Finite Group Databasebeta

← D11×#2318 #14912403

Subgroups — D11×#2318 #14912403

Order 2816.

3262 conjugacy classes of subgroups.

The subgroup lattice has 1108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D11C211yesmaximal, characteristic
2#13071252C211yesmaximal, characteristic, complemented
3#13071251C211yesmaximal, characteristic, complemented
4#13071250C211yesmaximal, characteristic, complemented
5#13071249C211yesmaximal, characteristic, complemented
6#13071248C212yesmaximal, complemented
7#13071247C211yesmaximal, characteristic, complemented
8#13071246C212yesmaximal, complemented
9#13071245C211yesmaximal, characteristic, complemented
10#13071244C212yesmaximal, complemented
11#13071243C211yesmaximal, characteristic, complemented
12#13071242C212yesmaximal, complemented
13D11×#388C212yesmaximal, complemented
14D11×#387C212yesmaximal, complemented
15D11×#386C212yesmaximal
16D11×#385C212yesmaximal, complemented
17D11×#383C211yesmaximal, characteristic, complemented
18D11×#382C211yesmaximal, characteristic, complemented
19D11×#381C211yesmaximal, characteristic, complemented
20D11×#380C211yesmaximal, characteristic, complemented
21C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
22C2×D11×#95C211yesmaximal, characteristic, complemented
23C11×#2318C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C23×C4×D11C2212yes—
26C23×C4×D11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×D4×Dic11C2211yescharacteristic
30C2×C4×C22⋊D11C2211yescharacteristic
31C2×C4×C22⋊D11C2211yescharacteristic
32C4×D4×D11C4116yescomplemented
33C2×#66946C2211yescharacteristic
34C2×C4⋊C4×D11C2212yes—
35C2×C4⋊C4×D11C2212yes—
36C2×C4⋊C4×D11C2211yescharacteristic
37C2×(C22⋊D11)⋊C4C2211yescharacteristic
38C2×(C22⋊D11)⋊C4C2211yescharacteristic
39C2×C22⋊C4×D11C2212yes—
40C2×C22⋊C4×D11C2212yes—
41C2×C22⋊C4×D11C2212yes—
42C2×C22⋊C4×D11C2211yescharacteristic
43C2×C22⋊C4×D11C2211yescharacteristic
44C2×C4×D44C2211yescharacteristic
45C2×C42×D11C2212yes—
46C2×C42×D11C2211yescharacteristic
47C11×#388C2212yescomplemented
48C11×#387C2212yescomplemented
49C11×#386C2212yes—
50C11×#385C2212yescomplemented
51C11×#383C2211yescharacteristic, complemented
52C11×#382C2211yescharacteristic, complemented
53C11×#381C2211yescharacteristic, complemented
54C11×#380C2211yescharacteristic, complemented
55C4×C11×C22⋊C4C2211yescharacteristic, complemented
56C2×C11×#95C2211yescharacteristic, complemented
57#10622833C2212yes—
58#10622826C2212yes—
59#10622825C2211yescharacteristic, complemented
60#10622824C2211yescharacteristic, complemented
61#10622823C2212yescomplemented
62C4×C22⋊Dic11C2211yescharacteristic, complemented
63C2×C11⋊#95C2212yescomplemented
64C2×C11⋊#95C2211yescharacteristic, complemented
65#10622603C2212yescomplemented
66#10622602C2212yescomplemented
67#10622602C2212yescomplemented
68#10622600C2212yescomplemented
69#10622594C2212yescomplemented
70#10622591C2212yescomplemented
71#10622590C2212yescomplemented
72#10622571C2212yes—
73#10622569C2212yes—
74#10622569C2212yes—
75#10622564C2212yescomplemented
76#10622563C2212yescomplemented
77#10622559C2212yescomplemented
78#10622558C2212yescomplemented
79#10622557C2212yescomplemented
80#10622556C2212yescomplemented
81#10622555C2212yescomplemented
82C22⋊C4×Dic11C2212yescomplemented
83#10622553C2212yescomplemented
84C4×(C2×D11)⋊C4C2212yescomplemented
85#10622550C2211yescharacteristic, complemented
86#10622549C2211yescharacteristic, complemented
87#10622546C2212yescomplemented
88#10622283C2212yescomplemented
89#10622282C2212yescomplemented
