Finite Group Databasebeta

← #14914087

Subgroups — #14914087

Order 2816.

3246 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623055C211yesmaximal, characteristic
2C2×#10623054C211yesmaximal, characteristic, complemented
3C2×D11×#117C211yesmaximal, characteristic, complemented
4#13071610C214yesmaximal, complemented
5#13071598C214yesmaximal, complemented
6#13071563C212yesmaximal, complemented
7#13071548C212yesmaximal, complemented
8#13071548C212yesmaximal, complemented
9C4⋊C4×D44C212yesmaximal, complemented
10#13071310C212yesmaximal, complemented
11#13071299C212yesmaximal, complemented
12#13071239C211yesmaximal, characteristic, complemented
13#13071209C211yesmaximal, characteristic, complemented
14C4×#66950C212yesmaximal, complemented
15C4×#66948C212yesmaximal, complemented
16C2×#10622600C211yesmaximal, characteristic, complemented
17C11×#2274C211yesmaximal, characteristic, complemented
18C22×#4339C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2212yes—
24C2×#66979C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26#10623055C4116yescomplemented
27#10623054—28no—
28D11×#117—28no—
29C2×#66950C2211yescharacteristic
30C2×#66950C2211yescharacteristic
31C2×#66948C2211yescharacteristic
32C2×#66948C2211yescharacteristic
33C2×#66945C2211yescharacteristic
34C2×#66945C2211yescharacteristic
35C2×#66945C2212yescomplemented
36C2×C4⋊C4×D11C2211yescharacteristic
37C2×C4⋊C4×D11C2211yescharacteristic
38C2×C4⋊C4×D11C2212yescomplemented
39C2×#66939C2212yes—
40C2×#66935C2212yes—
41C2×(C22⋊D11)⋊C4C2214yes—
42C2×C22⋊C4×D11C2212yes—
43C2×#66930C2212yes—
44C2×C4×D44C2214yes—
45C2×C4×D44C2212yes—
46C2×C4×D44C2212yes—
47C2×C4×D44C2212yescomplemented
48C2×#66925C2212yes—
49C2×C42×D11C2212yes—
50C2×C4×Dic22C2212yescomplemented
51C4×C11×C4⋊C4C2212yescomplemented
52C4×C11×C4⋊C4C2212yescomplemented
53C4×C11×C4⋊C4C2212yescomplemented
54C4×C11×C4⋊C4C2212yescomplemented
55C4×C11×C22⋊C4C2214yes—
56#10622826C2214yes—
57C2×C11⋊#95C2212yes—
58#10622601C2212yescomplemented
59#10622600C2212yes—
60#10622600C2212yes—
61#10622600C2212yes—
62#10622600C2212yes—
63#10622600C2212yescomplemented
64#10622600C2212yescomplemented
65#10622598C2212yescomplemented
66#10622598C2212yescomplemented
67#10622587C2212yescomplemented
68#10622563C2214yes—
69#10622553C2214yes—
70#10622553C2214yescomplemented
71#10622552C2214yes—
72C4×(C2×D11)⋊C4C2214yes—
73C4×(C2×D11)⋊C4C2214yescomplemented
74#10622549C2212yescomplemented
75#10622548C2212yescomplemented
76C4×C4⋊Dic11C2214yescomplemented
77#10622541C2214yescomplemented
78#10622283C2214yes—
79#10622283C2214yescomplemented
80#10622281C2214yes—
81#10622281C2214yescomplemented
