Finite Group Databasebeta

← D11×#2662 #14920500

Subgroups — D11×#2662 #14920500

Order 2816.

3002 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#126C211yesmaximal, characteristic, complemented
2C2×D11×#124C211yesmaximal, characteristic, complemented
3#13074762C211yesmaximal, characteristic, complemented
4#13074761C211yesmaximal, characteristic, complemented
5#13074760C211yesmaximal, characteristic, complemented
6#13074759C212yesmaximal, complemented
7#13074758C211yesmaximal, characteristic, complemented
8#13074757C212yesmaximal, complemented
9#13074756C211yesmaximal, characteristic, complemented
10#13074755C211yesmaximal, characteristic, complemented
11#13074754C212yesmaximal, complemented
12#13074753C211yesmaximal, characteristic, complemented
13#13074752C212yesmaximal, complemented
14D11×#396C212yesmaximal, complemented
15D11×#395C211yesmaximal, characteristic, complemented
16D11×#394C212yesmaximal, complemented
17D11×#394C211yesmaximal, characteristic, complemented
18D11×#393C211yesmaximal, characteristic, complemented
19D11×#392C211yesmaximal, characteristic
20D11×#390C212yesmaximal, complemented
21D11×#388C212yesmaximal, complemented
22C4×C4⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2662C211yesmaximal, characteristic, complemented
24C22×Q8×D11C2211yescharacteristic
25C22×D4×D11C2211yescharacteristic
26C22×D4×D11C2212yes—
27C2×C11×#126C2211yescharacteristic, complemented
28C2×C11×#124C2211yescharacteristic, complemented
29C2×#67000C2211yescharacteristic, complemented
30C2×#66989C2211yescharacteristic, complemented
31D11×#126—28no—
32D11×#124—28no—
33C2×#66951C2211yescharacteristic, complemented
34C2×#66951C2211yescharacteristic, complemented
35C2×#66951C2211yescharacteristic, complemented
36C2×C4⋊C4×D11C2211yescharacteristic
37C2×C4⋊C4×D11C2211yescharacteristic
38C2×C4⋊C4×D11C2211yescharacteristic
39C2×C4⋊C4×D11C2212yes—
40C2×C4⋊C4×D11C2212yes—
41C2×#66938C2212yescomplemented
42C2×#66938C2212yescomplemented
43C2×C22⋊C4×D11C2212yes—
44C2×C22⋊C4×D11C2212yes—
45C2×C22⋊C4×D11C2211yescharacteristic
46C2×C22⋊C4×D11C2211yescharacteristic
47C2×C22⋊C4×D11C2211yescharacteristic
48C2×C22⋊C4×D11C2212yes—
49C2×C22⋊C4×D11C2212yes—
50C2×C22⋊C4×D11C2212yes—
51C2×C22⋊C4×D11C2212yes—
52C2×#66932C2211yescharacteristic, complemented
53C2×#66932C2211yescharacteristic, complemented
54C2×#66932C2211yescharacteristic, complemented
55C2×#66929C2211yescharacteristic, complemented
56C2×#66928C2211yescharacteristic, complemented
57C2×C42×D11C2212yes—
58C2×C42×D11C2211yescharacteristic
59C11×#396C2212yescomplemented
60C11×#395C2211yescharacteristic, complemented
61C11×#394C2212yescomplemented
62C11×#394C2211yescharacteristic, complemented
63C11×#393C2211yescharacteristic, complemented
64C11×#392C2211yescharacteristic
65C11×#390C2212yescomplemented
66C11×#388C2212yescomplemented
67C4×C11×C4⋊C4C2211yescharacteristic, complemented
68#10622844C2211yescharacteristic, complemented
69#10622842C2211yescharacteristic, complemented
70#10622836C2212yes—
71#10622836C2211yescharacteristic
72#10622835C2211yescharacteristic, complemented
73#10622835C2212yescomplemented
74#10622834C2212yescomplemented
75#10622607C2212yescomplemented
76#10622607C2212yescomplemented
77#10622607C2212yescomplemented
78#10622604C2212yescomplemented
79#10622604C2211yescharacteristic, complemented
80#10622603C2212yescomplemented
81#10622601C2212yescomplemented
82#10622592C2212yescomplemented
83#10622592C2211yescharacteristic, complemented
