Finite Group Databasebeta

← C2×#13080158 #15628788

Subgroups — C2×#13080158 #15628788

Order 2816.

2966 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66967C211yesmaximal, characteristic, complemented
2C22×#66969C211yesmaximal, characteristic, complemented
3C2×#10623108C211yesmaximal, characteristic, complemented
4C2×#10623085C211yesmaximal, characteristic, complemented
5#13080158C2116yesmaximal, direct product factor
6C2×#10622325C211yesmaximal, characteristic, complemented
7C2×#10622499C211yesmaximal, characteristic, complemented
8C2×#10622496C211yesmaximal, characteristic, complemented
9C2×#10622641C211yesmaximal, characteristic, complemented
10C2×#10622628C211yesmaximal, characteristic, complemented
11C2×#10622423C211yesmaximal, characteristic, complemented
12C2×#10622424C211yesmaximal, characteristic, complemented
13C2×#10622394C211yesmaximal, characteristic, complemented
14C2×#10622386C211yesmaximal, characteristic, complemented
15C2×#10622319C211yesmaximal, characteristic, complemented
16C2×C11×#440C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×#4343C2211yescharacteristic, complemented
19C22×#4341C2211yescharacteristic
20C22×D4×D11C2211yescharacteristic
21C22×C11×SD16C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic, complemented
23C2×C4×D4×C11C2211yescharacteristic
24C22×#4326C2211yescharacteristic, complemented
25C22×#4325C2211yescharacteristic
26C22×#4323C2211yescharacteristic
27C22×#4323C2211yescharacteristic
28C2×#66983—21no—
29C22×(C2×D11)⋊C4—21no—
30C2×#66969—28no—
31C2×#66969C2218yescomplemented
32C2×#66967—28no—
33C2×#66967C2218yescomplemented
34C22×D88C2211yescharacteristic
35C22×D88C2211yescharacteristic
36C22×#4314C2211yescharacteristic, complemented
37C22×#4314C2211yescharacteristic, complemented
38C22×#4313C2211yescharacteristic
39C22×C8×D11C2211yescharacteristic, complemented
40#10623108—24no—
41#10623108C2218yescomplemented
42#10623085—24no—
43#10623085C2218yescomplemented
44C2×#66950C2211yescharacteristic
45C2×#66948—21no—
46C2×#66948—21no—
47C2×#66948C2211yescharacteristic
48C2×#66948C2211yescharacteristic
49C2×#66948C2211yescharacteristic, complemented
50C2×#66939—21no—
51C2×#66935—21no—
52C2×#66928C2211yescharacteristic
53C2×#66927—21no—
54C2×#66927C2211yescharacteristic, complemented
55C2×C4×D44—21no—
56C2×C4×D44C2211yescharacteristic
57C11×#440C2218yescomplemented
58C2×C11×#107C2211yescharacteristic, complemented
59C2×C11×#103C2211yescharacteristic, complemented
60C2×C11×#102C2211yescharacteristic
61C2×C11×#97C2211yescharacteristic, complemented
62C2×(C2×D11)⋊C8C2211yescharacteristic
63C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
64#10622641C2218yescomplemented
65#10622628C2218yescomplemented