82#10622278C2214yes—
83#10622278C2214yes—
84#10622266C2214yescomplemented
85#10622266C2214yescomplemented
86C24×D11C2311yescharacteristic
87C23×C4×C11C2312yes—
88C23×C4×C11C2311yescharacteristic
89C22×C22⋊D11C2312yes—
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2312yes—
92C2×#4339—24no—
93C2×#4339—24no—
94C2×#4339C2×C418yescomplemented
95C22×D44C2312yes—
96C22×D44C2311yescharacteristic
97C22×D44C2312yes—
98C22×C4×D11—24no—
99C22×C4×D11—24no—
100C22×C4×D11C2×C418yescomplemented
101C22×C4×D11C2312yes—
102C22×C4×D11C2312yes—
103C22×C4×D11C2311yescharacteristic
104C22×C4×D11C2311yescharacteristic
105C22×C4×D11C2311yescharacteristic
106C22×C4×D11C2312yes—
107C22×C4×D11C2311yescharacteristic
108C22×C4×D11C2314yes—
109C22×Dic22C2311yescharacteristic
110C11×#117C2×C418yescomplemented
111C11×#117D418yescomplemented
112C2×C11×C4⋊C4—24no—
113C2×C11×C4⋊C4C2312yes—
114C2×C11×C4⋊C4C2312yes—
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C4⋊C4C2311yescharacteristic
119C2×C11×C22⋊C4C2312yes—
120C2×C11×C22⋊C4C2312yes—
121C2×C42×C11C2314yes—
122C2×C42×C11C2314yes—
123C2×C42×C11C2312yes—
124C2×C42×C11C2312yes—
125C2×C22⋊Dic11C2312yes—
126C2×(C2×D11)⋊C4—44no—
127C2×(C2×D11)⋊C4C2312yes—
128C2×(C2×D11)⋊C4C2312yes—
129C2×(C2×D11)⋊C4C2314yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2312yes—
135C2×(C2×D11)⋊C4C2312yes—
136C2×(C2×D11)⋊C4C2312yes—
137C2×(C2×D11)⋊C4C2312yes—
138#66979—24no—
139C2×C4⋊Dic11—24no—
140C2×C4⋊Dic11C2312yes—
141C2×C4⋊Dic11C2311yescharacteristic
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4⋊Dic11C2312yes—
144C2×C4⋊Dic11C2314yes—
145C2×C4⋊Dic11C2314yes—
146C2×C4⋊Dic11C2312yes—
147C2×C4⋊Dic11C2312yes—
148C2×Dic11⋊C4C2314yes—
149C2×Dic11⋊C4C2312yes—
150C2×Dic11⋊C4C2312yes—
151C2×C4×Dic11C2314yes—
152C2×C4×Dic11C2312yes—
153C2×C4×Dic11C2312yes—
154C2×C4×Dic11C2312yes—
155#66950C2×C418yescomplemented
156#66950C2×C418yescomplemented
157#66948C2×C418yescomplemented
158#66948C2×C418yescomplemented
159#66945—24no—
160#66945—24no—
161#66945—28no—
162C4⋊C4×D11—24no—
163C4⋊C4×D11—24no—
164C4⋊C4×D11—28no—
165#66939C2×C4116yescomplemented
166#66935C2×C4116yescomplemented
167(C22⋊D11)⋊C4—216no—
168C22⋊C4×D11—28no—
169#66930—28no—
170C4×D44—28no—
171C4×D44—48no—
172C4×D44C2×C4116yescomplemented
173C4×D44C2×C4116yescomplemented
174#66925—28no—
175C42×D11—28no—
176C4×Dic22—28no—
177C11×#95C2314yes—
178C11×#95C2314yes—
179C11⋊#95C2314yes—
180C11⋊#95C2314yes—
181C11⋊#95C2314yes—
182C11⋊#95C2314yes—
183C11⋊#95C2314yes—
184C11⋊#95C2314yes—
185#34202—111nomaximal, Sylow
186C24×C11C2411yescharacteristic
187C23×D11—22no—
188C23×D11—22no—
189C23×D11—22no—
