Finite Group Databasebeta

← C2×#13080073 #15626734

Subgroups — C2×#13080073 #15626734

Order 2816.

1882 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×#10623174C211yesmaximal, characteristic, complemented
2C2×#10623134C211yesmaximal, characteristic, complemented
3#13080073C2116yesmaximal, direct product factor
4C2×#10622488C211yesmaximal, characteristic, complemented
5C2×#10622407C211yesmaximal, characteristic, complemented
6C2×#10622503C211yesmaximal, characteristic, complemented
7C2×#10622372C211yesmaximal, characteristic, complemented
8C2×#10622747C211yesmaximal, characteristic, complemented
9C2×#10622664C211yesmaximal, characteristic, complemented
10C2×#10622651C211yesmaximal, characteristic
11C2×#10622411C211yesmaximal, characteristic, complemented
12C2×#10622779C211yesmaximal, characteristic, complemented
13C2×#10622778C211yesmaximal, characteristic, complemented
14C2×#10622400C211yesmaximal, characteristic, complemented
15C2×#10622732C211yesmaximal, characteristic, complemented
16C2×C11×#468C211yesmaximal, characteristic, complemented
17C22×C11×SD16C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×#67000C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C22×#4326C2211yescharacteristic
24C2×#66989—21no—
25C2×#66989C2211yescharacteristic
26C2×#66988—21no—
27C2×D4×Dic11C2211yescharacteristic
28C22×#4323C2211yescharacteristic
29C2×#66983C2211yescharacteristic
30C2×#66979C2211yescharacteristic
31C2×#66977C2211yescharacteristic
32C23×C11⋊C8C2211yescharacteristic
33C22×#4314C2211yescharacteristic
34#10623174—24no—
35#10623174C2218yescomplemented
36#10623134—24no—
37#10623134C2218yescomplemented
38C2×#66951—21no—
39C2×#66950—21no—
40C2×#66946C2211yescharacteristic
41C2×#66941C2211yescharacteristic
42C2×#66941C2211yescharacteristic
43C2×#66940C2211yescharacteristic
44C2×#66938—21no—
45C2×#66936—21no—
46C2×#66932—21no—
47C2×#66931—21no—
48C11×#468C2218yescomplemented
49C2×C11×#107C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54#10622779C2218yescomplemented
55#10622778C2218yescomplemented
56#10622747C2218yescomplemented
57#10622732C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×#66882C2211yescharacteristic
60C2×#66880C2211yescharacteristic
61C2×Dic11⋊C8C2211yescharacteristic
62C2×Dic11⋊C8C2211yescharacteristic
63C2×Dic11⋊C8C2211yescharacteristic
64C2×Dic11⋊C8C2211yescharacteristic
65#10622664C2218yescomplemented
66#10622651C2218yes—
67C2×#66874C2211yescharacteristic
68C2×#66873C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71#10622503C2218yescomplemented
72#10622488C2218yescomplemented
73#10622411C2218yescomplemented
74#10622407C2218yescomplemented
75#10622400C2218yescomplemented
76#10622372C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C23×Dic11—21no—
83C22×D44C2311yescharacteristic
84C22×C4×D11—21no—
85C22×Dic22—21no—
86C22×Dic22—21no—
87C22×Dic22C2311yescharacteristic
88C2×C11×SD16—42no—
89C2×C11×SD16C2314yes—
90C2×C11×M16—42no—
91C2×C11×M16C2314yes—
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C11×C22⋊Q8—22no—
95C11×C22⋊Q8C2314yes—
96C11×#121—22no—
97C11×#121C2314yes—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11—21no—
