Finite Group Databasebeta

← #14914926

Subgroups — #14914926

Order 2816.

3586 conjugacy classes of subgroups.

The subgroup lattice has 1208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623246C211yesmaximal, characteristic
2C2×#10623077C211yesmaximal, characteristic, complemented
3C2×C4×D4×D11C211yesmaximal, characteristic, complemented
4#13071689C211yesmaximal, characteristic, complemented
5#13071687C211yesmaximal, characteristic, complemented
6#13071686C211yesmaximal, characteristic, complemented
7#13071685C211yesmaximal, characteristic, complemented
8#13071681C211yesmaximal, characteristic, complemented
9#13071678C211yesmaximal, characteristic, complemented
10#13071677C211yesmaximal, characteristic, complemented
11#13071657C212yesmaximal, complemented
12#13071651C212yesmaximal, complemented
13#13071633C212yesmaximal, complemented
14#13071627C212yesmaximal, complemented
15#13071275C212yesmaximal, complemented
16#13071272C212yesmaximal, complemented
17#13071195C211yesmaximal, characteristic, complemented
18#13071121C212yesmaximal, complemented
19C4×#66990C212yesmaximal, complemented
20#13071103C211yesmaximal, characteristic, complemented
21#13071096C211yesmaximal, characteristic, complemented
22#13070970C211yesmaximal, characteristic, complemented
23C11×#2366C211yesmaximal, characteristic, complemented
24C22×#4341C2211yescharacteristic
25C22×D4×D11C2211yescharacteristic
26C23×C4×D11C2212yes—
27C2×C11×#127C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic, complemented
30C2×C4×D4×C11C2212yescomplemented
31C2×#66993C2211yescharacteristic
32C2×#66992C2212yes—
33C2×#66992C2212yes—
34C2×#66990C2212yes—
35C2×#66990C2212yes—
36C2×#66989C2211yescharacteristic
37C2×D4×Dic11C2211yescharacteristic
38C2×D4×Dic11C2211yescharacteristic, complemented
39C2×D4×Dic11C2212yescomplemented
40C2×C4×C22⋊D11C2212yes—
41C2×C4×C22⋊D11C2212yes—
42C2×C4×C22⋊D11C2212yescomplemented
43C22×Dic11⋊C4C2212yescomplemented
44#10623246C4116yescomplemented
45#10623077—28no—
46C4×D4×D11—28no—
47C2×#66946C2211yescharacteristic
48C2×#66945C2211yescharacteristic
49C2×C4⋊C4×D11C2211yescharacteristic
50C2×#66940C2211yescharacteristic, complemented
51C2×(C22⋊D11)⋊C4C2212yes—
52C2×(C22⋊D11)⋊C4C2212yes—
53C2×(C22⋊D11)⋊C4C2212yescomplemented
54C2×C22⋊C4×D11C2212yes—
55C2×#66930C2212yescomplemented
56C2×#66928C2211yescharacteristic
57C2×C4×D44C2211yescharacteristic
58C2×#66925C2211yescharacteristic
59C2×#66925C2211yescharacteristic
60C2×C42×D11C2211yescharacteristic
61C2×C4×Dic22C2211yescharacteristic, complemented
62C11×#390C2211yescharacteristic
63C11×#390C2212yescomplemented
64C11×#390C2211yescharacteristic, complemented
65C11×#386C2212yescomplemented
66C11×#386C2212yescomplemented
67C4×C11×C4⋊C4C2211yescharacteristic, complemented
68C4×C11×C4⋊C4C2211yescharacteristic, complemented
69#10622834C2211yescharacteristic
70#10622834C2212yescomplemented
71#10622834C2211yescharacteristic, complemented
72#10622833C2212yescomplemented
73#10622833C2212yescomplemented
74#10622826C2212yescomplemented
75#10622823C2212yescomplemented
76C4×C22⋊Dic11C2212yescomplemented
77#10622603C2212yescomplemented
78#10622602C2211yescharacteristic
79#10622602C2211yescharacteristic
80#10622602C2212yescomplemented
81#10622601C2211yescharacteristic
82C4⋊C4×Dic11C2211yescharacteristic, complemented
83C4⋊C4×Dic11C2211yescharacteristic, complemented
84#10622587C2211yescharacteristic, complemented
85#10622585C2211yescharacteristic, complemented
86#10622585C2211yescharacteristic, complemented
87#10622571C2212yescomplemented
88#10622570C2212yes—
89#10622570C2212yes—
90#10622570C2212yescomplemented
91#10622570C2212yescomplemented
92#10622569C2212yes—
93#10622569C2212yes—
94#10622569C2212yescomplemented
95#10622569C2212yescomplemented
96#10622568C2212yes—
97#10622568C2212yes—
