Finite Group Databasebeta

← C2×#13079971 #15626610

Subgroups — C2×#13079971 #15626610

Order 2816.

2178 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623127C211yesmaximal, characteristic, complemented
2C2×#10623131C211yesmaximal, characteristic, complemented
3#13079971C2116yesmaximal, direct product factor
4C2×#10622467C211yesmaximal, characteristic, complemented
5C2×#10622484C211yesmaximal, characteristic, complemented
6C2×#10622379C211yesmaximal, characteristic, complemented
7C2×#10622372C211yesmaximal, characteristic, complemented
8C2×#10622652C211yesmaximal, characteristic, complemented
9C2×#10622747C211yesmaximal, characteristic, complemented
10C2×#10622655C211yesmaximal, characteristic, complemented
11C2×#10622375C211yesmaximal, characteristic, complemented
12C2×#10622400C211yesmaximal, characteristic, complemented
13C2×#10622766C211yesmaximal, characteristic, complemented
14C2×#10622763C211yesmaximal, characteristic, complemented
15C2×#10622731C211yesmaximal, characteristic, complemented
16C2×C11×#469C211yesmaximal, characteristic, complemented
17C22×#4341—21no—
18C22×C11×D8C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×#66993C2211yescharacteristic
23C2×#66992—21no—
24C2×#66989C2211yescharacteristic
25C2×#66988—21no—
26C2×D4×Dic11—21no—
27C2×D4×Dic11C2211yescharacteristic
28C2×D4×Dic11C2211yescharacteristic
29C22×#4324C2211yescharacteristic
30C22×#4323C2211yescharacteristic
31C2×#66983C2211yescharacteristic
32C2×#66977C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×#4318C2211yescharacteristic
35C22×#4314C2211yescharacteristic
36#10623131—24no—
37#10623131C2218yescomplemented
38#10623127—24no—
39#10623127C2218yescomplemented
40C2×#66946C2211yescharacteristic
41C2×#66943C2211yescharacteristic
42C2×#66941C2211yescharacteristic
43C2×#66940C2211yescharacteristic
44C2×#66938—21no—
45C2×(C22⋊D11)⋊C4—21no—
46C2×#66932—21no—
47C2×#66930—21no—
48C11×#469C2218yescomplemented
49C2×C11×#106C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54#10622766C2218yescomplemented
55#10622763C2218yescomplemented
56#10622747C2218yescomplemented
57#10622731C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×#66882C2211yescharacteristic
60C2×#66880C2211yescharacteristic
61C2×Dic11⋊C8C2211yescharacteristic
62C2×Dic11⋊C8C2211yescharacteristic
63C2×Dic11⋊C8C2211yescharacteristic
64C2×Dic11⋊C8C2211yescharacteristic
65#10622655C2218yescomplemented
66#10622652C2218yescomplemented
67C2×#66874C2211yescharacteristic
68C2×#66873C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71#10622484C2218yescomplemented
72#10622467C2218yescomplemented
73#10622400C2218yescomplemented
74#10622379C2218yescomplemented
75#10622375C2218yescomplemented
76#10622372C2218yescomplemented
77C22×D4×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C23×Dic11—21no—
86C23×Dic11—21no—
87C23×Dic11D411yescharacteristic
88C23×Dic11D411yescharacteristic
