Finite Group Databasebeta

← C2×#13080240 #15628896

Subgroups — C2×#13080240 #15628896

Order 2816.

2902 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66971C211yesmaximal, characteristic, complemented
2C22×#67002C211yesmaximal, characteristic, complemented
3C2×#10623362C211yesmaximal, characteristic, complemented
4C2×#10623161C211yesmaximal, characteristic, complemented
5#13080240C2116yesmaximal, direct product factor
6C2×#10622781C211yesmaximal, characteristic, complemented
7C2×#10622665C211yesmaximal, characteristic, complemented
8C2×#10622395C211yesmaximal, characteristic, complemented
9C2×#10622798C211yesmaximal, characteristic, complemented
10C2×#10622400C211yesmaximal, characteristic, complemented
11C2×#10622785C211yesmaximal, characteristic, complemented
12C2×#10622419C211yesmaximal, characteristic, complemented
13C2×#10622344C211yesmaximal, characteristic, complemented
14C2×#10622401C211yesmaximal, characteristic, complemented
15C2×#10622342C211yesmaximal, characteristic, complemented
16C2×C11×#452C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×#4343C2211yescharacteristic
19C22×Q8×D11C2211yescharacteristic, complemented
20C23×D44C2211yescharacteristic
21C22×C11×Q16C2211yescharacteristic, complemented
22C22×C11×SD16C2211yescharacteristic, complemented
23C2×C11×C22⋊Q8C2211yescharacteristic
24#10623362—24no—
25#10623362C2218yescomplemented
26C2×#67002—28no—
27C2×#67002C2218yescomplemented
28C2×#67000C2211yescharacteristic
29C2×Q8×Dic11C2211yescharacteristic, complemented
30C22×#4326C2211yescharacteristic, complemented
31C22×#4325C2211yescharacteristic
32C22×#4325C2211yescharacteristic
33C2×#66991—21no—
34C2×#66991C2211yescharacteristic, complemented
35C2×#66989—21no—
36C2×#66989C2211yescharacteristic, complemented
37C22×#4323C2211yescharacteristic
38C22×#4323C2211yescharacteristic
39C2×C4×C22⋊D11—21no—
40C2×C4×C22⋊D11C2211yescharacteristic
41C2×#66977—21no—
42C2×#66977C2211yescharacteristic
43C22×#4318C2211yescharacteristic
44C2×#66971—28no—
45C2×#66971C2218yescomplemented
46C22×#4314C2211yescharacteristic
47C22×#4314C2211yescharacteristic
48C22×#4313C2211yescharacteristic, complemented
49#10623161—24no—
50#10623161C2218yescomplemented
51C2×#66948—21no—
52C2×#66948C2211yescharacteristic
53C2×#66947—21no—
54C2×#66946C2211yescharacteristic
55C2×#66935—21no—
56C2×C22⋊C4×D11—21no—
57C11×#452C2218yescomplemented
58C2×C11×#103C2211yescharacteristic, complemented
59C2×C11×#102C2211yescharacteristic, complemented
60C2×C11×C22⋊C8C2211yescharacteristic
61C2×#66899C2211yescharacteristic, complemented
62#10622798C2218yescomplemented
63#10622785C2218yescomplemented
64#10622781C2218yescomplemented
65C2×#66885C2211yescharacteristic
