Finite Group Databasebeta

← C2×#13081115 #15632367

Subgroups — C2×#13081115 #15632367

Order 2816.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623265C211yesmaximal, characteristic, complemented
2C2×#10623226C211yesmaximal, characteristic, complemented
3#13081115C2116yesmaximal, direct product factor
4C2×#10622498C211yesmaximal, characteristic, complemented
5C2×#10622479C211yesmaximal, characteristic, complemented
6C2×#10622479C211yesmaximal, characteristic, complemented
7C2×#10622495C211yesmaximal, characteristic, complemented
8C2×#10622679C211yesmaximal, characteristic, complemented
9C2×#10622700C211yesmaximal, characteristic, complemented
10C2×#10622478C211yesmaximal, characteristic, complemented
11C2×#10622496C211yesmaximal, characteristic, complemented
12C2×#10622324C211yesmaximal, characteristic, complemented
13C2×#10622319C211yesmaximal, characteristic, complemented
14C2×#10622494C211yesmaximal, characteristic, complemented
15C2×#10622473C211yesmaximal, characteristic, complemented
16C2×C11×#501C211yesmaximal, characteristic, complemented
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×#125C2211yescharacteristic
19C2×#67000—21no—
20C2×#67000—21no—
21C22×D88C2211yescharacteristic
22C22×#4313C2211yescharacteristic
23C22×C8×D11C2211yescharacteristic
24#10623265—24no—
25#10623265C2218yescomplemented
26#10623226—24no—
27#10623226C2218yescomplemented
28C2×#66951—21no—
29C2×#66948—21no—
30C2×#66948—21no—
31C2×#66948C2211yescharacteristic
32C2×#66948C2211yescharacteristic
33C2×#66948C2211yescharacteristic
34C2×#66948C2211yescharacteristic
35C2×#66947—21no—
36C2×#66946—21no—
37C2×#66945—21no—
38C2×#66945C2211yescharacteristic
39C2×#66945C2211yescharacteristic
40C2×#66945C2211yescharacteristic
41C2×C4⋊C4×D11C2211yescharacteristic
42C2×C4×D44C2211yescharacteristic
43C2×C4×D44C2211yescharacteristic
44C2×C4×D44C2211yescharacteristic
45C11×#501C2218yescomplemented
46C2×C11×#107C2211yescharacteristic
47C2×C11×#107C2211yescharacteristic
48C2×C11×#106C2211yescharacteristic
49C2×C11×#106C2211yescharacteristic
50C2×C11×#97C2211yescharacteristic
51C2×#66885C2211yescharacteristic
52C2×#66885C2211yescharacteristic
53C2×(C2×D11)⋊C8C2211yescharacteristic
54C2×(C2×D11)⋊C8C2211yescharacteristic
55C2×#66881C2211yescharacteristic
56#10622700C2218yescomplemented
57#10622679C2218yescomplemented
58C2×#66873C2211yescharacteristic
59C2×#66873C2211yescharacteristic
60C2×#66873C2211yescharacteristic
61C2×#66873C2211yescharacteristic
62C2×#66872C2211yescharacteristic
63C2×#66871C2211yescharacteristic
64C2×#66871C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×C4⋊(C11⋊C8)C2211yescharacteristic
67#10622498C2218yescomplemented
68#10622496C2218yescomplemented
69#10622495C2218yescomplemented
70#10622494C2218yescomplemented
71#10622479C2218yescomplemented
72#10622479C2218yescomplemented
73#10622478C2218yescomplemented
74#10622473C2218yescomplemented
75#10622324C2218yescomplemented
76#10622319C2218yescomplemented
77C22×Q8×C11—21no—
78C22×D44—21no—
79C22×D44—21no—
80C22×D44—21no—
81C22×D44—21no—
82C22×D44D411yescharacteristic
83C22×D44C2311yescharacteristic
84C22×D44C2311yescharacteristic
85C22×C4×D11—21no—
86C22×C4×D11—21no—
87C22×C4×D11—21no—
88C22×C4×D11C2311yescharacteristic
