Finite Group Databasebeta

← D11×#2490 #14923211

Subgroups — D11×#2490 #14923211

Order 2816.

3158 conjugacy classes of subgroups.

The subgroup lattice has 1242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#125C211yesmaximal, characteristic, complemented
2C2×D11×#121C211yesmaximal, characteristic
3#13072971C211yesmaximal, characteristic, complemented
4#13072970C211yesmaximal, characteristic, complemented
5#13072969C211yesmaximal, characteristic, complemented
6#13072968C211yesmaximal, characteristic, complemented
7#13072967C212yesmaximal, complemented
8#13072966C211yesmaximal, characteristic, complemented
9#13072965C212yesmaximal, complemented
10#13072964C211yesmaximal, characteristic, complemented
11#13072963C212yesmaximal, complemented
12#13072962C211yesmaximal, characteristic, complemented
13#13072961C212yesmaximal, complemented
14D11×#397C212yesmaximal, complemented
15D11×#394C212yesmaximal, complemented
16D11×#390C211yesmaximal, characteristic, complemented
17D11×#390C211yesmaximal, characteristic, complemented
18D11×#390C212yesmaximal, complemented
19D11×#388C212yesmaximal, complemented
20D11×#380C211yesmaximal, characteristic, complemented
21C4×C4⋊C4×D11C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2490C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C22×D4×D11C2212yes—
26C23×C4×D11C2211yescharacteristic
27C2×C11×#125C2211yescharacteristic, complemented
28C2×C11×#121C2211yescharacteristic
29C2×#66992C2212yes—
30C2×#66991C2211yescharacteristic
31C2×#66983C2211yescharacteristic
32D11×#125—28no—
33D11×#121—28no—
34C2×#66948C2211yescharacteristic
35C2×C4⋊C4×D11C2211yescharacteristic
36C2×C4⋊C4×D11C2212yes—
37C2×C4⋊C4×D11C2212yes—
38C2×C4⋊C4×D11C2211yescharacteristic
39C2×C4⋊C4×D11C2211yescharacteristic
40C2×#66943C2211yescharacteristic, complemented
41C2×#66943C2211yescharacteristic, complemented
42C2×#66942C2212yescomplemented
43C2×#66942C2212yescomplemented
44C2×#66937C2212yes—
45C2×C22⋊C4×D11C2211yescharacteristic
46C2×C22⋊C4×D11C2211yescharacteristic
47C2×C22⋊C4×D11C2212yes—
48C2×C22⋊C4×D11C2212yes—
49C2×C22⋊C4×D11C2212yes—
50C2×C22⋊C4×D11C2212yes—
51C2×C22⋊C4×D11C2212yes—
52C2×C22⋊C4×D11C2212yes—
53C2×C42×D11C2211yescharacteristic
54C2×C42×D11C2211yescharacteristic
55C2×C42×D11C2212yes—
56C2×#66923C2211yescharacteristic, complemented
57C11×#397C2212yescomplemented
58C11×#394C2212yescomplemented
59C11×#390C2212yescomplemented
60C11×#390C2211yescharacteristic, complemented
61C11×#390C2211yescharacteristic, complemented
62C11×#388C2212yescomplemented
63C11×#380C2211yescharacteristic, complemented
64C4×C11×C4⋊C4C2211yescharacteristic, complemented
65C4×C11×C22⋊C4C2211yescharacteristic, complemented
66#10622835C2212yescomplemented
67#10622834C2212yescomplemented
68#10622834C2211yescharacteristic, complemented
69#10622834C2211yescharacteristic, complemented
70#10622825C2211yescharacteristic, complemented
71C4×C22⋊Dic11C2211yescharacteristic, complemented
72#10622606C2212yescomplemented
73#10622604C2212yescomplemented
74#10622603C2212yescomplemented
75#10622601C2211yescharacteristic, complemented
76#10622601C2212yescomplemented
77#10622601C2211yescharacteristic, complemented
78#10622600C2211yescharacteristic, complemented
79#10622600C2211yescharacteristic, complemented
80C4⋊C4×Dic11C2211yescharacteristic, complemented
81C4⋊C4×Dic11C2211yescharacteristic, complemented
82#10622574C2212yescomplemented
83#10622574C2212yescomplemented
84#10622572C2212yescomplemented
85#10622572C2212yescomplemented
86#10622570C2212yescomplemented
87#10622570C2212yescomplemented
88#10622570C2212yescomplemented
89#10622570C2212yescomplemented
90#10622570C2212yescomplemented
