Finite Group Databasebeta

← C2×#13080579 #15630285

Subgroups — C2×#13080579 #15630285

Order 2816.

2514 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623086C211yesmaximal, characteristic, complemented
2C2×#10623081C211yesmaximal, characteristic, complemented
3#13080579C2116yesmaximal, direct product factor
4C2×#10622327C211yesmaximal, characteristic, complemented
5C2×#10622348C211yesmaximal, characteristic, complemented
6C2×#10622334C211yesmaximal, characteristic, complemented
7C2×#10622455C211yesmaximal, characteristic, complemented
8C2×#10622748C211yesmaximal, characteristic, complemented
9C2×#10622727C211yesmaximal, characteristic, complemented
10C2×#10622457C211yesmaximal, characteristic, complemented
11C2×#10622347C211yesmaximal, characteristic, complemented
12C2×#10622345C211yesmaximal, characteristic, complemented
13C2×#10622324C211yesmaximal, characteristic, complemented
14C2×#10622746C211yesmaximal, characteristic, complemented
15C22×#66885C211yesmaximal, characteristic, complemented
16C2×C11×#435C211yesmaximal, characteristic, complemented
17C22×#4341—21no—
18C22×#4339C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C22×C11×M16C2211yescharacteristic, complemented
21C23×C8×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×#66990—21no—
24C2×#66983C2211yescharacteristic
25C2×#66983C2211yescharacteristic
26C2×#66983C2211yescharacteristic, complemented
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic, complemented
29C2×#66977C2211yescharacteristic
30C22×D88C2211yescharacteristic
31C22×D88C2211yescharacteristic
32C22×#4314C2211yescharacteristic, complemented
33#10623086—24no—
34#10623086C2218yescomplemented
35#10623081—24no—
36#10623081C2218yescomplemented
37C2×#66950—21no—
38C2×#66947—21no—
39C2×#66939—21no—
40C2×#66939—21no—
41C2×#66937—21no—
42C2×C22⋊C4×D11—21no—
43C2×#66928C2211yescharacteristic
44C2×C4×D44C2211yescharacteristic
45C2×C4×D44C2211yescharacteristic, complemented
46C2×#66922C2211yescharacteristic, complemented
47C11×#435C2218yescomplemented
48C2×C11×C4⋊C8C2211yescharacteristic, complemented
49C2×C11×C22⋊C8C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic, complemented
51C2×C11×#97C2211yescharacteristic, complemented
52#10622748C2218yescomplemented
53#10622746C2218yescomplemented
54#10622727C2218yescomplemented
55C2×#66885C2211yescharacteristic
56C2×#66885C2211yescharacteristic
57C2×#66885C2211yescharacteristic
58C2×#66885C2211yescharacteristic
59C2×#66885C2211yescharacteristic
60C2×#66885C2211yescharacteristic
61C2×#66885C2218yescomplemented
62C2×#66885C2211yescharacteristic, complemented
63C2×#66881C2211yescharacteristic, complemented
64C2×#66881C2211yescharacteristic, complemented
65C2×#66881C2211yescharacteristic, complemented
66C2×#66880C2211yescharacteristic, complemented
67C2×#66880C2211yescharacteristic, complemented
68C2×#66880C2211yescharacteristic, complemented
