Finite Group Databasebeta

← C2×#13080631 #15630309

Subgroups — C2×#13080631 #15630309

Order 2816.

2578 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×D44C211yesmaximal, characteristic
2#13080631C2116yesmaximal, direct product factor
3C2×#10622680C211yesmaximal, characteristic, complemented
4C2×#10622616C211yesmaximal, characteristic, complemented
5C2×#10622580C211yesmaximal, characteristic, complemented
6C2×#10622679C211yesmaximal, characteristic, complemented
7C2×#10622662C211yesmaximal, characteristic, complemented
8C2×#10622661C211yesmaximal, characteristic, complemented
9C2×#10622640C211yesmaximal, characteristic, complemented
10C2×#10622659C211yesmaximal, characteristic, complemented
11C2×#10622659C211yesmaximal, characteristic, complemented
12C2×#10622639C211yesmaximal, characteristic, complemented
13C2×#10622624C211yesmaximal, characteristic, complemented
14C2×#10622614C211yesmaximal, characteristic, complemented
15C22×#66873C211yesmaximal, characteristic, complemented
16C2×C11×#552C211yesmaximal, characteristic, complemented
17C22×D4×D11—21no—
18C23×D44C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C11×#552—24no—
21C11×#552C2218yescomplemented
22C2×C11×#126—21no—
23C2×C11×#125—21no—
24C2×C11×#125C2211yescharacteristic, complemented
25C2×C11×#123—21no—
26C2×C11×C22⋊Q8C2211yescharacteristic, complemented
27C2×C11×C22⋊Q8C2211yescharacteristic, complemented
28C2×C4×Q8×C11C2211yescharacteristic, complemented
29C2×C4×D4×C11C2211yescharacteristic
30C2×C11×#117—21no—
31C2×C11×#117C2211yescharacteristic, complemented
32C22×C11×C4⋊C4C2211yescharacteristic, complemented
33C22×#4325C2211yescharacteristic
34C22×#4325C2211yescharacteristic, complemented
35C22×#4325C2211yescharacteristic, complemented
36C2×#66983C2211yescharacteristic
37C2×#66983C2211yescharacteristic
38C22×#4318C2211yescharacteristic, complemented
39C23×C11⋊C8C2211yescharacteristic, complemented
40D4×D44—24no—
41D4×D44C2218yes—
42C2×#66948—21no—
43C2×#66935—21no—
44C2×#66935—21no—
45C2×#66927C2211yescharacteristic
46C2×C4×D44C2211yescharacteristic
47C2×#66899C2211yescharacteristic, complemented
48C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
49C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
50#10622680C2218yescomplemented
51#10622679C2218yescomplemented
52#10622662C2218yescomplemented
53#10622661C2218yescomplemented
54#10622659C2218yescomplemented
55#10622659C2218yescomplemented
56#10622640C2218yescomplemented
57#10622639C2218yescomplemented
58#10622624C2218yescomplemented
59#10622616C2218yescomplemented
60#10622614C2218yescomplemented
61#10622580C2218yescomplemented
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66873C2211yescharacteristic
65C2×#66873C2218yescomplemented
66C2×#66873C2211yescharacteristic, complemented
67C2×#66873C2211yescharacteristic, complemented
68C2×#66873C2211yescharacteristic, complemented
69C2×#66873C2211yescharacteristic, complemented