89C22×C4×D11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C11×C4⋊Q8—22no—
93C11×C4⋊Q8C2314yes—
94C11×#125—22no—
95C11×#125C2314yes—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C42×C11C2311yescharacteristic
104#67000—28no—
105#67000—28no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
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⋊Dic11D411yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119C2×C4⋊Dic11C2311yescharacteristic
120C2×Dic11⋊C4—21no—
121C2×C4×Dic11—21no—
122C2×C4×Dic11—21no—
123C2×C4×Dic11—21no—
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C2×D88—24no—
127C2×D88C2314yes—
128C2×#4313—24no—
129C2×#4313C2314yes—
130C2×C8×D11—24no—
131C2×C8×D11C2314yes—
132#66951—28no—
133#66948—28no—
134#66948—28no—
135#66948—22no—
136#66948—22no—
137#66948—22no—
138#66948—22no—
139#66948C2314yes—
140#66948C2314yes—
141#66948C2314yes—
142#66948C2314yes—
143#66947—28no—
144#66946—28no—
145#66945—22no—
146#66945—22no—
147#66945—22no—
148#66945—28no—
149#66945C2314yes—
150#66945C2314yes—
151#66945C2314yes—
152C4⋊C4×D11—22no—
153C4⋊C4×D11C2314yes—
154C4×D44—22no—
155C4×D44—22no—
156C4×D44D414yes—
157C4×D44C2314yes—
158C4×D44C2314yes—
159C4×D44C2314yes—
160C11×#107C2314yes—
161C11×#107C2314yes—
162C11×#106C2314yes—
163C11×#106C2314yes—
164C11×#97C2314yes—
165#66885C2314yes—
166#66885C2314yes—
167(C2×D11)⋊C8C2314yes—
168(C2×D11)⋊C8C2314yes—
169#66881C2314yes—
170#66873C2314yes—
171#66873C2314yes—
172#66873C2314yes—
173#66873C2314yes—
174#66872C2314yes—
175#66871C2314yes—
176#66871C2314yes—
177#66871C2314yes—
178C4⋊(C11⋊C8)C2314yes—
179C2×#3347—111nomaximal, Sylow
180C23×D11—21no—
181C23×D11—21no—
182C23×D11C2×D411yescharacteristic
183C23×D11C2×D411yescharacteristic
184C2×Q8×C11—24no—
185C2×Q8×C11—82no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2411yescharacteristic
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11C2×D411yescharacteristic
196C22×Dic11C2×D411yescharacteristic
197C2×D44—24no—
198C2×D44—24no—
199C2×D44—24no—
200C2×D44—24no—
201C2×D44—21no—
202C2×D44—21no—
203C2×D44—22no—
204C2×D44—22no—
205C2×D44—22no—
206C2×D44—22no—
207C2×D44—42no—
208C2×D44—44no—
209C2×D44—82no—
210C2×D44—82no—
211C2×D44—82no—
212C2×D44C2×D414yes—
213C2×D44C2412yes—
214C2×D44C2412yes—
215C2×C4×D11—24no—
216C2×C4×D11—24no—
217C2×C4×D11—24no—
218C2×C4×D11—22no—
219C2×C4×D11—22no—
220C2×C4×D11—22no—
221C2×C4×D11—22no—
222C2×C4×D11—44no—
223C2×C4×D11—82no—
224C2×C4×D11—82no—
225C2×C4×D11C2×D412yes—
226C2×C4×D11C2×D412yes—
227C2×C4×D11C2412yes—
228C2×C4×D11C2412yes—
229C2×C8×C11—22no—
230C2×C8×C11#4114yes—
231C2×C8×C11C2412yes—
232C2×C8×C11C2412yes—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—24no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—21no—
238C11×C4⋊C4—24no—
239C11×C4⋊C4—24no—
240C11×C4⋊C4C2412yes—
241C11×C4⋊C4C2412yes—
242C11×C4⋊C4C2412yes—
243C11×C4⋊C4C2412yes—
244C42×C11C2×D412yes—
245C42×C11C2412yes—
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—
253(C2×D11)⋊C4—24no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4C2×D414yes—
256(C2×D11)⋊C4C2×D414yes—
257C4⋊Dic11—21no—
258C4⋊Dic11—21no—
259C4⋊Dic11C2×D414yes—
260C4⋊Dic11C2412yes—
261C4⋊Dic11C2412yes—
262Dic11⋊C4—24no—
263C4×Dic11—24no—
264C4×Dic11—24no—
265C4×Dic11—24no—
266C2×C11⋊C8—22no—
267C2×C11⋊C8—22no—
