Finite Group Databasebeta

← #15622154

Subgroups — #15622154

Order 2816.

2570 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D44C211yesmaximal, characteristic, complemented
2#13078750C214yesmaximal, complemented
3#13078711C212yesmaximal, complemented
4#13078703C212yesmaximal, complemented
5#13078659C214yesmaximal, complemented
6#13078620C212yesmaximal, complemented
7#13078612C212yesmaximal, complemented
8#13078536C212yesmaximal, complemented
9#13078409C212yesmaximal, complemented
10#13078076C212yesmaximal, complemented
11#13077842C212yesmaximal, complemented
12C4×#67002C214yesmaximal, complemented
13#13077249C211yesmaximal, characteristic, complemented
14C11×#3444C211yesmaximal, characteristic, complemented
15C23×D44C2211yescharacteristic
16C23×C4×D11—21no—
17C11×#533C2211yescharacteristic, complemented
18C11×#533C2211yescharacteristic, complemented
19C11×#533C2211yescharacteristic, complemented
20C11×#532C2211yescharacteristic, complemented
21C11×#532C2211yescharacteristic, complemented
22C11×#532C2211yescharacteristic, complemented
23C11×#529—21no—
24C11×#529—21no—
25C11×#529—21no—
26C11×#529—21no—
27C11×#529C2212yescomplemented
28C11×#529C2212yescomplemented
29C11×#525—21no—
30C11×#525—21no—
31C11×#525C2212yes—
32C4×C11×#41—21no—
33C4×C11×#41—21no—
34C4×C11×#41C2212yescomplemented
35C22×C42×C11C2211yescharacteristic
36C2×#67002C2214yes—
37C22×(C2×D11)⋊C4—21no—
38C22×C4⋊Dic11C2211yescharacteristic
39C2×C4×D44—21no—
40C2×C4×D44—21no—
41C2×C4×D44—21no—
42C2×C4×D44—21no—
43C2×C4×D44—21no—
44C2×C4×D44—21no—
45C2×C4×D44C2212yes—
46C2×C4×D44C2212yes—
47C2×C4×D44C2212yes—
48C2×C4×D44C2212yes—
49C2×C4×D44C2212yes—
50C2×C4×D44C2212yes—
51#10622845C2214yescomplemented
52#10622820C2212yes—
53#10622700C2214yescomplemented
54#10622697C2214yescomplemented
55#10622696C2214yescomplemented
56#10622685C2214yescomplemented
57#10622679C2218yescomplemented
58#10622670C2218yescomplemented
59#10622659C2214yes—
60#10622659C2214yes—
61#10622657C2214yescomplemented
62#10622656C2214yescomplemented
63#10622649C2214yes—
64#10622649C2214yes—
65#10622647C2214yescomplemented
66#10622646C2214yescomplemented
67#10622639C2218yescomplemented
68C4×#4325C2218yescomplemented
69#10622627C2218yescomplemented
70C4×#4323C2218yescomplemented
71#10622614C2214yes—
72#10622608C2214yescomplemented
73#10622539C2212yescomplemented
74#10622539C2212yescomplemented
75#10622538C2212yescomplemented
76#10622538C2212yescomplemented
77#10622537C2212yescomplemented
78C4×#4318C2212yescomplemented
79C24×D11—21no—
80C2×C11×#41—21no—
81C2×C11×#41—21no—
82C2×C11×#41C2312yes—
83C23×C4×C11D411yescharacteristic
84C23×C4×C11D411yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×Dic11—21no—
