Finite Group Databasebeta

← #14914962

Subgroups — #14914962

Order 2816.

3154 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623358C211yesmaximal, characteristic, complemented
2C2×#41×Dic11C211yesmaximal, characteristic, complemented
3#13071668C214yesmaximal, complemented
4#13071658C212yesmaximal, complemented
5#13071647C212yesmaximal, complemented
6#13071636C212yesmaximal, complemented
7#13071636C214yesmaximal, complemented
8#13071625C212yesmaximal, complemented
9#13071311C212yesmaximal, complemented
10#13071300C212yesmaximal, complemented
11#13071208C211yesmaximal, characteristic, complemented
12C22⋊Q8×Dic11C212yesmaximal, complemented
13#121×Dic11C212yesmaximal, complemented
14#13071107C211yesmaximal, characteristic, complemented
15C2×#10622598C211yesmaximal, characteristic, complemented
16#13070973C211yesmaximal, characteristic, complemented
17C2×C11×#537C211yesmaximal, characteristic
18C22×C11×#41C2211yescharacteristic
19C22×C11×#41C2211yescharacteristic
20C11×#537C4116yescomplemented
21C2×C11×C22⋊Q8C2212yes—
22C2×C11×C22⋊Q8C2212yes—
23C2×C11×#121C2212yes—
24C2×C11×#121C2214yes—
25C2×C11×#121C2212yes—
26C22×C11×C4⋊C4C2211yescharacteristic
27#10623358—28no—
28#41×Dic11—28no—
29C2×Q8×Dic11C2211yescharacteristic
30C2×Q8×Dic11C2211yescharacteristic
31C2×Q8×Dic11C2212yes—
32C2×D4×Dic11C2212yes—
33C2×D4×Dic11C2211yescharacteristic
34C2×D4×Dic11C2214yes—
35C2×D4×Dic11C2212yes—
36C2×D4×Dic11C2211yescharacteristic
37C2×D4×Dic11C2212yes—
38C2×D4×Dic11C2214yes—
39C2×#66979C2211yescharacteristic
40C2×#66979C2212yes—
41C2×#66979C2212yes—
42C2×#66979C2211yescharacteristic
43C22×C4⋊Dic11C2212yes—
44C22×C4⋊Dic11C2211yescharacteristic
45C22×C4⋊Dic11C2212yes—
46C22×C4×Dic11C2211yescharacteristic
47C22×C4×Dic11C2212yes—
48#10622843C2211yescharacteristic
49#10622843C2211yescharacteristic
50#10622843C2212yes—
51#10622834C2211yescharacteristic
52#10622834C2211yescharacteristic
53#10622834C2212yes—
54#10622834C2214yes—
55#10622833C2212yes—
56#10622833C2212yes—
57#10622833C2214yes—
58#10622833C2214yes—
59#10622833C2214yes—
60#10622825C2212yes—
61#10622825C2212yes—
62C4×C22⋊Dic11C2212yes—
63C4×C22⋊Dic11C2212yes—
64C4×C22⋊Dic11C2214yes—
65C2×C11⋊#95C2212yes—
66#10622598C2214yes—
67#10622598C2212yes—
68#10622598C2212yes—
69#10622598C2212yes—
70#10622598C2212yes—
71#10622594C2214yes—
72#10622594C2214yes—
73C4⋊C4×Dic11C2212yes—
74C4⋊C4×Dic11C2214yes—
75C4⋊C4×Dic11C2212yes—
76C4⋊C4×Dic11C2212yes—
77C4⋊C4×Dic11C2212yes—
78#10622564C2214yes—
79#10622564C2214yes—
80#10622564C2214yes—
81#10622564C2214yes—
82#10622563C2214yes—
83#10622563C2214yes—
84C22⋊C4×Dic11C2214yes—
85C22⋊C4×Dic11C2214yes—
86C2×C11×#41—24no—
87C2×C11×#41—24no—
88C2×C11×#41—24no—
89C2×C11×#41—24no—