98#10622559C2212yescomplemented
99#10622558C2212yescomplemented
100#10622558C2212yescomplemented
101#10622557C2212yescomplemented
102#10622557C2212yescomplemented
103C22⋊C4×Dic11C2212yescomplemented
104C22⋊C4×Dic11C2212yescomplemented
105C22⋊C4×Dic11C2212yescomplemented
106#10622553C2212yescomplemented
107#10622552C2211yescharacteristic
108C4×(C2×D11)⋊C4C2212yes—
109C4×(C2×D11)⋊C4C2212yescomplemented
110C4×C4⋊Dic11C2211yescharacteristic, complemented
111C4×C4⋊Dic11C2211yescharacteristic, complemented
112C4×Dic11⋊C4C2212yescomplemented
113C4×Dic11⋊C4C2211yescharacteristic, complemented
114C4×Dic11⋊C4C2211yescharacteristic, complemented
115#10622542C2211yescharacteristic, complemented
116#10622283C2212yescomplemented
117#10622282C2212yescomplemented
118#10622281C2211yescharacteristic
119#10622281C2211yescharacteristic
120#10622281C2212yescomplemented
121#10622279C2212yes—
122#10622279C2212yescomplemented
123#10622262C2212yescomplemented
124#10622260C2211yescharacteristic, complemented
125#10622260C2211yescharacteristic, complemented
126C24×D11C2312yes—
127C22×D4×C11C2311yescharacteristic
128C22×D4×C11C2311yescharacteristic
129C22×D4×C11C2312yes—
130C22×D4×C11C2312yes—
131C23×C4×C11C2312yes—
132C23×C4×C11C2312yes—
133C22×C22⋊D11C2312yes—
134C22×C22⋊D11C2312yes—
135C22×C22⋊D11C2312yes—
136C22×C22⋊D11C2312yes—
137C23×Dic11C2312yes—
138C23×Dic11C2312yes—
139C23×Dic11C2312yes—
140C2×#4341—24no—
141C2×#4341—24no—
142C2×#4341C2×C418yescomplemented
143C2×D4×D11—24no—
144C2×D4×D11—24no—
145C2×D4×D11C2×C418yescomplemented
146C22×D44C2311yescharacteristic
147C22×C4×D11—28no—
148C22×C4×D11—44no—
149C22×C4×D11—44no—
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2312yes—
152C22×C4×D11C2312yes—
153C22×C4×D11C2311yescharacteristic
154C22×C4×D11C2312yes—
155C22×C4×D11C2311yescharacteristic
156C22×Dic22C2311yescharacteristic
157C11×#127C2×C418yescomplemented
158C4×D4×C11—24no—
159C4×D4×C11—24no—
160C4×D4×C11—44no—
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C4⋊C4C2311yescharacteristic
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2312yes—
169C2×C11×C22⋊C4C2312yes—
170C2×C11×C22⋊C4C2312yes—
171C2×C42×C11C2311yescharacteristic
172C2×C42×C11C2311yescharacteristic
173C2×C42×C11C2312yes—
174C2×C42×C11C2311yescharacteristic
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182C2×C22⋊Dic11C2312yes—
183#66993C2×C418yescomplemented
184#66992C2×C4116yescomplemented
185#66992C2×C4116yescomplemented
186#66990C2×C4116yescomplemented
187#66990C2×C4116yescomplemented
188#66989C2×C418yescomplemented
189D4×Dic11—24no—
190D4×Dic11—24no—
191D4×Dic11—44no—
192C4×C22⋊D11—28no—
193C4×C22⋊D11—28no—
194C4×C22⋊D11—44no—
195C2×(C2×D11)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2311yescharacteristic
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2311yescharacteristic
205C2×(C2×D11)⋊C4C2311yescharacteristic
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2312yes—
208C2×C4⋊Dic11C2311yescharacteristic
209C2×C4⋊Dic11C2311yescharacteristic
210C2×C4⋊Dic11C2311yescharacteristic
211C2×C4⋊Dic11C2311yescharacteristic
212C2×Dic11⋊C4—28no—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2311yescharacteristic
215C2×Dic11⋊C4C2311yescharacteristic
216C2×Dic11⋊C4C2312yes—
217C2×Dic11⋊C4C2311yescharacteristic
218C2×Dic11⋊C4C2311yescharacteristic
219C2×Dic11⋊C4C2311yescharacteristic
220C2×Dic11⋊C4C2311yescharacteristic
221C2×Dic11⋊C4C2311yescharacteristic
222C2×Dic11⋊C4C2311yescharacteristic
223C2×Dic11⋊C4C2312yes—
224C2×C4×Dic11C2312yes—
225C2×C4×Dic11C2311yescharacteristic
226C2×C4×Dic11C2311yescharacteristic
227C2×C4×Dic11C2311yescharacteristic
228C2×C4×Dic11C2311yescharacteristic
229C2×C4×Dic11C2312yes—
230C2×C4×Dic11C2312yes—
231C2×C4×Dic11C2312yes—
232C2×C4×Dic11C2312yes—
233C2×C4×Dic11C2312yes—
234C2×C4×Dic11C2311yescharacteristic
