Finite Group Databasebeta

← C2×#13080159 #15628789

Subgroups — C2×#13080159 #15628789

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×#67002C211yesmaximal, characteristic, complemented
2C22×#66972C211yesmaximal, characteristic, complemented
3C2×#10623365C211yesmaximal, characteristic, complemented
4C2×#10623161C211yesmaximal, characteristic, complemented
5#13080159C2116yesmaximal, direct product factor
6C2×#10622789C211yesmaximal, characteristic, complemented
7C2×#10622662C211yesmaximal, characteristic, complemented
8C2×#10622388C211yesmaximal, characteristic, complemented
9C2×#10622798C211yesmaximal, characteristic, complemented
10C2×#10622399C211yesmaximal, characteristic, complemented
11C2×#10622424C211yesmaximal, characteristic, complemented
12C2×#10622785C211yesmaximal, characteristic, complemented
13C2×#10622345C211yesmaximal, characteristic, complemented
14C2×#10622430C211yesmaximal, characteristic, complemented
15C2×#10622341C211yesmaximal, characteristic, complemented
16C2×C11×#452C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×#4343C2211yescharacteristic
19C22×#4343C2211yescharacteristic, complemented
20C23×D44C2211yescharacteristic
21C22×C11×Q16C2211yescharacteristic, complemented
22C22×C11×SD16C2211yescharacteristic, complemented
23C2×C11×C22⋊Q8C2211yescharacteristic
24#10623365—24no—
25#10623365C2218yescomplemented
26C2×#67002—28no—
27C2×#67002C2218yescomplemented
28C2×#67000C2211yescharacteristic
29C2×Q8×Dic11C2211yescharacteristic, complemented
30C22×#4325C2211yescharacteristic
31C22×#4325C2211yescharacteristic
32C22×#4325C2211yescharacteristic, complemented
33C2×#66993—21no—
34C2×#66993C2211yescharacteristic, complemented
35C2×#66991—21no—
36C2×#66991C2211yescharacteristic, complemented
37C22×#4323C2211yescharacteristic
38C22×#4323C2211yescharacteristic
39C2×#66983—21no—
40C2×#66983C2211yescharacteristic
41C2×C4×C22⋊D11—21no—
42C2×C4×C22⋊D11C2211yescharacteristic
43C22×#4318C2211yescharacteristic
44C2×#66972—28no—
45C2×#66972C2218yescomplemented
46C22×D88C2211yescharacteristic
47C22×D88C2211yescharacteristic
48C22×C8×D11C2211yescharacteristic, 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#10622789C2218yescomplemented
64#10622785C2218yescomplemented
65C2×#66885C2211yescharacteristic
66C2×#66885C2211yescharacteristic
67C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
68C2×#66879C2211yescharacteristic, complemented
69C2×Dic11⋊C8C2211yescharacteristic, complemented
70#10622662C2218yescomplemented
71C2×#66873C2211yescharacteristic, complemented
72C2×#66871C2211yescharacteristic, complemented
73#10622430C2218yescomplemented
74#10622424C2218yescomplemented
75#10622399C2218yescomplemented
76#10622388C2218yescomplemented
77#10622345C2218yescomplemented
78#10622341C2218yescomplemented
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⋊D11—21no—
