Finite Group Databasebeta

← #14914491

Subgroups — #14914491

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×#10623158C211yesmaximal, characteristic
2#13071632C211yesmaximal, characteristic, complemented
3#13071630C211yesmaximal, characteristic, complemented
4#13071625C211yesmaximal, characteristic, complemented
5#13071598C212yesmaximal, complemented
6#13071592C212yesmaximal, complemented
7#13071555C212yesmaximal, complemented
8#13071525C212yesmaximal, complemented
9#13071505C211yesmaximal, characteristic, complemented
10#13071500C211yesmaximal, characteristic, complemented
11#13071454C211yesmaximal, characteristic, complemented
12#13071445C211yesmaximal, characteristic, complemented
13#13071409C212yesmaximal, complemented
14#13071405C212yesmaximal, complemented
15#13071244C212yesmaximal, complemented
16#13071154C211yesmaximal, characteristic, complemented
17C4×#66999C211yesmaximal, characteristic, complemented
18C4×#66948C211yesmaximal, characteristic, complemented
19#13071124C211yesmaximal, characteristic, complemented
20C2×#10622600C211yesmaximal, characteristic, complemented
21#13070975C212yesmaximal, complemented
22C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2360C211yesmaximal, characteristic, complemented
24C22×#4343C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic, complemented
28C22×C11×C4⋊C4C2211yescharacteristic
29C2×#66999C2211yescharacteristic
30C2×Q8×Dic11C2211yescharacteristic, complemented
31C2×#66983C2211yescharacteristic
32C2×C4×C22⋊D11C2212yes—
33C22×(C2×D11)⋊C4C2212yes—
34C22×C4⋊Dic11C2211yescharacteristic
35#10623158C4116yescomplemented
36C2×#66948C2211yescharacteristic
37C2×#66947C2212yes—
38C2×#66946C2212yes—
39C2×#66946C2212yes—
40C2×#66946C2211yescharacteristic, complemented
41C2×#66945C2211yescharacteristic
42C2×#66935C2212yes—
43C2×(C22⋊D11)⋊C4C2212yes—
44C2×(C22⋊D11)⋊C4C2212yes—
45C2×C22⋊C4×D11C2211yescharacteristic
46C2×C22⋊C4×D11C2211yescharacteristic
47C2×C4×D44C2212yes—
48C2×C4×D44C2211yescharacteristic, complemented
49C2×C42×D11C2211yescharacteristic
50C2×C42×D11C2211yescharacteristic
51C11×#391C2211yescharacteristic, complemented
52C11×#389C2211yescharacteristic, complemented
53C11×#389C2212yescomplemented
54C11×#387C2212yescomplemented
55C11×#385C2212yes—
56C4×C11×C4⋊C4C2211yescharacteristic, complemented
57C4×C11×C22⋊C4C2211yescharacteristic
58C4×C11×C22⋊C4C2212yes—
59#10622843C2211yescharacteristic, complemented
60#10622826C2212yes—
61C4×C22⋊Dic11C2211yescharacteristic
62C2×C11⋊#95C2212yes—
63#10622603C2212yes—
64#10622603C2212yescomplemented
65#10622603C2212yescomplemented
66#10622602C2212yes—
67#10622602C2212yescomplemented
68#10622601C2212yes—
69#10622601C2211yescharacteristic, complemented
70#10622600C2211yescharacteristic
71#10622600C2211yescharacteristic
72#10622600C2212yes—
73#10622600C2211yescharacteristic
74#10622600C2211yescharacteristic
75#10622600C2212yes—
76#10622600C2212yescomplemented
77#10622598C2211yescharacteristic, complemented
78#10622598C2212yescomplemented
79#10622594C2212yescomplemented
80#10622591C2212yescomplemented
81#10622590C2212yescomplemented
82C4⋊C4×Dic11C2211yescharacteristic, complemented
83C4⋊C4×Dic11C2211yescharacteristic, complemented
84#10622586C2211yescharacteristic, complemented
85#10622571C2212yes—
86#10622563C2212yes—
87C22⋊C4×Dic11C2212yes—