89C2×#4341—28no—
90C2×#4341—48no—
91C22×D44C2311yescharacteristic
92C22×C4×D11—21no—
93C22×Dic22—21no—
94C22×Dic22C2311yescharacteristic
95C2×C11×D8—42no—
96C2×C11×D8C2314yes—
97C2×C11×M16—42no—
98C2×C11×M16C2314yes—
99C22×C8×C11C2311yescharacteristic
100C22×C8×C11C2311yescharacteristic
101C11×#121—22no—
102C11×#121—22no—
103C11×#121C2314yes—
104C11×#121C2314yes—
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C22⋊Dic11—21no—
110C2×C22⋊Dic11—21no—
111C2×C22⋊Dic11—21no—
112C2×C22⋊Dic11—21no—
113C2×C22⋊Dic11—21no—
114#66993—22no—
115#66993C2314yes—
116#66992—28no—
117#66989—22no—
118#66989C2314yes—
119#66988—28no—
120D4×Dic11—28no—
121D4×Dic11—22no—
122D4×Dic11—22no—
123D4×Dic11C2314yes—
124D4×Dic11C2314yes—
125C2×#4324—42no—
126C2×#4324C2314yes—
127C2×#4323—42no—
128C2×#4323C2314yes—
129#66983—22no—
130#66983C2314yes—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133C2×C4⋊Dic11—21no—
134C2×C4⋊Dic11C2311yescharacteristic
135C2×C4⋊Dic11C2311yescharacteristic
136#66977—22no—
137#66977C2314yes—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×Dic11⋊C4—21no—
142C2×C4×Dic11—21no—
143C2×C4×Dic11D411yescharacteristic
144C2×C4×Dic11D411yescharacteristic
145C2×C4×Dic11D414yes—
146C2×C4×Dic11C2314yes—
147C2×C4×Dic11C2311yescharacteristic
148C2×C4×Dic11C2311yescharacteristic
149C2×#4318—42no—
150C2×#4318C2314yes—
151C22×C11⋊C8C2311yescharacteristic
152C22×C11⋊C8C2311yescharacteristic
153C2×#4314—42no—
154C2×#4314C2314yes—
155#66946—22no—
156#66946C2314yes—
157#66943—22no—
158#66943C2314yes—
159#66941—22no—
160#66941C2314yes—
161#66940—22no—
162#66940C2314yes—
163#66938—28no—
164(C22⋊D11)⋊C4—28no—
165#66932—28no—
166#66930—28no—
167C11×#106C2314yes—
168C11×#102C2314yes—
169C11×#102C2314yes—
170#66896C2314yes—
171#66896C2314yes—
172#66885C2314yes—
173#66882C2314yes—
174#66880C2314yes—
175Dic11⋊C8C2314yes—
176Dic11⋊C8C2314yes—
177Dic11⋊C8C2314yes—
178Dic11⋊C8C2314yes—
179#66874C2314yes—
180#66873C2314yes—
181#66872C2314yes—
182#66871C2314yes—
183C2×#3251—111nomaximal, Sylow
184C24×C11—21no—
185C24×C11—21no—
186C24×C11C2×D411yescharacteristic
187C23×D11—21no—
188C2×D4×C11—24no—
189C2×D4×C11—24no—
190C2×D4×C11—21no—
191C2×D4×C11—21no—
192C2×D4×C11—22no—
193C2×D4×C11—22no—
194C2×D4×C11—22no—
195C2×D4×C11—22no—
196C2×D4×C11—44no—
197C2×D4×C11—44no—
198C2×D4×C11C2412yes—
199C2×D4×C11C2412yes—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2411yescharacteristic
208C2×C22⋊D11—24no—
209C2×C22⋊D11—24no—
210C2×C22⋊D11—24no—
211C2×C22⋊D11—44no—
212C2×C22⋊D11—44no—
213C2×C22⋊D11—44no—
214C22×Dic11—24no—
215C22×Dic11—24no—
216C22×Dic11—24no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—42no—
221C22×Dic11—44no—
222C22×Dic11—44no—
223C22×Dic11C2×D411yescharacteristic
224C22×Dic11C2×D411yescharacteristic
225C22×Dic11C2×D411yescharacteristic
226C22×Dic11C2×D414yes—
227C22×Dic11C2×D414yes—
