Finite Group Databasebeta

← C2×#13081108 #15632359

Subgroups — C2×#13081108 #15632359

Order 2816.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623110C211yesmaximal, characteristic, complemented
2C2×#10623226C211yesmaximal, characteristic
3#13081108C2116yesmaximal, direct product factor
4C2×#10622678C211yesmaximal, characteristic, complemented
5C2×#10622422C211yesmaximal, characteristic, complemented
6C2×#10622476C211yesmaximal, characteristic, complemented
7C2×#10622427C211yesmaximal, characteristic, complemented
8C2×#10622495C211yesmaximal, characteristic, complemented
9C2×#10622459C211yesmaximal, characteristic, complemented
10C2×#10622425C211yesmaximal, characteristic, complemented
11C2×#10622420C211yesmaximal, characteristic, complemented
12C2×#10622639C211yesmaximal, characteristic, complemented
13C2×#10622449C211yesmaximal, characteristic, complemented
14C2×#10622474C211yesmaximal, characteristic, complemented
15C2×D11×#107C211yesmaximal, characteristic, complemented
16C2×C11×#479C211yesmaximal, characteristic, complemented
17C2×C11×#125C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#66999C2211yescharacteristic
20C2×#66999C2211yescharacteristic
21C22×#4325C2211yescharacteristic
22C22×#4313C2211yescharacteristic
23C22×C8×D11C2211yescharacteristic
24#10623226—24no—
25#10623226C2218yes—
26#10623110—24no—
27#10623110C2218yescomplemented
28C2×#66951—21no—
29C2×#66949—21no—
30C2×#66949—21no—
31C2×#66948—21no—
32C2×#66948C2211yescharacteristic
33C2×#66948C2211yescharacteristic
34C2×#66947—21no—
35C2×#66946—21no—
36C2×#66945C2211yescharacteristic
37C2×C4⋊C4×D11C2211yescharacteristic
38C2×C4⋊C4×D11C2211yescharacteristic
39C2×C4⋊C4×D11C2211yescharacteristic
40C2×C4×D44—21no—
41C2×C4×D44C2211yescharacteristic
42C2×C4×D44C2211yescharacteristic
43C2×#66923—21no—
44C2×#66922C2211yescharacteristic
45C11×#479C2218yescomplemented
46C2×C11×#107C2211yescharacteristic
47C2×C11×#106C2211yescharacteristic
48C2×C11×C4⋊C8C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66885C2211yescharacteristic
53C2×#66885C2211yescharacteristic
54C2×(C2×D11)⋊C8C2211yescharacteristic
55C2×(C2×D11)⋊C8C2211yescharacteristic
56C2×#66882C2211yescharacteristic
57C2×#66882C2211yescharacteristic
58#10622678C2218yescomplemented
59#10622639C2218yescomplemented
60C2×#66873C2211yescharacteristic
61C2×#66872C2211yescharacteristic
62C2×#66872C2211yescharacteristic
63C2×#66871C2211yescharacteristic
64C2×#66871C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×#66867C2211yescharacteristic
67#10622495C2218yescomplemented
68D11×#107C2218yescomplemented
69#10622476C2218yescomplemented
70#10622474C2218yescomplemented
71#10622459C2218yescomplemented
72#10622449C2218yescomplemented
73#10622427C2218yescomplemented
74#10622425C2218yescomplemented
75#10622422C2218yescomplemented
76#10622420C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D44—21no—
79C22×D44—21no—
80C22×D44D411yescharacteristic
81C22×D44C2311yescharacteristic
82C22×C4×D11—21no—
83C22×C4×D11—21no—
84C22×C4×D11—21no—
85C22×C4×D11—21no—
86C22×C4×D11C2311yescharacteristic
87C22×C4×D11C2311yescharacteristic
88C22×Dic22—21no—
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C11×#125—22no—
92C11×#125C2314yes—
93C4×Q8×C11—22no—
