Finite Group Databasebeta

← #15624534

Subgroups — #15624534

Order 2816.

2342 conjugacy classes of subgroups.

The subgroup lattice has 1154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623158C211yesmaximal, characteristic
2C2×D11×C22⋊Q8C211yesmaximal, characteristic, complemented
3#13079447C214yesmaximal, complemented
4#13079437C211yesmaximal, characteristic, complemented
5#13079423C211yesmaximal, characteristic, complemented
6#13079418C211yesmaximal, characteristic, complemented
7#13079402C212yesmaximal, complemented
8#13079400C212yesmaximal, complemented
9#13079389C212yesmaximal, complemented
10#13079372C212yesmaximal, complemented
11#13078559C212yesmaximal, complemented
12#13078540C212yesmaximal, complemented
13#13078245C214yesmaximal, complemented
14#13077875C212yesmaximal, complemented
15#13077851C212yesmaximal, complemented
16D11×#407C211yesmaximal, characteristic, complemented
17C11×#3195C211yesmaximal, characteristic, complemented
18C22×#4343C2211yescharacteristic
19C22×Q8×D11C2211yescharacteristic, complemented
20C23×C4×D11C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×#66999C2211yescharacteristic
24C2×#66999C2211yescharacteristic, complemented
25C2×#66983C2211yescharacteristic
26C2×#66977C2211yescharacteristic
27C2×#66971C2214yescomplemented
28C2×M16×D11C2212yescomplemented
29#10623158—21no—
30#10623158—21no—
31#10623158—21no—
32#10623158—21no—
33#10623158C2212yes—
34#10623158C2212yes—
35#10623158C2212yes—
36#10623158C2212yes—
37D11×C22⋊Q8—21no—
38D11×C22⋊Q8—21no—
39D11×C22⋊Q8—21no—
40D11×C22⋊Q8—21no—
41D11×C22⋊Q8C2212yes—
42D11×C22⋊Q8C2212yes—
43D11×C22⋊Q8C2212yescomplemented
44D11×C22⋊Q8C2212yescomplemented
45C2×#66950C2211yescharacteristic, complemented
46C2×#66949—21no—
47C2×#66948C2211yescharacteristic
48C2×#66947—21no—
49C2×#66946—21no—
50C2×#66945C2211yescharacteristic
51C2×C4⋊C4×D11—21no—
52C2×C4⋊C4×D11C2211yescharacteristic, complemented
53C2×#66935—21no—
54C2×(C22⋊D11)⋊C4—21no—
55C2×C22⋊C4×D11—21no—
56C2×#66931—21no—
57C11×#483C2212yescomplemented
58C11×#483C2212yescomplemented
59C11×#470C2214yescomplemented
60C11×#451C2212yescomplemented
61C11×#451C2212yescomplemented
62C11×#407C2211yescharacteristic
63#10622841C2212yescomplemented
64#10622840C2212yescomplemented
65#10622820C2211yescharacteristic
66#10622801C2214yescomplemented
67#10622800C2214yescomplemented
68#10622799C2214yescomplemented
69#10622747C2214yescomplemented
70#10622739C2212yescomplemented
71#10622665C2214yescomplemented
72#10622663C2212yescomplemented
73#10622662C2214yescomplemented
74#10622659C2212yescomplemented
75#10622657C2212yescomplemented
76#10622656C2212yescomplemented
77#10622584C2212yescomplemented
78#10622580C2212yescomplemented
79#10622480C2214yescomplemented
80#10622477C2214yescomplemented
81#10622476C2214yescomplemented
82#10622474C2214yescomplemented
83#10622427C2214yescomplemented
84#10622426C2214yescomplemented
85#10622423C2214yescomplemented
86#10622422C2214yescomplemented
87#10622420C2214yescomplemented
88#10622419C2214yescomplemented
89#10622416C2214yescomplemented
90#10622415C2214yescomplemented
91#10622351C2212yescomplemented
92#10622349C2212yescomplemented
93#10622344C2212yescomplemented
94#10622339C2212yes—
95#10622339C2212yescomplemented
96D11×C22⋊C8C2212yes—
97D11×C22⋊C8C2212yescomplemented
98#10622335C2212yescomplemented
