Finite Group Databasebeta

← D11×#2610 #14924615

Subgroups — D11×#2610 #14924615

Order 2816.

3286 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#124C211yesmaximal, characteristic, complemented
2C2×D11×#117C211yesmaximal, characteristic, complemented
3#13074306C211yesmaximal, characteristic, complemented
4#13074305C211yesmaximal, characteristic, complemented
5#13074304C211yesmaximal, characteristic, complemented
6#13074303C211yesmaximal, characteristic, complemented
7#13074302C212yesmaximal, complemented
8#13074301C212yesmaximal, complemented
9#13074300C212yesmaximal, complemented
10#13074299C212yesmaximal, complemented
11#13074298C211yesmaximal, characteristic, complemented
12#13074297C211yesmaximal, characteristic, complemented
13#13074296C211yesmaximal, characteristic, complemented
14D11×#395C211yesmaximal, characteristic, complemented
15D11×#394C211yesmaximal, characteristic, complemented
16D11×#393C211yesmaximal, characteristic, complemented
17D11×#392C211yesmaximal, characteristic
18D11×#390C212yesmaximal, complemented
19D11×#388C212yesmaximal, complemented
20D11×#388C212yesmaximal, complemented
21D11×#386C212yesmaximal, complemented
22D11×#376C211yesmaximal, characteristic, complemented
23C11×#2610C211yesmaximal, characteristic, complemented
24C22×Q8×D11C2211yescharacteristic
25C22×D4×D11C2212yes—
26C22×D4×D11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic
28C2×C11×#124C2211yescharacteristic, complemented
29C2×C11×#117C2211yescharacteristic, complemented
30C2×#67000C2211yescharacteristic, complemented
31C2×#66989C2211yescharacteristic, complemented
32C2×#66979C2211yescharacteristic, complemented
33D11×#124—28no—
34D11×#117—28no—
35C2×#66945C2211yescharacteristic, complemented
36C2×#66945C2211yescharacteristic, complemented
37C2×C4⋊C4×D11C2211yescharacteristic
38C2×C4⋊C4×D11C2211yescharacteristic
39C2×C4⋊C4×D11C2212yes—
40C2×#66938C2212yescomplemented
41C2×#66938C2212yescomplemented
42C2×C22⋊C4×D11C2212yes—
43C2×C22⋊C4×D11C2212yes—
44C2×C22⋊C4×D11C2211yescharacteristic
45C2×C22⋊C4×D11C2211yescharacteristic
46C2×C22⋊C4×D11C2212yes—
47C2×C22⋊C4×D11C2212yes—
48C2×C22⋊C4×D11C2212yes—
49C2×C22⋊C4×D11C2212yes—
50C2×#66930C2211yescharacteristic, complemented
51C2×#66930C2211yescharacteristic, complemented
52C2×#66928C2211yescharacteristic, complemented
53C2×#66925C2211yescharacteristic, complemented
54C2×#66925C2211yescharacteristic, complemented
55C2×C42×D11C2212yes—
56C2×C42×D11C2211yescharacteristic
57C2×C42×D11C2211yescharacteristic
58C11×#395C2211yescharacteristic, complemented
59C11×#394C2211yescharacteristic, complemented
60C11×#393C2211yescharacteristic, complemented
61C11×#392C2211yescharacteristic
62C11×#390C2212yescomplemented
63C11×#388C2212yescomplemented
64C11×#388C2212yescomplemented
65C11×#386C2212yescomplemented
66C11×#376C2211yescharacteristic, complemented
67#10622844C2211yescharacteristic, complemented
68#10622842C2211yescharacteristic, complemented
69#10622836C2212yes—
70#10622836C2211yescharacteristic
71#10622835C2211yescharacteristic, complemented
72#10622834C2212yescomplemented
73#10622833C2212yescomplemented
74#10622826C2212yescomplemented
75#10622604C2211yescharacteristic, complemented
76#10622603C2212yescomplemented
77#10622603C2212yescomplemented
78#10622601C2212yescomplemented
79#10622592C2212yescomplemented
80#10622592C2211yescharacteristic, complemented
81#10622574C2212yescomplemented