84C4⋊C4×Dic11C2212yescomplemented
85#10622574C2212yescomplemented
86#10622574C2212yescomplemented
87#10622574C2212yescomplemented
88#10622573C2212yes—
89#10622573C2211yescharacteristic
90#10622572C2212yescomplemented
91#10622572C2212yescomplemented
92#10622572C2212yescomplemented
93#10622570C2212yescomplemented
94#10622570C2212yescomplemented
95#10622570C2212yescomplemented
96#10622570C2212yescomplemented
97#10622564C2212yescomplemented
98#10622561C2212yescomplemented
99#10622561C2212yescomplemented
100#10622561C2212yescomplemented
101#10622560C2212yescomplemented
102#10622560C2211yescharacteristic, complemented
103#10622558C2212yescomplemented
104#10622557C2212yescomplemented
105#10622553C2212yescomplemented
106#10622552C2212yescomplemented
107C4×C4⋊Dic11C2211yescharacteristic, complemented
108C4×Dic11⋊C4C2212yescomplemented
109#10622289C2212yescomplemented
110#10622286C2211yescharacteristic, complemented
111#10622286C2212yescomplemented
112#10622285C2211yescharacteristic, complemented
113#10622285C2212yescomplemented
114#10622284C2211yescharacteristic
115#10622283C2212yescomplemented
116#10622282C2212yescomplemented
117D11×#95C2211yescharacteristic
118D11×#95C2211yescharacteristic
119D11×#95C2212yes—
120D11×#95C2212yes—
121#10622269C2212yescomplemented
122#10622269C2211yescharacteristic, complemented
123#10622262C2211yescharacteristic, complemented
124#10622262C2211yescharacteristic, complemented
125C24×D11C2311yescharacteristic
126C24×D11C2312yes—
127C22×Q8×C11C2311yescharacteristic
128C22×D4×C11C2311yescharacteristic
129C22×D4×C11C2312yes—
130C22×C22⋊D11C2312yes—
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C2×Q8×D11—24no—
134C2×Q8×D11—44no—
135C2×D4×D11—24no—
136C2×D4×D11—28no—
137C2×D4×D11—44no—
138C2×D4×D11—44no—
139C2×D4×D11—44no—
140C22×D44C2311yescharacteristic
141C22×D44C2312yes—
142C22×C4×D11C2312yes—
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2312yes—
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2312yes—
151C22×Dic22C2311yescharacteristic
152C22×Dic22C2312yes—
153C11×#126—24no—
154C11×#124—24no—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2312yes—
159C2×C11×C4⋊C4C2312yes—
160C2×C11×C22⋊C4C2311yescharacteristic
161C2×C11×C22⋊C4C2311yescharacteristic
162C2×C11×C22⋊C4C2311yescharacteristic
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2312yes—
169C2×C42×C11C2312yes—
170C2×C42×C11C2311yescharacteristic
171C2×C22⋊Dic11C2311yescharacteristic
172C2×C22⋊Dic11C2311yescharacteristic
173C2×C22⋊Dic11C2311yescharacteristic
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180#67000—24no—
181#66989—24no—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2311yescharacteristic
185C2×(C2×D11)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2311yescharacteristic
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2311yescharacteristic
191C2×(C2×D11)⋊C4C2311yescharacteristic
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×C4⋊Dic11C2311yescharacteristic
201C2×C4⋊Dic11C2311yescharacteristic
202C2×C4⋊Dic11C2311yescharacteristic
203C2×C4⋊Dic11C2312yes—
204C2×C4⋊Dic11C2312yes—
205C2×Dic11⋊C4C2311yescharacteristic
206C2×Dic11⋊C4C2311yescharacteristic
207C2×Dic11⋊C4C2311yescharacteristic
208C2×Dic11⋊C4C2311yescharacteristic
209C2×Dic11⋊C4C2311yescharacteristic
210C2×Dic11⋊C4C2311yescharacteristic
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2312yes—
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2311yescharacteristic
