Finite Group Databasebeta

← C2×#13080014 #15626658

Subgroups — C2×#13080014 #15626658

Order 2816.

1930 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623088C211yesmaximal, characteristic, complemented
2C2×#10623211C211yesmaximal, characteristic, complemented
3#13080014C2116yesmaximal, direct product factor
4C2×#10622442C211yesmaximal, characteristic, complemented
5C2×#10622412C211yesmaximal, characteristic, complemented
6C2×#10622622C211yesmaximal, characteristic, complemented
7C2×#10622379C211yesmaximal, characteristic, complemented
8C2×#10622429C211yesmaximal, characteristic, complemented
9C2×#10622772C211yesmaximal, characteristic
10C2×#10622393C211yesmaximal, characteristic, complemented
11C2×#10622787C211yesmaximal, characteristic, complemented
12C2×#10622779C211yesmaximal, characteristic, complemented
13C2×#10622667C211yesmaximal, characteristic, complemented
14C2×#10622766C211yesmaximal, characteristic, complemented
15C2×#10622450C211yesmaximal, characteristic, complemented
16C2×C11×#463C211yesmaximal, characteristic, complemented
17C22×C11×SD16C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C2×C11×#124C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×#66999C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C22×#4326C2211yescharacteristic
24C2×#66991C2211yescharacteristic
25C2×#66991C2211yescharacteristic
26C2×#66989C2211yescharacteristic
27C2×D4×Dic11C2211yescharacteristic
28C22×#4324C2211yescharacteristic
29C2×C4×C22⋊D11—21no—
30C2×#66979—21no—
31C22×#4313C2211yescharacteristic
32C22×#4313C2211yescharacteristic
33#10623211—24no—
34#10623211C2218yescomplemented
35#10623088—24no—
36#10623088C2218yescomplemented
37C2×#66950C2211yescharacteristic
38C2×#66943C2211yescharacteristic
39C2×#66936—21no—
40C2×#66936—21no—
41C2×(C22⋊D11)⋊C4—21no—
42C2×#66932—21no—
43C2×#66932—21no—
44C2×#66930—21no—
45C2×C42×D11C2211yescharacteristic
46C2×#66923C2211yescharacteristic
47C2×C4×Dic22C2211yescharacteristic
48C11×#463C2218yescomplemented
49C2×C11×C4⋊C8C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×#66896C2211yescharacteristic
56#10622787C2218yescomplemented
57#10622779C2218yescomplemented
58#10622772C2218yes—
59#10622766C2218yescomplemented
60C2×#66882C2211yescharacteristic
61C2×#66881C2211yescharacteristic
62C2×#66880C2211yescharacteristic
63C2×#66880C2211yescharacteristic
64C2×Dic11⋊C8C2211yescharacteristic
65C2×Dic11⋊C8C2211yescharacteristic
66#10622667C2218yescomplemented
67#10622622C2218yescomplemented
68C2×#66872C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×C4⋊(C11⋊C8)C2211yescharacteristic
71#10622450C2218yescomplemented
72#10622442C2218yescomplemented
73#10622429C2218yescomplemented
74#10622412C2218yescomplemented
75#10622393C2218yescomplemented
76#10622379C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11C2311yescharacteristic
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11—21no—
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C23×Dic11—21no—
84C22×C4×D11D411yescharacteristic
85C22×C4×D11D411yescharacteristic
86C22×C4×D11C2311yescharacteristic
87C22×Dic22C2311yescharacteristic
88C2×C11×SD16—42no—
89C2×C11×SD16C2314yes—
90C2×C11×D8—42no—
91C2×C11×D8C2314yes—
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C11×#124—22no—
95C11×#124C2314yes—
96C4×D4×C11—22no—
97C4×D4×C11C2314yes—