90C2×C11×#41C2×C418yescomplemented
91C2×C11×#41C2×C418yescomplemented
92C22×Q8×C11C2311yescharacteristic
93C22×Q8×C11C2311yescharacteristic
94C22×D4×C11C2312yes—
95C22×D4×C11C2312yes—
96C22×D4×C11C2311yescharacteristic
97C22×D4×C11C2311yescharacteristic
98C22×D4×C11C2314yes—
99C23×C4×C11C2312yes—
100C23×C4×C11C2312yes—
101C23×C4×C11C2312yes—
102C23×C4×C11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2312yes—
105C23×Dic11C2312yes—
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2312yes—
108C23×Dic11C2314yes—
109C11×C22⋊Q8C2×C4116yescomplemented
110C11×C22⋊Q8C2×C4116yescomplemented
111C11×#121C2×C4116yescomplemented
112C11×#121C2×C4116yescomplemented
113C11×#121C2×C4132yescomplemented
114C2×C11×C4⋊C4C2×C418yescomplemented
115C2×C11×C4⋊C4C2312yes—
116C2×C11×C4⋊C4C2312yes—
117C2×C11×C4⋊C4C2314yes—
118C2×C11×C22⋊C4C2314yes—
119C2×C11×C22⋊C4C2314yes—
120C2×C22⋊Dic11C2312yes—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2312yes—
123C2×C22⋊Dic11C2312yes—
124C2×C22⋊Dic11C2312yes—
125C2×C22⋊Dic11C2312yes—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2314yes—
128C2×C22⋊Dic11C2312yes—
129C2×C22⋊Dic11C2312yes—
130C2×C22⋊Dic11C2312yes—
131Q8×Dic11—24no—
132Q8×Dic11—24no—
133Q8×Dic11—28no—
134D4×Dic11—28no—
135D4×Dic11—28no—
136D4×Dic11—216no—
137D4×Dic11—24no—
138D4×Dic11—24no—
139D4×Dic11—28no—
140D4×Dic11—48no—
141#66979—24no—
142#66979—28no—
143#66979—28no—
144#66979D418yescomplemented
145C2×C4⋊Dic11—24no—
146C2×C4⋊Dic11—28no—
147C2×C4⋊Dic11—44no—
148C2×C4⋊Dic11C2312yes—
149C2×C4⋊Dic11C2314yes—
150C2×C4⋊Dic11C2314yes—
151C2×C4⋊Dic11C2312yes—
152C2×C4⋊Dic11C2312yes—
153C2×C4⋊Dic11C2312yes—
154C2×C4⋊Dic11C2311yescharacteristic
155C2×C4⋊Dic11C2311yescharacteristic
156C2×C4⋊Dic11C2314yes—
157C2×C4⋊Dic11C2311yescharacteristic
158C2×C4⋊Dic11C2311yescharacteristic
159C2×C4×Dic11—24no—
160C2×C4×Dic11—28no—
161C2×C4×Dic11C2311yescharacteristic
162C2×C4×Dic11C2311yescharacteristic
163C2×C4×Dic11C2312yes—
164C2×C4×Dic11C2312yes—
165C2×C4×Dic11C2311yescharacteristic
166C2×C4×Dic11C2311yescharacteristic
167C2×C4×Dic11C2314yes—
168C2×C4×Dic11C2312yes—
169C2×C4×Dic11C2314yes—
170C2×C4×Dic11C2314yes—
171C2×C4×Dic11C2312yes—
172C11⋊#95C2314yes—
173C11⋊#95C2312yes—
174C11⋊#95C2314yes—
175C11⋊#95C2312yes—
176C11⋊#95C2314yes—
177C11⋊#95C2314yes—
178C11⋊#95C2314yes—
179C11⋊#95C2312yes—
180C11⋊#95C2312yes—
181C11⋊#95C2314yes—
182#34267—111nomaximal, Sylow
183C24×C11C2412yes—
184C24×C11C2412yes—
185C24×C11C2411yescharacteristic
186C11×#41—232no—
187C11×#41—232no—
188C2×Q8×C11—22no—
189C2×Q8×C11—22no—
190C2×Q8×C11—22no—
191C2×Q8×C11—22no—
192C2×Q8×C11C22×C414yes—
193C2×Q8×C11C22×C414yes—
194C2×D4×C11—24no—
195C2×D4×C11—24no—
196C2×D4×C11—24no—
197C2×D4×C11—24no—
198C2×D4×C11—22no—
