Finite Group Databasebeta

← #14925909

Subgroups — #14925909

Order 2816.

3206 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623117C211yesmaximal, characteristic, complemented
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
3#13074231C212yesmaximal, complemented
4#13074223C212yesmaximal, complemented
5#13074095C211yesmaximal, characteristic, complemented
6#13073995C211yesmaximal, characteristic, complemented
7#13073794C212yesmaximal, complemented
8#13073773C211yesmaximal, characteristic, complemented
9#13073580C212yesmaximal, complemented
10#13073546C211yesmaximal, characteristic, complemented
11#13072012C211yesmaximal, characteristic, complemented
12#13071991C211yesmaximal, characteristic, complemented
13#13071984C211yesmaximal, characteristic, complemented
14#13071874C212yesmaximal, complemented
15#13071830C212yesmaximal, complemented
16#123×Dic11C211yesmaximal, characteristic, complemented
17#13071133C211yesmaximal, characteristic, complemented
18#13071126C212yesmaximal, complemented
19#13071122C212yesmaximal, complemented
20#13071121C211yesmaximal, characteristic, complemented
21#13071117C211yesmaximal, characteristic, complemented
22C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
23C11×#2412C211yesmaximal, characteristic, complemented
24C23×C22⋊D11C2211yescharacteristic
25C24×Dic11C2211yescharacteristic
26C22×#4341C2211yescharacteristic, complemented
27C23×C4×D11C2211yescharacteristic
28C2×C11×#123C2211yescharacteristic
29C2×C11×#120C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C11×C22⋊C4C2211yescharacteristic
32C2×#67006C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C2×#66992C2212yes—
35C2×#66992C2211yescharacteristic
36C2×#66992C2211yescharacteristic, complemented
37C2×#66990C2211yescharacteristic
38C2×#66988C2211yescharacteristic, complemented
39C2×D4×Dic11C2211yescharacteristic
40C2×D4×Dic11C2211yescharacteristic, complemented
41C2×#66983C2212yes—
42C2×#66982C2211yescharacteristic
43C22×(C2×D11)⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C22×C4×Dic11C2212yescomplemented
47#10623117—28no—
48C2×#66946C2212yescomplemented
49C2×#66939C2211yescharacteristic, complemented
50C2×#66935C2211yescharacteristic
51C2×(C22⋊D11)⋊C4—28no—
52C2×(C22⋊D11)⋊C4C2212yes—
53C2×(C22⋊D11)⋊C4C2211yescharacteristic
54C2×(C22⋊D11)⋊C4C2212yes—
55C2×(C22⋊D11)⋊C4C2212yes—
56C2×(C22⋊D11)⋊C4C2212yes—
57C2×(C22⋊D11)⋊C4C2211yescharacteristic, complemented
58C2×(C22⋊D11)⋊C4C2212yescomplemented
59C2×#66931C2211yescharacteristic
60C2×#66931C2211yescharacteristic, complemented
61C2×#66930C2211yescharacteristic, complemented
62C11×#397C2212yescomplemented
63C11×#394C2212yescomplemented
64C11×#386C2211yescharacteristic
65C11×#386C2212yescomplemented
66C11×#385C2211yescharacteristic
67C11×#381C2211yescharacteristic
68C11×#380C2212yescomplemented
69#10622836C2212yes—
70#10622833C2211yescharacteristic
71#10622826C2211yescharacteristic
72#10622826C2212yes—
73#10622824C2211yescharacteristic
74#10622823C2211yescharacteristic
75C2×C11⋊#95C2212yescomplemented
76#10622605C2212yescomplemented
77#10622602C2212yescomplemented
78#10622601C2212yescomplemented
79#10622594C2212yescomplemented
80#10622592C2212yescomplemented
81C4⋊C4×Dic11C2212yescomplemented
82#10622586C2212yescomplemented
83#10622574C2212yes—
84#10622573C2212yes—
85#10622573C2212yescomplemented
86#10622572C2212yes—
87#10622572C2212yescomplemented
88#10622572C2212yescomplemented
89#10622571C2212yes—
90#10622571C2211yescharacteristic
91#10622571C2212yescomplemented
