Finite Group Databasebeta

← #14926030

Subgroups — #14926030

Order 2816.

3270 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4341C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3#13074181C212yesmaximal, complemented
4#13074179C212yesmaximal, complemented
5#13073973C212yesmaximal, complemented
6#13073516C212yesmaximal, complemented
7#13072932C211yesmaximal, characteristic, complemented
8#13072930C211yesmaximal, characteristic, complemented
9#13072889C211yesmaximal, characteristic, complemented
10#13072887C211yesmaximal, characteristic, complemented
11#13071971C211yesmaximal, characteristic, complemented
12#13071969C211yesmaximal, characteristic, complemented
13#13071934C211yesmaximal, characteristic, complemented
14#13071932C211yesmaximal, characteristic, complemented
15#13071903C212yesmaximal, complemented
16#13071895C212yesmaximal, complemented
17C4×#66937C212yesmaximal, complemented
18C4×#66992C212yesmaximal, complemented
19C4×#66935C211yesmaximal, characteristic, complemented
20C4×#67006C211yesmaximal, characteristic, complemented
21C4×#66990C211yesmaximal, characteristic, complemented
22#13071010C211yesmaximal, characteristic, complemented
23C4×C11×#120C211yesmaximal, characteristic, complemented
24C24×C4×C11C2211yescharacteristic
25C23×C22⋊D11C2211yescharacteristic
26C22×#4341C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic
28C2×C11×#120C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×C4×D4×C11C2212yescomplemented
31C2×#67006C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C2×#66992C2212yes—
34C2×#66990C2211yescharacteristic
35C2×D4×Dic11C2211yescharacteristic
36C2×C4×C22⋊D11—28no—
37C2×C4×C22⋊D11C2212yes—
38C2×C4×C22⋊D11C2211yescharacteristic
39C2×C4×C22⋊D11C2212yes—
40C2×C4×C22⋊D11C2212yes—
41C2×C4×C22⋊D11C2212yes—
42C2×C4×C22⋊D11C2211yescharacteristic, complemented
43C2×C4×C22⋊D11C2212yescomplemented
44C2×C4×C22⋊D11C2212yescomplemented
45C22×(C2×D11)⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48C22×C4×Dic11C2211yescharacteristic, complemented
49C4×#4341—28no—
50C2×#66945C2211yescharacteristic, complemented
51C2×#66940C2211yescharacteristic, complemented
52C2×#66937C2212yes—
53C2×#66935C2211yescharacteristic
54C2×(C22⋊D11)⋊C4C2211yescharacteristic
55C2×(C22⋊D11)⋊C4C2211yescharacteristic, complemented
56C2×#66930C2211yescharacteristic
57C2×#66930C2211yescharacteristic, complemented
58C2×C4×D44C2212yescomplemented
59C2×C42×D11C2211yescharacteristic, complemented
60C2×C4×Dic22C2211yescharacteristic, complemented
61C11×#386C2211yescharacteristic
62C11×#386C2212yescomplemented
63C11×#385C2211yescharacteristic
64C11×#385C2212yescomplemented
65C11×#379C2211yescharacteristic
66C4×C11×C22⋊C4C2211yescharacteristic
67C4×C11×C22⋊C4C2212yescomplemented
68#10622860C2211yescharacteristic
69#10622836C2212yes—
70#10622836C2212yescomplemented
71#10622833C2211yescharacteristic
72#10622833C2212yescomplemented
73#10622826C2211yescharacteristic
74#10622826C2212yescomplemented
75#10622823C2211yescharacteristic
76#10622823C2212yescomplemented
77C4×C22⋊Dic11C2211yescharacteristic
78C4×C22⋊Dic11C2212yescomplemented
79#10622605C2212yescomplemented
80#10622605C2212yescomplemented
81#10622603C2212yescomplemented
82#10622602C2212yescomplemented
83#10622585C2212yescomplemented
84#10622574C2212yes—
85#10622573C2212yes—
86#10622573C2212yescomplemented
87#10622572C2212yes—
88#10622571C2211yescharacteristic
89#10622571C2212yescomplemented
90#10622570C2212yes—
91#10622570C2212yes—
