Finite Group Databasebeta

← #14769655

Subgroups — #14769655

Order 2816.

1362 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623299C211yesmaximal, characteristic
2C2×#10622436C211yesmaximal, characteristic, complemented
3C2×#10622757C211yesmaximal, characteristic, complemented
4#13077064C211yesmaximal, characteristic, complemented
5#13077063C211yesmaximal, characteristic, complemented
6#13069506C211yesmaximal, characteristic, complemented
7#13069503C211yesmaximal, characteristic, complemented
8#13068945C211yesmaximal, characteristic, complemented
9#13068944C211yesmaximal, characteristic, complemented
10#13068942C211yesmaximal, characteristic, complemented
11#13068657C211yesmaximal, characteristic, complemented
12#13068558C211yesmaximal, characteristic, complemented
13#13068558C211yesmaximal, characteristic, complemented
14#13068398C211yesmaximal, characteristic, complemented
15C11×#1876C211yesmaximal, characteristic, complemented
16C2×#41×D11C2211yescharacteristic
17C2×#41×D11C2211yescharacteristic
18C2×C11×#135C2211yescharacteristic
19C2×C11×#131C2211yescharacteristic, complemented
20C2×#67003C2211yescharacteristic
21C2×#67003C2211yescharacteristic
22C2×#67001C2211yescharacteristic, complemented
23#10623299—24no—
24#10623299—24no—
25C2×#66971C411yescharacteristic, complemented
26C2×#66971C411yescharacteristic, complemented
27C2×#66968C411yescharacteristic, complemented
28C2×#66968C411yescharacteristic, complemented
29C2×#66967C411yescharacteristic, complemented
30C2×#66967C411yescharacteristic, complemented
31C2×#66964C411yescharacteristic, complemented
32C2×#66964C411yescharacteristic, complemented
33C2×#66960C2211yescharacteristic, complemented
34C2×#66957C2211yescharacteristic
35C2×#66954C2211yescharacteristic, complemented
36C22×#4313C2211yescharacteristic
37C2×C11×#104C2211yescharacteristic, complemented
38C2×C11×#104C2211yescharacteristic, complemented
39C11×#408C2211yescharacteristic, complemented
40C2×#66901C2211yescharacteristic, complemented
41C2×#66901C2211yescharacteristic, complemented
42#10622847C2211yescharacteristic, complemented
43#10622757—24no—
44C2×#66889C2211yescharacteristic, complemented
45C2×#66889C2211yescharacteristic, complemented
46#10622742—21no—
47#10622742C2211yescharacteristic, complemented
48#10622739—21no—
49#10622739C2211yescharacteristic
50#10622739C2211yescharacteristic
51C2×#66886C2211yescharacteristic, complemented
52C2×#66886C2211yescharacteristic, complemented
53#10622723—21no—
54#10622723C2211yescharacteristic, complemented
55C2×(C2×D11)⋊C8—21no—
56C2×(C2×D11)⋊C8C2211yescharacteristic
57C2×C8×Dic11C2211yescharacteristic, complemented
58C4×(C2×D11)⋊C4C2211yescharacteristic
59C2×#66869C2211yescharacteristic, complemented
60C2×#66869C2211yescharacteristic, complemented
61C2×#66867C2211yescharacteristic, complemented
62#10622436—24no—
63#10622340—21no—
64#10622340—21no—