190C23×D11—22no—
191C23×D11—41no—
192C23×D11—41no—
193C23×D11C22×C414yes—
194C23×D11C2411yescharacteristic
195C23×D11C2412yes—
196C23×D11C2411yescharacteristic
197C22×C4×C11—24no—
198C22×C4×C11—42no—
199C22×C4×C11—42no—
200C22×C4×C11C22×C414yes—
201C22×C4×C11C2×D414yes—
202C22×C4×C11#4114yes—
203C22×C4×C11C2414yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2411yescharacteristic
209C22×C4×C11C2411yescharacteristic
210C2×C22⋊D11—24no—
211C2×C22⋊D11—24no—
212C2×C22⋊D11C22×C418yes—
213C22×Dic11—22no—
214C22×Dic11—24no—
215C22×Dic11—22no—
216C22×Dic11—42no—
217C22×Dic11—42no—
218C22×Dic11C22×C414yes—
219C22×Dic11C2412yes—
220C22×Dic11C2414yes—
221C22×Dic11C2412yes—
222C22×Dic11C2411yescharacteristic
223C22×Dic11C2412yes—
224C22×Dic11C2411yescharacteristic
225#4339—232no—
226C2×D44—24no—
227C2×D44—24no—
228C2×D44—22no—
229C2×D44—22no—
230C2×D44—42no—
231C2×D44—42no—
232C2×D44C22×C418yes—
233C2×D44C22×C414yes—
234C2×D44C22×C418yes—
235C2×C4×D11—24no—
236C2×C4×D11—24no—
237C2×C4×D11—232no—
238C2×C4×D11—22no—
239C2×C4×D11—22no—
240C2×C4×D11—22no—
241C2×C4×D11—24no—
242C2×C4×D11—22no—
243C2×C4×D11—24no—
244C2×C4×D11—24no—
245C2×C4×D11—28no—
246C2×C4×D11—22no—
247C2×C4×D11—22no—
248C2×C4×D11—22no—
249C2×C4×D11—22no—
250C2×C4×D11—24no—
251C2×C4×D11—42no—
252C2×C4×D11—42no—
253C2×C4×D11—44no—
254C2×C4×D11—44no—
255C2×C4×D11C22×C414yes—
256C2×C4×D11C22×C414yes—
257C2×C4×D11C22×C418yes—
258C2×C4×D11C22×C414yes—
259C2×C4×D11C22×C414yes—
260C2×Dic22—22no—
261C2×Dic22—22no—
262C2×Dic22C22×C414yes—
263C11×C4⋊C4—24no—
264C11×C4⋊C4—24no—
265C11×C4⋊C4C22×C414yes—
266C11×C4⋊C4C22×C414yes—
267C11×C4⋊C4C2×D414yes—
268C11×C4⋊C4C2×D414yes—
269C11×C22⋊C4C22×C418yes—
270C11×C22⋊C4C2×D418yes—
271C42×C11—44no—
272C42×C11—44no—
273C42×C11C22×C418yes—
274C42×C11C2×D418yes—
275C22⋊Dic11—24no—
276(C2×D11)⋊C4—28no—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4—24no—
279(C2×D11)⋊C4—28no—
280(C2×D11)⋊C4—44no—
281(C2×D11)⋊C4—44no—
282(C2×D11)⋊C4—44no—
283(C2×D11)⋊C4C22×C418yes—
284(C2×D11)⋊C4C22×C418yes—
285(C2×D11)⋊C4C22×C418yes—
286(C2×D11)⋊C4C22×C418yes—
287C4⋊Dic11—24no—
288C4⋊Dic11—24no—
289C4⋊Dic11—22no—
290C4⋊Dic11—22no—
291C4⋊Dic11—44no—
292C4⋊Dic11—44no—
293C4⋊Dic11C22×C418yes—
294C4⋊Dic11C22×C418yes—
295Dic11⋊C4—28no—
296Dic11⋊C4—24no—
297Dic11⋊C4—24no—
298C4×Dic11—28no—
299C4×Dic11—24no—
300C4×Dic11—24no—
301C4×Dic11—24no—
302C2×#525—111no—
303C2×#520—111no—
304C22×#117—111no—
305#2359—114no—
306#2358—114no—
307#2354—112no—
308#2352—112no—
309#2352—112no—
310D4×C4⋊C4—112no—
311#2324—112no—
312#2323—112no—
313#2317—111no—
314#2311—111no—
315C4×C22⋊Q8—112no—
316C4×#121—112no—
317C2×#380—111no—
