Finite Group Databasebeta

← C2×#13078237 #15620921

Subgroups — C2×#13078237 #15620921

Order 2816.

3242 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67002C211yesmaximal, characteristic, complemented
2C23×#4318C211yesmaximal, characteristic, complemented
3C22×#66983C211yesmaximal, characteristic, complemented
4#13078237C2116yesmaximal, direct product factor
5C2×#10622652C212yesmaximal, complemented
6C2×#10622662C212yesmaximal, complemented
7C2×#10622651C212yesmaximal, complemented
8C2×#10622661C212yesmaximal, complemented
9C2×#10622608C211yesmaximal, characteristic, complemented
10C2×#10622845C211yesmaximal, characteristic, complemented
11C2×#10622614C211yesmaximal, characteristic, complemented
12C2×C11×#525C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C23×C22⋊D11—21no—
16C23×D44C2211yescharacteristic
17C11×#525—24no—
18C11×#525C2218yescomplemented
19C2×C11×#123—21no—
20C2×C11×C22⋊Q8C2211yescharacteristic, complemented
21C2×C11×C22⋊Q8C2211yescharacteristic, complemented
22C2×C11×#121C2211yescharacteristic, complemented
23C2×C11×#121C2211yescharacteristic, complemented
24C2×C11×#120—21no—
25C2×C4×D4×C11—21no—
26C2×C4×D4×C11—21no—
27C2×C11×#117C2211yescharacteristic
28C2×#67002—28no—
29C2×#67002C2218yescomplemented
30C22×#4325C2212yescomplemented
31C22×#4323C2212yescomplemented
32C2×#66983—21no—
33C2×#66983—21no—
34C2×#66983—24no—
35C2×#66983C2212yes—
36C2×#66983C2212yes—
37C2×#66983C2218yescomplemented
38C22×(C2×D11)⋊C4—21no—
39C22×C4⋊Dic11C2211yescharacteristic
40C22×#4318—28no—
41C22×#4318C2211yescharacteristic
42C22×#4318C2211yescharacteristic
43C22×#4318C2212yescomplemented
44C22×#4318C2218yescomplemented
45C23×C11⋊C8C2212yescomplemented
46#10622845C2218yescomplemented
47C2×#66899C2212yescomplemented
48C2×#66896C2212yescomplemented
49#10622662C22116yescomplemented
50#10622661C22116yescomplemented
51#10622652C22116yescomplemented
52#10622651C22116yescomplemented
53#10622614C2218yescomplemented
54#10622608C2218yescomplemented
55C2×#66873C2212yescomplemented
56C2×#66873C2212yescomplemented
57C2×#66872C2212yescomplemented
58C2×#66871C2212yescomplemented
59C25×C11D411yescharacteristic
60C24×D11—21no—
61C2×C11×#41—22no—
62C2×C11×#41—24no—
63C2×C11×#41—24no—
64C2×C11×#41C2314yes—
65C22×Q8×C11C2311yescharacteristic
66C22×D4×C11—21no—
67C22×D4×C11—21no—
68C22×D4×C11—21no—
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11—24no—
71C23×C4×C11—24no—
72C23×C4×C11—21no—
73C23×C4×C11D411yescharacteristic
74C23×C4×C11D411yescharacteristic
75C23×C4×C11D411yescharacteristic
76C23×C4×C11D414yes—
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2314yes—
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—22no—
82C22×C22⋊D11—22no—
83C22×C22⋊D11—28no—
84C22×C22⋊D11—48no—
85C23×Dic11—21no—
86C22×D44—24no—
87C22×D44—24no—
88C22×D44—21no—
89C22×D44—22no—
90C22×D44C2312yes—
91C22×D44C2314yes—
92C11×#123—28no—
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8—22no—
95C11×C22⋊Q8C2314yescomplemented