69#10622457C2218yescomplemented
70#10622455C2218yescomplemented
71#10622348C2218yescomplemented
72#10622347C2218yescomplemented
73#10622345C2218yescomplemented
74#10622334C2218yescomplemented
75#10622327C2218yescomplemented
76#10622324C2218yescomplemented
77C24×D11—21no—
78C22×D4×C11D411yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C23×Dic11—21no—
86C23×Dic11—21no—
87C2×#4341—28no—
88C2×#4341—48no—
89C2×#4339—22no—
90C2×#4339—24no—
91C2×#4339—42no—
92C2×#4339C2314yes—
93C22×D44—24no—
94C22×D44—21no—
95C22×D44—22no—
96C22×D44—42no—
97C22×D44C2311yescharacteristic
98C22×D44C2311yescharacteristic
99C22×D44C2314yes—
100C22×D44C2311yescharacteristic
101C22×C4×D11—21no—
102C22×C4×D11—21no—
103C22×C4×D11—21no—
104C22×Dic22—21no—
105C22×Dic22C2311yescharacteristic
106C2×C11×M16—42no—
107C2×C11×M16C2314yescomplemented
108C22×C8×C11—42no—
109C22×C8×C11C2311yescharacteristic
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2311yescharacteristic
112C22×C8×C11C2311yescharacteristic
113C22×C8×C11C2314yes—
114C4×D4×C11D414yes—
115C4×D4×C11C2314yes—
116C2×C11×C4⋊C4D411yescharacteristic
117C2×C11×C22⋊C4D411yescharacteristic
118C2×C11×C22⋊C4D411yescharacteristic
119C2×C42×C11C2311yescharacteristic
120C2×C22⋊Dic11—21no—
121#66990—28no—
122#66983—22no—
123#66983—22no—
124#66983—22no—
125#66983C2314yes—
126#66983C2314yes—
127#66983C2314yescomplemented
128C2×(C2×D11)⋊C4—21no—
129C2×(C2×D11)⋊C4—21no—
130C2×(C2×D11)⋊C4—21no—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—21no—
134C2×(C2×D11)⋊C4—21no—
135C2×C4⋊Dic11—21no—
136C2×C4⋊Dic11—21no—
137C2×C4⋊Dic11—21no—
138C2×C4⋊Dic11—22no—
139C2×C4⋊Dic11—22no—
140C2×C4⋊Dic11C2311yescharacteristic
141C2×C4⋊Dic11C2311yescharacteristic
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4⋊Dic11C2314yes—
144C2×C4⋊Dic11C2311yescharacteristic
145C2×C4⋊Dic11C2314yescomplemented
146#66977—22no—
147#66977C2314yes—
148C2×Dic11⋊C4—21no—
149C2×D88—24no—
150C2×D88—42no—
151C2×D88C2314yes—
152C2×D88C2314yes—
153C2×#4314—42no—
154C2×#4314C2314yescomplemented
155#66950—28no—
156#66947—28no—
157#66939—28no—
158#66939—28no—
159#66937—28no—
160C22⋊C4×D11—28no—
161#66928—22no—
162#66928C2314yes—
163C4×D44—22no—
164C4×D44—22no—
165C4×D44C2314yes—
166C4×D44C2314yescomplemented
167#66922—22no—
168#66922C2314yescomplemented
169C11×C4⋊C8C2314yescomplemented
170C11×C22⋊C8C2314yes—
171C11×C22⋊C8C2314yescomplemented
172C11×#97C2314yescomplemented
173#66885C2314yes—
174#66885C2314yes—
175#66885C2314yes—
176#66885C2314yes—
177#66885C2314yes—
178#66885C2314yes—
179#66885C2314yescomplemented
180#66881C2314yescomplemented
181#66881C2314yescomplemented
182#66881C2314yescomplemented
183#66880C2314yescomplemented
184#66880C2314yescomplemented
185#66880C2314yescomplemented
186C2×#3306—111nomaximal, Sylow
187C24×C11C2×D411yescharacteristic
188C24×C11C2×D411yescharacteristic
189C23×D11—21no—
