Finite Group Databasebeta

← D11×#2485 #14923282

Subgroups — D11×#2485 #14923282

Order 2816.

3070 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×C4×D4×D11C211yesmaximal, characteristic
2C2×D11×#117C211yesmaximal, characteristic, complemented
3#13072916C211yesmaximal, characteristic, complemented
4#13072915C211yesmaximal, characteristic, complemented
5#13072914C211yesmaximal, characteristic, complemented
6#13072913C211yesmaximal, characteristic, complemented
7#13072912C212yesmaximal, complemented
8#13072911C211yesmaximal, characteristic, complemented
9#13072910C212yesmaximal, complemented
10#13072909C211yesmaximal, characteristic, complemented
11#13072908C212yesmaximal, complemented
12#13072907C211yesmaximal, characteristic, complemented
13#13072906C212yesmaximal, complemented
14D11×#397C212yesmaximal, complemented
15D11×#394C212yesmaximal
16D11×#389C211yesmaximal, characteristic, complemented
17D11×#389C211yesmaximal, characteristic, complemented
18D11×#388C212yesmaximal, complemented
19D11×#387C212yesmaximal, complemented
20D11×#380C211yesmaximal, characteristic, complemented
21D11×#380C211yesmaximal, characteristic, complemented
22D11×#380C211yesmaximal, characteristic, complemented
23C11×#2485C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic, complemented
29C2×D4×Dic11C2211yescharacteristic
30C2×C4×C22⋊D11C2211yescharacteristic
31C2×C4×C22⋊D11C2211yescharacteristic
32C2×#66979C2211yescharacteristic, complemented
33C4×D4×D11—28no—
34D11×#117—28no—
35C2×#66946C2211yescharacteristic
36C2×#66945C2211yescharacteristic, complemented
37C2×#66945C2211yescharacteristic, complemented
38C2×C4⋊C4×D11C2211yescharacteristic
39C2×C4⋊C4×D11C2211yescharacteristic
40C2×C4⋊C4×D11C2211yescharacteristic
41C2×C4⋊C4×D11C2211yescharacteristic
42C2×C4⋊C4×D11C2211yescharacteristic
43C2×C4⋊C4×D11C2212yes—
44C2×C4⋊C4×D11C2212yes—
45C2×(C22⋊D11)⋊C4C2211yescharacteristic
46C2×(C22⋊D11)⋊C4C2211yescharacteristic
47C2×C22⋊C4×D11C2212yes—
48C2×C22⋊C4×D11C2212yes—
49C2×C22⋊C4×D11C2211yescharacteristic
50C2×C22⋊C4×D11C2211yescharacteristic
51C2×C22⋊C4×D11C2212yes—
52C2×C22⋊C4×D11C2212yes—
53C2×#66930C2212yescomplemented
54C2×C4×D44C2211yescharacteristic
55C2×#66925C2212yescomplemented
56C2×C42×D11C2212yes—
57C2×C42×D11C2211yescharacteristic
58C11×#397C2212yescomplemented
59C11×#394C2212yes—
60C11×#389C2211yescharacteristic, complemented
61C11×#389C2211yescharacteristic, complemented
62C11×#388C2212yescomplemented
63C11×#387C2212yescomplemented
64C11×#380C2211yescharacteristic, complemented
65C11×#380C2211yescharacteristic, complemented
66C11×#380C2211yescharacteristic, complemented
67#10622835C2212yes—
68#10622825C2211yescharacteristic, complemented
69#10622825C2211yescharacteristic, complemented
70#10622825C2211yescharacteristic, complemented
71#10622606C2212yescomplemented
72#10622604C2212yes—
73#10622603C2212yescomplemented
74#10622600C2211yescharacteristic, complemented
75#10622600C2211yescharacteristic, complemented
76#10622600C2211yescharacteristic, complemented
77#10622600C2211yescharacteristic, complemented
78#10622600C2211yescharacteristic, complemented
79#10622600C2211yescharacteristic, complemented
80#10622598C2211yescharacteristic, complemented
81#10622598C2211yescharacteristic, complemented
82#10622594C2212yescomplemented
83#10622591C2212yescomplemented
84#10622586C2211yescharacteristic, complemented
85#10622586C2211yescharacteristic, complemented
86#10622585C2212yescomplemented
87#10622585C2212yescomplemented
88#10622574C2212yes—
89#10622574C2212yes—
90#10622572C2212yes—
91#10622572C2212yes—
