Finite Group Databasebeta

← #15624532

Subgroups — #15624532

Order 2816.

2342 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic
2C22×#66977C211yesmaximal, characteristic, complemented
3#13079448C214yesmaximal, complemented
4#13079440C212yesmaximal, complemented
5#13079423C212yesmaximal, complemented
6#13079399C214yesmaximal, complemented
7#13079391C212yesmaximal, complemented
8#13079374C212yesmaximal, complemented
9#13078565C212yesmaximal, complemented
10#13078541C212yesmaximal, complemented
11#13078246C214yesmaximal, complemented
12#13077878C212yesmaximal, complemented
13#13077853C212yesmaximal, complemented
14C2×C11×#407C211yesmaximal, characteristic, complemented
15C24×C4×C11C2211yescharacteristic
16C22×#4339C2211yescharacteristic
17C23×Dic22C2211yescharacteristic, complemented
18C22×C11×M16C2212yescomplemented
19C2×#67006—21no—
20C22×C22⋊Dic11—21no—
21#10623322—21no—
22#10623322—21no—
23#10623322—21no—
24#10623322—21no—
25#10623322C2212yes—
26#10623322C2212yes—
27#10623322C2212yes—
28#10623322C2212yes—
29C2×#66983C2211yescharacteristic
30C2×#66983C2211yescharacteristic
31C2×#66982—21no—
32C2×C4×C22⋊D11—21no—
33C2×C4×C22⋊D11—21no—
34C2×#66979C2211yescharacteristic
35C22×C4⋊Dic11C2211yescharacteristic, complemented
36C2×#66977—21no—
37C2×#66977—21no—
38C2×#66977—21no—
39C2×#66977—21no—
40C2×#66977—21no—
41C2×#66977—21no—
42C2×#66977C2211yescharacteristic
43C2×#66977C2211yescharacteristic
44C2×#66977C2212yes—
45C2×#66977C2212yes—
46C2×#66977C2212yes—
47C2×#66977C2212yescomplemented
48C2×#66977C2212yescomplemented
49C2×#66977C2212yescomplemented
50C22×Dic11⋊C4—21no—
51C2×#66962C2214yescomplemented
52C11×#407C2212yes—
53C11×#407C2212yes—
54C11×#407C2212yescomplemented
55C11×#407C2212yescomplemented
56C2×C11×C22⋊C8C2212yes—
57C2×C11×C22⋊C8C2212yescomplemented
58#10622750C2218yescomplemented
59#10622747C2218yescomplemented
60#10622746C2214yescomplemented
61#10622734C2214yescomplemented
62#10622733C2214yescomplemented
63#10622729C2218yescomplemented
64#10622727C2218yescomplemented
65#10622352C2214yescomplemented
66#10622352C2214yescomplemented
67#10622352C2214yescomplemented
68#10622351C2214yescomplemented
69#10622351C2214yescomplemented
70#10622349C2214yescomplemented
71#10622348C2214yescomplemented
72#10622346C2218yescomplemented
73#10622344C2214yescomplemented
74#10622336C2218yescomplemented
75#10622335C2214yescomplemented
76#10622335C2214yescomplemented
77#10622334C2214yescomplemented
78#10622334C2214yescomplemented
79C25×C11D411yescharacteristic
80C23×C4×C11—44no—
81C23×C4×C11D411yescharacteristic
82C23×C4×C11D411yescharacteristic
83C23×C4×C11D411yescharacteristic
84C23×C4×C11D411yescharacteristic
