Finite Group Databasebeta

← #14923631

Subgroups — #14923631

Order 2816.

2926 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2C2×D11×#117C211yesmaximal, characteristic, complemented
3#13072929C212yesmaximal, complemented
4#13072920C212yesmaximal, complemented
5#13072915C212yesmaximal, complemented
6#13072909C212yesmaximal, complemented
7#13072900C212yesmaximal, complemented
8#13072895C212yesmaximal, complemented
9#13072887C212yesmaximal, complemented
10#13071941C212yesmaximal
11#13071877C214yesmaximal, complemented
12C4×#66936C214yesmaximal, complemented
13#13071100C211yesmaximal, characteristic, complemented
14#13071098C211yesmaximal, characteristic, complemented
15#13070999C211yesmaximal, characteristic, complemented
16#13070995C211yesmaximal, characteristic, complemented
17C11×#2280C211yesmaximal, characteristic, complemented
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C2×C4×C22⋊D11—28no—
25C2×C4×C22⋊D11C2212yes—
26C2×C4×C22⋊D11C2212yes—
27C2×C4×C22⋊D11C2212yes—
28C2×C4×C22⋊D11C2212yes—
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C2×#66979C2211yescharacteristic
31C2×#66979C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34D11×#117—28no—
35C2×#66945C2211yescharacteristic, complemented
36C2×#66945C2211yescharacteristic, complemented
37C2×C4⋊C4×D11C2211yescharacteristic, complemented
38C2×C4⋊C4×D11C2211yescharacteristic, complemented
39C2×#66936C2214yes—
40C2×C22⋊C4×D11C2212yes—
41C2×#66930C2212yes—
42C2×#66925C2212yescomplemented
43C2×C42×D11C2212yescomplemented
44C11×#381C2212yes—
45C11×#380C2212yescomplemented
46C11×#380C2212yescomplemented
47C11×#379C2212yes—
48C4×C11×C22⋊C4C2214yescomplemented
49#10622860C2212yes—
50#10622825C2212yescomplemented
51#10622825C2212yescomplemented
52#10622824C2212yes—
53C4×C22⋊Dic11C2214yescomplemented
54#10622600C2212yescomplemented
55#10622600C2212yescomplemented
56#10622598C2212yescomplemented
57#10622598C2212yescomplemented
58#10622586C2212yescomplemented
59#10622586C2212yescomplemented
60#10622574C2214yes—
61#10622572C2214yes—
62#10622569C2214yes—
63#10622568C2212yes—
64#10622565C2214yescomplemented
65#10622564C2214yescomplemented
66#10622563C2212yes—
67#10622563C2212yes—
68#10622562C2214yescomplemented
69#10622559C2212yes—
70#10622559C2212yes—
71#10622558C2214yescomplemented
72#10622556C2212yes—
73C4×(C2×D11)⋊C4C2212yescomplemented
74C4×(C2×D11)⋊C4C2212yescomplemented
75C4×C4⋊Dic11C2214yescomplemented
76C4×Dic11⋊C4C2214yescomplemented
77#10622288C2214yescomplemented
78#10622287C2214yescomplemented
79#10622281C2214yescomplemented
80#10622277C2214yescomplemented
81#10622271C2214yescomplemented
82#10622270C2214yescomplemented
83#10622267C2214yescomplemented
