Finite Group Databasebeta

← D11×#2431 #14922102

Subgroups — D11×#2431 #14922102

Order 2816.

6278 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
1C22×#41×D11C211yesmaximal, characteristic, complemented
2C2×D11×#127C211yesmaximal, characteristic, complemented
3C2×D11×#124C211yesmaximal, characteristic, complemented
4C2×D11×#121C211yesmaximal, characteristic, complemented
5#13072238C211yesmaximal, characteristic, complemented
6#13072237C211yesmaximal, characteristic, complemented
7#13072236C211yesmaximal, characteristic, complemented
8#13072235C211yesmaximal, characteristic, complemented
9#13072234C211yesmaximal, characteristic, complemented
10#13072233C214yesmaximal, complemented
11#13072232C211yesmaximal, characteristic, complemented
12#13072231C211yesmaximal, characteristic, complemented
13#13072230C214yesmaximal, complemented
14D11×#392C214yesmaximal, complemented
15D11×#391C211yesmaximal, characteristic, complemented
16D11×#390C211yesmaximal, characteristic, complemented
17D11×#386C214yesmaximal, complemented
18C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
19C11×#2431C211yesmaximal, characteristic, complemented
20C22×C11×#41C2211yescharacteristic, complemented
21C2×#41×D11—28no—
22C2×#41×D11—28no—
23C2×#41×D11—28no—
24C22×#4343C2211yescharacteristic, complemented
25C22×Q8×D11C2211yescharacteristic
26C22×#4341C2212yescomplemented
27C22×#4341C2211yescharacteristic, complemented
28C22×D4×D11C2211yescharacteristic
29C22×D4×D11C2212yes—
30C22×D4×D11C2214yes—
31C22×D4×D11C2211yescharacteristic
32C22×D4×D11C2212yes—
33C22×#4339C2212yescomplemented
34C22×#4339C2211yescharacteristic, complemented
35C23×C4×D11C2212yes—
36C23×C4×D11C2211yescharacteristic
37C2×C11×#127C2211yescharacteristic, complemented
38C2×C11×#124C2211yescharacteristic, complemented
39C2×C11×#121C2211yescharacteristic, complemented
40C2×#67000C2211yescharacteristic, complemented
41C2×#66993C2214yescomplemented
42C2×#66993C2211yescharacteristic, complemented
43C2×#66993C2211yescharacteristic, complemented
44C2×#66992C2212yescomplemented
45C2×#66991C2211yescharacteristic, complemented
46C2×#66989C2211yescharacteristic, complemented
47C2×#66983C2211yescharacteristic, complemented
48D11×#127—28no—
49D11×#124—28no—
50D11×#121—28no—
51C2×#66948C2211yescharacteristic, complemented
52C2×C4⋊C4×D11C2211yescharacteristic
53C2×#66938C2214yescomplemented
54C2×#66937C2212yescomplemented
55C2×C22⋊C4×D11C2214yes—
56C2×C22⋊C4×D11C2212yes—
57C2×C22⋊C4×D11C2212yes—
58C2×C22⋊C4×D11C2214yes—
59C2×#66928C2211yescharacteristic, complemented
60C2×#66927C2211yescharacteristic, complemented
61C2×C42×D11C2211yescharacteristic
62C2×C42×D11C2211yescharacteristic
63C11×#392C2214yescomplemented
64C11×#391C2211yescharacteristic, complemented
65C11×#390C2211yescharacteristic, complemented
66C11×#386C2214yescomplemented
67C4×C11×C22⋊C4C2211yescharacteristic, complemented
68#10622843C2211yescharacteristic, complemented
69#10622836C2214yescomplemented
70#10622836C2214yescomplemented
71#10622836C2214yescomplemented
72#10622834C2211yescharacteristic, complemented
73#10622833C2214yescomplemented
74#10622826C2214yescomplemented
75C4×C22⋊Dic11C2211yescharacteristic, complemented
76#10622601C2211yescharacteristic, complemented
77#10622587C2211yescharacteristic, complemented
78#10622573C2214yescomplemented
79#10622573C2214yescomplemented
80#10622573C2214yescomplemented
81#10622571C2214yescomplemented
82#10622570C2214yescomplemented
83#10622569C2214yescomplemented
84#10622569C2214yescomplemented