66C2×#66885C2211yescharacteristic
67C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
68C2×Dic11⋊C8C2211yescharacteristic, complemented
69C2×C8×Dic11C2211yescharacteristic, complemented
70#10622665C2218yescomplemented
71C2×#66874C2211yescharacteristic, complemented
72C2×#66872C2211yescharacteristic, complemented
73#10622419C2218yescomplemented
74#10622401C2218yescomplemented
75#10622400C2218yescomplemented
76#10622395C2218yescomplemented
77#10622344C2218yescomplemented
78#10622342C2218yescomplemented
79C24×D11—21no—
80C2×C11×#41—22no—
81C2×C11×#41—24no—
82C2×C11×#41—42no—
83C2×C11×#41C2314yes—
84C22×Q8×C11C2311yescharacteristic
85C22×Q8×C11C2311yescharacteristic
86C22×D4×C11—21no—
87C22×D4×C11C2311yescharacteristic
88C23×C4×C11—21no—
89C23×C4×C11C2311yescharacteristic
90C22×C22⋊D11—21no—
91C22×C22⋊D11D411yescharacteristic
92C2×#4343—22no—
93C2×#4343—24no—
94C2×#4343—42no—
95C2×#4343C2314yes—
96C2×Q8×D11—22no—
97C2×Q8×D11—24no—
98C2×Q8×D11—42no—
99C2×Q8×D11C2314yescomplemented
100C22×D44—24no—
101C22×D44—21no—
102C22×D44—21no—
103C22×D44—22no—
104C22×D44—21no—
105C22×D44—42no—
106C22×D44C2311yescharacteristic
107C22×D44C2314yes—
108C22×D44C2311yescharacteristic
109C22×C4×D11—21no—
110C22×C4×D11—21no—
111C22×C4×D11—21no—
112C22×C4×D11C2311yescharacteristic
113C22×Dic22—21no—
114C22×Dic22C2311yescharacteristic
115C2×C11×Q16—24no—
116C2×C11×Q16C2314yescomplemented
117C2×C11×SD16—42no—
118C2×C11×SD16C2314yescomplemented
119C22×C8×C11C2311yescharacteristic
120C22×C8×C11C2311yescharacteristic
121C11×C22⋊Q8—22no—
122C11×C22⋊Q8C2314yes—
123C2×C11×C4⋊C4—21no—
124C2×C11×C4⋊C4C2311yescharacteristic
125C2×C11×C22⋊C4—21no—
126C2×C22⋊Dic11—21no—
127C2×C22⋊Dic11—21no—
128C2×C22⋊Dic11—21no—
129C2×C22⋊Dic11—21no—
130C2×C22⋊Dic11D411yescharacteristic
131#67002—232no—
132#67000—22no—
133#67000C2314yes—
134Q8×Dic11—22no—
135Q8×Dic11C2314yescomplemented
136C2×#4326—24no—
137C2×#4326C2314yescomplemented
138C2×#4325—24no—
139C2×#4325D418yescomplemented
140C2×#4325C2314yes—
141C2×#4325C2314yes—
142#66991—28no—
143#66991—22no—
144#66991C2314yescomplemented
145#66989—28no—
146#66989—22no—
147#66989C2314yescomplemented
148C2×#4323—24no—
149C2×#4323—24no—
150C2×#4323C2314yes—
151C2×#4323C2314yes—
152C4×C22⋊D11—28no—
153C4×C22⋊D11D414yes—
154C4×C22⋊D11C2314yes—
155C2×(C2×D11)⋊C4—21no—
156C2×(C2×D11)⋊C4—21no—
157C2×(C2×D11)⋊C4—21no—
158C2×(C2×D11)⋊C4—21no—
159C2×(C2×D11)⋊C4D411yescharacteristic
160C2×C4⋊Dic11—21no—
161C2×C4⋊Dic11C2311yescharacteristic
162#66977—22no—
163#66977—28no—
164#66977C2314yes—
165C2×Dic11⋊C4—21no—
166C2×Dic11⋊C4D411yescharacteristic
167C2×C4×Dic11—21no—
168C2×C4×Dic11C2311yescharacteristic
169C2×#4318—24no—
170C2×#4318C2314yes—
171C22×C11⋊C8C2311yescharacteristic
