Finite Group Databasebeta

← C2×#13069106 #14755658

Subgroups — C2×#13069106 #14755658

Order 2816.

1894 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67002C211yesmaximal, characteristic
2C2×#10623052C211yesmaximal, characteristic, complemented
3C2×#10622849C211yesmaximal, characteristic, complemented
4C2×#10622614C211yesmaximal, characteristic, complemented
5#13069106C218yesmaximal, direct product factor
6C2×#10622171C211yesmaximal, characteristic, complemented
7C2×#10622169C211yesmaximal, characteristic, complemented
8C2×C11×#410C211yesmaximal, characteristic, complemented
9C22×C11×#41C2211yescharacteristic
10C23×D44C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×#67002—22no—
14C2×#67002—22no—
15C2×#67002—22no—
16C2×#67002—22no—
17C2×#67002C414yescomplemented
18C2×#67002C2214yes—
19C22×#4325C412yescomplemented
20C22×#4323C412yescomplemented
21C2×#66979C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24#10623052—22no—
25#10623052—22no—
26#10623052—22no—
27#10623052C2214yescomplemented
28C2×#66946—22no—
29C2×C22⋊C4×D11—22no—
30C2×C4×D44—22no—
31C11×#410—22no—
32C11×#410C2214yescomplemented
33C2×C11×#99—22no—
34#10622849—22no—
35#10622849C2214yescomplemented
36C2×#66901—22no—
37#10622614—22no—
38#10622614C2214yescomplemented
39C2×#66873—22no—
40#10622171C2214yescomplemented
41#10622169C2214yescomplemented
42C24×D11—21no—
43C2×C11×#41—21no—
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C2×C11×#41—21no—
48C2×C11×#41—21no—
49C2×C11×#41—21no—
50C2×C11×#41—21no—
51C2×C11×#41—21no—
52C2×C11×#41—21no—
53C2×C11×#41C2×C412yescomplemented
54C2×C11×#41C2312yes—
55C22×Q8×C11C2×C411yescharacteristic, complemented
56C22×D4×C11—21no—
57C22×D4×C11C2×C411yescharacteristic, complemented
58C23×C4×C11—21no—
59C23×C4×C11C2311yescharacteristic
60C22×D44—21no—
61C22×D44—21no—
62C22×D44—21no—
63C22×D44—21no—
64C22×D44—21no—
65C22×D44—21no—
66C22×D44—21no—
67C22×D44C2×C412yes—
68C22×D44C2×C412yes—
69C22×D44D412yes—
70C22×D44D412yes—
71C22×D44D412yes—
72C22×D44D412yes—
73C22×D44C2312yes—
74C22×C4×D11—24no—
75C11×#117—21no—
76C11×#117—21no—
77C11×#117—21no—
78C11×#117—21no—
79C11×#117—21no—
80C11×#117D412yes—
81C11×#117C2312yes—
82C11×#117C2312yes—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4D412yes—
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C2×C22⋊Dic11—21no—
90#67002—28no—
91#67002—28no—
92#67002—28no—
93#67002—28no—
94C2×#4325—24no—
95C2×#4325—24no—
96C2×#4325C2×C418yescomplemented
97C2×#4323—24no—
98C2×#4323—24no—
99C2×#4323C2×C418yescomplemented
100C2×(C2×D11)⋊C4—24no—
101#66979—21no—
102#66979—21no—
103#66979D412yes—
104#66979C2312yes—
105C2×C4⋊Dic11—21no—
106C2×C4×Dic11D412yes—
107C2×#4318—21no—
108C2×#4318—21no—
109C2×#4318—21no—
110C2×#4318—21no—
111C2×#4318—21no—
112C2×#4318—21no—
113C2×#4318—21no—
114C2×#4318—21no—
115C2×#4318—21no—
116C2×#4318C2×C412yescomplemented
117C2×#4318C2312yes—
118C2×#4318C2312yes—
119C22×C11⋊C8—21no—