65#10622339—21no—
66D11×C22⋊C8—21no—
67C11×#341C2211yescharacteristic, complemented
68C11×#336C2211yescharacteristic, complemented
69#10622190C2211yescharacteristic, complemented
70#10622188C2211yescharacteristic, complemented
71C2×C11×#41C2311yescharacteristic
72C2×C11×#41C2311yescharacteristic
73#41×D11—22no—
74#41×D11—22no—
75#41×D11—22no—
76#41×D11—22no—
77#41×D11—41no—
78#41×D11—41no—
79#41×D11—41no—
80#41×D11—41no—
81C2×#4343C2×C411yescharacteristic
82C2×#4343C2×C411yescharacteristic
83C2×Q8×D11C2×C411yescharacteristic
84C2×Q8×D11C2×C411yescharacteristic
85C2×#4341—21no—
86C2×#4341—21no—
87C2×#4341C2×C411yescharacteristic
88C2×#4341C2×C411yescharacteristic
89C2×D4×D11—21no—
90C2×D4×D11—21no—
91C2×D4×D11C2×C411yescharacteristic
92C2×D4×D11C2×C411yescharacteristic
93C2×#4339—21no—
94C2×#4339—21no—
95C2×#4339C2311yescharacteristic
96C2×#4339C2311yescharacteristic
97C22×C4×D11—21no—
98C22×C4×D11—21no—
99C22×C4×D11C2311yescharacteristic
100C11×#135—22no—
101C11×#135—22no—
102C2×C11×Q16C2×C411yescharacteristic
103C2×C11×SD16C2×C411yescharacteristic
104C2×C11×SD16C2×C411yescharacteristic
105C2×C11×D8C2×C411yescharacteristic
106C11×#131—22no—
107C11×#131—41no—
108C2×C11×M16—21no—
109C2×C11×M16C2311yescharacteristic
110C2×C11×M16C2311yescharacteristic
111C22×C8×C11—21no—
112C22×C8×C11C2311yescharacteristic
113C22×C8×C11C2311yescharacteristic
114C2×C42×C11C2311yescharacteristic
115#67003—22no—
116#67003—22no—
117#67003D414yes—
118#67003D414yes—
119#67001—22no—
120#67001—41no—
121C2×#4326C2×C411yescharacteristic
122C2×#4326C2×C411yescharacteristic
123C2×#4325C2×C411yescharacteristic
124C2×#4325C2×C411yescharacteristic
125C2×#4324C2×C411yescharacteristic
126C2×#4324C2×C411yescharacteristic
127C2×#4323C2×C411yescharacteristic
128C2×#4323C2×C411yescharacteristic
129C2×(C2×D11)⋊C4—21no—
130C2×C4×Dic11C2311yescharacteristic
131C2×#4318—21no—
132C2×#4318C2311yescharacteristic
133C2×#4318C2311yescharacteristic
134C22×C11⋊C8—21no—
135C22×C11⋊C8C2311yescharacteristic
136C22×C11⋊C8C2311yescharacteristic
137#66971—24no—
138#66971—24no—
139#66968—24no—
140#66968—24no—
141#66967—24no—
142#66967—24no—
143#66964—24no—
144#66964—24no—
145#66960—22no—
146#66960—41no—
147C2×Dic44C2×C411yescharacteristic
148#66957—22no—
149#66957—22no—
150C2×D88C2×C411yescharacteristic
151C2×#4314C2×C411yescharacteristic
152C2×#4314C2×C411yescharacteristic
153#66954—22no—
154#66954—41no—
155C2×#4313—22no—
156C2×#4313—22no—
157C2×#4313—21no—
158C2×#4313—21no—
159C2×#4313C2×C411yescharacteristic
160C2×#4313C2×C411yescharacteristic
161C2×#4313C2×C411yescharacteristic
162C2×#4313C2×C411yescharacteristic
163C2×C8×D11—21no—
164C2×C8×D11—21no—
165C11×#104—22no—
166C11×#104—41no—
167C11×C22⋊C8—21no—
168C11×C22⋊C8—21no—
169#66901—22no—
170#66901—41no—
171C11⋊#95—21no—
172C22⋊(C11⋊C8)—21no—
173C22⋊(C11⋊C8)—21no—
174#66889—22no—
175#66889—41no—
176#66886—22no—
177#66886—22no—