94C4×Q8×C11C2314yes—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C42×C11—21no—
102C2×C42×C11C2311yescharacteristic
103#66999—22no—
104#66999—22no—
105#66999C2314yes—
106#66999C2314yes—
107C2×#4325—24no—
108C2×#4325C2314yes—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4D411yescharacteristic
116C2×(C2×D11)⋊C4D411yescharacteristic
117C2×C4⋊Dic11—21no—
118C2×C4⋊Dic11D411yescharacteristic
119C2×C4⋊Dic11C2311yescharacteristic
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2311yescharacteristic
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4—21no—
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4—21no—
127C2×C4×Dic11—21no—
128C22×C11⋊C8C2311yescharacteristic
129C22×C11⋊C8C2311yescharacteristic
130C2×#4313—24no—
131C2×#4313C2314yes—
132C2×C8×D11—24no—
133C2×C8×D11C2314yes—
134#66951—28no—
135#66949—28no—
136#66949—28no—
137#66948—28no—
138#66948—22no—
139#66948—22no—
140#66948C2314yes—
141#66948C2314yes—
142#66947—28no—
143#66946—28no—
144#66945—22no—
145#66945C2314yes—
146C4⋊C4×D11—22no—
147C4⋊C4×D11—22no—
148C4⋊C4×D11—22no—
149C4⋊C4×D11C2314yes—
150C4⋊C4×D11C2314yes—
151C4⋊C4×D11C2314yes—
152C4×D44—28no—
153C4×D44—22no—
154C4×D44D414yes—
155C4×D44C2314yes—
156C4×D44C2314yes—
157#66923—28no—
158#66922—22no—
159#66922C2314yes—
160C11×#107C2314yes—
161C11×#106C2314yes—
162C11×C4⋊C8C2314yes—
163C11×#103C2314yes—
164C11×#103C2314yes—
165#66899C2314yes—
166#66885C2314yes—
167#66885C2314yes—
168(C2×D11)⋊C8C2314yes—
169(C2×D11)⋊C8C2314yes—
170#66882C2314yes—
171#66882C2314yes—
172#66873C2314yes—
173#66872C2314yes—
174#66872C2314yes—
175#66871C2314yes—
176#66871C2314yes—
177#66871C2314yes—
178#66867C2314yes—
179C2×#3346—111nomaximal, Sylow
180C23×D11—21no—
181C23×D11C2×D411yescharacteristic
182C23×D11C2×D411yescharacteristic
183C2×Q8×C11—21no—
184C2×Q8×C11—22no—
185C2×Q8×C11—22no—
186C2×Q8×C11C2412yes—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2411yescharacteristic
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11C2×D411yescharacteristic
198C22×Dic11C2×D411yescharacteristic
199C2×D44—24no—
200C2×D44—24no—
201C2×D44—24no—
202C2×D44—21no—
203C2×D44—22no—
204C2×D44—22no—
205C2×D44—44no—
206C2×D44—82no—
207C2×D44C2×D414yes—
208C2×D44C2412yes—
209C2×C4×D11—24no—
210C2×C4×D11—24no—
211C2×C4×D11—24no—
212C2×C4×D11—24no—
213C2×C4×D11—22no—
214C2×C4×D11—22no—
215C2×C4×D11—22no—
216C2×C4×D11—22no—
217C2×C4×D11—82no—
218C2×C4×D11—82no—
219C2×C4×D11—82no—
220C2×C4×D11—82no—
221C2×C4×D11C2×D412yes—
222C2×C4×D11C2×D412yes—
223C2×C4×D11C2412yes—
224C2×C4×D11C2412yes—
225C2×Dic22—24no—
226C2×Dic22—82no—
227C2×C8×C11—22no—
228C2×C8×C11—22no—
229C2×C8×C11C2412yes—
230C2×C8×C11C2412yes—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—21no—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—24no—
235C11×C4⋊C4—24no—
236C11×C4⋊C4—24no—
237C11×C4⋊C4C2412yes—
238C11×C4⋊C4C2412yes—
239C11×C4⋊C4C2412yes—
240C42×C11—24no—
241C42×C11C2×D412yes—
242C42×C11C2412yes—
243#4325—28no—
244(C2×D11)⋊C4—24no—
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)⋊C4C2×D414yes—
251(C2×D11)⋊C4C2×D414yes—
252C4⋊Dic11—21no—
253C4⋊Dic11—21no—
254C4⋊Dic11—24no—
255C4⋊Dic11—21no—
256C4⋊Dic11C2×D414yes—
257C4⋊Dic11C2412yes—
258C4⋊Dic11C2412yes—
259C4⋊Dic11C2412yes—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265C4×Dic11—24no—
