Finite Group Databasebeta

← #14914488

Subgroups — #14914488

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#13071637C211yesmaximal, characteristic, complemented
3#13071628C211yesmaximal, characteristic, complemented
4#13071623C211yesmaximal, characteristic, complemented
5#13071620C211yesmaximal, characteristic, complemented
6#13071596C212yesmaximal, complemented
7#13071593C212yesmaximal, complemented
8#13071554C212yesmaximal, complemented
9#13071521C212yesmaximal, complemented
10#13071505C211yesmaximal, characteristic, complemented
11#13071500C211yesmaximal, characteristic, complemented
12#13071455C211yesmaximal, characteristic, complemented
13#13071441C211yesmaximal, characteristic, complemented
14#13071408C212yesmaximal, complemented
15#13071404C212yesmaximal, complemented
16#13071246C212yesmaximal, complemented
17C4×#66977C211yesmaximal, characteristic, complemented
18#13071144C211yesmaximal, characteristic, complemented
19#121×Dic11C211yesmaximal, characteristic, complemented
20D11×#380C211yesmaximal, characteristic, complemented
21#13070975C212yesmaximal, complemented
22C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
23C4×C11×#121C211yesmaximal, characteristic, complemented
24C22×#4341C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C4×D4×C11C2212yes—
28C2×C4×D4×C11C2211yescharacteristic, complemented
29C22×C42×C11C2211yescharacteristic
30C2×#66991C2211yescharacteristic
31C2×#66990C2212yes—
32C2×D4×Dic11C2212yes—
33C2×D4×Dic11C2212yes—
34C2×D4×Dic11C2211yescharacteristic, complemented
35C2×C4×C22⋊D11C2212yes—
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C2×#66977C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40#10623137C4116yescomplemented
41C2×#66950C2211yescharacteristic
42C2×#66945C2211yescharacteristic
43C2×C4⋊C4×D11C2211yescharacteristic
44C2×C4⋊C4×D11C2211yescharacteristic
45C2×#66940C2211yescharacteristic, complemented
46C2×#66936C2212yes—
47C2×(C22⋊D11)⋊C4C2212yes—
48C2×(C22⋊D11)⋊C4C2212yes—
49C2×C22⋊C4×D11C2212yes—
50C2×C4×Dic22C2211yescharacteristic, complemented
51C11×#390C2211yescharacteristic, complemented
52C11×#389C2211yescharacteristic, complemented
53C11×#388C2212yescomplemented
54C11×#386C2212yes—
55C11×#380C2211yescharacteristic
56C4×C11×C4⋊C4C2211yescharacteristic, complemented
57C4×C11×C22⋊C4C2212yescomplemented
58#10622834C2211yescharacteristic, complemented
59#10622833C2212yes—
60#10622826C2212yes—
61#10622825C2211yescharacteristic
62#10622823C2212yes—
63#10622823C2212yescomplemented
64C4×C22⋊Dic11C2212yes—
65C2×C11⋊#95C2211yescharacteristic
66C2×C11⋊#95C2211yescharacteristic
67C2×C11⋊#95C2212yescomplemented
68#10622603C2212yes—
69#10622602C2212yes—
70#10622600C2211yescharacteristic
71#10622600C2211yescharacteristic
72#10622598C2211yescharacteristic, complemented
73#10622590C2212yescomplemented
74C4⋊C4×Dic11C2211yescharacteristic, complemented
75C4⋊C4×Dic11C2211yescharacteristic, complemented
76#10622587C2211yescharacteristic, complemented
77#10622586C2212yescomplemented
78#10622586C2211yescharacteristic, complemented
