Finite Group Databasebeta

← C2×#13081110 #15632362

Subgroups — C2×#13081110 #15632362

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×#10623094C211yesmaximal, characteristic, complemented
2#13081110C2116yesmaximal, direct product factor
3C2×#10622678C211yesmaximal, characteristic, complemented
4C2×#10622616C211yesmaximal, characteristic, complemented
5C2×#10622648C211yesmaximal, characteristic, complemented
6C2×#10622648C211yesmaximal, characteristic, complemented
7C2×#10622580C211yesmaximal, characteristic, complemented
8C2×#10622679C211yesmaximal, characteristic, complemented
9C2×#10622620C211yesmaximal, characteristic, complemented
10C2×#10622652C211yesmaximal, characteristic, complemented
11C2×#10622651C211yesmaximal, characteristic, complemented
12C2×#10622627C211yesmaximal, characteristic, complemented
13C2×#10622624C211yesmaximal, characteristic, complemented
14C2×#10622577C211yesmaximal, characteristic, complemented
15C2×#10622611C211yesmaximal, characteristic, complemented
16C2×C11×#553C211yesmaximal, characteristic, complemented
17C11×#553—24no—
18C11×#553C2218yescomplemented
19C2×C11×#126—21no—
20C2×C11×#125C2211yescharacteristic
21C2×C11×#123—21no—
22C2×C11×#121—21no—
23C2×C11×#121C2211yescharacteristic
24C2×C11×#121C2211yescharacteristic
25C2×C4×D4×C11—21no—
26C2×C4×D4×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic
29C22×C11×C4⋊C4C2211yescharacteristic
30C2×#66991—21no—
31C22×#4323C2211yescharacteristic
32C2×#66983C2211yescharacteristic
33C2×#66983C2211yescharacteristic
34C2×#66979C2211yescharacteristic
35C2×#66979C2211yescharacteristic
36C22×#4318C2211yescharacteristic
37C23×C11⋊C8C2211yescharacteristic
38#10623094—24no—
39#10623094C2218yescomplemented
40C2×#66945—21no—
41C2×#66938—21no—
42C2×#66938—21no—
43C2×C4×D44C2211yescharacteristic
44C2×#66922C2211yescharacteristic
45C2×#66896C2211yescharacteristic
46C2×#66896C2211yescharacteristic
47C2×#66896C2211yescharacteristic
48C2×C22⋊(C11⋊C8)C2211yescharacteristic
49C2×C22⋊(C11⋊C8)C2211yescharacteristic
50#10622679C2218yescomplemented
51#10622678C2218yescomplemented
52#10622652C2218yescomplemented
53#10622651C2218yescomplemented
54#10622648C2218yescomplemented
55#10622648C2218yescomplemented
56#10622627C2218yescomplemented
57#10622624C2218yescomplemented
58#10622620C2218yescomplemented
59#10622616C2218yescomplemented
60#10622611C2218yescomplemented
61#10622580C2218yescomplemented
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66873C2211yescharacteristic
65#10622577C2218yescomplemented
66C2×#66872C2211yescharacteristic
67C2×#66872C2211yescharacteristic
68C2×#66872C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71C2×#66871C2211yescharacteristic
72C2×#66871C2211yescharacteristic
73C2×#66871C2211yescharacteristic
74C2×#66871C2211yescharacteristic
75C2×C4⋊(C11⋊C8)C2211yescharacteristic
76C2×#66867C2211yescharacteristic
77C22×D4×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11D411yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11—21no—
82C23×C4×C11—21no—
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C22×C22⋊D11—21no—
86C22×C22⋊D11—21no—
87C22×D44C2311yescharacteristic
88C22×C4×D11—21no—
89C22×Dic22—21no—
90C11×#126—28no—
