Finite Group Databasebeta

← #14803178

Subgroups — #14803178

Order 2816.

822 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×#10622702C211yesmaximal, characteristic
2C2×#10622704C211yesmaximal, characteristic, complemented
3#13073596C211yesmaximal, characteristic
4#13070008C211yesmaximal, characteristic, complemented
5#13070001C211yesmaximal, characteristic
6#13069862C211yesmaximal, characteristic, complemented
7#13069857C211yesmaximal, characteristic
8#13069548C211yesmaximal, characteristic
9#13069548C211yesmaximal, characteristic
10#13069539C211yesmaximal, characteristic, complemented
11#13069340C211yesmaximal, characteristic, complemented
12#13069257C211yesmaximal, characteristic, complemented
13#13069236C211yesmaximal, characteristic
14#13068449C211yesmaximal, characteristic, complemented
15C11×#2365C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11—21no—
18C2×#66928C2211yescharacteristic
19C2×#66928C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C11×#391—21no—
23C11×#389C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C11×#387—21no—
26C11×#387—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C4×C11×C4⋊C4C2211yescharacteristic
30C4×C11×C4⋊C4C2211yescharacteristic
31#10622704—24no—
32#10622702—24no—
33#10622607—21no—
34#10622607—21no—
35C2×#66874C2211yescharacteristic
36C2×#66874C2211yescharacteristic
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45C2×#66873C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49#10622552C2211yescharacteristic
50#10622542C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×#66867C2211yescharacteristic
55#10622283—21no—
56#10622283—21no—
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×D44C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8D414yes—
67C4×Q8×C11—44no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C42×C11—21no—
78C2×C42×C11—21no—
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×C4×Dic11—21no—
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98#66928—22no—
99#66928—22no—
100#66928—22no—
101#66928—41no—
102#66922—22no—
103#66922—41no—
104C4×Dic22—22no—
105C4×Dic22—22no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95D411yescharacteristic
112C11×#95D411yescharacteristic
113C11⋊#95—21no—
114C11⋊#95—21no—
115#66874—22no—
116#66874—22no—
117#66874—22no—
118#66874—22no—
119#66874—22no—
120#66874—22no—
121#66874—22no—
122#66874—41no—
123#66873—22no—
124#66873—22no—
125#66873—22no—
126#66873—41no—
127#66871—22no—
128#66871—22no—
129C4⋊(C11⋊C8)—22no—
130C4⋊(C11⋊C8)—41no—
131C4⋊(C11⋊C8)—41no—
132#66867—22no—
133#25286—111nomaximal, Sylow
134C23×D11—21no—
135C2×Q8×C11—24no—
136C2×Q8×C11—42no—
137C2×Q8×C11—42no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—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#4112yes—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—41no—
178C11×C4⋊C4—42no—
179C11×C4⋊C4—42no—
180C11×C4⋊C4C2×D412yes—
181C11×C4⋊C4C2×D412yes—
182C11×C4⋊C4#4112yes—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—42no—
188C42×C11—42no—
189C42×C11—42no—
190C42×C11C2×D412yes—
191C42×C11#4112yes—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—42no—
197(C2×D11)⋊C4—42no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—42no—
201C4⋊Dic11—42no—
202Dic11⋊C4—42no—
203C4×Dic11—42no—
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×C11⋊C8—21no—
216C2×#489—111no—
217C2×#477—111no—
218#2545—111no—
219#2365D1111yescharacteristic, complemented
220#2068—111no—
221#2067—111no—
222#2043—111no—
223#2042—111no—
224#1983—111no—
225#1983—111no—
226#1981—111no—
227#1940—111no—
228#1928—111no—
229#1925—111no—
230#1763—111no—
