Finite Group Databasebeta

← #14914484

Subgroups — #14914484

Order 2816.

2826 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623137C211yesmaximal, characteristic
2#13071636C211yesmaximal, characteristic, complemented
3#13071621C211yesmaximal, characteristic, complemented
4#13071619C211yesmaximal, characteristic, complemented
5#13071596C212yesmaximal, complemented
6#13071593C212yesmaximal, complemented
7#13071551C212yesmaximal, complemented
8#13071522C212yesmaximal, complemented
9#13071508C211yesmaximal, characteristic, complemented
10#13071497C211yesmaximal, characteristic, complemented
11#13071455C211yesmaximal, characteristic, complemented
12#13071441C211yesmaximal, characteristic, complemented
13#13071413C212yesmaximal, complemented
14#13071401C212yesmaximal, complemented
15#13071242C212yesmaximal, complemented
16C4×#66950C211yesmaximal, characteristic, complemented
17#13071146C211yesmaximal, characteristic, complemented
18#13071132C211yesmaximal, characteristic, complemented
19C4×#66991C211yesmaximal, characteristic, complemented
20C2×#10622600C211yesmaximal, characteristic, complemented
21#13070977C212yesmaximal, complemented
22C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2361C211yesmaximal, characteristic, complemented
24C22×#4341C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C4×D4×C11C2212yes—
28C2×C4×D4×C11C2211yescharacteristic, complemented
29C22×C11×C4⋊C4C2211yescharacteristic
30C2×#66991C2211yescharacteristic
31C2×#66990C2212yes—
32C2×D4×Dic11C2212yes—
33C2×D4×Dic11C2212yes—
34C2×D4×Dic11C2211yescharacteristic, complemented
35C2×C4×C22⋊D11C2212yes—
36C22×(C2×D11)⋊C4C2212yes—
37C22×C4⋊Dic11C2211yescharacteristic
38C2×#66977C2211yescharacteristic
39#10623137C4116yescomplemented
40C2×#66950C2211yescharacteristic
41C2×#66945C2211yescharacteristic
42C2×#66940C2211yescharacteristic, complemented
43C2×#66936C2212yes—
44C2×(C22⋊D11)⋊C4C2212yes—
45C2×(C22⋊D11)⋊C4C2212yes—
46C2×C22⋊C4×D11C2211yescharacteristic
47C2×C22⋊C4×D11C2211yescharacteristic
48C2×C42×D11C2211yescharacteristic
49C2×C42×D11C2211yescharacteristic
50C2×C4×Dic22C2211yescharacteristic, complemented
51C11×#390C2211yescharacteristic, complemented
52C11×#389C2211yescharacteristic, complemented
53C11×#388C2212yescomplemented
54C11×#386C2212yes—
55C11×#385C2212yescomplemented
56C4×C11×C4⋊C4C2211yescharacteristic, complemented
57C4×C11×C22⋊C4C2211yescharacteristic
58#10622834C2211yescharacteristic, complemented
59#10622833C2212yes—
60#10622826C2212yes—
61#10622823C2212yes—
62C4×C22⋊Dic11C2211yescharacteristic
63C4×C22⋊Dic11C2212yes—
64C4×C22⋊Dic11C2212yescomplemented
65C2×C11⋊#95C2212yes—
66C2×C11⋊#95C2212yescomplemented
67#10622603C2212yes—
68#10622602C2212yes—
69#10622600C2211yescharacteristic
70#10622600C2211yescharacteristic
71#10622600C2212yes—
72#10622600C2211yescharacteristic
73#10622600C2211yescharacteristic
74#10622600C2212yes—
75#10622598C2211yescharacteristic, complemented
76#10622591C2212yescomplemented
77C4⋊C4×Dic11C2211yescharacteristic, complemented
78C4⋊C4×Dic11C2211yescharacteristic, complemented
79C4⋊C4×Dic11C2212yescomplemented
80C4⋊C4×Dic11C2212yescomplemented
81#10622587C2211yescharacteristic, complemented
82#10622586C2211yescharacteristic, complemented
83#10622585C2212yescomplemented
84#10622571C2212yes—
85#10622570C2212yes—
86#10622570C2212yes—
87#10622569C2212yes—
88#10622569C2212yes—
89#10622564C2212yescomplemented
90#10622563C2212yescomplemented
91#10622559C2212yes—
