Finite Group Databasebeta

← #14769656

Subgroups — #14769656

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×#10623353C211yesmaximal, characteristic
2C2×#10622758C211yesmaximal, characteristic, complemented
3C2×#10622757C211yesmaximal, characteristic, complemented
4#13077062C211yesmaximal, characteristic, complemented
5#13069508C211yesmaximal, characteristic, complemented
6#13069503C211yesmaximal, characteristic, complemented
7#13068946C211yesmaximal, characteristic, complemented
8#13068946C211yesmaximal, characteristic, complemented
9#13068943C211yesmaximal, characteristic, complemented
10#13068943C211yesmaximal, characteristic, complemented
11#13068656C211yesmaximal, characteristic, complemented
12#13068560C211yesmaximal, characteristic, complemented
13#13068559C211yesmaximal, characteristic, complemented
14#13068402C211yesmaximal, characteristic, complemented
15C11×#2880C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×#4339C2211yescharacteristic
18C2×C11×#131C2211yescharacteristic, complemented
19C2×C11×#131C2211yescharacteristic, complemented
20C2×#67004C411yescharacteristic, complemented
21C2×#67004C411yescharacteristic, complemented
22#10623353—24no—
23#10623353—24no—
24C2×#67003C2211yescharacteristic
25C2×#67003C2211yescharacteristic
26C2×#67003C2211yescharacteristic
27C2×#67003C2211yescharacteristic
28C2×#67002C411yescharacteristic, complemented
29C2×#67002C411yescharacteristic, complemented
30C2×#66995C411yescharacteristic, complemented
31C2×#66995C411yescharacteristic, complemented
32C2×#66985C411yescharacteristic, complemented
33C2×#66985C411yescharacteristic, complemented
34C22×#4318C2211yescharacteristic
35C2×#66954C2211yescharacteristic, complemented
36C2×#66954C2211yescharacteristic, complemented
37C11×#408—21no—
38C11×#408—21no—
39C11×#408C2211yescharacteristic, complemented
40C11×#408C2211yescharacteristic, complemented
41C11×#407—21no—
42C11×#407C2211yescharacteristic
43C2×C11×C22⋊C8—21no—
44C2×C11×C22⋊C8C2211yescharacteristic
45C2×#66901C2211yescharacteristic, complemented
46C2×#66901C2211yescharacteristic, complemented
47C2×#66901C2211yescharacteristic, complemented
48C2×#66901C2211yescharacteristic, complemented
49C4×C22⋊Dic11C2211yescharacteristic
50#10622820C2211yescharacteristic
51#10622758—24no—
52#10622757—24no—
53C2×#66889C2211yescharacteristic, complemented
54C2×#66889C2211yescharacteristic, complemented
55C2×#66889C2211yescharacteristic, complemented
56C2×#66889C2211yescharacteristic, complemented
57C2×#66886C2211yescharacteristic, complemented
58C2×#66886C2211yescharacteristic, complemented
59#10622723C2211yescharacteristic, complemented
60#10622723C2211yescharacteristic, complemented
61C2×#66879C2211yescharacteristic, complemented
62C2×C8×Dic11C2211yescharacteristic, complemented
63#10622340—21no—
64#10622340—21no—
65#10622339—21no—
66D11×C22⋊C8—21no—
67#10622196C2211yescharacteristic, complemented
68#10622196C2211yescharacteristic, complemented
69#10622188C2211yescharacteristic, complemented
70#10622188C2211yescharacteristic, complemented
71C2×C11×#41—21no—
72C2×C11×#41—21no—