91#10622570C2212yescomplemented
92#10622570C2212yescomplemented
93#10622570C2212yescomplemented
94#10622566C2212yescomplemented
95#10622565C2212yescomplemented
96#10622565C2212yescomplemented
97#10622564C2212yescomplemented
98#10622558C2212yescomplemented
99#10622557C2212yescomplemented
100#10622555C2212yescomplemented
101C22⋊C4×Dic11C2211yescharacteristic, complemented
102C22⋊C4×Dic11C2211yescharacteristic, complemented
103#10622553C2212yescomplemented
104#10622552C2212yescomplemented
105#10622552C2211yescharacteristic, complemented
106#10622552C2211yescharacteristic, complemented
107C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
108C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
109C4×C4⋊Dic11C2211yescharacteristic, complemented
110C4×Dic11⋊C4C2212yescomplemented
111#10622288C2212yescomplemented
112#10622288C2212yescomplemented
113#10622287C2212yescomplemented
114#10622285C2212yescomplemented
115#10622283C2212yescomplemented
116#10622282C2212yescomplemented
117#10622280C2212yescomplemented
118#10622279C2211yescharacteristic, complemented
119#10622279C2211yescharacteristic, complemented
120D11×#95C2211yescharacteristic
121D11×#95C2211yescharacteristic
122D11×#95C2212yes—
123D11×#95C2212yes—
124#10622262C2212yescomplemented
125C24×D11C2312yes—
126C24×D11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C22×D4×C11C2312yes—
129C23×C4×C11C2311yescharacteristic
130C22×C22⋊D11C2312yes—
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C23×Dic11C2311yescharacteristic
134C2×D4×D11—28no—
135C2×D4×D11—28no—
136C2×D4×D11—24no—
137C2×D4×D11—24no—
138C2×D4×D11—24no—
139C2×D4×D11—44no—
140C22×D44C2311yescharacteristic
141C22×D44C2312yes—
142C22×C4×D11—24no—
143C22×C4×D11—24no—
144C22×C4×D11—24no—
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2312yes—
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2312yes—
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2312yes—
154C22×C4×D11C2311yescharacteristic
155C22×C4×D11C2311yescharacteristic
156C11×#125—24no—
157C11×#121—24no—
158C2×C11×C4⋊C4C2312yes—
159C2×C11×C4⋊C4C2312yes—
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C4⋊C4C2311yescharacteristic
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2311yescharacteristic
165C2×C11×C22⋊C4C2311yescharacteristic
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×C22⋊Dic11C2311yescharacteristic
175C2×C22⋊Dic11C2311yescharacteristic
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182#66992—28no—
183#66991—24no—
184#66983—24no—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2311yescharacteristic
189C2×(C2×D11)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2311yescharacteristic
191C2×(C2×D11)⋊C4C2312yes—
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×(C2×D11)⋊C4C2312yes—
201C2×C4⋊Dic11C2311yescharacteristic
202C2×C4⋊Dic11C2312yes—
203C2×C4⋊Dic11C2312yes—
204C2×C4⋊Dic11C2311yescharacteristic
205C2×C4⋊Dic11C2311yescharacteristic
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2312yes—
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2312yes—
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221C2×C4×Dic11C2312yes—
222#66948—24no—
223C4⋊C4×D11—28no—
224C4⋊C4×D11—28no—
225C4⋊C4×D11—24no—
226C4⋊C4×D11—24no—
227C4⋊C4×D11D418yes—
228#66943—24no—
229#66943—24no—
230#66942—28no—
231#66942—28no—
232#66937—28no—
233C22⋊C4×D11—24no—
234C22⋊C4×D11—28no—
235C22⋊C4×D11—24no—
236C22⋊C4×D11—28no—
237C22⋊C4×D11—44no—
238C22⋊C4×D11—44no—
239C22⋊C4×D11—44no—
240C22⋊C4×D11—44no—
241C42×D11—24no—
242C42×D11—24no—
243C42×D11—44no—
244#66923—24no—
245C11×#95C2312yes—
246C11×#95C2311yescharacteristic
247C11×#95C2311yescharacteristic
