Finite Group Databasebeta

← #14912234

Subgroups — #14912234

Order 2816.

3902 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623078C211yesmaximal, characteristic
2C2×#10623053C211yesmaximal, characteristic, complemented
3C22×C42×D11C211yesmaximal, characteristic, complemented
4#13071150C212yesmaximal, complemented
5#13071148C212yesmaximal, complemented
6#13071143C212yesmaximal, complemented
7#13071137C212yesmaximal, complemented
8#13071128C212yesmaximal, complemented
9#13071126C212yesmaximal, complemented
10#13071121C212yesmaximal, complemented
11#13071117C212yesmaximal, complemented
12#13071102C211yesmaximal, characteristic, complemented
13#13071096C211yesmaximal, characteristic, complemented
14#13071060C211yesmaximal, characteristic, complemented
15#13071059C211yesmaximal, characteristic, complemented
16#13071053C211yesmaximal, characteristic, complemented
17#13070997C211yesmaximal, characteristic, complemented
18C4×D4×Dic11C211yesmaximal, characteristic, complemented
19C4×#66946C211yesmaximal, characteristic, complemented
20C4×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
21C4×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
22#13070955C211yesmaximal, characteristic, complemented
23C11×#2290C211yesmaximal, characteristic, complemented
24C22×#4339C2211yescharacteristic
25C23×C4×D11C2212yes—
26C23×C4×D11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic, complemented
29C22×C42×C11C2211yescharacteristic
30C2×#66992C2211yescharacteristic
31C2×#66990C2211yescharacteristic
32C2×D4×Dic11C2212yes—
33C2×C4×C22⋊D11C2211yescharacteristic
34C2×C4×C22⋊D11C2211yescharacteristic
35C22×C4×Dic11C2212yes—
36C22×C4×Dic11C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic, complemented
38#10623078C4116yescomplemented
39#10623053—28no—
40C2×#66949C2211yescharacteristic
41C2×#66947C2211yescharacteristic
42C2×#66946C2212yes—
43C2×#66946C2212yes—
44C2×#66940C2212yescomplemented
45C2×#66937C2211yescharacteristic
46C2×#66936C2211yescharacteristic
47C2×#66935C2211yescharacteristic
48C2×(C22⋊D11)⋊C4C2212yes—
49C2×(C22⋊D11)⋊C4C2212yes—
50C2×(C22⋊D11)⋊C4C2212yes—
51C2×(C22⋊D11)⋊C4C2212yescomplemented
52C2×#66931C2211yescharacteristic
53C2×C4×D44C2211yescharacteristic
54C2×#66925C2211yescharacteristic
55C2×#66925C2211yescharacteristic
56C2×#66925C2211yescharacteristic
57C2×#66925C2211yescharacteristic, complemented
58C2×C42×D11—28no—
59C2×C42×D11C2212yes—
60C2×C42×D11C2212yes—
61C2×C42×D11C2211yescharacteristic
62C2×C42×D11C2211yescharacteristic
63C2×C42×D11C2211yescharacteristic
64C2×C42×D11C2211yescharacteristic
65C2×C42×D11C2211yescharacteristic, complemented
66C11×#388C2212yescomplemented
67C11×#387C2212yescomplemented
68C11×#386C2212yes—
69C11×#385C2212yes—
70C4×C11×C4⋊C4C2211yescharacteristic, complemented
71C4×C11×C22⋊C4C2211yescharacteristic
72C4×C11×C22⋊C4C2211yescharacteristic, complemented
73C11×#376C2211yescharacteristic, complemented
74#10622826C2212yes—
75#10622823C2212yes—
76C4×C22⋊Dic11C2211yescharacteristic
77C4×C22⋊Dic11C2211yescharacteristic, complemented
78#10622602C2212yes—
79#10622602C2212yes—
80#10622591C2212yescomplemented
81C4⋊C4×Dic11C2212yescomplemented
82C4⋊C4×Dic11C2212yescomplemented
83#10622585C2212yescomplemented
84#10622570C2212yescomplemented
85#10622569C2212yes—
86#10622569C2212yes—
87#10622568C2212yes—
88#10622557C2212yescomplemented
89#10622555C2212yes—
90C22⋊C4×Dic11C2212yes—
91C22⋊C4×Dic11C2212yes—
92C22⋊C4×Dic11C2212yescomplemented
93C22⋊C4×Dic11C2212yescomplemented
94#10622553C2212yescomplemented
95C4×(C2×D11)⋊C4C2211yescharacteristic
96C4×(C2×D11)⋊C4C2211yescharacteristic
97C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
98C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