99C24×D11D411yescharacteristic
100C22×Q8×C11C2311yescharacteristic
101C22×Q8×C11C2311yescharacteristic
102C23×C4×C11C2311yescharacteristic
103C22×C22⋊D11—21no—
104C23×Dic11D411yescharacteristic
105C2×#4343—21no—
106C2×#4343—21no—
107C2×#4343—44no—
108C2×#4343C2312yes—
109C2×#4343C2312yes—
110C2×Q8×D11—21no—
111C2×Q8×D11—21no—
112C2×Q8×D11—44no—
113C2×Q8×D11C2312yes—
114C2×Q8×D11C2312yes—
115C22×D44—21no—
116C22×D44—21no—
117C22×D44C2311yescharacteristic
118C22×C4×D11—21no—
119C22×C4×D11—21no—
120C22×C4×D11—21no—
121C22×C4×D11—44no—
122C22×C4×D11D411yescharacteristic
123C22×C4×D11D411yescharacteristic
124C22×C4×D11D411yescharacteristic
125C22×C4×D11D411yescharacteristic
126C22×C4×D11D411yescharacteristic
127C22×C4×D11D411yescharacteristic
128C22×C4×D11C2311yescharacteristic
129C22×C4×D11C2311yescharacteristic
130C22×C4×D11C2311yescharacteristic
131C22×C4×D11C2311yescharacteristic
132C22×C4×D11C2311yescharacteristic
133C22×C4×D11C2311yescharacteristic
134C22×Dic22—21no—
135C22×Dic22C2311yescharacteristic
136C2×C11×Q16C2314yescomplemented
137C2×C11×M16C2312yes—
138C11×C22⋊Q8—21no—
139C11×C22⋊Q8—21no—
140C11×C22⋊Q8—21no—
141C11×C22⋊Q8—21no—
142C11×C22⋊Q8C2312yes—
143C11×C22⋊Q8C2312yes—
144C11×C22⋊Q8C2312yes—
145C11×C22⋊Q8C2312yes—
146C2×C11×C4⋊C4—21no—
147C2×C11×C4⋊C4—21no—
148C2×C11×C4⋊C4C2311yescharacteristic
149C2×C11×C4⋊C4C2311yescharacteristic
150C2×C11×C22⋊C4—21no—
151C2×C11×C22⋊C4—21no—
152C2×C22⋊Dic11—21no—
153#66999—21no—
154#66999—21no—
155#66999—21no—
156#66999—21no—
157#66999C2312yes—
158#66999C2312yes—
159#66999C2312yes—
160#66999C2312yes—
161C2×#4326C2314yescomplemented
162C2×#4325C2314yescomplemented
163#66983—21no—
164#66983—21no—
165#66983C2312yes—
166#66983C2312yes—
167C2×(C2×D11)⋊C4—21no—
168C2×(C2×D11)⋊C4—21no—
169C2×(C2×D11)⋊C4—21no—
170C2×(C2×D11)⋊C4—21no—
171C2×(C2×D11)⋊C4—21no—
172C2×(C2×D11)⋊C4—21no—
173C2×C4⋊Dic11—21no—
174C2×C4⋊Dic11C2311yescharacteristic
175C2×C4⋊Dic11C2311yescharacteristic
176#66977—21no—
177#66977—21no—
178#66977C2312yes—
179#66977C2312yes—
180C2×Dic11⋊C4—21no—
181C2×Dic11⋊C4—21no—
182C2×Dic11⋊C4—21no—
183C2×Dic11⋊C4—21no—
184C2×C4×Dic11—21no—
185C2×#4318C2312yes—
186#66971—48no—
187M16×D11—44no—
188C2×#4314C2314yescomplemented
189C2×#4313C2314yes—
190C2×C8×D11C2314yes—
191#66950—21no—
192#66950—21no—
193#66950C2312yes—
194#66950C2312yes—
195#66949—22no—
196#66949—22no—
197#66949—22no—
198#66949—22no—
199#66948—21no—
200#66948—21no—
201#66948C2312yes—
202#66948C2312yes—
203#66947—22no—
204#66947—22no—
205#66947—22no—
206#66947—22no—
207#66946—22no—
208#66946—22no—
209#66946—22no—
210#66946—22no—
211#66945—21no—
212#66945—21no—
213#66945C2312yes—
214#66945C2312yes—
215C4⋊C4×D11—22no—
216C4⋊C4×D11—22no—
217C4⋊C4×D11—22no—
218C4⋊C4×D11—22no—
219C4⋊C4×D11—21no—
220C4⋊C4×D11—21no—
221C4⋊C4×D11C2312yes—
222C4⋊C4×D11C2312yes—
223#66935—22no—
224#66935—22no—
225#66935—22no—
226#66935—22no—
227(C22⋊D11)⋊C4—22no—
228(C22⋊D11)⋊C4—22no—
229(C22⋊D11)⋊C4—22no—
230(C22⋊D11)⋊C4—22no—
231C22⋊C4×D11—22no—
232C22⋊C4×D11—22no—
233C22⋊C4×D11—22no—
234C22⋊C4×D11—22no—
235#66931—22no—
236#66931—22no—
237#66931—22no—
238#66931—22no—
239C11×#106C2314yescomplemented
240C11×#103C2314yescomplemented
241C11×#103C2314yescomplemented
242C11×C22⋊C8C2312yes—
243C11×C22⋊C8C2312yes—
244#66899C2314yescomplemented
245#66899C2314yescomplemented
246C22⋊(C11⋊C8)C2312yes—