266C2×C11⋊C8—22no—
267C2×C11⋊C8#4114yes—
268C2×C11⋊C8C2412yes—
269C2×C11⋊C8C2412yes—
270#4313—28no—
271C8×D11—28no—
272C2×#554—111no—
273C2×#553—111no—
274#3346—1116no—
275C2×#501—111no—
276C2×#484—111no—
277C2×#481—111no—
278C2×#485—111no—
279C2×#480—111no—
280C2×#479D1111yescharacteristic, complemented
281C2×#474—111no—
282C2×#468—111no—
283C2×#465—111no—
284C2×#440—111no—
285C2×#435—111no—
286C2×#428—111no—
287C22×#107—111no—
288C23×C11C22×D411yescharacteristic
289C22×D11—22no—
290C22×D11—22no—
291C22×D11—22no—
292C22×D11—22no—
293C22×D11—22no—
294C22×D11—22no—
295C22×D11—42no—
296C22×D11—42no—
297C22×D11—42no—
298C22×D11#13714yes—
299C22×D11C22×D412yes—
300C22×D11C22×D412yes—
301Q8×C11—22no—
302Q8×C11—22no—
303Q8×C11—42no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11C22×D412yes—
315C2×C4×C11C22×D412yes—
316C2×C4×C11C22×D411yescharacteristic
317C2×C4×C11C2×#4112yes—
318C2×C4×C112−1+412yes—
319C2×C4×C11C2511yescharacteristic
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—42no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11C22×D412yes—
329C2×Dic11C22×D412yes—
330D44—28no—
331D44—22no—
332D44—22no—
333D44—48no—
334D44—42no—
335D44—84no—
336C4×D11—24no—
337C4×D11—24no—
338C4×D11—22no—
339C4×D11—22no—
340C4×D11—22no—
341C4×D11—22no—
342C4×D11—84no—
343C4×D11—84no—
344C4×D11—84no—
345C4×D11—84no—
346Dic22—84no—
347C8×C11—22no—
348C8×C11—22no—
349C11⋊C8—22no—
350C11⋊C8C2×#4114yes—
351C22×SD16—111no—
352C22×M16—111no—
353C23×C8—111no—
354#554—118no—
355#554—224no—
356#553—118no—
357#553—224no—
358C2×C4⋊Q8—111no—
359C2×#126—221no—
360C2×#125—221no—
361C2×#125C2×D1111yescharacteristic
362C2×#123—221no—
363C2×C22⋊Q8—111no—
364C2×C22⋊Q8—111no—
365C2×C22⋊Q8—221no—
366C2×C22⋊Q8—221no—
367C2×#121—111no—
368C2×#121—111no—
369C2×#121—221no—
370C2×C4×Q8C2×D1111yescharacteristic
371C2×C4×D4—111no—
372C2×C4×D4—111no—
373C2×C4×D4—221no—
374C2×C4×D4—221no—
375C2×#117—111no—
376C22×C4⋊C4—111no—
377C22×C4⋊C4—111no—
378C22×C4⋊C4—111no—
379#501—118no—
380#485—118no—
381#484—118no—
382#481—118no—
383#480—118no—
384#479C2×D1118yescomplemented
385#474—118no—
386#468—118no—
387#465—118no—
388#440—118no—
389#435—118no—
390#428—118no—
391C2×#107—111no—
392C2×#107—111no—
393C2×#107—111no—
394C2×#107—111no—
395C2×#107—111no—
396C2×#107—118no—
397C2×#107C2×D1111yescharacteristic
398C2×#106—111no—
399C2×#106—111no—
400C2×#106C2×D1111yescharacteristic
401C2×C4⋊C8C2×D1111yescharacteristic
402C2×#103—111no—
403C2×#103C2×D1111yescharacteristic
404C2×#103C2×D1111yescharacteristic
405C2×#102—111no—
406C2×#102—111no—
407C2×#102—111no—
408C2×C22⋊C8—111no—
409C2×C22⋊C8—111no—
410C2×#97—111no—
411C22×C11#54712yes—
412C22×C11C2×#13712yes—
413C22×C11#57612yes—
414C22×C11C23×D411yescharacteristic
415C2×D11—28no—
416C2×D11—22no—
417C2×D11—22no—
418C2×D11—22no—
419C2×D11—22no—
420C2×D11—22no—
421C2×D11—44no—
422C2×D11—42no—
423C2×D11—42no—
424C2×D11—42no—
425C2×D11—84no—
426C2×D11C2×#13714yes—
427C4×C11—22no—
428C4×C11—22no—
429C4×C11—42no—
430C4×C11—42no—
431C4×C11—42no—
432C4×C11—42no—
433C4×C11#54712yes—
434C4×C11C22×#4111yescharacteristic
435C4×C11C2×2−1+411yescharacteristic
436Dic11—22no—
437Dic11—22no—
438Dic11—42no—
439Dic11—42no—
440Dic11—42no—
441C22×Q8—221no—
442C22×Q8C22×D1111yescharacteristic
443C22×D4—111no—
