Finite Group Databasebeta

← #15624410

Subgroups — #15624410

Order 2816.

2362 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic, complemented
2#13079453C214yesmaximal, complemented
3#13079446C212yesmaximal, complemented
4#13079442C212yesmaximal, complemented
5#13079437C211yesmaximal, characteristic, complemented
6#13079430C212yesmaximal, complemented
7#13079426C212yesmaximal, complemented
8#13079422C211yesmaximal, characteristic, complemented
9#13079418C211yesmaximal, characteristic, complemented
10#13079413C211yesmaximal, characteristic, complemented
11#13078529C212yesmaximal, complemented
12#13078525C212yesmaximal, complemented
13#13078222C214yesmaximal, complemented
14#13077834C212yesmaximal, complemented
15#13077832C212yesmaximal, complemented
16C2×#10622820C211yesmaximal, characteristic, complemented
17C2×C11×#525C211yesmaximal, characteristic, complemented
18C22×C11×#41C2211yescharacteristic, complemented
19C24×C4×C11C2211yescharacteristic
20C22×#4339C2211yescharacteristic, complemented
21C11×#525—21no—
22C11×#525—21no—
23C11×#525—21no—
24C11×#525—21no—
25C11×#525C2212yes—
26C11×#525C2212yes—
27C11×#525C2212yescomplemented
28C11×#525C2212yescomplemented
29C2×C11×#123—21no—
30C2×C11×C22⋊Q8C2211yescharacteristic
31C2×C11×C22⋊Q8C2211yescharacteristic, complemented
32C2×C11×#121C2211yescharacteristic
33C2×C11×#121C2211yescharacteristic, complemented
34C2×C11×#120—21no—
35C2×C4×D4×C11—21no—
36C2×C4×D4×C11—21no—
37C2×C11×#117C2211yescharacteristic, complemented
38C2×#67006—21no—
39C2×#67003C2214yescomplemented
40#10623322—21no—
41#10623322—21no—
42#10623322—21no—
43#10623322—21no—
44#10623322C2212yes—
45#10623322C2212yes—
46#10623322C2212yescomplemented
47#10623322C2212yescomplemented
48C2×#66983C2211yescharacteristic
49C2×#66983C2211yescharacteristic, complemented
50C2×#66982—21no—
51C2×C4×C22⋊D11—21no—
52C2×C4×C22⋊D11—21no—
53C2×#66979C2211yescharacteristic, complemented
54C2×#66977C2211yescharacteristic
55C2×#66977C2211yescharacteristic, complemented
56C22×#4318C2212yescomplemented
57#10622852C2214yescomplemented
58#10622851C2214yescomplemented
59#10622846C2214yescomplemented
60#10622841C2212yescomplemented
61#10622840C2212yescomplemented
62#10622831C2212yescomplemented
63#10622830C2212yescomplemented
64#10622820C2211yescharacteristic
65#10622820C2211yescharacteristic
66#10622820C2212yescomplemented
67#10622820C2212yescomplemented
68#10622820C2212yescomplemented
69C2×C22⋊(C11⋊C8)C2212yescomplemented
70C2×C22⋊(C11⋊C8)C2212yescomplemented
71#10622665C2214yescomplemented
72#10622665C2214yescomplemented
73#10622663C2212yescomplemented
74#10622662C2214yescomplemented
75#10622662C2214yescomplemented
76#10622660C2214yescomplemented
77#10622659C2212yescomplemented
78#10622658C2214yescomplemented
79#10622657C2212yescomplemented
80#10622656C2212yescomplemented
81#10622655C2214yescomplemented
82#10622655C2214yescomplemented
83#10622653C2212yescomplemented
84#10622652C2214yescomplemented
85#10622652C2214yescomplemented
86#10622650C2214yescomplemented
87#10622649C2212yescomplemented
88#10622648C2214yescomplemented
89#10622647C2212yescomplemented
90#10622646C2212yescomplemented
91#10622616C2214yescomplemented
92#10622615C2214yescomplemented
93#10622611C2214yescomplemented
94#10622609C2214yescomplemented
95#10622584C2212yescomplemented
96#10622583C2212yescomplemented
97#10622581C2212yescomplemented