172C22×C11⋊C8C2311yescharacteristic
173#66971—232no—
174C2×#4314—24no—
175C2×#4314—42no—
176C2×#4314C2314yes—
177C2×#4314C2314yes—
178C2×#4313—24no—
179C2×#4313C2314yescomplemented
180#66948—22no—
181#66948—28no—
182#66948C2314yes—
183#66947—28no—
184#66946—22no—
185#66946C2314yes—
186#66935—28no—
187C22⋊C4×D11—28no—
188C11×#103C2314yescomplemented
189C11×#102C2314yescomplemented
190C11×C22⋊C8C2314yes—
191#66899C2314yescomplemented
192#66885C2314yes—
193#66885C2314yes—
194(C2×D11)⋊C8C2314yescomplemented
195Dic11⋊C8C2314yescomplemented
196C8×Dic11C2314yescomplemented
197#66874C2314yescomplemented
198#66872C2314yescomplemented
199C2×#3275—111nomaximal, Sylow
200C24×C11—21no—
201C24×C11C2×D411yescharacteristic
202C23×D11—21no—
203C23×D11—21no—
204C23×D11—24no—
205C23×D11—44no—
206C23×D11—44no—
207C23×D11—82no—
208C23×D11C2×D411yescharacteristic
209C11×#41—28no—
210C11×#41—44no—
211C11×#41—48no—
212C2×Q8×C11—21no—
213C2×Q8×C11—21no—
214C2×Q8×C11—22no—
215C2×Q8×C11—22no—
216C2×Q8×C11—22no—
217C2×Q8×C11C2×D414yes—
218C2×Q8×C11C2412yes—
219C2×Q8×C11C2412yes—
220C2×D4×C11—24no—
221C2×D4×C11—22no—
222C2×D4×C11—21no—
223C2×D4×C11—22no—
224C2×D4×C11—44no—
225C2×D4×C11C2412yes—
226C22×C4×C11—21no—
227C22×C4×C11—22no—
228C22×C4×C11—22no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—24no—
232C22×C4×C11—44no—
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D412yes—
235C22×C4×C11C2412yes—
236C22×C4×C11C2411yescharacteristic
237C2×C22⋊D11—24no—
238C2×C22⋊D11—42no—
239C2×C22⋊D11—44no—
240C2×C22⋊D11C2×D414yes—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11C2×D411yescharacteristic
244C22×Dic11C2×D411yescharacteristic
245C22×Dic11C2×D411yescharacteristic
246#4343—28no—
247#4343—44no—
248#4343—48no—
249Q8×D11—28no—
250Q8×D11—44no—
251Q8×D11—48no—
252C2×D44—24no—
253C2×D44—24no—
254C2×D44—28no—
255C2×D44—21no—
256C2×D44—24no—
257C2×D44—21no—
258C2×D44—22no—
259C2×D44—22no—
260C2×D44—22no—
261C2×D44—44no—
262C2×D44—44no—
263C2×D44—48no—
264C2×D44—44no—
265C2×D44—82no—
266C2×D44C2×D414yes—
267C2×D44C2412yes—
268C2×D44C2412yes—
269C2×C4×D11—24no—
270C2×C4×D11—24no—
271C2×C4×D11—24no—
272C2×C4×D11—22no—
273C2×C4×D11—22no—
274C2×C4×D11—44no—
275C2×C4×D11—44no—
276C2×C4×D11—82no—
277C2×C4×D11C2×D412yes—
278C2×C4×D11C2412yes—
279C2×Dic22—24no—
280C2×Dic22—22no—
281C2×Dic22—21no—
282C2×Dic22—22no—
283C2×Dic22—44no—
284C2×Dic22C2412yes—
285C11×Q16—28no—
286C11×SD16—44no—
287C2×C8×C11—22no—
288C2×C8×C11—22no—
289C2×C8×C11C2412yes—
290C2×C8×C11C2412yes—
291C11×C4⋊C4—21no—
292C11×C4⋊C4—24no—
293C11×C4⋊C4C2412yes—
294C11×C22⋊C4—24no—
295C22⋊Dic11—24no—
296C22⋊Dic11—24no—
297C22⋊Dic11—24no—
298C22⋊Dic11—24no—
299C22⋊Dic11C2×D414yes—
300#4326—28no—
301#4325—28no—