120C22×C11⋊C8C2×C412yescomplemented
121#66946—28no—
122#66946—28no—
123C22⋊C4×D11—28no—
124C22⋊C4×D11—28no—
125C4×D44—28no—
126C4×D44—28no—
127C11×#99—28no—
128#66901—28no—
129#66873—28no—
130C2×#1904—111nomaximal, Sylow
131C24×C11—21no—
132C24×C11C2×D411yescharacteristic
133C23×D11—22no—
134C23×D11—22no—
135C23×D11—22no—
136C23×D11—22no—
137C23×D11—22no—
138C23×D11—22no—
139C23×D11—22no—
140C23×D11—84no—
141C11×#41—22no—
142C11×#41—22no—
143C11×#41—22no—
144C11×#41—22no—
145C11×#41—22no—
146C11×#41—22no—
147C11×#41—22no—
148C11×#41—22no—
149C11×#41—41no—
150C11×#41—41no—
151C11×#41—41no—
152C11×#41—41no—
153C11×#41—41no—
154C11×#41—41no—
155C11×#41—41no—
156C11×#41—41no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11C22×C412yescomplemented
163C2×D4×C11—22no—
164C2×D4×C11—22no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—41no—
171C2×D4×C11—41no—
172C2×D4×C11—41no—
173C2×D4×C11—41no—
174C2×D4×C11C22×C412yescomplemented
175C22×C4×C11—21no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—41no—
180C22×C4×C11—41no—
181C22×C4×C11—41no—
182C22×C4×C11—41no—
183C22×C4×C11—41no—
184C22×C4×C11C22×C411yescharacteristic
185C22×C4×C11C22×C411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11#4111yescharacteristic
194C22×C4×C11#4111yescharacteristic
195C22×C4×C11#4111yescharacteristic
196C22×C4×C11#4111yescharacteristic
197C22×C4×C11C2411yescharacteristic
198C22×Dic11—22no—
199C2×D44—22no—
200C2×D44—22no—
201C2×D44—22no—
202C2×D44—22no—
203C2×D44—22no—
204C2×D44—22no—
205C2×D44—22no—
206C2×D44—22no—
207C2×D44—22no—
208C2×D44—22no—
209C2×D44—22no—
210C2×D44—22no—
211C2×D44—22no—
212C2×D44—22no—
213C2×D44—22no—
214C2×D44—22no—
215C2×D44—22no—
216C2×D44—22no—
217C2×D44—22no—
218C2×D44—22no—
219C2×D44—22no—
220C2×D44C22⋊C414yes—
221C2×D44C22⋊C414yes—
222C2×D44C22⋊C414yes—
223C2×D44C22⋊C414yes—
224C2×D44C22×C414yes—
225C2×D44C2×D414yes—
226C2×D44C2×D414yes—
227C2×C4×D11—216no—
228C2×C4×D11—88no—
229C11×C4⋊C4—22no—
230C11×C4⋊C4—22no—
231C11×C4⋊C4—22no—
232C11×C4⋊C4—41no—
233C11×C22⋊C4—22no—
234C11×C22⋊C4—22no—
235C11×C22⋊C4—41no—
236C11×C22⋊C4C2×D414yes—
237C42×C11—22no—
238C42×C11—22no—
239C42×C11—22no—
240C42×C11—41no—
241C22⋊Dic11—22no—
242C22⋊Dic11—22no—
243#4325—216no—
244#4323—216no—
245(C2×D11)⋊C4—216no—
246C4⋊Dic11—22no—
247C4⋊Dic11—22no—
248C4×Dic11—22no—
249C4×Dic11C2×D414yes—
250#4318—22no—
251#4318—22no—
252#4318—22no—
253#4318—22no—
254#4318—22no—
255#4318—22no—
256#4318—41no—
257#4318—41no—
258C2×C11⋊C8—22no—
259C2×C11⋊C8—22no—
260C2×C11⋊C8—22no—
261C2×C11⋊C8—41no—
262C2×C11⋊C8—41no—
263C2×C11⋊C8C22×C414yescomplemented
264C22×AGL(1,ℤ/8)—111no—
265C2×#518—111no—
266C2×#421—111no—
267C2×#418—111no—
268C2×#410D1111yescharacteristic, complemented
269#1904—118no—
270C2×#344—111no—
271C2×H(3,ℤ/4)—111no—
272C23×C11—22no—
273C23×C11—42no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—82no—
277C23×C11C4×D411yescharacteristic
278C23×C11C4×D411yescharacteristic