91C11×#125—22no—
92C11×#125C2314yes—
93C11×#123—28no—
94C11×#121—28no—
95C11×#121—22no—
96C11×#121—22no—
97C11×#121C2314yes—
98C11×#121C2314yes—
99C4×D4×C11—28no—
100C4×D4×C11—22no—
101C4×D4×C11D414yes—
102C4×D4×C11C2314yes—
103C4×D4×C11C2314yes—
104C11×#117—22no—
105C11×#117C2314yes—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—22no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4D411yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2314yes—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4D411yescharacteristic
120C2×C11×C22⋊C4D411yescharacteristic
121C2×C42×C11—21no—
122C2×C42×C11C2311yescharacteristic
123C2×C22⋊Dic11—21no—
124C2×C22⋊Dic11—21no—
125#66991—28no—
126C2×#4323—24no—
127C2×#4323C2314yes—
128#66983—22no—
129#66983—22no—
130#66983C2314yes—
131#66983C2314yes—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—21no—
134C2×(C2×D11)⋊C4—21no—
135#66979—22no—
136#66979—22no—
137#66979C2314yes—
138#66979C2314yes—
139C2×C4⋊Dic11—21no—
140C2×C4⋊Dic11C2311yescharacteristic
141C2×C4⋊Dic11C2311yescharacteristic
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4×Dic11—21no—
144C2×C4×Dic11—21no—
145C2×#4318—24no—
146C2×#4318C2314yes—
147C22×C11⋊C8—24no—
148C22×C11⋊C8C2311yescharacteristic
149C22×C11⋊C8C2311yescharacteristic
150C22×C11⋊C8C2311yescharacteristic
151C22×C11⋊C8C2314yes—
152C22×C11⋊C8C2311yescharacteristic
153#66945—28no—
154#66938—28no—
155#66938—28no—
156C4×D44—22no—
157C4×D44C2314yes—
158#66922—22no—
159#66922C2314yes—
160#66896C2314yes—
161#66896C2314yes—
162#66896C2314yes—
163C22⋊(C11⋊C8)C2314yes—
164C22⋊(C11⋊C8)C2314yes—
165#66873C2314yes—
166#66873C2314yes—
167#66873C2314yes—
168#66872C2314yes—
169#66872C2314yes—
170#66872C2314yes—
171#66872C2314yes—
172#66871C2314yes—
173#66871C2314yes—
174#66871C2314yes—
175#66871C2314yes—
176#66871C2314yes—
177C4⋊(C11⋊C8)C2314yes—
178#66867C2314yes—
179C2×#3347—111nomaximal, Sylow
180C24×C11—21no—
181C24×C11C2×D411yescharacteristic
182C24×C11C2×D411yescharacteristic
183C23×D11—21no—
184C2×D4×C11—24no—
185C2×D4×C11—24no—
186C2×D4×C11—21no—
187C2×D4×C11—22no—
188C2×D4×C11—22no—
189C2×D4×C11—42no—
190C2×D4×C11—44no—
191C2×D4×C11—82no—
192C2×D4×C11C2×D414yes—
193C2×D4×C11C2412yes—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—24no—
202C22×C4×C11—24no—
203C22×C4×C11—82no—
204C22×C4×C11—82no—
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D412yes—
209C22×C4×C11C2×D412yes—
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2411yescharacteristic
214C2×C22⋊D11—24no—
215C2×C22⋊D11—24no—
216C2×C22⋊D11—82no—
217C2×C22⋊D11—82no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C2×D44—21no—
222C2×D44—22no—
223C2×D44—22no—
224C2×D44C2412yes—
225C2×C4×D11—24no—
226C2×C4×D11—44no—
227C2×Dic22—24no—
228C2×Dic22—82no—
229C11×C4⋊C4—21no—
230C11×C4⋊C4—21no—
231C11×C4⋊C4—24no—
232C11×C4⋊C4—24no—
233C11×C4⋊C4—24no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4C2×D414yes—
236C11×C4⋊C4C2412yes—
237C11×C4⋊C4C2412yes—
238C11×C4⋊C4C2412yes—
239C11×C22⋊C4—24no—
240C11×C22⋊C4—24no—
241C11×C22⋊C4—24no—
242C11×C22⋊C4—24no—
243C11×C22⋊C4C2×D414yes—
244C11×C22⋊C4C2×D414yes—
245C42×C11—24no—
246C42×C11C2×D412yes—
247C42×C11C2412yes—
248C22⋊Dic11—24no—