66C2×#66874C2211yescharacteristic, complemented
67C2×#66873C2211yescharacteristic
68C2×#66873C2211yescharacteristic, complemented
69C2×#66873C2211yescharacteristic, complemented
70C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
71#10622499C2218yescomplemented
72#10622496C2218yescomplemented
73#10622424C2218yescomplemented
74#10622423C2218yescomplemented
75#10622394C2218yescomplemented
76#10622386C2218yescomplemented
77#10622325C2218yescomplemented
78#10622319C2218yescomplemented
79C24×D11—21no—
80C22×Q8×C11C2311yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C23×C4×C11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C23×Dic11—21no—
86C2×#4343—22no—
87C2×#4343—22no—
88C2×#4343—24no—
89C2×#4343—24no—
90C2×#4343—42no—
91C2×#4343—42no—
92C2×#4343C2314yes—
93C2×#4343C2314yescomplemented
94C2×#4341—24no—
95C2×#4341—22no—
96C2×#4341—42no—
97C2×#4341C2314yes—
98C2×D4×D11—24no—
99C2×D4×D11—22no—
100C2×D4×D11—42no—
101C2×D4×D11C2314yes—
102C22×D44—21no—
103C22×D44—21no—
104C22×D44—21no—
105C22×D44—21no—
106C22×D44—21no—
107C22×D44—21no—
108C22×D44—21no—
109C22×D44D411yescharacteristic
110C22×D44C2311yescharacteristic
111C22×D44C2311yescharacteristic
112C22×D44C2311yescharacteristic
113C22×C4×D11—21no—
114C22×C4×D11—21no—
115C22×C4×D11C2311yescharacteristic
116C22×C4×D11C2311yescharacteristic
117C22×Dic22C2311yescharacteristic
118C2×C11×SD16D418yescomplemented
119C2×C11×SD16C2314yes—
120C22×C8×C11C2311yescharacteristic
121C22×C8×C11C2311yescharacteristic
122C4×Q8×C11—22no—
123C4×Q8×C11C2314yescomplemented
124C4×D4×C11—22no—
125C4×D4×C11C2314yes—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4C2311yescharacteristic
128C2×C11×C4⋊C4C2311yescharacteristic
129C2×C11×C22⋊C4—21no—
130C2×C42×C11—21no—
131C2×C42×C11C2311yescharacteristic
132C2×#4326—24no—
133C2×#4326C2314yescomplemented
134C2×#4325—24no—
135C2×#4325C2314yes—
136C2×#4323—24no—
137C2×#4323—24no—
138C2×#4323C2314yes—
139C2×#4323C2314yes—
140#66983—28no—
141C2×(C2×D11)⋊C4—21no—
142C2×(C2×D11)⋊C4—21no—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4—21no—
145C2×(C2×D11)⋊C4—21no—
146C2×(C2×D11)⋊C4—21no—
147C2×(C2×D11)⋊C4—28no—
148C2×(C2×D11)⋊C4D411yescharacteristic
149C2×(C2×D11)⋊C4D411yescharacteristic
150C2×C4⋊Dic11—21no—
151C2×C4⋊Dic11D411yescharacteristic
152C22×C11⋊C8C2311yescharacteristic
153C22×C11⋊C8C2311yescharacteristic
154#66969—232no—
155#66967—232no—
156C2×D88—24no—
157C2×D88—42no—
158C2×D88C2314yes—
159C2×D88C2314yes—
160C2×#4314—24no—
161C2×#4314—42no—
162C2×#4314C2314yescomplemented
163C2×#4314C2314yescomplemented
164C2×#4313—24no—
165C2×#4313C2314yes—
166C2×C8×D11—24no—
167C2×C8×D11C2314yescomplemented
168#66950—22no—
169#66950C2314yes—
170#66948—22no—
171#66948—22no—
172#66948—22no—
173#66948—28no—
174#66948—28no—
