Finite Group Databasebeta

← C2×#13078801 #15622005

Subgroups — C2×#13078801 #15622005

Order 2816.

2274 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623174C211yesmaximal, characteristic, complemented
2C2×#10623329C211yesmaximal, characteristic, complemented
3#13078801C2116yesmaximal, direct product factor
4C2×#10622658C211yesmaximal, characteristic, complemented
5C2×#10622350C211yesmaximal, characteristic, complemented
6C2×#10622374C211yesmaximal, characteristic, complemented
7C2×#10622372C211yesmaximal, characteristic, complemented
8C2×#10622778C211yesmaximal, characteristic, complemented
9C2×#10622778C211yesmaximal, characteristic, complemented
10C2×#10622830C211yesmaximal, characteristic
11C2×#10622398C211yesmaximal, characteristic, complemented
12C2×#10622777C211yesmaximal, characteristic, complemented
13C2×SD16×Dic11C211yesmaximal, characteristic, complemented
14C2×#10622369C211yesmaximal, characteristic, complemented
15C2×#10622333C211yesmaximal, characteristic, complemented
16C2×C11×#450C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Dic11—21no—
22C22×C22⋊Dic11—21no—
23C2×#67000C2211yescharacteristic, complemented
24C2×Q8×Dic11C2211yescharacteristic, complemented
25#10623329—24no—
26#10623329C2218yescomplemented
27C2×D4×Dic11—21no—
28C2×D4×Dic11—21no—
29C2×D4×Dic11C2211yescharacteristic
30C2×D4×Dic11C2211yescharacteristic
31C2×D4×Dic11C2211yescharacteristic
32C2×D4×Dic11C2211yescharacteristic
33C22×#4323C2211yescharacteristic
34C22×#4323C2211yescharacteristic
35C2×#66983C2211yescharacteristic
36C2×#66979C2211yescharacteristic
37C2×#66979C2211yescharacteristic
38#10623174—24no—
39#10623174C2218yescomplemented
40C2×#66951—21no—
41C2×#66950—21no—
42C2×#66946C2211yescharacteristic, complemented
43C2×#66941C2211yescharacteristic, complemented
44C2×#66938—21no—
45C2×#66936—21no—
46C11×#450C2218yescomplemented
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×C22⋊C8C2211yescharacteristic
50C2×#66899C2211yescharacteristic, complemented
51C2×#66899C2211yescharacteristic, complemented
52#10622830C2218yes—
53C2×#66896C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×C22⋊(C11⋊C8)C2211yescharacteristic
56#10622778C2218yescomplemented
57#10622778C2218yescomplemented
58#10622777C2218yescomplemented
59SD16×Dic11C2218yescomplemented
60C2×#66885C2211yescharacteristic, complemented
61C2×#66885C2211yescharacteristic, complemented
62C2×#66882C2211yescharacteristic, complemented
63C2×#66881C2211yescharacteristic, complemented
64C2×#66879C2211yescharacteristic, complemented
65C2×Dic11⋊C8C2211yescharacteristic, complemented
66C2×Dic11⋊C8C2211yescharacteristic, complemented
67C2×C8×Dic11C2211yescharacteristic, complemented
68#10622658C2218yescomplemented
69C2×#66872C2211yescharacteristic, complemented
70C2×#66871C2211yescharacteristic, complemented
71#10622398C2218yescomplemented
72#10622374C2218yescomplemented
73#10622372C2218yescomplemented
74#10622369C2218yescomplemented
75#10622350C2218yescomplemented
76#10622333C2218yescomplemented
77C25×C11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11—24no—
80C22×D4×C11—24no—
81C22×D4×C11—21no—
82C22×D4×C11—22no—