249C22⋊Dic11—24no—
250#4323—28no—
251(C2×D11)⋊C4—24no—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4—24no—
254C4⋊Dic11—21no—
255C4⋊Dic11—21no—
256C4⋊Dic11—24no—
257C4⋊Dic11—21no—
258C4⋊Dic11C2412yes—
259C4⋊Dic11C2412yes—
260C4⋊Dic11C2412yes—
261C4×Dic11—24no—
262C4×Dic11—24no—
263#4318—28no—
264C2×C11⋊C8—28no—
265C2×C11⋊C8—22no—
266C2×C11⋊C8—22no—
267C2×C11⋊C8—22no—
268C2×C11⋊C8#4114yes—
269C2×C11⋊C8C2412yes—
270C2×C11⋊C8C2412yes—
271C2×C11⋊C8C2412yes—
272C2×C11⋊C8C2412yes—
273C2×#555—111no—
274C2×#553D1111yescharacteristic, complemented
275#3347—1116no—
276C2×#501—111no—
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×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—42no—
297C23×C11—42no—
298C23×C11—42no—
299C23×C11C22×D412yes—
300C23×C11C22×D412yes—
301C23×C11C22×D411yescharacteristic
302C22×D11—22no—
303C22×D11—42no—
304C22×D11—42no—
305C22×D11—42no—
306D4×C11—22no—
307D4×C11—22no—
308D4×C11—44no—
309D4×C11—48no—
310D4×C11—42no—
311D4×C11—84no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—24no—
317C2×C4×C11—24no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11—42no—
328C2×C4×C11—84no—
329C2×C4×C11—84no—
330C2×C4×C11C22×D412yes—
331C2×C4×C11C22×D412yes—
332C2×C4×C11C22×D412yes—
333C2×C4×C11C22×D412yes—
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11C2×#4112yes—
336C2×C4×C112−1+412yes—
337C2×C4×C11C2511yescharacteristic
338C22⋊D11—84no—
339C22⋊D11—84no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346D44—22no—
347D44—22no—
348D44—42no—
349C4×D11—48no—
350Dic22—84no—
351C11⋊C8—22no—
352C11⋊C8—22no—
353C11⋊C8—22no—
354C11⋊C8C2×#4114yes—
355C22×D8—111no—
356C22×M16—111no—
357C23×C8—111no—
358#555—118no—
359#555—224no—
360#553—24no—
361#553C2×D1118yescomplemented
362C2×C4⋊Q8—111no—
363C2×#126—21no—
364C2×#125C2×D1111yescharacteristic
365C2×#124—221no—
366C2×#124—221no—
367C2×#123—21no—
368C2×#121—21no—
369C2×#121—111no—
370C2×#121—111no—
371C2×#121—221no—
372C2×#121C2×D1111yescharacteristic
373C2×#121C2×D1111yescharacteristic
374C2×C4×D4—21no—
375C2×C4×D4—111no—
376C2×C4×D4C2×D1111yescharacteristic
377C2×C4×D4C2×D1111yescharacteristic
378C2×#117—111no—
379C2×#117—111no—
380C2×#117—221no—
381C2×#117C2×D1111yescharacteristic
382C22×C4⋊C4C2×D1111yescharacteristic
383#501—118no—
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×#107—111no—
400C2×#107—111no—
401C2×#106—111no—
402C2×#106—111no—
403C2×#106—111no—
404C2×#106—111no—
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×#97—111no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—22no—
419C22×C11—22no—
420C22×C11—22no—
421C22×C11—44no—
422C22×C11—44no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11—42no—
426C22×C11—84no—
427C22×C11#54712yes—
428C22×C11#57512yes—
429C22×C11#57612yes—
430C22×C11C23×D411yescharacteristic
431C2×D11—42no—
432C2×D11—42no—
433C2×D11—42no—
434C2×D11—84no—
435C4×C11—22no—
436C4×C11—22no—
437C4×C11—22no—
438C4×C11—22no—
439C4×C11—42no—
440C4×C11—42no—
441C4×C11—42no—
442C4×C11#54712yes—
443C4×C11C22×#4111yescharacteristic
444C4×C11C2×2−1+411yescharacteristic
445Dic11—42no—
446Dic11—42no—
447Dic11—42no—
448C22×Q8—221no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—111no—