178(C2×D11)⋊C8—21no—
179(C2×D11)⋊C8—21no—
180(C2×D11)⋊C8—21no—
181(C2×D11)⋊C8—21no—
182(C2×D11)⋊C8—21no—
183(C2×D11)⋊C8—21no—
184(C2×D11)⋊C8—21no—
185(C2×D11)⋊C8—21no—
186(C2×D11)⋊C8D411yescharacteristic
187(C2×D11)⋊C8D411yescharacteristic
188(C2×D11)⋊C8D411yescharacteristic
189(C2×D11)⋊C8D411yescharacteristic
190C8×Dic11—22no—
191#66869—22no—
192#66869—41no—
193#66867—22no—
194#22453—111nomaximal, Sylow
195C23×D11—21no—
196C23×D11—21no—
197C23×D11#4111yescharacteristic
198C11×#41—21no—
199C11×#41—21no—
200C11×#41—21no—
201C11×#41—21no—
202C11×#41—21no—
203C11×#41—21no—
204C11×#41C2×D412yes—
205C11×#41C2×D412yes—
206C2×Q8×C11C22×C411yescharacteristic
207C2×Q8×C11C22×C411yescharacteristic
208C2×D4×C11—21no—
209C2×D4×C11—21no—
210C2×D4×C11C22×C411yescharacteristic
211C2×D4×C11C22×C411yescharacteristic
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11C2411yescharacteristic
216C2×C22⋊D11—21no—
217C2×C22⋊D11—21no—
218C2×C22⋊D11—21no—
219C2×C22⋊D11—21no—
220C2×C22⋊D11—21no—
221C2×C22⋊D11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11#4111yescharacteristic
226#4343—22no—
227#4343—22no—
228#4343—41no—
229#4343—41no—
230Q8×D11—22no—
231Q8×D11—22no—
232Q8×D11—41no—
233Q8×D11—41no—
234#4341—22no—
235#4341—22no—
236#4341—41no—
237#4341—41no—
238#4341—42no—
239#4341—42no—
240#4341—42no—
241#4341—42no—
242D4×D11—22no—
243D4×D11—22no—
244D4×D11—42no—
245D4×D11—42no—
246D4×D11—41no—
247D4×D11—41no—
248D4×D11—42no—
249D4×D11—42no—
250#4339—21no—
251#4339—21no—
252#4339—21no—
253#4339—21no—
254#4339—21no—
255#4339—21no—
256#4339—42no—
257#4339—42no—
258#4339—42no—
259#4339—42no—
260#4339C2×D412yes—
261#4339C2×D412yes—
262C2×D44—21no—
263C2×D44—21no—
264C2×D44C22×C411yescharacteristic
265C2×D44C22×C411yescharacteristic
266C2×C4×D11—21no—
267C2×C4×D11—21no—
268C2×C4×D11—21no—
269C2×C4×D11—21no—
270C2×C4×D11—21no—
271C2×C4×D11—21no—
272C2×C4×D11—21no—
273C2×C4×D11—21no—
274C2×C4×D11—21no—
275C2×C4×D11—21no—
276C2×C4×D11—42no—
277C2×C4×D11—42no—
278C2×C4×D11—42no—
279C2×C4×D11—42no—
280C2×C4×D11C22×C411yescharacteristic
281C2×C4×D11C22×C411yescharacteristic
282C2×C4×D11C2×D411yescharacteristic
283C2×C4×D11C2×D411yescharacteristic
284C2×Dic22—21no—
285C2×Dic22—21no—
286C2×Dic22C22×C411yescharacteristic
287C2×Dic22C22×C411yescharacteristic
288C11×Q16—22no—
289C11×SD16—22no—
290C11×SD16—22no—
291C11×D8—22no—
292C11×M16—21no—
293C11×M16—21no—
294C11×M16—21no—
295C11×M16—21no—
296C11×M16—42no—
297C2×C8×C11—21no—
298C2×C8×C11—21no—
299C2×C8×C11—21no—
300C2×C8×C11—21no—
301C2×C8×C11—21no—
302C2×C8×C11—21no—
303C2×C8×C11—42no—
304C2×C8×C11C22×C411yescharacteristic
305C2×C8×C11C22×C411yescharacteristic
306C2×C8×C11C2×D411yescharacteristic
307C2×C8×C11C2×D411yescharacteristic
308C42×C11—21no—
309C42×C11—21no—
310#4326—22no—
311#4326C22⋊C414yescomplemented
312#4325—22no—
313#4325C22⋊C414yescomplemented
314#4324—22no—
315#4324C22⋊C414yescomplemented