92#10622569C2212yescomplemented
93#10622569C2212yescomplemented
94#10622568C2211yescharacteristic
95#10622568C2211yescharacteristic
96#10622565C2212yescomplemented
97#10622564C2212yescomplemented
98#10622563C2211yescharacteristic
99#10622562C2212yescomplemented
100#10622562C2212yescomplemented
101#10622560C2212yescomplemented
102#10622559C2211yescharacteristic
103#10622558C2212yescomplemented
104#10622556C2211yescharacteristic
105#10622556C2211yescharacteristic
106#10622555C2211yescharacteristic
107#10622555C2211yescharacteristic
108#10622555C2212yescomplemented
109C4×(C2×D11)⋊C4C2212yescomplemented
110C4×(C2×D11)⋊C4C2212yescomplemented
111#10622545C2212yescomplemented
112C4×Dic11⋊C4C2212yescomplemented
113#10622288C2212yescomplemented
114#10622286C2212yescomplemented
115#10622282C2212yescomplemented
116#10622281C2212yescomplemented
117#10622280C2212yescomplemented
118#10622278C2212yescomplemented
119#10622278C2212yescomplemented
120#10622273C2212yescomplemented
121#10622271C2212yescomplemented
122#10622264C2212yescomplemented
123#10622263C2212yescomplemented
124#10622260C2212yescomplemented
125C25×C11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C22×D4×C11C2312yes—
128C22×D4×C11C2311yescharacteristic
129C23×C4×C11—24no—
130C23×C4×C11—44no—
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2312yes—
133C23×C4×C11C2311yescharacteristic
134C23×C4×C11C2311yescharacteristic
135C23×C4×C11C2312yes—
136C22×C22⋊D11—28no—
137C22×C22⋊D11—24no—
138C22×C22⋊D11C2311yescharacteristic
139C22×C22⋊D11C2312yes—
140C22×C22⋊D11C2312yes—
141C22×C22⋊D11C2312yes—
142C22×C22⋊D11C2311yescharacteristic
143C22×C22⋊D11C2312yes—
144C23×Dic11C2311yescharacteristic
145C23×Dic11C2311yescharacteristic
146C23×Dic11C2311yescharacteristic
147C23×Dic11C2311yescharacteristic
148C23×Dic11C2311yescharacteristic
149C2×#4341—24no—
150C2×#4341—24no—
151C2×#4341—24no—
152C22×D44C2312yes—
153C22×C4×D11—24no—
154C22×C4×D11—44no—
155C22×C4×D11C2311yescharacteristic
156C22×C4×D11C2311yescharacteristic
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2312yes—
159C22×C4×D11C2312yes—
160C22×Dic22C2311yescharacteristic
161C11×#120—24no—
162C4×D4×C11—24no—
163C4×D4×C11—44no—
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C4⋊C4C2312yes—
166C2×C11×C22⋊C4C2311yescharacteristic
167C2×C11×C22⋊C4C2311yescharacteristic
168C2×C11×C22⋊C4C2311yescharacteristic
169C2×C11×C22⋊C4C2312yes—
170C2×C11×C22⋊C4C2311yescharacteristic
171C2×C11×C22⋊C4C2312yes—
172C2×C11×C22⋊C4C2312yes—
173C2×C11×C22⋊C4C2312yes—
174C2×C42×C11C2311yescharacteristic
175C2×C42×C11C2312yes—
176#67006—24no—
177C2×C22⋊Dic11—24no—
178C2×C22⋊Dic11C2311yescharacteristic
179C2×C22⋊Dic11C2311yescharacteristic
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182C2×C22⋊Dic11C2311yescharacteristic
183C2×C22⋊Dic11C2311yescharacteristic
184C2×C22⋊Dic11C2312yes—
185C2×C22⋊Dic11C2312yes—
186C2×C22⋊Dic11C2312yes—
187C2×C22⋊Dic11C2312yes—
188#66992—28no—
189#66990—24no—
190D4×Dic11—24no—
191C4×C22⋊D11—24no—
192C4×C22⋊D11—28no—
193C4×C22⋊D11—28no—
194C4×C22⋊D11—28no—
195C4×C22⋊D11—28no—
196C4×C22⋊D11—24no—
197C4×C22⋊D11—44no—
198C4×C22⋊D11—44no—
199C2×(C2×D11)⋊C4—24no—
200C2×(C2×D11)⋊C4C2311yescharacteristic
201C2×(C2×D11)⋊C4C2311yescharacteristic
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2312yes—
208C2×(C2×D11)⋊C4C2312yes—
209C2×(C2×D11)⋊C4C2312yes—
210C2×(C2×D11)⋊C4C2312yes—
211C2×(C2×D11)⋊C4C2312yes—
212C2×C4⋊Dic11C2311yescharacteristic
213C2×C4⋊Dic11C2312yes—