279C23×C11#12011yescharacteristic
280C23×C11#12011yescharacteristic
281C23×C11#12111yescharacteristic
282C23×C11#12111yescharacteristic
283C23×C11C22×D411yescharacteristic
284C22×D11—24no—
285C22×D11—24no—
286C22×D11—24no—
287C22×D11—24no—
288C22×D11—24no—
289C22×D11—24no—
290C22×D11—24no—
291C22×D11—48no—
292C22×D11—84no—
293C22×D11—84no—
294C22×D11—84no—
295C22×D11—84no—
296C22×D11—84no—
297C22×D11—84no—
298Q8×C11—22no—
299Q8×C11—22no—
300Q8×C11—41no—
301Q8×C11—41no—
302D4×C11—22no—
303D4×C11—22no—
304D4×C11—42no—
305D4×C11—42no—
306D4×C11—42no—
307D4×C11—42no—
308D4×C11—41no—
309D4×C11—41no—
310C2×C4×C11—22no—
311C2×C4×C11—24no—
312C2×C4×C11—44no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11—42no—
319C2×C4×C11—42no—
320C2×C4×C11—82no—
321C2×C4×C11C2×C22⋊C411yescharacteristic
322C2×C4×C11C2×C22⋊C411yescharacteristic
323C2×C4×C11C2×C22⋊C411yescharacteristic
324C2×C4×C11C2×C22⋊C411yescharacteristic
325C2×C4×C11C4×D411yescharacteristic
326C2×C4×C11C4×D411yescharacteristic
327C2×C4×C11C4×D411yescharacteristic
328C2×C4×C11C4×D411yescharacteristic
329C2×C4×C11C4×D411yescharacteristic
330C2×C4×C11C4×D411yescharacteristic
331C2×C4×C11#12011yescharacteristic
332C2×C4×C11#12011yescharacteristic
333C2×C4×C11#12111yescharacteristic
334C2×C4×C11#12111yescharacteristic
335C2×C4×C11#12111yescharacteristic
336C2×C4×C11#12111yescharacteristic
337C2×C4×C11#12111yescharacteristic
338C2×C4×C11#12111yescharacteristic
339C2×C4×C11#12311yescharacteristic
340C2×C4×C11#12311yescharacteristic
341C2×C4×C11#12311yescharacteristic
342C2×C4×C11#12311yescharacteristic
343C2×C4×C11C23×C411yescharacteristic
344C2×C4×C11C22×D411yescharacteristic
345C2×C4×C11C22×D411yescharacteristic
346C2×C4×C11C22×D411yescharacteristic
347C2×C4×C11C2×#4111yescharacteristic
348C2×C4×C11C2×#4111yescharacteristic
349C2×Dic11—24no—
350C2×Dic11—44no—
351D44—24no—
352D44—24no—
353D44—24no—
354D44—24no—
355D44—24no—
356D44—24no—
357D44—24no—
358D44C2×C22⋊C418yes—
359C4×D11—816no—
360C11⋊C8—24no—
361C11⋊C8—42no—
362C22×#41C2×D1111yescharacteristic
363C23×D4—111no—
364C2×AGL(1,ℤ/8)—114no—
365C2×AGL(1,ℤ/8)—114no—
366C2×AGL(1,ℤ/8)—222no—
367C2×AGL(1,ℤ/8)—222no—
368C2×AGL(1,ℤ/8)—222no—
369C2×AGL(1,ℤ/8)—222no—
370C22×SD16—112no—
371C22×D8—112no—
372C22×M16—111no—
373C22×M16—111no—
374#518—114no—
375#518—222no—
376#518—222no—
377#518—222no—
378C2×C4×D4—222no—
379C2×C4×D4—222no—
380C2×#117—111no—
381C2×#117C2×D1111yescharacteristic
382C2×#117C2×D1111yescharacteristic
383C22×C22⋊C4—222no—
384#421—114no—
385#421—222no—
386C2×#104—222no—
387#418—114no—
388#418—222no—
389C2×#102—222no—
390#410—22no—
391#410C2×D1114yescomplemented
392C2×#99—22no—
393#344—114no—
394H(3,ℤ/4)—114no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—22no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—42no—
403C22×C11—82no—
404C22×C11—82no—
405C22×C11—82no—
406C22×C11#38611yescharacteristic
407C22×C11#38611yescharacteristic
408C22×C11#38611yescharacteristic
