Finite Group Databasebeta

← C2×#13081677 #15634774

Subgroups — C2×#13081677 #15634774

Order 2816.

2002 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623244C211yesmaximal, characteristic, complemented
2C2×#10623202C211yesmaximal, characteristic, complemented
3#13081677C2116yesmaximal, direct product factor
4C2×#10622780C211yesmaximal, characteristic, complemented
5C2×#10622768C211yesmaximal, characteristic, complemented
6C2×#10622779C211yesmaximal, characteristic, complemented
7C2×#10622667C211yesmaximal, characteristic, complemented
8C2×#10622688C211yesmaximal, characteristic, complemented
9C2×#10622766C211yesmaximal, characteristic, complemented
10C2×#10622766C211yesmaximal, characteristic, complemented
11C2×#10622775C211yesmaximal, characteristic, complemented
12C2×#10622314C211yesmaximal, characteristic, complemented
13C2×#10622765C211yesmaximal, characteristic, complemented
14C2×#10622329C211yesmaximal, characteristic, complemented
15C2×SD16×Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#496C211yesmaximal, characteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×D8C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic
21C2×C11×#127C2211yescharacteristic
22C2×C11×#124C2211yescharacteristic
23C2×Q8×Dic11C2211yescharacteristic
24C2×#66997C2211yescharacteristic
25C22×#4326C2211yescharacteristic
26C2×#66989—21no—
27C2×#66989C2211yescharacteristic
28C2×#66989C2211yescharacteristic
29C2×#66989C2211yescharacteristic
30C2×#66988—21no—
31C2×#66988—21no—
32C2×D4×Dic11—21no—
33C2×D4×Dic11C2211yescharacteristic
34C2×D4×Dic11C2211yescharacteristic
35C2×D4×Dic11C2211yescharacteristic
36C22×#4324C2211yescharacteristic
37C22×#4324C2211yescharacteristic
38C22×#4324C2211yescharacteristic
39C22×Dic44C2211yescharacteristic
40#10623244—24no—
41#10623244C2218yescomplemented
42#10623202—24no—
43#10623202C2218yescomplemented
44C2×#66932—21no—
45C2×#66932—21no—
46C2×#66931—21no—
47C2×#66930—21no—
48C2×C4×Dic22C2211yescharacteristic
49C2×C4×Dic22C2211yescharacteristic
50C2×C4×Dic22C2211yescharacteristic
51C11×#496C2218yes—
52C2×C11×#97C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×#66896C2211yescharacteristic
56C2×#66896C2211yescharacteristic
57#10622780C2218yescomplemented
58#10622779C2218yescomplemented
59#10622775C2218yescomplemented
60SD16×Dic11C2218yescomplemented
61#10622768C2218yescomplemented
62#10622766C2218yescomplemented
63#10622766C2218yescomplemented
64#10622765C2218yescomplemented
65C2×#66881C2211yescharacteristic
66C2×#66880C2211yescharacteristic
67C2×#66880C2211yescharacteristic
68C2×#66879C2211yescharacteristic
69C2×Dic11⋊C8C2211yescharacteristic
70C2×Dic11⋊C8C2211yescharacteristic
71C2×C8×Dic11C2211yescharacteristic
72#10622688C2218yescomplemented
73#10622667C2218yescomplemented
74C2×C4⋊(C11⋊C8)C2211yescharacteristic
75#10622329C2218yescomplemented