87C22×D44—21no—
88C22×D44—21no—
89C22×D44—21no—
90C22×D44—28no—
91C22×D44C2312yes—
92C22×D44C2312yes—
93C22×D44C2312yes—
94C22×C4×D11—22no—
95C22×C4×D11—22no—
96C22×C4×D11—22no—
97C22×C4×D11—22no—
98C22×C4×D11—22no—
99C22×C4×D11—22no—
100C22×C4×D11—48no—
101C11×C4⋊Q8C2311yescharacteristic, complemented
102C11×C4⋊Q8C2311yescharacteristic, complemented
103C11×C4⋊Q8C2311yescharacteristic, complemented
104C11×#127C2311yescharacteristic, complemented
105C11×#126—22no—
106C11×#126—22no—
107C11×#125—21no—
108C11×#125—21no—
109C11×#125C2312yescomplemented
110C11×#124—21no—
111C11×#124—21no—
112C11×#124C2312yescomplemented
113C11×#123—22no—
114C11×#123—22no—
115C11×#123—22no—
116C11×C22⋊Q8—21no—
117C11×C22⋊Q8—21no—
118C11×C22⋊Q8—21no—
119C11×C22⋊Q8—21no—
120C11×C22⋊Q8C2312yes—
121C11×C22⋊Q8C2312yes—
122C11×#121—21no—
123C11×#121—21no—
124C11×#121—21no—
125C11×#121—21no—
126C11×#121C2312yes—
127C11×#121C2312yes—
128C11×#120—22no—
129C4×Q8×C11—21no—
130C4×Q8×C11—21no—
131C4×Q8×C11—21no—
132C4×Q8×C11—21no—
133C4×Q8×C11C2312yescomplemented
134C4×Q8×C11C2312yescomplemented
135C4×D4×C11—22no—
136C4×D4×C11—22no—
137C4×D4×C11—22no—
138C4×D4×C11—22no—
139C4×D4×C11—22no—
140C4×D4×C11—22no—
141C4×D4×C11—21no—
142C4×D4×C11—21no—
143C4×D4×C11—21no—
144C4×D4×C11—21no—
145C4×D4×C11C2312yescomplemented
146C4×D4×C11C2312yescomplemented
147C11×#117—21no—
148C11×#117—21no—
149C11×#117—22no—
150C11×#117—22no—
151C11×#117—22no—
152C11×#117C2312yes—
153C2×C42×C11—22no—
154C2×C42×C11D411yescharacteristic
155C2×C42×C11D411yescharacteristic
156C2×C42×C11D411yescharacteristic
157C2×C42×C11D411yescharacteristic
158C2×C42×C11D411yescharacteristic
159C2×C42×C11D411yescharacteristic
160C2×C42×C11C2311yescharacteristic
161C2×C42×C11C2311yescharacteristic
162C2×C42×C11C2311yescharacteristic
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2311yescharacteristic
165C2×C42×C11C2311yescharacteristic
166#67002—216no—
167C2×#4325C2318yes—
168C2×#4323C2318yes—
169C2×(C2×D11)⋊C4—22no—
170C2×(C2×D11)⋊C4—22no—
171C2×(C2×D11)⋊C4—22no—
172C2×(C2×D11)⋊C4—22no—
173C2×(C2×D11)⋊C4—22no—
174C2×(C2×D11)⋊C4—22no—
175C2×C4⋊Dic11—21no—
176C2×C4⋊Dic11—21no—
177C2×C4⋊Dic11—21no—
178C2×C4⋊Dic11C2312yes—
179C2×C4⋊Dic11C2312yes—
180C2×C4⋊Dic11C2312yes—
181C2×#4318C2314yes—
182C4×D44—22no—
183C4×D44—22no—
184C4×D44—22no—
185C4×D44—22no—
186C4×D44—22no—
187C4×D44—22no—
188C4×D44—22no—
189C4×D44—22no—
190C4×D44—22no—
191C4×D44—22no—
192C4×D44—22no—
193C4×D44—22no—
194C4×D44C2314yes—
195C4×D44C2314yes—
196C4×D44C2314yes—
197C4×D44C2314yes—
198#66899C2318yescomplemented
199#66896C2318yescomplemented
200C22⋊(C11⋊C8)C2314yes—
201C22⋊(C11⋊C8)C2314yes—
202#66873C2318yes—
203#66873C2318yes—
204#66872C2318yescomplemented