409C22×C11#38611yescharacteristic
410C22×C11C2×C4×D411yescharacteristic
411C22×C11C2×#12011yescharacteristic
412C22×C11C2×#12111yescharacteristic
413C2×D11—28no—
414C2×D11—48no—
415C2×D11—48no—
416C2×D11—48no—
417C2×D11—84no—
418C2×D11—84no—
419C2×D11—84no—
420C2×D11—84no—
421C4×C11—44no—
422C4×C11—42no—
423C4×C11—82no—
424C4×C11#38611yescharacteristic
425C4×C11#38611yescharacteristic
426C4×C11#38611yescharacteristic
427C4×C11#38611yescharacteristic
428C4×C11C22×C22⋊C411yescharacteristic
429C4×C11C2×C4×D411yescharacteristic
430C4×C11C2×#12111yescharacteristic
431C4×C11C2×#12311yescharacteristic
432Dic11—44no—
433C25—221no—
434C2×#41—21no—
435C2×#41—21no—
436C2×#41—21no—
437C2×#41—21no—
438C2×#41—21no—
439C2×#41—21no—
440C2×#41—21no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41—21no—
444C2×#41C4×D1112yescomplemented
445C2×#41C22×D1112yes—
446C22×Q8C4×D1111yescharacteristic, complemented
447C22×D4—21no—
448C22×D4—112no—
449C22×D4—112no—
450C22×D4—112no—
451C22×D4—112no—
452C22×D4—112no—
453C22×D4—112no—
454C22×D4—112no—
455C22×D4—221no—
456C22×D4—221no—
457C22×D4—221no—
458C22×D4—221no—
459C22×D4—221no—
460C22×D4—221no—
461C22×D4—221no—
462C22×D4C4×D1111yescharacteristic, complemented
463C23×C4—21no—
464C23×C4—224no—
465C23×C4C22×D1111yescharacteristic
466AGL(1,ℤ/8)—228no—
467AGL(1,ℤ/8)—228no—
468AGL(1,ℤ/8)—228no—
469AGL(1,ℤ/8)—228no—
470C2×SD16—118no—
471C2×SD16—224no—
472C2×SD16—224no—
473C2×D8—118no—
474C2×D8—224no—
475C2×D8—224no—
476C2×M16—112no—
477C2×M16—112no—
478C2×M16—112no—
479C2×M16—221no—
480C2×M16—221no—
481C2×M16—221no—
482C2×M16—221no—
483C2×M16—221no—
484C2×M16—221no—
485C2×M16—221no—
486C2×M16—221no—
487C2×M16—221no—
488C22×C8—112no—
489C22×C8—221no—
490C4×D4—228no—
491C4×D4—228no—
492C4×D4—228no—
493C4×D4—228no—
494#117—21no—
495#117—21no—
496#117—21no—
497#117—21no—
498#117—21no—
499#117—112no—
500#117—112no—
501#117—221no—
502#117—221no—
503#117C22⋊D1112yes—
504#117C22×D1112yes—
505#117C22×D1112yes—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—221no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—228no—
511C2×C22⋊C4—224no—
512C2×C22⋊C4—221no—
513C2×C22⋊C4—228no—
514C2×C22⋊C4C22⋊D1112yes—
515C2×C42—21no—
516C2×C42—21no—
517C2×C42—112no—
518#104—228no—
519#102—228no—
520#99—28no—
521C2×C11—21no—
522C2×C11—21no—
523C2×C11—21no—
524C2×C11—21no—
525C2×C11—21no—
526C2×C11—21no—
527C2×C11—82no—
528C2×C11#190412yescomplemented
529C2×C11C2×#38611yescharacteristic
530D11—48no—
531C24—21no—
532C24—222no—
533C24—222no—
534C24—222no—
535C24—222no—
536C24—222no—
537C24—222no—
538C24—222no—
539C24—884no—
540C24C2×C22⋊D1111yescharacteristic
541#41—22no—
542#41—22no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—41no—
550#41—41no—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8C2×C4×D1112yescomplemented
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—41no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—114no—
575C2×D4—114no—
