Finite Group Databasebeta

← C2×#13081337 #15633451

Subgroups — C2×#13081337 #15633451

Order 2816.

2070 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623099C211yesmaximal, characteristic, complemented
2C2×#10623258C211yesmaximal, characteristic, complemented
3#13081337C2116yesmaximal, direct product factor
4C2×#10622702C211yesmaximal, characteristic, complemented
5C2×#10622408C211yesmaximal, characteristic, complemented
6C2×#10622405C211yesmaximal, characteristic, complemented
7C2×#10622488C211yesmaximal, characteristic, complemented
8C2×#10622503C211yesmaximal, characteristic, complemented
9C2×#10622432C211yesmaximal, characteristic
10C2×#10622457C211yesmaximal, characteristic
11C2×#10622431C211yesmaximal, characteristic, complemented
12C2×#10622441C211yesmaximal, characteristic, complemented
13C2×#10622502C211yesmaximal, characteristic, complemented
14C2×#10622639C211yesmaximal, characteristic, complemented
15C2×#10622485C211yesmaximal, characteristic
16C2×C11×#477C211yesmaximal, characteristic, complemented
17C22×Q8×D11—21no—
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×#67000C2211yescharacteristic
21C2×#66999—21no—
22C2×#66997C2211yescharacteristic
23C22×#4325C2211yescharacteristic
24C22×D88C2211yescharacteristic
25C22×#4314C2211yescharacteristic
26#10623258—24no—
27#10623258C2218yescomplemented
28#10623099—24no—
29#10623099C2218yescomplemented
30C2×#66951—21no—
31C2×#66949—21no—
32C2×#66949—21no—
33C2×#66949—21no—
34C2×#66946C2211yescharacteristic
35C2×#66946C2211yescharacteristic
36C2×#66946C2211yescharacteristic
37C2×#66941C2211yescharacteristic
38C2×#66941C2211yescharacteristic
39C2×#66940C2211yescharacteristic
40C2×#66929—21no—
41C2×#66928C2211yescharacteristic
42C2×C4×D44C2211yescharacteristic
43C2×#66925—21no—
44C2×C4×Dic22C2211yescharacteristic
45C11×#477C2218yescomplemented
46C2×C11×#107C2211yescharacteristic
47C2×C11×#107C2211yescharacteristic
48C2×C11×C4⋊C8C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66885C2211yescharacteristic
53C2×#66880C2211yescharacteristic
54C2×#66879C2211yescharacteristic
55C2×Dic11⋊C8C2211yescharacteristic
56C2×Dic11⋊C8C2211yescharacteristic
57C2×C8×Dic11C2211yescharacteristic
58#10622702C2218yescomplemented
59#10622639C2218yescomplemented
60C2×#66874C2211yescharacteristic
61C2×#66874C2211yescharacteristic
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66873C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×#66867C2211yescharacteristic
67#10622503C2218yescomplemented
68#10622502C2218yescomplemented
69#10622488C2218yescomplemented
70#10622485C2218yes—
71#10622457C2218yes—
72#10622441C2218yescomplemented
73#10622432C2218yes—
74#10622431C2218yescomplemented
75#10622408C2218yescomplemented
76#10622405C2218yescomplemented
77C22×Q8×C11—21no—
78C22×Q8×C11C2311yescharacteristic
79C2×Q8×D11—28no—
80C2×Q8×D11—48no—
81C22×D44C2311yescharacteristic
82C22×D44C2311yescharacteristic
83C22×C4×D11—21no—
84C22×C4×D11—21no—
85C22×C4×D11—21no—
86C22×C4×D11—21no—
87C22×Dic22—21no—
88C22×Dic22—21no—
89C22×Dic22D411yescharacteristic
90C22×Dic22C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C11×C4⋊Q8—22no—
94C11×C4⋊Q8C2314yes—
95C4×Q8×C11—22no—
96C4×Q8×C11C2314yes—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C42×C11—21no—