92#10622566C2212yescomplemented
93#10622565C2212yescomplemented
94#10622565C2212yescomplemented
95#10622564C2212yescomplemented
96#10622558C2212yescomplemented
97#10622557C2212yescomplemented
98#10622555C2212yescomplemented
99#10622555C2212yescomplemented
100#10622555C2212yescomplemented
101#10622553C2212yescomplemented
102#10622546C2212yescomplemented
103#10622541C2211yescharacteristic, complemented
104#10622541C2211yescharacteristic, complemented
105#10622288C2212yescomplemented
106#10622288C2212yescomplemented
107#10622287C2212yescomplemented
108#10622285C2212yes—
109#10622283C2212yescomplemented
110#10622282C2212yescomplemented
111#10622280C2212yescomplemented
112#10622280C2212yescomplemented
113#10622280C2212yescomplemented
114D11×#95C2212yes—
115D11×#95C2212yes—
116D11×#95C2212yes—
117D11×#95C2212yes—
118D11×#95C2212yes—
119#10622268C2212yescomplemented
120#10622267C2212yescomplemented
121#10622266C2212yescomplemented
122#10622265C2212yescomplemented
123#10622260C2212yescomplemented
124#10622260C2212yescomplemented
125C24×D11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C22×C22⋊D11C2311yescharacteristic
131C22×C22⋊D11C2311yescharacteristic
132C23×Dic11C2311yescharacteristic
133C23×Dic11C2311yescharacteristic
134C2×D4×D11—24no—
135C2×D4×D11—24no—
136C2×D4×D11—24no—
137C22×D44C2311yescharacteristic
138C22×C4×D11—24no—
139C22×C4×D11—24no—
140C22×C4×D11—24no—
141C22×C4×D11—24no—
142C22×C4×D11—24no—
143C22×C4×D11D418yes—
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2312yes—
146C22×C4×D11C2312yes—
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2312yes—
149C22×C4×D11C2312yes—
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2311yescharacteristic
154C22×C4×D11C2311yescharacteristic
155C22×C4×D11C2311yescharacteristic
156C22×C4×D11C2311yescharacteristic
157C4×D4×C11—24no—
158C11×#117—24no—
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C4⋊C4C2312yes—
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C4⋊C4C2312yes—
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2311yescharacteristic
168C2×C11×C22⋊C4C2311yescharacteristic
169C2×C11×C22⋊C4C2312yes—
170C2×C11×C22⋊C4C2312yes—
171C2×C11×C22⋊C4C2312yes—
172C2×C42×C11C2312yes—
173C2×C42×C11C2311yescharacteristic
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2311yescharacteristic
176C2×C22⋊Dic11C2311yescharacteristic
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180D4×Dic11—24no—
181C4×C22⋊D11—24no—
182C4×C22⋊D11—24no—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2311yescharacteristic
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2311yescharacteristic
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195#66979—24no—
196C2×C4⋊Dic11C2311yescharacteristic
197C2×C4⋊Dic11C2312yes—
198C2×C4⋊Dic11C2311yescharacteristic
199C2×C4⋊Dic11C2311yescharacteristic
200C2×C4⋊Dic11C2311yescharacteristic
201C2×C4⋊Dic11C2311yescharacteristic
202C2×C4⋊Dic11C2312yes—
203C2×Dic11⋊C4C2312yes—
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C2311yescharacteristic
206C2×Dic11⋊C4C2311yescharacteristic
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2312yes—
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2312yes—
213C2×C4×Dic11C2312yes—
214C2×C4×Dic11C2312yes—
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2311yescharacteristic
219#66946—24no—
220#66945—24no—
221#66945—24no—
222C4⋊C4×D11—24no—
223C4⋊C4×D11—24no—
224C4⋊C4×D11—24no—
225C4⋊C4×D11—24no—
226C4⋊C4×D11—24no—
227C4⋊C4×D11—28no—
228C4⋊C4×D11—44no—
229(C22⋊D11)⋊C4—24no—
230(C22⋊D11)⋊C4—24no—
231C22⋊C4×D11—28no—
232C22⋊C4×D11—24no—
