Finite Group Databasebeta

← C2×#13081694 #15634792

Subgroups — C2×#13081694 #15634792

Order 2816.

1938 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623073C211yesmaximal, characteristic, complemented
2C2×#10623202C211yesmaximal, characteristic, complemented
3#13081694C2116yesmaximal, direct product factor
4C2×#10622673C211yesmaximal, characteristic, complemented
5C2×#10622780C211yesmaximal, characteristic, complemented
6C2×#10622768C211yesmaximal, characteristic
7C2×#10622380C211yesmaximal, characteristic, complemented
8C2×#10622779C211yesmaximal, characteristic, complemented
9C2×#10622462C211yesmaximal, characteristic, complemented
10C2×#10622406C211yesmaximal, characteristic, complemented
11C2×#10622766C211yesmaximal, characteristic
12C2×#10622441C211yesmaximal, characteristic, complemented
13C2×#10622631C211yesmaximal, characteristic, complemented
14C2×#10622370C211yesmaximal, characteristic, complemented
15C2×#10622403C211yesmaximal, characteristic, complemented
16C2×C11×#463C211yesmaximal, characteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C2×C11×#124C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C2×#66997C2211yescharacteristic
23C22×#4326C2211yescharacteristic
24C22×#4326C2211yescharacteristic
25C2×#66989C2211yescharacteristic
26C2×#66989C2211yescharacteristic
27C2×#66989C2211yescharacteristic
28C2×D4×Dic11C2211yescharacteristic
29C22×#4324C2211yescharacteristic
30C22×#4324C2211yescharacteristic
31C22×#4324C2211yescharacteristic
32C2×#66979—21no—
33C2×#66977—21no—
34C22×Dic44C2211yescharacteristic
35C22×Dic44C2211yescharacteristic
36#10623202—24no—
37#10623202C2218yescomplemented
38#10623073—24no—
39#10623073C2218yescomplemented
40C2×#66940C2211yescharacteristic
41C2×#66940C2211yescharacteristic
42C2×#66932—21no—
43C2×#66932—21no—
44C2×#66932—21no—
45C2×#66932—21no—
46C2×#66931—21no—
47C2×#66930—21no—
48C2×#66922C2211yescharacteristic
49C2×C4×Dic22C2211yescharacteristic
50C2×C4×Dic22C2211yescharacteristic
51C11×#463C2218yes—
52C2×C11×C4⋊C8C2211yescharacteristic
53C2×C11×#103C2211yescharacteristic
54C2×C11×#102C2211yescharacteristic
55C2×#66896C2211yescharacteristic
56#10622780C2218yescomplemented
57#10622779C2218yescomplemented
58#10622768C2218yes—
59#10622766C2218yes—
60C2×#66880C2211yescharacteristic
61C2×#66880C2211yescharacteristic
62C2×#66879C2211yescharacteristic
63C2×Dic11⋊C8C2211yescharacteristic
64C2×Dic11⋊C8C2211yescharacteristic
65C2×C8×Dic11C2211yescharacteristic
66#10622673C2218yescomplemented
67#10622631C2218yescomplemented
68C2×#66874C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×#66867C2211yescharacteristic
71#10622462C2218yescomplemented
72#10622441C2218yescomplemented
73#10622406C2218yescomplemented
74#10622403C2218yescomplemented
75#10622380C2218yescomplemented
76#10622370C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11C2311yescharacteristic
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11—21no—
81C23×Dic11—21no—
82C22×Dic22D411yescharacteristic
83C22×Dic22C2311yescharacteristic
84C22×Dic22C2311yescharacteristic
85C22×Dic22C2311yescharacteristic
86C2×C11×SD16—42no—
87C2×C11×SD16C2314yes—
88C2×C11×D8—42no—
89C2×C11×D8C2314yes—
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C11×#124—22no—
93C11×#124C2314yes—
94C4×D4×C11—22no—