92#10622570C2212yescomplemented
93#10622569C2212yescomplemented
94#10622568C2211yescharacteristic
95#10622568C2211yescharacteristic
96#10622565C2212yescomplemented
97#10622564C2212yescomplemented
98#10622563C2211yescharacteristic
99#10622559C2211yescharacteristic
100#10622557C2212yescomplemented
101#10622555C2212yescomplemented
102C22⋊C4×Dic11C2211yescharacteristic
103C22⋊C4×Dic11C2211yescharacteristic
104C22⋊C4×Dic11C2211yescharacteristic
105C22⋊C4×Dic11C2211yescharacteristic
106C22⋊C4×Dic11C2212yescomplemented
107C22⋊C4×Dic11C2212yescomplemented
108C22⋊C4×Dic11C2212yescomplemented
109#10622288C2212yescomplemented
110#10622286C2212yescomplemented
111#10622283C2212yescomplemented
112#10622282C2212yescomplemented
113#10622282C2212yescomplemented
114#10622282C2212yescomplemented
115#10622281C2212yescomplemented
116#10622279C2212yescomplemented
117#10622279C2212yescomplemented
118#10622279C2212yescomplemented
119#10622278C2212yescomplemented
120#10622271C2212yescomplemented
121#10622270C2212yescomplemented
122#10622265C2212yescomplemented
123#10622262C2212yescomplemented
124#10622260C2212yescomplemented
125C25×C11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C22×D4×C11C2311yescharacteristic
129C22×D4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C23×C4×C11C2312yes—
132C23×C4×C11C2311yescharacteristic
133C22×C22⋊D11—24no—
134C22×C22⋊D11—28no—
135C22×C22⋊D11C2312yes—
136C22×C22⋊D11C2311yescharacteristic
137C22×C22⋊D11C2311yescharacteristic
138C22×C22⋊D11C2312yes—
139C22×C22⋊D11C2312yes—
140C22×C22⋊D11C2311yescharacteristic
141C22×C22⋊D11C2311yescharacteristic
142C23×Dic11—44no—
143C23×Dic11D418yescomplemented
144C23×Dic11C2311yescharacteristic
145C23×Dic11C2311yescharacteristic
146C23×Dic11C2312yes—
147C23×Dic11C2311yescharacteristic
148C23×Dic11C2311yescharacteristic
149C23×Dic11C2311yescharacteristic
150C23×Dic11C2311yescharacteristic
151C23×Dic11C2311yescharacteristic
152C23×Dic11C2311yescharacteristic
153C2×#4341—24no—
154C2×#4341—44no—
155C22×D44C2312yes—
156C22×C4×D11—24no—
157C22×C4×D11—44no—
158C22×C4×D11C2312yes—
159C22×C4×D11C2311yescharacteristic
160C22×C4×D11C2312yes—
161C22×Dic22C2311yescharacteristic
162C11×#123—24no—
163C11×#120—24no—
164C2×C11×C4⋊C4C2312yes—
165C2×C11×C4⋊C4C2312yes—
166C2×C11×C22⋊C4—24no—
167C2×C11×C22⋊C4—24no—
168C2×C11×C22⋊C4C2311yescharacteristic
169C2×C11×C22⋊C4C2311yescharacteristic
170C2×C11×C22⋊C4C2311yescharacteristic
171C2×C11×C22⋊C4C2312yes—
172C2×C11×C22⋊C4C2312yes—
173C2×C11×C22⋊C4C2311yescharacteristic
174C2×C11×C22⋊C4C2312yes—
175C2×C11×C22⋊C4C2312yes—
176C2×C11×C22⋊C4C2312yes—
177C2×C11×C22⋊C4C2311yescharacteristic
178#67006—24no—
179C2×C22⋊Dic11—24no—
180C2×C22⋊Dic11C2311yescharacteristic
181C2×C22⋊Dic11C2311yescharacteristic
182C2×C22⋊Dic11C2311yescharacteristic
183C2×C22⋊Dic11C2311yescharacteristic
184C2×C22⋊Dic11C2312yes—
185C2×C22⋊Dic11C2312yes—
186C2×C22⋊Dic11C2311yescharacteristic
187C2×C22⋊Dic11C2311yescharacteristic
188C2×C22⋊Dic11C2311yescharacteristic
189#66992—28no—
190#66992—24no—
191#66992—24no—
192#66990—24no—
193#66988—24no—
194D4×Dic11—24no—
195D4×Dic11—24no—
196#66983—28no—
197#66982—24no—
198C2×(C2×D11)⋊C4—24no—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2311yescharacteristic
202C2×(C2×D11)⋊C4C2311yescharacteristic
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2312yes—
208C2×(C2×D11)⋊C4C2312yes—
209C2×(C2×D11)⋊C4C2312yes—
210C2×(C2×D11)⋊C4C2312yes—
211C2×(C2×D11)⋊C4C2312yes—
212C2×C4⋊Dic11C2311yescharacteristic
213C2×C4⋊Dic11C2311yescharacteristic
