Finite Group Databasebeta

← C2×#13081340 #15633467

Subgroups — C2×#13081340 #15633467

Order 2816.

2122 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623100C211yesmaximal, characteristic, complemented
2C2×#10623249C211yesmaximal, characteristic
3#13081340C2116yesmaximal, direct product factor
4C2×#10622684C211yesmaximal, characteristic, complemented
5C2×#10622377C211yesmaximal, characteristic, complemented
6C2×#10622373C211yesmaximal, characteristic, complemented
7C2×#10622376C211yesmaximal, characteristic, complemented
8C2×#10622460C211yesmaximal, characteristic, complemented
9C2×#10622372C211yesmaximal, characteristic, complemented
10C2×#10622776C211yesmaximal, characteristic, complemented
11C2×#10622776C211yesmaximal, characteristic, complemented
12C2×#10622441C211yesmaximal, characteristic, complemented
13C2×#10622777C211yesmaximal, characteristic, complemented
14C2×#10622639C211yesmaximal, characteristic, complemented
15C2×SD16×Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#460C211yesmaximal, characteristic, complemented
17C22×#4341—21no—
18C22×C11×SD16C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C2×C11×#127C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C2×Q8×Dic11C2211yescharacteristic
24C22×#4325C2211yescharacteristic
25C2×#66993C2211yescharacteristic
26C2×#66993C2211yescharacteristic
27C2×#66992—21no—
28C2×#66992—21no—
29C2×#66991—21no—
30C2×D4×Dic11C2211yescharacteristic
31C2×D4×Dic11C2211yescharacteristic
32#10623249—24no—
33#10623249C2218yes—
34#10623100—24no—
35#10623100C2218yescomplemented
36C2×#66943—21no—
37C2×#66943C2211yescharacteristic
38C2×#66941—21no—
39C2×#66941C2211yescharacteristic
40C2×C4×D44C2211yescharacteristic
41C2×#66923—21no—
42C2×#66923C2211yescharacteristic
43C2×C4×Dic22—21no—
44C2×C4×Dic22C2211yescharacteristic
45C11×#460C2218yescomplemented
46C2×C11×C4⋊C8C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×#66899C2211yescharacteristic
50C2×#66896C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54#10622777C2218yescomplemented
55#10622776C2218yescomplemented
56#10622776C2218yescomplemented
57SD16×Dic11C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×#66885C2211yescharacteristic
60C2×#66882C2211yescharacteristic
61C2×#66881C2211yescharacteristic
62C2×#66879C2211yescharacteristic
63C2×Dic11⋊C8C2211yescharacteristic
64C2×Dic11⋊C8C2211yescharacteristic
65C2×C8×Dic11C2211yescharacteristic
66#10622684C2218yescomplemented
67#10622639C2218yescomplemented
68C2×#66873C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×#66867C2211yescharacteristic
71#10622460C2218yescomplemented
72#10622441C2218yescomplemented
73#10622377C2218yescomplemented
74#10622376C2218yescomplemented
75#10622373C2218yescomplemented
76#10622372C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11C2311yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C23×Dic11—21no—