70C2×#66873C2211yescharacteristic, complemented
71C2×#66873C2211yescharacteristic, complemented
72C2×#66872C2211yescharacteristic, complemented
73C2×#66871C2211yescharacteristic, complemented
74C2×#66871C2211yescharacteristic, complemented
75C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
76C2×#66867C2211yescharacteristic, complemented
77C24×D11—21no—
78C24×D11—21no—
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11D411yescharacteristic
81C23×C4×C11—21no—
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C2×D4×D11—28no—
87C2×D4×D11—48no—
88C22×D44—24no—
89C22×D44—24no—
90C22×D44—21no—
91C22×D44—21no—
92C22×D44—21no—
93C22×D44—22no—
94C22×D44—22no—
95C22×D44—21no—
96C22×D44—42no—
97C22×D44—42no—
98C22×D44C2311yescharacteristic
99C22×D44C2311yescharacteristic
100C22×D44C2314yes—
101C22×D44C2314yes—
102C22×D44C2311yescharacteristic
103C22×C4×D11—21no—
104C11×#126—28no—
105C11×#125—28no—
106C11×#125—22no—
107C11×#125C2314yescomplemented
108C11×#123—28no—
109C11×C22⋊Q8—22no—
110C11×C22⋊Q8—22no—
111C11×C22⋊Q8C2314yescomplemented
112C11×C22⋊Q8C2314yescomplemented
113C4×Q8×C11—22no—
114C4×Q8×C11C2314yescomplemented
115C4×D4×C11D414yes—
116C4×D4×C11C2314yes—
117C11×#117—22no—
118C11×#117—28no—
119C11×#117C2314yescomplemented
120C2×C11×C4⋊C4—21no—
121C2×C11×C4⋊C4—22no—
122C2×C11×C4⋊C4—21no—
123C2×C11×C4⋊C4—21no—
124C2×C11×C4⋊C4—21no—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4D411yescharacteristic
128C2×C11×C4⋊C4C2311yescharacteristic
129C2×C11×C4⋊C4C2311yescharacteristic
130C2×C11×C4⋊C4C2311yescharacteristic
131C2×C11×C4⋊C4C2314yescomplemented
132C2×C11×C22⋊C4—21no—
133C2×C11×C22⋊C4—21no—
134C2×C11×C22⋊C4—21no—
135C2×C11×C22⋊C4D411yescharacteristic
136C2×C11×C22⋊C4D411yescharacteristic
137C2×C42×C11—21no—
138C2×C42×C11—21no—
139C2×C42×C11C2311yescharacteristic
140C2×#4325—24no—
141C2×#4325—42no—
142C2×#4325—42no—
143C2×#4325C2314yes—
144C2×#4325C2314yescomplemented
145C2×#4325C2314yescomplemented
146#66983—22no—
147#66983—22no—
148#66983C2314yes—
149#66983C2314yes—
150C2×(C2×D11)⋊C4—21no—
151C2×(C2×D11)⋊C4—21no—
152C2×(C2×D11)⋊C4—21no—
153C2×C4⋊Dic11C2311yescharacteristic
154C2×#4318—42no—
155C2×#4318C2314yescomplemented
156C22×C11⋊C8—42no—
157C22×C11⋊C8C2311yescharacteristic
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C22×C11⋊C8C2311yescharacteristic
161C22×C11⋊C8C2314yescomplemented
162#66948—28no—
163#66935—28no—
164#66935—28no—
165#66927—22no—
166#66927C2314yes—
167C4×D44—22no—
168C4×D44C2314yes—
169#66899C2314yescomplemented
170C22⋊(C11⋊C8)C2314yescomplemented
171C22⋊(C11⋊C8)C2314yescomplemented
172#66873C2314yes—
173#66873C2314yes—
174#66873C2314yes—
175#66873C2314yescomplemented
176#66873C2314yescomplemented
177#66873C2314yescomplemented
178#66873C2314yescomplemented
179#66873C2314yescomplemented
180#66873C2314yescomplemented
181#66872C2314yescomplemented
182#66871C2314yescomplemented
183#66871C2314yescomplemented
184C4⋊(C11⋊C8)C2314yescomplemented