85C22⋊C4×Dic11C2212yescomplemented
86#10622552C2211yescharacteristic, complemented
87C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
88C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
89#10622542C2211yescharacteristic, complemented
90#10622284C2214yescomplemented
91#10622279C2212yescomplemented
92#10622278C2214yescomplemented
93#10622278C2214yescomplemented
94D11×#95C2212yes—
95D11×#95C2214yes—
96#10622259C2214yescomplemented
97C24×D11C2312yes—
98C24×D11C2311yescharacteristic
99C24×D11C2312yes—
100C2×C11×#41—24no—
101C2×C11×#41—24no—
102C2×C11×#41—24no—
103C22×Q8×C11C2311yescharacteristic
104C22×D4×C11C2311yescharacteristic
105C22×D4×C11C2312yes—
106C22×D4×C11C2314yes—
107C22×D4×C11C2311yescharacteristic
108C22×D4×C11C2312yes—
109C23×C4×C11C2312yes—
110C23×C4×C11C2311yescharacteristic
111C22×C22⋊D11C2312yes—
112C22×C22⋊D11C2312yes—
113C22×C22⋊D11C2312yes—
114C22×C22⋊D11C2314yes—
115C22×C22⋊D11C2314yes—
116C22×C22⋊D11C2312yes—
117C22×C22⋊D11C2312yes—
118C22×C22⋊D11C2312yes—
119C23×Dic11C2312yes—
120C23×Dic11C2311yescharacteristic
121#41×D11—2128no—
122C2×#4343—24no—
123C2×#4343—24no—
124C2×#4343—24no—
125C2×Q8×D11—24no—
126C2×Q8×D11—24no—
127C2×Q8×D11D418yescomplemented
128C2×#4341—24no—
129C2×#4341—28no—
130C2×#4341—28no—
131C2×#4341—24no—
132C2×#4341—24no—
133C2×#4341—28no—
134C2×D4×D11—28no—
135C2×D4×D11—28no—
136C2×D4×D11—216no—
137C2×D4×D11—28no—
138C2×D4×D11—28no—
139C2×D4×D11—24no—
140C2×D4×D11—24no—
141C2×D4×D11—24no—
142C2×D4×D11—24no—
143C2×D4×D11—24no—
144C2×D4×D11—216no—
145C2×D4×D11—48no—
146C2×D4×D11—48no—
147C2×D4×D11D418yescomplemented
148C2×#4339—24no—
149C2×#4339—28no—
150C2×#4339—24no—
151C2×#4339—28no—
152C2×#4339—24no—
153C2×#4339—28no—
154C22×D44C2311yescharacteristic
155C22×D44C2312yes—
156C22×D44C2314yes—
157C22×D44C2311yescharacteristic
158C22×D44C2312yes—
159C22×C4×D11—28no—
160C22×C4×D11—28no—
161C22×C4×D11—28no—
162C22×C4×D11—24no—
163C22×C4×D11—24no—
164C22×C4×D11D418yescomplemented
165C22×C4×D11C2312yes—
166C22×C4×D11C2312yes—
167C22×C4×D11C2312yes—
168C22×C4×D11C2312yes—
169C22×C4×D11C2311yescharacteristic
170C22×C4×D11C2312yes—
171C22×C4×D11C2311yescharacteristic
172C22×C4×D11C2311yescharacteristic
173C22×C4×D11C2312yes—
174C22×C4×D11C2311yescharacteristic
175C22×Dic22C2311yescharacteristic
176C22×Dic22C2312yes—
177C11×#127—24no—
178C11×#124—24no—
179C11×#121—24no—
180C2×C11×C4⋊C4C2311yescharacteristic
181C2×C11×C22⋊C4C2312yes—
182C2×C11×C22⋊C4C2314yes—
183C2×C11×C22⋊C4C2312yes—
184C2×C11×C22⋊C4C2314yes—
185C2×C42×C11C2311yescharacteristic
186C2×C42×C11C2311yescharacteristic
187C2×C22⋊Dic11C2314yes—
188C2×C22⋊Dic11C2312yes—
189C2×C22⋊Dic11C2312yes—
190C2×C22⋊Dic11C2314yes—
191#67000—24no—
192#66993—24no—
193#66993—216no—
194#66993—24no—
195#66992—28no—
196#66991—24no—
197#66989—24no—
198#66983—24no—
199C2×(C2×D11)⋊C4C2314yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2314yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2314yes—
206C2×(C2×D11)⋊C4C2314yes—
207C2×C4⋊Dic11C2311yescharacteristic
208C2×Dic11⋊C4C2312yes—
209C2×C4×Dic11C2312yes—
210C2×C4×Dic11C2312yes—
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2311yescharacteristic
213#66948—24no—
214C4⋊C4×D11—24no—
215#66938—216no—
216#66937—28no—
217C22⋊C4×D11—28no—
218C22⋊C4×D11—216no—
219C22⋊C4×D11—28no—
220C22⋊C4×D11—48no—
221#66928—24no—
222#66927—24no—
223C42×D11—24no—
224C42×D11—24no—
225C11×#95C2314yes—
226C11×#95C2312yes—
227C11⋊#95C2314yes—
228C11⋊#95C2314yes—
229C11⋊#95C2314yes—
