Finite Group Databasebeta

← D11×#2598 #14924397

Subgroups — D11×#2598 #14924397

Order 2816.

3502 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D11C211yesmaximal, characteristic, complemented
2C2×D11×#117C211yesmaximal, characteristic, complemented
3#13074185C211yesmaximal, characteristic, complemented
4#13074184C211yesmaximal, characteristic, complemented
5#13074183C211yesmaximal, characteristic, complemented
6#13074182C211yesmaximal, characteristic, complemented
7#13074181C212yesmaximal, complemented
8#13074180C212yesmaximal, complemented
9#13074179C212yesmaximal, complemented
10#13074178C212yesmaximal, complemented
11#13074177C211yesmaximal, characteristic, complemented
12#13074176C211yesmaximal, characteristic, complemented
13#13074175C211yesmaximal, characteristic, complemented
14D11×#400C211yesmaximal, characteristic, complemented
15D11×#399C211yesmaximal, characteristic, complemented
16D11×#394C211yesmaximal, characteristic, complemented
17D11×#392C211yesmaximal, characteristic
18D11×#388C212yesmaximal, complemented
19D11×#386C212yesmaximal, complemented
20D11×#386C212yesmaximal, complemented
21D11×#385C212yesmaximal, complemented
22D11×#383C211yesmaximal, characteristic, complemented
23C11×#2598C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C22×D4×D11C2212yes—
26C23×C4×D11C2211yescharacteristic
27C23×C4×D11C2212yes—
28C2×C4×D4×C11C2211yescharacteristic, complemented
29C2×C11×#117C2211yescharacteristic, complemented
30C2×D4×Dic11C2211yescharacteristic, complemented
31C2×C4×C22⋊D11C2212yescomplemented
32C2×#66979C2211yescharacteristic, complemented
33C4×D4×D11—28no—
34D11×#117—28no—
35C2×#66946C2211yescharacteristic, complemented
36C2×#66945C2211yescharacteristic, complemented
37C2×#66945C2211yescharacteristic, complemented
38C2×C4⋊C4×D11C2211yescharacteristic
39C2×C4⋊C4×D11C2211yescharacteristic
40C2×C4⋊C4×D11C2211yescharacteristic
41C2×C4⋊C4×D11C2212yes—
42C2×(C22⋊D11)⋊C4C2212yescomplemented
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×C4×D44C2211yescharacteristic, complemented
53C2×#66925C2211yescharacteristic, complemented
54C2×#66925C2211yescharacteristic, complemented
55C2×C42×D11C2211yescharacteristic
56C2×C42×D11C2211yescharacteristic
57C11×#400C2211yescharacteristic, complemented
58C11×#399C2211yescharacteristic, complemented
59C11×#394C2211yescharacteristic, complemented
60C11×#392C2211yescharacteristic
61C11×#388C2212yescomplemented
62C11×#386C2212yescomplemented
63C11×#386C2212yescomplemented
64C11×#385C2212yescomplemented
65C11×#383C2211yescharacteristic, complemented
66#10622836C2211yescharacteristic
67#10622836C2212yes—
68#10622835C2211yescharacteristic, complemented
69#10622833C2212yescomplemented
70#10622833C2212yescomplemented
71#10622826C2212yescomplemented
72#10622826C2212yescomplemented
73#10622823C2212yescomplemented
74#10622605C2211yescharacteristic, complemented
75#10622605C2212yescomplemented
76#10622604C2211yescharacteristic, complemented
77#10622603C2212yescomplemented
78#10622602C2212yescomplemented
79#10622602C2212yescomplemented
80#10622599C2211yescharacteristic, complemented
81#10622595C2211yescharacteristic, complemented
82#10622574C2212yescomplemented
83#10622573C2212yes—
84#10622573C2211yescharacteristic
85#10622572C2212yescomplemented
86#10622571C2212yescomplemented
87#10622571C2212yescomplemented
88#10622569C2212yescomplemented
89#10622569C2212yescomplemented