73C2×C11×#41—22no—
74C2×C11×#41—22no—
75C2×C11×#41—41no—
76C2×C11×#41—41no—
77C2×C11×#41C2×C411yescharacteristic
78C2×C11×#41C2×C411yescharacteristic
79C2×C11×#41C2311yescharacteristic
80C2×C11×#41C2311yescharacteristic
81C22×Q8×C11C2×C411yescharacteristic
82C22×D4×C11—21no—
83C22×D4×C11C2×C411yescharacteristic
84C23×C4×C11—21no—
85C23×C4×C11C2311yescharacteristic
86C22×C22⋊D11—21no—
87C2×#4339—21no—
88C2×#4339—21no—
89C2×#4339—22no—
90C2×#4339—22no—
91C2×#4339—41no—
92C2×#4339—41no—
93C2×#4339C2×C411yescharacteristic
94C2×#4339C2×C411yescharacteristic
95C2×#4339C2311yescharacteristic
96C2×#4339C2311yescharacteristic
97C22×D44C2×C411yescharacteristic
98C22×C4×D11—21no—
99C22×Dic22C2×C411yescharacteristic
100C11×#131—22no—
101C11×#131—22no—
102C11×#131—41no—
103C11×#131—41no—
104C2×C11×M16—21no—
105C2×C11×M16—21no—
106C2×C11×M16C2311yescharacteristic
107C2×C11×M16C2311yescharacteristic
108C22×C8×C11—21no—
109C22×C8×C11—21no—
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2311yescharacteristic
112C2×C22⋊Dic11—21no—
113#67004—24no—
114#67004—24no—
115#67003—22no—
116#67003—22no—
117#67003—22no—
118#67003—22no—
119#67003—22no—
120#67003—22no—
121#67003D414yes—
122#67003D414yes—
123#67002—24no—
124#67002—24no—
125C2×#4326C2×C411yescharacteristic
126C2×#4326C2×C411yescharacteristic
127C2×#4326C2×C411yescharacteristic
128C2×#4326C2×C411yescharacteristic
129#66995—24no—
130#66995—24no—
131C2×#4325C2×C411yescharacteristic
132C2×#4325C2×C411yescharacteristic
133C2×#4325C2×C411yescharacteristic
134C2×#4325C2×C411yescharacteristic
135C2×#4324C2×C411yescharacteristic
136C2×#4324C2×C411yescharacteristic
137C2×#4324C2×C411yescharacteristic
138C2×#4324C2×C411yescharacteristic
139#66985—24no—
140#66985—24no—
141C2×#4323C2×C411yescharacteristic
142C2×#4323C2×C411yescharacteristic
143C2×#4323C2×C411yescharacteristic
144C2×#4323C2×C411yescharacteristic
145C2×C4×Dic11C2311yescharacteristic
146C2×C4×Dic11C2311yescharacteristic
147C2×#4318—22no—
148C2×#4318—22no—
149C2×#4318C2×C411yescharacteristic
150C2×#4318C2×C411yescharacteristic
151C2×#4318C2×C411yescharacteristic
152C2×#4318C2×C411yescharacteristic
153C2×#4318C2311yescharacteristic
154C2×#4318C2311yescharacteristic
155C22×C11⋊C8C2311yescharacteristic
156C22×C11⋊C8C2311yescharacteristic
157#66954—22no—
158#66954—22no—
159#66954—41no—
160#66954—41no—
161C2×#4313—21no—
162C2×#4313—21no—
163C2×C8×D11—21no—
164C2×C8×D11—21no—
165C11×C22⋊C8—21no—
166C11×C22⋊C8—21no—
167C11×C22⋊C8—21no—
168C11×C22⋊C8—21no—
169C11×C22⋊C8—21no—
170C11×C22⋊C8—21no—
171C11×C22⋊C8D411yescharacteristic
172C11×C22⋊C8D411yescharacteristic
173C11×C22⋊C8D411yescharacteristic
174C11×C22⋊C8D411yescharacteristic
175#66901—22no—
176#66901—22no—
177#66901—41no—
178#66901—41no—
179C11⋊#95—21no—
180C22⋊(C11⋊C8)—21no—
181C22⋊(C11⋊C8)—21no—
182#66889—22no—
183#66889—22no—
184#66889—41no—
185#66889—41no—
186#66886—22no—
187#66886—22no—
188(C2×D11)⋊C8—21no—
189(C2×D11)⋊C8—21no—
190(C2×D11)⋊C8—21no—
191(C2×D11)⋊C8—21no—
192#66879—22no—
193C8×Dic11—22no—
194#22453—111nomaximal, Sylow
195C24×C11—21no—
196C24×C11#4111yescharacteristic