84#10622265C2214yescomplemented
85C25×C11C2311yescharacteristic
86C24×D11C2311yescharacteristic
87C23×C4×C11—24no—
88C23×C4×C11—24no—
89C23×C4×C11—24no—
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2312yes—
92C23×C4×C11C2312yes—
93C23×C4×C11C2311yescharacteristic
94C22×C22⋊D11—24no—
95C22×C22⋊D11—28no—
96C22×C22⋊D11C2312yes—
97C22×C22⋊D11C2312yes—
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C22×C4×D11—24no—
102C22×C4×D11—24no—
103C22×C4×D11D418yes—
104C22×C4×D11C2312yes—
105C22×C4×D11C2311yescharacteristic
106C22×C4×D11C2311yescharacteristic
107C22×C4×D11C2311yescharacteristic
108C22×C4×D11C2311yescharacteristic
109C22×C4×D11C2312yes—
110C11×#117—24no—
111C11×#117—24no—
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2312yes—
115C2×C11×C22⋊C4C2312yes—
116C2×C11×C22⋊C4C2314yes—
117C2×C11×C22⋊C4C2312yes—
118C2×C11×C22⋊C4C2314yes—
119C2×C42×C11C2312yes—
120C2×C42×C11C2312yes—
121C2×C22⋊Dic11—24no—
122C2×C22⋊Dic11C2312yes—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2312yes—
125C2×C22⋊Dic11C2312yes—
126C2×C22⋊Dic11C2312yes—
127C2×C22⋊Dic11C2314yes—
128C4×C22⋊D11—28no—
129C4×C22⋊D11—28no—
130C4×C22⋊D11—28no—
131C4×C22⋊D11—28no—
132C2×(C2×D11)⋊C4—24no—
133C2×(C2×D11)⋊C4C2312yes—
134C2×(C2×D11)⋊C4C2312yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2312yes—
137C2×(C2×D11)⋊C4C2312yes—
138C2×(C2×D11)⋊C4C2314yes—
139#66979—24no—
140#66979—24no—
141C2×C4⋊Dic11C2314yes—
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4⋊Dic11C2311yescharacteristic
144C2×C4⋊Dic11C2312yes—
145C2×C4⋊Dic11C2314yes—
146C2×Dic11⋊C4—24no—
147C2×Dic11⋊C4C2312yes—
148C2×Dic11⋊C4C2312yes—
149C2×Dic11⋊C4C2314yes—
150C2×Dic11⋊C4C2312yes—
151C2×Dic11⋊C4C2312yes—
152C2×Dic11⋊C4C2314yes—
153C2×C4×Dic11—24no—
154C2×C4×Dic11C2312yes—
155C2×C4×Dic11C2312yes—
156C2×C4×Dic11C2312yes—
157C2×C4×Dic11C2312yes—
158C2×C4×Dic11C2312yes—
159C2×C4×Dic11C2312yes—
160#66945—24no—
161#66945—24no—
162C4⋊C4×D11—24no—
163C4⋊C4×D11—24no—
164#66936—216no—
165C22⋊C4×D11—28no—
166#66930—28no—
167#66925—28no—
168C42×D11—28no—
169C11×#95C2314yes—
170C11×#95C2314yes—
171C11⋊#95C2314yes—
172C11⋊#95C2314yes—
173C11⋊#95C2314yes—
174C11⋊#95C2314yes—
175C11⋊#95C2314yes—
176C11⋊#95C2314yes—
177C11⋊#95C2314yes—
178C11⋊#95C2314yes—
179#34809—111nomaximal, Sylow
180C24×C11—22no—
181C24×C11—24no—
182C24×C11—22no—
183C24×C11—22no—
184C24×C11—42no—
185C24×C11C2412yes—
186C24×C11C2411yescharacteristic
187C23×D11—22no—
188C23×D11—22no—
189C23×D11—24no—
190C23×D11—42no—
191C23×D11C2×D414yes—
192C23×D11C2411yescharacteristic
193C23×D11C2411yescharacteristic
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—24no—
198C22×C4×C11—24no—
199C22×C4×C11—24no—
200C22×C4×C11—24no—
201C22×C4×C11—24no—
