Finite Group Databasebeta

← C2×#13080109 #15628736

Subgroups — C2×#13080109 #15628736

Order 2816.

3226 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66985C211yesmaximal, characteristic, complemented
2C22×SD16×D11C211yesmaximal, characteristic, complemented
3C2×#10623164C211yesmaximal, characteristic, complemented
4C2×D4×C22⋊D11C211yesmaximal, characteristic, complemented
5#13080109C2116yesmaximal, direct product factor
6C2×#10622789C211yesmaximal, characteristic, complemented
7C2×#10622662C211yesmaximal, characteristic, complemented
8C2×#10622388C211yesmaximal, characteristic, complemented
9C2×#10622375C211yesmaximal, characteristic, complemented
10C2×#10622778C211yesmaximal, characteristic, complemented
11C2×#10622347C211yesmaximal, characteristic, complemented
12C2×#10622783C211yesmaximal, characteristic, complemented
13C2×#10622386C211yesmaximal, characteristic, complemented
14C2×#10622370C211yesmaximal, characteristic, complemented
15C2×#10622341C211yesmaximal, characteristic, complemented
16C2×C11×#450C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11—21no—
19C22×Q8×D11C2211yescharacteristic, complemented
20C22×D4×D11C2211yescharacteristic
21C22×#4339C2211yescharacteristic, complemented
22C22×C11×SD16C2211yescharacteristic
23C22×C11×SD16C2211yescharacteristic, complemented
24C2×C11×C22⋊Q8C2211yescharacteristic, complemented
25C2×#67006—21no—
26C2×#67000C2211yescharacteristic, complemented
27C22×#4325C2211yescharacteristic, complemented
28C2×#66993C2211yescharacteristic
29C2×#66992—21no—
30D4×C22⋊D11—24no—
31D4×C22⋊D11C2218yescomplemented
32C2×#66991C2211yescharacteristic
33C2×#66990—21no—
34C2×D4×Dic11C2211yescharacteristic
35C22×#4324C2211yescharacteristic
36C22×#4324C2211yescharacteristic, complemented
37C2×#66985—28no—
38C2×#66985C2218yescomplemented
39C22×#4323C2211yescharacteristic
40C22×#4323C2211yescharacteristic, complemented
41C2×#66983C2211yescharacteristic
42C2×C4×C22⋊D11C2211yescharacteristic
43C22×#4318C2211yescharacteristic, complemented
44C2×SD16×D11—28no—
45C2×SD16×D11C2218yescomplemented
46C22×D88C2211yescharacteristic, complemented
47C22×#4314C2211yescharacteristic, complemented
48C22×C8×D11C2211yescharacteristic, complemented
49#10623164—24no—
50#10623164C2218yescomplemented
51C2×#66949—21no—
52C2×#66948C2211yescharacteristic, complemented
53C2×#66946—21no—
54C2×#66940C2211yescharacteristic, complemented
55C2×#66938—21no—
56C2×#66937—21no—
57C11×#450C2218yescomplemented
58C2×C11×#102C2211yescharacteristic
59C2×C11×#102C2211yescharacteristic, complemented
60C2×C11×C22⋊C8C2211yescharacteristic, complemented
61C2×#66899C2211yescharacteristic, complemented
62#10622789C2218yescomplemented
63#10622783C2218yescomplemented
64#10622778C2218yescomplemented
65C2×#66885C2211yescharacteristic, complemented
66C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
67C2×#66880C2211yescharacteristic, complemented