85C23×C4×C11D411yescharacteristic
86C23×C4×C11D411yescharacteristic
87C23×C4×C11D411yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C22×C22⋊D11—21no—
96C22×C22⋊D11—21no—
97C22×C22⋊D11—21no—
98C23×Dic11—21no—
99C23×Dic11—21no—
100C2×#4339—21no—
101C2×#4339—21no—
102C2×#4339—44no—
103C2×#4339C2312yes—
104C2×#4339C2312yes—
105C22×D44C2311yescharacteristic
106C22×C4×D11—21no—
107C22×Dic22—21no—
108C22×Dic22—21no—
109C22×Dic22—21no—
110C22×Dic22—44no—
111C22×Dic22C2312yes—
112C22×Dic22C2311yescharacteristic
113C22×Dic22C2312yes—
114C22×Dic22C2312yes—
115C2×C11×M16—44no—
116C2×C11×M16C2314yes—
117C2×C11×M16C2314yes—
118C22×C8×C11C2314yes—
119#67006—22no—
120#67006—22no—
121#67006—22no—
122#67006—22no—
123C2×C22⋊Dic11—22no—
124C2×C22⋊Dic11—22no—
125C2×C22⋊Dic11—22no—
126C2×C22⋊Dic11—22no—
127C2×C22⋊Dic11—22no—
128C2×C22⋊Dic11—22no—
129C2×C22⋊Dic11—21no—
130C2×C22⋊Dic11—21no—
131C2×C22⋊Dic11—21no—
132#66983—21no—
133#66983—21no—
134#66983—21no—
135#66983—21no—
136#66983C2312yes—
137#66983C2312yes—
138#66983C2312yes—
139#66983C2312yes—
140#66982—22no—
141#66982—22no—
142#66982—22no—
143#66982—22no—
144C4×C22⋊D11—22no—
145C4×C22⋊D11—22no—
146C4×C22⋊D11—22no—
147C4×C22⋊D11—22no—
148C4×C22⋊D11—22no—
149C4×C22⋊D11—22no—
150C4×C22⋊D11—22no—
151C4×C22⋊D11—22no—
152C2×(C2×D11)⋊C4—21no—
153C2×(C2×D11)⋊C4—21no—
154#66979—21no—
155#66979—21no—
156#66979C2312yes—
157#66979C2312yes—
158C2×C4⋊Dic11—21no—
159C2×C4⋊Dic11—21no—
160C2×C4⋊Dic11—21no—
161C2×C4⋊Dic11C2312yes—
162C2×C4⋊Dic11C2312yes—
163C2×C4⋊Dic11C2312yes—
164C2×C4⋊Dic11C2311yescharacteristic
165C2×C4⋊Dic11C2311yescharacteristic
166#66977—22no—
167#66977—22no—
168#66977—22no—
169#66977—22no—
170#66977—22no—
171#66977—22no—
172#66977—22no—
173#66977—22no—
174#66977—22no—
175#66977—22no—
176#66977—22no—
177#66977—22no—
178#66977—21no—
179#66977—21no—
180#66977—21no—
181#66977—21no—
182#66977C2314yes—
183#66977C2312yes—
184#66977C2314yes—
185#66977C2312yes—
186#66977C2314yes—
187#66977C2314yes—
188#66977C2312yes—
189#66977C2312yes—
190C2×Dic11⋊C4—22no—
191C2×Dic11⋊C4—22no—
192C2×Dic11⋊C4—22no—
193C2×Dic11⋊C4—22no—
194C2×Dic11⋊C4—22no—
195C2×Dic11⋊C4—22no—
196C2×Dic11⋊C4—21no—
197C2×Dic11⋊C4—21no—
198C2×C4×Dic11—21no—
199#66962—48no—
200C2×Dic44C2318yescomplemented
201C2×#4314C2318yescomplemented
202C11×C22⋊C8C2314yes—
203C11×C22⋊C8C2314yes—
204C11×C22⋊C8C2314yes—
205C11×C22⋊C8C2314yes—
206#66885C2318yescomplemented
207#66882C2318yescomplemented
208#66881C2318yescomplemented
209#66880C2318yescomplemented
210#66880C2318yescomplemented
211#66880C2318yescomplemented
212#60751—111nomaximal, Sylow
213C24×C11—24no—
214C24×C11—42no—
215C24×C11—42no—