87C23×Dic11—21no—
88C2×#4341—28no—
89C2×#4341—48no—
90C22×D44C2311yescharacteristic
91C22×C4×D11—21no—
92C22×Dic22—21no—
93C22×Dic22D411yescharacteristic
94C2×C11×SD16—24no—
95C2×C11×SD16—24no—
96C2×C11×SD16C2314yes—
97C2×C11×SD16C2314yes—
98C22×C8×C11C2311yescharacteristic
99C22×C8×C11C2311yescharacteristic
100C11×#127—22no—
101C11×#127C2314yes—
102C4×Q8×C11—22no—
103C4×Q8×C11C2314yes—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C42×C11—21no—
107C2×C42×C11C2311yescharacteristic
108C2×C22⋊Dic11—21no—
109C2×C22⋊Dic11—21no—
110Q8×Dic11—22no—
111Q8×Dic11—22no—
112Q8×Dic11C2314yes—
113Q8×Dic11C2314yes—
114C2×#4325—24no—
115C2×#4325C2314yes—
116#66993—22no—
117#66993—22no—
118#66993C2314yes—
119#66993C2314yes—
120#66992—28no—
121#66992—28no—
122#66991—28no—
123D4×Dic11—22no—
124D4×Dic11—22no—
125D4×Dic11C2314yes—
126D4×Dic11C2314yes—
127C2×(C2×D11)⋊C4—21no—
128C2×C4⋊Dic11—21no—
129C2×C4⋊Dic11—21no—
130C2×C4⋊Dic11—21no—
131C2×C4⋊Dic11D411yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
133C2×C4⋊Dic11C2311yescharacteristic
134C2×C4⋊Dic11C2311yescharacteristic
135C2×Dic11⋊C4—21no—
136C2×Dic11⋊C4—21no—
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4D411yescharacteristic
140C2×Dic11⋊C4D411yescharacteristic
141C2×C4×Dic11—21no—
142C2×C4×Dic11—21no—
143C2×C4×Dic11C2311yescharacteristic
144C2×C4×Dic11C2311yescharacteristic
145C22×C11⋊C8C2311yescharacteristic
146C22×C11⋊C8C2311yescharacteristic
147#66943—28no—
148#66943—22no—
149#66943C2314yes—
150#66941—28no—
151#66941—22no—
152#66941C2314yes—
153C4×D44—22no—
154C4×D44C2314yes—
155#66923—22no—
156#66923—28no—
157#66923C2314yes—
158C4×Dic22—28no—
159C4×Dic22D414yes—
160C4×Dic22C2314yes—
161C11×C4⋊C8C2314yes—
162C11×#102C2314yes—
163C11×#102C2314yes—
164#66899C2314yes—
165#66896C2314yes—
166#66896C2314yes—
167#66896C2314yes—
168#66896C2314yes—
169#66885C2314yes—
170#66885C2314yes—
171#66882C2314yes—
172#66881C2314yes—
173#66879C2314yes—
174Dic11⋊C8C2314yes—
175Dic11⋊C8C2314yes—
176C8×Dic11C2314yes—
177#66873C2314yes—
178#66871C2314yes—
179#66867C2314yes—
180C2×#3368—111nomaximal, Sylow
181C24×C11—21no—
182C24×C11—21no—
183C23×D11—21no—
184C2×Q8×C11—21no—
185C2×Q8×C11—22no—
186C2×Q8×C11#4114yescomplemented
187C2×Q8×C11C2412yes—
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—24no—
191C2×D4×C11—24no—
192C2×D4×C11—22no—
193C2×D4×C11—22no—
194C2×D4×C11—22no—
195C2×D4×C11—22no—
196C2×D4×C11—44no—
197C2×D4×C11—82no—
198C2×D4×C11C2412yes—
199C2×D4×C11C2412yes—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2411yescharacteristic
205C2×C22⋊D11—24no—
206C2×C22⋊D11—24no—
207C2×C22⋊D11—24no—
208C2×C22⋊D11—24no—
209C2×C22⋊D11—44no—
210C2×C22⋊D11—44no—
211C2×C22⋊D11—82no—
212C2×C22⋊D11—82no—
213C22×Dic11—24no—