68C2×#66879C2211yescharacteristic, complemented
69C2×Dic11⋊C8C2211yescharacteristic, complemented
70#10622662C2218yescomplemented
71C2×#66873C2211yescharacteristic, complemented
72C2×#66871C2211yescharacteristic, complemented
73#10622388C2218yescomplemented
74#10622386C2218yescomplemented
75#10622375C2218yescomplemented
76#10622370C2218yescomplemented
77#10622347C2218yescomplemented
78#10622341C2218yescomplemented
79C25×C11—21no—
80C24×D11—21no—
81C22×Q8×C11C2311yescharacteristic
82C22×D4×C11—24no—
83C22×D4×C11—21no—
84C22×D4×C11—22no—
85C22×D4×C11—42no—
86C22×D4×C11C2311yescharacteristic
87C22×D4×C11C2314yes—
88C22×D4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C22×C22⋊D11—21no—
91C22×C22⋊D11—21no—
92C22×C22⋊D11—21no—
93C22×C22⋊D11—28no—
94C22×C22⋊D11—21no—
95C22×C22⋊D11—21no—
96C22×C22⋊D11—21no—
97C22×C22⋊D11—48no—
98C22×C22⋊D11D411yescharacteristic
99C23×Dic11—21no—
100C2×Q8×D11—22no—
101C2×Q8×D11—24no—
102C2×Q8×D11—42no—
103C2×Q8×D11C2314yescomplemented
104C2×D4×D11—24no—
105C2×D4×D11—22no—
106C2×D4×D11—42no—
107C2×D4×D11C2314yes—
108C2×#4339—22no—
109C2×#4339—24no—
110C2×#4339—42no—
111C2×#4339C2314yescomplemented
112C22×D44—21no—
113C22×D44C2311yescharacteristic
114C22×D44C2311yescharacteristic
115C22×C4×D11—21no—
116C22×C4×D11—21no—
117C22×C4×D11C2311yescharacteristic
118C22×Dic22—21no—
119C22×Dic22C2311yescharacteristic
120C2×C11×SD16—24no—
121C2×C11×SD16—42no—
122C2×C11×SD16C2314yes—
123C2×C11×SD16C2314yescomplemented
124C22×C8×C11C2311yescharacteristic
125C22×C8×C11C2311yescharacteristic
126C11×C22⋊Q8—22no—
127C11×C22⋊Q8C2314yescomplemented
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4C2311yescharacteristic
130C2×C11×C22⋊C4—21no—
131#67006—28no—
132C2×C22⋊Dic11—21no—
133C2×C22⋊Dic11—21no—
134C2×C22⋊Dic11D411yescharacteristic
135#67000—22no—
136#67000C2314yescomplemented
137C2×#4325—24no—
138C2×#4325C2314yescomplemented
139#66993—22no—
140#66993C2314yes—
141#66992—28no—
142#66991—22no—
143#66991C2314yes—
144#66990—28no—
145D4×Dic11—22no—
146D4×Dic11C2314yes—
147C2×#4324—24no—
148C2×#4324D418yescomplemented
149C2×#4324C2314yes—
150C2×#4324C2314yescomplemented
151#66985—232no—
152C2×#4323—24no—
153C2×#4323—24no—
154C2×#4323C2314yes—
155C2×#4323C2314yescomplemented
156#66983—22no—
157#66983C2314yes—
158C4×C22⋊D11D414yes—
159C4×C22⋊D11C2314yes—
160C2×(C2×D11)⋊C4—21no—
161C2×(C2×D11)⋊C4—21no—
162C2×(C2×D11)⋊C4—21no—
163C2×(C2×D11)⋊C4—21no—
164C2×(C2×D11)⋊C4D411yescharacteristic
165C2×C4⋊Dic11C2311yescharacteristic
166C2×Dic11⋊C4—21no—
167C2×Dic11⋊C4D411yescharacteristic
168C2×C4×Dic11—21no—
169C2×C4×Dic11C2311yescharacteristic
170C2×#4318—24no—
171C2×#4318C2314yescomplemented
172C22×C11⋊C8C2311yescharacteristic
173C22×C11⋊C8C2311yescharacteristic
174SD16×D11—232no—
175C2×D88—42no—
176C2×D88C2314yescomplemented
177C2×#4314—24no—
178C2×#4314C2314yescomplemented
179C2×C8×D11—24no—
180C2×C8×D11C2314yescomplemented