576C2×D4—114no—
577C2×D4—114no—
578C2×D4—114no—
579C2×D4—114no—
580C2×D4—114no—
581C2×D4—222no—
582C2×D4—222no—
583C2×D4—222no—
584C2×D4—222no—
585C2×D4—222no—
586C2×D4—222no—
587C2×D4—222no—
588C2×D4—222no—
589C2×D4—222no—
590C2×D4—222no—
591C2×D4—222no—
592C2×D4—222no—
593C2×D4—222no—
594C2×D4—222no—
595C2×D4—222no—
596C2×D4—222no—
597C2×D4—222no—
598C2×D4—222no—
599C2×D4—222no—
600C2×D4—222no—
601C2×D4—222no—
602C2×D4C2×C4×D1112yescomplemented
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—2216no—
613C22×C4—222no—
614C22×C4—888no—
615C22×C4C2×C4×D1111yescharacteristic
616C22×C4C2×C4×D1111yescharacteristic
617C22×C4#433911yescharacteristic
618C22×C4#433911yescharacteristic
619C22×C4D4×D1111yescharacteristic
620C22×C4D4×D1111yescharacteristic
621C22×C4D4×D1111yescharacteristic
622C22×C4D4×D1111yescharacteristic
623C22×C4D4×D1111yescharacteristic
624C22×C4D4×D1111yescharacteristic
625C22×C4#434111yescharacteristic
626C22×C4#434111yescharacteristic
627C22×C4C2×C22⋊D1111yescharacteristic
628C22×C4C23×D1111yescharacteristic
629SD16—2216no—
630D8—2216no—
631M16—222no—
632M16—222no—
633M16—222no—
634M16—222no—
635M16—222no—
636M16—222no—
637M16—441no—
638M16—441no—
639C2×C8—114no—
640C2×C8—222no—
641C2×C8—222no—
642C2×C8—222no—
643C2×C8—441no—
644C2×C8—441no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—41no—
649C4⋊C4—222no—
650C4⋊C4—222no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—41no—
654C22⋊C4—2216no—
655C22⋊C4—222no—
656C22⋊C4—222no—
657C22⋊C4C2×C22⋊D1114yes—
658C42—22no—
659C42—22no—
660C42—22no—
661C42—41no—
662C42—114no—
663C42—222no—
664C11C2×#190411yescharacteristic, complemented, Sylow
665C23—22no—
666C23—42no—
667C23—41no—
668C23—41no—
669C23—82no—
670C23—224no—
671C23—224no—
672C23—224no—
673C23—224no—
674C23—224no—
675C23—224no—
676C23—224no—
677C23—448no—
678C23—884no—
679C23—884no—
680C23—884no—
681C23—884no—
682C23—884no—
683C23—884no—
684C23C4×C22⋊D1111yescharacteristic
685C23C4×C22⋊D1111yescharacteristic
686C23#6699011yescharacteristic
687C23#6699011yescharacteristic
688C23#6699111yescharacteristic
689C23#6699111yescharacteristic
690C23C22×C22⋊D1111yescharacteristic
691Q8—22no—
692Q8—22no—
693Q8—41no—
694Q8—41no—
695D4—22no—
696D4—22no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—41no—
702D4—41no—
703D4—118no—
704D4—224no—
705D4—224no—
706D4—224no—
707D4—224no—
708D4—224no—
709D4—224no—
710D4—224no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—44no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—82no—
722C2×C4—224no—
723C2×C4—444no—
724C2×C4—8816no—
725C2×C4C22⋊C4×D1111yescharacteristic
726C2×C4C22⋊C4×D1111yescharacteristic
727C2×C4C22⋊C4×D1111yescharacteristic
728C2×C4C22⋊C4×D1111yescharacteristic
729C2×C4(C22⋊D11)⋊C411yescharacteristic
730C2×C4(C22⋊D11)⋊C411yescharacteristic
731C2×C4(C22⋊D11)⋊C411yescharacteristic
732C2×C4(C22⋊D11)⋊C411yescharacteristic
733C2×C4#6693611yescharacteristic
734C2×C4#6693611yescharacteristic