82#10622573C2212yes—
83#10622573C2211yescharacteristic
84#10622572C2212yescomplemented
85#10622571C2212yescomplemented
86#10622570C2212yescomplemented
87#10622570C2212yescomplemented
88#10622570C2212yescomplemented
89#10622570C2212yescomplemented
90#10622569C2212yescomplemented
91#10622569C2212yescomplemented
92#10622564C2212yescomplemented
93#10622564C2212yescomplemented
94#10622560C2211yescharacteristic, complemented
95#10622560C2212yescomplemented
96#10622558C2212yescomplemented
97#10622558C2212yescomplemented
98#10622557C2212yescomplemented
99#10622557C2212yescomplemented
100#10622553C2212yescomplemented
101#10622553C2212yescomplemented
102#10622552C2212yescomplemented
103#10622545C2212yescomplemented
104#10622545C2211yescharacteristic, complemented
105#10622286C2211yescharacteristic, complemented
106#10622286C2212yescomplemented
107#10622285C2211yescharacteristic, complemented
108#10622284C2211yescharacteristic
109#10622283C2212yescomplemented
110#10622283C2212yescomplemented
111#10622282C2212yescomplemented
112#10622282C2212yescomplemented
113#10622278C2212yescomplemented
114#10622278C2212yescomplemented
115D11×#95C2212yes—
116D11×#95C2211yescharacteristic
117D11×#95C2211yescharacteristic
118D11×#95C2212yes—
119D11×#95C2212yes—
120#10622269C2211yescharacteristic, complemented
121#10622269C2212yescomplemented
122#10622261C2211yescharacteristic, complemented
123#10622261C2212yescomplemented
124#10622261C2211yescharacteristic, complemented
125C24×D11C2312yes—
126C24×D11C2311yescharacteristic
127C22×Q8×C11C2311yescharacteristic
128C22×D4×C11C2312yes—
129C22×D4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2312yes—
134C23×Dic11C2311yescharacteristic
135C2×Q8×D11—24no—
136C2×Q8×D11—44no—
137C2×D4×D11—28no—
138C2×D4×D11—24no—
139C2×D4×D11—28no—
140C2×D4×D11—44no—
141C2×D4×D11—44no—
142C22×D44C2312yes—
143C22×D44C2311yescharacteristic
144C22×C4×D11—24no—
145C22×C4×D11—24no—
146C22×C4×D11—24no—
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2312yes—
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2312yes—
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2311yescharacteristic
154C22×C4×D11C2311yescharacteristic
155C22×C4×D11C2311yescharacteristic
156C22×C4×D11C2312yes—
157C22×C4×D11C2311yescharacteristic
158C22×Dic22C2311yescharacteristic
159C22×Dic22C2312yes—
160C11×#124—24no—
161C11×#117—24no—
162C2×C11×C4⋊C4C2311yescharacteristic
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2312yes—
165C2×C11×C22⋊C4C2311yescharacteristic
166C2×C11×C22⋊C4C2311yescharacteristic
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2312yes—
169C2×C11×C22⋊C4C2312yes—
170C2×C11×C22⋊C4C2312yes—
171C2×C11×C22⋊C4C2312yes—
172C2×C11×C22⋊C4C2312yes—
173C2×C42×C11C2311yescharacteristic
174C2×C42×C11C2312yes—
175C2×C42×C11C2311yescharacteristic
176C2×C22⋊Dic11C2311yescharacteristic
177C2×C22⋊Dic11C2311yescharacteristic
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182C2×C22⋊Dic11C2312yes—
183C2×C22⋊Dic11C2312yes—
184#67000—24no—
185#66989—24no—
186C2×(C2×D11)⋊C4C2311yescharacteristic
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2311yescharacteristic
189C2×(C2×D11)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2312yes—
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×(C2×D11)⋊C4C2312yes—
202#66979—24no—
203C2×C4⋊Dic11C2311yescharacteristic
204C2×C4⋊Dic11C2311yescharacteristic
205C2×C4⋊Dic11C2312yes—
206C2×Dic11⋊C4C2311yescharacteristic