197C23×D11—21no—
198C11×#41—21no—
199C11×#41—21no—
200C11×#41—22no—
201C11×#41—22no—
202C11×#41—21no—
203C11×#41—21no—
204C11×#41—21no—
205C11×#41—21no—
206C11×#41—42no—
207C11×#41—42no—
208C11×#41—41no—
209C11×#41—41no—
210C11×#41—42no—
211C11×#41—42no—
212C11×#41C2×D412yes—
213C11×#41C2×D412yes—
214C2×Q8×C11—21no—
215C2×Q8×C11—22no—
216C2×Q8×C11—41no—
217C2×Q8×C11C22×C411yescharacteristic
218C2×Q8×C11C22×C411yescharacteristic
219C2×D4×C11—21no—
220C2×D4×C11—22no—
221C2×D4×C11—21no—
222C2×D4×C11—21no—
223C2×D4×C11—21no—
224C2×D4×C11—21no—
225C2×D4×C11—41no—
226C2×D4×C11—42no—
227C2×D4×C11—42no—
228C2×D4×C11C22×C411yescharacteristic
229C2×D4×C11C22×C411yescharacteristic
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—42no—
240C22×C4×C11—42no—
241C22×C4×C11C22×C411yescharacteristic
242C22×C4×C11C22×C411yescharacteristic
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11#4111yescharacteristic
246C22×C4×C11C2411yescharacteristic
247C2×C22⋊D11—21no—
248C2×C22⋊D11—21no—
249C2×C22⋊D11—21no—
250C2×C22⋊D11—21no—
251C2×C22⋊D11—42no—
252C2×C22⋊D11—42no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256#4339—22no—
257#4339—22no—
258#4339—21no—
259#4339—21no—
260#4339—21no—
261#4339—21no—
262#4339—21no—
263#4339—21no—
264#4339—41no—
265#4339—41no—
266#4339—42no—
267#4339—42no—
268#4339—42no—
269#4339—42no—
270#4339C2×D412yes—
271#4339C2×D412yes—
272C2×D44—22no—
273C2×D44—21no—
274C2×D44—41no—
275C2×D44C22×C411yescharacteristic
276C2×D44C22×C411yescharacteristic
277C2×C4×D11—21no—
278C2×C4×D11—21no—
279C2×C4×D11—21no—
280C2×C4×D11—21no—
281C2×C4×D11—42no—
282C2×C4×D11—42no—
283C2×Dic22—22no—
284C2×Dic22—21no—
285C2×Dic22—41no—
286C2×Dic22C22×C411yescharacteristic
287C2×Dic22C22×C411yescharacteristic
288C11×M16—21no—
289C11×M16—21no—
290C11×M16—21no—
291C11×M16—21no—
292C11×M16—42no—
293C11×M16—42no—
294C2×C8×C11—21no—
295C2×C8×C11—21no—
296C2×C8×C11—21no—
297C2×C8×C11—21no—
298C2×C8×C11—21no—
299C2×C8×C11—21no—
300C2×C8×C11—42no—
301C2×C8×C11—42no—
302C2×C8×C11C2×D411yescharacteristic
303C2×C8×C11C2×D411yescharacteristic
304C2×C8×C11C2×D411yescharacteristic
305C2×C8×C11C2×D411yescharacteristic
306C22⋊Dic11—42no—
307#4326—22no—
308#4326—22no—
309#4326—22no—
310#4326C22⋊C414yescomplemented
311#4325—22no—
312#4325—22no—
313#4325—22no—
314#4325C22⋊C414yescomplemented
315#4324—22no—
316#4324—22no—
317#4324—22no—
318#4324C22⋊C414yescomplemented
319#4323—22no—
320#4323—22no—
321#4323—22no—
322#4323C22⋊C414yescomplemented
323C4×Dic11—21no—
324C4×Dic11—21no—
325C4×Dic11—21no—
326C4×Dic11—21no—
327#4318—22no—
328#4318—22no—
329#4318—22no—
330#4318—22no—
331#4318—21no—
332#4318—21no—
333#4318—21no—
334#4318—21no—
335C2×C11⋊C8—21no—
336C2×C11⋊C8—21no—
337C2×C11⋊C8—21no—
338C2×C11⋊C8—21no—
339C2×C11⋊C8C22×C411yescharacteristic
340C2×C11⋊C8C22×C411yescharacteristic
341C2×C11⋊C8C22×C411yescharacteristic
342C2×C11⋊C8C22×C411yescharacteristic
343C2×C11⋊C8C2×D412yes—
344C2×C11⋊C8C2×D412yes—
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#2880D1111yescharacteristic, complemented
354#1975—111no—
355#1974—111no—
356#1876—111no—
