Finite Group Databasebeta

← #15624516

Subgroups — #15624516

Order 2816.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic, complemented
2#13079430C214yesmaximal, complemented
3#13079422C212yesmaximal, complemented
4#13079413C212yesmaximal, complemented
5#13079381C214yesmaximal, complemented
6#13079373C212yesmaximal, complemented
7#13079364C212yesmaximal, complemented
8#13078552C212yesmaximal, complemented
9#13078539C212yesmaximal, complemented
10#13078231C214yesmaximal, complemented
11#13077866C212yesmaximal, complemented
12#13077843C212yesmaximal, complemented
13C2×#10622820C211yesmaximal, characteristic, complemented
14C22×C11×#121C211yesmaximal, characteristic, complemented
15C23×D4×C11—21no—
16C23×D4×C11C2211yescharacteristic, complemented
17C24×C4×C11C2211yescharacteristic
18C22×#4339C2211yescharacteristic, complemented
19C2×C11×#121—21no—
20C2×C11×#121—21no—
21C2×C11×#121—21no—
22C2×C11×#121—21no—
23C2×C11×#121—21no—
24C2×C11×#121—21no—
25C2×C11×#121C2212yes—
26C2×C11×#121C2212yes—
27C2×C11×#121C2212yes—
28C2×C11×#121C2212yescomplemented
29C2×C11×#121C2212yescomplemented
30C2×C11×#121C2212yescomplemented
31C22×C11×C4⋊C4C2211yescharacteristic, complemented
32C22×C11×C22⋊C4—21no—
33C2×#67006—21no—
34C2×#66985C2214yescomplemented
35#10623322—21no—
36#10623322—21no—
37#10623322—21no—
38#10623322—21no—
39#10623322C2212yes—
40#10623322C2212yescomplemented
41#10623322C2212yescomplemented
42#10623322C2212yescomplemented
43C2×#66983C2211yescharacteristic, complemented
44C2×#66983C2211yescharacteristic, complemented
45C2×#66982—21no—
46C2×C4×C22⋊D11—21no—
47C2×C4×C22⋊D11—21no—
48C2×#66979C2211yescharacteristic, complemented
49C2×#66977C2211yescharacteristic, complemented
50C2×#66977C2211yescharacteristic, complemented
51C22×#4318C2212yescomplemented
52#10622831C2214yescomplemented
53#10622831C2214yescomplemented
54#10622830C2214yescomplemented
55#10622830C2214yescomplemented
56#10622828C2214yescomplemented
57#10622820C2212yescomplemented
58#10622820C2212yescomplemented
59#10622820C2212yescomplemented
60#10622820C2212yescomplemented
61C2×C22⋊(C11⋊C8)C2212yescomplemented
62C2×C22⋊(C11⋊C8)C2212yescomplemented
63#10622655C2218yescomplemented
64#10622654C2218yescomplemented
65#10622653C2214yescomplemented
66#10622652C2218yescomplemented
67#10622651C2218yescomplemented
68#10622650C2218yescomplemented
69#10622649C2214yescomplemented
70#10622648C2218yescomplemented
71#10622647C2214yescomplemented
72#10622646C2214yescomplemented
73#10622584C2214yescomplemented
74#10622583C2214yescomplemented
75#10622581C2214yescomplemented
76#10622580C2214yescomplemented
77#10622579C2214yescomplemented
78#10622577C2214yescomplemented
79C25×C11—21no—
80C25×C11D411yescharacteristic
81C22×D4×C11—22no—
82C22×D4×C11—22no—
83C22×D4×C11—22no—
84C22×D4×C11—22no—
85C22×D4×C11—22no—
86C22×D4×C11—22no—
87C22×D4×C11—21no—
88C22×D4×C11—21no—
89C22×D4×C11—21no—
90C22×D4×C11—44no—
91C22×D4×C11—48no—
92C22×D4×C11C2312yes—
93C22×D4×C11C2312yes—