207C2×Dic11⋊C4C2311yescharacteristic
208C2×Dic11⋊C4C2311yescharacteristic
209C2×Dic11⋊C4C2311yescharacteristic
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2312yes—
212C2×C4×Dic11C2311yescharacteristic
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2311yescharacteristic
221#66945—24no—
222#66945—24no—
223C4⋊C4×D11—24no—
224C4⋊C4×D11—24no—
225C4⋊C4×D11—44no—
226#66938—28no—
227#66938—28no—
228C22⋊C4×D11—24no—
229C22⋊C4×D11—24no—
230C22⋊C4×D11—28no—
231C22⋊C4×D11—28no—
232C22⋊C4×D11—28no—
233C22⋊C4×D11—28no—
234C22⋊C4×D11—44no—
235C22⋊C4×D11—44no—
236#66930—24no—
237#66930—24no—
238#66928—24no—
239#66925—24no—
240#66925—24no—
241C42×D11—24no—
242C42×D11—28no—
243C42×D11D418yescomplemented
244C11×#95C2311yescharacteristic
245C11×#95C2312yes—
246C11×#95C2311yescharacteristic
247C11×#95C2312yes—
248C11×#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2311yescharacteristic
255C11⋊#95C2311yescharacteristic
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C2×#2610—111nomaximal, Sylow
263C24×C11C2412yes—
264C24×C11C2411yescharacteristic
265C23×D11—22no—
266C23×D11—22no—
267C23×D11—24no—
268C23×D11—24no—
269C23×D11—24no—
270C23×D11—24no—
271C23×D11—24no—
272C23×D11—24no—
273C23×D11—24no—
274C23×D11—24no—
275C23×D11—24no—
276C23×D11#4114yes—
277C23×D11C2412yes—
278C23×D11C2411yescharacteristic
279C23×D11C2411yescharacteristic
280C2×Q8×C11—22no—
281C2×Q8×C11—42no—
282C2×D4×C11—24no—
283C2×D4×C11—22no—
284C2×D4×C11—24no—
285C2×D4×C11—42no—
286C2×D4×C11—42no—
287C22×C4×C11—22no—
288C22×C4×C11—22no—
289C22×C4×C11—22no—
290C22×C4×C11C2412yes—
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2412yes—
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2412yes—
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—42no—
305C2×C22⋊D11—42no—
306C2×C22⋊D11—42no—
307C2×C22⋊D11—42no—
308C22×Dic11—22no—
309C22×Dic11—22no—
310C22×Dic11—22no—
311C22×Dic11C2412yes—
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2412yes—
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2412yes—
319C22×Dic11C2411yescharacteristic
320Q8×D11—416no—
321D4×D11—432no—
322D4×D11—416no—
323C2×D44—24no—
324C2×D44—22no—
325C2×D44—24no—
326C2×D44—42no—
327C2×D44—42no—
328C2×C4×D11—232no—
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—24no—
336C2×C4×D11—22no—
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—24no—
344C2×C4×D11—24no—
345C2×C4×D11—24no—
346C2×C4×D11—24no—
347C2×C4×D11—24no—
348C2×C4×D11—24no—
349C2×C4×D11—24no—
350C2×C4×D11—24no—
351C2×C4×D11—22no—
352C2×C4×D11—22no—
353C2×C4×D11C2×D414yes—
354C2×C4×D11C2×D414yes—
355C2×C4×D11C2×D414yes—
356C2×C4×D11#4118yes—
357C2×C4×D11#4114yes—
358C2×Dic22—24no—
359C2×Dic22—22no—
360C2×Dic22—42no—
361C2×Dic22—42no—
362C2×Dic22—42no—
363C11×C4⋊C4—22no—
364C11×C4⋊C4—22no—
365C11×C4⋊C4—42no—
366C11×C22⋊C4—22no—
367C11×C22⋊C4—22no—
368C11×C22⋊C4—24no—
369C11×C22⋊C4—24no—
370C11×C22⋊C4—24no—
371C11×C22⋊C4—24no—
372C11×C22⋊C4—42no—
373C11×C22⋊C4—42no—
374C42×C11—22no—
375C42×C11—24no—
376C42×C11C2×D414yescomplemented
377C22⋊Dic11—22no—
378C22⋊Dic11—22no—
379C22⋊Dic11—24no—
380C22⋊Dic11—24no—
381C22⋊Dic11—24no—
382C22⋊Dic11—24no—
383C22⋊Dic11—42no—
384C22⋊Dic11—42no—
385(C2×D11)⋊C4—22no—
386(C2×D11)⋊C4—22no—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—24no—
390(C2×D11)⋊C4—24no—
391(C2×D11)⋊C4—22no—
392(C2×D11)⋊C4—22no—
393(C2×D11)⋊C4—24no—
394(C2×D11)⋊C4—24no—
395(C2×D11)⋊C4—24no—
