Finite Group Databasebeta

← C2×#13078231 #15620915

Subgroups — C2×#13078231 #15620915

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×#66985C211yesmaximal, characteristic, complemented
2C23×#4318C211yesmaximal, characteristic, complemented
3C2×#10623322C211yesmaximal, characteristic, complemented
4#13078231C2116yesmaximal, direct product factor
5C2×#10622652C212yesmaximal, complemented
6C2×#10622655C212yesmaximal, complemented
7C2×#10622651C212yesmaximal, complemented
8C2×#10622654C212yesmaximal, complemented
9C2×#10622577C211yesmaximal, characteristic, complemented
10C2×#10622579C211yesmaximal, characteristic, complemented
11C2×#10622828C211yesmaximal, characteristic, complemented
12C22×C11×#121C211yesmaximal, characteristic, complemented
13C23×D4×C11—21no—
14C23×D4×C11C2211yescharacteristic
15C24×C4×C11C2211yescharacteristic
16C22×#4339C2211yescharacteristic
17C2×C11×#121—21no—
18C2×C11×#121—21no—
19C2×C11×#121—24no—
20C2×C11×#121C2212yes—
21C2×C11×#121C2212yes—
22C2×C11×#121C2218yescomplemented
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4—21no—
25C2×#67006—21no—
26C22×#4324C2212yescomplemented
27C2×#66985—28no—
28C2×#66985C2218yescomplemented
29C22×#4323C2212yescomplemented
30#10623322—24no—
31#10623322C2218yescomplemented
32C2×#66983C2211yescharacteristic, complemented
33C2×#66983C2211yescharacteristic, complemented
34C2×#66982—21no—
35C2×C4×C22⋊D11—21no—
36C2×C4×C22⋊D11—21no—
37C2×#66979C2211yescharacteristic
38C2×#66977C2211yescharacteristic, complemented
39C2×#66977C2211yescharacteristic, complemented
40C22×#4318—28no—
41C22×#4318C2211yescharacteristic
42C22×#4318C2211yescharacteristic
43C22×#4318C2212yescomplemented
44C22×#4318C2218yescomplemented
45C23×C11⋊C8C2212yescomplemented
46#10622828C2218yescomplemented
47C2×#66896C2212yescomplemented
48C2×#66896C2212yescomplemented
49#10622655C22116yescomplemented
50#10622654C22116yescomplemented
51#10622652C22116yescomplemented
52#10622651C22116yescomplemented
53C2×#66874C2212yescomplemented
54#10622579C2218yescomplemented
55C2×#66873C2212yescomplemented
56#10622577C2218yescomplemented
57C2×#66872C2212yescomplemented
58C2×#66871C2212yescomplemented
59C25×C11—21no—
60C25×C11D411yescharacteristic
61C22×D4×C11—22no—
62C22×D4×C11—22no—
63C22×D4×C11—28no—
64C22×D4×C11—24no—
65C22×D4×C11—21no—
66C22×D4×C11—22no—
67C22×D4×C11—24no—
68C22×D4×C11—48no—
69C22×D4×C11C2312yes—
70C22×D4×C11C2314yes—
71C23×C4×C11—24no—
72C23×C4×C11—24no—
73C23×C4×C11—21no—
74C23×C4×C11D411yescharacteristic
75C23×C4×C11D411yescharacteristic
76C23×C4×C11D411yescharacteristic
77C23×C4×C11D414yes—
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2314yes—
81C23×C4×C11C2311yescharacteristic
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C2×#4339—22no—
86C2×#4339—24no—
87C2×#4339—24no—
88C2×#4339C2314yes—
89C22×D44C2311yescharacteristic
90C22×C4×D11—21no—
91C22×Dic22C2311yescharacteristic
92C11×#121—24no—
93C11×#121—24no—
94C11×#121—28no—
95C11×#121—28no—