90#10622281C2212yescomplemented
91#10622281C2212yescomplemented
92#10622280C2211yescharacteristic, complemented
93#10622280C2211yescharacteristic, complemented
94#10622279C2211yescharacteristic, complemented
95#10622279C2211yescharacteristic, complemented
96#10622278C2212yes—
97#10622278C2212yes—
98#10622277C2211yescharacteristic, complemented
99#10622277C2212yescomplemented
100#10622277C2211yescharacteristic, complemented
101D11×#95C2211yescharacteristic
102D11×#95C2211yescharacteristic
103D11×#95C2212yes—
104D11×#95C2211yescharacteristic
105D11×#95C2211yescharacteristic
106D11×#95C2212yes—
107D11×#95C2212yes—
108D11×#95C2212yes—
109D11×#95C2212yes—
110D11×#95C2211yescharacteristic, complemented
111D11×#95C2212yescomplemented
112D11×#95C2211yescharacteristic, complemented
113#10622268C2212yescomplemented
114#10622267C2212yescomplemented
115#10622266C2212yescomplemented
116#10622265C2212yescomplemented
117#10622264C2212yescomplemented
118#10622264C2211yescharacteristic, complemented
119#10622264C2212yescomplemented
120#10622264C2211yescharacteristic, complemented
121#10622263C2212yescomplemented
122#10622263C2211yescharacteristic, complemented
123#10622263C2211yescharacteristic, complemented
124C24×D11C2311yescharacteristic
125C24×D11C2311yescharacteristic
126C22×D4×C11C2311yescharacteristic
127C23×C4×C11C2312yes—
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C22×C22⋊D11C2311yescharacteristic
131C22×C22⋊D11C2311yescharacteristic
132C23×Dic11C2312yes—
133C23×Dic11C2311yescharacteristic
134C23×Dic11C2311yescharacteristic
135C2×D4×D11—28no—
136C2×D4×D11C2×C418yes—
137C22×D44C2311yescharacteristic
138C22×C4×D11—28no—
139C22×C4×D11—44no—
140C22×C4×D11—44no—
141C22×C4×D11—44no—
142C22×C4×D11—44no—
143C22×C4×D11C2×C418yes—
144C22×C4×D11C2×C418yescomplemented
145C22×C4×D11C2312yes—
146C22×C4×D11C2312yes—
147C22×C4×D11C2312yes—
148C22×C4×D11C2312yes—
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2311yescharacteristic
154C22×C4×D11C2312yes—
155C22×C4×D11C2312yes—
156C22×C4×D11C2311yescharacteristic
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C2311yescharacteristic
160C4×D4×C11C2×C418yescomplemented
161C2×C11×C4⋊C4C2312yes—
162C2×C11×C4⋊C4C2312yes—
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2311yescharacteristic
168C2×C11×C22⋊C4C2311yescharacteristic
169C2×C42×C11C2312yes—
170C2×C42×C11C2311yescharacteristic
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2311yescharacteristic
175C2×C22⋊Dic11C2311yescharacteristic
176D4×Dic11C2×C418yescomplemented
177C4×C22⋊D11C2×C418yescomplemented
178C4×C22⋊D11C2×C418yescomplemented
179C2×(C2×D11)⋊C4C2312yes—
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
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×C4⋊Dic11C2312yes—
190C2×C4⋊Dic11C2312yes—
191C2×C4⋊Dic11C2311yescharacteristic
192C2×Dic11⋊C4C2312yes—
193C2×Dic11⋊C4C2312yes—
194C2×Dic11⋊C4C2312yes—
195C2×Dic11⋊C4C2312yes—
196C2×Dic11⋊C4C2311yescharacteristic
197C2×Dic11⋊C4C2311yescharacteristic
198C2×C4×Dic11C2312yes—
199C2×C4×Dic11C2312yes—
200C2×C4×Dic11C2312yes—
201C2×C4×Dic11C2311yescharacteristic
202C2×C4×Dic11C2311yescharacteristic
203C2×C4×Dic11C2311yescharacteristic
204#66946C2×C418yescomplemented
205C4⋊C4×D11—44no—
206C4⋊C4×D11—44no—
207C4⋊C4×D11C2×C418yescomplemented
208(C22⋊D11)⋊C4C2×C418yescomplemented
209(C22⋊D11)⋊C4C2×C418yescomplemented
210C22⋊C4×D11—28no—
211C22⋊C4×D11—44no—
212C22⋊C4×D11—44no—
213C22⋊C4×D11C2×C418yes—
214C22⋊C4×D11C2×C418yescomplemented
215C4×D44C2×C418yescomplemented
216C42×D11—44no—