202C22×C4×C11—24no—
203C22×C4×C11—416no—
204C22×C4×C11C2×D414yes—
205C22×C4×C11#4114yes—
206C22×C4×C11#4114yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2414yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2411yescharacteristic
212C22×C4×C11C2411yescharacteristic
213C2×C22⋊D11—232no—
214C2×C22⋊D11—24no—
215C2×C22⋊D11—24no—
216C2×C22⋊D11—24no—
217C2×C22⋊D11—24no—
218C2×C22⋊D11—24no—
219C2×C22⋊D11#4118yes—
220C22×Dic11—24no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—42no—
226C22×Dic11C2×D414yes—
227C22×Dic11C2414yes—
228C22×Dic11C2412yes—
229C22×Dic11C2412yes—
230C22×Dic11C2412yes—
231C22×Dic11C2411yescharacteristic
232C22×Dic11C2411yescharacteristic
233C22×Dic11C2412yes—
234C2×C4×D11—24no—
235C2×C4×D11—24no—
236C2×C4×D11—28no—
237C2×C4×D11—232no—
238C2×C4×D11—22no—
239C2×C4×D11—22no—
240C2×C4×D11—22no—
241C2×C4×D11—22no—
242C2×C4×D11—22no—
243C2×C4×D11—22no—
244C2×C4×D11—22no—
245C2×C4×D11—22no—
246C2×C4×D11—44no—
247C2×C4×D11C2×D414yes—
248C2×C4×D11C2×D414yes—
249C2×C4×D11C2×D414yes—
250C2×C4×D11C2×D414yes—
251C11×C4⋊C4—22no—
252C11×C4⋊C4—22no—
253C11×C4⋊C4—24no—
254C11×C22⋊C4—24no—
255C11×C22⋊C4—28no—
256C11×C22⋊C4—24no—
257C11×C22⋊C4—44no—
258C42×C11—24no—
259C42×C11—24no—
260C22⋊Dic11—24no—
261C22⋊Dic11—24no—
262C22⋊Dic11—24no—
263C22⋊Dic11—28no—
264C22⋊Dic11—24no—
265C22⋊Dic11—44no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4—24no—
270(C2×D11)⋊C4—28no—
271(C2×D11)⋊C4—44no—
272C4⋊Dic11—28no—
273C4⋊Dic11—22no—
274C4⋊Dic11—22no—
275C4⋊Dic11—24no—
276C4⋊Dic11—44no—
277Dic11⋊C4—24no—
278Dic11⋊C4—24no—
279Dic11⋊C4—24no—
280Dic11⋊C4—24no—
281Dic11⋊C4—28no—
282Dic11⋊C4—44no—
283C4×Dic11—24no—
284C4×Dic11—24no—
285C4×Dic11—24no—
286C4×Dic11—24no—
287C4×Dic11—24no—
288C4×Dic11—24no—
289C22×C4×D4—111no—
290C22×#117—111no—
291#2487—112no—
292#2486—112no—
293#2485—112no—
294#2485—112no—
295#2484—112no—
296#2483—112no—
297#2482—112no—
298#2405—112no—
299#2395—114no—
300C4×#123—114no—
301#2296—111no—
302#2296—111no—
303#2280—111no—
304#2280—111no—
305#2280D1111yescharacteristic, complemented
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—28no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—48no—
316C23×C11—48no—
317C23×C11—44no—
318C23×C11—44no—
319C23×C11C22×D412yes—
320C23×C11C2×#4112yes—
321C23×C11C2×#4112yes—
322C23×C11C2×#4114yes—
323C23×C11C2511yescharacteristic
324C22×D11—21no—
325C22×D11—21no—
326C22×D11—22no—
327C22×D11—28no—
328C22×D11—21no—
329C22×D11—21no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—28no—
333C22×D11—44no—
334C22×D11—48no—
335C22×D11—48no—
336C22×D11C22×D412yes—
337C22×D11C22×D412yes—
338C22×D11C2×#4114yes—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—24no—