396(C2×D11)⋊C4—24no—
397(C2×D11)⋊C4—42no—
398(C2×D11)⋊C4—42no—
399(C2×D11)⋊C4—42no—
400(C2×D11)⋊C4—42no—
401C4⋊Dic11—22no—
402C4⋊Dic11—22no—
403C4⋊Dic11—42no—
404Dic11⋊C4—22no—
405Dic11⋊C4—22no—
406Dic11⋊C4—22no—
407Dic11⋊C4—22no—
408Dic11⋊C4—42no—
409Dic11⋊C4—42no—
410C4×Dic11—22no—
411C4×Dic11—22no—
412C4×Dic11—24no—
413C4×Dic11—24no—
414C4×Dic11—22no—
415C4×Dic11—24no—
416C4×Dic11C2×D414yescomplemented
417C4×Dic11C2×D414yescomplemented
418C4×Dic11C2×D414yescomplemented
419C22×#124—111no—
420C22×#117—111no—
421#2610—111no—
422#2610—111no—
423#2610—111no—
424#2610—111no—
425#2610—112no—
426#2610—112no—
427#2610—112no—
428#2610—112no—
429#2610—111no—
430#2610—111no—
431#2610—111no—
432#2610D1111yescharacteristic, direct product factor
433C2×#395—111no—
434C2×#394—111no—
435C2×#393—111no—
436C2×#392—111no—
437C2×#390—112no—
438C2×#388—112no—
439C2×#388—112no—
440C2×#386—112no—
441C2×#376—111no—
442C23×C11—21no—
443C23×C11—21no—
444C23×C11—22no—
445C23×C11—22no—
446C23×C11—22no—
447C23×C11—22no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11—22no—
451C23×C11—22no—
452C23×C11—22no—
453C23×C11C2×#4112yes—
454C23×C11C2511yescharacteristic
455C22×D11—21no—
456C22×D11—21no—
457C22×D11—22no—
458C22×D11—22no—
459C22×D11—28no—
460C22×D11—216no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—44no—
469C22×D11—44no—
470C22×D11—48no—
471C22×D11—48no—
472C22×D11—48no—
473C22×D11—48no—
474C22×D11—48no—
475C22×D11—48no—
476C22×D11—48no—
477C22×D11—48no—
478C22×D11C22×D412yes—
479C22×D11C2×#4112yes—
480C22×D11C2×#4112yes—
481C22×D11C2×#4112yes—
482C22×D11C2×#4114yes—
483C22×D11H(5,𝔽2)14yes—
484Q8×C11—44no—
485D4×C11—48no—
486D4×C11—44no—
487C2×C4×C11—28no—
488C2×C4×C11—21no—
489C2×C4×C11—22no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—21no—
497C2×C4×C11—21no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—22no—
506C2×C4×C11C22×D412yes—
507C2×C4×C11C22×D412yes—
508C2×C4×C11C22×D412yes—
509C2×C4×C11C2×#4114yes—
510C2×C4×C11C2×#4112yes—
511C22⋊D11—48no—
512C22⋊D11—48no—
513C22⋊D11—48no—
514C2×Dic11—28no—
515C2×Dic11—21no—
516C2×Dic11—22no—
517C2×Dic11—21no—
518C2×Dic11—21no—
519C2×Dic11—21no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—21no—
524C2×Dic11—21no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—22no—
532C2×Dic11—22no—
533C2×Dic11C22×D412yes—
534C2×Dic11C22×D412yes—
535C2×Dic11C22×D412yes—
536C2×Dic11C2×#4114yes—
537C2×Dic11C2×#4112yes—
538D44—48no—
539D44—44no—
540C4×D11—28no—
541C4×D11—28no—
542C4×D11—28no—
543C4×D11—28no—
544C4×D11—28no—
545C4×D11—28no—
546C4×D11—216no—
547C4×D11—44no—
548C4×D11—44no—
549C4×D11—48no—
550C4×D11—48no—
551Dic22—48no—
552Dic22—44no—
553C23×Q8—111no—
554C23×D4—112no—
555C23×D4—111no—
556C24×C4—111no—
557C2×#124—111no—
558C2×#124—111no—
559C2×#124—112no—
560C2×#124—112no—
561C2×#124—111no—
562C2×#124—228no—
563C2×#124C2×D1111yescharacteristic, complemented
564C2×#117—111no—
565C2×#117—111no—
566C2×#117—111no—
567C2×#117—111no—
568C2×#117—111no—
569C2×#117—111no—
570C2×#117—111no—
571C2×#117—228no—
572C2×#117C2×D1111yescharacteristic, complemented
573C22×C4⋊C4—111no—
574C22×C4⋊C4—111no—
575C22×C4⋊C4—112no—
576C22×C22⋊C4—111no—
577C22×C22⋊C4—112no—
578C22×C22⋊C4—112no—
579C22×C22⋊C4—111no—
580C22×C22⋊C4—112no—
581C22×C22⋊C4—112no—
582C22×C22⋊C4—112no—
583C22×C22⋊C4—112no—
584C22×C42—111no—
585C22×C42—111no—
586C22×C42—112no—
587#395—111no—
588#395—112no—
589#395—111no—
590#395—112no—
