Finite Group Databasebeta

← #14914263

Subgroups — #14914263

Order 2816.

3014 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623359C211yesmaximal, characteristic
2#13071695C212yesmaximal, complemented
3#13071665C212yesmaximal, complemented
4#13071614C212yesmaximal, complemented
5#13071602C212yesmaximal, complemented
6#13071559C211yesmaximal, characteristic, complemented
7#13071553C211yesmaximal, characteristic, complemented
8#13071523C211yesmaximal, characteristic, complemented
9#13071520C211yesmaximal, characteristic, complemented
10#13071478C211yesmaximal, characteristic, complemented
11#13071472C211yesmaximal, characteristic, complemented
12#13071446C211yesmaximal, characteristic, complemented
13#13071348C212yesmaximal, complemented
14#13071318C212yesmaximal, complemented
15#13071251C211yesmaximal, characteristic, complemented
16#13071245C211yesmaximal, characteristic, complemented
17#13071121C212yesmaximal, complemented
18C4×#66990C212yesmaximal, complemented
19#13070996C211yesmaximal, characteristic, complemented
20#13070975C211yesmaximal, characteristic, complemented
21#13070974C211yesmaximal, characteristic, complemented
22C2×D11×#95C211yesmaximal, characteristic, complemented
23C11×#2339C211yesmaximal, characteristic, complemented
24C22×C11×#41C2211yescharacteristic
25C23×C4×D11C2212yes—
26C23×C4×D11C2211yescharacteristic
27C2×C4×D4×C11C2212yes—
28#10623359C4116yescomplemented
29C2×#66999C2211yescharacteristic
30C2×#66999C2211yescharacteristic
31C2×#66991C2211yescharacteristic
32C2×#66991C2211yescharacteristic
33C2×#66990C2211yescharacteristic
34C2×#66990C2211yescharacteristic
35C2×#66988C2211yescharacteristic
36C2×#66988C2211yescharacteristic
37C2×D4×Dic11C2212yes—
38C2×C4×C22⋊D11C2212yes—
39C2×C4×C22⋊D11C2212yes—
40C2×C4×C22⋊D11C2211yescharacteristic
41C2×C4×C22⋊D11C2211yescharacteristic
42C2×C4×C22⋊D11C2211yescharacteristic
43C2×C4×C22⋊D11C2211yescharacteristic
44C2×#66979C2211yescharacteristic
45C2×(C22⋊D11)⋊C4C2212yes—
46C2×(C22⋊D11)⋊C4C2212yes—
47C2×#66930C2212yes—
48C11×#391C2212yescomplemented
49C11×#386C2212yes—
50C11×#386C2212yescomplemented
51C11×#381C2211yescharacteristic
52C11×#381C2211yescharacteristic, complemented
53C11×#380C2211yescharacteristic, complemented
54C4×C11×C22⋊C4C2211yescharacteristic, complemented
55C2×C11×#95C2211yescharacteristic
56C2×C11×#95C2211yescharacteristic, complemented
57#10622843C2212yescomplemented
58#10622833C2212yes—
59#10622833C2212yescomplemented
60#10622825C2211yescharacteristic, complemented
61#10622824C2211yescharacteristic
62#10622824C2211yescharacteristic, complemented
63#10622823C2212yes—
64#10622823C2212yescomplemented
65C4×C22⋊Dic11C2212yes—
66C4×C22⋊Dic11C2212yescomplemented
67C4×C22⋊Dic11C2211yescharacteristic, complemented
68C2×C11⋊#95C2211yescharacteristic
69C2×C11⋊#95C2212yes—
70C2×C11⋊#95C2211yescharacteristic, complemented
71#10622602C2212yes—
72#10622602C2212yes—
73#10622591C2212yescomplemented
74#10622585C2212yescomplemented
75#10622569C2212yes—
76#10622569C2212yes—
77#10622569C2212yes—
78#10622569C2212yes—
79#10622568C2212yes—
80#10622559C2212yes—
81#10622559C2212yescomplemented
82#10622558C2212yescomplemented
83#10622558C2212yescomplemented
84#10622557C2212yescomplemented
85#10622557C2212yescomplemented
86C22⋊C4×Dic11C2212yes—
87C22⋊C4×Dic11C2212yescomplemented
88C4×(C2×D11)⋊C4C2212yes—