247C22⋊(C11⋊C8)C2312yes—
248#66885C2314yescomplemented
249(C2×D11)⋊C8C2314yes—
250(C2×D11)⋊C8C2314yes—
251#66882C2314yescomplemented
252#66880C2314yescomplemented
253#66874C2314yescomplemented
254#66873C2314yescomplemented
255#66872C2314yescomplemented
256#66871C2314yescomplemented
257#60751—111nomaximal, Sylow
258C24×C11C2×D411yescharacteristic
259C23×D11—24no—
260C23×D11—21no—
261C23×D11—42no—
262C23×D11—42no—
263C23×D11C2×D411yescharacteristic
264C23×D11C2×D411yescharacteristic
265C23×D11C2×D411yescharacteristic
266C23×D11C2×D411yescharacteristic
267C23×D11C2×D411yescharacteristic
268C23×D11C2×D411yescharacteristic
269C2×Q8×C11—21no—
270C2×Q8×C11—21no—
271C2×Q8×C11—42no—
272C2×Q8×C11—42no—
273C2×Q8×C11C2412yes—
274C2×Q8×C11C2412yes—
275C22×C4×C11—21no—
276C22×C4×C11—21no—
277C22×C4×C11—21no—
278C22×C4×C11—21no—
279C22×C4×C11—42no—
280C22×C4×C11C2×D411yescharacteristic
281C22×C4×C11C2×D411yescharacteristic
282C22×C4×C11C2×D411yescharacteristic
283C22×C4×C11C2411yescharacteristic
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2411yescharacteristic
286C2×C22⋊D11—22no—
287C2×C22⋊D11—22no—
288C2×C22⋊D11—44no—
289C22×Dic11—21no—
290C22×Dic11—21no—
291C22×Dic11—21no—
292C22×Dic11—42no—
293C22×Dic11C2×D411yescharacteristic
294C22×Dic11C2×D411yescharacteristic
295C22×Dic11C2×D411yescharacteristic
296C22×Dic11C2×D411yescharacteristic
297C22×Dic11C2×D411yescharacteristic
298C22×Dic11C2×D411yescharacteristic
299#4343—28no—
300#4343—44no—
301#4343—44no—
302#4343—44no—
303Q8×D11—28no—
304Q8×D11—44no—
305Q8×D11—44no—
306Q8×D11—44no—
307C2×D44—22no—
308C2×D44—22no—
309C2×D44—22no—
310C2×D44—22no—
311C2×D44—21no—
312C2×D44—42no—
313C2×D44—44no—
314C2×D44—44no—
315C2×D44C2412yes—
316C2×C4×D11—24no—
317C2×C4×D11—24no—
318C2×C4×D11—24no—
319C2×C4×D11—22no—
320C2×C4×D11—22no—
321C2×C4×D11—22no—
322C2×C4×D11—22no—
323C2×C4×D11—22no—
324C2×C4×D11—22no—
325C2×C4×D11—42no—
326C2×C4×D11—42no—
327C2×C4×D11—42no—
328C2×C4×D11—42no—
329C2×C4×D11—42no—
330C2×C4×D11—42no—
331C2×C4×D11—44no—
332C2×C4×D11—44no—
333C2×C4×D11—42no—
334C2×C4×D11—42no—
335C2×C4×D11—42no—
336C2×C4×D11—44no—
337C2×C4×D11C2×D411yescharacteristic
338C2×C4×D11C2×D411yescharacteristic
339C2×C4×D11C2×D411yescharacteristic
340C2×C4×D11C2×D411yescharacteristic
341C2×C4×D11C2×D411yescharacteristic
342C2×C4×D11C2×D411yescharacteristic
343C2×C4×D11C2×D411yescharacteristic
344C2×C4×D11C2×D411yescharacteristic
345C2×C4×D11C2×D411yescharacteristic
346C2×C4×D11C2×D411yescharacteristic
347C2×C4×D11C2×D411yescharacteristic
348C2×C4×D11C2×D411yescharacteristic
349C2×C4×D11C2411yescharacteristic
350C2×C4×D11C2411yescharacteristic
351C2×C4×D11C2411yescharacteristic
352C2×C4×D11C2411yescharacteristic
353C2×Dic22—22no—
354C2×Dic22—22no—
355C2×Dic22—21no—
356C2×Dic22—42no—
357C2×Dic22—44no—
358C2×Dic22C2412yes—
359C11×Q16—44no—
360C11×M16—42no—
361C2×C8×C11C2414yes—
362C11×C4⋊C4—22no—
363C11×C4⋊C4—22no—
364C11×C4⋊C4—21no—
365C11×C4⋊C4—21no—
366C11×C4⋊C4—22no—
367C11×C4⋊C4—22no—
368C11×C4⋊C4C2412yes—
369C11×C4⋊C4C2412yes—
370C11×C22⋊C4—22no—
371C11×C22⋊C4—22no—
372C11×C22⋊C4—22no—
373C11×C22⋊C4—22no—
374C22⋊Dic11—22no—
375C22⋊Dic11—22no—
376#4326—44no—
377#4325—44no—
378(C2×D11)⋊C4—22no—
379(C2×D11)⋊C4—22no—
380(C2×D11)⋊C4—22no—
381(C2×D11)⋊C4—22no—
382(C2×D11)⋊C4—22no—
383(C2×D11)⋊C4—22no—
384(C2×D11)⋊C4—22no—