235#66946—24no—
236#66945—24no—
237C4⋊C4×D11D418yescomplemented
238#66940—24no—
239(C22⋊D11)⋊C4—28no—
240(C22⋊D11)⋊C4—28no—
241(C22⋊D11)⋊C4—44no—
242C22⋊C4×D11—28no—
243#66930—28no—
244#66928C2×C418yescomplemented
245C4×D44—24no—
246#66925—24no—
247#66925C2×C418yescomplemented
248C42×D11—24no—
249C4×Dic22—24no—
250C11×#95C2311yescharacteristic
251C11×#95C2311yescharacteristic
252C11×#95C2312yes—
253C11⋊#95C2311yescharacteristic
254C11⋊#95C2311yescharacteristic
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2311yescharacteristic
259C11⋊#95C2311yescharacteristic
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264C11⋊#95C2311yescharacteristic
265C11⋊#95C2311yescharacteristic
266#34265—111nomaximal, Sylow
267C24×C11C2412yes—
268C24×C11C2412yes—
269C23×D11—24no—
270C23×D11—24no—
271C23×D11—42no—
272C23×D11—42no—
273C23×D11—42no—
274C23×D11—42no—
275C23×D11C22×C418yes—
276C23×D11C2412yes—
277C23×D11C2411yescharacteristic
278C2×D4×C11—22no—
279C2×D4×C11—22no—
280C2×D4×C11—22no—
281C2×D4×C11—22no—
282C2×D4×C11—42no—
283C2×D4×C11—42no—
284C2×D4×C11—42no—
285C2×D4×C11—42no—
286C2×D4×C11C22×C414yes—
287C2×D4×C11C22×C414yescomplemented
288C2×D4×C11C22×C418yescomplemented
289C2×D4×C11C22×C418yescomplemented
290C22×C4×C11—24no—
291C22×C4×C11—24no—
292C22×C4×C11—24no—
293C22×C4×C11—42no—
294C22×C4×C11—42no—
295C22×C4×C11—42no—
296C22×C4×C11C2412yes—
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2411yescharacteristic
300C22×C4×C11C2411yescharacteristic
301C22×C4×C11C2411yescharacteristic
302C22×C4×C11C2412yes—
303C22×C4×C11C2411yescharacteristic
304C22×C4×C11C2411yescharacteristic
305C2×C22⋊D11—24no—
306C2×C22⋊D11—24no—
307C2×C22⋊D11—24no—
308C2×C22⋊D11—24no—
309C2×C22⋊D11—42no—
310C2×C22⋊D11—42no—
311C2×C22⋊D11—42no—
312C2×C22⋊D11—42no—
313C2×C22⋊D11C22×C418yes—
314C2×C22⋊D11C22×C418yes—
315C2×C22⋊D11C22×C418yescomplemented
316C2×C22⋊D11C22×C418yescomplemented
317C22×Dic11—24no—
318C22×Dic11—24no—
319C22×Dic11—24no—
320C22×Dic11—24no—
321C22×Dic11—24no—
322C22×Dic11—42no—
323C22×Dic11—42no—
324C22×Dic11—42no—
325C22×Dic11C22×C418yescomplemented
326C22×Dic11C2412yes—
327C22×Dic11C2411yescharacteristic
328C22×Dic11C2411yescharacteristic
329C22×Dic11C2411yescharacteristic
330C22×Dic11C2411yescharacteristic
331C22×Dic11C2411yescharacteristic
332C22×Dic11C2412yes—
333C22×Dic11C2412yes—
334C22×Dic11C2411yescharacteristic
335C22×Dic11C2411yescharacteristic
336#4341—232no—
337D4×D11—232no—
338C2×D44—22no—
339C2×D44—22no—
340C2×D44C22×C414yes—
341C2×C4×D11—22no—
342C2×C4×D11—24no—
343C2×C4×D11—24no—
344C2×C4×D11—22no—
345C2×C4×D11—22no—
346C2×C4×D11—24no—
347C2×C4×D11—22no—
348C2×C4×D11—24no—
349C2×C4×D11—42no—
350C2×C4×D11—42no—
351C2×C4×D11—42no—
352C2×C4×D11—42no—
353C2×C4×D11—41no—
354C2×C4×D11—41no—
355C2×C4×D11—432no—
356C2×C4×D11C22×C414yes—
357C2×C4×D11C2×D418yes—
358C2×C4×D11C2×D414yes—
359C2×C4×D11#4114yes—
360C2×Dic22—22no—
361C2×Dic22—22no—
362C2×Dic22C22×C414yescomplemented
363C11×C4⋊C4—22no—
364C11×C4⋊C4—22no—
365C11×C4⋊C4—41no—
366C11×C4⋊C4C2×D414yes—
367C11×C22⋊C4—24no—
368C11×C22⋊C4—24no—
369C11×C22⋊C4—24no—
370C11×C22⋊C4—42no—
371C11×C22⋊C4—42no—
372C11×C22⋊C4—42no—
373C42×C11—22no—
374C42×C11—22no—
375C42×C11—42no—
376C42×C11C22×C414yescomplemented
377C22⋊Dic11—24no—
378C22⋊Dic11—24no—
379C22⋊Dic11—24no—
380C22⋊Dic11—42no—
381C22⋊Dic11—42no—
382C22⋊Dic11—42no—
383C22⋊Dic11C22×C418yescomplemented
384C22⋊Dic11C22×C418yescomplemented
385(C2×D11)⋊C4—24no—
386(C2×D11)⋊C4—22no—
387(C2×D11)⋊C4—22no—
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—24no—
390(C2×D11)⋊C4—42no—
391(C2×D11)⋊C4—42no—
392(C2×D11)⋊C4—42no—
393(C2×D11)⋊C4—42no—
394(C2×D11)⋊C4C22×C414yes—
395(C2×D11)⋊C4C22×C414yes—
396(C2×D11)⋊C4C22×C418yescomplemented
397(C2×D11)⋊C4C22×C418yescomplemented
398C4⋊Dic11—22no—
399C4⋊Dic11—22no—
400C4⋊Dic11—41no—