95C4×D4×C11C2314yes—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C42×C11C2311yescharacteristic
101C2×C22⋊Dic11—21no—
102C2×C22⋊Dic11—21no—
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11—21no—
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11—21no—
108Q8×Dic11—22no—
109Q8×Dic11C2314yes—
110#66997—22no—
111#66997C2314yes—
112C2×#4326—24no—
113C2×#4326—42no—
114C2×#4326C2314yes—
115C2×#4326C2314yes—
116#66989—22no—
117#66989—22no—
118#66989—22no—
119#66989C2314yes—
120#66989C2314yes—
121#66989C2314yes—
122D4×Dic11—22no—
123D4×Dic11C2314yes—
124C2×#4324—24no—
125C2×#4324—24no—
126C2×#4324—42no—
127C2×#4324C2314yes—
128C2×#4324C2314yes—
129C2×#4324C2314yes—
130#66979—28no—
131C2×C4⋊Dic11—21no—
132C2×C4⋊Dic11—21no—
133C2×C4⋊Dic11—21no—
134C2×C4⋊Dic11D411yescharacteristic
135C2×C4⋊Dic11C2311yescharacteristic
136#66977—28no—
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4D411yescharacteristic
143C2×Dic11⋊C4D411yescharacteristic
144C2×C4×Dic11—21no—
145C2×C4×Dic11—21no—
146C2×C4×Dic11—21no—
147C2×C4×Dic11—21no—
148C2×C4×Dic11C2311yescharacteristic
149C2×C4×Dic11C2311yescharacteristic
150C22×C11⋊C8C2311yescharacteristic
151C22×C11⋊C8C2311yescharacteristic
152C2×Dic44—42no—
153C2×Dic44—42no—
154C2×Dic44C2314yes—
155C2×Dic44C2314yes—
156#66940—22no—
157#66940—22no—
158#66940C2314yes—
159#66940C2314yes—
160#66932—28no—
161#66932—28no—
162#66932—28no—
163#66932—28no—
164#66931—28no—
165#66930—28no—
166#66922—22no—
167#66922C2314yes—
168C4×Dic22—22no—
169C4×Dic22D414yes—
170C4×Dic22C2314yes—
171C4×Dic22C2314yes—
172C11×C4⋊C8C2314yes—
173C11×#103C2314yes—
174C11×#102C2314yes—
175#66896C2314yes—
176#66880C2314yes—
177#66880C2314yes—
178#66879C2314yes—
179Dic11⋊C8C2314yes—
180Dic11⋊C8C2314yes—
181C8×Dic11C2314yes—
182#66874C2314yes—
183#66871C2314yes—
184#66867C2314yes—
185C2×#3402—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11—21no—
188C2×Q8×C11—21no—
189C2×Q8×C11—22no—
190C2×Q8×C11—22no—
191C2×Q8×C11C2412yes—
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—22no—
195C2×D4×C11—22no—
196C2×D4×C11—22no—
197C2×D4×C11—22no—
198C2×D4×C11C2412yes—
199C2×D4×C11C2412yes—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—24no—
203C22×C4×C11—44no—
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2411yescharacteristic
207C22×Dic11—24no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—44no—
213C22×Dic11C2×D411yescharacteristic
214C22×Dic11C2×D411yescharacteristic
215C22×Dic11C2×D411yescharacteristic
216C22×Dic11C2×D411yescharacteristic
217C2×Dic22—21no—
218C2×Dic22—21no—
219C2×Dic22—21no—
220C2×Dic22—22no—
221C2×Dic22—22no—
222C2×Dic22—22no—
223C2×Dic22—22no—
224C2×Dic22—22no—
225C2×Dic22—22no—
226C2×Dic22—42no—
227C2×Dic22C2×D414yes—
228C2×Dic22C2412yes—
229C2×Dic22C2412yes—
230C2×Dic22C2412yes—
231C11×SD16—44no—
232C11×D8—44no—
233C2×C8×C11—22no—
234C2×C8×C11—22no—
235C2×C8×C11C2412yes—
236C2×C8×C11C2412yes—
237C11×C4⋊C4—21no—
238C11×C4⋊C4C2412yes—
239C11×C22⋊C4—24no—
240C11×C22⋊C4—24no—
241C11×C22⋊C4—24no—
242C42×C11C2×D412yes—
243C42×C11C2412yes—
244C22⋊Dic11—24no—
245C22⋊Dic11—24no—
246C22⋊Dic11—24no—
247C22⋊Dic11—24no—
248C22⋊Dic11—24no—
249C22⋊Dic11—24no—
250C22⋊Dic11—24no—
251#4326—28no—
252#4326—44no—
253#4324—28no—
254#4324—28no—
255#4324—44no—
256C4⋊Dic11—24no—
257C4⋊Dic11—21no—