217C42×D11C2×C418yescomplemented
218C11×#95C2312yes—
219C11×#95C2311yescharacteristic
220C11×#95C2311yescharacteristic
221C11×#95C2312yes—
222C11×#95C2311yescharacteristic
223C11×#95C2311yescharacteristic
224C11×#95C2312yes—
225C11×#95C2312yes—
226C11×#95C2312yes—
227C11⋊#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2311yescharacteristic
230C11⋊#95C2312yes—
231C11⋊#95C2311yescharacteristic
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2311yescharacteristic
242C11⋊#95C2311yescharacteristic
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C2×#2318—111nomaximal, Sylow
251C24×C11C2411yescharacteristic
252C24×C11C2411yescharacteristic
253C23×D11—24no—
254C23×D11—22no—
255C23×D11—22no—
256C23×D11—24no—
257C23×D11—22no—
258C23×D11—24no—
259C23×D11—22no—
260C23×D11C22×C414yes—
261C23×D11C22×C414yes—
262C23×D11#4118yes—
263C23×D11C2411yescharacteristic
264C23×D11C2411yescharacteristic
265C23×D11C2411yescharacteristic
266C2×D4×C11—24no—
267C2×D4×C11C22×C414yes—
268C22×C4×C11—24no—
269C22×C4×C11—42no—
270C22×C4×C11—42no—
271C22×C4×C11—42no—
272C22×C4×C11—42no—
273C22×C4×C11C22×C414yes—
274C22×C4×C11C22×C414yescomplemented
275C22×C4×C11C2412yes—
276C22×C4×C11C2412yes—
277C22×C4×C11C2412yes—
278C22×C4×C11C2412yes—
279C22×C4×C11C2411yescharacteristic
280C22×C4×C11C2411yescharacteristic
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2411yescharacteristic
283C22×C4×C11C2411yescharacteristic
284C2×C22⋊D11—24no—
285C2×C22⋊D11—24no—
286C2×C22⋊D11C22×C414yes—
287C2×C22⋊D11C22×C414yes—
288C22×Dic11—24no—
289C22×Dic11—42no—
290C22×Dic11—42no—
291C22×Dic11—42no—
292C22×Dic11—42no—
293C22×Dic11C22×C414yes—
294C22×Dic11C22×C414yescomplemented
295C22×Dic11C2412yes—
296C22×Dic11C2412yes—
297C22×Dic11C2412yes—
298C22×Dic11C2412yes—
299C22×Dic11C2411yescharacteristic
300C22×Dic11C2411yescharacteristic
301C22×Dic11C2411yescharacteristic
302C22×Dic11C2411yescharacteristic
303C22×Dic11C2411yescharacteristic
304D4×D11—232no—
305C2×D44—24no—
306C2×D44C22×C414yes—
307C2×C4×D11—24no—
308C2×C4×D11—24no—
309C2×C4×D11—24no—
310C2×C4×D11—24no—
311C2×C4×D11—24no—
312C2×C4×D11—24no—
313C2×C4×D11—24no—
314C2×C4×D11—24no—
315C2×C4×D11—22no—
316C2×C4×D11—24no—
317C2×C4×D11—24no—
318C2×C4×D11—24no—
319C2×C4×D11—24no—
320C2×C4×D11—24no—
321C2×C4×D11—24no—
322C2×C4×D11—24no—
323C2×C4×D11—24no—
324C2×C4×D11—24no—
325C2×C4×D11—22no—
326C2×C4×D11—24no—
327C2×C4×D11—42no—
328C2×C4×D11—42no—
329C2×C4×D11—42no—
330C2×C4×D11—42no—
331C2×C4×D11—42no—
332C2×C4×D11—42no—
333C2×C4×D11—42no—
334C2×C4×D11—42no—
335C2×C4×D11—416no—
336C2×C4×D11—416no—
337C2×C4×D11—432no—
338C2×C4×D11C22×C414yes—
339C2×C4×D11C22×C414yes—
340C2×C4×D11C22×C414yes—
341C2×C4×D11C22×C414yes—
342C2×C4×D11C22×C414yes—
343C2×C4×D11C22×C414yes—
344C2×C4×D11C22×C414yes—
345C2×C4×D11C22×C414yescomplemented
346C2×C4×D11C22×C414yescomplemented
347C11×C4⋊C4—42no—
348C11×C4⋊C4—42no—
349C11×C4⋊C4C22×C414yescomplemented
350C11×C22⋊C4—24no—
351C11×C22⋊C4—42no—
352C11×C22⋊C4—42no—
353C11×C22⋊C4C22×C414yes—
354C11×C22⋊C4C22×C414yescomplemented
355C42×C11—42no—
356C42×C11C22×C414yescomplemented
357C22⋊Dic11—24no—
358C22⋊Dic11—42no—
359C22⋊Dic11—42no—
360C22⋊Dic11C22×C414yes—
361C22⋊Dic11C22×C414yescomplemented
362(C2×D11)⋊C4—24no—
363(C2×D11)⋊C4—24no—
364(C2×D11)⋊C4—42no—
365(C2×D11)⋊C4—42no—
366(C2×D11)⋊C4—42no—
367(C2×D11)⋊C4—42no—
368(C2×D11)⋊C4C22×C414yes—
369(C2×D11)⋊C4C22×C414yes—
370(C2×D11)⋊C4C22×C414yescomplemented
371(C2×D11)⋊C4C22×C414yescomplemented
372C4⋊Dic11—42no—
373C4⋊Dic11—42no—
374C4⋊Dic11C22×C414yescomplemented