228C22×Dic11C2×D411yescharacteristic
229#4341—432no—
230C2×D44—21no—
231C2×D44—22no—
232C2×D44—22no—
233C2×D44C2412yes—
234C2×C4×D11—24no—
235C2×C4×D11—44no—
236C2×Dic22—24no—
237C2×Dic22—21no—
238C2×Dic22—22no—
239C2×Dic22—22no—
240C2×Dic22—44no—
241C2×Dic22C2412yes—
242C11×D8—44no—
243C11×M16—44no—
244C2×C8×C11—22no—
245C2×C8×C11—22no—
246C2×C8×C11C2412yes—
247C2×C8×C11C2412yes—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4C2412yes—
251C11×C4⋊C4C2412yes—
252C11×C22⋊C4—24no—
253C11×C22⋊C4—24no—
254C22⋊Dic11—24no—
255C22⋊Dic11—24no—
256C22⋊Dic11—24no—
257C22⋊Dic11—24no—
258C22⋊Dic11—24no—
259#4324—44no—
260#4323—44no—
261(C2×D11)⋊C4—24no—
262(C2×D11)⋊C4—24no—
263C4⋊Dic11—24no—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266C4⋊Dic11C2412yes—
267C4⋊Dic11C2412yes—
268Dic11⋊C4—24no—
269Dic11⋊C4—24no—
270Dic11⋊C4—24no—
271Dic11⋊C4—24no—
272C4×Dic11—24no—
273C4×Dic11C2×D414yes—
274C4×Dic11C2×D414yes—
275C4×Dic11C2×D412yes—
276C4×Dic11C2×D412yes—
277C4×Dic11C2412yes—
278C4×Dic11C2412yes—
279#4318—44no—
280C2×C11⋊C8—22no—
281C2×C11⋊C8—22no—
282C2×C11⋊C8C2412yes—
283C2×C11⋊C8C2412yes—
284#4314—44no—
285C2×#532—111no—
286C2×#529—111no—
287#3251—1116no—
288C2×#475—111no—
289C2×#478—111no—
290C2×#478—111no—
291C2×#474—111no—
292C2×#469—111no—
293C2×#469D1111yescharacteristic, complemented
294C2×#468—111no—
295C2×#468—111no—
296C2×#460—111no—
297C2×#463—111no—
298C2×#463—111no—
299C2×#459—111no—
300C2×#423—111no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—42no—
307C23×C11—42no—
308C23×C11—42no—
309C23×C11—42no—
310C23×C11—42no—
311C23×C11—42no—
312C23×C11C22×D412yes—
313C23×C11C22×D411yescharacteristic
314C22×D11—22no—
315C22×D11—42no—
316C22×D11—42no—
317C22×D11—42no—
318D4×C11—22no—
319D4×C11—22no—
320D4×C11—22no—
321D4×C11—22no—
322D4×C11—48no—
323D4×C11—48no—
324D4×C11—42no—
325D4×C11—42no—
326C2×C4×C11—22no—
327C2×C4×C11—24no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—42no—
333C2×C4×C11—42no—
334C2×C4×C11C22×D412yes—
335C2×C4×C11C22×D411yescharacteristic
336C2×C4×C11H(5,𝔽2)12yes—
337C2×C4×C112−1+412yes—
338C2×C4×C11C2511yescharacteristic
339C22⋊D11—48no—
340C22⋊D11—48no—
341C22⋊D11—48no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—28no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—44no—
350C2×Dic11—48no—
351C2×Dic11—42no—
352C2×Dic11—42no—
353C2×Dic11—42no—
354C2×Dic11—48no—
355C2×Dic11AGL(1,ℤ/8)14yes—
356C2×Dic11C22×D412yes—
357C2×Dic11C22×D412yes—
358C2×Dic11C22×D412yes—
359C2×Dic11C22×D412yes—
360D44—22no—
361D44—22no—
362D44—42no—
363C4×D11—48no—
364Dic22—22no—
365Dic22—22no—
366Dic22—42no—
367Dic22—48no—
368C8×C11—22no—
369C8×C11—22no—
370C11⋊C8—22no—
371C11⋊C8—22no—
372C22×#41—221no—
373C22×SD16—111no—
374C22×SD16—111no—
375C22×D8—111no—
376C22×D8C2×D1111yescharacteristic
377C22×M16—111no—
378C22×M16C2×D1111yescharacteristic
379#532—118no—
380#532—224no—
381C2×C4⋊Q8—111no—
382C2×#127—111no—