205#66871C2318yescomplemented
206C4⋊(C11⋊C8)C2314yescomplemented
207C4⋊(C11⋊C8)C2314yescomplemented
208#66867C2314yescomplemented
209C4×C11⋊C8C2314yescomplemented
210#60558—111nomaximal, Sylow
211C24×C11C2×D411yescharacteristic
212C23×D11—28no—
213C23×D11—22no—
214C23×D11—22no—
215C23×D11—22no—
216C23×D11—44no—
217C23×D11—44no—
218C11×#41—28no—
219C11×#41—44no—
220C11×#41—44no—
221C2×Q8×C11—21no—
222C2×Q8×C11—21no—
223C2×Q8×C11C2412yes—
224C2×D4×C11—22no—
225C2×D4×C11—22no—
226C2×D4×C11—22no—
227C2×D4×C11—21no—
228C2×D4×C11—21no—
229C2×D4×C11C2412yes—
230C22×C4×C11—24no—
231C22×C4×C11—24no—
232C22×C4×C11—22no—
233C22×C4×C11—22no—
234C22×C4×C11—22no—
235C22×C4×C11—42no—
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2×D411yescharacteristic
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×C11C2411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2411yescharacteristic
254C22×Dic11—22no—
255C22×Dic11—22no—
256C22×Dic11—22no—
257C22×Dic11—44no—
258C2×D44—28no—
259C2×D44—28no—
260C2×D44—28no—
261C2×D44—28no—
262C2×D44—28no—
263C2×D44—22no—
264C2×D44—22no—
265C2×D44—22no—
266C2×D44—24no—
267C2×D44#4118yescomplemented
268C2×D44C2414yes—
269C2×C4×D11—24no—
270C2×C4×D11—24no—
271C2×C4×D11—24no—
272C2×C4×D11—24no—
273C2×C4×D11—48no—
274C2×C4×D11—48no—
275C2×C4×D11—48no—
276C2×C4×D11—48no—
277C2×C4×D11—48no—
278C2×C4×D11—48no—
279C11×C4⋊C4—21no—
280C11×C4⋊C4—21no—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—21no—
283C11×C4⋊C4—22no—
284C11×C4⋊C4—22no—
285C11×C4⋊C4—22no—
286C11×C4⋊C4—22no—
287C11×C4⋊C4—22no—
288C11×C4⋊C4—22no—
289C11×C4⋊C4C2412yes—
290C11×C4⋊C4C2412yes—
291C11×C22⋊C4—22no—
292C11×C22⋊C4—22no—
293C11×C22⋊C4—22no—
294C11×C22⋊C4—22no—
295C11×C22⋊C4—22no—
296C11×C22⋊C4—22no—
297C11×C22⋊C4—22no—
298C11×C22⋊C4—22no—
299C11×C22⋊C4—22no—
300C42×C11—22no—
301C42×C11—22no—
302C42×C11—22no—
303C42×C11C2×D411yescharacteristic
304C42×C11C2×D411yescharacteristic
305C42×C11C2×D411yescharacteristic
306C42×C11C2×D411yescharacteristic
307C42×C11C2×D411yescharacteristic
308C42×C11C2×D411yescharacteristic
309C42×C11C2×D411yescharacteristic
310C42×C11C2×D411yescharacteristic
311C42×C11C2×D411yescharacteristic
312C42×C11C2×D411yescharacteristic
313C42×C11C2×D411yescharacteristic
314C42×C11C2×D411yescharacteristic
315C42×C11C2411yescharacteristic
316C42×C11C2411yescharacteristic
317C42×C11C2411yescharacteristic
318C42×C11C2411yescharacteristic
319#4325—216no—
320#4323—216no—
321(C2×D11)⋊C4—24no—
322(C2×D11)⋊C4—24no—
323(C2×D11)⋊C4—24no—
324(C2×D11)⋊C4—24no—
325C4⋊Dic11—22no—
326C4⋊Dic11—22no—
327C4⋊Dic11—22no—
328C4⋊Dic11C2414yes—
329#4318—28no—
330C2×C11⋊C8C2418yes—
331#3444D1111yescharacteristic, complemented
332C22×C4×D4—111no—