316#4323—22no—
317#4323C22⋊C414yescomplemented
318(C2×D11)⋊C4—42no—
319C4×Dic11—21no—
320C4×Dic11—21no—
321#4318—21no—
322#4318—21no—
323#4318—21no—
324#4318—21no—
325#4318—42no—
326C2×C11⋊C8—21no—
327C2×C11⋊C8—21no—
328C2×C11⋊C8—21no—
329C2×C11⋊C8—21no—
330C2×C11⋊C8—42no—
331C2×C11⋊C8C22×C411yescharacteristic
332C2×C11⋊C8C22×C411yescharacteristic
333C2×C11⋊C8C2×D411yescharacteristic
334C2×C11⋊C8C2×D411yescharacteristic
335C2×C11⋊C8C2×D412yes—
336C2×C11⋊C8C2×D412yes—
337Dic44—22no—
338D88—22no—
339#4314—22no—
340#4314—22no—
341#4313—22no—
342#4313—22no—
343#4313—22no—
344#4313—22no—
345#4313—42no—
346#4313—42no—
347C8×D11—42no—
348C8×D11—42no—
349C2×#575—111no—
350C2×#444—111no—
351C2×#443—111no—
352#2880—111no—
353#2880—111no—
354#1975—111no—
355#1974—111no—
356#1876—111no—
357#1876—111no—
358#1876—111no—
359#1876D1111yescharacteristic, complemented
360#1811—111no—
361#1789—111no—
362#1789—111no—
363#1753—111no—
364C23×C11—21no—
365C23×C11—21no—
366C23×C11C2×#4111yescharacteristic
367C22×D11—21no—
368C22×D11—21no—
369C22×D11—21no—
370C22×D11—21no—
371C22×D11—41no—
372C22×D11—41no—
373C22×D11—42no—
374C22×D11—42no—
375C22×D11—42no—
376C22×D11—42no—
377C22×D11—81no—
378C22×D11—81no—
379C22×D11C4×D411yescharacteristic
380C22×D11C4×D411yescharacteristic
381Q8×C11—21no—
382Q8×C11—21no—
383Q8×C11—21no—
384Q8×C11C2×C22⋊C412yes—
385D4×C11—22no—
386D4×C11—22no—
387D4×C11—21no—
388D4×C11—21no—
389D4×C11—21no—
390D4×C11—41no—
391D4×C11—41no—
392D4×C11C2×C22⋊C412yes—
393C2×C4×C11—21no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—21no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11C23×C411yescharacteristic
403C2×C4×C11C22×D411yescharacteristic
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C22×D411yescharacteristic
406C2×C4×C11H(5,𝔽2)11yescharacteristic
407C2×C4×C11H(5,𝔽2)11yescharacteristic
408C22⋊D11—22no—
409C22⋊D11—22no—
410C22⋊D11—42no—
411C22⋊D11—42no—
412C22⋊D11—42no—
413C22⋊D11—42no—
414C22⋊D11—41no—
415C22⋊D11—41no—
416C2×Dic11—21no—
417C2×Dic11—21no—
418C2×Dic11—21no—
419C2×Dic11—22no—
420C2×Dic11—21no—
421C2×Dic11—42no—
422C2×Dic11—42no—
423C2×Dic11—41no—
424C2×Dic11—41no—
425C2×Dic11C4×D411yescharacteristic
426C2×Dic11C4×D411yescharacteristic
427D44—21no—
428D44—21no—
429D44—21no—
430D44—42no—
431D44—42no—
432D44C2×C22⋊C412yes—
433C4×D11—21no—
434C4×D11—21no—
435C4×D11—21no—
436C4×D11—21no—
437C4×D11—22no—
438C4×D11—22no—
439C4×D11—21no—
440C4×D11—21no—
441C4×D11—21no—
442C4×D11—21no—
443C4×D11—42no—
444C4×D11—42no—
445C4×D11—42no—
446C4×D11—42no—
447C4×D11—41no—
448C4×D11—41no—
449Dic22—21no—
450Dic22—21no—
451Dic22—21no—
452Dic22—42no—
453Dic22—42no—
454Dic22C2×C22⋊C412yes—
455C8×C11—21no—
456C8×C11—21no—
457C8×C11—21no—
458C8×C11—21no—
459C8×C11—41no—
460C8×C11—41no—
461C11⋊C8—21no—
462C11⋊C8—21no—
463C11⋊C8—41no—
464C11⋊C8—41no—
465C11⋊C8C2×C22⋊C412yes—
466C11⋊C8C2×C22⋊C412yes—