103C2×C42×C11C2311yescharacteristic
104#67000—22no—
105#67000C2314yes—
106#66999—28no—
107#66997—22no—
108#66997C2314yes—
109C2×#4325—24no—
110C2×#4325C2314yes—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×C4⋊Dic11D411yescharacteristic
120C2×C4⋊Dic11C2311yescharacteristic
121C2×Dic11⋊C4—21no—
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4—21no—
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4D411yescharacteristic
127C2×Dic11⋊C4D411yescharacteristic
128C2×C4×Dic11—21no—
129C2×C4×Dic11C2311yescharacteristic
130C2×C4×Dic11C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133C2×D88—24no—
134C2×D88C2314yes—
135C2×#4314—24no—
136C2×#4314C2314yes—
137#66951—28no—
138#66949—28no—
139#66949—28no—
140#66949—28no—
141#66946—22no—
142#66946—22no—
143#66946—22no—
144#66946C2314yes—
145#66946C2314yes—
146#66946C2314yes—
147#66941—22no—
148#66941—22no—
149#66941C2314yes—
150#66941C2314yes—
151#66940—22no—
152#66940C2314yes—
153#66929—28no—
154#66928—22no—
155#66928C2314yes—
156C4×D44—22no—
157C4×D44C2314yes—
158#66925—28no—
159C4×Dic22D414yes—
160C4×Dic22C2314yes—
161C11×#107C2314yes—
162C11×#107C2314yes—
163C11×C4⋊C8C2314yes—
164C11×#103C2314yes—
165C11×#103C2314yes—
166#66899C2314yes—
167#66885C2314yes—
168#66880C2314yes—
169#66879C2314yes—
170Dic11⋊C8C2314yes—
171Dic11⋊C8C2314yes—
172C8×Dic11C2314yes—
173#66874C2314yes—
174#66874C2314yes—
175#66873C2314yes—
176#66873C2314yes—
177#66873C2314yes—
178#66871C2314yes—
179#66867C2314yes—
180C2×#3367—111nomaximal, Sylow
181C23×D11—21no—
182C23×D11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—24no—
185C2×Q8×C11—22no—
186C2×Q8×C11—22no—
187C2×Q8×C11—44no—
188C2×Q8×C11C2412yes—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2411yescharacteristic
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11C2×D411yescharacteristic
199C22×Dic11C2×D411yescharacteristic
200C22×Dic11C2×D411yescharacteristic
201C22×Dic11C2×D411yescharacteristic
202Q8×D11—432no—
203C2×D44—21no—
204C2×D44—21no—
205C2×D44—22no—
206C2×D44—22no—
207C2×D44—22no—
208C2×D44#4114yes—
209C2×D44C2412yes—
210C2×D44C2412yes—
211C2×C4×D11—24no—
212C2×C4×D11—24no—
213C2×C4×D11—24no—
214C2×C4×D11—24no—
215C2×C4×D11—44no—
216C2×C4×D11—44no—
217C2×C4×D11—44no—
218C2×C4×D11—44no—
219C2×Dic22—24no—
220C2×Dic22—24no—
221C2×Dic22—24no—
222C2×Dic22—21no—
223C2×Dic22—22no—
224C2×Dic22—22no—
225C2×Dic22—44no—
226C2×Dic22—44no—
227C2×Dic22C2×D414yes—
228C2×Dic22C2412yes—
229C2×C8×C11—22no—
230C2×C8×C11—22no—
231C2×C8×C11C2412yes—
232C2×C8×C11C2412yes—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—24no—
237C11×C4⋊C4—24no—
238C11×C4⋊C4C2412yes—
239C11×C4⋊C4C2412yes—
240C11×C4⋊C4C2412yes—
241C42×C11—24no—
242C42×C11C2×D412yes—
243C42×C11C2412yes—
244#4325—28no—
245(C2×D11)⋊C4—24no—
246(C2×D11)⋊C4—24no—
247(C2×D11)⋊C4—24no—
248(C2×D11)⋊C4—24no—
249(C2×D11)⋊C4—24no—
250(C2×D11)⋊C4—24no—
251(C2×D11)⋊C4—24no—
252(C2×D11)⋊C4—24no—
253C4⋊Dic11—21no—
254C4⋊Dic11C2×D414yes—
255C4⋊Dic11C2412yes—
256Dic11⋊C4—24no—
257Dic11⋊C4—24no—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4C2×D414yes—
262Dic11⋊C4C2×D414yes—
263C4×Dic11—24no—
264C4×Dic11C2×D412yes—
265C4×Dic11C2×D412yes—
266C4×Dic11C2412yes—
267C4×Dic11C2412yes—