96C11×C22⋊Q8C2314yescomplemented
97C11×#121—22no—
98C11×#121—22no—
99C11×#121C2314yescomplemented
100C11×#121C2314yescomplemented
101C11×#120—28no—
102C4×D4×C11—28no—
103C4×D4×C11—28no—
104C11×#117—22no—
105C11×#117C2314yes—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C42×C11—21no—
116#67002—232no—
117C2×#4325—28no—
118C2×#4325C2318yescomplemented
119C2×#4323—28no—
120C2×#4323C2318yescomplemented
121#66983—24no—
122#66983—24no—
123#66983—28no—
124#66983—28no—
125#66983C2318yes—
126#66983C2318yes—
127C2×(C2×D11)⋊C4—22no—
128C2×(C2×D11)⋊C4—22no—
129C2×(C2×D11)⋊C4—28no—
130C2×C4⋊Dic11—21no—
131C2×C4⋊Dic11—22no—
132C2×C4⋊Dic11C2312yes—
133C2×C4⋊Dic11C2314yes—
134C2×#4318—24no—
135C2×#4318—232no—
136C2×#4318—28no—
137C2×#4318D418yescomplemented
138C2×#4318C2314yes—
139C2×#4318C2314yes—
140C2×#4318C2318yescomplemented
141C22×C11⋊C8—28no—
142C22×C11⋊C8C2312yes—
143C22×C11⋊C8C2312yes—
144C22×C11⋊C8C2318yescomplemented
145#66899C2318yescomplemented
146#66896C2318yescomplemented
147#66873C2318yescomplemented
148#66873C2318yescomplemented
149#66872C2318yescomplemented
150#66871C2318yescomplemented
151C2×#3055—111nomaximal, Sylow
152C24×C11—24no—
153C24×C11—24no—
154C24×C11—21no—
155C24×C11—42no—
156C24×C11C2×D411yescharacteristic
157C24×C11C2×D414yes—
158C24×C11C2×D411yescharacteristic
159C24×C11C2×D411yescharacteristic
160C23×D11—24no—
161C23×D11—22no—
162C23×D11—44no—
163C23×D11—44no—
164C23×D11—44no—
165C11×#41—28no—
166C11×#41—28no—
167C11×#41—48no—
168C2×Q8×C11—21no—
169C2×Q8×C11—22no—
170C2×Q8×C11—22no—
171C2×Q8×C11C2412yes—
172C2×D4×C11—24no—
173C2×D4×C11—24no—
174C2×D4×C11—24no—
175C2×D4×C11—22no—
176C2×D4×C11—21no—
177C2×D4×C11—22no—
178C2×D4×C11—44no—
179C2×D4×C11—44no—
180C2×D4×C11—44no—
181C2×D4×C11C2412yes—
182C22×C4×C11—24no—
183C22×C4×C11—24no—
184C22×C4×C11—24no—
185C22×C4×C11—216no—
186C22×C4×C11—22no—
187C22×C4×C11—28no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—28no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—24no—
196C22×C4×C11—44no—
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D414yes—
200C22×C4×C11C2×D414yes—
201C22×C4×C11C2×D414yes—
202C22×C4×C11C2×D412yes—
203C22×C4×C11C2×D412yes—
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D412yes—
206C22×C4×C11C2×D414yes—
207C22×C4×C11#4114yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2411yescharacteristic
211C22×C4×C11C2412yes—
212C2×C22⋊D11—28no—
213C2×C22⋊D11—28no—
214C2×C22⋊D11—432no—
215C2×C22⋊D11—48no—
216C2×C22⋊D11—48no—
217C22×Dic11—24no—
218C22×Dic11—22no—
219C22×Dic11—44no—
220C2×D44—24no—
221C2×D44—22no—
222C2×D44—24no—
223C2×D44—28no—
224C2×D44—24no—
225C2×D44—28no—
226C2×D44—44no—
227C2×D44—48no—
228C2×D44C2414yes—
229C11×C4⋊C4—24no—
230C11×C4⋊C4—24no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—21no—
233C11×C4⋊C4C2412yes—
234C11×C4⋊C4C2412yes—
235C11×C22⋊C4—24no—
236C11×C22⋊C4—24no—
237C11×C22⋊C4—24no—
238C11×C22⋊C4—24no—
239C11×C22⋊C4—24no—
240C42×C11—24no—
241#4325—216no—
242#4323—216no—