221#66951—24no—
222#66951—24no—
223#66951—24no—
224C4⋊C4×D11—24no—
225C4⋊C4×D11—24no—
226C4⋊C4×D11—24no—
227C4⋊C4×D11—28no—
228C4⋊C4×D11—44no—
229#66938—28no—
230#66938—28no—
231C22⋊C4×D11—24no—
232C22⋊C4×D11—24no—
233C22⋊C4×D11—24no—
234C22⋊C4×D11—28no—
235C22⋊C4×D11—28no—
236C22⋊C4×D11—28no—
237C22⋊C4×D11—44no—
238C22⋊C4×D11—44no—
239C22⋊C4×D11—44no—
240#66932—24no—
241#66932—24no—
242#66932—24no—
243#66929—24no—
244#66928—24no—
245C42×D11—44no—
246C42×D11D418yescomplemented
247C11×#95C2311yescharacteristic
248C11×#95C2311yescharacteristic
249C11×#95C2312yes—
250C11×#95C2312yes—
251C11⋊#95C2311yescharacteristic
252C11⋊#95C2311yescharacteristic
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C2×#2662—111nomaximal, Sylow
262C24×C11C2411yescharacteristic
263C24×C11C2412yes—
264C23×D11—22no—
265C23×D11—24no—
266C23×D11—24no—
267C23×D11—24no—
268C23×D11—24no—
269C23×D11—24no—
270C23×D11—24no—
271C23×D11—24no—
272C23×D11—24no—
273C23×D11—22no—
274C23×D11—22no—
275C23×D11—24no—
276C23×D11C2411yescharacteristic
277C23×D11C2412yes—
278C23×D11C2411yescharacteristic
279C2×Q8×C11—22no—
280C2×Q8×C11—42no—
281C2×D4×C11—22no—
282C2×D4×C11—24no—
283C2×D4×C11—42no—
284C2×D4×C11—42no—
285C2×D4×C11—42no—
286C22×C4×C11C2412yes—
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2412yes—
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2412yes—
295C2×C22⋊D11—24no—
296C2×C22⋊D11—24no—
297C2×C22⋊D11—24no—
298C2×C22⋊D11—42no—
299C2×C22⋊D11—42no—
300C2×C22⋊D11—42no—
301C2×C22⋊D11—42no—
302C2×C22⋊D11—42no—
303C2×C22⋊D11—42no—
304C22×Dic11C2412yes—
305C22×Dic11C2411yescharacteristic
306C22×Dic11C2411yescharacteristic
307C22×Dic11C2412yes—
308C22×Dic11C2411yescharacteristic
309C22×Dic11C2411yescharacteristic
310C22×Dic11C2411yescharacteristic
311C22×Dic11C2411yescharacteristic
312C22×Dic11C2412yes—
313Q8×D11—416no—
314D4×D11—416no—
315D4×D11—432no—
316C2×D44—22no—
317C2×D44—24no—
318C2×D44—42no—
319C2×D44—42no—
320C2×D44—42no—
321C2×C4×D11—24no—
322C2×C4×D11—22no—
323C2×C4×D11—22no—
324C2×C4×D11—22no—
325C2×C4×D11—24no—
326C2×C4×D11—24no—
327C2×C4×D11—24no—
328C2×C4×D11—22no—
329C2×C4×D11—24no—
330C2×C4×D11—24no—
331C2×C4×D11—24no—
332C2×C4×D11—24no—
333C2×C4×D11—24no—
334C2×C4×D11—22no—
335C2×C4×D11—24no—
336C2×C4×D11—24no—
337C2×C4×D11—24no—
338C2×C4×D11—22no—
339C2×C4×D11—22no—
340C2×C4×D11C2×D414yes—
341C2×C4×D11C2×D414yes—
342C2×C4×D11C2×D414yes—
343C2×C4×D11#4118yes—
344C2×Dic22—24no—
345C2×Dic22—22no—
346C2×Dic22—42no—
347C2×Dic22—42no—
348C2×Dic22—42no—
349C11×C4⋊C4—22no—
350C11×C4⋊C4—22no—
351C11×C4⋊C4—22no—
352C11×C4⋊C4—24no—
353C11×C4⋊C4—42no—
354C11×C22⋊C4—22no—
355C11×C22⋊C4—22no—
356C11×C22⋊C4—22no—
357C11×C22⋊C4—24no—
358C11×C22⋊C4—24no—
359C11×C22⋊C4—24no—
360C11×C22⋊C4—42no—
361C11×C22⋊C4—42no—
362C11×C22⋊C4—42no—
363C42×C11—42no—
364C42×C11C2×D414yescomplemented
365C22⋊Dic11—22no—
366C22⋊Dic11—22no—
367C22⋊Dic11—22no—
368C22⋊Dic11—24no—
369C22⋊Dic11—24no—
370C22⋊Dic11—24no—
371C22⋊Dic11—42no—
372C22⋊Dic11—42no—
373C22⋊Dic11—42no—
374(C2×D11)⋊C4—24no—
375(C2×D11)⋊C4—24no—
376(C2×D11)⋊C4—22no—
377(C2×D11)⋊C4—22no—
378(C2×D11)⋊C4—22no—
379(C2×D11)⋊C4—24no—
380(C2×D11)⋊C4—24no—
381(C2×D11)⋊C4—24no—
382(C2×D11)⋊C4—22no—
383(C2×D11)⋊C4—22no—
384(C2×D11)⋊C4—22no—
385(C2×D11)⋊C4—24no—
386(C2×D11)⋊C4—42no—
387(C2×D11)⋊C4—42no—
388(C2×D11)⋊C4—42no—
389(C2×D11)⋊C4—42no—
390(C2×D11)⋊C4—42no—
391(C2×D11)⋊C4—42no—
392C4⋊Dic11—22no—
393C4⋊Dic11—22no—
394C4⋊Dic11—22no—
395C4⋊Dic11—24no—