181#66949—28no—
182#66948—22no—
183#66948C2314yescomplemented
184#66946—28no—
185#66940—22no—
186#66940C2314yescomplemented
187#66938—28no—
188#66937—28no—
189C11×#102C2314yes—
190C11×#102C2314yescomplemented
191C11×C22⋊C8C2314yescomplemented
192#66899C2314yescomplemented
193#66885C2314yescomplemented
194(C2×D11)⋊C8C2314yescomplemented
195#66880C2314yescomplemented
196#66879C2314yescomplemented
197Dic11⋊C8C2314yescomplemented
198#66873C2314yescomplemented
199#66871C2314yescomplemented
200C2×#3265—111nomaximal, Sylow
201C24×C11—21no—
202C24×C11—21no—
203C24×C11—24no—
204C24×C11—44no—
205C24×C11—44no—
206C24×C11—82no—
207C24×C11C2×D411yescharacteristic
208C23×D11—21no—
209C23×D11—21no—
210C23×D11—24no—
211C23×D11—44no—
212C23×D11—44no—
213C23×D11—82no—
214C23×D11C2×D411yescharacteristic
215C2×Q8×C11—21no—
216C2×Q8×C11—22no—
217C2×Q8×C11—22no—
218C2×Q8×C11C2412yes—
219C2×D4×C11—28no—
220C2×D4×C11—21no—
221C2×D4×C11—22no—
222C2×D4×C11—24no—
223C2×D4×C11—21no—
224C2×D4×C11—22no—
225C2×D4×C11—22no—
226C2×D4×C11—44no—
227C2×D4×C11—48no—
228C2×D4×C11—44no—
229C2×D4×C11C2×D414yes—
230C2×D4×C11C2412yes—
231C2×D4×C11C2412yes—
232C22×C4×C11—22no—
233C22×C4×C11—22no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2×D412yes—
238C22×C4×C11C2412yes—
239C22×C4×C11C2411yescharacteristic
240C2×C22⋊D11—24no—
241C2×C22⋊D11—24no—
242C2×C22⋊D11—24no—
243C2×C22⋊D11—24no—
244C2×C22⋊D11—24no—
245C2×C22⋊D11—24no—
246C2×C22⋊D11—24no—
247C2×C22⋊D11—44no—
248C2×C22⋊D11—44no—
249C2×C22⋊D11—44no—
250C2×C22⋊D11—44no—
251C2×C22⋊D11—432no—
252C2×C22⋊D11—44no—
253C2×C22⋊D11—82no—
254C2×C22⋊D11C2×D414yes—
255C22×Dic11—24no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—44no—
259C22×Dic11C2×D411yescharacteristic
260C22×Dic11C2×D411yescharacteristic
261C22×Dic11C2×D411yescharacteristic
262Q8×D11—28no—
263Q8×D11—44no—
264Q8×D11—48no—
265D4×D11—28no—
266D4×D11—44no—
267D4×D11—48no—
268#4339—28no—
269#4339—44no—
270#4339—48no—
271C2×D44—24no—
272C2×D44—21no—
273C2×D44—21no—
274C2×D44—22no—
275C2×D44—22no—
276C2×D44—22no—
277C2×D44—22no—
278C2×D44—44no—
279C2×D44C2412yes—
280C2×D44C2412yes—
281C2×C4×D11—24no—
282C2×C4×D11—22no—
283C2×C4×D11—24no—
284C2×C4×D11—22no—
285C2×C4×D11—44no—
286C2×C4×D11—44no—
287C2×C4×D11C2×D412yes—
288C2×C4×D11C2412yes—
289C2×Dic22—24no—
290C2×Dic22—21no—
291C2×Dic22—22no—
292C2×Dic22—44no—
293C2×Dic22C2×D414yescomplemented
294C2×Dic22C2412yes—
295C11×SD16—28no—
296C11×SD16—44no—
297C2×C8×C11—22no—
298C2×C8×C11—22no—
299C2×C8×C11C2412yes—
300C2×C8×C11C2412yes—
301C11×C4⋊C4—21no—
302C11×C4⋊C4—24no—
303C11×C4⋊C4C2412yes—
304C11×C22⋊C4—24no—
305C22⋊Dic11—24no—
306C22⋊Dic11—24no—
307C22⋊Dic11C2×D414yes—
308#4325—28no—
309#4324—28no—
310#4324C2×D4116yescomplemented
311#4323—28no—
312#4323—28no—
313(C2×D11)⋊C4—24no—
314(C2×D11)⋊C4—24no—
315(C2×D11)⋊C4—24no—
316(C2×D11)⋊C4—24no—
317(C2×D11)⋊C4C2×D414yes—
318C4⋊Dic11—21no—
319C4⋊Dic11C2412yes—