243(C2×D11)⋊C4—28no—
244(C2×D11)⋊C4—28no—
245C4⋊Dic11—24no—
246C4⋊Dic11—22no—
247C4⋊Dic11C2414yes—
248#4318—216no—
249#4318—28no—
250#4318C2×D4116yescomplemented
251C2×C11⋊C8—216no—
252C2×C11⋊C8—24no—
253C2×C11⋊C8C2×D418yescomplemented
254C2×C11⋊C8C2414yes—
255C2×C11⋊C8C2414yes—
256C22×AGL(1,ℤ/8)—111no—
257C23×M16—111no—
258C2×#525D1111yescharacteristic, complemented
259C22×#121—111no—
260#3055—1116no—
261C2×#469—112no—
262C2×#468—112no—
263C2×#466—112no—
264C2×#465—112no—
265C2×#428—111no—
266C2×#417—111no—
267C2×#418—111no—
268C23×C11—22no—
269C23×C11—22no—
270C23×C11—22no—
271C23×C11—22no—
272C23×C11—28no—
273C23×C11—22no—
274C23×C11—22no—
275C23×C11—28no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—44no—
279C23×C11—416no—
280C23×C11—42no—
281C23×C11—42no—
282C23×C11—42no—
283C23×C11#12114yes—
284C23×C11AGL(1,ℤ/8)14yescomplemented
285C23×C11C22×D412yes—
286C23×C11C22×D412yes—
287C23×C11C22×D412yes—
288C23×C11C22×D411yescharacteristic
289C22×D11—24no—
290C22×D11—48no—
291C22×D11—48no—
292C22×D11—48no—
293C22×D11—44no—
294C22×D11—44no—
295C22×D11—44no—
296C22×D11—816no—
297Q8×C11—22no—
298Q8×C11—22no—
299Q8×C11—42no—
300D4×C11—22no—
301D4×C11—22no—
302D4×C11—48no—
303D4×C11—48no—
304D4×C11—48no—
305D4×C11—42no—
306C2×C4×C11—28no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—28no—
310C2×C4×C11—28no—
311C2×C4×C11—24no—
312C2×C4×C11—24no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—42no—
321C2×C4×C11—42no—
322C2×C4×C11—42no—
323C2×C4×C11—48no—
324C2×C4×C11#12114yes—
325C2×C4×C11#12118yes—
326C2×C4×C11C22×D412yes—
327C2×C4×C11C22×D414yes—
328C2×C4×C11C22×D412yes—
329C2×C4×C11C22×D412yes—
330C2×C4×C11C22×D412yes—
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11C2×#4112yes—
333C2×C4×C11C2×#4114yes—
334C2×C4×C11C2511yescharacteristic
335C22⋊D11—416no—
336C22⋊D11—416no—
337C2×Dic11—24no—
338C2×Dic11—48no—
339C2×Dic11—44no—
340D44—24no—
341D44—24no—
342D44—48no—
343D44—44no—
344C11⋊C8—24no—
345C11⋊C8C22×D418yescomplemented
346C22×#41C2×D1111yescharacteristic
347C23×D4—111no—
348C23×D4—221no—
349C24×C4C2×D1111yescharacteristic
350C2×AGL(1,ℤ/8)—118no—
351C2×AGL(1,ℤ/8)—228no—
352C22×SD16—112no—
353C22×D8—112no—
354C22×M16—111no—
355C22×M16—111no—
356C22×M16—112no—
357C22×M16—118no—
358C22×M16—228no—
359C23×C8—112no—
360#525—24no—
361#525C2×D1118yescomplemented
362C2×#123—21no—
363C2×C22⋊Q8C2×D1111yescharacteristic, complemented
364C2×C22⋊Q8C2×D1111yescharacteristic, complemented
365C2×#121—112no—
366C2×#121—112no—
367C2×#121—118no—
368C2×#121—221no—
369C2×#121—221no—
370C2×#121—224no—
371C2×#121C2×D1111yescharacteristic, complemented
372C2×#121C2×D1111yescharacteristic, complemented
373C2×#120—21no—
374C2×C4×D4—21no—
375C2×C4×D4—21no—
376C2×#117C2×D1111yescharacteristic
377C22×C4⋊C4—111no—
378C22×C22⋊C4—221no—
379#469—1116no—
380#468—1116no—
381#466—1116no—
382#465—1116no—
383#428—118no—
384C2×#107—112no—
385C2×#106—112no—
386#418—118no—
387#417—118no—
388C2×#103—112no—
389C2×#102—112no—