214C22×Dic11—24no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—44no—
219C22×Dic11—44no—
220C22×Dic11C2×D411yescharacteristic
221C22×Dic11C2×D411yescharacteristic
222C22×Dic11C2×D411yescharacteristic
223C22×Dic11C2×D411yescharacteristic
224#4341—432no—
225C2×D44—21no—
226C2×D44—22no—
227C2×D44—22no—
228C2×D44C2412yes—
229C2×C4×D11—24no—
230C2×C4×D11—44no—
231C2×Dic22—24no—
232C2×Dic22—24no—
233C2×Dic22—44no—
234C2×Dic22C2×D414yes—
235C11×SD16—28no—
236C11×SD16—28no—
237C2×C8×C11—22no—
238C2×C8×C11—22no—
239C2×C8×C11C2412yes—
240C2×C8×C11C2412yes—
241C11×C4⋊C4—24no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4C2412yes—
244C42×C11—24no—
245C42×C11C2×D412yes—
246C42×C11C2412yes—
247C22⋊Dic11—24no—
248C22⋊Dic11—24no—
249#4325—28no—
250(C2×D11)⋊C4—24no—
251C4⋊Dic11—24no—
252C4⋊Dic11—24no—
253C4⋊Dic11—24no—
254C4⋊Dic11—21no—
255C4⋊Dic11—21no—
256C4⋊Dic11—21no—
257C4⋊Dic11C2×D414yes—
258C4⋊Dic11C2412yes—
259C4⋊Dic11C2412yes—
260C4⋊Dic11C2412yes—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265Dic11⋊C4C2×D414yes—
266Dic11⋊C4C2×D414yes—
267C4×Dic11—24no—
268C4×Dic11—24no—
269C4×Dic11C2×D412yes—
270C4×Dic11C2×D412yes—
271C4×Dic11C2412yes—
272C4×Dic11C2412yes—
273C2×C11⋊C8—22no—
274C2×C11⋊C8—22no—
275C2×C11⋊C8C2412yes—
276C2×C11⋊C8C2412yes—
277C2×#557—111no—
278C2×#550—111no—
279#3368—1116no—
280C2×#490—111no—
281C2×#490—111no—
282C2×#486—111no—
283C2×#478—111no—
284C2×#478—111no—
285C2×#474—111no—
286C2×#460—111no—
287C2×#460—111no—
288C2×#460D1111yescharacteristic, complemented
289C2×#446—111no—
290C2×#440—111no—
291C2×#440—111no—
292C2×C4×SD16—111no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—42no—
296C23×C11—42no—
297C23×C11—42no—
298C23×C11—42no—
299C23×C11—42no—
300C23×C11—42no—
301C23×C11C22×D411yescharacteristic
302C22×D11—22no—
303C22×D11—42no—
304C22×D11—42no—
305C22×D11—42no—
306Q8×C11—24no—
307Q8×C11—22no—
308Q8×C11C2×#4114yescomplemented
309D4×C11—22no—
310D4×C11—22no—
311D4×C11—22no—
312D4×C11—22no—
313D4×C11—48no—
314D4×C11—42no—
315D4×C11—42no—
316D4×C11—84no—
317C2×C4×C11—24no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—42no—
323C2×C4×C11C22×D412yes—
324C2×C4×C11C22×D412yes—
325C2×C4×C11C22×D411yescharacteristic
326C2×C4×C11C2×#4112yes—
327C2×C4×C112−1+412yes—
328C2×C4×C11C2511yescharacteristic
329C22⋊D11—48no—
330C22⋊D11—48no—
331C22⋊D11—84no—
332C22⋊D11—84no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—48no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11—48no—
344C2×Dic11AGL(1,ℤ/8)14yes—
345C2×Dic11C22×D412yes—
346C2×Dic11C22×D412yes—
347C2×Dic11C22×D412yes—
348C2×Dic11C22×D412yes—
349D44—22no—
350D44—22no—
351D44—42no—
352C4×D11—48no—
353Dic22—28no—
354Dic22—48no—
355C8×C11—22no—
356C8×C11—22no—
357C11⋊C8—22no—
358C11⋊C8—22no—
359C22×#41—221no—
360C22×SD16—111no—
361C22×SD16C2×D1111yescharacteristic
362C22×SD16C2×D1111yescharacteristic