185#66867C2314yescomplemented
186C2×#3310—111nomaximal, Sylow
187C24×C11C2×D411yescharacteristic
188C24×C11C2×D411yescharacteristic
189C23×D11—21no—
190C23×D11—21no—
191C23×D11—21no—
192C23×D11—24no—
193C23×D11—24no—
194C23×D11—44no—
195C23×D11—44no—
196C23×D11—44no—
197C23×D11—44no—
198C23×D11—82no—
199C23×D11—82no—
200C2×Q8×C11—21no—
201C2×Q8×C11—22no—
202C2×Q8×C11—22no—
203C2×Q8×C11C2412yes—
204C2×D4×C11—24no—
205C2×D4×C11C2×D414yes—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—24no—
215C22×C4×C11—44no—
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D412yes—
220C22×C4×C11C2×D412yes—
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2412yes—
223C22×C4×C11C2412yes—
224C22×C4×C11C2411yescharacteristic
225C2×C22⋊D11—24no—
226C2×C22⋊D11—24no—
227C2×C22⋊D11—44no—
228C2×C22⋊D11—44no—
229C22×Dic11—21no—
230D4×D11—432no—
231C2×D44—28no—
232C2×D44—28no—
233C2×D44—21no—
234C2×D44—21no—
235C2×D44—21no—
236C2×D44—24no—
237C2×D44—24no—
238C2×D44—24no—
239C2×D44—24no—
240C2×D44—22no—
241C2×D44—22no—
242C2×D44—22no—
243C2×D44—22no—
244C2×D44—22no—
245C2×D44—44no—
246C2×D44—44no—
247C2×D44—44no—
248C2×D44—44no—
249C2×D44—48no—
250C2×D44—48no—
251C2×D44—44no—
252C2×D44—82no—
253C2×D44#4114yes—
254C2×D44C2412yes—
255C2×D44C2412yes—
256C2×D44C2412yes—
257C2×C4×D11—24no—
258C2×C4×D11—44no—
259C11×C4⋊C4—21no—
260C11×C4⋊C4—21no—
261C11×C4⋊C4—24no—
262C11×C4⋊C4—24no—
263C11×C4⋊C4—24no—
264C11×C4⋊C4—24no—
265C11×C4⋊C4—24no—
266C11×C4⋊C4—24no—
267C11×C4⋊C4—21no—
268C11×C4⋊C4C2×D414yes—
269C11×C4⋊C4C2412yes—
270C11×C4⋊C4C2412yes—
271C11×C4⋊C4C2412yes—
272C11×C22⋊C4—24no—
273C11×C22⋊C4—24no—
274C11×C22⋊C4—24no—
275C11×C22⋊C4C2×D414yes—
276C11×C22⋊C4C2×D414yes—
277C42×C11—24no—
278C42×C11—24no—
279C42×C11C2×D412yes—
280C42×C11C2412yes—
281#4325—28no—
282#4325—44no—
283#4325—44no—
284(C2×D11)⋊C4—24no—
285(C2×D11)⋊C4—24no—
286(C2×D11)⋊C4—24no—
287C4⋊Dic11—21no—
288C4⋊Dic11C2412yes—
289#4318—44no—
290C2×C11⋊C8—22no—
291C2×C11⋊C8—22no—
292C2×C11⋊C8—22no—
293C2×C11⋊C8—22no—
294C2×C11⋊C8—44no—
295C2×C11⋊C8C2412yes—
296C2×C11⋊C8C2412yes—
297C2×C11⋊C8C2412yes—
298C2×C11⋊C8C2412yes—
299C2×#552D1111yescharacteristic, complemented
300C2×D42—111no—
301#3310—1116no—
302C2×#490—111no—
303C2×#482—111no—
304C2×#480—111no—
305C2×#478—111no—
306C2×#468—111no—
307C2×#465—111no—
308C2×#460—111no—
309C2×#450—111no—
310C2×#450—111no—
311C2×#440—111no—
312C2×#435—111no—
313C2×#418—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—48no—
330C22×D11—42no—
331C22×D11—42no—
332C22×D11—48no—
333C22×D11—42no—
334C22×D11—42no—
335C22×D11—42no—
336C22×D11—42no—
337C22×D11—48no—
338C22×D11—42no—
339C22×D11—42no—
340C22×D11—84no—
341C22×D11—84no—
342C22×D11—816no—
343C22×D11—816no—
344Q8×C11—22no—
345Q8×C11—22no—
346Q8×C11—42no—
347D4×C11—28no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—24no—
353C2×C4×C11—24no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—42no—
363C2×C4×C11—48no—
364C2×C4×C11—42no—