396C4⋊Dic11—42no—
397Dic11⋊C4—22no—
398Dic11⋊C4—22no—
399Dic11⋊C4—22no—
400Dic11⋊C4—24no—
401Dic11⋊C4—22no—
402Dic11⋊C4—22no—
403Dic11⋊C4—22no—
404Dic11⋊C4—24no—
405Dic11⋊C4—42no—
406Dic11⋊C4—42no—
407C4×Dic11—42no—
408C4×Dic11—42no—
409C4×Dic11—42no—
410C4×Dic11C2×D414yescomplemented
411C4×Dic11C2×D414yescomplemented
412C4×Dic11C2×D414yescomplemented
413C22×#126—111no—
414C22×#124—111no—
415#2662—112no—
416#2662—111no—
417#2662—112no—
418#2662—111no—
419#2662—111no—
420#2662—111no—
421#2662—112no—
422#2662—112no—
423#2662—111no—
424#2662—111no—
425#2662—111no—
426#2662D1111yescharacteristic, direct product factor
427C2×#396—112no—
428C2×#395—111no—
429C2×#394—112no—
430C2×#394—111no—
431C2×#393—111no—
432C2×#392—111no—
433C2×#390—112no—
434C2×#388—112no—
435C2×C4×C4⋊C4—111no—
436C23×C11—21no—
437C23×C11—22no—
438C23×C11—22no—
439C23×C11—22no—
440C23×C11—22no—
441C23×C11—22no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—21no—
446C23×C11—21no—
447C23×C11—22no—
448C23×C11C2511yescharacteristic
449C22×D11—21no—
450C22×D11—22no—
451C22×D11—22no—
452C22×D11—22no—
453C22×D11—22no—
454C22×D11—22no—
455C22×D11—22no—
456C22×D11—22no—
457C22×D11—22no—
458C22×D11—21no—
459C22×D11—21no—
460C22×D11—22no—
461C22×D11—44no—
462C22×D11—48no—
463C22×D11—48no—
464C22×D11—44no—
465C22×D11—44no—
466C22×D11—48no—
467C22×D11—48no—
468C22×D11—48no—
469C22×D11—48no—
470C22×D11—48no—
471C22×D11—48no—
472C22×D11—48no—
473C22×D11C22×D412yes—
474C22×D11C2×#4114yes—
475C22×D11H(5,𝔽2)14yes—
476C22×D11H(5,𝔽2)12yes—
477C22×D112−1+412yes—
478Q8×C11—44no—
479D4×C11—44no—
480D4×C11—48no—
481C2×C4×C11—22no—
482C2×C4×C11—21no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—21no—
487C2×C4×C11—21no—
488C2×C4×C11—21no—
489C2×C4×C11—21no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—21no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—21no—
500C2×C4×C11C22×D412yes—
501C2×C4×C11C22×D412yes—
502C2×C4×C11C22×D412yes—
503C2×C4×C11C2×#4114yes—
504C22⋊D11—48no—
505C22⋊D11—48no—
506C22⋊D11—48no—
507C2×Dic11—22no—
508C2×Dic11—21no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—21no—
513C2×Dic11—21no—
514C2×Dic11—21no—
515C2×Dic11—21no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—21no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—21no—
526C2×Dic11C22×D412yes—
527C2×Dic11C22×D412yes—
528C2×Dic11C22×D412yes—
529C2×Dic11C2×#4114yes—
530D44—44no—
531D44—48no—
532C4×D11—28no—
533C4×D11—28no—
534C4×D11—28no—
535C4×D11—216no—
536C4×D11—44no—
537C4×D11—44no—
538C4×D11—48no—
539C4×D11—44no—
540C4×D11—48no—
541Dic22—48no—
542Dic22—44no—
543C23×Q8—111no—
544C23×D4—111no—
545C23×D4—112no—
546C2×#126—111no—
547C2×#126—111no—
548C2×#126—111no—
549C2×#126—111no—
550C2×#126—111no—
551C2×#126—111no—
552C2×#126—111no—
553C2×#126—228no—
554C2×#126C2×D1111yescharacteristic, complemented
555C2×#124—111no—
556C2×#124—111no—
557C2×#124—112no—
558C2×#124—112no—
559C2×#124—111no—
560C2×#124—228no—
561C2×#124C2×D1111yescharacteristic, complemented
562C22×C4⋊C4—111no—
563C22×C4⋊C4—112no—
564C22×C4⋊C4—111no—
565C22×C4⋊C4—111no—
566C22×C4⋊C4—112no—
567C22×C22⋊C4—111no—
568C22×C22⋊C4—112no—
569C22×C22⋊C4—111no—
570C22×C22⋊C4—112no—
571C22×C22⋊C4—112no—
572C22×C22⋊C4—111no—
573C22×C22⋊C4—112no—
574C22×C22⋊C4—112no—
575C22×C22⋊C4—112no—
576C22×C42—111no—
577C22×C42—112no—
578#396—112no—
579#396—112no—
580#396—112no—
581#396—112no—
582#396—112no—
583#396—112no—
584#396—112no—
585#396C2×D1112yescomplemented