90#10622569C2212yescomplemented
91#10622569C2212yescomplemented
92#10622564C2212yescomplemented
93#10622563C2212yescomplemented
94#10622562C2212yescomplemented
95#10622562C2211yescharacteristic, complemented
96#10622559C2212yescomplemented
97#10622558C2212yescomplemented
98#10622557C2212yescomplemented
99#10622553C2212yescomplemented
100#10622550C2211yescharacteristic, complemented
101#10622290C2211yescharacteristic, complemented
102#10622285C2211yescharacteristic, complemented
103#10622284C2211yescharacteristic
104#10622283C2212yescomplemented
105#10622282C2212yescomplemented
106#10622281C2212yescomplemented
107#10622281C2212yescomplemented
108#10622278C2212yescomplemented
109#10622278C2212yescomplemented
110#10622278C2212yescomplemented
111#10622278C2212yescomplemented
112D11×#95C2212yes—
113D11×#95C2212yes—
114D11×#95C2211yescharacteristic
115D11×#95C2211yescharacteristic
116D11×#95C2212yes—
117D11×#95C2212yes—
118#10622273C2212yescomplemented
119#10622272C2211yescharacteristic, complemented
120#10622271C2212yescomplemented
121#10622264C2211yescharacteristic, complemented
122#10622264C2212yescomplemented
123#10622264C2212yescomplemented
124#10622264C2211yescharacteristic, complemented
125C24×D11C2311yescharacteristic
126C24×D11C2312yes—
127C22×D4×C11C2311yescharacteristic
128C22×D4×C11C2312yes—
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2312yes—
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2312yes—
134C23×Dic11C2311yescharacteristic
135C23×Dic11C2312yes—
136C2×D4×D11—28no—
137C2×D4×D11—28no—
138C2×D4×D11—28no—
139C2×D4×D11—24no—
140C2×D4×D11—44no—
141C22×D44C2311yescharacteristic
142C22×D44C2312yes—
143C22×C4×D11—24no—
144C22×C4×D11—24no—
145C22×C4×D11—24no—
146C22×C4×D11—28no—
147C22×C4×D11—44no—
148C22×C4×D11—44no—
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2312yes—
153C22×C4×D11C2312yes—
154C22×C4×D11C2312yes—
155C22×C4×D11C2311yescharacteristic
156C22×C4×D11C2311yescharacteristic
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C2311yescharacteristic
160C22×C4×D11C2312yes—
161C22×C4×D11C2312yes—
162C4×D4×C11—24no—
163C11×#117—24no—
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C4⋊C4C2311yescharacteristic
166C2×C11×C4⋊C4C2311yescharacteristic
167C2×C11×C4⋊C4C2312yes—
168C2×C11×C22⋊C4C2311yescharacteristic
169C2×C11×C22⋊C4C2311yescharacteristic
170C2×C11×C22⋊C4C2312yes—
171C2×C11×C22⋊C4C2312yes—
172C2×C11×C22⋊C4C2312yes—
173C2×C11×C22⋊C4C2312yes—
174C2×C11×C22⋊C4C2312yes—
175C2×C42×C11C2311yescharacteristic
176C2×C42×C11C2311yescharacteristic
177C2×C22⋊Dic11C2311yescharacteristic
178C2×C22⋊Dic11C2311yescharacteristic
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182C2×C22⋊Dic11C2312yes—
183C2×C22⋊Dic11C2312yes—
184D4×Dic11—24no—
185C4×C22⋊D11—28no—
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—
200#66979—24no—
201C2×C4⋊Dic11C2311yescharacteristic
202C2×C4⋊Dic11C2311yescharacteristic
203C2×C4⋊Dic11C2311yescharacteristic
204C2×C4⋊Dic11C2312yes—
205C2×Dic11⋊C4C2311yescharacteristic
206C2×Dic11⋊C4C2311yescharacteristic
207C2×Dic11⋊C4C2311yescharacteristic
208C2×Dic11⋊C4C2311yescharacteristic
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2312yes—
212C2×C4×Dic11C2311yescharacteristic
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218#66946—24no—
219#66945—24no—
220#66945—24no—
221C4⋊C4×D11—24no—
222C4⋊C4×D11—24no—
223C4⋊C4×D11—24no—
224C4⋊C4×D11—44no—
225(C22⋊D11)⋊C4—28no—
226C22⋊C4×D11—28no—
