Finite Group Databasebeta

← D11×#2623 #14920386

Subgroups — D11×#2623 #14920386

Order 2816.

3002 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#123C211yesmaximal, characteristic
2C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
3#13074403C212yesmaximal, complemented
4#13074402C212yesmaximal, complemented
5#13074401C212yesmaximal, complemented
6#13074400C212yesmaximal, complemented
7#13074399C211yesmaximal, characteristic, complemented
8#13074398C211yesmaximal, characteristic, complemented
9#13074397C212yesmaximal, complemented
10#13074396C211yesmaximal, characteristic, complemented
11#13074395C212yesmaximal, complemented
12D11×#400C212yesmaximal, complemented
13D11×#399C212yesmaximal, complemented
14D11×#398C212yesmaximal, complemented
15D11×#397C212yesmaximal, complemented
16D11×#386C212yesmaximal
17D11×#385C212yesmaximal, complemented
18D11×#381C211yesmaximal, characteristic, complemented
19C11×#2623C211yesmaximal, characteristic, complemented
20C22×D4×D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2212yes—
23C2×C11×#123C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic, complemented
25C2×#66988C2211yescharacteristic
26C2×#66982C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic, complemented
28C22×Dic11⋊C4C2212yescomplemented
29D11×#123—28no—
30C2×#66947C2211yescharacteristic
31C2×#66947C2211yescharacteristic
32C2×C4⋊C4×D11—28no—
33C2×C4⋊C4×D11C2212yes—
34C2×C4⋊C4×D11C2212yes—
35C2×C4⋊C4×D11C2211yescharacteristic
36C2×C4⋊C4×D11C2211yescharacteristic
37C2×C4⋊C4×D11C2214yes—
38C2×C4⋊C4×D11C2212yescomplemented
39C2×C4⋊C4×D11C2212yescomplemented
40C2×#66939C2211yescharacteristic
41C2×#66936C2211yescharacteristic
42C2×#66936C2211yescharacteristic
43C2×C22⋊C4×D11C2212yes—
44C2×C22⋊C4×D11C2211yescharacteristic
45C2×C22⋊C4×D11C2211yescharacteristic
46C2×C22⋊C4×D11C2211yescharacteristic
47C2×C22⋊C4×D11C2214yes—
48C11×#400C2212yescomplemented
49C11×#399C2212yescomplemented
50C11×#398C2212yescomplemented
51C11×#397C2212yescomplemented
52C11×#386C2212yes—
53C11×#385C2212yescomplemented
54C11×#381C2211yescharacteristic, complemented
55#10622833C2212yes—
56#10622826C2212yes—
57#10622824C2211yescharacteristic, complemented
58#10622823C2212yescomplemented
59#10622606C2212yescomplemented
60#10622605C2212yescomplemented
61#10622605C2214yescomplemented
62#10622602C2214yescomplemented
63#10622599C2212yescomplemented
64#10622597C2214yescomplemented
65#10622596C2212yescomplemented
66#10622595C2212yescomplemented
67#10622593C2212yescomplemented
68#10622571C2212yes—
69#10622569C2214yes—
70#10622566C2212yescomplemented
71#10622565C2214yescomplemented
72#10622563C2212yescomplemented
73#10622562C2214yescomplemented
74#10622562C2212yescomplemented
75#10622559C2212yescomplemented
76#10622556C2212yescomplemented
77#10622290C2212yescomplemented
78#10622288C2214yescomplemented
79#10622287C2212yescomplemented
80#10622281C2214yescomplemented
81#10622278C2214yes—