467C22×#41—111no—
468C22×#41—111no—
469#575—224no—
470#575—224no—
471C2×#137—111no—
472C2×#137—111no—
473C2×#137—111no—
474C2×#137—111no—
475C2×AGL(1,ℤ/8)—111no—
476C2×AGL(1,ℤ/8)—111no—
477C2×AGL(1,ℤ/8)—111no—
478C2×AGL(1,ℤ/8)—111no—
479C2×#135—111no—
480C2×#135—111no—
481C2×#135—111no—
482C2×#135C2×D1111yescharacteristic
483C2×#131—111no—
484C2×#131—111no—
485C2×#131—111no—
486C2×#131C2×D1111yescharacteristic, complemented
487C22×M16—111no—
488#444—224no—
489#443—224no—
490C2×#108—111no—
491C2×#108—111no—
492C2×#104—111no—
493C2×#104—111no—
494C2×#104—111no—
495C2×#104—111no—
496C2×#104—111no—
497C2×#104—111no—
498C2×#104C2×D1111yescharacteristic, complemented
499C2×#104C2×D1111yescharacteristic, complemented
500#408—111no—
501#408—111no—
502#408—111no—
503#408—221no—
504#408—221no—
505#408—221no—
506#408—221no—
507#408C2×D1111yescharacteristic, complemented
508#407—111no—
509#407—111no—
510#407—221no—
511#407—221no—
512C2×C22⋊C8—111no—
513C2×C22⋊C8—221no—
514C2×C22⋊C8—221no—
515C2×#97—111no—
516C2×C4×C8—111no—
517C4×C22⋊C4—111no—
518#341—111no—
519#341C2×D1111yescharacteristic, complemented
520#336—111no—
521#336C2×D1111yescharacteristic, complemented
522C22×C11—21no—
523C22×C11—21no—
524C22×C11—22no—
525C22×C11—41no—
526C22×C11—41no—
527C22×C11—41no—
528C22×C11—41no—
529C22×C11—41no—
530C22×C11C2×C4×D411yescharacteristic
531C22×C11#54611yescharacteristic
532C22×C11#54611yescharacteristic
533C2×D11—21no—
534C2×D11—21no—
535C2×D11—22no—
536C2×D11—21no—
537C2×D11—21no—
538C2×D11—21no—
539C2×D11—21no—
540C2×D11—41no—
541C2×D11—41no—
542C2×D11—41no—
543C2×D11—41no—
544C2×D11—41no—
545C2×D11—81no—
546C2×D11—81no—
547C2×D11—84no—
548C2×D11—84no—
549C4×C11—22no—
550C4×C11—41no—
551C4×C11—81no—
552C4×C11C22×C22⋊C411yescharacteristic
553C4×C11#51811yescharacteristic
554C4×C11D4211yescharacteristic
555C4×C11D4211yescharacteristic
556Dic11—22no—
557Dic11—21no—
558Dic11—21no—
559Dic11—42no—
560Dic11—41no—
561C2×#41—111no—
562C2×#41—111no—
563C2×#41—111no—
564C2×#41—111no—
565C2×#41—111no—
566C2×#41—111no—
567C2×#41—221no—
568C2×#41—221no—
569C2×#41—221no—
570C2×#41—221no—
571C2×#41—222no—
572C2×#41—222no—
573C2×#41—222no—
574C2×#41—222no—
575C2×#41—441no—
576C2×#41—441no—
577C2×#41—441no—
578C2×#41—441no—
579C2×#41C22×D1111yescharacteristic
580C2×#41C22×D1111yescharacteristic
581C22×Q8—111no—
582C22×Q8—111no—
583C22×D4—111no—
584C22×D4—111no—
585C22×D4—221no—
586C22×D4—221no—
587C23×C4—111no—
588C23×C4—221no—
589C23×C4—221no—
590#137—224no—
591#137—224no—
592#137—224no—
593#137—224no—
594AGL(1,ℤ/8)—224no—
595AGL(1,ℤ/8)—224no—
596AGL(1,ℤ/8)—224no—
597AGL(1,ℤ/8)—224no—
598#135—22no—
599#135—22no—
600#135—114no—
601#135—114no—
602#135—222no—
603#135—222no—
604#135—222no—
605#135—222no—
606C2×Q16—111no—
607C2×Q16—111no—
608C2×Q16—111no—
609C2×Q16C4×D1111yescharacteristic
610C2×SD16—111no—
611C2×SD16—111no—
612C2×SD16—111no—
613C2×SD16—111no—
