Finite Group Databasebeta

← C4×#10622419 #14759366

Subgroups — C4×#10622419 #14759366

Order 2816.

1532 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
2C2×#10622419C211yesmaximal, characteristic
3C2×C4×#4314C211yesmaximal, characteristic, complemented
4C2×C4×#4325C211yesmaximal, characteristic, complemented
5C4×#66948C211yesmaximal, characteristic
6#13068972C211yesmaximal, characteristic, complemented
7#13068969C211yesmaximal, characteristic, complemented
8#13068932C211yesmaximal, characteristic
9#13068886C211yesmaximal, characteristic, complemented
10#13068885C211yesmaximal, characteristic, complemented
11#13068810C211yesmaximal, characteristic, complemented
12#13068549C211yesmaximal, characteristic, complemented
13C4×#66874C211yesmaximal, characteristic, complemented
14C4×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
15C4×C11×#103C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C22×#4314C2211yescharacteristic
21C4×Q8×D11—24no—
22C4×Q8×D11—24no—
23C2×#66948C2211yescharacteristic
24C2×C4⋊C4×D11—21no—
25C2×C4⋊C4×D11C2211yescharacteristic
26C2×#66940—21no—
27C2×#66940C2211yescharacteristic
28C2×C4×D44—21no—
29C2×C4×D44C2211yescharacteristic
30C2×C42×D11—21no—
31C2×C42×D11C2211yescharacteristic
32C2×C4×Dic22—21no—
33C2×C4×Dic22C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C2×C4×C8×C11C2211yescharacteristic
37C4×C11×C4⋊C4C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×#66885C2211yescharacteristic
40C2×(C2×D11)⋊C8C2211yescharacteristic
41C2×(C2×D11)⋊C8C2211yescharacteristic
42C2×#66881C2211yescharacteristic
43C2×#66880C2211yescharacteristic
44C4×#4325—24no—
45#10622601C2211yescharacteristic
46#10622600C2211yescharacteristic
47#10622598C2211yescharacteristic
48C2×#66874C2211yescharacteristic
49C2×#66874C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51C2×#66872C2211yescharacteristic
52C4×(C2×D11)⋊C4—21no—
53C2×C4×C11⋊C8C2211yescharacteristic
54#10622419C418yesdirect product factor
55C4×#4314—24no—
56#10622283—21no—
57#10622278—21no—
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622188C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622167C2211yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C2×Q8×D11—22no—
66C2×Q8×D11—22no—
67C2×Q8×D11—22no—
68C2×Q8×D11—22no—
69C2×Q8×D11—22no—
70C2×Q8×D11C2×C414yescomplemented
71C22×D44—21no—
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×C4×D11—21no—
75C22×C4×D11—21no—
76C22×C4×D11D411yescharacteristic
77C22×C4×D11D411yescharacteristic
78C22×C4×D11C2311yescharacteristic
79C22×Dic22—21no—
80C22×Dic22C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C4×Q8×C11—22no—
84C4×Q8×C11D414yescomplemented
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C2×C42×C11C2311yescharacteristic
92Q8×Dic11—22no—
93Q8×Dic11—22no—
94C2×#4325—22no—
95C2×#4325—22no—
96C2×#4325C2×C414yescomplemented