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11D411yescharacteristic
108C2×C22⋊Dic11D411yescharacteristic
109#67000—22no—
110#67000C2314yes—
111Q8×Dic11—22no—
112Q8×Dic11C2314yes—
113C2×#4326—42no—
114C2×#4326C2314yes—
115#66989—28no—
116#66989—22no—
117#66989C2314yes—
118#66988—28no—
119D4×Dic11—22no—
120D4×Dic11C2314yes—
121C2×#4323—42no—
122C2×#4323C2314yes—
123#66983—22no—
124#66983C2314yes—
125C2×(C2×D11)⋊C4—21no—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
128C2×(C2×D11)⋊C4—21no—
129#66979D414yes—
130#66979C2314yes—
131C2×C4⋊Dic11—21no—
132C2×C4⋊Dic11D411yescharacteristic
133C2×C4⋊Dic11D411yescharacteristic
134C2×C4⋊Dic11C2311yescharacteristic
135C2×C4⋊Dic11C2311yescharacteristic
136#66977—22no—
137#66977C2314yes—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×Dic11⋊C4—21no—
142C2×C4×Dic11—21no—
143C2×C4×Dic11—21no—
144C2×C4×Dic11C2311yescharacteristic
145C2×C4×Dic11C2311yescharacteristic
146C22×C11⋊C8—42no—
147C22×C11⋊C8C2311yescharacteristic
148C22×C11⋊C8C2311yescharacteristic
149C22×C11⋊C8C2314yes—
150C2×#4314—42no—
151C2×#4314C2314yes—
152#66951—28no—
153#66950—28no—
154#66946—22no—
155#66946C2314yes—
156#66941—22no—
157#66941—22no—
158#66941C2314yes—
159#66941C2314yes—
160#66940—22no—
161#66940C2314yes—
162#66938—28no—
163#66936—28no—
164#66932—28no—
165#66931—28no—
166C11×#107C2314yes—
167C11×#103C2314yes—
168C11×#102C2314yes—
169#66899C2314yes—
170#66896C2314yes—
171#66885C2314yes—
172#66882C2314yes—
173#66880C2314yes—
174Dic11⋊C8C2314yes—
175Dic11⋊C8C2314yes—
176Dic11⋊C8C2314yes—
177Dic11⋊C8C2314yes—
178#66874C2314yes—
179#66873C2314yes—
180#66871C2314yes—
181#66871C2314yes—
182C2×#3262—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11C2×D411yescharacteristic
185C23×D11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—22no—
188C2×Q8×C11—22no—
189C2×Q8×C11C2412yes—
190C2×D4×C11—24no—
191C2×D4×C11—21no—
192C2×D4×C11—22no—
193C2×D4×C11—22no—
194C2×D4×C11—82no—
195C2×D4×C11C2412yes—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D412yes—
203C22×C4×C11C2412yes—
204C22×C4×C11C2411yescharacteristic
205C2×C22⋊D11—24no—
206C2×C22⋊D11—82no—
207C22×Dic11—24no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—82no—
212C22×Dic11C2×D411yescharacteristic
213C22×Dic11C2×D411yescharacteristic
214C22×Dic11C2×D411yescharacteristic
215C22×Dic11C2×D411yescharacteristic
216C2×D44—21no—
217C2×D44—22no—
218C2×D44—22no—
219C2×D44C2412yes—
220C2×C4×D11—24no—
221C2×C4×D11—82no—
222C2×Dic22—24no—
223C2×Dic22—24no—
224C2×Dic22—21no—
225C2×Dic22—22no—
226C2×Dic22—22no—
227C2×Dic22—82no—
228C2×Dic22—82no—
229C2×Dic22C2412yes—
230C11×SD16—44no—
231C11×M16—44no—
232C2×C8×C11—22no—
233C2×C8×C11—22no—
234C2×C8×C11C2412yes—
235C2×C8×C11C2412yes—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—21no—
238C11×C4⋊C4—24no—
239C11×C4⋊C4C2412yes—
240C11×C4⋊C4C2412yes—
241C11×C22⋊C4—24no—
242C11×C22⋊C4—24no—
243C22⋊Dic11—24no—
244C22⋊Dic11—24no—
245C22⋊Dic11—24no—
246C22⋊Dic11—24no—
247C22⋊Dic11C2×D414yes—
248C22⋊Dic11C2×D414yes—
249#4326—44no—
250#4323—44no—
251(C2×D11)⋊C4—24no—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4—24no—