96C11×#121C2318yes—
97C11×#121C2318yes—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—22no—
100C2×C11×C4⋊C4C2312yes—
101C2×C11×C4⋊C4C2314yes—
102C2×C11×C22⋊C4—22no—
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—28no—
105#67006—28no—
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11—21no—
109C2×#4324—28no—
110C2×#4324C2318yescomplemented
111#66985—232no—
112C2×#4323—28no—
113C2×#4323C2318yescomplemented
114#66983—22no—
115#66983—22no—
116#66983C2314yescomplemented
117#66983C2314yescomplemented
118#66982—28no—
119C4×C22⋊D11—28no—
120C4×C22⋊D11—28no—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4—21no—
123#66979—22no—
124#66979C2314yes—
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127#66977—22no—
128#66977—22no—
129#66977C2314yescomplemented
130#66977C2314yescomplemented
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×C4×Dic11—21no—
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#66896C2318yescomplemented
146#66896C2318yescomplemented
147#66874C2318yescomplemented
148#66873C2318yescomplemented
149#66872C2318yescomplemented
150#66871C2318yescomplemented
151C2×#3055—111nomaximal, Sylow
152C24×C11—24no—
153C24×C11—24no—
154C24×C11—24no—
155C24×C11—22no—
156C24×C11—42no—
157C24×C11—44no—
158C24×C11—44no—
159C24×C11—44no—
160C24×C11C2×D411yescharacteristic
161C24×C11C2×D414yes—
162C24×C11C2×D411yescharacteristic
163C24×C11C2×D411yescharacteristic
164C23×D11—21no—
165C2×D4×C11—28no—
166C2×D4×C11—28no—
167C2×D4×C11—24no—
168C2×D4×C11—28no—
169C2×D4×C11—24no—
170C2×D4×C11—22no—
171C2×D4×C11—24no—
172C2×D4×C11—28no—
173C2×D4×C11—432no—
174C2×D4×C11—48no—
175C2×D4×C11—48no—
176C2×D4×C11—44no—
177C2×D4×C11—48no—
178C2×D4×C11C2414yes—
179C22×C4×C11—24no—
180C22×C4×C11—24no—
181C22×C4×C11—24no—
182C22×C4×C11—216no—
183C22×C4×C11—22no—
184C22×C4×C11—28no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—28no—
189C22×C4×C11—24no—
190C22×C4×C11—22no—
191C22×C4×C11—44no—
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D412yes—
195C22×C4×C11C2×D412yes—
196C22×C4×C11C2×D414yes—
197C22×C4×C11C2×D414yes—
198C22×C4×C11C2×D414yes—
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D412yes—
201C22×C4×C11C2×D414yes—
202C22×C4×C11#4114yes—
203C22×C4×C11C2412yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2411yescharacteristic
206C22×C4×C11C2412yes—
207C2×C22⋊D11—24no—
208C2×C22⋊D11—24no—
209C2×C22⋊D11—24no—
210C2×C22⋊D11—44no—
211C2×C22⋊D11—44no—
212C2×C22⋊D11—44no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216#4339—28no—
217#4339—28no—
218#4339—48no—
219C2×D44—21no—
220C2×D44—22no—
221C2×D44—22no—
222C2×D44C2412yes—
223C2×C4×D11—24no—
224C2×C4×D11—44no—
225C2×Dic22—22no—
226C2×Dic22—21no—
227C2×Dic22—22no—
228C2×Dic22C2412yes—
229C11×C4⋊C4—24no—
230C11×C4⋊C4—22no—
231C11×C4⋊C4C2414yes—
232C11×C22⋊C4—28no—
233C11×C22⋊C4—28no—
234C22⋊Dic11—24no—
235C22⋊Dic11—24no—
236C22⋊Dic11—24no—
237#4324—216no—
238#4323—216no—
239(C2×D11)⋊C4—24no—
240(C2×D11)⋊C4—24no—
241C4⋊Dic11—21no—
