Finite Group Databasebeta

← #14913936

Subgroups — #14913936

Order 2816.

2914 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D11C211yesmaximal, characteristic
2#13071586C212yesmaximal, complemented
3#13071555C212yesmaximal, complemented
4#13071554C212yesmaximal, complemented
5#13071522C212yesmaximal, complemented
6#13071482C212yesmaximal, complemented
7#13071463C212yesmaximal, complemented
8#13071460C212yesmaximal, complemented
9#13071434C212yesmaximal
10#13071258C211yesmaximal, characteristic, complemented
11#13071256C211yesmaximal, characteristic, complemented
12#13071252C211yesmaximal, characteristic, complemented
13#13071249C211yesmaximal, characteristic, complemented
14#13071247C211yesmaximal, characteristic, complemented
15#13071013C211yesmaximal, characteristic, complemented
16#13071009C211yesmaximal, characteristic, complemented
17#13070998C211yesmaximal, characteristic, complemented
18#13070997C211yesmaximal, characteristic, complemented
19C2×#10622277C211yesmaximal, characteristic, complemented
20D11×#381C211yesmaximal, characteristic, complemented
21#13070975C211yesmaximal, characteristic, complemented
22#13070974C211yesmaximal, characteristic, complemented
23C11×#2318C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×D4×Dic11C2211yescharacteristic
29C2×C4×C22⋊D11C2212yes—
30C2×C4×C22⋊D11C2211yescharacteristic
31C2×C4×C22⋊D11C2211yescharacteristic
32C22×(C2×D11)⋊C4C2212yes—
33C4×D4×D11C4116yescomplemented
34C2×#66946C2211yescharacteristic
35C2×#66945C2212yes—
36C2×C4⋊C4×D11C2211yescharacteristic
37C2×(C22⋊D11)⋊C4C2212yes—
38C2×(C22⋊D11)⋊C4C2211yescharacteristic
39C2×(C22⋊D11)⋊C4C2211yescharacteristic
40C2×C22⋊C4×D11C2212yes—
41C2×C22⋊C4×D11C2211yescharacteristic
42C2×C22⋊C4×D11C2211yescharacteristic
43C2×C4×D44C2211yescharacteristic
44C2×#66925C2212yes—
45C2×C42×D11C2211yescharacteristic
46C11×#388C2212yescomplemented
47C11×#387C2212yescomplemented
48C11×#386C2212yes—
49C11×#385C2212yescomplemented
50C11×#383C2211yescharacteristic, complemented
51C11×#382C2211yescharacteristic, complemented
52C11×#381C2211yescharacteristic, complemented
53C11×#380C2211yescharacteristic, complemented
54C4×C11×C22⋊C4C2211yescharacteristic, complemented
55C2×C11×#95C2211yescharacteristic, complemented
56#10622833C2212yes—
57#10622825C2211yescharacteristic, complemented
58#10622824C2211yescharacteristic, complemented
59C4×C22⋊Dic11C2212yescomplemented
60C4×C22⋊Dic11C2211yescharacteristic, complemented
61C2×C11⋊#95C2211yescharacteristic, complemented
62C2×C11⋊#95C2212yescomplemented
63#10622603C2212yescomplemented
64#10622603C2212yescomplemented
65#10622602C2212yescomplemented
66#10622600C2212yes—
67#10622600C2212yescomplemented
68#10622594C2212yescomplemented
69C4⋊C4×Dic11C2212yescomplemented
70#10622585C2212yescomplemented
71#10622570C2212yes—
72#10622570C2212yes—
73#10622568C2212yes—
74#10622568C2212yes—
75#10622564C2212yescomplemented
76#10622563C2212yescomplemented
77#10622558C2212yescomplemented
78#10622557C2212yescomplemented
79#10622556C2212yescomplemented
80#10622555C2212yescomplemented
81C22⋊C4×Dic11C2212yescomplemented
82C22⋊C4×Dic11C2212yescomplemented
83C4×(C2×D11)⋊C4C2212yescomplemented
84C4×(C2×D11)⋊C4C2212yescomplemented
85#10622550C2211yescharacteristic, complemented
86#10622549C2211yescharacteristic, complemented