79#10622571C2212yes—
80#10622570C2212yes—
81#10622570C2212yes—
82#10622569C2212yes—
83#10622569C2212yes—
84#10622564C2212yescomplemented
85#10622559C2212yes—
86#10622559C2212yescomplemented
87#10622558C2212yescomplemented
88#10622557C2212yescomplemented
89#10622556C2212yescomplemented
90#10622555C2212yes—
91#10622555C2212yescomplemented
92C22⋊C4×Dic11C2212yes—
93C22⋊C4×Dic11C2212yescomplemented
94C22⋊C4×Dic11C2212yescomplemented
95#10622553C2212yes—
96C4×(C2×D11)⋊C4C2211yescharacteristic
97C4×(C2×D11)⋊C4C2211yescharacteristic
98C4×(C2×D11)⋊C4C2212yes—
99C4×(C2×D11)⋊C4C2211yescharacteristic
100C4×(C2×D11)⋊C4C2211yescharacteristic
101C4×(C2×D11)⋊C4C2211yescharacteristic
102C4×(C2×D11)⋊C4C2211yescharacteristic
103C4×(C2×D11)⋊C4C2211yescharacteristic
104C4×(C2×D11)⋊C4C2211yescharacteristic
105C4×C4⋊Dic11C2211yescharacteristic, complemented
106#10622546C2212yescomplemented
107C4×Dic11⋊C4C2212yescomplemented
108C4×Dic11⋊C4C2212yescomplemented
109#10622542C2211yescharacteristic, complemented
110#10622541C2212yescomplemented
111#10622541C2211yescharacteristic, complemented
112#10622283C2212yes—
113#10622282C2212yes—
114#10622281C2212yes—
115#10622280C2212yes—
116#10622279C2212yes—
117D11×#95C2212yes—
118#10622267C2212yescomplemented
119#10622266C2212yescomplemented
120#10622265C2212yescomplemented
121#10622264C2212yescomplemented
122#10622262C2212yescomplemented
123#10622261C2212yescomplemented
124C24×D11C2311yescharacteristic
125C22×D4×C11C2312yes—
126C22×D4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2312yes—
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C23×Dic11C2311yescharacteristic
134C23×Dic11C2311yescharacteristic
135C23×Dic11C2312yes—
136C23×Dic11C2312yes—
137C23×Dic11C2311yescharacteristic
138C2×#4341—42no—
139C2×#4341—42no—
140C2×#4341C2×C418yescomplemented
141C22×C4×D11—42no—
142C22×C4×D11—42no—
143C22×C4×D11C2×C418yescomplemented
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2312yes—
147C22×C4×D11C2312yes—
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×Dic22C2311yescharacteristic
151C11×#121C2×C418yescomplemented
152C4×D4×C11—42no—
153C4×D4×C11—44no—
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C42×C11—42no—
164C2×C42×C11C2311yescharacteristic
165C2×C42×C11C2311yescharacteristic
166C2×C42×C11C2312yes—
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2311yescharacteristic
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175#66991C2×C418yescomplemented
176#66990C2×C4116yescomplemented
177D4×Dic11—42no—
178D4×Dic11—44no—
179D4×Dic11C2×C4116yescomplemented
180C4×C22⋊D11—28no—
181C2×(C2×D11)⋊C4—24no—
182C2×(C2×D11)⋊C4—24no—
183C2×(C2×D11)⋊C4C2311yescharacteristic
184C2×(C2×D11)⋊C4C2311yescharacteristic
185C2×(C2×D11)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2311yescharacteristic
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2311yescharacteristic
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2311yescharacteristic
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×C4⋊Dic11C2311yescharacteristic