302#4325C2×D4116yescomplemented
303#4323—28no—
304#4323—28no—
305(C2×D11)⋊C4—24no—
306(C2×D11)⋊C4—24no—
307(C2×D11)⋊C4—24no—
308(C2×D11)⋊C4—24no—
309(C2×D11)⋊C4C2×D414yes—
310C4⋊Dic11—24no—
311C4⋊Dic11—21no—
312C4⋊Dic11C2412yes—
313Dic11⋊C4—24no—
314Dic11⋊C4C2×D414yes—
315C4×Dic11—24no—
316C4×Dic11C2×D412yes—
317C4×Dic11C2412yes—
318#4318—28no—
319C2×C11⋊C8—22no—
320C2×C11⋊C8C2×D414yes—
321C2×C11⋊C8C2412yes—
322C2×C11⋊C8C2412yes—
323#4314—28no—
324#4314—44no—
325#4313—28no—
326C22×#137—111no—
327C22×AGL(1,ℤ/8)—111no—
328C2×#548—111no—
329C2×#546—111no—
330#3275—1116no—
331C2×#495—111no—
332C2×#470—111no—
333C2×#469—111no—
334C2×#464—111no—
335C2×#463—111no—
336C2×#452D1111yescharacteristic, complemented
337C2×#449—111no—
338C2×#448—111no—
339C2×#450—111no—
340C2×C4×SD16—111no—
341C2×#436—111no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—42no—
347C23×C11—42no—
348C23×C11—42no—
349C23×C11C22×D412yes—
350C23×C11C22×D411yescharacteristic
351C22×D11—22no—
352C22×D11—24no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—48no—
358C22×D11—42no—
359C22×D11—42no—
360C22×D11—48no—
361C22×D11—42no—
362C22×D11—42no—
363C22×D11—42no—
364C22×D11—84no—
365C22×D11—816no—
366C22×D11C22×D412yes—
367Q8×C11—24no—
368Q8×C11—22no—
369Q8×C11—22no—
370Q8×C11—22no—
371Q8×C11—42no—
372Q8×C11C22×D414yes—
373D4×C11—22no—
374D4×C11—22no—
375D4×C11—48no—
376D4×C11—42no—
377C2×C4×C11—24no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—24no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—48no—
386C2×C4×C11—42no—
387C2×C4×C11—42no—
388C2×C4×C11C22×D412yes—
389C2×C4×C11C22×D411yescharacteristic
390C2×C4×C11C22×D412yes—
391C2×C4×C11H(5,𝔽2)12yes—
392C2×C4×C11C2511yescharacteristic
393C22⋊D11—44no—
394C22⋊D11—48no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—42no—
401C2×Dic11—42no—
402C2×Dic11C22×D412yes—
403C2×Dic11C22×D412yes—
404C2×Dic11C22×D412yes—
405D44—24no—
406D44—22no—
407D44—22no—
408D44—22no—
409D44—48no—
410D44—48no—
411D44—42no—
412D44—84no—
413D44C22×D414yes—
414C4×D11—24no—
415C4×D11—22no—
416C4×D11—22no—
417C4×D11—48no—
418C4×D11—48no—
419C4×D11—84no—
420Dic22—22no—
421Dic22—22no—
422Dic22—48no—
423Dic22—42no—
424C8×C11—22no—
425C8×C11—22no—
426C11⋊C8—22no—
427C11⋊C8C22×D414yes—
428C22×#41—111no—
429C22×#41C2×D1111yescharacteristic
430C23×Q8—111no—
431C23×D4—111no—
432C2×#137—118no—
433C2×#137—228no—
434C2×AGL(1,ℤ/8)—118no—
435C2×AGL(1,ℤ/8)—228no—
436C22×Q16—111no—
437C22×Q16C2×D1111yescharacteristic, complemented
438C22×SD16—111no—
439C22×SD16—111no—
440C22×SD16—111no—
441C22×SD16—111no—
442C22×SD16C2×D1111yescharacteristic, complemented
443C22×D8—111no—
444C22×D8—111no—
445C22×M16—111no—
446C22×M16—111no—
447#548—118no—
448#548—224no—