214C2×C4⋊Dic11C2312yes—
215C2×Dic11⋊C4—24no—
216C2×Dic11⋊C4C2311yescharacteristic
217C2×Dic11⋊C4C2311yescharacteristic
218C2×Dic11⋊C4C2311yescharacteristic
219C2×Dic11⋊C4C2311yescharacteristic
220C2×Dic11⋊C4C2312yes—
221C2×Dic11⋊C4C2312yes—
222C2×Dic11⋊C4C2312yes—
223C2×Dic11⋊C4C2312yes—
224C2×Dic11⋊C4C2312yes—
225C2×C4×Dic11—24no—
226C2×C4×Dic11—44no—
227C2×C4×Dic11C2311yescharacteristic
228C2×C4×Dic11C2311yescharacteristic
229C2×C4×Dic11C2312yes—
230C2×C4×Dic11C2312yes—
231C2×C4×Dic11C2312yes—
232C2×C4×Dic11C2312yes—
233C2×C4×Dic11C2312yes—
234C2×C4×Dic11C2312yes—
235#66946—44no—
236#66939—24no—
237#66935—24no—
238(C22⋊D11)⋊C4—28no—
239(C22⋊D11)⋊C4—28no—
240(C22⋊D11)⋊C4—28no—
241(C22⋊D11)⋊C4—28no—
242(C22⋊D11)⋊C4—24no—
243(C22⋊D11)⋊C4—24no—
244(C22⋊D11)⋊C4—44no—
245#66931—24no—
246#66931—24no—
247#66930—24no—
248C11×#95C2312yes—
249C11×#95C2312yes—
250C11×#95C2312yes—
251C11×#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264#34957—111nomaximal, Sylow
265C24×C11—22no—
266C24×C11—22no—
267C24×C11—24no—
268C24×C11—42no—
269C24×C11C2×D414yes—
270C24×C11C2411yescharacteristic
271C24×C11C2411yescharacteristic
272C24×C11C2411yescharacteristic
273C24×C11C2411yescharacteristic
274C23×D11—22no—
275C23×D11—24no—
276C23×D11—22no—
277C23×D11—22no—
278C23×D11—42no—
279C23×D11C2411yescharacteristic
280C23×D11C2412yes—
281C2×D4×C11—22no—
282C2×D4×C11—22no—
283C2×D4×C11—22no—
284C2×D4×C11—22no—
285C2×D4×C11—24no—
286C2×D4×C11—22no—
287C2×D4×C11—42no—
288C22×C4×C11—22no—
289C22×C4×C11—22no—
290C22×C4×C11—22no—
291C22×C4×C11—24no—
292C22×C4×C11—22no—
293C22×C4×C11—24no—
294C22×C4×C11—42no—
295C22×C4×C11—42no—
296C22×C4×C11C2412yes—
297C22×C4×C11C2412yes—
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2412yes—
300C22×C4×C11C2411yescharacteristic
301C22×C4×C11C2411yescharacteristic
302C22×C4×C11C2412yes—
303C2×C22⋊D11—232no—
304C2×C22⋊D11—22no—
305C2×C22⋊D11—24no—
306C2×C22⋊D11—24no—
307C2×C22⋊D11—24no—
308C2×C22⋊D11—24no—
309C2×C22⋊D11—22no—
310C2×C22⋊D11—22no—
311C2×C22⋊D11—22no—
312C2×C22⋊D11—24no—
313C2×C22⋊D11—22no—
314C2×C22⋊D11—22no—
315C2×C22⋊D11—24no—
316C2×C22⋊D11—24no—
317C2×C22⋊D11—24no—
318C2×C22⋊D11—42no—
319C2×C22⋊D11—42no—
320C2×C22⋊D11—42no—
321C2×C22⋊D11#4118yescomplemented
322C22×Dic11—24no—
323C22×Dic11—24no—
324C22×Dic11—24no—
325C22×Dic11—24no—
326C22×Dic11—22no—
327C22×Dic11—24no—
328C22×Dic11—24no—
329C22×Dic11—22no—
330C22×Dic11—24no—
331C22×Dic11—42no—
332C22×Dic11—42no—
333C22×Dic11—42no—
334C22×Dic11—42no—
335C22×Dic11—416no—
336C22×Dic11C2×D414yes—
337C22×Dic11C2×D414yes—
338C22×Dic11C2×D414yes—
339C22×Dic11C2×D414yes—
340C22×Dic11C2×D414yes—
341C22×Dic11C2×D414yes—
342C22×Dic11C2412yes—
343C22×Dic11C2411yescharacteristic
344C22×Dic11C2411yescharacteristic
345C22×Dic11C2411yescharacteristic
346C22×Dic11C2411yescharacteristic
347C22×Dic11C2411yescharacteristic
348C22×Dic11C2411yescharacteristic
349C22×Dic11C2412yes—
350C22×Dic11C2412yes—
351C22×Dic11C2411yescharacteristic
352#4341—416no—
353C2×D44—24no—
354C2×D44—24no—
355C2×D44—42no—
356C2×C4×D11—24no—
357C2×C4×D11—24no—
358C2×C4×D11—22no—
359C2×C4×D11—24no—
360C2×C4×D11—24no—
361C2×C4×D11—24no—
362C2×C4×D11—42no—
363C2×C4×D11—42no—
364C2×C4×D11—416no—
365C2×Dic22—22no—
366C2×Dic22—42no—
367C11×C4⋊C4—24no—
368C11×C4⋊C4—42no—
369C11×C22⋊C4—22no—
370C11×C22⋊C4—22no—
371C11×C22⋊C4—22no—
372C11×C22⋊C4—24no—
373C11×C22⋊C4—24no—
374C11×C22⋊C4—22no—
375C11×C22⋊C4—24no—
376C11×C22⋊C4—24no—
377C11×C22⋊C4—42no—
378C11×C22⋊C4#4114yescomplemented
379C22⋊Dic11—22no—