268C2×C11⋊C8—22no—
269C2×C11⋊C8—22no—
270C2×C11⋊C8C2412yes—
271C2×C11⋊C8C2412yes—
272D88—28no—
273#4314—28no—
274C2×#556—111no—
275C2×D4×Q8—111no—
276#3367—1116no—
277C2×#489—111no—
278C2×#489—111no—
279C2×#487—111no—
280C2×#477—111no—
281C2×#477D1111yescharacteristic, complemented
282C2×#474—111no—
283C2×#463—111no—
284C2×#463—111no—
285C2×#461—111no—
286C2×#446—111no—
287C2×#440—111no—
288C2×#440—111no—
289C2×C4×D8—111no—
290C23×C11C22×D411yescharacteristic
291C22×D11—24no—
292C22×D11—22no—
293C22×D11—22no—
294C22×D11—42no—
295C22×D11—42no—
296C22×D11—42no—
297C22×D11—42no—
298C22×D11—42no—
299Q8×C11—22no—
300Q8×C11—22no—
301Q8×C11—48no—
302Q8×C11—42no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11C22×D412yes—
314C2×C4×C11C22×D412yes—
315C2×C4×C11C22×D411yescharacteristic
316C2×C4×C11C2×#4112yes—
317C2×C4×C112−1+412yes—
318C2×C4×C11C2511yescharacteristic
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—42no—
325C2×Dic11—42no—
326C2×Dic11AGL(1,ℤ/8)14yes—
327C2×Dic11C22×D412yes—
328C2×Dic11C22×D412yes—
329C2×Dic11C22×D412yes—
330C2×Dic11C22×D412yes—
331D44—24no—
332D44—22no—
333D44—22no—
334D44—22no—
335D44—42no—
336D44C2×#4114yes—
337C4×D11—48no—
338C4×D11—48no—
339C4×D11—48no—
340C4×D11—48no—
341Dic22—28no—
342Dic22—22no—
343Dic22—22no—
344Dic22—48no—
345Dic22—42no—
346Dic22—48no—
347C8×C11—22no—
348C8×C11—22no—
349C11⋊C8—22no—
350C11⋊C8—22no—
351C23×Q8—221no—
352C22×SD16—111no—
353C22×SD16—111no—
354C22×D8—111no—
355#556—118no—
356#556—224no—
357D4×Q8—118no—
358D4×Q8—224no—
359C2×C4⋊Q8—111no—
360C2×C4⋊Q8—111no—
361C2×C4⋊Q8—111no—
362C2×C4⋊Q8C2×D1111yescharacteristic
363C2×#126—221no—
364C2×#126—221no—
365C2×#124—111no—
366C2×#124—111no—
367C2×C22⋊Q8—221no—
368C2×C22⋊Q8—221no—
369C2×C22⋊Q8—221no—
370C2×C22⋊Q8—221no—
371C2×C4×Q8—111no—
372C2×C4×Q8—111no—
373C2×C4×Q8C2×D1111yescharacteristic
374C2×C4×D4—111no—
375C2×C4×D4—111no—
376C2×C4×D4—111no—
377C2×C4×D4—111no—
378C2×#117—221no—
379#489—118no—
380#489—118no—
381#487—118no—
382#477—118no—
383#477C2×D1118yescomplemented
384#474—118no—
385#463—118no—
386#463—118no—
387#461—118no—
388#446—118no—
389#440—118no—
390#440—118no—
391C4×D8—118no—
392C2×#107—111no—
393C2×#107C2×D1111yescharacteristic
394C2×#107C2×D1111yescharacteristic
395C2×C4⋊C8—111no—
396C2×C4⋊C8—111no—
397C2×C4⋊C8C2×D1111yescharacteristic
398C2×#103—111no—
399C2×#103—111no—
400C2×#103—111no—
401C2×#103—111no—
402C2×#103C2×D1111yescharacteristic
403C2×#103C2×D1111yescharacteristic
404C2×#102—111no—
405C2×#102—111no—
406C2×#102—111no—
407C2×#102—111no—
408C2×#97—111no—
409C2×#97—111no—
410C2×C4×C8—111no—
411C22×C11#54812yes—
412C22×C11C2×AGL(1,ℤ/8)12yes—
413C22×C11#57812yes—
414C22×C11C23×D411yescharacteristic
415C2×D11—24no—
416C2×D11—48no—
417C2×D11—42no—
418C2×D11—42no—
419C2×D11—42no—
420C2×D11—42no—
421C2×D11—42no—
422C2×D11—84no—
423C4×C11—22no—
424C4×C11—22no—
425C4×C11—42no—
426C4×C11—42no—
427C4×C11—42no—
428C4×C11—42no—
429C4×C11#54812yes—
430C4×C11C22×#4111yescharacteristic
431C4×C11C2×2−1+411yescharacteristic
432Dic11—22no—
433Dic11—22no—
434Dic11—22no—
435Dic11—42no—
436Dic11—42no—
437Dic11C2×AGL(1,ℤ/8)14yes—
438C22×Q8—21no—
439C22×Q8—111no—
440C22×Q8—111no—
441C22×Q8—221no—
442C22×Q8—221no—
443C22×Q8—228no—