98#10622580C2212yescomplemented
99C25×C11D411yescharacteristic
100C2×C11×#41—21no—
101C2×C11×#41—21no—
102C2×C11×#41—44no—
103C2×C11×#41C2312yes—
104C2×C11×#41C2312yes—
105C22×Q8×C11C2311yescharacteristic
106C22×D4×C11—21no—
107C22×D4×C11—21no—
108C22×D4×C11—21no—
109C22×D4×C11C2311yescharacteristic
110C23×C4×C11—21no—
111C23×C4×C11—44no—
112C23×C4×C11D411yescharacteristic
113C23×C4×C11D411yescharacteristic
114C23×C4×C11D411yescharacteristic
115C23×C4×C11D411yescharacteristic
116C23×C4×C11D411yescharacteristic
117C23×C4×C11D411yescharacteristic
118C23×C4×C11D411yescharacteristic
119C23×C4×C11C2311yescharacteristic
120C23×C4×C11C2311yescharacteristic
121C23×C4×C11C2311yescharacteristic
122C23×C4×C11C2311yescharacteristic
123C23×C4×C11C2311yescharacteristic
124C23×C4×C11C2311yescharacteristic
125C23×C4×C11C2311yescharacteristic
126C22×C22⋊D11—21no—
127C22×C22⋊D11—21no—
128C22×C22⋊D11—21no—
129C2×#4339—21no—
130C2×#4339—21no—
131C2×#4339—44no—
132C2×#4339C2312yes—
133C2×#4339C2312yes—
134C22×D44C2311yescharacteristic
135C22×C4×D11—21no—
136C22×Dic22C2311yescharacteristic
137C11×#123—22no—
138C11×#123—22no—
139C11×#123—22no—
140C11×#123—22no—
141C11×C22⋊Q8—21no—
142C11×C22⋊Q8—21no—
143C11×C22⋊Q8—21no—
144C11×C22⋊Q8—21no—
145C11×C22⋊Q8C2312yes—
146C11×C22⋊Q8C2312yes—
147C11×C22⋊Q8C2312yes—
148C11×C22⋊Q8C2312yes—
149C11×#121—21no—
150C11×#121—21no—
151C11×#121—21no—
152C11×#121—21no—
153C11×#121C2312yes—
154C11×#121C2312yes—
155C11×#121C2312yes—
156C11×#121C2312yes—
157C11×#120—22no—
158C11×#120—22no—
159C11×#120—22no—
160C11×#120—22no—
161C4×D4×C11—22no—
162C4×D4×C11—22no—
163C4×D4×C11—22no—
164C4×D4×C11—22no—
165C4×D4×C11—22no—
166C4×D4×C11—22no—
167C4×D4×C11—22no—
168C4×D4×C11—22no—
169C11×#117—21no—
170C11×#117—21no—
171C11×#117C2312yes—
172C11×#117C2312yes—
173C2×C11×C4⋊C4—21no—
174C2×C11×C4⋊C4—21no—
175C2×C11×C4⋊C4C2311yescharacteristic
176C2×C11×C4⋊C4C2311yescharacteristic
177C2×C11×C22⋊C4—21no—
178C2×C11×C22⋊C4—21no—
179C2×C11×C22⋊C4—21no—
180C2×C11×C22⋊C4—21no—
181C2×C11×C22⋊C4—21no—
182C2×C42×C11—21no—
183#67006—22no—
184#67006—22no—
185#67006—22no—
186#67006—22no—
187C2×C22⋊Dic11—21no—
188C2×C22⋊Dic11—21no—
189C2×C22⋊Dic11—21no—
190#67003—48no—
191C2×#4326C2314yescomplemented
192C2×#4325C2314yescomplemented
193C2×#4324C2314yescomplemented
194C2×#4323C2314yescomplemented
195#66983—21no—
196#66983—21no—
197#66983—21no—
198#66983—21no—
199#66983C2312yes—
200#66983C2312yes—
201#66983C2312yes—
202#66983C2312yes—
203#66982—22no—
204#66982—22no—
205#66982—22no—
206#66982—22no—
207C4×C22⋊D11—22no—
208C4×C22⋊D11—22no—
209C4×C22⋊D11—22no—
210C4×C22⋊D11—22no—
211C4×C22⋊D11—22no—
212C4×C22⋊D11—22no—
213C4×C22⋊D11—22no—
214C4×C22⋊D11—22no—
215C2×(C2×D11)⋊C4—21no—
216C2×(C2×D11)⋊C4—21no—
217#66979—21no—
218#66979—21no—
219#66979C2312yes—
220#66979C2312yes—
221C2×C4⋊Dic11C2311yescharacteristic
222C2×C4⋊Dic11C2311yescharacteristic
223#66977—21no—
224#66977—21no—
225#66977—21no—
226#66977—21no—
227#66977C2312yes—
228#66977C2312yes—
229#66977C2312yes—
230#66977C2312yes—
231C2×Dic11⋊C4—21no—
232C2×Dic11⋊C4—21no—
233C2×C4×Dic11—21no—
234C2×#4318—44no—
235C2×#4318C2312yes—
236C2×#4318C2312yes—
237C2×#4318C2314yes—
238C22×C11⋊C8C2314yes—
239#66899C2314yescomplemented
240#66899C2314yescomplemented
241#66896C2314yescomplemented
242#66896C2314yescomplemented
243C22⋊(C11⋊C8)C2312yes—
244C22⋊(C11⋊C8)C2312yes—