227C22⋊C4×D11—24no—
228C22⋊C4×D11—24no—
229C22⋊C4×D11—28no—
230C22⋊C4×D11—28no—
231C22⋊C4×D11—44no—
232C22⋊C4×D11—44no—
233#66930—24no—
234#66930—24no—
235C4×D44—24no—
236#66925—24no—
237#66925—24no—
238C42×D11—24no—
239C42×D11D418yescomplemented
240C11×#95C2311yescharacteristic
241C11×#95C2312yes—
242C11×#95C2312yes—
243C11×#95C2311yescharacteristic
244C11×#95C2312yes—
245C11×#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2311yescharacteristic
254C11⋊#95C2312yes—
255C11⋊#95C2311yescharacteristic
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C2×#2598—111nomaximal, Sylow
263C24×C11C2411yescharacteristic
264C24×C11C2412yes—
265C23×D11—22no—
266C23×D11—24no—
267C23×D11—24no—
268C23×D11—22no—
269C23×D11—24no—
270C23×D11—24no—
271C23×D11—24no—
272C23×D11—24no—
273C23×D11—24no—
274C23×D11—24no—
275C23×D11#4118yes—
276C23×D11#4114yes—
277C23×D11C2411yescharacteristic
278C23×D11C2412yes—
279C23×D11C2411yescharacteristic
280C2×D4×C11—24no—
281C2×D4×C11—24no—
282C2×D4×C11—24no—
283C2×D4×C11—22no—
284C2×D4×C11—42no—
285C22×C4×C11—22no—
286C22×C4×C11—22no—
287C22×C4×C11—22no—
288C22×C4×C11—24no—
289C22×C4×C11—42no—
290C22×C4×C11—42no—
291C22×C4×C11C2412yes—
292C22×C4×C11C2412yes—
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2412yes—
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2411yescharacteristic
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—24no—
307C2×C22⋊D11—42no—
308C2×C22⋊D11—42no—
309C22×Dic11—22no—
310C22×Dic11—22no—
311C22×Dic11—24no—
312C22×Dic11—22no—
313C22×Dic11—42no—
314C22×Dic11—42no—
315C22×Dic11C2412yes—
316C22×Dic11C2412yes—
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2412yes—
319C22×Dic11C2411yescharacteristic
320C22×Dic11C2411yescharacteristic
321C22×Dic11C2411yescharacteristic
322C22×Dic11C2411yescharacteristic
323C22×Dic11C2411yescharacteristic
324D4×D11—232no—
325D4×D11—432no—
326C2×D44—24no—
327C2×D44—24no—
328C2×D44—24no—
329C2×D44—22no—
330C2×D44—42no—
331C2×C4×D11—232no—
332C2×C4×D11—22no—
333C2×C4×D11—22no—
334C2×C4×D11—24no—
335C2×C4×D11—22no—
336C2×C4×D11—22no—
337C2×C4×D11—22no—
338C2×C4×D11—24no—
339C2×C4×D11—22no—
340C2×C4×D11—22no—
341C2×C4×D11—22no—
342C2×C4×D11—22no—
343C2×C4×D11—22no—
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—24no—
352C2×C4×D11—24no—
353C2×C4×D11—24no—
354C2×C4×D11—24no—
355C2×C4×D11—24no—
356C2×C4×D11—22no—
357C2×C4×D11—24no—
358C2×C4×D11—22no—
359C2×C4×D11—42no—
360C2×C4×D11—42no—
361C2×C4×D11—42no—
362C2×C4×D11—42no—
363C2×C4×D11—432no—
364C2×C4×D11C2×D414yes—
365C2×C4×D11C2×D414yes—
366C2×C4×D11C2×D414yes—
367C2×C4×D11#4114yes—
368C11×C4⋊C4—22no—
369C11×C4⋊C4—22no—
370C11×C4⋊C4—22no—
371C11×C4⋊C4—42no—
372C11×C22⋊C4—24no—
373C11×C22⋊C4—22no—
374C11×C22⋊C4—22no—
375C11×C22⋊C4—24no—
376C11×C22⋊C4—24no—
377C11×C22⋊C4—42no—
378C11×C22⋊C4—42no—
379C42×C11—22no—
380C42×C11C2×D414yescomplemented
381C22⋊Dic11—22no—
382C22⋊Dic11—22no—
383C22⋊Dic11—24no—
384C22⋊Dic11—24no—
385C22⋊Dic11—24no—
386C22⋊Dic11—42no—
387C22⋊Dic11—42no—
388(C2×D11)⋊C4—22no—
389(C2×D11)⋊C4—22no—
390(C2×D11)⋊C4—24no—
391(C2×D11)⋊C4—24no—
392(C2×D11)⋊C4—24no—
393(C2×D11)⋊C4—24no—
394(C2×D11)⋊C4—22no—
395(C2×D11)⋊C4—22no—
396(C2×D11)⋊C4—24no—
397(C2×D11)⋊C4—24no—
398(C2×D11)⋊C4—42no—
399(C2×D11)⋊C4—42no—
400(C2×D11)⋊C4—42no—
401(C2×D11)⋊C4—42no—
402C4⋊Dic11—22no—
403C4⋊Dic11—22no—
404C4⋊Dic11—22no—
405C4⋊Dic11—42no—
406Dic11⋊C4—22no—
407Dic11⋊C4—22no—
408Dic11⋊C4—24no—