199C2×D4×C11—22no—
200C2×D4×C11—22no—
201C2×D4×C11—22no—
202C2×D4×C11—44no—
203C2×D4×C11—44no—
204C2×D4×C11C22×C418yes—
205C2×D4×C11C22×C418yes—
206C2×D4×C11C22×C414yes—
207C2×D4×C11C22×C414yes—
208C2×D4×C11C22×C4116yes—
209C22×C4×C11—24no—
210C22×C4×C11—24no—
211C22×C4×C11—24no—
212C22×C4×C11—24no—
213C22×C4×C11—42no—
214C22×C4×C11—42no—
215C22×C4×C11C22×C418yes—
216C22×C4×C11C22×C418yes—
217C22×C4×C11C22×C418yes—
218C22×C4×C11C22×C414yes—
219C22×C4×C11C2×D414yes—
220C22×C4×C11#4114yes—
221C22×C4×C11C2414yes—
222C22×C4×C11C2412yes—
223C22×C4×C11C2412yes—
224C22×C4×C11C2411yescharacteristic
225C22×C4×C11C2411yescharacteristic
226C22×Dic11—24no—
227C22×Dic11—24no—
228C22×Dic11—22no—
229C22×Dic11—24no—
230C22×Dic11—22no—
231C22×Dic11—24no—
232C22×Dic11—28no—
233C22×Dic11—22no—
234C22×Dic11—22no—
235C22×Dic11—24no—
236C22×Dic11—41no—
237C22×Dic11—41no—
238C22×Dic11—42no—
239C22×Dic11—42no—
240C22×Dic11—42no—
241C22×Dic11—44no—
242C22×Dic11—42no—
243C22×Dic11—44no—
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C22×Dic11C2411yescharacteristic
247C22×Dic11C2414yes—
248C22×Dic11C2411yescharacteristic
249C22×Dic11C2412yes—
250C22×Dic11C2412yes—
251C22×Dic11C2411yescharacteristic
252C22×Dic11C2411yescharacteristic
253C11×C4⋊C4C22×C418yes—
254C11×C4⋊C4C22×C418yes—
255C11×C4⋊C4C22×C4116yes—
256C11×C22⋊C4C22×C4116yes—
257C11×C22⋊C4C22×C4116yes—
258C22⋊Dic11—24no—
259C22⋊Dic11—24no—
260C22⋊Dic11—28no—
261C22⋊Dic11—24no—
262C22⋊Dic11—24no—
263C22⋊Dic11—24no—
264C22⋊Dic11—44no—
265C22⋊Dic11—44no—
266C22⋊Dic11—42no—
267C22⋊Dic11—42no—
268C22⋊Dic11C2×D418yes—
269C4⋊Dic11—28no—
270C4⋊Dic11—24no—
271C4⋊Dic11—24no—
272C4⋊Dic11—28no—
273C4⋊Dic11—24no—
274C4⋊Dic11—24no—
275C4⋊Dic11—22no—
276C4⋊Dic11—22no—
277C4⋊Dic11—44no—
278C4⋊Dic11C2×D414yes—
279C4⋊Dic11C2×D414yes—
280C4×Dic11—24no—
281C4×Dic11—24no—
282C4×Dic11—28no—
283C4×Dic11—22no—
284C4×Dic11—22no—
285C4×Dic11—22no—
286C4×Dic11—22no—
287C4×Dic11—24no—
288C4×Dic11—44no—
289C4×Dic11—44no—
290C4×Dic11C2×D418yes—
291C2×#537D1111yescharacteristic
292C2×#520—111no—
293C2×C4×#41—111no—
294#2364—114no—
295#2363—112no—
296#2362—112no—
297#2361—112no—
298#2361—114no—
299#2360—112no—
300#2324—112no—
301#2323—112no—
302#2311—111no—
303C4×C22⋊Q8—112no—
304C4×#121—112no—
305#2297—111no—
306C2×#389—111no—
307#2274—111no—
308C23×C11—21no—
309C23×C11—21no—
310C23×C11—21no—
311C23×C11—21no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11C23×C414yes—
325C23×C11C23×C414yes—
326C23×C11C23×C412yes—
327C23×C11C22×D412yes—
328C23×C11C2×#4112yes—
329C23×C11C2511yescharacteristic
330Q8×C11—28no—
331Q8×C11—28no—
332D4×C11—216no—
333D4×C11—216no—
334D4×C11—28no—
335D4×C11—28no—
336D4×C11—416no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—24no—