390C2×#102—112no—
391C2×#102—112no—
392C22×C11—22no—
393C22×C11—28no—
394C22×C11—28no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—22no—
400C22×C11—22no—
401C22×C11—416no—
402C22×C11—44no—
403C22×C11—42no—
404C22×C11—42no—
405C22×C11—42no—
406C22×C11—84no—
407C22×C11C2×#12114yes—
408C22×C11C2×#12112yes—
409C22×C11C2×AGL(1,ℤ/8)12yes—
410C22×C11C2×AGL(1,ℤ/8)14yescomplemented
411C22×C11#57512yes—
412C22×C11C23×D411yescharacteristic
413C2×D11—44no—
414C2×D11—44no—
415C2×D11—44no—
416C2×D11—816no—
417C2×D11—88no—
418C4×C11—22no—
419C4×C11—22no—
420C4×C11—42no—
421C4×C11—42no—
422C4×C11—42no—
423C4×C11C2×#12114yes—
424C4×C11C2×#12112yes—
425C4×C11C23×D411yescharacteristic
426C4×C11C22×#4111yescharacteristic
427Dic11—44no—
428C25—221no—
429C25C22⋊D1111yescharacteristic
430C2×#41—22no—
431C2×#41—24no—
432C2×#41—24no—
433C2×#41C22×D1114yes—
434C22×Q8C22×D1111yescharacteristic
435C22×D4—21no—
436C22×D4—21no—
437C22×D4—21no—
438C22×D4—112no—
439C22×D4—114no—
440C22×D4—228no—
441C22×D4—222no—
442C22×D4—222no—
443C22×D4—224no—
444C22×D4—224no—
445C22×D4—222no—
446C22×D4—221no—
447C22×D4—448no—
448C22×D4C22×D1111yescharacteristic
449C23×C4—24no—
450C23×C4—24no—
451C23×C4—21no—
452C23×C4—221no—
453C23×C4C22⋊D1111yescharacteristic
454C23×C4C22⋊D1111yescharacteristic
455C23×C4C22⋊D1111yescharacteristic
456C23×C4C22⋊D1114yes—
457C23×C4C22×D1111yescharacteristic
458C23×C4C22×D1111yescharacteristic
459C23×C4C22×D1114yes—
460C23×C4C22×D1111yescharacteristic
461AGL(1,ℤ/8)—2232no—
462C2×SD16—118no—
463C2×SD16—228no—
464C2×D8—118no—
465C2×D8—228no—
466C2×M16—118no—
467C2×M16—114no—
468C2×M16—114no—
469C2×M16—118no—
470C2×M16—228no—
471C2×M16—2232no—
472C2×M16—224no—
473C22×C8—112no—
474C22×C8—112no—
475C22×C8—118no—
476C22×C8—228no—
477#123—28no—
478C22⋊Q8—22no—
479C22⋊Q8—22no—
480C22⋊Q8C22×D1114yescomplemented
481C22⋊Q8C22×D1114yescomplemented
482#121—22no—
483#121—22no—
484#121—118no—
485#121—118no—
486#121—228no—
487#121—228no—
488#121—224no—
489#121—224no—
490#121C22×D1114yescomplemented
491#121C22×D1114yescomplemented
492#120—28no—
493C4×D4—28no—
494C4×D4—28no—
495#117—22no—
496#117C22×D1114yes—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—112no—
500C2×C4⋊C4—114no—
501C2×C4⋊C4—222no—
502C2×C4⋊C4—221no—
503C2×C4⋊C4C22×D1111yescharacteristic
504C2×C4⋊C4C22×D1111yescharacteristic
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—228no—
511C2×C22⋊C4—222no—
512C2×C22⋊C4—222no—
513C2×C42—21no—
514#107—118no—
515#106—118no—
516#103—118no—
517#102—118no—
518#102—118no—
519#102—118no—
520C2×C11—24no—
521C2×C11—24no—
522C2×C11—42no—
523C2×C11—82no—
524C2×C11#305514yescomplemented
525C2×C11C22×#12111yescharacteristic
526C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
527C2×C11C2×#57511yescharacteristic
528D11—84no—
529C24—24no—
530C24—24no—
531C24—21no—
532C24—42no—
533C24—224no—
534C24—222no—
535C24—444no—
536C24—444no—
537C24—444no—
538C24C2×C22⋊D1111yescharacteristic
539C24C2×C22⋊D1114yes—