87C4×Dic11⋊C4C2212yescomplemented
88#10622283C2212yescomplemented
89#10622283C2212yescomplemented
90#10622281C2212yescomplemented
91#10622280C2212yes—
92#10622280C2211yescharacteristic, complemented
93#10622280C2211yescharacteristic, complemented
94#10622279C2212yes—
95#10622279C2212yes—
96#10622279C2212yescomplemented
97#10622279C2211yescharacteristic, complemented
98#10622279C2211yescharacteristic, complemented
99#10622278C2212yes—
100#10622278C2212yes—
101#10622277C2212yes—
102#10622277C2212yes—
103#10622277C2211yescharacteristic
104#10622277C2211yescharacteristic
105#10622277C2211yescharacteristic
106#10622277C2211yescharacteristic
107#10622277C2211yescharacteristic, complemented
108#10622277C2211yescharacteristic, complemented
109#10622277C2212yescomplemented
110D11×#95C2211yescharacteristic, complemented
111D11×#95C2211yescharacteristic, complemented
112D11×#95C2212yescomplemented
113#10622267C2212yescomplemented
114#10622266C2212yescomplemented
115#10622264C2212yescomplemented
116#10622263C2212yescomplemented
117#10622262C2212yescomplemented
118#10622262C2211yescharacteristic, complemented
119#10622262C2211yescharacteristic, complemented
120#10622261C2211yescharacteristic, complemented
121#10622261C2211yescharacteristic, complemented
122#10622261C2212yescomplemented
123#10622260C2212yescomplemented
124C24×D11C2311yescharacteristic
125C24×D11C2311yescharacteristic
126C22×D4×C11C2311yescharacteristic
127C23×C4×C11C2312yes—
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C22×C22⋊D11C2311yescharacteristic
131C22×C22⋊D11C2311yescharacteristic
132C23×Dic11C2312yes—
133C23×Dic11C2311yescharacteristic
134C23×Dic11C2311yescharacteristic
135C2×D4×D11—28no—
136C2×D4×D11C2×C418yes—
137C22×D44C2311yescharacteristic
138C22×C4×D11—44no—
139C22×C4×D11—44no—
140C22×C4×D11C2×C418yescomplemented
141C22×C4×D11C2×C418yescomplemented
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2312yes—
147C22×C4×D11C2312yes—
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2311yescharacteristic
153C4×D4×C11C2×C418yescomplemented
154C2×C11×C4⋊C4C2312yes—
155C2×C11×C4⋊C4C2312yes—
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2311yescharacteristic
161C2×C11×C22⋊C4C2311yescharacteristic
162C2×C42×C11C2312yes—
163C2×C42×C11C2311yescharacteristic
164C2×C22⋊Dic11C2312yes—
165C2×C22⋊Dic11C2312yes—
166C2×C22⋊Dic11C2312yes—
167C2×C22⋊Dic11C2311yescharacteristic
168C2×C22⋊Dic11C2311yescharacteristic
169D4×Dic11C2×C418yescomplemented
170C4×C22⋊D11—28no—
171C4×C22⋊D11C2×C418yes—
172C4×C22⋊D11C2×C418yescomplemented
173C2×(C2×D11)⋊C4—44no—
174C2×(C2×D11)⋊C4C2312yes—
175C2×(C2×D11)⋊C4C2312yes—
176C2×(C2×D11)⋊C4C2312yes—
177C2×(C2×D11)⋊C4C2312yes—
178C2×(C2×D11)⋊C4C2312yes—
179C2×(C2×D11)⋊C4C2312yes—
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2311yescharacteristic
185C2×(C2×D11)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2311yescharacteristic
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×C4⋊Dic11C2312yes—
189C2×C4⋊Dic11C2312yes—
190C2×C4⋊Dic11C2311yescharacteristic
191C2×Dic11⋊C4C2312yes—
192C2×Dic11⋊C4C2312yes—
193C2×Dic11⋊C4C2312yes—
194C2×Dic11⋊C4C2312yes—
195C2×Dic11⋊C4C2311yescharacteristic
196C2×Dic11⋊C4C2311yescharacteristic
197C2×C4×Dic11C2312yes—
198C2×C4×Dic11C2312yes—
199C2×C4×Dic11C2312yes—
200C2×C4×Dic11C2312yes—