342C2×C4×C11—24no—
343C2×C4×C11—216no—
344C2×C4×C11—216no—
345C2×C4×C11—48no—
346C2×C4×C11C4×D4116yescomplemented
347C2×C4×C11C23×C418yes—
348C2×C4×C11C23×C414yes—
349C2×C4×C11C23×C414yes—
350C2×C4×C11C23×C412yes—
351C2×C4×C11C23×C412yes—
352C2×C4×C11C22×D412yes—
353C2×C4×C11C22×D412yes—
354C2×C4×C11C2×#4112yes—
355C2×C4×C11C2×#4112yes—
356C2×Dic11—21no—
357C2×Dic11—21no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—21no—
362C2×Dic11—21no—
363C2×Dic11—22no—
364C2×Dic11—21no—
365C2×Dic11—21no—
366C2×Dic11—24no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—24no—
371C2×Dic11—21no—
372C2×Dic11—22no—
373C2×Dic11—21no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—21no—
377C2×Dic11—21no—
378C2×Dic11—24no—
379C2×Dic11—48no—
380C2×Dic11—48no—
381C2×Dic11—44no—
382C2×Dic11—44no—
383C2×Dic11—88no—
384C2×Dic11—84no—
385C2×Dic11C22×D414yes—
386C2×Dic11C22×D414yes—
387C2×Dic11H(5,𝔽2)12yes—
388C2×Dic112−1+412yes—
389C22×#41C2×D1111yescharacteristic
390C22×#41C2×D1111yescharacteristic
391#537Dic11116yescomplemented
392C2×C22⋊Q8C2×D1112yes—
393C2×C22⋊Q8C2×D1112yes—
394C2×#121C2×D1112yes—
395C2×#121C2×D1112yes—
396C2×#121C2×D1114yes—
397#520—228no—
398C4×#41—228no—
399C2×C4×Q8—112no—
400C2×C4×Q8—111no—
401C2×C4×Q8—111no—
402C2×C4×D4—112no—
403C2×C4×D4—111no—
404C2×C4×D4—112no—
405C2×C4×D4—114no—
406C2×C4×D4—111no—
407C2×C4×D4—112no—
408C2×C4×D4—114no—
409C2×#117—111no—
410C2×#117—111no—
411C2×#117—112no—
412C2×#117—112no—
413C22×C4⋊C4—111no—
414C22×C4⋊C4—112no—
415C22×C4⋊C4—112no—
416C22×C4⋊C4C2×D1111yescharacteristic
417C22×C42—111no—
418C22×C42—112no—
419#391—112no—
420#391—111no—
421#391—111no—
422#390—112no—
423#390—111no—
424#390—114no—
425#390—111no—
426#389—112no—
427#389—114no—
428#389—112no—
429#389—112no—
430#389—112no—
431#388—114no—
432#388—114no—
433#388—114no—
434#388—114no—
435#387—114no—
436#387—114no—
437#386—114no—
438#386—114no—
439#386—112no—
440#386—114no—
441#386—112no—
442#385—114no—
443#385—114no—
444#380—112no—
445#380—112no—
446C4×C4⋊C4—112no—
447C4×C4⋊C4—112no—
448C4×C4⋊C4—112no—
449C4×C4⋊C4—114no—
450C4×C4⋊C4—112no—
451C4×C22⋊C4—112no—
452C4×C22⋊C4—112no—
453C4×C22⋊C4—114no—
454C4×C22⋊C4—114no—
455C4×C22⋊C4—114no—
456C2×#95—112no—
457C22×C11—22no—
458C22×C11—22no—
459C22×C11—22no—
460C22×C11—22no—
461C22×C11—22no—
462C22×C11—22no—
463C22×C11—24no—
464C22×C11—24no—
465C22×C11—24no—
466C22×C11—24no—
467C22×C11—24no—
468C22×C11—24no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11C2×C4×D414yes—
478C22×C11C24×C411yescharacteristic
479C22×C11C23×D411yescharacteristic
480C22×C11C22×#4111yescharacteristic
481C22×C11C2×H(5,𝔽2)11yescharacteristic
482C22×C11C2×2−1+411yescharacteristic
483C22×C11#58511yescharacteristic