363#557—118no—
364#557—224no—
365#550—118no—
366#550—224no—
367C2×C4⋊Q8—111no—
368C2×C4⋊Q8—221no—
369C2×#127—111no—
370C2×#127—111no—
371C2×#127C2×D1111yescharacteristic
372C2×#125—111no—
373C2×#125—111no—
374C2×#125—221no—
375C2×#125—221no—
376C2×#121—221no—
377C2×#121—221no—
378C2×#121—221no—
379C2×C4×Q8—111no—
380C2×C4×Q8—111no—
381C2×C4×Q8—111no—
382C2×C4×Q8—221no—
383C2×C4×Q8C2×D1111yescharacteristic
384C2×C4×D4—111no—
385C2×C4×D4—111no—
386C2×C4×D4—111no—
387#490—118no—
388#490—118no—
389#486—118no—
390#478—118no—
391#478—118no—
392#474—118no—
393#460—118no—
394#460—118no—
395#460C2×D1118yescomplemented
396#446—118no—
397#440—118no—
398#440—118no—
399C4×SD16—118no—
400C2×#107—111no—
401C2×#107—111no—
402C2×#106—111no—
403C2×C4⋊C8—111no—
404C2×C4⋊C8—111no—
405C2×C4⋊C8C2×D1111yescharacteristic
406C2×#103—111no—
407C2×#102—111no—
408C2×#102—111no—
409C2×#102—111no—
410C2×#102—111no—
411C2×#102—111no—
412C2×#102—111no—
413C2×#102—111no—
414C2×#102C2×D1111yescharacteristic
415C2×#102C2×D1111yescharacteristic
416C2×#97—111no—
417C2×#97—111no—
418C2×C4×C8—111no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11—84no—
426C22×C11—84no—
427C22×C11#54812yes—
428C22×C11C2×AGL(1,ℤ/8)12yes—
429C22×C11#57712yes—
430C22×C11C23×D411yescharacteristic
431C2×D11—42no—
432C2×D11—42no—
433C2×D11—42no—
434C2×D11—84no—
435C4×C11—24no—
436C4×C11—22no—
437C4×C11—22no—
438C4×C11—42no—
439C4×C11#54812yes—
440C4×C11C22×#4111yescharacteristic
441C4×C11C2×2−1+411yescharacteristic
442Dic11—22no—
443Dic11—22no—
444Dic11—22no—
445Dic11—42no—
446Dic11—42no—
447Dic11—42no—
448Dic11C2×AGL(1,ℤ/8)14yes—
449C2×#41—228no—
450C2×#41—448no—
451C22×Q8—111no—
452C22×Q8—221no—
453C22×Q8C22×D1111yescharacteristic
454C22×D4—21no—
455C22×D4—21no—
456C22×D4—111no—
457C22×D4—221no—
458C22×D4—221no—
459C22×D4—221no—
460C22×D4—221no—
461C22×D4C22×D1111yescharacteristic
462C22×D4C22×D1111yescharacteristic
463C23×C4—221no—
464C23×C4—221no—
465C23×C4—221no—
466C2×SD16—24no—
467C2×SD16—24no—
468C2×SD16—114no—
469C2×SD16—224no—
470C2×SD16C22×D1114yes—
471C2×SD16C22×D1114yes—
472C22×C8—111no—
473C22×C8—111no—
474C22×C8C22×D1111yescharacteristic
475C22×C8C22×D1111yescharacteristic
476C4⋊Q8—114no—
477C4⋊Q8—222no—
478C4⋊Q8—228no—
479#127—22no—
480#127—114no—
481#127—114no—
482#127—222no—
483#127—222no—
484#127C22×D1114yes—
485#125—114no—
486#125—114no—
487#125—228no—
488#125—222no—
489#125—228no—
490#125—222no—
491#121—228no—
492#121—228no—
493#121—228no—
494C4×Q8—22no—
495C4×Q8—114no—
496C4×Q8—114no—
497C4×Q8—114no—
498C4×Q8—114no—
499C4×Q8—228no—
500C4×Q8—222no—
501C4×Q8—222no—
502C4×Q8C22×D1114yes—
503C4×D4—114no—
504C4×D4—114no—
505C4×D4—114no—
506C4×D4—222no—
507C4×D4—222no—
508C4×D4—222no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—111no—
511C2×C4⋊C4—111no—
512C2×C4⋊C4—111no—