452C22×D4—221no—
453C22×D4—221no—
454C22×D4C22⋊D1111yescharacteristic
455C22×D4C22×D1111yescharacteristic
456C23×C4—21no—
457C23×C4—21no—
458C23×C4—221no—
459C23×C4C22×D1111yescharacteristic
460C23×C4C22×D1111yescharacteristic
461C2×D8—114no—
462C2×D8—224no—
463C2×M16—114no—
464C2×M16—224no—
465C22×C8—111no—
466C22×C8—111no—
467C22×C8—114no—
468C22×C8—111no—
469C22×C8—111no—
470C22×C8—224no—
471C4⋊Q8—114no—
472C4⋊Q8—222no—
473#126—28no—
474#125—22no—
475#125C22×D1114yes—
476#124—228no—
477#124—228no—
478#123—28no—
479#121—28no—
480#121—22no—
481#121—22no—
482#121—114no—
483#121—114no—
484#121—228no—
485#121—222no—
486#121—222no—
487#121C22×D1114yes—
488#121C22×D1114yes—
489C4×D4—28no—
490C4×D4—22no—
491C4×D4—114no—
492C4×D4—222no—
493C4×D4C22⋊D1114yes—
494C4×D4C22×D1114yes—
495C4×D4C22×D1114yes—
496#117—22no—
497#117—114no—
498#117—114no—
499#117—222no—
500#117—222no—
501#117—228no—
502#117C22×D1114yes—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—111no—
508C2×C4⋊C4—111no—
509C2×C4⋊C4—111no—
510C2×C4⋊C4—221no—
511C2×C4⋊C4C22⋊D1111yescharacteristic
512C2×C4⋊C4C22×D1111yescharacteristic
513C2×C4⋊C4C22×D1111yescharacteristic
514C2×C4⋊C4C22×D1114yes—
515C2×C4⋊C4C22×D1111yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—221no—
521C2×C22⋊C4—221no—
522C2×C22⋊C4—221no—
523C2×C22⋊C4—221no—
524C2×C22⋊C4—221no—
525C2×C22⋊C4C22⋊D1111yescharacteristic
526C2×C22⋊C4C22⋊D1111yescharacteristic
527C2×C42—21no—
528C2×C42—221no—
529C2×C42—221no—
530C2×C42C22×D1111yescharacteristic
531#107—114no—
532#107—114no—
533#107—114no—
534#107—114no—
535#107—114no—
536#106—114no—
537#106—114no—
538#106—114no—
539#106—114no—
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#97—114no—
550C2×C11—42no—
551C2×C11—42no—
552C2×C11—82no—
553C2×C11#334714yescomplemented
554C2×C11C2×#54711yescharacteristic
555C2×C11C2×#57511yescharacteristic
556C2×C11C2×#57611yescharacteristic
557D11—82no—
558C24—21no—
559C24—221no—
560C24C2×C22⋊D1111yescharacteristic
561C24C2×C22⋊D1111yescharacteristic
562C2×Q8—224no—
563C2×Q8—882no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—42no—
570C2×D4—44no—
571C2×D4—82no—
572C2×D4—112no—
573C2×D4—224no—
574C2×D4—224no—
575C2×D4—222no—
576C2×D4—222no—
577C2×D4—221no—
578C2×D4—882no—
579C2×D4—882no—
580C2×D4C2×C22⋊D1114yes—
581C2×D4C23×D1112yes—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—82no—
592C22×C4—82no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—221no—
596C22×C4—224no—
597C22×C4—444no—
598C22×C4C2×C22⋊D1112yes—
599C22×C4C2×C22⋊D1112yes—
600C22×C4C2×C22⋊D1111yescharacteristic
601C22×C4C2×C22⋊D1111yescharacteristic
602C22×C4C2×C22⋊D1111yescharacteristic
603C22×C4C2×C22⋊D1111yescharacteristic
604C22×C4C23×D1112yes—
605C22×C4C23×D1112yes—
606C22×C4C23×D1111yescharacteristic
607D8—228no—
608M16—228no—
609C2×C8—114no—
610C2×C8—112no—
611C2×C8—112no—
612C2×C8—112no—
613C2×C8—112no—
614C2×C8—228no—
615C2×C8—222no—
616C2×C8—222no—
617C2×C8—222no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—112no—
625C4⋊C4—112no—
626C4⋊C4—112no—
627C4⋊C4—221no—
628C4⋊C4—221no—
629C4⋊C4—221no—
630C4⋊C4—224no—
631C4⋊C4C2×C22⋊D1114yes—
632C4⋊C4C23×D1112yes—
633C4⋊C4C23×D1112yes—