82#10622277C2212yescomplemented
83#10622277C2212yescomplemented
84D11×#95C2212yes—
85D11×#95C2212yes—
86D11×#95C2214yes—
87D11×#95C2214yes—
88#10622274C2212yescomplemented
89#10622273C2214yescomplemented
90#10622272C2212yescomplemented
91#10622271C2214yescomplemented
92#10622270C2214yescomplemented
93C24×D11C2311yescharacteristic
94C24×D11C2311yescharacteristic
95C22×D4×C11C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C23×C4×C11C2312yes—
98C22×C22⋊D11C2311yescharacteristic
99C22×C22⋊D11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2312yes—
102C2×D4×D11—24no—
103C2×D4×D11—28no—
104C22×D44C2311yescharacteristic
105C22×C4×D11—28no—
106C22×C4×D11—28no—
107C22×C4×D11—48no—
108C22×C4×D11D418yes—
109C22×C4×D11C2311yescharacteristic
110C22×C4×D11C2311yescharacteristic
111C22×C4×D11C2314yes—
112C22×C4×D11C2314yes—
113C22×C4×D11C2311yescharacteristic
114C22×C4×D11C2311yescharacteristic
115C22×C4×D11C2311yescharacteristic
116C22×C4×D11C2311yescharacteristic
117C22×C4×D11C2311yescharacteristic
118C22×C4×D11C2314yes—
119C11×#123—24no—
120C2×C11×C4⋊C4—24no—
121C2×C11×C4⋊C4C2312yes—
122C2×C11×C4⋊C4C2312yes—
123C2×C11×C4⋊C4C2311yescharacteristic
124C2×C11×C4⋊C4C2311yescharacteristic
125C2×C11×C4⋊C4C2314yes—
126C2×C11×C22⋊C4C2311yescharacteristic
127C2×C11×C22⋊C4C2311yescharacteristic
128C2×C11×C22⋊C4C2311yescharacteristic
129C2×C11×C22⋊C4C2312yes—
130C2×C11×C22⋊C4C2314yes—
131C2×C22⋊Dic11C2311yescharacteristic
132C2×C22⋊Dic11C2311yescharacteristic
133C2×C22⋊Dic11C2311yescharacteristic
134C2×C22⋊Dic11C2312yes—
135C2×C22⋊Dic11C2314yes—
136#66988—24no—
137#66982—24no—
138C2×(C2×D11)⋊C4C2311yescharacteristic
139C2×(C2×D11)⋊C4C2311yescharacteristic
140C2×(C2×D11)⋊C4C2311yescharacteristic
141C2×(C2×D11)⋊C4C2311yescharacteristic
142C2×(C2×D11)⋊C4C2311yescharacteristic
143C2×(C2×D11)⋊C4C2311yescharacteristic
144C2×(C2×D11)⋊C4C2314yes—
145C2×(C2×D11)⋊C4C2314yes—
146C2×(C2×D11)⋊C4C2314yes—
147C2×C4⋊Dic11—24no—
148C2×C4⋊Dic11C2311yescharacteristic
149C2×C4⋊Dic11C2311yescharacteristic
150C2×C4⋊Dic11C2312yes—
151C2×C4⋊Dic11C2312yes—
152C2×C4⋊Dic11C2314yes—
153C2×Dic11⋊C4—28no—
154C2×Dic11⋊C4C2311yescharacteristic
155C2×Dic11⋊C4C2311yescharacteristic
156C2×Dic11⋊C4C2314yes—
157C2×Dic11⋊C4C2314yes—
158C2×Dic11⋊C4C2311yescharacteristic
159C2×Dic11⋊C4C2311yescharacteristic
160C2×Dic11⋊C4C2314yes—
161C2×Dic11⋊C4C2314yes—
162#66947—24no—
163#66947—24no—
164C4⋊C4×D11—28no—
165C4⋊C4×D11—28no—
166C4⋊C4×D11—28no—
167C4⋊C4×D11—28no—
168C4⋊C4×D11—24no—
169C4⋊C4×D11—24no—
170C4⋊C4×D11—48no—
171#66939—24no—
172#66936—24no—
173#66936—24no—
174C22⋊C4×D11—24no—
175C22⋊C4×D11—28no—
176C22⋊C4×D11—24no—
177C22⋊C4×D11—24no—
178C22⋊C4×D11—48no—
179C11×#95C2314yes—
180C11×#95C2312yes—
181C11×#95C2314yes—
182C11×#95C2312yes—
183C11⋊#95C2314yes—
184C11⋊#95C2314yes—
185C11⋊#95C2314yes—
186C11⋊#95C2314yes—
187C11⋊#95C2314yes—
188C11⋊#95C2314yes—
189C11⋊#95C2314yes—
190C11⋊#95C2314yes—
191C11⋊#95C2312yes—