401C4⋊Dic11C2×D414yes—
402Dic11⋊C4—24no—
403Dic11⋊C4—22no—
404Dic11⋊C4—22no—
405Dic11⋊C4—22no—
406Dic11⋊C4—24no—
407Dic11⋊C4—22no—
408Dic11⋊C4—41no—
409Dic11⋊C4—41no—
410Dic11⋊C4C22×C414yescomplemented
411Dic11⋊C4C22×C414yescomplemented
412Dic11⋊C4C2×D418yes—
413C4×Dic11—24no—
414C4×Dic11—22no—
415C4×Dic11—22no—
416C4×Dic11—24no—
417C4×Dic11—22no—
418C4×Dic11—22no—
419C4×Dic11—24no—
420C4×Dic11—42no—
421C4×Dic11—42no—
422C4×Dic11—42no—
423C4×Dic11C22×C414yescomplemented
424C2×#535—111no—
425C2×#520—111no—
426C22×C4×D4—111no—
427#2367—111no—
428#2367—111no—
429#2367—111no—
430#2367—111no—
431#2366—111no—
432#2366—111no—
433#2366—111no—
434#2366D1111yescharacteristic, complemented
435#2363—112no—
436#2363—112no—
437#2361—112no—
438#2361—112no—
439#2321—112no—
440#2321—112no—
441#2309—111no—
442C4×#120—112no—
443C4×#120—112no—
444#2297—111no—
445#2296—111no—
446#2274—111no—
447C23×C11—22no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11—22no—
451C23×C11—22no—
452C23×C11—22no—
453C23×C11—22no—
454C23×C11—22no—
455C23×C11—22no—
456C23×C11—22no—
457C23×C11—22no—
458C23×C11—22no—
459C23×C11C23×C414yes—
460C23×C11C23×C414yes—
461C23×C11C2511yescharacteristic
462C22×D11—21no—
463C22×D11—21no—
464C22×D11—21no—
465C22×D11—21no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—216no—
473C22×D11—48no—
474C22×D11—48no—
475C22×D11—48no—
476C22×D11—48no—
477C22×D11—48no—
478C22×D11—48no—
479C22×D11C23×C414yes—
480C22×D11C23×C412yes—
481C22×D11C22×D412yes—
482C22×D11C2×#4112yes—
483D4×C11—28no—
484D4×C11—28no—
485D4×C11—48no—
486D4×C11—48no—
487C2×C4×C11—21no—
488C2×C4×C11—21no—
489C2×C4×C11—22no—
490C2×C4×C11—21no—
491C2×C4×C11—22no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—21no—
495C2×C4×C11—21no—
496C2×C4×C11—21no—
497C2×C4×C11—21no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—21no—
501C2×C4×C11—21no—
502C2×C4×C11—21no—
503C2×C4×C11—21no—
504C2×C4×C11—21no—
505C2×C4×C11—22no—
506C2×C4×C11—21no—
507C2×C4×C11—48no—
508C2×C4×C11—84no—
509C2×C4×C11C23×C412yes—
510C2×C4×C11C23×C412yes—
511C2×C4×C11C23×C412yes—
512C2×C4×C11C22×D414yes—
513C2×C4×C11C22×D412yes—
514C2×C4×C11C2×#4112yes—
515C2×C4×C11H(5,𝔽2)12yes—
516C22⋊D11—216no—
517C22⋊D11—216no—
518C22⋊D11—48no—
519C22⋊D11—48no—
520C2×Dic11—22no—
521C2×Dic11—21no—
522C2×Dic11—22no—
523C2×Dic11—21no—
524C2×Dic11—21no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—21no—
528C2×Dic11—21no—
529C2×Dic11—21no—
530C2×Dic11—216no—
531C2×Dic11—21no—
532C2×Dic11—21no—
533C2×Dic11—21no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—21no—
537C2×Dic11—21no—
538C2×Dic11—21no—
539C2×Dic11—21no—
540C2×Dic11—21no—
541C2×Dic11—22no—
542C2×Dic11—21no—
543C2×Dic11—48no—
544C2×Dic11—84no—
545C2×Dic11C23×C412yes—
546C2×Dic11C23×C412yes—
547C2×Dic11C23×C414yes—
548C2×Dic11C23×C412yes—
549C2×Dic11C22×D414yes—
550C2×Dic11C22×D412yes—
551C2×Dic11C2×#4112yes—
552C2×Dic11H(5,𝔽2)12yes—
553D44—28no—
554C4×D11—28no—
555C4×D11—48no—
556C4×D11—48no—
557C4×D11—48no—
558C4×D11—44no—
559C4×D11C4×D4116yescomplemented
560Dic22—28no—
561C22×#41—111no—
562C23×D4—111no—
563C24×C4—112no—
564#535—1116no—
565C2×#127—111no—
566C2×#127C2×D1111yescharacteristic
567C2×#124—111no—
568C2×#124—111no—
569C2×#121—112no—
570C2×#121—112no—
571C2×#120—112no—
572C2×#120—112no—
573#520—228no—
574C2×C4×Q8—111no—
575C2×C4×Q8—111no—
576C2×C4×D4—111no—
577C2×C4×D4—111no—
578C2×C4×D4—112no—
579C2×C4×D4—112no—
580C2×C4×D4—112no—
581C2×C4×D4—112no—
582C2×C4×D4—111no—
583C2×C4×D4—112no—
584C2×C4×D4—112no—
585C2×C4×D4—112no—
586C2×C4×D4—111no—
587C2×C4×D4—228no—
588C2×C4×D4C2×D1111yescharacteristic
589C2×C4×D4C2×D1111yescharacteristic, complemented
590C2×C4×D4C2×D1112yescomplemented
591C2×#117—111no—
592C2×#117—112no—
593C2×#117—111no—
594C2×#117—111no—
595C22×C4⋊C4—111no—
596C22×C4⋊C4—112no—
597C22×C22⋊C4—112no—