245C22⋊(C11⋊C8)C2312yes—
246C22⋊(C11⋊C8)C2312yes—
247C22⋊(C11⋊C8)C2314yes—
248C22⋊(C11⋊C8)C2314yes—
249#66874C2314yescomplemented
250#66874C2314yescomplemented
251#66873C2314yescomplemented
252#66873C2314yescomplemented
253#66872C2314yescomplemented
254#66872C2314yescomplemented
255#66871C2314yescomplemented
256#66871C2314yescomplemented
257#60741—111nomaximal, Sylow
258C24×C11—21no—
259C24×C11—42no—
260C24×C11—42no—
261C24×C11—42no—
262C24×C11C2×D411yescharacteristic
263C24×C11C2×D411yescharacteristic
264C24×C11C2×D411yescharacteristic
265C24×C11C2×D411yescharacteristic
266C24×C11C2×D411yescharacteristic
267C24×C11C2×D411yescharacteristic
268C24×C11C2×D411yescharacteristic
269C23×D11—21no—
270C11×#41—28no—
271C11×#41—44no—
272C11×#41—44no—
273C11×#41—44no—
274C2×Q8×C11—21no—
275C2×Q8×C11—42no—
276C2×Q8×C11C2412yes—
277C2×D4×C11—22no—
278C2×D4×C11—22no—
279C2×D4×C11—22no—
280C2×D4×C11—22no—
281C2×D4×C11—22no—
282C2×D4×C11—22no—
283C2×D4×C11—21no—
284C2×D4×C11—42no—
285C2×D4×C11—44no—
286C2×D4×C11—44no—
287C2×D4×C11—44no—
288C2×D4×C11C2412yes—
289C22×C4×C11—24no—
290C22×C4×C11—24no—
291C22×C4×C11—24no—
292C22×C4×C11—21no—
293C22×C4×C11—21no—
294C22×C4×C11—21no—
295C22×C4×C11—22no—
296C22×C4×C11—22no—
297C22×C4×C11—42no—
298C22×C4×C11—42no—
299C22×C4×C11—42no—
300C22×C4×C11—42no—
301C22×C4×C11—42no—
302C22×C4×C11—42no—
303C22×C4×C11—42no—
304C22×C4×C11—42no—
305C22×C4×C11—42no—
306C22×C4×C11—42no—
307C22×C4×C11—42no—
308C22×C4×C11—44no—
309C22×C4×C11C2×D411yescharacteristic
310C22×C4×C11C2×D411yescharacteristic
311C22×C4×C11C2×D411yescharacteristic
312C22×C4×C11C2×D411yescharacteristic
313C22×C4×C11C2×D411yescharacteristic
314C22×C4×C11C2×D411yescharacteristic
315C22×C4×C11C2×D411yescharacteristic
316C22×C4×C11C2×D411yescharacteristic
317C22×C4×C11C2×D411yescharacteristic
318C22×C4×C11C2×D411yescharacteristic
319C22×C4×C11C2×D411yescharacteristic
320C22×C4×C11C2×D411yescharacteristic
321C22×C4×C11C2×D411yescharacteristic
322C22×C4×C11C2×D411yescharacteristic
323C22×C4×C11C2×D411yescharacteristic
324C22×C4×C11C2×D411yescharacteristic
325C22×C4×C11C2×D411yescharacteristic
326C22×C4×C11C2×D411yescharacteristic
327C22×C4×C11C2×D411yescharacteristic
328C22×C4×C11C2×D411yescharacteristic
329C22×C4×C11C2×D411yescharacteristic
330C22×C4×C11C2411yescharacteristic
331C22×C4×C11C2411yescharacteristic
332C22×C4×C11C2411yescharacteristic
333C22×C4×C11C2411yescharacteristic
334C22×C4×C11C2411yescharacteristic
335C22×C4×C11C2411yescharacteristic
336C22×C4×C11C2411yescharacteristic
337C2×C22⋊D11—22no—
338C2×C22⋊D11—22no—
339C2×C22⋊D11—22no—
340C2×C22⋊D11—22no—
341C2×C22⋊D11—22no—
342C2×C22⋊D11—22no—
343C2×C22⋊D11—44no—
344C2×C22⋊D11—44no—
345C2×C22⋊D11—44no—
346C22×Dic11—21no—
347C22×Dic11—21no—
348C22×Dic11—21no—
349#4339—28no—
350#4339—44no—
351#4339—44no—
352#4339—44no—
353C2×D44—21no—
354C2×D44—42no—
355C2×D44C2412yes—
356C2×C4×D11—22no—
357C2×C4×D11—22no—
358C2×C4×D11—44no—
359C2×Dic22—21no—
360C2×Dic22—42no—
361C2×Dic22C2412yes—
362C11×C4⋊C4—22no—
363C11×C4⋊C4—22no—
364C11×C4⋊C4—22no—
365C11×C4⋊C4—22no—
366C11×C4⋊C4—21no—
367C11×C4⋊C4—21no—
368C11×C4⋊C4C2412yes—
369C11×C4⋊C4C2412yes—
370C11×C22⋊C4—22no—
371C11×C22⋊C4—22no—
372C11×C22⋊C4—22no—
373C11×C22⋊C4—22no—
374C11×C22⋊C4—22no—
375C11×C22⋊C4—22no—
376C11×C22⋊C4—22no—
377C11×C22⋊C4—22no—
378C11×C22⋊C4—22no—
379C11×C22⋊C4—22no—
380C42×C11—22no—
381C42×C11—22no—
