42—221no—
424C2×C42C22×D1111yescharacteristic
425C2×C42C22×D1111yescharacteristic
426C2×C42C22×D1111yescharacteristic
427#107—222no—
428#107—441no—
429C4⋊C8—222no—
430#103—114no—
431#103—222no—
432#103—222no—
433#103—222no—
434#103—222no—
435#103—222no—
436#102—222no—
437#102—222no—
438#97—222no—
439#97—222no—
440C4×C8—222no—
441#95—21no—
442#95—21no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95C22⋊D1111yescharacteristic
451#95C22⋊D1111yescharacteristic
452C2×C11—82no—
453C2×C11#246111yescharacteristic
454C2×C11#317811yescharacteristic
455C2×C11#318211yescharacteristic
456C2×C11#326511yescharacteristic
457C2×C11#327011yescharacteristic
458C2×C11#336711yescharacteristic
459C2×C11#337211yescharacteristic
460C24—21no—
461C2×Q8—42no—
462C2×Q8—42no—
463C2×Q8—81no—
464C2×Q8—112no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×Q8—221no—
471C2×Q8—221no—
472C2×Q8—221no—
473C2×Q8—221no—
474C2×Q8—221no—
475C2×Q8—221no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4#434312yes—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—81no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4C2×C22⋊D1111yescharacteristic
493C22×C4C2×C22⋊D1111yescharacteristic
494C22×C4C2×C22⋊D1111yescharacteristic
495C22×C4C2×C22⋊D1111yescharacteristic
496C22×C4C2×C22⋊D1111yescharacteristic
497C22×C4C2×C22⋊D1111yescharacteristic
498C22×C4C23×D1111yescharacteristic
499SD16—228no—
500SD16—444no—
501C2×C8—112no—
502C2×C8—112no—
503C2×C8—112no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—42no—
521C4⋊C4—42no—
522C4⋊C4—42no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—442no—
528C4⋊C4—442no—
529C4⋊C4—442no—
530C4⋊C4—442no—
531C4⋊C4D4×D1112yes—
532C22⋊C4—42no—
533C22⋊C4—42no—
534C22⋊C4—42no—
535C22⋊C4—42no—
536C22⋊C4—81no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—442no—
544C11#2683611yescharacteristic, complemented, Sylow
545C23—22no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23C22×C22⋊D1111yescharacteristic
553Q8—84no—
554Q8—222no—
555Q8—222no—
556Q8—441no—
557Q8—441no—
558Q8—441no—
559Q8—441no—
560Q8—441no—
561Q8—441no—
562D4—22no—
563D4—22no—
564D4—41no—
565D4—41no—
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—22no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—84no—
592C2×C4—222no—
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—441no—
604C2×C4#6698512yes—
605C2×C4#6700412yes—
606C2×C4C2×D4×D1111yescharacteristic
607C2×C4#6703711yescharacteristic
608C2×C4C2×#434311yescharacteristic
609C2×C4#6704011yescharacteristic
610C2×C4#41×D1111yescharacteristic
611C2×C4#41×D1111yescharacteristic
612C8—222no—
613C8—222no—
614C8—222no—
615C8—441no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22—81no—
623C22C2×#6698511yescharacteristic
624C22D4×C22⋊D1111yescharacteristic
625C22#1062334811yescharacteristic
626C22C2×#6700411yescharacteristic
627C22#1062336311yescharacteristic
628C22#1062336711yescharacteristic
629C22#1062336911yescharacteristic
630C4—22no—
631C4—22no—
632C4—41no—
633C4—41no—
634C4—42no—
635C4—41no—
636C4—41no—
637C4—81no—
638C4—81no—
639C4—442no—
640C4—881no—
641C4—881no—
642C4—881no—
643C4#1062315811yescharacteristic
644C4#1062316211yescharacteristic
645C4#1062316811yescharacteristic
646C4#1062317111yescharacteristic
647C2—82no—
648C2#1307259011yescharacteristic
649C2#1307927811yescharacteristic
650C2#1307933011yescharacteristic
651C2#1308010711yescharacteristic
652C2#1308018211yescharacteristic
653C2#1308133411yescharacteristic
654C2#1308139711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2452C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2452D11
hypocenterC11#26836
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2452

Complements

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

NH ≅ G/Ntype
1. C2×#10622706C2semidirect
3. #13072392C2semidirect
4. #13070008C2semidirect
5. #13069941C2semidirect
9. #13069305C2semidirect
10. #13069305C2semidirect
13. #13068869C2semidirect
14. #13068491C2semidirect
544. C11#26836semidirect

Maximal subgroups

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

subgroupindex
C2×#106227062
C2×#106226312
#130723922
#130700082
#130699412
#130699332
#130696982
#130694962
#130693052
#130693022
#130689502
#130688692
#130684912
C11×#24522
#2683611