192C11⋊#95C2312yes—
193C2×#2623—111nomaximal, Sylow
194C24×C11C2411yescharacteristic
195C24×C11C2411yescharacteristic
196C23×D11—24no—
197C23×D11—24no—
198C23×D11—22no—
199C23×D11—24no—
200C23×D11—24no—
201C23×D11—24no—
202C23×D11C2×D414yes—
203C23×D11#4118yes—
204C23×D11C2411yescharacteristic
205C23×D11C2411yescharacteristic
206C23×D11C2411yescharacteristic
207C2×D4×C11—22no—
208C2×D4×C11—24no—
209C22×C4×C11—24no—
210C22×C4×C11—24no—
211C22×C4×C11—44no—
212C22×C4×C11C2×D414yes—
213C22×C4×C11C2411yescharacteristic
214C22×C4×C11C2411yescharacteristic
215C22×C4×C11C2414yes—
216C22×C4×C11C2414yes—
217C22×C4×C11C2411yescharacteristic
218C22×C4×C11C2411yescharacteristic
219C22×C4×C11C2411yescharacteristic
220C2×C22⋊D11—22no—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—22no—
223C2×C22⋊D11—24no—
224C22×Dic11—24no—
225C22×Dic11—24no—
226C22×Dic11—44no—
227C22×Dic11C2×D414yes—
228C22×Dic11C2411yescharacteristic
229C22×Dic11C2411yescharacteristic
230C22×Dic11C2414yes—
231C22×Dic11C2414yes—
232C22×Dic11C2411yescharacteristic
233C22×Dic11C2411yescharacteristic
234C22×Dic11C2411yescharacteristic
235D4×D11—416no—
236C2×D44—22no—
237C2×D44—24no—
238C2×C4×D11—232no—
239C2×C4×D11—22no—
240C2×C4×D11—22no—
241C2×C4×D11—28no—
242C2×C4×D11—28no—
243C2×C4×D11—22no—
244C2×C4×D11—24no—
245C2×C4×D11—24no—
246C2×C4×D11—24no—
247C2×C4×D11—24no—
248C2×C4×D11—28no—
249C2×C4×D11—24no—
250C2×C4×D11—28no—
251C2×C4×D11—28no—
252C2×C4×D11—24no—
253C2×C4×D11—28no—
254C2×C4×D11—24no—
255C2×C4×D11—28no—
256C2×C4×D11—44no—
257C2×C4×D11—44no—
258C2×C4×D11—432no—
259C2×C4×D11C2×D414yes—
260C2×C4×D11C2×D414yes—
261C2×C4×D11C2×D414yes—
262C2×C4×D11C2×D414yes—
263C11×C4⋊C4—24no—
264C11×C4⋊C4—24no—
265C11×C4⋊C4—22no—
266C11×C4⋊C4—22no—
267C11×C4⋊C4—44no—
268C11×C22⋊C4—22no—
269C11×C22⋊C4—24no—
270C11×C22⋊C4—22no—
271C11×C22⋊C4—22no—
272C11×C22⋊C4—44no—
273C22⋊Dic11—22no—
274C22⋊Dic11—22no—
275C22⋊Dic11—22no—
276C22⋊Dic11—24no—
277C22⋊Dic11—44no—
278(C2×D11)⋊C4—22no—
279(C2×D11)⋊C4—22no—
280(C2×D11)⋊C4—22no—
281(C2×D11)⋊C4—22no—
282(C2×D11)⋊C4—28no—
283(C2×D11)⋊C4—22no—
284(C2×D11)⋊C4—22no—
285(C2×D11)⋊C4—44no—
286(C2×D11)⋊C4—44no—
287C4⋊Dic11—22no—
288C4⋊Dic11—22no—
289C4⋊Dic11—24no—
290C4⋊Dic11—24no—
291C4⋊Dic11—44no—
292Dic11⋊C4—28no—
293Dic11⋊C4—28no—
294Dic11⋊C4—22no—
295Dic11⋊C4—22no—
296Dic11⋊C4—22no—
297Dic11⋊C4—22no—
298Dic11⋊C4—44no—
299Dic11⋊C4—44no—
300C22×#123—111no—
301C23×C4⋊C4—111no—
302#2623—112no—
303#2623—112no—
304#2623—112no—
305#2623—112no—
306#2623—112no—
307#2623—112no—
308#2623—111no—
309#2623—111no—
310#2623—111no—
311#2623D1111yescharacteristic, direct product factor
312C2×#400—112no—
313C2×#399—112no—
314C2×#398—112no—
315C2×#397—112no—
316C2×#386—112no—
317C2×#385—112no—
318C2×#381—111no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—21no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11C22×D412yes—
326C23×C11C2×#4114yes—
327C23×C11C2511yescharacteristic