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×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×C4×Dic11—42no—
209C2×C4×Dic11C2312yes—
210C2×C4×Dic11C2311yescharacteristic
211C2×C4×Dic11C2312yes—
212C2×C4×Dic11C2311yescharacteristic
213C2×C4×Dic11C2312yes—
214C2×C4×Dic11C2312yes—
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2312yes—
219#66950C2×C418yescomplemented
220#66945C2×C418yescomplemented
221C4⋊C4×D11—42no—
222C4⋊C4×D11—42no—
223#66940—42no—
224#66936C2×C4116yescomplemented
225(C22⋊D11)⋊C4—28no—
226(C22⋊D11)⋊C4C2×C4116yescomplemented
227C22⋊C4×D11—44no—
228C4×Dic22—42no—
229C11×#95C2312yes—
230C11×#95C2312yes—
231C11×#95C2312yes—
232C11⋊#95C2311yescharacteristic
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2311yescharacteristic
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2311yescharacteristic
244C11⋊#95C2312yes—
245C11⋊#95C2311yescharacteristic
246C11⋊#95C2312yes—
247C11⋊#95C2311yescharacteristic
248C11⋊#95C2312yes—
249C11⋊#95C2311yescharacteristic
250C11⋊#95C2312yes—
251C11⋊#95C2311yescharacteristic
252C11⋊#95C2311yescharacteristic
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—22no—
274C22×C4×C11—22no—
275C22×C4×C11—22no—
276C22×C4×C11—22no—
277C22×C4×C11—24no—
278C22×C4×C11—41no—
279C22×C4×C11—41no—
280C22×C4×C11—42no—
281C22×C4×C11—42no—
282C22×C4×C11C22×C414yes—
283C22×C4×C11C2411yescharacteristic
284C22×C4×C11C2412yes—
285C22×C4×C11C2411yescharacteristic
286C22×C4×C11C2412yes—
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2412yes—
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C2×C22⋊D11—24no—
293C2×C22⋊D11—24no—
294C2×C22⋊D11—42no—
295C2×C22⋊D11—42no—
296C2×C22⋊D11C22×C418yes—
297C2×C22⋊D11C22×C418yes—
298C22×Dic11—22no—
299C22×Dic11—22no—
300C22×Dic11—24no—
301C22×Dic11—22no—
302C22×Dic11—22no—
303C22×Dic11—41no—
304C22×Dic11—41no—
305C22×Dic11—41no—
306C22×Dic11—41no—
307C22×Dic11—42no—
308C22×Dic11—42no—
309C22×Dic11—42no—
310C22×Dic11—42no—
311C22×Dic11C22×C418yes—
312C22×Dic11C22×C414yes—
313C22×Dic11C2411yescharacteristic
314C22×Dic11C2412yes—
315C22×Dic11C2412yes—
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2412yes—
319C22×Dic11C2412yes—
320C22×Dic11C2411yescharacteristic
321C22×Dic11C2411yescharacteristic
322C22×Dic11C2411yescharacteristic
323#4341—416no—
324C2×C4×D11—24no—
325C2×C4×D11—24no—
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—42no—
335C2×C4×D11—42no—
336C2×C4×D11—42no—
337C2×C4×D11—42no—
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—22no—
347C11×C4⋊C4—22no—
348C11×C4⋊C4—42no—
349C11×C4⋊C4C22×C414yes—
350C11×C22⋊C4—24no—
351C11×C22⋊C4—24no—
352C11×C22⋊C4—42no—
353C11×C22⋊C4—42no—
354C11×C22⋊C4C22×C418yes—
355C42×C11—22no—
356C42×C11—22no—
357C42×C11—41no—
358C42×C11—41no—
359C42×C11—42no—
360C22⋊Dic11—24no—
361C22⋊Dic11—24no—
362C22⋊Dic11—42no—
363C22⋊Dic11—42no—
364C22⋊Dic11C22×C418yes—
365C22⋊Dic11C22×C418yes—
366(C2×D11)⋊C4—22no—
367(C2×D11)⋊C4—22no—
368(C2×D11)⋊C4—22no—
369(C2×D11)⋊C4—22no—
370(C2×D11)⋊C4—22no—
371(C2×D11)⋊C4—22no—
372(C2×D11)⋊C4—42no—
373(C2×D11)⋊C4—42no—
374(C2×D11)⋊C4C22×C418yes—