375Dic11⋊C4—42no—
376Dic11⋊C4—42no—
377Dic11⋊C4—42no—
378Dic11⋊C4—42no—
379Dic11⋊C4C22×C414yescomplemented
380Dic11⋊C4C22×C414yescomplemented
381C4×Dic11—42no—
382C4×Dic11—42no—
383C4×Dic11—42no—
384C4×Dic11C22×C414yescomplemented
385C4×Dic11C22×C414yescomplemented
386C4×Dic11C22×C414yescomplemented
387C22×C4×D4—111no—
388#2318—112no—
389#2318—112no—
390#2318—112no—
391#2318—112no—
392#2318—111no—
393#2318—111no—
394#2318—111no—
395#2318—111no—
396#2318—111no—
397#2318—111no—
398#2318—111no—
399#2318D1111yescharacteristic, direct product factor
400C2×#388—112no—
401C2×#387—112no—
402C2×#386—112no—
403C2×#385—112no—
404C2×#383—111no—
405C2×#382—111no—
406C2×#381—111no—
407C2×#380—111no—
408C2×C4×C22⋊C4—111no—
409C22×#95—111no—
410C23×C11—22no—
411C23×C11—21no—
412C23×C11—21no—
413C23×C11—22no—
414C23×C11—21no—
415C23×C11—22no—
416C23×C11—21no—
417C23×C11C23×C412yes—
418C23×C11C23×C412yes—
419C23×C11C2×#4114yes—
420C23×C11C2511yescharacteristic
421C22×D11—22no—
422C22×D11—21no—
423C22×D11—21no—
424C22×D11—28no—
425C22×D11—28no—
426C22×D11—216no—
427C22×D11—216no—
428C22×D11—22no—
429C22×D11—21no—
430C22×D11—22no—
431C22×D11—21no—
432C22×D11—28no—
433C22×D11—28no—
434C22×D11—28no—
435C22×D11—48no—
436C22×D11—48no—
437C22×D11#117116yes—
438C22×D11C23×C412yes—
439C22×D11C23×C412yes—
440C22×D11C23×C412yes—
441C22×D11C2×#4114yes—
442C22×D11C2×#4114yes—
443C22×D11H(5,𝔽2)14yes—
444C22×D11H(5,𝔽2)12yes—
445C22×D112−1+412yes—
446D4×C11—28no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—21no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—21no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
456C2×C4×C11—22no—
457C2×C4×C11—22no—
458C2×C4×C11—22no—
459C2×C4×C11—22no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
462C2×C4×C11—22no—
463C2×C4×C11—22no—
464C2×C4×C11—22no—
465C2×C4×C11—44no—
466C2×C4×C11—44no—
467C2×C4×C11—48no—
468C2×C4×C11C23×C412yes—
469C2×C4×C11C23×C412yes—
470C2×C4×C11C23×C412yes—
471C2×C4×C11C23×C412yes—
472C2×C4×C11C23×C412yes—
473C22⋊D11—28no—
474C22⋊D11—28no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—21no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—21no—
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—22no—
486C2×Dic11—22no—
487C2×Dic11—22no—
488C2×Dic11—22no—
489C2×Dic11—22no—
490C2×Dic11—22no—
491C2×Dic11—22no—
492C2×Dic11—22no—
493C2×Dic11—44no—
494C2×Dic11—44no—
495C2×Dic11—48no—
496C2×Dic11C23×C412yes—
497C2×Dic11C23×C412yes—
498C2×Dic11C23×C412yes—
499C2×Dic11C23×C412yes—
500C2×Dic11C23×C412yes—
501D44—28no—
502C4×D11—28no—
503C4×D11—28no—
504C4×D11—28no—
505C4×D11—28no—
506C4×D11—28no—
507C4×D11—44no—
508C4×D11—44no—
509C4×D11—44no—
510C4×D11—44no—
511C4×D11—48no—
512C4×D11—48no—
513C4×D11—48no—
514C4×D11—48no—
515C4×D11—48no—
516C4×D11—48no—
517C23×D4—111no—
518C24×C4—111no—
519C24×C4—111no—
520C24×C4—112no—
521C2×C4×D4—111no—
522C2×C4×D4—111no—
523C2×C4×D4—111no—
524C2×C4×D4—1116no—
525C2×C4×D4—111no—
526C2×C4×D4—111no—
527C2×C4×D4—111no—
528C2×C4×D4—111no—
529C2×C4×D4C2×D1111yescharacteristic
530C22×C4⋊C4—111no—
531C22×C4⋊C4—112no—
532C22×C4⋊C4—112no—
533C22×C22⋊C4—111no—
534C22×C22⋊C4—111no—
535C22×C22⋊C4—112no—
536C22×C22⋊C4—112no—
537C22×C22⋊C4—112no—
538C22×C42—111no—
539C22×C42—112no—
540#388—112no—
541#388—112no—
542#388—112no—
543#388—112no—
544#388—112no—
545#388—112no—
546#388—112no—
547#388C2×D1112yescomplemented
548#387—112no—
549#387—112no—
550#387—112no—
551#387—112no—
552#387—112no—
553#387—112no—
554#387—112no—
555#387C2×D1112yescomplemented
556#386—112no—
557#386—112no—