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4—21no—
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×Dic11⋊C4—21no—
107C2×Dic11⋊C4—21no—
108C2×Dic11⋊C4—21no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11—21no—
112C2×C4×Dic11D411yescharacteristic
113C2×C4×Dic11D411yescharacteristic
114C2×C4×Dic11C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C2×#4314—22no—
118C2×#4314—22no—
119C2×#4314C2×C414yescomplemented
120#66948—22no—
121#66948C2×C414yes—
122C4⋊C4×D11—28no—
123C4⋊C4×D11—22no—
124C4⋊C4×D11—22no—
125#66940—28no—
126#66940—22no—
127#66940—22no—
128C4×D44—22no—
129C4×D44—22no—
130C4×D44—44no—
131C42×D11—28no—
132C42×D11—22no—
133C42×D11—22no—
134C4×Dic22—28no—
135C4×Dic22—22no—
136C4×Dic22D414yescomplemented
137C11×#103—22no—
138C11×#103C2×C414yescomplemented
139C4×C8×C11—22no—
140C11×#95—21no—
141#66899—22no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144#66885—22no—
145(C2×D11)⋊C8—22no—
146(C2×D11)⋊C8C2×C414yescomplemented
147#66881—22no—
148#66880—22no—
149#66874—22no—
150#66874C2×C414yescomplemented
151#66873—22no—
152#66872—22no—
153C4×C11⋊C8—22no—
154C4×#448—111nomaximal, Sylow
155C23×D11—21no—
156C23×D11C2×D411yescharacteristic
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11C22×C412yes—
161C2×Q8×C11C2×D412yes—
162C2×Q8×C11#4112yes—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2411yescharacteristic
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11C2×D411yescharacteristic
174C22×Dic11C2×D411yescharacteristic
175C22×Dic11C2×D411yescharacteristic
176Q8×D11—28no—
177Q8×D11—28no—
178Q8×D11—28no—
179Q8×D11—28no—
180C2×D44—24no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—21no—
184C2×D44—21no—
185C2×D44—21no—
186C2×D44—42no—
187C2×D44—42no—
188C2×D44C22×C412yes—
189C2×C4×D11—24no—
190C2×C4×D11—24no—
191C2×C4×D11—24no—
192C2×C4×D11—24no—
193C2×C4×D11—22no—
194C2×C4×D11—22no—
195C2×C4×D11—22no—
196C2×C4×D11—22no—
197C2×C4×D11—21no—
198C2×C4×D11—21no—
199C2×C4×D11—21no—
200C2×C4×D11—21no—
201C2×C4×D11—41no—
202C2×C4×D11—42no—
203C2×C4×D11—42no—
204C2×C4×D11—42no—
205C2×C4×D11—42no—
206C2×C4×D11—42no—
207C2×C4×D11SD1614yescomplemented
208C2×C4×D11C22×C412yes—
209C2×C4×D11#4112yes—
210C2×Dic22—24no—
211C2×Dic22—24no—
212C2×Dic22—24no—
213C2×Dic22—21no—
214C2×Dic22—21no—
215C2×Dic22—21no—
216C2×Dic22C22×C412yes—
217C2×Dic22C2×D412yes—
218C2×Dic22#4112yes—
219C2×C8×C11—21no—
220C2×C8×C11—21no—
221C2×C8×C11—21no—
222C2×C8×C11—21no—
223C2×C8×C11—21no—
224C2×C8×C11C22×C412yes—
225C11×C4⋊C4—24no—
226C11×C4⋊C4—21no—
227C11×C4⋊C4—21no—
228C11×C4⋊C4—21no—
229C11×C4⋊C4—21no—
230C11×C4⋊C4C22×C412yes—
231C11×C4⋊C4C2×D412yes—
232C42×C11—24no—
233C42×C11—42no—
234C42×C11C2×D412yes—
235C42×C11C2×D412yes—
236#4325—28no—
237(C2×D11)⋊C4—24no—
238(C2×D11)⋊C4—42no—
239(C2×D11)⋊C4—42no—
240(C2×D11)⋊C4—42no—
241(C2×D11)⋊C4—42no—
242C4⋊Dic11—24no—