409Dic11⋊C4—22no—
410Dic11⋊C4—22no—
411Dic11⋊C4—42no—
412Dic11⋊C4—42no—
413C4×Dic11—22no—
414C4×Dic11—22no—
415C4×Dic11—22no—
416C4×Dic11C2×D414yescomplemented
417C4×Dic11C2×D414yescomplemented
418C4×Dic11C2×D414yescomplemented
419C22×C4×D4—111no—
420C22×#117—111no—
421#2598—111no—
422#2598—111no—
423#2598—111no—
424#2598—111no—
425#2598—112no—
426#2598—112no—
427#2598—112no—
428#2598—112no—
429#2598—111no—
430#2598—111no—
431#2598—111no—
432#2598D1111yescharacteristic, direct product factor
433C2×#400—111no—
434C2×#399—111no—
435C2×#394—111no—
436C2×#392—111no—
437C2×#388—112no—
438C2×#386—112no—
439C2×#386—112no—
440C2×#385—112no—
441C2×#383—111no—
442C23×C11—21no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—21no—
446C23×C11—22no—
447C23×C11—22no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11—22no—
451C23×C11—22no—
452C23×C11C2×#4114yes—
453C23×C11C2×#4112yes—
454C23×C11C2511yescharacteristic
455C22×D11—21no—
456C22×D11—22no—
457C22×D11—22no—
458C22×D11—21no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—28no—
466C22×D11—216no—
467C22×D11—216no—
468C22×D11—216no—
469C22×D11—216no—
470C22×D11—44no—
471C22×D11—48no—
472C22×D11—48no—
473C22×D11—44no—
474C22×D11—48no—
475C22×D11—48no—
476C22×D11—48no—
477C22×D11C22×D412yes—
478C22×D11C2×#4114yes—
479C22×D11C2×#4112yes—
480C22×D11C2×#4112yes—
481C22×D11C2×#4114yes—
482C22×D11C2×#4112yes—
483C22×D11H(5,𝔽2)14yes—
484D4×C11—28no—
485D4×C11—48no—
486C2×C4×C11—28no—
487C2×C4×C11—21no—
488C2×C4×C11—21no—
489C2×C4×C11—21no—
490C2×C4×C11—21no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—21no—
494C2×C4×C11—21no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
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×C11—48no—
507C2×C4×C11C22×D412yes—
508C2×C4×C11C22×D412yes—
509C2×C4×C11C22×D412yes—
510C2×C4×C11C2×#4112yes—
511C22⋊D11—216no—
512C22⋊D11—48no—
513C22⋊D11—48no—
514C2×Dic11—28no—
515C2×Dic11—21no—
516C2×Dic11—21no—
517C2×Dic11—21no—
518C2×Dic11—21no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—21no—
522C2×Dic11—21no—
523C2×Dic11—22no—
524C2×Dic11—22no—
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×Dic11—22no—
534C2×Dic11—48no—
535C2×Dic11C22×D412yes—
536C2×Dic11C22×D412yes—
537C2×Dic11C22×D412yes—
538C2×Dic11C2×#4112yes—
539D44—28no—
540D44—48no—
541C4×D11—28no—
542C4×D11—28no—
543C4×D11—28no—
544C4×D11—28no—
545C4×D11—28no—
546C4×D11—28no—
547C4×D11—48no—
548C4×D11—48no—
549C4×D11—44no—
550C4×D11—44no—
551C4×D11—48no—
552C4×D11—48no—
553C4×D11—48no—
554C23×D4—111no—
555C23×D4—112no—
556C24×C4—111no—
557C24×C4—112no—
558C2×C4×D4—111no—
559C2×C4×D4—112no—
560C2×C4×D4—111no—
561C2×C4×D4—112no—
562C2×C4×D4—111no—
563C2×C4×D4—228no—
564C2×C4×D4C2×D1111yescharacteristic, complemented
565C2×#117—111no—
566C2×#117—111no—
567C2×#117—111no—
568C2×#117—111no—
569C2×#117—111no—
570C2×#117—111no—
571C2×#117—111no—
572C2×#117—228no—
573C2×#117C2×D1111yescharacteristic, complemented
574C22×C4⋊C4—111no—
575C22×C4⋊C4—111no—
576C22×C4⋊C4—111no—
577C22×C4⋊C4—112no—
578C22×C22⋊C4—111no—
579C22×C22⋊C4—112no—
580C22×C22⋊C4—112no—
581C22×C22⋊C4—111no—
582C22×C22⋊C4—112no—
583C22×C22⋊C4—112no—
584C22×C22⋊C4—112no—
585C22×C42—111no—
586C22×C42—111no—
587#400—111no—
588#400—111no—
589#400—112no—
590#400—111no—
591#400—112no—
592#400C2×D1111yescharacteristic, complemented
593#399—112no—
594#399—111no—
595#399—112no—
596#399—111no—
597#399—111no—