88C22⋊C4×Dic11C2211yescharacteristic
89C22⋊C4×Dic11C2211yescharacteristic
90#10622553C2212yes—
91#10622552C2212yes—
92#10622552C2211yescharacteristic, complemented
93C4×(C2×D11)⋊C4C2212yes—
94C4×(C2×D11)⋊C4C2211yescharacteristic
95C4×(C2×D11)⋊C4C2211yescharacteristic
96C4×(C2×D11)⋊C4C2212yescomplemented
97C4×(C2×D11)⋊C4C2212yescomplemented
98C4×C4⋊Dic11C2211yescharacteristic, complemented
99C4×Dic11⋊C4C2212yescomplemented
100C4×Dic11⋊C4C2212yescomplemented
101#10622541C2211yescharacteristic, complemented
102#10622283C2212yes—
103#10622283C2212yescomplemented
104#10622283C2212yescomplemented
105#10622282C2212yes—
106#10622281C2212yes—
107#10622281C2212yescomplemented
108#10622279C2211yescharacteristic
109#10622279C2211yescharacteristic
110#10622279C2212yes—
111#10622279C2212yescomplemented
112#10622278C2212yes—
113#10622278C2212yes—
114#10622278C2212yes—
115#10622278C2212yes—
116#10622277C2212yescomplemented
117D11×#95C2211yescharacteristic
118D11×#95C2211yescharacteristic
119D11×#95C2212yescomplemented
120#10622268C2212yescomplemented
121#10622264C2212yescomplemented
122#10622262C2212yescomplemented
123#10622261C2212yescomplemented
124C24×D11C2311yescharacteristic
125C22×Q8×C11C2311yescharacteristic
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2312yes—
128C22×C22⋊D11C2312yes—
129C23×Dic11C2312yes—
130C23×Dic11C2311yescharacteristic
131C2×#4343—42no—
132C2×#4343—42no—
133C2×#4343C2×C418yescomplemented
134C22×D44C2312yes—
135C22×D44C2311yescharacteristic
136C22×D44C2312yes—
137C22×C4×D11—42no—
138C22×C4×D11—42no—
139C22×C4×D11C2×C418yescomplemented
140C22×C4×D11C2311yescharacteristic
141C22×C4×D11C2311yescharacteristic
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2312yes—
147C22×C4×D11C2312yes—
148C22×C4×D11C2312yes—
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2311yescharacteristic
151C11×C22⋊Q8C2×C418yescomplemented
152C4×Q8×C11—42no—
153C2×C11×C4⋊C4—42no—
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C4⋊C4C2312yes—
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C4⋊C4C2312yes—
161C2×C11×C22⋊C4C2311yescharacteristic
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2311yescharacteristic
164C2×C42×C11C2311yescharacteristic
165C2×C42×C11C2311yescharacteristic
166C2×C42×C11C2312yes—
167C2×C42×C11C2312yes—
168C2×C22⋊Dic11C2311yescharacteristic
169C2×C22⋊Dic11C2311yescharacteristic
170#66999C2×C418yescomplemented
171Q8×Dic11—42no—
172#66983C2×C418yescomplemented
173C4×C22⋊D11—28no—
174C2×(C2×D11)⋊C4—44no—
175C2×(C2×D11)⋊C4C2312yes—
176C2×(C2×D11)⋊C4C2311yescharacteristic
177C2×(C2×D11)⋊C4C2311yescharacteristic
178C2×(C2×D11)⋊C4C2311yescharacteristic
179C2×(C2×D11)⋊C4C2311yescharacteristic
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
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⋊Dic11C2311yescharacteristic
196C2×C4⋊Dic11C2312yes—
197C2×C4⋊Dic11C2312yes—
198C2×C4⋊Dic11C2312yes—
199C2×C4⋊Dic11C2311yescharacteristic
200C2×Dic11⋊C4C2312yes—
201C2×Dic11⋊C4C2312yes—
202C2×Dic11⋊C4C2312yes—
203C2×C4×Dic11C2311yescharacteristic
204C2×C4×Dic11C2311yescharacteristic
205C2×C4×Dic11C2312yes—
206C2×C4×Dic11C2312yes—
207C2×C4×Dic11C2311yescharacteristic
208C2×C4×Dic11C2311yescharacteristic
209C2×C4×Dic11C2311yescharacteristic
210C2×C4×Dic11C2311yescharacteristic
211C2×C4×Dic11C2312yes—
212C2×C4×Dic11C2312yes—
213C2×C4×Dic11C2312yes—