318#2274D1111yescharacteristic, complemented
319C23×C11—21no—
320C23×C11—21no—
321C23×C11—21no—
322C23×C11—21no—
323C23×C11C23×C412yes—
324C23×C11C22×D412yes—
325C23×C11C2×#4112yes—
326C23×C11C2511yescharacteristic
327C22×D11—21no—
328C22×D11—21no—
329C22×D11—21no—
330C22×D11—21no—
331C22×D11—28no—
332C22×D11—21no—
333C22×D11—22no—
334C22×D11—21no—
335C22×D11—22no—
336C22×D11—21no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—21no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—21no—
343C22×D11—21no—
344C22×D11—28no—
345C22×D11—44no—
346C22×D11—44no—
347C22×D11—44no—
348C22×D11—44no—
349C22×D11—44no—
350C22×D11C23×C412yes—
351C22×D11C23×C414yes—
352C22×D11C23×C412yes—
353C22×D11H(5,𝔽2)12yes—
354C22×D112−1+412yes—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—24no—
364C2×C4×C11—24no—
365C2×C4×C11—24no—
366C2×C4×C11—84no—
367C2×C4×C11C4×D4116yescomplemented
368C2×C4×C11C23×C414yes—
369C2×C4×C11C23×C414yes—
370C2×C4×C11C23×C412yes—
371C2×C4×C11C23×C412yes—
372C2×C4×C11C22×D414yes—
373C2×C4×C11C22×D414yes—
374C2×C4×C11C22×D412yes—
375C2×C4×C11C22×D412yes—
376C2×C4×C11C2×#4112yes—
377C2×C4×C11C2×#4112yes—
378C22⋊D11—216no—
379C2×Dic11—28no—
380C2×Dic11—21no—
381C2×Dic11—22no—
382C2×Dic11—21no—
383C2×Dic11—22no—
384C2×Dic11—21no—
385C2×Dic11—21no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—24no—
389C2×Dic11—22no—
390C2×Dic11—24no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—24no—
394C2×Dic11—22no—
395C2×Dic11—84no—
396C2×Dic11C23×C414yes—
397C2×Dic11C23×C412yes—
398C2×Dic11C23×C412yes—
399D44—216no—
400D44—28no—
401D44—48no—
402C4×D11—28no—
403C4×D11—28no—
404C4×D11—28no—
405C4×D11—28no—
406C4×D11—216no—
407C4×D11—48no—
408C4×D11—48no—
409C4×D11—88no—
410Dic22—28no—
411C22×#41—111no—
412C24×C4—111no—
413#525—1116no—
414C2×#123—112no—
415C2×C22⋊Q8—111no—
416C2×C22⋊Q8—111no—
417C2×#121—111no—
418C2×#121—111no—
419C2×#120—112no—
420#520—228no—
421C2×C4×Q8—112no—
422C2×C4×D4—114no—
423C2×C4×D4—112no—
424C2×C4×D4—112no—
425C2×C4×D4—112no—
426C2×C4×D4—114no—
427C2×#117—111no—
428C2×#117—111no—
429C2×#117—112no—
430C2×#117—111no—
431C2×#117—112no—
432C2×#117—112no—
433C2×#117—228no—
434C2×#117C2×D1111yescharacteristic
435C2×#117C2×D1111yescharacteristic
436C22×C4⋊C4—111no—
437C22×C4⋊C4—111no—
438C22×C4⋊C4—112no—
439C22×C4⋊C4—111no—
440C22×C4⋊C4C2×D1111yescharacteristic
441C22×C22⋊C4—112no—
442C22×C22⋊C4—112no—
443C22×C42—112no—
444#391—112no—
445#390—112no—
446#390—114no—
447#389—112no—
448#389—112no—
449#389—114no—
450#388—114no—
451#388—114no—
452#388—114no—
453#388—114no—
454#387—114no—
455#387—114no—
456#386—114no—
457#386—114no—