268C2×C11⋊C8C2412yes—
269C2×C11⋊C8C2412yes—
270D88—28no—
271#4313—28no—
272C8×D11—28no—
273C2×#555—111no—
274C2×#553—111no—
275#3347—1116no—
276C2×#501D1111yescharacteristic, complemented
277C2×#482—111no—
278C2×#482—111no—
279C2×#482—111no—
280C2×#480—111no—
281C2×#478—111no—
282C2×#474—111no—
283C2×#469—111no—
284C2×#466—111no—
285C2×#442—111no—
286C2×#435—111no—
287C2×#428—111no—
288C2×#427—111no—
289C23×C11C22×D411yescharacteristic
290C22×D11—22no—
291C22×D11—22no—
292C22×D11—22no—
293C22×D11—22no—
294C22×D11—22no—
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—22no—
298C22×D11—42no—
299C22×D11—42no—
300C22×D11—42no—
301C22×D11—42no—
302C22×D11—42no—
303C22×D11—42no—
304C22×D11C22×D412yes—
305C22×D11C22×D412yes—
306Q8×C11—84no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11C22×D412yes—
318C2×C4×C11C22×D412yes—
319C2×C4×C11C22×D411yescharacteristic
320C2×C4×C11C2×#4112yes—
321C2×C4×C112−1+412yes—
322C2×C4×C11C2511yescharacteristic
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11C22×D412yes—
330C2×Dic11C22×D412yes—
331D44—22no—
332D44—22no—
333D44—22no—
334D44—22no—
335D44—44no—
336D44—48no—
337D44—42no—
338D44—42no—
339D44—84no—
340D44—84no—
341D44—84no—
342C4×D11—24no—
343C4×D11—24no—
344C4×D11—22no—
345C4×D11—22no—
346C4×D11—22no—
347C4×D11—22no—
348C4×D11—48no—
349C4×D11—84no—
350C4×D11—84no—
351C8×C11—22no—
352C8×C11C2×#4114yes—
353C11⋊C8—22no—
354C11⋊C8—22no—
355C22×D8—111no—
356C22×M16—111no—
357C23×C8—111no—
358#555—118no—
359#555—224no—
360#553—118no—
361#553—224no—
362C2×C4⋊Q8C2×D1111yescharacteristic
363C2×#126—221no—
364C2×#125C2×D1111yescharacteristic
365C2×#124—221no—
366C2×#124—221no—
367C2×#123—221no—
368C2×#121—111no—
369C2×#121—111no—
370C2×#121—111no—
371C2×#121—111no—
372C2×#121—221no—
373C2×#121—221no—
374C2×C4×D4—111no—
375C2×C4×D4—111no—
376C2×C4×D4—111no—
377C2×C4×D4—221no—
378C2×#117—111no—
379C2×#117—111no—
380C2×#117—111no—
381C2×#117—221no—
382C22×C4⋊C4—111no—
383#501C2×D1118yescomplemented
384#482—118no—
385#482—118no—
386#482—118no—
387#480—118no—
388#478—118no—
389#474—118no—
390#469—118no—
391#466—118no—
392#442—118no—
393#435—118no—
394#428—118no—
395#427—118no—
396C2×#107—111no—
397C2×#107—111no—
398C2×#107—111no—
399C2×#107C2×D1111yescharacteristic
400C2×#107C2×D1111yescharacteristic
401C2×#106—111no—
402C2×#106—111no—
403C2×#106C2×D1111yescharacteristic
404C2×#106C2×D1111yescharacteristic
405C2×C4⋊C8—111no—
406C2×#102—111no—
407C2×#102—111no—
408C2×#102—111no—
409C2×#102—111no—
410C2×#102—111no—
411C2×#102—111no—
412C2×C22⋊C8—111no—
413C2×C22⋊C8—111no—
414C2×#97C2×D1111yescharacteristic
415C22×C11#54712yes—
416C22×C11#57512yes—
417C22×C11#57612yes—
418C22×C11C23×D411yescharacteristic
419C2×D11—22no—
420C2×D11—22no—
421C2×D11—22no—
422C2×D11—22no—
423C2×D11—22no—
424C2×D11—22no—
425C2×D11—44no—
426C2×D11—44no—
427C2×D11—42no—
428C2×D11—42no—
429C2×D11—42no—
430C2×D11—42no—
431C2×D11—42no—
432C2×D11—42no—
433C2×D11—84no—
434C2×D11—84no—
435C4×C11—22no—
436C4×C11—22no—
437C4×C11—42no—
438C4×C11—42no—
439C4×C11—42no—
440C4×C11—42no—
441C4×C11#54712yes—
442C4×C11C22×#4111yescharacteristic
443C4×C11C2×2−1+411yescharacteristic
444Dic11—22no—
445Dic11—22no—
446Dic11—42no—
447Dic11—42no—
448C22×Q8—21no—
449C22×D4—111no—
450C22×D4—111no—