214#66948C2×C418yescomplemented
215#66947C2×C4116yescomplemented
216#66946—42no—
217#66946—44no—
218#66946C2×C4116yescomplemented
219#66945C2×C418yescomplemented
220#66935C2×C4116yescomplemented
221(C22⋊D11)⋊C4—28no—
222(C22⋊D11)⋊C4C2×C4116yescomplemented
223C22⋊C4×D11—24no—
224C22⋊C4×D11—24no—
225C4×D44—42no—
226C4×D44—44no—
227C42×D11—42no—
228C42×D11—42no—
229C11×#95C2312yes—
230C11×#95C2312yes—
231C11×#95C2312yes—
232C11×#95C2312yes—
233C11×#95C2311yescharacteristic
234C11×#95C2311yescharacteristic
235C11⋊#95C2311yescharacteristic
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2311yescharacteristic
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2311yescharacteristic
246C11⋊#95C2311yescharacteristic
247C11⋊#95C2311yescharacteristic
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253#34233—111nomaximal, Sylow
254C24×C11C2411yescharacteristic
255C23×D11—22no—
256C23×D11—22no—
257C23×D11—22no—
258C23×D11—22no—
259C23×D11—41no—
260C23×D11—41no—
261C23×D11C22×C414yes—
262C23×D11C2411yescharacteristic
263C23×D11C2412yes—
264C23×D11C2411yescharacteristic
265C2×Q8×C11—22no—
266C2×Q8×C11—22no—
267C2×Q8×C11C22×C414yes—
268C22×C4×C11—22no—
269C22×C4×C11—22no—
270C22×C4×C11—24no—
271C22×C4×C11—42no—
272C22×C4×C11—42no—
273C22×C4×C11C22×C414yes—
274C22×C4×C11C2411yescharacteristic
275C22×C4×C11C2412yes—
276C22×C4×C11C2411yescharacteristic
277C22×C4×C11C2412yes—
278C22×C4×C11C2412yes—
279C22×C4×C11C2412yes—
280C22×C4×C11C2411yescharacteristic
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2411yescharacteristic
283C22×C4×C11C2411yescharacteristic
284C2×C22⋊D11—24no—
285C2×C22⋊D11—24no—
286C2×C22⋊D11C22×C418yes—
287C22×Dic11—24no—
288C22×Dic11—41no—
289C22×Dic11—41no—
290C22×Dic11—42no—
291C22×Dic11—42no—
292C22×Dic11C22×C414yes—
293C22×Dic11C2411yescharacteristic
294C22×Dic11C2412yes—
295C22×Dic11C2412yes—
296C22×Dic11C2411yescharacteristic
297C22×Dic11C2411yescharacteristic
298C22×Dic11C2411yescharacteristic
299C22×Dic11C2412yes—
300C22×Dic11C2411yescharacteristic
301C22×Dic11C2411yescharacteristic
302#4343—416no—
303C2×D44—24no—
304C2×D44—24no—
305C2×D44—22no—
306C2×D44—22no—
307C2×D44—42no—
308C2×D44—42no—
309C2×D44C22×C418yes—
310C2×D44C22×C414yes—
311C2×D44C22×C418yes—
312C2×C4×D11—22no—
313C2×C4×D11—22no—
314C2×C4×D11—24no—
315C2×C4×D11—22no—
316C2×C4×D11—22no—
317C2×C4×D11—22no—
318C2×C4×D11—22no—
319C2×C4×D11—22no—
320C2×C4×D11—22no—
321C2×C4×D11—24no—
322C2×C4×D11—22no—
323C2×C4×D11—22no—
324C2×C4×D11—22no—
325C2×C4×D11—22no—
326C2×C4×D11—41no—
327C2×C4×D11—41no—
328C2×C4×D11—41no—
329C2×C4×D11—41no—
330C2×C4×D11—41no—
331C2×C4×D11—41no—
332C2×C4×D11—41no—
333C2×C4×D11—41no—
334C2×C4×D11—42no—
335C2×C4×D11—42no—
336C2×C4×D11—42no—
337C2×C4×D11—42no—
338C2×C4×D11—42no—
339C2×C4×D11—42no—
340C2×C4×D11—416no—
341C2×C4×D11C22×C414yes—
342C2×C4×D11C22×C414yes—
343C2×C4×D11C22×C418yes—
344C2×C4×D11C22×C414yes—
345C2×C4×D11C22×C414yes—
346C11×C4⋊C4—22no—
347C11×C4⋊C4—22no—
348C11×C4⋊C4—42no—
349C11×C4⋊C4—42no—
350C11×C4⋊C4—42no—
351C11×C4⋊C4C22×C414yes—
352C11×C4⋊C4C22×C418yes—
353C11×C22⋊C4—22no—
354C11×C22⋊C4C22×C418yes—
355C11×C22⋊C4#4114yescomplemented
356C42×C11—22no—
357C42×C11—22no—
358C42×C11—42no—
359C42×C11—42no—
360C22⋊Dic11—22no—
361C22⋊Dic11#4114yescomplemented
362(C2×D11)⋊C4—22no—
363(C2×D11)⋊C4—22no—
364(C2×D11)⋊C4—24no—