83C22×D4×C11C2314yes—
84C22×D4×C11C2311yescharacteristic
85C22×D4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—21no—
88C23×Dic11—21no—
89C23×Dic11—21no—
90C23×Dic11—21no—
91C23×Dic11—21no—
92C22×D44C2311yescharacteristic
93C22×C4×D11—21no—
94C22×Dic22—21no—
95C2×C11×SD16—24no—
96C2×C11×SD16—24no—
97C2×C11×SD16C2314yes—
98C2×C11×SD16C2314yes—
99C22×C8×C11C2311yescharacteristic
100C22×C8×C11C2311yescharacteristic
101C11×C22⋊Q8—22no—
102C11×C22⋊Q8C2314yes—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C22⋊C4—21no—
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11—21no—
109C2×C22⋊Dic11—21no—
110C2×C22⋊Dic11—21no—
111C2×C22⋊Dic11—28no—
112C2×C22⋊Dic11—28no—
113C2×C22⋊Dic11D411yescharacteristic
114C2×C22⋊Dic11D411yescharacteristic
115#67000—22no—
116#67000C2314yescomplemented
117Q8×Dic11—22no—
118Q8×Dic11C2314yescomplemented
119D4×Dic11—28no—
120D4×Dic11—28no—
121D4×Dic11—22no—
122D4×Dic11—22no—
123D4×Dic11—22no—
124D4×Dic11—22no—
125D4×Dic11C2314yes—
126D4×Dic11C2314yes—
127D4×Dic11C2314yes—
128D4×Dic11C2314yes—
129C2×#4323—24no—
130C2×#4323—24no—
131C2×#4323C2314yes—
132C2×#4323C2314yes—
133#66983—22no—
134#66983C2314yes—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4—21no—
138C2×(C2×D11)⋊C4—21no—
139#66979—22no—
140#66979D414yes—
141#66979C2314yes—
142#66979C2314yes—
143C2×C4⋊Dic11—21no—
144C2×C4⋊Dic11D411yescharacteristic
145C2×C4⋊Dic11D411yescharacteristic
146C2×C4⋊Dic11C2311yescharacteristic
147C2×C4⋊Dic11C2311yescharacteristic
148C2×C4⋊Dic11C2311yescharacteristic
149C2×Dic11⋊C4—21no—
150C2×C4×Dic11—21no—
151C2×C4×Dic11—21no—
152C2×C4×Dic11C2311yescharacteristic
153C2×C4×Dic11C2311yescharacteristic
154C22×C11⋊C8C2311yescharacteristic
155C22×C11⋊C8C2311yescharacteristic
156#66951—28no—
157#66950—28no—
158#66946—22no—
159#66946C2314yescomplemented
160#66941—22no—
161#66941C2314yescomplemented
162#66938—28no—
163#66936—28no—
164C11×#102C2314yes—
165C11×#102C2314yes—
166C11×C22⋊C8C2314yes—
167#66899C2314yescomplemented
168#66899C2314yescomplemented
169#66896C2314yes—
170#66896C2314yes—
171C22⋊(C11⋊C8)C2314yes—
172#66885C2314yescomplemented
173#66885C2314yescomplemented
174#66882C2314yescomplemented
175#66881C2314yescomplemented
176#66879C2314yescomplemented
177Dic11⋊C8C2314yescomplemented
178Dic11⋊C8C2314yescomplemented
179C8×Dic11C2314yescomplemented
180#66872C2314yescomplemented
181#66871C2314yescomplemented
182C2×#3118—111nomaximal, Sylow
183C24×C11—28no—
184C24×C11—21no—
185C24×C11—21no—
186C24×C11—24no—
187C24×C11—82no—
188C24×C11—82no—
189C24×C11C2×D411yescharacteristic
190C23×D11—21no—
191C2×Q8×C11—21no—
192C2×Q8×C11—22no—
193C2×Q8×C11—22no—
194C2×Q8×C11C2412yes—
195C2×D4×C11—28no—
196C2×D4×C11—216no—
197C2×D4×C11—28no—
198C2×D4×C11—28no—
199C2×D4×C11—24no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—22no—
203C2×D4×C11—22no—
204C2×D4×C11#4114yes—
205C2×D4×C11#4114yes—
206C2×D4×C11C2412yes—
207C2×D4×C11C2412yes—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D412yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2411yescharacteristic
216C2×C22⋊D11—24no—
217C2×C22⋊D11—82no—
218C22×Dic11—24no—
219C22×Dic11—24no—
220C22×Dic11—24no—