89C4×(C2×D11)⋊C4C2212yes—
90#10622546C2212yescomplemented
91C4×Dic11⋊C4C2212yescomplemented
92#10622281C2212yes—
93#10622281C2212yes—
94#10622280C2211yescharacteristic
95#10622280C2211yescharacteristic
96#10622280C2212yes—
97#10622279C2212yes—
98#10622279C2212yes—
99#10622279C2212yes—
100#10622279C2211yescharacteristic
101#10622279C2211yescharacteristic
102D11×#95C2212yes—
103D11×#95C2211yescharacteristic
104D11×#95C2211yescharacteristic
105D11×#95C2211yescharacteristic
106D11×#95C2211yescharacteristic
107D11×#95C2212yes—
108#10622268C2212yescomplemented
109#10622267C2212yescomplemented
110#10622267C2212yescomplemented
111#10622266C2212yescomplemented
112#10622266C2212yescomplemented
113#10622265C2212yescomplemented
114#10622264C2211yescharacteristic, complemented
115#10622264C2211yescharacteristic, complemented
116#10622263C2211yescharacteristic, complemented
117#10622263C2211yescharacteristic, complemented
118#10622262C2212yescomplemented
119#10622262C2211yescharacteristic, complemented
120#10622262C2211yescharacteristic, complemented
121#10622261C2211yescharacteristic, complemented
122#10622261C2211yescharacteristic, complemented
123#10622260C2212yescomplemented
124C24×D11C2311yescharacteristic
125C2×C11×#41—44no—
126C2×C11×#41C2×C418yescomplemented
127C22×Q8×C11C2311yescharacteristic
128C22×D4×C11C2311yescharacteristic
129C22×D4×C11C2311yescharacteristic
130C22×D4×C11C2311yescharacteristic
131C23×C4×C11C2312yes—
132C23×C4×C11C2311yescharacteristic
133C23×C4×C11C2312yes—
134C23×C4×C11C2311yescharacteristic
135C23×C4×C11C2311yescharacteristic
136C22×C22⋊D11C2311yescharacteristic
137C22×C22⋊D11C2311yescharacteristic
138C22×C22⋊D11C2311yescharacteristic
139C22×C22⋊D11C2311yescharacteristic
140C23×Dic11C2312yes—
141C23×Dic11C2311yescharacteristic
142C23×Dic11C2312yes—
143C22×C4×D11—28no—
144C22×C4×D11—44no—
145C22×C4×D11—44no—
146C22×C4×D11—44no—
147C22×C4×D11C2×C418yescomplemented
148C22×C4×D11C2312yes—
149C22×C4×D11C2312yes—
150C22×C4×D11C2312yes—
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2311yescharacteristic
154C22×C4×D11C2311yescharacteristic
155C22×C4×D11C2312yes—
156C4×D4×C11—44no—
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C42×C11C2312yes—
163C2×C22⋊Dic11C2312yes—
164C2×C22⋊Dic11C2312yes—
165C2×C22⋊Dic11C2312yes—
166C2×C22⋊Dic11C2312yes—
167C2×C22⋊Dic11C2311yescharacteristic
168C2×C22⋊Dic11C2311yescharacteristic
169C2×C22⋊Dic11C2311yescharacteristic
170C2×C22⋊Dic11C2311yescharacteristic
171C2×C22⋊Dic11C2311yescharacteristic
172C2×C22⋊Dic11C2311yescharacteristic
173#66999C2×C418yescomplemented
174#66999C2×C418yescomplemented
175#66991C2×C418yescomplemented
176#66991C2×C418yescomplemented
177#66990C2×C418yescomplemented
178#66990C2×C418yescomplemented
179#66988C2×C418yescomplemented
180#66988C2×C418yescomplemented
181D4×Dic11—44no—
182C4×C22⋊D11—28no—
183C4×C22⋊D11—44no—
184C4×C22⋊D11C2×C418yescomplemented
185C4×C22⋊D11C2×C418yescomplemented
186C4×C22⋊D11C2×C418yescomplemented
187C4×C22⋊D11C2×C418yescomplemented
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2311yescharacteristic
193C2×(C2×D11)⋊C4C2311yescharacteristic
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2311yescharacteristic
196#66979C2×C418yescomplemented
197C2×C4⋊Dic11C2312yes—
198C2×C4⋊Dic11C2311yescharacteristic
199C2×C4⋊Dic11C2311yescharacteristic
200C2×Dic11⋊C4C2312yes—