214C2×Dic11⋊C4—24no—
215C2×Dic11⋊C4C2311yescharacteristic
216C2×Dic11⋊C4C2311yescharacteristic
217C2×Dic11⋊C4C2311yescharacteristic
218C2×Dic11⋊C4C2311yescharacteristic
219C2×Dic11⋊C4C2312yes—
220C2×Dic11⋊C4C2312yes—
221C2×Dic11⋊C4C2312yes—
222C2×Dic11⋊C4C2312yes—
223C2×Dic11⋊C4C2312yes—
224C2×Dic11⋊C4C2312yes—
225C2×C4×Dic11—24no—
226C2×C4×Dic11D418yescomplemented
227C2×C4×Dic11C2311yescharacteristic
228C2×C4×Dic11C2311yescharacteristic
229C2×C4×Dic11C2311yescharacteristic
230C2×C4×Dic11C2311yescharacteristic
231C2×C4×Dic11C2311yescharacteristic
232C2×C4×Dic11C2312yes—
233C2×C4×Dic11C2311yescharacteristic
234C2×C4×Dic11C2311yescharacteristic
235C2×C4×Dic11C2311yescharacteristic
236C2×C4×Dic11C2311yescharacteristic
237#66945—24no—
238#66940—24no—
239#66937—28no—
240#66935—24no—
241(C22⋊D11)⋊C4—24no—
242(C22⋊D11)⋊C4—24no—
243#66930—24no—
244#66930—24no—
245C4×D44—44no—
246C42×D11—24no—
247C4×Dic22—24no—
248C11×#95C2312yes—
249C11×#95C2312yes—
250C11×#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264#34963—111nomaximal, Sylow
265C24×C11—22no—
266C24×C11—24no—
267C24×C11—22no—
268C24×C11—22no—
269C24×C11—42no—
270C24×C11C2412yes—
271C24×C11C2411yescharacteristic
272C24×C11C2411yescharacteristic
273C23×D11—22no—
274C23×D11—24no—
275C23×D11—22no—
276C23×D11—22no—
277C23×D11—42no—
278C23×D11C2412yes—
279C23×D11C2411yescharacteristic
280C2×D4×C11—22no—
281C2×D4×C11—22no—
282C2×D4×C11—24no—
283C2×D4×C11—24no—
284C2×D4×C11—42no—
285C2×D4×C11#4114yes—
286C22×C4×C11—24no—
287C22×C4×C11—22no—
288C22×C4×C11—22no—
289C22×C4×C11—24no—
290C22×C4×C11—24no—
291C22×C4×C11—24no—
292C22×C4×C11—24no—
293C22×C4×C11—24no—
294C22×C4×C11—42no—
295C22×C4×C11—42no—
296C22×C4×C11—42no—
297C22×C4×C11—416no—
298C22×C4×C11C2×D414yes—
299C22×C4×C11C2412yes—
300C22×C4×C11C2412yes—
301C22×C4×C11C2411yescharacteristic
302C22×C4×C11C2412yes—
303C22×C4×C11C2411yescharacteristic
304C22×C4×C11C2411yescharacteristic
305C22×C4×C11C2411yescharacteristic
306C22×C4×C11C2411yescharacteristic
307C2×C22⋊D11—232no—
308C2×C22⋊D11—22no—
309C2×C22⋊D11—24no—
310C2×C22⋊D11—24no—
311C2×C22⋊D11—24no—
312C2×C22⋊D11—22no—
313C2×C22⋊D11—22no—
314C2×C22⋊D11—22no—
315C2×C22⋊D11—24no—
316C2×C22⋊D11—24no—
317C2×C22⋊D11—24no—
318C2×C22⋊D11—22no—
319C2×C22⋊D11—24no—
320C2×C22⋊D11—24no—
321C2×C22⋊D11—24no—
322C2×C22⋊D11—42no—
323C2×C22⋊D11—42no—
324C2×C22⋊D11#4114yes—
325C2×C22⋊D11#4118yescomplemented
326C22×Dic11—22no—
327C22×Dic11—22no—
328C22×Dic11—24no—
329C22×Dic11—22no—
330C22×Dic11—24no—
331C22×Dic11—22no—
332C22×Dic11—22no—
333C22×Dic11—22no—
334C22×Dic11—22no—
335C22×Dic11—42no—
336C22×Dic11C2×D414yes—
337C22×Dic11C2×D414yes—
338C22×Dic11C2412yes—
339C22×Dic11C2412yes—
340C22×Dic11C2411yescharacteristic
341C22×Dic11C2412yes—
342C22×Dic11C2411yescharacteristic
343C22×Dic11C2411yescharacteristic
344C22×Dic11C2411yescharacteristic
345C22×Dic11C2411yescharacteristic
346C22×Dic11C2411yescharacteristic
347C22×Dic11C2411yescharacteristic
348#4341—232no—
349C2×D44—24no—
350C2×D44—24no—
351C2×D44—42no—
352C2×C4×D11—22no—
353C2×C4×D11—22no—
354C2×C4×D11—24no—
355C2×C4×D11—22no—
356C2×C4×D11—22no—
357C2×C4×D11—24no—
358C2×C4×D11—24no—
359C2×C4×D11—22no—
360C2×C4×D11—24no—
361C2×C4×D11—24no—
362C2×C4×D11—24no—
363C2×C4×D11—42no—
364C2×C4×D11—42no—
365C2×C4×D11—416no—
366C2×Dic22—22no—
367C2×Dic22—22no—
368C2×Dic22—22no—
369C11×C4⋊C4—22no—
370C11×C4⋊C4—42no—
371C11×C22⋊C4—22no—
372C11×C22⋊C4—22no—
373C11×C22⋊C4—24no—
374C11×C22⋊C4—22no—
375C11×C22⋊C4—22no—