586#395—111no—
587#395—112no—
588#395—111no—
589#395—112no—
590#395—111no—
591#395C2×D1111yescharacteristic, complemented
592#394—111no—
593#394—112no—
594#394—111no—
595#394—112no—
596#394—112no—
597#394—112no—
598#394—112no—
599#394—112no—
600#394—112no—
601#394—112no—
602#394—111no—
603#394—112no—
604#394C2×D1111yescharacteristic, complemented
605#394C2×D1112yescomplemented
606#393—111no—
607#393—112no—
608#393—111no—
609#393—112no—
610#393—111no—
611#393C2×D1111yescharacteristic, complemented
612#392—112no—
613#392—111no—
614#392—112no—
615#392—111no—
616#392—111no—
617#392C2×D1111yescharacteristic
618#390—112no—
619#390—112no—
620#390—112no—
621#390—112no—
622#390—112no—
623#390—112no—
624#390—112no—
625#390C2×D1112yescomplemented
626#388—112no—
627#388—112no—
628#388—112no—
629#388—112no—
630#388—112no—
631#388—112no—
632#388—112no—
633#388C2×D1112yescomplemented
634C4×C4⋊C4—112no—
635C4×C4⋊C4—112no—
636C4×C4⋊C4—111no—
637C4×C4⋊C4—111no—
638C4×C4⋊C4—111no—
639C4×C4⋊C4C2×D1111yescharacteristic, complemented
640C2×#95—111no—
641C2×#95—111no—
642C2×#95—112no—
643C2×#95—112no—
644C22×C11—41no—
645C22×C11—42no—
646C22×C11—42no—
647C22×C11—41no—
648C22×C11—41no—
649C22×C11—42no—
650C22×C11—42no—
651C22×C11—42no—
652C22×C11—42no—
653C22×C11—42no—
654C22×C11—42no—
655C22×C11—42no—
656C22×C11C23×D411yescharacteristic
657C22×C11C22×#4112yes—
658C22×C11C2×H(5,𝔽2)12yes—
659C22×C11C2×H(5,𝔽2)11yescharacteristic
660C22×C11C2×2−1+411yescharacteristic
661C2×D11—41no—
662C2×D11—42no—
663C2×D11—41no—
664C2×D11—42no—
665C2×D11—41no—
666C2×D11—42no—
667C2×D11—42no—
668C2×D11—42no—
669C2×D11—42no—
670C2×D11—42no—
671C2×D11—42no—
672C2×D11—42no—
673C2×D11—816no—
674C2×D11—88no—
675C2×D11#53214yes—
676C2×D11#53514yes—
677C2×D11#53714yes—
678C2×D11#53818yes—
679C2×D11#54218yes—
680C4×C11—22no—
681C4×C11—22no—
682C4×C11—22no—
683C4×C11—24no—
684C4×C11—41no—
685C4×C11—42no—
686C4×C11—41no—
687C4×C11—41no—
688C4×C11—42no—
689Dic11—22no—
690Dic11—22no—
691Dic11—22no—
692Dic11—24no—
693Dic11—41no—
694Dic11—42no—
695Dic11—41no—
696Dic11—41no—
697Dic11—42no—
698C25—111no—
699C25—112no—
700C22×Q8—112no—
701C22×Q8—111no—
702C22×Q8—224no—
703C22×Q8—444no—
704C22×Q8C22×D1111yescharacteristic
705C22×D4—112no—
706C22×D4—112no—
707C22×D4—112no—
708C22×D4—111no—
709C22×D4—112no—
710C22×D4—224no—
711C22×D4—228no—
712C22×D4—444no—
713C22×D4—444no—
714C22×D4—444no—
715C22×D4C22×D1111yescharacteristic
716C22×D4C22×D1112yes—
717C23×C4—111no—
718C23×C4—111no—
719C23×C4—112no—
720C23×C4—111no—
721C23×C4—111no—
722C23×C4—111no—
723C23×C4—111no—
724C23×C4—112no—
725C23×C4—112no—
726#126—24no—
727#126—224no—
728#126—224no—
729#126—224no—
730#126—224no—
731#126—224no—
732#126—224no—
733#126—224no—
734#124—24no—
735#124—228no—
736#124—228no—
737#124—224no—
738#124—224no—
739#124—224no—
740C2×C4⋊C4—111no—
741C2×C4⋊C4—111no—
742C2×C4⋊C4—111no—
743C2×C4⋊C4—111no—
744C2×C4⋊C4—111no—
745C2×C4⋊C4—111no—
746C2×C4⋊C4—111no—
747C2×C4⋊C4—111no—
748C2×C4⋊C4—111no—
749C2×C4⋊C4—112no—
750C2×C4⋊C4—112no—
751C2×C4⋊C4—112no—
752C2×C4⋊C4—112no—
753C2×C4⋊C4—112no—
754C2×C4⋊C4—112no—
755C2×C4⋊C4—224no—
756C2×C4⋊C4—224no—
757C2×C4⋊C4—224no—
758C2×C4⋊C4—228no—
759C2×C4⋊C4—444no—
760C2×C4⋊C4C22×D1111yescharacteristic
761C2×C4⋊C4C22×D1111yescharacteristic
762C2×C4⋊C4C22×D1111yescharacteristic
763C2×C4⋊C4C22×D1112yes—
764C2×C4⋊C4C22×D1112yes—
765C2×C22⋊C4—112no—
766C2×C22⋊C4—112no—
767C2×C22⋊C4—111no—
768C2×C22⋊C4—111no—
769C2×C22⋊C4—111no—