484C22×C11#58511yescharacteristic
485C4×C11—24no—
486C4×C11—24no—
487C4×C11—28no—
488C4×C11C2×C4×D414yes—
489C4×C11C2×C4×D414yes—
490Dic11—22no—
491Dic11—24no—
492Dic11—22no—
493Dic11—24no—
494Dic11—41no—
495Dic11—44no—
496Dic11—41no—
497Dic11—42no—
498Dic11—42no—
499C2×#41—24no—
500C2×#41—24no—
501C2×#41—24no—
502C2×#41—24no—
503C2×#41C2×Dic1118yescomplemented
504C2×#41C2×Dic1118yescomplemented
505C22×Q8C22×D1111yescharacteristic
506C22×Q8C22×D1111yescharacteristic
507C22×D4C22×D1112yes—
508C22×D4C22×D1112yes—
509C22×D4C22×D1111yescharacteristic
510C22×D4C22×D1111yescharacteristic
511C22×D4C22×D1114yes—
512C23×C4—111no—
513C23×C4—112no—
514C23×C4—111no—
515C23×C4—112no—
516C23×C4—112no—
517C23×C4—114no—
518C23×C4C22×D1112yes—
519C23×C4C22×D1112yes—
520C23×C4C22×D1112yes—
521C23×C4C22×D1111yescharacteristic
522C22⋊Q8C2×Dic11116yescomplemented
523C22⋊Q8C2×Dic11116yescomplemented
524#121C2×Dic11116yescomplemented
525#121C2×Dic11116yescomplemented
526#121C2×Dic11132yescomplemented
527C4×Q8—228no—
528C4×Q8—224no—
529C4×Q8—224no—
530C4×D4—228no—
531C4×D4—228no—
532C4×D4—228no—
533C4×D4—2216no—
534C4×D4—224no—
535C4×D4—224no—
536C4×D4—448no—
537#117—118no—
538#117—228no—
539#117—228no—
540#117—224no—
541C2×C4⋊C4—111no—
542C2×C4⋊C4—111no—
543C2×C4⋊C4—112no—
544C2×C4⋊C4—112no—
545C2×C4⋊C4—114no—
546C2×C4⋊C4—114no—
547C2×C4⋊C4—112no—
548C2×C4⋊C4—112no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—114no—
552C2×C4⋊C4—228no—
553C2×C4⋊C4—224no—
554C2×C4⋊C4—444no—
555C2×C4⋊C4C2×Dic1118yescomplemented
556C2×C4⋊C4C22×D1112yes—
557C2×C4⋊C4C22×D1112yes—
558C2×C4⋊C4C22×D1114yes—
559C2×C22⋊C4—112no—
560C2×C22⋊C4—112no—
561C2×C22⋊C4—114no—
562C2×C22⋊C4—112no—
563C2×C22⋊C4—112no—
564C2×C22⋊C4—112no—
565C2×C22⋊C4—112no—
566C2×C22⋊C4—114no—
567C2×C22⋊C4—114no—
568C2×C22⋊C4—112no—
569C2×C22⋊C4—112no—
570C2×C22⋊C4C22×D1114yes—
571C2×C22⋊C4C22×D1114yes—
572C2×C42—112no—
573C2×C42—111no—
574C2×C42—114no—
575C2×C42—112no—
576C2×C42—112no—
577C2×C42—111no—
578C2×C42—111no—
579C2×C42—112no—
580C2×C42—111no—
581C2×C42—114no—
582C2×C42—114no—
583C2×C42—228no—
584C2×C42—224no—
585#95—114no—
586#95—114no—
587#95—112no—
588#95—114no—
589#95—112no—
590#95—114no—
591#95—114no—
592#95—112no—
593#95—112no—
594#95—114no—
595C2×C11—24no—
596C2×C11—44no—
597C2×C11—44no—
598C2×C11C22×C4×D411yescharacteristic
599C2×C11C4×H(5,𝔽2)11yescharacteristic
600C2×C11C4×2−1+411yescharacteristic
601C2×C11#348811yescharacteristic
602C2×C11#348911yescharacteristic
603C2×C11#351111yescharacteristic
604C2×C11#351211yescharacteristic
605C24C23×D1112yes—
606C24C23×D1112yes—
607C24C23×D1111yescharacteristic
608#41—232no—
609#41—232no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—22no—
613C2×Q8—22no—