449#546—118no—
450#546—224no—
451C2×#124—111no—
452C2×#124—111no—
453C2×#124—221no—
454C2×#123—221no—
455C2×C22⋊Q8—111no—
456C2×C22⋊Q8—221no—
457C2×C22⋊Q8C2×D1111yescharacteristic
458C2×#121—111no—
459C2×#121—111no—
460C2×#121—221no—
461C2×#121—221no—
462C2×#120—221no—
463C2×C4×Q8—111no—
464C2×C4×D4—111no—
465C2×C4×D4—111no—
466C2×C4×D4—221no—
467C22×C22⋊C4—221no—
468#495—118no—
469#470—118no—
470#469—118no—
471#464—118no—
472#463—118no—
473#452C2×D1118yescomplemented
474#450—118no—
475#449—118no—
476#448—118no—
477C4×SD16—118no—
478#436—118no—
479C2×#106—111no—
480C2×C4⋊C8—111no—
481C2×#103—111no—
482C2×#103—111no—
483C2×#103C2×D1111yescharacteristic, complemented
484C2×#102—111no—
485C2×#102—111no—
486C2×#102C2×D1111yescharacteristic, complemented
487C2×C22⋊C8—111no—
488C2×C22⋊C8C2×D1111yescharacteristic
489C2×C4×C8—111no—
490C22×C11—22no—
491C22×C11—22no—
492C22×C11—22no—
493C22×C11—44no—
494C22×C11—42no—
495C22×C11—42no—
496C22×C11—42no—
497C22×C11—84no—
498C22×C11D4212yes—
499C22×C11#57512yes—
500C22×C11#57712yes—
501C22×C11C23×D411yescharacteristic
502C2×D11—24no—
503C2×D11—22no—
504C2×D11—22no—
505C2×D11—22no—
506C2×D11—44no—
507C2×D11—48no—
508C2×D11—42no—
509C2×D11—42no—
510C2×D11—42no—
511C2×D11—42no—
512C2×D11—42no—
513C2×D11—816no—
514C2×D11—84no—
515C4×C11—22no—
516C4×C11—24no—
517C4×C11—42no—
518C4×C11—42no—
519C4×C11D4212yes—
520C4×C11C23×D411yescharacteristic
521C4×C11C2×H(5,𝔽2)11yescharacteristic
522Dic11—22no—
523Dic11—22no—
524Dic11—22no—
525Dic11—42no—
526Dic11—42no—
527C25—221no—
528C2×#41—22no—
529C2×#41—24no—
530C2×#41—42no—
531C2×#41—114no—
532C2×#41—222no—
533C2×#41—224no—
534C2×#41—442no—
535C2×#41C22×D1114yes—
536C22×Q8—114no—
537C22×Q8—111no—
538C22×Q8—221no—
539C22×Q8—222no—
540C22×Q8—224no—
541C22×Q8—442no—
542C22×Q8C22×D1111yescharacteristic
543C22×Q8C22×D1111yescharacteristic
544C22×D4—21no—
545C22×D4—111no—
546C22×D4—111no—
547C22×D4—111no—
548C22×D4—114no—
549C22×D4—224no—
550C22×D4—221no—
551C22×D4—221no—
552C22×D4—221no—
553C22×D4—221no—
554C22×D4—222no—
555C22×D4—442no—
556C22×D4C22×D1111yescharacteristic
557C23×C4—21no—
558C23×C4—111no—
559C23×C4—221no—
560C23×C4—221no—
561C23×C4—221no—
562C23×C4C22×D1111yescharacteristic
563#137—2232no—
564AGL(1,ℤ/8)—2232no—
565C2×Q16—24no—
566C2×Q16—114no—
567C2×Q16—224no—
568C2×Q16C22×D1114yescomplemented
569C2×SD16—42no—
570C2×SD16—118no—
571C2×SD16—114no—
572C2×SD16—114no—
573C2×SD16—114no—
574C2×SD16—114no—
575C2×SD16—224no—
576C2×SD16—224no—
577C2×SD16—442no—
578C2×SD16C22×D1114yescomplemented
579C2×D8—114no—
580C2×D8—114no—
581C2×D8—224no—
582C2×D8—224no—
583C2×M16—114no—
584C2×M16—114no—
585C2×M16—224no—
586C2×M16—224no—
587C22×C8—111no—
588C22×C8—111no—