201C2×C4×Dic11C2312yes—
202C2×C4×Dic11C2312yes—
203C2×C4×Dic11C2312yes—
204C2×C4×Dic11C2311yescharacteristic
205C2×C4×Dic11C2311yescharacteristic
206C2×C4×Dic11C2311yescharacteristic
207#66946C2×C418yescomplemented
208#66945—44no—
209C4⋊C4×D11C2×C418yescomplemented
210(C22⋊D11)⋊C4—28no—
211(C22⋊D11)⋊C4C2×C418yes—
212(C22⋊D11)⋊C4C2×C418yescomplemented
213C22⋊C4×D11—44no—
214C22⋊C4×D11C2×C418yescomplemented
215C22⋊C4×D11C2×C418yescomplemented
216C4×D44C2×C418yescomplemented
217#66925—44no—
218C42×D11C2×C418yescomplemented
219C11×#95C2312yes—
220C11×#95C2312yes—
221C11×#95C2311yescharacteristic
222C11×#95C2311yescharacteristic
223C11×#95C2311yescharacteristic
224C11×#95C2311yescharacteristic
225C11×#95C2312yes—
226C11×#95C2312yes—
227C11×#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2311yescharacteristic
235C11⋊#95C2311yescharacteristic
236C11⋊#95C2312yes—
237C11⋊#95C2311yescharacteristic
238C11⋊#95C2311yescharacteristic
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247#34190—111nomaximal, Sylow
248C24×C11C2411yescharacteristic
249C24×C11C2411yescharacteristic
250C23×D11—24no—
251C23×D11—24no—
252C23×D11—24no—
253C23×D11—24no—
254C23×D11—41no—
255C23×D11—41no—
256C23×D11—41no—
257C23×D11—41no—
258C23×D11C22×C414yes—
259C23×D11C22×C414yes—
260C23×D11C2411yescharacteristic
261C23×D11C2411yescharacteristic
262C23×D11C2411yescharacteristic
263C2×D4×C11—24no—
264C2×D4×C11C22×C414yes—
265C22×C4×C11—24no—
266C22×C4×C11—42no—
267C22×C4×C11—42no—
268C22×C4×C11—42no—
269C22×C4×C11—42no—
270C22×C4×C11C22×C414yes—
271C22×C4×C11C22×C414yes—
272C22×C4×C11C2412yes—
273C22×C4×C11C2412yes—
274C22×C4×C11C2412yes—
275C22×C4×C11C2412yes—
276C22×C4×C11C2411yescharacteristic
277C22×C4×C11C2411yescharacteristic
278C22×C4×C11C2411yescharacteristic
279C22×C4×C11C2411yescharacteristic
280C22×C4×C11C2411yescharacteristic
281C2×C22⋊D11—24no—
282C2×C22⋊D11C22×C414yes—
283C2×C22⋊D11C22×C414yes—
284C2×C22⋊D11#4118yes—
285C22×Dic11—24no—
286C22×Dic11—42no—
287C22×Dic11—42no—
288C22×Dic11—42no—
289C22×Dic11—42no—
290C22×Dic11C22×C414yes—
291C22×Dic11C22×C414yes—
292C22×Dic11C2412yes—
293C22×Dic11C2412yes—
294C22×Dic11C2412yes—
295C22×Dic11C2412yes—
296C22×Dic11C2411yescharacteristic
297C22×Dic11C2411yescharacteristic
298C22×Dic11C2411yescharacteristic
299C22×Dic11C2411yescharacteristic
300C22×Dic11C2411yescharacteristic
301D4×D11—232no—
302C2×D44—24no—
303C2×D44C22×C414yes—
304C2×C4×D11—24no—
305C2×C4×D11—24no—
306C2×C4×D11—24no—
307C2×C4×D11—24no—
308C2×C4×D11—24no—
309C2×C4×D11—24no—
310C2×C4×D11—42no—
311C2×C4×D11—42no—
312C2×C4×D11—42no—
313C2×C4×D11—42no—
314C2×C4×D11—41no—
315C2×C4×D11—41no—
316C2×C4×D11—42no—
317C2×C4×D11—42no—
318C2×C4×D11—42no—
319C2×C4×D11—42no—
320C2×C4×D11—416no—
321C2×C4×D11—416no—
322C2×C4×D11C22×C414yes—
323C2×C4×D11C22×C414yes—
324C2×C4×D11C22×C414yes—
325C2×C4×D11C22×C414yes—
326C2×C4×D11C22×C414yes—
327C2×C4×D11C22×C414yes—
328C2×C4×D11C22×C414yes—
329C2×C4×D11C22×C414yes—
330C2×C4×D11C22×C414yes—
331C11×C4⋊C4—42no—
332C11×C4⋊C4—42no—
333C11×C4⋊C4C22×C414yes—
334C11×C22⋊C4—24no—
335C11×C22⋊C4—42no—
336C11×C22⋊C4—42no—
337C11×C22⋊C4C22×C414yes—
338C11×C22⋊C4C22×C414yes—
339C42×C11—42no—
340C42×C11C22×C414yes—
341C22⋊Dic11—24no—
342C22⋊Dic11—42no—
343C22⋊Dic11—42no—
344C22⋊Dic11C22×C414yes—
345C22⋊Dic11C22×C414yes—