383#529—118no—
384#529—224no—
385C2×#126—221no—
386C2×#125—111no—
387C2×#124—111no—
388C2×#124—221no—
389C2×#123—221no—
390C2×C22⋊Q8—111no—
391C2×#121—111no—
392C2×#121—221no—
393C2×#121C2×D1111yescharacteristic
394C2×#121C2×D1111yescharacteristic
395C2×C4×Q8—111no—
396C2×C4×D4—111no—
397C2×C4×D4—111no—
398C2×C4×D4—111no—
399C2×C4×D4—221no—
400C2×C4×D4—221no—
401C2×#117—221no—
402C22×C42—111no—
403#478—118no—
404#478—118no—
405#475—118no—
406#474—118no—
407#469—118no—
408#469C2×D1118yescomplemented
409#468—118no—
410#468—118no—
411#463—118no—
412#463—118no—
413#460—118no—
414#459—118no—
415C2×#107—111no—
416C2×#107—111no—
417C2×#106—111no—
418C2×#106C2×D1111yescharacteristic
419#423—118no—
420C2×C4⋊C8—111no—
421C2×C4⋊C8—111no—
422C2×C4⋊C8—111no—
423C2×C4⋊C8—111no—
424C2×#103—111no—
425C2×#103—111no—
426C2×#102—111no—
427C2×#102—111no—
428C2×#102—111no—
429C2×#102—111no—
430C2×#102C2×D1111yescharacteristic
431C2×#102C2×D1111yescharacteristic
432C22×C11—22no—
433C22×C11—22no—
434C22×C11—22no—
435C22×C11—44no—
436C22×C11—42no—
437C22×C11—42no—
438C22×C11—42no—
439C22×C11—42no—
440C22×C11—42no—
441C22×C11—42no—
442C22×C11—84no—
443C22×C11—84no—
444C22×C11#53712yes—
445C22×C11C2×AGL(1,ℤ/8)12yes—
446C22×C11#57512yes—
447C22×C11C23×D411yescharacteristic
448C2×D11—42no—
449C2×D11—42no—
450C2×D11—42no—
451C2×D11—84no—
452C4×C11—22no—
453C4×C11—42no—
454C4×C11—42no—
455C4×C11#53712yes—
456C4×C11C2×H(5,𝔽2)11yescharacteristic
457C4×C11C2×2−1+411yescharacteristic
458Dic11—22no—
459Dic11—22no—
460Dic11—22no—
461Dic11—42no—
462Dic11—42no—
463Dic11—42no—
464Dic11C2×AGL(1,ℤ/8)14yes—
465C2×#41—228no—
466C2×#41—448no—
467C22×Q8—111no—
468C22×Q8—221no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—111no—
472C22×D4—221no—
473C22×D4—221no—
474C22×D4—221no—
475C22×D4C22×D1111yescharacteristic
476C22×D4C22×D1111yescharacteristic
477C23×C4—111no—
478C23×C4—111no—
479C23×C4—221no—
480C23×C4—221no—
481C23×C4—221no—
482C23×C4C22×D1111yescharacteristic
483C2×SD16—114no—
484C2×SD16—114no—
485C2×SD16—442no—
486C2×SD16—442no—
487C2×D8—42no—
488C2×D8—114no—
489C2×D8—442no—
490C2×D8C22×D1114yes—
491C2×M16—42no—
492C2×M16—114no—
493C2×M16—442no—
494C2×M16C22×D1114yes—
495C22×C8—111no—
496C22×C8—111no—
497C22×C8C22×D1111yescharacteristic
498C22×C8C22×D1111yescharacteristic
499C4⋊Q8—114no—
500C4⋊Q8—222no—
501#127—114no—
502#127—222no—
503#126—228no—
504#125—114no—
505#125—222no—
506#124—114no—
507#124—228no—
508#124—222no—
509#123—228no—
510C22⋊Q8—114no—
511C22⋊Q8—222no—
512#121—22no—
513#121—22no—
514#121—114no—
515#121—228no—
516#121—222no—
517#121C22×D1114yes—
518#121C22×D1114yes—
519C4×Q8—114no—
520C4×Q8—222no—
521C4×D4—114no—
522C4×D4—114no—
523C4×D4—114no—
524C4×D4—228no—
525C4×D4—222no—
526C4×D4—222no—
527C4×D4—222no—
528C4×D4—228no—
529#117—228no—
530C2×C4⋊C4—111no—
531C2×C4⋊C4—111no—
532C2×C4⋊C4—221no—
533C2×C4⋊C4—221no—