92#10622558C2212yescomplemented
93#10622557C2212yescomplemented
94#10622556C2212yescomplemented
95#10622555C2212yescomplemented
96C22⋊C4×Dic11C2212yes—
97C22⋊C4×Dic11C2211yescharacteristic
98C22⋊C4×Dic11C2211yescharacteristic
99C22⋊C4×Dic11C2212yescomplemented
100C22⋊C4×Dic11C2212yescomplemented
101#10622553C2212yes—
102C4×(C2×D11)⋊C4C2212yes—
103C4×(C2×D11)⋊C4C2211yescharacteristic
104C4×(C2×D11)⋊C4C2211yescharacteristic
105C4×C4⋊Dic11C2211yescharacteristic, complemented
106C4×C4⋊Dic11C2212yescomplemented
107#10622545C2212yescomplemented
108#10622542C2211yescharacteristic, complemented
109#10622541C2211yescharacteristic, complemented
110#10622283C2212yes—
111#10622282C2212yes—
112#10622281C2212yes—
113#10622279C2211yescharacteristic
114#10622279C2212yes—
115#10622279C2211yescharacteristic
116D11×#95C2211yescharacteristic
117D11×#95C2211yescharacteristic
118#10622268C2212yescomplemented
119#10622267C2212yescomplemented
120#10622266C2212yescomplemented
121#10622264C2212yescomplemented
122#10622263C2212yescomplemented
123#10622260C2212yescomplemented
124C24×D11C2311yescharacteristic
125C22×D4×C11C2312yes—
126C22×D4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2312yes—
129C23×C4×C11C2312yes—
130C22×C22⋊D11C2312yes—
131C22×C22⋊D11C2312yes—
132C23×Dic11C2312yes—
133C23×Dic11C2312yes—
134C23×Dic11C2312yes—
135C23×Dic11C2311yescharacteristic
136C2×#4341—42no—
137C2×#4341—42no—
138C2×#4341C2×C418yescomplemented
139C22×C4×D11—42no—
140C22×C4×D11—42no—
141C22×C4×D11C2×C418yescomplemented
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×Dic22C2311yescharacteristic
151C11×#121C2×C418yescomplemented
152C4×D4×C11—28no—
153C4×D4×C11—42no—
154C2×C11×C4⋊C4—42no—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C4⋊C4C2312yes—
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C22⋊C4C2311yescharacteristic
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2311yescharacteristic
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2312yes—
169C2×C22⋊Dic11C2311yescharacteristic
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2311yescharacteristic
176#66991C2×C418yescomplemented
177#66990C2×C4116yescomplemented
178D4×Dic11—28no—
179D4×Dic11—42no—
180D4×Dic11C2×C4116yescomplemented
181C4×C22⋊D11—44no—
182C2×(C2×D11)⋊C4—44no—
183C2×(C2×D11)⋊C4C2311yescharacteristic
184C2×(C2×D11)⋊C4C2311yescharacteristic
185C2×(C2×D11)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2311yescharacteristic
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×C4⋊Dic11—42no—
194C2×C4⋊Dic11C2311yescharacteristic
195C2×C4⋊Dic11C2312yes—
196C2×C4⋊Dic11C2311yescharacteristic
197C2×C4⋊Dic11C2312yes—
198C2×C4⋊Dic11C2312yes—
199C2×C4⋊Dic11C2311yescharacteristic
200#66977C2×C418yescomplemented
201C2×Dic11⋊C4C2312yes—
202C2×Dic11⋊C4C2312yes—
203C2×Dic11⋊C4C2312yes—
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C2312yes—
206C2×C4×Dic11C2311yescharacteristic
207C2×C4×Dic11C2311yescharacteristic
208C2×C4×Dic11C2312yes—
209C2×C4×Dic11C2312yes—
210C2×C4×Dic11C2311yescharacteristic
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2311yescharacteristic
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2312yes—
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2312yes—
218#66950C2×C418yescomplemented
219#66945C2×C418yescomplemented
220#66940—42no—
221#66936C2×C4116yescomplemented
222(C22⋊D11)⋊C4—44no—
223(C22⋊D11)⋊C4C2×C4116yescomplemented
224C22⋊C4×D11—24no—
225C22⋊C4×D11—24no—
226C42×D11—42no—
227C42×D11—42no—