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C42×C11C2311yescharacteristic
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11—21no—
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11—21no—
108#66999—22no—
109#66999C2314yes—
110Q8×Dic11—22no—
111Q8×Dic11C2314yes—
112C2×#4326—42no—
113C2×#4326C2314yes—
114#66991—22no—
115#66991—22no—
116#66991C2314yes—
117#66991C2314yes—
118#66989—22no—
119#66989C2314yes—
120D4×Dic11—22no—
121D4×Dic11C2314yes—
122C2×#4324—42no—
123C2×#4324C2314yes—
124C4×C22⋊D11—28no—
125C2×(C2×D11)⋊C4—21no—
126C2×(C2×D11)⋊C4—21no—
127#66979—28no—
128C2×C4⋊Dic11—21no—
129C2×C4⋊Dic11—21no—
130C2×C4⋊Dic11—21no—
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
133C2×C4⋊Dic11C2311yescharacteristic
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4—21no—
136C2×Dic11⋊C4—21no—
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4—21no—
139C2×C4×Dic11—21no—
140C2×C4×Dic11—21no—
141C2×C4×Dic11D411yescharacteristic
142C2×C4×Dic11D411yescharacteristic
143C2×C4×Dic11C2311yescharacteristic
144C22×C11⋊C8C2311yescharacteristic
145C22×C11⋊C8C2311yescharacteristic
146C2×#4313—42no—
147C2×#4313—42no—
148C2×#4313C2314yes—
149C2×#4313C2314yes—
150#66950—22no—
151#66950C2314yes—
152#66943—22no—
153#66943C2314yes—
154#66936—28no—
155#66936—28no—
156(C22⋊D11)⋊C4—28no—
157#66932—28no—
158#66932—28no—
159#66930—28no—
160C42×D11D414yes—
161C42×D11C2314yes—
162#66923—22no—
163#66923C2314yes—
164C4×Dic22—22no—
165C4×Dic22C2314yes—
166C11×C4⋊C8C2314yes—
167C11×#103C2314yes—
168C11×#102C2314yes—
169#66899C2314yes—
170#66896C2314yes—
171#66896C2314yes—
172#66896C2314yes—
173#66882C2314yes—
174#66881C2314yes—
175#66880C2314yes—
176#66880C2314yes—
177Dic11⋊C8C2314yes—
178Dic11⋊C8C2314yes—
179#66872C2314yes—
180#66871C2314yes—
181C4⋊(C11⋊C8)C2314yes—
182C2×#3256—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11—21no—
185C23×D11C2×D411yescharacteristic
186C2×Q8×C11—21no—
187C2×Q8×C11—22no—
188C2×Q8×C11—22no—
189C2×Q8×C11C2412yes—
190C2×D4×C11—21no—
191C2×D4×C11—21no—
192C2×D4×C11—22no—
193C2×D4×C11—22no—
194C2×D4×C11—22no—
195C2×D4×C11—22no—
196C2×D4×C11C2412yes—
197C2×D4×C11C2412yes—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—24no—
201C22×C4×C11—44no—
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2411yescharacteristic
205C2×C22⋊D11—24no—
206C2×C22⋊D11—24no—
207C2×C22⋊D11—44no—
208C2×C22⋊D11—44no—
209C22×Dic11—24no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—44no—
215C22×Dic11C2×D411yescharacteristic
216C22×Dic11C2×D411yescharacteristic
217C22×Dic11C2×D411yescharacteristic
218C2×C4×D11—22no—
219C2×C4×D11—22no—
220C2×C4×D11—42no—
221C2×C4×D11—42no—
222C2×C4×D11C2×D412yes—
223C2×C4×D11C2×D414yes—
224C2×C4×D11C2×D414yes—
225C2×C4×D11C2412yes—
226C2×Dic22—21no—
227C2×Dic22—22no—
228C2×Dic22—22no—
229C2×Dic22C2412yes—
230C11×SD16—44no—
231C11×D8—44no—
232C2×C8×C11—22no—
233C2×C8×C11—22no—
234C2×C8×C11C2412yes—
235C2×C8×C11C2412yes—
236C11×C4⋊C4—21no—
237C11×C4⋊C4C2412yes—
238C11×C22⋊C4—24no—
239C11×C22⋊C4—24no—
240C11×C22⋊C4—24no—
241C42×C11C2×D412yes—
242C42×C11C2412yes—
243C22⋊Dic11—24no—
244C22⋊Dic11—24no—
245C22⋊Dic11—24no—
246C22⋊Dic11—24no—
247C22⋊Dic11—24no—
248#4326—44no—
249#4324—44no—
250(C2×D11)⋊C4—24no—
251(C2×D11)⋊C4—24no—
252C4⋊Dic11—24no—
253C4⋊Dic11—24no—
254C4⋊Dic11—24no—
255C4⋊Dic11—21no—
256C4⋊Dic11—21no—
257C4⋊Dic11—21no—
258C4⋊Dic11C2412yes—