258C4⋊Dic11—24no—
259C4⋊Dic11—24no—
260C4⋊Dic11C2×D414yes—
261C4⋊Dic11C2412yes—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267Dic11⋊C4C2×D414yes—
268Dic11⋊C4C2×D414yes—
269C4×Dic11—24no—
270C4×Dic11—24no—
271C4×Dic11—24no—
272C4×Dic11—24no—
273C4×Dic11C2×D412yes—
274C4×Dic11C2×D412yes—
275C4×Dic11C2412yes—
276C4×Dic11C2412yes—
277C2×C11⋊C8—22no—
278C2×C11⋊C8#4114yes—
279C2×C11⋊C8C2412yes—
280C2×C11⋊C8C2412yes—
281Dic44—44no—
282Dic44—44no—
283C2×#556—111no—
284C2×#556—111no—
285#3402—1116no—
286C2×#497—111no—
287C2×#497—111no—
288C2×#495—111no—
289C2×#464—111no—
290C2×#464—111no—
291C2×#462—111no—
292C2×#462—111no—
293C2×#463—111no—
294C2×#463D1111yescharacteristic
295C2×#446—111no—
296C2×#440—111no—
297C2×#440—111no—
298C2×C4×Q16—111no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—42no—
302C23×C11—42no—
303C23×C11—42no—
304C23×C11—42no—
305C23×C11—42no—
306C23×C11—42no—
307C23×C11C22×D411yescharacteristic
308Q8×C11—22no—
309Q8×C11—22no—
310Q8×C11—42no—
311D4×C11—22no—
312D4×C11—22no—
313D4×C11—22no—
314D4×C11—22no—
315D4×C11—42no—
316D4×C11—42no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—48no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11C22×D412yes—
325C2×C4×C11C22×D412yes—
326C2×C4×C11C22×D411yescharacteristic
327C2×C4×C11C2×#4112yes—
328C2×C4×C11H(5,𝔽2)12yes—
329C2×C4×C11C2511yescharacteristic
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—48no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11C22×D412yes—
344C2×Dic11C22×D412yes—
345C2×Dic11C22×D412yes—
346C2×Dic11C22×D412yes—
347Dic22—22no—
348Dic22—22no—
349Dic22—22no—
350Dic22—22no—
351Dic22—22no—
352Dic22—22no—
353Dic22—44no—
354Dic22—42no—
355Dic22—42no—
356Dic22—42no—
357C8×C11—22no—
358C8×C11—22no—
359C11⋊C8—22no—
360C11⋊C8C2×#4114yes—
361C22×Q16—111no—
362C22×Q16—111no—
363C22×Q16—111no—
364C22×Q16—111no—
365C22×SD16—111no—
366C22×SD16—111no—
367C22×SD16—111no—
368C22×SD16C2×D1111yescharacteristic
369C22×D8C2×D1111yescharacteristic
370#556—118no—
371#556—118no—
372#556—224no—
373#556—224no—
374C2×C4⋊Q8—111no—
375C2×C4⋊Q8—111no—
376C2×#126—221no—
377C2×#126—221no—
378C2×#126—221no—
379C2×#126—221no—
380C2×#124—111no—
381C2×#124—111no—
382C2×#124—111no—
383C2×#124C2×D1111yescharacteristic
384C2×C22⋊Q8—221no—
385C2×C22⋊Q8—221no—
386C2×C4×Q8—111no—
387C2×C4×Q8—111no—
388C2×C4×Q8—111no—
389C2×C4×Q8—111no—
390C2×C4×Q8—111no—
391C2×C4×D4—111no—
392C2×C4×D4C2×D1111yescharacteristic
393C2×#117—221no—
394C2×#117—221no—
395#497—118no—
396#497—118no—
397#495—118no—
398#464—118no—
399#464—118no—
400#463—118no—
401#463C2×D1118yes—
402#462—118no—
403#462—118no—
404#446—118no—
405#440—118no—
406#440—118no—
407C4×Q16—118no—
408C2×#107—111no—
409C2×C4⋊C8—111no—
410C2×C4⋊C8—111no—
411C2×C4⋊C8C2×D1111yescharacteristic
412C2×#103—111no—
413C2×#103—111no—
414C2×#103—111no—
415C2×#103C2×D1111yescharacteristic
416C2×#102—111no—
417C2×#102C2×D1111yescharacteristic
418C2×#97—111no—
419C2×#97—111no—
420C2×C4×C8—111no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11—42no—
426C22×C11—42no—
427C22×C11—84no—
428C22×C11—84no—
429C22×C11#55012yes—
430C22×C11#57512yes—
431C22×C11#57812yes—
432C22×C11C23×D411yescharacteristic
433C4×C11—22no—
434C4×C11—22no—
435C4×C11—42no—
436C4×C11—42no—
437C4×C11#55012yes—
438C4×C11C22×#4111yescharacteristic