228C4×Dic22—42no—
229C11×#95C2311yescharacteristic
230C11×#95C2312yes—
231C11×#95C2312yes—
232C11×#95C2311yescharacteristic
233C11⋊#95C2312yes—
234C11⋊#95C2311yescharacteristic
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2311yescharacteristic
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2311yescharacteristic
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2311yescharacteristic
250C11⋊#95C2311yescharacteristic
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253#34233—111nomaximal, Sylow
254C24×C11C2412yes—
255C24×C11C2411yescharacteristic
256C23×D11—22no—
257C23×D11—22no—
258C23×D11—22no—
259C23×D11—22no—
260C23×D11—41no—
261C23×D11—41no—
262C23×D11C22×C414yes—
263C23×D11C2411yescharacteristic
264C23×D11C2411yescharacteristic
265C2×D4×C11—24no—
266C2×D4×C11—24no—
267C2×D4×C11—22no—
268C2×D4×C11—22no—
269C2×D4×C11C22×C418yes—
270C2×D4×C11C22×C414yes—
271C22×C4×C11—22no—
272C22×C4×C11—22no—
273C22×C4×C11—24no—
274C22×C4×C11—24no—
275C22×C4×C11—42no—
276C22×C4×C11—42no—
277C22×C4×C11—42no—
278C22×C4×C11—42no—
279C22×C4×C11C22×C414yes—
280C22×C4×C11C2411yescharacteristic
281C22×C4×C11C2412yes—
282C22×C4×C11C2412yes—
283C22×C4×C11C2411yescharacteristic
284C22×C4×C11C2412yes—
285C22×C4×C11C2411yescharacteristic
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2411yescharacteristic
289C2×C22⋊D11—24no—
290C2×C22⋊D11—24no—
291C2×C22⋊D11—42no—
292C2×C22⋊D11—42no—
293C2×C22⋊D11C22×C418yes—
294C2×C22⋊D11C22×C418yes—
295C22×Dic11—24no—
296C22×Dic11—24no—
297C22×Dic11—41no—
298C22×Dic11—41no—
299C22×Dic11—42no—
300C22×Dic11—42no—
301C22×Dic11—42no—
302C22×Dic11—42no—
303C22×Dic11—42no—
304C22×Dic11—42no—
305C22×Dic11C22×C418yes—
306C22×Dic11C22×C414yes—
307C22×Dic11C2411yescharacteristic
308C22×Dic11C2412yes—
309C22×Dic11C2411yescharacteristic
310C22×Dic11C2412yes—
311C22×Dic11C2411yescharacteristic
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2412yes—
314C22×Dic11C2412yes—
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2411yescharacteristic
317#4341—416no—
318C2×C4×D11—22no—
319C2×C4×D11—22no—
320C2×C4×D11—22no—
321C2×C4×D11—22no—
322C2×C4×D11—22no—
323C2×C4×D11—22no—
324C2×C4×D11—22no—
325C2×C4×D11—22no—
326C2×C4×D11—22no—
327C2×C4×D11—22no—
328C2×C4×D11—22no—
329C2×C4×D11—22no—
330C2×C4×D11—41no—
331C2×C4×D11—41no—
332C2×C4×D11—41no—
333C2×C4×D11—41no—
334C2×C4×D11—41no—
335C2×C4×D11—41no—
336C2×C4×D11—41no—
337C2×C4×D11—41no—
338C2×C4×D11—416no—
339C2×C4×D11C22×C414yes—
340C2×C4×D11C22×C414yes—
341C2×C4×D11C22×C414yes—
342C2×C4×D11C22×C414yes—
343C2×Dic22—22no—
344C2×Dic22—22no—
345C2×Dic22C22×C414yes—
346C11×C4⋊C4—24no—
347C11×C4⋊C4—22no—
348C11×C4⋊C4—22no—
349C11×C4⋊C4—42no—
350C11×C4⋊C4C22×C414yes—
351C11×C22⋊C4—22no—
352C11×C22⋊C4—24no—
353C11×C22⋊C4—42no—
354C11×C22⋊C4—42no—
355C11×C22⋊C4C22×C418yes—
356C11×C22⋊C4#4114yescomplemented
357C42×C11—24no—
358C42×C11—22no—
359C42×C11—22no—
360C22⋊Dic11—24no—
361C22⋊Dic11—22no—
362C22⋊Dic11—42no—
363C22⋊Dic11—42no—
364C22⋊Dic11C22×C418yes—
365C22⋊Dic11C22×C418yes—
366C22⋊Dic11#4114yescomplemented
367(C2×D11)⋊C4—22no—
368(C2×D11)⋊C4—22no—
369(C2×D11)⋊C4—24no—
370(C2×D11)⋊C4—24no—
371(C2×D11)⋊C4—22no—
372(C2×D11)⋊C4—22no—
373(C2×D11)⋊C4—42no—
374(C2×D11)⋊C4—42no—
375(C2×D11)⋊C4C22×C418yes—
376(C2×D11)⋊C4C22×C418yes—
377C4⋊Dic11—24no—
378C4⋊Dic11—22no—
379C4⋊Dic11—22no—
380C4⋊Dic11—42no—
381C4⋊Dic11C22×C418yes—
382C4⋊Dic11C22×C414yes—
383Dic11⋊C4—42no—
384Dic11⋊C4—42no—
385Dic11⋊C4—42no—
386Dic11⋊C4—42no—