382C22⋊Dic11—22no—
383C22⋊Dic11—22no—
384C22⋊Dic11—22no—
385C22⋊Dic11—22no—
386C22⋊Dic11—22no—
387C22⋊Dic11—22no—
388#4326—44no—
389#4325—44no—
390#4324—44no—
391#4323—44no—
392(C2×D11)⋊C4—22no—
393(C2×D11)⋊C4—22no—
394(C2×D11)⋊C4—22no—
395(C2×D11)⋊C4—22no—
396C4⋊Dic11—21no—
397C4⋊Dic11—21no—
398C4⋊Dic11C2412yes—
399C4⋊Dic11C2412yes—
400Dic11⋊C4—22no—
401Dic11⋊C4—22no—
402Dic11⋊C4—22no—
403Dic11⋊C4—22no—
404C4×Dic11—22no—
405C4×Dic11—22no—
406#4318—42no—
407#4318—44no—
408#4318—42no—
409C2×C11⋊C8—28no—
410C2×C11⋊C8C2414yes—
411C2×C11⋊C8C2414yes—
412C2×#525—111no—
413C2×#525D1111yescharacteristic, complemented
414#3197—114no—
415#3196—112no—
416#3196—112no—
417#3195—111no—
418#3194—112no—
419#3194—112no—
420#3193—111no—
421#3193—111no—
422#3192—111no—
423#3091—112no—
424#3091—112no—
425#3054—114no—
426#3002—112no—
427#3002—112no—
428C2×#407—111no—
429C23×C11—22no—
430C23×C11—22no—
431C23×C11—22no—
432C23×C11—22no—
433C23×C11—22no—
434C23×C11—22no—
435C23×C11—22no—
436C23×C11—22no—
437C23×C11—22no—
438C23×C11—22no—
439C23×C11—41no—
440C23×C11—41no—
441C23×C11—41no—
442C23×C11—41no—
443C23×C11—41no—
444C23×C11—41no—
445C23×C11—41no—
446C23×C11—41no—
447C23×C11—41no—
448C23×C11—41no—
449C23×C11—41no—
450C23×C11—41no—
451C23×C11—42no—
452C23×C11—42no—
453C23×C11—416no—
454C23×C11—42no—
455C23×C11C22×D411yescharacteristic
456C23×C11C22×D411yescharacteristic
457C23×C11C22×D411yescharacteristic
458C23×C11C22×D411yescharacteristic
459C23×C11C22×D411yescharacteristic
460C23×C11C22×D411yescharacteristic
461C23×C11C22×D411yescharacteristic
462C22×D11—22no—
463C22×D11—42no—
464C22×D11—42no—
465C22×D11—42no—
466Q8×C11—24no—
467Q8×C11—42no—
468D4×C11—24no—
469D4×C11—42no—
470D4×C11—44no—
471D4×C11—44no—
472D4×C11—44no—
473D4×C11—44no—
474D4×C11—44no—
475D4×C11—44no—
476C2×C4×C11—22no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—22no—
480C2×C4×C11—22no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—41no—
495C2×C4×C11—41no—
496C2×C4×C11—41no—
497C2×C4×C11—41no—
498C2×C4×C11—41no—
499C2×C4×C11—41no—
500C2×C4×C11—41no—
501C2×C4×C11—41no—
502C2×C4×C11—41no—
503C2×C4×C11—41no—
504C2×C4×C11—41no—
505C2×C4×C11—41no—
506C2×C4×C11—44no—
507C2×C4×C11—42no—
508C2×C4×C11—42no—
509C2×C4×C11—42no—
510C2×C4×C11—44no—
511C2×C4×C11C22×D411yescharacteristic
512C2×C4×C11C22×D411yescharacteristic
513C2×C4×C11C22×D411yescharacteristic
514C2×C4×C11C22×D411yescharacteristic
515C2×C4×C11C22×D411yescharacteristic
516C2×C4×C11C22×D411yescharacteristic
517C2×C4×C11C22×D411yescharacteristic
518C2×C4×C11H(5,𝔽2)14yes—
519C2×C4×C11C2511yescharacteristic
520C22⋊D11—44no—
521C22⋊D11—44no—
522C22⋊D11—44no—
523C22⋊D11—44no—
524C22⋊D11—44no—
525C22⋊D11—44no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—42no—
530C2×Dic11—42no—
531C2×Dic11—42no—
532D44—24no—
533D44—42no—
534C4×D11—44no—
535C4×D11—44no—
536Dic22—24no—
537Dic22—42no—
538C11⋊C8—24no—
539C11⋊C8—24no—
540C22×#41—111no—
541C22×#41C2×D1111yescharacteristic, complemented
542C24×C4C2×D1111yescharacteristic
543C2×#135—114no—
544C22×M16—112no—
545#525—21no—
546#525—21no—
547#525—21no—
548#525—21no—
549#525—112no—
550#525—112no—
551#525—112no—
552#525—112no—
553#525—221no—
554#525—221no—
555#525—221no—
556#525—221no—
557#525C2×D1112yes—
558#525C2×D1112yes—
559#525C2×D1112yescomplemented
560#525C2×D1112yescomplemented
561C2×#123—21no—
562C2×#123—221no—
563C2×C22⋊Q8—111no—