233C22⋊C4×D11—28no—
234C22⋊C4×D11—24no—
235C22⋊C4×D11—44no—
236C22⋊C4×D11—44no—
237#66930—28no—
238C4×D44—24no—
239#66925—28no—
240C42×D11—28no—
241C42×D11—24no—
242C11×#95C2312yes—
243C11×#95C2312yes—
244C11×#95C2312yes—
245C11×#95C2312yes—
246C11×#95C2312yes—
247C11⋊#95C2312yes—
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—
262C2×#2485—111nomaximal, Sylow
263C24×C11C2411yescharacteristic
264C24×C11C2411yescharacteristic
265C23×D11—22no—
266C23×D11—22no—
267C23×D11—22no—
268C23×D11—22no—
269C23×D11—22no—
270C23×D11—22no—
271C23×D11—22no—
272C23×D11—22no—
273C23×D11—22no—
274C23×D11—22no—
275C23×D11—22no—
276C23×D11—22no—
277C23×D11C2×D414yes—
278C23×D11#4114yes—
279C23×D11C2411yescharacteristic
280C23×D11C2411yescharacteristic
281C23×D11C2411yescharacteristic
282C2×D4×C11—22no—
283C2×D4×C11—22no—
284C2×D4×C11—22no—
285C22×C4×C11—22no—
286C22×C4×C11—22no—
287C22×C4×C11—22no—
288C22×C4×C11—22no—
289C22×C4×C11—22no—
290C22×C4×C11C2×D414yes—
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2412yes—
293C22×C4×C11C2412yes—
294C22×C4×C11C2412yes—
295C22×C4×C11C2412yes—
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2411yescharacteristic
300C2×C22⋊D11—22no—
301C2×C22⋊D11—22no—
302C2×C22⋊D11—22no—
303C2×C22⋊D11—22no—
304C2×C22⋊D11—22no—
305C2×C22⋊D11—22no—
306C22×Dic11—22no—
307C22×Dic11—22no—
308C22×Dic11—22no—
309C22×Dic11—22no—
310C22×Dic11—22no—
311C22×Dic11C2×D414yes—
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2412yes—
314C22×Dic11C2412yes—
315C22×Dic11C2412yes—
316C22×Dic11C2412yes—
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2411yescharacteristic
319C22×Dic11C2411yescharacteristic
320C22×Dic11C2411yescharacteristic
321D4×D11—232no—
322C2×D44—22no—
323C2×D44—22no—
324C2×D44—22no—
325C2×C4×D11—22no—
326C2×C4×D11—22no—
327C2×C4×D11—232no—
328C2×C4×D11—22no—
329C2×C4×D11—22no—
330C2×C4×D11—22no—
331C2×C4×D11—22no—
332C2×C4×D11—22no—
333C2×C4×D11—24no—
334C2×C4×D11—24no—
335C2×C4×D11—22no—
336C2×C4×D11—22no—
337C2×C4×D11—22no—
338C2×C4×D11—22no—
339C2×C4×D11—24no—
340C2×C4×D11—24no—
341C2×C4×D11—24no—
342C2×C4×D11—24no—
343C2×C4×D11—24no—
344C2×C4×D11—24no—
345C2×C4×D11—22no—
346C2×C4×D11—22no—
347C2×C4×D11—24no—
348C2×C4×D11—24no—
349C2×C4×D11—24no—
350C2×C4×D11—22no—
351C2×C4×D11—22no—
352C2×C4×D11—24no—
353C2×C4×D11—22no—
354C2×C4×D11—22no—
355C2×C4×D11—22no—
356C2×C4×D11—22no—
357C2×C4×D11—22no—
358C2×C4×D11—416no—
359C2×C4×D11C2×D414yes—
360C2×C4×D11C2×D414yes—
361C2×C4×D11C2×D414yes—
362C2×C4×D11C2×D414yes—
363C2×C4×D11#4114yes—
364C2×C4×D11#4114yes—
365C2×C4×D11#4114yes—
366C11×C4⋊C4—22no—
367C11×C4⋊C4—22no—
368C11×C4⋊C4—22no—
369C11×C4⋊C4—22no—
370C11×C4⋊C4—22no—
371C11×C4⋊C4—24no—
372C11×C4⋊C4—42no—
373C11×C22⋊C4—24no—
374C11×C22⋊C4—22no—
375C11×C22⋊C4—24no—
376C11×C22⋊C4—22no—
377C11×C22⋊C4—42no—
378C11×C22⋊C4—42no—
379C42×C11—24no—
380C42×C11—22no—
381C22⋊Dic11—22no—
382C22⋊Dic11—24no—
383C22⋊Dic11—22no—
384C22⋊Dic11—24no—
385C22⋊Dic11—42no—
386C22⋊Dic11—42no—
387(C2×D11)⋊C4—22no—
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—22no—
395(C2×D11)⋊C4—42no—
396(C2×D11)⋊C4—42no—
397(C2×D11)⋊C4—42no—
398(C2×D11)⋊C4—42no—
399C4⋊Dic11—22no—
400C4⋊Dic11—24no—
401C4⋊Dic11—22no—
402C4⋊Dic11—22no—
403C4⋊Dic11—22no—
404C4⋊Dic11—22no—
405C4⋊Dic11—42no—
406Dic11⋊C4—24no—
407Dic11⋊C4—24no—
408Dic11⋊C4—22no—
409Dic11⋊C4—24no—
410Dic11⋊C4—24no—
411Dic11⋊C4—24no—
412Dic11⋊C4—22no—
413Dic11⋊C4—24no—
414Dic11⋊C4—42no—
415Dic11⋊C4—42no—
416C4×Dic11—24no—
417C4×Dic11—24no—
418C4×Dic11—22no—
419C4×Dic11—22no—
420C4×Dic11—24no—
421C4×Dic11—22no—
422C22×C4×D4—111no—
423C22×#117—111no—