540C24C2×C22⋊D1111yescharacteristic
541C24C2×C22⋊D1111yescharacteristic
542#41—28no—
543#41—28no—
544#41—48no—
545C2×Q8—21no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8C23×D1112yes—
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—21no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—114no—
559C2×D4—228no—
560C2×D4—228no—
561C2×D4—224no—
562C2×D4—228no—
563C2×D4—224no—
564C2×D4—228no—
565C2×D4—224no—
566C2×D4—222no—
567C2×D4—4432no—
568C2×D4—448no—
569C2×D4—448no—
570C2×D4—444no—
571C2×D4—448no—
572C2×D4C23×D1112yes—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—216no—
577C22×C4—22no—
578C22×C4—28no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—28no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—24no—
587C22×C4—44no—
588C22×C4—224no—
589C22×C4—222no—
590C22×C4—444no—
591C22×C4D4×D1114yes—
592C22×C4#434114yes—
593C22×C4C2×C22⋊D1114yes—
594C22×C4C2×C22⋊D1114yes—
595C22×C4C2×C22⋊D1114yes—
596C22×C4C2×C22⋊D1112yes—
597C22×C4C2×C22⋊D1112yes—
598C22×C4C2×C22⋊D1111yescharacteristic
599C22×C4C2×C22⋊D1111yescharacteristic
600C22×C4C2×C22⋊D1112yes—
601C22×C4C2×C22⋊D1111yescharacteristic
602C22×C4C23×D1112yes—
603C22×C4C23×D1112yes—
604C22×C4C23×D1112yes—
605C22×C4C23×D1111yescharacteristic
606SD16—2216no—
607D8—2216no—
608M16—1116no—
609M16—2216no—
610M16—228no—
611C2×C8—118no—
612C2×C8—114no—
613C2×C8—114no—
614C2×C8—2216no—
615C2×C8—224no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—114no—
621C4⋊C4—224no—
622C4⋊C4—222no—
623C4⋊C4C23×D1112yes—
624C4⋊C4C23×D1112yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—228no—
631C22⋊C4—228no—
632C42—24no—
633C11C2×#305511yescharacteristic, complemented, Sylow
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—28no—
639C23—22no—
640C23—22no—
641C23—28no—
642C23—22no—
643C23—22no—
644C23—44no—
645C23—416no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—224no—
650C23—448no—
651C23—448no—
652C23—448no—
653C23—444no—
654C23—444no—
655C23—444no—
656C23—8816no—
657C23#6699214yes—
658C23#6700214yescomplemented
659C23C22×C22⋊D1112yes—
660C23C22×C22⋊D1112yes—
661C23C22×C22⋊D1112yes—
662C23C22×C22⋊D1111yescharacteristic
663Q8—22no—
664Q8—22no—
665Q8—42no—
666D4—22no—
667D4—22no—
668D4—48no—
669D4—48no—
670D4—48no—
671D4—42no—
672D4—224no—
673D4—224no—
674D4—4416no—
675D4—4416no—
676D4—448no—
677D4—444no—
678C2×C4—28no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—28no—
682C2×C4—28no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—48no—
696C2×C4—224no—
697C2×C4—448no—
698C2×C4—444no—
699C2×C4#6699214yes—
700C2×C4#6699218yes—
701C2×C4C2×D4×D1112yes—
702C2×C4C2×D4×D1114yes—
703C2×C4C2×#434112yes—
704C2×C4C2×#434114yes—
705C2×C4C22×C22⋊D1112yes—
706C2×C4C22×C22⋊D1112yes—
707C2×C4C22×C22⋊D1112yes—
708C2×C4C22×C22⋊D1111yescharacteristic
709C2×C4C24×D1111yescharacteristic
710C8—118no—
711C8—224no—
712C22—22no—
713C22—28no—
714C22—28no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—416no—
722C22—44no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—84no—