243C4⋊Dic11—21no—
244C4⋊Dic11—21no—
245C4⋊Dic11—21no—
246C4⋊Dic11—42no—
247C4⋊Dic11C2×D412yes—
248Dic11⋊C4—24no—
249Dic11⋊C4—24no—
250Dic11⋊C4—24no—
251C4×Dic11—24no—
252C4×Dic11—24no—
253C4×Dic11—22no—
254C4×Dic11—24no—
255C4×Dic11—22no—
256C4×Dic11—21no—
257C4×Dic11—21no—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8—21no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8C22×C412yes—
264#4314—28no—
265C22×C4×Q8—111no—
266C2×#448—111no—
267C2×C4×SD16—111no—
268C2×C4×SD16—111no—
269C4×#121—111no—
270#1880—111no—
271#1880—111no—
272#1874—111no—
273#1865—111no—
274#1865—111no—
275#1853—111no—
276#1787—111no—
277C4×#103—111no—
278C4×#103D1111yescharacteristic, complemented
279C4×C22⋊C8—111no—
280C23×C11C22×D411yescharacteristic
281C22×D11—21no—
282C22×D11—21no—
283C22×D11—21no—
284C22×D11—21no—
285C22×D11—22no—
286C22×D11—41no—
287C22×D11—41no—
288C22×D11—41no—
289C22×D11—41no—
290C22×D11—41no—
291C22×D11—41no—
292C22×D11C4×D412yes—
293C22×D11C2×SD1612yes—
294C22×D11#13512yes—
295Q8×C11—22no—
296Q8×C11—22no—
297Q8×C11—22no—
298Q8×C11C4×D414yescomplemented
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11#12012yes—
314C2×C4×C11#12012yes—
315C2×C4×C11C2×SD1612yes—
316C2×C4×C11#13712yes—
317C2×C4×C11C23×C411yescharacteristic
318C2×C4×C11C22×D411yescharacteristic
319C2×C4×C11C22×D411yescharacteristic
320C2×C4×C11C2×#4111yescharacteristic
321C2×C4×C11C2×#4111yescharacteristic
322C2×C4×C11C2×#4111yescharacteristic
323C2×Dic11—22no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—22no—
327C2×Dic11—21no—
328C2×Dic11—22no—
329C2×Dic11—21no—
330C2×Dic11—21no—
331C2×Dic11—22no—
332C2×Dic11—21no—
333C2×Dic11—21no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11C4×D412yes—
340C2×Dic11C2×SD1612yes—
341D44—22no—
342D44—22no—
343D44—48no—
344D44—41no—
345D44—41no—
346C4×D11—216no—
347C4×D11—22no—
348C4×D11—22no—
349C4×D11—22no—
350C4×D11—22no—
351C4×D11—28no—
352C4×D11—44no—
353C4×D11—48no—
354C4×D11—84no—
355Dic22—216no—
356Dic22—22no—
357Dic22—22no—
358Dic22—22no—
359Dic22C4×D414yescomplemented
360C8×C11—22no—
361C8×C11—41no—
362C11⋊C8—22no—
363C11⋊C8—41no—
364C23×Q8—111no—
365C22×SD16—111no—
366C22×SD16—111no—
367C2×#121—111no—
368C2×C4×Q8—111no—
369C2×C4×Q8—111no—
370C2×C4×Q8—111no—
371C2×C4×Q8—221no—
372C2×C4×Q8—221no—
373C2×C4×Q8—224no—
374C2×C4×Q8—224no—
375C2×C4×Q8C2×D1111yescharacteristic
376C2×C4×D4—111no—
377C2×C4×D4—221no—
378C22×C4⋊C4—111no—
379C22×C4⋊C4—221no—
380C22×C42—111no—
381C22×C42—221no—
382#448—118no—
383C4×SD16—224no—
384C4×SD16—224no—
385C2×#106—111no—
386C2×#106—111no—
387C2×#103—111no—
388C2×#103—111no—
389C2×#103—111no—
390C2×#103—111no—
391C2×#103C2×D1111yescharacteristic
392C2×#103C2×D1111yescharacteristic
393C2×#102—111no—
394C2×#102—111no—
395C2×C22⋊C8—111no—
396C2×C22⋊C8—111no—
397C2×C4×C8—111no—
398C2×C4×C8C2×D1111yescharacteristic