231C23×C11C22×D411yescharacteristic
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239Q8×C11—48no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
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—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×C11#12112yes—
269C2×C4×C11AGL(1,ℤ/8)12yes—
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11H(5,𝔽2)11yescharacteristic
275C2×C4×C112−1+411yescharacteristic
276C2×Dic11—22no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285D44—41no—
286D44—41no—
287D44—41no—
288D44—41no—
289Dic22—22no—
290Dic22—22no—
291Dic22—41no—
292Dic22—41no—
293Dic22—41no—
294Dic22—41no—
295Dic22—41no—
296Dic22—41no—
297C11⋊C8—41no—
298C11⋊C8—41no—
299C11⋊C8—41no—
300C11⋊C8—41no—
301C2×C4⋊Q8—111no—
302C2×C4⋊Q8C2×D1111yescharacteristic
303C2×#124—111no—
304C2×#124—111no—
305C2×C4×Q8—21no—
306C2×C4×Q8—111no—
307#489—224no—
308#477—224no—
309C2×#107—111no—
310C2×#107—111no—
311C2×C4⋊C8—111no—
312C2×C4⋊C8—111no—
313C2×C4⋊C8—111no—
314C2×#103—111no—
315C2×#103—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×#102—111no—
325C2×#102—111no—
326C2×#97—111no—
327#396—221no—
328#396—221no—
329#391—21no—
330#391—111no—
331#390—111no—
332#389C2×D1111yescharacteristic
333#389C2×D1111yescharacteristic
334#388—221no—
335#388—221no—
336#387—21no—
337#387—21no—
338C4×C4⋊C4C2×D1111yescharacteristic
339C4×C4⋊C4C2×D1111yescharacteristic
340C4×C4⋊C4C2×D1111yescharacteristic
341C4×C4⋊C4C2×D1111yescharacteristic
342#340—111no—
343#340—111no—
344#336—111no—
345#336—111no—
346C22×C11C2×#12111yescharacteristic
347C22×C11#54611yescharacteristic
348C22×C11#54811yescharacteristic
349C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
350C22×C11#57511yescharacteristic
351C22×C11#57811yescharacteristic
352C22×C11#57811yescharacteristic
353C2×D11—81no—
354C2×D11—81no—
355C2×D11—81no—
356C2×D11—81no—
357C2×D11—81no—
358C2×D11—81no—
359C2×D11—81no—
360C4×C11—22no—
361C4×C11—22no—
362C4×C11—22no—
363C4×C11—42no—
364C4×C11—42no—
365C4×C11—42no—
366C4×C11—41no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11—81no—
370C4×C11#52911yescharacteristic
371C4×C11#54211yescharacteristic
372C4×C11#54811yescharacteristic
373C4×C11#55011yescharacteristic
374Dic11—42no—
375Dic11—81no—
376Dic11—81no—
377C22×Q8—21no—
378C22×Q8—111no—
379C22×Q8—111no—
380C22×D4—111no—
381C22×C8—111no—
382C22×C8—111no—
383C22×C8—111no—
384C22×C8—111no—
385C4⋊Q8—22no—
386C4⋊Q8—222no—
387C4⋊Q8—441no—
388C4⋊Q8D4414yes—
389#124—222no—
390#124—222no—
391#124—222no—
392#124—441no—
393C4×Q8—44no—
394C4×Q8—222no—
395C4×Q8—222no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4C22⋊D1111yescharacteristic
404C2×C4⋊C4C22⋊D1111yescharacteristic
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C22⋊C4—221no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42—21no—
418C2×C42—221no—
419C2×C42C22×D1111yescharacteristic
420C2×C42C22×D1111yescharacteristic
421C2×C42C22×D1111yescharacteristic
422#107—222no—
423#107—222no—
424C4⋊C8—222no—
425C4⋊C8—441no—
426C4⋊C8—441no—
427#103—222no—
428#103—222no—
429#103—222no—
430#103—222no—
431#103—222no—
432#103—222no—
433#103—222no—
434#103—441no—
435#102—222no—
436#102—222no—
437#102—222no—
438#102—441no—
439#97—222no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—221no—
446#95—221no—
447#95C22⋊D1111yescharacteristic
448#95C22⋊D1111yescharacteristic
449C2×C11#242611yescharacteristic
450C2×C11#303611yescharacteristic
451C2×C11#304411yescharacteristic
452C2×C11#330811yescharacteristic
453C2×C11#331311yescharacteristic
454C2×C11#336711yescharacteristic
455C2×C11#337711yescharacteristic
456D11—161no—
457C24—221no—