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C2×#2431—111nomaximal, Sylow
234C24×C11C2412yes—
235C24×C11C2411yescharacteristic
236C24×C11C2412yes—
237C23×D11—24no—
238C23×D11—22no—
239C23×D11—24no—
240C23×D11—22no—
241C23×D11—24no—
242C23×D11—28no—
243C23×D11—28no—
244C23×D11—24no—
245C23×D11—24no—
246C23×D11—24no—
247C23×D11—24no—
248C23×D11—28no—
249C23×D11—28no—
250C23×D11C2×D418yes—
251C23×D11C2×D414yes—
252C23×D11C2412yes—
253C23×D11C2411yescharacteristic
254C23×D11C2412yes—
255C23×D11C2411yescharacteristic
256C11×#41—232no—
257C2×Q8×C11—22no—
258C2×Q8×C11—22no—
259C2×Q8×C11C2×D414yescomplemented
260C2×D4×C11—24no—
261C2×D4×C11—24no—
262C2×D4×C11—24no—
263C2×D4×C11—28no—
264C2×D4×C11—24no—
265C2×D4×C11—22no—
266C2×D4×C11—22no—
267C2×D4×C11—22no—
268C2×D4×C11—22no—
269C2×D4×C11—22no—
270C2×D4×C11—28no—
271C2×D4×C11—44no—
272C2×D4×C11—44no—
273C2×D4×C11C2×D414yescomplemented
274C22×C4×C11—24no—
275C22×C4×C11—24no—
276C22×C4×C11—24no—
277C22×C4×C11—22no—
278C22×C4×C11—22no—
279C22×C4×C11C2×D414yescomplemented
280C22×C4×C11C2412yes—
281C22×C4×C11C2412yes—
282C22×C4×C11C2412yes—
283C22×C4×C11C2411yescharacteristic
284C22×C4×C11C2412yes—
285C22×C4×C11C2411yescharacteristic
286C2×C22⋊D11—24no—
287C2×C22⋊D11—24no—
288C2×C22⋊D11—24no—
289C2×C22⋊D11—24no—
290C2×C22⋊D11—24no—
291C2×C22⋊D11—24no—
292C2×C22⋊D11—24no—
293C2×C22⋊D11—28no—
294C2×C22⋊D11—28no—
295C2×C22⋊D11—24no—
296C2×C22⋊D11—24no—
297C2×C22⋊D11—24no—
298C2×C22⋊D11—28no—
299C2×C22⋊D11—24no—
300C2×C22⋊D11—24no—
301C2×C22⋊D11—24no—
302C2×C22⋊D11—28no—
303C2×C22⋊D11—44no—
304C2×C22⋊D11—44no—
305C2×C22⋊D11—44no—
306C2×C22⋊D11—44no—
307C2×C22⋊D11C2×D418yescomplemented
308C22×Dic11—24no—
309C22×Dic11—24no—
310C22×Dic11—22no—
311C22×Dic11—22no—
312C22×Dic11—24no—
313C22×Dic11C2×D414yescomplemented
314C22×Dic11C2412yes—
315C22×Dic11C2412yes—
316C22×Dic11C2412yes—
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2412yes—
319C22×Dic11C2411yescharacteristic
320#4343—232no—
321Q8×D11—232no—
322#4341—264no—
323#4341—232no—
324D4×D11—264no—
325D4×D11—232no—
326D4×D11—464no—
327D4×D11—432no—
328D4×D11—416no—
329#4339—264no—
330#4339—232no—
331C2×D44—24no—
332C2×D44—24no—
333C2×D44—28no—
334C2×D44—24no—
335C2×D44—24no—
336C2×D44—22no—
337C2×D44—22no—
338C2×D44—22no—
339C2×D44—22no—
340C2×D44—22no—
341C2×D44—28no—
342C2×D44—44no—
343C2×D44—44no—
344C2×D44C2×D414yescomplemented
345C2×C4×D11—264no—
346C2×C4×D11—24no—
347C2×C4×D11—22no—
348C2×C4×D11—22no—
349C2×C4×D11—24no—
350C2×C4×D11—232no—
351C2×C4×D11—24no—
352C2×C4×D11—22no—
353C2×C4×D11—22no—
354C2×C4×D11—24no—
355C2×C4×D11—24no—
356C2×C4×D11—24no—
357C2×C4×D11—24no—
358C2×C4×D11—24no—
359C2×C4×D11—24no—
360C2×C4×D11—24no—
361C2×C4×D11—24no—
362C2×C4×D11—24no—
363C2×C4×D11—28no—
364C2×C4×D11—24no—
365C2×C4×D11—24no—
366C2×C4×D11—22no—
367C2×C4×D11—22no—
368C2×C4×D11C2×D414yes—
369C2×C4×D11C2×D418yes—
370C2×C4×D11C2×D414yes—
371C2×C4×D11C2×D414yes—
372C2×C4×D11C2×D414yes—
373C2×C4×D11C2×D414yescomplemented
374C2×C4×D11C2×D414yescomplemented
375C2×C4×D11#4118yescomplemented
376C2×Dic22—24no—
377C2×Dic22—24no—
378C2×Dic22—22no—
379C2×Dic22—22no—
380C2×Dic22C2×D414yescomplemented
381C2×Dic22C2×D418yescomplemented
382C11×C4⋊C4—22no—
383C11×C22⋊C4—24no—
384C11×C22⋊C4—28no—
385C11×C22⋊C4—24no—
386C11×C22⋊C4—44no—
387C42×C11—22no—
388C42×C11—22no—
389C22⋊Dic11—28no—
390C22⋊Dic11—24no—
391C22⋊Dic11—24no—
392C22⋊Dic11—44no—
393(C2×D11)⋊C4—28no—
394(C2×D11)⋊C4—24no—
395(C2×D11)⋊C4—24no—
396(C2×D11)⋊C4—24no—
397(C2×D11)⋊C4—28no—
398(C2×D11)⋊C4—24no—
