Finite Group Databasebeta

← #14914717

Subgroups — #14914717

Order 2816.

3106 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623035C211yesmaximal, characteristic
2C2×#10623054C211yesmaximal, characteristic
3C2×#10623053C211yesmaximal, characteristic
4#13071535C212yesmaximal, complemented
5#13071530C212yesmaximal, complemented
6#13071525C212yesmaximal, complemented
7#13071520C214yesmaximal, complemented
8#13071517C212yesmaximal, complemented
9#13071512C214yesmaximal, complemented
10#13071238C212yesmaximal, complemented
11#13071236C211yesmaximal, characteristic, complemented
12#13071231C212yesmaximal, complemented
13#13071098C211yesmaximal, characteristic, complemented
14#13071097C212yesmaximal, complemented
15C2×#10622598C211yesmaximal, characteristic, complemented
16D11×#389C212yesmaximal, complemented
17C11×#2316C211yesmaximal, characteristic, complemented
18C22×#4339C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C2×C4×C22⋊D11C2214yes—
23C2×#66979C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2212yes—
26C22×C4×Dic11C2211yescharacteristic
27#10623054—28no—
28#10623053—28no—
29#10623035C4116yescomplemented
30C2×#66946C2211yescharacteristic
31C2×#66946C2211yescharacteristic
32C2×#66946C2212yes—
33C2×#66945C2212yes—
34C2×#66945C2212yes—
35C2×C4⋊C4×D11C2212yes—
36C2×C4⋊C4×D11C2214yes—
37C2×C4⋊C4×D11C2212yes—
38C2×#66940C2211yescharacteristic
39C2×#66940C2211yescharacteristic
40C2×#66940C2212yes—
41C2×(C22⋊D11)⋊C4C2212yes—
42C2×(C22⋊D11)⋊C4C2214yes—
43C2×(C22⋊D11)⋊C4C2212yes—
44C2×C4×D44C2212yes—
45C2×#66925C2212yes—
46C2×C42×D11C2212yes—
47C2×C4×Dic22C2212yes—
48C11×#389C2212yes—
49C11×#389C2212yes—
50C11×#389C2212yes—
51C11×#389C2212yes—
52C11×#380C2214yes—
53C2×C11⋊#95C2212yes—
54#10622602C2214yes—
55#10622602C2214yes—
56#10622600C2214yes—
57#10622598C2212yes—
58#10622598C2212yes—
59#10622598C2212yes—
60#10622598C2212yes—
61#10622590C2212yes—
62#10622589C2212yes—
63#10622589C2214yes—
64C4⋊C4×Dic11C2214yes—
65#10622586C2211yescharacteristic
66#10622586C2211yescharacteristic
67#10622586C2211yescharacteristic
68#10622586C2211yescharacteristic
69#10622585C2214yes—
70#10622585C2214yes—
71#10622559C2214yes—
72#10622559C2212yes—
73#10622559C2212yes—
74C4×Dic11⋊C4C2212yes—
75C4×Dic11⋊C4C2212yes—
76#10622541C2212yes—
77#10622541C2212yes—
78#10622281C2214yes—
79#10622281C2214yes—
80#10622280C2214yes—
81D11×#95C2214yes—
82#10622263C2214yes—
83#10622262C2214yes—
84#10622260C2214yes—
85#10622260C2214yes—
86C23×C4×C11C2312yes—
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11C2312yes—
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2312yes—