375(C2×D11)⋊C4C22×C418yes—
376(C2×D11)⋊C4#4114yescomplemented
377(C2×D11)⋊C4#4114yescomplemented
378C4⋊Dic11—22no—
379C4⋊Dic11—22no—
380C4⋊Dic11—42no—
381C4⋊Dic11C22×C418yes—
382C4⋊Dic11C22×C414yes—
383Dic11⋊C4—24no—
384Dic11⋊C4—24no—
385Dic11⋊C4—42no—
386Dic11⋊C4—42no—
387Dic11⋊C4—42no—
388Dic11⋊C4—42no—
389Dic11⋊C4C22×C418yes—
390C4×Dic11—24no—
391C4×Dic11—24no—
392C4×Dic11—22no—
393C4×Dic11—22no—
394C4×Dic11—42no—
395C4×Dic11—42no—
396C4×Dic11—41no—
397C4×Dic11—41no—
398C4×Dic11—42no—
399C4×Dic11C22×C418yes—
400C2×#525—111no—
401#2361—111no—
402#2361—111no—
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×#121D1111yescharacteristic, complemented
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×C11H(5,𝔽2)12yes—
436C23×C112−1+412yes—
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×D11C2×#4112yes—
458C22×D11C2×#4112yes—
459D4×C11—216no—
460D4×C11—28no—
461C2×C4×C11—21no—
462C2×C4×C11—21no—
463C2×C4×C11—22no—
464C2×C4×C11—21no—
465C2×C4×C11—21no—
466C2×C4×C11—21no—
467C2×C4×C11—21no—
468C2×C4×C11—22no—
469C2×C4×C11—28no—
470C2×C4×C11—22no—
471C2×C4×C11—22no—
472C2×C4×C11—21no—
473C2×C4×C11—21no—
474C2×C4×C11—22no—
475C2×C4×C11—21no—
476C2×C4×C11—22no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—21no—
480C2×C4×C11—21no—
481C2×C4×C11—21no—
482C2×C4×C11—44no—
483C2×C4×C11—44no—
484C2×C4×C11—84no—
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—
493C22⋊D11—48no—
494C2×Dic11—22no—
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—21no—
505C2×Dic11—21no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—21no—
509C2×Dic11—21no—
510C2×Dic11—21no—
511C2×Dic11—21no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—21no—
516C2×Dic11—22no—
517C2×Dic11—21no—
518C2×Dic11—44no—
519C2×Dic11—48no—
520C2×Dic11—44no—
521C2×Dic11—44no—
522C2×Dic11—84no—
523C2×Dic11C23×C412yes—
524C2×Dic11C23×C414yes—
525C2×Dic11C23×C414yes—
526C2×Dic11C23×C412yes—
527C2×Dic11C2×#4112yes—
528C2×Dic11C2×#4112yes—
529C4×D11—28no—
530C4×D11—28no—
531C4×D11—44no—
532C4×D11—44no—
533C4×D11—84no—
534C4×D11—84no—
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⋊C4—111no—
558C22×C22⋊C4—111no—
559C22×C22⋊C4—111no—
560C22×C22⋊C4—112no—
561C22×C42—111no—
562C22×C42C2×D1111yescharacteristic
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—112no—
573#389—111no—
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#385—112no—
599#383—112no—
600#382—112no—
601#381—112no—
602#380—111no—
603#380—111no—
604#380—111no—
605#380—112no—
606#380—112no—
607#380—112no—
608#380C2×D1111yescharacteristic
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—112no—
617C4×C22⋊C4—112no—
618C4×C22⋊C4—112no—
619C4×C22⋊C4—112no—
620C4×C22⋊C4—111no—
621C4×C22⋊C4—111no—
622C4×C22⋊C4—111no—
623C4×C22⋊C4—111no—
624C4×C22⋊C4—111no—
625C4×C22⋊C4—112no—
626C4×C22⋊C4—111no—
627C4×C22⋊C4—111no—
628C4×C22⋊C4—111no—
629C4×C22⋊C4—112no—
630C4×C22⋊C4C2×D1112yescomplemented
631#376—112no—
632C2×#95—112no—
633C2×#95—111no—
634C2×#95—111no—
635C2×#95—112no—
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×C11#52014yes—