92C22×C22⋊D11—21no—
93C22×C22⋊D11—21no—
94C22×C22⋊D11D411yescharacteristic
95C2×#4343—22no—
96C2×#4343—22no—
97C2×#4343—24no—
98C2×#4343—24no—
99C2×#4343—42no—
100C2×#4343—42no—
101C2×#4343C2314yes—
102C2×#4343C2314yescomplemented
103C22×D44—24no—
104C22×D44—21no—
105C22×D44—21no—
106C22×D44—21no—
107C22×D44—22no—
108C22×D44—21no—
109C22×D44—42no—
110C22×D44C2311yescharacteristic
111C22×D44C2311yescharacteristic
112C22×D44C2314yes—
113C22×D44C2311yescharacteristic
114C22×C4×D11—21no—
115C22×C4×D11—21no—
116C22×C4×D11—21no—
117C22×C4×D11C2311yescharacteristic
118C2×C11×Q16—24no—
119C2×C11×Q16C2314yescomplemented
120C2×C11×SD16—42no—
121C2×C11×SD16C2314yescomplemented
122C22×C8×C11C2311yescharacteristic
123C22×C8×C11C2311yescharacteristic
124C11×C22⋊Q8—22no—
125C11×C22⋊Q8C2314yes—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4C2311yescharacteristic
128C2×C11×C22⋊C4—21no—
129C2×C22⋊Dic11—21no—
130C2×C22⋊Dic11D411yescharacteristic
131#67002—232no—
132#67000—22no—
133#67000C2314yes—
134Q8×Dic11—22no—
135Q8×Dic11C2314yescomplemented
136C2×#4325—24no—
137C2×#4325—24no—
138C2×#4325D418yescomplemented
139C2×#4325C2314yes—
140C2×#4325C2314yes—
141C2×#4325C2314yescomplemented
142#66993—28no—
143#66993—22no—
144#66993C2314yescomplemented
145#66991—22no—
146#66991—28no—
147#66991C2314yescomplemented
148C2×#4323—24no—
149C2×#4323—24no—
150C2×#4323C2314yes—
151C2×#4323C2314yes—
152#66983—22no—
153#66983—28no—
154#66983C2314yes—
155C4×C22⋊D11—28no—
156C4×C22⋊D11D414yes—
157C4×C22⋊D11C2314yes—
158C2×(C2×D11)⋊C4—21no—
159C2×(C2×D11)⋊C4—21no—
160C2×(C2×D11)⋊C4—21no—
161C2×(C2×D11)⋊C4—21no—
162C2×(C2×D11)⋊C4—21no—
163C2×(C2×D11)⋊C4D411yescharacteristic
164C2×C4⋊Dic11—21no—
165C2×C4⋊Dic11C2311yescharacteristic
166C2×Dic11⋊C4D411yescharacteristic
167C2×C4×Dic11—21no—
168C2×C4×Dic11C2311yescharacteristic
169C2×#4318—24no—
170C2×#4318C2314yes—
171C22×C11⋊C8C2311yescharacteristic
172C22×C11⋊C8C2311yescharacteristic
173#66972—232no—
174C2×D88—24no—
175C2×D88—42no—
176C2×D88C2314yes—
177C2×D88C2314yes—
178C2×C8×D11—24no—
179C2×C8×D11C2314yescomplemented
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
195#66879C2314yescomplemented
196Dic11⋊C8C2314yescomplemented
197#66873C2314yescomplemented
198#66871C2314yescomplemented
199C2×#3268—111nomaximal, Sylow
200C24×C11—21no—
201C24×C11C2×D411yescharacteristic
202C23×D11—21no—
203C23×D11—21no—
204C23×D11—21no—
205C23×D11—24no—
206C23×D11—44no—
207C23×D11—44no—
208C23×D11—82no—
209C23×D11C2×D411yescharacteristic
210C11×#41—28no—
211C11×#41—44no—
212C11×#41—48no—
213C2×Q8×C11—21no—
214C2×Q8×C11—21no—
215C2×Q8×C11—22no—
216C2×Q8×C11—22no—
217C2×Q8×C11—22no—
218C2×Q8×C11C2×D414yes—
219C2×Q8×C11C2412yes—
220C2×Q8×C11C2412yes—
221C2×D4×C11—24no—
222C2×D4×C11—22no—
223C2×D4×C11—21no—
224C2×D4×C11—22no—
225C2×D4×C11—44no—