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—28no—
331C22×D11—28no—
332C22×D11—232no—
333C22×D11—21no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—44no—
338C22×D11—44no—
339C22×D11—44no—
340C22×D11—416no—
341C22×D11#123116yes—
342C22×D11C22×D412yes—
343C22×D11C22×D412yes—
344C22×D11C2×#4114yes—
345C22×D11C2×#4114yes—
346C22×D11H(5,𝔽2)14yes—
347C22×D112−1+414yes—
348D4×C11—44no—
349C2×C4×C11—28no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—24no—
353C2×C4×C11—21no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—24no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—24no—
360C2×C4×C11—24no—
361C2×C4×C11—24no—
362C2×C4×C11—22no—
363C2×C4×C11—24no—
364C2×C4×C11—48no—
365C2×C4×C11C22×D412yes—
366C2×C4×C11C22×D412yes—
367C22⋊D11—44no—
368C22⋊D11—44no—
369C2×Dic11—28no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—24no—
373C2×Dic11—21no—
374C2×Dic11—21no—
375C2×Dic11—21no—
376C2×Dic11—24no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—24no—
380C2×Dic11—24no—
381C2×Dic11—24no—
382C2×Dic11—22no—
383C2×Dic11—24no—
384C2×Dic11—48no—
385C2×Dic11C22×D412yes—
386C2×Dic11C22×D412yes—
387D44—44no—
388C4×D11—28no—
389C4×D11—28no—
390C4×D11—28no—
391C4×D11—28no—
392C4×D11—416no—
393C4×D11—44no—
394C4×D11—44no—
395C4×D11—416no—
396C4×D11—44no—
397C4×D11—416no—
398C23×D4—111no—
399C24×C4—111no—
400C24×C4—112no—
401C2×#123—111no—
402C2×#123—111no—
403C2×#123—111no—
404C2×#123—111no—
405C2×#123—111no—
406C2×#123—111no—
407C2×#123—111no—
408C2×#123—228no—
409C2×#123C2×D1111yescharacteristic
410C22×C4⋊C4—112no—
411C22×C4⋊C4—111no—
412C22×C4⋊C4—112no—
413C22×C4⋊C4—111no—
414C22×C4⋊C4—112no—
415C22×C4⋊C4—111no—
416C22×C4⋊C4—112no—
417C22×C4⋊C4—112no—
418C22×C4⋊C4—114no—
419C22×C4⋊C4—228no—
420C22×C4⋊C4C2×D1111yescharacteristic, complemented
421C22×C22⋊C4—111no—
422C22×C22⋊C4—111no—
423C22×C22⋊C4—111no—
424C22×C22⋊C4—112no—
425C22×C22⋊C4—114no—
426#400—112no—
427#400—112no—
428#400—114no—
429#400—112no—
430#400—114no—
431#400C2×D1112yescomplemented
432#399—114no—
433#399—112no—
434#399—114no—
435#399—112no—
436#399—112no—
437#399C2×D1112yescomplemented
438#398—112no—
439#398—112no—
440#398—114no—
441#398—114no—
442#398—112no—
443#398C2×D1112yescomplemented
444#397—112no—
445#397—114no—
446#397—112no—
447#397—112no—
448#397—114no—
449#397C2×D1112yescomplemented
450#386—112no—
451#386—112no—
452#386—114no—
453#386—112no—
454#386—114no—
455#386C2×D1112yes—
456#385—112no—
457#385—114no—
458#385—112no—
459#385—112no—
460#385—114no—
461#385C2×D1112yescomplemented
462#381—111no—
463#381—112no—
464#381—112no—
465#381—112no—
466#381C2×D1111yescharacteristic, complemented
467C2×#95—112no—
468C2×#95—114no—
469C2×#95—114no—
470C2×#95—112no—
471C22×C11—22no—
472C22×C11—22no—
473C22×C11—28no—
474C22×C11—41no—
475C22×C11—41no—
476C22×C11—41no—
477C22×C11—44no—
478C22×C11C2×#12314yes—
479C22×C11C23×D411yescharacteristic
480C22×C11C22×#4112yes—
481C22×C11C2×H(5,𝔽2)12yes—
482C22×C11C2×2−1+412yes—