201C2×Dic11⋊C4C2312yes—
202C2×Dic11⋊C4C2312yes—
203C2×Dic11⋊C4C2312yes—
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C2312yes—
206C2×Dic11⋊C4C2311yescharacteristic
207C2×Dic11⋊C4C2311yescharacteristic
208C2×Dic11⋊C4C2311yescharacteristic
209C2×Dic11⋊C4C2311yescharacteristic
210C2×C4×Dic11C2312yes—
211C2×C4×Dic11C2312yes—
212C2×C4×Dic11C2312yes—
213C2×C4×Dic11C2312yes—
214C2×C4×Dic11C2312yes—
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2311yescharacteristic
219(C22⋊D11)⋊C4—28no—
220(C22⋊D11)⋊C4—44no—
221#66930—44no—
222C11×#95C2312yes—
223C11×#95C2311yescharacteristic
224C11×#95C2311yescharacteristic
225C11×#95C2311yescharacteristic
226C11×#95C2311yescharacteristic
227C11×#95C2312yes—
228C11×#95C2312yes—
229C11×#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2311yescharacteristic
232C11⋊#95C2311yescharacteristic
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2311yescharacteristic
236C11⋊#95C2312yes—
237C11⋊#95C2311yescharacteristic
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250#34218—111nomaximal, Sylow
251C24×C11C2411yescharacteristic
252C24×C11C2411yescharacteristic
253C24×C11C2411yescharacteristic
254C23×D11—24no—
255C23×D11—24no—
256C23×D11—22no—
257C23×D11—22no—
258C23×D11C22×C414yes—
259C23×D11C2411yescharacteristic
260C23×D11C2411yescharacteristic
261C11×#41—416no—
262C2×Q8×C11—42no—
263C2×Q8×C11C22×C414yescomplemented
264C2×D4×C11—24no—
265C2×D4×C11—24no—
266C2×D4×C11—42no—
267C2×D4×C11C22×C414yes—
268C2×D4×C11C22×C414yes—
269C2×D4×C11C22×C414yescomplemented
270C22×C4×C11—24no—
271C22×C4×C11—24no—
272C22×C4×C11—24no—
273C22×C4×C11—24no—
274C22×C4×C11—42no—
275C22×C4×C11—42no—
276C22×C4×C11—42no—
277C22×C4×C11—42no—
278C22×C4×C11—42no—
279C22×C4×C11C22×C414yes—
280C22×C4×C11C22×C414yescomplemented
281C22×C4×C11C22×C414yescomplemented
282C22×C4×C11C2412yes—
283C22×C4×C11C2412yes—
284C22×C4×C11C2412yes—
285C22×C4×C11C2411yescharacteristic
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2412yes—
290C2×C22⋊D11—24no—
291C2×C22⋊D11—24no—
292C2×C22⋊D11—22no—
293C2×C22⋊D11—22no—
294C2×C22⋊D11—22no—
295C2×C22⋊D11—22no—
296C2×C22⋊D11C22×C414yes—
297C2×C22⋊D11C22×C414yes—
298C2×C22⋊D11C22×C414yes—
299C2×C22⋊D11C22×C414yes—
300C22×Dic11—24no—
301C22×Dic11—24no—
302C22×Dic11—24no—
303C22×Dic11—24no—
304C22×Dic11—42no—
305C22×Dic11—42no—
306C22×Dic11—42no—
307C22×Dic11C22×C414yes—
308C22×Dic11C2412yes—
309C22×Dic11C2412yes—
310C22×Dic11C2412yes—
311C22×Dic11C2411yescharacteristic
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2411yescharacteristic
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2412yes—
318C2×C4×D11—24no—
319C2×C4×D11—24no—
320C2×C4×D11—24no—
321C2×C4×D11—24no—
322C2×C4×D11—24no—
323C2×C4×D11—416no—
324C2×C4×D11—42no—
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—42no—
332C2×C4×D11—42no—
333C2×C4×D11—42no—
334C2×C4×D11—432no—
335C2×C4×D11C22×C414yes—
336C2×C4×D11C22×C414yes—
337C2×C4×D11C22×C414yes—
338C2×C4×D11C22×C414yes—
339C2×C4×D11#4118yescomplemented
340C11×C4⋊C4—42no—
341C11×C22⋊C4—24no—
342C11×C22⋊C4—24no—
343C11×C22⋊C4—42no—
344C11×C22⋊C4—42no—
345C42×C11—42no—
346C22⋊Dic11—24no—
347C22⋊Dic11—24no—
348C22⋊Dic11—42no—
349C22⋊Dic11—42no—
350C22⋊Dic11C22×C414yes—
351C22⋊Dic11C22×C414yes—
352C22⋊Dic11C22×C414yescomplemented
353C22⋊Dic11C22×C414yescomplemented
354C22⋊Dic11C22×C414yescomplemented