385(C2×D11)⋊C4—22no—
386(C2×D11)⋊C4—22no—
387(C2×D11)⋊C4—22no—
388(C2×D11)⋊C4—22no—
389(C2×D11)⋊C4—22no—
390C4⋊Dic11—22no—
391C4⋊Dic11—22no—
392C4⋊Dic11—21no—
393C4⋊Dic11—21no—
394C4⋊Dic11C2412yes—
395C4⋊Dic11C2412yes—
396Dic11⋊C4—22no—
397Dic11⋊C4—22no—
398Dic11⋊C4—22no—
399Dic11⋊C4—22no—
400Dic11⋊C4—22no—
401Dic11⋊C4—22no—
402Dic11⋊C4—22no—
403Dic11⋊C4—22no—
404C4×Dic11—22no—
405C4×Dic11—22no—
406#4318—42no—
407C2×C11⋊C8C2414yes—
408#4314—44no—
409#4313—28no—
410C8×D11—44no—
411C2×#525—111no—
412C22×C22⋊Q8—111no—
413#3196—114no—
414#3195—111no—
415#3195D1111yescharacteristic, complemented
416#3193—111no—
417#3193—111no—
418#3190—112no—
419#3190—112no—
420#3189—112no—
421#3187—112no—
422#3095—112no—
423#3092—112no—
424#3056—114no—
425#3007—112no—
426#3004—112no—
427C2×#407—111no—
428C23×C11—22no—
429C23×C11—22no—
430C23×C11—41no—
431C23×C11C22×D411yescharacteristic
432C23×C11C22×D411yescharacteristic
433C23×C11C22×D411yescharacteristic
434C22×D11—22no—
435C22×D11—22no—
436C22×D11—22no—
437C22×D11—22no—
438C22×D11—22no—
439C22×D11—22no—
440C22×D11—22no—
441C22×D11—22no—
442C22×D11—22no—
443C22×D11—22no—
444C22×D11—22no—
445C22×D11—41no—
446C22×D11—41no—
447C22×D11—41no—
448C22×D11—41no—
449C22×D11—41no—
450C22×D11—41no—
451C22×D11—41no—
452C22×D11—416no—
453C22×D11—42no—
454C22×D11—42no—
455C22×D11—42no—
456C22×D11#13714yescomplemented
457C22×D11C22×D411yescharacteristic
458C22×D11C22×D411yescharacteristic
459C22×D11C22×D411yescharacteristic
460C22×D11C22×D411yescharacteristic
461Q8×C11—24no—
462Q8×C11—24no—
463Q8×C11—42no—
464Q8×C11—42no—
465C2×C4×C11—22no—
466C2×C4×C11—22no—
467C2×C4×C11—22no—
468C2×C4×C11—22no—
469C2×C4×C11—22no—
470C2×C4×C11—22no—
471C2×C4×C11—22no—
472C2×C4×C11—41no—
473C2×C4×C11—41no—
474C2×C4×C11—41no—
475C2×C4×C11—42no—
476C2×C4×C11—42no—
477C2×C4×C11—42no—
478C2×C4×C11—42no—
479C2×C4×C11C22×D411yescharacteristic
480C2×C4×C11C22×D411yescharacteristic
481C2×C4×C11C22×D411yescharacteristic
482C2×C4×C11C2511yescharacteristic
483C22⋊D11—44no—
484C22⋊D11—44no—
485C2×Dic11—22no—
486C2×Dic11—22no—
487C2×Dic11—22no—
488C2×Dic11—22no—
489C2×Dic11—22no—
490C2×Dic11—22no—
491C2×Dic11—41no—
492C2×Dic11—41no—
493C2×Dic11—41no—
494C2×Dic11—42no—
495C2×Dic11—42no—
496C2×Dic11—42no—
497C2×Dic11C22×D411yescharacteristic
498C2×Dic11C22×D411yescharacteristic
499C2×Dic11C22×D411yescharacteristic
500C2×Dic11C22×D411yescharacteristic
501D44—24no—
502D44—42no—
503D44—44no—
504D44—44no—
505D44—44no—
506D44—44no—
507C4×D11—22no—
508C4×D11—22no—
509C4×D11—22no—
510C4×D11—22no—
511C4×D11—22no—
512C4×D11—22no—
513C4×D11—22no—
514C4×D11—22no—
515C4×D11—22no—
516C4×D11—41no—
517C4×D11—41no—
518C4×D11—41no—
519C4×D11—41no—
520C4×D11—41no—
521C4×D11—41no—
522C4×D11—44no—
523C4×D11—44no—
524C4×D11—44no—
525C4×D11—44no—
526C4×D11—44no—
527C4×D11—44no—
528C4×D11H(5,𝔽2)14yes—
529Dic22—24no—
530Dic22—44no—
531Dic22—42no—
532Dic22—44no—
533C8×C11—24no—
534C11⋊C8—24no—
535C22×#41—111no—
536C23×Q8—111no—
537C24×C4—111no—
538C2×#137—114no—
539C22×M16—112no—
540#525—112no—
541#525—112no—
542#525—112no—
543#525—112no—
544#525—221no—
545#525—221no—
546#525—221no—
547#525—221no—
548C2×#123—221no—
549C2×C22⋊Q8—111no—
550C2×C22⋊Q8—111no—
551C2×C22⋊Q8—111no—
552C2×C22⋊Q8—112no—
553C2×C22⋊Q8—112no—
554C2×C22⋊Q8—112no—
555C2×C22⋊Q8—112no—
556C2×C22⋊Q8—111no—
557C2×C22⋊Q8—221no—
558C2×C22⋊Q8—221no—