598#399C2×D1111yescharacteristic, complemented
599#394—111no—
600#394—111no—
601#394—112no—
602#394—112no—
603#394—111no—
604#394C2×D1111yescharacteristic, complemented
605#392—112no—
606#392—111no—
607#392—112no—
608#392—111no—
609#392—111no—
610#392C2×D1111yescharacteristic
611#388—112no—
612#388—112no—
613#388—112no—
614#388—112no—
615#388—112no—
616#388—112no—
617#388—112no—
618#388C2×D1112yescomplemented
619#386—112no—
620#386—112no—
621#386—112no—
622#386—112no—
623#386—112no—
624#386—112no—
625#386—112no—
626#386—112no—
627#386—112no—
628#386—112no—
629#386—112no—
630#386—112no—
631#386—112no—
632#386—112no—
633#386C2×D1112yescomplemented
634#386C2×D1112yescomplemented
635#385—112no—
636#385—112no—
637#385—112no—
638#385—112no—
639#385—112no—
640#385—112no—
641#385—112no—
642#385C2×D1112yescomplemented
643#383—111no—
644#383—111no—
645#383—111no—
646#383—112no—
647#383—112no—
648#383C2×D1111yescharacteristic, complemented
649C2×#95—111no—
650C2×#95—111no—
651C2×#95—112no—
652C2×#95—112no—
653C2×#95—112no—
654C2×#95—112no—
655C22×C11—22no—
656C22×C11—24no—
657C22×C11—24no—
658C22×C11—24no—
659C22×C11—24no—
660C22×C11—42no—
661C22×C11—41no—
662C22×C11—42no—
663C22×C11—41no—
664C22×C11—42no—
665C22×C11—42no—
666C22×C11—42no—
667C22×C11C23×D411yescharacteristic
668C22×C11C22×#4111yescharacteristic
669C22×C11C22×#4112yes—
670C22×C11C22×#4111yescharacteristic
671C22×C11C2×H(5,𝔽2)12yes—
672C2×D11—22no—
673C2×D11—24no—
674C2×D11—24no—
675C2×D11—24no—
676C2×D11—24no—
677C2×D11—42no—
678C2×D11—41no—
679C2×D11—41no—
680C2×D11—42no—
681C2×D11—42no—
682C2×D11—42no—
683C2×D11—42no—
684C2×D11—416no—
685C2×D11—432no—
686C2×D11#52514yes—
687C2×D11#52514yes—
688C2×D11#53514yes—
689C2×D11#55118yes—
690C2×D11#55318yes—
691C4×C11—22no—
692C4×C11—22no—
693C4×C11—22no—
694C4×C11—22no—
695C4×C11—41no—
696C4×C11—42no—
697C4×C11—41no—
698C4×C11—42no—
699C4×C11—42no—
700Dic11—22no—
701Dic11—22no—
702Dic11—22no—
703Dic11—22no—
704Dic11—41no—
705Dic11—42no—
706Dic11—41no—
707Dic11—42no—
708Dic11—42no—
709C25—112no—
710C25—111no—
711C22×D4—112no—
712C22×D4—112no—
713C22×D4—112no—
714C22×D4—111no—
715C22×D4—112no—
716C22×D4—224no—
717C22×D4—228no—
718C22×D4—228no—
719C22×D4—228no—
720C22×D4—444no—
721C22×D4C22×D1111yescharacteristic
722C22×D4C22×D1112yes—
723C23×C4—111no—
724C23×C4—111no—
725C23×C4—111no—
726C23×C4—111no—
727C23×C4—111no—
728C23×C4—112no—
729C23×C4—111no—
730C23×C4—112no—
731C23×C4—111no—
732C23×C4—112no—
733C23×C4—112no—
734C23×C4—111no—
735C23×C4—111no—
736C23×C4—112no—
737C23×C4—112no—
738C23×C4—224no—
739C23×C4—224no—
740C23×C4—228no—
741C23×C4—224no—
742C23×C4—444no—
743C23×C4—444no—
744C23×C4C22×D1111yescharacteristic
745C23×C4C22×D1112yes—
746C4×D4—24no—
747C4×D4—228no—
748C4×D4—224no—
749C4×D4—228no—
750C4×D4—224no—
751C4×D4—224no—
752#117—24no—
753#117—224no—
754#117—224no—
755#117—224no—
756#117—224no—
757#117—224no—
758#117—224no—
759#117—224no—
760C2×C4⋊C4—111no—
761C2×C4⋊C4—111no—
762C2×C4⋊C4—111no—
763C2×C4⋊C4—111no—
764C2×C4⋊C4—111no—
765C2×C4⋊C4—111no—
766C2×C4⋊C4—112no—
767C2×C4⋊C4—111no—
768C2×C4⋊C4—112no—
769C2×C4⋊C4—112no—
770C2×C4⋊C4—112no—
771C2×C4⋊C4—224no—
772C2×C4⋊C4—224no—
773C2×C4⋊C4—224no—
774C2×C4⋊C4—444no—
775C2×C4⋊C4C22×D1111yescharacteristic
776C2×C4⋊C4C22×D1111yescharacteristic
777C2×C4⋊C4C22×D1111yescharacteristic
778C2×C4⋊C4C22×D1112yes—
779C2×C22⋊C4—111no—
780C2×C22⋊C4—111no—
781C2×C22⋊C4—112no—
782C2×C22⋊C4—112no—
783C2×C22⋊C4—112no—