248C11×#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2311yescharacteristic
251C11⋊#95C2311yescharacteristic
252C11⋊#95C2312yes—
253C11⋊#95C2311yescharacteristic
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2311yescharacteristic
258C11⋊#95C2311yescharacteristic
259C11⋊#95C2311yescharacteristic
260C11⋊#95C2312yes—
261C2×#2490—111nomaximal, Sylow
262C24×C11C2412yes—
263C24×C11C2411yescharacteristic
264C23×D11—22no—
265C23×D11—22no—
266C23×D11—22no—
267C23×D11—22no—
268C23×D11—22no—
269C23×D11—22no—
270C23×D11—24no—
271C23×D11—24no—
272C23×D11—24no—
273C23×D11—24no—
274C23×D11—24no—
275C23×D11—24no—
276C23×D11—24no—
277C23×D11#4114yes—
278C23×D11C2412yes—
279C23×D11C2411yescharacteristic
280C23×D11C2411yescharacteristic
281C2×D4×C11—24no—
282C2×D4×C11—22no—
283C2×D4×C11—24no—
284C2×D4×C11—22no—
285C2×D4×C11—22no—
286C2×D4×C11—42no—
287C22×C4×C11—22no—
288C22×C4×C11—22no—
289C22×C4×C11—22no—
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2412yes—
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2412yes—
296C22×C4×C11C2412yes—
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2411yescharacteristic
299C2×C22⋊D11—24no—
300C2×C22⋊D11—24no—
301C2×C22⋊D11—24no—
302C2×C22⋊D11—24no—
303C2×C22⋊D11—24no—
304C2×C22⋊D11—24no—
305C2×C22⋊D11—24no—
306C2×C22⋊D11—42no—
307C2×C22⋊D11—42no—
308C22×Dic11—22no—
309C22×Dic11—22no—
310C22×Dic11—22no—
311C22×Dic11C2411yescharacteristic
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2412yes—
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2412yes—
317C22×Dic11C2412yes—
318C22×Dic11C2411yescharacteristic
319C22×Dic11C2411yescharacteristic
320D4×D11—432no—
321D4×D11—416no—
322C2×D44—24no—
323C2×D44—24no—
324C2×D44—22no—
325C2×D44—22no—
326C2×D44—22no—
327C2×D44—42no—
328C2×C4×D11—22no—
329C2×C4×D11—22no—
330C2×C4×D11—22no—
331C2×C4×D11—22no—
332C2×C4×D11—22no—
333C2×C4×D11—22no—
334C2×C4×D11—24no—
335C2×C4×D11—22no—
336C2×C4×D11—24no—
337C2×C4×D11—22no—
338C2×C4×D11—22no—
339C2×C4×D11—22no—
340C2×C4×D11—22no—
341C2×C4×D11—24no—
342C2×C4×D11—24no—
343C2×C4×D11—22no—
344C2×C4×D11—22no—
345C2×C4×D11—22no—
346C2×C4×D11—24no—
347C2×C4×D11—24no—
348C2×C4×D11—22no—
349C2×C4×D11—24no—
350C2×C4×D11—22no—
351C2×C4×D11—24no—
352C2×C4×D11—22no—
353C2×C4×D11—22no—
354C2×C4×D11—22no—
355C2×C4×D11—22no—
356C2×C4×D11—416no—
357C2×C4×D11C2×D418yes—
358C2×C4×D11C2×D414yes—
359C2×C4×D11#4114yes—
360C2×C4×D11#4114yes—
361C2×C4×D11#4114yes—
362C11×C4⋊C4—24no—
363C11×C4⋊C4—24no—
364C11×C4⋊C4—22no—
365C11×C4⋊C4—22no—
366C11×C4⋊C4C2×D414yes—
367C11×C22⋊C4—22no—
368C11×C22⋊C4—24no—
369C11×C22⋊C4—22no—
370C11×C22⋊C4—24no—
371C11×C22⋊C4—42no—
372C11×C22⋊C4—42no—
373C11×C22⋊C4—42no—
374C11×C22⋊C4—42no—
375C42×C11—22no—
376C42×C11—22no—
377C42×C11—42no—
378C22⋊Dic11—24no—
379C22⋊Dic11—22no—
380C22⋊Dic11—24no—
381C22⋊Dic11—22no—
382C22⋊Dic11—42no—
383C22⋊Dic11—42no—
384C22⋊Dic11—42no—
385C22⋊Dic11—42no—
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—22no—
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—22no—
390(C2×D11)⋊C4—22no—
391(C2×D11)⋊C4—24no—
392(C2×D11)⋊C4—22no—
393(C2×D11)⋊C4—24no—
394(C2×D11)⋊C4—42no—
395(C2×D11)⋊C4—42no—
396(C2×D11)⋊C4—42no—
397(C2×D11)⋊C4—42no—
398(C2×D11)⋊C4—42no—
399(C2×D11)⋊C4—42no—
400(C2×D11)⋊C4—42no—
401(C2×D11)⋊C4—42no—
402C4⋊Dic11—24no—
403C4⋊Dic11—22no—
404C4⋊Dic11—24no—
405C4⋊Dic11—22no—
406C4⋊Dic11C2×D414yes—
407Dic11⋊C4—24no—
408Dic11⋊C4—24no—
409Dic11⋊C4—24no—
410Dic11⋊C4—24no—
411Dic11⋊C4—24no—
412Dic11⋊C4—24no—
413Dic11⋊C4C2×D418yes—
414C4×Dic11—22no—
415C4×Dic11—22no—
416C4×Dic11—22no—
417C4×Dic11—22no—
418C4×Dic11—22no—
419C4×Dic11—22no—
420C4×Dic11—42no—