770C2×C22⋊C4—112no—
771C2×C22⋊C4—112no—
772C2×C22⋊C4—112no—
773C2×C22⋊C4—112no—
774C2×C22⋊C4—112no—
775C2×C22⋊C4—111no—
776C2×C22⋊C4—111no—
777C2×C22⋊C4—111no—
778C2×C22⋊C4—111no—
779C2×C22⋊C4—111no—
780C2×C22⋊C4—111no—
781C2×C22⋊C4—112no—
782C2×C22⋊C4—112no—
783C2×C22⋊C4—112no—
784C2×C22⋊C4—112no—
785C2×C22⋊C4—112no—
786C2×C22⋊C4—112no—
787C2×C22⋊C4—112no—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—112no—
790C2×C22⋊C4—112no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—228no—
793C2×C22⋊C4—228no—
794C2×C22⋊C4—224no—
795C2×C22⋊C4—224no—
796C2×C22⋊C4—224no—
797C2×C22⋊C4—228no—
798C2×C22⋊C4—444no—
799C2×C22⋊C4—444no—
800C2×C22⋊C4—444no—
801C2×C22⋊C4C22×D1112yes—
802C2×C22⋊C4C22×D1112yes—
803C2×C22⋊C4C22×D1111yescharacteristic
804C2×C22⋊C4C22×D1111yescharacteristic
805C2×C22⋊C4C22×D1111yescharacteristic
806C2×C22⋊C4C22×D1112yes—
807C2×C22⋊C4C22×D1112yes—
808C2×C22⋊C4C22×D1112yes—
809C2×C22⋊C4C22×D1112yes—
810C2×C42—111no—
811C2×C42—111no—
812C2×C42—111no—
813C2×C42—118no—
814C2×C42—112no—
815C2×C42—112no—
816C2×C42—112no—
817C2×C42—444no—
818C2×C42C22×D1112yes—
819C2×C42C22×D1111yescharacteristic
820#95—111no—
821#95—112no—
822#95—112no—
823#95—111no—
824#95—112no—
825#95—112no—
826#95—112no—
827#95—112no—
828#95—112no—
829#95—112no—
830#95C22×D1111yescharacteristic
831#95C22×D1111yescharacteristic
832#95C22×D1112yes—
833#95C22×D1112yes—
834C2×C11—82no—
835C2×C11—81no—
836C2×C11C2×#53211yescharacteristic
837C2×C11C2×#53511yescharacteristic
838C2×C11C2×#53711yescharacteristic
839C2×C11C2×#53812yes—
840C2×C11C2×#54212yes—
841D11—81no—
842D11—82no—
843D11#266218yesdirect product factor
844C24—111no—
845C24—111no—
846C24—112no—
847C24—222no—
848C24—224no—
849C24—224no—
850C24—224no—
851C24—224no—
852C24—224no—
853C24—224no—
854C24—224no—
855C24—224no—
856C24—222no—
857C24—222no—
858C24—224no—
859C24C23×D1111yescharacteristic
860C24C23×D1112yes—
861C2×Q8—22no—
862C2×Q8—42no—
863C2×Q8—224no—
864C2×Q8—222no—
865C2×Q8—442no—
866C2×Q8—442no—
867C2×Q8—442no—
868C2×Q8—4416no—
869C2×D4—22no—
870C2×D4—24no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—224no—
875C2×D4—224no—
876C2×D4—224no—
877C2×D4—222no—
878C2×D4—224no—
879C2×D4—442no—
880C2×D4—442no—
881C2×D4—442no—
882C2×D4—4416no—
883C2×D4—4432no—
884C2×D4—442no—
885C2×D4—442no—
886C2×D4—442no—
887C2×D4—442no—
888C2×D4—442no—
889C2×D4—442no—
890C22×C4—112no—
891C22×C4—111no—
892C22×C4—111no—
893C22×C4—111no—
894C22×C4—114no—
895C22×C4—114no—
896C22×C4—114no—
897C22×C4—118no—
898C22×C4—112no—
899C22×C4—111no—
900C22×C4—111no—
901C22×C4—112no—
902C22×C4—111no—
903C22×C4—222no—
904C22×C4—224no—
905C22×C4—224no—
906C22×C4—224no—
907C22×C4—224no—
908C22×C4—222no—
909C22×C4—224no—
910C22×C4—224no—
911C22×C4—222no—
912C22×C4—222no—
913C22×C4—222no—
914C22×C4—224no—
915C22×C4—222no—
916C22×C4—224no—
917C22×C4—224no—
918C22×C4—224no—
919C22×C4—224no—
920C22×C4—224no—
921C22×C4—222no—
922C22×C4C23×D1112yes—
923C22×C4C23×D1111yescharacteristic
924C22×C4C23×D1111yescharacteristic
925C22×C4C23×D1112yes—
926C22×C4C23×D1111yescharacteristic
927C22×C4C23×D1111yescharacteristic
928C22×C4C23×D1111yescharacteristic
929C22×C4C23×D1111yescharacteristic
930C22×C4C23×D1112yes—
931C4⋊C4—22no—
932C4⋊C4—22no—
933C4⋊C4—22no—
934C4⋊C4—24no—
935C4⋊C4—42no—
936C4⋊C4—222no—
937C4⋊C4—222no—
938C4⋊C4—222no—
939C4⋊C4—222no—
940C4⋊C4—222no—
941C4⋊C4—222no—
942C4⋊C4—224no—
943C4⋊C4—224no—
944C4⋊C4—222no—
945C4⋊C4—222no—
946C4⋊C4—222no—
947C4⋊C4—224no—
948C4⋊C4—442no—