399#390—111no—
400#389—111no—
401#388—221no—
402#386—221no—
403#380—111no—
404C4×C4⋊C4C2×D1111yescharacteristic
405C4×C22⋊C4—221no—
406#340—111no—
407#340—111no—
408#340C2×D1111yescharacteristic
409#340C2×D1111yescharacteristic
410#336—111no—
411#336—111no—
412C22×C11C2×C4×D411yescharacteristic
413C22×C11C2×#12011yescharacteristic
414C22×C11#52511yescharacteristic
415C22×C11C22×SD1611yescharacteristic
416C22×C11C2×#13511yescharacteristic
417C22×C11C2×#13711yescharacteristic
418C22×C11#57511yescharacteristic
419C2×D11—22no—
420C2×D11—22no—
421C2×D11—22no—
422C2×D11—22no—
423C2×D11—22no—
424C2×D11—22no—
425C2×D11—42no—
426C2×D11—42no—
427C2×D11—42no—
428C2×D11—81no—
429C2×D11—81no—
430C2×D11—81no—
431C2×D11—81no—
432C2×D11C4×SD1614yescomplemented
433C4×C11—22no—
434C4×C11—24no—
435C4×C11—42no—
436C4×C11—42no—
437C4×C11—81no—
438C4×C11#44814yescomplemented
439C4×C11C2×C4×D411yescharacteristic
440C4×C11C2×C4×D411yescharacteristic
441C4×C11#52511yescharacteristic
442C4×C11#52511yescharacteristic
443Dic11—22no—
444Dic11—22no—
445Dic11—24no—
446Dic11—41no—
447Dic11—42no—
448Dic11—81no—
449C22×Q8—114no—
450C22×Q8—111no—
451C22×Q8—221no—
452C22×Q8—222no—
453C22×Q8—222no—
454C22×Q8—222no—
455C22×Q8—222no—
456C22×Q8—222no—
457C22×Q8C22×D1111yescharacteristic
458C22×D4—111no—
459C22×D4—221no—
460C23×C4—111no—
461C23×C4—111no—
462C23×C4—111no—
463C23×C4—221no—
464C23×C4—221no—
465C23×C4—221no—
466C2×SD16—114no—
467C2×SD16—114no—
468C2×SD16—222no—
469C2×SD16—222no—
470C2×SD16—222no—
471C2×SD16—222no—
472C22×C8—111no—
473C22×C8—111no—
474C22×C8C22×D1111yescharacteristic
475C22×C8C22×D1111yescharacteristic
476#121—114no—
477#121—222no—
478C4×Q8—22no—
479C4×Q8—114no—
480C4×Q8—228no—
481C4×Q8—222no—
482C4×Q8—228no—
483C4×Q8—222no—
484C4×Q8—222no—
485C4×Q8—222no—
486C4×Q8—222no—
487C4×Q8D4414yescomplemented
488C4×D4—222no—
489C4×D4—222no—
490C4×D4—444no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—111no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—222no—
495C2×C4⋊C4—228no—
496C2×C4⋊C4—221no—
497C2×C4⋊C4—221no—
498C2×C4⋊C4—221no—
499C2×C4⋊C4—221no—
500C2×C4⋊C4—222no—
501C2×C4⋊C4—221no—
502C2×C4⋊C4C22×D1111yescharacteristic
503C2×C4⋊C4C22×D1111yescharacteristic
504C2×C4⋊C4C22×D1111yescharacteristic
505C2×C22⋊C4—221no—
506C2×C22⋊C4—221no—
507C2×C22⋊C4—221no—
508C2×C22⋊C4—221no—
509C2×C22⋊C4—221no—
510C2×C42—21no—
511C2×C42—21no—
512C2×C42—111no—
513C2×C42—111no—
514C2×C42—111no—
515C2×C42—228no—
516C2×C42—221no—
517C2×C42—221no—
518C2×C42—221no—
519C2×C42—222no—
520C2×C42—222no—
521C2×C42C22×D1111yescharacteristic
522#106—222no—
523#106—222no—
524#103—22no—
525#103—114no—
526#103—222no—
527#103—222no—
528#103—222no—
529#103C4×D1114yescomplemented
530#102—222no—
531#102—222no—
532C22⋊C8—114no—
533C22⋊C8—222no—
534C4×C8—22no—
535C4×C8—222no—
536#95—21no—
537#95—221no—
538#95—221no—