513C2×C4⋊C4—111no—
514C2×C4⋊C4—111no—
515C2×C4⋊C4—111no—
516C2×C4⋊C4—221no—
517C2×C4⋊C4—221no—
518C2×C4⋊C4—221no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4—221no—
523C2×C4⋊C4C22×D1111yescharacteristic
524C2×C22⋊C4—221no—
525C2×C22⋊C4—221no—
526C2×C22⋊C4—221no—
527C2×C42—21no—
528C2×C42—111no—
529C2×C42—111no—
530C2×C42—221no—
531C2×C42—221no—
532C2×C42C22×D1111yescharacteristic
533#107—114no—
534#107—114no—
535#106—114no—
536C4⋊C8—114no—
537C4⋊C8—114no—
538C4⋊C8C22×D1114yes—
539#103—114no—
540#102—114no—
541#102—114no—
542#102—114no—
543#102—114no—
544#102—114no—
545#102—114no—
546#102—114no—
547#102C22×D1114yes—
548#102C22×D1114yes—
549#97—114no—
550#97—114no—
551C4×C8—114no—
552C2×C11—82no—
553C2×C11—82no—
554C2×C11#336814yescomplemented
555C2×C11C2×#54811yescharacteristic
556C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
557C2×C11C2×#57711yescharacteristic
558D11—82no—
559C24—21no—
560C24—21no—
561C24—221no—
562#41—4432no—
563C2×Q8—21no—
564C2×Q8—22no—
565C2×Q8—114no—
566C2×Q8—224no—
567C2×Q8—224no—
568C2×Q8—444no—
569C2×Q8#434114yescomplemented
570C2×Q8C23×D1112yes—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—44no—
580C2×D4—82no—
581C2×D4—112no—
582C2×D4—224no—
583C2×D4—224no—
584C2×D4—224no—
585C2×D4—224no—
586C2×D4—221no—
587C2×D4—222no—
588C2×D4—222no—
589C2×D4—444no—
590C2×D4—444no—
591C2×D4—882no—
592C2×D4—882no—
593C2×D4C23×D1112yes—
594C2×D4C23×D1112yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—111no—
598C22×C4—111no—
599C22×C4—111no—
600C22×C4—111no—
601C22×C4—224no—
602C22×C4—224no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—224no—
607C22×C4—444no—
608C22×C4—444no—
609C22×C4—444no—
610C22×C4D4×D1111yescharacteristic
611C22×C4D4×D1111yescharacteristic
612C22×C4C23×D1111yescharacteristic
613SD16—28no—
614SD16—28no—
615SD16—228no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—112no—
619C2×C8—112no—
620C2×C8—222no—
621C2×C8—222no—
622C2×C8C23×D1112yes—
623C2×C8C23×D1112yes—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—114no—
627C4⋊C4—114no—
628C4⋊C4—114no—
629C4⋊C4—112no—
630C4⋊C4—112no—
631C4⋊C4—112no—
632C4⋊C4—224no—
633C4⋊C4—224no—
634C4⋊C4—224no—
635C4⋊C4—224no—
636C4⋊C4—224no—
637C4⋊C4—221no—
638C4⋊C4—221no—
639C4⋊C4—221no—
640C4⋊C4—224no—
641C4⋊C4—224no—
642C4⋊C4C23×D1112yes—
643C22⋊C4—224no—
644C22⋊C4—224no—
645C22⋊C4—224no—
646C42—24no—
647C42—112no—
648C42—112no—
649C42—112no—
650C42—112no—
651C42—224no—
652C42—224no—
653C42D4×D1112yes—
654C42C23×D1112yes—
655C11C2×#336811yescharacteristic, complemented, Sylow
656C23—22no—
657C23—22no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—222no—
665C23—442no—
666C23—442no—
667C23—442no—
668C23C2×D4×D1111yescharacteristic
669Q8—24no—
670Q8—22no—
671Q8—228no—
672Q8—448no—
673Q8C2×#434114yescomplemented
674D4—22no—
675D4—22no—
676D4—22no—