175#66948C2314yes—
176#66948C2314yes—
177#66948C2314yescomplemented
178#66939—28no—
179#66935—28no—
180#66928—22no—
181#66928C2314yes—
182#66927—28no—
183#66927—22no—
184#66927C2314yescomplemented
185C4×D44—28no—
186C4×D44D414yes—
187C4×D44C2314yes—
188C11×#107C2314yescomplemented
189C11×#103C2314yescomplemented
190C11×#102C2314yes—
191C11×#97C2314yescomplemented
192(C2×D11)⋊C8C2314yes—
193(C2×D11)⋊C8C2314yescomplemented
194#66874C2314yescomplemented
195#66873C2314yes—
196#66873C2314yescomplemented
197#66873C2314yescomplemented
198C4⋊(C11⋊C8)C2314yescomplemented
199C2×#3268—111nomaximal, Sylow
200C24×C11—21no—
201C23×D11—21no—
202C23×D11—21no—
203C23×D11—21no—
204C23×D11—24no—
205C23×D11—44no—
206C23×D11—44no—
207C23×D11—82no—
208C23×D11C2×D411yescharacteristic
209C23×D11C2×D411yescharacteristic
210C2×Q8×C11—21no—
211C2×Q8×C11—22no—
212C2×Q8×C11C2×D414yes—
213C2×Q8×C11C2412yes—
214C2×D4×C11—21no—
215C2×D4×C11—22no—
216C2×D4×C11C2×D414yes—
217C2×D4×C11C2412yes—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—24no—
222C22×C4×C11—82no—
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2411yescharacteristic
226C2×C22⋊D11—24no—
227C2×C22⋊D11—24no—
228C2×C22⋊D11—44no—
229C2×C22⋊D11—44no—
230C22×Dic11—24no—
231C22×Dic11—21no—
232C22×Dic11—44no—
233C22×Dic11C2×D411yescharacteristic
234C22×Dic11C2×D411yescharacteristic
235#4343—28no—
236#4343—28no—
237#4343—44no—
238#4343—44no—
239#4343—48no—
240#4343—48no—
241#4341—28no—
242#4341—44no—
243#4341—48no—
244D4×D11—28no—
245D4×D11—44no—
246D4×D11—48no—
247C2×D44—24no—
248C2×D44—24no—
249C2×D44—24no—
250C2×D44—24no—
251C2×D44—24no—
252C2×D44—24no—
253C2×D44—21no—
254C2×D44—21no—
255C2×D44—21no—
256C2×D44—24no—
257C2×D44—22no—
258C2×D44—22no—
259C2×D44—22no—
260C2×D44—22no—
261C2×D44—22no—
262C2×D44—22no—
263C2×D44—42no—
264C2×D44—44no—
265C2×D44—44no—
266C2×D44—44no—
267C2×D44—82no—
268C2×D44—82no—
269C2×D44—82no—
270C2×D44—82no—
271C2×D44C2×D414yes—
272C2×D44C2412yes—
273C2×D44C2412yes—
274C2×D44C2412yes—
275C2×C4×D11—24no—
276C2×C4×D11—24no—
277C2×C4×D11—22no—
278C2×C4×D11—22no—
279C2×C4×D11—22no—
280C2×C4×D11—22no—
281C2×C4×D11—44no—
282C2×C4×D11—44no—
283C2×C4×D11C2×D412yes—
284C2×C4×D11C2×D412yes—
285C2×C4×D11C2412yes—
286C2×C4×D11C2412yes—
287C2×Dic22—22no—
288C2×Dic22—21no—
289C2×Dic22—22no—
290C2×Dic22C2412yes—
291C11×SD16C2×D4116yescomplemented
292C2×C8×C11—22no—
293C2×C8×C11C2×D414yes—
294C2×C8×C11C2412yes—
295C2×C8×C11C2412yes—
296C11×C4⋊C4—24no—
297C11×C4⋊C4—21no—
298C11×C4⋊C4—21no—
299C11×C4⋊C4C2412yes—
300C11×C4⋊C4C2412yes—
301C11×C22⋊C4—24no—
302C42×C11—24no—
303C42×C11C2×D412yes—
304C42×C11C2412yes—
305#4326—28no—
306#4325—28no—
307#4323—28no—
308#4323—28no—
309(C2×D11)⋊C4—24no—
310(C2×D11)⋊C4—24no—
311(C2×D11)⋊C4—24no—