591#395—111no—
592#395C2×D1111yescharacteristic, complemented
593#394—111no—
594#394—111no—
595#394—112no—
596#394—112no—
597#394—111no—
598#394C2×D1111yescharacteristic, complemented
599#393—111no—
600#393—112no—
601#393—111no—
602#393—112no—
603#393—111no—
604#393C2×D1111yescharacteristic, complemented
605#392—112no—
606#392—111no—
607#392—112no—
608#392—111no—
609#392—111no—
610#392C2×D1111yescharacteristic
611#390—112no—
612#390—112no—
613#390—112no—
614#390—112no—
615#390—112no—
616#390—112no—
617#390—112no—
618#390C2×D1112yescomplemented
619#388—112no—
620#388—112no—
621#388—112no—
622#388—112no—
623#388—112no—
624#388—112no—
625#388—112no—
626#388—112no—
627#388—112no—
628#388—112no—
629#388—112no—
630#388—112no—
631#388—112no—
632#388—112no—
633#388C2×D1112yescomplemented
634#388C2×D1112yescomplemented
635#386—112no—
636#386—112no—
637#386—112no—
638#386—112no—
639#386—112no—
640#386—112no—
641#386—112no—
642#386C2×D1112yescomplemented
643#376—112no—
644#376—111no—
645#376—111no—
646#376—111no—
647#376—112no—
648#376C2×D1111yescharacteristic, complemented
649C2×#95—111no—
650C2×#95—111no—
651C2×#95—112no—
652C2×#95—112no—
653C2×#95—112no—
654C22×C11—22no—
655C22×C11—24no—
656C22×C11—41no—
657C22×C11—41no—
658C22×C11—42no—
659C22×C11—42no—
660C22×C11—42no—
661C22×C11—42no—
662C22×C11—42no—
663C22×C11—42no—
664C22×C11—42no—
665C22×C11—42no—
666C22×C11C23×D411yescharacteristic
667C22×C11C22×#4111yescharacteristic
668C22×C11C22×#4111yescharacteristic
669C22×C11C22×#4112yes—
670C22×C11C2×H(5,𝔽2)12yes—
671C2×D11—22no—
672C2×D11—24no—
673C2×D11—41no—
674C2×D11—41no—
675C2×D11—42no—
676C2×D11—416no—
677C2×D11—42no—
678C2×D11—42no—
679C2×D11—42no—
680C2×D11—42no—
681C2×D11—42no—
682C2×D11—42no—
683C2×D11—42no—
684C2×D11—816no—
685C2×D11#52514yes—
686C2×D11#53214yes—
687C2×D11#53514yes—
688C2×D11#55118yes—
689C2×D11#55518yes—
690C4×C11—22no—
691C4×C11—22no—
692C4×C11—22no—
693C4×C11—22no—
694C4×C11—24no—
695C4×C11—41no—
696C4×C11—42no—
697C4×C11—41no—
698C4×C11—42no—
699Dic11—22no—
700Dic11—22no—
701Dic11—22no—
702Dic11—22no—
703Dic11—24no—
704Dic11—41no—
705Dic11—42no—
706Dic11—41no—
707Dic11—42no—
708C25—111no—
709C25—112no—
710C22×Q8—112no—
711C22×Q8—111no—
712C22×Q8—224no—
713C22×Q8—444no—
714C22×Q8C22×D1111yescharacteristic
715C22×D4—112no—
716C22×D4—112no—
717C22×D4—112no—
718C22×D4—112no—
719C22×D4—111no—
720C22×D4—224no—
721C22×D4—228no—
722C22×D4—228no—
723C22×D4—444no—
724C22×D4—444no—
725C22×D4C22×D1112yes—
726C22×D4C22×D1111yescharacteristic
727C23×C4—111no—
728C23×C4—111no—
729C23×C4—111no—
730C23×C4—111no—
731C23×C4—112no—
732C23×C4—111no—
733C23×C4—111no—
734C23×C4—112no—
735C23×C4—111no—
736C23×C4—112no—
737C23×C4—111no—
738C23×C4—111no—
739C23×C4—224no—
740C23×C4—224no—
741C23×C4—224no—
742C23×C4C22×D1111yescharacteristic
743#124—24no—
744#124—228no—
745#124—228no—
746#124—224no—
747#124—224no—
748#124—224no—
749#117—24no—
750#117—224no—
751#117—224no—
752#117—224no—
753#117—224no—
754#117—224no—
755#117—224no—
756#117—224no—
757C2×C4⋊C4—111no—
758C2×C4⋊C4—111no—
759C2×C4⋊C4—111no—
760C2×C4⋊C4—111no—
761C2×C4⋊C4—111no—
762C2×C4⋊C4—111no—
763C2×C4⋊C4—112no—
764C2×C4⋊C4—112no—
765C2×C4⋊C4—112no—
766C2×C4⋊C4—224no—
767C2×C4⋊C4—224no—
768C2×C4⋊C4—444no—
769C2×C4⋊C4C22×D1111yescharacteristic
770C2×C4⋊C4C22×D1111yescharacteristic
771C2×C4⋊C4C22×D1112yes—
772C2×C22⋊C4—111no—
773C2×C22⋊C4—111no—
774C2×C22⋊C4—112no—
775C2×C22⋊C4—112no—