190C23×D11—21no—
191C23×D11—21no—
192C23×D11—24no—
193C23×D11—44no—
194C23×D11—44no—
195C23×D11—82no—
196C2×D4×C11—24no—
197C2×D4×C11C2×D414yes—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D412yes—
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D412yes—
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2412yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2411yescharacteristic
211C2×C22⋊D11—24no—
212C2×C22⋊D11—24no—
213C2×C22⋊D11—24no—
214C2×C22⋊D11—24no—
215C2×C22⋊D11—44no—
216C2×C22⋊D11—44no—
217C2×C22⋊D11—44no—
218C2×C22⋊D11—82no—
219C22×Dic11—24no—
220C22×Dic11—24no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—44no—
227C22×Dic11—44no—
228#4341—432no—
229#4339—28no—
230#4339—44no—
231#4339—48no—
232C2×D44—28no—
233C2×D44—21no—
234C2×D44—21no—
235C2×D44—21no—
236C2×D44—24no—
237C2×D44—22no—
238C2×D44—22no—
239C2×D44—22no—
240C2×D44—22no—
241C2×D44—22no—
242C2×D44—44no—
243C2×D44—44no—
244C2×D44—48no—
245C2×D44#4114yescomplemented
246C2×D44C2412yes—
247C2×D44C2412yes—
248C2×D44C2412yes—
249C2×C4×D11—24no—
250C2×C4×D11—24no—
251C2×C4×D11—24no—
252C2×C4×D11—44no—
253C2×C4×D11—44no—
254C2×C4×D11—82no—
255C2×Dic22—24no—
256C2×Dic22—21no—
257C2×Dic22—22no—
258C2×Dic22—22no—
259C2×Dic22—44no—
260C2×Dic22C2412yes—
261C11×M16—44no—
262C2×C8×C11—22no—
263C2×C8×C11—22no—
264C2×C8×C11—22no—
265C2×C8×C11—22no—
266C2×C8×C11—44no—
267C2×C8×C11C2412yes—
268C2×C8×C11C2412yes—
269C2×C8×C11C2412yes—
270C2×C8×C11C2412yes—
271C11×C4⋊C4C2×D414yes—
272C11×C22⋊C4C2×D414yes—
273C11×C22⋊C4C2×D414yes—
274C42×C11C2×D412yes—
275C42×C11C2412yes—
276C22⋊Dic11—24no—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4—24no—
279(C2×D11)⋊C4—24no—
280(C2×D11)⋊C4—24no—
281(C2×D11)⋊C4—24no—
282(C2×D11)⋊C4—24no—
283(C2×D11)⋊C4—24no—
284C4⋊Dic11—21no—
285C4⋊Dic11—21no—
286C4⋊Dic11—24no—
287C4⋊Dic11—21no—
288C4⋊Dic11—21no—
289C4⋊Dic11—24no—
290C4⋊Dic11—24no—
291C4⋊Dic11C2412yes—
292C4⋊Dic11C2412yes—
293C4⋊Dic11C2412yes—
294C4⋊Dic11C2412yes—
295Dic11⋊C4—24no—
296D88—28no—
297D88—44no—
298#4314—44no—
299C2×#547—111no—
300C2×#546—111no—
301#3306—1116no—
302C2×#489—111no—
303C2×#481—111no—
304C2×#483—111no—
305C2×#476—111no—
306C2×#469—111no—
307C2×#465—111no—
308C2×#463—111no—
309C2×#449—111no—
310C2×#447—111no—
311C2×#442—111no—
312C2×#435D1111yescharacteristic, complemented
313C2×#417—111no—
314C22×#102—111no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11AGL(1,ℤ/8)14yes—
321C23×C11C22×D412yes—
322C23×C11C22×D412yes—
323C23×C11C22×D411yescharacteristic
324C22×D11—24no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—48no—
329C22×D11—42no—
330C22×D11—42no—
331C22×D11—42no—
332C22×D11—42no—
333C22×D11—42no—
334C22×D11—48no—
335C22×D11—42no—
336C22×D11—42no—
337C22×D11—42no—
338C22×D11—84no—
339C22×D11—816no—
340D4×C11—28no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—24no—