376C11×C22⋊C4—24no—
377C11×C22⋊C4—42no—
378C11×C22⋊C4—42no—
379C42×C11—22no—
380C42×C11—24no—
381C22⋊Dic11—22no—
382C22⋊Dic11—24no—
383C22⋊Dic11—24no—
384C22⋊Dic11—24no—
385C22⋊Dic11—22no—
386C22⋊Dic11—22no—
387C22⋊Dic11—24no—
388C22⋊Dic11—22no—
389C22⋊Dic11—42no—
390C22⋊Dic11—42no—
391(C2×D11)⋊C4—22no—
392(C2×D11)⋊C4—24no—
393(C2×D11)⋊C4—24no—
394(C2×D11)⋊C4—24no—
395(C2×D11)⋊C4—24no—
396(C2×D11)⋊C4—24no—
397(C2×D11)⋊C4—22no—
398(C2×D11)⋊C4—24no—
399(C2×D11)⋊C4—42no—
400(C2×D11)⋊C4—42no—
401(C2×D11)⋊C4—42no—
402(C2×D11)⋊C4—42no—
403C4⋊Dic11—22no—
404C4⋊Dic11—42no—
405Dic11⋊C4—22no—
406Dic11⋊C4—22no—
407Dic11⋊C4—22no—
408Dic11⋊C4—24no—
409Dic11⋊C4—24no—
410Dic11⋊C4—24no—
411Dic11⋊C4—24no—
412Dic11⋊C4—22no—
413Dic11⋊C4—42no—
414Dic11⋊C4—42no—
415C4×Dic11—22no—
416C4×Dic11—22no—
417C4×Dic11—22no—
418C4×Dic11—22no—
419C4×Dic11—22no—
420C4×Dic11—24no—
421C4×Dic11C2×D414yes—
422C4×Dic11C2×D414yes—
423C4×Dic11C2×D414yes—
424C4×Dic11C2×D414yes—
425C2×C4×#41—111no—
426C22×C4×D4—111no—
427#2598—112no—
428#2598—112no—
429#2580—112no—
430#2535—112no—
431#2487—111no—
432#2487—111no—
433#2482—111no—
434#2482—111no—
435#2408—111no—
436#2408—111no—
437#2404—111no—
438#2404—111no—
439#2398—112no—
440#2397—112no—
441C4×#121—112no—
442C4×#121—112no—
443C4×#120—111no—
444C4×#120—111no—
445C4×#120—111no—
446C4×#120D1111yescharacteristic, complemented
447#2283—111no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11—28no—
451C23×C11—22no—
452C23×C11—21no—
453C23×C11—22no—
454C23×C11—22no—
455C23×C11—21no—
456C23×C11—22no—
457C23×C11—22no—
458C23×C11—22no—
459C23×C11—22no—
460C23×C11—22no—
461C23×C11—48no—
462C23×C11—48no—
463C23×C11—44no—
464C23×C11—44no—
465C23×C11C22×D412yes—
466C23×C11C2×#4112yes—
467C23×C11C2×#4112yes—
468C23×C11C2×#4114yes—
469C23×C11C2×#4112yes—
470C23×C11C2511yescharacteristic
471C22×D11—28no—
472C22×D11—21no—
473C22×D11—22no—
474C22×D11—22no—
475C22×D11—22no—
476C22×D11—22no—
477C22×D11—21no—
478C22×D11—22no—
479C22×D11—22no—
480C22×D11—22no—
481C22×D11—22no—
482C22×D11—48no—
483C22×D11—48no—
484C22×D11—44no—
485C22×D11—44no—
486C22×D11C2×#4114yes—
487C22×D11C2×#4112yes—
488D4×C11—28no—
489D4×C11—48no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—22no—
493C2×C4×C11—28no—
494C2×C4×C11—21no—
495C2×C4×C11—21no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—22no—
506C2×C4×C11—22no—
507C2×C4×C11—48no—
508C2×C4×C11—44no—
509C2×C4×C11—44no—
510C2×C4×C11—48no—
511C2×C4×C11C22×D412yes—
512C2×C4×C11C22×D412yes—
513C2×C4×C11C2×#4112yes—
514C2×C4×C11H(5,𝔽2)14yes—
515C22⋊D11—28no—
516C22⋊D11—216no—
517C22⋊D11—28no—
518C22⋊D11—216no—
519C22⋊D11—48no—
520C22⋊D11—48no—
521C2×Dic11—28no—
522C2×Dic11—28no—
523C2×Dic11—21no—
524C2×Dic11—21no—
525C2×Dic11—21no—
526C2×Dic11—21no—
527C2×Dic11—21no—
528C2×Dic11—21no—
529C2×Dic11—22no—
530C2×Dic11—28no—
531C2×Dic11—21no—
532C2×Dic11—21no—
533C2×Dic11—22no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—22no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—22no—
543C2×Dic11—22no—
544C2×Dic11—44no—
545C2×Dic11—44no—
546C2×Dic11C22×D412yes—
547C2×Dic11C22×D412yes—
548C2×Dic11C22×D412yes—
549C2×Dic11C22×D412yes—
550C2×Dic11C2×#4112yes—
551C2×Dic11C2×#4114yes—
552D44—48no—
553C4×D11—28no—
554C4×D11—48no—
555C4×D11—44no—
556C4×D11—48no—
557C4×D11—44no—
558Dic22—28no—
559C22×#41—111no—
560C23×D4—111no—
561C24×C4—111no—
562C24×C4C2×D1111yescharacteristic
563C2×#121—112no—
564C2×#121—112no—
565C2×#120—111no—
566C2×#120—111no—
567C2×#120—111no—