343C2×C4×C11—24no—
344C2×C4×C11—24no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—24no—
348C2×C4×C11—24no—
349C2×C4×C11—44no—
350C2×C4×C11—48no—
351C2×C4×C11—48no—
352C2×C4×C11#123116yescomplemented
353C2×C4×C11C22×D412yes—
354C2×C4×C11C22×D412yes—
355C2×C4×C11C2×#4112yes—
356C2×C4×C11C2×#4112yes—
357C2×C4×C11C2×#4112yes—
358C2×C4×C11C2×#4112yes—
359C22⋊D11—216no—
360C22⋊D11—216no—
361C2×Dic11—28no—
362C2×Dic11—28no—
363C2×Dic11—22no—
364C2×Dic11—21no—
365C2×Dic11—21no—
366C2×Dic11—21no—
367C2×Dic11—21no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—24no—
373C2×Dic11—24no—
374C2×Dic11—24no—
375C2×Dic11—22no—
376C2×Dic11—24no—
377C2×Dic11—22no—
378C2×Dic11—24no—
379C2×Dic11—44no—
380C2×Dic11C22×D412yes—
381C2×Dic11C22×D412yes—
382C2×Dic11C2×#4114yes—
383C4×D11—28no—
384C4×D11—28no—
385C4×D11—28no—
386C4×D11—28no—
387C4×D11—48no—
388C4×D11—48no—
389C23×D4—111no—
390C24×C4—111no—
391C24×C4C2×D1111yescharacteristic
392C2×#123—114no—
393C2×C4×D4—112no—
394C2×C4×D4—112no—
395C2×C4×D4—112no—
396C2×C4×D4—112no—
397C2×C4×D4—228no—
398C2×#117—111no—
399C2×#117—111no—
400C2×#117—111no—
401C2×#117—111no—
402C2×#117—112no—
403C2×#117—112no—
404C2×#117—228no—
405C2×#117C2×D1111yescharacteristic
406C2×#117C2×D1111yescharacteristic
407C22×C4⋊C4—111no—
408C22×C4⋊C4—111no—
409C22×C4⋊C4—111no—
410C22×C22⋊C4—111no—
411C22×C22⋊C4—111no—
412C22×C22⋊C4—112no—
413C22×C42—111no—
414C22×C42—112no—
415#400—114no—
416#399—114no—
417#398—114no—
418#397—114no—
419#397—114no—
420#397—114no—
421#394—114no—
422#394—114no—
423#389—112no—
424#389—112no—
425#389—112no—
426#389—112no—
427#388—114no—
428#388—114no—
429#387—114no—
430#387—114no—
431#386—114no—
432#385—112no—
433#385—112no—
434#385—112no—
435#385—112no—
436#385—114no—
437#381—112no—
438#381—112no—
439#381—114no—
440#381C2×D1112yes—
441#380—112no—
442#380—112no—
443#380—112no—
444#380—112no—
445#380C2×D1112yescomplemented
446#380C2×D1112yescomplemented
447#379—112no—
448#379—112no—
449#379C2×D1112yes—
450C4×C4⋊C4—114no—
451C4×C4⋊C4—114no—
452C4×C22⋊C4—114no—
453C4×C22⋊C4—112no—
454C4×C22⋊C4—112no—
455C4×C22⋊C4C2×D1114yescomplemented
456C22×C11—22no—
457C22×C11—22no—
458C22×C11—24no—
459C22×C11—24no—
460C22×C11—24no—
461C22×C11—24no—
462C22×C11—24no—
463C22×C11—416no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11C2×#12314yes—
469C22×C11C23×D411yescharacteristic
470C22×C11C22×#4111yescharacteristic
471C22×C11C22×#4111yescharacteristic
472C22×C11C22×#4112yes—
473C22×C11#58512yes—
474C2×D11—22no—
475C2×D11—22no—
476C2×D11—24no—
477C2×D11—24no—
478C2×D11—22no—
479C2×D11—22no—
480C2×D11—22no—
481C2×D11—416no—
482C2×D11—42no—
483C2×D11—42no—
484C2×D11#52514yes—
485C4×C11—42no—
486C4×C11—42no—
487C4×C11—42no—