226C2×D4×C11C2412yes—
227C22×C4×C11—21no—
228C22×C4×C11—22no—
229C22×C4×C11—22no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—24no—
233C22×C4×C11—44no—
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D412yes—
236C22×C4×C11C2412yes—
237C22×C4×C11C2411yescharacteristic
238C2×C22⋊D11—24no—
239C2×C22⋊D11—24no—
240C2×C22⋊D11—24no—
241C2×C22⋊D11—24no—
242C2×C22⋊D11—42no—
243C2×C22⋊D11—44no—
244C2×C22⋊D11—82no—
245C2×C22⋊D11—82no—
246C2×C22⋊D11—82no—
247C2×C22⋊D11C2×D414yes—
248C22×Dic11—21no—
249C22×Dic11C2×D411yescharacteristic
250C22×Dic11C2×D411yescharacteristic
251C22×Dic11C2×D411yescharacteristic
252#4343—28no—
253#4343—28no—
254#4343—44no—
255#4343—44no—
256#4343—48no—
257#4343—48no—
258C2×D44—24no—
259C2×D44—24no—
260C2×D44—24no—
261C2×D44—28no—
262C2×D44—21no—
263C2×D44—24no—
264C2×D44—21no—
265C2×D44—21no—
266C2×D44—22no—
267C2×D44—22no—
268C2×D44—22no—
269C2×D44—22no—
270C2×D44—22no—
271C2×D44—44no—
272C2×D44—44no—
273C2×D44—44no—
274C2×D44—48no—
275C2×D44—44no—
276C2×D44—82no—
277C2×D44C2×D414yes—
278C2×D44C2412yes—
279C2×D44C2412yes—
280C2×D44C2412yes—
281C2×C4×D11—24no—
282C2×C4×D11—24no—
283C2×C4×D11—24no—
284C2×C4×D11—22no—
285C2×C4×D11—22no—
286C2×C4×D11—44no—
287C2×C4×D11—44no—
288C2×C4×D11—82no—
289C2×C4×D11C2×D412yes—
290C2×C4×D11C2412yes—
291C11×Q16—28no—
292C11×SD16—44no—
293C2×C8×C11—22no—
294C2×C8×C11—22no—
295C2×C8×C11C2412yes—
296C2×C8×C11C2412yes—
297C11×C4⋊C4—21no—
298C11×C4⋊C4—24no—
299C11×C4⋊C4C2412yes—
300C11×C22⋊C4—24no—
301C22⋊Dic11—24no—
302C22⋊Dic11C2×D414yes—
303#4325—28no—
304#4325—28no—
305#4325C2×D4116yescomplemented
306#4323—28no—
307#4323—28no—
308(C2×D11)⋊C4—24no—
309(C2×D11)⋊C4—24no—
310(C2×D11)⋊C4—24no—
311(C2×D11)⋊C4—24no—
312(C2×D11)⋊C4—24no—
313(C2×D11)⋊C4C2×D414yes—
314C4⋊Dic11—24no—
315C4⋊Dic11—21no—
316C4⋊Dic11C2412yes—
317Dic11⋊C4C2×D414yes—
318C4×Dic11—24no—
319C4×Dic11C2×D412yes—
320C4×Dic11C2412yes—
321#4318—28no—
322C2×C11⋊C8—22no—
323C2×C11⋊C8C2×D414yes—
324C2×C11⋊C8C2412yes—
325C2×C11⋊C8C2412yes—
326D88—28no—
327D88—44no—
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×#452D1111yescharacteristic, complemented
340C2×#449—111no—
341C2×#449—111no—
342C2×#447—111no—
343C2×#440—111no—
344C2×#435—111no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—42no—
350C23×C11—42no—
351C23×C11—42no—
352C23×C11C22×D412yes—
353C23×C11C22×D411yescharacteristic
354C22×D11—22no—
355C22×D11—24no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—48no—
362C22×D11—42no—
363C22×D11—42no—
364C22×D11—48no—
365C22×D11—42no—
366C22×D11—42no—
367C22×D11—42no—
368C22×D11—42no—
369C22×D11—42no—
370C22×D11—42no—
371C22×D11—84no—
372C22×D11—816no—
373C22×D11C22×D412yes—
374Q8×C11—24no—
375Q8×C11—22no—
376Q8×C11—22no—
377Q8×C11—22no—
378Q8×C11—42no—
379Q8×C11C22×D414yes—
380D4×C11—22no—
381D4×C11—22no—
382D4×C11—48no—
383D4×C11—42no—