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×D11C4×#4114yes—
672C4×C11—22no—
673C4×C11—24no—
674C4×C11—22no—
675C4×C11—22no—
676C4×C11—41no—
677C4×C11—42no—
678C4×C11—42no—
679C4×C11—41no—
680C4×C11#51814yes—
681Dic11—24no—
682Dic11—24no—
683Dic11—22no—
684Dic11—22no—
685Dic11—22no—
686Dic11—22no—
687Dic11—42no—
688Dic11—42no—
689Dic11—41no—
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—111no—
708C23×C4—111no—
709C23×C4—112no—
710C23×C4—112no—
711C23×C4—112no—
712C23×C4—442no—
713C23×C4—442no—
714C23×C4C22×D1111yescharacteristic
715C23×C4C22×D1111yescharacteristic
716C23×C4C22×D1111yescharacteristic
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—42no—
727C4×D4—44no—
728C4×D4—1116no—
729C4×D4—1116no—
730C4×D4—228no—
731C4×D4—228no—
732C4×D4—442no—
733C4×D4—444no—
734#117—118no—
735C2×C4⋊C4—111no—
736C2×C4⋊C4—112no—
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—112no—
746C2×C4⋊C4—112no—
747C2×C4⋊C4—442no—
748C2×C4⋊C4—442no—
749C2×C4⋊C4C22×D1111yescharacteristic
750C2×C4⋊C4C22×D1111yescharacteristic
751C2×C4⋊C4C22×D1112yes—
752C2×C4⋊C4C22×D1111yescharacteristic
753C2×C22⋊C4—112no—
754C2×C22⋊C4—112no—
755C2×C22⋊C4—111no—
756C2×C22⋊C4—111no—
757C2×C22⋊C4—112no—
758C2×C22⋊C4—112no—
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—111no—
766C2×C22⋊C4—111no—
767C2×C22⋊C4—112no—
768C2×C22⋊C4—112no—
769C2×C22⋊C4—112no—
770C2×C22⋊C4—112no—
771C2×C22⋊C4—224no—
772C2×C22⋊C4—224no—
773C2×C22⋊C4—444no—
774C2×C22⋊C4C22×D1112yes—
775C2×C22⋊C4C22×D1112yes—
776C2×C22⋊C4C22×D1112yes—
777C2×C22⋊C4C22×D1112yes—
778C2×C22⋊C4C22×D1112yes—
779C2×C42—42no—
780C2×C42—112no—
781C2×C42—112no—
782C2×C42—112no—
783C2×C42—111no—
784C2×C42—111no—
785C2×C42—112no—
786C2×C42—112no—
787C2×C42—112no—
788C2×C42—111no—
789C2×C42—111no—
790C2×C42—442no—
791C2×C42C22×D1111yescharacteristic
792C2×C42C22×D1111yescharacteristic
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—111no—
804#95—111no—
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#95—112no—
817#95C22×D1112yes—
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—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—24no—
865C22×C4—41no—
866C22×C4—41no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—111no—
870C22×C4—111no—
871C22×C4—111no—
872C22×C4—112no—
873C22×C4—112no—
874C22×C4—111no—
875C22×C4—114no—
876C22×C4—118no—
877C22×C4—114no—
878C22×C4—114no—
879C22×C4—114no—
880C22×C4—114no—
881C22×C4—111no—
882C22×C4—112no—
883C22×C4—112no—
884C22×C4—111no—
885C22×C4—224no—
886C22×C4—224no—
887C22×C4—222no—
888C22×C4—222no—
889C22×C4—224no—
890C22×C4—222no—
891C22×C4—222no—
892C22×C4—222no—
893C22×C4—222no—
894C22×C4—222no—
895C22×C4—222no—
896C22×C4—4416no—
897C22×C4—441no—
898C22×C4—441no—
899C22×C4—441no—
900C22×C4—441no—
901C22×C4—442no—
902C22×C4—442no—
903C22×C4—442no—
904C22×C4—442no—
905C22×C4—441no—
906C22×C4—441no—
907C22×C4—441no—
908C22×C4—441no—
909C22×C4—442no—
910C22×C4—442no—
911C22×C4—442no—
912C22×C4—442no—
913C22×C4C2×C4×D1114yes—
914C22×C4C23×D1111yescharacteristic
915C22×C4C23×D1112yes—