221C22×Dic11—24no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—82no—
226C22×Dic11—82no—
227C22×Dic11—82no—
228C22×Dic11—82no—
229C22×Dic11C2×D411yescharacteristic
230C22×Dic11C2×D411yescharacteristic
231C22×Dic11C2×D411yescharacteristic
232C22×Dic11C2×D411yescharacteristic
233C2×D44—21no—
234C2×D44—22no—
235C2×D44—22no—
236C2×D44C2412yes—
237C2×C4×D11—24no—
238C2×C4×D11—82no—
239C2×Dic22—24no—
240C2×Dic22—82no—
241C11×SD16—28no—
242C11×SD16—28no—
243C2×C8×C11—22no—
244C2×C8×C11—22no—
245C2×C8×C11C2412yes—
246C2×C8×C11C2412yes—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—24no—
249C11×C4⋊C4C2412yes—
250C11×C22⋊C4—24no—
251C22⋊Dic11—24no—
252C22⋊Dic11—24no—
253C22⋊Dic11—24no—
254C22⋊Dic11—24no—
255C22⋊Dic11—24no—
256C22⋊Dic11C2×D414yes—
257C22⋊Dic11C2×D414yes—
258#4323—28no—
259#4323—28no—
260(C2×D11)⋊C4—24no—
261(C2×D11)⋊C4—24no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—24no—
264C4⋊Dic11—24no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11C2×D414yes—
269C4⋊Dic11C2×D414yes—
270C4⋊Dic11C2412yes—
271C4⋊Dic11C2412yes—
272C4⋊Dic11C2412yes—
273Dic11⋊C4—24no—
274C4×Dic11—24no—
275C4×Dic11—24no—
276C4×Dic11C2×D412yes—
277C4×Dic11C2×D412yes—
278C4×Dic11C2412yes—
279C4×Dic11C2412yes—
280C2×C11⋊C8—22no—
281C2×C11⋊C8—22no—
282C2×C11⋊C8C2412yes—
283C2×C11⋊C8C2412yes—
284C2×#542—111no—
285C2×#518—111no—
286#3118—1116no—
287C2×#485—111no—
288C2×#482—111no—
289C2×#476—111no—
290C2×#474—111no—
291C2×#463—111no—
292C2×#463—111no—
293C2×#450D1111yescharacteristic, complemented
294C2×#447—111no—
295C2×#442—111no—
296C2×#440—111no—
297C2×C4×SD16—111no—
298C2×C4×D8—111no—
299C2×#433—111no—
300C23×C11—216no—
301C23×C11—22no—
302C23×C11—24no—
303C23×C11—24no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—42no—
309C23×C11—42no—
310C23×C11—42no—
311C23×C11—42no—
312C23×C11—84no—
313C23×C11—84no—
314C23×C11—816no—
315C23×C11C22×D412yes—
316C23×C11C22×D411yescharacteristic
317C22×D11—22no—
318C22×D11—42no—
319C22×D11—42no—
320C22×D11—42no—
321Q8×C11—22no—
322Q8×C11—22no—
323Q8×C11—42no—
324D4×C11—216no—
325D4×C11—24no—
326D4×C11—24no—
327D4×C11—22no—
328D4×C11—22no—
329D4×C11C2×#4114yes—
330D4×C11C2×#4114yes—
331C2×C4×C11—22no—
332C2×C4×C11—24no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—42no—
338C2×C4×C11—42no—
339C2×C4×C11C22×D412yes—
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11C2×#4112yes—
342C2×C4×C11C2×#4112yes—
343C2×C4×C11C2511yescharacteristic
344C22⋊D11—84no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—42no—
353C2×Dic11—42no—
354C2×Dic11—42no—
355C2×Dic11—84no—
356C2×Dic11—84no—
357C2×Dic11—84no—
358C2×Dic11—84no—
359C2×Dic11C22×D412yes—
360C2×Dic11C22×D412yes—
361C2×Dic11C22×D412yes—
362C2×Dic11C22×D412yes—
363D44—22no—
364D44—22no—
365D44—42no—
366C4×D11—84no—
367Dic22—84no—
368C8×C11—22no—
369C8×C11—22no—
370C11⋊C8—22no—
371C11⋊C8—22no—
372C23×D4C2×D1111yescharacteristic
373C22×SD16C2×D1111yescharacteristic
374C22×SD16C2×D1111yescharacteristic
375C22×D8—111no—
376C22×D8—111no—
377#542—118no—
378#542—224no—
379C2×C4⋊Q8—111no—
380C2×#126—221no—
381C2×#124—111no—
382C2×#124—221no—
383C2×#123—221no—
384C2×C22⋊Q8—221no—