92C2×#4339C2×C418yes—
93C2×#4339D418yes—
94C2×#4339Q818yes—
95C22×D44C2311yescharacteristic
96C22×C4×D11C2312yes—
97C22×C4×D11C2312yes—
98C22×C4×D11C2314yes—
99C22×C4×D11C2314yes—
100C22×C4×D11C2312yes—
101C22×Dic22C2311yescharacteristic
102C11×#117—24no—
103C11×#117—24no—
104C2×C11×C4⋊C4C2×C418yescomplemented
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2314yes—
110C2×C11×C4⋊C4C2314yes—
111C2×C11×C4⋊C4C2312yes—
112C2×C11×C4⋊C4C2312yes—
113C2×C11×C22⋊C4C2312yes—
114C2×C11×C22⋊C4C2312yes—
115C2×C42×C11C2312yes—
116C2×C42×C11C2312yes—
117C2×C22⋊Dic11C2312yes—
118C4×C22⋊D11C2×C4132yescomplemented
119C2×(C2×D11)⋊C4C2312yes—
120C2×(C2×D11)⋊C4C2312yes—
121C2×(C2×D11)⋊C4C2314yes—
122C2×(C2×D11)⋊C4C2314yes—
123#66979C2×C418yescomplemented
124C2×C4⋊Dic11—24no—
125C2×C4⋊Dic11—44no—
126C2×C4⋊Dic11C2312yes—
127C2×C4⋊Dic11C2314yes—
128C2×C4⋊Dic11C2312yes—
129C2×C4⋊Dic11C2314yes—
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4⋊Dic11C2311yescharacteristic
132C2×Dic11⋊C4C2314yes—
133C2×Dic11⋊C4C2312yes—
134C2×Dic11⋊C4C2312yes—
135C2×Dic11⋊C4C2312yes—
136C2×Dic11⋊C4C2312yes—
137C2×Dic11⋊C4C2314yes—
138C2×Dic11⋊C4C2314yes—
139C2×Dic11⋊C4C2312yes—
140C2×Dic11⋊C4C2312yes—
141C2×Dic11⋊C4C2314yes—
142C2×C4×Dic11—24no—
143C2×C4×Dic11C2314yes—
144C2×C4×Dic11C2311yescharacteristic
145C2×C4×Dic11C2312yes—
146C2×C4×Dic11C2312yes—
147C2×C4×Dic11C2311yescharacteristic
148C2×C4×Dic11C2311yescharacteristic
149C2×C4×Dic11C2311yescharacteristic
150C2×C4×Dic11C2314yes—
151C2×C4×Dic11C2312yes—
152#66946—24no—
153#66946—24no—
154#66946C2×C4116yescomplemented
155#66945—28no—
156#66945C2×C4116yescomplemented
157C4⋊C4×D11—28no—
158C4⋊C4×D11—48no—
159C4⋊C4×D11C2×C4116yescomplemented
160#66940—24no—
161#66940—24no—
162#66940C2×C4116yescomplemented
163(C22⋊D11)⋊C4—28no—
164(C22⋊D11)⋊C4—28no—
165(C22⋊D11)⋊C4—216no—
166C4×D44—28no—
167#66925—28no—
168C42×D11—28no—
169C4×Dic22—28no—
170C11×#95C2314yes—
171C11×#95C2314yes—
172C11⋊#95C2312yes—
173C11⋊#95C2314yes—
174C11⋊#95C2314yes—
175C11⋊#95C2312yes—
176C11⋊#95C2314yes—
177C11⋊#95C2314yes—
178C11⋊#95C2312yes—
179C11⋊#95C2312yes—
180#34250—111nomaximal, Sylow
181C24×C11C2411yescharacteristic
182C23×D11C2412yes—
183C22×C4×C11—42no—
184C22×C4×C11—42no—
185C22×C4×C11C22×C418yes—
186C22×C4×C11C22×C414yes—
187C22×C4×C11C2×D414yes—
188C22×C4×C11C2×Q814yes—
189C22×C4×C11C2412yes—
190C22×C4×C11C2412yes—
191C22×C4×C11C2412yes—
192C22×C4×C11C2412yes—
193C22×C4×C11C2414yes—
194C22×C4×C11C2411yescharacteristic
195C22×C4×C11C2411yescharacteristic
196C2×C22⋊D11C22×C418yes—
197C2×C22⋊D11C2×D418yes—