242C4⋊Dic11—21no—
243C4⋊Dic11C2412yes—
244C4⋊Dic11C2412yes—
245Dic11⋊C4—24no—
246Dic11⋊C4—24no—
247C4×Dic11—24no—
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×#525—111no—
259C22×#121D1111yescharacteristic, complemented
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—24no—
278C23×C11—44no—
279C23×C11—416no—
280C23×C11—48no—
281C23×C11—48no—
282C23×C11—48no—
283C23×C11—44no—
284C23×C11—44no—
285C23×C11—44no—
286C23×C11—816no—
287C23×C11#12114yes—
288C23×C11AGL(1,ℤ/8)14yescomplemented
289C23×C11C22×D412yes—
290C23×C11C22×D412yes—
291C23×C11C22×D412yes—
292C23×C11C22×D411yescharacteristic
293C22×D11—22no—
294C22×D11—42no—
295C22×D11—42no—
296C22×D11—42no—
297D4×C11—24no—
298D4×C11—24no—
299D4×C11—416no—
300D4×C11—416no—
301D4×C11—44no—
302D4×C11—48no—
303C2×C4×C11—28no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—24no—
307C2×C4×C11—24no—
308C2×C4×C11—28no—
309C2×C4×C11—28no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—24no—
315C2×C4×C11—48no—
316C2×C4×C11—44no—
317C2×C4×C11#12114yes—
318C2×C4×C11#12118yes—
319C2×C4×C11C22×D412yes—
320C2×C4×C11C22×D414yes—
321C2×C4×C11C22×D412yes—
322C2×C4×C11C22×D412yes—
323C2×C4×C11C22×D412yes—
324C2×C4×C11C22×D411yescharacteristic
325C2×C4×C11C2×#4112yes—
326C2×C4×C11C2×#4114yes—
327C2×C4×C11C2511yescharacteristic
328C22⋊D11—48no—
329C22⋊D11—48no—
330C22⋊D11—48no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337D44—22no—
338D44—22no—
339D44—42no—
340C4×D11—48no—
341Dic22—22no—
342Dic22—22no—
343Dic22—42no—
344C11⋊C8—24no—
345C11⋊C8C22×D418yescomplemented
346C22×#41—111no—
347C23×D4—21no—
348C23×D4C2×D1111yescharacteristic
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—118no—
361#525—224no—
362C2×#123—221no—
363C2×C22⋊Q8—111no—
364C2×C22⋊Q8—111no—
365C2×#121—21no—
366C2×#121—21no—
367C2×#121—24no—
368C2×#121—111no—
369C2×#121—111no—
370C2×#121C2×D1112yes—
371C2×#121C2×D1112yes—
372C2×#121C2×D1118yescomplemented
373C2×#120—221no—
374C2×C4×D4—221no—
375C2×C4×D4—221no—
376C2×#117—111no—
377C22×C4⋊C4C2×D1111yescharacteristic
378C22×C22⋊C4—21no—
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—44no—
404C22×C11—44no—
405C22×C11—44no—
406C22×C11—816no—
407C22×C11—88no—
408C22×C11C2×#12114yes—
409C22×C11C2×#12112yes—
410C22×C11C2×AGL(1,ℤ/8)12yes—
411C22×C11C2×AGL(1,ℤ/8)14yescomplemented
412C22×C11#57512yes—
413C22×C11C23×D411yescharacteristic
414C2×D11—42no—
415C2×D11—42no—
416C2×D11—42no—
417C2×D11—84no—
418C4×C11—22no—
419C4×C11—22no—
420C4×C11—44no—
421C4×C11C2×#12112yes—
422C4×C11C2×#12114yes—
423C4×C11C23×D411yescharacteristic
424C4×C11C22×#4111yescharacteristic
425Dic11—42no—
426Dic11—42no—
427Dic11—42no—
428C25—21no—
429C25C22⋊D1111yescharacteristic
430C2×#41—114no—
431C2×#41—222no—
432C2×#41—224no—
433C2×#41—224no—
434C22×Q8—111no—
435C22×D4—22no—
436C22×D4—22no—
437C22×D4—28no—
438C22×D4—24no—
439C22×D4—24no—
440C22×D4—22no—
441C22×D4—21no—
442C22×D4—48no—
443C22×D4—111no—
444C22×D4—221no—
445C22×D4—221no—
446C22×D4—221no—