488C4×C11—44no—
489C4×C11C2×#12314yes—
490C4×C11C2×#12314yes—
491Dic11—22no—
492Dic11—22no—
493Dic11—24no—
494Dic11—42no—
495Dic11—42no—
496Dic11—42no—
497Dic11—44no—
498C25—111no—
499C25C22×D1111yescharacteristic
500C22×D4—112no—
501C22×D4—112no—
502C22×D4—228no—
503C22×D4—224no—
504C23×C4—24no—
505C23×C4—24no—
506C23×C4—24no—
507C23×C4—111no—
508C23×C4—118no—
509C23×C4—111no—
510C23×C4—111no—
511C23×C4—111no—
512C23×C4—111no—
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—112no—
516C23×C4—112no—
517C23×C4—224no—
518C23×C4—224no—
519C23×C4C22×D1111yescharacteristic
520C23×C4C22×D1112yes—
521C23×C4C22×D1112yes—
522C23×C4C22×D1111yescharacteristic
523#123—2216no—
524C4×D4—228no—
525C4×D4—228no—
526C4×D4—228no—
527C4×D4—228no—
528#117—24no—
529#117—24no—
530#117—228no—
531#117—228no—
532#117—224no—
533#117—224no—
534#117—224no—
535#117—224no—
536C2×C4⋊C4—111no—
537C2×C4⋊C4—111no—
538C2×C4⋊C4—112no—
539C2×C4⋊C4—112no—
540C2×C4⋊C4—112no—
541C2×C4⋊C4—112no—
542C2×C4⋊C4—112no—
543C2×C4⋊C4—114no—
544C2×C4⋊C4—114no—
545C2×C4⋊C4—114no—
546C2×C4⋊C4—114no—
547C2×C4⋊C4—224no—
548C2×C4⋊C4—224no—
549C2×C4⋊C4—224no—
550C2×C4⋊C4C22×D1111yescharacteristic
551C2×C4⋊C4C22×D1111yescharacteristic
552C2×C4⋊C4C22×D1112yes—
553C2×C22⋊C4—112no—
554C2×C22⋊C4—112no—
555C2×C22⋊C4—112no—
556C2×C22⋊C4—112no—
557C2×C22⋊C4—114no—
558C2×C22⋊C4—112no—
559C2×C22⋊C4—112no—
560C2×C22⋊C4—112no—
561C2×C22⋊C4—112no—
562C2×C22⋊C4—114no—
563C2×C22⋊C4—114no—
564C2×C22⋊C4—114no—
565C2×C22⋊C4—228no—
566C2×C22⋊C4—224no—
567C2×C22⋊C4—224no—
568C2×C22⋊C4C22×D1112yes—
569C2×C22⋊C4C22×D1112yes—
570C2×C22⋊C4C22×D1114yes—
571C2×C22⋊C4C22×D1114yes—
572C2×C42—112no—
573C2×C42—112no—
574C2×C42—112no—
575C2×C42—112no—
576C2×C42—112no—
577C2×C42—112no—
578C2×C42—228no—
579C2×C42—224no—
580C2×C42C22×D1112yes—
581C2×C42C22×D1112yes—
582#95—114no—
583#95—114no—
584#95—114no—
585#95—114no—
586#95—114no—
587#95—114no—
588#95—114no—
589#95—114no—
590#95C22×D1114yes—
591#95C22×D1114yes—
592C2×C11—24no—
593C2×C11—44no—
594C2×C11C22×#12311yescharacteristic
595C2×C11C2×#52511yescharacteristic
596C2×C11#344911yescharacteristic
597C2×C11#347512yes—
598C2×C11#347512yes—
599D11—24no—
600D11—42no—
601C24—22no—
602C24—24no—
603C24—22no—
604C24—22no—
605C24—42no—
606C24—111no—
607C24—111no—
608C24—114no—
609C24—224no—
610C24—222no—
611C24—222no—
612C24—442no—
613C24C23×D1112yes—
614C24C23×D1111yescharacteristic
615C2×D4—118no—
616C2×D4—224no—
617C2×D4—224no—
618C2×D4—224no—
619C2×D4—224no—
620C2×D4—2232no—
621C2×D4—224no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—24no—
626C22×C4—24no—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—416no—
632C22×C4—114no—
633C22×C4—111no—
634C22×C4—112no—