564C2×C22⋊Q8—111no—
565C2×C22⋊Q8C2×D1111yescharacteristic
566C2×C22⋊Q8C2×D1111yescharacteristic, complemented
567C2×#121—111no—
568C2×#121—111no—
569C2×#121C2×D1111yescharacteristic
570C2×#121C2×D1111yescharacteristic, complemented
571C2×#120—21no—
572C2×#120—221no—
573C2×C4×D4—21no—
574C2×C4×D4—21no—
575C2×C4×D4—221no—
576C2×C4×D4—221no—
577C2×#117—111no—
578C2×#117C2×D1111yescharacteristic, complemented
579#485—114no—
580#485—114no—
581#484—112no—
582#484—112no—
583#483—112no—
584#483—112no—
585#482—114no—
586#482—114no—
587#481—112no—
588#481—112no—
589#480—112no—
590#480—112no—
591#470—114no—
592#470—114no—
593#469—114no—
594#469—114no—
595#468—114no—
596#468—114no—
597#468—114no—
598#468—114no—
599#452—114no—
600#452—114no—
601#451—112no—
602#451—112no—
603#450—112no—
604#450—112no—
605#449—114no—
606#449—114no—
607#448—112no—
608#448—112no—
609#447—112no—
610#447—112no—
611#427—114no—
612#416—114no—
613#416—114no—
614#407—111no—
615#407—111no—
616#407—112no—
617#407—112no—
618#407—112no—
619C2×C22⋊C8—112no—
620C2×C22⋊C8—112no—
621C22×C11—21no—
622C22×C11—21no—
623C22×C11—21no—
624C22×C11—21no—
625C22×C11—21no—
626C22×C11—21no—
627C22×C11—21no—
628C22×C11—21no—
629C22×C11—21no—
630C22×C11—21no—
631C22×C11—21no—
632C22×C11—21no—
633C22×C11—21no—
634C22×C11—21no—
635C22×C11—21no—
636C22×C11—21no—
637C22×C11—21no—
638C22×C11—21no—
639C22×C11—44no—
640C22×C11—44no—
641C22×C11—44no—
642C22×C11—44no—
643C22×C11—44no—
644C22×C11—44no—
645C22×C11—44no—
646C22×C11—42no—
647C22×C11—42no—
648C22×C11—42no—
649C22×C11—84no—
650C22×C11#53412yes—
651C22×C11#57512yes—
652C22×C11#57512yes—
653C22×C11C23×D411yescharacteristic
654C2×D11—42no—
655C2×D11—42no—
656C2×D11—42no—
657C2×D11—84no—
658C4×C11—21no—
659C4×C11—21no—
660C4×C11—21no—
661C4×C11—21no—
662C4×C11—21no—
663C4×C11—21no—
664C4×C11—42no—
665C4×C11—42no—
666C4×C11—42no—
667C4×C11#53412yes—
668C4×C11C2×H(5,𝔽2)12yes—
669Dic11—42no—
670Dic11—42no—
671Dic11—42no—
672C25C22⋊D1111yescharacteristic
673C2×#41—21no—
674C2×#41—21no—
675C2×#41—44no—
676C2×#41—112no—
677C2×#41—112no—
678C2×#41—221no—
679C2×#41—221no—
680C2×#41—444no—
681C2×#41C22×D1112yes—
682C2×#41C22×D1112yes—
683C22×Q8—111no—
684C22×Q8C22×D1111yescharacteristic
685C22×D4—21no—
686C22×D4—21no—
687C22×D4—21no—
688C22×D4—111no—
689C22×D4—221no—
690C22×D4—221no—
691C22×D4—221no—
692C22×D4C22×D1111yescharacteristic
693C23×C4—21no—
694C23×C4—44no—
695C23×C4—221no—
696C23×C4C22⋊D1111yescharacteristic
697C23×C4C22⋊D1111yescharacteristic
698C23×C4C22⋊D1111yescharacteristic
699C23×C4C22⋊D1111yescharacteristic
700C23×C4C22⋊D1111yescharacteristic
701C23×C4C22⋊D1111yescharacteristic
702C23×C4C22⋊D1111yescharacteristic
703C23×C4C22×D1111yescharacteristic
704C23×C4C22×D1111yescharacteristic
705C23×C4C22×D1111yescharacteristic
706C23×C4C22×D1111yescharacteristic
707C23×C4C22×D1111yescharacteristic
708C23×C4C22×D1111yescharacteristic
709C23×C4C22×D1111yescharacteristic
710#135—448no—
711C2×Q16—114no—
712C2×SD16—114no—
713C2×SD16—114no—
714C2×D8—114no—
715C2×M16—112no—
716C2×M16—114no—
717C2×M16—112no—
718C2×M16—444no—
719C22×C8—114no—
720#123—22no—
721#123—22no—
722#123—22no—
723#123—22no—
724#123—222no—
725#123—222no—
726#123—222no—
727#123—222no—
728C22⋊Q8—21no—
729C22⋊Q8—21no—
730C22⋊Q8—21no—
731C22⋊Q8—21no—
732C22⋊Q8—112no—
733C22⋊Q8—112no—
734C22⋊Q8—112no—
735C22⋊Q8—112no—
736C22⋊Q8—221no—
737C22⋊Q8—221no—