727C22—444no—
728C22—444no—
729C22—444no—
730C22—8816no—
731C22—888no—
732C22C2×#6699214yes—
733C22C2×#6699212yes—
734C22C2×#6700212yes—
735C22C2×#6700214yescomplemented
736C22#1062335312yes—
737C22C23×C22⋊D1111yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—444no—
744C4C2×#6699214yes—
745C4C2×#6699212yes—
746C4C22×D4×D1111yescharacteristic
747C4C22×#434111yescharacteristic
748C2—24no—
749C2—24no—
750C2—42no—
751C2—82no—
752C2—884no—
753C2#1307823714yesdirect product factor
754C2C22×#6699211yescharacteristic
755C2C22×#6700211yescharacteristic
756C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#525C2
socleC23×C11C22×D4
hypercenterC2×#525D11
hypocenterC11C2×#3055
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C22×#67002C2semidirect
2. C23×#4318C2semidirect
3. C22×#66983C2semidirect
4. #13078237C2direct (N × H)
5. C2×#10622652C2semidirect
6. C2×#10622662C2semidirect
7. C2×#10622651C2semidirect
8. C2×#10622661C2semidirect
9. C2×#10622608C2semidirect
10. C2×#10622845C2semidirect
11. C2×#10622614C2semidirect
12. C2×C11×#525C2semidirect
18. C11×#525C22semidirect
20. C2×C11×C22⋊Q8C22semidirect
21. C2×C11×C22⋊Q8C22semidirect
22. C2×C11×#121C22semidirect
23. C2×C11×#121C22semidirect
29. C2×#67002C22semidirect
30. C22×#4325C22semidirect
31. C22×#4323C22semidirect
37. C2×#66983C22semidirect
43. C22×#4318C22semidirect
44. C22×#4318C22semidirect
45. C23×C11⋊C8C22semidirect
46. #10622845C22semidirect
47. C2×#66899C22semidirect
48. C2×#66896C22semidirect
49. #10622662C22semidirect
50. #10622661C22semidirect
51. #10622652C22semidirect
52. #10622651C22semidirect
53. #10622614C22semidirect
54. #10622608C22semidirect
55. C2×#66873C22semidirect
56. C2×#66873C22semidirect
57. C2×#66872C22semidirect
58. C2×#66871C22semidirect
95. C11×C22⋊Q8C23semidirect
96. C11×C22⋊Q8C23semidirect
99. C11×#121C23semidirect
100. C11×#121C23semidirect
118. C2×#4325C23semidirect
120. C2×#4323C23semidirect
137. C2×#4318D4semidirect
140. C2×#4318C23semidirect
144. C22×C11⋊C8C23semidirect
145. #66899C23semidirect
146. #66896C23semidirect
147. #66873C23semidirect
148. #66873C23semidirect
149. #66872C23semidirect
150. #66871C23semidirect
250. #4318C2×D4semidirect
253. C2×C11⋊C8C2×D4semidirect
258. C2×#525D11semidirect
284. C23×C11AGL(1,ℤ/8)semidirect
345. C11⋊C8C22×D4semidirect
361. #525C2×D11semidirect
363. C2×C22⋊Q8C2×D11semidirect
364. C2×C22⋊Q8C2×D11semidirect
371. C2×#121C2×D11semidirect
372. C2×#121C2×D11semidirect
410. C22×C11C2×AGL(1,ℤ/8)semidirect
480. C22⋊Q8C22×D11semidirect
481. C22⋊Q8C22×D11semidirect
490. #121C22×D11semidirect
491. #121C22×D11semidirect
524. C2×C11#3055semidirect
633. C11C2×#3055semidirect
658. C23#67002semidirect
735. C22C2×#67002semidirect
753. C2#13078237direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670022
C23×#43182
C22×#669832
#130782372
C2×#106226522
C2×#106226622
C2×#106226512
C2×#106226612
C2×#106226082
C2×#106228452
C2×#106226142
C2×C11×#5252
C2×#305511