365(C2×D11)⋊C4—24no—
366(C2×D11)⋊C4—24no—
367(C2×D11)⋊C4—22no—
368(C2×D11)⋊C4—22no—
369(C2×D11)⋊C4—24no—
370(C2×D11)⋊C4—42no—
371(C2×D11)⋊C4—42no—
372(C2×D11)⋊C4—42no—
373(C2×D11)⋊C4—42no—
374(C2×D11)⋊C4—42no—
375(C2×D11)⋊C4—42no—
376(C2×D11)⋊C4C22×C418yes—
377(C2×D11)⋊C4C22×C418yes—
378(C2×D11)⋊C4C22×C418yes—
379(C2×D11)⋊C4C22×C418yes—
380C4⋊Dic11—22no—
381C4⋊Dic11—22no—
382C4⋊Dic11—42no—
383C4⋊Dic11—42no—
384C4⋊Dic11—42no—
385C4⋊Dic11C22×C414yes—
386Dic11⋊C4—24no—
387Dic11⋊C4—24no—
388Dic11⋊C4C22×C418yes—
389C4×Dic11—24no—
390C4×Dic11—24no—
391C4×Dic11—22no—
392C4×Dic11—22no—
393C4×Dic11—41no—
394C4×Dic11—41no—
395C4×Dic11—41no—
396C4×Dic11—41no—
397C4×Dic11—42no—
398C4×Dic11—42no—
399C4×Dic11C22×C418yes—
400C2×#525—111no—
401#2361—111no—
402#2361—111no—
403#2360—111no—
404#2360D1111yescharacteristic, complemented
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×C11C23×C412yes—
428C23×C11C2×#4112yes—
429C23×C11C2×#4112yes—
430C23×C11C2511yescharacteristic
431C22×D11—21no—
432C22×D11—21no—
433C22×D11—21no—
434C22×D11—21no—
435C22×D11—28no—
436C22×D11—21no—
437C22×D11—21no—
438C22×D11—22no—
439C22×D11—22no—
440C22×D11—21no—
441C22×D11—22no—
442C22×D11—22no—
443C22×D11—22no—
444C22×D11—21no—
445C22×D11—21no—
446C22×D11—22no—
447C22×D11—21no—
448C22×D11—28no—
449C22×D11—44no—
450C22×D11—44no—
451C22×D11—44no—
452C22×D11—44no—
453C22×D11—44no—
454C22×D11C23×C412yes—
455C22×D11C23×C414yes—
456C22×D11C23×C412yes—
457C22×D11H(5,𝔽2)12yes—
458C22×D112−1+412yes—
459Q8×C11—28no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
462C2×C4×C11—21no—
463C2×C4×C11—21no—
464C2×C4×C11—21no—
465C2×C4×C11—21no—
466C2×C4×C11—22no—
467C2×C4×C11—21no—
468C2×C4×C11—21no—
469C2×C4×C11—22no—
470C2×C4×C11—28no—
471C2×C4×C11—22no—
472C2×C4×C11—22no—
473C2×C4×C11—21no—
474C2×C4×C11—21no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—21no—
480C2×C4×C11—22no—
481C2×C4×C11—22no—
482C2×C4×C11—21no—
483C2×C4×C11—84no—
484C2×C4×C11C23×C414yes—
485C2×C4×C11C23×C414yes—
486C2×C4×C11C23×C412yes—
487C2×C4×C11C23×C412yes—
488C2×C4×C11C2×#4112yes—
489C2×C4×C11C2×#4112yes—
490C2×C4×C11H(5,𝔽2)12yes—
491C2×C4×C11H(5,𝔽2)12yes—
492C22⋊D11—216no—
493C2×Dic11—22no—
494C2×Dic11—22no—
495C2×Dic11—21no—
496C2×Dic11—21no—
497C2×Dic11—21no—
498C2×Dic11—21no—
499C2×Dic11—21no—
500C2×Dic11—21no—
501C2×Dic11—21no—
502C2×Dic11—21no—
503C2×Dic11—22no—
504C2×Dic11—22no—
505C2×Dic11—21no—
506C2×Dic11—21no—
507C2×Dic11—21no—
508C2×Dic11—21no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—21no—
513C2×Dic11—22no—
514C2×Dic11—21no—
515C2×Dic11—44no—
516C2×Dic11—84no—
517C2×Dic11C23×C412yes—
518C2×Dic11C23×C414yes—
519C2×Dic11C23×C412yes—
520C2×Dic11C2×#4112yes—
521C2×Dic11C2×#4112yes—
522D44—216no—
523D44—28no—
524D44—48no—
525C4×D11—28no—
526C4×D11—28no—
527C4×D11—44no—
528C4×D11—44no—
529C4×D11—48no—
530C4×D11—44no—
531C4×D11—44no—
532C4×D11—44no—
533C4×D11—44no—
534C4×D11—84no—
535C4×D11—84no—
536C22×#41—111no—
537C24×C4—111no—
538#525—1116no—
539C2×#123—112no—
540C2×C22⋊Q8—111no—
541C2×C22⋊Q8C2×D1111yescharacteristic
542C2×#121—111no—
543C2×#121—111no—
544C2×#120—112no—
545C2×C4×Q8—111no—
546C2×C4×Q8C2×D1111yescharacteristic, complemented
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×D4—112no—
554C2×C4×D4—111no—
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#391C2×D1111yescharacteristic, complemented