94C22×D4×C11C2312yes—
95C23×C4×C11—21no—
96C23×C4×C11—44no—
97C23×C4×C11D411yescharacteristic
98C23×C4×C11D411yescharacteristic
99C23×C4×C11D411yescharacteristic
100C23×C4×C11D411yescharacteristic
101C23×C4×C11D411yescharacteristic
102C23×C4×C11D411yescharacteristic
103C23×C4×C11D411yescharacteristic
104C23×C4×C11C2311yescharacteristic
105C23×C4×C11C2311yescharacteristic
106C23×C4×C11C2311yescharacteristic
107C23×C4×C11C2311yescharacteristic
108C23×C4×C11C2311yescharacteristic
109C23×C4×C11C2311yescharacteristic
110C23×C4×C11C2311yescharacteristic
111C22×C22⋊D11—21no—
112C22×C22⋊D11—21no—
113C22×C22⋊D11—21no—
114C2×#4339—21no—
115C2×#4339—21no—
116C2×#4339—44no—
117C2×#4339C2312yes—
118C2×#4339C2312yescomplemented
119C22×D44C2311yescharacteristic, complemented
120C22×C4×D11—21no—
121C22×Dic22C2311yescharacteristic, complemented
122C11×#121—22no—
123C11×#121—22no—
124C11×#121—22no—
125C11×#121—22no—
126C11×#121—22no—
127C11×#121—22no—
128C11×#121—22no—
129C11×#121—22no—
130C11×#121—22no—
131C11×#121—22no—
132C11×#121—22no—
133C11×#121—22no—
134C11×#121C2314yes—
135C11×#121C2314yes—
136C11×#121C2314yes—
137C11×#121C2314yes—
138C2×C11×C4⋊C4—21no—
139C2×C11×C4⋊C4—21no—
140C2×C11×C4⋊C4—21no—
141C2×C11×C4⋊C4C2312yes—
142C2×C11×C4⋊C4C2312yes—
143C2×C11×C4⋊C4C2312yes—
144C2×C11×C22⋊C4—22no—
145C2×C11×C22⋊C4—22no—
146C2×C11×C22⋊C4—22no—
147C2×C11×C22⋊C4—22no—
148C2×C11×C22⋊C4—22no—
149C2×C11×C22⋊C4—22no—
150#67006—22no—
151#67006—22no—
152#67006—22no—
153#67006—22no—
154C2×C22⋊Dic11—21no—
155C2×C22⋊Dic11—21no—
156C2×C22⋊Dic11—21no—
157C2×#4324C2318yescomplemented
158#66985—48no—
159C2×#4323C2318yescomplemented
160#66983—21no—
161#66983—21no—
162#66983—21no—
163#66983—21no—
164#66983C2312yes—
165#66983C2312yes—
166#66983C2312yescomplemented
167#66983C2312yescomplemented
168#66982—22no—
169#66982—22no—
170#66982—22no—
171#66982—22no—
172C4×C22⋊D11—22no—
173C4×C22⋊D11—22no—
174C4×C22⋊D11—22no—
175C4×C22⋊D11—22no—
176C4×C22⋊D11—22no—
177C4×C22⋊D11—22no—
178C4×C22⋊D11—22no—
179C4×C22⋊D11—22no—
180C2×(C2×D11)⋊C4—21no—
181C2×(C2×D11)⋊C4—21no—
182#66979—21no—
183#66979—21no—
184#66979C2312yes—
185#66979C2312yescomplemented
186C2×C4⋊Dic11C2311yescharacteristic, complemented
187C2×C4⋊Dic11C2311yescharacteristic, complemented
188#66977—21no—
189#66977—21no—
190#66977—21no—
191#66977—21no—
192#66977C2312yes—
193#66977C2312yes—
194#66977C2312yescomplemented
195#66977C2312yescomplemented
196C2×Dic11⋊C4—21no—
197C2×Dic11⋊C4—21no—
198C2×C4×Dic11—21no—
199C2×#4318—44no—
200C2×#4318C2314yes—
201C2×#4318C2314yescomplemented
202C22×C11⋊C8C2314yescomplemented
203#66896C2318yescomplemented
204#66896C2318yescomplemented
205C22⋊(C11⋊C8)C2314yes—
206C22⋊(C11⋊C8)C2314yes—
207C22⋊(C11⋊C8)C2314yescomplemented
208C22⋊(C11⋊C8)C2314yescomplemented
209#66874C2318yescomplemented
210#66873C2318yescomplemented
211#66872C2318yescomplemented
212#66871C2318yescomplemented
213#60750—111nomaximal, Sylow
214C24×C11—24no—
215C24×C11—22no—