346(C2×D11)⋊C4—24no—
347(C2×D11)⋊C4—24no—
348(C2×D11)⋊C4—24no—
349(C2×D11)⋊C4—24no—
350(C2×D11)⋊C4—24no—
351(C2×D11)⋊C4—24no—
352(C2×D11)⋊C4—42no—
353(C2×D11)⋊C4—42no—
354(C2×D11)⋊C4—42no—
355(C2×D11)⋊C4—42no—
356(C2×D11)⋊C4C22×C414yes—
357(C2×D11)⋊C4C22×C414yes—
358(C2×D11)⋊C4C22×C414yes—
359(C2×D11)⋊C4C22×C414yes—
360C4⋊Dic11—42no—
361C4⋊Dic11—42no—
362C4⋊Dic11C22×C414yes—
363Dic11⋊C4—24no—
364Dic11⋊C4—24no—
365Dic11⋊C4—42no—
366Dic11⋊C4—42no—
367Dic11⋊C4C22×C414yes—
368Dic11⋊C4C22×C414yes—
369C4×Dic11—24no—
370C4×Dic11—24no—
371C4×Dic11—42no—
372C4×Dic11—42no—
373C4×Dic11—42no—
374C4×Dic11—42no—
375C4×Dic11—42no—
376C4×Dic11C22×C414yes—
377C4×Dic11C22×C414yes—
378C4×Dic11C22×C414yes—
379C22×C4×D4—111no—
380#2357—112no—
381#2353—112no—
382#2353—112no—
383#2349—112no—
384#2344—112no—
385#2342—112no—
386#2342—112no—
387D4×C22⋊C4—112no—
388#2319—111no—
389#2319—111no—
390#2318—111no—
391#2318—111no—
392#2318—111no—
393#2318D1111yescharacteristic, complemented
394#2283—111no—
395#2283—111no—
396#2280—111no—
397#2280—111no—
398C2×#381—111no—
399C2×#381—111no—
400#2275—111no—
401#2275—111no—
402C23×C11—22no—
403C23×C11—21no—
404C23×C11—21no—
405C23×C11—22no—
406C23×C11—22no—
407C23×C11—21no—
408C23×C11—21no—
409C23×C11C23×C412yes—
410C23×C11C23×C412yes—
411C23×C11C2×#4114yes—
412C23×C11C2511yescharacteristic
413C22×D11—22no—
414C22×D11—22no—
415C22×D11—21no—
416C22×D11—21no—
417C22×D11—21no—
418C22×D11—21no—
419C22×D11—28no—
420C22×D11—22no—
421C22×D11—22no—
422C22×D11—21no—
423C22×D11—21no—
424C22×D11—28no—
425C22×D11—28no—
426C22×D11—28no—
427C22×D11—44no—
428C22×D11—44no—
429C22×D11—48no—
430C22×D11—48no—
431C22×D11—48no—
432C22×D11—48no—
433C22×D11C23×C412yes—
434C22×D11C23×C412yes—
435C22×D11C23×C412yes—
436C22×D11C2×#4114yes—
437C22×D11H(5,𝔽2)14yes—
438D4×C11—28no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—21no—
444C2×C4×C11—21no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
456C2×C4×C11—22no—
457C2×C4×C11—44no—
458C2×C4×C11—44no—
459C2×C4×C11—84no—
460C2×C4×C11C23×C412yes—
461C2×C4×C11C23×C412yes—
462C2×C4×C11C23×C412yes—
463C2×C4×C11C23×C412yes—
464C2×C4×C11C23×C412yes—
465C22⋊D11—28no—
466C22⋊D11#117116yescomplemented
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—21no—
471C2×Dic11—21no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—44no—
485C2×Dic11—44no—
486C2×Dic11—84no—
487C2×Dic11C23×C412yes—
488C2×Dic11C23×C412yes—
489C2×Dic11C23×C412yes—
490C2×Dic11C23×C412yes—
491C2×Dic11C23×C412yes—
492C2×Dic11C2×#4114yes—
493D44—28no—
494C4×D11—28no—
495C4×D11—28no—
496C4×D11—28no—
497C4×D11—28no—
498C4×D11—44no—
499C4×D11—44no—
500C4×D11—44no—
501C4×D11—44no—
502C4×D11—44no—
503C4×D11—84no—
504C4×D11—84no—
505C23×D4—111no—
506C24×C4—111no—
507C24×C4—111no—
508C2×C4×D4—111no—
509C2×C4×D4—111no—
510C2×C4×D4—111no—
511C2×C4×D4—1116no—
512C2×C4×D4—112no—
513C2×C4×D4—111no—
514C2×C4×D4—111no—
515C2×C4×D4—111no—
516C2×C4×D4—112no—
517C2×C4×D4—111no—
518C2×C4×D4C2×D1111yescharacteristic
519C2×#117—112no—
520C2×#117—112no—
521C22×C4⋊C4—111no—
522C22×C22⋊C4—111no—
523C22×C22⋊C4—111no—
524C22×C22⋊C4—112no—
525C22×C22⋊C4—112no—
526C22×C42—111no—
527#390—112no—
528#390—112no—
529#389—112no—
530#389—112no—
531#388—112no—
532#388—112no—
533#388—112no—
534#388—112no—
535#388—112no—
536#388—112no—
537#388—112no—