76#10622314C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11C2311yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C23×Dic11—21no—
84C23×Dic11—21no—
85C23×Dic11—21no—
86C22×Dic22D411yescharacteristic
87C22×Dic22C2311yescharacteristic
88C22×Dic22C2311yescharacteristic
89C2×C11×SD16—24no—
90C2×C11×SD16—42no—
91C2×C11×SD16C2314yes—
92C2×C11×SD16C2314yes—
93C2×C11×D8—24no—
94C2×C11×D8—42no—
95C2×C11×D8C2314yes—
96C2×C11×D8C2314yes—
97C22×C8×C11C2311yescharacteristic
98C22×C8×C11C2311yescharacteristic
99C11×#127—22no—
100C11×#127C2314yes—
101C11×#124—22no—
102C11×#124C2314yes—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C42×C11C2311yescharacteristic
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11—21no—
109C2×C22⋊Dic11—21no—
110C2×C22⋊Dic11—21no—
111C2×C22⋊Dic11—21no—
112C2×C22⋊Dic11—21no—
113C2×C22⋊Dic11—21no—
114C2×C22⋊Dic11—21no—
115Q8×Dic11—22no—
116Q8×Dic11C2314yes—
117#66997—22no—
118#66997C2314yes—
119C2×#4326—42no—
120C2×#4326C2314yes—
121#66989—28no—
122#66989—22no—
123#66989—22no—
124#66989—22no—
125#66989C2314yes—
126#66989C2314yes—
127#66989C2314yes—
128#66988—28no—
129#66988—28no—
130D4×Dic11—28no—
131D4×Dic11—22no—
132D4×Dic11—22no—
133D4×Dic11—22no—
134D4×Dic11C2314yes—
135D4×Dic11C2314yes—
136D4×Dic11C2314yes—
137C2×#4324—42no—
138C2×#4324—42no—
139C2×#4324—42no—
140C2×#4324C2314yes—
141C2×#4324C2314yes—
142C2×#4324C2314yes—
143C2×C4⋊Dic11—21no—
144C2×C4⋊Dic11D411yescharacteristic
145C2×C4⋊Dic11C2311yescharacteristic
146C2×C4⋊Dic11C2311yescharacteristic
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4—21no—
149C2×Dic11⋊C4—21no—
150C2×Dic11⋊C4—21no—
151C2×Dic11⋊C4D411yescharacteristic
152C2×Dic11⋊C4D411yescharacteristic
153C2×C4×Dic11—21no—
154C2×C4×Dic11—21no—
155C2×C4×Dic11—21no—
156C2×C4×Dic11C2311yescharacteristic
157C2×C4×Dic11C2311yescharacteristic
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C2×Dic44—24no—
161C2×Dic44C2314yes—
162#66932—28no—
163#66932—28no—
164#66931—28no—
165#66930—28no—
166C4×Dic22—22no—
167C4×Dic22—22no—
168C4×Dic22D414yes—
169C4×Dic22C2314yes—
170C4×Dic22C2314yes—
171C4×Dic22C2314yes—
172C11×#97C2314yes—
173#66899C2314yes—
174#66896C2314yes—
175#66896C2314yes—
176#66896C2314yes—
177#66881C2314yes—
178#66880C2314yes—
179#66880C2314yes—
180#66879C2314yes—
181Dic11⋊C8C2314yes—
182Dic11⋊C8C2314yes—
183C8×Dic11C2314yes—
184C4⋊(C11⋊C8)C2314yes—
185C2×#3401—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—21no—
189C2×Q8×C11—21no—
190C2×Q8×C11—22no—
191C2×Q8×C11—22no—
192C2×Q8×C11C2412yes—
193C2×D4×C11—21no—
194C2×D4×C11—21no—
195C2×D4×C11—21no—
196C2×D4×C11—24no—
197C2×D4×C11—24no—
198C2×D4×C11—22no—
199C2×D4×C11—22no—
200C2×D4×C11—22no—
201C2×D4×C11—22no—
202C2×D4×C11—22no—
203C2×D4×C11—22no—
204C2×D4×C11—44no—
205C2×D4×C11—82no—
206C2×D4×C11C2412yes—
207C2×D4×C11C2412yes—
208C2×D4×C11C2412yes—
209C22×C4×C11—21no—