483C2×D11—22no—
484C2×D11—22no—
485C2×D11—28no—
486C2×D11—232no—
487C2×D11—41no—
488C2×D11—41no—
489C2×D11—41no—
490C2×D11—44no—
491C2×D11—88no—
492C2×D11C2×#12314yes—
493C2×D11C2×#12314yes—
494C2×D11#53514yes—
495C2×D11#53614yes—
496C2×D11#539116yes—
497C4×C11—22no—
498C4×C11—22no—
499C4×C11—41no—
500C4×C11—44no—
501C4×C11—41no—
502C4×C11—41no—
503C4×C11—44no—
504Dic11—22no—
505Dic11—22no—
506Dic11—41no—
507Dic11—44no—
508Dic11—41no—
509Dic11—41no—
510Dic11—44no—
511C25—111no—
512C25—111no—
513C22×D4—111no—
514C22×D4—111no—
515C22×D4—111no—
516C22×D4—224no—
517C22×D4—228no—
518C22×D4C22×D1111yescharacteristic
519C23×C4—111no—
520C23×C4—118no—
521C23×C4—111no—
522C23×C4—111no—
523C23×C4—111no—
524C23×C4—111no—
525C23×C4—112no—
526C23×C4—111no—
527C23×C4—111no—
528C23×C4—114no—
529C23×C4—114no—
530C23×C4—111no—
531C23×C4—114no—
532C23×C4—228no—
533C23×C4—228no—
534C23×C4—448no—
535C23×C4C22×D1111yescharacteristic
536C23×C4C22×D1112yes—
537#123—24no—
538#123—224no—
539#123—224no—
540#123—224no—
541#123—224no—
542#123—224no—
543#123—224no—
544#123—224no—
545C2×C4⋊C4—24no—
546C2×C4⋊C4—114no—
547C2×C4⋊C4—112no—
548C2×C4⋊C4—114no—
549C2×C4⋊C4—112no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—111no—
553C2×C4⋊C4—111no—
554C2×C4⋊C4—111no—
555C2×C4⋊C4—111no—
556C2×C4⋊C4—114no—
557C2×C4⋊C4—114no—
558C2×C4⋊C4—114no—
559C2×C4⋊C4—228no—
560C2×C4⋊C4—228no—
561C2×C4⋊C4—228no—
562C2×C4⋊C4—228no—
563C2×C4⋊C4—224no—
564C2×C4⋊C4—224no—
565C2×C4⋊C4—228no—
566C2×C4⋊C4—224no—
567C2×C4⋊C4—448no—
568C2×C4⋊C4C22×D1112yes—
569C2×C4⋊C4C22×D1112yes—
570C2×C4⋊C4C22×D1111yescharacteristic
571C2×C4⋊C4C22×D1111yescharacteristic
572C2×C4⋊C4C22×D1114yes—
573C2×C22⋊C4—111no—
574C2×C22⋊C4—111no—
575C2×C22⋊C4—111no—
576C2×C22⋊C4—112no—
577C2×C22⋊C4—111no—
578C2×C22⋊C4—111no—
579C2×C22⋊C4—111no—
580C2×C22⋊C4—111no—
581C2×C22⋊C4—111no—
582C2×C22⋊C4—111no—
583C2×C22⋊C4—114no—
584C2×C22⋊C4—114no—
585C2×C22⋊C4—114no—
586C2×C22⋊C4—114no—
587C2×C22⋊C4—224no—
588C2×C22⋊C4—224no—
589C2×C22⋊C4—224no—
590C2×C22⋊C4—228no—
591C2×C22⋊C4—448no—
592C2×C22⋊C4C22×D1111yescharacteristic
593C2×C22⋊C4C22×D1111yescharacteristic
594C2×C22⋊C4C22×D1111yescharacteristic
595C2×C22⋊C4C22×D1112yes—
596C2×C22⋊C4C22×D1114yes—
597#95—114no—
598#95—112no—
599#95—114no—
600#95—112no—
601#95—114no—
602#95—114no—
603#95—114no—
604#95—114no—
605#95—114no—
606#95—114no—
607#95C22×D1112yes—
608#95C22×D1112yes—
609#95C22×D1114yes—
610#95C22×D1114yes—
611C2×C11—24no—
612C2×C11—81no—
613C2×C11C22×#12311yescharacteristic
614C2×C11C2×#53511yescharacteristic
615C2×C11C2×#53611yescharacteristic
616C2×C11C2×#53914yes—
617D11—24no—
618D11—81no—
619D11#262318yesdirect product factor
620C24—111no—
621C24—114no—
622C24—118no—
623C24—111no—
624C24—111no—
625C24—224no—
626C24—224no—
627C24—222no—
628C24—224no—
629C24—224no—
630C24—224no—
631C24C23×D1111yescharacteristic
632C24C23×D1111yescharacteristic
633C2×D4—22no—
634C2×D4—24no—
635C2×D4—222no—