589C22×C8C22×D1111yescharacteristic
590C22×C8C22×D1111yescharacteristic
591#124—114no—
592#124—114no—
593#124—222no—
594#124—222no—
595#124—228no—
596#123—228no—
597C22⋊Q8—22no—
598C22⋊Q8—114no—
599C22⋊Q8—228no—
600C22⋊Q8—222no—
601C22⋊Q8C22×D1114yes—
602#121—114no—
603#121—114no—
604#121—228no—
605#121—222no—
606#121—222no—
607#121—228no—
608#120—228no—
609C4×Q8—114no—
610C4×Q8—222no—
611C4×D4—114no—
612C4×D4—114no—
613C4×D4—114no—
614C4×D4—222no—
615C4×D4—228no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—111no—
618C2×C4⋊C4—111no—
619C2×C4⋊C4—221no—
620C2×C4⋊C4—221no—
621C2×C4⋊C4C22×D1111yescharacteristic
622C2×C22⋊C4—21no—
623C2×C22⋊C4—111no—
624C2×C22⋊C4—111no—
625C2×C22⋊C4—228no—
626C2×C22⋊C4—221no—
627C2×C22⋊C4—221no—
628C2×C22⋊C4—221no—
629C2×C22⋊C4—221no—
630C2×C22⋊C4—221no—
631C2×C22⋊C4—221no—
632C2×C22⋊C4—221no—
633C2×C22⋊C4—221no—
634C2×C42—111no—
635C2×C42—221no—
636#106—114no—
637C4⋊C8—114no—
638#103—114no—
639#103—114no—
640#103C22×D1114yescomplemented
641#102—114no—
642#102—114no—
643#102C22×D1114yescomplemented
644C22⋊C8—114no—
645C22⋊C8C22×D1114yes—
646C4×C8—114no—
647C2×C11—42no—
648C2×C11—82no—
649C2×C11#327514yescomplemented
650C2×C11C2×D4211yescharacteristic
651C2×C11C2×#57511yescharacteristic
652C2×C11C2×#57711yescharacteristic
653D11—42no—
654D11—44no—
655D11—82no—
656C24—21no—
657C24—111no—
658C24—221no—
659C24—221no—
660C24—224no—
661C24—444no—
662C24—444no—
663C24—882no—
664C24D4×D1111yescharacteristic
665#41—28no—
666#41—44no—
667#41—48no—
668#41—228no—
669#41—444no—
670#41—448no—
671C2×Q8—21no—
672C2×Q8—21no—
673C2×Q8—22no—
674C2×Q8—22no—
675C2×Q8—22no—
676C2×Q8—112no—
677C2×Q8—224no—
678C2×Q8—221no—
679C2×Q8—228no—
680C2×Q8—222no—
681C2×Q8—222no—
682C2×Q8—444no—
683C2×Q8—444no—
684C2×Q8—448no—
685C2×Q8D4×D1114yes—
686C2×Q8C23×D1112yes—
687C2×Q8C23×D1112yes—
688C2×D4—24no—
689C2×D4—22no—
690C2×D4—21no—
691C2×D4—22no—
692C2×D4—44no—
693C2×D4—114no—
694C2×D4—114no—
695C2×D4—112no—
696C2×D4—112no—
697C2×D4—228no—
698C2×D4—224no—
699C2×D4—224no—
700C2×D4—224no—
701C2×D4—221no—
702C2×D4—222no—
703C2×D4—224no—
704C2×D4—221no—
705C2×D4—222no—
706C2×D4—222no—
707C2×D4—444no—
708C2×D4—448no—
709C2×D4—444no—
710C2×D4—444no—
711C2×D4—442no—
712C2×D4—444no—
713C2×D4—882no—
714C2×D4C23×D1112yes—
715C22×C4—21no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—24no—
721C22×C4—44no—
722C22×C4—111no—
723C22×C4—111no—
724C22×C4—111no—
725C22×C4—112no—
726C22×C4—112no—
727C22×C4—224no—
728C22×C4—224no—
729C22×C4—224no—
730C22×C4—222no—
731C22×C4—222no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4—444no—
735C22×C4—444no—
736C22×C4—882no—
737C22×C4D4×D1112yes—
738C22×C4D4×D1111yescharacteristic
739C22×C4C23×D1112yes—