259C4⋊Dic11C2412yes—
260C4⋊Dic11C2412yes—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266C4×Dic11—24no—
267C4×Dic11—24no—
268C4×Dic11C2×D412yes—
269C4×Dic11C2×D414yes—
270C4×Dic11C2×D414yes—
271C4×Dic11C2412yes—
272C2×C11⋊C8—22no—
273C2×C11⋊C8—22no—
274C2×C11⋊C8C2412yes—
275C2×C11⋊C8C2412yes—
276#4313—44no—
277#4313—44no—
278C2×#529—111no—
279C2×#529—111no—
280#3256—1116no—
281C2×#479—111no—
282C2×#479—111no—
283C2×#478—111no—
284C2×#478—111no—
285C2×#470—111no—
286C2×#469—111no—
287C2×#468—111no—
288C2×#468—111no—
289C2×#464—111no—
290C2×#464—111no—
291C2×#463—111no—
292C2×#463D1111yescharacteristic, complemented
293C2×#423—111no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—42no—
297C23×C11—42no—
298C23×C11—42no—
299C23×C11—42no—
300C23×C11—42no—
301C23×C11—42no—
302C23×C11C22×D411yescharacteristic
303C22×D11—22no—
304C22×D11—22no—
305C22×D11—22no—
306C22×D11C22×D412yes—
307Q8×C11—22no—
308Q8×C11—22no—
309Q8×C11—42no—
310D4×C11—22no—
311D4×C11—22no—
312D4×C11—22no—
313D4×C11—22no—
314D4×C11—42no—
315D4×C11—42no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—48no—
321C2×C4×C11—42no—
322C2×C4×C11—42no—
323C2×C4×C11C22×D412yes—
324C2×C4×C11C22×D412yes—
325C2×C4×C11C22×D411yescharacteristic
326C2×C4×C11H(5,𝔽2)12yes—
327C2×C4×C112−1+412yes—
328C2×C4×C11C2511yescharacteristic
329C22⋊D11—48no—
330C22⋊D11—48no—
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—
346C4×D11—24no—
347C4×D11—22no—
348C4×D11—22no—
349C4×D11—44no—
350C4×D11—44no—
351Dic22—22no—
352Dic22—22no—
353Dic22—42no—
354C8×C11—22no—
355C8×C11—22no—
356C11⋊C8—22no—
357C11⋊C8—22no—
358C22×Q16—111no—
359C22×SD16—111no—
360C22×SD16C2×D1111yescharacteristic
361C22×D8C2×D1111yescharacteristic
362C22×M16—111no—
363C22×M16—111no—
364#529—118no—
365#529—118no—
366#529—224no—
367#529—224no—
368C2×#126—221no—
369C2×#126—221no—
370C2×#125—111no—
371C2×#125—111no—
372C2×#124—111no—
373C2×#124C2×D1111yescharacteristic
374C2×#123—221no—
375C2×#123—221no—
376C2×C22⋊Q8—111no—
377C2×C22⋊Q8—111no—
378C2×#121—111no—
379C2×#121—111no—
380C2×C4×Q8—111no—
381C2×C4×Q8—111no—
382C2×C4×D4—111no—
383C2×C4×D4—221no—
384C2×C4×D4—221no—
385C2×C4×D4C2×D1111yescharacteristic
386C2×#117—221no—
387C2×#117—221no—
388C22×C42—111no—
389#479—118no—
390#479—118no—
391#478—118no—
392#478—118no—
393#470—118no—
394#469—118no—
395#468—118no—
396#468—118no—
397#464—118no—
398#464—118no—
399#463—118no—
400#463C2×D1118yescomplemented
401C2×#107—111no—
402C2×#107—111no—
403C2×#106—111no—
404C2×#106—111no—
405#423—118no—
406C2×C4⋊C8—111no—
407C2×C4⋊C8—111no—
408C2×C4⋊C8—111no—
409C2×C4⋊C8C2×D1111yescharacteristic
410C2×#103—111no—
411C2×#103—111no—
412C2×#103—111no—
413C2×#103C2×D1111yescharacteristic
414C2×#102—111no—
415C2×#102—111no—
416C2×#102—111no—
417C2×#102C2×D1111yescharacteristic
418C22×C11—42no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—84no—
425C22×C11—84no—
426C22×C11#53712yes—
427C22×C11#57512yes—
428C22×C11#57512yes—
429C22×C11C23×D411yescharacteristic
430C2×D11—22no—
431C2×D11—22no—
432C2×D11—22no—
433C2×D11—44no—
434C4×C11—22no—
435C4×C11—22no—
436C4×C11—42no—
437C4×C11—42no—
438C4×C11#53712yes—
439C4×C11C2×H(5,𝔽2)11yescharacteristic
440C4×C11C2×2−1+411yescharacteristic
441Dic11—22no—
442Dic11—22no—
443Dic11—22no—
444Dic11—42no—
445Dic11—42no—
446Dic11—42no—
447Dic11—42no—
448C22×Q8—111no—