784C2×C22⋊C4—111no—
785C2×C22⋊C4—111no—
786C2×C22⋊C4—111no—
787C2×C22⋊C4—111no—
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—112no—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—224no—
801C2×C22⋊C4—224no—
802C2×C22⋊C4—228no—
803C2×C22⋊C4—228no—
804C2×C22⋊C4—228no—
805C2×C22⋊C4—444no—
806C2×C22⋊C4—444no—
807C2×C22⋊C4C22×D1111yescharacteristic
808C2×C22⋊C4C22×D1111yescharacteristic
809C2×C22⋊C4C22×D1112yes—
810C2×C22⋊C4C22×D1112yes—
811C2×C22⋊C4C22×D1112yes—
812C2×C22⋊C4C22×D1112yes—
813C2×C22⋊C4C22×D1112yes—
814C2×C42—111no—
815C2×C42—111no—
816C2×C42—111no—
817C2×C42—118no—
818C2×C42—111no—
819C2×C42—111no—
820C2×C42—111no—
821C2×C42—224no—
822C2×C42C22×D1111yescharacteristic
823C2×C42C22×D1111yescharacteristic
824#95—112no—
825#95—112no—
826#95—112no—
827#95—112no—
828#95—112no—
829#95—112no—
830#95—112no—
831#95—111no—
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×D1112yes—
842#95C22×D1111yescharacteristic
843#95C22×D1111yescharacteristic
844#95C22×D1112yes—
845#95C22×D1112yes—
846C2×C11—42no—
847C2×C11—44no—
848C2×C11C2×#52511yescharacteristic
849C2×C11C2×#52511yescharacteristic
850C2×C11C2×#53511yescharacteristic
851C2×C11C2×#55112yes—
852C2×C11C2×#55312yes—
853D11—42no—
854D11—44no—
855D11#259818yesdirect product factor
856C24—111no—
857C24—118no—
858C24—114no—
859C24—112no—
860C24—111no—
861C24—222no—
862C24—224no—
863C24—224no—
864C24—224no—
865C24—224no—
866C24—222no—
867C24—224no—
868C24—224no—
869C24—224no—
870C24—224no—
871C24C23×D1111yescharacteristic
872C24C23×D1112yes—
873C2×D4—24no—
874C2×D4—24no—
875C2×D4—24no—
876C2×D4—22no—
877C2×D4—42no—
878C2×D4—224no—
879C2×D4—224no—
880C2×D4—224no—
881C2×D4—224no—
882C2×D4—2232no—
883C2×D4—224no—
884C2×D4—224no—
885C2×D4—224no—
886C2×D4—224no—
887C2×D4—224no—
888C2×D4—224no—
889C2×D4—222no—
890C2×D4—442no—
891C2×D4—442no—
892C2×D4—442no—
893C2×D4—4432no—
894C22×C4—22no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—24no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—111no—
901C22×C4—111no—
902C22×C4—111no—
903C22×C4—111no—
904C22×C4—114no—
905C22×C4—114no—
906C22×C4—114no—
907C22×C4—114no—
908C22×C4—112no—
909C22×C4—112no—
910C22×C4—111no—
911C22×C4—112no—
912C22×C4—111no—
913C22×C4—222no—
914C22×C4—222no—
915C22×C4—224no—
916C22×C4—222no—
917C22×C4—222no—
918C22×C4—222no—
919C22×C4—222no—
920C22×C4—222no—
921C22×C4—222no—
922C22×C4—224no—
923C22×C4—224no—
924C22×C4—2232no—
925C22×C4—222no—
926C22×C4—222no—
927C22×C4—224no—
928C22×C4—224no—
929C22×C4—224no—
930C22×C4—224no—
931C22×C4—224no—
932C22×C4—224no—
933C22×C4—224no—
934C22×C4—224no—
935C22×C4—224no—
936C22×C4—224no—
937C22×C4—224no—
938C22×C4—222no—
939C22×C4—222no—
940C22×C4—224no—
941C22×C4—222no—
942C22×C4—222no—
943C22×C4—222no—
944C22×C4—224no—
945C22×C4—442no—
946C22×C4—442no—
947C22×C4—442no—
948C22×C4—442no—
949C22×C4—4432no—
950C22×C4—442no—
951C22×C4—442no—
952C22×C4C23×D1112yes—
953C22×C4C23×D1112yes—
954C22×C4C23×D1111yescharacteristic
955C22×C4C23×D1112yes—
956C22×C4C23×D1111yescharacteristic
957C22×C4C23×D1111yescharacteristic
958C22×C4C23×D1111yescharacteristic
959C22×C4C23×D1111yescharacteristic
960C22×C4C23×D1111yescharacteristic
961C4⋊C4—22no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—42no—
965C4⋊C4—222no—
966C4⋊C4—222no—
967C4⋊C4—222no—
968C4⋊C4—222no—
969C4⋊C4—224no—
970C4⋊C4—222no—
971C4⋊C4—222no—
972C4⋊C4—222no—
973C4⋊C4—442no—
974C4⋊C4—442no—
975C4⋊C4—442no—