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2411yescharacteristic
213C22×Dic11—24no—
214C22×Dic11—24no—
215C22×Dic11—24no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—44no—
221C22×Dic11—82no—
222C22×Dic11—82no—
223C22×Dic11C2×D411yescharacteristic
224C22×Dic11C2×D411yescharacteristic
225C22×Dic11C2×D411yescharacteristic
226C22×Dic11C2×D411yescharacteristic
227C2×Dic22—21no—
228C2×Dic22—21no—
229C2×Dic22—22no—
230C2×Dic22—22no—
231C2×Dic22—22no—
232C2×Dic22—22no—
233C2×Dic22—42no—
234C2×Dic22C2×D414yes—
235C2×Dic22C2412yes—
236C2×Dic22C2412yes—
237C11×SD16—28no—
238C11×SD16—44no—
239C11×D8—28no—
240C11×D8—44no—
241C2×C8×C11—22no—
242C2×C8×C11#4114yes—
243C2×C8×C11C2412yes—
244C2×C8×C11C2412yes—
245C11×C22⋊C4—24no—
246C11×C22⋊C4—24no—
247C42×C11C2×D412yes—
248C42×C11C2412yes—
249C22⋊Dic11—24no—
250C22⋊Dic11—24no—
251C22⋊Dic11—24no—
252C22⋊Dic11—24no—
253C22⋊Dic11—24no—
254C22⋊Dic11—24no—
255C22⋊Dic11—24no—
256C22⋊Dic11—24no—
257C22⋊Dic11—24no—
258#4326—44no—
259#4324—44no—
260#4324—44no—
261#4324—44no—
262C4⋊Dic11—24no—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265C4⋊Dic11C2×D414yes—
266C4⋊Dic11C2412yes—
267C4⋊Dic11C2412yes—
268Dic11⋊C4—24no—
269Dic11⋊C4—24no—
270Dic11⋊C4—24no—
271Dic11⋊C4—24no—
272Dic11⋊C4C2×D414yes—
273Dic11⋊C4C2×D414yes—
274C4×Dic11—24no—
275C4×Dic11—24no—
276C4×Dic11—24no—
277C4×Dic11C2×D412yes—
278C4×Dic11C2×D412yes—
279C4×Dic11C2412yes—
280C4×Dic11C2412yes—
281C2×C11⋊C8—22no—
282C2×C11⋊C8—22no—
283C2×C11⋊C8C2412yes—
284C2×C11⋊C8C2412yes—
285Dic44—28no—
286C2×#559—111no—
287C2×#556—111no—
288#3401—1116no—
289C2×#497—111no—
290C2×#496D1111yescharacteristic
291C2×#495—111no—
292C2×#464—111no—
293C2×#464—111no—
294C2×#460—111no—
295C2×#463—111no—
296C2×#463—111no—
297C2×#461—111no—
298C2×#446—111no—
299C2×#442—111no—
300C2×#441—111no—
301C2×C4×SD16—111no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—42no—
306C23×C11—42no—
307C23×C11—42no—
308C23×C11—42no—
309C23×C11—42no—
310C23×C11—42no—
311C23×C11—42no—
312C23×C11—42no—
313C23×C11—42no—
314C23×C11C22×D411yescharacteristic
315Q8×C11—22no—
316Q8×C11—22no—
317Q8×C11—42no—
318D4×C11—22no—
319D4×C11—22no—
320D4×C11—22no—
321D4×C11—22no—
322D4×C11—22no—
323D4×C11—22no—
324D4×C11—48no—
325D4×C11—42no—
326D4×C11—42no—
327D4×C11—42no—
328D4×C11—84no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—42no—
333C2×C4×C11C22×D412yes—
334C2×C4×C11C22×D412yes—
335C2×C4×C11C22×D411yescharacteristic
336C2×C4×C11C2×#4112yes—
337C2×C4×C11H(5,𝔽2)12yes—
338C2×C4×C11C2511yescharacteristic
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—48no—
348C2×Dic11—42no—
349C2×Dic11—42no—
350C2×Dic11—42no—
351C2×Dic11—42no—
352C2×Dic11—84no—
353C2×Dic11—84no—
354C2×Dic11C22×D412yes—
355C2×Dic11C22×D412yes—
356C2×Dic11C22×D412yes—
357C2×Dic11C22×D412yes—
358Dic22—22no—
359Dic22—22no—
360Dic22—22no—