357#1876—111no—
358#1876—111no—
359#1876—111no—
360#1811—111no—
361#1789—111no—
362#1789—111no—
363#1753—111no—
364C23×C11—21no—
365C23×C11—21no—
366C23×C11—21no—
367C23×C11—21no—
368C23×C11—41no—
369C23×C11—41no—
370C23×C11—42no—
371C23×C11—42no—
372C23×C11—81no—
373C23×C11C4×D411yescharacteristic
374C23×C11C4×D411yescharacteristic
375C23×C11C2×#4111yescharacteristic
376C22×D11—21no—
377C22×D11—21no—
378C22×D11—42no—
379C22×D11—42no—
380C22×D11—81no—
381Q8×C11—21no—
382Q8×C11—21no—
383Q8×C11—21no—
384Q8×C11—42no—
385Q8×C11C2×C22⋊C412yes—
386D4×C11—22no—
387D4×C11—22no—
388D4×C11—21no—
389D4×C11—21no—
390D4×C11—21no—
391D4×C11—42no—
392D4×C11—42no—
393D4×C11—42no—
394D4×C11—41no—
395D4×C11—41no—
396D4×C11C2×C22⋊C412yes—
397C2×C4×C11—21no—
398C2×C4×C11—21no—
399C2×C4×C11—21no—
400C2×C4×C11—21no—
401C2×C4×C11—21no—
402C2×C4×C11—21no—
403C2×C4×C11—21no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—21no—
407C2×C4×C11—21no—
408C2×C4×C11—21no—
409C2×C4×C11—21no—
410C2×C4×C11—21no—
411C2×C4×C11—42no—
412C2×C4×C11—42no—
413C2×C4×C11—42no—
414C2×C4×C11—41no—
415C2×C4×C11—41no—
416C2×C4×C11C4×D411yescharacteristic
417C2×C4×C11C4×D411yescharacteristic
418C2×C4×C11C23×C411yescharacteristic
419C2×C4×C11C22×D411yescharacteristic
420C2×C4×C11C22×D411yescharacteristic
421C2×C4×C11C22×D411yescharacteristic
422C2×C4×C11H(5,𝔽2)11yescharacteristic
423C2×C4×C11H(5,𝔽2)11yescharacteristic
424C22⋊D11—22no—
425C22⋊D11—22no—
426C22⋊D11—42no—
427C22⋊D11—42no—
428C22⋊D11—41no—
429C22⋊D11—41no—
430C2×Dic11—21no—
431C2×Dic11—22no—
432C2×Dic11—21no—
433C2×Dic11—42no—
434C2×Dic11—41no—
435C2×Dic11—41no—
436C2×Dic11—41no—
437C2×Dic11—41no—
438C2×Dic11—41no—
439D44—21no—
440D44—21no—
441D44—21no—
442D44—42no—
443D44C2×C22⋊C412yes—
444C4×D11—22no—
445C4×D11—22no—
446C4×D11—42no—
447C4×D11—42no—
448C4×D11—41no—
449C4×D11—41no—
450Dic22—21no—
451Dic22—21no—
452Dic22—21no—
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×#41C2×D1111yescharacteristic
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×#135—111no—
483C2×#131—111no—
484C2×#131—111no—
485C2×#131C2×D1111yescharacteristic, complemented
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×#104—111no—
499C2×#104—111no—
500#408—21no—
501#408—21no—
502#408—111no—
503#408—111no—
504#408—221no—
505#408—221no—
506#408C2×D1111yescharacteristic, complemented
507#408C2×D1111yescharacteristic, complemented
508#407—21no—
509#407—111no—
510#407—221no—
511#407C2×D1111yescharacteristic
512C2×C22⋊C8—21no—
513C2×C22⋊C8—221no—
514C2×C22⋊C8C2×D1111yescharacteristic
515C2×#97—111no—
516C2×C4×C8—111no—
517C4×C22⋊C4—111no—
518#341—111no—
519#341—111no—
520#336—111no—
521#336—111no—
522C22×C11—21no—
523C22×C11—21no—
524C22×C11—21no—
525C22×C11—21no—
526C22×C11—22no—
527C22×C11—21no—
528C22×C11—21no—
529C22×C11—21no—
530C22×C11—21no—
531C22×C11—41no—
532C22×C11—41no—
533C22×C11—41no—
534C22×C11—41no—
535C22×C11—41no—
536C22×C11—81no—
537C22×C11—81no—
538C22×C11—84no—
539C22×C11C2×C4×D411yescharacteristic
540C22×C11#54611yescharacteristic
541C22×C11#54611yescharacteristic
542C2×D11—22no—
543C2×D11—41no—