598C22×C42—111no—
599#391—111no—
600#391—111no—
601#390—111no—
602#390—112no—
603#390—111no—
604#390—111no—
605#390—112no—
606#390—112no—
607#390—112no—
608#390—112no—
609#390—111no—
610#390C2×D1111yescharacteristic
611#390C2×D1112yescomplemented
612#390C2×D1111yescharacteristic, complemented
613#389—111no—
614#389—111no—
615#389—111no—
616#389—111no—
617#388—112no—
618#388—112no—
619#388—112no—
620#388—112no—
621#388—112no—
622#388—112no—
623#388—112no—
624#388—112no—
625#386—112no—
626#386—112no—
627#386—112no—
628#386—112no—
629#386—112no—
630#386—112no—
631#386—112no—
632#386—112no—
633#386C2×D1112yescomplemented
634#386C2×D1112yescomplemented
635#385—112no—
636#385—111no—
637#385—112no—
638#385—111no—
639#385—112no—
640#385—111no—
641#385—112no—
642#385—111no—
643#379—112no—
644#379—112no—
645C4×C4⋊C4—111no—
646C4×C4⋊C4—111no—
647C4×C4⋊C4—112no—
648C4×C4⋊C4—111no—
649C4×C4⋊C4—111no—
650C4×C4⋊C4—111no—
651C4×C4⋊C4—111no—
652C4×C4⋊C4—112no—
653C4×C4⋊C4C2×D1111yescharacteristic, complemented
654C4×C4⋊C4C2×D1111yescharacteristic, complemented
655C4×C22⋊C4—112no—
656C4×C22⋊C4—112no—
657C4×C22⋊C4—112no—
658C4×C22⋊C4—112no—
659C4×C22⋊C4—112no—
660C4×C22⋊C4—112no—
661C4×C22⋊C4—112no—
662C4×C22⋊C4—112no—
663C22×C11—24no—
664C22×C11—24no—
665C22×C11—24no—
666C22×C11—24no—
667C22×C11—24no—
668C22×C11—24no—
669C22×C11—42no—
670C22×C11—42no—
671C22×C11—42no—
672C22×C11—42no—
673C22×C11—42no—
674C22×C11—42no—
675C22×C11—42no—
676C22×C11—42no—
677C22×C11C24×C411yescharacteristic
678C22×C11C23×D411yescharacteristic
679C22×C11C22×#4111yescharacteristic
680C22×C11C2×H(5,𝔽2)11yescharacteristic
681C22×C11C2×H(5,𝔽2)11yescharacteristic
682C22×C11#58511yescharacteristic
683C22×C11#58511yescharacteristic
684C2×D11—22no—
685C2×D11—22no—
686C2×D11—22no—
687C2×D11—22no—
688C2×D11—22no—
689C2×D11—22no—
690C2×D11—24no—
691C2×D11—24no—
692C2×D11—24no—
693C2×D11—432no—
694C2×D11—42no—
695C2×D11—42no—
696C2×D11—42no—
697C2×D11—42no—
698C2×D11C2×C4×D414yes—
699C4×C11—22no—
700C4×C11—22no—
701C4×C11—22no—
702C4×C11—24no—
703C4×C11—41no—
704C4×C11—41no—
705C4×C11—41no—
706C4×C11—42no—
707C4×C11C2×C4×D414yes—
708Dic11—24no—
709Dic11—22no—
710Dic11—22no—
711Dic11—22no—
712Dic11—24no—
713Dic11—41no—
714Dic11—41no—
715Dic11—41no—
716Dic11—42no—
717Dic11C2×C4×D414yes—
718C25—112no—
719C2×#41—118no—
720C2×#41—224no—
721C2×#41—224no—
722C22×Q8—111no—
723C22×D4—112no—
724C22×D4—112no—
725C22×D4—112no—
726C22×D4—112no—
727C22×D4—118no—
728C22×D4—111no—
729C22×D4—224no—
730C22×D4—224no—
731C22×D4C22×D1111yescharacteristic
732C22×D4C22×D1111yescharacteristic
733C22×D4C22×D1112yes—
734C22×D4C22×D1112yes—
735C23×C4—111no—
736C23×C4—112no—
737C23×C4—112no—
738C23×C4—112no—
739C23×C4—112no—
740C23×C4—111no—
741C23×C4—112no—
742C23×C4—112no—
743C23×C4—111no—
744C23×C4—228no—
745C23×C4—444no—
746C23×C4—444no—
747C23×C4C22×D1112yes—
748C23×C4C22×D1112yes—
749#127—118no—
750#127C4×D1118yescomplemented
751#124—118no—
752#124—118no—
753#121—1116no—
754#121—1116no—
755#120—1116no—
756#120—1116no—
757C4×Q8—224no—
758C4×Q8—224no—
759C4×D4—24no—
760C4×D4—24no—
761C4×D4—44no—
762C4×D4—224no—
763C4×D4—228no—
764C4×D4—228no—
765C4×D4—228no—
766C4×D4—224no—
767C4×D4—224no—
768C4×D4—228no—
769C4×D4—224no—
770C4×D4—444no—
771C4×D4—444no—
772C4×D4—444no—
773#117—118no—
774#117—224no—
775#117—228no—
776#117—224no—
777C2×C4⋊C4—112no—
778C2×C4⋊C4—111no—
779C2×C4⋊C4—111no—
780C2×C4⋊C4—111no—
781C2×C4⋊C4—118no—
782C2×C4⋊C4—111no—
783C2×C4⋊C4—112no—
784C2×C4⋊C4—112no—
785C2×C4⋊C4—111no—
786C2×C4⋊C4—111no—
787C2×C4⋊C4—111no—
788C2×C4⋊C4—111no—
789C2×C4⋊C4—111no—
790C2×C4⋊C4—111no—
791C2×C4⋊C4—111no—
792C2×C4⋊C4—111no—
793C2×C4⋊C4—228no—
794C2×C4⋊C4C22×D1111yescharacteristic
795C2×C4⋊C4C22×D1111yescharacteristic
796C2×C4⋊C4C22×D1111yescharacteristic
797C2×C4⋊C4C22×D1111yescharacteristic