312(C2×D11)⋊C4—24no—
313(C2×D11)⋊C4—24no—
314(C2×D11)⋊C4—24no—
315(C2×D11)⋊C4C2×D414yes—
316(C2×D11)⋊C4C2×D414yes—
317C4⋊Dic11—24no—
318C4⋊Dic11C2×D414yes—
319C2×C11⋊C8—22no—
320C2×C11⋊C8—22no—
321C2×C11⋊C8C2412yes—
322C2×C11⋊C8C2412yes—
323D88—28no—
324D88—44no—
325#4314—28no—
326#4314—44no—
327#4313—28no—
328C8×D11—28no—
329C22×AGL(1,ℤ/8)—111no—
330C22×#135—111no—
331C2×#550—111no—
332C2×#546—111no—
333#3268—1116no—
334C2×#496—111no—
335C2×#468—111no—
336C2×#466—111no—
337C2×#464—111no—
338C2×#459—111no—
339C2×#452—111no—
340C2×#449—111no—
341C2×#449—111no—
342C2×#447—111no—
343C2×#440D1111yescharacteristic, complemented
344C2×#435—111no—
345C23×C11—24no—
346C23×C11—22no—
347C23×C11—42no—
348C23×C11—42no—
349C23×C11C22×D411yescharacteristic
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—48no—
360C22×D11—48no—
361C22×D11—42no—
362C22×D11—42no—
363C22×D11—42no—
364C22×D11—42no—
365C22×D11—42no—
366C22×D11—42no—
367C22×D11—42no—
368C22×D11—42no—
369C22×D11—42no—
370C22×D11—84no—
371C22×D11—816no—
372C22×D11C22×D412yes—
373C22×D11C22×D412yes—
374Q8×C11—24no—
375Q8×C11—22no—
376Q8×C11C22×D414yes—
377D4×C11—24no—
378D4×C11—22no—
379D4×C11C22×D414yes—
380C2×C4×C11—24no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—42no—
387C2×C4×C11—42no—
388C2×C4×C11—84no—
389C2×C4×C11C22×D412yes—
390C2×C4×C11C22×D412yes—
391C2×C4×C11C22×D412yes—
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11H(5,𝔽2)12yes—
394C2×C4×C11C2511yescharacteristic
395C22⋊D11—48no—
396C22⋊D11—48no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—48no—
401C2×Dic11—42no—
402C2×Dic11C22×D412yes—
403C2×Dic11C22×D412yes—
404D44—22no—
405D44—22no—
406D44—22no—
407D44—22no—
408D44—22no—
409D44—22no—
410D44—44no—
411D44—48no—
412D44—48no—
413D44—48no—
414D44—42no—
415D44—42no—
416D44—42no—
417D44—84no—
418D44—84no—
419D44—84no—
420D44—84no—
421C4×D11—24no—
422C4×D11—24no—
423C4×D11—22no—
424C4×D11—22no—
425C4×D11—22no—
426C4×D11—22no—
427C4×D11—48no—
428C4×D11—48no—
429Dic22—22no—
430Dic22—22no—
431Dic22—42no—
432C8×C11—22no—
433C8×C11C22×D414yes—
434C11⋊C8—22no—
435C11⋊C8—22no—
436C22×#41—111no—
437C22×#41—111no—
438C22×#41—111no—
439C23×D4—111no—
440C2×AGL(1,ℤ/8)—118no—
441C2×AGL(1,ℤ/8)—228no—
442C2×#135—118no—
443C2×#135—228no—
444C22×Q16—111no—
445C22×SD16—111no—
446C22×SD16—111no—
447C22×SD16—111no—
448C22×SD16C2×D1111yescharacteristic
449C22×D8—111no—
450C22×D8—111no—
451C22×D8—111no—
452C22×D8—111no—
453C22×M16—111no—
454C23×C8—111no—
455#550—118no—
456#550—224no—
457#546—118no—
458#546—224no—
459C2×#127—111no—
460C2×#127—221no—
461C2×#124—111no—
462C2×#123—221no—
463C2×C22⋊Q8—111no—
464C2×#121—111no—
465C2×#121—111no—
466C2×#121—111no—
467C2×#121—221no—
468C2×#121—221no—
469C2×#121—221no—