99C4×C4⋊Dic11C2211yescharacteristic, complemented
100#10622546C2212yescomplemented
101#10622545C2211yescharacteristic, complemented
102C4×Dic11⋊C4C2211yescharacteristic, complemented
103C4×Dic11⋊C4C2211yescharacteristic, complemented
104C42×Dic11C2211yescharacteristic, complemented
105C42×Dic11C2211yescharacteristic, complemented
106#10622283C2212yescomplemented
107#10622281C2212yes—
108#10622281C2212yes—
109#10622280C2212yes—
110#10622279C2212yes—
111#10622279C2212yes—
112#10622279C2212yes—
113#10622279C2212yes—
114#10622279C2212yescomplemented
115#10622279C2212yescomplemented
116#10622278C2212yes—
117#10622278C2212yes—
118#10622277C2212yes—
119#10622266C2212yescomplemented
120#10622262C2212yescomplemented
121#10622262C2212yescomplemented
122#10622262C2212yescomplemented
123#10622262C2212yescomplemented
124#10622260C2212yescomplemented
125#10622259C2212yescomplemented
126C24×D11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C23×C4×C11C2312yes—
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C22×C22⋊D11C2311yescharacteristic
132C22×C22⋊D11C2311yescharacteristic
133C22×C22⋊D11C2311yescharacteristic
134C22×C22⋊D11C2311yescharacteristic
135C23×Dic11C2312yes—
136C23×Dic11C2311yescharacteristic
137C23×Dic11C2312yes—
138C2×#4339—24no—
139C2×#4339—24no—
140C2×#4339C2×C418yescomplemented
141C22×D44C2311yescharacteristic
142C22×D44C2311yescharacteristic
143C22×C4×D11—28no—
144C22×C4×D11—28no—
145C22×C4×D11—24no—
146C22×C4×D11—24no—
147C22×C4×D11—28no—
148C22×C4×D11C2×C418yescomplemented
149C22×C4×D11C2312yes—
150C22×C4×D11C2312yes—
151C22×C4×D11C2312yes—
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2311yescharacteristic
154C22×C4×D11C2311yescharacteristic
155C22×C4×D11C2311yescharacteristic
156C22×C4×D11C2312yes—
157C22×C4×D11C2312yes—
158C22×C4×D11C2311yescharacteristic
159C22×Dic22C2311yescharacteristic
160C4×D4×C11C2×C418yescomplemented
161C11×#117—24no—
162C2×C11×C4⋊C4C2312yes—
163C2×C11×C4⋊C4C2312yes—
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2311yescharacteristic
169C2×C11×C22⋊C4C2311yescharacteristic
170C2×C42×C11—24no—
171C2×C42×C11C2311yescharacteristic
172C2×C42×C11C2312yes—
173C2×C42×C11C2311yescharacteristic
174C2×C42×C11C2311yescharacteristic
175C2×C42×C11C2311yescharacteristic
176C2×C42×C11C2311yescharacteristic
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2311yescharacteristic
180C2×C22⋊Dic11C2311yescharacteristic
181#66992C2×C418yescomplemented
182#66990C2×C418yescomplemented
183D4×Dic11—28no—
184C4×C22⋊D11C2×C418yescomplemented
185C4×C22⋊D11C2×C418yescomplemented
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×(C2×D11)⋊C4C2311yescharacteristic
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2311yescharacteristic
197C2×(C2×D11)⋊C4C2311yescharacteristic
198C2×(C2×D11)⋊C4C2311yescharacteristic
199C2×C4⋊Dic11C2312yes—
200C2×C4⋊Dic11C2311yescharacteristic
201C2×Dic11⋊C4C2312yes—
202C2×Dic11⋊C4C2312yes—
203C2×Dic11⋊C4C2312yes—
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C2312yes—
206C2×Dic11⋊C4C2311yescharacteristic
207C2×Dic11⋊C4C2311yescharacteristic
208C2×Dic11⋊C4C2311yescharacteristic
209C2×Dic11⋊C4C2311yescharacteristic
210C2×C4×Dic11—24no—
211C2×C4×Dic11—28no—
212C2×C4×Dic11—24no—
213C2×C4×Dic11C2312yes—
214C2×C4×Dic11C2312yes—
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2312yes—
222C2×C4×Dic11C2312yes—
223C2×C4×Dic11C2312yes—
224C2×C4×Dic11C2312yes—
225C2×C4×Dic11C2312yes—
226C2×C4×Dic11C2311yescharacteristic
227C2×C4×Dic11C2311yescharacteristic
228C2×C4×Dic11C2312yes—
229#66949C2×C418yescomplemented
230#66947C2×C418yescomplemented
231#66946—28no—
232#66946—28no—
233#66940—28no—
234#66937C2×C418yescomplemented
235#66936C2×C418yescomplemented