447C22×D4C22×D1112yes—
448C22×D4C22×D1114yes—
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—228no—
478C22⋊Q8—114no—
479C22⋊Q8—114no—
480C22⋊Q8—222no—
481C22⋊Q8—222no—
482#121—24no—
483#121—24no—
484#121—28no—
485#121—28no—
486#121—114no—
487#121—114no—
488#121—222no—
489#121—222no—
490#121C22×D1118yes—
491#121C22×D1118yes—
492#120—228no—
493C4×D4—228no—
494C4×D4—228no—
495#117—114no—
496#117—222no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—111no—
500C2×C4⋊C4—111no—
501C2×C4⋊C4—221no—
502C2×C4⋊C4—221no—
503C2×C4⋊C4C22×D1112yes—
504C2×C4⋊C4C22×D1114yes—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—28no—
508C2×C22⋊C4—221no—
509C2×C22⋊C4—221no—
510C2×C22⋊C4—221no—
511C2×C22⋊C4—221no—
512C2×C22⋊C4—221no—
513C2×C42—221no—
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—84no—
524C2×C11#305514yescomplemented
525C2×C11C22×#12111yescharacteristic
526C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
527C2×C11C2×#57511yescharacteristic
528D11—82no—
529C24—24no—
530C24—24no—
531C24—24no—
532C24—22no—
533C24—42no—
534C24—44no—
535C24—44no—
536C24—44no—
537C24—221no—
538C24C2×C22⋊D1111yescharacteristic
539C24C2×C22⋊D1114yes—
540C24C2×C22⋊D1111yescharacteristic
541C24C2×C22⋊D1111yescharacteristic
542#41—228no—
543#41—228no—
544#41—448no—
545C2×Q8—112no—
546C2×Q8—221no—
547C2×Q8—222no—
548C2×Q8—222no—
549C2×D4—28no—
550C2×D4—28no—
551C2×D4—24no—
552C2×D4—28no—
553C2×D4—24no—
554C2×D4—28no—
555C2×D4—24no—
556C2×D4—22no—
557C2×D4—432no—
558C2×D4—48no—
559C2×D4—48no—
560C2×D4—44no—
561C2×D4—48no—
562C2×D4—112no—
563C2×D4—224no—
564C2×D4—224no—
565C2×D4—224no—
566C2×D4—222no—
567C2×D4—222no—
568C2×D4—221no—
569C2×D4—444no—
570C2×D4—444no—
571C2×D4—444no—
572C2×D4C23×D1114yes—
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—24no—
584C22×C4—22no—
585C22×C4—44no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—221no—
589C22×C4—224no—
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—22no—
618C4⋊C4—112no—
619C4⋊C4—112no—
620C4⋊C4—221no—
621C4⋊C4—221no—
622C4⋊C4—224no—
623C4⋊C4—224no—
624C4⋊C4C23×D1114yes—
625C22⋊C4—28no—
626C22⋊C4—28no—
627C22⋊C4—224no—
628C22⋊C4—224no—
629C22⋊C4—224no—
630C22⋊C4—224no—
631C22⋊C4—224no—
632C42—224no—
633C11C2×#305511yescharacteristic, complemented, Sylow
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—28no—
640C23—28no—
641C23—22no—
642C23—22no—
643C23—24no—
644C23—44no—
645C23—416no—
646C23—48no—
647C23—48no—
648C23—44no—
649C23—48no—
650C23—44no—
651C23—44no—
652C23—816no—
653C23—222no—
654C23—442no—
655C23—442no—
656C23—442no—
657C23#6698514yescomplemented
658C23#6699214yes—
659C23C22×C22⋊D1112yes—
660C23C22×C22⋊D1112yes—
661C23C22×C22⋊D1112yes—
662C23C22×C22⋊D1111yescharacteristic
663Q8—222no—
664Q8—222no—
665Q8—442no—
666D4—24no—
667D4—24no—
668D4—416no—
669D4—416no—
670D4—48no—
671D4—44no—
672D4—222no—
673D4—222no—
674D4—448no—
675D4—448no—
676D4—448no—
677D4—442no—
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—24no—
690C2×C4—48no—