216C24×C11—22no—
217C24×C11—22no—
218C24×C11—42no—
219C24×C11—42no—
220C24×C11—44no—
221C24×C11—44no—
222C24×C11—44no—
223C24×C11C2×D411yescharacteristic
224C24×C11C2×D411yescharacteristic
225C24×C11C2×D411yescharacteristic
226C24×C11C2×D411yescharacteristic
227C24×C11C2×D411yescharacteristic
228C24×C11C2×D411yescharacteristic
229C24×C11C2×D411yescharacteristic
230C23×D11—21no—
231C2×D4×C11—24no—
232C2×D4×C11—24no—
233C2×D4×C11—24no—
234C2×D4×C11—24no—
235C2×D4×C11—22no—
236C2×D4×C11—22no—
237C2×D4×C11—22no—
238C2×D4×C11—28no—
239C2×D4×C11—44no—
240C2×D4×C11—44no—
241C2×D4×C11—44no—
242C2×D4×C11—44no—
243C2×D4×C11—44no—
244C2×D4×C11—48no—
245C2×D4×C11—48no—
246C2×D4×C11—48no—
247C2×D4×C11—48no—
248C2×D4×C11—48no—
249C2×D4×C11—48no—
250C2×D4×C11C2414yes—
251C22×C4×C11—24no—
252C22×C4×C11—24no—
253C22×C4×C11—24no—
254C22×C4×C11—22no—
255C22×C4×C11—22no—
256C22×C4×C11—22no—
257C22×C4×C11—42no—
258C22×C4×C11—42no—
259C22×C4×C11—42no—
260C22×C4×C11—42no—
261C22×C4×C11—42no—
262C22×C4×C11—42no—
263C22×C4×C11—42no—
264C22×C4×C11—42no—
265C22×C4×C11—42no—
266C22×C4×C11—42no—
267C22×C4×C11—42no—
268C22×C4×C11—44no—
269C22×C4×C11C2×D411yescharacteristic
270C22×C4×C11C2×D411yescharacteristic
271C22×C4×C11C2×D411yescharacteristic
272C22×C4×C11C2×D411yescharacteristic
273C22×C4×C11C2×D411yescharacteristic
274C22×C4×C11C2×D411yescharacteristic
275C22×C4×C11C2×D411yescharacteristic
276C22×C4×C11C2×D411yescharacteristic
277C22×C4×C11C2×D411yescharacteristic
278C22×C4×C11C2×D411yescharacteristic
279C22×C4×C11C2×D411yescharacteristic
280C22×C4×C11C2×D411yescharacteristic
281C22×C4×C11C2×D411yescharacteristic
282C22×C4×C11C2×D411yescharacteristic
283C22×C4×C11C2×D411yescharacteristic
284C22×C4×C11C2×D411yescharacteristic
285C22×C4×C11C2×D411yescharacteristic
286C22×C4×C11C2×D411yescharacteristic
287C22×C4×C11C2×D411yescharacteristic
288C22×C4×C11C2×D411yescharacteristic
289C22×C4×C11C2×D411yescharacteristic
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C2×C22⋊D11—22no—
298C2×C22⋊D11—22no—
299C2×C22⋊D11—22no—
300C2×C22⋊D11—22no—
301C2×C22⋊D11—22no—
302C2×C22⋊D11—22no—
303C2×C22⋊D11—44no—
304C2×C22⋊D11—44no—
305C2×C22⋊D11—44no—
306C22×Dic11—21no—
307C22×Dic11—21no—
308C22×Dic11—21no—
309#4339—28no—
310#4339—44no—
311#4339—44no—
312#4339—44no—
313C2×D44—21no—
314C2×D44—42no—
315C2×D44C2412yes—
316C2×C4×D11—22no—
317C2×C4×D11—22no—
318C2×C4×D11—44no—
319C2×Dic22—21no—
320C2×Dic22—42no—
321C2×Dic22C2412yes—
322C11×C4⋊C4—22no—
323C11×C4⋊C4—22no—
324C11×C4⋊C4—22no—
325C11×C4⋊C4C2414yes—
326C11×C22⋊C4—24no—
327C11×C22⋊C4—24no—
328C11×C22⋊C4—24no—
329C11×C22⋊C4—24no—
330C22⋊Dic11—22no—
331C22⋊Dic11—22no—
332C22⋊Dic11—22no—
333C22⋊Dic11—22no—
334C22⋊Dic11—22no—
335C22⋊Dic11—22no—
336#4324—48no—
337#4323—48no—
338(C2×D11)⋊C4—22no—
339(C2×D11)⋊C4—22no—
340(C2×D11)⋊C4—22no—
341(C2×D11)⋊C4—22no—
342C4⋊Dic11—21no—
343C4⋊Dic11—21no—
344C4⋊Dic11C2412yes—
345C4⋊Dic11C2412yes—
346Dic11⋊C4—22no—
347Dic11⋊C4—22no—
348Dic11⋊C4—22no—