236#66935C2×C418yescomplemented
237(C22⋊D11)⋊C4—28no—
238(C22⋊D11)⋊C4—28no—
239(C22⋊D11)⋊C4—28no—
240(C22⋊D11)⋊C4—28no—
241#66931C2×C418yescomplemented
242C4×D44C2×C418yescomplemented
243#66925—24no—
244#66925—24no—
245#66925—24no—
246#66925C2×C418yescomplemented
247C42×D11—28no—
248C42×D11—24no—
249C42×D11—24no—
250C42×D11—24no—
251C42×D11—28no—
252C42×D11—24no—
253C42×D11D418yescomplemented
254C11×#95C2312yes—
255C11×#95C2312yes—
256C11×#95C2312yes—
257C11×#95C2312yes—
258C11×#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264C11⋊#95C2312yes—
265C11⋊#95C2312yes—
266C11⋊#95C2312yes—
267C11⋊#95C2312yes—
268C11⋊#95C2312yes—
269C11⋊#95C2312yes—
270C4×#525—111nomaximal, Sylow
271C24×C11C2411yescharacteristic
272C24×C11C2411yescharacteristic
273C23×D11—24no—
274C23×D11—22no—
275C23×D11—24no—
276C23×D11—22no—
277C23×D11C22×C414yes—
278C23×D11C2411yescharacteristic
279C23×D11C2411yescharacteristic
280C23×D11C2411yescharacteristic
281C2×D4×C11—24no—
282C2×D4×C11C22×C414yes—
283C22×C4×C11—24no—
284C22×C4×C11—24no—
285C22×C4×C11—22no—
286C22×C4×C11—22no—
287C22×C4×C11—24no—
288C22×C4×C11—22no—
289C22×C4×C11—22no—
290C22×C4×C11C22×C414yes—
291C22×C4×C11C22×C414yescomplemented
292C22×C4×C11C2412yes—
293C22×C4×C11C2412yes—
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2412yes—
299C22×C4×C11C2412yes—
300C22×C4×C11C2411yescharacteristic
301C2×C22⋊D11—22no—
302C2×C22⋊D11—22no—
303C2×C22⋊D11—24no—
304C2×C22⋊D11—22no—
305C2×C22⋊D11—24no—
306C2×C22⋊D11—22no—
307C2×C22⋊D11C22×C414yes—
308C2×C22⋊D11C22×C414yes—
309C2×C22⋊D11C22×C414yes—
310C2×C22⋊D11C22×C414yescomplemented
311C22×Dic11—22no—
312C22×Dic11—24no—
313C22×Dic11—22no—
314C22×Dic11—24no—
315C22×Dic11—24no—
316C22×Dic11—24no—
317C22×Dic11—24no—
318C22×Dic11C22×C414yes—
319C22×Dic11#4118yescomplemented
320C22×Dic11C2412yes—
321C22×Dic11C2412yes—
322C22×Dic11C2411yescharacteristic
323C22×Dic11C2411yescharacteristic
324C22×Dic11C2411yescharacteristic
325C22×Dic11C2411yescharacteristic
326C22×Dic11C2412yes—
327C22×Dic11C2411yescharacteristic
328C22×Dic11C2412yes—
329#4339—232no—
330C2×D44—22no—
331C2×D44—24no—
332C2×D44—22no—
333C2×D44C22×C414yes—
334C2×D44C22×C414yes—
335C2×C4×D11—264no—
336C2×C4×D11—22no—
337C2×C4×D11—24no—
338C2×C4×D11—24no—
339C2×C4×D11—24no—
340C2×C4×D11—22no—
341C2×C4×D11—24no—
342C2×C4×D11—24no—
343C2×C4×D11—24no—
344C2×C4×D11—232no—
345C2×C4×D11—24no—
346C2×C4×D11—24no—
347C2×C4×D11—24no—
348C2×C4×D11—24no—
349C2×C4×D11—22no—
350C2×C4×D11—22no—
351C2×C4×D11—24no—
352C2×C4×D11—24no—
353C2×C4×D11—22no—
354C2×C4×D11—22no—
355C2×C4×D11—24no—
356C2×C4×D11—22no—
357C2×C4×D11—22no—
358C2×C4×D11C22×C414yes—
359C2×C4×D11C22×C414yes—
360C2×C4×D11C22×C414yes—
361C2×C4×D11C22×C414yes—
362C2×C4×D11C22×C414yescomplemented
363C2×C4×D11C2×D418yes—
364C2×C4×D11C2×D414yes—
365C2×C4×D11#4114yes—
366C2×C4×D11#4118yescomplemented
367C2×Dic22—22no—
368C2×Dic22—22no—
369C2×Dic22C22×C414yescomplemented
370C11×C4⋊C4—24no—
371C11×C4⋊C4—24no—
372C11×C4⋊C4C22×C414yescomplemented
373C11×C22⋊C4—24no—
374C11×C22⋊C4—24no—
375C11×C22⋊C4—24no—
376C11×C22⋊C4C22×C414yes—
377C11×C22⋊C4C22×C414yescomplemented
378C42×C11—24no—
379C42×C11—22no—
380C42×C11—22no—
381C42×C11—22no—
382C42×C11C22×C414yescomplemented
383C42×C11C2×D414yes—
384C22⋊Dic11—24no—
385C22⋊Dic11—24no—
386C22⋊Dic11C22×C414yes—
387C22⋊Dic11C22×C414yescomplemented
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—24no—
390(C2×D11)⋊C4—24no—
391(C2×D11)⋊C4—24no—
392(C2×D11)⋊C4—24no—
393(C2×D11)⋊C4—24no—
394(C2×D11)⋊C4—24no—
395(C2×D11)⋊C4C22×C414yes—
396(C2×D11)⋊C4C22×C414yes—
397(C2×D11)⋊C4C22×C414yes—
398(C2×D11)⋊C4C22×C414yes—
399(C2×D11)⋊C4C22×C414yescomplemented
400(C2×D11)⋊C4C22×C414yescomplemented
401C4⋊Dic11—24no—