361Dic22—22no—
362Dic22—44no—
363Dic22—42no—
364Dic22—42no—
365C8×C11—22no—
366C8×C11C2×#4114yes—
367C11⋊C8—22no—
368C11⋊C8—22no—
369C22×Q16—111no—
370C22×Q16—111no—
371C22×SD16—111no—
372C22×SD16—111no—
373C22×SD16—111no—
374C22×SD16C2×D1111yescharacteristic
375C22×SD16C2×D1111yescharacteristic
376C22×D8C2×D1111yescharacteristic
377C22×D8C2×D1111yescharacteristic
378#559—118no—
379#559—224no—
380#556—118no—
381#556—224no—
382C2×C4⋊Q8—111no—
383C2×#127C2×D1111yescharacteristic
384C2×#126—221no—
385C2×#126—221no—
386C2×#124—111no—
387C2×#124—111no—
388C2×#124—111no—
389C2×#124—221no—
390C2×#124C2×D1111yescharacteristic
391C2×#123—221no—
392C2×#123—221no—
393C2×C22⋊Q8—221no—
394C2×C4×Q8—111no—
395C2×C4×Q8—111no—
396C2×C4×Q8—111no—
397C2×C4×Q8—111no—
398C2×C4×D4—111no—
399C2×C4×D4—111no—
400C2×C4×D4—111no—
401C2×C4×D4—221no—
402C2×#117—221no—
403#497—118no—
404#496C2×D1118yes—
405#495—118no—
406#464—118no—
407#464—118no—
408#463—118no—
409#463—118no—
410#461—118no—
411#460—118no—
412#446—118no—
413#442—118no—
414#441—118no—
415C4×SD16—118no—
416C2×#106—111no—
417C2×C4⋊C8—111no—
418C2×C4⋊C8—111no—
419C2×C4⋊C8—111no—
420C2×#103—111no—
421C2×#103—111no—
422C2×#103—111no—
423C2×#102—111no—
424C2×#102—111no—
425C2×#102—111no—
426C2×#97—111no—
427C2×#97C2×D1111yescharacteristic
428C2×C4×C8—111no—
429C22×C11—42no—
430C22×C11—42no—
431C22×C11—42no—
432C22×C11—42no—
433C22×C11—42no—
434C22×C11—42no—
435C22×C11—42no—
436C22×C11—42no—
437C22×C11—42no—
438C22×C11—84no—
439C22×C11—84no—
440C22×C11—84no—
441C22×C11#55012yes—
442C22×C11#57512yes—
443C22×C11#57712yes—
444C22×C11C23×D411yescharacteristic
445C4×C11—22no—
446C4×C11—22no—
447C4×C11—42no—
448C4×C11#55012yes—
449C4×C11C22×#4111yescharacteristic
450C4×C11C2×H(5,𝔽2)11yescharacteristic
451Dic11—22no—
452Dic11—22no—
453Dic11—22no—
454Dic11—22no—
455Dic11—42no—
456Dic11—42no—
457Dic11—42no—
458Dic11—42no—
459C22×Q8—111no—
460C22×Q8—111no—
461C22×Q8—111no—
462C22×Q8C22×D1111yescharacteristic
463C22×D4—21no—
464C22×D4—21no—
465C22×D4C22×D1111yescharacteristic
466C22×D4C22×D1111yescharacteristic
467C22×D4C22×D1111yescharacteristic
468C23×C4—221no—
469C23×C4—221no—
470C23×C4—221no—
471C2×Q16—114no—
472C2×Q16—114no—
473C2×Q16—224no—
474C2×Q16—442no—
475C2×SD16—24no—
476C2×SD16—42no—
477C2×SD16—114no—
478C2×SD16—114no—
479C2×SD16—114no—
480C2×SD16—442no—
481C2×SD16—442no—
482C2×SD16—442no—
483C2×SD16C22×D1114yes—
484C2×SD16C22×D1114yes—
485C2×D8—24no—
486C2×D8—42no—
487C2×D8C22×D1114yes—
488C2×D8C22×D1114yes—
489C22×C8—111no—
490C22×C8—111no—
491C22×C8C22×D1111yescharacteristic
492C22×C8C22×D1111yescharacteristic
493C4⋊Q8—114no—
494C4⋊Q8—222no—
495#127—22no—
496#127C22×D1114yes—
497#126—228no—
498#126—228no—
499#124—22no—
500#124—114no—
501#124—114no—
502#124—114no—
503#124—222no—
504#124—222no—
505#124—222no—
506#124—228no—
507#124C22×D1114yes—