346C2×C4×C11—24no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11C22×D412yes—
352C2×C4×C11C22×D412yes—
353C2×C4×C11C22×D412yes—
354C2×C4×C11C22×D412yes—
355C2×C4×C11C22×D411yescharacteristic
356C2×C4×C11C2×#4112yes—
357C2×C4×C11H(5,𝔽2)12yes—
358C2×C4×C11C2511yescharacteristic
359C22⋊D11—48no—
360C22⋊D11—48no—
361C22⋊D11—48no—
362C22⋊D11—84no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—48no—
369C2×Dic11—42no—
370C2×Dic11—42no—
371C2×Dic11—42no—
372C2×Dic11—42no—
373C2×Dic11—48no—
374C2×Dic11—42no—
375D44—24no—
376D44—22no—
377D44—22no—
378D44—22no—
379D44—22no—
380D44—22no—
381D44—48no—
382D44—42no—
383D44—42no—
384D44C2×#4114yescomplemented
385C4×D11—48no—
386C4×D11—48no—
387C4×D11—84no—
388Dic22—22no—
389Dic22—22no—
390Dic22—48no—
391Dic22—42no—
392C8×C11—22no—
393C8×C11—22no—
394C8×C11—22no—
395C8×C11—22no—
396C22×#41—111no—
397C22×#41—221no—
398C23×D4—111no—
399C22×SD16—111no—
400C22×D8—111no—
401C22×D8—111no—
402C22×M16C2×D1111yescharacteristic, complemented
403C23×C8C2×D1111yescharacteristic
404#547—118no—
405#547—224no—
406#546—118no—
407#546—224no—
408C2×C4⋊Q8—111no—
409C2×#124—111no—
410C2×#123—221no—
411C2×#123—221no—
412C2×#123—221no—
413C2×C22⋊Q8—111no—
414C2×C22⋊Q8—221no—
415C2×#121—111no—
416C2×#121—111no—
417C2×#121—111no—
418C2×#121—221no—
419C2×#120—221no—
420C2×C4×D4—111no—
421C2×C4×D4—111no—
422C2×C4×D4C2×D1111yescharacteristic
423C22×C4⋊C4—111no—
424C22×C4⋊C4—111no—
425C22×C22⋊C4—221no—
426#489—118no—
427#483—118no—
428#481—118no—
429#476—118no—
430#469—118no—
431#465—118no—
432#463—118no—
433#449—118no—
434#447—118no—
435#442—118no—
436#435C2×D1118yescomplemented
437C2×#106—111no—
438C2×#106—111no—
439C2×#106—111no—
440C2×C4⋊C8C2×D1111yescharacteristic, complemented
441#417—118no—
442C2×#103—111no—
443C2×#103—111no—
444C2×#103—111no—
445C2×#102—111no—
446C2×#102—111no—
447C2×#102—111no—
448C2×#102—111no—
449C2×#102—111no—
450C2×#102—111no—
451C2×#102—118no—
452C2×#102—111no—
453C2×C22⋊C8C2×D1111yescharacteristic
454C2×C22⋊C8C2×D1111yescharacteristic, complemented
455C2×#97C2×D1111yescharacteristic, complemented
456C22×C11—22no—
457C22×C11—28no—
458C22×C11—22no—
459C22×C11—22no—
460C22×C11—22no—
461C22×C11—22no—
462C22×C11—44no—
463C22×C11#54612yes—
464C22×C11C2×AGL(1,ℤ/8)14yes—
465C22×C11C2×AGL(1,ℤ/8)12yes—
466C22×C11#57712yes—
467C22×C11C23×D411yescharacteristic
468C2×D11—24no—
469C2×D11—48no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—816no—
479C2×D11—84no—
480C2×D11—84no—
481C4×C11—22no—
482C4×C11—22no—
483C4×C11—22no—
484C4×C11—22no—
485C4×C11#54612yes—
486C4×C11C22×#4111yescharacteristic
487C4×C11C2×H(5,𝔽2)11yescharacteristic
488Dic11—42no—
489Dic11—42no—
490Dic11—42no—
491Dic11—42no—
492Dic11—42no—
493C25—221no—
494C2×#41—114no—
495C2×#41—224no—
496C2×#41—228no—
497C2×#41—222no—
498C2×#41—442no—
499C2×#41—448no—
500C22×Q8—111no—
501C22×Q8—221no—
502C22×D4—111no—
503C22×D4—111no—
504C22×D4—111no—