254(C2×D11)⋊C4—24no—
255C4⋊Dic11—24no—
256C4⋊Dic11—21no—
257C4⋊Dic11—21no—
258C4⋊Dic11C2×D414yes—
259C4⋊Dic11C2×D414yes—
260C4⋊Dic11C2412yes—
261C4⋊Dic11C2412yes—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266C4×Dic11—24no—
267C4×Dic11—24no—
268C4×Dic11C2×D412yes—
269C4×Dic11C2×D412yes—
270C4×Dic11C2412yes—
271C4×Dic11C2412yes—
272C2×C11⋊C8—22no—
273C2×C11⋊C8—22no—
274C2×C11⋊C8—44no—
275C2×C11⋊C8C2412yes—
276C2×C11⋊C8C2412yes—
277#4314—44no—
278C2×#542—111no—
279C2×#542—111no—
280#3262—1116no—
281C2×#477—111no—
282C2×#477—111no—
283C2×#474—111no—
284C2×#474—111no—
285C2×#468—111no—
286C2×#468D1111yescharacteristic, complemented
287C2×#467—111no—
288C2×#466—111no—
289C2×#464—111no—
290C2×#464—111no—
291C2×#463—111no—
292C2×#463—111no—
293C2×#424—111no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—42no—
299C23×C11—42no—
300C23×C11—42no—
301C23×C11C22×D412yes—
302C23×C11C22×D411yescharacteristic
303C22×D11—22no—
304C22×D11—42no—
305C22×D11—42no—
306C22×D11—42no—
307Q8×C11—22no—
308Q8×C11—22no—
309Q8×C11—42no—
310D4×C11—22no—
311D4×C11—22no—
312D4×C11—42no—
313D4×C11—84no—
314C2×C4×C11—22no—
315C2×C4×C11—24no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—42no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11C22×D412yes—
325C2×C4×C11C22×D411yescharacteristic
326C2×C4×C11H(5,𝔽2)12yes—
327C2×C4×C112−1+412yes—
328C2×C4×C11C2511yescharacteristic
329C22⋊D11—84no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—84no—
341C2×Dic11C22×D412yes—
342C2×Dic11C22×D412yes—
343C2×Dic11C22×D412yes—
344C2×Dic11C22×D412yes—
345D44—22no—
346D44—22no—
347D44—42no—
348C4×D11—84no—
349Dic22—22no—
350Dic22—22no—
351Dic22—42no—
352Dic22—84no—
353Dic22—84no—
354C8×C11—22no—
355C8×C11—22no—
356C11⋊C8—22no—
357C11⋊C8—22no—
358C22×Q16—111no—
359C22×SD16—111no—
360C22×SD16C2×D1111yescharacteristic
361C22×D8—111no—
362C22×M16C2×D1111yescharacteristic
363C23×C8—111no—
364#542—118no—
365#542—118no—
366#542—224no—
367#542—224no—
368C2×C4⋊Q8—111no—
369C2×C4⋊Q8—111no—
370C2×#126—221no—
371C2×#126—221no—
372C2×#124—111no—
373C2×#124—111no—
374C2×#124—221no—
375C2×#124—221no—
376C2×#123—221no—
377C2×#123—221no—
378C2×C22⋊Q8—111no—
379C2×C22⋊Q8—221no—
380C2×C22⋊Q8—221no—
381C2×C22⋊Q8C2×D1111yescharacteristic
382C2×#121—111no—
383C2×#121C2×D1111yescharacteristic
384C2×C4×Q8—111no—
385C2×C4×Q8—111no—
386C2×C4×D4—111no—
387C2×C4×D4—111no—
388C2×#117—111no—
389#477—118no—
390#477—118no—
391#474—118no—
392#474—118no—
393#468—118no—
394#468C2×D1118yescomplemented
395#467—118no—
396#466—118no—
397#464—118no—
398#464—118no—
399#463—118no—
400#463—118no—
401C2×#107—111no—
402C2×#107—111no—
403C2×#107—111no—
404C2×#107C2×D1111yescharacteristic
405#424—118no—
406C2×C4⋊C8—111no—
407C2×C4⋊C8—111no—
408C2×C4⋊C8—111no—
409C2×C4⋊C8—111no—
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—22no—
419C22×C11—22no—
420C22×C11—22no—
421C22×C11—44no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11—84no—
426C22×C11#53712yes—
427C22×C11#57612yes—
428C22×C11#57812yes—
429C22×C11C23×D411yescharacteristic
430C2×D11—42no—
431C2×D11—42no—
432C2×D11—42no—
433C2×D11—84no—
434C4×C11—22no—
435C4×C11—42no—