776C2×C22⋊C4—112no—
777C2×C22⋊C4—112no—
778C2×C22⋊C4—111no—
779C2×C22⋊C4—111no—
780C2×C22⋊C4—111no—
781C2×C22⋊C4—111no—
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—112no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—112no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—224no—
797C2×C22⋊C4—224no—
798C2×C22⋊C4—228no—
799C2×C22⋊C4—228no—
800C2×C22⋊C4—228no—
801C2×C22⋊C4—228no—
802C2×C22⋊C4—444no—
803C2×C22⋊C4—444no—
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×C22⋊C4C22×D1112yes—
811C2×C22⋊C4C22×D1112yes—
812C2×C42—111no—
813C2×C42—111no—
814C2×C42—111no—
815C2×C42—118no—
816C2×C42—111no—
817C2×C42—111no—
818C2×C42—111no—
819C2×C42—112no—
820C2×C42—112no—
821C2×C42—112no—
822C2×C42—224no—
823C2×C42—228no—
824C2×C42C22×D1111yescharacteristic
825C2×C42C22×D1112yes—
826C2×C42C22×D1111yescharacteristic
827#95—112no—
828#95—112no—
829#95—112no—
830#95—111no—
831#95—112no—
832#95—112no—
833#95—111no—
834#95—112no—
835#95—112no—
836#95—112no—
837#95—112no—
838#95—112no—
839#95—112no—
840#95C22×D1112yes—
841#95C22×D1111yescharacteristic
842#95C22×D1111yescharacteristic
843#95C22×D1112yes—
844#95C22×D1112yes—
845C2×C11—42no—
846C2×C11—82no—
847C2×C11C2×#52511yescharacteristic
848C2×C11C2×#53211yescharacteristic
849C2×C11C2×#53511yescharacteristic
850C2×C11C2×#55112yes—
851C2×C11C2×#55512yes—
852D11—42no—
853D11—82no—
854D11#261018yesdirect product factor
855C24—111no—
856C24—114no—
857C24—111no—
858C24—112no—
859C24—222no—
860C24—224no—
861C24—222no—
862C24—224no—
863C24—224no—
864C24—224no—
865C24—224no—
866C24—224no—
867C24—224no—
868C24—224no—
869C24—224no—
870C24C23×D1112yes—
871C24C23×D1111yescharacteristic
872C2×Q8—22no—
873C2×Q8—42no—
874C2×Q8—224no—
875C2×Q8—222no—
876C2×Q8—442no—
877C2×Q8—442no—
878C2×Q8—442no—
879C2×Q8—4416no—
880C2×D4—24no—
881C2×D4—22no—
882C2×D4—24no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—224no—
886C2×D4—224no—
887C2×D4—224no—
888C2×D4—224no—
889C2×D4—224no—
890C2×D4—224no—
891C2×D4—222no—
892C2×D4—224no—
893C2×D4—442no—
894C2×D4—442no—
895C2×D4—4432no—
896C2×D4—4416no—
897C2×D4—442no—
898C2×D4—442no—
899C2×D4—442no—
900C2×D4—442no—
901C22×C4—22no—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4—112no—
905C22×C4—111no—
906C22×C4—111no—
907C22×C4—111no—
908C22×C4—111no—
909C22×C4—114no—
910C22×C4—114no—
911C22×C4—114no—
912C22×C4—118no—
913C22×C4—114no—
914C22×C4—112no—
915C22×C4—111no—
916C22×C4—112no—
917C22×C4—111no—
918C22×C4—222no—
919C22×C4—222no—
920C22×C4—224no—
921C22×C4—222no—
922C22×C4—224no—
923C22×C4—222no—
924C22×C4—222no—
925C22×C4—222no—
926C22×C4—222no—
927C22×C4—222no—
928C22×C4—224no—
929C22×C4—224no—
930C22×C4—2232no—
931C22×C4—222no—
932C22×C4—222no—
933C22×C4—224no—
934C22×C4—224no—
935C22×C4—224no—
936C22×C4—224no—
937C22×C4—224no—
938C22×C4—224no—
939C22×C4—224no—
940C22×C4—224no—
941C22×C4—222no—
942C22×C4—222no—
943C22×C4—222no—
944C22×C4—222no—
945C22×C4—222no—
946C22×C4C23×D1112yes—
947C22×C4C23×D1111yescharacteristic
948C22×C4C23×D1112yes—
949C22×C4C23×D1111yescharacteristic
950C22×C4C23×D1111yescharacteristic
951C22×C4C23×D1111yescharacteristic
952C22×C4C23×D1111yescharacteristic
953C22×C4C23×D1112yes—
954C22×C4C23×D1111yescharacteristic
955C4⋊C4—22no—
956C4⋊C4—22no—
957C4⋊C4—42no—
958C4⋊C4—222no—
959C4⋊C4—222no—
960C4⋊C4—222no—
961C4⋊C4—222no—
962C4⋊C4—222no—
963C4⋊C4—222no—
964C4⋊C4—442no—
965C4⋊C4—442no—
966C4⋊C4—442no—
967C22⋊C4—22no—
968C22⋊C4—22no—