355C22⋊Dic11C22×C414yescomplemented
356(C2×D11)⋊C4—24no—
357(C2×D11)⋊C4—24no—
358(C2×D11)⋊C4—24no—
359(C2×D11)⋊C4—24no—
360(C2×D11)⋊C4C22×C414yes—
361(C2×D11)⋊C4C22×C414yes—
362(C2×D11)⋊C4C22×C414yes—
363(C2×D11)⋊C4C22×C414yes—
364C4⋊Dic11—42no—
365C4⋊Dic11C22×C414yescomplemented
366C4⋊Dic11C22×C414yescomplemented
367Dic11⋊C4—24no—
368Dic11⋊C4—24no—
369Dic11⋊C4—42no—
370Dic11⋊C4—42no—
371Dic11⋊C4—42no—
372Dic11⋊C4—42no—
373Dic11⋊C4C22×C414yescomplemented
374Dic11⋊C4C22×C414yescomplemented
375Dic11⋊C4C22×C414yescomplemented
376Dic11⋊C4C22×C414yescomplemented
377C4×Dic11—24no—
378C4×Dic11—24no—
379C4×Dic11—42no—
380C4×Dic11—42no—
381C4×Dic11—42no—
382C4×Dic11—42no—
383C4×Dic11—42no—
384C4×Dic11C22×C414yescomplemented
385C4×Dic11C22×C414yescomplemented
386C2×#525—111no—
387#2368—112no—
388#2364—112no—
389#2359—112no—
390#2359—112no—
391#2353—111no—
392#2353—111no—
393#2349—111no—
394#2349—111no—
395#2343—111no—
396#2343—111no—
397#2339—111no—
398#2339D1111yescharacteristic, complemented
399#2329—112no—
400#2325—112no—
401#2318—111no—
402#2318—111no—
403C4×#120—112no—
404C4×#120—112no—
405#2280—111no—
406#2275—111no—
407#2275—111no—
408C22×#95—111no—
409C23×C11—22no—
410C23×C11—21no—
411C23×C11—21no—
412C23×C11—22no—
413C23×C11—22no—
414C23×C11—21no—
415C23×C11—22no—
416C23×C11—21no—
417C23×C11—22no—
418C23×C11—21no—
419C23×C11—21no—
420C23×C11C23×C412yes—
421C23×C11C23×C412yes—
422C23×C11C23×C412yes—
423C23×C11H(5,𝔽2)14yes—
424C23×C11C2511yescharacteristic
425C22×D11—216no—
426C22×D11—216no—
427C22×D11—28no—
428C22×D11—22no—
429C22×D11—22no—
430C22×D11—22no—
431C22×D11—21no—
432C22×D11—21no—
433C22×D11—28no—
434C22×D11—28no—
435C22×D11C23×C412yes—
436C22×D11C23×C412yes—
437C22×D11C2×#4114yes—
438C22×D11H(5,𝔽2)12yes—
439C22×D112−1+412yes—
440Q8×C11—44no—
441D4×C11—28no—
442D4×C11—28no—
443D4×C11—44no—
444C2×C4×C11—28no—
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—22no—
458C2×C4×C11—22no—
459C2×C4×C11—22no—
460C2×C4×C11—44no—
461C2×C4×C11—44no—
462C2×C4×C11—48no—
463C2×C4×C11—84no—
464C2×C4×C11C23×C412yes—
465C2×C4×C11C23×C412yes—
466C2×C4×C11C23×C412yes—
467C2×C4×C11C23×C412yes—
468C2×C4×C11C2×#4114yes—
469C22⋊D11—28no—
470C22⋊D11—28no—
471C22⋊D11—28no—
472C22⋊D11—28no—
473C2×Dic11—28no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—21no—
477C2×Dic11—21no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—21no—
483C2×Dic11—21no—
484C2×Dic11—22no—
485C2×Dic11—22no—
486C2×Dic11—22no—
487C2×Dic11—22no—
488C2×Dic11—22no—
489C2×Dic11—22no—
490C2×Dic11—22no—
491C2×Dic11—22no—
492C2×Dic11—22no—
493C2×Dic11—48no—
494C2×Dic11—84no—
495C2×Dic11C23×C412yes—
496C2×Dic11C23×C412yes—
497C2×Dic11C23×C412yes—
498C2×Dic11C23×C412yes—
499C2×Dic11C23×C412yes—
500C2×Dic11C23×C412yes—
501C2×Dic11C2×#4114yes—
502C4×D11—44no—
503C4×D11—44no—
504C4×D11—44no—
505C4×D11—44no—
506C4×D11—48no—
507C4×D11—48no—
508C4×D11—48no—
509C4×D11—48no—
510C22×#41C2×D1111yescharacteristic
511C24×C4—111no—
512C24×C4—112no—
513#525—1116no—
514C2×#123—111no—
515C2×#123—111no—
516C2×C22⋊Q8—111no—
517C2×C22⋊Q8—111no—
518C2×#121—111no—
519C2×#121—111no—
520C2×#120—111no—
521C2×#120—111no—
522C2×C4×D4—111no—
523C2×C4×D4—111no—
524C2×C4×D4—111no—
525C2×C4×D4—111no—
526C2×C4×D4—112no—
527C2×C4×D4—112no—
528C2×C4×D4—112no—
529C2×C4×D4—112no—
530C2×C4×D4—112no—
531C2×C4×D4C2×D1112yes—
532C2×#117—111no—