421C4×Dic11—42no—
422C4×Dic11—42no—
423C22×#125—111no—
424C22×#121—111no—
425#2490—112no—
426#2490—112no—
427#2490—112no—
428#2490—111no—
429#2490—111no—
430#2490—112no—
431#2490—111no—
432#2490—111no—
433#2490—111no—
434#2490—111no—
435#2490—111no—
436#2490D1111yescharacteristic, direct product factor
437C2×#397—112no—
438C2×#394—112no—
439C2×#390—112no—
440C2×#390—111no—
441C2×#390—111no—
442C2×#388—112no—
443C2×#380—111no—
444C2×C4×C4⋊C4—111no—
445C2×C4×C22⋊C4—111no—
446C23×C11—21no—
447C23×C11—21no—
448C23×C11—21no—
449C23×C11—21no—
450C23×C11—21no—
451C23×C11—21no—
452C23×C11—22no—
453C23×C11—22no—
454C23×C11—22no—
455C23×C11—22no—
456C23×C11—22no—
457C23×C11—22no—
458C23×C11—22no—
459C23×C11C2×#4112yes—
460C23×C11C2511yescharacteristic
461C22×D11—21no—
462C22×D11—21no—
463C22×D11—21no—
464C22×D11—21no—
465C22×D11—21no—
466C22×D11—21no—
467C22×D11—28no—
468C22×D11—28no—
469C22×D11—28no—
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—22no—
475C22×D11—22no—
476C22×D11—22no—
477C22×D11—44no—
478C22×D11—44no—
479C22×D11—44no—
480C22×D11—44no—
481C22×D11—48no—
482C22×D11—48no—
483C22×D11—48no—
484C22×D11—48no—
485C22×D11—48no—
486C22×D11—48no—
487C22×D11—48no—
488C22×D11C22×D412yes—
489C22×D11C2×#4112yes—
490C22×D11C2×#4112yes—
491C22×D11C2×#4112yes—
492C22×D11C2×#4112yes—
493C22×D11C2×#4112yes—
494C22×D11H(5,𝔽2)12yes—
495C22×D11H(5,𝔽2)12yes—
496D4×C11—48no—
497D4×C11—44no—
498C2×C4×C11—21no—
499C2×C4×C11—22no—
500C2×C4×C11—21no—
501C2×C4×C11—22no—
502C2×C4×C11—21no—
503C2×C4×C11—21no—
504C2×C4×C11—22no—
505C2×C4×C11—21no—
506C2×C4×C11—21no—
507C2×C4×C11—22no—
508C2×C4×C11—21no—
509C2×C4×C11—21no—
510C2×C4×C11—22no—
511C2×C4×C11—21no—
512C2×C4×C11—21no—
513C2×C4×C11—21no—
514C2×C4×C11—22no—
515C2×C4×C11—22no—
516C2×C4×C11—21no—
517C2×C4×C11—21no—
518C2×C4×C11—22no—
519C2×C4×C11—21no—
520C2×C4×C11—44no—
521C2×C4×C11C22×D414yes—
522C2×C4×C11C22×D412yes—
523C2×C4×C11C2×#4112yes—
524C2×C4×C11C2×#4112yes—
525C2×C4×C11C2×#4112yes—
526C22⋊D11—48no—
527C22⋊D11—48no—
528C22⋊D11—48no—
529C2×Dic11—21no—
530C2×Dic11—22no—
531C2×Dic11—21no—
532C2×Dic11—22no—
533C2×Dic11—21no—
534C2×Dic11—21no—
535C2×Dic11—22no—
536C2×Dic11—21no—
537C2×Dic11—21no—
538C2×Dic11—22no—
539C2×Dic11—21no—
540C2×Dic11—21no—
541C2×Dic11—22no—
542C2×Dic11—21no—
543C2×Dic11—21no—
544C2×Dic11—21no—
545C2×Dic11—22no—
546C2×Dic11—22no—
547C2×Dic11—21no—
548C2×Dic11—21no—
549C2×Dic11—22no—
550C2×Dic11—21no—
551C2×Dic11—44no—
552C2×Dic11C22×D414yes—
553C2×Dic11C22×D412yes—
554C2×Dic11C2×#4112yes—
555C2×Dic11C2×#4112yes—
556C2×Dic11C2×#4112yes—
557D44—48no—
558D44—44no—
559C4×D11—216no—
560C4×D11—28no—
561C4×D11—44no—
562C4×D11—48no—
563C4×D11—44no—
564C4×D11—44no—
565C4×D11—48no—
566C4×D11—44no—
567C4×D11—44no—
568C4×D11—44no—
569C4×D11#124116yes—
570C23×D4—111no—
571C23×D4—112no—
572C24×C4—111no—
573C2×#125—112no—
574C2×#125—112no—
575C2×#125—111no—
576C2×#125—111no—
577C2×#125—111no—
578C2×#125—228no—
579C2×#125C2×D1111yescharacteristic, complemented
580C2×#121—111no—
581C2×#121—112no—
582C2×#121—111no—
583C2×#121—111no—
584C2×#121—112no—
585C2×#121—228no—
586C2×#121C2×D1111yescharacteristic
587C22×C4⋊C4—111no—
588C22×C4⋊C4—112no—
589C22×C4⋊C4—112no—
590C22×C4⋊C4—111no—
591C22×C4⋊C4—111no—
592C22×C22⋊C4—111no—
593C22×C22⋊C4—112no—
594C22×C22⋊C4—111no—
595C22×C22⋊C4—112no—
596C22×C22⋊C4—112no—
597C22×C22⋊C4—112no—
598C22×C22⋊C4—112no—
599C22×C22⋊C4—112no—
600C22×C42—111no—
601C22×C42—111no—
602C22×C42—112no—
603#397—112no—
604#397—112no—
605#397—112no—
606#397—112no—
607#397—112no—
608#397—112no—
609#397—112no—
610#397C2×D1112yescomplemented
611#394—112no—
612#394—112no—
613#394—112no—
614#394—112no—