424#2485—112no—
425#2485—112no—
426#2485—111no—
427#2485—111no—
428#2485—112no—
429#2485—112no—
430#2485—111no—
431#2485—111no—
432#2485—111no—
433#2485—111no—
434#2485—111no—
435#2485D1111yescharacteristic, direct product factor
436C2×#397—112no—
437C2×#394—112no—
438C2×#389—111no—
439C2×#389—111no—
440C2×#388—112no—
441C2×#387—112no—
442C2×#380—111no—
443C2×#380—111no—
444C2×#380—111no—
445C23×C11—21no—
446C23×C11—21no—
447C23×C11—21no—
448C23×C11—21no—
449C23×C11—21no—
450C23×C11—21no—
451C23×C11—21no—
452C23×C11—21no—
453C23×C11—21no—
454C23×C11—21no—
455C23×C11—21no—
456C23×C11—21no—
457C23×C11C22×D412yes—
458C23×C11C2×#4112yes—
459C23×C11C2511yescharacteristic
460C22×D11—21no—
461C22×D11—21no—
462C22×D11—21no—
463C22×D11—21no—
464C22×D11—21no—
465C22×D11—21no—
466C22×D11—21no—
467C22×D11—21no—
468C22×D11—21no—
469C22×D11—21no—
470C22×D11—21no—
471C22×D11—21no—
472C22×D11—28no—
473C22×D11—28no—
474C22×D11—28no—
475C22×D11—28no—
476C22×D11—28no—
477C22×D11—28no—
478C22×D11—44no—
479C22×D11—44no—
480C22×D11—44no—
481C22×D11—44no—
482C22×D11—44no—
483C22×D11—44no—
484C22×D11—44no—
485C22×D11—44no—
486C22×D11C22×D412yes—
487C22×D11C22×D412yes—
488C22×D11C2×#4112yes—
489C22×D11C2×#4112yes—
490C22×D11C2×#4112yes—
491C22×D11C2×#4112yes—
492C22×D11C2×#4112yes—
493C22×D11H(5,𝔽2)12yes—
494C22×D112−1+412yes—
495D4×C11—28no—
496C2×C4×C11—21no—
497C2×C4×C11—21no—
498C2×C4×C11—21no—
499C2×C4×C11—21no—
500C2×C4×C11—28no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—21no—
504C2×C4×C11—21no—
505C2×C4×C11—22no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11—22no—
509C2×C4×C11—22no—
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—22no—
517C2×C4×C11—22no—
518C2×C4×C11—21no—
519C2×C4×C11—44no—
520C2×C4×C11C22×D412yes—
521C2×C4×C11C22×D412yes—
522C2×C4×C11C2×#4112yes—
523C2×C4×C11C2×#4112yes—
524C2×C4×C11C2×#4112yes—
525C22⋊D11—28no—
526C22⋊D11—28no—
527C2×Dic11—21no—
528C2×Dic11—21no—
529C2×Dic11—21no—
530C2×Dic11—21no—
531C2×Dic11—28no—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—21no—
535C2×Dic11—21no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—22no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—21no—
543C2×Dic11—21no—
544C2×Dic11—21no—
545C2×Dic11—22no—
546C2×Dic11—22no—
547C2×Dic11—22no—
548C2×Dic11—22no—
549C2×Dic11—21no—
550C2×Dic11—44no—
551C2×Dic11C22×D412yes—
552C2×Dic11C22×D412yes—
553C2×Dic11C2×#4112yes—
554C2×Dic11C2×#4112yes—
555C2×Dic11C2×#4112yes—
556D44—28no—
557C4×D11—28no—
558C4×D11—28no—
559C4×D11—28no—
560C4×D11—28no—
561C4×D11—44no—
562C4×D11—48no—
563C4×D11—44no—
564C4×D11—48no—
565C4×D11—48no—
566C4×D11—48no—
567C4×D11—44no—
568C4×D11—44no—
569C4×D11#123116yes—
570C23×D4—111no—
571C24×C4—111no—
572C24×C4—111no—
573C2×C4×D4—111no—
574C2×C4×D4—111no—
575C2×C4×D4—111no—
576C2×C4×D4—111no—
577C2×C4×D4—111no—
578C2×C4×D4—111no—
579C2×C4×D4—111no—
580C2×C4×D4—228no—
581C2×C4×D4C2×D1111yescharacteristic
582C2×#117—111no—
583C2×#117—111no—
584C2×#117—111no—
585C2×#117—112no—
586C2×#117—112no—
587C2×#117—228no—
588C2×#117C2×D1111yescharacteristic, complemented
589C22×C4⋊C4—112no—
590C22×C4⋊C4—111no—
591C22×C4⋊C4—111no—
592C22×C4⋊C4—111no—
593C22×C4⋊C4—111no—
594C22×C4⋊C4—111no—
595C22×C4⋊C4—112no—
596C22×C22⋊C4—112no—
597C22×C22⋊C4—112no—
598C22×C22⋊C4—111no—
599C22×C22⋊C4—111no—
600C22×C22⋊C4—112no—
601C22×C22⋊C4—112no—
602C22×C42—112no—
603C22×C42—111no—
604#397—112no—
605#397—112no—
606#397—112no—
607#397—112no—
608#397—112no—
609#397—112no—
610#397—112no—
611#397C2×D1112yescomplemented
612#394—112no—
613#394—112no—
614#394—112no—
615#394—112no—