798C2×C22⋊C4—112no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—111no—
801C2×C22⋊C4—111no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—111no—
810C2×C22⋊C4—111no—
811C2×C22⋊C4—112no—
812C2×C22⋊C4—112no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—112no—
815C2×C22⋊C4—112no—
816C2×C22⋊C4—112no—
817C2×C22⋊C4—112no—
818C2×C22⋊C4—112no—
819C2×C22⋊C4—228no—
820C2×C22⋊C4C22×D1112yes—
821C2×C22⋊C4C22×D1112yes—
822C2×C22⋊C4C22×D1112yes—
823C2×C22⋊C4C22×D1112yes—
824C2×C22⋊C4C22×D1112yes—
825C2×C22⋊C4C22×D1112yes—
826C2×C42—111no—
827C2×C42—112no—
828C2×C42—112no—
829C2×C42—111no—
830C2×C42—112no—
831C2×C42—111no—
832C2×C42—111no—
833C2×C42—111no—
834C2×C42—112no—
835C2×C42—112no—
836C2×C42—112no—
837C2×C42—224no—
838C2×C42C22×D1111yescharacteristic
839C2×C42C22×D1111yescharacteristic
840C2×C42C22×D1112yes—
841C2×C42C22×D1111yescharacteristic
842#95—112no—
843#95—112no—
844#95—111no—
845#95—111no—
846#95—111no—
847#95—112no—
848#95—112no—
849#95—112no—
850#95—112no—
851#95—112no—
852#95—111no—
853#95—111no—
854#95—111no—
855#95C22×D1111yescharacteristic
856#95C22×D1112yes—
857#95C22×D1111yescharacteristic
858C2×C11—44no—
859C2×C11—44no—
860C2×C11C22×C4×D411yescharacteristic
861C2×C11C4×H(5,𝔽2)11yescharacteristic
862C2×C11C4×H(5,𝔽2)11yescharacteristic
863C2×C11#348411yescharacteristic
864C2×C11#348711yescharacteristic
865C2×C11#350611yescharacteristic
866C2×C11#350611yescharacteristic
867D11—24no—
868D11—44no—
869C24—111no—
870C24—112no—
871C24—118no—
872C24—224no—
873C24—224no—
874C24—442no—
875C24—442no—
876C24—442no—
877C24—442no—
878C24C23×D1112yes—
879C24C23×D1112yes—
880#41—2232no—
881C2×Q8—114no—
882C2×Q8—222no—
883C2×Q8—222no—
884C2×D4—22no—
885C2×D4—22no—
886C2×D4—22no—
887C2×D4—22no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—118no—
893C2×D4—118no—
894C2×D4—118no—
895C2×D4—118no—
896C2×D4—114no—
897C2×D4—2232no—
898C2×D4—224no—
899C2×D4—224no—
900C2×D4—224no—
901C2×D4—224no—
902C2×D4—222no—
903C2×D4—222no—
904C2×D4—442no—
905C2×D4—442no—
906C2×D4—442no—
907C2×D4—442no—
908C2×D4C2×C4×D1114yes—
909C2×D4C2×C4×D1114yescomplemented
910C2×D4C2×C4×D1118yescomplemented
911C2×D4C2×C4×D1118yescomplemented
912C22×C4—24no—
913C22×C4—24no—
914C22×C4—24no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—111no—
919C22×C4—114no—
920C22×C4—114no—
921C22×C4—114no—
922C22×C4—118no—
923C22×C4—111no—
924C22×C4—111no—
925C22×C4—112no—
926C22×C4—111no—
927C22×C4—112no—
928C22×C4—118no—
929C22×C4—112no—
930C22×C4—111no—
931C22×C4—111no—
932C22×C4—111no—
933C22×C4—222no—
934C22×C4—224no—
935C22×C4—224no—
936C22×C4—222no—
937C22×C4—222no—
938C22×C4—224no—
939C22×C4—224no—
940C22×C4—224no—
941C22×C4—224no—
942C22×C4—224no—
943C22×C4—222no—
944C22×C4—224no—
945C22×C4—224no—
946C22×C4—442no—
947C22×C4—442no—
948C22×C4—442no—
949C22×C4—442no—
950C22×C4—441no—
951C22×C4—441no—
952C22×C4—4432no—
953C22×C4—442no—
954C22×C4—442no—
955C22×C4—442no—
956C22×C4C23×D1112yes—
957C22×C4C23×D1111yescharacteristic
958C22×C4C23×D1111yescharacteristic
959C22×C4C23×D1111yescharacteristic
960C22×C4C23×D1111yescharacteristic
961C22×C4C23×D1111yescharacteristic
962C22×C4C23×D1112yes—
963C22×C4C23×D1111yescharacteristic
964C22×C4C23×D1111yescharacteristic
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—41no—
968C4⋊C4—114no—
969C4⋊C4—114no—
970C4⋊C4—118no—
971C4⋊C4—114no—
972C4⋊C4—222no—
973C4⋊C4—224no—
974C4⋊C4—222no—
975C4⋊C4—222no—
976C4⋊C4—222no—
977C4⋊C4—224no—
978C4⋊C4—222no—
979C4⋊C4—222no—
980C4⋊C4—441no—
981C4⋊C4—441no—
982C4⋊C4—441no—
983C4⋊C4D4×D1114yes—
984C22⋊C4—24no—
985C22⋊C4—24no—
986C22⋊C4—24no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—118no—
991C22⋊C4—118no—
992C22⋊C4—114no—
993C22⋊C4—114no—
994C22⋊C4—118no—
995C22⋊C4—118no—
996C22⋊C4—224no—
997C22⋊C4—222no—
998C22⋊C4—222no—
999C22⋊C4—224no—
1000C22⋊C4—224no—