216C24×C11C2×D411yescharacteristic
217C24×C11C2×D411yescharacteristic
218C24×C11C2×D411yescharacteristic
219C24×C11C2×D411yescharacteristic
220C24×C11C2×D411yescharacteristic
221C24×C11C2×D411yescharacteristic
222C24×C11C2×D411yescharacteristic
223C23×D11—21no—
224C22×C4×C11—24no—
225C22×C4×C11—24no—
226C22×C4×C11—24no—
227C22×C4×C11—42no—
228C22×C4×C11—42no—
229C22×C4×C11—42no—
230C22×C4×C11—42no—
231C22×C4×C11—42no—
232C22×C4×C11—42no—
233C22×C4×C11—42no—
234C22×C4×C11—42no—
235C22×C4×C11—42no—
236C22×C4×C11—42no—
237C22×C4×C11—42no—
238C22×C4×C11C2×D411yescharacteristic
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2×D411yescharacteristic
258C22×C4×C11C2×D411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C22×C4×C11C2411yescharacteristic
261C22×C4×C11C2411yescharacteristic
262C22×C4×C11C2411yescharacteristic
263C22×C4×C11C2411yescharacteristic
264C22×C4×C11C2411yescharacteristic
265C22×C4×C11C2411yescharacteristic
266C2×C22⋊D11—22no—
267C2×C22⋊D11—22no—
268C2×C22⋊D11—22no—
269C2×C22⋊D11—22no—
270C2×C22⋊D11—22no—
271C2×C22⋊D11—22no—
272C2×C22⋊D11—44no—
273C2×C22⋊D11—44no—
274C2×C22⋊D11—44no—
275C22×Dic11—21no—
276C22×Dic11—21no—
277C22×Dic11—22no—
278C22×Dic11—22no—
279C22×Dic11—22no—
280C22×Dic11—22no—
281C22×Dic11—22no—
282C22×Dic11—22no—
283C22×Dic11—21no—
284C22×Dic11—44no—
285C22×Dic11—44no—
286#4339—28no—
287#4339—44no—
288#4339—44no—
289#4339—44no—
290C2×D44—21no—
291C2×D44—42no—
292C2×D44C2412yes—
293C2×C4×D11—22no—
294C2×C4×D11—22no—
295C2×C4×D11—44no—
296C2×Dic22—22no—
297C2×Dic22—22no—
298C2×Dic22—22no—
299C2×Dic22—21no—
300C2×Dic22—28no—
301C2×Dic22—44no—
302C2×Dic22—44no—
303C2×Dic22—42no—
304C2×Dic22—44no—
305C2×Dic22—44no—
306C2×Dic22—44no—
307C2×Dic22C2414yes—
308C2×Dic22C2412yes—
309C11×M16—28no—
310C11×M16—44no—
311C2×C8×C11—44no—
312C2×C8×C11C2418yes—
313C22⋊Dic11—24no—
314C22⋊Dic11—24no—
315C22⋊Dic11—24no—
316C22⋊Dic11—24no—
317C22⋊Dic11—22no—
318C22⋊Dic11—22no—
319C22⋊Dic11—22no—
320C22⋊Dic11—22no—
321C22⋊Dic11—22no—
322C22⋊Dic11—22no—
323(C2×D11)⋊C4—22no—
324(C2×D11)⋊C4—22no—
325(C2×D11)⋊C4—22no—
326(C2×D11)⋊C4—22no—
327C4⋊Dic11—22no—
328C4⋊Dic11—22no—
329C4⋊Dic11—22no—
330C4⋊Dic11—21no—
331C4⋊Dic11—21no—
332C4⋊Dic11C2412yes—
333C4⋊Dic11C2412yes—
334C4⋊Dic11C2414yes—
335Dic11⋊C4—24no—
336Dic11⋊C4—24no—
337Dic11⋊C4—24no—
338Dic11⋊C4—24no—
339Dic11⋊C4—22no—
340Dic11⋊C4—22no—
341Dic11⋊C4—22no—
342Dic11⋊C4—22no—
343C4×Dic11—22no—
344C4×Dic11—22no—
345Dic44—48no—
346#4314—48no—
347C2×#525—111no—
348C22×C22⋊Q8—111no—
349#3196—114no—
350#3195—112no—
351#3193—112no—
352#3190—114no—
353#3189—112no—
354#3187—112no—
355#3095—112no—
356#3092—112no—
357#3056—114no—