402C4⋊Dic11C22×C414yescomplemented
403Dic11⋊C4—24no—
404Dic11⋊C4—24no—
405Dic11⋊C4—24no—
406Dic11⋊C4—24no—
407Dic11⋊C4—24no—
408Dic11⋊C4C22×C414yescomplemented
409Dic11⋊C4C22×C414yescomplemented
410Dic11⋊C4C22×C414yescomplemented
411Dic11⋊C4C22×C414yescomplemented
412C4×Dic11—24no—
413C4×Dic11—24no—
414C4×Dic11—24no—
415C4×Dic11—24no—
416C4×Dic11—24no—
417C4×Dic11—24no—
418C4×Dic11—24no—
419C4×Dic11—24no—
420C4×Dic11—24no—
421C4×Dic11—24no—
422C4×Dic11—22no—
423C4×Dic11—22no—
424C4×Dic11—22no—
425C4×Dic11C22×C414yescomplemented
426C4×Dic11C2×D414yes—
427C4×Dic11C2×D418yes—
428C2×#525—111no—
429C2×C4×#41—111no—
430C23×C42—111no—
431C4×C22⋊Q8—112no—
432C4×C22⋊Q8—112no—
433C4×#123—112no—
434C4×#123—112no—
435C4×#121—112no—
436C4×#121—112no—
437C4×#120—112no—
438C4×#120—112no—
439#2297—111no—
440#2296—111no—
441#2290—111no—
442#2290—111no—
443#2290—111no—
444#2290D1111yescharacteristic, complemented
445#2280—111no—
446C42×D4—111no—
447C42×D4—111no—
448C42×D4—111no—
449C42×D4—111no—
450C4×#117—111no—
451C23×C11—21no—
452C23×C11—21no—
453C23×C11—22no—
454C23×C11—21no—
455C23×C11—22no—
456C23×C11—22no—
457C23×C11—21no—
458C23×C11C23×C412yes—
459C23×C11C23×C412yes—
460C23×C11C2×#4114yes—
461C23×C11C2511yescharacteristic
462C22×D11—216no—
463C22×D11—216no—
464C22×D11—28no—
465C22×D11—21no—
466C22×D11—21no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—28no—
471C22×D11—28no—
472C22×D11—21no—
473C22×D11—22no—
474C22×D11—22no—
475C22×D11—21no—
476C22×D11C23×C412yes—
477C22×D11C23×C412yes—
478C22×D11C23×C412yes—
479C22×D11C22×D412yes—
480C22×D11C2×#4112yes—
481C22×D11C2×#4114yes—
482D4×C11—28no—
483C2×C4×C11—216no—
484C2×C4×C11—21no—
485C2×C4×C11—22no—
486C2×C4×C11—21no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—21no—
490C2×C4×C11—21no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—28no—
495C2×C4×C11—28no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11C23×C412yes—
503C2×C4×C11C23×C412yes—
504C2×C4×C11C23×C412yes—
505C2×C4×C11C23×C412yes—
506C2×C4×C11C23×C412yes—
507C2×C4×C11C22×D414yes—
508C2×C4×C11C22×D412yes—
509C2×C4×C11C2×#4114yes—
510C2×C4×C11C2×#4112yes—
511C22⋊D11—28no—
512C22⋊D11—28no—
513C22⋊D11—28no—
514C22⋊D11—28no—
515C2×Dic11—21no—
516C2×Dic11—22no—
517C2×Dic11—21no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—21no—
521C2×Dic11—21no—
522C2×Dic11—22no—
523C2×Dic11—28no—
524C2×Dic11—216no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—48no—
532C2×Dic11C23×C412yes—
533C2×Dic11C23×C412yes—
534C2×Dic11C23×C412yes—
535C2×Dic11C23×C412yes—
536C2×Dic11C23×C412yes—
537C2×Dic11C22×D412yes—
538C2×Dic11C22×D414yes—
539C2×Dic11C2×#4114yes—
540C2×Dic11C2×#4112yes—
541C2×Dic11C2×#4114yes—
542C2×Dic11C2×#4114yes—
543D44—28no—
544D44—28no—
545C4×D11—216no—
546C4×D11—216no—
547C4×D11—28no—
548C4×D11—28no—
549C4×D11—28no—
550C4×D11—28no—
551C4×D11—216no—
552C4×D11—216no—
553C4×D11—48no—
554C4×D11C4×D4116yescomplemented
555Dic22—28no—
556C22×#41—111no—
557C24×C4—111no—
558C24×C4—112no—
559#525—1116no—
560C2×#123—111no—
561C2×#123—111no—
562C2×C22⋊Q8—111no—
563C2×C22⋊Q8—111no—
564C2×#121—111no—
565C2×#121—111no—
566C2×#120—111no—
567C2×#120—111no—
568C4×#41—228no—
569C2×C4×Q8—112no—
570C2×C4×D4—111no—
571C2×C4×D4—111no—
572C2×C4×D4—112no—
573C2×C4×D4—112no—
574C2×C4×D4—112no—
575C2×C4×D4—112no—
576C2×C4×D4—112no—
577C2×C4×D4—112no—
578C2×C4×D4—112no—
579C2×C4×D4—111no—
580C2×C4×D4C2×D1111yescharacteristic
581C2×#117—111no—
582C2×#117—111no—
583C2×#117—111no—
584C2×#117—111no—
585C2×#117C2×D1111yescharacteristic, complemented
586C22×C42—111no—
587C22×C42—111no—
588C22×C42—112no—
589C22×C42—111no—
590C22×C42—111no—
591C22×C42—111no—
592C22×C42—111no—
593C22×C42—112no—
594C22×C42—112no—
595C22×C42—111no—