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—22no—
445Dic11—42no—
446Dic11—42no—
447Dic11—42no—
448C22×Q8—111no—
449C22×Q8—221no—
450C22×Q8—221no—
451C22×Q8C22×D1111yescharacteristic
452C22×D4—21no—
453C22×D4—111no—
454C22×D4—221no—
455C22×D4C22×D1111yescharacteristic
456C23×C4—221no—
457C23×C4—221no—
458C23×C4C22×D1111yescharacteristic
459C2×Q16—114no—
460C2×Q16—442no—
461C2×SD16—42no—
462C2×SD16—114no—
463C2×SD16—442no—
464C2×SD16C22×D1114yes—
465C2×D8—114no—
466C2×D8—442no—
467C2×M16—42no—
468C2×M16C22×D1114yes—
469C22×C8—111no—
470C22×C8—111no—
471C22×C8—114no—
472C22×C8—442no—
473C22×C8C22×D1111yescharacteristic
474C22×C8C22×D1111yescharacteristic
475C4⋊Q8—114no—
476C4⋊Q8—114no—
477C4⋊Q8—222no—
478C4⋊Q8—222no—
479#126—228no—
480#126—228no—
481#124—114no—
482#124—114no—
483#124—222no—
484#124—222no—
485#124—228no—
486#124—228no—
487#123—228no—
488#123—228no—
489C22⋊Q8—22no—
490C22⋊Q8—114no—
491C22⋊Q8—228no—
492C22⋊Q8—228no—
493C22⋊Q8—222no—
494C22⋊Q8C22×D1114yes—
495#121—22no—
496#121—114no—
497#121—222no—
498#121C22×D1114yes—
499C4×Q8—114no—
500C4×Q8—114no—
501C4×Q8—222no—
502C4×Q8—222no—
503C4×D4—114no—
504C4×D4—114no—
505C4×D4—222no—
506C4×D4—222no—
507#117—114no—
508#117—114no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—111no—
511C2×C4⋊C4—111no—
512C2×C4⋊C4—111no—
513C2×C4⋊C4—111no—
514C2×C4⋊C4—221no—
515C2×C4⋊C4—221no—
516C2×C4⋊C4—221no—
517C2×C4⋊C4—221no—
518C2×C4⋊C4—221no—
519C2×C4⋊C4C22×D1111yescharacteristic
520C2×C4⋊C4C22×D1111yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—111no—
524C2×C22⋊C4—111no—
525C2×C22⋊C4—221no—
526C2×C22⋊C4—221no—
527C2×C22⋊C4—221no—
528C2×C22⋊C4—221no—
529C2×C22⋊C4—221no—
530C2×C22⋊C4—221no—
531C2×C22⋊C4—221no—
532C2×C22⋊C4—221no—
533C2×C42—111no—
534C2×C42—111no—
535C2×C42—221no—
536C2×C42—221no—
537#107—114no—
538#107—114no—
539#107—114no—
540#107C22×D1114yes—
541C4⋊C8—114no—
542C4⋊C8—114no—
543C4⋊C8—114no—
544C4⋊C8—114no—
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—42no—
554C2×C11—82no—
555C2×C11#326214yescomplemented
556C2×C11C2×#53711yescharacteristic
557C2×C11C2×#57611yescharacteristic
558C2×C11C2×#57811yescharacteristic
559D11—82no—
560C24—21no—
561C24—221no—
562C24D4×D1111yescharacteristic
563C2×Q8—21no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—112no—
567C2×Q8—224no—
568C2×Q8—224no—
569C2×Q8—221no—
570C2×Q8—222no—
571C2×Q8—222no—
572C2×Q8—882no—
573C2×Q8—882no—
574C2×Q8C23×D1112yes—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—82no—
580C2×D4—112no—
581C2×D4—224no—
582C2×D4—221no—
583C2×D4—222no—
584C2×D4—222no—
585C2×D4—882no—
586C2×D4C23×D1112yes—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—111no—
593C22×C4—111no—
594C22×C4—111no—
595C22×C4—111no—
596C22×C4—224no—
597C22×C4—224no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—882no—
602C22×C4—882no—
603C22×C4D4×D1112yes—
604C22×C4D4×D1111yescharacteristic
605C22×C4C23×D1112yes—
606C22×C4C23×D1111yescharacteristic
607Q16—444no—
608SD16—44no—
609SD16—444no—
610D8—444no—
611M16—44no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—112no—
615C2×C8—112no—
616C2×C8—222no—
617C2×C8—222no—
618C2×C8—444no—