568C2×#120C2×D1111yescharacteristic
569C4×#41—228no—
570C2×C4×Q8—111no—
571C2×C4×Q8—111no—
572C2×C4×D4—111no—
573C2×C4×D4—112no—
574C2×C4×D4—112no—
575C2×C4×D4—112no—
576C2×C4×D4—112no—
577C2×C4×D4—111no—
578C2×C4×D4—111no—
579C2×C4×D4—112no—
580C2×C4×D4—112no—
581C2×C4×D4—111no—
582C2×C4×D4—111no—
583C2×C4×D4—112no—
584C2×C4×D4—228no—
585C2×C4×D4C2×D1111yescharacteristic
586C2×C4×D4C2×D1112yescomplemented
587C2×#117—111no—
588C2×#117—111no—
589C2×#117—111no—
590C22×C4⋊C4—111no—
591C22×C22⋊C4—111no—
592C22×C22⋊C4—111no—
593C22×C42—111no—
594C22×C42—111no—
595C22×C42—111no—
596#400—112no—
597#400—112no—
598#399—112no—
599#399—112no—
600#399—112no—
601#399—112no—
602#397—112no—
603#397—112no—
604#394—112no—
605#394—112no—
606#393—112no—
607#393—112no—
608#392—112no—
609#392—112no—
610#392—112no—
611#392—112no—
612#390—112no—
613#390—112no—
614#389—112no—
615#389—112no—
616#388—112no—
617#388—112no—
618#388—112no—
619#388—112no—
620#386—112no—
621#386—111no—
622#386—112no—
623#386—111no—
624#386—112no—
625#386—112no—
626#386—112no—
627#386—111no—
628#386—112no—
629#386—112no—
630#386C2×D1111yescharacteristic
631#386C2×D1112yescomplemented
632#385—112no—
633#385—111no—
634#385—112no—
635#385—111no—
636#385—111no—
637#385—112no—
638#385C2×D1111yescharacteristic
639#385C2×D1112yescomplemented
640#383—112no—
641#382—112no—
642#381—111no—
643#381—111no—
644#380—111no—
645#380—111no—
646#380—112no—
647#380—112no—
648#379—111no—
649#379—111no—
650#379—111no—
651#379C2×D1111yescharacteristic
652C4×C4⋊C4—112no—
653C4×C22⋊C4—112no—
654C4×C22⋊C4—111no—
655C4×C22⋊C4—112no—
656C4×C22⋊C4—112no—
657C4×C22⋊C4C2×D1111yescharacteristic
658C4×C22⋊C4C2×D1112yescomplemented
659#376—112no—
660C22×C11—22no—
661C22×C11—22no—
662C22×C11—24no—
663C22×C11—24no—
664C22×C11—22no—
665C22×C11—24no—
666C22×C11—24no—
667C22×C11—24no—
668C22×C11—24no—
669C22×C11—416no—
670C22×C11—42no—
671C22×C11—41no—
672C22×C11—42no—
673C22×C11—41no—
674C22×C11—42no—
675C22×C11—42no—
676C22×C11—42no—
677C22×C11#52514yes—
678C22×C11C23×D411yescharacteristic
679C22×C11C22×#4111yescharacteristic
680C22×C11C22×#4111yescharacteristic
681C22×C11C22×#4112yes—
682C22×C11C2×H(5,𝔽2)12yes—
683C2×D11—24no—
684C2×D11—22no—
685C2×D11—24no—
686C2×D11—24no—
687C2×D11—24no—
688C2×D11—416no—
689C2×D11—42no—
690C2×D11—41no—
691C2×D11—42no—
692C2×D11—41no—
693C2×D11—42no—
694C2×D11—42no—
695C2×D11—42no—
696C4×C11—22no—
697C4×C11—22no—
698C4×C11—41no—
699C4×C11—41no—
700C4×C11—42no—
701C4×C11—42no—
702C4×C11—42no—
703C4×C11#53514yes—
704Dic11—22no—
705Dic11—22no—
706Dic11—22no—
707Dic11—22no—
708Dic11—41no—
709Dic11—42no—
710Dic11—41no—
711Dic11—42no—
712Dic11—42no—
713Dic11#52514yes—
714C25—111no—
715C25C22×D1111yescharacteristic
716C2×#41—224no—
717C2×#41—224no—
718C2×#41—224no—
719C22×Q8—111no—
720C22×D4—111no—
721C22×D4—112no—
722C22×D4—112no—
723C22×D4—111no—
724C22×D4—112no—
725C22×D4—112no—
726C22×D4—112no—
727C22×D4—224no—
728C22×D4—228no—
729C22×D4C22×D1112yes—
730C22×D4C22×D1111yescharacteristic
731C23×C4—24no—
732C23×C4—44no—
733C23×C4—111no—
734C23×C4—111no—
735C23×C4—111no—
736C23×C4—111no—
737C23×C4—111no—
738C23×C4—111no—
739C23×C4—111no—
740C23×C4—111no—
741C23×C4—112no—
742C23×C4—112no—
743C23×C4—224no—
744C23×C4—444no—
745C23×C4C22×D1111yescharacteristic
746C23×C4C22×D1112yes—
747C23×C4C22×D1111yescharacteristic
748C23×C4C22×D1111yescharacteristic
749C23×C4C22×D1112yes—
750#121—228no—
751#121—228no—
752#120—24no—
753#120—224no—
754#120—224no—