976C22⋊C4—24no—
977C22⋊C4—22no—
978C22⋊C4—22no—
979C22⋊C4—24no—
980C22⋊C4—24no—
981C22⋊C4—42no—
982C22⋊C4—42no—
983C22⋊C4—222no—
984C22⋊C4—222no—
985C22⋊C4—224no—
986C22⋊C4—224no—
987C22⋊C4—224no—
988C22⋊C4—224no—
989C22⋊C4—222no—
990C22⋊C4—222no—
991C22⋊C4—224no—
992C22⋊C4—224no—
993C22⋊C4—224no—
994C22⋊C4—222no—
995C22⋊C4—222no—
996C22⋊C4—224no—
997C22⋊C4—224no—
998C22⋊C4—442no—
999C22⋊C4—442no—
1000C22⋊C4—442no—
1001C22⋊C4—442no—
1002C22⋊C4—442no—
1003C22⋊C4—442no—
1004C42—22no—
1005C42—114no—
1006C42—114no—
1007C42—114no—
1008C42—222no—
1009C42—222no—
1010C42—222no—
1011C42D4×D1114yescomplemented
1012C11C2×#259811yescharacteristic, complemented, Sylow
1013C23—21no—
1014C23—22no—
1015C23—22no—
1016C23—21no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—112no—
1024C23—112no—
1025C23—114no—
1026C23—112no—
1027C23—114no—
1028C23—114no—
1029C23—112no—
1030C23—228no—
1031C23—2216no—
1032C23—2216no—
1033C23—2216no—
1034C23—2216no—
1035C23—221no—
1036C23—222no—
1037C23—222no—
1038C23—221no—
1039C23—222no—
1040C23—222no—
1041C23—222no—
1042C23—222no—
1043C23—222no—
1044C23—222no—
1045C23—448no—
1046C23—448no—
1047C23—448no—
1048C23—444no—
1049C23—448no—
1050C23—444no—
1051C23—448no—
1052C23#41×D1114yes—
1053C23#41×D1112yes—
1054C23C24×D1111yescharacteristic
1055D4—28no—
1056D4—48no—
1057D4—228no—
1058D4—2216no—
1059D4—448no—
1060D4—448no—
1061D4—448no—
1062C2×C4—28no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—48no—
1083C2×C4—112no—
1084C2×C4—112no—
1085C2×C4—112no—
1086C2×C4—112no—
1087C2×C4—228no—
1088C2×C4—228no—
1089C2×C4—228no—
1090C2×C4—228no—
1091C2×C4—228no—
1092C2×C4—228no—
1093C2×C4—228no—
1094C2×C4—221no—
1095C2×C4—221no—
1096C2×C4—221no—
1097C2×C4—221no—
1098C2×C4—222no—
1099C2×C4—222no—
1100C2×C4—221no—
1101C2×C4—221no—
1102C2×C4—222no—
1103C2×C4—222no—
1104C2×C4—222no—
1105C2×C4—222no—
1106C2×C4—222no—
1107C2×C4—222no—
1108C2×C4—222no—
1109C2×C4—222no—
1110C2×C4—222no—
1111C2×C4—222no—
1112C2×C4—222no—
1113C2×C4—448no—
1114C2×C4—448no—
1115C2×C4—448no—
1116C2×C4—448no—
1117C2×C4—448no—
1118C2×C4—444no—
1119C2×C4—444no—
1120C2×C4—448no—
1121C2×C4C2×D4×D1112yes—
1122C2×C4C2×D4×D1112yes—
1123C2×C4C2×D4×D1112yes—
1124C2×C4#41×D1112yes—
1125C22—24no—
1126C22—22no—
1127C22—24no—
1128C22—24no—
1129C22—24no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—41no—
1134C22—42no—
1135C22—41no—
1136C22—42no—
1137C22—118no—
1138C22—114no—
1139C22—114no—
1140C22—114no—
1141C22—118no—
1142C22—224no—
1143C22—222no—
1144C22—224no—
1145C22—224no—
1146C22—224no—
1147C22—4416no—
1148C22—4432no—
1149C22—442no—
1150C22—442no—
1151C22—442no—
1152C22—441no—
1153C22—442no—
1154C22—441no—
1155C22—442no—
1156C22C22×D4×D1111yescharacteristic
1157C22C2×#41×D1111yescharacteristic
1158C22C2×#41×D1112yes—
1159C22C2×#41×D1111yescharacteristic
1160C22D11×H(5,𝔽2)12yes—
1161C4—22no—
1162C4—22no—
1163C4—22no—
1164C4—22no—
1165C4—42no—
1166C4—42no—
1167C4—41no—
1168C4—41no—
1169C4—42no—
1170C4—222no—
1171C4—222no—
1172C4—222no—
1173C4—222no—
1174C4—442no—
1175C4—442no—
1176C4—441no—
1177C4—441no—
1178C4—442no—
1179C2—44no—
1180C2—42no—
1181C2—118no—
1182C2—444no—
1183C2—442no—
1184C2D11×#52511yescharacteristic
1185C2D11×#52511yescharacteristic
1186C2D11×#53511yescharacteristic
1187C2D11×#55112yes—
1188C2D11×#55312yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2598C2
prime radicalD11×#392C2
hypercenter#2598D11
hypocenterC11C2×#2598