444C22×D4—111no—
445C22×D4—221no—
446C22×D4—221no—
447C23×C4—111no—
448C23×C4—111no—
449C23×C4—221no—
450C23×C4—221no—
451C23×C4—221no—
452C23×C4—221no—
453C2×SD16—114no—
454C2×SD16—224no—
455C2×M16—114no—
456C2×M16—224no—
457C22×C8—111no—
458C22×C8—111no—
459C22×C8—114no—
460C22×C8—224no—
461C22×C8C22×D1111yescharacteristic
462C22×C8C22×D1111yescharacteristic
463C4⋊Q8—114no—
464C4⋊Q8—222no—
465#126—228no—
466#125—22no—
467#125—228no—
468#125C22×D1114yes—
469#123—228no—
470C22⋊Q8—114no—
471C22⋊Q8—114no—
472C22⋊Q8—228no—
473C22⋊Q8—228no—
474C22⋊Q8—222no—
475C22⋊Q8—222no—
476#121—114no—
477#121—114no—
478#121—222no—
479#121—222no—
480#121—228no—
481C4×Q8—22no—
482C4×Q8C22×D1114yes—
483C4×D4—114no—
484C4×D4—114no—
485C4×D4—114no—
486C4×D4—228no—
487C4×D4—228no—
488C4×D4—222no—
489#117—114no—
490#117—222no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—111no—
495C2×C4⋊C4—111no—
496C2×C4⋊C4—111no—
497C2×C4⋊C4—111no—
498C2×C4⋊C4—114no—
499C2×C4⋊C4—114no—
500C2×C4⋊C4—114no—
501C2×C4⋊C4—222no—
502C2×C4⋊C4—222no—
503C2×C4⋊C4—222no—
504C2×C4⋊C4—221no—
505C2×C4⋊C4—221no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4—221no—
508C2×C4⋊C4—221no—
509C2×C4⋊C4—221no—
510C2×C4⋊C4C22×D1111yescharacteristic
511C2×C4⋊C4C22×D1111yescharacteristic
512C2×C4⋊C4C22×D1111yescharacteristic
513C2×C22⋊C4—111no—
514C2×C22⋊C4—111no—
515C2×C22⋊C4—221no—
516C2×C22⋊C4—221no—
517C2×C22⋊C4—221no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C42—21no—
522C2×C42—221no—
523C2×C42C22×D1111yescharacteristic
524#107—114no—
525#107—114no—
526#107—114no—
527#107—114no—
528#107—114no—
529#107C22×D1114yes—
530#106—114no—
531#106—114no—
532#106C22×D1114yes—
533C4⋊C8C22×D1114yes—
534#103—114no—
535#103C22×D1114yes—
536#103C22×D1114yes—
537#102—114no—
538#102—114no—
539#102—114no—
540C22⋊C8—114no—
541C22⋊C8—114no—
542#97—114no—
543C2×C11#334614yescomplemented
544C2×C11C2×#54711yescharacteristic
545C2×C11C22×#13711yescharacteristic
546C2×C11C2×#57611yescharacteristic
547D11—24no—
548D11—42no—
549D11—82no—
550C24—111no—
551C24—111no—
552C24—221no—
553C2×Q8—21no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—224no—
557C2×Q8—882no—
558C2×Q8C23×D1112yes—
559C2×D4—114no—
560C2×D4—112no—
561C2×D4—224no—
562C2×D4—224no—
563C2×D4—224no—
564C2×D4—221no—
565C2×D4—222no—
566C2×D4—222no—
567C2×D4—444no—
568C2×D4—882no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—111no—
574C22×C4—111no—
575C22×C4—112no—
576C22×C4—112no—
577C22×C4—112no—
578C22×C4—112no—
579C22×C4—224no—
580C22×C4—224no—
581C22×C4—224no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—221no—
589C22×C4—224no—
590C22×C4—882no—
591C22×C4—882no—
592C22×C4—882no—
593C22×C4—882no—
594C22×C4D4×D1111yescharacteristic
595C22×C4D4×D1111yescharacteristic
596C22×C4C23×D1111yescharacteristic
597SD16—228no—
598M16—228no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—114no—
602C2×C8—112no—
603C2×C8—112no—
604C2×C8—228no—
605C2×C8—222no—
606C2×C8C23×D1112yes—
607C2×C8C23×D1112yes—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—114no—
615C4⋊C4—112no—
616C4⋊C4—112no—
617C4⋊C4—112no—
618C4⋊C4—224no—
619C4⋊C4—224no—
620C4⋊C4—224no—
621C4⋊C4—224no—
622C4⋊C4—224no—
623C4⋊C4—221no—
624C4⋊C4—221no—
625C4⋊C4—221no—
626C4⋊C4—224no—
627C4⋊C4C23×D1112yes—
628C4⋊C4C23×D1112yes—