916C22×C4C23×D1111yescharacteristic
917C22×C4C23×D1112yes—
918C22×C4C23×D1111yescharacteristic
919C22×C4C23×D1112yes—
920C22×C4C23×D1111yescharacteristic
921C22×C4C23×D1111yescharacteristic
922C22×C4C23×D1111yescharacteristic
923C4⋊C4—22no—
924C4⋊C4—22no—
925C4⋊C4—42no—
926C4⋊C4—114no—
927C4⋊C4—118no—
928C4⋊C4—118no—
929C4⋊C4—224no—
930C4⋊C4—222no—
931C4⋊C4—224no—
932C4⋊C4—222no—
933C4⋊C4—442no—
934C4⋊C4—442no—
935C4⋊C4—442no—
936C4⋊C4—442no—
937C4⋊C4—442no—
938C4⋊C4C2×C4×D1114yes—
939C22⋊C4—24no—
940C22⋊C4—24no—
941C22⋊C4—42no—
942C22⋊C4—42no—
943C22⋊C4—118no—
944C22⋊C4—118no—
945C22⋊C4—118no—
946C22⋊C4—118no—
947C22⋊C4—114no—
948C22⋊C4—114no—
949C22⋊C4—222no—
950C22⋊C4—222no—
951C22⋊C4—222no—
952C22⋊C4—222no—
953C22⋊C4—224no—
954C22⋊C4—224no—
955C22⋊C4—222no—
956C22⋊C4—222no—
957C22⋊C4—442no—
958C22⋊C4—442no—
959C22⋊C4—442no—
960C22⋊C4—442no—
961C22⋊C4C2×C4×D1118yes—
962C42—22no—
963C42—22no—
964C42—41no—
965C42—41no—
966C42—42no—
967C42—118no—
968C42—224no—
969C42—224no—
970C42—222no—
971C42—222no—
972C42—441no—
973C42—441no—
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—
1011C23#6703712yes—
1012C23#6704312yes—
1013C23C24×D1111yescharacteristic
1014Q8—228no—
1015D4—216no—
1016D4—28no—
1017D4—2216no—
1018D4—448no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—22no—
1027C2×C4—28no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—21no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—22no—
1039C2×C4—21no—
1040C2×C4—44no—
1041C2×C4—44no—
1042C2×C4—84no—
1043C2×C4—112no—
1044C2×C4—114no—
1045C2×C4—112no—
1046C2×C4—114no—
1047C2×C4—112no—
1048C2×C4—112no—
1049C2×C4—221no—
1050C2×C4—222no—
1051C2×C4—221no—
1052C2×C4—221no—
1053C2×C4—222no—
1054C2×C4—222no—
1055C2×C4—221no—
1056C2×C4—221no—
1057C2×C4—222no—
1058C2×C4—221no—
1059C2×C4—221no—
1060C2×C4—221no—
1061C2×C4—228no—
1062C2×C4—228no—
1063C2×C4—222no—
1064C2×C4—222no—
1065C2×C4—222no—
1066C2×C4—221no—
1067C2×C4—222no—
1068C2×C4—221no—
1069C2×C4—221no—
1070C2×C4—222no—
1071C2×C4—221no—
1072C2×C4—221no—
1073C2×C4—222no—
1074C2×C4—221no—
1075C2×C4—444no—
1076C2×C4—444no—
1077C2×C4—444no—
1078C2×C4—448no—
1079C2×C4—444no—
1080C2×C4—444no—
1081C2×C4—884no—
1082C2×C4—884no—
1083C2×C4—884no—
1084C2×C4C22×C4×D1114yes—
1085C2×C4C22×C4×D1112yes—
1086C2×C4C22×C4×D1112yes—
1087C2×C4#6703712yes—
1088C2×C4#41×D1112yes—
1089C2×C4#41×D1112yes—
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—
1119C22#1062307714yes—
1120C22C23×C4×D1111yescharacteristic
1121C22C2×#6703711yescharacteristic
1122C22C2×#6703711yescharacteristic
1123C22C2×#41×D1111yescharacteristic
1124C22C2×#41×D1111yescharacteristic
1125C22C2×#6704211yescharacteristic
1126C22C2×#6704311yescharacteristic
1127C4—22no—
1128C4—22no—
1129C4—22no—
1130C4—24no—
1131C4—41no—
1132C4—42no—
1133C4—42no—
1134C4—41no—
1135C4—222no—
1136C4—222no—
1137C4—224no—
1138C4—222no—
1139C4—222no—
1140C4—224no—
1141C4—442no—
1142C4—441no—
1143C4—442no—
1144C4—441no—
1145C4#1062307614yes—
1146C2—24no—
1147C2—44no—
1148C2—224no—
1149C2—442no—
1150C2C4×#41×D1111yescharacteristic