565#390—112no—
566#390—111no—
567#390—112no—
568#390—111no—
569#389—112no—
570#389—111no—
571#389—111no—
572#389—111no—
573#389C2×D1112yescomplemented
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#388—112no—
583#387—112no—
584#387—112no—
585#387—112no—
586#387C2×D1112yescomplemented
587#386—112no—
588#386—112no—
589#386—112no—
590#386—112no—
591#386—112no—
592#386—112no—
593#385—112no—
594#385—112no—
595#385—112no—
596#385—112no—
597#385—112no—
598#385C2×D1112yes—
599#383—112no—
600#382—112no—
601#381—112no—
602#380—112no—
603#380—112no—
604#380—111no—
605#380—111no—
606#380—112no—
607#380—111no—
608#380—111no—
609C4×C4⋊C4—111no—
610C4×C4⋊C4—111no—
611C4×C4⋊C4—112no—
612C4×C4⋊C4—111no—
613C4×C4⋊C4—112no—
614C4×C4⋊C4—112no—
615C4×C4⋊C4C2×D1111yescharacteristic, complemented
616C4×C22⋊C4—111no—
617C4×C22⋊C4—111no—
618C4×C22⋊C4—112no—
619C4×C22⋊C4—111no—
620C4×C22⋊C4—112no—
621C4×C22⋊C4—111no—
622C4×C22⋊C4—111no—
623C4×C22⋊C4—112no—
624C4×C22⋊C4—112no—
625C4×C22⋊C4—111no—
626C4×C22⋊C4—111no—
627C4×C22⋊C4—112no—
628C4×C22⋊C4—112no—
629C4×C22⋊C4C2×D1112yes—
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×C11C4×#4114yes—
643C22×C11C24×C411yescharacteristic
644C22×C11C22×#4111yescharacteristic
645C22×C11C22×#4111yescharacteristic
646C22×C11C2×H(5,𝔽2)11yescharacteristic
647C22×C11C2×H(5,𝔽2)11yescharacteristic
648C22×C11C2×H(5,𝔽2)11yescharacteristic
649C22×C11C2×2−1+411yescharacteristic
650C2×D11—22no—
651C2×D11—22no—
652C2×D11—22no—
653C2×D11—22no—
654C2×D11—22no—
655C2×D11—22no—
656C2×D11—22no—
657C2×D11—24no—
658C2×D11—22no—
659C2×D11—24no—
660C2×D11—22no—
661C2×D11—24no—
662C2×D11—416no—
663C2×D11—41no—
664C2×D11—41no—
665C2×D11—42no—
666C2×D11—42no—
667C2×D11—42no—
668C2×D11—42no—
669C2×D11—41no—
670C2×D11—41no—
671C2×D11#52014yes—
672C4×C11—22no—
673C4×C11—24no—
674C4×C11—24no—
675C4×C11—22no—
676C4×C11—22no—
677C4×C11—42no—
678C4×C11—42no—
679C4×C11—41no—
680C4×C11—41no—
681C4×C11#51814yes—
682Dic11—24no—
683Dic11—22no—
684Dic11—22no—
685Dic11—22no—
686Dic11—22no—
687Dic11—41no—
688Dic11—42no—
689Dic11—42no—
690Dic11—41no—
691C25—111no—
692C2×#41—118no—
693C2×#41—442no—
694C2×#41—442no—
695C22×Q8C22×D1111yescharacteristic
696C22×D4—112no—
697C22×D4—112no—
698C22×D4—111no—
699C22×D4—112no—
700C23×C4—111no—
701C23×C4—111no—
702C23×C4—111no—
703C23×C4—118no—
704C23×C4—111no—
705C23×C4—112no—
706C23×C4—111no—
707C23×C4—112no—
708C23×C4—111no—
709C23×C4—111no—
710C23×C4—111no—
711C23×C4—111no—
712C23×C4—112no—
713C23×C4—112no—
714C23×C4—442no—
715C23×C4—442no—
716C23×C4C22×D1111yescharacteristic
717C23×C4C22×D1112yes—
718#123—1116no—
719C22⋊Q8—118no—
720C22⋊Q8C4×D1118yescomplemented
721#121—118no—
722#121—118no—
723#120—1116no—
724C4×Q8—42no—
725C4×Q8—442no—
726C4×D4—1116no—
727C4×D4—1116no—
728C4×D4—228no—
729C4×D4—228no—
730C4×D4—442no—
731C4×D4—444no—
732C4×D4—442no—
733C4×D4—444no—
734#117—118no—
735C2×C4⋊C4—42no—
736C2×C4⋊C4—111no—
737C2×C4⋊C4—112no—
738C2×C4⋊C4—111no—
739C2×C4⋊C4—111no—
740C2×C4⋊C4—112no—
741C2×C4⋊C4—112no—
742C2×C4⋊C4—112no—
743C2×C4⋊C4—112no—
744C2×C4⋊C4—112no—
745C2×C4⋊C4—442no—
746C2×C4⋊C4C22×D1111yescharacteristic
747C2×C4⋊C4C22×D1111yescharacteristic
748C2×C4⋊C4C22×D1112yes—
749C2×C4⋊C4C22×D1112yes—
750C2×C4⋊C4C22×D1112yes—
751C2×C4⋊C4C22×D1111yescharacteristic
752C2×C4⋊C4C22×D1112yes—