615#394—112no—
616#394—112no—
617#394—112no—
618#394C2×D1112yescomplemented
619#390—111no—
620#390—111no—
621#390—112no—
622#390—111no—
623#390—111no—
624#390—112no—
625#390—112no—
626#390—112no—
627#390—112no—
628#390—112no—
629#390—112no—
630#390—112no—
631#390—112no—
632#390—112no—
633#390—111no—
634#390—111no—
635#390—112no—
636#390C2×D1111yescharacteristic, complemented
637#390C2×D1111yescharacteristic, complemented
638#390C2×D1112yescomplemented
639#388—112no—
640#388—112no—
641#388—112no—
642#388—112no—
643#388—112no—
644#388—112no—
645#388—112no—
646#388C2×D1112yescomplemented
647#380—111no—
648#380—111no—
649#380—111no—
650#380—112no—
651#380—112no—
652#380C2×D1111yescharacteristic, complemented
653C4×C4⋊C4—111no—
654C4×C4⋊C4—111no—
655C4×C4⋊C4—112no—
656C4×C4⋊C4—111no—
657C4×C4⋊C4—112no—
658C4×C4⋊C4C2×D1111yescharacteristic, complemented
659C4×C22⋊C4—111no—
660C4×C22⋊C4—111no—
661C4×C22⋊C4—111no—
662C4×C22⋊C4—111no—
663C4×C22⋊C4—111no—
664C4×C22⋊C4—111no—
665C4×C22⋊C4—111no—
666C4×C22⋊C4C2×D1111yescharacteristic, complemented
667C2×#95—112no—
668C2×#95—111no—
669C2×#95—112no—
670C2×#95—111no—
671C22×C11—22no—
672C22×C11—22no—
673C22×C11—22no—
674C22×C11—41no—
675C22×C11—41no—
676C22×C11—41no—
677C22×C11—41no—
678C22×C11—42no—
679C22×C11—42no—
680C22×C11—42no—
681C22×C11—42no—
682C22×C11—42no—
683C22×C11—42no—
684C22×C11—42no—
685C22×C11C23×D411yescharacteristic
686C22×C11C22×#4111yescharacteristic
687C22×C11C22×#4111yescharacteristic
688C22×C11C22×#4111yescharacteristic
689C22×C11C22×#4111yescharacteristic
690C22×C11C2×H(5,𝔽2)11yescharacteristic
691C22×C11C2×H(5,𝔽2)11yescharacteristic
692C2×D11—22no—
693C2×D11—22no—
694C2×D11—22no—
695C2×D11—41no—
696C2×D11—41no—
697C2×D11—41no—
698C2×D11—41no—
699C2×D11—416no—
700C2×D11—42no—
701C2×D11—42no—
702C2×D11—42no—
703C2×D11—42no—
704C2×D11—42no—
705C2×D11—42no—
706C2×D11—42no—
707C2×D11—816no—
708C2×D11C2×#12414yes—
709C2×D11#52914yes—
710C2×D11#54014yes—
711C2×D11#54614yes—
712C2×D11#55014yes—
713C2×D11#55314yes—
714C2×D11#55314yes—
715C4×C11—24no—
716C4×C11—22no—
717C4×C11—41no—
718C4×C11—42no—
719C4×C11—41no—
720C4×C11—41no—
721C4×C11—42no—
722C4×C11—41no—
723C4×C11C2×#12414yes—
724Dic11—24no—
725Dic11—22no—
726Dic11—41no—
727Dic11—42no—
728Dic11—41no—
729Dic11—41no—
730Dic11—42no—
731Dic11—41no—
732Dic11C2×#12414yes—
733C25—111no—
734C25—112no—
735C22×D4—112no—
736C22×D4—112no—
737C22×D4—112no—
738C22×D4—111no—
739C22×D4—112no—
740C22×D4—224no—
741C22×D4—228no—
742C22×D4—224no—
743C22×D4—224no—
744C22×D4—228no—
745C22×D4—444no—
746C22×D4C22×D1111yescharacteristic
747C22×D4C22×D1112yes—
748C23×C4—111no—
749C23×C4—111no—
750C23×C4—112no—
751C23×C4—111no—
752C23×C4—112no—
753C23×C4—111no—
754C23×C4—111no—
755C23×C4—112no—
756C23×C4—111no—
757C23×C4—111no—
758C23×C4—111no—
759C23×C4—111no—
760C23×C4—224no—
761C23×C4—224no—
762C23×C4—224no—
763C23×C4C22×D1111yescharacteristic
764#125—24no—
765#125—224no—
766#125—228no—
767#125—228no—
768#125—224no—
769#125—224no—
770#121—24no—
771#121—228no—
772#121—224no—
773#121—224no—
774#121—228no—
775#121—224no—
776C2×C4⋊C4—112no—
777C2×C4⋊C4—111no—
778C2×C4⋊C4—118no—
779C2×C4⋊C4—112no—
780C2×C4⋊C4—111no—
781C2×C4⋊C4—112no—
782C2×C4⋊C4—112no—
783C2×C4⋊C4—112no—
784C2×C4⋊C4—112no—
785C2×C4⋊C4—112no—
786C2×C4⋊C4—112no—
787C2×C4⋊C4—112no—
788C2×C4⋊C4—111no—
789C2×C4⋊C4—224no—
790C2×C4⋊C4—228no—
791C2×C4⋊C4—228no—
792C2×C4⋊C4—224no—
793C2×C4⋊C4C22×D1111yescharacteristic
794C2×C4⋊C4C22×D1112yes—
795C2×C4⋊C4C22×D1112yes—
796C2×C4⋊C4C22×D1111yescharacteristic
797C2×C4⋊C4C22×D1111yescharacteristic
798C2×C22⋊C4—112no—
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—111no—
