Finite Group Databasebeta

← #14914083

Subgroups — #14914083

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×#10623035C211yesmaximal, characteristic, complemented
3C2×D11×#117C211yesmaximal, characteristic, complemented
4#13071606C214yesmaximal, complemented
5#13071592C214yesmaximal, complemented
6#13071567C212yesmaximal, complemented
7#13071542C212yesmaximal, complemented
8#13071542C212yesmaximal, complemented
9#13071516C212yesmaximal, complemented
10#13071307C212yesmaximal, complemented
11#13071296C212yesmaximal, complemented
12#13071204C211yesmaximal, characteristic, complemented
13#13071146C212yesmaximal, complemented
14#13071124C212yesmaximal, complemented
15C2×#10622600C211yesmaximal, characteristic, complemented
16#13070972C211yesmaximal, characteristic, complemented
17C11×#2317C211yesmaximal, characteristic, complemented
18C22×#4339C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C2×C4×C22⋊D11C2214yes—
24C22×(C2×D11)⋊C4C2212yes—
25C2×#66979C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27#10623055C4116yescomplemented
28D11×#117—28no—
29C2×#66950C2211yescharacteristic
30C2×#66950C2211yescharacteristic
31C2×#66948C2211yescharacteristic
32C2×#66948C2211yescharacteristic
33#10623035—28no—
34C2×#66946C2214yes—
35C2×#66946C2212yescomplemented
36C2×#66945C2211yescharacteristic
37C2×#66945C2211yescharacteristic
38C2×#66945C2212yescomplemented
39C2×C4⋊C4×D11C2211yescharacteristic
40C2×C4⋊C4×D11C2211yescharacteristic
41C2×C4⋊C4×D11C2212yescomplemented
42C2×#66940C2212yescomplemented
43C2×#66939C2212yes—
44C2×#66935C2212yes—
45C2×C22⋊C4×D11C2212yes—
46C2×#66930C2212yes—
47C2×C4×D44C2212yes—
48C2×C4×D44C2212yes—
49C2×#66925C2212yes—
50C2×C42×D11C2212yes—
51C11×#389C2212yescomplemented
52C11×#389C2212yescomplemented
53C11×#385C2214yes—
54C11×#384C2212yescomplemented
55C11×#382C2212yescomplemented
56C2×C11⋊#95C2212yes—
57#10622603C2214yes—
58#10622603C2214yescomplemented
59#10622602C2214yes—
60#10622602C2214yescomplemented
61#10622601C2214yes—
62#10622600C2212yes—
63#10622600C2212yes—
64#10622600C2212yes—
65#10622600C2212yes—
66#10622600C2212yescomplemented
67#10622600C2212yescomplemented
68C4⋊C4×Dic11C2212yescomplemented
69C4⋊C4×Dic11C2212yescomplemented
70C4⋊C4×Dic11C2214yescomplemented
71#10622586C2214yescomplemented
72#10622571C2214yes—
73C22⋊C4×Dic11C2214yes—
74#10622552C2212yescomplemented
75C4×C4⋊Dic11C2212yescomplemented
76C4×C4⋊Dic11C2212yescomplemented
77#10622542C2212yescomplemented
78#10622282C2214yes—
79#10622282C2214yescomplemented
80#10622279C2214yes—
81#10622279C2214yescomplemented
82#10622278C2214yes—
83#10622278C2214yes—
84#10622267C2214yescomplemented
85#10622267C2214yescomplemented
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×#117—24no—
111C11×#117C2×C418yescomplemented
112C2×C11×C4⋊C4—24no—
113C2×C11×C4⋊C4C2312yes—
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2312yes—
117C2×C11×C4⋊C4C2314yes—
118C2×C11×C4⋊C4C2314yes—
119C2×C11×C4⋊C4C2311yescharacteristic
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C11×C22⋊C4C2312yes—
122C2×C11×C22⋊C4C2312yes—
123C2×C42×C11C2312yes—
124C2×C42×C11C2312yes—
125C2×C22⋊Dic11C2312yes—
126C4×C22⋊D11—216no—
127C2×(C2×D11)⋊C4—44no—
128C2×(C2×D11)⋊C4C2312yes—
129C2×(C2×D11)⋊C4C2312yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2312yes—
136C2×(C2×D11)⋊C4C2312yes—
137C2×(C2×D11)⋊C4C2312yes—
138C2×(C2×D11)⋊C4C2312yes—
139#66979D418yescomplemented
140C2×C4⋊Dic11—24no—
141C2×C4⋊Dic11C2312yes—
142C2×C4⋊Dic11C2312yes—
143C2×C4⋊Dic11C2312yes—
144C2×C4⋊Dic11C2312yes—
145C2×C4⋊Dic11C2311yescharacteristic
146C2×C4⋊Dic11C2311yescharacteristic
147C2×Dic11⋊C4C2312yes—
148C2×Dic11⋊C4C2312yes—
149C2×Dic11⋊C4C2314yes—
150C2×C4×Dic11C2312yes—
151C2×C4×Dic11C2312yes—
152C2×C4×Dic11C2314yes—
153C2×C4×Dic11C2314yes—
154C2×C4×Dic11C2314yes—
155C2×C4×Dic11C2312yes—
156#66950C2×C418yescomplemented