538#388C2×D1112yescomplemented
539#387—112no—
540#387—112no—
541#387—112no—
542#387C2×D1112yescomplemented
543#386—112no—
544#386—112no—
545#386—112no—
546#386C2×D1112yes—
547#385—112no—
548#385—112no—
549#385—112no—
550#385C2×D1112yescomplemented
551#383—111no—
552#383—112no—
553#383C2×D1111yescharacteristic, complemented
554#382—111no—
555#382—112no—
556#382C2×D1111yescharacteristic, complemented
557#381—111no—
558#381—112no—
559#381—111no—
560#381—111no—
561#381—112no—
562#381—112no—
563#381—112no—
564#381—111no—
565#381—111no—
566#381—111no—
567#381—111no—
568#381C2×D1111yescharacteristic, complemented
569#380—111no—
570#380—112no—
571#380—112no—
572#380—112no—
573#380—111no—
574#380—111no—
575#380—112no—
576#380C2×D1111yescharacteristic, complemented
577#379—112no—
578#379—112no—
579C4×C4⋊C4—112no—
580C4×C4⋊C4—112no—
581C4×C4⋊C4—111no—
582C4×C4⋊C4—111no—
583C4×C4⋊C4—112no—
584C4×C22⋊C4—111no—
585C4×C22⋊C4—112no—
586C4×C22⋊C4—112no—
587C4×C22⋊C4—112no—
588C4×C22⋊C4—112no—
589C4×C22⋊C4—112no—
590C4×C22⋊C4—111no—
591C4×C22⋊C4—111no—
592C4×C22⋊C4—112no—
593C4×C22⋊C4—112no—
594C4×C22⋊C4—112no—
595C4×C22⋊C4C2×D1111yescharacteristic, complemented
596#376—111no—
597#376—111no—
598#376—112no—
599C2×#95—111no—
600C2×#95—112no—
601C2×#95—111no—
602C2×#95—111no—
603C2×#95—112no—
604C2×#95C2×D1111yescharacteristic, complemented
605C22×C11—22no—
606C22×C11—22no—
607C22×C11—24no—
608C22×C11—24no—
609C22×C11—22no—
610C22×C11—22no—
611C22×C11—22no—
612C22×C11—42no—
613C22×C11—42no—
614C22×C11C2×#11714yes—
615C22×C11C24×C411yescharacteristic
616C22×C11C22×#4112yes—
617C22×C11C2×H(5,𝔽2)12yes—
618C22×C11#58511yescharacteristic
619C22×C11#58511yescharacteristic
620C2×D11—22no—
621C2×D11—22no—
622C2×D11—22no—
623C2×D11—22no—
624C2×D11—24no—
625C2×D11—24no—
626C2×D11—24no—
627C2×D11—24no—
628C2×D11—22no—
629C2×D11—22no—
630C2×D11—22no—
631C2×D11—416no—
632C2×D11—416no—
633C2×D11—42no—
634C2×D11—42no—
635C2×D11C2×#11714yes—
636C2×D11#51814yes—
637C4×C11—22no—
638C4×C11—22no—
639C4×C11—22no—
640C4×C11—22no—
641C4×C11—22no—
642C4×C11—42no—
643C4×C11—42no—
644C4×C11—42no—
645C4×C11—42no—
646Dic11—22no—
647Dic11—22no—
648Dic11—22no—
649Dic11—22no—
650Dic11—42no—
651Dic11—42no—
652Dic11—42no—
653Dic11—42no—
654Dic11C2×#11714yes—
655C25—111no—
656C25—111no—
657C22×D4—111no—
658C22×D4—111no—
659C22×D4—118no—
660C22×D4—111no—
661C22×D4—228no—
662C22×D4C22×D1111yescharacteristic
663C23×C4—111no—
664C23×C4—111no—
665C23×C4—111no—
666C23×C4—111no—
667C23×C4—111no—
668C23×C4—111no—
669C23×C4—118no—
670C23×C4—118no—
671C23×C4—111no—
672C23×C4—111no—
673C23×C4—111no—
674C23×C4—111no—
675C23×C4—111no—
676C23×C4—112no—
677C23×C4—112no—
678C23×C4—112no—
679C23×C4—444no—
680C23×C4—444no—
681C23×C4C22×D1112yes—
682C23×C4C22×D1111yescharacteristic
683C23×C4C22×D1111yescharacteristic
684C4×D4—118no—
685C4×D4—118no—
686C4×D4—118no—
687C4×D4—118no—
688C4×D4—118no—
689C4×D4—118no—
690C4×D4—118no—
691C4×D4—228no—
692C4×D4—228no—
693C4×D4C4×D1118yescomplemented
694#117—444no—
695#117—444no—
696C2×C4⋊C4—111no—
697C2×C4⋊C4—111no—
698C2×C4⋊C4—111no—
699C2×C4⋊C4—118no—
700C2×C4⋊C4—112no—
701C2×C4⋊C4—112no—
702C2×C4⋊C4—112no—
703C2×C4⋊C4—112no—
704C2×C4⋊C4—112no—
705C2×C4⋊C4—112no—
706C2×C4⋊C4C22×D1112yes—
707C2×C4⋊C4C22×D1112yes—
708C2×C4⋊C4C22×D1111yescharacteristic
709C2×C22⋊C4—111no—