807C2×C22⋊C4—111no—
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—112no—
816C2×C22⋊C4—112no—
817C2×C22⋊C4—112no—
818C2×C22⋊C4—112no—
819C2×C22⋊C4—112no—
820C2×C22⋊C4—112no—
821C2×C22⋊C4—112no—
822C2×C22⋊C4—228no—
823C2×C22⋊C4—224no—
824C2×C22⋊C4—228no—
825C2×C22⋊C4—224no—
826C2×C22⋊C4—444no—
827C2×C22⋊C4—444no—
828C2×C22⋊C4—444no—
829C2×C22⋊C4—444no—
830C2×C22⋊C4C22×D1112yes—
831C2×C22⋊C4C22×D1111yescharacteristic
832C2×C22⋊C4C22×D1111yescharacteristic
833C2×C22⋊C4C22×D1112yes—
834C2×C22⋊C4C22×D1112yes—
835C2×C22⋊C4C22×D1112yes—
836C2×C22⋊C4C22×D1112yes—
837C2×C22⋊C4C22×D1112yes—
838C2×C42—111no—
839C2×C42—111no—
840C2×C42—111no—
841C2×C42—111no—
842C2×C42—111no—
843C2×C42—111no—
844C2×C42—112no—
845C2×C42—112no—
846C2×C42—112no—
847C2×C42—224no—
848C2×C42—224no—
849C2×C42—444no—
850C2×C42C22×D1111yescharacteristic
851C2×C42C22×D1111yescharacteristic
852C2×C42C22×D1112yes—
853#95—111no—
854#95—111no—
855#95—111no—
856#95—111no—
857#95—111no—
858#95—111no—
859#95—112no—
860#95—112no—
861#95—112no—
862#95—112no—
863#95—112no—
864#95—112no—
865#95C22×D1111yescharacteristic
866#95C22×D1111yescharacteristic
867#95C22×D1112yes—
868#95C22×D1112yes—
869C2×C11—42no—
870C2×C11—82no—
871C2×C11C22×#12411yescharacteristic
872C2×C11C2×#52911yescharacteristic
873C2×C11C2×#54011yescharacteristic
874C2×C11C2×#54611yescharacteristic
875C2×C11C2×#55011yescharacteristic
876C2×C11C2×#55311yescharacteristic
877C2×C11C2×#55311yescharacteristic
878D11—42no—
879D11—82no—
880D11#249018yesdirect product factor
881C24—111no—
882C24—114no—
883C24—111no—
884C24—112no—
885C24—222no—
886C24—222no—
887C24—222no—
888C24—222no—
889C24—222no—
890C24—222no—
891C24—224no—
892C24—224no—
893C24—224no—
894C24—224no—
895C24—224no—
896C24—224no—
897C24—224no—
898C24C23×D1112yes—
899C24C23×D1111yescharacteristic
900C2×D4—24no—
901C2×D4—24no—
902C2×D4—22no—
903C2×D4—22no—
904C2×D4—22no—
905C2×D4—42no—
906C2×D4—224no—
907C2×D4—224no—
908C2×D4—224no—
909C2×D4—224no—
910C2×D4—224no—
911C2×D4—224no—
912C2×D4—224no—
913C2×D4—224no—
914C2×D4—224no—
915C2×D4—222no—
916C2×D4—222no—
917C2×D4—222no—
918C2×D4—442no—
919C2×D4—4416no—
920C2×D4—4432no—
921C2×D4—442no—
922C2×D4—442no—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—111no—
927C22×C4—114no—
928C22×C4—114no—
929C22×C4—114no—
930C22×C4—111no—
931C22×C4—112no—
932C22×C4—118no—
933C22×C4—114no—
934C22×C4—111no—
935C22×C4—111no—
936C22×C4—112no—
937C22×C4—111no—
938C22×C4—111no—
939C22×C4—112no—
940C22×C4—222no—
941C22×C4—222no—
942C22×C4—222no—
943C22×C4—222no—
944C22×C4—222no—
945C22×C4—224no—
946C22×C4—224no—
947C22×C4—222no—
948C22×C4—222no—
949C22×C4—222no—
950C22×C4—224no—
951C22×C4—222no—
952C22×C4—224no—
953C22×C4—222no—
954C22×C4—222no—
955C22×C4—222no—
956C22×C4—224no—
957C22×C4—222no—
958C22×C4—222no—
959C22×C4—224no—
960C22×C4—222no—
961C22×C4—224no—
962C22×C4—224no—
963C22×C4—222no—
964C22×C4—222no—
965C22×C4—222no—
966C22×C4—222no—
967C22×C4—222no—
968C22×C4—222no—
969C22×C4—222no—
970C22×C4—222no—
971C22×C4—4416no—
972C22×C4C23×D1111yescharacteristic
973C22×C4C23×D1111yescharacteristic
974C22×C4C23×D1112yes—
975C22×C4C23×D1111yescharacteristic
976C22×C4C23×D1111yescharacteristic
977C22×C4C23×D1112yes—
978C22×C4C23×D1112yes—
979C22×C4C23×D1111yescharacteristic
980C22×C4C23×D1111yescharacteristic
981C4⋊C4—24no—
982C4⋊C4—24no—
983C4⋊C4—22no—
984C4⋊C4—22no—
985C4⋊C4—118no—
986C4⋊C4—114no—
987C4⋊C4—224no—
988C4⋊C4—224no—
989C4⋊C4—224no—
990C4⋊C4—224no—
991C4⋊C4—224no—
992C4⋊C4—224no—
993C4⋊C4—224no—
994C4⋊C4—224no—
995C4⋊C4—222no—
996C4⋊C4—222no—
997C4⋊C4D4×D1114yes—
998C22⋊C4—22no—
999C22⋊C4—24no—
1000C22⋊C4—22no—