157#66950C2×C418yescomplemented
158#66948C2×C418yescomplemented
159#66948C2×C418yescomplemented
160#66946—28no—
161#66946—48no—
162#66945—24no—
163#66945—24no—
164#66945—28no—
165C4⋊C4×D11—24no—
166C4⋊C4×D11—24no—
167C4⋊C4×D11—28no—
168#66940—28no—
169#66939C2×C4116yescomplemented
170#66935C2×C4116yescomplemented
171C22⋊C4×D11—28no—
172#66930—28no—
173C4×D44C2×C4116yescomplemented
174C4×D44C2×C4116yescomplemented
175#66925—28no—
176C42×D11—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×C11C2412yes—
204C22×C4×C11C2414yes—
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—22no—
215C22×Dic11—24no—
216C22×Dic11—42no—
217C22×Dic11—42no—
218C22×Dic11C22×C414yes—
219C22×Dic11C2414yes—
220C22×Dic11C2411yescharacteristic
221C22×Dic11C2412yes—
222C22×Dic11C2411yescharacteristic
223C22×Dic11C2412yes—
224C22×Dic11C2412yes—
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—28no—
238C2×C4×D11—24no—
239C2×C4×D11—24no—
240C2×C4×D11—232no—
241C2×C4×D11—22no—
242C2×C4×D11—22no—
243C2×C4×D11—22no—
244C2×C4×D11—24no—
245C2×C4×D11—22no—
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⋊C4—22no—
266C11×C4⋊C4—22no—
267C11×C4⋊C4—44no—
268C11×C4⋊C4—44no—
269C11×C4⋊C4C22×C414yes—
270C11×C4⋊C4C22×C414yes—
271C11×C22⋊C4—24no—
272C11×C22⋊C4C22×C418yes—
273C42×C11—24no—
274C42×C11C22×C418yes—
275C22⋊Dic11C2×D418yes—
276(C2×D11)⋊C4—24no—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4—28no—
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⋊Dic11C22×C418yes—
290C4⋊Dic11C22×C418yes—
291C4⋊Dic11C2×D414yes—
292C4⋊Dic11C2×D414yes—
293Dic11⋊C4—24no—
294Dic11⋊C4—24no—
295Dic11⋊C4—28no—
296C4×Dic11—24no—
297C4×Dic11—24no—
298C4×Dic11—28no—
299C4×Dic11—44no—
300C4×Dic11—44no—
301C4×Dic11C2×D418yes—
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#2317D1111yescharacteristic, complemented
314#2311—111no—
315C4×C22⋊Q8—112no—
316C4×#121—112no—
317C2×#380—111no—
318#2274—111no—
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—24no—
362C2×C4×C11—24no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—24no—
368C2×C4×C11—84no—
369C2×C4×C11C4×D4116yescomplemented
370C2×C4×C11C23×C414yes—
371C2×C4×C11C23×C414yes—
372C2×C4×C11C23×C412yes—
373C2×C4×C11C23×C412yes—
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—22no—
389C2×Dic11—22no—
390C2×Dic11—24no—
391C2×Dic11—24no—
392C2×Dic11—24no—
393C2×Dic11—84no—
394C2×Dic11C23×C414yes—
395C2×Dic11C23×C412yes—
396C2×Dic11C23×C412yes—
397C2×Dic11C22×D414yes—
398C2×Dic11C22×D414yes—
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—114no—
425C2×C4×D4—112no—
426C2×C4×D4—112no—
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—114no—
446#390—112no—
447#389—114no—
448#389C2×D1112yescomplemented
449#389C2×D1112yescomplemented
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#385C2×D1114yes—
462#384C2×D1112yescomplemented
463#382C2×D1112yescomplemented
464#380—112no—
465#380—112no—
466#380—112no—
467#380—112no—
468#380—112no—
469#380—112no—
470C4×C4⋊C4—112no—
471C4×C4⋊C4—112no—
472C4×C4⋊C4—114no—
473C4×C4⋊C4—112no—
474C4×C4⋊C4—112no—
475C4×C22⋊C4—114no—
476C4×C22⋊C4—114no—
477C4×C22⋊C4—114no—
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—44no—
518C4×C11—42no—
519C4×C11—42no—
520C4×C11C2×C4×D414yes—
521C4×C11C2×C4×D414yes—
522Dic11—24no—
523Dic11—22no—
524Dic11—22no—
525Dic11—24no—
526Dic11—24no—
527Dic11—44no—
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—228no—
562C4×D4—2216no—
563C4×D4—448no—
564#117—24no—
565#117—118no—
566#117—228no—
567#117—228no—
568#117—224no—
569#117—224no—
570#117—228no—
571#117C4×D1118yescomplemented
572C2×C4⋊C4—24no—
573C2×C4⋊C4—111no—
574C2×C4⋊C4—111no—
575C2×C4⋊C4—112no—
576C2×C4⋊C4—112no—
577C2×C4⋊C4—112no—
578C2×C4⋊C4—112no—
579C2×C4⋊C4—114no—
580C2×C4⋊C4—112no—
581C2×C4⋊C4—112no—
582C2×C4⋊C4—224no—
583C2×C4⋊C4—224no—
584C2×C4⋊C4—228no—
585C2×C4⋊C4—224no—