198C2×C22⋊D11C2×Q818yes—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—24no—
204C22×Dic11—41no—
205C22×Dic11—41no—
206C22×Dic11—42no—
207C22×Dic11—42no—
208C22×Dic11C2411yescharacteristic
209C22×Dic11C2414yes—
210C22×Dic11C2411yescharacteristic
211C22×Dic11C2412yes—
212C22×Dic11C2412yes—
213C22×Dic11C2411yescharacteristic
214C22×Dic11C2411yescharacteristic
215C22×Dic11C2412yes—
216#4339C4⋊C4164yescomplemented
217C2×D44C22×C414yes—
218C2×D44C2×D414yes—
219C2×D44C2×Q814yes—
220C2×C4×D11—24no—
221C2×C4×D11—24no—
222C2×C4×D11—24no—
223C2×C4×D11—24no—
224C2×C4×D11—28no—
225C2×C4×D11—44no—
226C2×C4×D11—44no—
227C2×C4×D11—42no—
228C2×C4×D11—42no—
229C2×C4×D11—44no—
230C2×C4×D11—44no—
231C2×C4×D11C22×C4116yes—
232C2×C4×D11C22×C418yes—
233C2×C4×D11C2×D418yes—
234C2×C4×D11C2×Q818yes—
235C2×Dic22C22×C414yes—
236C2×Dic22C2×D414yes—
237C2×Dic22C2×Q814yes—
238C11×C4⋊C4—22no—
239C11×C4⋊C4—22no—
240C11×C4⋊C4—22no—
241C11×C4⋊C4—22no—
242C11×C4⋊C4—44no—
243C11×C4⋊C4—44no—
244C11×C4⋊C4C22×C418yes—
245C11×C4⋊C4C22×C418yes—
246C11×C22⋊C4—24no—
247C11×C22⋊C4—24no—
248C42×C11—24no—
249C42×C11—24no—
250C22⋊Dic11C22×C418yes—
251(C2×D11)⋊C4—24no—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4—28no—
254(C2×D11)⋊C4C22×C4116yes—
255C4⋊Dic11—28no—
256C4⋊Dic11—24no—
257C4⋊Dic11—24no—
258C4⋊Dic11—44no—
259C4⋊Dic11C22×C414yes—
260C4⋊Dic11C22×C414yes—
261Dic11⋊C4—28no—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266Dic11⋊C4—44no—
267Dic11⋊C4—44no—
268Dic11⋊C4—42no—
269Dic11⋊C4—42no—
270Dic11⋊C4C22×C4116yes—
271C4×Dic11—28no—
272C4×Dic11—24no—
273C4×Dic11—24no—
274C4×Dic11—22no—
275C4×Dic11—22no—
276C4×Dic11—22no—
277C4×Dic11—22no—
278C4×Dic11C22×C4116yes—
279C4×Dic11C22×C418yes—
280C2×#520—111no—
281C2×#520—111no—
282C2×C4×#41—111no—
283#2351—112no—
284Q8×C4⋊C4—112no—
285#2349—112no—
286#2349—114no—
287D4×C4⋊C4—112no—
288D4×C4⋊C4—114no—
289#2317—112no—
290#2317—111no—
291#2316—112no—
292#2316D1111yescharacteristic, complemented
293#2296—112no—
294#2296—111no—
295C2×#389—112no—
296C2×#389—111no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11C23×C412yes—
302C23×C11C22×D412yes—
303C23×C11C22×Q812yes—
304C23×C11C2511yescharacteristic
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11C23×C414yes—
310C22×D11C22×D414yes—
311C22×D11C22×Q814yes—
312C2×C4×C11—24no—
313C2×C4×C11—24no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—48no—
327C2×C4×C11C2×C4⋊C4116yescomplemented
328C2×C4×C11C23×C418yes—
329C2×C4×C11C23×C412yes—
330C2×C4×C11C23×C412yes—
331C2×C4×C11C22×D412yes—
332C2×C4×C11C22×D412yes—
333C2×C4×C11C22×Q812yes—
334C2×C4×C11C22×Q812yes—
335C22⋊D11C2×C4⋊C4132yescomplemented