614C2×SD16—111no—
615C2×SD16—111no—
616C2×SD16C4×D1111yescharacteristic
617C2×SD16C4×D1111yescharacteristic
618C2×D8—111no—
619C2×D8—111no—
620C2×D8—111no—
621C2×D8C4×D1111yescharacteristic
622#131—22no—
623#131—41no—
624#131—222no—
625#131—222no—
626#131—222no—
627#131—441no—
628#131—441no—
629#131—441no—
630C2×M16—21no—
631C2×M16—111no—
632C2×M16—111no—
633C2×M16—111no—
634C2×M16—111no—
635C2×M16—111no—
636C2×M16—111no—
637C2×M16—222no—
638C2×M16—222no—
639C2×M16—221no—
640C2×M16—221no—
641C2×M16—221no—
642C2×M16C22×D1111yescharacteristic
643C2×M16C22×D1111yescharacteristic
644C22×C8—21no—
645C22×C8—111no—
646C22×C8—111no—
647C22×C8—221no—
648C22×C8—221no—
649C22×C8—221no—
650C22×C8C22×D1111yescharacteristic
651C22×C8C22×D1111yescharacteristic
652C2×C22⋊C4—221no—
653C2×C42—111no—
654C2×C42C22×D1111yescharacteristic
655#108—222no—
656#108—222no—
657#104—22no—
658#104—41no—
659#104—222no—
660#104—222no—
661#104—222no—
662#104—441no—
663#104—441no—
664#104—441no—
665C22⋊C8—21no—
666C22⋊C8—21no—
667C22⋊C8—111no—
668C22⋊C8—111no—
669C22⋊C8—111no—
670C22⋊C8—111no—
671C22⋊C8—221no—
672C22⋊C8—221no—
673C22⋊C8—221no—
674C22⋊C8—221no—
675C22⋊C8—221no—
676C22⋊C8—221no—
677C22⋊C8—221no—
678C22⋊C8—221no—
679C22⋊C8—221no—
680C22⋊C8—221no—
681#97—222no—
682C4×C8—222no—
683#95—221no—
684C2×C11—21no—
685C2×C11—21no—
686C2×C11—42no—
687C2×C11—81no—
688C2×C11D4×C22⋊C411yescharacteristic
689C2×C11#295511yescharacteristic
690C2×C11#295611yescharacteristic
691D11—41no—
692D11—41no—
693D11—42no—
694D11—81no—
695C24—111no—
696C24—221no—
697C24—221no—
698#41—21no—
699#41—21no—
700#41—21no—
701#41—21no—
702#41—21no—
703#41—21no—
704#41—112no—
705#41—112no—
706#41—221no—
707#41—221no—
708#41—222no—
709#41—222no—
710#41—222no—
711#41—222no—
712#41—221no—
713#41—221no—
714#41—221no—
715#41—221no—
716#41—442no—
717#41—442no—
718#41—442no—
719#41—442no—
720#41—441no—
721#41—441no—
722#41—442no—
723#41—442no—
724#41—442no—
725#41—442no—
726#41—441no—
727#41—441no—
728#41D4×D1112yes—
729#41D4×D1112yes—
730C2×Q8—111no—
731C2×Q8—111no—
732C2×Q8—221no—
733C2×Q8—221no—
734C2×Q8—222no—
735C2×Q8—222no—
736C2×Q8—441no—
737C2×Q8—441no—
738C2×Q8C2×C4×D1111yescharacteristic
739C2×Q8C2×C4×D1111yescharacteristic
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—111no—
743C2×D4—111no—
744C2×D4—221no—
745C2×D4—221no—
746C2×D4—221no—
747C2×D4—221no—
748C2×D4—222no—
749C2×D4—221no—
750C2×D4—222no—
751C2×D4—221no—
752C2×D4—221no—
753C2×D4—221no—
754C2×D4—441no—
755C2×D4—441no—
756C2×D4—442no—
757C2×D4—442no—
758C2×D4—442no—
759C2×D4—442no—
760C2×D4C2×C4×D1111yescharacteristic
761C2×D4C2×C4×D1111yescharacteristic
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—111no—
766C22×C4—111no—
767C22×C4—111no—
768C22×C4—111no—
769C22×C4—111no—
770C22×C4—221no—
771C22×C4—221no—
772C22×C4—221no—
773C22×C4—221no—
774C22×C4—221no—
775C22×C4—221no—
776C22×C4—221no—