533C2×#117—112no—
534#391—112no—
535#391C2×D1112yescomplemented
536#389—112no—
537#389—112no—
538#388—112no—
539#388—112no—
540#388—112no—
541#388—112no—
542#387—112no—
543#387—112no—
544#387—112no—
545#387—112no—
546#387—112no—
547#387—112no—
548#387—112no—
549#387—112no—
550#386—112no—
551#386—112no—
552#386—112no—
553#386—112no—
554#386—112no—
555#386—112no—
556#386C2×D1112yes—
557#386C2×D1112yescomplemented
558#385—112no—
559#385—112no—
560#385—112no—
561#385—112no—
562#385—112no—
563#385—112no—
564#385—112no—
565#385—112no—
566#383—111no—
567#383—111no—
568#382—111no—
569#382—111no—
570#381—111no—
571#381—111no—
572#381C2×D1111yescharacteristic
573#381C2×D1111yescharacteristic, complemented
574#380—111no—
575#380—112no—
576#380—111no—
577#380—111no—
578#380C2×D1111yescharacteristic, complemented
579#379—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—112no—
591C4×C22⋊C4—111no—
592C4×C22⋊C4—111no—
593C4×C22⋊C4—112no—
594C4×C22⋊C4—112no—
595C4×C22⋊C4—112no—
596C4×C22⋊C4C2×D1111yescharacteristic, complemented
597#376—111no—
598#376—111no—
599C2×#95—111no—
600C2×#95—111no—
601C2×#95—112no—
602C2×#95—111no—
603C2×#95—112no—
604C2×#95—111no—
605C2×#95—111no—
606C2×#95—112no—
607C2×#95—111no—
608C2×#95C2×D1111yescharacteristic
609C2×#95C2×D1111yescharacteristic, complemented
610C22×C11—22no—
611C22×C11—22no—
612C22×C11—24no—
613C22×C11—24no—
614C22×C11—22no—
615C22×C11—22no—
616C22×C11—22no—
617C22×C11—22no—
618C22×C11—22no—
619C22×C11—22no—
620C22×C11—42no—
621C22×C11—42no—
622C22×C11—42no—
623C22×C11—42no—
624C22×C11#51814yes—
625C22×C11C24×C411yescharacteristic
626C22×C11C22×#4112yes—
627C22×C11C2×H(5,𝔽2)12yes—
628C22×C11C2×H(5,𝔽2)11yescharacteristic
629C22×C11C2×2−1+411yescharacteristic
630C2×D11—232no—
631C2×D11—22no—
632C2×D11—22no—
633C2×D11—22no—
634C2×D11—22no—
635C2×D11—24no—
636C2×D11—24no—
637C2×D11—24no—
638C2×D11—24no—
639C2×D11C4×#4114yes—
640C2×D11#52014yes—
641C4×C11—22no—
642C4×C11—22no—
643C4×C11—22no—
644C4×C11—22no—
645C4×C11—24no—
646C4×C11—42no—
647C4×C11—42no—
648C4×C11—42no—
649Dic11—22no—
650Dic11—22no—
651Dic11—22no—
652Dic11—22no—
653Dic11—22no—
654Dic11—22no—
655Dic11—24no—
656Dic11—42no—
657Dic11—42no—
658Dic11—42no—
659C25—111no—
660C2×#41—44no—
661C2×#41C4×D1118yescomplemented
662C22×Q8C22×D1111yescharacteristic
663C22×D4—111no—
664C22×D4—111no—
665C22×D4—111no—
666C22×D4—111no—
667C22×D4C22×D1111yescharacteristic
668C22×D4C22×D1111yescharacteristic
669C22×D4C22×D1111yescharacteristic
670C23×C4—111no—
671C23×C4—118no—
672C23×C4—112no—
673C23×C4—111no—
674C23×C4—111no—
675C23×C4—111no—
676C23×C4—111no—
677C23×C4—112no—
678C23×C4—112no—
679C23×C4—112no—
680C23×C4—112no—
681C23×C4—112no—
682C23×C4—228no—
683C23×C4—444no—
684C23×C4—444no—
685C23×C4—444no—
686C23×C4C22×D1112yes—
687C23×C4C22×D1111yescharacteristic
688C23×C4C22×D1112yes—
689C23×C4C22×D1111yescharacteristic
690C23×C4C22×D1111yescharacteristic
691#123—118no—
692#123—118no—
693C22⋊Q8—118no—
694C22⋊Q8—118no—
695#121—118no—
696#121—118no—
697#120—118no—
698#120—118no—
699C4×D4—44no—
700C4×D4—118no—
701C4×D4—118no—
702C4×D4—118no—
703C4×D4—118no—
704C4×D4—228no—
705C4×D4—228no—
706C4×D4—444no—
707C4×D4—444no—
708C4×D4—444no—
709#117—118no—
710#117—444no—
711C2×C4⋊C4—111no—
712C2×C4⋊C4—111no—
713C2×C4⋊C4—111no—
714C2×C4⋊C4—111no—
715C2×C4⋊C4—111no—
716C2×C4⋊C4—111no—
717C2×C4⋊C4—112no—