387Dic11⋊C4C22×C418yes—
388C4×Dic11—24no—
389C4×Dic11—22no—
390C4×Dic11—22no—
391C4×Dic11—42no—
392C4×Dic11—41no—
393C4×Dic11—41no—
394C4×Dic11—41no—
395C4×Dic11—41no—
396C4×Dic11—42no—
397C4×Dic11—42no—
398C4×Dic11—42no—
399C4×Dic11C22×C418yes—
400C2×#525—111no—
401#2361—111no—
402#2361D1111yescharacteristic, complemented
403#2360—111no—
404#2360—111no—
405#2358—112no—
406#2358—112no—
407#2353—112no—
408#2349—112no—
409#2347—111no—
410#2346—111no—
411#2341—111no—
412#2339—111no—
413#2335—112no—
414#2335—112no—
415#2318—112no—
416C4×C22⋊Q8—111no—
417C4×C22⋊Q8—111no—
418C4×#121—111no—
419C4×#121—111no—
420C2×#380—111no—
421#2275—112no—
422C2×C4×C22⋊C4—111no—
423C23×C11—21no—
424C23×C11—21no—
425C23×C11—21no—
426C23×C11—21no—
427C23×C11—22no—
428C23×C11—22no—
429C23×C11—22no—
430C23×C11—22no—
431C23×C11—22no—
432C23×C11—22no—
433C23×C11C23×C414yes—
434C23×C11C23×C412yes—
435C23×C11C2×#4112yes—
436C23×C11C2×#4112yes—
437C23×C11C2511yescharacteristic
438C22×D11—21no—
439C22×D11—21no—
440C22×D11—21no—
441C22×D11—21no—
442C22×D11—28no—
443C22×D11—21no—
444C22×D11—21no—
445C22×D11—21no—
446C22×D11—21no—
447C22×D11—21no—
448C22×D11—21no—
449C22×D11—28no—
450C22×D11—44no—
451C22×D11—44no—
452C22×D11—44no—
453C22×D11—44no—
454C22×D11—44no—
455C22×D11C23×C412yes—
456C22×D11C23×C412yes—
457C22×D11H(5,𝔽2)12yes—
458C22×D112−1+412yes—
459D4×C11—216no—
460D4×C11—28no—
461C2×C4×C11—22no—
462C2×C4×C11—22no—
463C2×C4×C11—21no—
464C2×C4×C11—21no—
465C2×C4×C11—21no—
466C2×C4×C11—21no—
467C2×C4×C11—21no—
468C2×C4×C11—21no—
469C2×C4×C11—28no—
470C2×C4×C11—21no—
471C2×C4×C11—21no—
472C2×C4×C11—22no—
473C2×C4×C11—22no—
474C2×C4×C11—21no—
475C2×C4×C11—22no—
476C2×C4×C11—22no—
477C2×C4×C11—21no—
478C2×C4×C11—21no—
479C2×C4×C11—22no—
480C2×C4×C11—22no—
481C2×C4×C11—21no—
482C2×C4×C11—84no—
483C2×C4×C11—84no—
484C2×C4×C11C23×C414yes—
485C2×C4×C11C23×C412yes—
486C2×C4×C11C23×C412yes—
487C2×C4×C11C2×#4112yes—
488C2×C4×C11C2×#4112yes—
489C2×C4×C11H(5,𝔽2)12yes—
490C2×C4×C11H(5,𝔽2)12yes—
491C22⋊D11—216no—
492C22⋊D11—48no—
493C2×Dic11—21no—
494C2×Dic11—21no—
495C2×Dic11—22no—
496C2×Dic11—21no—
497C2×Dic11—21no—
498C2×Dic11—21no—
499C2×Dic11—22no—
500C2×Dic11—22no—
501C2×Dic11—21no—
502C2×Dic11—21no—
503C2×Dic11—21no—
504C2×Dic11—22no—
505C2×Dic11—22no—
506C2×Dic11—22no—
507C2×Dic11—21no—
508C2×Dic11—21no—
509C2×Dic11—21no—
510C2×Dic11—21no—
511C2×Dic11—22no—
512C2×Dic11—22no—
513C2×Dic11—21no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—21no—
517C2×Dic11—44no—
518C2×Dic11—48no—
519C2×Dic11—84no—
520C2×Dic11—84no—
521C2×Dic11C23×C412yes—
522C2×Dic11C23×C414yes—
523C2×Dic11C23×C414yes—
524C2×Dic11C23×C412yes—
525C2×Dic11C2×#4112yes—
526C2×Dic11C2×#4112yes—
527C4×D11—28no—
528C4×D11—28no—
529C4×D11—44no—
530C4×D11—44no—
531C4×D11—44no—
532C4×D11—44no—
533C4×D11—44no—
534C4×D11—44no—
535Dic22—28no—
536C22×#41—111no—
537C24×C4—111no—
538#525—1116no—
539C2×#123—112no—
540C2×C22⋊Q8—111no—
541C2×C22⋊Q8—111no—
542C2×#121—111no—
543C2×#121C2×D1111yescharacteristic
544C2×#120—112no—
545C2×C4×Q8—111no—
546C2×C4×Q8—111no—
547C2×C4×D4—112no—
548C2×C4×D4—112no—
549C2×C4×D4—111no—
550C2×C4×D4—112no—
551C2×C4×D4—112no—
552C2×C4×D4—112no—
553C2×C4×D4C2×D1112yes—
554C2×C4×D4C2×D1111yescharacteristic, complemented
555C2×#117—111no—
556C22×C4⋊C4—111no—
557C22×C4⋊C4C2×D1111yescharacteristic
558C22×C22⋊C4—112no—
559C22×C22⋊C4—111no—
560C22×C22⋊C4—111no—
561C22×C42—111no—
562C22×C42—111no—
563#391—111no—
564#391—111no—
565#390—111no—