1001C22⋊C4—24no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—224no—
1007C22⋊C4—222no—
1008C22⋊C4—224no—
1009C22⋊C4—222no—
1010C22⋊C4—222no—
1011C22⋊C4—224no—
1012C22⋊C4—222no—
1013C22⋊C4—224no—
1014C22⋊C4—222no—
1015C22⋊C4—224no—
1016C22⋊C4—222no—
1017C22⋊C4—224no—
1018C22⋊C4—442no—
1019C22⋊C4—442no—
1020C22⋊C4—442no—
1021C22⋊C4—442no—
1022C22⋊C4—442no—
1023C22⋊C4—442no—
1024C22⋊C4—442no—
1025C22⋊C4—442no—
1026C22⋊C4—442no—
1027C22⋊C4—442no—
1028C22⋊C4—442no—
1029C22⋊C4—442no—
1030C42—22no—
1031C42—22no—
1032C42—42no—
1033C42—222no—
1034C42—222no—
1035C42—222no—
1036C42—222no—
1037C42—222no—
1038C42—222no—
1039C42—442no—
1040C42—442no—
1041C42—442no—
1042C11C2×#249011yescharacteristic, complemented, Sylow
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—112no—
1057C23—112no—
1058C23—112no—
1059C23—112no—
1060C23—112no—
1061C23—112no—
1062C23—112no—
1063C23—112no—
1064C23—228no—
1065C23—228no—
1066C23—228no—
1067C23—221no—
1068C23—221no—
1069C23—221no—
1070C23—221no—
1071C23—221no—
1072C23—221no—
1073C23—222no—
1074C23—222no—
1075C23—222no—
1076C23—222no—
1077C23—222no—
1078C23—222no—
1079C23—222no—
1080C23—444no—
1081C23—444no—
1082C23—444no—
1083C23—444no—
1084C23—448no—
1085C23—448no—
1086C23—448no—
1087C23—448no—
1088C23—448no—
1089C23—448no—
1090C23—448no—
1091C23#41×D1112yes—
1092C23C24×D1111yescharacteristic
1093D4—48no—
1094D4—44no—
1095D4—448no—
1096D4—448no—
1097D4—448no—
1098D4—448no—
1099D4—444no—
1100C2×C4—21no—
1101C2×C4—22no—
1102C2×C4—21no—
1103C2×C4—22no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—22no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—22no—
1117C2×C4—21no—
1118C2×C4—22no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—22no—
1122C2×C4—44no—
1123C2×C4—112no—
1124C2×C4—112no—
1125C2×C4—112no—
1126C2×C4—1116no—
1127C2×C4—114no—
1128C2×C4—112no—
1129C2×C4—2216no—
1130C2×C4—228no—
1131C2×C4—221no—
1132C2×C4—222no—
1133C2×C4—221no—
1134C2×C4—222no—
1135C2×C4—221no—
1136C2×C4—221no—
1137C2×C4—221no—
1138C2×C4—222no—
1139C2×C4—221no—
1140C2×C4—221no—
1141C2×C4—221no—
1142C2×C4—221no—
1143C2×C4—222no—
1144C2×C4—222no—
1145C2×C4—221no—
1146C2×C4—221no—
1147C2×C4—222no—
1148C2×C4—221no—
1149C2×C4—222no—
1150C2×C4—221no—
1151C2×C4—221no—
1152C2×C4—222no—
1153C2×C4—444no—
1154C2×C4—444no—
1155C2×C4—444no—
1156C2×C4—448no—
1157C2×C4—444no—
1158C2×C4—444no—
1159C2×C4—448no—
1160C2×C4—444no—
1161C2×C4—444no—
1162C2×C4C2×D4×D1114yes—
1163C2×C4C2×D4×D1112yes—
1164C2×C4#41×D1112yes—
1165C2×C4#41×D1112yes—
1166C2×C4#41×D1112yes—
1167C22—22no—
1168C22—22no—
1169C22—22no—
1170C22—41no—
1171C22—41no—
1172C22—41no—
1173C22—41no—
1174C22—42no—
1175C22—42no—
1176C22—42no—
1177C22—42no—
1178C22—42no—
1179C22—42no—
1180C22—42no—
1181C22—114no—
1182C22—114no—
1183C22—114no—
1184C22—114no—
1185C22—114no—
1186C22—114no—
1187C22—114no—
1188C22—222no—
1189C22—222no—
1190C22—222no—
1191C22—4416no—
1192C22—441no—
1193C22—441no—
1194C22—441no—
1195C22—441no—
1196C22—442no—
1197C22—442no—
1198C22—442no—
1199C22—442no—
1200C22—442no—
1201C22—442no—
1202C22—442no—
1203C22—8816no—
1204C22C22×D4×D1111yescharacteristic
1205C22C2×#41×D1111yescharacteristic
1206C22C2×#41×D1111yescharacteristic
1207C22C2×#41×D1111yescharacteristic
1208C22C2×#41×D1111yescharacteristic
1209C22D11×H(5,𝔽2)11yescharacteristic
1210C22D11×H(5,𝔽2)11yescharacteristic
1211C4—22no—
1212C4—24no—
1213C4—41no—
1214C4—41no—
1215C4—42no—
1216C4—41no—
1217C4—41no—
1218C4—42no—
1219C4—114no—
1220C4—222no—
1221C4—224no—
1222C4—441no—
1223C4—441no—
1224C4—442no—
1225C4—441no—
1226C4—441no—
1227C4—442no—
1228C4D11×#12414yes—
1229C2—42no—
1230C2—82no—
1231C2—118no—
1232C2—442no—
1233C2—882no—