1001C22⋊C4—224no—
1002C22⋊C4—224no—
1003C22⋊C4—224no—
1004C22⋊C4—442no—
1005C22⋊C4—442no—
1006C22⋊C4—442no—
1007C22⋊C4—442no—
1008C22⋊C4—442no—
1009C22⋊C4—442no—
1010C22⋊C4—442no—
1011C42—22no—
1012C42—22no—
1013C42—42no—
1014C42—114no—
1015C42—222no—
1016C42—222no—
1017C42—224no—
1018C42—224no—
1019C42—222no—
1020C42—224no—
1021C42—222no—
1022C42—442no—
1023C42—442no—
1024C42—442no—
1025C42C2×C4×D1114yescomplemented
1026C11#3426511yescharacteristic, complemented, Sylow
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—112no—
1040C23—112no—
1041C23—112no—
1042C23—114no—
1043C23—2216no—
1044C23—221no—
1045C23—221no—
1046C23—221no—
1047C23—221no—
1048C23—222no—
1049C23—222no—
1050C23—222no—
1051C23—222no—
1052C23—222no—
1053C23—222no—
1054C23—448no—
1055C23—448no—
1056C23—448no—
1057C23—448no—
1058C23—448no—
1059C23—448no—
1060C23C22×C4×D1114yes—
1061C23C22×C4×D1114yes—
1062C23C24×D1111yescharacteristic
1063Q8—228no—
1064D4—28no—
1065D4—28no—
1066D4—48no—
1067D4—48no—
1068D4—2216no—
1069D4—2216no—
1070D4—228no—
1071D4—448no—
1072D4—448no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—22no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—22no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—22no—
1085C2×C4—21no—
1086C2×C4—22no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—22no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—48no—
1094C2×C4—84no—
1095C2×C4—112no—
1096C2×C4—112no—
1097C2×C4—112no—
1098C2×C4—1116no—
1099C2×C4—112no—
1100C2×C4—112no—
1101C2×C4—114no—
1102C2×C4—114no—
1103C2×C4—112no—
1104C2×C4—228no—
1105C2×C4—2216no—
1106C2×C4—222no—
1107C2×C4—221no—
1108C2×C4—221no—
1109C2×C4—222no—
1110C2×C4—221no—
1111C2×C4—222no—
1112C2×C4—221no—
1113C2×C4—221no—
1114C2×C4—222no—
1115C2×C4—221no—
1116C2×C4—221no—
1117C2×C4—221no—
1118C2×C4—221no—
1119C2×C4—221no—
1120C2×C4—222no—
1121C2×C4—222no—
1122C2×C4—221no—
1123C2×C4—221no—
1124C2×C4—222no—
1125C2×C4—221no—
1126C2×C4—221no—
1127C2×C4—221no—
1128C2×C4—448no—
1129C2×C4—448no—
1130C2×C4—448no—
1131C2×C4—444no—
1132C2×C4—448no—
1133C2×C4—884no—
1134C2×C4C22×C4×D1112yes—
1135C2×C4C22×C4×D1112yes—
1136C2×C4C22×C4×D1112yes—
1137C2×C4C2×D4×D1114yes—
1138C2×C4C2×D4×D1112yes—
1139C2×C4#6703712yes—
1140C2×C4#41×D1112yes—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—24no—
1146C22—24no—
1147C22—42no—
1148C22—42no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—42no—
1154C22—42no—
1155C22—114no—
1156C22—222no—
1157C22—222no—
1158C22—222no—
1159C22—222no—
1160C22—222no—
1161C22—222no—
1162C22—224no—
1163C22—224no—
1164C22—224no—
1165C22—4432no—
1166C22—442no—
1167C22—442no—
1168C22—442no—
1169C22—442no—
1170C22C23×C4×D1111yescharacteristic
1171C22C22×D4×D1111yescharacteristic
1172C22C2×#6703711yescharacteristic
1173C22C2×#41×D1111yescharacteristic
1174C22#1062345311yescharacteristic
1175C22D11×H(5,𝔽2)11yescharacteristic
1176C22#1062345511yescharacteristic
1177C4—22no—
1178C4—24no—
1179C4—22no—
1180C4—22no—
1181C4—42no—
1182C4—41no—
1183C4—41no—
1184C4—41no—
1185C4—114no—
1186C4—222no—
1187C4—224no—
1188C4—224no—
1189C4—222no—
1190C4—222no—
1191C4—442no—
1192C4—441no—
1193C4—441no—
1194C4—441no—
1195C4C4×D4×D1114yes—
1196C2—44no—
1197C2—44no—
1198C2—224no—
1199C2—444no—
1200C2C2×C4×D4×D1111yescharacteristic
1201C2#1308182011yescharacteristic
1202C2C4×#6703711yescharacteristic
1203C2#1308224411yescharacteristic
1204C2#1308226911yescharacteristic
1205C2#1308246011yescharacteristic
1206C2#1308246411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2366C2
socle, cosocleC23×C11C25
prime radicalC2×#10623246C2
hypercenter#2366D11
hypocenterC11#34265
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2366

Complements

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

NH ≅ G/Ntype
2. C2×#10623077C2semidirect
3. C2×C4×D4×D11C2semidirect