534C2×C4⋊C4—221no—
535C2×C4⋊C4—221no—
536C2×C4⋊C4—221no—
537C2×C4⋊C4C22×D1111yescharacteristic
538C2×C4⋊C4C22×D1111yescharacteristic
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—221no—
542C2×C22⋊C4—221no—
543C2×C22⋊C4—221no—
544C2×C22⋊C4—221no—
545C2×C22⋊C4—221no—
546C2×C22⋊C4—221no—
547C2×C22⋊C4—221no—
548C2×C42—111no—
549C2×C42—111no—
550C2×C42—114no—
551C2×C42—111no—
552C2×C42—111no—
553C2×C42—114no—
554C2×C42—221no—
555#107—114no—
556#107—114no—
557#106—114no—
558#106C22×D1114yes—
559C4⋊C8—114no—
560C4⋊C8—114no—
561C4⋊C8—114no—
562C4⋊C8—114no—
563#103—114no—
564#103—114no—
565#102—114no—
566#102—114no—
567#102—114no—
568#102—114no—
569#102C22×D1114yes—
570#102C22×D1114yes—
571C2×C11—42no—
572C2×C11—82no—
573C2×C11—82no—
574C2×C11#325114yescomplemented
575C2×C11C2×#53711yescharacteristic
576C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
577C2×C11C2×#57511yescharacteristic
578D11—82no—
579C24—21no—
580C24—21no—
581C24—221no—
582C24D4×D1111yescharacteristic
583#41—4432no—
584C2×Q8—112no—
585C2×Q8—224no—
586C2×Q8—221no—
587C2×Q8—222no—
588C2×Q8—222no—
589C2×Q8—444no—
590C2×D4—24no—
591C2×D4—24no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—44no—
599C2×D4—44no—
600C2×D4—112no—
601C2×D4—224no—
602C2×D4—224no—
603C2×D4—224no—
604C2×D4—221no—
605C2×D4—222no—
606C2×D4—222no—
607C2×D4—444no—
608C2×D4—444no—
609C2×D4—444no—
610C2×D4C23×D1112yes—
611C2×D4C23×D1112yes—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—111no—
617C22×C4—114no—
618C22×C4—111no—
619C22×C4—111no—
620C22×C4—111no—
621C22×C4—114no—
622C22×C4—224no—
623C22×C4—224no—
624C22×C4—224no—
625C22×C4—224no—
626C22×C4—221no—
627C22×C4—221no—
628C22×C4—221no—
629C22×C4—444no—
630C22×C4—444no—
631C22×C4—442no—
632C22×C4—444no—
633C22×C4D4×D1112yes—
634C22×C4D4×D1111yescharacteristic
635C22×C4C23×D1112yes—
636C22×C4C23×D1111yescharacteristic
637SD16—444no—
638SD16—444no—
639D8—44no—
640D8—444no—
641M16—44no—
642M16—444no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—112no—
646C2×C8—112no—
647C2×C8—222no—
648C2×C8—222no—
649C2×C8C23×D1112yes—
650C2×C8C23×D1112yes—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—112no—
654C4⋊C4—112no—
655C4⋊C4—224no—
656C4⋊C4—224no—
657C4⋊C4—224no—
658C4⋊C4—224no—
659C4⋊C4—221no—
660C4⋊C4—221no—
661C4⋊C4—224no—
662C4⋊C4C23×D1112yes—
663C4⋊C4C23×D1112yes—
664C22⋊C4—24no—
665C22⋊C4—24no—
666C22⋊C4—224no—
667C22⋊C4—224no—
668C22⋊C4—224no—
669C22⋊C4—224no—
670C22⋊C4—224no—
671C22⋊C4—224no—
672C22⋊C4—224no—
673C42—114no—
674C42—112no—
675C42—114no—
676C42—112no—
677C42—112no—
678C42—112no—
679C42—224no—
680C11C2×#325111yescharacteristic, complemented, Sylow
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—222no—
693C23—442no—
694C23—442no—
695C23—442no—
696C23C2×D4×D1112yes—
697C23C2×D4×D1111yescharacteristic
698Q8—222no—
699Q8—222no—
700Q8—448no—
701Q8—442no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—22no—