740C22×C4C23×D1111yescharacteristic
741Q16—28no—
742Q16—228no—
743SD16—44no—
744SD16—1116no—
745SD16—228no—
746SD16—228no—
747SD16—444no—
748D8—228no—
749D8—228no—
750M16—228no—
751M16—228no—
752C2×C8—22no—
753C2×C8—22no—
754C2×C8—114no—
755C2×C8—112no—
756C2×C8—112no—
757C2×C8—222no—
758C2×C8C23×D1112yes—
759C2×C8C23×D1112yes—
760C4⋊C4—24no—
761C4⋊C4—21no—
762C4⋊C4—114no—
763C4⋊C4—112no—
764C4⋊C4—224no—
765C4⋊C4—221no—
766C4⋊C4—224no—
767C4⋊C4C23×D1112yes—
768C22⋊C4—24no—
769C22⋊C4—114no—
770C22⋊C4—114no—
771C22⋊C4—224no—
772C22⋊C4—224no—
773C22⋊C4—224no—
774C22⋊C4—224no—
775C22⋊C4—224no—
776C22⋊C4—224no—
777C22⋊C4—224no—
778C22⋊C4—224no—
779C42—112no—
780C42—112no—
781C42—224no—
782C11C2×#327511yescharacteristic, complemented, Sylow
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—112no—
791C23—222no—
792C23—222no—
793C23—222no—
794C23—224no—
795C23—222no—
796C23—222no—
797C23—448no—
798C23—448no—
799C23—442no—
800C23—442no—
801C23—442no—
802C23—442no—
803C23—442no—
804C23—884no—
805C23—8816no—
806C23C2×D4×D1112yes—
807C23C2×D4×D1111yescharacteristic
808Q8—24no—
809Q8—22no—
810Q8—22no—
811Q8—22no—
812Q8—42no—
813Q8—222no—
814Q8—222no—
815Q8—448no—
816Q8—442no—
817Q8C2×D4×D1114yes—
818D4—22no—
819D4—22no—
820D4—48no—
821D4—42no—
822D4—114no—
823D4—224no—
824D4—222no—
825D4—222no—
826D4—222no—
827D4—448no—
828D4—448no—
829D4—444no—
830D4—448no—
831D4—442no—
832D4—884no—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—22no—
836C2×C4—24no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—48no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—112no—
845C2×C4—112no—
846C2×C4—112no—
847C2×C4—222no—
848C2×C4—222no—
849C2×C4—222no—
850C2×C4—224no—
851C2×C4—222no—
852C2×C4—222no—
853C2×C4—222no—
854C2×C4—222no—
855C2×C4—448no—
856C2×C4—448no—
857C2×C4—442no—
858C2×C4—442no—
859C2×C4—884no—
860C2×C4C2×D4×D1112yes—
861C2×C4C2×D4×D1111yescharacteristic
862C2×C4C2×D4×D1112yes—
863C2×C4#6703712yes—
864C2×C4C24×D1111yescharacteristic
865C8—22no—
866C8—22no—
867C8—114no—
868C8—222no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—44no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—84no—
877C22—222no—
878C22—224no—
879C22—222no—
880C22—222no—
881C22—444no—
882C22—448no—
883C22—442no—
884C22—442no—
885C22—442no—
886C22—442no—
887C22—442no—
888C22—8816no—
889C22—884no—
890C22#1062312112yes—
891C22#1062330112yes—
892C22#1062330812yes—
893C22C22×D4×D1111yescharacteristic
894C4—22no—
895C4—24no—
896C4—42no—
897C4—42no—
898C4—222no—
899C4—222no—
900C4—222no—
901C4—442no—
902C4—442no—
903C4#1062312112yes—
904C4C22×D4×D1111yescharacteristic
905C4C2×#6703711yescharacteristic
906C2—42no—
907C2—82no—
908C2—442no—
909C2—444no—
910C2—882no—