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—111no—
762C2×C22⋊C4—111no—
763C2×C22⋊C4—111no—
764C2×C22⋊C4—111no—
765C2×C22⋊C4—112no—
766C2×C22⋊C4—112no—
767C2×C22⋊C4—112no—
768C2×C22⋊C4—112no—
769C2×C22⋊C4—112no—
770C2×C22⋊C4—112no—
771C2×C22⋊C4—112no—
772C2×C22⋊C4—112no—
773C2×C22⋊C4—224no—
774C2×C22⋊C4—224no—
775C2×C22⋊C4—444no—
776C2×C22⋊C4C22×D1111yescharacteristic
777C2×C22⋊C4C22×D1112yes—
778C2×C22⋊C4C22×D1111yescharacteristic
779C2×C42—112no—
780C2×C42—112no—
781C2×C42—112no—
782C2×C42—111no—
783C2×C42—111no—
784C2×C42—112no—
785C2×C42—112no—
786C2×C42—111no—
787C2×C42—111no—
788C2×C42—111no—
789C2×C42—111no—
790C2×C42—442no—
791C2×C42—442no—
792C2×C42C22×D1111yescharacteristic
793C2×C42C22×D1111yescharacteristic
794C2×C42C22×D1112yes—
795C2×C42C22×D1112yes—
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#95C22×D1111yescharacteristic
815#95C22×D1111yescharacteristic
816#95C22×D1112yes—
817#95C22×D1112yes—
818#95C22×D1112yes—
819#95C22×D1112yes—
820C2×C11—24no—
821C2×C11C2×C4×#4111yescharacteristic
822C2×C11C2×#51811yescharacteristic
823C2×C11C2×#52011yescharacteristic
824C2×C11#351911yescharacteristic
825C2×C11#351911yescharacteristic
826C2×C11#352011yescharacteristic
827C2×C11#352011yescharacteristic
828D11—24no—
829D11—44no—
830D11—42no—
831C24—111no—
832C24—111no—
833C24—112no—
834C24—114no—
835C24—222no—
836C24—222no—
837C24—222no—
838C24—222no—
839C24—441no—
840C24—441no—
841C24C23×D1111yescharacteristic
842#41—4416no—
843C2×Q8—22no—
844C2×Q8—22no—
845C2×Q8C2×C4×D1114yes—
846C2×D4—118no—
847C2×D4—118no—
848C2×D4—114no—
849C2×D4—118no—
850C2×D4—224no—
851C2×D4—224no—
852C2×D4—224no—
853C2×D4—224no—
854C2×D4—222no—
855C2×D4—222no—
856C2×D4—442no—
857C2×D4—442no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—24no—
861C22×C4—42no—
862C22×C4—42no—
863C22×C4—111no—
864C22×C4—111no—
865C22×C4—111no—
866C22×C4—111no—
867C22×C4—112no—
868C22×C4—114no—
869C22×C4—114no—
870C22×C4—114no—
871C22×C4—114no—
872C22×C4—118no—
873C22×C4—114no—
874C22×C4—111no—
875C22×C4—112no—
876C22×C4—111no—
877C22×C4—112no—
878C22×C4—222no—
879C22×C4—222no—
880C22×C4—224no—
881C22×C4—222no—
882C22×C4—222no—
883C22×C4—222no—
884C22×C4—222no—
885C22×C4—222no—
886C22×C4—222no—
887C22×C4—222no—
888C22×C4—222no—
889C22×C4—224no—
890C22×C4—222no—
891C22×C4—222no—
892C22×C4—224no—
893C22×C4—4416no—
894C22×C4—441no—
895C22×C4—441no—
896C22×C4—441no—
897C22×C4—441no—
898C22×C4—441no—
899C22×C4—441no—
900C22×C4—441no—
901C22×C4—441no—
902C22×C4—442no—
903C22×C4—442no—
904C22×C4—442no—
905C22×C4—442no—
906C22×C4—442no—
907C22×C4—442no—
908C22×C4—441no—
909C22×C4—441no—
910C22×C4—442no—
911C22×C4—442no—
912C22×C4C2×C4×D1114yes—
913C22×C4C23×D1111yescharacteristic
914C22×C4C23×D1112yes—
915C22×C4C23×D1111yescharacteristic
916C22×C4C23×D1112yes—
917C22×C4C23×D1112yes—
918C22×C4C23×D1112yes—
919C22×C4C23×D1111yescharacteristic
920C22×C4C23×D1111yescharacteristic
921C22×C4C23×D1111yescharacteristic
922C22×C4C23×D1111yescharacteristic
923C4⋊C4—22no—
924C4⋊C4—22no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—114no—
929C4⋊C4—118no—
930C4⋊C4—224no—
931C4⋊C4—224no—
932C4⋊C4—222no—
933C4⋊C4—222no—
934C4⋊C4—442no—
935C4⋊C4—442no—
936C4⋊C4—442no—
937C4⋊C4C2×C4×D1114yes—
938C4⋊C4C2×C4×D1118yes—
939C22⋊C4—22no—
940C22⋊C4—114no—
941C22⋊C4—118no—
942C22⋊C4—118no—
943C22⋊C4—118no—