777C22×C4—221no—
778C22×C4—221no—
779C22×C4—221no—
780C22×C4—221no—
781C22×C4—221no—
782C22×C4—221no—
783C22×C4—442no—
784C22×C4—442no—
785C22×C4—442no—
786C22×C4—442no—
787C22×C4C23×D1111yescharacteristic
788Q16—22no—
789Q16—114no—
790Q16—222no—
791Q16—222no—
792SD16—22no—
793SD16—22no—
794SD16—114no—
795SD16—114no—
796SD16—222no—
797SD16—222no—
798SD16—222no—
799SD16—222no—
800D8—22no—
801D8—114no—
802D8—222no—
803D8—222no—
804M16—21no—
805M16—21no—
806M16—21no—
807M16—21no—
808M16—42no—
809M16—222no—
810M16—222no—
811M16—222no—
812M16—222no—
813M16—221no—
814M16—221no—
815M16—221no—
816M16—221no—
817M16—442no—
818M16—442no—
819M16—442no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—42no—
827C2×C8—111no—
828C2×C8—111no—
829C2×C8—112no—
830C2×C8—112no—
831C2×C8—111no—
832C2×C8—111no—
833C2×C8—221no—
834C2×C8—221no—
835C2×C8—221no—
836C2×C8—221no—
837C2×C8—442no—
838C2×C8—442no—
839C2×C8—442no—
840C2×C8C2×C4×D1111yescharacteristic
841C2×C8C2×C4×D1111yescharacteristic
842C2×C8D4×D1111yescharacteristic
843C2×C8D4×D1111yescharacteristic
844C22⋊C4—442no—
845C42—21no—
846C42—21no—
847C42—221no—
848C42—221no—
849C11#2245311yescharacteristic, complemented, Sylow
850C23—21no—
851C23—21no—
852C23—111no—
853C23—111no—
854C23—221no—
855C23—221no—
856C23—221no—
857C23—221no—
858C23—441no—
859C23—441no—
860C23—442no—
861C23—442no—
862C23—442no—
863C23—442no—
864C23—881no—
865C23—881no—
866C23#41×D1111yescharacteristic
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—112no—
871Q8—221no—
872Q8—221no—
873Q8—221no—
874Q8—442no—
875Q8—442no—
876Q8C22⋊C4×D1112yes—
877D4—22no—
878D4—22no—
879D4—21no—
880D4—21no—
881D4—21no—
882D4—41no—
883D4—41no—
884D4—112no—
885D4—222no—
886D4—222no—
887D4—221no—
888D4—221no—
889D4—221no—
890D4—442no—
891D4—442no—
892D4—442no—
893D4—442no—
894D4—442no—
895D4—442no—
896D4—441no—
897D4—441no—
898D4C22⋊C4×D1112yes—
899C2×C4—21no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—21no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—111no—
909C2×C4—111no—
910C2×C4—221no—
911C2×C4—221no—
912C2×C4—221no—
913C2×C4—221no—
914C2×C4—221no—
915C2×C4—221no—
916C2×C4—221no—
917C2×C4—222no—
918C2×C4—221no—
919C2×C4—221no—
920C2×C4—222no—
921C2×C4—221no—
922C2×C4—221no—
923C2×C4—222no—
924C2×C4—221no—
925C2×C4—442no—
926C2×C4—442no—
927C2×C4—442no—
928C2×C4—442no—
929C2×C4—442no—
930C2×C4—442no—
931C2×C4—441no—
932C2×C4—441no—
933C2×C4—441no—
934C2×C4—441no—
935C2×C4C22×C4×D1111yescharacteristic
936C2×C4C2×D4×D1111yescharacteristic
937C2×C4C2×D4×D1111yescharacteristic
938C2×C4C2×D4×D1111yescharacteristic
939C2×C4#6703711yescharacteristic
940C2×C4#6704211yescharacteristic
941C8—21no—
942C8—21no—
943C8—21no—
944C8—21no—
945C8—41no—
946C8—41no—
947C8—112no—
948C8—112no—
949C8—221no—
950C8—221no—
951C8—441no—
952C8—441no—
953C22—21no—
954C22—21no—
955C22—22no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—221no—