634C4⋊C4C23×D1112yes—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—24no—
639C22⋊C4—224no—
640C22⋊C4—224no—
641C22⋊C4—224no—
642C22⋊C4—224no—
643C22⋊C4—224no—
644C22⋊C4C2×C22⋊D1114yes—
645C22⋊C4C2×C22⋊D1114yes—
646C42—24no—
647C42—224no—
648C42—224no—
649C42C2×C22⋊D1112yes—
650C42C23×D1112yes—
651C11C2×#334711yescharacteristic, complemented, Sylow
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—222no—
663C23—442no—
664C23—442no—
665C23—442no—
666C23C22×C22⋊D1112yes—
667C23C22×C22⋊D1112yes—
668C23C22×C22⋊D1111yescharacteristic
669Q8—884no—
670D4—22no—
671D4—22no—
672D4—44no—
673D4—48no—
674D4—42no—
675D4—84no—
676D4—222no—
677D4—222no—
678D4—442no—
679D4—884no—
680D4—884no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—84no—
698C2×C4—84no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—448no—
703C2×C4—442no—
704C2×C4—442no—
705C2×C4—442no—
706C2×C4#41×D1112yes—
707C2×C4#6704312yes—
708C2×C4C22×C22⋊D1112yes—
709C2×C4C22×C22⋊D1112yes—
710C2×C4C22×C22⋊D1112yes—
711C2×C4C22×C22⋊D1112yes—
712C2×C4C22×C22⋊D1111yescharacteristic
713C2×C4C24×D1111yescharacteristic
714C8—114no—
715C8—222no—
716C8—222no—
717C8—222no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—44no—
725C22—44no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—84no—
730C22—442no—
731C22—442no—
732C22—442no—
733C22—884no—
734C22#1062335312yes—
735C22#1062335512yes—
736C22#1062336612yes—
737C22C23×C22⋊D1111yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—42no—
743C4—42no—
744C4—42no—
745C4—442no—
746C4—442no—
747C4—442no—
748C4#1062335512yes—
749C4C2×#41×D1111yescharacteristic
750C4C2×#6704311yescharacteristic
751C2—42no—
752C2—42no—
753C2—82no—
754C2—882no—
755C2#1308111014yesdirect product factor
756C2C2×#1062335511yescharacteristic
757C2C2×#1062335311yescharacteristic
758C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#553C2
socleC23×C11C22×D4
hypercenterC2×#553D11
hypocenterC11C2×#3347
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#10623094C2semidirect
2. #13081110C2direct (N × H)
3. C2×#10622678C2semidirect
4. C2×#10622616C2semidirect
5. C2×#10622648C2semidirect
6. C2×#10622648C2semidirect
7. C2×#10622580C2semidirect
8. C2×#10622679C2semidirect
9. C2×#10622620C2semidirect
10. C2×#10622652C2semidirect
11. C2×#10622651C2semidirect
12. C2×#10622627C2semidirect
13. C2×#10622624C2semidirect
14. C2×#10622577C2semidirect
15. C2×#10622611C2semidirect
16. C2×C11×#553C2semidirect
18. C11×#553C22semidirect
39. #10623094C22semidirect
50. #10622679C22semidirect
51. #10622678C22semidirect
52. #10622652C22semidirect
53. #10622651C22semidirect
54. #10622648C22semidirect
55. #10622648C22semidirect
56. #10622627C22semidirect
57. #10622624C22semidirect
58. #10622620C22semidirect
59. #10622616C22semidirect
60. #10622611C22semidirect
61. #10622580C22semidirect
65. #10622577C22semidirect
274. C2×#553D11semidirect
361. #553C2×D11semidirect
553. C2×C11#3347semidirect
651. C11C2×#3347semidirect
755. C2#13081110direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230942
#130811102
C2×#106226782
C2×#106226162
C2×#106226482
C2×#106225802
C2×#106226792
C2×#106226202
C2×#106226522
C2×#106226512
C2×#106226272
C2×#106226242
C2×#106225772
C2×#106226112
C2×C11×#5532
C2×#334711