738C22⋊Q8—221no—
739C22⋊Q8—221no—
740C22⋊Q8C22×D1112yes—
741C22⋊Q8C22×D1112yes—
742C22⋊Q8C22×D1112yes—
743C22⋊Q8C22×D1112yes—
744#121—21no—
745#121—21no—
746#121—21no—
747#121—21no—
748#121—112no—
749#121—112no—
750#121—112no—
751#121—112no—
752#121—221no—
753#121—221no—
754#121—221no—
755#121—221no—
756#121C22×D1112yes—
757#121C22×D1112yes—
758#121C22×D1112yes—
759#121C22×D1112yes—
760#120—22no—
761#120—22no—
762#120—22no—
763#120—22no—
764#120—222no—
765#120—222no—
766#120—222no—
767#120—222no—
768C4×D4—22no—
769C4×D4—22no—
770C4×D4—22no—
771C4×D4—22no—
772C4×D4—22no—
773C4×D4—22no—
774C4×D4—22no—
775C4×D4—22no—
776C4×D4—222no—
777C4×D4—222no—
778C4×D4—222no—
779C4×D4—222no—
780C4×D4—222no—
781C4×D4—222no—
782C4×D4—222no—
783C4×D4—222no—
784#117—21no—
785#117—21no—
786#117—112no—
787#117—112no—
788#117—221no—
789#117—221no—
790#117C22×D1112yes—
791#117C22×D1112yes—
792C2×C4⋊C4—21no—
793C2×C4⋊C4—21no—
794C2×C4⋊C4—111no—
795C2×C4⋊C4—111no—
796C2×C4⋊C4—221no—
797C2×C4⋊C4—221no—
798C2×C4⋊C4C22×D1111yescharacteristic
799C2×C4⋊C4C22×D1111yescharacteristic
800C2×C22⋊C4—21no—
801C2×C22⋊C4—21no—
802C2×C22⋊C4—21no—
803C2×C22⋊C4—21no—
804C2×C22⋊C4—21no—
805C2×C22⋊C4—221no—
806C2×C22⋊C4—221no—
807C2×C22⋊C4—221no—
808C2×C22⋊C4—221no—
809C2×C22⋊C4—221no—
810C2×C42—21no—
811C2×C42—221no—
812#107—114no—
813#107—114no—
814#106—114no—
815#106—114no—
816#103—114no—
817#103—114no—
818#103—114no—
819#103—114no—
820#102—114no—
821#102—114no—
822#102—114no—
823#102—114no—
824C22⋊C8—112no—
825C22⋊C8—112no—
826C22⋊C8—112no—
827C22⋊C8—112no—
828C22⋊C8—114no—
829C22⋊C8—114no—
830C2×C11—22no—
831C2×C11—22no—
832C2×C11—22no—
833C2×C11—41no—
834C2×C11—41no—
835C2×C11—41no—
836C2×C11—41no—
837C2×C11—82no—
838C2×C11C2×#53411yescharacteristic
839C2×C11C2×#57511yescharacteristic
840C2×C11C2×#57511yescharacteristic
841D11—82no—
842C24—21no—
843C24—42no—
844C24—42no—
845C24—42no—
846C24—221no—
847C24C2×C22⋊D1111yescharacteristic
848C24C2×C22⋊D1111yescharacteristic
849C24C2×C22⋊D1111yescharacteristic
850C24C2×C22⋊D1111yescharacteristic
851C24C2×C22⋊D1111yescharacteristic
852C24C2×C22⋊D1111yescharacteristic
853C24C2×C22⋊D1111yescharacteristic
854#41—28no—
855#41—44no—
856#41—44no—
857#41—44no—
858#41—228no—
859#41—444no—
860#41—444no—
861#41—444no—
862C2×Q8—21no—
863C2×Q8—42no—
864C2×Q8—112no—
865C2×Q8—221no—
866C2×Q8—442no—
867C2×Q8C23×D1112yes—
868C2×D4—22no—
869C2×D4—22no—
870C2×D4—22no—
871C2×D4—22no—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—21no—
875C2×D4—42no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—112no—
880C2×D4—222no—
881C2×D4—222no—
882C2×D4—222no—
883C2×D4—222no—
884C2×D4—222no—
885C2×D4—222no—
886C2×D4—221no—
887C2×D4—442no—
888C2×D4—444no—
889C2×D4—444no—
890C2×D4—444no—
891C2×D4C23×D1112yes—
892C22×C4—24no—
893C22×C4—24no—
894C22×C4—24no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—44no—
912C22×C4—221no—
913C22×C4—221no—
914C22×C4—221no—
915C22×C4—222no—
916C22×C4—222no—
917C22×C4—444no—
918C22×C4C2×C22⋊D1111yescharacteristic
919C22×C4C2×C22⋊D1111yescharacteristic
920C22×C4C2×C22⋊D1111yescharacteristic
921C22×C4C2×C22⋊D1111yescharacteristic
922C22×C4C2×C22⋊D1111yescharacteristic
923C22×C4C2×C22⋊D1111yescharacteristic
924C22×C4C2×C22⋊D1111yescharacteristic
925C22×C4C2×C22⋊D1111yescharacteristic
926C22×C4C2×C22⋊D1111yescharacteristic
927C22×C4C2×C22⋊D1111yescharacteristic