616#394—112no—
617#394—112no—
618#394—112no—
619#394C2×D1112yes—
620#389—112no—
621#389—112no—
622#389—111no—
623#389—111no—
624#389—111no—
625#389—111no—
626#389—111no—
627#389—111no—
628#389—112no—
629#389—112no—
630#389C2×D1111yescharacteristic, complemented
631#389C2×D1111yescharacteristic, complemented
632#388—112no—
633#388—112no—
634#388—112no—
635#388—112no—
636#388—112no—
637#388—112no—
638#388—112no—
639#388C2×D1112yescomplemented
640#387—112no—
641#387—112no—
642#387—112no—
643#387—112no—
644#387—112no—
645#387—112no—
646#387—112no—
647#387C2×D1112yescomplemented
648#380—111no—
649#380—111no—
650#380—111no—
651#380—111no—
652#380—111no—
653#380—111no—
654#380—111no—
655#380—111no—
656#380—111no—
657#380—112no—
658#380—112no—
659#380—112no—
660#380—112no—
661#380—112no—
662#380—112no—
663#380C2×D1111yescharacteristic, complemented
664#380C2×D1111yescharacteristic, complemented
665#380C2×D1111yescharacteristic, complemented
666C2×#95—112no—
667C2×#95—112no—
668C2×#95—112no—
669C2×#95—112no—
670C2×#95—112no—
671C22×C11—22no—
672C22×C11—22no—
673C22×C11—22no—
674C22×C11—22no—
675C22×C11—22no—
676C22×C11—22no—
677C22×C11—41no—
678C22×C11—41no—
679C22×C11—41no—
680C22×C11—41no—
681C22×C11—41no—
682C22×C11—41no—
683C22×C11—41no—
684C22×C11—41no—
685C22×C11C23×D411yescharacteristic
686C22×C11C22×#4111yescharacteristic
687C22×C11C22×#4111yescharacteristic
688C22×C11C22×#4111yescharacteristic
689C22×C11C22×#4111yescharacteristic
690C22×C11C2×H(5,𝔽2)11yescharacteristic
691C22×C11C2×2−1+411yescharacteristic
692C2×D11—22no—
693C2×D11—22no—
694C2×D11—22no—
695C2×D11—22no—
696C2×D11—22no—
697C2×D11—22no—
698C2×D11—41no—
699C2×D11—41no—
700C2×D11—41no—
701C2×D11—41no—
702C2×D11—41no—
703C2×D11—41no—
704C2×D11—41no—
705C2×D11—41no—
706C2×D11—416no—
707C2×D11—416no—
708C2×D11C2×#12314yes—
709C2×D11#52514yes—
710C2×D11#53714yes—
711C2×D11#55214yes—
712C2×D11#55314yes—
713C2×D11#55514yes—
714C2×D11#55614yes—
715C4×C11—22no—
716C4×C11—22no—
717C4×C11—41no—
718C4×C11—42no—
719C4×C11—42no—
720C4×C11—41no—
721C4×C11—42no—
722C4×C11—42no—
723C4×C11C2×#12314yes—
724Dic11—22no—
725Dic11—22no—
726Dic11—41no—
727Dic11—42no—
728Dic11—42no—
729Dic11—41no—
730Dic11—42no—
731Dic11—42no—
732Dic11C2×#12314yes—
733C25—111no—
734C25—111no—
735C22×D4—111no—
736C22×D4—111no—
737C22×D4—111no—
738C22×D4—224no—
739C22×D4—224no—
740C22×D4—224no—
741C22×D4C22×D1111yescharacteristic
742C23×C4—111no—
743C23×C4—111no—
744C23×C4—118no—
745C23×C4—111no—
746C23×C4—111no—
747C23×C4—111no—
748C23×C4—111no—
749C23×C4—111no—
750C23×C4—112no—
751C23×C4—112no—
752C23×C4—111no—
753C23×C4—112no—
754C23×C4—112no—
755C23×C4—111no—
756C23×C4—111no—
757C23×C4—111no—
758C23×C4—224no—
759C23×C4—224no—
760C23×C4—224no—
761C23×C4—224no—
762C23×C4—224no—
763C23×C4C22×D1111yescharacteristic
764C23×C4C22×D1111yescharacteristic
765C4×D4—24no—
766C4×D4—224no—
767C4×D4—224no—
768C4×D4—224no—
769C4×D4—224no—
770C4×D4—224no—
771C4×D4—224no—
772C4×D4—224no—
773#117—24no—
774#117—228no—
775#117—228no—
776#117—224no—
777#117—224no—
778#117—224no—
779C2×C4⋊C4—112no—
780C2×C4⋊C4—112no—
781C2×C4⋊C4—111no—
782C2×C4⋊C4—111no—
783C2×C4⋊C4—111no—
784C2×C4⋊C4—111no—
785C2×C4⋊C4—111no—
786C2×C4⋊C4—112no—
787C2×C4⋊C4—112no—
788C2×C4⋊C4—111no—
789C2×C4⋊C4—111no—
790C2×C4⋊C4—112no—
791C2×C4⋊C4—112no—
792C2×C4⋊C4—112no—
793C2×C4⋊C4—112no—
794C2×C4⋊C4—112no—
795C2×C4⋊C4—112no—
796C2×C4⋊C4—224no—
797C2×C4⋊C4—224no—
798C2×C4⋊C4—224no—
799C2×C4⋊C4—224no—
800C2×C4⋊C4—224no—
801C2×C4⋊C4—228no—
802C2×C4⋊C4—444no—
803C2×C4⋊C4C22×D1111yescharacteristic
804C2×C4⋊C4C22×D1111yescharacteristic