349Dic11⋊C4—22no—
350C4×Dic11—22no—
351C4×Dic11—22no—
352#4318—28no—
353#4318—44no—
354C2×C11⋊C8—44no—
355C2×C11⋊C8C2418yes—
356C2×#525—111no—
357C22×#121D1111yescharacteristic, complemented
358#3194—114no—
359#3193—112no—
360#3192—112no—
361#3188—114no—
362#3187—112no—
363#3186—112no—
364#3094—112no—
365#3092—112no—
366#3055—114no—
367#3006—112no—
368#3003—112no—
369C2×#407—111no—
370C23×C11—22no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—22no—
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—22no—
379C23×C11—22no—
380C23×C11—22no—
381C23×C11—22no—
382C23×C11—24no—
383C23×C11—41no—
384C23×C11—41no—
385C23×C11—41no—
386C23×C11—41no—
387C23×C11—41no—
388C23×C11—41no—
389C23×C11—41no—
390C23×C11—41no—
391C23×C11—416no—
392C23×C11—44no—
393C23×C11—44no—
394C23×C11—44no—
395C23×C11—44no—
396C23×C11—44no—
397C23×C11—44no—
398C23×C11—44no—
399C23×C11—44no—
400C23×C11—44no—
401C23×C11—816no—
402C23×C11AGL(1,ℤ/8)14yescomplemented
403C23×C11C22×D411yescharacteristic
404C23×C11C22×D411yescharacteristic
405C23×C11C22×D411yescharacteristic
406C23×C11C22×D411yescharacteristic
407C23×C11C22×D411yescharacteristic
408C23×C11C22×D411yescharacteristic
409C23×C11C22×D411yescharacteristic
410C22×D11—22no—
411C22×D11—42no—
412C22×D11—42no—
413C22×D11—42no—
414D4×C11—28no—
415D4×C11—44no—
416D4×C11—44no—
417D4×C11—48no—
418D4×C11—48no—
419D4×C11—48no—
420D4×C11—48no—
421D4×C11—44no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—24no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—44no—
451C2×C4×C11—44no—
452C2×C4×C11—44no—
453C2×C4×C11C22×D411yescharacteristic
454C2×C4×C11C22×D411yescharacteristic
455C2×C4×C11C22×D411yescharacteristic
456C2×C4×C11C22×D411yescharacteristic
457C2×C4×C11C22×D411yescharacteristic
458C2×C4×C11C22×D411yescharacteristic
459C2×C4×C11C22×D411yescharacteristic
460C2×C4×C11H(5,𝔽2)14yes—
461C2×C4×C11C2511yescharacteristic
462C22⋊D11—44no—
463C22⋊D11—44no—
464C22⋊D11—44no—
465C22⋊D11—44no—
466C22⋊D11—44no—
467C22⋊D11—44no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—42no—
472C2×Dic11—42no—
473C2×Dic11—42no—
474D44—24no—
475D44—42no—
476C4×D11—44no—
477C4×D11—44no—
478Dic22—24no—
479Dic22—42no—
480C11⋊C8—28no—
481C22×#41—111no—
482C23×D4—21no—
483C23×D4C2×D1111yescharacteristic, complemented
484C24×C4C2×D1111yescharacteristic
485C2×AGL(1,ℤ/8)—114no—
486C22×M16—112no—
487#525—112no—
488#525—112no—
489#525—112no—
490#525—112no—
491#525—221no—
492#525—221no—
493#525—221no—
494#525—221no—
495C2×#123—221no—
496C2×C22⋊Q8—111no—
497C2×C22⋊Q8—111no—
498C2×#121—21no—
499C2×#121—21no—
500C2×#121—21no—
501C2×#121—21no—
502C2×#121—21no—
503C2×#121—21no—
504C2×#121—111no—
505C2×#121—111no—
506C2×#121C2×D1112yes—
507C2×#121C2×D1112yes—
508C2×#121C2×D1112yes—
509C2×#121C2×D1112yescomplemented
510C2×#121C2×D1112yescomplemented
511C2×#121C2×D1112yescomplemented
512C2×#120—221no—
513C2×C4×D4—221no—
514C2×C4×D4—221no—
515C2×#117—111no—
516C22×C4⋊C4C2×D1111yescharacteristic, complemented