596C22×C42—228no—
597C22×C42C2×D1111yescharacteristic
598#391—112no—
599#390—112no—
600#389—112no—
601#389—112no—
602#388—112no—
603#388—112no—
604#388—112no—
605#388C2×D1112yescomplemented
606#387—112no—
607#387—112no—
608#387—112no—
609#387C2×D1112yescomplemented
610#386—112no—
611#386—112no—
612#386—112no—
613#386—112no—
614#386—112no—
615#386C2×D1112yes—
616#385—112no—
617#385—112no—
618#385—112no—
619#385—112no—
620#385—112no—
621#385C2×D1112yes—
622#381—112no—
623#380—112no—
624#380—112no—
625#379—112no—
626C4×C4⋊C4—112no—
627C4×C4⋊C4—112no—
628C4×C4⋊C4—111no—
629C4×C4⋊C4—111no—
630C4×C4⋊C4—111no—
631C4×C4⋊C4—112no—
632C4×C4⋊C4—112no—
633C4×C4⋊C4—112no—
634C4×C4⋊C4—112no—
635C4×C4⋊C4C2×D1111yescharacteristic, complemented
636C4×C22⋊C4—111no—
637C4×C22⋊C4—111no—
638C4×C22⋊C4—112no—
639C4×C22⋊C4—112no—
640C4×C22⋊C4—112no—
641C4×C22⋊C4—112no—
642C4×C22⋊C4—111no—
643C4×C22⋊C4—111no—
644C4×C22⋊C4—111no—
645C4×C22⋊C4—111no—
646C4×C22⋊C4—112no—
647C4×C22⋊C4—112no—
648C4×C22⋊C4—112no—
649C4×C22⋊C4—112no—
650C4×C22⋊C4—112no—
651C4×C22⋊C4—112no—
652C4×C22⋊C4C2×D1111yescharacteristic
653C4×C22⋊C4C2×D1111yescharacteristic, complemented
654#376—111no—
655#376C2×D1111yescharacteristic, complemented
656C43—111no—
657C43—111no—
658C22×C11—22no—
659C22×C11—22no—
660C22×C11—24no—
661C22×C11—24no—
662C22×C11—22no—
663C22×C11—22no—
664C22×C11—22no—
665C22×C11—42no—
666C22×C11—42no—
667C22×C11C4×#4114yescomplemented
668C22×C11C24×C411yescharacteristic
669C22×C11C23×D411yescharacteristic
670C22×C11C22×#4111yescharacteristic
671C22×C11C22×#4112yes—
672C22×C11C22×#4112yes—
673C2×D11—232no—
674C2×D11—22no—
675C2×D11—22no—
676C2×D11—22no—
677C2×D11—22no—
678C2×D11—24no—
679C2×D11—24no—
680C2×D11—24no—
681C2×D11—24no—
682C2×D11—22no—
683C2×D11—22no—
684C2×D11—22no—
685C2×D11—42no—
686C2×D11—42no—
687C2×D11C2×C4×D414yes—
688C2×D11C4×#4114yescomplemented
689C4×C11—22no—
690C4×C11—22no—
691C4×C11—22no—
692C4×C11—22no—
693C4×C11—24no—
694C4×C11—24no—
695C4×C11—42no—
696C4×C11—42no—
697C4×C11C2×C4×D414yes—
698Dic11—22no—
699Dic11—22no—
700Dic11—22no—
701Dic11—22no—
702Dic11—24no—
703Dic11—42no—
704Dic11—42no—
705Dic11C2×C4×D414yes—
706Dic11#52518yescomplemented
707C25—111no—
708C2×#41—118no—
709C2×#41—224no—
710C2×#41—224no—
711C22×Q8—111no—
712C22×D4—111no—
713C22×D4—111no—
714C22×D4—111no—
715C22×D4—111no—
716C22×D4—111no—
717C22×D4—111no—
718C22×D4C22×D1111yescharacteristic
719C23×C4—111no—
720C23×C4—112no—
721C23×C4—111no—
722C23×C4—118no—
723C23×C4—112no—
724C23×C4—112no—
725C23×C4—111no—
726C23×C4—111no—
727C23×C4—111no—
728C23×C4—111no—
729C23×C4—112no—
730C23×C4—112no—
731C23×C4—112no—
732C23×C4—112no—
733C23×C4—228no—
734C23×C4—224no—
735C23×C4—228no—
736C23×C4—224no—
737C23×C4—228no—
738C23×C4C22×D1112yes—
739C23×C4C22×D1111yescharacteristic
740C23×C4C22×D1111yescharacteristic
741#123—118no—
742#123—118no—
743C22⋊Q8—118no—
744C22⋊Q8—118no—
745#121—118no—
746#121—118no—
747#120—118no—
748#120—118no—
749C4×Q8—228no—
750C4×D4—118no—
751C4×D4—118no—
752C4×D4—118no—
753C4×D4—228no—
754C4×D4—228no—
755C4×D4—228no—
756C4×D4—228no—
757C4×D4—228no—
758C4×D4—228no—
759C4×D4—228no—
760C4×D4C4×D1118yescomplemented
761#117—24no—
762#117—118no—
763#117—224no—
764#117—224no—
765#117—224no—
766C2×C4⋊C4—111no—
767C2×C4⋊C4—111no—
768C2×C4⋊C4—111no—
769C2×C4⋊C4—111no—
770C2×C4⋊C4—111no—
771C2×C4⋊C4—112no—
772C2×C4⋊C4—112no—
773C2×C4⋊C4—112no—
774C2×C4⋊C4—112no—
775C2×C4⋊C4—112no—
776C2×C4⋊C4—112no—
777C2×C4⋊C4C22×D1112yes—
778C2×C4⋊C4C22×D1112yes—
779C2×C4⋊C4C22×D1111yescharacteristic
780C2×C22⋊C4—111no—
781C2×C22⋊C4—111no—
782C2×C22⋊C4—111no—
783C2×C22⋊C4—111no—
784C2×C22⋊C4—111no—
785C2×C22⋊C4—111no—
786C2×C22⋊C4—111no—