505C22×D4—114no—
506C22×D4—224no—
507C22×D4—221no—
508C22×D4—221no—
509C22×D4—221no—
510C22×D4—221no—
511C22×D4—221no—
512C22×D4—222no—
513C22×D4—442no—
514C22×D4D4411yescharacteristic
515C23×C4—221no—
516C23×C4—221no—
517C23×C4—221no—
518C23×C4—221no—
519C23×C4—221no—
520C23×C4C22×D1111yescharacteristic
521C23×C4C22×D1111yescharacteristic
522C2×SD16—114no—
523C2×SD16—442no—
524C2×D8—114no—
525C2×D8—114no—
526C2×D8—224no—
527C2×D8—442no—
528C2×M16—42no—
529C2×M16C22×D1114yescomplemented
530C22×C8—42no—
531C22×C8C22×D1111yescharacteristic
532C22×C8C22×D1111yescharacteristic
533C22×C8C22×D1111yescharacteristic
534C22×C8C22×D1111yescharacteristic
535C22×C8C22×D1114yes—
536C4⋊Q8—114no—
537C4⋊Q8—222no—
538#124—114no—
539#124—222no—
540#123—228no—
541#123—228no—
542#123—228no—
543C22⋊Q8—114no—
544C22⋊Q8—222no—
545C22⋊Q8—228no—
546#121—114no—
547#121—114no—
548#121—114no—
549#121—222no—
550#121—222no—
551#121—222no—
552#121—228no—
553#120—228no—
554C4×D4—114no—
555C4×D4—114no—
556C4×D4—222no—
557C4×D4—222no—
558C4×D4D4414yes—
559C4×D4C22×D1114yes—
560C2×C4⋊C4—111no—
561C2×C4⋊C4—111no—
562C2×C4⋊C4—111no—
563C2×C4⋊C4—114no—
564C2×C4⋊C4—114no—
565C2×C4⋊C4—111no—
566C2×C4⋊C4—221no—
567C2×C4⋊C4—221no—
568C2×C4⋊C4—222no—
569C2×C4⋊C4—222no—
570C2×C4⋊C4—221no—
571C2×C4⋊C4—221no—
572C2×C4⋊C4D4411yescharacteristic
573C2×C22⋊C4—221no—
574C2×C22⋊C4—221no—
575C2×C22⋊C4—221no—
576C2×C22⋊C4—221no—
577C2×C22⋊C4—221no—
578C2×C22⋊C4—221no—
579C2×C22⋊C4—221no—
580C2×C22⋊C4—221no—
581C2×C22⋊C4—228no—
582C2×C22⋊C4D4411yescharacteristic
583C2×C22⋊C4D4411yescharacteristic
584C2×C42C22×D1111yescharacteristic
585#106—114no—
586#106—114no—
587#106—114no—
588C4⋊C8C22×D1114yescomplemented
589#103—114no—
590#103—114no—
591#103—114no—
592#102—114no—
593#102—114no—
594#102—114no—
595#102—114no—
596#102—114no—
597#102—114no—
598#102—114no—
599C22⋊C8C22×D1114yes—
600C22⋊C8C22×D1114yescomplemented
601#97C22×D1114yescomplemented
602C2×C11—24no—
603C2×C11—42no—
604C2×C11#330614yescomplemented
605C2×C11C2×#54611yescharacteristic
606C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
607C2×C11C2×#57711yescharacteristic
608D11—44no—
609D11—82no—
610D11—82no—
611C24—221no—
612C24—221no—
613C24—221no—
614C24—224no—
615C24—444no—
616C24—444no—
617C24—882no—
618C24C2×D4411yescharacteristic
619C24C2×D4411yescharacteristic
620#41—228no—
621#41—444no—
622#41—448no—
623#41—4432no—
624C2×Q8—112no—
625C2×Q8—221no—
626C2×Q8—224no—
627C2×Q8—222no—
628C2×Q8—222no—
629C2×Q8—444no—
630C2×D4—24no—
631C2×D4—114no—
632C2×D4—112no—
633C2×D4—112no—
634C2×D4—112no—
635C2×D4—228no—
636C2×D4—224no—
637C2×D4—224no—
638C2×D4—224no—
639C2×D4—224no—
640C2×D4—221no—
641C2×D4—221no—
642C2×D4—224no—
643C2×D4—221no—
644C2×D4—222no—
645C2×D4—222no—
646C2×D4—222no—
647C2×D4—222no—
648C2×D4—222no—
649C2×D4—444no—
650C2×D4—448no—
651C2×D4—444no—
652C2×D4—444no—
653C2×D4—444no—
654C2×D4—444no—