539C2×C11C4×#12011yescharacteristic
540C2×C11C2×C4×SD1611yescharacteristic
541C2×C11C4×#13711yescharacteristic
542C2×C11C2×#44811yescharacteristic
543C2×C11#300211yescharacteristic
544C2×C11#310311yescharacteristic
545C2×C11#310811yescharacteristic
546D11—24no—
547D11—82no—
548C24—111no—
549C24—221no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—112no—
554C2×Q8—112no—
555C2×Q8—112no—
556C2×Q8—224no—
557C2×Q8—224no—
558C2×Q8—224no—
559C2×Q8—228no—
560C2×Q8—228no—
561C2×Q8—228no—
562C2×Q8—228no—
563C2×Q8—221no—
564C2×Q8—221no—
565C2×Q8—221no—
566C2×Q8C2×C4×D1112yes—
567C2×Q8C2×D4412yes—
568C2×Q8#433912yes—
569C2×D4—112no—
570C2×D4—224no—
571C2×D4—221no—
572C2×D4—221no—
573C2×D4—221no—
574C2×D4—221no—
575C2×D4—221no—
576C2×D4—442no—
577C2×D4—442no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—111no—
583C22×C4—111no—
584C22×C4—114no—
585C22×C4—112no—
586C22×C4—112no—
587C22×C4—111no—
588C22×C4—224no—
589C22×C4—224no—
590C22×C4—224no—
591C22×C4—222no—
592C22×C4—224no—
593C22×C4—221no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—221no—
597C22×C4—221no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—222no—
602C22×C4—221no—
603C22×C4—441no—
604C22×C4—442no—
605C22×C4—442no—
606C22×C4—442no—
607C22×C4—442no—
608C22×C4—442no—
609C22×C4D4×D1111yescharacteristic
610C22×C4D4×D1111yescharacteristic
611C22×C4C23×D1111yescharacteristic
612SD16—228no—
613SD16—228no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—112no—
620C2×C8—221no—
621C2×C8—221no—
622C2×C8—221no—
623C2×C8—221no—
624C2×C8—221no—
625C2×C8C2×C4×D1112yes—
626C4⋊C4—24no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—112no—
632C4⋊C4—224no—
633C4⋊C4—224no—
634C4⋊C4—224no—
635C4⋊C4—224no—
636C4⋊C4—221no—
637C4⋊C4—221no—
638C4⋊C4—221no—
639C4⋊C4—442no—
640C4⋊C4C2×C4×D1112yes—
641C4⋊C4C2×D4412yes—
642C22⋊C4—224no—
643C22⋊C4—442no—
644C22⋊C4—442no—
645C22⋊C4—442no—
646C22⋊C4—442no—
647C42—24no—
648C42—42no—
649C42—224no—
650C42—224no—
651C42—222no—
652C42—222no—
653C42—224no—
654C42—221no—
655C42—221no—
656C42C2×D4412yes—
657C42D4×D1112yes—
658C11C4×#44811yescharacteristic, complemented, Sylow
659C23—112no—
660C23—112no—
661C23—112no—
662C23—221no—
663C23—221no—
664C23—221no—
665C23—221no—
666C23—222no—
667C23—441no—
668C23—441no—
669C23—441no—
670C23—441no—
671C23—441no—
672C23—441no—
673C23C2×D4×D1111yescharacteristic
674Q8—22no—
675Q8—22no—
676Q8—22no—
677Q8—114no—
678Q8—2216no—
679Q8—222no—
680Q8—222no—
681Q8—222no—
682Q8C4×D4414yescomplemented
683D4—222no—
684D4—222no—
685D4—448no—
686D4—441no—
687D4—441no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—112no—
703C2×C4—112no—
704C2×C4—2216no—
705C2×C4—221no—
706C2×C4—221no—
707C2×C4—222no—
708C2×C4—221no—
709C2×C4—222no—
710C2×C4—221no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—228no—
717C2×C4—222no—
718C2×C4—221no—
719C2×C4—221no—