385C2×C22⋊Q8C2×D1111yescharacteristic
386C2×#121—111no—
387#518—118no—
388#518—224no—
389C2×C4×Q8—111no—
390C2×C4×D4—111no—
391C2×C4×D4—111no—
392C2×C4×D4—111no—
393C2×C4×D4—111no—
394C2×C4×D4—111no—
395C2×C4×D4—221no—
396C2×C4×D4—221no—
397C2×#117—111no—
398C2×#117—111no—
399C22×C22⋊C4—221no—
400C22×C22⋊C4—221no—
401#485—118no—
402#482—118no—
403#476—118no—
404#474—118no—
405#463—118no—
406#463—118no—
407#450C2×D1118yescomplemented
408#447—118no—
409#442—118no—
410#440—118no—
411C4×SD16—118no—
412C4×D8—118no—
413#433—118no—
414C2×#107—111no—
415C2×#107—111no—
416C2×#106—111no—
417C2×#106—111no—
418C2×C4⋊C8—111no—
419C2×C4⋊C8—111no—
420C2×#103—111no—
421C2×#103—111no—
422C2×#102—111no—
423C2×#102—111no—
424C2×#102—111no—
425C2×#102—111no—
426C2×#102C2×D1111yescharacteristic
427C2×#102C2×D1111yescharacteristic
428C2×C22⋊C8—111no—
429C2×C22⋊C8C2×D1111yescharacteristic
430C2×#97—111no—
431C2×C4×C8—111no—
432C22×C11—22no—
433C22×C11—24no—
434C22×C11—24no—
435C22×C11—22no—
436C22×C11—22no—
437C22×C11—44no—
438C22×C11—48no—
439C22×C11—48no—
440C22×C11—42no—
441C22×C11—42no—
442C22×C11—42no—
443C22×C11—42no—
444C22×C11—816no—
445C22×C11#52512yes—
446C22×C11#57612yes—
447C22×C11#57712yes—
448C22×C11C23×D411yescharacteristic
449C2×D11—42no—
450C2×D11—42no—
451C2×D11—42no—
452C2×D11—84no—
453C4×C11—22no—
454C4×C11—42no—
455C4×C11—42no—
456C4×C11#52512yes—
457C4×C11C22×#4111yescharacteristic
458C4×C11C22×#4111yescharacteristic
459Dic11—22no—
460Dic11—22no—
461Dic11—22no—
462Dic11—22no—
463Dic11—42no—
464Dic11—42no—
465Dic11—42no—
466C25—21no—
467C22×Q8—221no—
468C22×Q8C22×D1111yescharacteristic
469C22×D4—24no—
470C22×D4—24no—
471C22×D4—21no—
472C22×D4—22no—
473C22×D4—111no—
474C22×D4—221no—
475C22×D4C22×D1114yes—
476C22×D4C22×D1111yescharacteristic
477C22×D4C22×D1111yescharacteristic
478C23×C4—221no—
479C23×C4—221no—
480C23×C4—221no—
481C23×C4—221no—
482C23×C4—221no—
483C23×C4C22×D1111yescharacteristic
484C2×SD16—24no—
485C2×SD16—24no—
486C2×SD16C22×D1114yes—
487C2×SD16C22×D1114yes—
488C2×D8—114no—
489C2×D8—114no—
490C2×D8—224no—
491C2×D8—224no—
492C22×C8—111no—
493C22×C8—111no—
494C22×C8C22×D1111yescharacteristic
495C22×C8C22×D1111yescharacteristic
496C4⋊Q8—114no—
497C4⋊Q8—222no—
498#126—228no—
499#124—114no—
500#124—222no—
501#124—228no—
502#123—228no—
503C22⋊Q8—22no—
504C22⋊Q8—228no—
505C22⋊Q8C22×D1114yes—
506#121—114no—
507#121—222no—
508C4×Q8—114no—
509C4×Q8—222no—
510C4×D4—114no—
511C4×D4—114no—
512C4×D4—114no—
513C4×D4—114no—
514C4×D4—114no—
515C4×D4—222no—
516C4×D4—222no—
517C4×D4—222no—
518C4×D4—222no—
519C4×D4—222no—
520C4×D4—228no—
521C4×D4—228no—
522#117—114no—
523#117—114no—
524#117—114no—
525#117—222no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—111no—
528C2×C4⋊C4—111no—
529C2×C4⋊C4—111no—
530C2×C4⋊C4—111no—
531C2×C4⋊C4—111no—
532C2×C4⋊C4—221no—
533C2×C4⋊C4—221no—
534C2×C4⋊C4C22×D1111yescharacteristic
535C2×C22⋊C4—21no—
536C2×C22⋊C4—111no—
537C2×C22⋊C4—111no—
538C2×C22⋊C4—228no—
539C2×C22⋊C4—228no—
540C2×C22⋊C4—221no—
541C2×C22⋊C4—221no—
542C2×C22⋊C4—221no—
543C2×C22⋊C4—221no—
544C2×C22⋊C4—221no—
545C2×C22⋊C4—221no—
546C2×C22⋊C4—221no—
547C2×C22⋊C4—221no—