458#386—114no—
459#385—114no—
460#385—114no—
461#385—114no—
462#384—112no—
463#382—112no—
464#380—112no—
465#380—112no—
466#380—112no—
467#380—112no—
468#380—112no—
469#380—112no—
470C4×C4⋊C4—114no—
471C4×C4⋊C4C2×D1112yescomplemented
472C4×C4⋊C4C2×D1112yescomplemented
473C4×C4⋊C4C2×D1112yescomplemented
474C4×C4⋊C4C2×D1112yescomplemented
475C4×C22⋊C4—114no—
476C4×C22⋊C4—114no—
477C4×C22⋊C4C2×D1114yes—
478C2×#95—112no—
479C22×C11—22no—
480C22×C11—22no—
481C22×C11—22no—
482C22×C11—22no—
483C22×C11—22no—
484C22×C11—22no—
485C22×C11C2×C4×D414yes—
486C22×C11C24×C411yescharacteristic
487C22×C11C23×D411yescharacteristic
488C22×C11C22×#4111yescharacteristic
489C22×C11C2×H(5,𝔽2)11yescharacteristic
490C22×C11C2×2−1+411yescharacteristic
491C22×C11#58511yescharacteristic
492C22×C11#58511yescharacteristic
493C2×D11—22no—
494C2×D11—22no—
495C2×D11—22no—
496C2×D11—22no—
497C2×D11—22no—
498C2×D11—22no—
499C2×D11—22no—
500C2×D11—24no—
501C2×D11—22no—
502C2×D11—24no—
503C2×D11—22no—
504C2×D11—24no—
505C2×D11—416no—
506C2×D11—41no—
507C2×D11—42no—
508C2×D11—42no—
509C2×D11—41no—
510C2×D11—42no—
511C2×D11—41no—
512C2×D11—42no—
513C2×D11—41no—
514C2×D11#52014yescomplemented
515C4×C11—24no—
516C4×C11—24no—
517C4×C11—24no—
518C4×C11—24no—
519C4×C11—44no—
520C4×C11C2×C4×D414yes—
521C4×C11C2×C4×D414yes—
522Dic11—24no—
523Dic11—22no—
524Dic11—22no—
525Dic11—42no—
526Dic11—44no—
527Dic11—42no—
528C25—111no—
529C2×#41—118no—
530C2×#41—224no—
531C2×#41—224no—
532C22×Q8—111no—
533C22×D4—112no—
534C22×D4—112no—
535C22×D4—111no—
536C22×D4—112no—
537C23×C4—111no—
538C23×C4—118no—
539C23×C4—111no—
540C23×C4—112no—
541C23×C4—111no—
542C23×C4—111no—
543C23×C4—111no—
544C23×C4—112no—
545C23×C4—112no—
546C23×C4—112no—
547C23×C4—114no—
548C23×C4—224no—
549C23×C4—224no—
550C23×C4C22×D1112yes—
551C23×C4C22×D1111yescharacteristic
552#123—1116no—
553C22⋊Q8—118no—
554C22⋊Q8—118no—
555#121—118no—
556#121—118no—
557#120—1116no—
558C4×Q8—228no—
559C4×D4—1116no—
560C4×D4—1116no—
561C4×D4—2216no—
562C4×D4—228no—
563C4×D4—448no—
564#117—224no—
565#117—224no—
566#117—224no—
567#117—228no—
568#117—228no—
569#117—228no—
570#117C4×D1118yescomplemented
571#117D4418yescomplemented
572C2×C4⋊C4—24no—
573C2×C4⋊C4—112no—
574C2×C4⋊C4—112no—
575C2×C4⋊C4—112no—
576C2×C4⋊C4—111no—
577C2×C4⋊C4—111no—
578C2×C4⋊C4—112no—
579C2×C4⋊C4—112no—
580C2×C4⋊C4—112no—
581C2×C4⋊C4—114no—
582C2×C4⋊C4—114no—
583C2×C4⋊C4—114no—
584C2×C4⋊C4—224no—
585C2×C4⋊C4—224no—
586C2×C4⋊C4—224no—
587C2×C4⋊C4—228no—
588C2×C4⋊C4C22×D1112yes—
589C2×C4⋊C4C22×D1112yes—
590C2×C4⋊C4C22×D1111yescharacteristic
591C2×C4⋊C4C22×D1111yescharacteristic
592C2×C4⋊C4C22×D1111yescharacteristic