735C2×C4#6693611yescharacteristic
736C2×C4#6693611yescharacteristic
737C2×C4#6693711yescharacteristic
738C2×C4#6693711yescharacteristic
739C2×C4#6693711yescharacteristic
740C2×C4#6693711yescharacteristic
741C2×C4C4×C22⋊D1111yescharacteristic
742C2×C4C4×C22⋊D1111yescharacteristic
743C2×C4#6699011yescharacteristic
744C2×C4#6699011yescharacteristic
745C2×C4#6699111yescharacteristic
746C2×C4#6699111yescharacteristic
747C2×C4C22×C4×D1111yescharacteristic
748C2×C4C2×#433911yescharacteristic
749C2×C4C2×D4×D1111yescharacteristic
750C2×C4C2×D4×D1111yescharacteristic
751C2×C4C2×D4×D1111yescharacteristic
752C2×C4C2×#434111yescharacteristic
753C8—224no—
754C8—442no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—228no—
767C22—448no—
768C22—448no—
769C22—448no—
770C22—884no—
771C22—884no—
772C22—884no—
773C22—884no—
774C22#1062256911yescharacteristic
775C22#1062256911yescharacteristic
776C22#1062256911yescharacteristic
777C22#1062256911yescharacteristic
778C22C2×C4×C22⋊D1111yescharacteristic
779C22C2×#6699011yescharacteristic
780C22C2×#6699111yescharacteristic
781C4—44no—
782C4—42no—
783C4—82no—
784C4—444no—
785C4#1062256911yescharacteristic
786C4#1062256911yescharacteristic
787C4#1062256911yescharacteristic
788C4#1062256911yescharacteristic
789C4C2×C22⋊C4×D1111yescharacteristic
790C4C2×(C22⋊D11)⋊C411yescharacteristic
791C4C2×#6693611yescharacteristic
792C4C2×#6693711yescharacteristic
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—82no—
800C2—448no—
801C2#1306910612yesdirect product factor
802C2C2×#1062256911yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#410C2
socleC22×C11#386
prime radicalC22×#67002C2
cosocleC22×C4×C11C24
hypercenterC2×#410D11
hypocenterC11C2×#1904
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. C2×#10623052C2semidirect
3. C2×#10622849C2semidirect
4. C2×#10622614C2semidirect
5. #13069106C2direct (N × H)
6. C2×#10622171C2semidirect
7. C2×#10622169C2semidirect
8. C2×C11×#410C2semidirect
17. C2×#67002C4semidirect
19. C22×#4325C4semidirect
20. C22×#4323C4semidirect
27. #10623052C22semidirect
32. C11×#410C22semidirect
35. #10622849C22semidirect
38. #10622614C22semidirect
40. #10622171C22semidirect
41. #10622169C22semidirect
53. C2×C11×#41C2×C4semidirect
55. C22×Q8×C11C2×C4semidirect
57. C22×D4×C11C2×C4semidirect
96. C2×#4325C2×C4semidirect
99. C2×#4323C2×C4semidirect
116. C2×#4318C2×C4semidirect
120. C22×C11⋊C8C2×C4semidirect
162. C2×Q8×C11C22×C4semidirect
174. C2×D4×C11C22×C4semidirect
263. C2×C11⋊C8C22×C4semidirect
268. C2×#410D11semidirect
391. #410C2×D11semidirect
444. C2×#41C4×D11semidirect
446. C22×Q8C4×D11semidirect
462. C22×D4C4×D11semidirect
528. C2×C11#1904semidirect
562. C2×Q8C2×C4×D11semidirect
602. C2×D4C2×C4×D11semidirect
664. C11C2×#1904semidirect
801. C2#13069106direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670022
C2×#106230522
C2×#106228492
C2×#106226142
#130691062
C2×#106221712
C2×#106221692
C2×C11×#4102
C2×#190411