444C22×Q8—448no—
445C22×Q8C22×D1111yescharacteristic
446C22×D4—111no—
447C22×D4—111no—
448C23×C4—221no—
449C23×C4—221no—
450C23×C4—221no—
451C23×C4—221no—
452C2×SD16—114no—
453C2×SD16—114no—
454C2×SD16—224no—
455C2×SD16—224no—
456C2×D8—114no—
457C2×D8—224no—
458C22×C8—111no—
459C22×C8—111no—
460C22×C8C22×D1111yescharacteristic
461C22×C8C22×D1111yescharacteristic
462C4⋊Q8—22no—
463C4⋊Q8—114no—
464C4⋊Q8—114no—
465C4⋊Q8—114no—
466C4⋊Q8—222no—
467C4⋊Q8—222no—
468C4⋊Q8—222no—
469C4⋊Q8C22×D1114yes—
470#126—228no—
471#126—228no—
472#124—114no—
473#124—114no—
474#124—222no—
475#124—222no—
476C22⋊Q8—228no—
477C22⋊Q8—228no—
478C22⋊Q8—228no—
479C22⋊Q8—228no—
480C4×Q8—22no—
481C4×Q8—114no—
482C4×Q8—114no—
483C4×Q8—114no—
484C4×Q8—222no—
485C4×Q8C22×D1114yes—
486C4×D4—114no—
487C4×D4—114no—
488C4×D4—114no—
489C4×D4—114no—
490C4×D4—222no—
491C4×D4—222no—
492C4×D4—222no—
493C4×D4—222no—
494#117—228no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—111no—
498C2×C4⋊C4—111no—
499C2×C4⋊C4—111no—
500C2×C4⋊C4—111no—
501C2×C4⋊C4—221no—
502C2×C4⋊C4—221no—
503C2×C4⋊C4—221no—
504C2×C4⋊C4—221no—
505C2×C4⋊C4—221no—
506C2×C4⋊C4C22×D1111yescharacteristic
507C2×C4⋊C4C22×D1111yescharacteristic
508C2×C4⋊C4C22×D1111yescharacteristic
509C2×C22⋊C4—221no—
510C2×C22⋊C4—221no—
511C2×C22⋊C4—221no—
512C2×C22⋊C4—221no—
513C2×C22⋊C4—221no—
514C2×C22⋊C4—221no—
515C2×C22⋊C4—221no—
516C2×C22⋊C4—221no—
517C2×C42—21no—
518C2×C42—111no—
519C2×C42—111no—
520C2×C42—221no—
521C2×C42C22×D1111yescharacteristic
522#107—114no—
523#107C22×D1114yes—
524#107C22×D1114yes—
525C4⋊C8—114no—
526C4⋊C8—114no—
527C4⋊C8C22×D1114yes—
528#103—114no—
529#103—114no—
530#103—114no—
531#103—114no—
532#103C22×D1114yes—
533#103C22×D1114yes—
534#102—114no—
535#102—114no—
536#102—114no—
537#102—114no—
538#97—114no—
539#97—114no—
540C4×C8—114no—
541C2×C11#336714yescomplemented
542C2×C11C2×#54811yescharacteristic
543C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
544C2×C11C2×#57811yescharacteristic
545D11—44no—
546D11—82no—
547C24—221no—
548C24—221no—
549C2×Q8—21no—
550C2×Q8—24no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—44no—
554C2×Q8—114no—
555C2×Q8—112no—
556C2×Q8—224no—
557C2×Q8—224no—
558C2×Q8—224no—
559C2×Q8—221no—
560C2×Q8—222no—
561C2×Q8—222no—
562C2×Q8—444no—
563C2×Q8—444no—
564C2×Q8—4432no—
565C2×Q8C23×D1112yes—
566C2×D4—114no—
567C2×D4—112no—
568C2×D4—112no—
569C2×D4—221no—
570C2×D4—221no—
571C2×D4—222no—
572C2×D4—222no—
573C2×D4—222no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—111no—
579C22×C4—111no—
580C22×C4—111no—
581C22×C4—111no—
582C22×C4—224no—
583C22×C4—224no—
584C22×C4—224no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—224no—
588C22×C4—444no—
589C22×C4—444no—
590C22×C4—444no—
591C22×C4—444no—
592C22×C4D4×D1111yescharacteristic
593C22×C4D4×D1111yescharacteristic
594C22×C4C23×D1111yescharacteristic
595SD16—228no—
596SD16—228no—
597D8—228no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—112no—
601C2×C8—112no—
602C2×C8—222no—
603C2×C8—222no—
604C2×C8C23×D1112yes—
605C2×C8C23×D1112yes—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—114no—
612C4⋊C4—114no—
613C4⋊C4—114no—
614C4⋊C4—112no—
615C4⋊C4—224no—
616C4⋊C4—224no—
617C4⋊C4—224no—
618C4⋊C4—224no—
619C4⋊C4—224no—