333#3114—114no—
334#3110—112no—
335#3109—112no—
336#3105—114no—
337#3101—112no—
338#3100—112no—
339#3092—112no—
340#3077—112no—
341#3036—112no—
342#3003—112no—
343C4×AGL(1,ℤ/8)—114no—
344#2920—111no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11C22×D411yescharacteristic
350C23×C11C22×D411yescharacteristic
351C23×C11C22×D411yescharacteristic
352C22×D11—28no—
353C22×D11—28no—
354C22×D11—28no—
355C22×D11—24no—
356C22×D11—44no—
357C22×D11—44no—
358C22×D11—432no—
359C22×D11—44no—
360C22×D11—44no—
361C22×D11—44no—
362C22×D11—44no—
363Q8×C11—24no—
364Q8×C11—42no—
365Q8×C11—42no—
366D4×C11—24no—
367D4×C11—42no—
368D4×C11—44no—
369D4×C11—44no—
370D4×C11—44no—
371D4×C11—42no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—44no—
392C2×C4×C11—44no—
393C2×C4×C11—44no—
394C2×C4×C11AGL(1,ℤ/8)14yescomplemented
395C2×C4×C11C22×D411yescharacteristic
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C22×D411yescharacteristic
398C2×C4×C11C22×D411yescharacteristic
399C2×C4×C11C22×D411yescharacteristic
400C2×C4×C11C22×D411yescharacteristic
401C2×C4×C11C22×D411yescharacteristic
402C2×C4×C11C22×D411yescharacteristic
403C2×C4×C11C22×D411yescharacteristic
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C22×D411yescharacteristic
406C2×C4×C11C2×#4114yes—
407C2×C4×C11C2511yescharacteristic
408C2×Dic11—24no—
409C2×Dic11—44no—
410C2×Dic11—44no—
411C2×Dic11—44no—
412D44—28no—
413D44—28no—
414D44—28no—
415D44—24no—
416D44C2×#4118yes—
417C4×D11—48no—
418C4×D11—48no—
419C4×D11—48no—
420C4×D11—48no—
421C11⋊C8—28no—
422C23×D4—111no—
423C24×C4—221no—
424C2×AGL(1,ℤ/8)—114no—
425#533C2×D1111yescharacteristic, complemented
426#533C2×D1111yescharacteristic, complemented
427#533C2×D1111yescharacteristic, complemented
428#532C2×D1111yescharacteristic, complemented
429#532C2×D1111yescharacteristic, complemented
430#532C2×D1111yescharacteristic, complemented
431#529—21no—
432#529—21no—
433#529—21no—
434#529—21no—
435#529C2×D1112yescomplemented
436#529C2×D1112yescomplemented
437#525—21no—
438#525—21no—
439#525C2×D1112yes—
440C4×#41—21no—
441C4×#41—21no—
442C4×#41C2×D1112yescomplemented
443C2×C4×D4—112no—
444C2×C4×D4—112no—
445C2×C4×D4—112no—
446C2×C4×D4—112no—
447C2×C4×D4—112no—
448C2×C4×D4—112no—
449C2×C4×D4—221no—
450C2×C4×D4—221no—
451C2×C4×D4—221no—
452C2×C4×D4—221no—
453C2×C4×D4—221no—
454C2×C4×D4—221no—
455C22×C4⋊C4—111no—
456C22×C22⋊C4—221no—
457C22×C42C2×D1111yescharacteristic
458#484—114no—
459#483—114no—
460#481—114no—
461#480—114no—
462#478—118no—
463#476—114no—
464#474—114no—
465#463—118no—
466#461—114no—
467#459—114no—
468#450—114no—
469#450—114no—
470#447—114no—
471#447—114no—
472#442—118no—
473#440—118no—
474C4×SD16—118no—
475C4×D8—118no—
476#432—112no—