559C2×C22⋊Q8—221no—
560C2×C22⋊Q8—221no—
561C2×C22⋊Q8—221no—
562C2×C22⋊Q8—221no—
563C2×C22⋊Q8C2×D1111yescharacteristic
564C2×C22⋊Q8C2×D1111yescharacteristic
565C2×#121—111no—
566C2×#121—111no—
567C2×#120—221no—
568C2×C4×D4—221no—
569C2×C4×D4—221no—
570C2×#117—111no—
571C22×C4⋊C4—111no—
572C22×C4⋊C4—221no—
573C22×C22⋊C4—221no—
574#485—114no—
575#485—114no—
576#484—112no—
577#484—114no—
578#484—112no—
579#483—112no—
580#483—112no—
581#483C2×D1112yescomplemented
582#483C2×D1112yescomplemented
583#481—114no—
584#480—112no—
585#480—112no—
586#470—114no—
587#470C2×D1114yescomplemented
588#468—114no—
589#468—114no—
590#467—114no—
591#467—114no—
592#465—114no—
593#465—114no—
594#452—114no—
595#452—114no—
596#451—112no—
597#451—114no—
598#451—112no—
599#451C2×D1112yescomplemented
600#451C2×D1112yescomplemented
601#450—112no—
602#450—112no—
603#448—112no—
604#448—114no—
605#448—112no—
606#428—114no—
607#419—114no—
608#417—114no—
609#407—111no—
610#407—112no—
611#407—112no—
612#407—112no—
613#407C2×D1111yescharacteristic
614C2×C22⋊C8—112no—
615C2×C22⋊C8—112no—
616C22×C11—21no—
617C22×C11—21no—
618C22×C11—21no—
619C22×C11—21no—
620C22×C11—21no—
621C22×C11—21no—
622C22×C11—21no—
623C22×C11—44no—
624C22×C11C2×#13712yes—
625C22×C11#57512yes—
626C22×C11C23×D411yescharacteristic
627C2×D11—28no—
628C2×D11—21no—
629C2×D11—21no—
630C2×D11—21no—
631C2×D11—21no—
632C2×D11—21no—
633C2×D11—21no—
634C2×D11—21no—
635C2×D11—21no—
636C2×D11—21no—
637C2×D11—44no—
638C2×D11—44no—
639C2×D11—44no—
640C2×D11—44no—
641C2×D11—44no—
642C2×D11—42no—
643C2×D11—42no—
644C2×D11—42no—
645C2×D11—84no—
646C2×D11#53412yes—
647C2×D11C2×#13712yes—
648C2×D11C2×#13712yes—
649C4×C11—21no—
650C4×C11—21no—
651C4×C11—21no—
652C4×C11—42no—
653C4×C11—42no—
654C4×C11—42no—
655C4×C11—42no—
656C4×C11C2×H(5,𝔽2)12yes—
657Dic11—21no—
658Dic11—21no—
659Dic11—21no—
660Dic11—42no—
661Dic11—42no—
662Dic11—42no—
663Dic11#53412yes—
664C25—111no—
665C2×#41—112no—
666C2×#41—112no—
667C2×#41—221no—
668C2×#41—221no—
669C2×#41—444no—
670C22×Q8—112no—
671C22×Q8—112no—
672C22×Q8—111no—
673C22×Q8—221no—
674C22×Q8—221no—
675C22×Q8—221no—
676C22×Q8—444no—
677C22×Q8C22×D1111yescharacteristic
678C22×Q8C22×D1111yescharacteristic
679C22×D4—111no—
680C22×D4—221no—
681C22×D4—221no—
682C22×D4—221no—
683C23×C4—111no—
684C23×C4—111no—
685C23×C4—111no—
686C23×C4—111no—
687C23×C4—111no—
688C23×C4—111no—
689C23×C4—111no—
690C23×C4—111no—
691C23×C4—111no—
692C23×C4—111no—
693C23×C4—111no—
694C23×C4—111no—
695C23×C4—111no—
696C23×C4—221no—
697C23×C4—221no—
698C23×C4—221no—
699C23×C4—444no—
700C23×C4C22×D1111yescharacteristic
701#137—448no—
702C2×Q16—114no—
703C2×Q16C22×D1114yescomplemented
704C2×SD16—114no—
705C2×SD16—114no—
706C2×M16—112no—
707C2×M16—114no—
708C2×M16—444no—
709C2×M16C22×D1112yes—
710C22×C8—114no—
711#123—222no—
712#123—222no—
713#123—222no—
714#123—222no—
715C22⋊Q8—21no—
716C22⋊Q8—21no—
717C22⋊Q8—21no—
718C22⋊Q8—21no—
719C22⋊Q8—112no—
720C22⋊Q8—112no—
721C22⋊Q8—112no—
722C22⋊Q8—112no—
723C22⋊Q8—112no—
724C22⋊Q8—112no—
725C22⋊Q8—112no—
726C22⋊Q8—112no—
727C22⋊Q8—222no—
728C22⋊Q8—222no—
729C22⋊Q8—222no—
730C22⋊Q8—222no—
731C22⋊Q8—222no—
732C22⋊Q8—222no—
733C22⋊Q8—222no—
734C22⋊Q8—222no—
735C22⋊Q8—221no—
736C22⋊Q8—221no—
737C22⋊Q8—221no—
738C22⋊Q8—221no—
739C22⋊Q8—221no—
740C22⋊Q8—221no—
741C22⋊Q8—221no—
742C22⋊Q8—221no—