969C22⋊C4—24no—
970C22⋊C4—24no—
971C22⋊C4—24no—
972C22⋊C4—24no—
973C22⋊C4—42no—
974C22⋊C4—42no—
975C22⋊C4—222no—
976C22⋊C4—222no—
977C22⋊C4—224no—
978C22⋊C4—224no—
979C22⋊C4—224no—
980C22⋊C4—224no—
981C22⋊C4—222no—
982C22⋊C4—222no—
983C22⋊C4—224no—
984C22⋊C4—224no—
985C22⋊C4—224no—
986C22⋊C4—224no—
987C22⋊C4—222no—
988C22⋊C4—222no—
989C22⋊C4—224no—
990C22⋊C4—224no—
991C22⋊C4—224no—
992C22⋊C4—224no—
993C22⋊C4—442no—
994C22⋊C4—442no—
995C22⋊C4—442no—
996C22⋊C4—442no—
997C22⋊C4—442no—
998C22⋊C4—442no—
999C42—22no—
1000C42—24no—
1001C42—114no—
1002C42—114no—
1003C42—114no—
1004C42—222no—
1005C42—222no—
1006C42—224no—
1007C42—224no—
1008C42—222no—
1009C42—224no—
1010C42D4×D1114yescomplemented
1011C11C2×#261011yescharacteristic, complemented, Sylow
1012C23—21no—
1013C23—21no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—112no—
1024C23—114no—
1025C23—112no—
1026C23—112no—
1027C23—114no—
1028C23—112no—
1029C23—228no—
1030C23—2216no—
1031C23—221no—
1032C23—221no—
1033C23—222no—
1034C23—222no—
1035C23—222no—
1036C23—222no—
1037C23—222no—
1038C23—222no—
1039C23—222no—
1040C23—222no—
1041C23—222no—
1042C23—444no—
1043C23—448no—
1044C23—444no—
1045C23—448no—
1046C23—448no—
1047C23—448no—
1048C23—448no—
1049C23—448no—
1050C23—448no—
1051C23—448no—
1052C23#41×D1112yes—
1053C23C24×D1111yescharacteristic
1054Q8—44no—
1055Q8—444no—
1056Q8—448no—
1057D4—48no—
1058D4—44no—
1059D4—448no—
1060D4—444no—
1061D4—448no—
1062D4—448no—
1063D4—448no—
1064C2×C4—28no—
1065C2×C4—21no—
1066C2×C4—22no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—112no—
1084C2×C4—112no—
1085C2×C4—112no—
1086C2×C4—114no—
1087C2×C4—112no—
1088C2×C4—228no—
1089C2×C4—228no—
1090C2×C4—228no—
1091C2×C4—2216no—
1092C2×C4—228no—
1093C2×C4—228no—
1094C2×C4—228no—
1095C2×C4—228no—
1096C2×C4—221no—
1097C2×C4—222no—
1098C2×C4—221no—
1099C2×C4—221no—
1100C2×C4—221no—
1101C2×C4—222no—
1102C2×C4—222no—
1103C2×C4—222no—
1104C2×C4—221no—
1105C2×C4—221no—
1106C2×C4—222no—
1107C2×C4—222no—
1108C2×C4—222no—
1109C2×C4—222no—
1110C2×C4—222no—
1111C2×C4—222no—
1112C2×C4—222no—
1113C2×C4—222no—
1114C2×C4—448no—
1115C2×C4—444no—
1116C2×C4—448no—
1117C2×C4—444no—
1118C2×C4C2×D4×D1112yes—
1119C2×C4C2×D4×D1112yes—
1120C2×C4C2×D4×D1112yes—
1121C2×C4#41×D1114yes—
1122C2×C4#41×D1112yes—
1123C22—22no—
1124C22—24no—
1125C22—41no—
1126C22—42no—
1127C22—41no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—114no—
1136C22—118no—
1137C22—114no—
1138C22—114no—
1139C22—118no—
1140C22—222no—
1141C22—224no—
1142C22—4416no—
1143C22—441no—
1144C22—442no—
1145C22—441no—
1146C22—442no—
1147C22—442no—
1148C22—442no—
1149C22—442no—
1150C22—442no—
1151C22—442no—
1152C22—442no—
1153C22—8816no—
1154C22C22×D4×D1111yescharacteristic
1155C22C2×#41×D1112yes—
1156C22C2×#41×D1111yescharacteristic
1157C22C2×#41×D1111yescharacteristic
1158C22D11×H(5,𝔽2)12yes—
1159C4—22no—
1160C4—22no—
1161C4—22no—
1162C4—22no—
1163C4—24no—
1164C4—41no—
1165C4—42no—
1166C4—42no—
1167C4—41no—
1168C4—222no—
1169C4—222no—
1170C4—222no—
1171C4—222no—
1172C4—224no—
1173C4—441no—
1174C4—442no—
1175C4—442no—
1176C4—441no—
1177C2—42no—
1178C2—82no—
1179C2—118no—
1180C2—442no—
1181C2—882no—
1182C2D11×#52511yescharacteristic
1183C2D11×#53211yescharacteristic
1184C2D11×#53511yescharacteristic
1185C2D11×#55112yes—
1186C2D11×#55512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2610C2
prime radicalD11×#392C2
hypercenter#2610D11
hypocenterC11C2×#2610