439C4×C11C2×H(5,𝔽2)11yescharacteristic
440Dic11—22no—
441Dic11—22no—
442Dic11—22no—
443Dic11—22no—
444Dic11—42no—
445Dic11—42no—
446Dic11—42no—
447Dic11—42no—
448C22×Q8—111no—
449C22×Q8—111no—
450C22×Q8—111no—
451C22×Q8—111no—
452C22×Q8C22×D1111yescharacteristic
453C22×D4C22×D1111yescharacteristic
454C22×D4C22×D1111yescharacteristic
455C23×C4—21no—
456C23×C4—221no—
457C2×Q16—114no—
458C2×Q16—114no—
459C2×Q16—114no—
460C2×Q16—114no—
461C2×Q16—224no—
462C2×Q16—442no—
463C2×Q16—442no—
464C2×Q16—442no—
465C2×SD16—42no—
466C2×SD16—114no—
467C2×SD16—114no—
468C2×SD16—114no—
469C2×SD16—224no—
470C2×SD16—224no—
471C2×SD16—442no—
472C2×SD16C22×D1114yes—
473C2×D8—42no—
474C2×D8C22×D1114yes—
475C22×C8—111no—
476C22×C8—111no—
477C22×C8C22×D1111yescharacteristic
478C22×C8C22×D1111yescharacteristic
479C4⋊Q8—114no—
480C4⋊Q8—114no—
481C4⋊Q8—222no—
482C4⋊Q8—222no—
483#126—228no—
484#126—228no—
485#126—228no—
486#126—228no—
487#124—22no—
488#124—114no—
489#124—114no—
490#124—114no—
491#124—222no—
492#124—222no—
493#124—222no—
494#124C22×D1114yes—
495C22⋊Q8—228no—
496C22⋊Q8—228no—
497C4×Q8—114no—
498C4×Q8—114no—
499C4×Q8—114no—
500C4×Q8—114no—
501C4×Q8—114no—
502C4×Q8—114no—
503C4×Q8—222no—
504C4×Q8—222no—
505C4×Q8—222no—
506C4×Q8—222no—
507C4×D4—22no—
508C4×D4—114no—
509C4×D4—222no—
510C4×D4C22×D1114yes—
511#117—228no—
512#117—228no—
513C2×C4⋊C4—111no—
514C2×C4⋊C4—111no—
515C2×C4⋊C4—111no—
516C2×C4⋊C4—111no—
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⋊C4—221no—
524C2×C4⋊C4—221no—
525C2×C4⋊C4C22×D1111yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—221no—
530C2×C22⋊C4—221no—
531C2×C22⋊C4—221no—
532C2×C22⋊C4—221no—
533C2×C22⋊C4—221no—
534C2×C22⋊C4—221no—
535C2×C22⋊C4—221no—
536C2×C42—111no—
537C2×C42—111no—
538C2×C42—221no—
539C2×C42—221no—
540C2×C42—221no—
541C2×C42—221no—
542C2×C42C22×D1111yescharacteristic
543#107—114no—
544C4⋊C8—114no—
545C4⋊C8—114no—
546C4⋊C8C22×D1114yes—
547#103—114no—
548#103—114no—
549#103—114no—
550#103C22×D1114yes—
551#102—114no—
552#102C22×D1114yes—
553#97—114no—
554#97—114no—
555C4×C8—114no—
556C2×C11—82no—
557C2×C11—82no—
558C2×C11#340214yescomplemented
559C2×C11C2×#55011yescharacteristic
560C2×C11C2×#57511yescharacteristic
561C2×C11C2×#57811yescharacteristic
562C24—21no—
563C24—21no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—114no—
568C2×Q8—112no—
569C2×Q8—112no—
570C2×Q8—112no—
571C2×Q8—221no—
572C2×Q8—221no—
573C2×Q8—221no—
574C2×Q8—222no—
575C2×Q8—222no—
576C2×Q8—222no—
577C2×Q8—222no—
578C2×Q8—222no—
579C2×Q8—222no—
580C2×Q8—442no—
581C2×Q8C23×D1112yes—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4C23×D1112yes—
589C2×D4C23×D1112yes—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—24no—
593C22×C4—44no—
594C22×C4—111no—
595C22×C4—111no—
596C22×C4—111no—
597C22×C4—111no—
598C22×C4—224no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—221no—
603C22×C4—444no—
604C22×C4D4×D1111yescharacteristic
605C22×C4D4×D1111yescharacteristic
606C22×C4C23×D1111yescharacteristic
607Q16—228no—
608Q16—444no—
609Q16—444no—
610Q16—444no—
611SD16—44no—
612SD16—228no—
613SD16—228no—
614SD16—444no—
615D8—44no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—114no—
619C2×C8—112no—
620C2×C8—112no—
621C2×C8—222no—
622C2×C8C23×D1112yes—
623C2×C8C23×D1112yes—