720C2×C4—221no—
721C2×C4—444no—
722C2×C4—448no—
723C2×C4—441no—
724C2×C4—441no—
725C2×C4—441no—
726C2×C4—441no—
727C2×C4—441no—
728C2×C4—884no—
729C2×C4#6693512yes—
730C2×C4#6693512yes—
731C2×C4SD16×D1112yes—
732C2×C4#6697112yes—
733C2×C4C22×C4×D1111yescharacteristic
734C2×C4C22×D4411yescharacteristic
735C2×C4C2×#433911yescharacteristic
736C2×C4C2×D4×D1111yescharacteristic
737C2×C4#41×D1111yescharacteristic
738C2×C4#41×D1111yescharacteristic
739C8—22no—
740C8—41no—
741C8—222no—
742C8—441no—
743C22—114no—
744C22—222no—
745C22—222no—
746C22—222no—
747C22—222no—
748C22—222no—
749C22—222no—
750C22—442no—
751C22—442no—
752C22—442no—
753C22—881no—
754C22—881no—
755C22—881no—
756C22—881no—
757C22C2×#6693511yescharacteristic
758C22C4×D4×D1111yescharacteristic
759C22#1062307811yescharacteristic
760C22C2×SD16×D1111yescharacteristic
761C22C2×#6697111yescharacteristic
762C22D11×#13511yescharacteristic
763C22#1062329911yescharacteristic
764C4—24no—
765C4—22no—
766C4—42no—
767C4—42no—
768C4—81no—
769C4—222no—
770C4—224no—
771C4—222no—
772C4—441no—
773C4—442no—
774C4—881no—
775C4#1062241914yesdirect product factor
776C4C2×C4×D4411yescharacteristic
777C4#1062305511yescharacteristic
778C4C4×D4×D1111yescharacteristic
779C4#1062307811yescharacteristic
780C2—224no—
781C2—882no—
782C2C4×#6693511yescharacteristic
783C2C4×SD16×D1111yescharacteristic
784C2C4×#6697111yescharacteristic
785C2C2×#1062241911yescharacteristic
786C2#1307783611yescharacteristic
787C2#1307864511yescharacteristic
788C2#1307870011yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#103C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
cosocleC22×C4×C11C24
hypercenterC4×#103D11
hypocenterC11C4×#448
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
1. C2×C4×Q8×D11C2semidirect
3. C2×C4×#4314C2semidirect
4. C2×C4×#4325C2semidirect
6. #13068972C2semidirect
7. #13068969C2semidirect
9. #13068886C2semidirect
10. #13068885C2semidirect
11. #13068810C2semidirect
12. #13068549C2semidirect
13. C4×#66874C2semidirect
14. C4×(C2×D11)⋊C8C2semidirect
15. C4×C11×#103C2semidirect
54. #10622419C4direct (N × H)
70. C2×Q8×D11C2×C4semidirect
84. C4×Q8×C11D4semidirect
96. C2×#4325C2×C4semidirect
119. C2×#4314C2×C4semidirect
136. C4×Dic22D4semidirect
138. C11×#103C2×C4semidirect
146. (C2×D11)⋊C8C2×C4semidirect
150. #66874C2×C4semidirect
207. C2×C4×D11SD16semidirect
278. C4×#103D11semidirect
298. Q8×C11C4×D4semidirect
359. Dic22C4×D4semidirect
432. C2×D11C4×SD16semidirect
438. C4×C11#448semidirect
487. C4×Q8D44semidirect
529. #103C4×D11semidirect
658. C11C4×#448semidirect
682. Q8C4×D44semidirect
775. C4#10622419direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D112
C2×#106224192
C2×C4×#43142
C2×C4×#43252
C4×#669482
#130689722
#130689692
#130689322
#130688862
#130688852
#130688102
#130685492
C4×#668742
C4×(C2×D11)⋊C82
C4×C11×#1032
C4×#44811