449C22×Q8C22×D1111yescharacteristic
450C22×D4—221no—
451C22×D4—221no—
452C22×D4C22×D1111yescharacteristic
453C22×D4C22×D1111yescharacteristic
454C23×C4—21no—
455C23×C4—111no—
456C23×C4—111no—
457C23×C4—111no—
458C23×C4—221no—
459C2×Q16—114no—
460C2×Q16—442no—
461C2×SD16—42no—
462C2×SD16—114no—
463C2×SD16—442no—
464C2×SD16C22×D1114yes—
465C2×D8—42no—
466C2×D8C22×D1114yes—
467C2×M16—114no—
468C2×M16—114no—
469C2×M16—442no—
470C2×M16—442no—
471C22×C8—111no—
472C22×C8—111no—
473C22×C8C22×D1111yescharacteristic
474C22×C8C22×D1111yescharacteristic
475#126—228no—
476#126—228no—
477#125—114no—
478#125—114no—
479#125—222no—
480#125—222no—
481#124—22no—
482#124—114no—
483#124—222no—
484#124C22×D1114yes—
485#123—228no—
486#123—228no—
487C22⋊Q8—114no—
488C22⋊Q8—114no—
489C22⋊Q8—222no—
490C22⋊Q8—222no—
491#121—114no—
492#121—114no—
493#121—222no—
494#121—222no—
495C4×Q8—114no—
496C4×Q8—114no—
497C4×Q8—222no—
498C4×Q8—222no—
499C4×D4—22no—
500C4×D4—114no—
501C4×D4—222no—
502C4×D4—228no—
503C4×D4—228no—
504C4×D4C22×D1114yes—
505#117—228no—
506#117—228no—
507C2×C4⋊C4—111no—
508C2×C4⋊C4—111no—
509C2×C4⋊C4—111no—
510C2×C4⋊C4—221no—
511C2×C4⋊C4—221no—
512C2×C4⋊C4—221no—
513C2×C4⋊C4—221no—
514C2×C4⋊C4—221no—
515C2×C4⋊C4—221no—
516C2×C4⋊C4—221no—
517C2×C4⋊C4—221no—
518C2×C4⋊C4C22×D1111yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—221no—
523C2×C22⋊C4—221no—
524C2×C22⋊C4—221no—
525C2×C22⋊C4—221no—
526C2×C22⋊C4—221no—
527C2×C22⋊C4—221no—
528C2×C22⋊C4—221no—
529C2×C42—111no—
530C2×C42—111no—
531C2×C42—111no—
532C2×C42—114no—
533C2×C42—114no—
534C2×C42—221no—
535C2×C42—221no—
536C2×C42C22×D1111yescharacteristic
537#107—114no—
538#107—114no—
539#106—114no—
540#106—114no—
541C4⋊C8—114no—
542C4⋊C8—114no—
543C4⋊C8—114no—
544C4⋊C8C22×D1114yes—
545#103—114no—
546#103—114no—
547#103—114no—
548#103C22×D1114yes—
549#102—114no—
550#102—114no—
551#102—114no—
552#102C22×D1114yes—
553C2×C11—82no—
554C2×C11—82no—
555C2×C11#325614yescomplemented
556C2×C11C2×#53711yescharacteristic
557C2×C11C2×#57511yescharacteristic
558C2×C11C2×#57511yescharacteristic
559D11—42no—
560C24—21no—
561C24—21no—
562C24—111no—
563C2×Q8—21no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—112no—
567C2×Q8—221no—
568C2×Q8—222no—
569C2×Q8—222no—
570C2×Q8C23×D1112yes—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—224no—
578C2×D4—224no—
579C2×D4—444no—
580C2×D4—444no—
581C2×D4C23×D1112yes—
582C2×D4C23×D1112yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—24no—
586C22×C4—44no—
587C22×C4—111no—
588C22×C4—111no—
589C22×C4—111no—
590C22×C4—112no—
591C22×C4—112no—
592C22×C4—114no—
593C22×C4—114no—
594C22×C4—224no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—221no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—442no—
602C22×C4—442no—
603C22×C4—444no—
604C22×C4D4×D1111yescharacteristic
605C22×C4D4×D1111yescharacteristic
606C22×C4C23×D1111yescharacteristic
607Q16—444no—
608SD16—44no—
609SD16—444no—
610D8—44no—
611M16—444no—
612M16—444no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—112no—
616C2×C8—112no—
617C2×C8—222no—
618C2×C8—222no—
619C2×C8C23×D1112yes—
620C2×C8C23×D1112yes—
621C4⋊C4—21no—
622C4⋊C4—112no—
623C4⋊C4—112no—
624C4⋊C4—112no—
625C4⋊C4—224no—
626C4⋊C4—224no—
627C4⋊C4—224no—
628C4⋊C4—224no—
629C4⋊C4—224no—
630C4⋊C4—221no—
631C4⋊C4—221no—
632C4⋊C4—221no—
633C4⋊C4—224no—
634C4⋊C4—224no—
635C4⋊C4—224no—