365C2×C4×C11—42no—
366C2×C4×C11—42no—
367C2×C4×C11C22×D412yes—
368C2×C4×C11C22×D412yes—
369C2×C4×C11C22×D412yes—
370C2×C4×C11C22×D412yes—
371C2×C4×C11C22×D411yescharacteristic
372C2×C4×C11C2×#4112yes—
373C2×C4×C11H(5,𝔽2)12yes—
374C2×C4×C11C2511yescharacteristic
375C22⋊D11—48no—
376C22⋊D11—48no—
377C2×Dic11—22no—
378C2×Dic11—42no—
379D44—24no—
380D44—22no—
381D44—22no—
382D44—22no—
383D44—22no—
384D44—22no—
385D44—48no—
386D44—48no—
387D44—48no—
388D44—42no—
389D44—42no—
390D44—84no—
391D44C2×#4114yes—
392C4×D11—48no—
393C11⋊C8—22no—
394C11⋊C8—22no—
395C11⋊C8—22no—
396C11⋊C8—22no—
397C23×D4—111no—
398C23×D4—111no—
399C23×D4—221no—
400C22×SD16—111no—
401C22×SD16—111no—
402C22×SD16—111no—
403C22×M16—111no—
404C23×C8—111no—
405#552—24no—
406#552C2×D1118yescomplemented
407D42—118no—
408D42—224no—
409C2×#127—111no—
410C2×#126—21no—
411C2×#125—21no—
412C2×#125C2×D1111yescharacteristic, complemented
413C2×#123—21no—
414C2×C22⋊Q8C2×D1111yescharacteristic, complemented
415C2×C22⋊Q8C2×D1111yescharacteristic, complemented
416C2×#121—111no—
417C2×#121—111no—
418C2×#121—221no—
419C2×#120—221no—
420C2×#120—221no—
421C2×C4×Q8C2×D1111yescharacteristic, complemented
422C2×C4×D4—111no—
423C2×C4×D4C2×D1111yescharacteristic
424C2×#117—21no—
425C2×#117C2×D1111yescharacteristic, complemented
426C22×C4⋊C4C2×D1111yescharacteristic, complemented
427#490—118no—
428#482—118no—
429#480—118no—
430#478—118no—
431#468—118no—
432#465—118no—
433#460—118no—
434#450—118no—
435#450—118no—
436#440—118no—
437#435—118no—
438C2×#107—111no—
439C2×#107—111no—
440C2×#106—111no—
441C2×C4⋊C8—111no—
442#418—118no—
443C2×#103—111no—
444C2×#102—111no—
445C2×#102—111no—
446C2×#102—111no—
447C2×#102—111no—
448C2×#102—111no—
449C2×#102—111no—
450C2×#102—111no—
451C2×#102—111no—
452C2×#102—111no—
453C2×#102—118no—
454C2×C22⋊C8—111no—
455C2×C22⋊C8—111no—
456C2×#97—111no—
457C22×C11—22no—
458C22×C11—28no—
459C22×C11—22no—
460C22×C11—22no—
461C22×C11—22no—
462C22×C11—22no—
463C22×C11—44no—
464C22×C11#54612yes—
465C22×C11C2×AGL(1,ℤ/8)14yes—
466C22×C11C2×AGL(1,ℤ/8)12yes—
467C22×C11#57712yes—
468C22×C11C23×D411yescharacteristic
469C2×D11—24no—
470C2×D11—48no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—816no—
480C2×D11—816no—
481C2×D11—84no—
482C2×D11—84no—
483C4×C11—22no—
484C4×C11—22no—
485C4×C11—22no—
486C4×C11—22no—
487C4×C11—42no—
488C4×C11—42no—
489C4×C11—42no—
490C4×C11—42no—
491C4×C11#54612yes—
492C4×C11C22×#4111yescharacteristic
493C4×C11C2×H(5,𝔽2)11yescharacteristic
494Dic11—42no—
495C25—221no—
496C25—221no—
497C22×Q8C22×D1111yescharacteristic
498C22×D4—111no—
499C22×D4—111no—
500C22×D4—111no—
501C22×D4—114no—
502C22×D4—114no—
503C22×D4—224no—
504C22×D4—224no—
505C22×D4—221no—
506C22×D4—221no—
507C22×D4—228no—
508C22×D4—221no—
509C22×D4—221no—
510C22×D4—221no—
511C22×D4—222no—
512C22×D4—222no—
513C22×D4—221no—
514C22×D4—442no—
515C22×D4—442no—
516C22×D4—448no—
517C22×D4C22⋊D1111yescharacteristic