635C22×C4—111no—
636C22×C4—114no—
637C22×C4—114no—
638C22×C4—114no—
639C22×C4—114no—
640C22×C4—114no—
641C22×C4—112no—
642C22×C4—112no—
643C22×C4—112no—
644C22×C4—224no—
645C22×C4—224no—
646C22×C4—228no—
647C22×C4—224no—
648C22×C4—222no—
649C22×C4—222no—
650C22×C4—222no—
651C22×C4—2232no—
652C22×C4—222no—
653C22×C4—222no—
654C22×C4—222no—
655C22×C4—222no—
656C22×C4—222no—
657C22×C4—222no—
658C22×C4—222no—
659C22×C4—222no—
660C22×C4—222no—
661C22×C4—444no—
662C22×C4—442no—
663C22×C4#433914yes—
664C22×C4D4×D1114yes—
665C22×C4#434114yes—
666C22×C4C23×D1112yes—
667C22×C4C23×D1114yes—
668C22×C4C23×D1112yes—
669C22×C4C23×D1112yes—
670C22×C4C23×D1111yescharacteristic
671C22×C4C23×D1111yescharacteristic
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—24no—
675C4⋊C4—224no—
676C4⋊C4—224no—
677C4⋊C4—224no—
678C4⋊C4—224no—
679C4⋊C4—228no—
680C4⋊C4—228no—
681C4⋊C4—224no—
682C4⋊C4—222no—
683C4⋊C4—222no—
684C4⋊C4—444no—
685C4⋊C4—444no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—28no—
689C22⋊C4—44no—
690C22⋊C4—224no—
691C22⋊C4—224no—
692C22⋊C4—224no—
693C22⋊C4—224no—
694C22⋊C4—228no—
695C22⋊C4—224no—
696C22⋊C4—224no—
697C22⋊C4—224no—
698C22⋊C4—224no—
699C22⋊C4—228no—
700C22⋊C4—444no—
701C22⋊C4—444no—
702C42—24no—
703C42—24no—
704C42—224no—
705C42—224no—
706C42—224no—
707C42—224no—
708C42—224no—
709C42—224no—
710C11#3480911yescharacteristic, complemented, Sylow
711C23—22no—
712C23—22no—
713C23—28no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—48no—
721C23—48no—
722C23—44no—
723C23—44no—
724C23—112no—
725C23—114no—
726C23—112no—
727C23—228no—
728C23—221no—
729C23—221no—
730C23—222no—
731C23—228no—
732C23—221no—
733C23—221no—
734C23—222no—
735C23—222no—
736C23—444no—
737C23—448no—
738C23—448no—
739C23C2×#433912yes—
740C23C2×D4×D1112yes—
741C23C2×#434112yes—
742C23#41×D1114yes—
743C23C24×D1111yescharacteristic
744D4—2216no—
745D4—2216no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—44no—
757C2×C4—48no—
758C2×C4—48no—
759C2×C4—112no—
760C2×C4—112no—
761C2×C4—114no—
762C2×C4—228no—
763C2×C4—228no—
764C2×C4—221no—
765C2×C4—221no—
766C2×C4—222no—
767C2×C4—221no—
768C2×C4—221no—
769C2×C4—222no—
770C2×C4—228no—
771C2×C4—228no—
772C2×C4—228no—
773C2×C4—228no—
774C2×C4—224no—
775C2×C4—222no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—224no—
779C2×C4—224no—
780C2×C4—224no—
781C2×C4—224no—
782C2×C4—222no—
783C2×C4—222no—
784C2×C4—448no—
785C2×C4—448no—
786C2×C4—444no—
787C2×C4#66936116yescomplemented
788C2×C4C2×#433912yes—
789C2×C4C2×#433912yes—
790C2×C4C2×D4×D1112yes—
791C2×C4C2×D4×D1112yes—
792C2×C4C2×#434112yes—
793C2×C4C2×#434112yes—
794C22—24no—
795C22—24no—
796C22—22no—
797C22—22no—
798C22—24no—
799C22—24no—
800C22—24no—