593C2×C4⋊C4C22×D1111yescharacteristic
594C2×C22⋊C4—112no—
595C2×C22⋊C4—112no—
596C2×C22⋊C4—112no—
597C2×C22⋊C4—112no—
598C2×C22⋊C4—112no—
599C2×C22⋊C4—112no—
600C2×C22⋊C4—112no—
601C2×C22⋊C4—114no—
602C2×C22⋊C4—114no—
603C2×C22⋊C4—114no—
604C2×C22⋊C4—114no—
605C2×C22⋊C4—114no—
606C2×C22⋊C4—228no—
607C2×C22⋊C4—444no—
608C2×C22⋊C4C22×D1112yes—
609C2×C22⋊C4C22×D1112yes—
610C2×C42—112no—
611C2×C42—112no—
612C2×C42—112no—
613C2×C42—114no—
614C2×C42—228no—
615C2×C42C22×D1114yes—
616C2×C42C22×D1114yes—
617C2×C42C22×D1112yes—
618C2×C42C22×D1112yes—
619#95—114no—
620#95—114no—
621#95—114no—
622#95—114no—
623#95—114no—
624#95—114no—
625#95C22×D1114yes—
626#95C22×D1114yes—
627C2×C11—24no—
628C2×C11C22×C4×D411yescharacteristic
629C2×C11C2×#52011yescharacteristic
630C2×C11#342811yescharacteristic
631C2×C11#348811yescharacteristic
632C2×C11#348911yescharacteristic
633C2×C11#349411yescharacteristic
634C2×C11#349511yescharacteristic
635D11—24no—
636D11—44no—
637D11—42no—
638C24—111no—
639C24—111no—
640C24—112no—
641C24—114no—
642C24—222no—
643C24—222no—
644C24—222no—
645C24—222no—
646C24—441no—
647C24—441no—
648C24C23×D1111yescharacteristic
649#41—2232no—
650C2×Q8—114no—
651C2×Q8—222no—
652C2×Q8—222no—
653C2×D4—118no—
654C2×D4—118no—
655C2×D4—114no—
656C2×D4—118no—
657C2×D4—224no—
658C2×D4—224no—
659C2×D4—224no—
660C2×D4—224no—
661C2×D4—222no—
662C2×D4—222no—
663C2×D4—442no—
664C2×D4—442no—
665C22×C4—24no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—114no—
669C22×C4—111no—
670C22×C4—112no—
671C22×C4—111no—
672C22×C4—114no—
673C22×C4—114no—
674C22×C4—118no—
675C22×C4—114no—
676C22×C4—114no—
677C22×C4—112no—
678C22×C4—114no—
679C22×C4—112no—
680C22×C4—224no—
681C22×C4—224no—
682C22×C4—222no—
683C22×C4—222no—
684C22×C4—2232no—
685C22×C4—222no—
686C22×C4—222no—
687C22×C4—224no—
688C22×C4—222no—
689C22×C4—222no—
690C22×C4—222no—
691C22×C4—222no—
692C22×C4—222no—
693C22×C4—222no—
694C22×C4—224no—
695C22×C4—224no—
696C22×C4—224no—
697C22×C4—224no—
698C22×C4—228no—
699C22×C4—442no—
700C22×C4—442no—
701C22×C4—444no—
702C22×C4—444no—
703C22×C4—442no—
704C22×C4—442no—
705C22×C4C2×C4×D1114yes—
706C22×C4C2×D4414yes—
707C22×C4#433914yes—
708C22×C4C23×D1114yes—
709C22×C4C23×D1112yes—
710C22×C4C23×D1112yes—
711C22×C4C23×D1112yes—
712C22×C4C23×D1112yes—
713C22×C4C23×D1111yescharacteristic
714C22×C4C23×D1111yescharacteristic
715C4⋊C4—24no—
716C4⋊C4—24no—
717C4⋊C4—118no—
718C4⋊C4—118no—
719C4⋊C4—224no—
720C4⋊C4—224no—
721C4⋊C4—224no—
722C4⋊C4—222no—
723C4⋊C4—222no—
724C4⋊C4—228no—
725C4⋊C4—224no—
726C4⋊C4—444no—
727C4⋊C4—444no—
728C4⋊C4C2×C4×D1114yes—
729C4⋊C4C2×C4×D1114yes—
730C4⋊C4C2×D4414yes—