384C2×C4×C11—24no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—24no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—48no—
393C2×C4×C11—42no—
394C2×C4×C11—42no—
395C2×C4×C11C22×D412yes—
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C22×D412yes—
398C2×C4×C11H(5,𝔽2)12yes—
399C2×C4×C11C2511yescharacteristic
400C22⋊D11—44no—
401C22⋊D11—48no—
402C22⋊D11—84no—
403C22⋊D11—84no—
404C22⋊D11—84no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—42no—
410C2×Dic11C22×D412yes—
411C2×Dic11C22×D412yes—
412C2×Dic11C22×D412yes—
413D44—24no—
414D44—22no—
415D44—22no—
416D44—22no—
417D44—22no—
418D44—22no—
419D44—48no—
420D44—48no—
421D44—48no—
422D44—42no—
423D44—42no—
424D44—84no—
425D44C22×D414yes—
426C4×D11—24no—
427C4×D11—22no—
428C4×D11—22no—
429C4×D11—48no—
430C4×D11—48no—
431C4×D11—84no—
432C8×C11—22no—
433C8×C11—22no—
434C11⋊C8—22no—
435C11⋊C8C22×D414yes—
436C22×#41—111no—
437C22×#41—111no—
438C22×#41C2×D1111yescharacteristic
439C23×D4—111no—
440C2×AGL(1,ℤ/8)—118no—
441C2×AGL(1,ℤ/8)—228no—
442C2×#135—118no—
443C2×#135—228no—
444C22×Q16C2×D1111yescharacteristic, complemented
445C22×SD16—111no—
446C22×SD16—111no—
447C22×SD16—111no—
448C22×SD16C2×D1111yescharacteristic, complemented
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⋊Q8C2×D1111yescharacteristic
464C2×#121—111no—
465C2×#121—111no—
466C2×#121—111no—
467C2×#121—221no—
468C2×#121—221no—
469C2×#121—221no—
470C2×#120—221no—
471C2×C4×Q8—111no—
472C2×C4×D4—111no—
473C2×C4×D4—111no—
474C2×C4×D4—221no—
475C22×C22⋊C4—221no—
476#496—118no—
477#468—118no—
478#466—118no—
479#464—118no—
480#459—118no—
481#452C2×D1118yescomplemented
482#449—118no—
483#449—118no—
484#447—118no—
485#440—118no—
486#435—118no—
487C2×#107—111no—
488C2×C4⋊C8—111no—
489C2×#103—111no—
490C2×#103C2×D1111yescharacteristic, complemented
491C2×#102—111no—
492C2×#102—111no—
493C2×#102—111no—
494C2×#102C2×D1111yescharacteristic, complemented
495C2×C22⋊C8—111no—
496C2×C22⋊C8C2×D1111yescharacteristic
497C2×#97—111no—
498C22×C11—22no—
499C22×C11—22no—
500C22×C11—22no—
501C22×C11—44no—
502C22×C11—42no—
503C22×C11—42no—
504C22×C11—42no—
505C22×C11—84no—
506C22×C11D4212yes—
507C22×C11#57512yes—
508C22×C11#57612yes—
509C22×C11C23×D411yescharacteristic
510C2×D11—24no—
511C2×D11—22no—
512C2×D11—22no—
513C2×D11—22no—
514C2×D11—44no—
515C2×D11—48no—
516C2×D11—42no—
517C2×D11—42no—
518C2×D11—42no—
519C2×D11—42no—
520C2×D11—42no—
521C2×D11—42no—
522C2×D11—42no—
523C2×D11—42no—
524C2×D11—816no—
525C2×D11—84no—
526C2×D11—84no—
527C4×C11—22no—
528C4×C11—24no—
529C4×C11—42no—
530C4×C11—42no—
531C4×C11D4212yes—
532C4×C11C23×D411yescharacteristic
533C4×C11C2×H(5,𝔽2)11yescharacteristic
534Dic11—22no—
535Dic11—22no—
536Dic11—22no—
537Dic11—42no—
538C25—221no—
539C2×#41—22no—
540C2×#41—24no—
541C2×#41—42no—
542C2×#41—114no—
543C2×#41—114no—
544C2×#41—222no—