691C2×C4—44no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—222no—
695C2×C4—442no—
696C2×C4—442no—
697C2×C4—442no—
698C2×C4—448no—
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—44no—
724C22—44no—
725C22—44no—
726C22—816no—
727C22—88no—
728C22—442no—
729C22—442no—
730C22—442no—
731C22—884no—
732C22C2×#6698512yes—
733C22C2×#6698514yescomplemented
734C22C2×#6699214yes—
735C22C2×#6699212yes—
736C22#1062335312yes—
737C22C23×C22⋊D1111yescharacteristic
738C4—22no—
739C4—22no—
740C4—44no—
741C4—442no—
742C4—442no—
743C4—442no—
744C4C2×#6699214yes—
745C4C2×#6699212yes—
746C4C22×D4×D1111yescharacteristic
747C4C22×#434111yescharacteristic
748C2—24no—
749C2—24no—
750C2—42no—
751C2—84no—
752C2—882no—
753C2#1307823114yesdirect product factor
754C2C22×#6699211yescharacteristic
755C2C22×#6698511yescharacteristic
756C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#121C2
socleC23×C11C22×D4
hypercenterC22×#121D11
hypocenterC11C2×#3055
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×#66985C2semidirect
2. C23×#4318C2semidirect
3. C2×#10623322C2semidirect
4. #13078231C2direct (N × H)
5. C2×#10622652C2semidirect
6. C2×#10622655C2semidirect
7. C2×#10622651C2semidirect
8. C2×#10622654C2semidirect
9. C2×#10622577C2semidirect
10. C2×#10622579C2semidirect
11. C2×#10622828C2semidirect
12. C22×C11×#121C2semidirect
22. C2×C11×#121C22semidirect
26. C22×#4324C22semidirect
28. C2×#66985C22semidirect
29. C22×#4323C22semidirect
31. #10623322C22semidirect
32. C2×#66983C22semidirect
33. C2×#66983C22semidirect
38. C2×#66977C22semidirect
39. C2×#66977C22semidirect
43. C22×#4318C22semidirect
44. C22×#4318C22semidirect
45. C23×C11⋊C8C22semidirect
46. #10622828C22semidirect
47. C2×#66896C22semidirect
48. C2×#66896C22semidirect
49. #10622655C22semidirect
50. #10622654C22semidirect
51. #10622652C22semidirect
52. #10622651C22semidirect
53. C2×#66874C22semidirect
54. #10622579C22semidirect
55. C2×#66873C22semidirect
56. #10622577C22semidirect
57. C2×#66872C22semidirect
58. C2×#66871C22semidirect
110. C2×#4324C23semidirect
113. C2×#4323C23semidirect
116. #66983C23semidirect
117. #66983C23semidirect
129. #66977C23semidirect
130. #66977C23semidirect
137. C2×#4318D4semidirect
140. C2×#4318C23semidirect
144. C22×C11⋊C8C23semidirect
145. #66896C23semidirect
146. #66896C23semidirect
147. #66874C23semidirect
148. #66873C23semidirect
149. #66872C23semidirect
150. #66871C23semidirect
250. #4318C2×D4semidirect
253. C2×C11⋊C8C2×D4semidirect
259. C22×#121D11semidirect
288. C23×C11AGL(1,ℤ/8)semidirect
345. C11⋊C8C22×D4semidirect
372. C2×#121C2×D11semidirect
411. C22×C11C2×AGL(1,ℤ/8)semidirect
524. C2×C11#3055semidirect
633. C11C2×#3055semidirect
657. C23#66985semidirect
733. C22C2×#66985semidirect
753. C2#13078231direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669852
C23×#43182
C2×#106233222
#130782312
C2×#106226522
C2×#106226552
C2×#106226512
C2×#106226542
C2×#106225772
C2×#106225792
C2×#106228282
C22×C11×#1212
C2×#305511