517C22×C22⋊C4—21no—
518#484—114no—
519#483—114no—
520#482—118no—
521#481—114no—
522#481—114no—
523#480—114no—
524#480—114no—
525#469—118no—
526#468—118no—
527#466—118no—
528#465—118no—
529#450—114no—
530#450—114no—
531#449—118no—
532#448—114no—
533#447—114no—
534#447—114no—
535#447—114no—
536#428—114no—
537#418—114no—
538#417—114no—
539#407—112no—
540#407—112no—
541#407—112no—
542#407—112no—
543C2×C22⋊C8—112no—
544C2×C22⋊C8—112no—
545C22×C11—28no—
546C22×C11—21no—
547C22×C11—21no—
548C22×C11—21no—
549C22×C11—21no—
550C22×C11—21no—
551C22×C11—21no—
552C22×C11—21no—
553C22×C11—21no—
554C22×C11—21no—
555C22×C11—21no—
556C22×C11—21no—
557C22×C11—21no—
558C22×C11—21no—
559C22×C11—21no—
560C22×C11—21no—
561C22×C11—21no—
562C22×C11—44no—
563C22×C11—44no—
564C22×C11—44no—
565C22×C11—44no—
566C22×C11—44no—
567C22×C11—44no—
568C22×C11—44no—
569C22×C11—44no—
570C22×C11—44no—
571C22×C11—88no—
572C22×C11—88no—
573C22×C11—88no—
574C22×C11#53412yes—
575C22×C11C2×AGL(1,ℤ/8)12yes—
576C22×C11C2×AGL(1,ℤ/8)12yes—
577C22×C11C2×AGL(1,ℤ/8)12yes—
578C22×C11#57512yes—
579C22×C11C23×D411yescharacteristic
580C2×D11—42no—
581C2×D11—42no—
582C2×D11—42no—
583C2×D11—84no—
584C4×C11—21no—
585C4×C11—21no—
586C4×C11—21no—
587C4×C11—21no—
588C4×C11—21no—
589C4×C11—21no—
590C4×C11—44no—
591C4×C11#53412yes—
592C4×C11C2×H(5,𝔽2)12yes—
593Dic11—42no—
594Dic11—42no—
595Dic11—42no—
596C25—21no—
597C25C22⋊D1111yescharacteristic
598C2×#41—112no—
599C2×#41—112no—
600C2×#41—221no—
601C2×#41—221no—
602C2×#41—444no—
603C22×Q8—111no—
604C22×D4—22no—
605C22×D4—22no—
606C22×D4—22no—
607C22×D4—22no—
608C22×D4—22no—
609C22×D4—22no—
610C22×D4—21no—
611C22×D4—21no—
612C22×D4—21no—
613C22×D4—44no—
614C22×D4—48no—
615C22×D4—111no—
616C22×D4—221no—
617C22×D4—221no—
618C22×D4—221no—
619C22×D4C22×D1112yes—
620C22×D4C22×D1112yes—
621C22×D4C22×D1112yes—
622C23×C4—21no—
623C23×C4—44no—
624C23×C4—221no—
625C23×C4C22⋊D1111yescharacteristic
626C23×C4C22⋊D1111yescharacteristic
627C23×C4C22⋊D1111yescharacteristic
628C23×C4C22⋊D1111yescharacteristic
629C23×C4C22⋊D1111yescharacteristic
630C23×C4C22⋊D1111yescharacteristic
631C23×C4C22⋊D1111yescharacteristic
632C23×C4C22×D1111yescharacteristic
633C23×C4C22×D1111yescharacteristic
634C23×C4C22×D1111yescharacteristic
635C23×C4C22×D1111yescharacteristic
636C23×C4C22×D1111yescharacteristic
637C23×C4C22×D1111yescharacteristic
638C23×C4C22×D1111yescharacteristic
639AGL(1,ℤ/8)—448no—
640C2×SD16—118no—
641C2×D8—118no—
642C2×M16—114no—
643C2×M16—114no—
644C2×M16—444no—
645C22×C8—114no—
646#123—222no—
647#123—222no—
648#123—222no—
649#123—222no—
650C22⋊Q8—112no—
651C22⋊Q8—112no—
652C22⋊Q8—112no—
653C22⋊Q8—112no—
654C22⋊Q8—221no—
655C22⋊Q8—221no—
656C22⋊Q8—221no—
657C22⋊Q8—221no—
658#121—22no—
659#121—22no—
660#121—22no—
661#121—22no—
662#121—22no—
663#121—22no—
664#121—22no—
665#121—22no—
666#121—22no—
667#121—22no—
668#121—22no—
669#121—22no—
670#121—112no—
671#121—112no—
672#121—112no—
673#121—112no—
674#121—221no—
675#121—221no—