518C23×C4—21no—
519C23×C4—221no—
520C23×C4C22×D1111yescharacteristic
521C23×C4C22×D1111yescharacteristic
522C2×SD16—114no—
523C2×SD16—114no—
524C2×SD16—114no—
525C2×SD16—224no—
526C2×SD16—442no—
527C2×SD16—442no—
528C2×M16—114no—
529C2×M16—442no—
530C22×C8—111no—
531C22×C8—111no—
532C22×C8—111no—
533C22×C8—111no—
534C22×C8—114no—
535C22×C8—442no—
536#127—114no—
537#127—222no—
538#126—28no—
539#125—28no—
540#125—22no—
541#125C22×D1114yescomplemented
542#123—28no—
543C22⋊Q8—22no—
544C22⋊Q8—22no—
545C22⋊Q8C22×D1114yescomplemented
546C22⋊Q8C22×D1114yescomplemented
547#121—114no—
548#121—114no—
549#121—222no—
550#121—222no—
551#121—228no—
552#120—228no—
553#120—228no—
554C4×Q8—22no—
555C4×Q8C22×D1114yescomplemented
556C4×D4—114no—
557C4×D4—222no—
558C4×D4C22⋊D1114yes—
559C4×D4C22×D1114yes—
560#117—22no—
561#117—28no—
562#117C22×D1114yescomplemented
563C2×C4⋊C4—21no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—111no—
571C2×C4⋊C4C22⋊D1111yescharacteristic
572C2×C4⋊C4C22×D1111yescharacteristic
573C2×C4⋊C4C22×D1111yescharacteristic
574C2×C4⋊C4C22×D1111yescharacteristic
575C2×C4⋊C4C22×D1114yescomplemented
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—221no—
580C2×C22⋊C4—221no—
581C2×C22⋊C4—221no—
582C2×C22⋊C4C22⋊D1111yescharacteristic
583C2×C22⋊C4C22⋊D1111yescharacteristic
584C2×C42—21no—
585C2×C42—21no—
586C2×C42C22×D1111yescharacteristic
587#107—114no—
588#107—114no—
589#106—114no—
590C4⋊C8—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—
599#102—114no—
600#102—114no—
601C22⋊C8—114no—
602C22⋊C8—114no—
603#97—114no—
604C2×C11—24no—
605C2×C11—42no—
606C2×C11#331014yescomplemented
607C2×C11C2×#54611yescharacteristic
608C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
609C2×C11C2×#57711yescharacteristic
610D11—44no—
611D11—82no—
612D11—82no—
613C24—221no—
614C24—221no—
615C24—221no—
616C24—224no—
617C24—224no—
618C24—444no—
619C24—444no—
620C24—444no—
621C24—444no—
622C24—882no—
623C24—882no—
624C24C2×C22⋊D1111yescharacteristic
625C24C2×C22⋊D1111yescharacteristic
626C2×Q8—21no—
627C2×Q8—22no—
628C2×Q8—22no—
629C2×Q8C23×D1112yes—
630C2×D4—24no—
631C2×D4—114no—
632C2×D4—112no—
633C2×D4—112no—
634C2×D4—112no—
635C2×D4—228no—
636C2×D4—228no—
637C2×D4—224no—
638C2×D4—224no—
639C2×D4—222no—
640C2×D4—222no—
641C2×D4—222no—
642C2×D4—222no—
643C2×D4—222no—
644C2×D4—221no—
645C2×D4—224no—
646C2×D4—224no—
647C2×D4—224no—
648C2×D4—221no—
649C2×D4—221no—
650C2×D4—224no—
651C2×D4—444no—
652C2×D4—444no—
653C2×D4—448no—
654C2×D4—448no—
655C2×D4—444no—
656C2×D4—444no—
657C2×D4—444no—
658C2×D4—4432no—
659C2×D4—444no—
660C2×D4—444no—
661C2×D4—882no—
662C2×D4C2×C22⋊D1114yes—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—24no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—44no—
673C22×C4—221no—
674C22×C4—224no—
675C22×C4—444no—
676C22×C4C2×C22⋊D1112yes—
677C22×C4C2×C22⋊D1112yes—
678C22×C4C2×C22⋊D1111yescharacteristic
679C22×C4C2×C22⋊D1111yescharacteristic