787C2×C22⋊C4—111no—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—112no—
790C2×C22⋊C4—112no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—112no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—112no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—112no—
797C2×C22⋊C4C22×D1112yes—
798C2×C22⋊C4C22×D1112yes—
799C2×C22⋊C4C22×D1112yes—
800C2×C22⋊C4C22×D1111yescharacteristic
801C2×C22⋊C4C22×D1111yescharacteristic
802C2×C42—24no—
803C2×C42—112no—
804C2×C42—111no—
805C2×C42—111no—
806C2×C42—118no—
807C2×C42—112no—
808C2×C42—112no—
809C2×C42—112no—
810C2×C42—112no—
811C2×C42—112no—
812C2×C42—112no—
813C2×C42—112no—
814C2×C42—112no—
815C2×C42—112no—
816C2×C42—112no—
817C2×C42—111no—
818C2×C42—111no—
819C2×C42—111no—
820C2×C42—224no—
821C2×C42—224no—
822C2×C42—228no—
823C2×C42—224no—
824C2×C42—228no—
825C2×C42—224no—
826C2×C42—224no—
827C2×C42—228no—
828C2×C42—224no—
829C2×C42C22×D1112yes—
830C2×C42C22×D1111yescharacteristic
831C2×C42C22×D1111yescharacteristic
832C2×C42C22×D1111yescharacteristic
833C2×C42C22×D1111yescharacteristic
834C2×C42C22×D1111yescharacteristic
835#95—112no—
836#95—112no—
837#95—112no—
838#95—112no—
839#95—112no—
840#95—112no—
841#95—112no—
842#95—112no—
843#95—112no—
844#95—112no—
845#95—112no—
846#95C22×D1112yes—
847#95C22×D1112yes—
848#95C22×D1112yes—
849#95C22×D1112yes—
850#95C22×D1112yes—
851C2×C11—24no—
852C2×C11—42no—
853C2×C11C22×C4×D411yescharacteristic
854C2×C11C2×C4×#4111yescharacteristic
855C2×C11C2×C4×#4111yescharacteristic
856C2×C11C2×#52512yes—
857C2×C11#344412yes—
858D11—24no—
859D11—24no—
860D11—42no—
861C24—111no—
862C24—111no—
863C24—114no—
864C24—111no—
865C24—222no—
866C24—222no—
867C24—224no—
868C24—224no—
869C24C23×D1111yescharacteristic
870C24C23×D1111yescharacteristic
871#41—2232no—
872C2×Q8—114no—
873C2×Q8—222no—
874C2×Q8—222no—
875C2×D4—24no—
876C2×D4—114no—
877C2×D4—114no—
878C2×D4—114no—
879C2×D4—114no—
880C2×D4—114no—
881C2×D4—114no—
882C2×D4—222no—
883C2×D4—224no—
884C2×D4—222no—
885C2×D4—222no—
886C2×D4—222no—
887C2×D4—222no—
888C2×D4—224no—
889C2×D4—222no—
890C2×D4—224no—
891C2×D4C2×C4×D1114yes—
892C22×C4—24no—
893C22×C4—24no—
894C22×C4—22no—
895C22×C4—22no—
896C22×C4—24no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—112no—
900C22×C4—111no—
901C22×C4—114no—
902C22×C4—114no—
903C22×C4—114no—
904C22×C4—114no—
905C22×C4—118no—
906C22×C4—111no—
907C22×C4—112no—
908C22×C4—111no—
909C22×C4—111no—
910C22×C4—111no—
911C22×C4—114no—
912C22×C4—114no—
913C22×C4—114no—
914C22×C4—114no—
915C22×C4—118no—
916C22×C4—118no—
917C22×C4—112no—
918C22×C4—112no—
919C22×C4—224no—
920C22×C4—222no—
921C22×C4—224no—
922C22×C4—224no—
923C22×C4—224no—
924C22×C4—222no—
925C22×C4—224no—
926C22×C4—224no—
927C22×C4—2232no—
928C22×C4—224no—
929C22×C4—224no—
930C22×C4—224no—
931C22×C4—222no—
932C22×C4—224no—
933C22×C4—222no—
934C22×C4—224no—
935C22×C4—2264no—
936C22×C4—224no—
937C22×C4—222no—
938C22×C4—224no—
939C22×C4—222no—
940C22×C4—224no—
941C22×C4—224no—
942C22×C4—224no—
943C22×C4—224no—
944C22×C4—222no—
945C22×C4—222no—
946C22×C4—224no—
947C22×C4—222no—
948C22×C4—222no—
949C22×C4C2×C4×D1114yes—
950C22×C4C2×C4×D1114yescomplemented
951C22×C4C23×D1112yes—
952C22×C4C23×D1112yes—
953C22×C4C23×D1111yescharacteristic
954C22×C4C23×D1111yescharacteristic
955C22×C4C23×D1111yescharacteristic
956C22×C4C23×D1111yescharacteristic
957C22×C4C23×D1112yes—
958C22×C4C23×D1112yes—
959C22×C4C23×D1111yescharacteristic
960C4⋊C4—24no—
961C4⋊C4—24no—
962C4⋊C4—114no—
963C4⋊C4—114no—
964C4⋊C4—114no—
965C4⋊C4—114no—
966C4⋊C4—114no—
967C4⋊C4—224no—
968C4⋊C4—224no—
969C4⋊C4—224no—
970C4⋊C4—224no—
971C4⋊C4—224no—
972C4⋊C4—224no—
973C4⋊C4C2×C4×D1114yescomplemented
974C22⋊C4—24no—
975C22⋊C4—24no—
976C22⋊C4—24no—
977C22⋊C4—114no—