949C4⋊C4—442no—
950C4⋊C4—442no—
951C22⋊C4—24no—
952C22⋊C4—24no—
953C22⋊C4—22no—
954C22⋊C4—22no—
955C22⋊C4—22no—
956C22⋊C4—24no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—224no—
961C22⋊C4—224no—
962C22⋊C4—222no—
963C22⋊C4—222no—
964C22⋊C4—222no—
965C22⋊C4—224no—
966C22⋊C4—224no—
967C22⋊C4—224no—
968C22⋊C4—222no—
969C22⋊C4—222no—
970C22⋊C4—222no—
971C22⋊C4—224no—
972C22⋊C4—224no—
973C22⋊C4—224no—
974C22⋊C4—222no—
975C22⋊C4—222no—
976C22⋊C4—222no—
977C22⋊C4—224no—
978C22⋊C4—442no—
979C22⋊C4—442no—
980C22⋊C4—442no—
981C22⋊C4—442no—
982C22⋊C4—442no—
983C22⋊C4—442no—
984C22⋊C4—442no—
985C22⋊C4—442no—
986C22⋊C4—442no—
987C42—42no—
988C42—114no—
989C42—114no—
990C42—114no—
991C42—442no—
992C42—442no—
993C42—442no—
994C42D4×D1114yescomplemented
995C11C2×#266211yescharacteristic, complemented, Sylow
996C23—21no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—21no—
1006C23—21no—
1007C23—22no—
1008C23—112no—
1009C23—114no—
1010C23—114no—
1011C23—112no—
1012C23—112no—
1013C23—221no—
1014C23—222no—
1015C23—222no—
1016C23—222no—
1017C23—222no—
1018C23—222no—
1019C23—222no—
1020C23—222no—
1021C23—222no—
1022C23—221no—
1023C23—221no—
1024C23—222no—
1025C23—448no—
1026C23—448no—
1027C23—448no—
1028C23—444no—
1029C23—448no—
1030C23—444no—
1031C23—444no—
1032C23—448no—
1033C23—448no—
1034C23—448no—
1035C23—448no—
1036C23—448no—
1037C23C24×D1111yescharacteristic
1038Q8—44no—
1039Q8—444no—
1040Q8—448no—
1041D4—44no—
1042D4—48no—
1043D4—444no—
1044D4—448no—
1045D4—448no—
1046D4—448no—
1047D4—448no—
1048C2×C4—22no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—21no—
1054C2×C4—22no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—21no—
1067C2×C4—112no—
1068C2×C4—112no—
1069C2×C4—112no—
1070C2×C4—114no—
1071C2×C4—228no—
1072C2×C4—2216no—
1073C2×C4—228no—
1074C2×C4—228no—
1075C2×C4—222no—
1076C2×C4—221no—
1077C2×C4—222no—
1078C2×C4—222no—
1079C2×C4—222no—
1080C2×C4—221no—
1081C2×C4—222no—
1082C2×C4—221no—
1083C2×C4—221no—
1084C2×C4—221no—
1085C2×C4—222no—
1086C2×C4—222no—
1087C2×C4—222no—
1088C2×C4—221no—
1089C2×C4—222no—
1090C2×C4—222no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—221no—
1094C2×C4—448no—
1095C2×C4—444no—
1096C2×C4—444no—
1097C2×C4—444no—
1098C2×C4—448no—
1099C2×C4C2×D4×D1112yes—
1100C2×C4C2×D4×D1112yes—
1101C2×C4C2×D4×D1112yes—
1102C2×C4#41×D1114yes—
1103C22—41no—
1104C22—42no—
1105C22—42no—
1106C22—41no—
1107C22—41no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—114no—
1116C22—114no—
1117C22—114no—
1118C22—118no—
1119C22—118no—
1120C22—441no—
1121C22—442no—
1122C22—442no—
1123C22—441no—
1124C22—441no—
1125C22—442no—
1126C22—442no—
1127C22—442no—
1128C22—442no—
1129C22—442no—
1130C22—442no—
1131C22—442no—
1132C22—8816no—
1133C22—888no—
1134C22C22×D4×D1111yescharacteristic
1135C22C2×#41×D1112yes—
1136C22D11×H(5,𝔽2)12yes—
1137C22D11×H(5,𝔽2)11yescharacteristic
1138C22D11×2−1+411yescharacteristic
1139C4—22no—
1140C4—22no—
1141C4—22no—
1142C4—24no—
1143C4—41no—
1144C4—42no—
1145C4—41no—
1146C4—41no—
1147C4—42no—
1148C4—222no—
1149C4—222no—
1150C4—222no—
1151C4—224no—
1152C4—441no—
1153C4—442no—
1154C4—441no—
1155C4—441no—
1156C4—442no—
1157C2—82no—
1158C2—81no—
1159C2—118no—
1160C2—882no—
1161C2—881no—
1162C2D11×#53211yescharacteristic
1163C2D11×#53511yescharacteristic
1164C2D11×#53711yescharacteristic
1165C2D11×#53812yes—
1166C2D11×#54212yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2662C2
prime radicalD11×#392C2
hypercenter#2662D11