399(C2×D11)⋊C4—44no—
400(C2×D11)⋊C4—44no—
401C4⋊Dic11—22no—
402Dic11⋊C4—24no—
403C4×Dic11—24no—
404C4×Dic11—24no—
405C4×Dic11—22no—
406C4×Dic11—22no—
407C23×#41—111no—
408C22×#127—111no—
409C22×#124—111no—
410C22×#121—111no—
411#2431—114no—
412#2431—111no—
413#2431—111no—
414#2431—114no—
415#2431—111no—
416#2431—111no—
417#2431—111no—
418#2431—111no—
419#2431—111no—
420#2431D1111yescharacteristic, direct product factor
421C2×#392—114no—
422C2×#391—111no—
423C2×#390—111no—
424C2×#386—114no—
425C2×C4×C22⋊C4—111no—
426C23×C11—22no—
427C23×C11—21no—
428C23×C11—22no—
429C23×C11—21no—
430C23×C11—22no—
431C23×C11—24no—
432C23×C11—24no—
433C23×C11—22no—
434C23×C11—22no—
435C23×C11—22no—
436C23×C11—22no—
437C23×C11—24no—
438C23×C11—24no—
439C23×C11C22×D414yes—
440C23×C11C22×D412yes—
441C23×C11C2511yescharacteristic
442C22×D11—22no—
443C22×D11—21no—
444C22×D11—22no—
445C22×D11—21no—
446C22×D11—22no—
447C22×D11—24no—
448C22×D11—24no—
449C22×D11—22no—
450C22×D11—216no—
451C22×D11—28no—
452C22×D11—28no—
453C22×D11—28no—
454C22×D11—232no—
455C22×D11—22no—
456C22×D11—22no—
457C22×D11—22no—
458C22×D11—24no—
459C22×D11—24no—
460C22×D11—48no—
461C22×D11—48no—
462C22×D11—48no—
463C22×D11—48no—
464C22×D11—416no—
465C22×D11—48no—
466C22×D11—48no—
467C22×D11—48no—
468C22×D11—416no—
469C22×D11—416no—
470C22×D11C22×D414yes—
471C22×D11C22×D412yes—
472C22×D11C22×D412yes—
473C22×D11C22×D412yes—
474C22×D11C22×D412yes—
475C22×D11C2×#4114yes—
476C22×D11H(5,𝔽2)14yes—
477Q8×C11—28no—
478D4×C11—216no—
479D4×C11—28no—
480D4×C11—416no—
481D4×C11—48no—
482D4×C11—44no—
483C2×C4×C11—216no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—21no—
488C2×C4×C11—21no—
489C2×C4×C11—22no—
490C2×C4×C11—28no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—24no—
496C2×C4×C11C22×D414yes—
497C2×C4×C11C22×D412yes—
498C2×C4×C11C22×D412yes—
499C2×C4×C11C22×D412yes—
500C2×C4×C11C22×D412yes—
501C2×C4×C11C2×#4114yescomplemented
502C22⋊D11—216no—
503C22⋊D11—216no—
504C22⋊D11—216no—
505C22⋊D11—416no—
506C22⋊D11—416no—
507C22⋊D11—48no—
508C22⋊D11—48no—
509C22⋊D11—48no—
510C2×Dic11—216no—
511C2×Dic11—22no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—21no—
515C2×Dic11—21no—
516C2×Dic11—22no—
517C2×Dic11—28no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—24no—
523C2×Dic11C22×D414yes—
524C2×Dic11C22×D412yes—
525C2×Dic11C22×D412yes—
526C2×Dic11C22×D412yes—
527C2×Dic11C22×D412yes—
528C2×Dic11C2×#4114yescomplemented
529D44—216no—
530D44—28no—
531D44—416no—
532D44—48no—
533D44—44no—
534C4×D11—216no—
535C4×D11—216no—
536C4×D11—28no—
537C4×D11—216no—
538C4×D11—216no—
539C4×D11—28no—
540C4×D11—28no—
541C4×D11—48no—
542C4×D11—48no—
543C4×D11#120116yes—
544Dic22—28no—
545Dic22—216no—
546C22×#41—111no—
547C22×#41—112no—
548C22×#41—111no—
549C22×#41—112no—
550C22×#41—111no—
551C22×#41—228no—
552C22×#41—228no—
553C22×#41—228no—
554C22×#41C2×D1111yescharacteristic, complemented
555C23×Q8—111no—
556C23×D4—111no—
557C23×D4—112no—
558C23×D4—111no—
559C23×D4—114no—
560C23×D4—112no—
561C24×C4—111no—
562C24×C4—112no—
563C2×#127—114no—
564C2×#127—111no—
565C2×#127—111no—
566C2×#127—111no—
567C2×#127—228no—
568C2×#127C2×D1111yescharacteristic, complemented
569C2×#124—111no—
570C2×#124—111no—
571C2×#124—114no—
572C2×#124—111no—
573C2×#124—228no—
574C2×#124C2×D1111yescharacteristic, complemented
575C2×#121—111no—
576C2×#121—112no—
577C2×#121—111no—
578C2×#121—111no—
579C2×#121—112no—
580C2×#121—228no—
581C2×#121C2×D1111yescharacteristic, complemented
582C22×C4⋊C4—111no—
583C22×C22⋊C4—112no—