619C2×C8C23×D1112yes—
620C2×C8C23×D1112yes—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—114no—
625C4⋊C4—114no—
626C4⋊C4—112no—
627C4⋊C4—112no—
628C4⋊C4—224no—
629C4⋊C4—224no—
630C4⋊C4—224no—
631C4⋊C4—224no—
632C4⋊C4—221no—
633C4⋊C4—221no—
634C4⋊C4—224no—
635C4⋊C4C23×D1112yes—
636C4⋊C4C23×D1112yes—
637C22⋊C4—24no—
638C22⋊C4—24no—
639C22⋊C4—114no—
640C22⋊C4—114no—
641C22⋊C4—224no—
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—
655C11C2×#326211yescharacteristic, complemented, Sylow
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—222no—
664C23—442no—
665C23—442no—
666C23—442no—
667C23C2×D4×D1112yes—
668C23C2×D4×D1111yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—222no—
673Q8—222no—
674Q8—442no—
675Q8—884no—
676Q8—884no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—84no—
681D4—222no—
682D4—222no—
683D4—442no—
684D4—884no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—42no—
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—442no—
707C2×C4—442no—
708C2×C4—442no—
709C2×C4—884no—
710C2×C4—884no—
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—22no—
721C22—22no—
722C22—22no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—84no—
728C22—442no—
729C22—442no—
730C22—442no—
731C22—884no—
732C22#1062312812yes—
733C22#1062330512yes—
734C22#1062331012yes—
735C22C22×D4×D1111yescharacteristic
736C4—22no—
737C4—42no—
738C4—42no—
739C4—42no—
740C4—222no—
741C4—222no—
742C4—222no—
743C4—222no—
744C4—442no—
745C4—442no—
746C4—442no—
747C4#1062312812yes—
748C4C2×#6703711yescharacteristic
749C4C2×#6704311yescharacteristic
750C2—42no—
751C2—82no—
752C2—882no—
753C2#1308007314yesdirect product factor
754C2C2×#1062312811yescharacteristic
755C2C2×#1062330511yescharacteristic
756C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#468C2
socleC23×C11C22×D4
prime radicalC2×#10622651C2
hypercenterC2×#468D11
hypocenterC11C2×#3262
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#10623174C2semidirect
2. C2×#10623134C2semidirect
3. #13080073C2direct (N × H)
4. C2×#10622488C2semidirect
5. C2×#10622407C2semidirect
6. C2×#10622503C2semidirect
7. C2×#10622372C2semidirect
8. C2×#10622747C2semidirect
9. C2×#10622664C2semidirect
11. C2×#10622411C2semidirect
12. C2×#10622779C2semidirect
13. C2×#10622778C2semidirect
14. C2×#10622400C2semidirect
15. C2×#10622732C2semidirect
16. C2×C11×#468C2semidirect
35. #10623174C22semidirect
37. #10623134C22semidirect
48. C11×#468C22semidirect
54. #10622779C22semidirect
55. #10622778C22semidirect
56. #10622747C22semidirect
57. #10622732C22semidirect
65. #10622664C22semidirect
71. #10622503C22semidirect
72. #10622488C22semidirect
73. #10622411C22semidirect
74. #10622407C22semidirect
75. #10622400C22semidirect
76. #10622372C22semidirect
286. C2×#468D11semidirect
394. #468C2×D11semidirect
555. C2×C11#3262semidirect
655. C11C2×#3262semidirect
753. C2#13080073direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231742
C2×#106231342
#130800732
C2×#106224882
C2×#106224072
C2×#106225032
C2×#106223722
C2×#106227472
C2×#106226642
C2×#106226512
C2×#106224112
C2×#106227792
C2×#106227782
C2×#106224002
C2×#106227322
C2×C11×#4682
C2×#326211