636C2×D4—224no—
637C2×D4—222no—
638C2×D4—224no—
639C2×D4—222no—
640C2×D4—224no—
641C2×D4—4416no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—44no—
645C22×C4—114no—
646C22×C4—111no—
647C22×C4—111no—
648C22×C4—114no—
649C22×C4—114no—
650C22×C4—114no—
651C22×C4—114no—
652C22×C4—111no—
653C22×C4—114no—
654C22×C4—111no—
655C22×C4—114no—
656C22×C4—111no—
657C22×C4—2232no—
658C22×C4—224no—
659C22×C4—224no—
660C22×C4—224no—
661C22×C4—224no—
662C22×C4—222no—
663C22×C4—222no—
664C22×C4—228no—
665C22×C4—228no—
666C22×C4—228no—
667C22×C4—228no—
668C22×C4—228no—
669C22×C4—222no—
670C22×C4—224no—
671C22×C4—228no—
672C22×C4—224no—
673C22×C4—224no—
674C22×C4—228no—
675C22×C4—224no—
676C22×C4—224no—
677C22×C4—444no—
678C22×C4—444no—
679C22×C4—4432no—
680C22×C4—444no—
681C22×C4D4×D1114yes—
682C22×C4C23×D1111yescharacteristic
683C22×C4C23×D1114yes—
684C22×C4C23×D1111yescharacteristic
685C22×C4C23×D1114yes—
686C22×C4C23×D1111yescharacteristic
687C22×C4C23×D1111yescharacteristic
688C22×C4C23×D1111yescharacteristic
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—44no—
694C4⋊C4—228no—
695C4⋊C4—228no—
696C4⋊C4—222no—
697C4⋊C4—222no—
698C4⋊C4—222no—
699C4⋊C4—222no—
700C4⋊C4—224no—
701C4⋊C4—224no—
702C4⋊C4—222no—
703C4⋊C4—222no—
704C4⋊C4—444no—
705C4⋊C4—444no—
706C4⋊C4—444no—
707C22⋊C4—22no—
708C22⋊C4—24no—
709C22⋊C4—22no—
710C22⋊C4—22no—
711C22⋊C4—44no—
712C22⋊C4—222no—
713C22⋊C4—222no—
714C22⋊C4—222no—
715C22⋊C4—222no—
716C22⋊C4—228no—
717C22⋊C4—222no—
718C22⋊C4—222no—
719C22⋊C4—222no—
720C22⋊C4—224no—
721C22⋊C4—222no—
722C22⋊C4—222no—
723C22⋊C4—444no—
724C22⋊C4—444no—
725C22⋊C4—444no—
726C11C2×#262311yescharacteristic, complemented, Sylow
727C23—22no—
728C23—22no—
729C23—21no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—112no—
734C23—114no—
735C23—114no—
736C23—114no—
737C23—1116no—
738C23—112no—
739C23—114no—
740C23—228no—
741C23—228no—
742C23—2232no—
743C23—222no—
744C23—222no—
745C23—221no—
746C23—222no—
747C23—222no—
748C23—222no—
749C23—444no—
750C23—444no—
751C23—444no—
752C23—4416no—
753C23C2×D4×D1112yes—
754C23#41×D1114yes—
755C23C24×D1111yescharacteristic
756D4—44no—
757D4—444no—
758D4—444no—
759D4—444no—
760C2×C4—28no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—24no—
766C2×C4—21no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—48no—
776C2×C4—112no—
777C2×C4—112no—
778C2×C4—228no—
779C2×C4—228no—
780C2×C4—228no—
781C2×C4—228no—
782C2×C4—228no—
783C2×C4—222no—
784C2×C4—222no—
785C2×C4—221no—
786C2×C4—221no—
787C2×C4—224no—
788C2×C4—221no—
789C2×C4—224no—
790C2×C4—222no—
791C2×C4—224no—
792C2×C4—224no—
793C2×C4—222no—
794C2×C4—224no—
795C2×C4—222no—
796C2×C4—224no—
797C2×C4—4416no—
798C2×C4—444no—
799C2×C4—444no—
800C2×C4—444no—
801C2×C4—4416no—
802C2×C4—4416no—
803C2×C4—448no—
804C2×C4C2×D4×D1112yes—
805C2×C4C2×D4×D1112yes—
806C22—22no—
807C22—22no—
808C22—28no—
809C22—41no—
810C22—41no—
811C22—44no—
812C22—41no—
813C22—114no—
814C22—114no—