544C2×D11—41no—
545C2×D11—41no—
546C2×D11—41no—
547C2×D11—41no—
548C2×D11—84no—
549C4×C11—21no—
550C4×C11—21no—
551C4×C11—22no—
552C4×C11—41no—
553C4×C11C22×C22⋊C411yescharacteristic
554C4×C11#51811yescharacteristic
555C4×C11D4211yescharacteristic
556C4×C11D4211yescharacteristic
557Dic11—22no—
558Dic11—42no—
559Dic11—41no—
560Dic11—81no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—22no—
564C2×#41—22no—
565C2×#41—41no—
566C2×#41—41no—
567C2×#41—111no—
568C2×#41—111no—
569C2×#41—111no—
570C2×#41—111no—
571C2×#41—222no—
572C2×#41—222no—
573C2×#41—221no—
574C2×#41—221no—
575C2×#41—441no—
576C2×#41—441no—
577C2×#41C4×D1111yescharacteristic
578C2×#41C4×D1111yescharacteristic
579C2×#41C22×D1111yescharacteristic
580C2×#41C22×D1111yescharacteristic
581C22×Q8—111no—
582C22×Q8C4×D1111yescharacteristic
583C22×D4—21no—
584C22×D4—111no—
585C22×D4—221no—
586C22×D4C4×D1111yescharacteristic
587C23×C4—21no—
588C23×C4—221no—
589C23×C4C22×D1111yescharacteristic
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—114no—
599#135—114no—
600#135—222no—
601#135—222no—
602#135—222no—
603#135—222no—
604#135—222no—
605#135—222no—
606C2×Q16—111no—
607C2×Q16—111no—
608C2×Q16—111no—
609C2×Q16—111no—
610C2×SD16—111no—
611C2×SD16—111no—
612C2×SD16—111no—
613C2×SD16—111no—
614C2×SD16—111no—
615C2×SD16—111no—
616C2×SD16—111no—
617C2×SD16—111no—
618C2×D8—111no—
619C2×D8—111no—
620C2×D8—111no—
621C2×D8—111no—
622#131—22no—
623#131—22no—
624#131—41no—
625#131—41no—
626#131—222no—
627#131—222no—
628#131—441no—
629#131—441no—
630C2×M16—21no—
631C2×M16—21no—
632C2×M16—111no—
633C2×M16—111no—
634C2×M16—111no—
635C2×M16—111no—
636C2×M16—111no—
637C2×M16—111no—
638C2×M16—222no—
639C2×M16—222no—
640C2×M16—221no—
641C2×M16—221no—
642C2×M16C22×D1111yescharacteristic
643C2×M16C22×D1111yescharacteristic
644C22×C8—21no—
645C22×C8—21no—
646C22×C8—111no—
647C22×C8—111no—
648C22×C8—221no—
649C22×C8—221no—
650C22×C8C22×D1111yescharacteristic
651C22×C8C22×D1111yescharacteristic
652C2×C22⋊C4—221no—
653C2×C42—111no—
654C2×C42—111no—
655#108—222no—
656#108—222no—
657#104—222no—
658#104—222no—
659#104—222no—
660#104—222no—
661#104—441no—
662#104—441no—
663#104—441no—
664#104—441no—
665C22⋊C8—21no—
666C22⋊C8—21no—
667C22⋊C8—21no—
668C22⋊C8—21no—
669C22⋊C8—21no—
670C22⋊C8—21no—
671C22⋊C8—221no—
672C22⋊C8—221no—
673C22⋊C8—221no—
674C22⋊C8—221no—
675C22⋊C8—221no—
676C22⋊C8—221no—
677C22⋊C8C22⋊D1111yescharacteristic
678C22⋊C8C22⋊D1111yescharacteristic
679C22⋊C8C22⋊D1111yescharacteristic
680C22⋊C8C22⋊D1111yescharacteristic
681#97—222no—
682C4×C8—222no—
683#95—221no—
684C2×C11—21no—
685C2×C11—21no—
686C2×C11—41no—
687C2×C11—41no—
688C2×C11—42no—
689C2×C11—81no—
690C2×C11D4×C22⋊C411yescharacteristic
691C2×C11#295511yescharacteristic
692C2×C11#295611yescharacteristic
693D11—42no—
694D11—81no—
695C24—21no—
696C24—221no—
697C24#433911yescharacteristic
698#41—21no—
699#41—21no—
700#41—22no—
701#41—22no—
702#41—21no—
703#41—21no—
704#41—21no—
705#41—21no—
706#41—42no—
707#41—42no—
708#41—41no—
709#41—41no—
710#41—42no—
711#41—42no—
712#41—112no—
713#41—112no—
714#41—222no—
715#41—222no—