584C22×C22⋊C4—114no—
585C22×C22⋊C4—112no—
586C22×C22⋊C4—114no—
587C22×C42—111no—
588C22×C42—111no—
589#392—114no—
590#392—114no—
591#392—114no—
592#392—114no—
593#392—114no—
594#392—114no—
595#392—114no—
596#392C2×D1114yescomplemented
597#391—111no—
598#391—111no—
599#391—111no—
600#391—114no—
601#391C2×D1111yescharacteristic, complemented
602#390—111no—
603#390—111no—
604#390—114no—
605#390—111no—
606#390C2×D1111yescharacteristic, complemented
607#386—114no—
608#386—114no—
609#386—114no—
610#386—114no—
611#386—114no—
612#386—114no—
613#386—114no—
614#386C2×D1114yescomplemented
615C4×C22⋊C4—111no—
616C4×C22⋊C4—112no—
617C4×C22⋊C4—111no—
618C4×C22⋊C4—111no—
619C4×C22⋊C4—112no—
620C4×C22⋊C4C2×D1111yescharacteristic, complemented
621C2×#95—114no—
622C2×#95—112no—
623C22×C11—24no—
624C22×C11—22no—
625C22×C11—22no—
626C22×C11—22no—
627C22×C11—28no—
628C22×C11—42no—
629C22×C11—42no—
630C22×C11—42no—
631C22×C11—42no—
632C22×C11—44no—
633C22×C11—42no—
634C22×C11—42no—
635C22×C11—42no—
636C22×C11—44no—
637C22×C11—44no—
638C22×C11C23×D411yescharacteristic
639C22×C11C23×D411yescharacteristic
640C22×C11C23×D411yescharacteristic
641C22×C11C22×#4112yes—
642C22×C11C2×H(5,𝔽2)12yes—
643C2×D11—24no—
644C2×D11—22no—
645C2×D11—22no—
646C2×D11—22no—
647C2×D11—28no—
648C2×D11—42no—
649C2×D11—42no—
650C2×D11—42no—
651C2×D11—42no—
652C2×D11—44no—
653C2×D11—416no—
654C2×D11—432no—
655C2×D11—42no—
656C2×D11—42no—
657C2×D11—42no—
658C2×D11—44no—
659C2×D11—44no—
660C2×D11—816no—
661C2×D11C2×#12014yes—
662C2×D11#53214yes—
663C2×D11#53514yes—
664C2×D11#54618yes—
665C2×D11#55018yes—
666C4×C11—22no—
667C4×C11—24no—
668C4×C11—24no—
669C4×C11—42no—
670C4×C11—42no—
671C4×C11C2×#12014yes—
672Dic11—24no—
673Dic11—22no—
674Dic11—24no—
675Dic11—42no—
676Dic11—42no—
677Dic11C2×#12014yes—
678C25—111no—
679C25—112no—
680C25—112no—
681C2×#41—24no—
682C2×#41—24no—
683C2×#41—24no—
684C2×#41—228no—
685C2×#41—228no—
686C2×#41—224no—
687C2×#41—228no—
688C2×#41—224no—
689C2×#41—228no—
690C2×#41—224no—
691C2×#41—224no—
692C2×#41—228no—
693C2×#41—228no—
694C2×#41—224no—
695C2×#41—224no—
696C2×#41—22128no—
697C2×#41—224no—
698C2×#41—224no—
699C2×#41—224no—
700C22×Q8—118no—
701C22×Q8—112no—
702C22×Q8—111no—
703C22×Q8—224no—
704C22×Q8—224no—
705C22×Q8C22×D1111yescharacteristic
706C22×D4—112no—
707C22×D4—118no—
708C22×D4—112no—
709C22×D4—112no—
710C22×D4—112no—
711C22×D4—114no—
712C22×D4—114no—
713C22×D4—112no—
714C22×D4—112no—
715C22×D4—111no—
716C22×D4—111no—
717C22×D4—112no—
718C22×D4—114no—
719C22×D4—112no—
720C22×D4—224no—
721C22×D4—224no—
722C22×D4—228no—
723C22×D4—224no—
724C22×D4—224no—
725C22×D4—224no—
726C22×D4—2216no—
727C22×D4—228no—
728C22×D4—228no—
729C22×D4—228no—
730C22×D4—2216no—
731C22×D4—448no—
732C22×D4—448no—
733C22×D4C22×D1111yescharacteristic
734C22×D4C22×D1112yes—
735C22×D4C22×D1114yes—
736C22×D4C22×D1111yescharacteristic
737C22×D4C22×D1112yes—
738C23×C4—111no—
739C23×C4—111no—
740C23×C4—118no—
741C23×C4—111no—
742C23×C4—112no—
743C23×C4—112no—
744C23×C4—111no—
745C23×C4—111no—
746C23×C4—112no—
747C23×C4—112no—
748C23×C4—112no—
749C23×C4—112no—
750C23×C4—112no—
751C23×C4—224no—
752C23×C4—224no—
753C23×C4—228no—
754C23×C4—228no—
755C23×C4—228no—
756C23×C4C22×D1112yes—
757C23×C4C22×D1111yescharacteristic
758#127—24no—
759#127—224no—
760#127—2216no—
761#127—224no—
762#127—224no—
763#124—24no—
764#124—224no—
765#124—2216no—
766#124—224no—
767#124—224no—
768#121—24no—
769#121—228no—
770#121—224no—
771#121—224no—
772#121—228no—
773#121—224no—
774C2×C4⋊C4—112no—
775C2×C4⋊C4—111no—