677D4—22no—
678D4—48no—
679D4—42no—
680D4—42no—
681D4—84no—
682D4—222no—
683D4—222no—
684D4—448no—
685D4—448no—
686D4—442no—
687D4—884no—
688D4—884no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—42no—
695C2×C4—114no—
696C2×C4—112no—
697C2×C4—112no—
698C2×C4—112no—
699C2×C4—112no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—222no—
706C2×C4—448no—
707C2×C4—448no—
708C2×C4—448no—
709C2×C4—442no—
710C2×C4—442no—
711C2×C4—442no—
712C2×C4C2×D4×D1112yes—
713C2×C4C2×D4×D1112yes—
714C2×C4C2×D4×D1111yescharacteristic
715C2×C4C2×#434112yes—
716C2×C4#6704312yes—
717C2×C4C24×D1111yescharacteristic
718C8—22no—
719C8—22no—
720C8—222no—
721C8—222no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—84no—
729C22—84no—
730C22—442no—
731C22—442no—
732C22—442no—
733C22—884no—
734C22#1062312912yes—
735C22#1062329312yes—
736C22D11×AGL(1,ℤ/8)12yes—
737C22C22×D4×D1111yescharacteristic
738C4—22no—
739C4—24no—
740C4—22no—
741C4—42no—
742C4—114no—
743C4—222no—
744C4—222no—
745C4—222no—
746C4—442no—
747C4—442no—
748C4—442no—
749C4#1062312912yes—
750C4C22×#434111yescharacteristic
751C4C2×#6704311yescharacteristic
752C2—82no—
753C2—82no—
754C2—882no—
755C2#1308134014yesdirect product factor
756C2C2×#1062312911yescharacteristic
757C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
758C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#460C2
socleC23×C11C22×D4
prime radicalC2×#10623249C2
hypercenterC2×#460D11
hypocenterC11C2×#3368
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
1. C2×#10623100C2semidirect
3. #13081340C2direct (N × H)
4. C2×#10622684C2semidirect
5. C2×#10622377C2semidirect
6. C2×#10622373C2semidirect
7. C2×#10622376C2semidirect
8. C2×#10622460C2semidirect
9. C2×#10622372C2semidirect
10. C2×#10622776C2semidirect
11. C2×#10622776C2semidirect
12. C2×#10622441C2semidirect
13. C2×#10622777C2semidirect
14. C2×#10622639C2semidirect
15. C2×SD16×Dic11C2semidirect
16. C2×C11×#460C2semidirect
35. #10623100C22semidirect
45. C11×#460C22semidirect
54. #10622777C22semidirect
55. #10622776C22semidirect
56. #10622776C22semidirect
57. SD16×Dic11C22semidirect
66. #10622684C22semidirect
67. #10622639C22semidirect
71. #10622460C22semidirect
72. #10622441C22semidirect
73. #10622377C22semidirect
74. #10622376C22semidirect
75. #10622373C22semidirect
76. #10622372C22semidirect
186. C2×Q8×C11#41semidirect
288. C2×#460D11semidirect
308. Q8×C11C2×#41semidirect
395. #460C2×D11semidirect
554. C2×C11#3368semidirect
569. C2×Q8#4341semidirect
655. C11C2×#3368semidirect
673. Q8C2×#4341semidirect
755. C2#13081340direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231002
C2×#106232492
#130813402
C2×#106226842
C2×#106223772
C2×#106223732
C2×#106223762
C2×#106224602
C2×#106223722
C2×#106227762
C2×#106224412
C2×#106227772
C2×#106226392
C2×SD16×Dic112
C2×C11×#4602
C2×#336811