545C2×#41—222no—
546C2×#41—224no—
547C2×#41—224no—
548C2×#41—442no—
549C2×#41—442no—
550C2×#41C22×D1114yes—
551C22×Q8C22×D1111yescharacteristic
552C22×Q8C22×D1111yescharacteristic
553C22×D4—21no—
554C22×D4—111no—
555C22×D4—111no—
556C22×D4—111no—
557C22×D4—111no—
558C22×D4—114no—
559C22×D4—224no—
560C22×D4—221no—
561C22×D4—221no—
562C22×D4—221no—
563C22×D4—221no—
564C22×D4—221no—
565C22×D4—221no—
566C22×D4—221no—
567C22×D4—221no—
568C22×D4—222no—
569C22×D4—442no—
570C22×D4C22×D1111yescharacteristic
571C23×C4—21no—
572C23×C4—111no—
573C23×C4—221no—
574C23×C4—221no—
575C23×C4—221no—
576C23×C4C22×D1111yescharacteristic
577AGL(1,ℤ/8)—2232no—
578#135—2232no—
579C2×Q16—24no—
580C2×Q16C22×D1114yescomplemented
581C2×SD16—42no—
582C2×SD16—118no—
583C2×SD16—114no—
584C2×SD16—114no—
585C2×SD16—114no—
586C2×SD16—224no—
587C2×SD16—224no—
588C2×SD16C22×D1114yescomplemented
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—222no—
607#127—228no—
608#124—114no—
609#124—222no—
610#123—228no—
611C22⋊Q8—22no—
612C22⋊Q8C22×D1114yes—
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—114no—
624C4×Q8—222no—
625C4×D4—114no—
626C4×D4—114no—
627C4×D4—114no—
628C4×D4—222no—
629C4×D4—228no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—111no—
632C2×C4⋊C4—111no—
633C2×C4⋊C4—221no—
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—111no—
646C2×C42—221no—
647#107—114no—
648C4⋊C8—114no—
649#103—114no—
650#103C22×D1114yescomplemented
651#102—114no—
652#102—114no—
653#102—114no—
654#102C22×D1114yescomplemented
655C22⋊C8—114no—
656C22⋊C8C22×D1114yes—
657#97—114no—
658C2×C11—42no—
659C2×C11—82no—
660C2×C11#326814yescomplemented
661C2×C11C2×D4211yescharacteristic
662C2×C11C2×#57511yescharacteristic
663C2×C11C2×#57611yescharacteristic
664D11—42no—
665D11—44no—
666D11—82no—
667D11—82no—
668C24—21no—
669C24—111no—
670C24—221no—
671C24—221no—
672C24—221no—
673C24—224no—
674C24—444no—
675C24—444no—
676C24—882no—
677C24D4×D1111yescharacteristic
678#41—28no—
679#41—44no—
680#41—48no—
681#41—228no—
682#41—228no—
683#41—444no—
684#41—444no—
685#41—448no—
686#41—448no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—22no—
690C2×Q8—22no—
691C2×Q8—22no—
692C2×Q8D4×D1114yes—
693C2×Q8C23×D1112yes—
694C2×Q8C23×D1112yes—
695C2×D4—24no—
696C2×D4—22no—
697C2×D4—21no—
698C2×D4—22no—
699C2×D4—44no—
700C2×D4—114no—
701C2×D4—114no—
702C2×D4—112no—
703C2×D4—112no—
704C2×D4—112no—
705C2×D4—228no—
706C2×D4—224no—
707C2×D4—224no—
708C2×D4—224no—
709C2×D4—224no—
710C2×D4—224no—
711C2×D4—224no—
712C2×D4—224no—
713C2×D4—221no—
714C2×D4—222no—
715C2×D4—222no—
716C2×D4—224no—
717C2×D4—221no—
718C2×D4—221no—
719C2×D4—222no—
720C2×D4—222no—
721C2×D4—222no—
722C2×D4—444no—
723C2×D4—448no—
724C2×D4—444no—
725C2×D4—444no—
726C2×D4—444no—
727C2×D4—442no—
728C2×D4—444no—
729C2×D4—882no—
730C2×D4—882no—
731C2×D4—882no—
732C2×D4—882no—