380C22⋊Dic11—22no—
381C22⋊Dic11—24no—
382C22⋊Dic11—24no—
383C22⋊Dic11—22no—
384C22⋊Dic11—22no—
385C22⋊Dic11—22no—
386C22⋊Dic11—22no—
387C22⋊Dic11#4114yescomplemented
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—24no—
390(C2×D11)⋊C4—22no—
391(C2×D11)⋊C4—22no—
392(C2×D11)⋊C4—24no—
393(C2×D11)⋊C4—24no—
394(C2×D11)⋊C4—24no—
395(C2×D11)⋊C4—24no—
396(C2×D11)⋊C4—24no—
397(C2×D11)⋊C4—24no—
398(C2×D11)⋊C4—42no—
399(C2×D11)⋊C4—42no—
400(C2×D11)⋊C4—42no—
401C4⋊Dic11—22no—
402C4⋊Dic11—22no—
403C4⋊Dic11—24no—
404Dic11⋊C4—22no—
405Dic11⋊C4—22no—
406Dic11⋊C4—22no—
407Dic11⋊C4—22no—
408Dic11⋊C4—24no—
409Dic11⋊C4—24no—
410Dic11⋊C4—24no—
411Dic11⋊C4—24no—
412Dic11⋊C4—42no—
413C4×Dic11—22no—
414C4×Dic11—22no—
415C4×Dic11—24no—
416C4×Dic11—24no—
417C4×Dic11—24no—
418C4×Dic11—24no—
419C4×Dic11—42no—
420C4×Dic11—42no—
421C2×#525—111no—
422C22×C4×D4—111no—
423#2602—112no—
424#2602—112no—
425#2591—111no—
426#2583—111no—
427#2564—112no—
428#2561—111no—
429#2543—112no—
430#2539—111no—
431#2412—111no—
432#2412D1111yescharacteristic, complemented
433#2410—111no—
434#2410—111no—
435#2395—112no—
436#2388—112no—
437C4×#123—111no—
438C4×#123—111no—
439C4×#121—112no—
440C4×#121—112no—
441C4×#120—111no—
442C4×#120—111no—
443C2×C4×C22⋊C4—111no—
444C23×C11—21no—
445C23×C11—22no—
446C23×C11—21no—
447C23×C11—22no—
448C23×C11—22no—
449C23×C11—28no—
450C23×C11—28no—
451C23×C11—21no—
452C23×C11—21no—
453C23×C11—22no—
454C23×C11—22no—
455C23×C11—21no—
456C23×C11—22no—
457C23×C11—21no—
458C23×C11—21no—
459C23×C11—22no—
460C23×C11—44no—
461C23×C11—48no—
462C23×C11—48no—
463C23×C11C22×D412yes—
464C23×C11C22×D412yes—
465C23×C11C22×D412yes—
466C23×C11C2×#4112yes—
467C23×C11C2×#4114yes—
468C23×C11C2×#4112yes—
469C23×C11C2511yescharacteristic
470C22×D11—28no—
471C22×D11—22no—
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—22no—
475C22×D11—22no—
476C22×D11—22no—
477C22×D11—21no—
478C22×D11—21no—
479C22×D11—22no—
480C22×D11—21no—
481C22×D11—22no—
482C22×D11—48no—
483C22×D11—48no—
484C22×D11—44no—
485C22×D11—44no—
486C22×D11C2×#4114yes—
487D4×C11—44no—
488D4×C11—44no—
489D4×C11—44no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—21no—
494C2×C4×C11—21no—
495C2×C4×C11—21no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—21no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—21no—
504C2×C4×C11—22no—
505C2×C4×C11—22no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11—48no—
509C2×C4×C11—44no—
510C2×C4×C11—44no—
511C2×C4×C11C2×#4114yes—
512C22⋊D11—216no—
513C22⋊D11—216no—
514C22⋊D11—48no—
515C22⋊D11—44no—
516C22⋊D11—44no—
517C22⋊D11—44no—
518C22⋊D11—44no—
519C2×Dic11—28no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—28no—
528C2×Dic11—28no—
529C2×Dic11—28no—
530C2×Dic11—21no—
531C2×Dic11—21no—
532C2×Dic11—21no—
533C2×Dic11—21no—
534C2×Dic11—22no—
535C2×Dic11—21no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—22no—
539C2×Dic11—22no—
540C2×Dic11—44no—
541C2×Dic11—44no—
542C2×Dic11—44no—
543C2×Dic11—48no—
544C2×Dic11—44no—
545C2×Dic11C22×D412yes—
546C2×Dic11C22×D412yes—
547C2×Dic11C22×D412yes—
548C2×Dic11C22×D412yes—
549C2×Dic11C2×#4114yes—
550C2×Dic11C2×#4114yes—
551C2×Dic11H(5,𝔽2)14yes—
552D44—48no—
553C4×D11—48no—
554C4×D11—48no—
555C4×D11—44no—
556Dic22—44no—
557C22×#41—111no—
558C23×D4—111no—
559C24×C4—111no—
560C24×C4—111no—
561#525—228no—
562C2×#123—111no—
563C2×#123—111no—
564C2×#123—111no—
565C2×#123C2×D1111yescharacteristic
566C2×C22⋊Q8—111no—
567C2×C22⋊Q8—111no—
568C2×#121—111no—
569C2×#121—112no—
570C2×#121—111no—
571C2×#121—112no—