731C4⋊C4C2×D4414yes—
732C22⋊C4—118no—
733C22⋊C4—118no—
734C22⋊C4—118no—
735C22⋊C4—118no—
736C22⋊C4—228no—
737C22⋊C4—224no—
738C22⋊C4—224no—
739C22⋊C4—224no—
740C22⋊C4—228no—
741C22⋊C4—444no—
742C22⋊C4—444no—
743C22⋊C4—444no—
744C22⋊C4C2×C4×D1118yes—
745C22⋊C4C2×D4418yes—
746C42—44no—
747C42—44no—
748C42—224no—
749C42—224no—
750C42—224no—
751C42—228no—
752C42C2×C4×D1118yes—
753C42C2×D4418yes—
754C11#3420211yescharacteristic, complemented, Sylow
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—112no—
760C23—112no—
761C23—112no—
762C23—112no—
763C23—114no—
764C23—228no—
765C23—221no—
766C23—221no—
767C23—221no—
768C23—221no—
769C23—228no—
770C23—221no—
771C23—222no—
772C23—221no—
773C23—222no—
774C23—221no—
775C23—222no—
776C23—222no—
777C23—221no—
778C23—222no—
779C23—221no—
780C23—222no—
781C23—221no—
782C23—444no—
783C23—444no—
784C23—444no—
785C23—444no—
786C23—444no—
787C23C22×C4×D1112yes—
788C23C22×D4412yes—
789C23C2×#433912yes—
790C23C24×D1111yescharacteristic
791Q8—228no—
792D4—2216no—
793D4—2216no—
794D4—228no—
795D4—448no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—84no—
808C2×C4—112no—
809C2×C4—112no—
810C2×C4—114no—
811C2×C4—228no—
812C2×C4—221no—
813C2×C4—222no—
814C2×C4—221no—
815C2×C4—221no—
816C2×C4—221no—
817C2×C4—222no—
818C2×C4—228no—
819C2×C4—228no—
820C2×C4—228no—
821C2×C4—228no—
822C2×C4—2216no—
823C2×C4—222no—
824C2×C4—222no—
825C2×C4—224no—
826C2×C4—224no—
827C2×C4—222no—
828C2×C4—222no—
829C2×C4—222no—
830C2×C4—222no—
831C2×C4—224no—
832C2×C4—448no—
833C2×C4—448no—
834C2×C4—888no—
835C2×C4—884no—
836C2×C4C4×D44116yescomplemented
837C2×C4C22×C4×D1114yes—
838C2×C4C22×C4×D1114yes—
839C2×C4C22×C4×D1112yes—
840C2×C4C22×C4×D1112yes—
841C2×C4C22×D4414yes—
842C2×C4C22×D4414yes—
843C2×C4C22×D4412yes—
844C2×C4C22×D4412yes—
845C2×C4C2×#433912yes—
846C2×C4C2×#433912yes—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—114no—
854C22—222no—
855C22—222no—
856C22—222no—
857C22—222no—
858C22—222no—
859C22—222no—
860C22—222no—
861C22—224no—
862C22—224no—
863C22—222no—
864C22—222no—
865C22—224no—
866C22—4416no—
867C22—442no—
868C22—441no—
869C22—441no—
870C22—442no—
871C22—441no—
872C22—442no—
873C22—441no—
874C22—442no—
875C22C2×C4×D4414yes—
876C22C23×C4×D1111yescharacteristic
877C22C23×D4411yescharacteristic
878C22C22×#433911yescharacteristic
879C22D11×H(5,𝔽2)11yescharacteristic
880C22#1062345511yescharacteristic
881C22D11×2−1+411yescharacteristic
882C22#1062345711yescharacteristic
883C4—24no—
884C4—24no—
885C4—24no—
886C4—24no—
887C4—44no—
888C4—222no—
889C4—222no—
890C4—224no—
891C4—442no—
892C4—444no—
893C4—442no—
894C4C2×C4×D4414yes—