614C2×Q8C22×Dic1114yes—
615C2×Q8C22×Dic1114yes—
616C2×D4—24no—
617C2×D4—24no—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—44no—
625C2×D4—44no—
626C2×D4C22×Dic1118yes—
627C2×D4C22×Dic1118yes—
628C2×D4C22×Dic1114yes—
629C2×D4C22×Dic1114yes—
630C2×D4C22×Dic11116yes—
631C22×C4—24no—
632C22×C4—24no—
633C22×C4—24no—
634C22×C4—24no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—111no—
638C22×C4—112no—
639C22×C4—112no—
640C22×C4—111no—
641C22×C4—112no—
642C22×C4—112no—
643C22×C4—111no—
644C22×C4—114no—
645C22×C4—111no—
646C22×C4—224no—
647C22×C4—224no—
648C22×C4—222no—
649C22×C4—224no—
650C22×C4—224no—
651C22×C4—222no—
652C22×C4—228no—
653C22×C4—222no—
654C22×C4—222no—
655C22×C4—224no—
656C22×C4—442no—
657C22×C4—441no—
658C22×C4—442no—
659C22×C4—441no—
660C22×C4—442no—
661C22×C4—444no—
662C22×C4—444no—
663C22×C4—442no—
664C22×C4D4×D1114yes—
665C22×C4#434114yes—
666C22×C4C22×Dic1118yes—
667C22×C4C22×Dic1118yes—
668C22×C4C22×Dic1118yes—
669C22×C4C22×Dic1114yes—
670C22×C4C23×D1114yes—
671C22×C4C23×D1112yes—
672C22×C4C23×D1112yes—
673C22×C4C23×D1111yescharacteristic
674C22×C4C23×D1111yescharacteristic
675C4⋊C4—114no—
676C4⋊C4—114no—
677C4⋊C4—228no—
678C4⋊C4—228no—
679C4⋊C4—224no—
680C4⋊C4—224no—
681C4⋊C4—224no—
682C4⋊C4—224no—
683C4⋊C4—222no—
684C4⋊C4—222no—
685C4⋊C4—444no—
686C4⋊C4C22×Dic1118yes—
687C4⋊C4C22×Dic1118yes—
688C4⋊C4C22×Dic11116yes—
689C22⋊C4—118no—
690C22⋊C4—224no—
691C22⋊C4—228no—
692C22⋊C4—224no—
693C22⋊C4—224no—
694C22⋊C4—224no—
695C22⋊C4—224no—
696C22⋊C4—444no—
697C22⋊C4—442no—
698C22⋊C4—442no—
699C22⋊C4—444no—
700C22⋊C4C22×Dic11116yes—
701C22⋊C4C22×Dic11116yes—
702C42—118no—
703C42—224no—
704C42—224no—
705C42—228no—
706C42—222no—
707C42—222no—
708C42—222no—
709C42—222no—
710C42—224no—
711C42—444no—
712C42—444no—
713C11#3426711yescharacteristic, complemented, Sylow
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23C2×D4×D1112yes—
731C23C2×#434112yes—
732C23C23×Dic1114yes—
733C23C23×Dic1114yes—
734C23C23×Dic1112yes—
735C23C24×D1111yescharacteristic
736Q8—28no—
737Q8—28no—
738D4—216no—
739D4—216no—
740D4—28no—
741D4—28no—
742D4—416no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—216no—
750C2×C4—216no—
751C2×C4—48no—
752C2×C4—114no—
753C2×C4—114no—
754C2×C4—112no—
755C2×C4—112no—
756C2×C4—221no—
757C2×C4—221no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—221no—
761C2×C4—222no—
762C2×C4—221no—
763C2×C4—222no—
764C2×C4—221no—
765C2×C4—221no—
766C2×C4—224no—
767C2×C4—222no—
768C2×C4—222no—
769C2×C4—222no—
770C2×C4—224no—
771C2×C4—221no—
772C2×C4—222no—
773C2×C4—221no—
774C2×C4—222no—
775C2×C4—221no—
776C2×C4—222no—
777C2×C4—221no—
778C2×C4—224no—
779C2×C4—448no—
780C2×C4—448no—
781C2×C4—444no—
782C2×C4—444no—
783C2×C4—888no—
784C2×C4—884no—