928C22×C4C2×C22⋊D1111yescharacteristic
929C22×C4C2×C22⋊D1111yescharacteristic
930C22×C4C2×C22⋊D1111yescharacteristic
931C22×C4C2×C22⋊D1111yescharacteristic
932C22×C4C2×C22⋊D1111yescharacteristic
933C22×C4C2×C22⋊D1111yescharacteristic
934C22×C4C2×C22⋊D1111yescharacteristic
935C22×C4C2×C22⋊D1111yescharacteristic
936C22×C4C2×C22⋊D1111yescharacteristic
937C22×C4C2×C22⋊D1111yescharacteristic
938C22×C4C2×C22⋊D1111yescharacteristic
939C22×C4C23×D1111yescharacteristic
940C22×C4C23×D1111yescharacteristic
941C22×C4C23×D1111yescharacteristic
942C22×C4C23×D1111yescharacteristic
943C22×C4C23×D1111yescharacteristic
944C22×C4C23×D1111yescharacteristic
945C22×C4C23×D1111yescharacteristic
946Q16—444no—
947SD16—444no—
948SD16—444no—
949D8—444no—
950M16—442no—
951M16—444no—
952M16—442no—
953C2×C8—114no—
954C2×C8—114no—
955C2×C8—228no—
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—112no—
963C4⋊C4—112no—
964C4⋊C4—221no—
965C4⋊C4—221no—
966C4⋊C4—222no—
967C4⋊C4—222no—
968C4⋊C4—222no—
969C4⋊C4—222no—
970C4⋊C4C23×D1112yes—
971C4⋊C4C23×D1112yes—
972C22⋊C4—22no—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—22no—
976C22⋊C4—22no—
977C22⋊C4—22no—
978C22⋊C4—22no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—222no—
983C22⋊C4—222no—
984C22⋊C4—222no—
985C22⋊C4—222no—
986C22⋊C4—222no—
987C22⋊C4—222no—
988C22⋊C4—222no—
989C22⋊C4—222no—
990C22⋊C4—222no—
991C22⋊C4—222no—
992C42—22no—
993C42—22no—
994C42—222no—
995C42—222no—
996C11#6074111yescharacteristic, complemented, Sylow
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—42no—
1020C23—42no—
1021C23—416no—
1022C23—42no—
1023C23—222no—
1024C23—442no—
1025C23—442no—
1026C23—442no—
1027C23C22×C22⋊D1111yescharacteristic
1028C23C22×C22⋊D1111yescharacteristic
1029C23C22×C22⋊D1111yescharacteristic
1030C23C22×C22⋊D1111yescharacteristic
1031C23C22×C22⋊D1111yescharacteristic
1032C23C22×C22⋊D1111yescharacteristic
1033C23C22×C22⋊D1111yescharacteristic
1034Q8—24no—
1035Q8—42no—
1036Q8—224no—
1037Q8—442no—
1038D4—24no—
1039D4—42no—
1040D4—44no—
1041D4—44no—
1042D4—44no—
1043D4—44no—
1044D4—44no—
1045D4—44no—
1046D4—224no—
1047D4—442no—
1048D4—444no—
1049D4—444no—
1050D4—444no—
1051D4—444no—
1052D4—444no—
1053D4—444no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—44no—
1085C2×C4—42no—
1086C2×C4—42no—
1087C2×C4—42no—
1088C2×C4—44no—
1089C2×C4—222no—
1090C2×C4—222no—
1091C2×C4—222no—
1092C2×C4—444no—
1093C2×C4—442no—
1094C2×C4—442no—
1095C2×C4—442no—
1096C2×C4—444no—
1097C2×C4#6703714yes—
1098C2×C4C22×C22⋊D1111yescharacteristic
1099C2×C4C22×C22⋊D1111yescharacteristic
1100C2×C4C22×C22⋊D1111yescharacteristic
1101C2×C4C22×C22⋊D1111yescharacteristic
1102C2×C4C22×C22⋊D1111yescharacteristic
1103C2×C4C22×C22⋊D1111yescharacteristic
1104C2×C4C22×C22⋊D1111yescharacteristic
1105C2×C4C24×D1111yescharacteristic
1106C8—224no—
1107C8—224no—
1108C22—21no—
1109C22—21no—
1110C22—21no—
1111C22—21no—
1112C22—21no—
1113C22—21no—
1114C22—21no—
1115C22—21no—
1116C22—21no—
1117C22—21no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—21no—
1124C22—21no—
1125C22—21no—
1126C22—44no—
1127C22—44no—
1128C22—44no—
1129C22—44no—
1130C22—44no—
1131C22—44no—
1132C22—44no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22—84no—
1137C22—442no—
1138C22—442no—
1139C22—442no—
1140C22—884no—
1141C22#1062333512yes—
1142C22#1062335312yes—
1143C22#1062335312yes—
1144C22C23×C22⋊D1111yescharacteristic
1145C4—21no—