680C22×C4C2×C22⋊D1111yescharacteristic
681C22×C4C2×C22⋊D1111yescharacteristic
682C22×C4C23×D1112yes—
683C22×C4C23×D1112yes—
684C22×C4C23×D1111yescharacteristic
685SD16—228no—
686SD16—444no—
687SD16—444no—
688M16—444no—
689C2×C8—112no—
690C2×C8—112no—
691C2×C8—112no—
692C2×C8—112no—
693C2×C8—222no—
694C2×C8—222no—
695C2×C8—222no—
696C2×C8—222no—
697C2×C8—444no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—24no—
701C4⋊C4—24no—
702C4⋊C4—24no—
703C4⋊C4—24no—
704C4⋊C4—24no—
705C4⋊C4—24no—
706C4⋊C4—21no—
707C4⋊C4—112no—
708C4⋊C4—221no—
709C4⋊C4C2×C22⋊D1114yes—
710C4⋊C4C23×D1112yes—
711C4⋊C4C23×D1112yes—
712C4⋊C4C23×D1112yes—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—224no—
717C22⋊C4—224no—
718C22⋊C4—224no—
719C22⋊C4C2×C22⋊D1114yes—
720C22⋊C4C2×C22⋊D1114yes—
721C42—24no—
722C42—24no—
723C42C2×C22⋊D1112yes—
724C42C23×D1112yes—
725C11C2×#331011yescharacteristic, complemented, Sylow
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—224no—
732C23—222no—
733C23—222no—
734C23—222no—
735C23—448no—
736C23—448no—
737C23—448no—
738C23—442no—
739C23—442no—
740C23—448no—
741C23—442no—
742C23—442no—
743C23—442no—
744C23—442no—
745C23—442no—
746C23—442no—
747C23—884no—
748C23—884no—
749C23—8816no—
750C23—8816no—
751C23#6700214yes—
752C23C22×C22⋊D1112yes—
753C23C22×C22⋊D1112yes—
754C23C22×C22⋊D1111yescharacteristic
755Q8—22no—
756Q8—22no—
757Q8—42no—
758D4—28no—
759D4—114no—
760D4—224no—
761D4—222no—
762D4—222no—
763D4—222no—
764D4—222no—
765D4—222no—
766D4—448no—
767D4—448no—
768D4—448no—
769D4—448no—
770D4—448no—
771D4—442no—
772D4—442no—
773D4—884no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—48no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—222no—
794C2×C4—448no—
795C2×C4—442no—
796C2×C4#41×D1112yes—
797C2×C4#6704212yes—
798C2×C4C22×C22⋊D1112yes—
799C2×C4C22×C22⋊D1112yes—
800C2×C4C22×C22⋊D1112yes—
801C2×C4C22×C22⋊D1112yes—
802C2×C4C22×C22⋊D1111yescharacteristic
803C2×C4C24×D1111yescharacteristic
804C8—222no—
805C8—222no—
806C8—222no—
807C8—222no—
808C22—28no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—44no—
815C22—224no—
816C22—448no—
817C22—442no—
818C22—442no—
819C22—442no—
820C22—442no—
821C22—442no—
822C22—442no—
823C22—442no—
824C22—442no—
825C22—8816no—
826C22—8816no—
827C22—884no—
828C22—884no—
829C22C2×#6700214yes—
830C22C2×#6700212yes—
831C22#1062336012yes—
832C22#1062336812yes—
833C22C23×C22⋊D1111yescharacteristic
834C4—22no—
835C4—22no—
836C4—22no—
837C4—22no—
838C4—42no—
839C4—42no—
840C4—42no—
841C4—42no—
842C4—442no—
843C4#1062336012yes—
844C4C2×#41×D1111yescharacteristic
845C4C2×#6704211yescharacteristic
846C2—24no—
847C2—42no—
848C2—444no—
849C2—882no—
850C2—882no—
851C2#1308063114yesdirect product factor
852C2C2×#1062336011yescharacteristic
853C2C22×#6700211yescharacteristic
854C2C2×#1062336811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#552C2
socleC23×C11C22×D4
prime radicalC2×D4×D44C2
hypercenterC2×#552D11
hypocenterC11C2×#3310