558#386—112no—
559#386—112no—
560#386—112no—
561#386—112no—
562#386—112no—
563#386C2×D1112yes—
564#385—112no—
565#385—112no—
566#385—112no—
567#385—112no—
568#385—112no—
569#385—112no—
570#385—112no—
571#385C2×D1112yescomplemented
572#383—111no—
573#383—112no—
574#383—112no—
575#383—111no—
576#383—111no—
577#383C2×D1111yescharacteristic, complemented
578#382—112no—
579#382—111no—
580#382—112no—
581#382—111no—
582#382—111no—
583#382C2×D1111yescharacteristic, complemented
584#381—111no—
585#381—112no—
586#381—112no—
587#381—111no—
588#381—111no—
589#381C2×D1111yescharacteristic, complemented
590#380—111no—
591#380—112no—
592#380—112no—
593#380—111no—
594#380—111no—
595#380C2×D1111yescharacteristic, complemented
596C4×C22⋊C4—111no—
597C4×C22⋊C4—112no—
598C4×C22⋊C4—112no—
599C4×C22⋊C4—111no—
600C4×C22⋊C4—111no—
601C4×C22⋊C4C2×D1111yescharacteristic, complemented
602C2×#95—112no—
603C2×#95—111no—
604C2×#95—112no—
605C2×#95—111no—
606C2×#95—111no—
607C2×#95—111no—
608C2×#95—111no—
609C2×#95—112no—
610C2×#95—111no—
611C2×#95—111no—
612C2×#95—112no—
613C2×#95—112no—
614C2×#95—112no—
615C2×#95—112no—
616C2×#95C2×D1111yescharacteristic, complemented
617C22×C11—22no—
618C22×C11—22no—
619C22×C11—24no—
620C22×C11—24no—
621C22×C11—22no—
622C22×C11—22no—
623C22×C11—22no—
624C22×C11—42no—
625C22×C11—42no—
626C22×C11C2×#11714yes—
627C22×C11C24×C411yescharacteristic
628C22×C11C22×#4112yes—
629C22×C11C2×H(5,𝔽2)12yes—
630C22×C11C2×H(5,𝔽2)11yescharacteristic
631C22×C11C2×2−1+411yescharacteristic
632C2×D11—22no—
633C2×D11—22no—
634C2×D11—24no—
635C2×D11—24no—
636C2×D11—232no—
637C2×D11—22no—
638C2×D11—22no—
639C2×D11—22no—
640C2×D11—42no—
641C2×D11—42no—
642C2×D11—416no—
643C2×D11C2×#11714yes—
644C2×D11C2×#11714yes—
645C2×D11#51814yes—
646C2×D11#52014yes—
647C2×D11#53818yes—
648C2×D11#53918yes—
649C4×C11—22no—
650C4×C11—22no—
651C4×C11—22no—
652C4×C11—22no—
653C4×C11—22no—
654C4×C11—42no—
655C4×C11—42no—
656C4×C11—42no—
657C4×C11—42no—
658Dic11—22no—
659Dic11—22no—
660Dic11—22no—
661Dic11—22no—
662Dic11—22no—
663Dic11—42no—
664Dic11—42no—
665Dic11—42no—
666Dic11—42no—
667C25—111no—
668C25—111no—
669C22×D4—111no—
670C22×D4—111no—
671C22×D4—118no—
672C22×D4—111no—
673C22×D4—228no—
674C22×D4C22×D1111yescharacteristic
675C23×C4—111no—
676C23×C4—111no—
677C23×C4—111no—
678C23×C4—111no—
679C23×C4—111no—
680C23×C4—111no—
681C23×C4—111no—
682C23×C4—118no—
683C23×C4—118no—
684C23×C4—111no—
685C23×C4—111no—
686C23×C4—111no—
687C23×C4—111no—
688C23×C4—112no—
689C23×C4—112no—
690C23×C4—112no—
691C23×C4—112no—
692C23×C4—112no—
693C23×C4—112no—
694C23×C4—112no—
695C23×C4—228no—
696C23×C4—444no—
697C23×C4—444no—
698C23×C4—444no—
699C23×C4—444no—
700C23×C4C22×D1112yes—
701C23×C4C22×D1111yescharacteristic
702C23×C4C22×D1111yescharacteristic
703C4×D4—118no—
704C4×D4—118no—
705C4×D4—118no—
706C4×D4—118no—
707C4×D4—118no—
708C4×D4—118no—
709C4×D4—118no—
710C4×D4C4×D1118yescomplemented
711C2×C4⋊C4—111no—
712C2×C4⋊C4—111no—
713C2×C4⋊C4—111no—
714C2×C4⋊C4—118no—
715C2×C4⋊C4—112no—
716C2×C4⋊C4—112no—
717C2×C4⋊C4—112no—
718C2×C4⋊C4—112no—
719C2×C4⋊C4—112no—
720C2×C4⋊C4—112no—
721C2×C4⋊C4—444no—
722C2×C4⋊C4—444no—
723C2×C4⋊C4C22×D1112yes—
724C2×C4⋊C4C22×D1112yes—
725C2×C4⋊C4C22×D1111yescharacteristic
726C2×C22⋊C4—111no—
727C2×C22⋊C4—111no—
728C2×C22⋊C4—111no—
729C2×C22⋊C4—111no—
730C2×C22⋊C4—111no—
731C2×C22⋊C4—111no—
732C2×C22⋊C4—118no—
733C2×C22⋊C4—118no—
734C2×C22⋊C4—112no—
735C2×C22⋊C4—112no—
736C2×C22⋊C4—112no—
737C2×C22⋊C4—112no—
738C2×C22⋊C4—112no—
739C2×C22⋊C4—112no—
740C2×C22⋊C4—112no—