676#121—221no—
677#121—221no—
678#121C22×D1114yes—
679#121C22×D1114yes—
680#121C22×D1114yes—
681#121C22×D1114yes—
682#120—222no—
683#120—222no—
684#120—222no—
685#120—222no—
686C4×D4—222no—
687C4×D4—222no—
688C4×D4—222no—
689C4×D4—222no—
690C4×D4—222no—
691C4×D4—222no—
692C4×D4—222no—
693C4×D4—222no—
694#117—112no—
695#117—112no—
696#117—221no—
697#117—221no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—21no—
700C2×C4⋊C4—21no—
701C2×C4⋊C4—111no—
702C2×C4⋊C4—111no—
703C2×C4⋊C4—221no—
704C2×C4⋊C4—221no—
705C2×C4⋊C4C22×D1112yes—
706C2×C4⋊C4C22×D1112yes—
707C2×C4⋊C4C22×D1112yes—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—221no—
715C2×C22⋊C4—221no—
716C2×C22⋊C4—221no—
717C2×C22⋊C4—221no—
718C2×C22⋊C4—221no—
719C2×C42—221no—
720#107—118no—
721#106—118no—
722#103—118no—
723#102—118no—
724#102—118no—
725#102—118no—
726C22⋊C8—114no—
727C22⋊C8—114no—
728C22⋊C8—114no—
729C22⋊C8—114no—
730C2×C11—22no—
731C2×C11—22no—
732C2×C11—22no—
733C2×C11—22no—
734C2×C11—22no—
735C2×C11—41no—
736C2×C11—41no—
737C2×C11—84no—
738C2×C11C2×#53411yescharacteristic
739C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
740C2×C11C2×#57511yescharacteristic
741D11—82no—
742C24—24no—
743C24—22no—
744C24—22no—
745C24—22no—
746C24—42no—
747C24—42no—
748C24—44no—
749C24—44no—
750C24—44no—
751C24—221no—
752C24C2×C22⋊D1111yescharacteristic
753C24C2×C22⋊D1111yescharacteristic
754C24C2×C22⋊D1111yescharacteristic
755C24C2×C22⋊D1111yescharacteristic
756C24C2×C22⋊D1111yescharacteristic
757C24C2×C22⋊D1111yescharacteristic
758C24C2×C22⋊D1111yescharacteristic
759#41—228no—
760#41—444no—
761#41—444no—
762#41—444no—
763C2×Q8—112no—
764C2×Q8—221no—
765C2×Q8—442no—
766C2×D4—24no—
767C2×D4—24no—
768C2×D4—24no—
769C2×D4—24no—
770C2×D4—28no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—44no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—44no—
779C2×D4—48no—
780C2×D4—48no—
781C2×D4—48no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4—48no—
785C2×D4—112no—
786C2×D4—222no—
787C2×D4—222no—
788C2×D4—222no—
789C2×D4—222no—
790C2×D4—222no—
791C2×D4—222no—
792C2×D4—221no—
793C2×D4—442no—
794C2×D4—444no—
795C2×D4—444no—
796C2×D4—444no—
797C2×D4C23×D1114yes—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—42no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—44no—
816C22×C4—221no—
817C22×C4—221no—
818C22×C4—221no—
819C22×C4—222no—
820C22×C4—222no—
821C22×C4—444no—
822C22×C4C2×C22⋊D1111yescharacteristic
823C22×C4C2×C22⋊D1111yescharacteristic
824C22×C4C2×C22⋊D1111yescharacteristic
825C22×C4C2×C22⋊D1111yescharacteristic
826C22×C4C2×C22⋊D1111yescharacteristic
827C22×C4C2×C22⋊D1111yescharacteristic
828C22×C4C2×C22⋊D1111yescharacteristic
829C22×C4C2×C22⋊D1111yescharacteristic
830C22×C4C2×C22⋊D1111yescharacteristic
831C22×C4C2×C22⋊D1111yescharacteristic
832C22×C4C2×C22⋊D1111yescharacteristic
833C22×C4C2×C22⋊D1111yescharacteristic
834C22×C4C2×C22⋊D1111yescharacteristic
835C22×C4C2×C22⋊D1111yescharacteristic