755#120—224no—
756C4×Q8—224no—
757C4×Q8—224no—
758C4×D4—24no—
759C4×D4—44no—
760C4×D4—224no—
761C4×D4—228no—
762C4×D4—228no—
763C4×D4—228no—
764C4×D4—228no—
765C4×D4—224no—
766C4×D4—224no—
767C4×D4—224no—
768C4×D4—224no—
769C4×D4—444no—
770C4×D4—444no—
771C4×D4—444no—
772#117—224no—
773#117—224no—
774#117—224no—
775C2×C4⋊C4—112no—
776C2×C4⋊C4—112no—
777C2×C4⋊C4—111no—
778C2×C4⋊C4—111no—
779C2×C4⋊C4—111no—
780C2×C4⋊C4—111no—
781C2×C4⋊C4—111no—
782C2×C4⋊C4—112no—
783C2×C4⋊C4—112no—
784C2×C4⋊C4—112no—
785C2×C4⋊C4—112no—
786C2×C4⋊C4—112no—
787C2×C4⋊C4—224no—
788C2×C4⋊C4C22×D1111yescharacteristic
789C2×C4⋊C4C22×D1112yes—
790C2×C22⋊C4—112no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—111no—
793C2×C22⋊C4—111no—
794C2×C22⋊C4—111no—
795C2×C22⋊C4—111no—
796C2×C22⋊C4—112no—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—111no—
801C2×C22⋊C4—111no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—112no—
811C2×C22⋊C4—112no—
812C2×C22⋊C4—224no—
813C2×C22⋊C4—224no—
814C2×C22⋊C4C22×D1111yescharacteristic
815C2×C22⋊C4C22×D1111yescharacteristic
816C2×C22⋊C4C22×D1111yescharacteristic
817C2×C22⋊C4C22×D1111yescharacteristic
818C2×C22⋊C4C22×D1112yes—
819C2×C22⋊C4C22×D1112yes—
820C2×C22⋊C4C22×D1112yes—
821C2×C22⋊C4C22×D1112yes—
822C2×C42—118no—
823C2×C42—111no—
824C2×C42—111no—
825C2×C42—111no—
826C2×C42—111no—
827C2×C42—111no—
828C2×C42—111no—
829C2×C42—111no—
830C2×C42—111no—
831C2×C42—112no—
832C2×C42—111no—
833C2×C42—224no—
834C2×C42—224no—
835C2×C42C22×D1112yes—
836C2×C42C22×D1111yescharacteristic
837#95—112no—
838#95—112no—
839#95—112no—
840#95—112no—
841#95—112no—
842#95—112no—
843#95—112no—
844#95—112no—
845#95—112no—
846#95—112no—
847#95—112no—
848#95—112no—
849#95—112no—
850#95C22×D1112yes—
851#95C22×D1112yes—
852#95C22×D1112yes—
853C2×C11—24no—
854C2×C11—42no—
855C2×C11—44no—
856C2×C11C2×#52511yescharacteristic
857C2×C11C2×#52511yescharacteristic
858C2×C11C2×#53511yescharacteristic
859C2×C11#348112yes—
860C2×C11#348112yes—
861D11—42no—
862D11—44no—
863C24—22no—
864C24—24no—
865C24—22no—
866C24—22no—
867C24—42no—
868C24—112no—
869C24—111no—
870C24—224no—
871C24—222no—
872C24—222no—
873C24—222no—
874C24—442no—
875C24C23×D1111yescharacteristic
876C24C23×D1112yes—
877C24C23×D1111yescharacteristic
878#41—2232no—
879C2×Q8—222no—
880C2×Q8—222no—
881C2×Q8—222no—
882C2×D4—22no—
883C2×D4—22no—
884C2×D4—24no—
885C2×D4—24no—
886C2×D4—42no—
887C2×D4—114no—
888C2×D4—118no—
889C2×D4—224no—
890C2×D4—224no—
891C2×D4—224no—
892C2×D4—224no—
893C2×D4—222no—
894C2×D4—224no—
895C2×D4—224no—
896C2×D4—222no—
897C2×D4—2232no—
898C2×D4—222no—
899C2×D4—222no—
900C2×D4—222no—
901C2×D4—224no—
902C2×D4—224no—
903C2×D4—224no—
904C2×D4—224no—
905C2×D4—224no—
906C2×D4—442no—
907C2×D4—442no—
908C2×D4—442no—
909C2×D4#433914yes—
910C22×C4—24no—
911C22×C4—22no—
912C22×C4—22no—
913C22×C4—24no—
914C22×C4—24no—
915C22×C4—24no—
916C22×C4—24no—
917C22×C4—24no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—416no—
922C22×C4—111no—
923C22×C4—114no—
924C22×C4—114no—
925C22×C4—111no—
926C22×C4—111no—
927C22×C4—111no—
928C22×C4—111no—
929C22×C4—112no—
930C22×C4—112no—
931C22×C4—111no—
932C22×C4—112no—
933C22×C4—111no—
934C22×C4—222no—
935C22×C4—222no—
936C22×C4—224no—
937C22×C4—222no—
938C22×C4—222no—
939C22×C4—224no—
940C22×C4—222no—
941C22×C4—222no—
942C22×C4—224no—
943C22×C4—222no—
944C22×C4—222no—
945C22×C4—222no—
946C22×C4—222no—
947C22×C4—222no—
948C22×C4—222no—
949C22×C4—224no—
950C22×C4—224no—
951C22×C4—224no—