566#390—112no—
567#390—112no—
568#390C2×D1111yescharacteristic, complemented
569#389—112no—
570#389—111no—
571#389—111no—
572#389—111no—
573#389—112no—
574#389C2×D1111yescharacteristic, complemented
575#388—112no—
576#388—112no—
577#388—112no—
578#388—112no—
579#388—112no—
580#388—112no—
581#388—112no—
582#388C2×D1112yescomplemented
583#387—112no—
584#387—112no—
585#387—112no—
586#387—112no—
587#386—112no—
588#386—112no—
589#386—112no—
590#386—112no—
591#386—112no—
592#386C2×D1112yes—
593#385—112no—
594#385—112no—
595#385—112no—
596#385—112no—
597#385—112no—
598#385C2×D1112yescomplemented
599#383—112no—
600#382—112no—
601#381—112no—
602#380—112no—
603#380—111no—
604#380—111no—
605#380—112no—
606#380—111no—
607#380—111no—
608#380—112no—
609C4×C4⋊C4—112no—
610C4×C4⋊C4—111no—
611C4×C4⋊C4—112no—
612C4×C4⋊C4—111no—
613C4×C4⋊C4—112no—
614C4×C4⋊C4—111no—
615C4×C4⋊C4C2×D1111yescharacteristic, complemented
616C4×C22⋊C4—112no—
617C4×C22⋊C4—112no—
618C4×C22⋊C4—111no—
619C4×C22⋊C4—111no—
620C4×C22⋊C4—112no—
621C4×C22⋊C4—112no—
622C4×C22⋊C4—112no—
623C4×C22⋊C4—111no—
624C4×C22⋊C4—111no—
625C4×C22⋊C4—111no—
626C4×C22⋊C4—112no—
627C4×C22⋊C4—111no—
628C4×C22⋊C4—111no—
629C4×C22⋊C4—112no—
630C4×C22⋊C4C2×D1111yescharacteristic
631#376—112no—
632C2×#95—112no—
633C2×#95—112no—
634C2×#95—111no—
635C2×#95—111no—
636C22×C11—22no—
637C22×C11—22no—
638C22×C11—22no—
639C22×C11—22no—
640C22×C11—22no—
641C22×C11—22no—
642C22×C11—24no—
643C22×C11—24no—
644C22×C11—24no—
645C22×C11—42no—
646C22×C11—42no—
647C22×C11—42no—
648C22×C11—42no—
649C22×C11C4×#4114yes—
650C22×C11C24×C411yescharacteristic
651C22×C11C22×#4111yescharacteristic
652C22×C11C22×#4111yescharacteristic
653C22×C11C2×H(5,𝔽2)11yescharacteristic
654C22×C11C2×H(5,𝔽2)11yescharacteristic
655C22×C11C2×H(5,𝔽2)11yescharacteristic
656C22×C11C2×2−1+411yescharacteristic
657C2×D11—22no—
658C2×D11—22no—
659C2×D11—22no—
660C2×D11—22no—
661C2×D11—22no—
662C2×D11—22no—
663C2×D11—22no—
664C2×D11—22no—
665C2×D11—22no—
666C2×D11—416no—
667C2×D11—41no—
668C2×D11—41no—
669C2×D11—41no—
670C2×D11—41no—
671C2×D11#52014yes—
672C4×C11—24no—
673C4×C11—22no—
674C4×C11—22no—
675C4×C11—22no—
676C4×C11—42no—
677C4×C11—42no—
678C4×C11—41no—
679C4×C11—41no—
680C4×C11#51814yes—
681Dic11—24no—
682Dic11—22no—
683Dic11—22no—
684Dic11—24no—
685Dic11—22no—
686Dic11—22no—
687Dic11—41no—
688Dic11—42no—
689Dic11—42no—
690Dic11—41no—
691C25—111no—
692C2×#41—118no—
693C2×#41—442no—
694C2×#41—442no—
695C22×Q8—111no—
696C22×D4—112no—
697C22×D4—112no—
698C22×D4C22×D1112yes—
699C22×D4C22×D1111yescharacteristic
700C23×C4—111no—
701C23×C4—112no—
702C23×C4—111no—
703C23×C4—111no—
704C23×C4—118no—
705C23×C4—111no—
706C23×C4—111no—
707C23×C4—112no—
708C23×C4—112no—
709C23×C4—111no—
710C23×C4—111no—
711C23×C4—111no—
712C23×C4—111no—
713C23×C4—442no—
714C23×C4—442no—
715C23×C4C22×D1111yescharacteristic
716C23×C4C22×D1112yes—
717C23×C4C22×D1112yes—
718#123—1116no—
719C22⋊Q8—118no—
720C22⋊Q8—118no—
721#121—118no—
722#121C4×D1118yescomplemented
723#120—1116no—
724C4×Q8—442no—
725C4×Q8—442no—
726C4×D4—28no—
727C4×D4—42no—
728C4×D4—1116no—
729C4×D4—1116no—
730C4×D4—228no—
731C4×D4—442no—
732C4×D4—444no—
733C4×D4—444no—
734#117—118no—
735C2×C4⋊C4—42no—
736C2×C4⋊C4—111no—
737C2×C4⋊C4—112no—
738C2×C4⋊C4—112no—
739C2×C4⋊C4—111no—
740C2×C4⋊C4—111no—
741C2×C4⋊C4—112no—
742C2×C4⋊C4—112no—
743C2×C4⋊C4—112no—
744C2×C4⋊C4—112no—
745C2×C4⋊C4—112no—
746C2×C4⋊C4—112no—
747C2×C4⋊C4—442no—
748C2×C4⋊C4C22×D1111yescharacteristic