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2598

Complements

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

NH ≅ G/Ntype
1. C2×C4×D4×D11C2semidirect
2. C2×D11×#117C2semidirect
3. #13074185C2semidirect
4. #13074184C2semidirect
5. #13074183C2semidirect
6. #13074182C2semidirect
7. #13074181C2semidirect
8. #13074180C2semidirect
9. #13074179C2semidirect
10. #13074178C2semidirect
11. #13074177C2semidirect
12. #13074176C2semidirect
13. #13074175C2semidirect
14. D11×#400C2semidirect
15. D11×#399C2semidirect
16. D11×#394C2semidirect
18. D11×#388C2semidirect
19. D11×#386C2semidirect
20. D11×#386C2semidirect
21. D11×#385C2semidirect
22. D11×#383C2semidirect
23. C11×#2598C2semidirect
28. C2×C4×D4×C11C22semidirect
29. C2×C11×#117C22semidirect
30. C2×D4×Dic11C22semidirect
31. C2×C4×C22⋊D11C22semidirect
32. C2×#66979C22semidirect
35. C2×#66946C22semidirect
36. C2×#66945C22semidirect
37. C2×#66945C22semidirect
42. C2×(C22⋊D11)⋊C4C22semidirect
50. C2×#66930C22semidirect
51. C2×#66930C22semidirect
52. C2×C4×D44C22semidirect
53. C2×#66925C22semidirect
54. C2×#66925C22semidirect
57. C11×#400C22semidirect
58. C11×#399C22semidirect
59. C11×#394C22semidirect
61. C11×#388C22semidirect
62. C11×#386C22semidirect
63. C11×#386C22semidirect
64. C11×#385C22semidirect
65. C11×#383C22semidirect
68. #10622835C22semidirect
69. #10622833C22semidirect
70. #10622833C22semidirect
71. #10622826C22semidirect
72. #10622826C22semidirect
73. #10622823C22semidirect
74. #10622605C22semidirect
75. #10622605C22semidirect
76. #10622604C22semidirect
77. #10622603C22semidirect
78. #10622602C22semidirect
79. #10622602C22semidirect
80. #10622599C22semidirect
81. #10622595C22semidirect
82. #10622574C22semidirect
85. #10622572C22semidirect
86. #10622571C22semidirect
87. #10622571C22semidirect
88. #10622569C22semidirect
89. #10622569C22semidirect
90. #10622569C22semidirect
91. #10622569C22semidirect
92. #10622564C22semidirect
93. #10622563C22semidirect
94. #10622562C22semidirect
95. #10622562C22semidirect
96. #10622559C22semidirect
97. #10622558C22semidirect
98. #10622557C22semidirect
99. #10622553C22semidirect
100. #10622550C22semidirect
101. #10622290C22semidirect
102. #10622285C22semidirect
104. #10622283C22semidirect
105. #10622282C22semidirect
106. #10622281C22semidirect
107. #10622281C22semidirect
108. #10622278C22semidirect
109. #10622278C22semidirect
110. #10622278C22semidirect
111. #10622278C22semidirect
118. #10622273C22semidirect
119. #10622272C22semidirect
120. #10622271C22semidirect
121. #10622264C22semidirect
122. #10622264C22semidirect
123. #10622264C22semidirect
124. #10622264C22semidirect
239. C42×D11D4semidirect
380. C42×C11C2×D4semidirect
416. C4×Dic11C2×D4semidirect
417. C4×Dic11C2×D4semidirect
418. C4×Dic11C2×D4semidirect
432. #2598D11direct (N × H)
564. C2×C4×D4C2×D11semidirect
573. C2×#117C2×D11semidirect
592. #400C2×D11semidirect
598. #399C2×D11semidirect
604. #394C2×D11semidirect
618. #388C2×D11semidirect
633. #386C2×D11semidirect
634. #386C2×D11semidirect
642. #385C2×D11semidirect
648. #383C2×D11semidirect
855. D11#2598direct (N × H)
1011. C42D4×D11semidirect
1012. C11C2×#2598semidirect

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
#130741852
#130741842
#130741832
#130741822
#130741812
#130741802
#130741792
#130741782
#130741772
#130741762
#130741752
D11×#4002
D11×#3992
D11×#3942
D11×#3922
D11×#3882
D11×#3862
D11×#3852
D11×#3832
C11×#25982
C2×#259811