741C2×C22⋊C4—112no—
742C2×C22⋊C4—112no—
743C2×C22⋊C4—228no—
744C2×C22⋊C4—444no—
745C2×C22⋊C4—444no—
746C2×C22⋊C4C22×D1112yes—
747C2×C22⋊C4C22×D1112yes—
748C2×C22⋊C4C22×D1112yes—
749C2×C22⋊C4C22×D1111yescharacteristic
750C2×C22⋊C4C22×D1111yescharacteristic
751C2×C42—111no—
752C2×C42—111no—
753C2×C42—111no—
754C2×C42—118no—
755C2×C42—112no—
756C2×C42—112no—
757C2×C42—112no—
758C2×C42—444no—
759C2×C42C22×D1112yes—
760C2×C42C22×D1111yescharacteristic
761#95—112no—
762#95—111no—
763#95—112no—
764#95—111no—
765#95—112no—
766#95—112no—
767#95—112no—
768#95—112no—
769#95—111no—
770#95—112no—
771#95—111no—
772#95—112no—
773#95—112no—
774#95—112no—
775#95—112no—
776#95—112no—
777#95—112no—
778#95—112no—
779#95—112no—
780#95—112no—
781#95—112no—
782#95—112no—
783#95—112no—
784#95C22×D1111yescharacteristic
785#95C22×D1111yescharacteristic
786#95C22×D1112yes—
787#95C22×D1111yescharacteristic
788#95C22×D1111yescharacteristic
789#95C22×D1112yes—
790#95C22×D1112yes—
791#95C22×D1112yes—
792#95C22×D1112yes—
793C2×C11—24no—
794C2×C11—42no—
795C2×C11C22×#11711yescharacteristic
796C2×C11C2×#51811yescharacteristic
797C2×C11C2×#52011yescharacteristic
798C2×C11C2×#53812yes—
799C2×C11C2×#53912yes—
800D11—24no—
801D11—42no—
802D11#231818yesdirect product factor
803C24—111no—
804C24—114no—
805C24—118no—
806C24—111no—
807C24—114no—
808C24—111no—
809C24—222no—
810C24—224no—
811C24—222no—
812C24—222no—
813C24—224no—
814C24—224no—
815C24—222no—
816C24C23×D1111yescharacteristic
817C24C23×D1111yescharacteristic
818C2×D4—24no—
819C2×D4—114no—
820C2×D4—114no—
821C2×D4—114no—
822C2×D4—224no—
823C2×D4—2232no—
824C2×D4—224no—
825C2×D4—224no—
826C2×D4C2×C4×D1114yes—
827C22×C4—24no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—111no—
833C22×C4—111no—
834C22×C4—111no—
835C22×C4—111no—
836C22×C4—111no—
837C22×C4—114no—
838C22×C4—114no—
839C22×C4—114no—
840C22×C4—114no—
841C22×C4—114no—
842C22×C4—114no—
843C22×C4—114no—
844C22×C4—114no—
845C22×C4—114no—
846C22×C4—114no—
847C22×C4—114no—
848C22×C4—112no—
849C22×C4—112no—
850C22×C4—112no—
851C22×C4—112no—
852C22×C4—224no—
853C22×C4—222no—
854C22×C4—224no—
855C22×C4—224no—
856C22×C4—224no—
857C22×C4—222no—
858C22×C4—224no—
859C22×C4—224no—
860C22×C4—224no—
861C22×C4—224no—
862C22×C4—224no—
863C22×C4—224no—
864C22×C4—224no—
865C22×C4—224no—
866C22×C4—224no—
867C22×C4—224no—
868C22×C4—224no—
869C22×C4—224no—
870C22×C4—224no—
871C22×C4—224no—
872C22×C4—224no—
873C22×C4—442no—
874C22×C4—442no—
875C22×C4—442no—
876C22×C4—442no—
877C22×C4—442no—
878C22×C4—442no—
879C22×C4—442no—
880C22×C4—442no—
881C22×C4—4416no—
882C22×C4—4416no—
883C22×C4—4432no—
884C22×C4—442no—
885C22×C4—442no—
886C22×C4—442no—
887C22×C4—442no—
888C22×C4C2×C4×D1114yes—
889C22×C4C2×C4×D1114yescomplemented
890C22×C4C23×D1112yes—
891C22×C4C23×D1112yes—
892C22×C4C23×D1112yes—
893C22×C4C23×D1112yes—
894C22×C4C23×D1111yescharacteristic
895C22×C4C23×D1111yescharacteristic
896C22×C4C23×D1111yescharacteristic
897C22×C4C23×D1111yescharacteristic
898C22×C4C23×D1111yescharacteristic
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—114no—
902C4⋊C4—114no—
903C4⋊C4—114no—
904C4⋊C4—442no—
905C4⋊C4—442no—
906C4⋊C4—442no—
907C4⋊C4—442no—
908C4⋊C4—442no—
909C4⋊C4—442no—
910C4⋊C4C2×C4×D1114yescomplemented
911C22⋊C4—24no—
912C22⋊C4—42no—
913C22⋊C4—42no—
914C22⋊C4—114no—
915C22⋊C4—114no—
916C22⋊C4—114no—
917C22⋊C4—114no—
918C22⋊C4—114no—
919C22⋊C4—114no—
920C22⋊C4—224no—
921C22⋊C4—224no—
922C22⋊C4—224no—
923C22⋊C4—442no—
924C22⋊C4—442no—
925C22⋊C4—442no—
926C22⋊C4—442no—
927C22⋊C4—442no—