1146C4—21no—
1147C4—21no—
1148C4—21no—
1149C4—21no—
1150C4—21no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—442no—
1155C4—442no—
1156C4—442no—
1157C4#1062333512yes—
1158C4C2×#6703712yes—
1159C2—22no—
1160C2—22no—
1161C2—22no—
1162C2—41no—
1163C2—41no—
1164C2—41no—
1165C2—41no—
1166C2—82no—
1167C2—882no—
1168C2C2×#1062333511yescharacteristic
1169C2C2×#1062335311yescharacteristic
1170C2C2×#1062335311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#525C2
socleC22×C11C23×D4
hypercenterC2×#525D11
hypocenterC11#60741
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#10623322C2semidirect
2. #13079453C2semidirect
3. #13079446C2semidirect
4. #13079442C2semidirect
5. #13079437C2semidirect
6. #13079430C2semidirect
7. #13079426C2semidirect
8. #13079422C2semidirect
9. #13079418C2semidirect
10. #13079413C2semidirect
11. #13078529C2semidirect
12. #13078525C2semidirect
13. #13078222C2semidirect
14. #13077834C2semidirect
15. #13077832C2semidirect
16. C2×#10622820C2semidirect
17. C2×C11×#525C2semidirect
18. C22×C11×#41C22semidirect
20. C22×#4339C22semidirect
27. C11×#525C22semidirect
28. C11×#525C22semidirect
31. C2×C11×C22⋊Q8C22semidirect
33. C2×C11×#121C22semidirect
37. C2×C11×#117C22semidirect
39. C2×#67003C22semidirect
46. #10623322C22semidirect
47. #10623322C22semidirect
49. C2×#66983C22semidirect
53. C2×#66979C22semidirect
55. C2×#66977C22semidirect
56. C22×#4318C22semidirect
57. #10622852C22semidirect
58. #10622851C22semidirect
59. #10622846C22semidirect
60. #10622841C22semidirect
61. #10622840C22semidirect
62. #10622831C22semidirect
63. #10622830C22semidirect
66. #10622820C22semidirect
67. #10622820C22semidirect
68. #10622820C22semidirect
69. C2×C22⋊(C11⋊C8)C22semidirect
70. C2×C22⋊(C11⋊C8)C22semidirect
71. #10622665C22semidirect
72. #10622665C22semidirect
73. #10622663C22semidirect
74. #10622662C22semidirect
75. #10622662C22semidirect
76. #10622660C22semidirect
77. #10622659C22semidirect
78. #10622658C22semidirect
79. #10622657C22semidirect
80. #10622656C22semidirect
81. #10622655C22semidirect
82. #10622655C22semidirect
83. #10622653C22semidirect
84. #10622652C22semidirect
85. #10622652C22semidirect
86. #10622650C22semidirect
87. #10622649C22semidirect
88. #10622648C22semidirect
89. #10622647C22semidirect
90. #10622646C22semidirect
91. #10622616C22semidirect
92. #10622615C22semidirect
93. #10622611C22semidirect
94. #10622609C22semidirect
95. #10622584C22semidirect
96. #10622583C22semidirect
97. #10622581C22semidirect
98. #10622580C22semidirect
191. C2×#4326C23semidirect
192. C2×#4325C23semidirect
193. C2×#4324C23semidirect
194. C2×#4323C23semidirect
239. #66899C23semidirect
240. #66899C23semidirect
241. #66896C23semidirect
242. #66896C23semidirect
249. #66874C23semidirect
250. #66874C23semidirect
251. #66873C23semidirect
252. #66873C23semidirect
253. #66872C23semidirect
254. #66872C23semidirect
255. #66871C23semidirect
256. #66871C23semidirect
413. C2×#525D11semidirect
541. C22×#41C2×D11semidirect
559. #525C2×D11semidirect
560. #525C2×D11semidirect
566. C2×C22⋊Q8C2×D11semidirect
570. C2×#121C2×D11semidirect
578. C2×#117C2×D11semidirect
996. C11#60741semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
#130794532
#130794462
#130794422
#130794372
#130794302
#130794262
#130794222
#130794182
#130794132
#130785292
#130785252
#130782222
#130778342
#130778322
C2×#106228202
C2×C11×#5252
#6074111