620C4⋊C4—221no—
621C4⋊C4C23×D1112yes—
622C4⋊C4C23×D1112yes—
623C4⋊C4C23×D1112yes—
624C22⋊C4—224no—
625C22⋊C4—224no—
626C22⋊C4—224no—
627C22⋊C4—224no—
628C22⋊C4—224no—
629C22⋊C4—224no—
630C22⋊C4—224no—
631C22⋊C4—224no—
632C42—24no—
633C42—112no—
634C42—112no—
635C42—112no—
636C42—112no—
637C42—224no—
638C42D4×D1112yes—
639C42C23×D1112yes—
640C11C2×#336711yescharacteristic, complemented, Sylow
641C23—224no—
642C23—222no—
643C23—222no—
644C23—442no—
645C23—442no—
646C23—442no—
647C23—442no—
648C23—442no—
649C23C2×D4×D1111yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—48no—
653Q8—42no—
654Q8—228no—
655Q8—222no—
656Q8—222no—
657Q8—448no—
658Q8—448no—
659Q8—442no—
660D4—114no—
661D4—224no—
662D4—222no—
663D4—222no—
664D4—222no—
665D4—442no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—114no—
677C2×C4—112no—
678C2×C4—112no—
679C2×C4—112no—
680C2×C4—112no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—222no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—448no—
687C2×C4—448no—
688C2×C4—448no—
689C2×C4—448no—
690C2×C4—442no—
691C2×C4—442no—
692C2×C4C2×D4×D1112yes—
693C2×C4C2×D4×D1112yes—
694C2×C4C2×D4×D1111yescharacteristic
695C2×C4#6704012yes—
696C2×C4#41×D1112yes—
697C2×C4C24×D1111yescharacteristic
698C8—22no—
699C8—22no—
700C8—222no—
701C8—222no—
702C22—224no—
703C22—442no—
704C22—442no—
705C22—448no—
706C22—442no—
707C22—442no—
708C22—442no—
709C22—884no—
710C22#1062316412yes—
711C22#1062329712yes—
712C22D11×AGL(1,ℤ/8)12yes—
713C22C22×D4×D1111yescharacteristic
714C4—22no—
715C4—22no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—114no—
721C4—222no—
722C4—222no—
723C4—222no—
724C4—442no—
725C4—442no—
726C4#1062316412yes—
727C4C2×#6704011yescharacteristic
728C4C2×#41×D1111yescharacteristic
729C2—444no—
730C2—882no—
731C2#1308133714yesdirect product factor
732C2C2×#1062316411yescharacteristic
733C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
734C2C2×#1062329711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#477C2
socleC23×C11C22×D4
prime radicalC22×D88C22
hypercenterC2×#477D11
hypocenterC11C2×#3367
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
1. C2×#10623099C2semidirect
2. C2×#10623258C2semidirect
3. #13081337C2direct (N × H)
4. C2×#10622702C2semidirect
5. C2×#10622408C2semidirect
6. C2×#10622405C2semidirect
7. C2×#10622488C2semidirect
8. C2×#10622503C2semidirect
11. C2×#10622431C2semidirect
12. C2×#10622441C2semidirect
13. C2×#10622502C2semidirect
14. C2×#10622639C2semidirect
16. C2×C11×#477C2semidirect
27. #10623258C22semidirect
29. #10623099C22semidirect
45. C11×#477C22semidirect
58. #10622702C22semidirect
59. #10622639C22semidirect
67. #10622503C22semidirect
68. #10622502C22semidirect
69. #10622488C22semidirect
72. #10622441C22semidirect
74. #10622431C22semidirect
75. #10622408C22semidirect
76. #10622405C22semidirect
281. C2×#477D11semidirect
383. #477C2×D11semidirect
541. C2×C11#3367semidirect
640. C11C2×#3367semidirect
731. C2#13081337direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230992
C2×#106232582
#130813372
C2×#106227022
C2×#106224082
C2×#106224052
C2×#106224882
C2×#106225032
C2×#106224322
C2×#106224572
C2×#106224312
C2×#106224412
C2×#106225022
C2×#106226392
C2×#106224852
C2×C11×#4772
C2×#336711