358#3007—112no—
359#3004—112no—
360C2×#407D1111yescharacteristic, complemented
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—41no—
374C23×C11—41no—
375C23×C11—41no—
376C23×C11—41no—
377C23×C11—41no—
378C23×C11—41no—
379C23×C11—41no—
380C23×C11—41no—
381C23×C11—416no—
382C23×C11#13714yescomplemented
383C23×C11C22×D411yescharacteristic
384C23×C11C22×D411yescharacteristic
385C23×C11C22×D411yescharacteristic
386C23×C11C22×D411yescharacteristic
387C23×C11C22×D411yescharacteristic
388C23×C11C22×D411yescharacteristic
389C23×C11C22×D411yescharacteristic
390C22×D11—22no—
391C22×D11—42no—
392C22×D11—42no—
393C22×D11—42no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—41no—
410C2×C4×C11—41no—
411C2×C4×C11—41no—
412C2×C4×C11—41no—
413C2×C4×C11—41no—
414C2×C4×C11—41no—
415C2×C4×C11—41no—
416C2×C4×C11—41no—
417C2×C4×C11—41no—
418C2×C4×C11—41no—
419C2×C4×C11—41no—
420C2×C4×C11—41no—
421C2×C4×C11C22×D411yescharacteristic
422C2×C4×C11C22×D411yescharacteristic
423C2×C4×C11C22×D411yescharacteristic
424C2×C4×C11C22×D411yescharacteristic
425C2×C4×C11C22×D411yescharacteristic
426C2×C4×C11C22×D411yescharacteristic
427C2×C4×C11C22×D411yescharacteristic
428C2×C4×C11H(5,𝔽2)14yes—
429C2×C4×C11C2511yescharacteristic
430C22⋊D11—44no—
431C22⋊D11—44no—
432C22⋊D11—44no—
433C22⋊D11—44no—
434C22⋊D11—44no—
435C22⋊D11—44no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—24no—
439C2×Dic11—24no—
440C2×Dic11—22no—
441C2×Dic11—44no—
442C2×Dic11—44no—
443C2×Dic11—42no—
444C2×Dic11—44no—
445C2×Dic11—44no—
446C2×Dic11—42no—
447C2×Dic11—44no—
448C2×Dic11—42no—
449C2×Dic11—44no—
450D44—24no—
451D44—42no—
452C4×D11—44no—
453C4×D11—44no—
454Dic22—28no—
455Dic22—24no—
456Dic22—44no—
457Dic22—44no—
458Dic22—42no—
459Dic22—44no—
460C8×C11—28no—
461C22×#41—111no—
462C23×Q8—111no—
463C24×C4C2×D1111yescharacteristic
464C2×#137—114no—
465C22×M16C2×D1112yescomplemented
466#525—112no—
467#525—112no—
468#525—112no—
469#525—112no—
470#525—221no—
471#525—221no—
472#525—221no—
473#525—221no—
474C2×#123—221no—
475C2×C22⋊Q8—112no—
476C2×C22⋊Q8—112no—
477C2×C22⋊Q8—112no—
478C2×C22⋊Q8—111no—
479C2×C22⋊Q8—111no—
480C2×C22⋊Q8—112no—
481C2×C22⋊Q8—112no—
482C2×C22⋊Q8—112no—
483C2×C22⋊Q8—221no—
484C2×C22⋊Q8—221no—
485C2×C22⋊Q8—221no—
486C2×C22⋊Q8—221no—
487C2×C22⋊Q8—221no—
488C2×C22⋊Q8—221no—
489C2×#121—111no—
490C2×#121—111no—
491C2×#120—221no—
492C2×C4×D4—221no—
493C2×C4×D4—221no—
494C2×#117—111no—
495C22×C4⋊C4—111no—
496C22×C4⋊C4—221no—
497C22×C22⋊C4—221no—
498#485—118no—
499#484—114no—
500#484—114no—
501#483—114no—
502#483—114no—
503#481—114no—
504#480—114no—
505#470—118no—
506#468—118no—
507#467—118no—
508#465—118no—
509#452—118no—
510#451—114no—