477#432—112no—
478#431—112no—
479#431—112no—
480#428—114no—
481#423—112no—
482#418—114no—
483#417—114no—
484#407—112no—
485C4×M16—112no—
486C22×C11—28no—
487C22×C11—21no—
488C22×C11—21no—
489C22×C11—21no—
490C22×C11—21no—
491C22×C11—21no—
492C22×C11—21no—
493C22×C11—42no—
494C22×C11—42no—
495C22×C11—42no—
496C22×C11#52512yes—
497C22×C11C2×AGL(1,ℤ/8)12yes—
498C22×C11#57512yes—
499C22×C11C23×D411yescharacteristic
500C2×D11—28no—
501C2×D11—416no—
502C2×D11—416no—
503C2×D11—416no—
504C2×D11—44no—
505C2×D11—44no—
506C4×C11—21no—
507C4×C11—21no—
508C4×C11—21no—
509C4×C11—21no—
510C4×C11—21no—
511C4×C11—21no—
512C4×C11—21no—
513C4×C11—21no—
514C4×C11—42no—
515C4×C11—42no—
516C4×C11—42no—
517C4×C11#52512yes—
518C4×C11C2×AGL(1,ℤ/8)12yes—
519C4×C11C2×AGL(1,ℤ/8)12yes—
520C4×C11C22×#4112yes—
521Dic11—44no—
522C25—221no—
523C2×#41—21no—
524C2×#41—21no—
525C2×#41C22×D1112yes—
526C22×D4—112no—
527C22×D4—112no—
528C22×D4—112no—
529C22×D4—228no—
530C22×D4—221no—
531C22×D4—221no—
532C22×D4—221no—
533C23×C4—221no—
534C23×C4—222no—
535C23×C4—222no—
536C23×C4—222no—
537C23×C4—222no—
538C23×C4—222no—
539C23×C4—222no—
540C23×C4—448no—
541C23×C4C22⋊D1111yescharacteristic
542C23×C4C22⋊D1111yescharacteristic
543C23×C4C22×D1111yescharacteristic
544AGL(1,ℤ/8)—2216no—
545C2×SD16—118no—
546C2×D8—118no—
547C2×M16—114no—
548C4⋊Q8C22×D1111yescharacteristic, complemented
549C4⋊Q8C22×D1111yescharacteristic, complemented
550C4⋊Q8C22×D1111yescharacteristic, complemented
551#127C22×D1111yescharacteristic, complemented
552#126—22no—
553#126—22no—
554#125—21no—
555#125—21no—
556#125C22×D1112yescomplemented
557#124—21no—
558#124—21no—
559#124C22×D1112yescomplemented
560#123—22no—
561#123—22no—
562#123—22no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566C22⋊Q8—21no—
567C22⋊Q8C22×D1112yes—
568C22⋊Q8C22×D1112yes—
569#121—21no—
570#121—21no—
571#121—21no—
572#121—21no—
573#121C22×D1112yes—
574#121C22×D1112yes—
575#120—22no—
576C4×Q8—21no—
577C4×Q8—21no—
578C4×Q8—21no—
579C4×Q8—21no—
580C4×Q8C22×D1112yescomplemented
581C4×Q8C22×D1112yescomplemented
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—21no—
589C4×D4—21no—
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—114no—
593C4×D4—114no—
594C4×D4—114no—
595C4×D4—114no—
596C4×D4—222no—
597C4×D4—222no—
598C4×D4—222no—
599C4×D4—222no—
600C4×D4—222no—
601C4×D4—222no—
602C4×D4—222no—
603C4×D4—222no—
604C4×D4—222no—
605C4×D4—222no—
606C4×D4—222no—
607C4×D4—222no—
608C4×D4C22×D1112yescomplemented
609C4×D4C22×D1112yescomplemented
610#117—21no—
611#117—21no—
612#117—22no—
613#117—22no—
614#117—22no—
615#117C22×D1112yes—
616C2×C4⋊C4—112no—
617C2×C4⋊C4—112no—
618C2×C4⋊C4—112no—
619C2×C4⋊C4—221no—
620C2×C4⋊C4—221no—
621C2×C4⋊C4—221no—