952C22×C4—224no—
953C22×C4—224no—
954C22×C4—442no—
955C22×C4—442no—
956C22×C4—4416no—
957C22×C4—442no—
958C22×C4D4×D1114yes—
959C22×C4C23×D1112yes—
960C22×C4C23×D1112yes—
961C22×C4C23×D1111yescharacteristic
962C22×C4C23×D1112yes—
963C22×C4C23×D1111yescharacteristic
964C22×C4C23×D1111yescharacteristic
965C22×C4C23×D1111yescharacteristic
966C22×C4C23×D1111yescharacteristic
967C4⋊C4—22no—
968C4⋊C4—42no—
969C4⋊C4—224no—
970C4⋊C4—224no—
971C4⋊C4—222no—
972C4⋊C4—222no—
973C4⋊C4—222no—
974C4⋊C4—222no—
975C4⋊C4—224no—
976C4⋊C4—224no—
977C4⋊C4—222no—
978C4⋊C4—442no—
979C4⋊C4—442no—
980C4⋊C4—442no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—24no—
985C22⋊C4—24no—
986C22⋊C4—22no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—224no—
990C22⋊C4—224no—
991C22⋊C4—222no—
992C22⋊C4—224no—
993C22⋊C4—224no—
994C22⋊C4—224no—
995C22⋊C4—224no—
996C22⋊C4—224no—
997C22⋊C4—222no—
998C22⋊C4—224no—
999C22⋊C4—222no—
1000C22⋊C4—222no—
1001C22⋊C4—222no—
1002C22⋊C4—224no—
1003C22⋊C4—224no—
1004C22⋊C4—222no—
1005C22⋊C4—442no—
1006C22⋊C4—442no—
1007C22⋊C4—442no—
1008C22⋊C4—442no—
1009C22⋊C4—442no—
1010C22⋊C4—442no—
1011C42—22no—
1012C42—24no—
1013C42—114no—
1014C42—114no—
1015C42—114no—
1016C42—114no—
1017C42—222no—
1018C42—222no—
1019C42—222no—
1020C42—222no—
1021C42—222no—
1022C42—224no—
1023C11#3496311yescharacteristic, complemented, Sylow
1024C23—22no—
1025C23—22no—
1026C23—28no—
1027C23—22no—
1028C23—21no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—21no—
1035C23—22no—
1036C23—22no—
1037C23—48no—
1038C23—48no—
1039C23—44no—
1040C23—44no—
1041C23—114no—
1042C23—112no—
1043C23—228no—
1044C23—222no—
1045C23—221no—
1046C23—221no—
1047C23—222no—
1048C23—222no—
1049C23—222no—
1050C23—222no—
1051C23—222no—
1052C23—222no—
1053C23—222no—
1054C23—448no—
1055C23—448no—
1056C23—444no—
1057C23—444no—
1058C23C2×#433912yes—
1059C23C2×#433912yes—
1060C23C2×D4×D1112yes—
1061C23#41×D1114yes—
1062C23#41×D1112yes—
1063C23C24×D1111yescharacteristic
1064Q8—228no—
1065D4—28no—
1066D4—48no—
1067D4—2216no—
1068D4—2216no—
1069D4—228no—
1070D4—228no—
1071D4—448no—
1072D4—448no—
1073D4—448no—
1074C2×C4—21no—
1075C2×C4—22no—
1076C2×C4—21no—
1077C2×C4—28no—
1078C2×C4—22no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—48no—
1092C2×C4—44no—
1093C2×C4—44no—
1094C2×C4—48no—
1095C2×C4—112no—
1096C2×C4—114no—
1097C2×C4—112no—
1098C2×C4—112no—
1099C2×C4—112no—
1100C2×C4—112no—
1101C2×C4—228no—
1102C2×C4—228no—
1103C2×C4—228no—
1104C2×C4—228no—
1105C2×C4—221no—
1106C2×C4—221no—
1107C2×C4—221no—
1108C2×C4—221no—
1109C2×C4—221no—
1110C2×C4—222no—
1111C2×C4—221no—
1112C2×C4—222no—
1113C2×C4—221no—
1114C2×C4—221no—
1115C2×C4—222no—
1116C2×C4—222no—
1117C2×C4—222no—
1118C2×C4—222no—
1119C2×C4—222no—
1120C2×C4—222no—
1121C2×C4—222no—
1122C2×C4—222no—
1123C2×C4—222no—
1124C2×C4—222no—
1125C2×C4—448no—
1126C2×C4—444no—
1127C2×C4—444no—
1128C2×C4—444no—
1129C2×C4—448no—
1130C2×C4—444no—
1131C2×C4C2×#433912yes—
1132C2×C4C2×D4×D1112yes—
1133C2×C4C2×D4×D1112yes—
1134C2×C4#6703714yes—
1135C22—22no—
1136C22—24no—
1137C22—24no—
1138C22—22no—
1139C22—22no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—416no—
1145C22—42no—
1146C22—42no—
1147C22—41no—
1148C22—42no—
1149C22—42no—
1150C22—42no—
1151C22—41no—
1152C22—222no—
1153C22—224no—
1154C22—224no—
1155C22—224no—
1156C22—224no—
1157C22—4416no—
1158C22—442no—
1159C22—442no—
1160C22—441no—
1161C22—442no—
1162C22—442no—
1163C22—442no—
1164C22—441no—
1165C22#1062307814yes—
1166C22C22×#433911yescharacteristic