743C22⋊Q8C22×D1112yes—
744C22⋊Q8C22×D1112yes—
745C22⋊Q8C22×D1112yes—
746C22⋊Q8C22×D1112yes—
747#121—112no—
748#121—112no—
749#121—112no—
750#121—112no—
751#121—221no—
752#121—221no—
753#121—221no—
754#121—221no—
755#120—222no—
756#120—222no—
757#120—222no—
758#120—222no—
759C4×D4—222no—
760C4×D4—222no—
761C4×D4—222no—
762C4×D4—222no—
763C4×D4—222no—
764C4×D4—222no—
765C4×D4—222no—
766C4×D4—222no—
767#117—112no—
768#117—112no—
769#117—221no—
770#117—221no—
771C2×C4⋊C4—21no—
772C2×C4⋊C4—21no—
773C2×C4⋊C4—111no—
774C2×C4⋊C4—111no—
775C2×C4⋊C4—112no—
776C2×C4⋊C4—112no—
777C2×C4⋊C4—221no—
778C2×C4⋊C4—221no—
779C2×C4⋊C4—222no—
780C2×C4⋊C4—222no—
781C2×C4⋊C4—222no—
782C2×C4⋊C4—222no—
783C2×C4⋊C4—221no—
784C2×C4⋊C4—221no—
785C2×C4⋊C4—221no—
786C2×C4⋊C4—221no—
787C2×C4⋊C4—221no—
788C2×C4⋊C4C22×D1111yescharacteristic
789C2×C4⋊C4C22×D1111yescharacteristic
790C2×C22⋊C4—21no—
791C2×C22⋊C4—21no—
792C2×C22⋊C4—222no—
793C2×C22⋊C4—222no—
794C2×C22⋊C4—222no—
795C2×C22⋊C4—222no—
796C2×C22⋊C4—221no—
797C2×C22⋊C4—221no—
798C2×C22⋊C4—221no—
799C2×C22⋊C4—221no—
800C2×C22⋊C4—221no—
801C2×C22⋊C4—221no—
802C2×C22⋊C4—221no—
803C2×C42—221no—
804#107—114no—
805#107—114no—
806#106—114no—
807#106C22×D1114yescomplemented
808#103—114no—
809#103—114no—
810#103—114no—
811#103—114no—
812#103C22×D1114yescomplemented
813#103C22×D1114yescomplemented
814#102—114no—
815#102—114no—
816C22⋊C8—112no—
817C22⋊C8—112no—
818C22⋊C8—114no—
819C22⋊C8—114no—
820C22⋊C8C22×D1112yes—
821C22⋊C8C22×D1112yes—
822C2×C11—22no—
823C2×C11—22no—
824C2×C11—41no—
825C2×C11C2×#53411yescharacteristic
826C2×C11C22×#13711yescharacteristic
827C2×C11C2×#57511yescharacteristic
828D11—22no—
829D11—22no—
830D11—22no—
831D11—41no—
832D11—82no—
833C24—111no—
834C24—111no—
835C24—111no—
836C24—111no—
837C24—111no—
838C24—111no—
839C24—224no—
840C24—221no—
841C24—442no—
842C24—442no—
843C24D4×D1111yescharacteristic
844#41—228no—
845#41—444no—
846#41—444no—
847#41—444no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—42no—
851C2×Q8—42no—
852C2×Q8—112no—
853C2×Q8—222no—
854C2×Q8—222no—
855C2×Q8—228no—
856C2×Q8—221no—
857C2×Q8—442no—
858C2×Q8—444no—
859C2×Q8—444no—
860C2×Q8—444no—
861C2×Q8—444no—
862C2×Q8C23×D1112yes—
863C2×Q8C23×D1112yes—
864C2×D4—112no—
865C2×D4—222no—
866C2×D4—222no—
867C2×D4—222no—
868C2×D4—222no—
869C2×D4—222no—
870C2×D4—222no—
871C2×D4—221no—
872C2×D4—442no—
873C2×D4—444no—
874C2×D4—444no—
875C2×D4—444no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—42no—
881C22×C4—111no—
882C22×C4—111no—
883C22×C4—111no—
884C22×C4—111no—
885C22×C4—111no—
886C22×C4—111no—
887C22×C4—111no—
888C22×C4—111no—
889C22×C4—111no—
890C22×C4—111no—
891C22×C4—111no—
892C22×C4—111no—
893C22×C4—111no—
894C22×C4—111no—
895C22×C4—111no—
896C22×C4—111no—
897C22×C4—111no—
898C22×C4—111no—
899C22×C4—111no—
900C22×C4—111no—
901C22×C4—111no—
902C22×C4—111no—
903C22×C4—224no—
904C22×C4—224no—
905C22×C4—224no—
906C22×C4—222no—
907C22×C4—222no—
908C22×C4—222no—
909C22×C4—222no—
910C22×C4—222no—
911C22×C4—222no—
912C22×C4—221no—
913C22×C4—221no—
914C22×C4—221no—
915C22×C4—442no—
916C22×C4—442no—
917C22×C4—442no—
918C22×C4—442no—
919C22×C4—442no—
920C22×C4—442no—
921C22×C4—442no—
922C22×C4—442no—
923C22×C4—442no—
924C22×C4—444no—
925C22×C4—444no—
926C22×C4—444no—
927C22×C4—442no—
928C22×C4D4×D1111yescharacteristic
929C22×C4D4×D1111yescharacteristic