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #13080631C2direct (N × H)
3. C2×#10622680C2semidirect
4. C2×#10622616C2semidirect
5. C2×#10622580C2semidirect
6. C2×#10622679C2semidirect
7. C2×#10622662C2semidirect
8. C2×#10622661C2semidirect
9. C2×#10622640C2semidirect
10. C2×#10622659C2semidirect
11. C2×#10622659C2semidirect
12. C2×#10622639C2semidirect
13. C2×#10622624C2semidirect
14. C2×#10622614C2semidirect
15. C22×#66873C2semidirect
16. C2×C11×#552C2semidirect
21. C11×#552C22semidirect
24. C2×C11×#125C22semidirect
26. C2×C11×C22⋊Q8C22semidirect
27. C2×C11×C22⋊Q8C22semidirect
28. C2×C4×Q8×C11C22semidirect
31. C2×C11×#117C22semidirect
32. C22×C11×C4⋊C4C22semidirect
34. C22×#4325C22semidirect
35. C22×#4325C22semidirect
38. C22×#4318C22semidirect
39. C23×C11⋊C8C22semidirect
47. C2×#66899C22semidirect
48. C2×C22⋊(C11⋊C8)C22semidirect
49. C2×C22⋊(C11⋊C8)C22semidirect
50. #10622680C22semidirect
51. #10622679C22semidirect
52. #10622662C22semidirect
53. #10622661C22semidirect
54. #10622659C22semidirect
55. #10622659C22semidirect
56. #10622640C22semidirect
57. #10622639C22semidirect
58. #10622624C22semidirect
59. #10622616C22semidirect
60. #10622614C22semidirect
61. #10622580C22semidirect
65. C2×#66873C22semidirect
66. C2×#66873C22semidirect
67. C2×#66873C22semidirect
68. C2×#66873C22semidirect
69. C2×#66873C22semidirect
70. C2×#66873C22semidirect
71. C2×#66873C22semidirect
72. C2×#66872C22semidirect
73. C2×#66871C22semidirect
74. C2×#66871C22semidirect
75. C2×C4⋊(C11⋊C8)C22semidirect
76. C2×#66867C22semidirect
107. C11×#125C23semidirect
111. C11×C22⋊Q8C23semidirect
112. C11×C22⋊Q8C23semidirect
114. C4×Q8×C11C23semidirect
119. C11×#117C23semidirect
131. C2×C11×C4⋊C4C23semidirect
144. C2×#4325C23semidirect
145. C2×#4325C23semidirect
155. C2×#4318C23semidirect
161. C22×C11⋊C8C23semidirect
169. #66899C23semidirect
170. C22⋊(C11⋊C8)C23semidirect
171. C22⋊(C11⋊C8)C23semidirect
175. #66873C23semidirect
176. #66873C23semidirect
177. #66873C23semidirect
178. #66873C23semidirect
179. #66873C23semidirect
180. #66873C23semidirect
181. #66872C23semidirect
182. #66871C23semidirect
183. #66871C23semidirect
184. C4⋊(C11⋊C8)C23semidirect
185. #66867C23semidirect
299. C2×#552D11semidirect
406. #552C2×D11semidirect
412. C2×#125C2×D11semidirect
414. C2×C22⋊Q8C2×D11semidirect
415. C2×C22⋊Q8C2×D11semidirect
421. C2×C4×Q8C2×D11semidirect
425. C2×#117C2×D11semidirect
426. C22×C4⋊C4C2×D11semidirect
541. #125C22×D11semidirect
545. C22⋊Q8C22×D11semidirect
546. C22⋊Q8C22×D11semidirect
555. C4×Q8C22×D11semidirect
562. #117C22×D11semidirect
575. C2×C4⋊C4C22×D11semidirect
606. C2×C11#3310semidirect
725. C11C2×#3310semidirect
851. C2#13080631direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×D442
#130806312
C2×#106226802
C2×#106226162
C2×#106225802
C2×#106226792
C2×#106226622
C2×#106226612
C2×#106226402
C2×#106226592
C2×#106226392
C2×#106226242
C2×#106226142
C22×#668732
C2×C11×#5522
C2×#331011