636C4⋊C4C23×D1112yes—
637C22⋊C4—24no—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—224no—
641C22⋊C4—224no—
642C22⋊C4—224no—
643C22⋊C4—224no—
644C22⋊C4—224no—
645C22⋊C4—224no—
646C22⋊C4—224no—
647C42—114no—
648C42—112no—
649C42—114no—
650C42—112no—
651C42—224no—
652C42—224no—
653C42D4×D1112yes—
654C42C23×D1112yes—
655C11C2×#325611yescharacteristic, complemented, Sylow
656C23—22no—
657C23—22no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—112no—
665C23—222no—
666C23—222no—
667C23—222no—
668C23C2×D4×D1111yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—222no—
673Q8—222no—
674Q8—442no—
675D4—22no—
676D4—22no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—42no—
681D4—448no—
682D4—448no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—48no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—112no—
691C2×C4—112no—
692C2×C4—112no—
693C2×C4—222no—
694C2×C4—222no—
695C2×C4—222no—
696C2×C4—224no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—444no—
704C2×C4—444no—
705C2×C4—448no—
706C2×C4—442no—
707C2×C4—442no—
708C2×C4—442no—
709C2×C4—442no—
710C2×C4C2×D4×D1112yes—
711C2×C4C2×D4×D1112yes—
712C2×C4C2×D4×D1111yescharacteristic
713C2×C4#6703712yes—
714C2×C4#6704312yes—
715C2×C4C24×D1111yescharacteristic
716C8—22no—
717C8—22no—
718C8—222no—
719C8—222no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—84no—
727C22—84no—
728C22—222no—
729C22—222no—
730C22—222no—
731C22—444no—
732C22#1062313912yes—
733C22#1062329912yes—
734C22#1062330412yes—
735C22C22×D4×D1111yescharacteristic
736C4—22no—
737C4—22no—
738C4—42no—
739C4—42no—
740C4—222no—
741C4—222no—
742C4—222no—
743C4—442no—
744C4—442no—
745C4—442no—
746C4—442no—
747C4#1062313912yes—
748C4C2×#6703711yescharacteristic
749C4C2×#6704311yescharacteristic
750C2—82no—
751C2—82no—
752C2—442no—
753C2#1308001414yesdirect product factor
754C2C2×#1062313911yescharacteristic
755C2C2×#1062330411yescharacteristic
756C2C2×#1062329911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#463C2
socleC23×C11C22×D4
prime radicalC2×#10622772C2
hypercenterC2×#463D11
hypocenterC11C2×#3256
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×#10623088C2semidirect
2. C2×#10623211C2semidirect
3. #13080014C2direct (N × H)
4. C2×#10622442C2semidirect
5. C2×#10622412C2semidirect
6. C2×#10622622C2semidirect
7. C2×#10622379C2semidirect
8. C2×#10622429C2semidirect
10. C2×#10622393C2semidirect
11. C2×#10622787C2semidirect
12. C2×#10622779C2semidirect
13. C2×#10622667C2semidirect
14. C2×#10622766C2semidirect
15. C2×#10622450C2semidirect
16. C2×C11×#463C2semidirect
34. #10623211C22semidirect
36. #10623088C22semidirect
48. C11×#463C22semidirect
56. #10622787C22semidirect
57. #10622779C22semidirect
59. #10622766C22semidirect
66. #10622667C22semidirect
67. #10622622C22semidirect
71. #10622450C22semidirect
72. #10622442C22semidirect
73. #10622429C22semidirect
74. #10622412C22semidirect
75. #10622393C22semidirect
76. #10622379C22semidirect
292. C2×#463D11semidirect
400. #463C2×D11semidirect
555. C2×C11#3256semidirect
655. C11C2×#3256semidirect
753. C2#13080014direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230882
C2×#106232112
#130800142
C2×#106224422
C2×#106224122
C2×#106226222
C2×#106223792
C2×#106224292
C2×#106227722
C2×#106223932
C2×#106227872
C2×#106227792
C2×#106226672
C2×#106227662
C2×#106224502
C2×C11×#4632
C2×#325611