718C2×C4⋊C4—112no—
719C2×C4⋊C4—112no—
720C2×C4⋊C4—112no—
721C2×C4⋊C4—112no—
722C2×C4⋊C4—112no—
723C2×C4⋊C4—112no—
724C2×C4⋊C4C22×D1112yes—
725C2×C22⋊C4—111no—
726C2×C22⋊C4—111no—
727C2×C22⋊C4—111no—
728C2×C22⋊C4—111no—
729C2×C22⋊C4—111no—
730C2×C22⋊C4—111no—
731C2×C22⋊C4—111no—
732C2×C22⋊C4—111no—
733C2×C22⋊C4—111no—
734C2×C22⋊C4—111no—
735C2×C22⋊C4—112no—
736C2×C22⋊C4—112no—
737C2×C22⋊C4—112no—
738C2×C22⋊C4—112no—
739C2×C22⋊C4—112no—
740C2×C22⋊C4—112no—
741C2×C22⋊C4—112no—
742C2×C22⋊C4—112no—
743C2×C22⋊C4C22×D1112yes—
744C2×C22⋊C4C22×D1112yes—
745C2×C22⋊C4C22×D1112yes—
746C2×C22⋊C4C22×D1112yes—
747C2×C42—111no—
748C2×C42—111no—
749C2×C42—112no—
750C2×C42—112no—
751C2×C42—112no—
752C2×C42—112no—
753C2×C42—112no—
754C2×C42—112no—
755C2×C42—112no—
756C2×C42C22×D1112yes—
757#95—111no—
758#95—112no—
759#95—111no—
760#95—112no—
761#95—112no—
762#95—112no—
763#95—112no—
764#95—111no—
765#95—112no—
766#95—111no—
767#95—112no—
768#95—112no—
769#95—112no—
770#95—112no—
771#95—112no—
772#95—112no—
773#95—112no—
774#95—112no—
775#95—112no—
776#95—112no—
777#95C22×D1111yescharacteristic
778#95C22×D1111yescharacteristic
779#95C22×D1112yes—
780#95C22×D1111yescharacteristic
781#95C22×D1112yes—
782#95C22×D1111yescharacteristic
783#95C22×D1112yes—
784#95C22×D1112yes—
785C2×C11—24no—
786C2×C11—42no—
787C2×C11—42no—
788C2×C11C2×C4×#4111yescharacteristic
789C2×C11C2×#51811yescharacteristic
790C2×C11C2×#52011yescharacteristic
791C2×C11#349012yes—
792C2×C11#349212yes—
793D11—24no—
794D11—24no—
795C24—111no—
796C24—111no—
797C24—114no—
798C24—224no—
799C24—222no—
800C24—222no—
801C24—224no—
802C24C23×D1111yescharacteristic
803C24C23×D1111yescharacteristic
804C24C23×D1111yescharacteristic
805#41—416no—
806C2×Q8—42no—
807C2×Q8C2×C4×D1114yescomplemented
808C2×D4—24no—
809C2×D4—24no—
810C2×D4—42no—
811C2×D4—114no—
812C2×D4—114no—
813C2×D4—114no—
814C2×D4—114no—
815C2×D4—224no—
816C2×D4—224no—
817C2×D4—222no—
818C2×D4—222no—
819C2×D4—222no—
820C2×D4—222no—
821C2×D4C2×C4×D1114yes—
822C2×D4C2×C4×D1114yes—
823C2×D4C2×C4×D1114yescomplemented
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—114no—
834C22×C4—112no—
835C22×C4—111no—
836C22×C4—111no—
837C22×C4—111no—
838C22×C4—111no—
839C22×C4—111no—
840C22×C4—111no—
841C22×C4—114no—
842C22×C4—114no—
843C22×C4—114no—
844C22×C4—114no—
845C22×C4—118no—
846C22×C4—112no—
847C22×C4—112no—
848C22×C4—112no—
849C22×C4—224no—
850C22×C4—224no—
851C22×C4—224no—
852C22×C4—224no—
853C22×C4—224no—
854C22×C4—224no—
855C22×C4—224no—
856C22×C4—224no—
857C22×C4—224no—
858C22×C4—4416no—
859C22×C4—442no—
860C22×C4—442no—
861C22×C4—442no—
862C22×C4—442no—
863C22×C4—442no—
864C22×C4—442no—
865C22×C4—442no—
866C22×C4—442no—
867C22×C4—442no—
868C22×C4—442no—
869C22×C4—4432no—
870C22×C4—442no—
871C22×C4—442no—
872C22×C4—442no—
873C22×C4C2×C4×D1114yes—
874C22×C4C2×C4×D1114yescomplemented
875C22×C4C2×C4×D1114yescomplemented
876C22×C4C23×D1112yes—
877C22×C4C23×D1112yes—
878C22×C4C23×D1112yes—
879C22×C4C23×D1111yescharacteristic
880C22×C4C23×D1111yescharacteristic
881C22×C4C23×D1111yescharacteristic
882C22×C4C23×D1111yescharacteristic
883C22×C4C23×D1112yes—
884C4⋊C4—42no—
885C4⋊C4—114no—
886C4⋊C4—114no—
887C4⋊C4—114no—
888C4⋊C4—114no—
889C4⋊C4—114no—
890C4⋊C4—114no—
891C4⋊C4—224no—
892C4⋊C4—224no—
893C4⋊C4—442no—
894C4⋊C4—442no—
895C4⋊C4—442no—
896C4⋊C4—442no—
897C4⋊C4—442no—