930C22×C4D4×D1111yescharacteristic
931C22×C4C23×D1111yescharacteristic
932C22×C4C23×D1111yescharacteristic
933C22×C4C23×D1111yescharacteristic
934Q16—44no—
935Q16—444no—
936SD16—444no—
937SD16—444no—
938M16—42no—
939M16—228no—
940M16—442no—
941C2×C8—114no—
942C2×C8—444no—
943C2×C8C23×D1114yes—
944C4⋊C4—22no—
945C4⋊C4—22no—
946C4⋊C4—22no—
947C4⋊C4—22no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—112no—
951C4⋊C4—112no—
952C4⋊C4—222no—
953C4⋊C4—222no—
954C4⋊C4—222no—
955C4⋊C4—222no—
956C4⋊C4—222no—
957C4⋊C4—222no—
958C4⋊C4—222no—
959C4⋊C4—222no—
960C4⋊C4—221no—
961C4⋊C4—221no—
962C4⋊C4—222no—
963C4⋊C4—222no—
964C4⋊C4C23×D1112yes—
965C4⋊C4C23×D1112yes—
966C22⋊C4—22no—
967C22⋊C4—22no—
968C22⋊C4—22no—
969C22⋊C4—22no—
970C22⋊C4—222no—
971C22⋊C4—222no—
972C22⋊C4—222no—
973C22⋊C4—222no—
974C22⋊C4—222no—
975C22⋊C4—222no—
976C22⋊C4—222no—
977C22⋊C4—222no—
978C22⋊C4—222no—
979C22⋊C4—222no—
980C22⋊C4—222no—
981C22⋊C4—222no—
982C22⋊C4—222no—
983C22⋊C4—222no—
984C42—222no—
985C42—222no—
986C11#6075111yescharacteristic, complemented, Sylow
987C23—22no—
988C23—22no—
989C23—41no—
990C23—111no—
991C23—111no—
992C23—111no—
993C23—114no—
994C23—111no—
995C23—222no—
996C23—222no—
997C23—222no—
998C23—222no—
999C23—222no—
1000C23—222no—
1001C23—222no—
1002C23—222no—
1003C23—222no—
1004C23—222no—
1005C23—222no—
1006C23—441no—
1007C23—441no—
1008C23—441no—
1009C23—441no—
1010C23—441no—
1011C23—441no—
1012C23—441no—
1013C23—442no—
1014C23—442no—
1015C23—4416no—
1016C23—442no—
1017C23C2×D4×D1111yescharacteristic
1018C23C2×D4×D1111yescharacteristic
1019C23C2×D4×D1111yescharacteristic
1020Q8—24no—
1021Q8—24no—
1022Q8—42no—
1023Q8—42no—
1024Q8—224no—
1025Q8—442no—
1026Q8—444no—
1027Q8—444no—
1028D4—224no—
1029D4—442no—
1030D4—444no—
1031D4—444no—
1032D4—444no—
1033D4—444no—
1034D4—444no—
1035D4—444no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—42no—
1047C2×C4—42no—
1048C2×C4—42no—
1049C2×C4—42no—
1050C2×C4—111no—
1051C2×C4—114no—
1052C2×C4—111no—
1053C2×C4—111no—
1054C2×C4—111no—
1055C2×C4—222no—
1056C2×C4—222no—
1057C2×C4—222no—
1058C2×C4—222no—
1059C2×C4—222no—
1060C2×C4—222no—
1061C2×C4—222no—
1062C2×C4—222no—
1063C2×C4—222no—
1064C2×C4—222no—
1065C2×C4—222no—
1066C2×C4—222no—
1067C2×C4—222no—
1068C2×C4—222no—
1069C2×C4—222no—
1070C2×C4—441no—
1071C2×C4—441no—
1072C2×C4—441no—
1073C2×C4—441no—
1074C2×C4—441no—
1075C2×C4—441no—
1076C2×C4—444no—
1077C2×C4—444no—
1078C2×C4—444no—
1079C2×C4—444no—
1080C2×C4—444no—
1081C2×C4—444no—
1082C2×C4—441no—
1083C2×C4—441no—
1084C2×C4—441no—
1085C2×C4—442no—
1086C2×C4—442no—
1087C2×C4—442no—
1088C2×C4C2×D4×D1111yescharacteristic
1089C2×C4C2×D4×D1111yescharacteristic
1090C2×C4C2×D4×D1111yescharacteristic
1091C2×C4C24×D1111yescharacteristic
1092C8—24no—
1093C8—224no—
1094C22—21no—
1095C22—21no—
1096C22—21no—
1097C22—21no—
1098C22—21no—
1099C22—21no—
1100C22—21no—
1101C22—44no—
1102C22—112no—
1103C22—112no—
1104C22—112no—
1105C22—228no—
1106C22—221no—
1107C22—221no—
1108C22—221no—
1109C22—221no—
1110C22—221no—
1111C22—221no—
1112C22—221no—
1113C22—221no—
1114C22—221no—
1115C22—444no—
1116C22—444no—
1117C22—444no—
1118C22—444no—
1119C22—444no—
1120C22—442no—
1121C22—442no—
1122C22—442no—
1123C22—884no—
1124C22D11×#13712yes—
1125C22#1062330812yes—
1126C22C22×D4×D1111yescharacteristic
1127C4—21no—
1128C4—21no—