508#123—228no—
509#123—228no—
510C22⋊Q8—228no—
511C4×Q8—114no—
512C4×Q8—114no—
513C4×Q8—114no—
514C4×Q8—114no—
515C4×Q8—114no—
516C4×Q8—222no—
517C4×Q8—222no—
518C4×Q8—222no—
519C4×D4—114no—
520C4×D4—114no—
521C4×D4—114no—
522C4×D4—222no—
523C4×D4—222no—
524C4×D4—222no—
525C4×D4—228no—
526#117—228no—
527C2×C4⋊C4—111no—
528C2×C4⋊C4—111no—
529C2×C4⋊C4—111no—
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×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—221no—
540C2×C22⋊C4—221no—
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—221no—
551C2×C42—221no—
552C2×C42—221no—
553C2×C42C22×D1111yescharacteristic
554#106—114no—
555C4⋊C8—114no—
556C4⋊C8—114no—
557C4⋊C8—114no—
558#103—114no—
559#103—114no—
560#103—114no—
561#102—114no—
562#102—114no—
563#102—114no—
564#97—114no—
565#97C22×D1114yes—
566C4×C8—114no—
567C2×C11—82no—
568C2×C11—82no—
569C2×C11—82no—
570C2×C11#340114yescomplemented
571C2×C11C2×#55011yescharacteristic
572C2×C11C2×#57511yescharacteristic
573C2×C11C2×#57711yescharacteristic
574C24—21no—
575C24—21no—
576C24—21no—
577C2×Q8—21no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—114no—
581C2×Q8—112no—
582C2×Q8—112no—
583C2×Q8—221no—
584C2×Q8—221no—
585C2×Q8—222no—
586C2×Q8—222no—
587C2×Q8—222no—
588C2×Q8—222no—
589C2×Q8—442no—
590C2×Q8C23×D1112yes—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—24no—
595C2×D4—24no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—44no—
603C2×D4—82no—
604C2×D4C23×D1112yes—
605C2×D4C23×D1112yes—
606C2×D4C23×D1112yes—
607C22×C4—21no—
608C22×C4—111no—
609C22×C4—111no—
610C22×C4—111no—
611C22×C4—111no—
612C22×C4—224no—
613C22×C4—224no—
614C22×C4—224no—
615C22×C4—221no—
616C22×C4—221no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—444no—
620C22×C4—882no—
621C22×C4—882no—
622C22×C4D4×D1111yescharacteristic
623C22×C4D4×D1111yescharacteristic
624C22×C4C23×D1111yescharacteristic
625Q16—228no—
626Q16—444no—
627SD16—28no—
628SD16—44no—
629SD16—444no—
630SD16—444no—
631SD16—444no—
632D8—28no—
633D8—44no—
634C2×C8—22no—
635C2×C8—112no—
636C2×C8—112no—
637C2×C8—222no—
638C2×C8—222no—
639C2×C8#434114yes—
640C2×C8C23×D1112yes—
641C2×C8C23×D1112yes—
642C4⋊C4—114no—
643C4⋊C4—114no—
644C4⋊C4—114no—
645C4⋊C4—112no—
646C4⋊C4—112no—
647C4⋊C4—224no—
648C4⋊C4—224no—
649C4⋊C4—224no—
650C4⋊C4—221no—
651C4⋊C4—221no—
652C4⋊C4—224no—
653C4⋊C4—224no—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—224no—
657C22⋊C4—224no—
658C22⋊C4—224no—
659C22⋊C4—224no—
660C22⋊C4—224no—
661C22⋊C4—224no—
662C22⋊C4—224no—
663C22⋊C4—224no—
664C22⋊C4—224no—
665C42—112no—
666C42—112no—
667C42—112no—
668C42—112no—
669C42—224no—
670C42—224no—
671C42—224no—
672C42D4×D1112yes—
673C42C23×D1112yes—
674C11C2×#340111yescharacteristic, complemented, Sylow
675C23—22no—
676C23—22no—
677C23—22no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23C2×D4×D1111yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—42no—