4. #13071689C2semidirect
5. #13071687C2semidirect
6. #13071686C2semidirect
7. #13071685C2semidirect
8. #13071681C2semidirect
9. #13071678C2semidirect
10. #13071677C2semidirect
11. #13071657C2semidirect
12. #13071651C2semidirect
13. #13071633C2semidirect
14. #13071627C2semidirect
15. #13071275C2semidirect
16. #13071272C2semidirect
17. #13071195C2semidirect
18. #13071121C2semidirect
19. C4×#66990C2semidirect
20. #13071103C2semidirect
21. #13071096C2semidirect
22. #13070970C2semidirect
23. C11×#2366C2semidirect
29. C2×C4×D4×C11C22semidirect
30. C2×C4×D4×C11C22semidirect
38. C2×D4×Dic11C22semidirect
39. C2×D4×Dic11C22semidirect
42. C2×C4×C22⋊D11C22semidirect
43. C22×Dic11⋊C4C22semidirect
44. #10623246C4semidirect
50. C2×#66940C22semidirect
53. C2×(C22⋊D11)⋊C4C22semidirect
55. C2×#66930C22semidirect
61. C2×C4×Dic22C22semidirect
63. C11×#390C22semidirect
64. C11×#390C22semidirect
65. C11×#386C22semidirect
66. C11×#386C22semidirect
67. C4×C11×C4⋊C4C22semidirect
68. C4×C11×C4⋊C4C22semidirect
70. #10622834C22semidirect
71. #10622834C22semidirect
72. #10622833C22semidirect
73. #10622833C22semidirect
74. #10622826C22semidirect
75. #10622823C22semidirect
76. C4×C22⋊Dic11C22semidirect
77. #10622603C22semidirect
80. #10622602C22semidirect
82. C4⋊C4×Dic11C22semidirect
83. C4⋊C4×Dic11C22semidirect
84. #10622587C22semidirect
85. #10622585C22semidirect
86. #10622585C22semidirect
87. #10622571C22semidirect
90. #10622570C22semidirect
91. #10622570C22semidirect
94. #10622569C22semidirect
95. #10622569C22semidirect
98. #10622559C22semidirect
99. #10622558C22semidirect
100. #10622558C22semidirect
101. #10622557C22semidirect
102. #10622557C22semidirect
103. C22⋊C4×Dic11C22semidirect
104. C22⋊C4×Dic11C22semidirect
105. C22⋊C4×Dic11C22semidirect
106. #10622553C22semidirect
109. C4×(C2×D11)⋊C4C22semidirect
110. C4×C4⋊Dic11C22semidirect
111. C4×C4⋊Dic11C22semidirect
112. C4×Dic11⋊C4C22semidirect
113. C4×Dic11⋊C4C22semidirect
114. C4×Dic11⋊C4C22semidirect
115. #10622542C22semidirect
116. #10622283C22semidirect
117. #10622282C22semidirect
120. #10622281C22semidirect
122. #10622279C22semidirect
123. #10622262C22semidirect
124. #10622260C22semidirect
125. #10622260C22semidirect
142. C2×#4341C2×C4semidirect
145. C2×D4×D11C2×C4semidirect
157. C11×#127C2×C4semidirect
183. #66993C2×C4semidirect
184. #66992C2×C4semidirect
185. #66992C2×C4semidirect
186. #66990C2×C4semidirect
187. #66990C2×C4semidirect
188. #66989C2×C4semidirect
237. C4⋊C4×D11D4semidirect
244. #66928C2×C4semidirect
247. #66925C2×C4semidirect
287. C2×D4×C11C22×C4semidirect
288. C2×D4×C11C22×C4semidirect
289. C2×D4×C11C22×C4semidirect
315. C2×C22⋊D11C22×C4semidirect
316. C2×C22⋊D11C22×C4semidirect
325. C22×Dic11C22×C4semidirect
362. C2×Dic22C22×C4semidirect
376. C42×C11C22×C4semidirect
383. C22⋊Dic11C22×C4semidirect
384. C22⋊Dic11C22×C4semidirect
396. (C2×D11)⋊C4C22×C4semidirect
397. (C2×D11)⋊C4C22×C4semidirect
410. Dic11⋊C4C22×C4semidirect
411. Dic11⋊C4C22×C4semidirect
423. C4×Dic11C22×C4semidirect
434. #2366D11semidirect
559. C4×D11C4×D4semidirect
589. C2×C4×D4C2×D11semidirect
590. C2×C4×D4C2×D11semidirect
611. #390C2×D11semidirect
612. #390C2×D11semidirect
633. #386C2×D11semidirect
634. #386C2×D11semidirect
653. C4×C4⋊C4C2×D11semidirect
654. C4×C4⋊C4C2×D11semidirect
750. #127C4×D11semidirect
909. C2×D4C2×C4×D11semidirect
910. C2×D4C2×C4×D11semidirect
911. C2×D4C2×C4×D11semidirect
1025. C42C2×C4×D11semidirect
1026. C11#34265semidirect

Maximal subgroups

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

subgroupindex
C2×#106232462
C2×#106230772
C2×C4×D4×D112
#130716892
#130716872
#130716862
#130716852
#130716812
#130716782
#130716772
#130716572
#130716512
#130716332
#130716272
#130712752
#130712722
#130711952
#130711212
C4×#669902
#130711032
#130710962
#130709702
C11×#23662
#3426511