805C2×C4⋊C4C22×D1111yescharacteristic
806C2×C4⋊C4C22×D1111yescharacteristic
807C2×C4⋊C4C22×D1111yescharacteristic
808C2×C4⋊C4C22×D1112yes—
809C2×C4⋊C4C22×D1112yes—
810C2×C22⋊C4—112no—
811C2×C22⋊C4—111no—
812C2×C22⋊C4—111no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—112no—
815C2×C22⋊C4—112no—
816C2×C22⋊C4—111no—
817C2×C22⋊C4—111no—
818C2×C22⋊C4—111no—
819C2×C22⋊C4—111no—
820C2×C22⋊C4—112no—
821C2×C22⋊C4—112no—
822C2×C22⋊C4—112no—
823C2×C22⋊C4—112no—
824C2×C22⋊C4—112no—
825C2×C22⋊C4—112no—
826C2×C22⋊C4—112no—
827C2×C22⋊C4—112no—
828C2×C22⋊C4—224no—
829C2×C22⋊C4—228no—
830C2×C22⋊C4—224no—
831C2×C22⋊C4—228no—
832C2×C22⋊C4—444no—
833C2×C22⋊C4—444no—
834C2×C22⋊C4C22×D1112yes—
835C2×C22⋊C4C22×D1111yescharacteristic
836C2×C22⋊C4C22×D1111yescharacteristic
837C2×C22⋊C4C22×D1112yes—
838C2×C22⋊C4C22×D1112yes—
839C2×C22⋊C4C22×D1112yes—
840C2×C42—112no—
841C2×C42—112no—
842C2×C42—112no—
843C2×C42—111no—
844C2×C42—111no—
845C2×C42—111no—
846C2×C42—228no—
847C2×C42—224no—
848C2×C42C22×D1112yes—
849C2×C42C22×D1111yescharacteristic
850#95—112no—
851#95—112no—
852#95—112no—
853#95—112no—
854#95—112no—
855#95—112no—
856#95—112no—
857#95—112no—
858#95—112no—
859#95—112no—
860#95—112no—
861#95—112no—
862#95—112no—
863#95—112no—
864#95—112no—
865#95C22×D1112yes—
866#95C22×D1112yes—
867#95C22×D1112yes—
868#95C22×D1112yes—
869#95C22×D1112yes—
870C2×C11—42no—
871C2×C11—42no—
872C2×C11C22×#12311yescharacteristic
873C2×C11C2×#52511yescharacteristic
874C2×C11C2×#53711yescharacteristic
875C2×C11C2×#55211yescharacteristic
876C2×C11C2×#55311yescharacteristic
877C2×C11C2×#55511yescharacteristic
878C2×C11C2×#55611yescharacteristic
879D11—42no—
880D11—42no—
881D11#248518yesdirect product factor
882C24—111no—
883C24—114no—
884C24—114no—
885C24—111no—
886C24—111no—
887C24—222no—
888C24—222no—
889C24—222no—
890C24—222no—
891C24—222no—
892C24—222no—
893C24—222no—
894C24—222no—
895C24—222no—
896C24—222no—
897C24—222no—
898C24—222no—
899C24C23×D1111yescharacteristic
900C24C23×D1111yescharacteristic
901C2×D4—22no—
902C2×D4—22no—
903C2×D4—22no—
904C2×D4—222no—
905C2×D4—222no—
906C2×D4—222no—
907C2×D4—222no—
908C2×D4—2232no—
909C2×D4—222no—
910C2×D4—222no—
911C2×D4—222no—
912C2×D4—222no—
913C2×D4—222no—
914C22×C4—22no—
915C22×C4—22no—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4—22no—
919C22×C4—111no—
920C22×C4—114no—
921C22×C4—114no—
922C22×C4—114no—
923C22×C4—114no—
924C22×C4—111no—
925C22×C4—111no—
926C22×C4—114no—
927C22×C4—114no—
928C22×C4—114no—
929C22×C4—114no—
930C22×C4—111no—
931C22×C4—112no—
932C22×C4—112no—
933C22×C4—111no—
934C22×C4—112no—
935C22×C4—112no—
936C22×C4—222no—
937C22×C4—222no—
938C22×C4—2232no—
939C22×C4—222no—
940C22×C4—222no—
941C22×C4—222no—
942C22×C4—222no—
943C22×C4—222no—
944C22×C4—222no—
945C22×C4—222no—
946C22×C4—222no—
947C22×C4—224no—
948C22×C4—224no—
949C22×C4—222no—
950C22×C4—224no—
951C22×C4—224no—
952C22×C4—224no—
953C22×C4—224no—
954C22×C4—224no—
955C22×C4—224no—
956C22×C4—224no—
957C22×C4—224no—
958C22×C4—224no—
959C22×C4—222no—
960C22×C4—222no—
961C22×C4—222no—
962C22×C4—222no—
963C22×C4—224no—
964C22×C4—222no—
965C22×C4—222no—
966C22×C4—222no—
967C22×C4—222no—
968C22×C4—222no—
969C22×C4—222no—
970C22×C4—222no—
971C22×C4—222no—
972C22×C4—222no—
973C22×C4—222no—
974C22×C4—4416no—
975C22×C4D4×D1114yes—
976C22×C4C23×D1111yescharacteristic
977C22×C4C23×D1112yes—
978C22×C4C23×D1112yes—
979C22×C4C23×D1111yescharacteristic
980C22×C4C23×D1112yes—
981C22×C4C23×D1112yes—
982C22×C4C23×D1111yescharacteristic
983C22×C4C23×D1111yescharacteristic
984C22×C4C23×D1111yescharacteristic