836C22×C4C2×C22⋊D1111yescharacteristic
837C22×C4C2×C22⋊D1111yescharacteristic
838C22×C4C2×C22⋊D1111yescharacteristic
839C22×C4C2×C22⋊D1111yescharacteristic
840C22×C4C2×C22⋊D1111yescharacteristic
841C22×C4C2×C22⋊D1111yescharacteristic
842C22×C4C2×C22⋊D1111yescharacteristic
843C22×C4C23×D1111yescharacteristic
844C22×C4C23×D1111yescharacteristic
845C22×C4C23×D1111yescharacteristic
846C22×C4C23×D1111yescharacteristic
847C22×C4C23×D1111yescharacteristic
848C22×C4C23×D1111yescharacteristic
849C22×C4C23×D1111yescharacteristic
850SD16—448no—
851D8—448no—
852M16—228no—
853M16—444no—
854C2×C8—118no—
855C2×C8—444no—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—112no—
860C4⋊C4—112no—
861C4⋊C4—221no—
862C4⋊C4—221no—
863C4⋊C4—222no—
864C4⋊C4—222no—
865C4⋊C4—222no—
866C4⋊C4—222no—
867C4⋊C4C23×D1114yes—
868C22⋊C4—24no—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—24no—
872C22⋊C4—222no—
873C22⋊C4—222no—
874C22⋊C4—222no—
875C22⋊C4—222no—
876C22⋊C4—222no—
877C22⋊C4—222no—
878C22⋊C4—222no—
879C22⋊C4—222no—
880C22⋊C4—222no—
881C22⋊C4—222no—
882C42—222no—
883C42—222no—
884C11#6075011yescharacteristic, complemented, Sylow
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—24no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—416no—
907C23—44no—
908C23—44no—
909C23—44no—
910C23—44no—
911C23—44no—
912C23—44no—
913C23—44no—
914C23—44no—
915C23—44no—
916C23—816no—
917C23—222no—
918C23—442no—
919C23—442no—
920C23—442no—
921C23#6698514yescomplemented
922C23C22×C22⋊D1111yescharacteristic
923C23C22×C22⋊D1111yescharacteristic
924C23C22×C22⋊D1111yescharacteristic
925C23C22×C22⋊D1111yescharacteristic
926C23C22×C22⋊D1111yescharacteristic
927C23C22×C22⋊D1111yescharacteristic
928C23C22×C22⋊D1111yescharacteristic
929Q8—224no—
930Q8—442no—
931D4—28no—
932D4—44no—
933D4—44no—
934D4—48no—
935D4—48no—
936D4—48no—
937D4—48no—
938D4—44no—
939D4—224no—
940D4—442no—
941D4—444no—
942D4—444no—
943D4—444no—
944D4—444no—
945D4—444no—
946D4—444no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—44no—
976C2×C4—44no—
977C2×C4—44no—
978C2×C4—222no—
979C2×C4—222no—
980C2×C4—222no—
981C2×C4—444no—
982C2×C4—442no—
983C2×C4—442no—
984C2×C4—442no—
985C2×C4—444no—
986C2×C4#6703714yes—
987C2×C4C22×C22⋊D1111yescharacteristic
988C2×C4C22×C22⋊D1111yescharacteristic
989C2×C4C22×C22⋊D1111yescharacteristic
990C2×C4C22×C22⋊D1111yescharacteristic
991C2×C4C22×C22⋊D1111yescharacteristic
992C2×C4C22×C22⋊D1111yescharacteristic
993C2×C4C22×C22⋊D1111yescharacteristic
994C2×C4C24×D1111yescharacteristic
995C8—228no—
996C22—28no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—44no—
1020C22—44no—
1021C22—44no—
1022C22—88no—
1023C22—88no—
1024C22—88no—
1025C22—442no—
1026C22—442no—
1027C22—442no—
1028C22—884no—
1029C22C2×#6698512yes—
1030C22C2×#6698512yes—
1031C22C2×#6698512yes—
1032C22#1062333512yes—
1033C22#1062335312yes—
1034C22C23×C22⋊D1111yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—44no—
1042C4—442no—
1043C4—442no—
1044C4—442no—
1045C4#1062333512yes—