470C2×#120—221no—
471C2×C4×Q8C2×D1111yescharacteristic, complemented
472C2×C4×D4—111no—
473C2×C4×D4—221no—
474C2×C4×D4C2×D1111yescharacteristic
475C22×C22⋊C4—221no—
476#496—118no—
477#468—118no—
478#466—118no—
479#464—118no—
480#459—118no—
481#452—118no—
482#449—118no—
483#449—118no—
484#447—118no—
485#440C2×D1118yescomplemented
486#435—118no—
487C2×#107C2×D1111yescharacteristic, complemented
488C2×C4⋊C8—111no—
489C2×#103—111no—
490C2×#103C2×D1111yescharacteristic, complemented
491C2×#102—111no—
492C2×#102—111no—
493C2×#102—111no—
494C2×#102C2×D1111yescharacteristic
495C2×C22⋊C8—111no—
496C2×C22⋊C8—111no—
497C2×#97C2×D1111yescharacteristic, complemented
498C22×C11—24no—
499C22×C11—48no—
500C22×C11—42no—
501C22×C11—42no—
502C22×C11D4212yes—
503C22×C11#57512yes—
504C22×C11#57612yes—
505C22×C11C23×D411yescharacteristic
506C2×D11—22no—
507C2×D11—22no—
508C2×D11—22no—
509C2×D11—22no—
510C2×D11—22no—
511C2×D11—22no—
512C2×D11—44no—
513C2×D11—44no—
514C2×D11—42no—
515C2×D11—42no—
516C2×D11—42no—
517C2×D11—42no—
518C2×D11—42no—
519C2×D11—42no—
520C2×D11—42no—
521C2×D11—42no—
522C2×D11—42no—
523C2×D11—816no—
524C2×D11—84no—
525C2×D11—84no—
526C2×D11—84no—
527C4×C11—24no—
528C4×C11—22no—
529C4×C11—22no—
530C4×C11—42no—
531C4×C11—42no—
532C4×C11D4212yes—
533C4×C11C23×D411yescharacteristic
534C4×C11C2×H(5,𝔽2)11yescharacteristic
535Dic11—22no—
536Dic11—22no—
537Dic11—42no—
538C25—221no—
539C2×#41—114no—
540C2×#41—114no—
541C2×#41—114no—
542C2×#41—222no—
543C2×#41—222no—
544C2×#41—222no—
545C2×#41—224no—
546C2×#41—224no—
547C2×#41—224no—
548C2×#41—442no—
549C2×#41—442no—
550C2×#41—442no—
551C22×Q8—111no—
552C22×Q8C22×D1111yescharacteristic
553C22×D4—114no—
554C22×D4—111no—
555C22×D4—111no—
556C22×D4—111no—
557C22×D4—111no—
558C22×D4—221no—
559C22×D4—221no—
560C22×D4—221no—
561C22×D4—221no—
562C22×D4—221no—
563C22×D4—222no—
564C22×D4—221no—
565C22×D4—224no—
566C22×D4—221no—
567C22×D4—221no—
568C22×D4—221no—
569C22×D4—442no—
570C22×D4C22×D1111yescharacteristic
571C23×C4—21no—
572C23×C4—111no—
573C23×C4—111no—
574C23×C4—221no—
575C23×C4—221no—
576C23×C4—221no—
577AGL(1,ℤ/8)—2232no—
578#135—2232no—
579C2×Q16—114no—
580C2×Q16—224no—
581C2×SD16—114no—
582C2×SD16—114no—
583C2×SD16—114no—
584C2×SD16—224no—
585C2×SD16—224no—
586C2×SD16—442no—
587C2×SD16D4418yescomplemented
588C2×SD16C22×D1114yes—
589C2×D8—114no—
590C2×D8—114no—
591C2×D8—114no—
592C2×D8—114no—
593C2×D8—224no—
594C2×D8—224no—
595C2×D8—224no—
596C2×D8—442no—
597C2×M16—114no—
598C2×M16—224no—
599C22×C8—111no—
600C22×C8—111no—
601C22×C8—114no—
602C22×C8—224no—
603C22×C8C22×D1111yescharacteristic
604C22×C8C22×D1111yescharacteristic
605#127—114no—
606#127—228no—
607#127—222no—
608#124—114no—
609#124—222no—
610#123—228no—
611C22⋊Q8—114no—
612C22⋊Q8—222no—