776C2×C4⋊C4—224no—
777C2×C4⋊C4C22×D1111yescharacteristic
778C2×C22⋊C4—112no—
779C2×C22⋊C4—114no—
780C2×C22⋊C4—112no—
781C2×C22⋊C4—112no—
782C2×C22⋊C4—112no—
783C2×C22⋊C4—114no—
784C2×C22⋊C4—114no—
785C2×C22⋊C4—112no—
786C2×C22⋊C4—112no—
787C2×C22⋊C4—114no—
788C2×C22⋊C4—114no—
789C2×C22⋊C4—114no—
790C2×C22⋊C4—228no—
791C2×C22⋊C4—2216no—
792C2×C22⋊C4—228no—
793C2×C22⋊C4—448no—
794C2×C22⋊C4C22×D1112yes—
795C2×C22⋊C4C22×D1114yes—
796C2×C22⋊C4C22×D1112yes—
797C2×C22⋊C4C22×D1114yes—
798C2×C42—112no—
799C2×C42—111no—
800C2×C42—112no—
801C2×C42—111no—
802C2×C42—224no—
803C2×C42—224no—
804C2×C42C22×D1111yescharacteristic
805C2×C42C22×D1111yescharacteristic
806#95—112no—
807#95—112no—
808#95—112no—
809#95—114no—
810#95—114no—
811#95—114no—
812#95C22×D1112yes—
813#95C22×D1114yes—
814C2×C11—42no—
815C2×C11—44no—
816C2×C11—82no—
817C2×C11C22×#12011yescharacteristic
818C2×C11C2×#53211yescharacteristic
819C2×C11C2×#53511yescharacteristic
820C2×C11C2×#54612yes—
821C2×C11C2×#55012yes—
822D11—42no—
823D11—44no—
824D11—82no—
825D11#243118yesdirect product factor
826C24—111no—
827C24—114no—
828C24—118no—
829C24—111no—
830C24—112no—
831C24—112no—
832C24—224no—
833C24—228no—
834C24—222no—
835C24—224no—
836C24—224no—
837C24—222no—
838C24—228no—
839C24—224no—
840C24—224no—
841C24—224no—
842C24—224no—
843C24—228no—
844C24—228no—
845C24C23×D1112yes—
846C24C23×D1111yescharacteristic
847C24C23×D1112yes—
848#41—232no—
849#41—2264no—
850#41—2232no—
851#41—2264no—
852#41—2232no—
853#41—2232no—
854C2×Q8—22no—
855C2×Q8—22no—
856C2×Q8—118no—
857C2×Q8—114no—
858C2×Q8—224no—
859C2×Q8—224no—
860C2×Q8—2232no—
861C2×Q8—222no—
862C2×Q8—222no—
863C2×Q8D4×D1114yescomplemented
864C2×D4—24no—
865C2×D4—24no—
866C2×D4—24no—
867C2×D4—28no—
868C2×D4—24no—
869C2×D4—22no—
870C2×D4—22no—
871C2×D4—22no—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—28no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—118no—
878C2×D4—114no—
879C2×D4—224no—
880C2×D4—224no—
881C2×D4—224no—
882C2×D4—228no—
883C2×D4—2232no—
884C2×D4—224no—
885C2×D4—224no—
886C2×D4—224no—
887C2×D4—224no—
888C2×D4—224no—
889C2×D4—224no—
890C2×D4—224no—
891C2×D4—228no—
892C2×D4—228no—
893C2×D4—2264no—
894C2×D4—224no—
895C2×D4—224no—
896C2×D4—224no—
897C2×D4—224no—
898C2×D4—224no—
899C2×D4—228no—
900C2×D4—224no—
901C2×D4—228no—
902C2×D4—224no—
903C2×D4—222no—
904C2×D4—222no—
905C2×D4—222no—
906C2×D4—222no—
907C2×D4—222no—
908C2×D4—228no—
909C2×D4—444no—
910C2×D4—444no—
911C2×D4—4416no—
912C2×D4—4464no—
913C2×D4—444no—
914C2×D4—444no—
915C2×D4—444no—
916C2×D4—444no—
917C2×D4—4432no—
918C2×D4D4×D1114yescomplemented
919C22×C4—24no—
920C22×C4—24no—
921C22×C4—24no—
922C22×C4—22no—
923C22×C4—22no—
924C22×C4—111no—
925C22×C4—114no—
926C22×C4—114no—
927C22×C4—114no—
928C22×C4—114no—
929C22×C4—112no—
930C22×C4—111no—
931C22×C4—112no—
932C22×C4—114no—
933C22×C4—118no—
934C22×C4—114no—
935C22×C4—114no—
936C22×C4—118no—
937C22×C4—112no—
938C22×C4—112no—
939C22×C4—222no—
940C22×C4—222no—
941C22×C4—224no—
942C22×C4—224no—
943C22×C4—2232no—
944C22×C4—224no—
945C22×C4—222no—
946C22×C4—222no—
947C22×C4—224no—
948C22×C4—224no—
949C22×C4—224no—
950C22×C4—224no—
951C22×C4—224no—
952C22×C4—2264no—
953C22×C4—224no—
954C22×C4—224no—
955C22×C4—224no—
956C22×C4—224no—
957C22×C4—228no—
958C22×C4—222no—
959C22×C4—222no—
960C22×C4—224no—
961C22×C4—224no—
962C22×C4—224no—
963C22×C4—224no—
964C22×C4—224no—
965C22×C4—222no—
966C22×C4—222no—
967C22×C4D4×D1114yescomplemented
968C22×C4C23×D1112yes—
969C22×C4C23×D1112yes—