710C2×C22⋊C4—111no—
711C2×C22⋊C4—111no—
712C2×C22⋊C4—111no—
713C2×C22⋊C4—111no—
714C2×C22⋊C4—111no—
715C2×C22⋊C4—118no—
716C2×C22⋊C4—118no—
717C2×C22⋊C4—112no—
718C2×C22⋊C4—112no—
719C2×C22⋊C4—112no—
720C2×C22⋊C4—112no—
721C2×C22⋊C4—112no—
722C2×C22⋊C4—112no—
723C2×C22⋊C4—112no—
724C2×C22⋊C4—112no—
725C2×C22⋊C4—112no—
726C2×C22⋊C4—112no—
727C2×C22⋊C4—112no—
728C2×C22⋊C4—112no—
729C2×C22⋊C4—112no—
730C2×C22⋊C4—444no—
731C2×C22⋊C4—444no—
732C2×C22⋊C4C22×D1112yes—
733C2×C22⋊C4C22×D1112yes—
734C2×C22⋊C4C22×D1112yes—
735C2×C22⋊C4C22×D1111yescharacteristic
736C2×C22⋊C4C22×D1111yescharacteristic
737C2×C42—111no—
738C2×C42—111no—
739C2×C42—111no—
740C2×C42—118no—
741C2×C42—112no—
742C2×C42—112no—
743C2×C42—112no—
744C2×C42—112no—
745C2×C42—112no—
746C2×C42—112no—
747C2×C42—112no—
748C2×C42C22×D1112yes—
749C2×C42C22×D1111yescharacteristic
750#95—111no—
751#95—112no—
752#95—112no—
753#95—112no—
754#95—111no—
755#95—111no—
756#95—112no—
757#95—112no—
758#95—112no—
759#95—112no—
760#95—112no—
761#95—112no—
762#95—111no—
763#95—112no—
764#95—112no—
765#95—112no—
766#95—112no—
767#95—112no—
768#95—112no—
769#95C22×D1111yescharacteristic
770#95C22×D1111yescharacteristic
771#95C22×D1112yes—
772#95C22×D1111yescharacteristic
773#95C22×D1112yes—
774#95C22×D1111yescharacteristic
775#95C22×D1112yes—
776#95C22×D1112yes—
777#95C22×D1112yes—
778C2×C11—24no—
779C2×C11—42no—
780C2×C11C22×#11711yescharacteristic
781C2×C11C2×#51811yescharacteristic
782C2×C11#342811yescharacteristic
783C2×C11#351312yes—
784C2×C11#351312yes—
785D11—24no—
786D11—24no—
787D11—42no—
788C24—111no—
789C24—111no—
790C24—111no—
791C24—114no—
792C24—114no—
793C24—224no—
794C24—224no—
795C24—224no—
796C24—224no—
797C24—441no—
798C24—441no—
799C24—441no—
800C24—441no—
801C24C23×D1111yescharacteristic
802C24C23×D1111yescharacteristic
803C2×D4—24no—
804C2×D4—114no—
805C2×D4—118no—
806C2×D4—114no—
807C2×D4—114no—
808C2×D4—224no—
809C2×D4—224no—
810C2×D4—2232no—
811C2×D4C2×C4×D1114yes—
812C22×C4—24no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—111no—
818C22×C4—111no—
819C22×C4—111no—
820C22×C4—111no—
821C22×C4—111no—
822C22×C4—114no—
823C22×C4—114no—
824C22×C4—114no—
825C22×C4—114no—
826C22×C4—114no—
827C22×C4—114no—
828C22×C4—114no—
829C22×C4—114no—
830C22×C4—114no—
831C22×C4—114no—
832C22×C4—114no—
833C22×C4—112no—
834C22×C4—112no—
835C22×C4—112no—
836C22×C4—112no—
837C22×C4—224no—
838C22×C4—224no—
839C22×C4—224no—
840C22×C4—224no—
841C22×C4—224no—
842C22×C4—224no—
843C22×C4—224no—
844C22×C4—442no—
845C22×C4—442no—
846C22×C4—442no—
847C22×C4—442no—
848C22×C4—441no—
849C22×C4—441no—
850C22×C4—442no—
851C22×C4—442no—
852C22×C4—442no—
853C22×C4—442no—
854C22×C4—4416no—
855C22×C4—4416no—
856C22×C4—442no—
857C22×C4—442no—
858C22×C4—442no—
859C22×C4—442no—
860C22×C4C2×C4×D1114yes—
861C22×C4C2×C4×D1114yes—
862C22×C4C23×D1112yes—
863C22×C4C23×D1112yes—
864C22×C4C23×D1112yes—
865C22×C4C23×D1112yes—
866C22×C4C23×D1111yescharacteristic
867C22×C4C23×D1111yescharacteristic
868C22×C4C23×D1111yescharacteristic
869C22×C4C23×D1111yescharacteristic
870C22×C4C23×D1111yescharacteristic
871C4⋊C4—42no—
872C4⋊C4—42no—
873C4⋊C4—114no—
874C4⋊C4—114no—
875C4⋊C4—114no—
876C4⋊C4—224no—
877C4⋊C4—224no—
878C4⋊C4—442no—
879C4⋊C4—442no—
880C4⋊C4—442no—
881C4⋊C4—442no—
882C4⋊C4C2×C4×D1114yes—
883C22⋊C4—24no—
884C22⋊C4—42no—