613#121—114no—
614#121—114no—
615#121—114no—
616#121—228no—
617#121—228no—
618#121—228no—
619#121—222no—
620#121—222no—
621#121—222no—
622#120—228no—
623C4×Q8—22no—
624C4×Q8C22×D1114yescomplemented
625C4×D4—22no—
626C4×D4—114no—
627C4×D4—114no—
628C4×D4—228no—
629C4×D4C22×D1114yes—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—111no—
632C2×C4⋊C4—221no—
633C2×C4⋊C4C22×D1111yescharacteristic
634C2×C4⋊C4C22×D1111yescharacteristic
635C2×C22⋊C4—21no—
636C2×C22⋊C4—111no—
637C2×C22⋊C4—111no—
638C2×C22⋊C4—228no—
639C2×C22⋊C4—221no—
640C2×C22⋊C4—221no—
641C2×C22⋊C4—221no—
642C2×C22⋊C4—221no—
643C2×C22⋊C4—221no—
644C2×C22⋊C4—221no—
645C2×C42—21no—
646C2×C42C22×D1111yescharacteristic
647#107C22×D1114yescomplemented
648C4⋊C8—114no—
649#103—114no—
650#103C22×D1114yescomplemented
651#102—114no—
652#102—114no—
653#102—114no—
654#102C22×D1114yes—
655C22⋊C8—114no—
656C22⋊C8—114no—
657#97C22×D1114yescomplemented
658C2×C11—44no—
659C2×C11#326814yescomplemented
660C2×C11C2×D4211yescharacteristic
661C2×C11C2×#57511yescharacteristic
662C2×C11C2×#57611yescharacteristic
663D11—42no—
664D11—42no—
665D11—82no—
666D11—82no—
667D11—82no—
668C24—21no—
669C24—111no—
670C24—111no—
671C24—224no—
672C24—221no—
673C24—221no—
674C24—221no—
675C24—444no—
676C24—444no—
677C24—882no—
678#41—228no—
679#41—228no—
680#41—228no—
681#41—444no—
682#41—448no—
683#41—444no—
684#41—444no—
685#41—448no—
686#41—448no—
687C2×Q8—21no—
688C2×Q8—22no—
689C2×Q8—112no—
690C2×Q8—221no—
691C2×Q8—222no—
692C2×Q8—222no—
693C2×Q8C2×D4414yes—
694C2×Q8C23×D1112yes—
695C2×D4—21no—
696C2×D4—22no—
697C2×D4—114no—
698C2×D4—112no—
699C2×D4—112no—
700C2×D4—112no—
701C2×D4—224no—
702C2×D4—224no—
703C2×D4—224no—
704C2×D4—224no—
705C2×D4—224no—
706C2×D4—224no—
707C2×D4—228no—
708C2×D4—224no—
709C2×D4—222no—
710C2×D4—222no—
711C2×D4—222no—
712C2×D4—224no—
713C2×D4—221no—
714C2×D4—221no—
715C2×D4—221no—
716C2×D4—224no—
717C2×D4—222no—
718C2×D4—222no—
719C2×D4—222no—
720C2×D4—442no—
721C2×D4—444no—
722C2×D4—444no—
723C2×D4—444no—
724C2×D4—444no—
725C2×D4—448no—
726C2×D4—444no—
727C2×D4—444no—
728C2×D4—882no—
729C2×D4—882no—
730C2×D4—882no—
731C2×D4—882no—
732C2×D4C2×D4414yes—
733C2×D4C23×D1112yes—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—24no—
738C22×C4—82no—
739C22×C4—111no—
740C22×C4—111no—
741C22×C4—112no—
742C22×C4—112no—
743C22×C4—112no—
744C22×C4—112no—
745C22×C4—224no—
746C22×C4—224no—
747C22×C4—224no—
748C22×C4—222no—
749C22×C4—222no—
750C22×C4—222no—
751C22×C4—222no—
752C22×C4—221no—
753C22×C4—444no—
754C22×C4—444no—
755C22×C4—444no—
756C22×C4D4×D1111yescharacteristic
757C22×C4D4×D1111yescharacteristic
758C22×C4C23×D1111yescharacteristic
759Q16—228no—
760SD16—228no—
761SD16—228no—
762SD16—444no—
763SD16C2×D44116yescomplemented