716#41—221no—
717#41—221no—
718#41—221no—
719#41—221no—
720#41—221no—
721#41—221no—
722#41—442no—
723#41—442no—
724#41—441no—
725#41—441no—
726#41—442no—
727#41—442no—
728#41D4×D1112yes—
729#41D4×D1112yes—
730C2×Q8—21no—
731C2×Q8—22no—
732C2×Q8—41no—
733C2×Q8—111no—
734C2×Q8—111no—
735C2×Q8—222no—
736C2×Q8—221no—
737C2×Q8—441no—
738C2×Q8C2×C4×D1111yescharacteristic
739C2×Q8C2×C4×D1111yescharacteristic
740C2×D4—21no—
741C2×D4—22no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—21no—
745C2×D4—21no—
746C2×D4—41no—
747C2×D4—42no—
748C2×D4—42no—
749C2×D4—111no—
750C2×D4—111no—
751C2×D4—222no—
752C2×D4—221no—
753C2×D4—221no—
754C2×D4—221no—
755C2×D4—221no—
756C2×D4—221no—
757C2×D4—441no—
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—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—221no—
774C22×C4—221no—
775C22×C4—221no—
776C22×C4—221no—
777C22×C4—221no—
778C22×C4—221no—
779C22×C4—221no—
780C22×C4—442no—
781C22×C4—442no—
782C22×C4C2×C4×D1111yescharacteristic
783C22×C4C2×C4×D1111yescharacteristic
784C22×C4#433911yescharacteristic
785C22×C4C2×C22⋊D1111yescharacteristic
786C22×C4C2×C22⋊D1111yescharacteristic
787C22×C4C23×D1111yescharacteristic
788Q16—114no—
789Q16—222no—
790Q16—222no—
791Q16—222no—
792SD16—114no—
793SD16—114no—
794SD16—222no—
795SD16—222no—
796SD16—222no—
797SD16—222no—
798SD16—222no—
799SD16—222no—
800D8—114no—
801D8—222no—
802D8—222no—
803D8—222no—
804M16—21no—
805M16—21no—
806M16—21no—
807M16—21no—
808M16—42no—
809M16—42no—
810M16—222no—
811M16—222no—
812M16—222no—
813M16—222no—
814M16—221no—
815M16—221no—
816M16—221no—
817M16—221no—
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—42no—
828C2×C8—111no—
829C2×C8—111no—
830C2×C8—112no—
831C2×C8—112no—
832C2×C8—111no—
833C2×C8—111no—
834C2×C8—221no—
835C2×C8—221no—
836C2×C8—221no—
837C2×C8—221no—
838C2×C8—442no—
839C2×C8—442no—
840C2×C8C2×C22⋊D1111yescharacteristic
841C2×C8C2×C22⋊D1111yescharacteristic
842C2×C8C2×C22⋊D1111yescharacteristic
843C2×C8C2×C22⋊D1111yescharacteristic
844C22⋊C4—442no—
845C42—221no—
846C42—221no—
847C42—221no—
848C42—221no—
849C11#2245311yescharacteristic, complemented, Sylow
850C23—21no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—41no—
855C23—41no—
856C23—42no—
857C23—42no—
858C23—81no—
859C23—221no—
860C23—221no—
861C23—442no—
862C23—442no—
863C23—881no—
864C23C4×C22⋊D1111yescharacteristic
865C23C4×C22⋊D1111yescharacteristic
866C23C2×#433911yescharacteristic
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—42no—
871Q8—112no—
872Q8—221no—
873Q8—221no—
874Q8—221no—
875Q8—442no—
876Q8C22⋊C4×D1112yes—
877D4—22no—
878D4—22no—
879D4—21no—
880D4—21no—
881D4—21no—
882D4—42no—
883D4—42no—
884D4—42no—
885D4—41no—
886D4—41no—
887D4—112no—
888D4—222no—
889D4—222no—
890D4—221no—
891D4—221no—
892D4—221no—
893D4—442no—
894D4—442no—
895D4—442no—
896D4—441no—
897D4—441no—
898D4C22⋊C4×D1112yes—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—221no—
919C2×C4—222no—
920C2×C4—222no—
921C2×C4—222no—
922C2×C4—221no—
923C2×C4—442no—
924C2×C4—442no—
925C2×C4—442no—
926C2×C4—441no—
927C2×C4—441no—
928C2×C4—441no—