320Dic11⋊C4—24no—
321Dic11⋊C4C2×D414yes—
322C4×Dic11—24no—
323C4×Dic11C2×D412yes—
324C4×Dic11C2412yes—
325#4318—28no—
326C2×C11⋊C8—22no—
327C2×C11⋊C8C2×D414yescomplemented
328C2×C11⋊C8C2412yes—
329C2×C11⋊C8C2412yes—
330D88—44no—
331#4314—28no—
332C8×D11—28no—
333C22×AGL(1,ℤ/8)—111no—
334C23×SD16—111no—
335C2×#548—111no—
336C2×D42—111no—
337#3265—1116no—
338C2×#496—111no—
339C2×#468—111no—
340C2×#466—111no—
341C2×#460—111no—
342C2×#463—111no—
343C2×#449—111no—
344C2×#448—111no—
345C2×#450D1111yescharacteristic, complemented
346C2×#447—111no—
347C2×#440—111no—
348C2×#435—111no—
349C23×C11—22no—
350C23×C11—24no—
351C23×C11—22no—
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—48no—
356C23×C11—48no—
357C23×C11—42no—
358C23×C11—42no—
359C23×C11—42no—
360C23×C11—42no—
361C23×C11—42no—
362C23×C11—84no—
363C23×C11—816no—
364C23×C11C22×D412yes—
365C23×C11C22×D411yescharacteristic
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—48no—
371C22×D11—42no—
372C22×D11—42no—
373C22×D11—42no—
374C22×D11—42no—
375C22×D11—42no—
376C22×D11—42no—
377C22×D11—48no—
378C22×D11—84no—
379C22×D11—816no—
380C22×D11AGL(1,ℤ/8)14yescomplemented
381C22×D11C22×D412yes—
382Q8×C11—22no—
383Q8×C11—22no—
384Q8×C11—42no—
385D4×C11—24no—
386D4×C11—22no—
387D4×C11—22no—
388D4×C11—22no—
389D4×C11—48no—
390D4×C11—42no—
391D4×C11C22×D414yes—
392C2×C4×C11—22no—
393C2×C4×C11—24no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—42no—
399C2×C4×C11—42no—
400C2×C4×C11C22×D412yes—
401C2×C4×C11C22×D411yescharacteristic
402C2×C4×C11C22×D412yes—
403C2×C4×C11H(5,𝔽2)12yes—
404C2×C4×C11C2511yescharacteristic
405C22⋊D11—28no—
406C22⋊D11—48no—
407C22⋊D11—48no—
408C22⋊D11—48no—
409C22⋊D11—48no—
410C22⋊D11—48no—
411C22⋊D11—84no—
412C2×Dic11—24no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—48no—
419C2×Dic11—42no—
420C2×Dic11C22×D412yes—
421C2×Dic11C22×D412yes—
422C2×Dic11C22×D412yes—
423D44—22no—
424D44—22no—
425D44—22no—
426D44—22no—
427D44—48no—
428D44—42no—
429D44—42no—
430C4×D11—24no—
431C4×D11—22no—
432C4×D11—22no—
433C4×D11—48no—
434C4×D11—48no—
435Dic22—24no—
436Dic22—22no—
437Dic22—48no—
438Dic22C22×D414yescomplemented
439C8×C11—22no—
440C8×C11—22no—
441C11⋊C8—22no—
442C11⋊C8C22×D414yescomplemented
443C22×#41—111no—
444C23×Q8—111no—
445C23×D4—111no—
446C23×D4—221no—
447C23×D4C2×D1111yescharacteristic
448C2×AGL(1,ℤ/8)—118no—
449C2×AGL(1,ℤ/8)—228no—
450C22×SD16—111no—
451C22×SD16—111no—
452C22×SD16—111no—
453C22×SD16—118no—
454C22×SD16—111no—
455C22×SD16—228no—
456C22×SD16C2×D1111yescharacteristic
457C22×SD16C2×D1111yescharacteristic, complemented
458C22×D8—111no—
459C22×D8—111no—
460C22×D8—111no—
461C22×M16—111no—
462C23×C8—111no—
463#548—118no—
464#548—224no—
465D42—118no—
466D42—224no—
467C2×#127—111no—
468C2×#124—111no—
469C2×#124—221no—
470C2×C22⋊Q8—221no—
471C2×C22⋊Q8C2×D1111yescharacteristic, complemented
472C2×#121—111no—
473C2×#121—111no—
474C2×#121—111no—