749C2×C4⋊C4C22×D1111yescharacteristic
750C2×C4⋊C4C22×D1112yes—
751C2×C4⋊C4C22×D1112yes—
752C2×C4⋊C4C22×D1111yescharacteristic
753C2×C22⋊C4—111no—
754C2×C22⋊C4—112no—
755C2×C22⋊C4—112no—
756C2×C22⋊C4—112no—
757C2×C22⋊C4—112no—
758C2×C22⋊C4—111no—
759C2×C22⋊C4—112no—
760C2×C22⋊C4—112no—
761C2×C22⋊C4—112no—
762C2×C22⋊C4—111no—
763C2×C22⋊C4—111no—
764C2×C22⋊C4—111no—
765C2×C22⋊C4—111no—
766C2×C22⋊C4—112no—
767C2×C22⋊C4—112no—
768C2×C22⋊C4—112no—
769C2×C22⋊C4—112no—
770C2×C22⋊C4—224no—
771C2×C22⋊C4—224no—
772C2×C22⋊C4—444no—
773C2×C22⋊C4C22×D1111yescharacteristic
774C2×C22⋊C4C22×D1112yes—
775C2×C22⋊C4C22×D1112yes—
776C2×C22⋊C4C22×D1112yes—
777C2×C22⋊C4C22×D1112yes—
778C2×C22⋊C4C22×D1111yescharacteristic
779C2×C42—112no—
780C2×C42—112no—
781C2×C42—111no—
782C2×C42—111no—
783C2×C42—112no—
784C2×C42—112no—
785C2×C42—112no—
786C2×C42—112no—
787C2×C42—111no—
788C2×C42—111no—
789C2×C42—111no—
790C2×C42—111no—
791C2×C42—442no—
792C2×C42—442no—
793C2×C42C22×D1112yes—
794C2×C42C22×D1111yescharacteristic
795C2×C42C22×D1111yescharacteristic
796#95—111no—
797#95—112no—
798#95—111no—
799#95—111no—
800#95—111no—
801#95—111no—
802#95—111no—
803#95—112no—
804#95—112no—
805#95—112no—
806#95—112no—
807#95—112no—
808#95—112no—
809#95—112no—
810#95—112no—
811#95—112no—
812#95—112no—
813#95—112no—
814#95—112no—
815#95—112no—
816#95C22×D1111yescharacteristic
817#95C22×D1111yescharacteristic
818#95C22×D1112yes—
819#95C22×D1112yes—
820C2×C11—24no—
821C2×C11—44no—
822C2×C11C2×C4×#4111yescharacteristic
823C2×C11C2×#51811yescharacteristic
824C2×C11C2×#52011yescharacteristic
825C2×C11#351911yescharacteristic
826C2×C11#351911yescharacteristic
827C2×C11#352011yescharacteristic
828C2×C11#352011yescharacteristic
829D11—24no—
830D11—42no—
831C24—111no—
832C24—111no—
833C24—114no—
834C24—222no—
835C24—222no—
836C24—222no—
837C24—222no—
838C24—441no—
839C24—441no—
840C24C23×D1112yes—
841C24C23×D1111yescharacteristic
842#41—4416no—
843C2×Q8—114no—
844C2×Q8—222no—
845C2×Q8—222no—
846C2×D4—24no—
847C2×D4—24no—
848C2×D4—22no—
849C2×D4—22no—
850C2×D4—118no—
851C2×D4—118no—
852C2×D4—224no—
853C2×D4—224no—
854C2×D4—442no—
855C2×D4—442no—
856C2×D4C2×C4×D1118yes—
857C2×D4C2×C4×D1114yes—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—24no—
861C22×C4—24no—
862C22×C4—42no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—111no—
867C22×C4—111no—
868C22×C4—111no—
869C22×C4—111no—
870C22×C4—112no—
871C22×C4—112no—
872C22×C4—114no—
873C22×C4—118no—
874C22×C4—114no—
875C22×C4—114no—
876C22×C4—114no—
877C22×C4—114no—
878C22×C4—111no—
879C22×C4—112no—
880C22×C4—111no—
881C22×C4—112no—
882C22×C4—222no—
883C22×C4—222no—
884C22×C4—222no—
885C22×C4—222no—
886C22×C4—222no—
887C22×C4—222no—
888C22×C4—224no—
889C22×C4—222no—
890C22×C4—222no—
891C22×C4—222no—
892C22×C4—222no—
893C22×C4—224no—
894C22×C4—222no—
895C22×C4—222no—
896C22×C4—4416no—
897C22×C4—441no—
898C22×C4—441no—
899C22×C4—441no—
900C22×C4—441no—
901C22×C4—441no—
902C22×C4—441no—
903C22×C4—441no—
904C22×C4—441no—
905C22×C4—441no—
906C22×C4—441no—
907C22×C4—442no—
908C22×C4—442no—
909C22×C4—442no—
910C22×C4—442no—
911C22×C4—442no—
912C22×C4—442no—
913C22×C4C2×C4×D1114yes—
914C22×C4C23×D1111yescharacteristic
915C22×C4C23×D1112yes—
916C22×C4C23×D1112yes—
917C22×C4C23×D1111yescharacteristic
918C22×C4C23×D1112yes—
919C22×C4C23×D1111yescharacteristic
920C22×C4C23×D1111yescharacteristic
921C22×C4C23×D1111yescharacteristic
922C22×C4C23×D1111yescharacteristic
923C4⋊C4—24no—
924C4⋊C4—22no—