572C2×#120—111no—
573C2×#120—111no—
574C2×#120—111no—
575C2×#120C2×D1111yescharacteristic
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—112no—
583C2×C4×D4—111no—
584C2×C4×D4—111no—
585C2×C4×D4—112no—
586C2×C4×D4—228no—
587C2×#117—111no—
588C22×C4⋊C4—111no—
589C22×C22⋊C4—111no—
590C22×C22⋊C4—111no—
591C22×C22⋊C4C2×D1111yescharacteristic
592C22×C22⋊C4C2×D1111yescharacteristic
593C22×C42—111no—
594C22×C42—112no—
595#400—112no—
596#399—112no—
597#398—112no—
598#397—112no—
599#397—112no—
600#397C2×D1112yescomplemented
601#395—112no—
602#394—112no—
603#394—112no—
604#394—112no—
605#394—112no—
606#394C2×D1112yescomplemented
607#393—112no—
608#392—112no—
609#392—112no—
610#392—112no—
611#390—112no—
612#390—112no—
613#389—112no—
614#389—112no—
615#388—112no—
616#388—112no—
617#388—112no—
618#388—112no—
619#388—112no—
620#388—112no—
621#387—112no—
622#387—112no—
623#386—111no—
624#386—112no—
625#386—111no—
626#386—112no—
627#386—111no—
628#386—112no—
629#386—112no—
630#386—112no—
631#386C2×D1111yescharacteristic
632#386C2×D1112yescomplemented
633#385—111no—
634#385—112no—
635#385—111no—
636#385—111no—
637#385—112no—
638#385C2×D1111yescharacteristic
639#381—111no—
640#381C2×D1111yescharacteristic
641#380—112no—
642#380C2×D1112yescomplemented
643#379—111no—
644#379—111no—
645C4×C4⋊C4—112no—
646C4×C4⋊C4—112no—
647C4×C22⋊C4—111no—
648C4×C22⋊C4—111no—
649C4×C22⋊C4—112no—
650C4×C22⋊C4—112no—
651C4×C22⋊C4—112no—
652C4×C22⋊C4—111no—
653C4×C22⋊C4—111no—
654C4×C22⋊C4—112no—
655C4×C22⋊C4—112no—
656C4×C22⋊C4—112no—
657C2×#95—112no—
658C22×C11—22no—
659C22×C11—22no—
660C22×C11—22no—
661C22×C11—22no—
662C22×C11—24no—
663C22×C11—24no—
664C22×C11—24no—
665C22×C11—24no—
666C22×C11—22no—
667C22×C11—22no—
668C22×C11—22no—
669C22×C11—416no—
670C22×C11—42no—
671C22×C11—42no—
672C22×C11—41no—
673C22×C11—41no—
674C22×C11—41no—
675C22×C11—42no—
676C22×C11—42no—
677C22×C11#52514yes—
678C22×C11#53214yes—
679C22×C11C23×D411yescharacteristic
680C22×C11C22×#4111yescharacteristic
681C22×C11C22×#4112yes—
682C22×C11C22×#4111yescharacteristic
683C22×C11C2×H(5,𝔽2)12yes—
684C2×D11—24no—
685C2×D11—24no—
686C2×D11—24no—
687C2×D11—416no—
688C2×D11—42no—
689C2×D11—42no—
690C2×D11—42no—
691C2×D11—42no—
692C2×D11—41no—
693C2×D11—41no—
694C2×D11—41no—
695C2×D11—42no—
696C2×D11—42no—
697C4×C11—24no—
698C4×C11—41no—
699C4×C11—42no—
700C4×C11—41no—
701C4×C11—42no—
702C4×C11—41no—
703C4×C11—42no—
704Dic11—24no—
705Dic11—22no—
706Dic11—22no—
707Dic11—22no—
708Dic11—24no—
709Dic11—41no—
710Dic11—41no—
711Dic11—41no—
712Dic11—42no—
713Dic11#53414yes—
714C25—111no—
715C25C22×D1111yescharacteristic
716C2×#41—224no—
717C2×#41—444no—
718C22×Q8—111no—
719C22×D4—112no—
720C22×D4—112no—
721C22×D4—111no—
722C22×D4—111no—
723C22×D4—112no—
724C22×D4—111no—
725C22×D4—111no—
726C22×D4—112no—
727C22×D4—228no—
728C22×D4—224no—
729C22×D4C22×D1111yescharacteristic
730C22×D4C22×D1111yescharacteristic
731C22×D4C22×D1111yescharacteristic
732C23×C4—111no—
733C23×C4—111no—
734C23×C4—111no—
735C23×C4—118no—
736C23×C4—111no—
737C23×C4—111no—
738C23×C4—111no—
739C23×C4—111no—
740C23×C4—111no—
741C23×C4—112no—
742C23×C4—112no—
743C23×C4—111no—
744C23×C4—112no—
745C23×C4—224no—
746C23×C4—444no—
747C23×C4—444no—
748C23×C4C22×D1111yescharacteristic
749C23×C4C22×D1112yes—
750C23×C4C22×D1111yescharacteristic
751#123—24no—
752#123—224no—
753#123—224no—
754#123—224no—
755C22⋊Q8—224no—
756C22⋊Q8—224no—
757#121—228no—
758#121—224no—
759#121—224no—
760#121—228no—
761#120—24no—
762#120—224no—
763#120—224no—