895C4C2×C4×D4414yes—
896C2—24no—
897C2—224no—
898C2—442no—
899C2—444no—
900C2C22×C4×D4411yescharacteristic
901C2D11×#52011yescharacteristic
902C2#1308181611yescharacteristic
903C2#1308228611yescharacteristic
904C2#1308229711yescharacteristic
905C2#1308234111yescharacteristic
906C2#1308235811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2274C2
socle, cosocleC23×C11C25
prime radicalC2×#10623055C2
hypercenter#2274D11
hypocenterC11#34202
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2274

Complements

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

NH ≅ G/Ntype
2. C2×#10623054C2semidirect
3. C2×D11×#117C2semidirect
4. #13071610C2semidirect
5. #13071598C2semidirect
6. #13071563C2semidirect
7. #13071548C2semidirect
8. #13071548C2semidirect
9. C4⋊C4×D44C2semidirect
10. #13071310C2semidirect
11. #13071299C2semidirect
12. #13071239C2semidirect
13. #13071209C2semidirect
14. C4×#66950C2semidirect
15. C4×#66948C2semidirect
16. C2×#10622600C2semidirect
17. C11×#2274C2semidirect
26. #10623055C4semidirect
35. C2×#66945C22semidirect
38. C2×C4⋊C4×D11C22semidirect
47. C2×C4×D44C22semidirect
50. C2×C4×Dic22C22semidirect
51. C4×C11×C4⋊C4C22semidirect
52. C4×C11×C4⋊C4C22semidirect
53. C4×C11×C4⋊C4C22semidirect
54. C4×C11×C4⋊C4C22semidirect
58. #10622601C22semidirect
63. #10622600C22semidirect
64. #10622600C22semidirect
65. #10622598C22semidirect
66. #10622598C22semidirect
67. #10622587C22semidirect
70. #10622553C22semidirect
73. C4×(C2×D11)⋊C4C22semidirect
74. #10622549C22semidirect
75. #10622548C22semidirect
76. C4×C4⋊Dic11C22semidirect
77. #10622541C22semidirect
79. #10622283C22semidirect
81. #10622281C22semidirect
84. #10622266C22semidirect
85. #10622266C22semidirect
94. C2×#4339C2×C4semidirect
100. C22×C4×D11C2×C4semidirect
110. C11×#117C2×C4semidirect
111. C11×#117D4semidirect
155. #66950C2×C4semidirect
156. #66950C2×C4semidirect
157. #66948C2×C4semidirect
158. #66948C2×C4semidirect
165. #66939C2×C4semidirect
166. #66935C2×C4semidirect
172. C4×D44C2×C4semidirect
173. C4×D44C2×C4semidirect
318. #2274D11semidirect
367. C2×C4×C11C4×D4semidirect
471. C4×C4⋊C4C2×D11semidirect
472. C4×C4⋊C4C2×D11semidirect
473. C4×C4⋊C4C2×D11semidirect
474. C4×C4⋊C4C2×D11semidirect
514. C2×D11#520semidirect
570. #117C4×D11semidirect
571. #117D44semidirect
754. C11#34202semidirect
836. C2×C4C4×D44semidirect

Maximal subgroups

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

subgroupindex
C2×#106230552
C2×#106230542
C2×D11×#1172
#130716102
#130715982
#130715632
#130715482
C4⋊C4×D442
#130713102
#130712992
#130712392
#130712092
C4×#669502
C4×#669482
C2×#106226002
C11×#22742
#3420211