970C22×C4C23×D1111yescharacteristic
971C22×C4C23×D1112yes—
972C22×C4C23×D1112yes—
973C22×C4C23×D1111yescharacteristic
974C4⋊C4—22no—
975C4⋊C4—224no—
976C4⋊C4—222no—
977C22⋊C4—24no—
978C22⋊C4—28no—
979C22⋊C4—24no—
980C22⋊C4—44no—
981C22⋊C4—224no—
982C22⋊C4—228no—
983C22⋊C4—224no—
984C22⋊C4—224no—
985C22⋊C4—228no—
986C22⋊C4—224no—
987C22⋊C4—224no—
988C22⋊C4—228no—
989C22⋊C4—224no—
990C22⋊C4—444no—
991C22⋊C4—444no—
992C22⋊C4—444no—
993C42—22no—
994C42—22no—
995C42—224no—
996C42—224no—
997C42—222no—
998C42—222no—
999C11C2×#243111yescharacteristic, complemented, Sylow
1000C23—22no—
1001C23—21no—
1002C23—22no—
1003C23—21no—
1004C23—22no—
1005C23—24no—
1006C23—24no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—24no—
1012C23—24no—
1013C23—112no—
1014C23—112no—
1015C23—112no—
1016C23—114no—
1017C23—114no—
1018C23—112no—
1019C23—114no—
1020C23—228no—
1021C23—2216no—
1022C23—228no—
1023C23—2232no—
1024C23—228no—
1025C23—222no—
1026C23—221no—
1027C23—221no—
1028C23—222no—
1029C23—222no—
1030C23—224no—
1031C23—224no—
1032C23—222no—
1033C23—222no—
1034C23—222no—
1035C23—222no—
1036C23—224no—
1037C23—224no—
1038C23—448no—
1039C23—448no—
1040C23—448no—
1041C23—448no—
1042C23—4416no—
1043C23—448no—
1044C23—4416no—
1045C23—448no—
1046C23—448no—
1047C23—4416no—
1048C23C2×D4×D1114yes—
1049C23C2×D4×D1112yes—
1050C23C24×D1111yescharacteristic
1051Q8—28no—
1052Q8—2216no—
1053Q8—228no—
1054D4—216no—
1055D4—28no—
1056D4—416no—
1057D4—48no—
1058D4—44no—
1059D4—2216no—
1060D4—2216no—
1061D4—2216no—
1062D4—2216no—
1063D4—228no—
1064D4—4416no—
1065D4—448no—
1066D4—448no—
1067D4—4416no—
1068D4—4416no—
1069D4—448no—
1070D4—448no—
1071D4—444no—
1072C2×C4—216no—
1073C2×C4—22no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—28no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—112no—
1086C2×C4—112no—
1087C2×C4—112no—
1088C2×C4—1116no—
1089C2×C4—112no—
1090C2×C4—114no—
1091C2×C4—114no—
1092C2×C4—228no—
1093C2×C4—228no—
1094C2×C4—2216no—
1095C2×C4—2216no—
1096C2×C4—2216no—
1097C2×C4—2216no—
1098C2×C4—228no—
1099C2×C4—2216no—
1100C2×C4—222no—
1101C2×C4—221no—
1102C2×C4—221no—
1103C2×C4—222no—
1104C2×C4—222no—
1105C2×C4—222no—
1106C2×C4—228no—
1107C2×C4—222no—
1108C2×C4—222no—
1109C2×C4—222no—
1110C2×C4—222no—
1111C2×C4—224no—
1112C2×C4—448no—
1113C2×C4—448no—
1114C2×C4C2×D4×D1112yes—
1115C2×C4C2×D4×D1114yes—
1116C2×C4C2×D4×D1112yes—
1117C2×C4C2×D4×D1112yes—
1118C2×C4C2×D4×D1112yes—
1119C2×C4#41×D1114yescomplemented
1120C22—22no—
1121C22—22no—
1122C22—28no—
1123C22—24no—
1124C22—22no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—44no—
1130C22—42no—
1131C22—42no—
1132C22—44no—
1133C22—42no—
1134C22—44no—
1135C22—114no—
1136C22—114no—
1137C22—118no—
1138C22—114no—
1139C22—118no—
1140C22—222no—
1141C22—222no—
1142C22—228no—
1143C22—222no—
1144C22—224no—
1145C22—4416no—
1146C22—4432no—
1147C22—442no—
1148C22—442no—
1149C22—442no—
1150C22—442no—
1151C22—444no—
1152C22—442no—
1153C22—442no—
1154C22—444no—
1155C22—442no—
1156C22—444no—
1157C22—8816no—
1158C22C22×D4×D1111yescharacteristic
1159C22C22×D4×D1111yescharacteristic
1160C22C22×D4×D1111yescharacteristic
1161C22C2×#41×D1112yes—
1162C22D11×H(5,𝔽2)12yes—
1163C4—24no—
1164C4—22no—
1165C4—24no—
1166C4—42no—
1167C4—42no—
1168C4—114no—
1169C4—224no—
1170C4—222no—
1171C4—224no—
1172C4—442no—
1173C4—442no—
1174C4D11×#12014yes—
1175C2—42no—
1176C2—44no—
1177C2—82no—
1178C2—118no—
1179C2—442no—
1180C2—444no—
1181C2—882no—
1182C2C2×D11×#12011yescharacteristic
1183C2D11×#53211yescharacteristic
1184C2D11×#53511yescharacteristic