1046C4C2×#6703712yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—84no—
1055C2—882no—
1056C2C2×#1062333511yescharacteristic
1057C2C22×#6698511yescharacteristic
1058C2C2×#1062335311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#121C2
socleC22×C11C23×D4
hypercenterC22×#121D11
hypocenterC11#60750
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10623322C2semidirect
2. #13079430C2semidirect
3. #13079422C2semidirect
4. #13079413C2semidirect
5. #13079381C2semidirect
6. #13079373C2semidirect
7. #13079364C2semidirect
8. #13078552C2semidirect
9. #13078539C2semidirect
10. #13078231C2semidirect
11. #13077866C2semidirect
12. #13077843C2semidirect
13. C2×#10622820C2semidirect
14. C22×C11×#121C2semidirect
16. C23×D4×C11C22semidirect
18. C22×#4339C22semidirect
28. C2×C11×#121C22semidirect
29. C2×C11×#121C22semidirect
30. C2×C11×#121C22semidirect
31. C22×C11×C4⋊C4C22semidirect
34. C2×#66985C22semidirect
40. #10623322C22semidirect
41. #10623322C22semidirect
42. #10623322C22semidirect
43. C2×#66983C22semidirect
44. C2×#66983C22semidirect
48. C2×#66979C22semidirect
49. C2×#66977C22semidirect
50. C2×#66977C22semidirect
51. C22×#4318C22semidirect
52. #10622831C22semidirect
53. #10622831C22semidirect
54. #10622830C22semidirect
55. #10622830C22semidirect
56. #10622828C22semidirect
57. #10622820C22semidirect
58. #10622820C22semidirect
59. #10622820C22semidirect
60. #10622820C22semidirect
61. C2×C22⋊(C11⋊C8)C22semidirect
62. C2×C22⋊(C11⋊C8)C22semidirect
63. #10622655C22semidirect
64. #10622654C22semidirect
65. #10622653C22semidirect
66. #10622652C22semidirect
67. #10622651C22semidirect
68. #10622650C22semidirect
69. #10622649C22semidirect
70. #10622648C22semidirect
71. #10622647C22semidirect
72. #10622646C22semidirect
73. #10622584C22semidirect
74. #10622583C22semidirect
75. #10622581C22semidirect
76. #10622580C22semidirect
77. #10622579C22semidirect
78. #10622577C22semidirect
118. C2×#4339C23semidirect
119. C22×D44C23semidirect
121. C22×Dic22C23semidirect
157. C2×#4324C23semidirect
159. C2×#4323C23semidirect
166. #66983C23semidirect
167. #66983C23semidirect
185. #66979C23semidirect
186. C2×C4⋊Dic11C23semidirect
187. C2×C4⋊Dic11C23semidirect
194. #66977C23semidirect
195. #66977C23semidirect
201. C2×#4318C23semidirect
202. C22×C11⋊C8C23semidirect
203. #66896C23semidirect
204. #66896C23semidirect
207. C22⋊(C11⋊C8)C23semidirect
208. C22⋊(C11⋊C8)C23semidirect
209. #66874C23semidirect
210. #66873C23semidirect
211. #66872C23semidirect
212. #66871C23semidirect
357. C22×#121D11semidirect
402. C23×C11AGL(1,ℤ/8)semidirect
483. C23×D4C2×D11semidirect
509. C2×#121C2×D11semidirect
510. C2×#121C2×D11semidirect
511. C2×#121C2×D11semidirect
516. C22×C4⋊C4C2×D11semidirect
884. C11#60750semidirect
921. C23#66985semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
#130794302
#130794222
#130794132
#130793812
#130793732
#130793642
#130785522
#130785392
#130782312
#130778662
#130778432
C2×#106228202
C22×C11×#1212
#6075011