1234C2C2×D11×#12411yescharacteristic
1235C2D11×#52911yescharacteristic
1236C2D11×#54011yescharacteristic
1237C2D11×#54611yescharacteristic
1238C2D11×#55011yescharacteristic
1239C2D11×#55311yescharacteristic
1240C2D11×#55311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2490C2
prime radicalC2×D11×#121C2
hypercenter#2490D11
hypocenterC11C2×#2490
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2490

Complements

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

NH ≅ G/Ntype
1. C2×D11×#125C2semidirect
3. #13072971C2semidirect
4. #13072970C2semidirect
5. #13072969C2semidirect
6. #13072968C2semidirect
7. #13072967C2semidirect
8. #13072966C2semidirect
9. #13072965C2semidirect
10. #13072964C2semidirect
11. #13072963C2semidirect
12. #13072962C2semidirect
13. #13072961C2semidirect
14. D11×#397C2semidirect
15. D11×#394C2semidirect
16. D11×#390C2semidirect
17. D11×#390C2semidirect
18. D11×#390C2semidirect
19. D11×#388C2semidirect
20. D11×#380C2semidirect
21. C4×C4⋊C4×D11C2semidirect
22. C4×C22⋊C4×D11C2semidirect
23. C11×#2490C2semidirect
27. C2×C11×#125C22semidirect
40. C2×#66943C22semidirect
41. C2×#66943C22semidirect
42. C2×#66942C22semidirect
43. C2×#66942C22semidirect
56. C2×#66923C22semidirect
57. C11×#397C22semidirect
58. C11×#394C22semidirect
59. C11×#390C22semidirect
60. C11×#390C22semidirect
61. C11×#390C22semidirect
62. C11×#388C22semidirect
63. C11×#380C22semidirect
64. C4×C11×C4⋊C4C22semidirect
65. C4×C11×C22⋊C4C22semidirect
66. #10622835C22semidirect
67. #10622834C22semidirect
68. #10622834C22semidirect
69. #10622834C22semidirect
70. #10622825C22semidirect
71. C4×C22⋊Dic11C22semidirect
72. #10622606C22semidirect
73. #10622604C22semidirect
74. #10622603C22semidirect
75. #10622601C22semidirect
76. #10622601C22semidirect
77. #10622601C22semidirect
78. #10622600C22semidirect
79. #10622600C22semidirect
80. C4⋊C4×Dic11C22semidirect
81. C4⋊C4×Dic11C22semidirect
82. #10622574C22semidirect
83. #10622574C22semidirect
84. #10622572C22semidirect
85. #10622572C22semidirect
86. #10622570C22semidirect
87. #10622570C22semidirect
88. #10622570C22semidirect
89. #10622570C22semidirect
90. #10622570C22semidirect
91. #10622570C22semidirect
92. #10622570C22semidirect
93. #10622570C22semidirect
94. #10622566C22semidirect
95. #10622565C22semidirect
96. #10622565C22semidirect
97. #10622564C22semidirect
98. #10622558C22semidirect
99. #10622557C22semidirect
100. #10622555C22semidirect
101. C22⋊C4×Dic11C22semidirect
102. C22⋊C4×Dic11C22semidirect
103. #10622553C22semidirect
104. #10622552C22semidirect
105. #10622552C22semidirect
106. #10622552C22semidirect
107. C4×(C2×D11)⋊C4C22semidirect
108. C4×(C2×D11)⋊C4C22semidirect
109. C4×C4⋊Dic11C22semidirect
110. C4×Dic11⋊C4C22semidirect
111. #10622288C22semidirect
112. #10622288C22semidirect
113. #10622287C22semidirect
114. #10622285C22semidirect
115. #10622283C22semidirect
116. #10622282C22semidirect
117. #10622280C22semidirect
118. #10622279C22semidirect
119. #10622279C22semidirect
124. #10622262C22semidirect
436. #2490D11direct (N × H)
579. C2×#125C2×D11semidirect
610. #397C2×D11semidirect
618. #394C2×D11semidirect
636. #390C2×D11semidirect
637. #390C2×D11semidirect
638. #390C2×D11semidirect
646. #388C2×D11semidirect
652. #380C2×D11semidirect
658. C4×C4⋊C4C2×D11semidirect
666. C4×C22⋊C4C2×D11semidirect
880. D11#2490direct (N × H)
1042. C11C2×#2490semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1252
C2×D11×#1212
#130729712
#130729702
#130729692
#130729682
#130729672
#130729662
#130729652
#130729642
#130729632
#130729622
#130729612
D11×#3972
D11×#3942
D11×#3902
D11×#3882
D11×#3802
C4×C4⋊C4×D112
C4×C22⋊C4×D112
C11×#24902
C2×#249011