764D8—228no—
765D8—228no—
766D8—228no—
767D8—444no—
768M16—228no—
769C2×C8—22no—
770C2×C8—112no—
771C2×C8—112no—
772C2×C8—222no—
773C2×C8—222no—
774C2×C8—228no—
775C2×C8C2×D4414yes—
776C2×C8C23×D1112yes—
777C2×C8C23×D1112yes—
778C4⋊C4—24no—
779C4⋊C4—21no—
780C4⋊C4—21no—
781C4⋊C4—114no—
782C4⋊C4—224no—
783C4⋊C4C23×D1112yes—
784C4⋊C4C23×D1112yes—
785C22⋊C4—24no—
786C22⋊C4—114no—
787C22⋊C4—114no—
788C22⋊C4—224no—
789C22⋊C4—224no—
790C22⋊C4—224no—
791C22⋊C4—224no—
792C22⋊C4—224no—
793C22⋊C4—224no—
794C42—24no—
795C42D4×D1112yes—
796C42C23×D1112yes—
797C11C2×#326811yescharacteristic, complemented, Sylow
798C23—24no—
799C23—22no—
800C23—42no—
801C23—42no—
802C23—112no—
803C23—112no—
804C23—222no—
805C23—222no—
806C23—222no—
807C23—222no—
808C23—222no—
809C23—222no—
810C23—222no—
811C23—222no—
812C23—222no—
813C23—448no—
814C23—448no—
815C23—442no—
816C23—442no—
817C23—442no—
818C23—442no—
819C23—442no—
820C23—442no—
821C23—442no—
822C23—442no—
823C23—442no—
824C23—884no—
825C23—8816no—
826C23C2×D4×D1111yescharacteristic
827Q8—24no—
828Q8—22no—
829Q8—222no—
830Q8—222no—
831Q8—442no—
832Q8C22×D4414yes—
833D4—24no—
834D4—22no—
835D4—222no—
836D4—222no—
837D4—222no—
838D4—222no—
839D4—222no—
840D4—222no—
841D4—444no—
842D4—448no—
843D4—448no—
844D4—448no—
845D4—448no—
846D4—448no—
847D4—442no—
848D4—442no—
849D4—442no—
850D4—884no—
851D4—884no—
852D4—884no—
853D4—884no—
854D4C22×D4414yes—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—24no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—84no—
864C2×C4—112no—
865C2×C4—112no—
866C2×C4—222no—
867C2×C4—222no—
868C2×C4—224no—
869C2×C4—224no—
870C2×C4—222no—
871C2×C4—222no—
872C2×C4—222no—
873C2×C4—222no—
874C2×C4—222no—
875C2×C4—448no—
876C2×C4—448no—
877C2×C4—448no—
878C2×C4—442no—
879C2×C4C22×D4412yes—
880C2×C4C2×D4×D1112yes—
881C2×C4C2×D4×D1112yes—
882C2×C4C2×D4×D1111yescharacteristic
883C2×C4#6704212yes—
884C2×C4C24×D1111yescharacteristic
885C8—22no—
886C8—222no—
887C8—222no—
888C8C22×D4414yes—
889C22—24no—
890C22—48no—
891C22—42no—
892C22—42no—
893C22—222no—
894C22—222no—
895C22—222no—
896C22—222no—
897C22—222no—
898C22—222no—
899C22—444no—
900C22—444no—
901C22—442no—
902C22—442no—
903C22—442no—
904C22—442no—
905C22—442no—
906C22—442no—
907C22—442no—
908C22—442no—
909C22—442no—
910C22—8816no—
911C22—884no—
912C22—884no—
913C22—884no—
914C22D4×D4412yes—
915C22#1062330512yes—
916C22#1062330812yes—
917C22C22×D4×D1111yescharacteristic
918C4—24no—
919C4—22no—
920C4—22no—
921C4—42no—
922C4—42no—
923C4—222no—
924C4—222no—
925C4—442no—
926C4D4×D4412yes—
927C4C23×D4411yescharacteristic
928C4C2×#6704211yescharacteristic
929C2—44no—
930C2—442no—
931C2—442no—
932C2—882no—
933C2—882no—
934C2—882no—
935C2#1308015814yesdirect product factor