985C4⋊C4—22no—
986C4⋊C4—22no—
987C4⋊C4—22no—
988C4⋊C4—24no—
989C4⋊C4—22no—
990C4⋊C4—22no—
991C4⋊C4—42no—
992C4⋊C4—224no—
993C4⋊C4—224no—
994C4⋊C4—222no—
995C4⋊C4—222no—
996C4⋊C4—224no—
997C4⋊C4—224no—
998C4⋊C4—224no—
999C4⋊C4—224no—
1000C4⋊C4—222no—
1001C4⋊C4—222no—
1002C4⋊C4—222no—
1003C4⋊C4—224no—
1004C4⋊C4—222no—
1005C4⋊C4—222no—
1006C4⋊C4—442no—
1007C4⋊C4—442no—
1008C4⋊C4—442no—
1009C22⋊C4—24no—
1010C22⋊C4—22no—
1011C22⋊C4—24no—
1012C22⋊C4—22no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—222no—
1016C22⋊C4—224no—
1017C22⋊C4—224no—
1018C22⋊C4—222no—
1019C22⋊C4—222no—
1020C22⋊C4—224no—
1021C22⋊C4—224no—
1022C22⋊C4—222no—
1023C22⋊C4—224no—
1024C22⋊C4—222no—
1025C22⋊C4—224no—
1026C22⋊C4—222no—
1027C22⋊C4—442no—
1028C22⋊C4—442no—
1029C22⋊C4—442no—
1030C22⋊C4—442no—
1031C22⋊C4—442no—
1032C22⋊C4—442no—
1033C42—24no—
1034C42—22no—
1035C42—224no—
1036C42—224no—
1037C42—222no—
1038C42—222no—
1039C42—224no—
1040C42—222no—
1041C11C2×#248511yescharacteristic, complemented, Sylow
1042C23—21no—
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—112no—
1055C23—112no—
1056C23—112no—
1057C23—112no—
1058C23—112no—
1059C23—112no—
1060C23—112no—
1061C23—112no—
1062C23—112no—
1063C23—228no—
1064C23—228no—
1065C23—228no—
1066C23—228no—
1067C23—228no—
1068C23—228no—
1069C23—221no—
1070C23—221no—
1071C23—221no—
1072C23—221no—
1073C23—221no—
1074C23—221no—
1075C23—221no—
1076C23—221no—
1077C23—221no—
1078C23—221no—
1079C23—221no—
1080C23—221no—
1081C23—444no—
1082C23—444no—
1083C23—444no—
1084C23—444no—
1085C23—444no—
1086C23—444no—
1087C23—444no—
1088C23—444no—
1089C23C2×D4×D1112yes—
1090C23#41×D1112yes—
1091C23C24×D1111yescharacteristic
1092D4—28no—
1093D4—228no—
1094D4—228no—
1095D4—228no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—28no—
1101C2×C4—21no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—21no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—22no—
1119C2×C4—44no—
1120C2×C4—112no—
1121C2×C4—112no—
1122C2×C4—112no—
1123C2×C4—1116no—
1124C2×C4—112no—
1125C2×C4—112no—
1126C2×C4—228no—
1127C2×C4—228no—
1128C2×C4—228no—
1129C2×C4—228no—
1130C2×C4—221no—
1131C2×C4—221no—
1132C2×C4—221no—
1133C2×C4—221no—
1134C2×C4—228no—
1135C2×C4—221no—
1136C2×C4—222no—
1137C2×C4—222no—
1138C2×C4—221no—
1139C2×C4—222no—
1140C2×C4—222no—
1141C2×C4—222no—
1142C2×C4—222no—
1143C2×C4—222no—
1144C2×C4—222no—
1145C2×C4—221no—
1146C2×C4—221no—
1147C2×C4—222no—
1148C2×C4—222no—
1149C2×C4—222no—
1150C2×C4—221no—
1151C2×C4—221no—
1152C2×C4—222no—
1153C2×C4—444no—
1154C2×C4—444no—
1155C2×C4—448no—
1156C2×C4—448no—
1157C2×C4—444no—
1158C2×C4—448no—
1159C2×C4—448no—
1160C2×C4—444no—
1161C2×C4—444no—
1162C2×C4C2×D4×D1112yes—
1163C2×C4C2×D4×D1112yes—
1164C2×C4#41×D1112yes—
1165C2×C4#41×D1112yes—
1166C2×C4#41×D1112yes—
1167C22—22no—
1168C22—22no—
1169C22—22no—
1170C22—22no—
1171C22—22no—
1172C22—22no—
1173C22—41no—
1174C22—41no—
1175C22—41no—
1176C22—41no—
1177C22—41no—
1178C22—41no—
1179C22—41no—
1180C22—41no—
1181C22—114no—
1182C22—114no—
1183C22—114no—
1184C22—114no—
1185C22—114no—
1186C22—114no—
1187C22—114no—
1188C22—222no—
1189C22—222no—
1190C22—222no—
1191C22—222no—
1192C22—222no—
1193C22—222no—
1194C22—4416no—
1195C22—4416no—
1196C22—441no—
1197C22—441no—
1198C22—441no—
1199C22—441no—
1200C22—441no—
1201C22—441no—
1202C22—441no—
1203C22—441no—
1204C22C22×D4×D1111yescharacteristic
1205C22C2×#41×D1111yescharacteristic
1206C22C2×#41×D1111yescharacteristic
1207C22C2×#41×D1111yescharacteristic
1208C22C2×#41×D1111yescharacteristic
1209C22D11×H(5,𝔽2)11yescharacteristic
1210C22D11×2−1+411yescharacteristic