978C22⋊C4—114no—
979C22⋊C4—114no—
980C22⋊C4—114no—
981C22⋊C4—114no—
982C22⋊C4—114no—
983C22⋊C4—114no—
984C22⋊C4—114no—
985C22⋊C4—224no—
986C22⋊C4—224no—
987C22⋊C4—224no—
988C22⋊C4—224no—
989C22⋊C4—224no—
990C22⋊C4—224no—
991C22⋊C4—224no—
992C22⋊C4—224no—
993C22⋊C4—224no—
994C22⋊C4C2×C4×D1114yes—
995C22⋊C4C2×C4×D1114yescomplemented
996C42—24no—
997C42—22no—
998C42—22no—
999C42—22no—
1000C42—114no—
1001C42—114no—
1002C42—118no—
1003C42—224no—
1004C42—224no—
1005C42—224no—
1006C42—224no—
1007C42—224no—
1008C42—224no—
1009C42—224no—
1010C42—224no—
1011C42—224no—
1012C42—224no—
1013C42—222no—
1014C42—222no—
1015C42—222no—
1016C42C2×C4×D1114yescomplemented
1017C42D4×D1114yes—
1018C11C4×#52511yescharacteristic, complemented, Sylow
1019C23—21no—
1020C23—21no—
1021C23—22no—
1022C23—21no—
1023C23—22no—
1024C23—22no—
1025C23—21no—
1026C23—112no—
1027C23—112no—
1028C23—112no—
1029C23—112no—
1030C23—114no—
1031C23—112no—
1032C23—228no—
1033C23—228no—
1034C23—2216no—
1035C23—2216no—
1036C23—228no—
1037C23—221no—
1038C23—221no—
1039C23—222no—
1040C23—222no—
1041C23—222no—
1042C23—221no—
1043C23—222no—
1044C23—222no—
1045C23—221no—
1046C23C22×C4×D1112yes—
1047C23C22×C4×D1112yes—
1048C23#41×D1114yes—
1049C23C24×D1111yescharacteristic
1050Q8—228no—
1051D4—28no—
1052D4—228no—
1053D4—228no—
1054D4—228no—
1055D4—228no—
1056D4—228no—
1057D4—228no—
1058C2×C4—216no—
1059C2×C4—21no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—21no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—21no—
1069C2×C4—28no—
1070C2×C4—28no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—112no—
1078C2×C4—114no—
1079C2×C4—112no—
1080C2×C4—114no—
1081C2×C4—114no—
1082C2×C4—112no—
1083C2×C4—1116no—
1084C2×C4—112no—
1085C2×C4—112no—
1086C2×C4—112no—
1087C2×C4—112no—
1088C2×C4—114no—
1089C2×C4—228no—
1090C2×C4—2216no—
1091C2×C4—2216no—
1092C2×C4—228no—
1093C2×C4—2216no—
1094C2×C4—2216no—
1095C2×C4—228no—
1096C2×C4—2216no—
1097C2×C4—221no—
1098C2×C4—222no—
1099C2×C4—221no—
1100C2×C4—222no—
1101C2×C4—222no—
1102C2×C4—221no—
1103C2×C4—222no—
1104C2×C4—221no—
1105C2×C4—228no—
1106C2×C4—228no—
1107C2×C4—222no—
1108C2×C4—222no—
1109C2×C4—222no—
1110C2×C4—222no—
1111C2×C4—222no—
1112C2×C4—222no—
1113C2×C4—448no—
1114C2×C4—448no—
1115C2×C4C22×C4×D1112yes—
1116C2×C4C22×C4×D1112yes—
1117C2×C4C22×C4×D1112yes—
1118C2×C4C22×C4×D1112yes—
1119C2×C4C22×C4×D1112yes—
1120C2×C4C2×D4×D1114yes—
1121C2×C4C2×D4×D1112yes—
1122C2×C4#41×D1114yes—
1123C2×C4#41×D1112yes—
1124C22—24no—
1125C22—22no—
1126C22—22no—
1127C22—24no—
1128C22—22no—
1129C22—22no—
1130C22—22no—
1131C22—42no—
1132C22—42no—
1133C22—114no—
1134C22—114no—
1135C22—2232no—
1136C22—224no—
1137C22—224no—
1138C22—222no—
1139C22—222no—
1140C22—222no—
1141C22—222no—
1142C22—224no—
1143C22—224no—
1144C22—222no—
1145C22—222no—
1146C22—222no—
1147C22—442no—
1148C22—442no—
1149C22#1062305314yescomplemented
1150C22C23×C4×D1111yescharacteristic
1151C22C22×D4×D1111yescharacteristic
1152C22C2×#41×D1111yescharacteristic
1153C22C2×#41×D1112yes—
1154C22C2×#41×D1112yes—
1155C4—22no—
1156C4—22no—
1157C4—22no—
1158C4—22no—
1159C4—24no—
1160C4—24no—
1161C4—42no—
1162C4—42no—
1163C4—114no—
1164C4—118no—
1165C4—222no—
1166C4—222no—
1167C4—222no—
1168C4—222no—
1169C4—224no—
1170C4—442no—
1171C4—442no—
1172C4C4×D4×D1114yes—
1173C2—24no—
1174C2—42no—
1175C2—224no—
1176C2—224no—
1177C2—442no—
1178C2C2×C4×D4×D1111yescharacteristic
1179C2C4×#41×D1111yescharacteristic
1180C2C2×#1062305311yescharacteristic
1181C2D11×#52512yes—
1182C2#1308191012yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC11×#2290C2
socle, cosocleC23×C11C25
prime radicalC2×#10623078C2
hypercenter#2290D11
hypocenterC11C4×#525
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2290