511#451—114no—
512#451—114no—
513#450—114no—
514#448—114no—
515#448—114no—
516#428—114no—
517#419—114no—
518#417—114no—
519#407C2×D1112yes—
520#407C2×D1112yes—
521#407C2×D1112yescomplemented
522#407C2×D1112yescomplemented
523C2×C22⋊C8C2×D1112yes—
524C2×C22⋊C8C2×D1112yescomplemented
525C22×C11—28no—
526C22×C11—21no—
527C22×C11—21no—
528C22×C11—21no—
529C22×C11—21no—
530C22×C11—21no—
531C22×C11—21no—
532C22×C11—21no—
533C22×C11—21no—
534C22×C11—21no—
535C22×C11—21no—
536C22×C11—21no—
537C22×C11—21no—
538C22×C11—21no—
539C22×C11—21no—
540C22×C11—21no—
541C22×C11—21no—
542C22×C11—44no—
543C22×C11—44no—
544C22×C11—44no—
545C22×C11—44no—
546C22×C11—44no—
547C22×C11—44no—
548C22×C11#53412yes—
549C22×C11C2×#13712yes—
550C22×C11C2×#13712yes—
551C22×C11C2×#13712yes—
552C22×C11#57512yes—
553C22×C11C23×D411yescharacteristic
554C2×D11—42no—
555C2×D11—42no—
556C2×D11—42no—
557C2×D11—84no—
558C4×C11—21no—
559C4×C11—21no—
560C4×C11—21no—
561C4×C11—21no—
562C4×C11—21no—
563C4×C11—21no—
564C4×C11#53412yes—
565C4×C11C2×H(5,𝔽2)12yes—
566Dic11—44no—
567Dic11—42no—
568Dic11—42no—
569Dic11—44no—
570Dic11—42no—
571C25D4411yescharacteristic
572C2×#41—112no—
573C2×#41—112no—
574C2×#41—221no—
575C2×#41—221no—
576C2×#41—444no—
577C22×Q8—112no—
578C22×Q8—112no—
579C22×Q8—112no—
580C22×Q8—111no—
581C22×Q8—221no—
582C22×Q8—221no—
583C22×Q8—221no—
584C22×Q8—444no—
585C22×D4—111no—
586C22×D4—221no—
587C22×D4—221no—
588C22×D4—221no—
589C23×C4—44no—
590C23×C4—221no—
591C23×C4—221no—
592C23×C4—221no—
593C23×C4D4411yescharacteristic
594C23×C4D4411yescharacteristic
595C23×C4D4411yescharacteristic
596C23×C4D4411yescharacteristic
597C23×C4D4411yescharacteristic
598C23×C4D4411yescharacteristic
599C23×C4D4411yescharacteristic
600C23×C4C22×D1111yescharacteristic
601C23×C4C22×D1111yescharacteristic
602C23×C4C22×D1111yescharacteristic
603C23×C4C22×D1111yescharacteristic
604C23×C4C22×D1111yescharacteristic
605C23×C4C22×D1111yescharacteristic
606C23×C4C22×D1111yescharacteristic
607#137—448no—
608C2×Q16—118no—
609C2×SD16—118no—
610C2×M16—44no—
611C2×M16C22×D1114yes—
612C2×M16C22×D1114yes—
613C22×C8C22×D1114yes—
614#123—222no—
615#123—222no—
616#123—222no—
617#123—222no—
618C22⋊Q8—114no—
619C22⋊Q8—114no—
620C22⋊Q8—114no—
621C22⋊Q8—114no—
622C22⋊Q8—112no—
623C22⋊Q8—112no—
624C22⋊Q8—112no—
625C22⋊Q8—112no—
626C22⋊Q8—222no—
627C22⋊Q8—222no—
628C22⋊Q8—222no—
629C22⋊Q8—222no—
630C22⋊Q8—222no—
631C22⋊Q8—222no—
632C22⋊Q8—222no—
633C22⋊Q8—222no—
634C22⋊Q8—222no—
635C22⋊Q8—222no—
636C22⋊Q8—222no—
637C22⋊Q8—222no—
638C22⋊Q8—221no—
639C22⋊Q8—221no—
640C22⋊Q8—221no—
641C22⋊Q8—221no—
642#121—112no—
643#121—112no—
644#121—112no—
645#121—112no—
646#121—221no—