622C2×C22⋊C4—222no—
623C2×C22⋊C4—222no—
624C2×C22⋊C4—222no—
625C2×C22⋊C4—222no—
626C2×C22⋊C4—222no—
627C2×C22⋊C4—222no—
628C2×C42—22no—
629C2×C42C22⋊D1111yescharacteristic
630C2×C42C22⋊D1111yescharacteristic
631C2×C42C22⋊D1111yescharacteristic
632C2×C42C22⋊D1111yescharacteristic
633C2×C42C22⋊D1111yescharacteristic
634C2×C42C22⋊D1111yescharacteristic
635C2×C42C22×D1111yescharacteristic
636C2×C42C22×D1111yescharacteristic
637C2×C42C22×D1111yescharacteristic
638C2×C42C22×D1111yescharacteristic
639C2×C42C22×D1111yescharacteristic
640C2×C42C22×D1111yescharacteristic
641#107—118no—
642#106—118no—
643C4⋊C8—114no—
644C4⋊C8—114no—
645#103—118no—
646#102—118no—
647#102—118no—
648#102—118no—
649C22⋊C8—114no—
650C22⋊C8—114no—
651#97—114no—
652C4×C8—114no—
653C2×C11—22no—
654C2×C11—22no—
655C2×C11—22no—
656C2×C11—82no—
657C2×C11C2×#52511yescharacteristic
658C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
659C2×C11C2×#57511yescharacteristic
660D11—48no—
661C24—228no—
662C24—222no—
663C24—222no—
664C24—222no—
665C24—444no—
666C24—444no—
667C24C2×C22⋊D1111yescharacteristic
668#41—28no—
669#41—44no—
670#41—44no—
671C2×Q8—21no—
672C2×Q8—21no—
673C2×Q8C23×D1112yes—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—118no—
680C2×D4—114no—
681C2×D4—228no—
682C2×D4—228no—
683C2×D4—228no—
684C2×D4—228no—
685C2×D4—228no—
686C2×D4—224no—
687C2×D4—222no—
688C2×D4—222no—
689C2×D4—222no—
690C2×D4C23×D1112yes—
691C22×C4—24no—
692C22×C4—24no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—42no—
697C22×C4—222no—
698C22×C4—222no—
699C22×C4—222no—
700C22×C4—224no—
701C22×C4—224no—
702C22×C4—224no—
703C22×C4—224no—
704C22×C4—448no—
705C22×C4—448no—
706C22×C4—448no—
707C22×C4—448no—
708C22×C4—448no—
709C22×C4—444no—
710C22×C4—448no—
711C22×C4C2×C22⋊D1111yescharacteristic
712C22×C4C2×C22⋊D1111yescharacteristic
713C22×C4C2×C22⋊D1111yescharacteristic
714C22×C4C2×C22⋊D1111yescharacteristic
715C22×C4C2×C22⋊D1111yescharacteristic
716C22×C4C2×C22⋊D1111yescharacteristic
717C22×C4C2×C22⋊D1111yescharacteristic
718C22×C4C2×C22⋊D1111yescharacteristic
719C22×C4C2×C22⋊D1111yescharacteristic
720C22×C4C2×C22⋊D1111yescharacteristic
721C22×C4C2×C22⋊D1111yescharacteristic
722C22×C4C2×C22⋊D1111yescharacteristic
723C22×C4C2×C22⋊D1111yescharacteristic
724C22×C4C2×C22⋊D1111yescharacteristic
725C22×C4C2×C22⋊D1111yescharacteristic
726C22×C4C23×D1111yescharacteristic
727C22×C4C23×D1111yescharacteristic
728C22×C4C23×D1111yescharacteristic
729SD16—2216no—
730D8—2216no—
731M16—228no—
732C2×C8—118no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—22no—
738C4⋊C4—22no—
739C4⋊C4—22no—
740C4⋊C4—22no—
741C4⋊C4—22no—
742C4⋊C4—22no—
743C4⋊C4—114no—
744C4⋊C4—222no—
745C4⋊C4—222no—
746C4⋊C4—222no—