898C22⋊C4—24no—
899C22⋊C4—24no—
900C22⋊C4—42no—
901C22⋊C4—42no—
902C22⋊C4—114no—
903C22⋊C4—114no—
904C22⋊C4—114no—
905C22⋊C4—114no—
906C22⋊C4—114no—
907C22⋊C4—114no—
908C22⋊C4—114no—
909C22⋊C4—114no—
910C22⋊C4—114no—
911C22⋊C4—114no—
912C22⋊C4—224no—
913C22⋊C4—224no—
914C22⋊C4—224no—
915C22⋊C4—224no—
916C22⋊C4—224no—
917C22⋊C4—224no—
918C22⋊C4—442no—
919C22⋊C4—442no—
920C42—42no—
921C42—114no—
922C42—114no—
923C42—224no—
924C42—224no—
925C42—442no—
926C42—442no—
927C42—442no—
928C42—442no—
929C42—442no—
930C11#3421811yescharacteristic, complemented, Sylow
931C23—22no—
932C23—21no—
933C23—21no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—21no—
939C23—21no—
940C23—21no—
941C23—21no—
942C23—112no—
943C23—112no—
944C23—114no—
945C23—112no—
946C23—112no—
947C23—228no—
948C23—228no—
949C23—2216no—
950C23—2216no—
951C23—228no—
952C23—222no—
953C23—222no—
954C23—222no—
955C23—221no—
956C23—221no—
957C23C22×C4×D1112yes—
958C23C22×C4×D1112yes—
959C23C22×C4×D1112yes—
960C23#6703714yes—
961C23C24×D1111yescharacteristic
962Q8—44no—
963D4—28no—
964D4—28no—
965D4—44no—
966D4—228no—
967D4—228no—
968D4—228no—
969D4—228no—
970C2×C4—28no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—44no—
987C2×C4—44no—
988C2×C4—48no—
989C2×C4—84no—
990C2×C4—112no—
991C2×C4—112no—
992C2×C4—112no—
993C2×C4—112no—
994C2×C4—112no—
995C2×C4—112no—
996C2×C4—114no—
997C2×C4—228no—
998C2×C4—222no—
999C2×C4—222no—
1000C2×C4—222no—
1001C2×C4—222no—
1002C2×C4—222no—
1003C2×C4—221no—
1004C2×C4—221no—
1005C2×C4—222no—
1006C2×C4—221no—
1007C2×C4—221no—
1008C2×C4—222no—
1009C2×C4—222no—
1010C2×C4—222no—
1011C2×C4—222no—
1012C2×C4—222no—
1013C2×C4—222no—
1014C2×C4—222no—
1015C2×C4—222no—
1016C2×C4—222no—
1017C2×C4—448no—
1018C2×C4—444no—
1019C2×C4—444no—
1020C2×C4—444no—
1021C2×C4—444no—
1022C2×C4—448no—
1023C2×C4—448no—
1024C2×C4—448no—
1025C2×C4—448no—
1026C2×C4—884no—
1027C2×C4C22×C4×D1112yes—
1028C2×C4C22×C4×D1112yes—
1029C2×C4C22×C4×D1112yes—
1030C2×C4C22×C4×D1112yes—
1031C2×C4#41×D1114yes—
1032C22—24no—
1033C22—22no—
1034C22—24no—
1035C22—22no—
1036C22—22no—
1037C22—22no—
1038C22—22no—
1039C22—22no—
1040C22—22no—
1041C22—22no—
1042C22—42no—
1043C22—42no—
1044C22—42no—
1045C22—42no—
1046C22—114no—
1047C22—114no—
1048C22—2232no—
1049C22—224no—
1050C22—224no—
1051C22—222no—
1052C22—222no—
1053C22—222no—
1054C22—224no—
1055C22—224no—
1056C22—222no—
1057C22#1062301714yes—
1058C22C23×C4×D1111yescharacteristic
1059C22C2×#6703712yes—
1060C22C2×#41×D1112yes—
1061C22D11×H(5,𝔽2)11yescharacteristic
1062C22D11×2−1+411yescharacteristic
1063C4—24no—
1064C4—22no—
1065C4—22no—
1066C4—22no—
1067C4—22no—
1068C4—42no—
1069C4—42no—
1070C4—42no—
1071C4—224no—
1072C4—222no—
1073C4—222no—
1074C4—222no—
1075C4—222no—
1076C4—222no—
1077C4—222no—
1078C4—442no—
1079C4—442no—
1080C4—442no—
1081C2—24no—
1082C2—42no—
1083C2—42no—
1084C2—224no—
1085C2—224no—
1086C2C4×#41×D1111yescharacteristic
1087C2C2×#1062301711yescharacteristic
1088C2D11×#52011yescharacteristic
1089C2#1308229812yes—
1090C2#1308231812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2339C2
socle, cosocleC23×C11C25
prime radicalC2×#10623359C2
hypercenter#2339D11
hypocenterC11#34218
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2339

Complements

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

NH ≅ G/Ntype
2. #13071695C2semidirect