706D4—48no—
707D4—48no—
708D4—42no—
709D4—42no—
710D4—222no—
711D4—222no—
712D4—448no—
713D4—448no—
714D4—448no—
715D4—442no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—114no—
725C2×C4—112no—
726C2×C4—112no—
727C2×C4—112no—
728C2×C4—112no—
729C2×C4—228no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—448no—
737C2×C4—448no—
738C2×C4—444no—
739C2×C4—448no—
740C2×C4—442no—
741C2×C4—442no—
742C2×C4—442no—
743C2×C4C2×D4×D1112yes—
744C2×C4C2×D4×D1111yescharacteristic
745C2×C4#6703712yes—
746C2×C4#6704312yes—
747C2×C4C24×D1111yescharacteristic
748C8—22no—
749C8—22no—
750C8—222no—
751C8—222no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—44no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—84no—
763C22—84no—
764C22—442no—
765C22—442no—
766C22—442no—
767C22—884no—
768C22#1062312812yes—
769C22D11×AGL(1,ℤ/8)12yes—
770C22#1062330412yes—
771C22C22×D4×D1111yescharacteristic
772C4—22no—
773C4—42no—
774C4—42no—
775C4—114no—
776C4—222no—
777C4—222no—
778C4—222no—
779C4—442no—
780C4—442no—
781C4—442no—
782C4#1062312812yes—
783C4C2×#6703711yescharacteristic
784C4C2×#6704311yescharacteristic
785C2—42no—
786C2—82no—
787C2—82no—
788C2—882no—
789C2#1307997114yesdirect product factor
790C2C2×#1062312811yescharacteristic
791C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
792C2C2×#1062330411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#469C2
socleC23×C11C22×D4
hypercenterC2×#469D11
hypocenterC11C2×#3251
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#469

Complements

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

NH ≅ G/Ntype
1. C2×#10623127C2semidirect
2. C2×#10623131C2semidirect
3. #13079971C2direct (N × H)
4. C2×#10622467C2semidirect
5. C2×#10622484C2semidirect
6. C2×#10622379C2semidirect
7. C2×#10622372C2semidirect
8. C2×#10622652C2semidirect
9. C2×#10622747C2semidirect
10. C2×#10622655C2semidirect
11. C2×#10622375C2semidirect
12. C2×#10622400C2semidirect
13. C2×#10622766C2semidirect
14. C2×#10622763C2semidirect
15. C2×#10622731C2semidirect
16. C2×C11×#469C2semidirect
37. #10623131C22semidirect
39. #10623127C22semidirect
48. C11×#469C22semidirect
54. #10622766C22semidirect
55. #10622763C22semidirect
56. #10622747C22semidirect
57. #10622731C22semidirect
65. #10622655C22semidirect
66. #10622652C22semidirect
71. #10622484C22semidirect
72. #10622467C22semidirect
73. #10622400C22semidirect
74. #10622379C22semidirect
75. #10622375C22semidirect
76. #10622372C22semidirect
293. C2×#469D11semidirect
408. #469C2×D11semidirect
574. C2×C11#3251semidirect
680. C11C2×#3251semidirect
789. C2#13079971direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231272
C2×#106231312
#130799712
C2×#106224672
C2×#106224842
C2×#106223792
C2×#106223722
C2×#106226522
C2×#106227472
C2×#106226552
C2×#106223752
C2×#106224002
C2×#106227662
C2×#106227632
C2×#106227312
C2×C11×#4692
C2×#325111