747C4⋊C4C23×D1112yes—
748C4⋊C4C23×D1112yes—
749C22⋊C4—22no—
750C22⋊C4—22no—
751C22⋊C4—22no—
752C22⋊C4—22no—
753C22⋊C4—22no—
754C22⋊C4—22no—
755C22⋊C4—22no—
756C22⋊C4—22no—
757C22⋊C4—22no—
758C22⋊C4—224no—
759C22⋊C4—224no—
760C22⋊C4—224no—
761C22⋊C4—224no—
762C42—22no—
763C42—22no—
764C42—22no—
765C42C2×C22⋊D1111yescharacteristic
766C42C2×C22⋊D1111yescharacteristic
767C42C2×C22⋊D1111yescharacteristic
768C42C2×C22⋊D1111yescharacteristic
769C42C2×C22⋊D1111yescharacteristic
770C42C2×C22⋊D1111yescharacteristic
771C42C2×C22⋊D1111yescharacteristic
772C42C2×C22⋊D1111yescharacteristic
773C42C2×C22⋊D1111yescharacteristic
774C42C2×C22⋊D1111yescharacteristic
775C42C2×C22⋊D1111yescharacteristic
776C42C2×C22⋊D1111yescharacteristic
777C42C23×D1111yescharacteristic
778C42C23×D1111yescharacteristic
779C42C23×D1111yescharacteristic
780C42C23×D1111yescharacteristic
781C11#6055811yescharacteristic, complemented, Sylow
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—228no—
787C23—228no—
788C23—228no—
789C23—224no—
790C23—444no—
791C23—444no—
792C23—4432no—
793C23—444no—
794C23—444no—
795C23—444no—
796C23—444no—
797C23C22×C22⋊D1111yescharacteristic
798C23C22×C22⋊D1111yescharacteristic
799C23C22×C22⋊D1111yescharacteristic
800Q8—24no—
801Q8—42no—
802Q8—42no—
803D4—24no—
804D4—42no—
805D4—44no—
806D4—44no—
807D4—44no—
808D4—42no—
809D4—118no—
810D4—228no—
811D4—228no—
812D4—228no—
813D4—224no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—44no—
834C2×C4—44no—
835C2×C4—44no—
836C2×C4—224no—
837C2×C4—448no—
838C2×C4—448no—
839C2×C4—444no—
840C2×C4—444no—
841C2×C4—444no—
842C2×C4—448no—
843C2×C4—448no—
844C2×C4#6700214yescomplemented
845C2×C4#41×D1114yes—
846C2×C4C22×C22⋊D1111yescharacteristic
847C2×C4C22×C22⋊D1111yescharacteristic
848C2×C4C22×C22⋊D1111yescharacteristic
849C2×C4C22×C22⋊D1111yescharacteristic
850C2×C4C22×C22⋊D1111yescharacteristic
851C2×C4C22×C22⋊D1111yescharacteristic
852C2×C4C22×C22⋊D1111yescharacteristic
853C2×C4C22×C22⋊D1111yescharacteristic
854C2×C4C22×C22⋊D1111yescharacteristic
855C2×C4C22×C22⋊D1111yescharacteristic
856C2×C4C22×C22⋊D1111yescharacteristic
857C2×C4C24×D1111yescharacteristic
858C8—228no—
859C22—28no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—228no—
870C22—4416no—
871C22—4416no—
872C22—4416no—
873C22—444no—
874C22—444no—
875C22C2×#6700212yes—
876C22#1062335312yes—
877C22#1062335912yes—
878C22C23×C22⋊D1111yescharacteristic
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—444no—
891C4C2×#6700212yes—
892C4C2×#6700212yes—
893C4#1062335912yes—
894C4C2×#41×D1112yes—
895C2—22no—
896C2—22no—
897C2—22no—
898C2—82no—
899C2—448no—
900C2C2×#1062335911yescharacteristic
901C2C22×#6700211yescharacteristic