647#121—221no—
648#121—221no—
649#121—221no—
650#120—222no—
651#120—222no—
652#120—222no—
653#120—222no—
654C4×D4—222no—
655C4×D4—222no—
656C4×D4—222no—
657C4×D4—222no—
658C4×D4—222no—
659C4×D4—222no—
660C4×D4—222no—
661C4×D4—222no—
662#117—112no—
663#117—112no—
664#117—221no—
665#117—221no—
666C2×C4⋊C4—112no—
667C2×C4⋊C4—112no—
668C2×C4⋊C4—112no—
669C2×C4⋊C4—111no—
670C2×C4⋊C4—111no—
671C2×C4⋊C4—221no—
672C2×C4⋊C4—221no—
673C2×C4⋊C4—221no—
674C2×C4⋊C4—222no—
675C2×C4⋊C4—222no—
676C2×C4⋊C4—222no—
677C2×C4⋊C4—222no—
678C2×C4⋊C4—222no—
679C2×C4⋊C4—222no—
680C2×C4⋊C4—221no—
681C2×C4⋊C4—221no—
682C2×C22⋊C4—222no—
683C2×C22⋊C4—222no—
684C2×C22⋊C4—222no—
685C2×C22⋊C4—222no—
686C2×C22⋊C4—222no—
687C2×C22⋊C4—222no—
688C2×C22⋊C4—221no—
689C2×C22⋊C4—221no—
690C2×C22⋊C4—221no—
691C2×C22⋊C4—221no—
692C2×C22⋊C4—221no—
693C2×C42—221no—
694#107—118no—
695#106—118no—
696#103—118no—
697#103—118no—
698#103—118no—
699#102—118no—
700C22⋊C8C22×D1114yes—
701C22⋊C8C22×D1114yes—
702C22⋊C8C22×D1114yes—
703C22⋊C8C22×D1114yes—
704C2×C11—22no—
705C2×C11—22no—
706C2×C11—22no—
707C2×C11—22no—
708C2×C11—22no—
709C2×C11—41no—
710C2×C11—41no—
711C2×C11C2×#53411yescharacteristic
712C2×C11C22×#13711yescharacteristic
713C2×C11C2×#57511yescharacteristic
714D11—82no—
715C24—24no—
716C24—42no—
717C24—42no—
718C24—221no—
719C24C2×D4411yescharacteristic
720C24C2×D4411yescharacteristic
721C24C2×D4411yescharacteristic
722C24C2×D4411yescharacteristic
723C24C2×D4411yescharacteristic
724C24C2×D4411yescharacteristic
725C24C2×D4411yescharacteristic
726#41—228no—
727#41—444no—
728#41—444no—
729#41—444no—
730C2×Q8—114no—
731C2×Q8—112no—
732C2×Q8—222no—
733C2×Q8—222no—
734C2×Q8—222no—
735C2×Q8—221no—
736C2×Q8—228no—
737C2×Q8—444no—
738C2×Q8—444no—
739C2×Q8—442no—
740C2×Q8—444no—
741C2×Q8—444no—
742C2×Q8—444no—
743C2×D4—112no—
744C2×D4—222no—
745C2×D4—222no—
746C2×D4—222no—
747C2×D4—222no—
748C2×D4—222no—
749C2×D4—222no—
750C2×D4—221no—
751C2×D4—442no—
752C2×D4—444no—
753C2×D4—444no—
754C2×D4—444no—
755C22×C4—24no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—42no—
759C22×C4—42no—
760C22×C4—42no—
761C22×C4—42no—
762C22×C4—42no—
763C22×C4—42no—
764C22×C4—42no—
765C22×C4—42no—
766C22×C4—42no—
767C22×C4—42no—
768C22×C4—42no—
769C22×C4—221no—
770C22×C4—221no—
771C22×C4—222no—
772C22×C4—222no—
773C22×C4—222no—
774C22×C4—221no—
775C22×C4—222no—
776C22×C4—222no—
777C22×C4—222no—
778C22×C4—222no—
779C22×C4—222no—
780C22×C4—444no—
781C22×C4—444no—
782C22×C4—444no—
783C22×C4C2×D4411yescharacteristic
784C22×C4C2×D4411yescharacteristic
785C22×C4C2×D4411yescharacteristic
786C22×C4C2×D4411yescharacteristic
787C22×C4C2×D4411yescharacteristic