475C2×#121—221no—
476C2×#121—221no—
477C2×#120—221no—
478C2×#120—221no—
479C2×C4×Q8—111no—
480C2×C4×D4—111no—
481C2×C4×D4—111no—
482C2×C4×D4—221no—
483#496—118no—
484#468—118no—
485#466—118no—
486#463—118no—
487#460—118no—
488#450C2×D1118yescomplemented
489#449—118no—
490#448—118no—
491#447—118no—
492#440—118no—
493#435—118no—
494C2×#107—111no—
495C2×C4⋊C8—111no—
496C2×#103—111no—
497C2×#103—111no—
498C2×#102—111no—
499C2×#102—111no—
500C2×#102C2×D1111yescharacteristic
501C2×#102C2×D1111yescharacteristic, complemented
502C2×C22⋊C8—111no—
503C2×C22⋊C8C2×D1111yescharacteristic, complemented
504C2×#97—111no—
505C22×C11—22no—
506C22×C11—24no—
507C22×C11—22no—
508C22×C11—22no—
509C22×C11—48no—
510C22×C11—44no—
511C22×C11—42no—
512C22×C11—42no—
513C22×C11—42no—
514C22×C11—42no—
515C22×C11—42no—
516C22×C11—816no—
517C22×C11—84no—
518C22×C11D4212yes—
519C22×C11C2×AGL(1,ℤ/8)12yes—
520C22×C11#57712yes—
521C22×C11C23×D411yescharacteristic
522C2×D11—22no—
523C2×D11—28no—
524C2×D11—22no—
525C2×D11—42no—
526C2×D11—42no—
527C2×D11—42no—
528C2×D11—42no—
529C2×D11—42no—
530C2×D11—42no—
531C2×D11—816no—
532C2×D11—84no—
533C2×D11—84no—
534C2×D11C2×AGL(1,ℤ/8)14yescomplemented
535C4×C11—22no—
536C4×C11—42no—
537C4×C11—42no—
538C4×C11D4212yes—
539C4×C11C23×D411yescharacteristic
540C4×C11C2×H(5,𝔽2)11yescharacteristic
541Dic11—24no—
542Dic11—22no—
543Dic11—22no—
544Dic11—22no—
545Dic11—42no—
546C25—21no—
547C25—221no—
548C2×#41—114no—
549C2×#41—224no—
550C2×#41—222no—
551C2×#41—442no—
552C22×Q8—114no—
553C22×Q8—111no—
554C22×Q8—221no—
555C22×Q8—222no—
556C22×Q8—224no—
557C22×Q8—442no—
558C22×Q8C22×D1111yescharacteristic
559C22×D4—24no—
560C22×D4—21no—
561C22×D4—22no—
562C22×D4—42no—
563C22×D4—111no—
564C22×D4—114no—
565C22×D4—111no—
566C22×D4—111no—
567C22×D4—221no—
568C22×D4—222no—
569C22×D4—221no—
570C22×D4—221no—
571C22×D4—221no—
572C22×D4—228no—
573C22×D4—224no—
574C22×D4—221no—
575C22×D4—221no—
576C22×D4—221no—
577C22×D4—442no—
578C22×D4—448no—
579C22×D4C22×D1111yescharacteristic
580C22×D4C22×D1114yes—
581C22×D4C22×D1111yescharacteristic
582C23×C4—111no—
583C23×C4—221no—
584C23×C4—221no—
585C23×C4—221no—
586C23×C4C22×D1111yescharacteristic
587AGL(1,ℤ/8)—2232no—
588C2×SD16—24no—
589C2×SD16—42no—
590C2×SD16—118no—
591C2×SD16—114no—
592C2×SD16—114no—
593C2×SD16—114no—
594C2×SD16—114no—
595C2×SD16—224no—
596C2×SD16—224no—
597C2×SD16—2232no—
598C2×SD16—224no—
599C2×SD16C22×D1114yes—
600C2×SD16C22×D1114yescomplemented
601C2×D8—114no—
602C2×D8—114no—
603C2×D8—114no—
604C2×D8—224no—
605C2×D8—224no—
606C2×D8—442no—
607C2×M16—114no—
608C2×M16—224no—
609C22×C8—111no—
610C22×C8—111no—
611C22×C8—114no—
612C22×C8—224no—
613C22×C8C22×D1111yescharacteristic
614C22×C8C22×D1111yescharacteristic
615#127—114no—
616#127—222no—
617#124—114no—
618#124—222no—
619#124—228no—
620C22⋊Q8—22no—
621C22⋊Q8—228no—
622C22⋊Q8C22×D1114yescomplemented
623#121—114no—
624#121—114no—