925C4⋊C4—22no—
926C4⋊C4—42no—
927C4⋊C4—114no—
928C4⋊C4—118no—
929C4⋊C4—118no—
930C4⋊C4—224no—
931C4⋊C4—222no—
932C4⋊C4—222no—
933C4⋊C4—442no—
934C4⋊C4—442no—
935C4⋊C4—442no—
936C4⋊C4—442no—
937C4⋊C4—442no—
938C4⋊C4C2×C4×D1114yes—
939C22⋊C4—22no—
940C22⋊C4—24no—
941C22⋊C4—42no—
942C22⋊C4—42no—
943C22⋊C4—118no—
944C22⋊C4—118no—
945C22⋊C4—114no—
946C22⋊C4—118no—
947C22⋊C4—118no—
948C22⋊C4—222no—
949C22⋊C4—222no—
950C22⋊C4—224no—
951C22⋊C4—224no—
952C22⋊C4—224no—
953C22⋊C4—222no—
954C22⋊C4—222no—
955C22⋊C4—222no—
956C22⋊C4—442no—
957C22⋊C4—442no—
958C22⋊C4—442no—
959C22⋊C4—442no—
960C22⋊C4C2×C4×D1118yes—
961C22⋊C4#434114yescomplemented
962C42—24no—
963C42—22no—
964C42—22no—
965C42—118no—
966C42—224no—
967C42—222no—
968C42—222no—
969C42—441no—
970C42—441no—
971C42—441no—
972C42—441no—
973C42—442no—
974C42—442no—
975C42—442no—
976C42—442no—
977C11#3423311yescharacteristic, complemented, Sylow
978C23—21no—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—112no—
989C23—112no—
990C23—112no—
991C23—112no—
992C23—228no—
993C23—221no—
994C23—221no—
995C23—221no—
996C23—221no—
997C23—228no—
998C23—221no—
999C23—221no—
1000C23—221no—
1001C23—221no—
1002C23—221no—
1003C23—221no—
1004C23—444no—
1005C23—444no—
1006C23—444no—
1007C23—444no—
1008C23—444no—
1009C23C22×C4×D1114yes—
1010C23C22×C4×D1112yes—
1011C23C2×#434112yes—
1012C23#41×D1112yes—
1013C23C24×D1111yescharacteristic
1014Q8—228no—
1015D4—216no—
1016D4—28no—
1017D4—2216no—
1018D4—448no—
1019C2×C4—22no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—22no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—28no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—21no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—22no—
1037C2×C4—21no—
1038C2×C4—22no—
1039C2×C4—21no—
1040C2×C4—84no—
1041C2×C4—84no—
1042C2×C4—112no—
1043C2×C4—114no—
1044C2×C4—112no—
1045C2×C4—114no—
1046C2×C4—112no—
1047C2×C4—112no—
1048C2×C4—221no—
1049C2×C4—221no—
1050C2×C4—222no—
1051C2×C4—221no—
1052C2×C4—221no—
1053C2×C4—221no—
1054C2×C4—222no—
1055C2×C4—221no—
1056C2×C4—222no—
1057C2×C4—221no—
1058C2×C4—221no—
1059C2×C4—222no—
1060C2×C4—228no—
1061C2×C4—228no—
1062C2×C4—221no—
1063C2×C4—221no—
1064C2×C4—221no—
1065C2×C4—222no—
1066C2×C4—222no—
1067C2×C4—221no—
1068C2×C4—222no—
1069C2×C4—222no—
1070C2×C4—222no—
1071C2×C4—222no—
1072C2×C4—221no—
1073C2×C4—221no—
1074C2×C4—444no—
1075C2×C4—444no—
1076C2×C4—444no—
1077C2×C4—444no—
1078C2×C4—444no—
1079C2×C4—444no—
1080C2×C4—444no—
1081C2×C4—448no—
1082C2×C4—884no—
1083C2×C4—884no—
1084C2×C4C22×C4×D1114yes—
1085C2×C4C22×C4×D1112yes—
1086C2×C4C22×C4×D1112yes—
1087C2×C4C2×#434112yes—
1088C2×C4C2×#434112yes—
1089C2×C4#6703712yes—
1090C2×C4#6704212yes—
1091C22—22no—
1092C22—22no—
1093C22—22no—
1094C22—22no—
1095C22—22no—
1096C22—22no—
1097C22—24no—
1098C22—24no—
1099C22—24no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—114no—
1105C22—222no—
1106C22—222no—
1107C22—222no—
1108C22—222no—
1109C22—222no—
1110C22—222no—
1111C22—222no—
1112C22—222no—
1113C22—222no—
1114C22—4416no—
1115C22—441no—
1116C22—441no—
1117C22—441no—
1118C22—441no—
1119C22C4×#434114yes—
1120C22C23×C4×D1111yescharacteristic
1121C22C22×#434111yescharacteristic
1122C22C2×#6703711yescharacteristic
1123C22C2×#41×D1111yescharacteristic
1124C22C2×#6704211yescharacteristic
1125C22D11×H(5,𝔽2)11yescharacteristic
1126C22D11×2−1+411yescharacteristic
1127C4—22no—
1128C4—22no—
1129C4—24no—
1130C4—22no—
1131C4—42no—
1132C4—42no—
1133C4—41no—
1134C4—41no—