548C2×C22⋊C4—221no—
549C2×C42—111no—
550C2×C42—111no—
551C2×C42—221no—
552C2×C42—221no—
553#107—114no—
554#107—114no—
555#106—114no—
556#106—114no—
557C4⋊C8—114no—
558C4⋊C8—114no—
559#103—114no—
560#103—114no—
561#102—114no—
562#102—114no—
563#102—114no—
564#102—114no—
565#102C22×D1114yes—
566#102C22×D1114yes—
567C22⋊C8—114no—
568C22⋊C8C22×D1114yes—
569#97—114no—
570C4×C8—114no—
571C2×C11—42no—
572C2×C11—44no—
573C2×C11—44no—
574C2×C11#311814yescomplemented
575C2×C11C2×#52511yescharacteristic
576C2×C11C2×#57611yescharacteristic
577C2×C11C2×#57711yescharacteristic
578D11—82no—
579C24—28no—
580C24—21no—
581C24—21no—
582C24—24no—
583C24—82no—
584C24—82no—
585C24—221no—
586C24D4×D1111yescharacteristic
587C2×Q8—21no—
588C2×Q8—22no—
589C2×Q8—22no—
590C2×Q8—224no—
591C2×Q8—882no—
592C2×Q8C23×D1112yes—
593C2×D4—28no—
594C2×D4—216no—
595C2×D4—28no—
596C2×D4—28no—
597C2×D4—24no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—112no—
603C2×D4—224no—
604C2×D4—221no—
605C2×D4—222no—
606C2×D4—222no—
607C2×D4—882no—
608C2×D4#434114yes—
609C2×D4#434114yes—
610C2×D4C23×D1112yes—
611C2×D4C23×D1112yes—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—111no—
617C22×C4—111no—
618C22×C4—111no—
619C22×C4—111no—
620C22×C4—224no—
621C22×C4—224no—
622C22×C4—224no—
623C22×C4—224no—
624C22×C4—224no—
625C22×C4—221no—
626C22×C4—221no—
627C22×C4—221no—
628C22×C4—882no—
629C22×C4—882no—
630C22×C4—882no—
631C22×C4—882no—
632C22×C4—882no—
633C22×C4D4×D1112yes—
634C22×C4D4×D1111yescharacteristic
635C22×C4C23×D1112yes—
636C22×C4C23×D1111yescharacteristic
637SD16—28no—
638SD16—28no—
639D8—228no—
640D8—228no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—112no—
644C2×C8—112no—
645C2×C8—222no—
646C2×C8—222no—
647C2×C8C23×D1112yes—
648C2×C8C23×D1112yes—
649C4⋊C4—24no—
650C4⋊C4—21no—
651C4⋊C4—114no—
652C4⋊C4—114no—
653C4⋊C4—112no—
654C4⋊C4—112no—
655C4⋊C4—112no—
656C4⋊C4—224no—
657C4⋊C4—224no—
658C4⋊C4—221no—
659C4⋊C4—221no—
660C4⋊C4—221no—
661C4⋊C4C23×D1112yes—
662C22⋊C4—24no—
663C22⋊C4—114no—
664C22⋊C4—114no—
665C22⋊C4—224no—
666C22⋊C4—224no—
667C22⋊C4—224no—
668C22⋊C4—224no—
669C22⋊C4—224no—
670C22⋊C4—224no—
671C22⋊C4—224no—
672C22⋊C4—224no—
673C22⋊C4—224no—
674C42—112no—
675C42—112no—
676C42—112no—
677C42—112no—
678C42—224no—
679C42—224no—
680C11C2×#311811yescharacteristic, complemented, Sylow
681C23—216no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—24no—
686C23—24no—
687C23—22no—
688C23—22no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—84no—
694C23—84no—
695C23—816no—
696C23—222no—
697C23—442no—
698C23—442no—
699C23—442no—
700C23C2×D4×D1112yes—
701C23C2×D4×D1111yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—42no—
705Q8—884no—
706D4—216no—
707D4—24no—
708D4—24no—
709D4—22no—
710D4—22no—
711D4—222no—
712D4—222no—
713D4—442no—
714D4—884no—
715D4C2×#434114yes—
716D4C2×#434114yes—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—112no—
726C2×C4—112no—
727C2×C4—112no—
728C2×C4—112no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—442no—
737C2×C4—442no—
738C2×C4—442no—
739C2×C4—884no—
740C2×C4—884no—
741C2×C4—884no—
742C2×C4—884no—
743C2×C4—884no—
744C2×C4C2×D4×D1112yes—