655C2×D4—882no—
656C2×D4C2×D4414yes—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—224no—
662C22×C4—224no—
663C22×C4—221no—
664C22×C4—221no—
665C22×C4—221no—
666C22×C4—221no—
667C22×C4—221no—
668C22×C4—224no—
669C22×C4—224no—
670C22×C4—224no—
671C22×C4—444no—
672C22×C4—444no—
673C22×C4—444no—
674C22×C4—444no—
675C22×C4—882no—
676C22×C4C2×D4412yes—
677C22×C4C2×D4412yes—
678C22×C4C2×D4411yescharacteristic
679C22×C4C2×D4411yescharacteristic
680C22×C4C2×D4411yescharacteristic
681C22×C4C2×D4411yescharacteristic
682C22×C4C23×D1112yes—
683C22×C4C23×D1112yes—
684C22×C4C23×D1111yescharacteristic
685SD16—444no—
686D8—228no—
687D8—444no—
688M16—44no—
689C2×C8—22no—
690C2×C8—22no—
691C2×C8—22no—
692C2×C8—22no—
693C2×C8—44no—
694C2×C8C23×D1112yes—
695C2×C8C23×D1112yes—
696C2×C8C23×D1112yes—
697C2×C8C23×D1112yes—
698C4⋊C4—112no—
699C4⋊C4—112no—
700C4⋊C4—112no—
701C4⋊C4—112no—
702C4⋊C4—221no—
703C4⋊C4—221no—
704C4⋊C4—221no—
705C4⋊C4—224no—
706C4⋊C4—224no—
707C4⋊C4—221no—
708C4⋊C4—224no—
709C4⋊C4—224no—
710C4⋊C4C2×D4414yes—
711C22⋊C4—224no—
712C22⋊C4—224no—
713C22⋊C4—224no—
714C22⋊C4—224no—
715C22⋊C4—224no—
716C22⋊C4—224no—
717C22⋊C4—224no—
718C22⋊C4—224no—
719C22⋊C4C2×D4414yes—
720C22⋊C4C2×D4414yes—
721C42C2×D4412yes—
722C42C23×D1112yes—
723C11C2×#330611yescharacteristic, complemented, Sylow
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—224no—
730C23—222no—
731C23—222no—
732C23—222no—
733C23—448no—
734C23—442no—
735C23—442no—
736C23—442no—
737C23—448no—
738C23—442no—
739C23—442no—
740C23—442no—
741C23—442no—
742C23—442no—
743C23—884no—
744C23—8816no—
745C23#6696114yes—
746C23C22×D4412yes—
747C23C22×D4412yes—
748C23C22×D4411yescharacteristic
749Q8—222no—
750Q8—222no—
751Q8—448no—
752Q8—442no—
753D4—28no—
754D4—114no—
755D4—224no—
756D4—222no—
757D4—222no—
758D4—222no—
759D4—222no—
760D4—222no—
761D4—448no—
762D4—448no—
763D4—448no—
764D4—448no—
765D4—442no—
766D4—442no—
767D4—884no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—222no—
783C2×C4—448no—
784C2×C4—448no—
785C2×C4—448no—
786C2×C4—442no—
787C2×C4—442no—
788C2×C4—442no—
789C2×C4—448no—
790C2×C4—442no—
791C2×C4—442no—
792C2×C4—884no—
793C2×C4C22×D4412yes—
794C2×C4C22×D4412yes—
795C2×C4C22×D4412yes—
796C2×C4C22×D4412yes—
797C2×C4C22×D4411yescharacteristic
798C2×C4#6703712yes—
799C2×C4#41×D1112yes—
800C2×C4C24×D1111yescharacteristic
801C8—22no—
802C8—22no—
803C8—22no—
804C8—22no—
805C22—28no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—44no—
812C22—224no—
813C22—448no—
814C22—442no—
815C22—442no—
816C22—442no—
817C22—442no—
818C22—442no—
819C22—442no—
820C22—442no—
821C22—442no—
822C22—8816no—
823C22—884no—
824C22—884no—
825C22#1062308512yes—
826C22C2×#6696114yes—
827C22C2×#6696112yes—
828C22#1062328212yes—
829C22C23×D4411yescharacteristic
830C4—22no—
831C4—22no—
832C4—22no—
833C4—22no—
834C4—442no—
835C4—442no—
836C4—442no—
837C4—442no—