785C2×C4D4×Dic11116yescomplemented
786C2×C4C2×D4×D1112yes—
787C2×C4C2×D4×D1112yes—
788C2×C4C2×#434112yes—
789C2×C4C2×#434112yes—
790C2×C4C23×Dic1118yes—
791C2×C4C23×Dic1114yes—
792C2×C4C23×Dic1114yes—
793C2×C4C23×Dic1112yes—
794C2×C4C23×Dic1112yes—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—24no—
802C22—24no—
803C22—24no—
804C22—24no—
805C22—24no—
806C22—24no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22C2×D4×Dic1114yes—
816C22C22×D4×D1111yescharacteristic
817C22C22×#434111yescharacteristic
818C22D11×H(5,𝔽2)11yescharacteristic
819C22#1062345511yescharacteristic
820C22D11×2−1+411yescharacteristic
821C22#1062345711yescharacteristic
822C22C24×Dic1111yescharacteristic
823C4—24no—
824C4—24no—
825C4—28no—
826C4—222no—
827C4—224no—
828C4—222no—
829C4—224no—
830C4—442no—
831C4—441no—
832C4—444no—
833C4—442no—
834C4—441no—
835C4C2×D4×Dic1114yes—
836C4C2×D4×Dic1114yes—
837C2—24no—
838C2—44no—
839C2—44no—
840C2C22×D4×Dic1111yescharacteristic
841C2H(5,𝔽2)×Dic1111yescharacteristic
842C22−1+4×Dic1111yescharacteristic
843C2#1308228011yescharacteristic
844C2#1308229111yescharacteristic
845C2#1308252511yescharacteristic
846C2#1308253711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
Fitting, prime radicalC2×C11×#537C2
socle, cosocleC23×C11C25
hypercenterC2×#537D11
hypocenterC11#34267
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#10623358C2semidirect
2. C2×#41×Dic11C2semidirect
3. #13071668C2semidirect
4. #13071658C2semidirect
5. #13071647C2semidirect
6. #13071636C2semidirect
7. #13071636C2semidirect
8. #13071625C2semidirect
9. #13071311C2semidirect
10. #13071300C2semidirect
11. #13071208C2semidirect
12. C22⋊Q8×Dic11C2semidirect
13. #121×Dic11C2semidirect
14. #13071107C2semidirect
15. C2×#10622598C2semidirect
16. #13070973C2semidirect
20. C11×#537C4semidirect
90. C2×C11×#41C2×C4semidirect
91. C2×C11×#41C2×C4semidirect
109. C11×C22⋊Q8C2×C4semidirect
110. C11×C22⋊Q8C2×C4semidirect
111. C11×#121C2×C4semidirect
112. C11×#121C2×C4semidirect
113. C11×#121C2×C4semidirect
114. C2×C11×C4⋊C4C2×C4semidirect
144. #66979D4semidirect
346. C2×C4×C11C4×D4semidirect
391. #537Dic11semidirect
503. C2×#41C2×Dic11semidirect
504. C2×#41C2×Dic11semidirect
522. C22⋊Q8C2×Dic11semidirect
523. C22⋊Q8C2×Dic11semidirect
524. #121C2×Dic11semidirect
525. #121C2×Dic11semidirect
526. #121C2×Dic11semidirect
555. C2×C4⋊C4C2×Dic11semidirect
713. C11#34267semidirect
785. C2×C4D4×Dic11semidirect

Maximal subgroups

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

subgroupindex
C2×#106233582
C2×#41×Dic112
#130716682
#130716582
#130716472
#130716362
#130716252
#130713112
#130713002
#130712082
C22⋊Q8×Dic112
#121×Dic112
#130711072
C2×#106225982
#130709732
C2×C11×#5372
#3426711