911C2#1308024014yesdirect product factor
912C2C2×#1062312111yescharacteristic
913C2C2×#1062330811yescharacteristic
914C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#452C2
socleC23×C11C22×D4
hypercenterC2×#452D11
hypocenterC11C2×#3275
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C22×#66971C2semidirect
2. C22×#67002C2semidirect
3. C2×#10623362C2semidirect
4. C2×#10623161C2semidirect
5. #13080240C2direct (N × H)
6. C2×#10622781C2semidirect
7. C2×#10622665C2semidirect
8. C2×#10622395C2semidirect
9. C2×#10622798C2semidirect
10. C2×#10622400C2semidirect
11. C2×#10622785C2semidirect
12. C2×#10622419C2semidirect
13. C2×#10622344C2semidirect
14. C2×#10622401C2semidirect
15. C2×#10622342C2semidirect
16. C2×C11×#452C2semidirect
19. C22×Q8×D11C22semidirect
21. C22×C11×Q16C22semidirect
22. C22×C11×SD16C22semidirect
25. #10623362C22semidirect
27. C2×#67002C22semidirect
29. C2×Q8×Dic11C22semidirect
30. C22×#4326C22semidirect
34. C2×#66991C22semidirect
36. C2×#66989C22semidirect
45. C2×#66971C22semidirect
48. C22×#4313C22semidirect
50. #10623161C22semidirect
57. C11×#452C22semidirect
58. C2×C11×#103C22semidirect
59. C2×C11×#102C22semidirect
61. C2×#66899C22semidirect
62. #10622798C22semidirect
63. #10622785C22semidirect
64. #10622781C22semidirect
67. C2×(C2×D11)⋊C8C22semidirect
68. C2×Dic11⋊C8C22semidirect
69. C2×C8×Dic11C22semidirect
70. #10622665C22semidirect
71. C2×#66874C22semidirect
72. C2×#66872C22semidirect
73. #10622419C22semidirect
74. #10622401C22semidirect
75. #10622400C22semidirect
76. #10622395C22semidirect
77. #10622344C22semidirect
78. #10622342C22semidirect
99. C2×Q8×D11C23semidirect
116. C2×C11×Q16C23semidirect
118. C2×C11×SD16C23semidirect
135. Q8×Dic11C23semidirect
137. C2×#4326C23semidirect
139. C2×#4325D4semidirect
144. #66991C23semidirect
147. #66989C23semidirect
179. C2×#4313C23semidirect
188. C11×#103C23semidirect
189. C11×#102C23semidirect
191. #66899C23semidirect
194. (C2×D11)⋊C8C23semidirect
195. Dic11⋊C8C23semidirect
196. C8×Dic11C23semidirect
197. #66874C23semidirect
198. #66872C23semidirect
302. #4325C2×D4semidirect
336. C2×#452D11semidirect
437. C22×Q16C2×D11semidirect
442. C22×SD16C2×D11semidirect
473. #452C2×D11semidirect
483. C2×#103C2×D11semidirect
486. C2×#102C2×D11semidirect
568. C2×Q16C22×D11semidirect
578. C2×SD16C22×D11semidirect
640. #103C22×D11semidirect
643. #102C22×D11semidirect
649. C2×C11#3275semidirect
782. C11C2×#3275semidirect
911. C2#13080240direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669712
C22×#670022
C2×#106233622
C2×#106231612
#130802402
C2×#106227812
C2×#106226652
C2×#106223952
C2×#106227982
C2×#106224002
C2×#106227852
C2×#106224192
C2×#106223442
C2×#106224012
C2×#106223422
C2×C11×#4522
C2×#327511