451C22×D4—111no—
452C22×D4—221no—
453C22×D4—221no—
454C22×D4—221no—
455C22×D4—221no—
456C23×C4—111no—
457C23×C4—111no—
458C23×C4—221no—
459C23×C4—221no—
460C23×C4—221no—
461C2×D8—114no—
462C2×D8—224no—
463C2×M16—114no—
464C2×M16—224no—
465C22×C8—111no—
466C22×C8—111no—
467C22×C8—114no—
468C22×C8—224no—
469C22×C8C22×D1111yescharacteristic
470C22×C8C22×D1111yescharacteristic
471C4⋊Q8—22no—
472C4⋊Q8C22×D1114yes—
473#126—228no—
474#125—22no—
475#125C22×D1114yes—
476#124—228no—
477#124—228no—
478#123—228no—
479#121—114no—
480#121—114no—
481#121—114no—
482#121—114no—
483#121—222no—
484#121—222no—
485#121—222no—
486#121—222no—
487#121—228no—
488#121—228no—
489C4×D4—114no—
490C4×D4—114no—
491C4×D4—114no—
492C4×D4—114no—
493C4×D4—228no—
494C4×D4—222no—
495C4×D4—222no—
496#117—114no—
497#117—114no—
498#117—114no—
499#117—228no—
500#117—222no—
501#117—222no—
502#117—222no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—111no—
507C2×C4⋊C4—111no—
508C2×C4⋊C4—111no—
509C2×C4⋊C4—114no—
510C2×C4⋊C4—222no—
511C2×C4⋊C4—221no—
512C2×C4⋊C4C22×D1111yescharacteristic
513C2×C4⋊C4C22×D1111yescharacteristic
514C2×C4⋊C4C22×D1111yescharacteristic
515C2×C4⋊C4C22×D1111yescharacteristic
516C2×C22⋊C4—111no—
517C2×C22⋊C4—111no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C22⋊C4—221no—
522C2×C22⋊C4—221no—
523C2×C22⋊C4—221no—
524C2×C22⋊C4—221no—
525C2×C22⋊C4—221no—
526C2×C22⋊C4—221no—
527C2×C42—221no—
528C2×C42—221no—
529C2×C42—221no—
530C2×C42C22×D1111yescharacteristic
531#107—114no—
532#107—114no—
533#107—114no—
534#107C22×D1114yes—
535#107C22×D1114yes—
536#106—114no—
537#106—114no—
538#106C22×D1114yes—
539#106C22×D1114yes—
540C4⋊C8—114no—
541#102—114no—
542#102—114no—
543#102—114no—
544#102—114no—
545#102—114no—
546#102—114no—
547C22⋊C8—114no—
548C22⋊C8—114no—
549#97C22×D1114yes—
550C2×C11#334714yescomplemented
551C2×C11C2×#54711yescharacteristic
552C2×C11C2×#57511yescharacteristic
553C2×C11C2×#57611yescharacteristic
554D11—42no—
555D11—42no—
556D11—82no—
557D11—82no—
558C24—111no—
559C24—111no—
560C24—221no—
561C24—221no—
562C2×Q8—24no—
563C2×Q8—82no—
564C2×D4—114no—
565C2×D4—112no—
566C2×D4—112no—
567C2×D4—224no—
568C2×D4—224no—
569C2×D4—224no—
570C2×D4—224no—
571C2×D4—221no—
572C2×D4—221no—
573C2×D4—222no—
574C2×D4—222no—
575C2×D4—222no—
576C2×D4—222no—
577C2×D4—442no—
578C2×D4—444no—
579C2×D4—882no—
580C2×D4—882no—
581C2×D4—882no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—111no—
587C22×C4—111no—
588C22×C4—112no—
589C22×C4—112no—
590C22×C4—112no—
591C22×C4—112no—
592C22×C4—224no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—221no—
598C22×C4—221no—
599C22×C4—224no—
600C22×C4—224no—
601C22×C4—444no—
602C22×C4—882no—
603C22×C4—882no—
604C22×C4D4×D1111yescharacteristic
605C22×C4D4×D1111yescharacteristic
606C22×C4C23×D1111yescharacteristic
607D8—228no—
608M16—228no—
609C2×C8—22no—
610C2×C8—112no—
611C2×C8—112no—
612C2×C8—222no—
613C2×C8—222no—
614C2×C8—228no—
615C2×C8#434314yes—
616C2×C8C23×D1112yes—
617C2×C8C23×D1112yes—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—114no—
626C4⋊C4—112no—
627C4⋊C4—112no—
628C4⋊C4—224no—
629C4⋊C4—221no—
630C4⋊C4—221no—
631C4⋊C4C23×D1112yes—
632C4⋊C4C23×D1112yes—
633C4⋊C4C23×D1112yes—
634C4⋊C4C23×D1112yes—
635C22⋊C4—114no—
636C22⋊C4—114no—
637C22⋊C4—224no—