Complements

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

NH ≅ G/Ntype
2. C2×#10623053C2semidirect
3. C22×C42×D11C2semidirect
4. #13071150C2semidirect
5. #13071148C2semidirect
6. #13071143C2semidirect
7. #13071137C2semidirect
8. #13071128C2semidirect
9. #13071126C2semidirect
10. #13071121C2semidirect
11. #13071117C2semidirect
12. #13071102C2semidirect
13. #13071096C2semidirect
14. #13071060C2semidirect
15. #13071059C2semidirect
16. #13071053C2semidirect
17. #13070997C2semidirect
18. C4×D4×Dic11C2semidirect
19. C4×#66946C2semidirect
20. C4×(C22⋊D11)⋊C4C2semidirect
21. C4×(C22⋊D11)⋊C4C2semidirect
22. #13070955C2semidirect
23. C11×#2290C2semidirect
28. C2×C11×#117C22semidirect
37. C22×C4×Dic11C22semidirect
38. #10623078C4semidirect
44. C2×#66940C22semidirect
51. C2×(C22⋊D11)⋊C4C22semidirect
57. C2×#66925C22semidirect
65. C2×C42×D11C22semidirect
66. C11×#388C22semidirect
67. C11×#387C22semidirect
70. C4×C11×C4⋊C4C22semidirect
72. C4×C11×C22⋊C4C22semidirect
73. C11×#376C22semidirect
77. C4×C22⋊Dic11C22semidirect
80. #10622591C22semidirect
81. C4⋊C4×Dic11C22semidirect
82. C4⋊C4×Dic11C22semidirect
83. #10622585C22semidirect
84. #10622570C22semidirect
88. #10622557C22semidirect
92. C22⋊C4×Dic11C22semidirect
93. C22⋊C4×Dic11C22semidirect
94. #10622553C22semidirect
97. C4×(C2×D11)⋊C4C22semidirect
98. C4×(C2×D11)⋊C4C22semidirect
99. C4×C4⋊Dic11C22semidirect
100. #10622546C22semidirect
101. #10622545C22semidirect
102. C4×Dic11⋊C4C22semidirect
103. C4×Dic11⋊C4C22semidirect
104. C42×Dic11C22semidirect
105. C42×Dic11C22semidirect
106. #10622283C22semidirect
114. #10622279C22semidirect
115. #10622279C22semidirect
119. #10622266C22semidirect
120. #10622262C22semidirect
121. #10622262C22semidirect
122. #10622262C22semidirect
123. #10622262C22semidirect
124. #10622260C22semidirect
125. #10622259C22semidirect
140. C2×#4339C2×C4semidirect
148. C22×C4×D11C2×C4semidirect
160. C4×D4×C11C2×C4semidirect
181. #66992C2×C4semidirect
182. #66990C2×C4semidirect
184. C4×C22⋊D11C2×C4semidirect
185. C4×C22⋊D11C2×C4semidirect
229. #66949C2×C4semidirect
230. #66947C2×C4semidirect
234. #66937C2×C4semidirect
235. #66936C2×C4semidirect
236. #66935C2×C4semidirect
241. #66931C2×C4semidirect
242. C4×D44C2×C4semidirect
246. #66925C2×C4semidirect
253. C42×D11D4semidirect
291. C22×C4×C11C22×C4semidirect
310. C2×C22⋊D11C22×C4semidirect
319. C22×Dic11#41semidirect
362. C2×C4×D11C22×C4semidirect
366. C2×C4×D11#41semidirect
369. C2×Dic22C22×C4semidirect
372. C11×C4⋊C4C22×C4semidirect
377. C11×C22⋊C4C22×C4semidirect
382. C42×C11C22×C4semidirect
387. C22⋊Dic11C22×C4semidirect
399. (C2×D11)⋊C4C22×C4semidirect
400. (C2×D11)⋊C4C22×C4semidirect
402. C4⋊Dic11C22×C4semidirect
408. Dic11⋊C4C22×C4semidirect
409. Dic11⋊C4C22×C4semidirect
410. Dic11⋊C4C22×C4semidirect
411. Dic11⋊C4C22×C4semidirect
425. C4×Dic11C22×C4semidirect
444. #2290D11semidirect
554. C4×D11C4×D4semidirect
585. C2×#117C2×D11semidirect
605. #388C2×D11semidirect
609. #387C2×D11semidirect
635. C4×C4⋊C4C2×D11semidirect
653. C4×C22⋊C4C2×D11semidirect
655. #376C2×D11semidirect
667. C22×C11C4×#41semidirect
688. C2×D11C4×#41semidirect
706. Dic11#525semidirect
760. C4×D4C4×D11semidirect
950. C22×C4C2×C4×D11semidirect
973. C4⋊C4C2×C4×D11semidirect
995. C22⋊C4C2×C4×D11semidirect
1016. C42C2×C4×D11semidirect
1018. C11C4×#525semidirect
1149. C22#10623053semidirect

Maximal subgroups

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

subgroupindex
C2×#106230782
C2×#106230532
C22×C42×D112
#130711502
#130711482
#130711432
#130711372
#130711282
#130711262
#130711212
#130711172
#130711022
#130710962
#130710602
#130710592
#130710532
#130709972
C4×D4×Dic112
C4×#669462
C4×(C22⋊D11)⋊C42
#130709552
C11×#22902
C4×#52511