745C2×C4C2×D4×D1111yescharacteristic
746C2×C4C2×#434112yes—
747C2×C4C2×#434112yes—
748C2×C4C24×D1111yescharacteristic
749C8—22no—
750C8—22no—
751C8—222no—
752C8—222no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—24no—
757C22—24no—
758C22—44no—
759C22—48no—
760C22—48no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—816no—
766C22—442no—
767C22—442no—
768C22—442no—
769C22—884no—
770C22#1062311712yes—
771C22#1062329312yes—
772C22#1062330512yes—
773C22C22×D4×D1111yescharacteristic
774C4—22no—
775C4—42no—
776C4—42no—
777C4—222no—
778C4—222no—
779C4—222no—
780C4—222no—
781C4—442no—
782C4—442no—
783C4—442no—
784C4#1062311712yes—
785C4C22×#434111yescharacteristic
786C4C22×#434111yescharacteristic
787C2—42no—
788C2—44no—
789C2—44no—
790C2—882no—
791C2#1307880114yesdirect product factor
792C2C2×#1062311711yescharacteristic
793C2C2×#1062330511yescharacteristic
794C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#450C2
socleC23×C11C22×D4
prime radicalC2×#10622830C2
hypercenterC2×#450D11
hypocenterC11C2×#3118
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. C2×#10623174C2semidirect
2. C2×#10623329C2semidirect
3. #13078801C2direct (N × H)
4. C2×#10622658C2semidirect
5. C2×#10622350C2semidirect
6. C2×#10622374C2semidirect
7. C2×#10622372C2semidirect
8. C2×#10622778C2semidirect
9. C2×#10622778C2semidirect
11. C2×#10622398C2semidirect
12. C2×#10622777C2semidirect
13. C2×SD16×Dic11C2semidirect
14. C2×#10622369C2semidirect
15. C2×#10622333C2semidirect
16. C2×C11×#450C2semidirect
23. C2×#67000C22semidirect
24. C2×Q8×Dic11C22semidirect
26. #10623329C22semidirect
39. #10623174C22semidirect
42. C2×#66946C22semidirect
43. C2×#66941C22semidirect
46. C11×#450C22semidirect
50. C2×#66899C22semidirect
51. C2×#66899C22semidirect
56. #10622778C22semidirect
57. #10622778C22semidirect
58. #10622777C22semidirect
59. SD16×Dic11C22semidirect
60. C2×#66885C22semidirect
61. C2×#66885C22semidirect
62. C2×#66882C22semidirect
63. C2×#66881C22semidirect
64. C2×#66879C22semidirect
65. C2×Dic11⋊C8C22semidirect
66. C2×Dic11⋊C8C22semidirect
67. C2×C8×Dic11C22semidirect
68. #10622658C22semidirect
69. C2×#66872C22semidirect
70. C2×#66871C22semidirect
71. #10622398C22semidirect
72. #10622374C22semidirect
73. #10622372C22semidirect
74. #10622369C22semidirect
75. #10622350C22semidirect
76. #10622333C22semidirect
116. #67000C23semidirect
118. Q8×Dic11C23semidirect
159. #66946C23semidirect
161. #66941C23semidirect
167. #66899C23semidirect
168. #66899C23semidirect
172. #66885C23semidirect
173. #66885C23semidirect
174. #66882C23semidirect
175. #66881C23semidirect
176. #66879C23semidirect
177. Dic11⋊C8C23semidirect
178. Dic11⋊C8C23semidirect
179. C8×Dic11C23semidirect
180. #66872C23semidirect
181. #66871C23semidirect
293. C2×#450D11semidirect
407. #450C2×D11semidirect
574. C2×C11#3118semidirect
680. C11C2×#3118semidirect
791. C2#13078801direct (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×#106233292
#130788012
C2×#106226582
C2×#106223502
C2×#106223742
C2×#106223722
C2×#106227782
C2×#106228302
C2×#106223982
C2×#106227772
C2×SD16×Dic112
C2×#106223692
C2×#106223332
C2×C11×#4502
C2×#311811