733C2×D4C23×D1112yes—
734C22×C4—21no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—24no—
740C22×C4—44no—
741C22×C4—111no—
742C22×C4—111no—
743C22×C4—111no—
744C22×C4—112no—
745C22×C4—112no—
746C22×C4—224no—
747C22×C4—224no—
748C22×C4—224no—
749C22×C4—222no—
750C22×C4—222no—
751C22×C4—221no—
752C22×C4—444no—
753C22×C4—444no—
754C22×C4—882no—
755C22×C4D4×D1112yes—
756C22×C4D4×D1111yescharacteristic
757C22×C4C23×D1112yes—
758C22×C4C23×D1111yescharacteristic
759Q16—28no—
760SD16—44no—
761SD16—1116no—
762SD16—228no—
763SD16—228no—
764D8—228no—
765D8—228no—
766D8—228no—
767D8—444no—
768M16—228no—
769C2×C8—22no—
770C2×C8—22no—
771C2×C8—114no—
772C2×C8—112no—
773C2×C8—112no—
774C2×C8—228no—
775C2×C8—222no—
776C2×C8C23×D1112yes—
777C2×C8C23×D1112yes—
778C4⋊C4—24no—
779C4⋊C4—21no—
780C4⋊C4—114no—
781C4⋊C4—112no—
782C4⋊C4—224no—
783C4⋊C4—221no—
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—112no—
795C42—112no—
796C42—224no—
797C11C2×#326811yescharacteristic, complemented, Sylow
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—112no—
806C23—222no—
807C23—222no—
808C23—222no—
809C23—224no—
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—884no—
824C23—8816no—
825C23C2×D4×D1112yes—
826C23C2×D4×D1111yescharacteristic
827Q8—24no—
828Q8—22no—
829Q8—22no—
830Q8—22no—
831Q8—42no—
832Q8C2×D4×D1114yes—
833D4—22no—
834D4—22no—
835D4—48no—
836D4—42no—
837D4—114no—
838D4—224no—
839D4—222no—
840D4—222no—
841D4—222no—
842D4—222no—
843D4—222no—
844D4—448no—
845D4—448no—
846D4—448no—
847D4—444no—
848D4—448no—
849D4—442no—
850D4—442no—
851D4—884no—
852D4—884no—
853D4—884no—
854D4—884no—
855C2×C4—22no—
856C2×C4—24no—
857C2×C4—22no—
858C2×C4—24no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—48no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—112no—
867C2×C4—112no—
868C2×C4—112no—
869C2×C4—222no—
870C2×C4—222no—
871C2×C4—222no—
872C2×C4—224no—
873C2×C4—222no—
874C2×C4—222no—
875C2×C4—222no—
876C2×C4—448no—
877C2×C4—448no—
878C2×C4—442no—
879C2×C4—884no—
880C2×C4C2×D4×D1112yes—
881C2×C4C2×D4×D1111yescharacteristic
882C2×C4C2×D4×D1112yes—
883C2×C4#6703712yes—
884C2×C4C24×D1111yescharacteristic
885C8—22no—
886C8—22no—
887C8—114no—
888C8—222no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—44no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—84no—
897C22—222no—
898C22—224no—
899C22—222no—
900C22—222no—
901C22—444no—
902C22—448no—
903C22—442no—
904C22—442no—
905C22—442no—
906C22—442no—
907C22—442no—
908C22—442no—
909C22—442no—
910C22—442no—
911C22—8816no—
912C22—884no—
913C22—884no—
914C22#1062312112yes—
915C22#1062330012yes—
916C22#1062330812yes—
917C22C22×D4×D1111yescharacteristic
918C4—22no—
919C4—24no—
920C4—42no—
921C4—42no—
922C4—222no—
923C4—222no—
924C4—222no—
925C4—442no—
926C4#1062312112yes—
927C4C22×D4×D1111yescharacteristic