625#121—114no—
626#121—228no—
627#121—222no—
628#121—228no—
629#121—222no—
630#121—222no—
631#120—228no—
632#120—228no—
633C4×Q8—114no—
634C4×Q8—222no—
635C4×D4—114no—
636C4×D4—114no—
637C4×D4—114no—
638C4×D4—222no—
639C4×D4—228no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—111no—
642C2×C4⋊C4—111no—
643C2×C4⋊C4—221no—
644C2×C4⋊C4C22×D1111yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—111no—
647C2×C22⋊C4—111no—
648C2×C22⋊C4—221no—
649C2×C22⋊C4—221no—
650C2×C22⋊C4—221no—
651C2×C22⋊C4—221no—
652C2×C22⋊C4—221no—
653C2×C22⋊C4—221no—
654C2×C42—111no—
655C2×C42—221no—
656#107—114no—
657C4⋊C8—114no—
658#103—114no—
659#103—114no—
660#102—114no—
661#102—114no—
662#102C22×D1114yes—
663#102C22×D1114yescomplemented
664C22⋊C8—114no—
665C22⋊C8C22×D1114yescomplemented
666#97—114no—
667C2×C11—44no—
668C2×C11—42no—
669C2×C11—82no—
670C2×C11#326514yescomplemented
671C2×C11C2×D4211yescharacteristic
672C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
673C2×C11C2×#57711yescharacteristic
674D11—24no—
675D11—82no—
676D11—82no—
677C24—21no—
678C24—21no—
679C24—24no—
680C24—44no—
681C24—44no—
682C24—82no—
683C24—111no—
684C24—224no—
685C24—221no—
686C24—221no—
687C24—444no—
688C24—444no—
689C24—882no—
690C24D4×D1111yescharacteristic
691#41—228no—
692#41—444no—
693#41—448no—
694C2×Q8—21no—
695C2×Q8—22no—
696C2×Q8—22no—
697C2×Q8—114no—
698C2×Q8—112no—
699C2×Q8—224no—
700C2×Q8—221no—
701C2×Q8—222no—
702C2×Q8—228no—
703C2×Q8—444no—
704C2×Q8—444no—
705C2×Q8—448no—
706C2×Q8C23×D1112yes—
707C2×D4—28no—
708C2×D4—21no—
709C2×D4—22no—
710C2×D4—24no—
711C2×D4—21no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—44no—
715C2×D4—48no—
716C2×D4—44no—
717C2×D4—114no—
718C2×D4—112no—
719C2×D4—112no—
720C2×D4—224no—
721C2×D4—224no—
722C2×D4—224no—
723C2×D4—224no—
724C2×D4—224no—
725C2×D4—228no—
726C2×D4—224no—
727C2×D4—224no—
728C2×D4—224no—
729C2×D4—222no—
730C2×D4—222no—
731C2×D4—221no—
732C2×D4—221no—
733C2×D4—222no—
734C2×D4—222no—
735C2×D4—444no—
736C2×D4—444no—
737C2×D4—448no—
738C2×D4—444no—
739C2×D4—444no—
740C2×D4—444no—
741C2×D4—4432no—
742C2×D4—444no—
743C2×D4—444no—
744C2×D4—882no—
745C2×D4D4×D1114yes—
746C2×D4C23×D1112yes—
747C2×D4C23×D1112yes—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—111no—
753C22×C4—111no—
754C22×C4—111no—
755C22×C4—112no—
756C22×C4—112no—
757C22×C4—224no—
758C22×C4—224no—
759C22×C4—221no—
760C22×C4—222no—
761C22×C4—222no—
762C22×C4—221no—
763C22×C4—224no—
764C22×C4—444no—
765C22×C4—444no—
766C22×C4—444no—
767C22×C4D4×D1112yes—
768C22×C4D4×D1111yescharacteristic
769C22×C4C23×D1112yes—
770C22×C4C23×D1111yescharacteristic
771SD16—28no—
772SD16—44no—
773SD16—1116no—
774SD16—228no—
775SD16—228no—
776SD16—228no—
777D8—228no—
778D8—228no—
779D8—444no—
780M16—228no—
781C2×C8—22no—
782C2×C8—22no—
783C2×C8—114no—
784C2×C8—112no—
785C2×C8—112no—
786C2×C8—228no—
787C2×C8—222no—
788C2×C8C23×D1112yes—
789C2×C8C23×D1112yes—