586C2×C4⋊C4C22×D1112yes—
587C2×C4⋊C4C22×D1111yescharacteristic
588C2×C4⋊C4C22×D1111yescharacteristic
589C2×C4⋊C4C22×D1112yes—
590C2×C4⋊C4C22×D1114yes—
591C2×C4⋊C4C22×D1114yes—
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—114no—
615C2×C42—114no—
616C2×C42—228no—
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—112no—
673C22×C4—112no—
674C22×C4—114no—
675C22×C4—114no—
676C22×C4—118no—
677C22×C4—114no—
678C22×C4—114no—
679C22×C4—114no—
680C22×C4—224no—
681C22×C4—224no—
682C22×C4—228no—
683C22×C4—224no—
684C22×C4—224no—
685C22×C4—222no—
686C22×C4—222no—
687C22×C4—2232no—
688C22×C4—222no—
689C22×C4—222no—
690C22×C4—224no—
691C22×C4—222no—
692C22×C4—222no—
693C22×C4—222no—
694C22×C4—222no—
695C22×C4—222no—
696C22×C4—222no—
697C22×C4—224no—
698C22×C4—224no—
699C22×C4—442no—
700C22×C4—442no—
701C22×C4—444no—
702C22×C4—444no—
703C22×C4—442no—
704C22×C4—442no—
705C22×C4C2×C4×D1114yes—
706C22×C4D4×D1114yes—
707C22×C4#434314yes—
708C22×C4C23×D1112yes—
709C22×C4C23×D1114yes—
710C22×C4C23×D1112yes—
711C22×C4C23×D1112yes—
712C22×C4C23×D1112yes—
713C22×C4C23×D1111yescharacteristic
714C22×C4C23×D1111yescharacteristic
715C4⋊C4—24no—
716C4⋊C4—24no—
717C4⋊C4—22no—
718C4⋊C4—22no—
719C4⋊C4—44no—
720C4⋊C4—44no—
721C4⋊C4—118no—
722C4⋊C4—118no—
723C4⋊C4—114no—
724C4⋊C4—114no—
725C4⋊C4—224no—
726C4⋊C4—224no—
727C4⋊C4—228no—
728C4⋊C4—224no—
729C4⋊C4—224no—
730C4⋊C4C2×C4×D1114yes—
731C4⋊C4C2×C4×D1114yes—
732C22⋊C4—24no—
733C22⋊C4—118no—
734C22⋊C4—118no—
735C22⋊C4—118no—
736C22⋊C4—118no—
737C22⋊C4—118no—
738C22⋊C4—224no—
739C22⋊C4—224no—
740C22⋊C4—228no—
741C22⋊C4—228no—
742C22⋊C4—444no—
743C22⋊C4—444no—
744C22⋊C4—444no—
745C22⋊C4C2×C4×D1118yes—
746C42—24no—
747C42—118no—
748C42—224no—
749C42—224no—
750C42—228no—
751C42—444no—
752C42—444no—
753C42C2×C4×D1118yes—
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—
788C23C2×D4×D1112yes—
789C23C2×#434312yes—
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—24no—
803C2×C4—24no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—24no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—84no—
810C2×C4—112no—
811C2×C4—112no—
812C2×C4—114no—
813C2×C4—114no—
814C2×C4—114no—
815C2×C4—228no—
816C2×C4—221no—
817C2×C4—222no—
818C2×C4—221no—
819C2×C4—221no—
820C2×C4—221no—
821C2×C4—222no—
822C2×C4—222no—
823C2×C4—222no—
824C2×C4—222no—
825C2×C4—222no—
826C2×C4—228no—
827C2×C4—228no—
828C2×C4—228no—
829C2×C4—228no—
830C2×C4—2216no—
831C2×C4—224no—
832C2×C4—224no—
833C2×C4—224no—
834C2×C4—448no—
835C2×C4—448no—
836C2×C4—888no—
837C2×C4—884no—
838C2×C4#66946116yescomplemented
839C2×C4C22×C4×D1114yes—
840C2×C4C22×C4×D1114yes—
841C2×C4C22×C4×D1112yes—
842C2×C4C22×C4×D1112yes—
843C2×C4C2×D4×D1112yes—
844C2×C4C2×D4×D1112yes—
845C2×C4C2×#434312yes—
846C2×C4C2×#434312yes—
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—441no—
868C22—442no—
869C22—442no—
870C22—441no—
871C22—441no—
872C22—442no—
873C22—441no—
874C22—442no—
875C22C2×#6694614yes—
876C22C23×C4×D1111yescharacteristic
877C22C22×D4×D1111yescharacteristic
878C22C22×#434311yescharacteristic
879C22D11×H(5,𝔽2)11yescharacteristic
880C22#1062345511yescharacteristic
881C22D11×2−1+411yescharacteristic
882C22#1062345711yescharacteristic
883C4—24no—
884C4—24no—
885C4—44no—
886C4—42no—
887C4—42no—
888C4—224no—
889C4—224no—
890C4—222no—
891C4—222no—
892C4—224no—
893C4—444no—
894C4C2×#6694614yes—
895C4C2×#6694614yes—
896C2—24no—
897C2—224no—
898C2—442no—
899C2—444no—
900C2C22×#6694611yescharacteristic
901C2D11×#52011yescharacteristic
902C2#1308181611yescharacteristic
903C2#1308228311yescharacteristic
904C2#1308229411yescharacteristic
905C2#1308235411yescharacteristic
906C2#1308237111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2317C2
socle, cosocleC23×C11C25
prime radicalC2×#10623055C2
hypercenter#2317D11
hypocenterC11#34202
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2317