629C4⋊C4C23×D1112yes—
630C22⋊C4—114no—
631C22⋊C4—114no—
632C22⋊C4—224no—
633C22⋊C4—224no—
634C22⋊C4—224no—
635C22⋊C4—224no—
636C22⋊C4—224no—
637C22⋊C4—224no—
638C42—24no—
639C42—224no—
640C42D4×D1112yes—
641C42C23×D1112yes—
642C11C2×#334611yescharacteristic, complemented, Sylow
643C23—114no—
644C23—112no—
645C23—112no—
646C23—222no—
647C23—222no—
648C23—222no—
649C23—222no—
650C23—222no—
651C23—222no—
652C23—442no—
653C23—442no—
654C23—442no—
655C23C2×D4×D1111yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—884no—
660D4—228no—
661D4—222no—
662D4—222no—
663D4—448no—
664D4—442no—
665D4—884no—
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—112no—
677C2×C4—112no—
678C2×C4—222no—
679C2×C4—222no—
680C2×C4—224no—
681C2×C4—224no—
682C2×C4—222no—
683C2×C4—222no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—222no—
688C2×C4—222no—
689C2×C4—442no—
690C2×C4—442no—
691C2×C4—442no—
692C2×C4—884no—
693C2×C4—884no—
694C2×C4—884no—
695C2×C4—884no—
696C2×C4C2×D4×D1112yes—
697C2×C4C2×D4×D1112yes—
698C2×C4C2×D4×D1111yescharacteristic
699C2×C4#6704012yes—
700C2×C4#41×D1112yes—
701C2×C4C24×D1111yescharacteristic
702C8—22no—
703C8—22no—
704C8—114no—
705C8—222no—
706C22—114no—
707C22—228no—
708C22—222no—
709C22—222no—
710C22—222no—
711C22—222no—
712C22—222no—
713C22—444no—
714C22—442no—
715C22—442no—
716C22—442no—
717C22—884no—
718C22#1062316212yes—
719C22#1062330012yes—
720C22D11×#13712yes—
721C22C22×D4×D1111yescharacteristic
722C4—22no—
723C4—22no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—222no—
729C4—222no—
730C4—442no—
731C4—442no—
732C4—442no—
733C4#1062316212yes—
734C4C2×#6704011yescharacteristic
735C4C2×#41×D1111yescharacteristic
736C2—224no—
737C2—442no—
738C2—882no—
739C2#1308110814yesdirect product factor
740C2C2×#1062316211yescharacteristic
741C2C2×D11×#13711yescharacteristic
742C2C2×#1062330011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#479C2
socleC23×C11C22×D4
prime radicalC2×#10623226C2
hypercenterC2×#479D11
hypocenterC11C2×#3346
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
1. C2×#10623110C2semidirect
3. #13081108C2direct (N × H)
4. C2×#10622678C2semidirect
5. C2×#10622422C2semidirect
6. C2×#10622476C2semidirect
7. C2×#10622427C2semidirect
8. C2×#10622495C2semidirect
9. C2×#10622459C2semidirect
10. C2×#10622425C2semidirect
11. C2×#10622420C2semidirect
12. C2×#10622639C2semidirect
13. C2×#10622449C2semidirect
14. C2×#10622474C2semidirect
15. C2×D11×#107C2semidirect
16. C2×C11×#479C2semidirect
27. #10623110C22semidirect
45. C11×#479C22semidirect
58. #10622678C22semidirect
59. #10622639C22semidirect
67. #10622495C22semidirect
68. D11×#107C22semidirect
69. #10622476C22semidirect
70. #10622474C22semidirect
71. #10622459C22semidirect
72. #10622449C22semidirect
73. #10622427C22semidirect
74. #10622425C22semidirect
75. #10622422C22semidirect
76. #10622420C22semidirect
280. C2×#479D11semidirect
384. #479C2×D11semidirect
543. C2×C11#3346semidirect
642. C11C2×#3346semidirect
739. C2#13081108direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231102
C2×#106232262
#130811082
C2×#106226782
C2×#106224222
C2×#106224762
C2×#106224272
C2×#106224952
C2×#106224592
C2×#106224252
C2×#106224202
C2×#106226392
C2×#106224492
C2×#106224742
C2×D11×#1072
C2×C11×#4792
C2×#334611