936C2C2×D4×D4411yescharacteristic
937C2C2×#1062330811yescharacteristic
938C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#440C2
socleC23×C11C22×D4
hypercenterC2×#440D11
hypocenterC11C2×#3268
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C22×#66967C2semidirect
2. C22×#66969C2semidirect
3. C2×#10623108C2semidirect
4. C2×#10623085C2semidirect
5. #13080158C2direct (N × H)
6. C2×#10622325C2semidirect
7. C2×#10622499C2semidirect
8. C2×#10622496C2semidirect
9. C2×#10622641C2semidirect
10. C2×#10622628C2semidirect
11. C2×#10622423C2semidirect
12. C2×#10622424C2semidirect
13. C2×#10622394C2semidirect
14. C2×#10622386C2semidirect
15. C2×#10622319C2semidirect
16. C2×C11×#440C2semidirect
18. C22×#4343C22semidirect
22. C2×C4×Q8×C11C22semidirect
24. C22×#4326C22semidirect
31. C2×#66969C22semidirect
33. C2×#66967C22semidirect
36. C22×#4314C22semidirect
37. C22×#4314C22semidirect
39. C22×C8×D11C22semidirect
41. #10623108C22semidirect
43. #10623085C22semidirect
49. C2×#66948C22semidirect
54. C2×#66927C22semidirect
57. C11×#440C22semidirect
58. C2×C11×#107C22semidirect
59. C2×C11×#103C22semidirect
61. C2×C11×#97C22semidirect
63. C2×(C2×D11)⋊C8C22semidirect
64. #10622641C22semidirect
65. #10622628C22semidirect
66. C2×#66874C22semidirect
68. C2×#66873C22semidirect
69. C2×#66873C22semidirect
70. C2×C4⋊(C11⋊C8)C22semidirect
71. #10622499C22semidirect
72. #10622496C22semidirect
73. #10622424C22semidirect
74. #10622423C22semidirect
75. #10622394C22semidirect
76. #10622386C22semidirect
77. #10622325C22semidirect
78. #10622319C22semidirect
93. C2×#4343C23semidirect
118. C2×C11×SD16D4semidirect
123. C4×Q8×C11C23semidirect
133. C2×#4326C23semidirect
162. C2×#4314C23semidirect
163. C2×#4314C23semidirect
167. C2×C8×D11C23semidirect
177. #66948C23semidirect
184. #66927C23semidirect
188. C11×#107C23semidirect
189. C11×#103C23semidirect
191. C11×#97C23semidirect
193. (C2×D11)⋊C8C23semidirect
194. #66874C23semidirect
196. #66873C23semidirect
197. #66873C23semidirect
198. C4⋊(C11⋊C8)C23semidirect
291. C11×SD16C2×D4semidirect
343. C2×#440D11semidirect
471. C2×C4×Q8C2×D11semidirect
485. #440C2×D11semidirect
487. C2×#107C2×D11semidirect
490. C2×#103C2×D11semidirect
497. C2×#97C2×D11semidirect
587. C2×SD16D44semidirect
624. C4×Q8C22×D11semidirect
647. #107C22×D11semidirect
650. #103C22×D11semidirect
657. #97C22×D11semidirect
659. C2×C11#3268semidirect
763. SD16C2×D44semidirect
797. C11C2×#3268semidirect
935. C2#13080158direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669672
C22×#669692
C2×#106231082
C2×#106230852
#130801582
C2×#106223252
C2×#106224992
C2×#106224962
C2×#106226412
C2×#106226282
C2×#106224232
C2×#106224242
C2×#106223942
C2×#106223862
C2×#106223192
C2×C11×#4402
C2×#326811