691Q8—222no—
692Q8—222no—
693Q8—222no—
694Q8—222no—
695Q8—444no—
696Q8—442no—
697Q8—442no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—22no—
703D4—22no—
704D4—48no—
705D4—42no—
706D4—42no—
707D4—42no—
708D4—84no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—42no—
713C2×C4—112no—
714C2×C4—112no—
715C2×C4—112no—
716C2×C4—112no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—222no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—222no—
725C2×C4—448no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—442no—
729C2×C4—442no—
730C2×C4—884no—
731C2×C4—884no—
732C2×C4C2×D4×D1112yes—
733C2×C4C2×D4×D1112yes—
734C2×C4C2×D4×D1111yescharacteristic
735C2×C4C2×#434112yes—
736C2×C4#6703712yes—
737C2×C4C24×D1111yescharacteristic
738C8—22no—
739C8—222no—
740C8—222no—
741C8C2×#434114yes—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—84no—
752C22—84no—
753C22—84no—
754C22#1062324912yes—
755C22#1062330412yes—
756C22#1062330612yes—
757C22C22×D4×D1111yescharacteristic
758C4—22no—
759C4—22no—
760C4—42no—
761C4—222no—
762C4—222no—
763C4—222no—
764C4—222no—
765C4—442no—
766C4—442no—
767C4—442no—
768C4—442no—
769C4#1062324912yes—
770C4C22×#434111yescharacteristic
771C4C2×#6703711yescharacteristic
772C2—82no—
773C2—82no—
774C2—82no—
775C2#1308167714yesdirect product factor
776C2C2×#1062324911yescharacteristic
777C2C2×#1062330411yescharacteristic
778C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#496C2
socleC23×C11C22×D4
hypercenterC2×#496D11
hypocenterC11C2×#3401
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#496

Complements

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

NH ≅ G/Ntype
1. C2×#10623244C2semidirect
2. C2×#10623202C2semidirect
3. #13081677C2direct (N × H)
4. C2×#10622780C2semidirect
5. C2×#10622768C2semidirect
6. C2×#10622779C2semidirect
7. C2×#10622667C2semidirect
8. C2×#10622688C2semidirect
9. C2×#10622766C2semidirect
10. C2×#10622766C2semidirect
11. C2×#10622775C2semidirect
12. C2×#10622314C2semidirect
13. C2×#10622765C2semidirect
14. C2×#10622329C2semidirect
15. C2×SD16×Dic11C2semidirect
41. #10623244C22semidirect
43. #10623202C22semidirect
57. #10622780C22semidirect
58. #10622779C22semidirect
59. #10622775C22semidirect
60. SD16×Dic11C22semidirect
61. #10622768C22semidirect
62. #10622766C22semidirect
63. #10622766C22semidirect
64. #10622765C22semidirect
72. #10622688C22semidirect
73. #10622667C22semidirect
75. #10622329C22semidirect
76. #10622314C22semidirect
570. C2×C11#3401semidirect
674. C11C2×#3401semidirect
775. C2#13081677direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232442
C2×#106232022
#130816772
C2×#106227802
C2×#106227682
C2×#106227792
C2×#106226672
C2×#106226882
C2×#106227662
C2×#106227752
C2×#106223142
C2×#106227652
C2×#106223292
C2×SD16×Dic112
C2×C11×#4962
C2×#340111