788C22×C4C2×D4411yescharacteristic
789C22×C4C2×D4411yescharacteristic
790C22×C4C2×D4411yescharacteristic
791C22×C4C2×D4411yescharacteristic
792C22×C4C2×D4411yescharacteristic
793C22×C4C2×D4411yescharacteristic
794C22×C4C2×D4411yescharacteristic
795C22×C4C2×D4411yescharacteristic
796C22×C4C2×D4411yescharacteristic
797C22×C4C2×D4411yescharacteristic
798C22×C4C2×D4411yescharacteristic
799C22×C4C2×D4411yescharacteristic
800C22×C4C2×D4411yescharacteristic
801C22×C4C2×D4411yescharacteristic
802C22×C4C2×D4411yescharacteristic
803C22×C4C2×D4411yescharacteristic
804C22×C4C23×D1111yescharacteristic
805C22×C4C23×D1111yescharacteristic
806C22×C4C23×D1111yescharacteristic
807C22×C4C23×D1111yescharacteristic
808C22×C4C23×D1111yescharacteristic
809C22×C4C23×D1111yescharacteristic
810C22×C4C23×D1111yescharacteristic
811Q16—448no—
812SD16—448no—
813M16—28no—
814M16—44no—
815C2×C8—44no—
816C2×C8C23×D1118yes—
817C4⋊C4—114no—
818C4⋊C4—112no—
819C4⋊C4—112no—
820C4⋊C4—222no—
821C4⋊C4—222no—
822C4⋊C4—222no—
823C4⋊C4—221no—
824C4⋊C4—221no—
825C4⋊C4—224no—
826C4⋊C4—224no—
827C4⋊C4—224no—
828C4⋊C4—224no—
829C4⋊C4—222no—
830C4⋊C4—222no—
831C4⋊C4—222no—
832C4⋊C4—222no—
833C22⋊C4—224no—
834C22⋊C4—224no—
835C22⋊C4—224no—
836C22⋊C4—224no—
837C22⋊C4—222no—
838C22⋊C4—222no—
839C22⋊C4—222no—
840C22⋊C4—222no—
841C22⋊C4—222no—
842C22⋊C4—222no—
843C22⋊C4—222no—
844C22⋊C4—222no—
845C22⋊C4—222no—
846C22⋊C4—222no—
847C42—222no—
848C42—222no—
849C11#6075111yescharacteristic, complemented, Sylow
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—416no—
871C23—222no—
872C23—442no—
873C23—442no—
874C23—442no—
875C23#6696214yescomplemented
876C23C22×D4411yescharacteristic
877C23C22×D4411yescharacteristic
878C23C22×D4411yescharacteristic
879C23C22×D4411yescharacteristic
880C23C22×D4411yescharacteristic
881C23C22×D4411yescharacteristic
882C23C22×D4411yescharacteristic
883Q8—228no—
884Q8—224no—
885Q8—444no—
886Q8—444no—
887Q8—442no—
888Q8—444no—
889D4—224no—
890D4—442no—
891D4—444no—
892D4—444no—
893D4—444no—
894D4—444no—
895D4—444no—
896D4—444no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—222no—
925C2×C4—222no—
926C2×C4—224no—
927C2×C4—222no—
928C2×C4—224no—
929C2×C4—444no—
930C2×C4—442no—
931C2×C4—444no—
932C2×C4—444no—
933C2×C4—444no—
934C2×C4—444no—
935C2×C4—442no—
936C2×C4—442no—
937C2×C4—444no—
938C2×C4—444no—
939C2×C4—444no—
940C2×C4C22×D4411yescharacteristic
941C2×C4C22×D4411yescharacteristic
942C2×C4C22×D4411yescharacteristic
943C2×C4C22×D4411yescharacteristic
944C2×C4C22×D4411yescharacteristic
945C2×C4C22×D4411yescharacteristic
946C2×C4C22×D4411yescharacteristic
947C2×C4#6703714yes—
948C2×C4C24×D1111yescharacteristic
949C8—28no—