764#120—224no—
765C4×D4—228no—
766C4×D4—228no—
767C4×D4—228no—
768C4×D4—228no—
769C4×D4—224no—
770C4×D4—224no—
771C4×D4—224no—
772C4×D4—224no—
773C4×D4—444no—
774C4×D4—444no—
775#117—224no—
776C2×C4⋊C4—112no—
777C2×C4⋊C4—112no—
778C2×C4⋊C4—111no—
779C2×C4⋊C4—111no—
780C2×C4⋊C4—111no—
781C2×C4⋊C4—111no—
782C2×C4⋊C4—111no—
783C2×C4⋊C4—111no—
784C2×C4⋊C4—112no—
785C2×C4⋊C4—112no—
786C2×C4⋊C4—112no—
787C2×C4⋊C4—112no—
788C2×C4⋊C4—224no—
789C2×C4⋊C4C22×D1112yes—
790C2×C4⋊C4C22×D1112yes—
791C2×C22⋊C4—24no—
792C2×C22⋊C4—24no—
793C2×C22⋊C4—111no—
794C2×C22⋊C4—111no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—111no—
797C2×C22⋊C4—111no—
798C2×C22⋊C4—111no—
799C2×C22⋊C4—111no—
800C2×C22⋊C4—111no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—111no—
805C2×C22⋊C4—111no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—112no—
811C2×C22⋊C4—112no—
812C2×C22⋊C4—112no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—112no—
815C2×C22⋊C4—224no—
816C2×C22⋊C4—224no—
817C2×C22⋊C4C22×D1112yes—
818C2×C22⋊C4C22×D1112yes—
819C2×C22⋊C4C22×D1111yescharacteristic
820C2×C22⋊C4C22×D1112yes—
821C2×C22⋊C4C22×D1111yescharacteristic
822C2×C22⋊C4C22×D1111yescharacteristic
823C2×C22⋊C4C22×D1111yescharacteristic
824C2×C22⋊C4C22×D1112yes—
825C2×C22⋊C4C22×D1112yes—
826C2×C22⋊C4C22×D1111yescharacteristic
827C2×C42—111no—
828C2×C42—111no—
829C2×C42—112no—
830C2×C42—112no—
831C2×C42—112no—
832C2×C42—112no—
833C2×C42—112no—
834C2×C42—112no—
835C2×C42—224no—
836C2×C42—444no—
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#95—112no—
847#95—112no—
848#95—112no—
849#95C22×D1112yes—
850#95C22×D1112yes—
851#95C22×D1112yes—
852#95C22×D1112yes—
853C2×C11—24no—
854C2×C11—24no—
855C2×C11—42no—
856C2×C11—81no—
857C2×C11C2×#52511yescharacteristic
858C2×C11C2×#53211yescharacteristic
859C2×C11C2×#53411yescharacteristic
860C2×C11#348112yes—
861C2×C11#348112yes—
862D11—44no—
863D11—81no—
864C24—22no—
865C24—22no—
866C24—24no—
867C24—42no—
868C24—112no—
869C24—111no—
870C24—224no—
871C24—222no—
872C24—222no—
873C24—222no—
874C24—442no—
875C24D4×D1114yes—
876C24C23×D1111yescharacteristic
877C24C23×D1111yescharacteristic
878C24C23×D1111yescharacteristic
879C24C23×D1111yescharacteristic
880#41—4416no—
881C2×Q8—222no—
882C2×Q8—442no—
883C2×D4—22no—
884C2×D4—22no—
885C2×D4—22no—
886C2×D4—22no—
887C2×D4—22no—
888C2×D4—24no—
889C2×D4—42no—
890C2×D4—118no—
891C2×D4—224no—
892C2×D4—224no—
893C2×D4—224no—
894C2×D4—222no—
895C2×D4—224no—
896C2×D4—2232no—
897C2×D4—224no—
898C2×D4—224no—
899C2×D4—224no—
900C2×D4—224no—
901C2×D4—222no—
902C2×D4—222no—
903C2×D4—222no—
904C2×D4—222no—
905C2×D4—224no—
906C2×D4—222no—
907C2×D4—224no—
908C2×D4—442no—
909C2×D4—442no—
910C2×D4—442no—
911C2×D4—442no—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—22no—
915C22×C4—24no—
916C22×C4—22no—
917C22×C4—24no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—111no—
921C22×C4—114no—
922C22×C4—114no—
923C22×C4—114no—
924C22×C4—112no—
925C22×C4—112no—
926C22×C4—111no—
927C22×C4—111no—
928C22×C4—111no—
929C22×C4—114no—
930C22×C4—114no—
931C22×C4—114no—
932C22×C4—112no—
933C22×C4—111no—
934C22×C4—111no—
935C22×C4—111no—
936C22×C4—224no—
937C22×C4—224no—
938C22×C4—222no—
939C22×C4—224no—
940C22×C4—224no—
941C22×C4—224no—
942C22×C4—224no—
943C22×C4—224no—
944C22×C4—224no—
945C22×C4—224no—
946C22×C4—224no—
947C22×C4—222no—
948C22×C4—224no—
949C22×C4—222no—
950C22×C4—224no—
951C22×C4—442no—
952C22×C4—442no—
953C22×C4—4416no—
954C22×C4—4416no—
955C22×C4—442no—
956C22×C4—442no—
957C22×C4—442no—