885C22⋊C4—42no—
886C22⋊C4—114no—
887C22⋊C4—114no—
888C22⋊C4—114no—
889C22⋊C4—114no—
890C22⋊C4—114no—
891C22⋊C4—114no—
892C22⋊C4—224no—
893C22⋊C4—224no—
894C22⋊C4—224no—
895C22⋊C4—224no—
896C22⋊C4—224no—
897C22⋊C4—224no—
898C22⋊C4—224no—
899C22⋊C4—442no—
900C22⋊C4—442no—
901C22⋊C4—442no—
902C22⋊C4—442no—
903C22⋊C4—442no—
904C22⋊C4—442no—
905C22⋊C4C2×C4×D1114yes—
906C22⋊C4C2×C4×D1114yes—
907C42—42no—
908C42—114no—
909C42—114no—
910C42—114no—
911C42—224no—
912C42—224no—
913C42—442no—
914C42—442no—
915C42—442no—
916C42—442no—
917C42—442no—
918C42C2×C4×D1114yes—
919C11#3419011yescharacteristic, complemented, Sylow
920C23—22no—
921C23—21no—
922C23—21no—
923C23—22no—
924C23—22no—
925C23—21no—
926C23—21no—
927C23—112no—
928C23—112no—
929C23—114no—
930C23—114no—
931C23—112no—
932C23—228no—
933C23—228no—
934C23—228no—
935C23—222no—
936C23—222no—
937C23—221no—
938C23—221no—
939C23—221no—
940C23—221no—
941C23—228no—
942C23—222no—
943C23—222no—
944C23—221no—
945C23—221no—
946C23—444no—
947C23—444no—
948C23—448no—
949C23—448no—
950C23—448no—
951C23—448no—
952C23C22×C4×D1112yes—
953C23C22×C4×D1112yes—
954C23#41×D1114yes—
955C23C24×D1111yescharacteristic
956D4—28no—
957D4—1116no—
958D4—228no—
959D4—228no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—44no—
979C2×C4—44no—
980C2×C4—84no—
981C2×C4—112no—
982C2×C4—114no—
983C2×C4—112no—
984C2×C4—112no—
985C2×C4—112no—
986C2×C4—112no—
987C2×C4—228no—
988C2×C4—228no—
989C2×C4—228no—
990C2×C4—228no—
991C2×C4—222no—
992C2×C4—222no—
993C2×C4—222no—
994C2×C4—221no—
995C2×C4—221no—
996C2×C4—222no—
997C2×C4—222no—
998C2×C4—222no—
999C2×C4—222no—
1000C2×C4—222no—
1001C2×C4—222no—
1002C2×C4—222no—
1003C2×C4—222no—
1004C2×C4—222no—
1005C2×C4—222no—
1006C2×C4—222no—
1007C2×C4—222no—
1008C2×C4—444no—
1009C2×C4—444no—
1010C2×C4—444no—
1011C2×C4—444no—
1012C2×C4—444no—
1013C2×C4—444no—
1014C2×C4—444no—
1015C2×C4—884no—
1016C2×C4—884no—
1017C2×C4—884no—
1018C2×C4C22×C4×D1112yes—
1019C2×C4C22×C4×D1112yes—
1020C2×C4C22×C4×D1112yes—
1021C2×C4C22×C4×D1112yes—
1022C2×C4C22×C4×D1112yes—
1023C22—24no—
1024C22—24no—
1025C22—22no—
1026C22—22no—
1027C22—22no—
1028C22—22no—
1029C22—22no—
1030C22—42no—
1031C22—42no—
1032C22—114no—
1033C22—114no—
1034C22—222no—
1035C22—224no—
1036C22—224no—
1037C22—224no—
1038C22—224no—
1039C22—222no—
1040C22—222no—
1041C22—222no—
1042C22—222no—
1043C22—222no—
1044C22—222no—
1045C22—4416no—
1046C22—4416no—
1047C22—442no—
1048C22—442no—
1049C22D11×#11714yes—
1050C22C23×C4×D1111yescharacteristic
1051C22C2×#41×D1112yes—
1052C22D11×H(5,𝔽2)12yes—
1053C22#1062345511yescharacteristic
1054C22#1062345711yescharacteristic
1055C4—22no—
1056C4—22no—
1057C4—22no—
1058C4—22no—
1059C4—22no—
1060C4—42no—
1061C4—42no—
1062C4—42no—
1063C4—42no—
1064C4—114no—
1065C4—222no—
1066C4—222no—
1067C4—222no—
1068C4—222no—
1069C4—442no—
1070C4—442no—
1071C4—442no—
1072C4—442no—
1073C2—24no—
1074C2—42no—
1075C2—224no—
1076C2—224no—
1077C2—442no—
1078C2C2×D11×#11711yescharacteristic
1079C2D11×#51811yescharacteristic
1080C2#1308181611yescharacteristic
1081C2#1308254612yes—
1082C2#1308255212yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2318C2
socle, cosocleC23×C11C25
prime radicalC22×D4×D11C22
hypercenter#2318D11
hypocenterC11#34190
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2318

Complements