928C22⋊C4—442no—
929C22⋊C4C2×C4×D1114yes—
930C22⋊C4C2×C4×D1114yescomplemented
931C42—42no—
932C42—114no—
933C42—114no—
934C42—114no—
935C42—442no—
936C42—442no—
937C42—442no—
938C42C2×C4×D1114yescomplemented
939C11C2×#231811yescharacteristic, complemented, Sylow
940C23—21no—
941C23—22no—
942C23—21no—
943C23—22no—
944C23—21no—
945C23—22no—
946C23—21no—
947C23—112no—
948C23—114no—
949C23—112no—
950C23—114no—
951C23—112no—
952C23—1116no—
953C23—112no—
954C23—114no—
955C23—112no—
956C23—2216no—
957C23—228no—
958C23—2216no—
959C23—228no—
960C23—228no—
961C23—228no—
962C23—228no—
963C23—221no—
964C23—222no—
965C23—221no—
966C23—222no—
967C23—221no—
968C23—222no—
969C23—221no—
970C23—448no—
971C23—448no—
972C23C22×C4×D1112yes—
973C23C22×C4×D1112yes—
974C23#41×D1114yes—
975C23C24×D1111yescharacteristic
976D4—28no—
977D4—228no—
978D4—228no—
979D4—228no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—21no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—21no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—44no—
999C2×C4—44no—
1000C2×C4—48no—
1001C2×C4—112no—
1002C2×C4—112no—
1003C2×C4—112no—
1004C2×C4—112no—
1005C2×C4—112no—
1006C2×C4—228no—
1007C2×C4—228no—
1008C2×C4—228no—
1009C2×C4—228no—
1010C2×C4—228no—
1011C2×C4—222no—
1012C2×C4—222no—
1013C2×C4—221no—
1014C2×C4—222no—
1015C2×C4—222no—
1016C2×C4—221no—
1017C2×C4—222no—
1018C2×C4—222no—
1019C2×C4—222no—
1020C2×C4—222no—
1021C2×C4—222no—
1022C2×C4—222no—
1023C2×C4—222no—
1024C2×C4—222no—
1025C2×C4—222no—
1026C2×C4—222no—
1027C2×C4—222no—
1028C2×C4—222no—
1029C2×C4—444no—
1030C2×C4—444no—
1031C2×C4—444no—
1032C2×C4—444no—
1033C2×C4—448no—
1034C2×C4—448no—
1035C2×C4—448no—
1036C2×C4—448no—
1037C2×C4—448no—
1038C2×C4—448no—
1039C2×C4—444no—
1040C2×C4—444no—
1041C2×C4—448no—
1042C2×C4C22×C4×D1112yes—
1043C2×C4C22×C4×D1112yes—
1044C2×C4C22×C4×D1112yes—
1045C2×C4C22×C4×D1112yes—
1046C2×C4C22×C4×D1112yes—
1047C22—24no—
1048C22—24no—
1049C22—22no—
1050C22—22no—
1051C22—22no—
1052C22—22no—
1053C22—22no—
1054C22—42no—
1055C22—42no—
1056C22—118no—
1057C22—118no—
1058C22—114no—
1059C22—114no—
1060C22—114no—
1061C22—114no—
1062C22—2232no—
1063C22—224no—
1064C22—224no—
1065C22—222no—
1066C22—222no—
1067C22—222no—
1068C22—222no—
1069C22—222no—
1070C22—4416no—
1071C22—442no—
1072C22—442no—
1073C22D11×#11714yes—
1074C22C23×C4×D1111yescharacteristic
1075C22C2×#41×D1112yes—
1076C22D11×H(5,𝔽2)11yescharacteristic
1077C22D11×H(5,𝔽2)12yes—
1078C22D11×2−1+411yescharacteristic
1079C4—22no—
1080C4—22no—
1081C4—22no—
1082C4—22no—
1083C4—22no—
1084C4—42no—
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—222no—
1089C4—222no—
1090C4—222no—
1091C4—222no—
1092C4—222no—
1093C4—442no—
1094C4—442no—
1095C4—442no—
1096C4—442no—
1097C2—24no—
1098C2—42no—
1099C2—118no—
1100C2—224no—
1101C2—442no—
1102C2C2×D11×#11711yescharacteristic
1103C2D11×#51811yescharacteristic
1104C2D11×#52011yescharacteristic
1105C2D11×#53812yes—
1106C2D11×#53912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2318C2
socle, cosocleC23×C11C25
prime radicalC22×D4×D11C22
hypercenter#2318D11
hypocenterC11C2×#2318
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2318

Complements

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

NH ≅ G/Ntype
2. #13071252C2semidirect
3. #13071251C2semidirect
4. #13071250C2semidirect
5. #13071249C2semidirect
6. #13071248C2semidirect
7. #13071247C2semidirect
8. #13071246C2semidirect
9. #13071245C2semidirect
10. #13071244C2semidirect
11. #13071243C2semidirect
12. #13071242C2semidirect
13. D11×#388C2semidirect