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2610

Complements

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

NH ≅ G/Ntype
1. C2×D11×#124C2semidirect
2. C2×D11×#117C2semidirect
3. #13074306C2semidirect
4. #13074305C2semidirect
5. #13074304C2semidirect
6. #13074303C2semidirect
7. #13074302C2semidirect
8. #13074301C2semidirect
9. #13074300C2semidirect
10. #13074299C2semidirect
11. #13074298C2semidirect
12. #13074297C2semidirect
13. #13074296C2semidirect
14. D11×#395C2semidirect
15. D11×#394C2semidirect
16. D11×#393C2semidirect
18. D11×#390C2semidirect
19. D11×#388C2semidirect
20. D11×#388C2semidirect
21. D11×#386C2semidirect
22. D11×#376C2semidirect
23. C11×#2610C2semidirect
28. C2×C11×#124C22semidirect
29. C2×C11×#117C22semidirect
30. C2×#67000C22semidirect
31. C2×#66989C22semidirect
32. C2×#66979C22semidirect
35. C2×#66945C22semidirect
36. C2×#66945C22semidirect
40. C2×#66938C22semidirect
41. C2×#66938C22semidirect
50. C2×#66930C22semidirect
51. C2×#66930C22semidirect
52. C2×#66928C22semidirect
53. C2×#66925C22semidirect
54. C2×#66925C22semidirect
58. C11×#395C22semidirect
59. C11×#394C22semidirect
60. C11×#393C22semidirect
62. C11×#390C22semidirect
63. C11×#388C22semidirect
64. C11×#388C22semidirect
65. C11×#386C22semidirect
66. C11×#376C22semidirect
67. #10622844C22semidirect
68. #10622842C22semidirect
71. #10622835C22semidirect
72. #10622834C22semidirect
73. #10622833C22semidirect
74. #10622826C22semidirect
75. #10622604C22semidirect
76. #10622603C22semidirect
77. #10622603C22semidirect
78. #10622601C22semidirect
79. #10622592C22semidirect
80. #10622592C22semidirect
81. #10622574C22semidirect
84. #10622572C22semidirect
85. #10622571C22semidirect
86. #10622570C22semidirect
87. #10622570C22semidirect
88. #10622570C22semidirect
89. #10622570C22semidirect
90. #10622569C22semidirect
91. #10622569C22semidirect
92. #10622564C22semidirect
93. #10622564C22semidirect
94. #10622560C22semidirect
95. #10622560C22semidirect
96. #10622558C22semidirect
97. #10622558C22semidirect
98. #10622557C22semidirect
99. #10622557C22semidirect
100. #10622553C22semidirect
101. #10622553C22semidirect
102. #10622552C22semidirect
103. #10622545C22semidirect
104. #10622545C22semidirect
105. #10622286C22semidirect
106. #10622286C22semidirect
107. #10622285C22semidirect
109. #10622283C22semidirect
110. #10622283C22semidirect
111. #10622282C22semidirect
112. #10622282C22semidirect
113. #10622278C22semidirect
114. #10622278C22semidirect
120. #10622269C22semidirect
121. #10622269C22semidirect
122. #10622261C22semidirect
123. #10622261C22semidirect
124. #10622261C22semidirect
243. C42×D11D4semidirect
376. C42×C11C2×D4semidirect
416. C4×Dic11C2×D4semidirect
417. C4×Dic11C2×D4semidirect
418. C4×Dic11C2×D4semidirect
432. #2610D11direct (N × H)
563. C2×#124C2×D11semidirect
572. C2×#117C2×D11semidirect
592. #395C2×D11semidirect
598. #394C2×D11semidirect
604. #393C2×D11semidirect
618. #390C2×D11semidirect
633. #388C2×D11semidirect
634. #388C2×D11semidirect
642. #386C2×D11semidirect
648. #376C2×D11semidirect
854. D11#2610direct (N × H)
1010. C42D4×D11semidirect
1011. C11C2×#2610semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1242
C2×D11×#1172
#130743062
#130743052
#130743042
#130743032
#130743022
#130743012
#130743002
#130742992
#130742982
#130742972
#130742962
D11×#3952
D11×#3942
D11×#3932
D11×#3922
D11×#3902
D11×#3882
D11×#3862
D11×#3762
C11×#26102
C2×#261011