950C22—28no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—442no—
974C22—442no—
975C22—442no—
976C22—884no—
977C22#1062302412yes—
978C22C2×#6696212yes—
979C22C2×#6696212yes—
980C22C2×#6696212yes—
981C22#1062327912yes—
982C22C23×D4411yescharacteristic
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—442no—
990C4—444no—
991C4—442no—
992C4—444no—
993C4—442no—
994C4#1062302412yes—
995C4C2×#6703712yes—
996C2—22no—
997C2—22no—
998C2—22no—
999C2—22no—
1000C2—22no—
1001C2—41no—
1002C2—41no—
1003C2—882no—
1004C2C2×#1062302411yescharacteristic
1005C2C22×#6696211yescharacteristic
1006C2C2×#1062327911yescharacteristic
subgroupG/H
centerC22C23×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#407C2
socleC22×C11C23×D4
prime radicalC2×#10623322C2
hypercenterC2×#407D11
hypocenterC11#60751
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C22×#66977C2semidirect
3. #13079448C2semidirect
4. #13079440C2semidirect
5. #13079423C2semidirect
6. #13079399C2semidirect
7. #13079391C2semidirect
8. #13079374C2semidirect
9. #13078565C2semidirect
10. #13078541C2semidirect
11. #13078246C2semidirect
12. #13077878C2semidirect
13. #13077853C2semidirect
14. C2×C11×#407C2semidirect
17. C23×Dic22C22semidirect
18. C22×C11×M16C22semidirect
35. C22×C4⋊Dic11C22semidirect
47. C2×#66977C22semidirect
48. C2×#66977C22semidirect
49. C2×#66977C22semidirect
51. C2×#66962C22semidirect
54. C11×#407C22semidirect
55. C11×#407C22semidirect
57. C2×C11×C22⋊C8C22semidirect
58. #10622750C22semidirect
59. #10622747C22semidirect
60. #10622746C22semidirect
61. #10622734C22semidirect
62. #10622733C22semidirect
63. #10622729C22semidirect
64. #10622727C22semidirect
65. #10622352C22semidirect
66. #10622352C22semidirect
67. #10622352C22semidirect
68. #10622351C22semidirect
69. #10622351C22semidirect
70. #10622349C22semidirect
71. #10622348C22semidirect
72. #10622346C22semidirect
73. #10622344C22semidirect
74. #10622336C22semidirect
75. #10622335C22semidirect
76. #10622335C22semidirect
77. #10622334C22semidirect
78. #10622334C22semidirect
200. C2×Dic44C23semidirect
201. C2×#4314C23semidirect
206. #66885C23semidirect
207. #66882C23semidirect
208. #66881C23semidirect
209. #66880C23semidirect
210. #66880C23semidirect
211. #66880C23semidirect
360. C2×#407D11semidirect
382. C23×C11#137semidirect
465. C22×M16C2×D11semidirect
521. #407C2×D11semidirect
522. #407C2×D11semidirect
524. C2×C22⋊C8C2×D11semidirect
849. C11#60751semidirect
875. C23#66962semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
C22×#669772
#130794482
#130794402
#130794232
#130793992
#130793912
#130793742
#130785652
#130785412
#130782462
#130778782
#130778532
C2×C11×#4072
#6075111