929C2×C4—441no—
930C2×C4—441no—
931C2×C4—441no—
932C2×C4—441no—
933C2×C4C4×C22⋊D1111yescharacteristic
934C2×C4C4×C22⋊D1111yescharacteristic
935C2×C4C22×C4×D1111yescharacteristic
936C2×C4C2×D4×D1111yescharacteristic
937C2×C4C2×D4×D1111yescharacteristic
938C2×C4#6703711yescharacteristic
939C2×C4#6703711yescharacteristic
940C2×C4C22×C22⋊D1111yescharacteristic
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—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—22no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—81no—
968C22—81no—
969C22—84no—
970C22—222no—
971C22—441no—
972C22—441no—
973C22—441no—
974C22—441no—
975C22—441no—
976C22—884no—
977C22#1062302111yescharacteristic
978C22#1062302111yescharacteristic
979C22C2×C4×C22⋊D1111yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—41no—
984C4—222no—
985C4—442no—
986C4—441no—
987C4—881no—
988C4C2×C22⋊C4×D1111yescharacteristic
989C4#1062301711yescharacteristic
990C4D4×C22⋊D1111yescharacteristic
991C4D4×C22⋊D1111yescharacteristic
992C2—21no—
993C2—21no—
994C2—41no—
995C2—41no—
996C2—42no—
997C2—81no—
998C2—442no—
999C2—881no—
1000C2C22⋊C4×C22⋊D1111yescharacteristic
1001C2#1307751711yescharacteristic
1002C2#1307752311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2880C2
socleC22×C11C2×C4×D4
prime radicalC2×#10623353C2
cosocleC22×C4×C11C24
hypercenter#2880D11
hypocenterC11#22453
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. C2×#10622758C2semidirect
3. C2×#10622757C2semidirect
4. #13077062C2semidirect
5. #13069508C2semidirect
6. #13069503C2semidirect
7. #13068946C2semidirect
8. #13068946C2semidirect
9. #13068943C2semidirect
10. #13068943C2semidirect
11. #13068656C2semidirect
12. #13068560C2semidirect
13. #13068559C2semidirect
14. #13068402C2semidirect
15. C11×#2880C2semidirect
18. C2×C11×#131C22semidirect
19. C2×C11×#131C22semidirect
20. C2×#67004C4semidirect
21. C2×#67004C4semidirect
28. C2×#67002C4semidirect
29. C2×#67002C4semidirect
30. C2×#66995C4semidirect
31. C2×#66995C4semidirect
32. C2×#66985C4semidirect
33. C2×#66985C4semidirect
35. C2×#66954C22semidirect
36. C2×#66954C22semidirect
39. C11×#408C22semidirect
40. C11×#408C22semidirect
45. C2×#66901C22semidirect
46. C2×#66901C22semidirect
47. C2×#66901C22semidirect
48. C2×#66901C22semidirect
53. C2×#66889C22semidirect
54. C2×#66889C22semidirect
55. C2×#66889C22semidirect
56. C2×#66889C22semidirect
57. C2×#66886C22semidirect
58. C2×#66886C22semidirect
59. #10622723C22semidirect
60. #10622723C22semidirect
61. C2×#66879C22semidirect
62. C2×C8×Dic11C22semidirect
67. #10622196C22semidirect
68. #10622196C22semidirect
69. #10622188C22semidirect
70. #10622188C22semidirect
310. #4326C22⋊C4semidirect
314. #4325C22⋊C4semidirect
318. #4324C22⋊C4semidirect
322. #4323C22⋊C4semidirect
353. #2880D11semidirect
485. C2×#131C2×D11semidirect
486. C2×#131C2×D11semidirect
506. #408C2×D11semidirect
507. #408C2×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×#106233532
C2×#106227582
C2×#106227572
#130770622
#130695082
#130695032
#130689462
#130689432
#130686562
#130685602
#130685592
#130684022
C11×#28802
#2245311