hypocenterC11C2×#2662
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2662

Complements

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

NH ≅ G/Ntype
1. C2×D11×#126C2semidirect
2. C2×D11×#124C2semidirect
3. #13074762C2semidirect
4. #13074761C2semidirect
5. #13074760C2semidirect
6. #13074759C2semidirect
7. #13074758C2semidirect
8. #13074757C2semidirect
9. #13074756C2semidirect
10. #13074755C2semidirect
11. #13074754C2semidirect
12. #13074753C2semidirect
13. #13074752C2semidirect
14. D11×#396C2semidirect
15. D11×#395C2semidirect
16. D11×#394C2semidirect
17. D11×#394C2semidirect
18. D11×#393C2semidirect
20. D11×#390C2semidirect
21. D11×#388C2semidirect
22. C4×C4⋊C4×D11C2semidirect
23. C11×#2662C2semidirect
27. C2×C11×#126C22semidirect
28. C2×C11×#124C22semidirect
29. C2×#67000C22semidirect
30. C2×#66989C22semidirect
33. C2×#66951C22semidirect
34. C2×#66951C22semidirect
35. C2×#66951C22semidirect
41. C2×#66938C22semidirect
42. C2×#66938C22semidirect
52. C2×#66932C22semidirect
53. C2×#66932C22semidirect
54. C2×#66932C22semidirect
55. C2×#66929C22semidirect
56. C2×#66928C22semidirect
59. C11×#396C22semidirect
60. C11×#395C22semidirect
61. C11×#394C22semidirect
62. C11×#394C22semidirect
63. C11×#393C22semidirect
65. C11×#390C22semidirect
66. C11×#388C22semidirect
67. C4×C11×C4⋊C4C22semidirect
68. #10622844C22semidirect
69. #10622842C22semidirect
72. #10622835C22semidirect
73. #10622835C22semidirect
74. #10622834C22semidirect
75. #10622607C22semidirect
76. #10622607C22semidirect
77. #10622607C22semidirect
78. #10622604C22semidirect
79. #10622604C22semidirect
80. #10622603C22semidirect
81. #10622601C22semidirect
82. #10622592C22semidirect
83. #10622592C22semidirect
84. C4⋊C4×Dic11C22semidirect
85. #10622574C22semidirect
86. #10622574C22semidirect
87. #10622574C22semidirect
90. #10622572C22semidirect
91. #10622572C22semidirect
92. #10622572C22semidirect
93. #10622570C22semidirect
94. #10622570C22semidirect
95. #10622570C22semidirect
96. #10622570C22semidirect
97. #10622564C22semidirect
98. #10622561C22semidirect
99. #10622561C22semidirect
100. #10622561C22semidirect
101. #10622560C22semidirect
102. #10622560C22semidirect
103. #10622558C22semidirect
104. #10622557C22semidirect
105. #10622553C22semidirect
106. #10622552C22semidirect
107. C4×C4⋊Dic11C22semidirect
108. C4×Dic11⋊C4C22semidirect
109. #10622289C22semidirect
110. #10622286C22semidirect
111. #10622286C22semidirect
112. #10622285C22semidirect
113. #10622285C22semidirect
115. #10622283C22semidirect
116. #10622282C22semidirect
121. #10622269C22semidirect
122. #10622269C22semidirect
123. #10622262C22semidirect
124. #10622262C22semidirect
246. C42×D11D4semidirect
364. C42×C11C2×D4semidirect
410. C4×Dic11C2×D4semidirect
411. C4×Dic11C2×D4semidirect
412. C4×Dic11C2×D4semidirect
426. #2662D11direct (N × H)
554. C2×#126C2×D11semidirect
561. C2×#124C2×D11semidirect
585. #396C2×D11semidirect
591. #395C2×D11semidirect
604. #394C2×D11semidirect
605. #394C2×D11semidirect
611. #393C2×D11semidirect
625. #390C2×D11semidirect
633. #388C2×D11semidirect
639. C4×C4⋊C4C2×D11semidirect
843. D11#2662direct (N × H)
994. C42D4×D11semidirect
995. C11C2×#2662semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1262
C2×D11×#1242
#130747622
#130747612
#130747602
#130747592
#130747582
#130747572
#130747562
#130747552
#130747542
#130747532
#130747522
D11×#3962
D11×#3952
D11×#3942
D11×#3932
D11×#3922
D11×#3902
D11×#3882
C4×C4⋊C4×D112
C11×#26622
C2×#266211