958C22×C4—442no—
959C22×C4C23×D1112yes—
960C22×C4C23×D1112yes—
961C22×C4C23×D1111yescharacteristic
962C22×C4C23×D1111yescharacteristic
963C22×C4C23×D1112yes—
964C22×C4C23×D1111yescharacteristic
965C22×C4C23×D1112yes—
966C4⋊C4—24no—
967C4⋊C4—42no—
968C4⋊C4—224no—
969C4⋊C4—224no—
970C4⋊C4—222no—
971C4⋊C4—222no—
972C4⋊C4—222no—
973C4⋊C4—222no—
974C4⋊C4—222no—
975C4⋊C4—222no—
976C4⋊C4—224no—
977C4⋊C4—224no—
978C4⋊C4—224no—
979C4⋊C4—442no—
980C22⋊C4—24no—
981C22⋊C4—24no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4—24no—
987C22⋊C4—24no—
988C22⋊C4—42no—
989C22⋊C4—114no—
990C22⋊C4—224no—
991C22⋊C4—224no—
992C22⋊C4—222no—
993C22⋊C4—222no—
994C22⋊C4—224no—
995C22⋊C4—224no—
996C22⋊C4—224no—
997C22⋊C4—224no—
998C22⋊C4—224no—
999C22⋊C4—224no—
1000C22⋊C4—222no—
1001C22⋊C4—222no—
1002C22⋊C4—224no—
1003C22⋊C4—222no—
1004C22⋊C4—222no—
1005C22⋊C4—222no—
1006C22⋊C4—222no—
1007C22⋊C4—224no—
1008C22⋊C4—442no—
1009C22⋊C4—442no—
1010C22⋊C4—442no—
1011C22⋊C4#434114yescomplemented
1012C42—224no—
1013C42—224no—
1014C42—224no—
1015C42—224no—
1016C42—222no—
1017C42—222no—
1018C42—442no—
1019C42—442no—
1020C11#3495711yescharacteristic, complemented, Sylow
1021C23—21no—
1022C23—21no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—28no—
1027C23—28no—
1028C23—21no—
1029C23—21no—
1030C23—22no—
1031C23—22no—
1032C23—21no—
1033C23—21no—
1034C23—22no—
1035C23—21no—
1036C23—22no—
1037C23—44no—
1038C23—48no—
1039C23—48no—
1040C23—114no—
1041C23—228no—
1042C23—222no—
1043C23—222no—
1044C23—222no—
1045C23—222no—
1046C23—222no—
1047C23—222no—
1048C23—221no—
1049C23—221no—
1050C23—221no—
1051C23—222no—
1052C23—222no—
1053C23—448no—
1054C23—448no—
1055C23—444no—
1056C23—444no—
1057C23C2×D4×D1112yes—
1058C23C2×D4×D1112yes—
1059C23C2×D4×D1112yes—
1060C23C2×#434112yes—
1061C23#41×D1112yes—
1062C23#41×D1114yes—
1063C23C24×D1111yescharacteristic
1064Q8—444no—
1065D4—44no—
1066D4—44no—
1067D4—44no—
1068D4—2216no—
1069D4—2216no—
1070D4—448no—
1071D4—448no—
1072D4—444no—
1073D4—444no—
1074D4—444no—
1075D4—444no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—22no—
1082C2×C4—21no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—21no—
1086C2×C4—22no—
1087C2×C4—21no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—48no—
1095C2×C4—44no—
1096C2×C4—44no—
1097C2×C4—112no—
1098C2×C4—114no—
1099C2×C4—112no—
1100C2×C4—112no—
1101C2×C4—112no—
1102C2×C4—114no—
1103C2×C4—114no—
1104C2×C4—228no—
1105C2×C4—228no—
1106C2×C4—228no—
1107C2×C4—228no—
1108C2×C4—222no—
1109C2×C4—222no—
1110C2×C4—222no—
1111C2×C4—222no—
1112C2×C4—222no—
1113C2×C4—222no—
1114C2×C4—222no—
1115C2×C4—221no—
1116C2×C4—221no—
1117C2×C4—221no—
1118C2×C4—221no—
1119C2×C4—222no—
1120C2×C4—222no—
1121C2×C4—222no—
1122C2×C4—221no—
1123C2×C4—222no—
1124C2×C4—222no—
1125C2×C4—448no—
1126C2×C4—444no—
1127C2×C4—448no—
1128C2×C4—444no—
1129C2×C4—444no—
1130C2×C4—444no—
1131C2×C4—444no—
1132C2×C4—448no—
1133C2×C4C2×#434114yes—
1134C22—22no—
1135C22—22no—
1136C22—22no—
1137C22—24no—
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—22no—
1142C22—22no—
1143C22—22no—
1144C22—22no—
1145C22—416no—
1146C22—42no—
1147C22—42no—
1148C22—41no—
1149C22—41no—
1150C22—42no—
1151C22—42no—
1152C22—41no—
1153C22—224no—
1154C22—224no—
1155C22—224no—
1156C22—4416no—
1157C22—442no—
1158C22—442no—
1159C22—442no—
1160C22—442no—
1161C22—441no—
1162C22—441no—
1163C22—442no—
1164C22—442no—
1165C22—441no—
1166C22#1062312714yes—
1167C22#1062318714yes—
1168C22C22×D4×D1111yescharacteristic
1169C22C22×#434111yescharacteristic