944C22⋊C4—118no—
945C22⋊C4—222no—
946C22⋊C4—222no—
947C22⋊C4—224no—
948C22⋊C4—224no—
949C22⋊C4—224no—
950C22⋊C4—222no—
951C22⋊C4—222no—
952C22⋊C4—222no—
953C22⋊C4—224no—
954C22⋊C4—442no—
955C22⋊C4—442no—
956C22⋊C4—442no—
957C22⋊C4—442no—
958C22⋊C4—442no—
959C22⋊C4—442no—
960C22⋊C4C2×C4×D1118yes—
961C22⋊C4#434314yescomplemented
962C42—22no—
963C42—22no—
964C42—42no—
965C42—42no—
966C42—118no—
967C42—224no—
968C42—222no—
969C42—224no—
970C42—222no—
971C42—441no—
972C42—441no—
973C42—441no—
974C42—441no—
975C42—442no—
976C42—442no—
977C11#3423311yescharacteristic, complemented, Sylow
978C23—21no—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—112no—
983C23—112no—
984C23—112no—
985C23—112no—
986C23—114no—
987C23—228no—
988C23—221no—
989C23—221no—
990C23—221no—
991C23—221no—
992C23—228no—
993C23—222no—
994C23—221no—
995C23—221no—
996C23—222no—
997C23—221no—
998C23—222no—
999C23—222no—
1000C23—221no—
1001C23—221no—
1002C23—222no—
1003C23—222no—
1004C23—221no—
1005C23—444no—
1006C23—444no—
1007C23—444no—
1008C23—444no—
1009C23—444no—
1010C23C22×C4×D1112yes—
1011C23C2×#434312yes—
1012C23#41×D1112yes—
1013C23C24×D1111yescharacteristic
1014Q8—28no—
1015D4—2216no—
1016D4—2216no—
1017D4—228no—
1018D4—448no—
1019C2×C4—21no—
1020C2×C4—22no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—22no—
1027C2×C4—21no—
1028C2×C4—22no—
1029C2×C4—28no—
1030C2×C4—21no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—22no—
1037C2×C4—21no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—84no—
1043C2×C4—112no—
1044C2×C4—114no—
1045C2×C4—112no—
1046C2×C4—112no—
1047C2×C4—112no—
1048C2×C4—221no—
1049C2×C4—221no—
1050C2×C4—221no—
1051C2×C4—222no—
1052C2×C4—222no—
1053C2×C4—221no—
1054C2×C4—221no—
1055C2×C4—221no—
1056C2×C4—221no—
1057C2×C4—221no—
1058C2×C4—228no—
1059C2×C4—228no—
1060C2×C4—221no—
1061C2×C4—222no—
1062C2×C4—221no—
1063C2×C4—221no—
1064C2×C4—222no—
1065C2×C4—221no—
1066C2×C4—222no—
1067C2×C4—222no—
1068C2×C4—222no—
1069C2×C4—222no—
1070C2×C4—221no—
1071C2×C4—221no—
1072C2×C4—444no—
1073C2×C4—444no—
1074C2×C4—448no—
1075C2×C4—444no—
1076C2×C4—444no—
1077C2×C4—444no—
1078C2×C4—444no—
1079C2×C4—444no—
1080C2×C4—884no—
1081C2×C4—884no—
1082C2×C4—884no—
1083C2×C4C22×C4×D1114yes—
1084C2×C4C22×C4×D1112yes—
1085C2×C4C22×C4×D1114yes—
1086C2×C4C22×C4×D1112yes—
1087C2×C4#6703712yes—
1088C2×C4C2×#434312yes—
1089C2×C4C2×#434312yes—
1090C2×C4#6704212yes—
1091C22—22no—
1092C22—22no—
1093C22—22no—
1094C22—22no—
1095C22—22no—
1096C22—22no—
1097C22—114no—
1098C22—222no—
1099C22—222no—
1100C22—222no—
1101C22—222no—
1102C22—222no—
1103C22—222no—
1104C22—224no—
1105C22—222no—
1106C22—222no—
1107C22—224no—
1108C22—224no—
1109C22—222no—
1110C22—4416no—
1111C22—442no—
1112C22—441no—
1113C22—442no—
1114C22—441no—
1115C22—441no—
1116C22—442no—
1117C22—441no—
1118C22—442no—
1119C22C4×#434314yes—
1120C22C23×C4×D1111yescharacteristic
1121C22C2×#6703711yescharacteristic
1122C22C22×#434311yescharacteristic
1123C22C2×#41×D1111yescharacteristic
1124C22C2×#6704211yescharacteristic
1125C22D11×H(5,𝔽2)11yescharacteristic
1126C22D11×2−1+411yescharacteristic
1127C4—22no—
1128C4—22no—
1129C4—22no—
1130C4—24no—
1131C4—24no—
1132C4—42no—
1133C4—42no—
1134C4—41no—
1135C4—41no—
1136C4—222no—
1137C4—222no—
1138C4—224no—
1139C4—222no—
1140C4—222no—
1141C4—441no—
1142C4—442no—
1143C4—442no—
1144C4—441no—