962C22—221no—
963C22—221no—
964C22—221no—
965C22—221no—
966C22—221no—
967C22—222no—
968C22—441no—
969C22—441no—
970C22—441no—
971C22—441no—
972C22—441no—
973C22—881no—
974C22—881no—
975C22—884no—
976C22—884no—
977C22C4×D4×D1111yescharacteristic
978C22#1062314111yescharacteristic
979C22#1062318511yescharacteristic
980C4—22no—
981C4—41no—
982C4—81no—
983C4—221no—
984C4—221no—
985C4—222no—
986C4—442no—
987C4—441no—
988C4C2×C22⋊C4×D1111yescharacteristic
989C4#1062307611yescharacteristic
990C4#1062312111yescharacteristic
991C4#1062314011yescharacteristic
992C2—21no—
993C2—21no—
994C2—42no—
995C2—81no—
996C2—441no—
997C2—441no—
998C2—442no—
999C2—881no—
1000C2#1307143411yescharacteristic
1001C2#1307751411yescharacteristic
1002C2#1307752411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1876C2
socleC22×C11C2×C4×D4
prime radicalC2×#10623299C2
cosocleC22×C4×C11C24
hypercenter#1876D11
hypocenterC11#22453
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1876

Complements

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

NH ≅ G/Ntype
2. C2×#10622436C2semidirect
3. C2×#10622757C2semidirect
4. #13077064C2semidirect
5. #13077063C2semidirect
6. #13069506C2semidirect
7. #13069503C2semidirect
8. #13068945C2semidirect
9. #13068944C2semidirect
10. #13068942C2semidirect
11. #13068657C2semidirect
12. #13068558C2semidirect
13. #13068558C2semidirect
14. #13068398C2semidirect
15. C11×#1876C2semidirect
19. C2×C11×#131C22semidirect
22. C2×#67001C22semidirect
25. C2×#66971C4semidirect
26. C2×#66971C4semidirect
27. C2×#66968C4semidirect
28. C2×#66968C4semidirect
29. C2×#66967C4semidirect
30. C2×#66967C4semidirect
31. C2×#66964C4semidirect
32. C2×#66964C4semidirect
33. C2×#66960C22semidirect
35. C2×#66954C22semidirect
37. C2×C11×#104C22semidirect
38. C2×C11×#104C22semidirect
39. C11×#408C22semidirect
40. C2×#66901C22semidirect
41. C2×#66901C22semidirect
42. #10622847C22semidirect
44. C2×#66889C22semidirect
45. C2×#66889C22semidirect
47. #10622742C22semidirect
51. C2×#66886C22semidirect
52. C2×#66886C22semidirect
54. #10622723C22semidirect
57. C2×C8×Dic11C22semidirect
59. C2×#66869C22semidirect
60. C2×#66869C22semidirect
61. C2×#66867C22semidirect
67. C11×#341C22semidirect
68. C11×#336C22semidirect
69. #10622190C22semidirect
70. #10622188C22semidirect
311. #4326C22⋊C4semidirect
313. #4325C22⋊C4semidirect
315. #4324C22⋊C4semidirect
317. #4323C22⋊C4semidirect
359. #1876D11semidirect
486. C2×#131C2×D11semidirect
498. C2×#104C2×D11semidirect
499. C2×#104C2×D11semidirect
507. #408C2×D11semidirect
519. #341C2×D11semidirect
521. #336C2×D11semidirect
849. C11#22453semidirect

Maximal subgroups

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

subgroupindex
C2×#106232992
C2×#106224362
C2×#106227572
#130770642
#130770632
#130695062
#130695032
#130689452
#130689442
#130689422
#130686572
#130685582
#130683982
C11×#18762
#2245311