624C4⋊C4—21no—
625C4⋊C4—114no—
626C4⋊C4—114no—
627C4⋊C4—114no—
628C4⋊C4—112no—
629C4⋊C4—224no—
630C4⋊C4—224no—
631C4⋊C4—224no—
632C4⋊C4—224no—
633C4⋊C4—224no—
634C4⋊C4—221no—
635C4⋊C4—224no—
636C4⋊C4—224no—
637C4⋊C4—224no—
638C4⋊C4C23×D1112yes—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—224no—
643C22⋊C4—224no—
644C22⋊C4—224no—
645C22⋊C4—224no—
646C22⋊C4—224no—
647C22⋊C4—224no—
648C22⋊C4—224no—
649C42—112no—
650C42—112no—
651C42—112no—
652C42—112no—
653C42—224no—
654C42—224no—
655C42—224no—
656C42—224no—
657C42D4×D1112yes—
658C42C23×D1112yes—
659C11C2×#340211yescharacteristic, complemented, Sylow
660C23—22no—
661C23—22no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23C2×D4×D1111yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—222no—
673Q8—222no—
674Q8—222no—
675Q8—222no—
676Q8—222no—
677Q8—222no—
678Q8—444no—
679Q8—442no—
680Q8—442no—
681Q8—442no—
682D4—22no—
683D4—22no—
684D4—22no—
685D4—22no—
686D4—42no—
687D4—42no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—48no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—112no—
696C2×C4—112no—
697C2×C4—112no—
698C2×C4—112no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—222no—
706C2×C4—222no—
707C2×C4—448no—
708C2×C4—442no—
709C2×C4—442no—
710C2×C4—442no—
711C2×C4—442no—
712C2×C4C2×D4×D1112yes—
713C2×C4C2×D4×D1112yes—
714C2×C4C2×D4×D1111yescharacteristic
715C2×C4#6703712yes—
716C2×C4#41×D1112yes—
717C2×C4C24×D1111yescharacteristic
718C8—22no—
719C8—22no—
720C8—114no—
721C8—222no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—84no—
729C22—84no—
730C22#1062313012yes—
731C22#1062330212yes—
732C22#1062330412yes—
733C22C22×D4×D1111yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—222no—
739C4—222no—
740C4—222no—
741C4—222no—
742C4—442no—
743C4—442no—
744C4—442no—
745C4—442no—
746C4#1062313012yes—
747C4C2×#6703711yescharacteristic
748C4C2×#41×D1111yescharacteristic
749C2—82no—
750C2—82no—
751C2#1308169414yesdirect product factor
752C2C2×#1062313011yescharacteristic
753C2C2×#1062330411yescharacteristic
754C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#463C2
socleC23×C11C22×D4
prime radicalC22×C11×D8C22
hypercenterC2×#463D11
hypocenterC11C2×#3402
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#10623073C2semidirect
2. C2×#10623202C2semidirect
3. #13081694C2direct (N × H)
4. C2×#10622673C2semidirect
5. C2×#10622780C2semidirect
7. C2×#10622380C2semidirect
8. C2×#10622779C2semidirect
9. C2×#10622462C2semidirect
10. C2×#10622406C2semidirect
12. C2×#10622441C2semidirect
13. C2×#10622631C2semidirect
14. C2×#10622370C2semidirect
15. C2×#10622403C2semidirect
37. #10623202C22semidirect
39. #10623073C22semidirect
56. #10622780C22semidirect
57. #10622779C22semidirect
66. #10622673C22semidirect
67. #10622631C22semidirect
71. #10622462C22semidirect
72. #10622441C22semidirect
73. #10622406C22semidirect
74. #10622403C22semidirect
75. #10622380C22semidirect
76. #10622370C22semidirect
558. C2×C11#3402semidirect
659. C11C2×#3402semidirect
751. C2#13081694direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230732
C2×#106232022
#130816942
C2×#106226732
C2×#106227802
C2×#106227682
C2×#106223802
C2×#106227792
C2×#106224622
C2×#106224062
C2×#106227662
C2×#106224412
C2×#106226312
C2×#106223702
C2×#106224032
C2×C11×#4632
C2×#340211