1151C2C2×#1062307611yescharacteristic
1152C2C2×#1062307711yescharacteristic
1153C2#1308264211yescharacteristic
1154C2#1308264311yescharacteristic
1155C2#1308265311yescharacteristic
1156C2#1308266711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC4×C11×#121C2
socle, cosocleC23×C11C25
prime radicalC2×#10623137C2
hypercenterC4×#121D11
hypocenterC11#34233
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
2. #13071637C2semidirect
3. #13071628C2semidirect
4. #13071623C2semidirect
5. #13071620C2semidirect
6. #13071596C2semidirect
7. #13071593C2semidirect
8. #13071554C2semidirect
9. #13071521C2semidirect
10. #13071505C2semidirect
11. #13071500C2semidirect
12. #13071455C2semidirect
13. #13071441C2semidirect
14. #13071408C2semidirect
15. #13071404C2semidirect
16. #13071246C2semidirect
17. C4×#66977C2semidirect
18. #13071144C2semidirect
19. #121×Dic11C2semidirect
20. D11×#380C2semidirect
21. #13070975C2semidirect
22. C2×C4×(C2×D11)⋊C4C2semidirect
23. C4×C11×#121C2semidirect
28. C2×C4×D4×C11C22semidirect
34. C2×D4×Dic11C22semidirect
40. #10623137C4semidirect
45. C2×#66940C22semidirect
50. C2×C4×Dic22C22semidirect
51. C11×#390C22semidirect
52. C11×#389C22semidirect
53. C11×#388C22semidirect
56. C4×C11×C4⋊C4C22semidirect
57. C4×C11×C22⋊C4C22semidirect
58. #10622834C22semidirect
63. #10622823C22semidirect
67. C2×C11⋊#95C22semidirect
72. #10622598C22semidirect
73. #10622590C22semidirect
74. C4⋊C4×Dic11C22semidirect
75. C4⋊C4×Dic11C22semidirect
76. #10622587C22semidirect
77. #10622586C22semidirect
78. #10622586C22semidirect
84. #10622564C22semidirect
86. #10622559C22semidirect
87. #10622558C22semidirect
88. #10622557C22semidirect
89. #10622556C22semidirect
91. #10622555C22semidirect
93. C22⋊C4×Dic11C22semidirect
94. C22⋊C4×Dic11C22semidirect
105. C4×C4⋊Dic11C22semidirect
106. #10622546C22semidirect
107. C4×Dic11⋊C4C22semidirect
108. C4×Dic11⋊C4C22semidirect
109. #10622542C22semidirect
110. #10622541C22semidirect
111. #10622541C22semidirect
118. #10622267C22semidirect
119. #10622266C22semidirect
120. #10622265C22semidirect
121. #10622264C22semidirect
122. #10622262C22semidirect
123. #10622261C22semidirect
140. C2×#4341C2×C4semidirect
143. C22×C4×D11C2×C4semidirect
151. C11×#121C2×C4semidirect
175. #66991C2×C4semidirect
176. #66990C2×C4semidirect
179. D4×Dic11C2×C4semidirect
200. #66977C2×C4semidirect
219. #66950C2×C4semidirect
220. #66945C2×C4semidirect
224. #66936C2×C4semidirect
226. (C22⋊D11)⋊C4C2×C4semidirect
376. (C2×D11)⋊C4#41semidirect
377. (C2×D11)⋊C4#41semidirect
419. C4×#121D11semidirect
554. C2×C4×D4C2×D11semidirect
568. #390C2×D11semidirect
574. #389C2×D11semidirect
582. #388C2×D11semidirect
615. C4×C4⋊C4C2×D11semidirect
630. C4×C22⋊C4C2×D11semidirect
722. #121C4×D11semidirect
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
#130716372
#130716282
#130716232
#130716202
#130715962
#130715932
#130715542
#130715212
#130715052
#130715002
#130714552
#130714412
#130714082
#130714042
#130712462
C4×#669772
#130711442
#121×Dic112
D11×#3802
#130709752
C2×C4×(C2×D11)⋊C42
C4×C11×#1212
#3423311