1211C4—22no—
1212C4—22no—
1213C4—42no—
1214C4—42no—
1215C4—41no—
1216C4—42no—
1217C4—41no—
1218C4—42no—
1219C4—114no—
1220C4—222no—
1221C4—222no—
1222C4—442no—
1223C4—442no—
1224C4—441no—
1225C4—442no—
1226C4—441no—
1227C4—442no—
1228C4D11×#12314yes—
1229C2—42no—
1230C2—42no—
1231C2—118no—
1232C2—442no—
1233C2—442no—
1234C2C2×D11×#12311yescharacteristic
1235C2D11×#52511yescharacteristic
1236C2D11×#53711yescharacteristic
1237C2D11×#55211yescharacteristic
1238C2D11×#55311yescharacteristic
1239C2D11×#55511yescharacteristic
1240C2D11×#55611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2485C2
prime radicalC22×D4×D11C22
hypercenter#2485D11
hypocenterC11C2×#2485
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2485

Complements

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

NH ≅ G/Ntype
2. C2×D11×#117C2semidirect
3. #13072916C2semidirect
4. #13072915C2semidirect
5. #13072914C2semidirect
6. #13072913C2semidirect
7. #13072912C2semidirect
8. #13072911C2semidirect
9. #13072910C2semidirect
10. #13072909C2semidirect
11. #13072908C2semidirect
12. #13072907C2semidirect
13. #13072906C2semidirect
14. D11×#397C2semidirect
16. D11×#389C2semidirect
17. D11×#389C2semidirect
18. D11×#388C2semidirect
19. D11×#387C2semidirect
20. D11×#380C2semidirect
21. D11×#380C2semidirect
22. D11×#380C2semidirect
23. C11×#2485C2semidirect
28. C2×C11×#117C22semidirect
32. C2×#66979C22semidirect
36. C2×#66945C22semidirect
37. C2×#66945C22semidirect
53. C2×#66930C22semidirect
55. C2×#66925C22semidirect
58. C11×#397C22semidirect
60. C11×#389C22semidirect
61. C11×#389C22semidirect
62. C11×#388C22semidirect
63. C11×#387C22semidirect
64. C11×#380C22semidirect
65. C11×#380C22semidirect
66. C11×#380C22semidirect
68. #10622825C22semidirect
69. #10622825C22semidirect
70. #10622825C22semidirect
71. #10622606C22semidirect
73. #10622603C22semidirect
74. #10622600C22semidirect
75. #10622600C22semidirect
76. #10622600C22semidirect
77. #10622600C22semidirect
78. #10622600C22semidirect
79. #10622600C22semidirect
80. #10622598C22semidirect
81. #10622598C22semidirect
82. #10622594C22semidirect
83. #10622591C22semidirect
84. #10622586C22semidirect
85. #10622586C22semidirect
86. #10622585C22semidirect
87. #10622585C22semidirect
92. #10622566C22semidirect
93. #10622565C22semidirect
94. #10622565C22semidirect
95. #10622564C22semidirect
96. #10622558C22semidirect
97. #10622557C22semidirect
98. #10622555C22semidirect
99. #10622555C22semidirect
100. #10622555C22semidirect
101. #10622553C22semidirect
102. #10622546C22semidirect
103. #10622541C22semidirect
104. #10622541C22semidirect
105. #10622288C22semidirect
106. #10622288C22semidirect
107. #10622287C22semidirect
109. #10622283C22semidirect
110. #10622282C22semidirect
111. #10622280C22semidirect
112. #10622280C22semidirect
113. #10622280C22semidirect
119. #10622268C22semidirect
120. #10622267C22semidirect
121. #10622266C22semidirect
122. #10622265C22semidirect
123. #10622260C22semidirect
124. #10622260C22semidirect
435. #2485D11direct (N × H)
588. C2×#117C2×D11semidirect
611. #397C2×D11semidirect
630. #389C2×D11semidirect
631. #389C2×D11semidirect
639. #388C2×D11semidirect
647. #387C2×D11semidirect
663. #380C2×D11semidirect
664. #380C2×D11semidirect
665. #380C2×D11semidirect
881. D11#2485direct (N × H)
1041. C11C2×#2485semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D112
C2×D11×#1172
#130729162
#130729152
#130729142
#130729132
#130729122
#130729112
#130729102
#130729092
#130729082
#130729072
#130729062
D11×#3972
D11×#3942
D11×#3892
D11×#3882
D11×#3872
D11×#3802
C11×#24852
C2×#248511