838C4—442no—
839C4#1062308512yes—
840C4C2×#6703711yescharacteristic
841C4C2×#41×D1111yescharacteristic
842C2—24no—
843C2—42no—
844C2—444no—
845C2—882no—
846C2—882no—
847C2#1308057914yesdirect product factor
848C2C2×#1062308511yescharacteristic
849C2C22×#6696111yescharacteristic
850C2C2×#1062328211yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#435C2
socleC23×C11C22×D4
hypercenterC2×#435D11
hypocenterC11C2×#3306
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#10623086C2semidirect
2. C2×#10623081C2semidirect
3. #13080579C2direct (N × H)
4. C2×#10622327C2semidirect
5. C2×#10622348C2semidirect
6. C2×#10622334C2semidirect
7. C2×#10622455C2semidirect
8. C2×#10622748C2semidirect
9. C2×#10622727C2semidirect
10. C2×#10622457C2semidirect
11. C2×#10622347C2semidirect
12. C2×#10622345C2semidirect
13. C2×#10622324C2semidirect
14. C2×#10622746C2semidirect
15. C22×#66885C2semidirect
16. C2×C11×#435C2semidirect
20. C22×C11×M16C22semidirect
26. C2×#66983C22semidirect
28. C22×C4⋊Dic11C22semidirect
32. C22×#4314C22semidirect
34. #10623086C22semidirect
36. #10623081C22semidirect
45. C2×C4×D44C22semidirect
46. C2×#66922C22semidirect
47. C11×#435C22semidirect
48. C2×C11×C4⋊C8C22semidirect
50. C2×C11×C22⋊C8C22semidirect
51. C2×C11×#97C22semidirect
52. #10622748C22semidirect
53. #10622746C22semidirect
54. #10622727C22semidirect
61. C2×#66885C22semidirect
62. C2×#66885C22semidirect
63. C2×#66881C22semidirect
64. C2×#66881C22semidirect
65. C2×#66881C22semidirect
66. C2×#66880C22semidirect
67. C2×#66880C22semidirect
68. C2×#66880C22semidirect
69. #10622457C22semidirect
70. #10622455C22semidirect
71. #10622348C22semidirect
72. #10622347C22semidirect
73. #10622345C22semidirect
74. #10622334C22semidirect
75. #10622327C22semidirect
76. #10622324C22semidirect
107. C2×C11×M16C23semidirect
127. #66983C23semidirect
145. C2×C4⋊Dic11C23semidirect
154. C2×#4314C23semidirect
166. C4×D44C23semidirect
168. #66922C23semidirect
169. C11×C4⋊C8C23semidirect
171. C11×C22⋊C8C23semidirect
172. C11×#97C23semidirect
179. #66885C23semidirect
180. #66881C23semidirect
181. #66881C23semidirect
182. #66881C23semidirect
183. #66880C23semidirect
184. #66880C23semidirect
185. #66880C23semidirect
245. C2×D44#41semidirect
312. C2×#435D11semidirect
384. D44C2×#41semidirect
402. C22×M16C2×D11semidirect
436. #435C2×D11semidirect
440. C2×C4⋊C8C2×D11semidirect
454. C2×C22⋊C8C2×D11semidirect
455. C2×#97C2×D11semidirect
529. C2×M16C22×D11semidirect
588. C4⋊C8C22×D11semidirect
600. C22⋊C8C22×D11semidirect
601. #97C22×D11semidirect
604. C2×C11#3306semidirect
723. C11C2×#3306semidirect
847. C2#13080579direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230862
C2×#106230812
#130805792
C2×#106223272
C2×#106223482
C2×#106223342
C2×#106224552
C2×#106227482
C2×#106227272
C2×#106224572
C2×#106223472
C2×#106223452
C2×#106223242
C2×#106227462
C22×#668852
C2×C11×#4352
C2×#330611