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

NH ≅ G/Ntype
2. #13071586C2semidirect
3. #13071555C2semidirect
4. #13071554C2semidirect
5. #13071522C2semidirect
6. #13071482C2semidirect
7. #13071463C2semidirect
8. #13071460C2semidirect
10. #13071258C2semidirect
11. #13071256C2semidirect
12. #13071252C2semidirect
13. #13071249C2semidirect
14. #13071247C2semidirect
15. #13071013C2semidirect
16. #13071009C2semidirect
17. #13070998C2semidirect
18. #13070997C2semidirect
19. C2×#10622277C2semidirect
20. D11×#381C2semidirect
21. #13070975C2semidirect
22. #13070974C2semidirect
23. C11×#2318C2semidirect
33. C4×D4×D11C4semidirect
46. C11×#388C22semidirect
47. C11×#387C22semidirect
49. C11×#385C22semidirect
50. C11×#383C22semidirect
51. C11×#382C22semidirect
52. C11×#381C22semidirect
53. C11×#380C22semidirect
54. C4×C11×C22⋊C4C22semidirect
55. C2×C11×#95C22semidirect
57. #10622825C22semidirect
58. #10622824C22semidirect
59. C4×C22⋊Dic11C22semidirect
60. C4×C22⋊Dic11C22semidirect
61. C2×C11⋊#95C22semidirect
62. C2×C11⋊#95C22semidirect
63. #10622603C22semidirect
64. #10622603C22semidirect
65. #10622602C22semidirect
67. #10622600C22semidirect
68. #10622594C22semidirect
69. C4⋊C4×Dic11C22semidirect
70. #10622585C22semidirect
75. #10622564C22semidirect
76. #10622563C22semidirect
77. #10622558C22semidirect
78. #10622557C22semidirect
79. #10622556C22semidirect
80. #10622555C22semidirect
81. C22⋊C4×Dic11C22semidirect
82. C22⋊C4×Dic11C22semidirect
83. C4×(C2×D11)⋊C4C22semidirect
84. C4×(C2×D11)⋊C4C22semidirect
85. #10622550C22semidirect
86. #10622549C22semidirect
87. C4×Dic11⋊C4C22semidirect
88. #10622283C22semidirect
89. #10622283C22semidirect
90. #10622281C22semidirect
92. #10622280C22semidirect
93. #10622280C22semidirect
96. #10622279C22semidirect
97. #10622279C22semidirect
98. #10622279C22semidirect
107. #10622277C22semidirect
108. #10622277C22semidirect
109. #10622277C22semidirect
110. D11×#95C22semidirect
111. D11×#95C22semidirect
112. D11×#95C22semidirect
113. #10622267C22semidirect
114. #10622266C22semidirect
115. #10622264C22semidirect
116. #10622263C22semidirect
117. #10622262C22semidirect
118. #10622262C22semidirect
119. #10622262C22semidirect
120. #10622261C22semidirect
121. #10622261C22semidirect
122. #10622261C22semidirect
123. #10622260C22semidirect
140. C22×C4×D11C2×C4semidirect
141. C22×C4×D11C2×C4semidirect
153. C4×D4×C11C2×C4semidirect
169. D4×Dic11C2×C4semidirect
172. C4×C22⋊D11C2×C4semidirect
207. #66946C2×C4semidirect
209. C4⋊C4×D11C2×C4semidirect
212. (C22⋊D11)⋊C4C2×C4semidirect
214. C22⋊C4×D11C2×C4semidirect
215. C22⋊C4×D11C2×C4semidirect
216. C4×D44C2×C4semidirect
218. C42×D11C2×C4semidirect
393. #2318D11semidirect
466. C22⋊D11#117semidirect
538. #388C2×D11semidirect
542. #387C2×D11semidirect
550. #385C2×D11semidirect
553. #383C2×D11semidirect
556. #382C2×D11semidirect
568. #381C2×D11semidirect
576. #380C2×D11semidirect
595. C4×C22⋊C4C2×D11semidirect
604. C2×#95C2×D11semidirect
693. C4×D4C4×D11semidirect
919. C11#34190semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D112
#130715862
#130715552
#130715542
#130715222
#130714822
#130714632
#130714602
#130714342
#130712582
#130712562
#130712522
#130712492
#130712472
#130710132
#130710092
#130709982
#130709972
C2×#106222772
D11×#3812
#130709752
#130709742
C11×#23182
#3419011