1170C22C2×#41×D1111yescharacteristic
1171C22C2×#41×D1112yes—
1172C22D11×H(5,𝔽2)12yes—
1173C4—24no—
1174C4—42no—
1175C4—41no—
1176C4—42no—
1177C4—41no—
1178C4—42no—
1179C4—41no—
1180C4—114no—
1181C4—222no—
1182C4—222no—
1183C4—222no—
1184C4—224no—
1185C4—224no—
1186C4—441no—
1187C4—441no—
1188C4—442no—
1189C4—441no—
1190C2—24no—
1191C2—24no—
1192C2—42no—
1193C2—81no—
1194C2—444no—
1195C2—881no—
1196C2C2×#1062318711yescharacteristic
1197C2C2×#1062312711yescharacteristic
1198C2D11×#53411yescharacteristic
1199C2#1308221912yes—
1200C2#1308222112yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2412C2
hypercenter#2412D11
hypocenterC11#34957
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2412

Complements

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

NH ≅ G/Ntype
1. C2×#10623117C2semidirect
2. C22×(C22⋊D11)⋊C4C2semidirect
3. #13074231C2semidirect
4. #13074223C2semidirect
5. #13074095C2semidirect
6. #13073995C2semidirect
7. #13073794C2semidirect
8. #13073773C2semidirect
9. #13073580C2semidirect
10. #13073546C2semidirect
11. #13072012C2semidirect
12. #13071991C2semidirect
13. #13071984C2semidirect
14. #13071874C2semidirect
15. #13071830C2semidirect
16. #123×Dic11C2semidirect
17. #13071133C2semidirect
18. #13071126C2semidirect
19. #13071122C2semidirect
20. #13071121C2semidirect
21. #13071117C2semidirect
22. C2×C22⋊C4×Dic11C2semidirect
23. C11×#2412C2semidirect
26. C22×#4341C22semidirect
36. C2×#66992C22semidirect
38. C2×#66988C22semidirect
40. C2×D4×Dic11C22semidirect
46. C22×C4×Dic11C22semidirect
48. C2×#66946C22semidirect
49. C2×#66939C22semidirect
57. C2×(C22⋊D11)⋊C4C22semidirect
58. C2×(C22⋊D11)⋊C4C22semidirect
60. C2×#66931C22semidirect
61. C2×#66930C22semidirect
62. C11×#397C22semidirect
63. C11×#394C22semidirect
65. C11×#386C22semidirect
68. C11×#380C22semidirect
75. C2×C11⋊#95C22semidirect
76. #10622605C22semidirect
77. #10622602C22semidirect
78. #10622601C22semidirect
79. #10622594C22semidirect
80. #10622592C22semidirect
81. C4⋊C4×Dic11C22semidirect
82. #10622586C22semidirect
85. #10622573C22semidirect
87. #10622572C22semidirect
88. #10622572C22semidirect
91. #10622571C22semidirect
92. #10622570C22semidirect
93. #10622569C22semidirect
96. #10622565C22semidirect
97. #10622564C22semidirect
100. #10622557C22semidirect
101. #10622555C22semidirect
106. C22⋊C4×Dic11C22semidirect
107. C22⋊C4×Dic11C22semidirect
108. C22⋊C4×Dic11C22semidirect
109. #10622288C22semidirect
110. #10622286C22semidirect
111. #10622283C22semidirect
112. #10622282C22semidirect
113. #10622282C22semidirect
114. #10622282C22semidirect
115. #10622281C22semidirect
116. #10622279C22semidirect
117. #10622279C22semidirect
118. #10622279C22semidirect
119. #10622278C22semidirect
120. #10622271C22semidirect
121. #10622270C22semidirect
122. #10622265C22semidirect
123. #10622262C22semidirect
124. #10622260C22semidirect
143. C23×Dic11D4semidirect
321. C2×C22⋊D11#41semidirect
378. C11×C22⋊C4#41semidirect
387. C22⋊Dic11#41semidirect
432. #2412D11semidirect
600. #397C2×D11semidirect
606. #394C2×D11semidirect
632. #386C2×D11semidirect
642. #380C2×D11semidirect
1011. C22⋊C4#4341semidirect
1020. C11#34957semidirect

Maximal subgroups

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

subgroupindex
C2×#106231172
C22×(C22⋊D11)⋊C42
#130742312
#130742232
#130740952
#130739952
#130737942
#130737732
#130735802
#130735462
#130720122
#130719912
#130719842
#130718742
#130718302
#123×Dic112
#130711332
#130711262
#130711222
#130711212
#130711172
C2×C22⋊C4×Dic112
C11×#24122
#3495711