336C2×Dic11—21no—
337C2×Dic11—21no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—21no—
343C2×Dic11—21no—
344C2×Dic11—21no—
345C2×Dic11—21no—
346C2×Dic11—24no—
347C2×Dic11—24no—
348C2×Dic11—21no—
349C2×Dic11—21no—
350C2×Dic11—21no—
351C2×Dic11—21no—
352C2×Dic11—24no—
353C2×Dic11—44no—
354C2×Dic11—44no—
355C2×Dic11—84no—
356C2×Dic11C23×C414yes—
357C2×Dic11C23×C414yes—
358C2×Dic11C23×C414yes—
359C2×Dic11C22×D414yes—
360C2×Dic11C22×Q814yes—
361C2×Dic11H(5,𝔽2)12yes—
362C2×Dic112−1+412yes—
363D44C2×C4⋊C4116yescomplemented
364C4×D11—416no—
365C4×D11—48no—
366C4×D11—48no—
367C4×D11—88no—
368C4×D11C2×C4⋊C4132yescomplemented
369Dic22C2×C4⋊C4116yescomplemented
370C22×#41—111no—
371#520—1116no—
372#520—228no—
373C4×#41—228no—
374C2×C4×Q8—112no—
375C2×C4×Q8—111no—
376C2×C4×Q8—111no—
377C2×C4×Q8—112no—
378C2×C4×D4—114no—
379C2×C4×D4—112no—
380C2×C4×D4—111no—
381C2×C4×D4—111no—
382C2×C4×D4—112no—
383C2×C4×D4—114no—
384C2×C4×D4—112no—
385C2×C4×D4—112no—
386C2×#117—111no—
387C2×#117—112no—
388C2×#117—112no—
389C2×#117—112no—
390C2×#117C2×D1111yescharacteristic
391C2×#117C2×D1111yescharacteristic
392C22×C4⋊C4—112no—
393C22×C4⋊C4—111no—
394C22×C4⋊C4—112no—
395C22×C4⋊C4—112no—
396C22×C4⋊C4—114no—
397C22×C4⋊C4C2×D1111yescharacteristic
398C22×C42—111no—
399C22×C42—112no—
400#389—111no—
401#389—112no—
402#389—114no—
403#389—111no—
404#389—112no—
405#389—114no—
406#389—112no—
407#389—111no—
408#389—111no—
409#389—112no—
410#389—112no—
411#389—112no—
412#389—114no—
413#389—114no—
414#389C2×D1112yes—
415#389C2×D1112yes—
416#389C2×D1112yes—
417#389C2×D1112yes—
418#385—114no—
419#385—114no—
420#385—114no—
421#385—112no—
422#385—112no—
423#385—114no—
424#385—114no—
425#384—114no—
426#384—112no—
427#382—112no—
428#382—114no—
429#380—114no—
430#380—114no—
431#380C2×D1114yes—
432C4×C4⋊C4—114no—
433C4×C4⋊C4—112no—
434C4×C4⋊C4—112no—
435C4×C4⋊C4—114no—
436C2×#95—112no—
437C2×#95—114no—
438C22×C11—22no—
439C22×C11—22no—
440C22×C11—22no—
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—22no—
444C22×C11C22×C4⋊C414yes—
445C22×C11C24×C411yescharacteristic
446C22×C11C23×D411yescharacteristic
447C22×C11C23×Q811yescharacteristic
448C22×C11C2×H(5,𝔽2)11yescharacteristic
449C22×C11C2×2−1+411yescharacteristic
450C22×C11#58511yescharacteristic
451C22×C11#58511yescharacteristic
452C2×D11—24no—
453C2×D11—24no—
454C2×D11—24no—
455C2×D11—24no—
456C2×D11—24no—
457C2×D11—24no—
458C2×D11C22×C4⋊C418yes—
459C4×C11—28no—
460C4×C11—42no—
461C4×C11—42no—
462C4×C11—42no—
463C4×C11—42no—
464C4×C11C22×C4⋊C414yes—
465C4×C11C22×C4⋊C414yes—
466Dic11—24no—
467Dic11—24no—
468Dic11—22no—