815C22—1116no—
816C22—114no—
817C22—114no—
818C22—2232no—
819C22—222no—
820C22—222no—
821C22—228no—
822C22—441no—
823C22—441no—
824C22—444no—
825C22—441no—
826C22—888no—
827C22D11×#12314yes—
828C22C22×D4×D1111yescharacteristic
829C22C2×#41×D1112yes—
830C22D11×H(5,𝔽2)12yes—
831C22D11×2−1+412yes—
832C4—22no—
833C4—22no—
834C4—44no—
835C4—41no—
836C4—41no—
837C4—44no—
838C4—41no—
839C4—222no—
840C4—222no—
841C4—444no—
842C4—441no—
843C4—441no—
844C4—444no—
845C4—441no—
846C2—24no—
847C2—81no—
848C2—118no—
849C2—224no—
850C2—881no—
851C2C2×D11×#12311yescharacteristic
852C2D11×#53511yescharacteristic
853C2D11×#53611yescharacteristic
854C2D11×#53914yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2623C2
prime radicalC22×D4×D11C22
hypercenter#2623D11
hypocenterC11C2×#2623
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2623

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D11C2semidirect
3. #13074403C2semidirect
4. #13074402C2semidirect
5. #13074401C2semidirect
6. #13074400C2semidirect
7. #13074399C2semidirect
8. #13074398C2semidirect
9. #13074397C2semidirect
10. #13074396C2semidirect
11. #13074395C2semidirect
12. D11×#400C2semidirect
13. D11×#399C2semidirect
14. D11×#398C2semidirect
15. D11×#397C2semidirect
17. D11×#385C2semidirect
18. D11×#381C2semidirect
19. C11×#2623C2semidirect
24. C22×C11×C4⋊C4C22semidirect
27. C22×C4⋊Dic11C22semidirect
28. C22×Dic11⋊C4C22semidirect
38. C2×C4⋊C4×D11C22semidirect
39. C2×C4⋊C4×D11C22semidirect
48. C11×#400C22semidirect
49. C11×#399C22semidirect
50. C11×#398C22semidirect
51. C11×#397C22semidirect
53. C11×#385C22semidirect
54. C11×#381C22semidirect
57. #10622824C22semidirect
58. #10622823C22semidirect
59. #10622606C22semidirect
60. #10622605C22semidirect
61. #10622605C22semidirect
62. #10622602C22semidirect
63. #10622599C22semidirect
64. #10622597C22semidirect
65. #10622596C22semidirect
66. #10622595C22semidirect
67. #10622593C22semidirect
70. #10622566C22semidirect
71. #10622565C22semidirect
72. #10622563C22semidirect
73. #10622562C22semidirect
74. #10622562C22semidirect
75. #10622559C22semidirect
76. #10622556C22semidirect
77. #10622290C22semidirect
78. #10622288C22semidirect
79. #10622287C22semidirect
80. #10622281C22semidirect
82. #10622277C22semidirect
83. #10622277C22semidirect
88. #10622274C22semidirect
89. #10622273C22semidirect
90. #10622272C22semidirect
91. #10622271C22semidirect
92. #10622270C22semidirect
311. #2623D11direct (N × H)
420. C22×C4⋊C4C2×D11semidirect
431. #400C2×D11semidirect
437. #399C2×D11semidirect
443. #398C2×D11semidirect
449. #397C2×D11semidirect
461. #385C2×D11semidirect
466. #381C2×D11semidirect
619. D11#2623direct (N × H)
726. C11C2×#2623semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1232
C22×C4⋊C4×D112
#130744032
#130744022
#130744012
#130744002
#130743992
#130743982
#130743972
#130743962
#130743952
D11×#4002
D11×#3992
D11×#3982
D11×#3972
D11×#3862
D11×#3852
D11×#3812
C11×#26232
C2×#262311