928C4C2×#6703711yescharacteristic
929C2—42no—
930C2—82no—
931C2—442no—
932C2—444no—
933C2—882no—
934C2—882no—
935C2#1308015914yesdirect product factor
936C2C2×#1062312111yescharacteristic
937C2C2×#1062330811yescharacteristic
938C2C2×#1062330011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#452C2
socleC23×C11C22×D4
hypercenterC2×#452D11
hypocenterC11C2×#3268
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×#67002C2semidirect
2. C22×#66972C2semidirect
3. C2×#10623365C2semidirect
4. C2×#10623161C2semidirect
5. #13080159C2direct (N × H)
6. C2×#10622789C2semidirect
7. C2×#10622662C2semidirect
8. C2×#10622388C2semidirect
9. C2×#10622798C2semidirect
10. C2×#10622399C2semidirect
11. C2×#10622424C2semidirect
12. C2×#10622785C2semidirect
13. C2×#10622345C2semidirect
14. C2×#10622430C2semidirect
15. C2×#10622341C2semidirect
16. C2×C11×#452C2semidirect
19. C22×#4343C22semidirect
21. C22×C11×Q16C22semidirect
22. C22×C11×SD16C22semidirect
25. #10623365C22semidirect
27. C2×#67002C22semidirect
29. C2×Q8×Dic11C22semidirect
32. C22×#4325C22semidirect
34. C2×#66993C22semidirect
36. C2×#66991C22semidirect
45. C2×#66972C22semidirect
48. C22×C8×D11C22semidirect
50. #10623161C22semidirect
57. C11×#452C22semidirect
58. C2×C11×#103C22semidirect
59. C2×C11×#102C22semidirect
61. C2×#66899C22semidirect
62. #10622798C22semidirect
63. #10622789C22semidirect
64. #10622785C22semidirect
67. C2×(C2×D11)⋊C8C22semidirect
68. C2×#66879C22semidirect
69. C2×Dic11⋊C8C22semidirect
70. #10622662C22semidirect
71. C2×#66873C22semidirect
72. C2×#66871C22semidirect
73. #10622430C22semidirect
74. #10622424C22semidirect
75. #10622399C22semidirect
76. #10622388C22semidirect
77. #10622345C22semidirect
78. #10622341C22semidirect
102. C2×#4343C23semidirect
119. C2×C11×Q16C23semidirect
121. C2×C11×SD16C23semidirect
135. Q8×Dic11C23semidirect
138. C2×#4325D4semidirect
141. C2×#4325C23semidirect
144. #66993C23semidirect
147. #66991C23semidirect
179. C2×C8×D11C23semidirect
188. C11×#103C23semidirect
189. C11×#102C23semidirect
191. #66899C23semidirect
194. (C2×D11)⋊C8C23semidirect
195. #66879C23semidirect
196. Dic11⋊C8C23semidirect
197. #66873C23semidirect
198. #66871C23semidirect
305. #4325C2×D4semidirect
339. C2×#452D11semidirect
444. C22×Q16C2×D11semidirect
448. C22×SD16C2×D11semidirect
481. #452C2×D11semidirect
490. C2×#103C2×D11semidirect
494. C2×#102C2×D11semidirect
580. C2×Q16C22×D11semidirect
588. C2×SD16C22×D11semidirect
650. #103C22×D11semidirect
654. #102C22×D11semidirect
660. C2×C11#3268semidirect
797. C11C2×#3268semidirect
935. C2#13080159direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670022
C22×#669722
C2×#106233652
C2×#106231612
#130801592
C2×#106227892
C2×#106226622
C2×#106223882
C2×#106227982
C2×#106223992
C2×#106224242
C2×#106227852
C2×#106223452
C2×#106224302
C2×#106223412
C2×C11×#4522
C2×#326811