1185C2D11×#54612yes—
1186C2D11×#55012yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2431C2
hypercenter#2431D11
hypocenterC11C2×#2431
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2431

Complements

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

NH ≅ G/Ntype
1. C22×#41×D11C2semidirect
2. C2×D11×#127C2semidirect
3. C2×D11×#124C2semidirect
4. C2×D11×#121C2semidirect
5. #13072238C2semidirect
6. #13072237C2semidirect
7. #13072236C2semidirect
8. #13072235C2semidirect
9. #13072234C2semidirect
10. #13072233C2semidirect
11. #13072232C2semidirect
12. #13072231C2semidirect
13. #13072230C2semidirect
14. D11×#392C2semidirect
15. D11×#391C2semidirect
16. D11×#390C2semidirect
17. D11×#386C2semidirect
18. C4×C22⋊C4×D11C2semidirect
19. C11×#2431C2semidirect
20. C22×C11×#41C22semidirect
24. C22×#4343C22semidirect
26. C22×#4341C22semidirect
27. C22×#4341C22semidirect
33. C22×#4339C22semidirect
34. C22×#4339C22semidirect
37. C2×C11×#127C22semidirect
38. C2×C11×#124C22semidirect
39. C2×C11×#121C22semidirect
40. C2×#67000C22semidirect
41. C2×#66993C22semidirect
42. C2×#66993C22semidirect
43. C2×#66993C22semidirect
44. C2×#66992C22semidirect
45. C2×#66991C22semidirect
46. C2×#66989C22semidirect
47. C2×#66983C22semidirect
51. C2×#66948C22semidirect
53. C2×#66938C22semidirect
54. C2×#66937C22semidirect
59. C2×#66928C22semidirect
60. C2×#66927C22semidirect
63. C11×#392C22semidirect
64. C11×#391C22semidirect
65. C11×#390C22semidirect
66. C11×#386C22semidirect
67. C4×C11×C22⋊C4C22semidirect
68. #10622843C22semidirect
69. #10622836C22semidirect
70. #10622836C22semidirect
71. #10622836C22semidirect
72. #10622834C22semidirect
73. #10622833C22semidirect
74. #10622826C22semidirect
75. C4×C22⋊Dic11C22semidirect
76. #10622601C22semidirect
77. #10622587C22semidirect
78. #10622573C22semidirect
79. #10622573C22semidirect
80. #10622573C22semidirect
81. #10622571C22semidirect
82. #10622570C22semidirect
83. #10622569C22semidirect
84. #10622569C22semidirect
85. C22⋊C4×Dic11C22semidirect
86. #10622552C22semidirect
87. C4×(C2×D11)⋊C4C22semidirect
88. C4×(C2×D11)⋊C4C22semidirect
89. #10622542C22semidirect
90. #10622284C22semidirect
91. #10622279C22semidirect
92. #10622278C22semidirect
93. #10622278C22semidirect
96. #10622259C22semidirect
127. C2×Q8×D11D4semidirect
147. C2×D4×D11D4semidirect
164. C22×C4×D11D4semidirect
259. C2×Q8×C11C2×D4semidirect
273. C2×D4×C11C2×D4semidirect
279. C22×C4×C11C2×D4semidirect
307. C2×C22⋊D11C2×D4semidirect
313. C22×Dic11C2×D4semidirect
344. C2×D44C2×D4semidirect
373. C2×C4×D11C2×D4semidirect
374. C2×C4×D11C2×D4semidirect
375. C2×C4×D11#41semidirect
380. C2×Dic22C2×D4semidirect
381. C2×Dic22C2×D4semidirect
420. #2431D11direct (N × H)
501. C2×C4×C11C2×#41semidirect
528. C2×Dic11C2×#41semidirect
554. C22×#41C2×D11semidirect
568. C2×#127C2×D11semidirect
574. C2×#124C2×D11semidirect
581. C2×#121C2×D11semidirect
596. #392C2×D11semidirect
601. #391C2×D11semidirect
606. #390C2×D11semidirect
614. #386C2×D11semidirect
620. C4×C22⋊C4C2×D11semidirect
825. D11#2431direct (N × H)
863. C2×Q8D4×D11semidirect
918. C2×D4D4×D11semidirect
967. C22×C4D4×D11semidirect
999. C11C2×#2431semidirect
1119. C2×C4#41×D11semidirect

Maximal subgroups

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

subgroupindex
C22×#41×D112
C2×D11×#1272
C2×D11×#1242
C2×D11×#1212
#130722382
#130722372
#130722362
#130722352
#130722342
#130722332
#130722322
#130722312
#130722302
D11×#3922
D11×#3912
D11×#3902
D11×#3862
C4×C22⋊C4×D112
C11×#24312
C2×#243111