1135C4—222no—
1136C4—222no—
1137C4—222no—
1138C4—222no—
1139C4—224no—
1140C4—224no—
1141C4—441no—
1142C4—442no—
1143C4—442no—
1144C4—441no—
1145C4#1062307614yes—
1146C2—24no—
1147C2—44no—
1148C2—224no—
1149C2—442no—
1150C2C2×C4×#434111yescharacteristic
1151C2C2×#1062307611yescharacteristic
1152C2D11×#52011yescharacteristic
1153C2#1308263911yescharacteristic
1154C2#1308264111yescharacteristic
1155C2#1308265611yescharacteristic
1156C2#1308265811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2361C2
socle, cosocleC23×C11C25
prime radicalC2×#10623137C2
hypercenter#2361D11
hypocenterC11#34233
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2361

Complements

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

NH ≅ G/Ntype
2. #13071636C2semidirect
3. #13071621C2semidirect
4. #13071619C2semidirect
5. #13071596C2semidirect
6. #13071593C2semidirect
7. #13071551C2semidirect
8. #13071522C2semidirect
9. #13071508C2semidirect
10. #13071497C2semidirect
11. #13071455C2semidirect
12. #13071441C2semidirect
13. #13071413C2semidirect
14. #13071401C2semidirect
15. #13071242C2semidirect
16. C4×#66950C2semidirect
17. #13071146C2semidirect
18. #13071132C2semidirect
19. C4×#66991C2semidirect
20. C2×#10622600C2semidirect
21. #13070977C2semidirect
22. C4×C22⋊C4×D11C2semidirect
23. C11×#2361C2semidirect
28. C2×C4×D4×C11C22semidirect
34. C2×D4×Dic11C22semidirect
39. #10623137C4semidirect
42. C2×#66940C22semidirect
50. C2×C4×Dic22C22semidirect
51. C11×#390C22semidirect
52. C11×#389C22semidirect
53. C11×#388C22semidirect
55. C11×#385C22semidirect
56. C4×C11×C4⋊C4C22semidirect
58. #10622834C22semidirect
64. C4×C22⋊Dic11C22semidirect
66. C2×C11⋊#95C22semidirect
75. #10622598C22semidirect
76. #10622591C22semidirect
77. C4⋊C4×Dic11C22semidirect
78. C4⋊C4×Dic11C22semidirect
79. C4⋊C4×Dic11C22semidirect
80. C4⋊C4×Dic11C22semidirect
81. #10622587C22semidirect
82. #10622586C22semidirect
83. #10622585C22semidirect
89. #10622564C22semidirect
90. #10622563C22semidirect
92. #10622558C22semidirect
93. #10622557C22semidirect
94. #10622556C22semidirect
95. #10622555C22semidirect
99. C22⋊C4×Dic11C22semidirect
100. C22⋊C4×Dic11C22semidirect
105. C4×C4⋊Dic11C22semidirect
106. C4×C4⋊Dic11C22semidirect
107. #10622545C22semidirect
108. #10622542C22semidirect
109. #10622541C22semidirect
118. #10622268C22semidirect
119. #10622267C22semidirect
120. #10622266C22semidirect
121. #10622264C22semidirect
122. #10622263C22semidirect
123. #10622260C22semidirect
138. C2×#4341C2×C4semidirect
141. C22×C4×D11C2×C4semidirect
151. C11×#121C2×C4semidirect
176. #66991C2×C4semidirect
177. #66990C2×C4semidirect
180. D4×Dic11C2×C4semidirect
200. #66977C2×C4semidirect
218. #66950C2×C4semidirect
219. #66945C2×C4semidirect
221. #66936C2×C4semidirect
223. (C22⋊D11)⋊C4C2×C4semidirect
356. C11×C22⋊C4#41semidirect
366. C22⋊Dic11#41semidirect
402. #2361D11semidirect
554. C2×C4×D4C2×D11semidirect
568. #390C2×D11semidirect
574. #389C2×D11semidirect
582. #388C2×D11semidirect
598. #385C2×D11semidirect
615. C4×C4⋊C4C2×D11semidirect
722. #121C4×D11semidirect
961. C22⋊C4#4341semidirect
977. C11#34233semidirect

Maximal subgroups

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

subgroupindex
C2×#106231372
#130716362
#130716212
#130716192
#130715962
#130715932
#130715512
#130715222
#130715082
#130714972
#130714552
#130714412
#130714132
#130714012
#130712422
C4×#669502
#130711462
#130711322
C4×#669912
C2×#106226002
#130709772
C4×C22⋊C4×D112
C11×#23612
#3423311