902C2C2×#1062335311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3444C2
socleC22×C11C23×D4
hypercenter#3444D11
hypocenterC11#60558
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. C22×C4×D44C2semidirect
2. #13078750C2semidirect
3. #13078711C2semidirect
4. #13078703C2semidirect
5. #13078659C2semidirect
6. #13078620C2semidirect
7. #13078612C2semidirect
8. #13078536C2semidirect
9. #13078409C2semidirect
10. #13078076C2semidirect
11. #13077842C2semidirect
12. C4×#67002C2semidirect
13. #13077249C2semidirect
14. C11×#3444C2semidirect
17. C11×#533C22semidirect
18. C11×#533C22semidirect
19. C11×#533C22semidirect
20. C11×#532C22semidirect
21. C11×#532C22semidirect
22. C11×#532C22semidirect
27. C11×#529C22semidirect
28. C11×#529C22semidirect
34. C4×C11×#41C22semidirect
51. #10622845C22semidirect
53. #10622700C22semidirect
54. #10622697C22semidirect
55. #10622696C22semidirect
56. #10622685C22semidirect
57. #10622679C22semidirect
58. #10622670C22semidirect
61. #10622657C22semidirect
62. #10622656C22semidirect
65. #10622647C22semidirect
66. #10622646C22semidirect
67. #10622639C22semidirect
68. C4×#4325C22semidirect
69. #10622627C22semidirect
70. C4×#4323C22semidirect
72. #10622608C22semidirect
73. #10622539C22semidirect
74. #10622539C22semidirect
75. #10622538C22semidirect
76. #10622538C22semidirect
77. #10622537C22semidirect
78. C4×#4318C22semidirect
101. C11×C4⋊Q8C23semidirect
102. C11×C4⋊Q8C23semidirect
103. C11×C4⋊Q8C23semidirect
104. C11×#127C23semidirect
109. C11×#125C23semidirect
112. C11×#124C23semidirect
133. C4×Q8×C11C23semidirect
134. C4×Q8×C11C23semidirect
145. C4×D4×C11C23semidirect
146. C4×D4×C11C23semidirect
198. #66899C23semidirect
199. #66896C23semidirect
204. #66872C23semidirect
205. #66871C23semidirect
206. C4⋊(C11⋊C8)C23semidirect
207. C4⋊(C11⋊C8)C23semidirect
208. #66867C23semidirect
209. C4×C11⋊C8C23semidirect
267. C2×D44#41semidirect
331. #3444D11semidirect
394. C2×C4×C11AGL(1,ℤ/8)semidirect
425. #533C2×D11semidirect
426. #533C2×D11semidirect
427. #533C2×D11semidirect
428. #532C2×D11semidirect
429. #532C2×D11semidirect
430. #532C2×D11semidirect
435. #529C2×D11semidirect
436. #529C2×D11semidirect
442. C4×#41C2×D11semidirect
548. C4⋊Q8C22×D11semidirect
549. C4⋊Q8C22×D11semidirect
550. C4⋊Q8C22×D11semidirect
551. #127C22×D11semidirect
556. #125C22×D11semidirect
559. #124C22×D11semidirect
580. C4×Q8C22×D11semidirect
581. C4×Q8C22×D11semidirect
608. C4×D4C22×D11semidirect
609. C4×D4C22×D11semidirect
781. C11#60558semidirect
844. C2×C4#67002semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D442
#130787502
#130787112
#130787032
#130786592
#130786202
#130786122
#130785362
#130784092
#130780762
#130778422
C4×#670022
#130772492
C11×#34442
#6055811