458C2×Q8—24no—
459C2×Q8—42no—
460C2×Q8—42no—
461C2×Q8—112no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×Q8—221no—
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×D4—221no—
474C2×D4—221no—
475C2×D4—221no—
476C2×D4—221no—
477C2×D4—221no—
478C2×D4—221no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4C2×C22⋊D1111yescharacteristic
487C22×C4C2×C22⋊D1111yescharacteristic
488C22×C4C2×C22⋊D1111yescharacteristic
489C22×C4C2×C22⋊D1111yescharacteristic
490C22×C4C2×C22⋊D1111yescharacteristic
491C22×C4C2×C22⋊D1111yescharacteristic
492C22×C4C23×D1111yescharacteristic
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—
503C2×C8—221no—
504C2×C8—221no—
505C4⋊C4—24no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—41no—
513C4⋊C4—42no—
514C4⋊C4—42no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—442no—
518C4⋊C4—442no—
519C4⋊C4—442no—
520C4⋊C4C2×D4412yes—
521C4⋊C4C2×D4412yes—
522C4⋊C4#434312yes—
523C22⋊C4—442no—
524C22⋊C4—442no—
525C22⋊C4—442no—
526C22⋊C4—442no—
527C22⋊C4—442no—
528C22⋊C4—442no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—42no—
534C42—42no—
535C42—42no—
536C42—442no—
537C42C2×D4412yes—
538C42#433912yes—
539C11#2528611yescharacteristic, complemented, Sylow
540C23—441no—
541C23—441no—
542C23—441no—
543C23—441no—
544C23—441no—
545C23—441no—
546C23—441no—
547C23C22×C22⋊D1111yescharacteristic
548Q8—48no—
549Q8—222no—
550Q8—222no—
551Q8—441no—
552Q8—441no—
553Q8—441no—
554Q8—441no—
555Q8—441no—
556Q8—441no—
557D4—441no—
558D4—441no—
559D4—441no—
560D4—441no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
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#6698312yes—
598C2×C4#6698312yes—
599C2×C4#6698512yes—
600C2×C4C22×D4411yescharacteristic
601C2×C4C2×#433911yescharacteristic
602C2×C4C2×#434311yescharacteristic
603C2×C4#6704011yescharacteristic
604C2×C4#41×D1111yescharacteristic
605C2×C4#6704211yescharacteristic
606C8—441no—
607C8—441no—
608C8—441no—
609C8—441no—
610C22—881no—
611C22—881no—
612C22—881no—
613C22—881no—
614C22—881no—
615C22—881no—
616C22—881no—
617C22C2×#6698311yescharacteristic
618C22C2×#6698511yescharacteristic
619C22#1062334811yescharacteristic
620C22#1062335311yescharacteristic
621C22#1062336011yescharacteristic
622C22#1062336911yescharacteristic
623C22#1062336911yescharacteristic
624C4—22no—
625C4—22no—
626C4—22no—
627C4—41no—
628C4—42no—
629C4—42no—
630C4—41no—
631C4—41no—
632C4—42no—
633C4—81no—
634C4—442no—
635C4—881no—
636C4—881no—
637C4#1062310711yescharacteristic
638C4#1062310811yescharacteristic
639C4#1062311111yescharacteristic
640C4#1062311311yescharacteristic
641C2—1761no—
642C2#1307217611yescharacteristic
643C2#1307808011yescharacteristic
644C2#1307814611yescharacteristic
645C2#1308060111yescharacteristic
646C2#1308067611yescharacteristic
647C2#1308133411yescharacteristic
648C2#1308145811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2365C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2365D11
hypocenterC11#25286
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2365

Complements

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

NH ≅ G/Ntype
2. C2×#10622704C2semidirect
4. #13070008C2semidirect
6. #13069862C2semidirect
10. #13069539C2semidirect
11. #13069340C2semidirect
12. #13069257C2semidirect
14. #13068449C2semidirect
15. C11×#2365C2semidirect
219. #2365D11semidirect
539. C11#25286semidirect

Maximal subgroups

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

subgroupindex
C2×#106227022
C2×#106227042
#130735962
#130700082
#130700012
#130698622
#130698572
#130695482
#130695392
#130693402
#130692572
#130692362
#130684492
C11×#23652
#2528611