801C22—416no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—114no—
807C22—224no—
808C22—224no—
809C22—222no—
810C22—222no—
811C22—222no—
812C22—222no—
813C22—222no—
814C22—4416no—
815C22—442no—
816C22—442no—
817C22C2×#6693614yes—
818C22C22×#433911yescharacteristic
819C22C22×D4×D1111yescharacteristic
820C22C22×#434111yescharacteristic
821C22C2×#41×D1112yes—
822C22#1062345312yes—
823C4—44no—
824C4—42no—
825C4—42no—
826C4—42no—
827C4—222no—
828C4—222no—
829C4—224no—
830C4—444no—
831C4—442no—
832C4—442no—
833C4—442no—
834C4C2×#6693614yes—
835C4C2×#6693614yes—
836C2—24no—
837C2—44no—
838C2—224no—
839C2—442no—
840C2C22×#6693611yescharacteristic
841C2D11×#52511yescharacteristic
842C2#1308194611yescharacteristic
843C2#1308217012yes—
844C2#1308217612yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2280C2
prime radicalC23×C22⋊D11C22
hypercenter#2280D11
hypocenterC11#34809
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C2×D11×#117C2semidirect
3. #13072929C2semidirect
4. #13072920C2semidirect
5. #13072915C2semidirect
6. #13072909C2semidirect
7. #13072900C2semidirect
8. #13072895C2semidirect
9. #13072887C2semidirect
11. #13071877C2semidirect
12. C4×#66936C2semidirect
13. #13071100C2semidirect
14. #13071098C2semidirect
15. #13070999C2semidirect
16. #13070995C2semidirect
17. C11×#2280C2semidirect
35. C2×#66945C22semidirect
36. C2×#66945C22semidirect
37. C2×C4⋊C4×D11C22semidirect
38. C2×C4⋊C4×D11C22semidirect
42. C2×#66925C22semidirect
43. C2×C42×D11C22semidirect
45. C11×#380C22semidirect
46. C11×#380C22semidirect
48. C4×C11×C22⋊C4C22semidirect
50. #10622825C22semidirect
51. #10622825C22semidirect
53. C4×C22⋊Dic11C22semidirect
54. #10622600C22semidirect
55. #10622600C22semidirect
56. #10622598C22semidirect
57. #10622598C22semidirect
58. #10622586C22semidirect
59. #10622586C22semidirect
64. #10622565C22semidirect
65. #10622564C22semidirect
68. #10622562C22semidirect
71. #10622558C22semidirect
73. C4×(C2×D11)⋊C4C22semidirect
74. C4×(C2×D11)⋊C4C22semidirect
75. C4×C4⋊Dic11C22semidirect
76. C4×Dic11⋊C4C22semidirect
77. #10622288C22semidirect
78. #10622287C22semidirect
79. #10622281C22semidirect
80. #10622277C22semidirect
81. #10622271C22semidirect
82. #10622270C22semidirect
83. #10622267C22semidirect
84. #10622265C22semidirect
305. #2280D11semidirect
352. C2×C4×C11#123semidirect
445. #380C2×D11semidirect
446. #380C2×D11semidirect
455. C4×C22⋊C4C2×D11semidirect
710. C11#34809semidirect
787. C2×C4#66936semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
C2×D11×#1172
#130729292
#130729202
#130729152
#130729092
#130729002
#130728952
#130728872
#130719412
#130718772
C4×#669362
#130711002
#130710982
#130709992
#130709952
C11×#22802
#3480911