638C22⋊C4—224no—
639C22⋊C4—224no—
640C22⋊C4—224no—
641C22⋊C4—224no—
642C22⋊C4—224no—
643C22⋊C4—224no—
644C22⋊C4—224no—
645C22⋊C4—224no—
646C42—224no—
647C42—224no—
648C42—224no—
649C42D4×D1112yes—
650C42C23×D1112yes—
651C11C2×#334711yescharacteristic, complemented, Sylow
652C23—112no—
653C23—112no—
654C23—222no—
655C23—222no—
656C23—222no—
657C23—222no—
658C23—222no—
659C23—222no—
660C23—222no—
661C23—222no—
662C23—442no—
663C23—442no—
664C23—442no—
665C23—442no—
666C23—442no—
667C23—442no—
668C23C2×D4×D1111yescharacteristic
669Q8—84no—
670D4—222no—
671D4—222no—
672D4—222no—
673D4—222no—
674D4—444no—
675D4—448no—
676D4—442no—
677D4—442no—
678D4—884no—
679D4—884no—
680D4—884no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—112no—
692C2×C4—112no—
693C2×C4—222no—
694C2×C4—222no—
695C2×C4—224no—
696C2×C4—224no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—448no—
704C2×C4—442no—
705C2×C4—442no—
706C2×C4—884no—
707C2×C4—884no—
708C2×C4C2×D4×D1112yes—
709C2×C4C2×D4×D1112yes—
710C2×C4C2×D4×D1111yescharacteristic
711C2×C4C2×#434312yes—
712C2×C4#6704012yes—
713C2×C4C24×D1111yescharacteristic
714C8—22no—
715C8—222no—
716C8—222no—
717C8C2×#434314yes—
718C22—222no—
719C22—222no—
720C22—222no—
721C22—222no—
722C22—222no—
723C22—222no—
724C22—444no—
725C22—444no—
726C22—442no—
727C22—442no—
728C22—442no—
729C22—442no—
730C22—442no—
731C22—442no—
732C22—884no—
733C22—884no—
734C22#1062325712yes—
735C22#1062330512yes—
736C22#1062330812yes—
737C22C22×D4×D1111yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—222no—
745C4—222no—
746C4—442no—
747C4—442no—
748C4#1062325712yes—
749C4C22×#434311yescharacteristic
750C4C2×#6704011yescharacteristic
751C2—442no—
752C2—442no—
753C2—882no—
754C2—882no—
755C2#1308111514yesdirect product factor
756C2C2×#1062325711yescharacteristic
757C2C2×#1062330811yescharacteristic
758C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#501C2
socleC23×C11C22×D4
hypercenterC2×#501D11
hypocenterC11C2×#3347
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#10623265C2semidirect
2. C2×#10623226C2semidirect
3. #13081115C2direct (N × H)
4. C2×#10622498C2semidirect
5. C2×#10622479C2semidirect
6. C2×#10622479C2semidirect
7. C2×#10622495C2semidirect
8. C2×#10622679C2semidirect
9. C2×#10622700C2semidirect
10. C2×#10622478C2semidirect
11. C2×#10622496C2semidirect
12. C2×#10622324C2semidirect
13. C2×#10622319C2semidirect
14. C2×#10622494C2semidirect
15. C2×#10622473C2semidirect
16. C2×C11×#501C2semidirect
25. #10623265C22semidirect
27. #10623226C22semidirect
45. C11×#501C22semidirect
56. #10622700C22semidirect
57. #10622679C22semidirect
67. #10622498C22semidirect
68. #10622496C22semidirect
69. #10622495C22semidirect
70. #10622494C22semidirect
71. #10622479C22semidirect
72. #10622479C22semidirect
73. #10622478C22semidirect
74. #10622473C22semidirect
75. #10622324C22semidirect
76. #10622319C22semidirect
276. C2×#501D11semidirect
383. #501C2×D11semidirect
550. C2×C11#3347semidirect
651. C11C2×#3347semidirect
755. C2#13081115direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232652
C2×#106232262
#130811152
C2×#106224982
C2×#106224792
C2×#106224952
C2×#106226792
C2×#106227002
C2×#106224782
C2×#106224962
C2×#106223242
C2×#106223192
C2×#106224942
C2×#106224732
C2×C11×#5012
C2×#334711