790C4⋊C4—24no—
791C4⋊C4—21no—
792C4⋊C4—114no—
793C4⋊C4—112no—
794C4⋊C4—224no—
795C4⋊C4—221no—
796C4⋊C4C23×D1112yes—
797C22⋊C4—24no—
798C22⋊C4—114no—
799C22⋊C4—114no—
800C22⋊C4—224no—
801C22⋊C4—224no—
802C22⋊C4—224no—
803C22⋊C4—224no—
804C22⋊C4—224no—
805C22⋊C4—224no—
806C42—112no—
807C42—112no—
808C42—224no—
809C11C2×#326511yescharacteristic, complemented, Sylow
810C23—22no—
811C23—22no—
812C23—22no—
813C23—24no—
814C23—22no—
815C23—22no—
816C23—48no—
817C23—48no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—84no—
824C23—816no—
825C23—114no—
826C23—112no—
827C23—222no—
828C23—222no—
829C23—222no—
830C23—222no—
831C23—448no—
832C23—448no—
833C23—442no—
834C23—442no—
835C23—442no—
836C23—442no—
837C23—442no—
838C23—442no—
839C23—884no—
840C23—8816no—
841C23C2×D4×D1112yes—
842C23C2×D4×D1111yescharacteristic
843Q8—22no—
844Q8—22no—
845Q8—42no—
846Q8—114no—
847Q8—224no—
848Q8—222no—
849Q8—448no—
850D4—24no—
851D4—22no—
852D4—22no—
853D4—22no—
854D4—48no—
855D4—42no—
856D4—228no—
857D4—222no—
858D4—222no—
859D4—222no—
860D4—222no—
861D4—448no—
862D4—448no—
863D4—448no—
864D4—448no—
865D4—448no—
866D4—448no—
867D4—442no—
868D4—442no—
869D4—884no—
870D4C2×D4×D1114yes—
871C2×C4—22no—
872C2×C4—24no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—112no—
880C2×C4—112no—
881C2×C4—112no—
882C2×C4—222no—
883C2×C4—222no—
884C2×C4—222no—
885C2×C4—224no—
886C2×C4—222no—
887C2×C4—224no—
888C2×C4—222no—
889C2×C4—222no—
890C2×C4—222no—
891C2×C4—448no—
892C2×C4—448no—
893C2×C4—448no—
894C2×C4—442no—
895C2×C4C2×D4×D1112yes—
896C2×C4C2×D4×D1111yescharacteristic
897C2×C4C2×D4×D1112yes—
898C2×C4#6703712yes—
899C2×C4C24×D1111yescharacteristic
900C8—22no—
901C8—22no—
902C8—114no—
903C8—222no—
904C22—22no—
905C22—24no—
906C22—22no—
907C22—22no—
908C22—44no—
909C22—48no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—816no—
916C22—84no—
917C22—114no—
918C22—228no—
919C22—222no—
920C22—222no—
921C22—442no—
922C22—442no—
923C22—442no—
924C22—442no—
925C22—442no—
926C22—442no—
927C22—8816no—
928C22—884no—
929C22—884no—
930C22#1062312112yes—
931C22#1062329312yes—
932C22D11×AGL(1,ℤ/8)12yes—
933C22C22×D4×D1111yescharacteristic
934C4—22no—
935C4—42no—
936C4—42no—
937C4—222no—
938C4—224no—
939C4—222no—
940C4—222no—
941C4—442no—
942C4#1062312112yes—
943C4C22×D4×D1111yescharacteristic
944C4C2×#6703711yescharacteristic
945C2—42no—
946C2—44no—
947C2—82no—
948C2—224no—
949C2—882no—
950C2—882no—
951C2#1308010914yesdirect product factor
952C2C2×#1062312111yescharacteristic
953C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
954C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#450C2
socleC23×C11C22×D4
hypercenterC2×#450D11
hypocenterC11C2×#3265
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. C22×#66985C2semidirect
2. C22×SD16×D11C2semidirect
3. C2×#10623164C2semidirect
4. C2×D4×C22⋊D11C2semidirect
5. #13080109C2direct (N × H)
6. C2×#10622789C2semidirect