1145C4#1062307614yes—
1146C2—24no—
1147C2—224no—
1148C2—442no—
1149C2—444no—
1150C2C2×C4×#434311yescharacteristic
1151C2C2×#1062307611yescharacteristic
1152C2D11×#52011yescharacteristic
1153C2#1308264511yescharacteristic
1154C2#1308264911yescharacteristic
1155C2#1308266211yescharacteristic
1156C2#1308266611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2360C2
socle, cosocleC23×C11C25
prime radicalC2×#10623158C2
hypercenter#2360D11
hypocenterC11#34233
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2360

Complements

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

NH ≅ G/Ntype
2. #13071632C2semidirect
3. #13071630C2semidirect
4. #13071625C2semidirect
5. #13071598C2semidirect
6. #13071592C2semidirect
7. #13071555C2semidirect
8. #13071525C2semidirect
9. #13071505C2semidirect
10. #13071500C2semidirect
11. #13071454C2semidirect
12. #13071445C2semidirect
13. #13071409C2semidirect
14. #13071405C2semidirect
15. #13071244C2semidirect
16. #13071154C2semidirect
17. C4×#66999C2semidirect
18. C4×#66948C2semidirect
19. #13071124C2semidirect
20. C2×#10622600C2semidirect
21. #13070975C2semidirect
22. C4×C22⋊C4×D11C2semidirect
23. C11×#2360C2semidirect
27. C2×C4×Q8×C11C22semidirect
30. C2×Q8×Dic11C22semidirect
35. #10623158C4semidirect
40. C2×#66946C22semidirect
48. C2×C4×D44C22semidirect
51. C11×#391C22semidirect
52. C11×#389C22semidirect
53. C11×#389C22semidirect
54. C11×#387C22semidirect
56. C4×C11×C4⋊C4C22semidirect
59. #10622843C22semidirect
64. #10622603C22semidirect
65. #10622603C22semidirect
67. #10622602C22semidirect
69. #10622601C22semidirect
76. #10622600C22semidirect
77. #10622598C22semidirect
78. #10622598C22semidirect
79. #10622594C22semidirect
80. #10622591C22semidirect
81. #10622590C22semidirect
82. C4⋊C4×Dic11C22semidirect
83. C4⋊C4×Dic11C22semidirect
84. #10622586C22semidirect
92. #10622552C22semidirect
96. C4×(C2×D11)⋊C4C22semidirect
97. C4×(C2×D11)⋊C4C22semidirect
98. C4×C4⋊Dic11C22semidirect
99. C4×Dic11⋊C4C22semidirect
100. C4×Dic11⋊C4C22semidirect
101. #10622541C22semidirect
103. #10622283C22semidirect
104. #10622283C22semidirect
107. #10622281C22semidirect
111. #10622279C22semidirect
116. #10622277C22semidirect
119. D11×#95C22semidirect
120. #10622268C22semidirect
121. #10622264C22semidirect
122. #10622262C22semidirect
123. #10622261C22semidirect
133. C2×#4343C2×C4semidirect
139. C22×C4×D11C2×C4semidirect
151. C11×C22⋊Q8C2×C4semidirect
170. #66999C2×C4semidirect
172. #66983C2×C4semidirect
214. #66948C2×C4semidirect
215. #66947C2×C4semidirect
218. #66946C2×C4semidirect
219. #66945C2×C4semidirect
220. #66935C2×C4semidirect
222. (C22⋊D11)⋊C4C2×C4semidirect
355. C11×C22⋊C4#41semidirect
361. C22⋊Dic11#41semidirect
404. #2360D11semidirect
546. C2×C4×Q8C2×D11semidirect
564. #391C2×D11semidirect
573. #389C2×D11semidirect
574. #389C2×D11semidirect
586. #387C2×D11semidirect
615. C4×C4⋊C4C2×D11semidirect
720. C22⋊Q8C4×D11semidirect
961. C22⋊C4#4343semidirect
977. C11#34233semidirect

Maximal subgroups

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

subgroupindex
C2×#106231582
#130716322
#130716302
#130716252
#130715982
#130715922
#130715552
#130715252
#130715052
#130715002
#130714542
#130714452
#130714092
#130714052
#130712442
#130711542
C4×#669992
C4×#669482
#130711242
C2×#106226002
#130709752
C4×C22⋊C4×D112
C11×#23602
#3423311