1167C22C22×D4×D1111yescharacteristic
1168C22C2×#6703712yes—
1169C22C2×#41×D1111yescharacteristic
1170C22C2×#41×D1112yes—
1171C4—22no—
1172C4—22no—
1173C4—42no—
1174C4—41no—
1175C4—42no—
1176C4—42no—
1177C4—41no—
1178C4—114no—
1179C4—222no—
1180C4—222no—
1181C4—222no—
1182C4—222no—
1183C4—442no—
1184C4—441no—
1185C4—442no—
1186C4—442no—
1187C4—441no—
1188C4#1062312314yes—
1189C2—24no—
1190C2—44no—
1191C2—42no—
1192C2—444no—
1193C2—442no—
1194C2D11×#52511yescharacteristic
1195C2C2×#1062307811yescharacteristic
1196C2C2×#1062312311yescharacteristic
1197C2#1308221812yes—
1198C2#1308222012yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC4×C11×#120C2
hypercenterC4×#120D11
hypocenterC11#34963
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#120

Complements

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

NH ≅ G/Ntype
1. C2×C4×#4341C2semidirect
2. C22×C4×C22⋊D11C2semidirect
3. #13074181C2semidirect
4. #13074179C2semidirect
5. #13073973C2semidirect
6. #13073516C2semidirect
7. #13072932C2semidirect
8. #13072930C2semidirect
9. #13072889C2semidirect
10. #13072887C2semidirect
11. #13071971C2semidirect
12. #13071969C2semidirect
13. #13071934C2semidirect
14. #13071932C2semidirect
15. #13071903C2semidirect
16. #13071895C2semidirect
17. C4×#66937C2semidirect
18. C4×#66992C2semidirect
19. C4×#66935C2semidirect
20. C4×#67006C2semidirect
21. C4×#66990C2semidirect
22. #13071010C2semidirect
23. C4×C11×#120C2semidirect
30. C2×C4×D4×C11C22semidirect
42. C2×C4×C22⋊D11C22semidirect
43. C2×C4×C22⋊D11C22semidirect
44. C2×C4×C22⋊D11C22semidirect
48. C22×C4×Dic11C22semidirect
50. C2×#66945C22semidirect
51. C2×#66940C22semidirect
55. C2×(C22⋊D11)⋊C4C22semidirect
57. C2×#66930C22semidirect
58. C2×C4×D44C22semidirect
59. C2×C42×D11C22semidirect
60. C2×C4×Dic22C22semidirect
62. C11×#386C22semidirect
64. C11×#385C22semidirect
67. C4×C11×C22⋊C4C22semidirect
70. #10622836C22semidirect
72. #10622833C22semidirect
74. #10622826C22semidirect
76. #10622823C22semidirect
78. C4×C22⋊Dic11C22semidirect
79. #10622605C22semidirect
80. #10622605C22semidirect
81. #10622603C22semidirect
82. #10622602C22semidirect
83. #10622585C22semidirect
86. #10622573C22semidirect
89. #10622571C22semidirect
92. #10622569C22semidirect
93. #10622569C22semidirect
96. #10622565C22semidirect
97. #10622564C22semidirect
99. #10622562C22semidirect
100. #10622562C22semidirect
101. #10622560C22semidirect
103. #10622558C22semidirect
108. #10622555C22semidirect
109. C4×(C2×D11)⋊C4C22semidirect
110. C4×(C2×D11)⋊C4C22semidirect
111. #10622545C22semidirect
112. C4×Dic11⋊C4C22semidirect
113. #10622288C22semidirect
114. #10622286C22semidirect
115. #10622282C22semidirect
116. #10622281C22semidirect
117. #10622280C22semidirect
118. #10622278C22semidirect
119. #10622278C22semidirect
120. #10622273C22semidirect
121. #10622271C22semidirect
122. #10622264C22semidirect
123. #10622263C22semidirect
124. #10622260C22semidirect
226. C2×C4×Dic11D4semidirect
325. C2×C22⋊D11#41semidirect
446. C4×#120D11semidirect
586. C2×C4×D4C2×D11semidirect
631. #386C2×D11semidirect
639. #385C2×D11semidirect
658. C4×C22⋊C4C2×D11semidirect
1023. C11#34963semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43412
C22×C4×C22⋊D112
#130741812
#130741792
#130739732
#130735162
#130729322
#130729302
#130728892
#130728872
#130719712
#130719692
#130719342
#130719322
#130719032
#130718952
C4×#669372
C4×#669922
C4×#669352
C4×#670062
C4×#669902
#130710102
C4×C11×#1202
#3496311