7. C2×#10622662C2semidirect
8. C2×#10622388C2semidirect
9. C2×#10622375C2semidirect
10. C2×#10622778C2semidirect
11. C2×#10622347C2semidirect
12. C2×#10622783C2semidirect
13. C2×#10622386C2semidirect
14. C2×#10622370C2semidirect
15. C2×#10622341C2semidirect
16. C2×C11×#450C2semidirect
19. C22×Q8×D11C22semidirect
21. C22×#4339C22semidirect
23. C22×C11×SD16C22semidirect
24. C2×C11×C22⋊Q8C22semidirect
26. C2×#67000C22semidirect
27. C22×#4325C22semidirect
31. D4×C22⋊D11C22semidirect
36. C22×#4324C22semidirect
38. C2×#66985C22semidirect
40. C22×#4323C22semidirect
43. C22×#4318C22semidirect
45. C2×SD16×D11C22semidirect
46. C22×D88C22semidirect
47. C22×#4314C22semidirect
48. C22×C8×D11C22semidirect
50. #10623164C22semidirect
52. C2×#66948C22semidirect
54. C2×#66940C22semidirect
57. C11×#450C22semidirect
59. C2×C11×#102C22semidirect
60. C2×C11×C22⋊C8C22semidirect
61. C2×#66899C22semidirect
62. #10622789C22semidirect
63. #10622783C22semidirect
64. #10622778C22semidirect
65. C2×#66885C22semidirect
66. C2×(C2×D11)⋊C8C22semidirect
67. C2×#66880C22semidirect
68. C2×#66879C22semidirect
69. C2×Dic11⋊C8C22semidirect
70. #10622662C22semidirect
71. C2×#66873C22semidirect
72. C2×#66871C22semidirect
73. #10622388C22semidirect
74. #10622386C22semidirect
75. #10622375C22semidirect
76. #10622370C22semidirect
77. #10622347C22semidirect
78. #10622341C22semidirect
103. C2×Q8×D11C23semidirect
111. C2×#4339C23semidirect
123. C2×C11×SD16C23semidirect
127. C11×C22⋊Q8C23semidirect
136. #67000C23semidirect
138. C2×#4325C23semidirect
148. C2×#4324D4semidirect
150. C2×#4324C23semidirect
155. C2×#4323C23semidirect
171. C2×#4318C23semidirect
176. C2×D88C23semidirect
178. C2×#4314C23semidirect
180. C2×C8×D11C23semidirect
183. #66948C23semidirect
186. #66940C23semidirect
190. C11×#102C23semidirect
191. C11×C22⋊C8C23semidirect
192. #66899C23semidirect
193. #66885C23semidirect
194. (C2×D11)⋊C8C23semidirect
195. #66880C23semidirect
196. #66879C23semidirect
197. Dic11⋊C8C23semidirect
198. #66873C23semidirect
199. #66871C23semidirect
293. C2×Dic22C2×D4semidirect
310. #4324C2×D4semidirect
327. C2×C11⋊C8C2×D4semidirect
345. C2×#450D11semidirect
380. C22×D11AGL(1,ℤ/8)semidirect
438. Dic22C22×D4semidirect
442. C11⋊C8C22×D4semidirect
457. C22×SD16C2×D11semidirect
471. C2×C22⋊Q8C2×D11semidirect
488. #450C2×D11semidirect
501. C2×#102C2×D11semidirect
503. C2×C22⋊C8C2×D11semidirect
534. C2×D11C2×AGL(1,ℤ/8)semidirect
600. C2×SD16C22×D11semidirect
622. C22⋊Q8C22×D11semidirect
663. #102C22×D11semidirect
665. C22⋊C8C22×D11semidirect
670. C2×C11#3265semidirect
809. C11C2×#3265semidirect
951. C2#13080109direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669852
C22×SD16×D112
C2×#106231642
C2×D4×C22⋊D112
#130801092
C2×#106227892
C2×#106226622
C2×#106223882
C2×#106223752
C2×#106227782
C2×#106223472
C2×#106227832
C2×#106223862
C2×#106223702
C2×#106223412
C2×C11×#4502
C2×#326511