14. D11×#387C2semidirect
16. D11×#385C2semidirect
17. D11×#383C2semidirect
18. D11×#382C2semidirect
19. D11×#381C2semidirect
20. D11×#380C2semidirect
21. C4×C22⋊C4×D11C2semidirect
22. C2×D11×#95C2semidirect
23. C11×#2318C2semidirect
32. C4×D4×D11C4semidirect
47. C11×#388C22semidirect
48. C11×#387C22semidirect
50. C11×#385C22semidirect
51. C11×#383C22semidirect
52. C11×#382C22semidirect
53. C11×#381C22semidirect
54. C11×#380C22semidirect
55. C4×C11×C22⋊C4C22semidirect
56. C2×C11×#95C22semidirect
59. #10622825C22semidirect
60. #10622824C22semidirect
61. #10622823C22semidirect
62. C4×C22⋊Dic11C22semidirect
63. C2×C11⋊#95C22semidirect
64. C2×C11⋊#95C22semidirect
65. #10622603C22semidirect
66. #10622602C22semidirect
67. #10622602C22semidirect
68. #10622600C22semidirect
69. #10622594C22semidirect
70. #10622591C22semidirect
71. #10622590C22semidirect
75. #10622564C22semidirect
76. #10622563C22semidirect
77. #10622559C22semidirect
78. #10622558C22semidirect
79. #10622557C22semidirect
80. #10622556C22semidirect
81. #10622555C22semidirect
82. C22⋊C4×Dic11C22semidirect
83. #10622553C22semidirect
84. C4×(C2×D11)⋊C4C22semidirect
85. #10622550C22semidirect
86. #10622549C22semidirect
87. #10622546C22semidirect
88. #10622283C22semidirect
89. #10622282C22semidirect
90. #10622281C22semidirect
91. #10622281C22semidirect
92. #10622280C22semidirect
93. #10622280C22semidirect
94. #10622279C22semidirect
95. #10622279C22semidirect
98. #10622277C22semidirect
99. #10622277C22semidirect
100. #10622277C22semidirect
110. D11×#95C22semidirect
111. D11×#95C22semidirect
112. D11×#95C22semidirect
113. #10622268C22semidirect
114. #10622267C22semidirect
115. #10622266C22semidirect
116. #10622265C22semidirect
117. #10622264C22semidirect
118. #10622264C22semidirect
119. #10622264C22semidirect
120. #10622264C22semidirect
121. #10622263C22semidirect
122. #10622263C22semidirect
123. #10622263C22semidirect
144. C22×C4×D11C2×C4semidirect
160. C4×D4×C11C2×C4semidirect
176. D4×Dic11C2×C4semidirect
177. C4×C22⋊D11C2×C4semidirect
178. C4×C22⋊D11C2×C4semidirect
204. #66946C2×C4semidirect
207. C4⋊C4×D11C2×C4semidirect
208. (C22⋊D11)⋊C4C2×C4semidirect
209. (C22⋊D11)⋊C4C2×C4semidirect
214. C22⋊C4×D11C2×C4semidirect
215. C4×D44C2×C4semidirect
217. C42×D11C2×C4semidirect
274. C22×C4×C11C22×C4semidirect
294. C22×Dic11C22×C4semidirect
345. C2×C4×D11C22×C4semidirect
346. C2×C4×D11C22×C4semidirect
349. C11×C4⋊C4C22×C4semidirect
354. C11×C22⋊C4C22×C4semidirect
356. C42×C11C22×C4semidirect
361. C22⋊Dic11C22×C4semidirect
370. (C2×D11)⋊C4C22×C4semidirect
371. (C2×D11)⋊C4C22×C4semidirect
374. C4⋊Dic11C22×C4semidirect
379. Dic11⋊C4C22×C4semidirect
380. Dic11⋊C4C22×C4semidirect
384. C4×Dic11C22×C4semidirect
385. C4×Dic11C22×C4semidirect
386. C4×Dic11C22×C4semidirect
399. #2318D11direct (N × H)
547. #388C2×D11semidirect
555. #387C2×D11semidirect
571. #385C2×D11semidirect
577. #383C2×D11semidirect
583. #382C2×D11semidirect
589. #381C2×D11semidirect
595. #380C2×D11semidirect
601. C4×C22⋊C4C2×D11semidirect
616. C2×#95C2×D11semidirect
710. C4×D4C4×D11semidirect
802. D11#2318direct (N × H)
889. C22×C4C2×C4×D11semidirect
910. C4⋊C4C2×C4×D11semidirect
930. C22⋊C4C2×C4×D11semidirect
938. C42C2×C4×D11semidirect
939. C11C2×#2318semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D112
#130712522
#130712512
#130712502
#130712492
#130712482
#130712472
#130712462
#130712452
#130712442
#130712432
#130712422
D11×#3882
D11×#3872
D11×#3862
D11×#3852
D11×#3832
D11×#3822
D11×#3812
D11×#3802
C4×C22⋊C4×D112
C2×D11×#952
C11×#23182
C2×#231811