3. #13071665C2semidirect
4. #13071614C2semidirect
5. #13071602C2semidirect
6. #13071559C2semidirect
7. #13071553C2semidirect
8. #13071523C2semidirect
9. #13071520C2semidirect
10. #13071478C2semidirect
11. #13071472C2semidirect
12. #13071446C2semidirect
13. #13071348C2semidirect
14. #13071318C2semidirect
15. #13071251C2semidirect
16. #13071245C2semidirect
17. #13071121C2semidirect
18. C4×#66990C2semidirect
19. #13070996C2semidirect
20. #13070975C2semidirect
21. #13070974C2semidirect
22. C2×D11×#95C2semidirect
23. C11×#2339C2semidirect
28. #10623359C4semidirect
48. C11×#391C22semidirect
50. C11×#386C22semidirect
52. C11×#381C22semidirect
53. C11×#380C22semidirect
54. C4×C11×C22⋊C4C22semidirect
56. C2×C11×#95C22semidirect
57. #10622843C22semidirect
59. #10622833C22semidirect
60. #10622825C22semidirect
62. #10622824C22semidirect
64. #10622823C22semidirect
66. C4×C22⋊Dic11C22semidirect
67. C4×C22⋊Dic11C22semidirect
70. C2×C11⋊#95C22semidirect
73. #10622591C22semidirect
74. #10622585C22semidirect
81. #10622559C22semidirect
82. #10622558C22semidirect
83. #10622558C22semidirect
84. #10622557C22semidirect
85. #10622557C22semidirect
87. C22⋊C4×Dic11C22semidirect
90. #10622546C22semidirect
91. C4×Dic11⋊C4C22semidirect
108. #10622268C22semidirect
109. #10622267C22semidirect
110. #10622267C22semidirect
111. #10622266C22semidirect
112. #10622266C22semidirect
113. #10622265C22semidirect
114. #10622264C22semidirect
115. #10622264C22semidirect
116. #10622263C22semidirect
117. #10622263C22semidirect
118. #10622262C22semidirect
119. #10622262C22semidirect
120. #10622262C22semidirect
121. #10622261C22semidirect
122. #10622261C22semidirect
123. #10622260C22semidirect
126. C2×C11×#41C2×C4semidirect
147. C22×C4×D11C2×C4semidirect
173. #66999C2×C4semidirect
174. #66999C2×C4semidirect
175. #66991C2×C4semidirect
176. #66991C2×C4semidirect
177. #66990C2×C4semidirect
178. #66990C2×C4semidirect
179. #66988C2×C4semidirect
180. #66988C2×C4semidirect
184. C4×C22⋊D11C2×C4semidirect
185. C4×C22⋊D11C2×C4semidirect
186. C4×C22⋊D11C2×C4semidirect
187. C4×C22⋊D11C2×C4semidirect
196. #66979C2×C4semidirect
263. C2×Q8×C11C22×C4semidirect
269. C2×D4×C11C22×C4semidirect
280. C22×C4×C11C22×C4semidirect
281. C22×C4×C11C22×C4semidirect
339. C2×C4×D11#41semidirect
352. C22⋊Dic11C22×C4semidirect
353. C22⋊Dic11C22×C4semidirect
354. C22⋊Dic11C22×C4semidirect
355. C22⋊Dic11C22×C4semidirect
365. C4⋊Dic11C22×C4semidirect
366. C4⋊Dic11C22×C4semidirect
373. Dic11⋊C4C22×C4semidirect
374. Dic11⋊C4C22×C4semidirect
375. Dic11⋊C4C22×C4semidirect
376. Dic11⋊C4C22×C4semidirect
384. C4×Dic11C22×C4semidirect
385. C4×Dic11C22×C4semidirect
398. #2339D11semidirect
535. #391C2×D11semidirect
557. #386C2×D11semidirect
573. #381C2×D11semidirect
578. #380C2×D11semidirect
596. C4×C22⋊C4C2×D11semidirect
609. C2×#95C2×D11semidirect
661. C2×#41C4×D11semidirect
807. C2×Q8C2×C4×D11semidirect
823. C2×D4C2×C4×D11semidirect
874. C22×C4C2×C4×D11semidirect
875. C22×C4C2×C4×D11semidirect
930. C11#34218semidirect

Maximal subgroups

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

subgroupindex
C2×#106233592
#130716952
#130716652
#130716142
#130716022
#130715592
#130715532
#130715232
#130715202
#130714782
#130714722
#130714462
#130713482
#130713182
#130712512
#130712452
#130711212
C4×#669902
#130709962
#130709752
#130709742
C2×D11×#952
C11×#23392
#3421811