1129C4—21no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—112no—
1135C4—221no—
1136C4—221no—
1137C4—221no—
1138C4—442no—
1139C4—442no—
1140C4—442no—
1141C4D11×H(5,𝔽2)12yes—
1142C2—22no—
1143C2—22no—
1144C2—41no—
1145C2—222no—
1146C2—222no—
1147C2—222no—
1148C2—441no—
1149C2—882no—
1150C2D11×#53411yescharacteristic
1151C2C2×D11×#13711yescharacteristic
1152C2C2×#1062330811yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3195C2
socleC22×C11C23×D4
prime radicalC2×#10623158C2
hypercenter#3195D11
hypocenterC11#60751
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3195

Complements

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

NH ≅ G/Ntype
2. C2×D11×C22⋊Q8C2semidirect
3. #13079447C2semidirect
4. #13079437C2semidirect
5. #13079423C2semidirect
6. #13079418C2semidirect
7. #13079402C2semidirect
8. #13079400C2semidirect
9. #13079389C2semidirect
10. #13079372C2semidirect
11. #13078559C2semidirect
12. #13078540C2semidirect
13. #13078245C2semidirect
14. #13077875C2semidirect
15. #13077851C2semidirect
16. D11×#407C2semidirect
17. C11×#3195C2semidirect
19. C22×Q8×D11C22semidirect
24. C2×#66999C22semidirect
27. C2×#66971C22semidirect
28. C2×M16×D11C22semidirect
43. D11×C22⋊Q8C22semidirect
44. D11×C22⋊Q8C22semidirect
45. C2×#66950C22semidirect
52. C2×C4⋊C4×D11C22semidirect
57. C11×#483C22semidirect
58. C11×#483C22semidirect
59. C11×#470C22semidirect
60. C11×#451C22semidirect
61. C11×#451C22semidirect
63. #10622841C22semidirect
64. #10622840C22semidirect
66. #10622801C22semidirect
67. #10622800C22semidirect
68. #10622799C22semidirect
69. #10622747C22semidirect
70. #10622739C22semidirect
71. #10622665C22semidirect
72. #10622663C22semidirect
73. #10622662C22semidirect
74. #10622659C22semidirect
75. #10622657C22semidirect
76. #10622656C22semidirect
77. #10622584C22semidirect
78. #10622580C22semidirect
79. #10622480C22semidirect
80. #10622477C22semidirect
81. #10622476C22semidirect
82. #10622474C22semidirect
83. #10622427C22semidirect
84. #10622426C22semidirect
85. #10622423C22semidirect
86. #10622422C22semidirect
87. #10622420C22semidirect
88. #10622419C22semidirect
89. #10622416C22semidirect
90. #10622415C22semidirect
91. #10622351C22semidirect
92. #10622349C22semidirect
93. #10622344C22semidirect
95. #10622339C22semidirect
97. D11×C22⋊C8C22semidirect
98. #10622335C22semidirect
136. C2×C11×Q16C23semidirect
161. C2×#4326C23semidirect
162. C2×#4325C23semidirect
188. C2×#4314C23semidirect
239. C11×#106C23semidirect
240. C11×#103C23semidirect
241. C11×#103C23semidirect
244. #66899C23semidirect
245. #66899C23semidirect
248. #66885C23semidirect
251. #66882C23semidirect
252. #66880C23semidirect
253. #66874C23semidirect
254. #66873C23semidirect
255. #66872C23semidirect
256. #66871C23semidirect
415. #3195D11semidirect
456. C22×D11#137semidirect
581. #483C2×D11semidirect
582. #483C2×D11semidirect
587. #470C2×D11semidirect
599. #451C2×D11semidirect
600. #451C2×D11semidirect
703. C2×Q16C22×D11semidirect
807. #106C22×D11semidirect
812. #103C22×D11semidirect
813. #103C22×D11semidirect
986. C11#60751semidirect

Maximal subgroups

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

subgroupindex
C2×#106231582
C2×D11×C22⋊Q82
#130794472
#130794372
#130794232
#130794182
#130794022
#130794002
#130793892
#130793722
#130785592
#130785402
#130782452
#130778752
#130778512
D11×#4072
C11×#31952
#6075111