Complements

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

NH ≅ G/Ntype
2. C2×#10623035C2semidirect
3. C2×D11×#117C2semidirect
4. #13071606C2semidirect
5. #13071592C2semidirect
6. #13071567C2semidirect
7. #13071542C2semidirect
8. #13071542C2semidirect
9. #13071516C2semidirect
10. #13071307C2semidirect
11. #13071296C2semidirect
12. #13071204C2semidirect
13. #13071146C2semidirect
14. #13071124C2semidirect
15. C2×#10622600C2semidirect
16. #13070972C2semidirect
17. C11×#2317C2semidirect
27. #10623055C4semidirect
35. C2×#66946C22semidirect
38. C2×#66945C22semidirect
41. C2×C4⋊C4×D11C22semidirect
42. C2×#66940C22semidirect
51. C11×#389C22semidirect
52. C11×#389C22semidirect
54. C11×#384C22semidirect
55. C11×#382C22semidirect
58. #10622603C22semidirect
60. #10622602C22semidirect
66. #10622600C22semidirect
67. #10622600C22semidirect
68. C4⋊C4×Dic11C22semidirect
69. C4⋊C4×Dic11C22semidirect
70. C4⋊C4×Dic11C22semidirect
71. #10622586C22semidirect
74. #10622552C22semidirect
75. C4×C4⋊Dic11C22semidirect
76. C4×C4⋊Dic11C22semidirect
77. #10622542C22semidirect
79. #10622282C22semidirect
81. #10622279C22semidirect
84. #10622267C22semidirect
85. #10622267C22semidirect
94. C2×#4339C2×C4semidirect
100. C22×C4×D11C2×C4semidirect
111. C11×#117C2×C4semidirect
139. #66979D4semidirect
156. #66950C2×C4semidirect
157. #66950C2×C4semidirect
158. #66948C2×C4semidirect
159. #66948C2×C4semidirect
169. #66939C2×C4semidirect
170. #66935C2×C4semidirect
173. C4×D44C2×C4semidirect
174. C4×D44C2×C4semidirect
313. #2317D11semidirect
369. C2×C4×C11C4×D4semidirect
448. #389C2×D11semidirect
449. #389C2×D11semidirect
462. #384C2×D11semidirect
463. #382C2×D11semidirect
514. C2×D11#520semidirect
571. #117C4×D11semidirect
754. C11#34202semidirect
838. C2×C4#66946semidirect

Maximal subgroups

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

subgroupindex
C2×#106230552
C2×#106230352
C2×D11×#1172
#130716062
#130715922
#130715672
#130715422
#130715162
#130713072
#130712962
#130712042
#130711462
#130711242
C2×#106226002
#130709722
C11×#23172
#3420211