469Dic11—22no—
470Dic11—44no—
471Dic11—41no—
472Dic11—41no—
473Dic11C22×C4⋊C418yes—
474C2×#41—118no—
475C2×#41—118no—
476C2×#41—118no—
477C22×Q8—111no—
478C22×D4—112no—
479C22×D4—111no—
480C23×C4—112no—
481C23×C4—114no—
482C23×C4—111no—
483C23×C4—111no—
484C23×C4—112no—
485C23×C4—112no—
486C23×C4—112no—
487C23×C4—114no—
488C23×C4C22×D1112yes—
489C23×C4C22×D1111yescharacteristic
490C4×Q8—1116no—
491C4×Q8—228no—
492C4×Q8—224no—
493C4×Q8—224no—
494C4×D4—1132no—
495C4×D4—1116no—
496C4×D4—228no—
497C4×D4—228no—
498C4×D4—228no—
499C4×D4—2216no—
500C4×D4—224no—
501C4×D4—224no—
502#117—24no—
503#117—24no—
504#117—118no—
505#117—1116no—
506#117—228no—
507#117—228no—
508C2×C4⋊C4—111no—
509C2×C4⋊C4—114no—
510C2×C4⋊C4—111no—
511C2×C4⋊C4—1116no—
512C2×C4⋊C4—112no—
513C2×C4⋊C4—112no—
514C2×C4⋊C4—114no—
515C2×C4⋊C4—114no—
516C2×C4⋊C4—112no—
517C2×C4⋊C4—112no—
518C2×C4⋊C4—112no—
519C2×C4⋊C4—112no—
520C2×C4⋊C4—114no—
521C2×C4⋊C4—114no—
522C2×C4⋊C4—112no—
523C2×C4⋊C4—114no—
524C2×C4⋊C4—112no—
525C2×C4⋊C4—228no—
526C2×C4⋊C4—224no—
527C2×C4⋊C4—448no—
528C2×C4⋊C4—444no—
529C2×C4⋊C4C4×D1118yescomplemented
530C2×C4⋊C4C22×D1111yescharacteristic
531C2×C4⋊C4C22×D1111yescharacteristic
532C2×C4⋊C4C22×D1111yescharacteristic
533C2×C4⋊C4C22×D1111yescharacteristic
534C2×C4⋊C4C22×D1114yes—
535C2×C4⋊C4C22×D1114yes—
536C2×C4⋊C4C22×D1112yes—
537C2×C4⋊C4C22×D1112yes—
538C2×C22⋊C4—112no—
539C2×C22⋊C4—114no—
540C2×C22⋊C4—112no—
541C2×C22⋊C4—114no—
542C2×C22⋊C4—112no—
543C2×C22⋊C4C22×D1112yes—
544C2×C22⋊C4C22×D1112yes—
545C2×C42—114no—
546C2×C42—112no—
547C2×C42—111no—
548C2×C42—114no—
549C2×C42—112no—
550C2×C42—112no—
551C2×C42—111no—
552C2×C42—111no—
553C2×C42—111no—
554C2×C42—228no—
555C2×C42—224no—
556C2×C42C22×D1112yes—
557C2×C42C22×D1112yes—
558#95—112no—
559#95—114no—
560#95—114no—
561#95—114no—
562#95—112no—
563#95—112no—
564#95—112no—
565#95—114no—
566#95C22×D1114yes—
567#95C22×D1114yes—
568C2×C11—24no—
569C2×C11C23×C4⋊C411yescharacteristic
570C2×C11C4×H(5,𝔽2)11yescharacteristic
571C2×C11C4×2−1+411yescharacteristic
572C2×C11#348811yescharacteristic
573C2×C11#348911yescharacteristic
574C2×C11#350311yescharacteristic
575C2×C11#350411yescharacteristic
576D11—28no—
577C24—112no—
578C24C23×D1111yescharacteristic
579#41—1164no—
580C2×Q8—114no—
581C2×Q8—114no—
582C2×Q8—114no—
583C2×D4—118no—
584C2×D4—118no—
585C2×D4—118no—
586C2×D4—114no—
587C2×D4—114no—
588C2×D4—114no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—112no—
592C22×C4—118no—
593C22×C4—118no—
594C22×C4—118no—
595C22×C4—111no—
596C22×C4—112no—
597C22×C4—112no—
598C22×C4—111no—
599C22×C4—1116no—
600C22×C4—111no—
601C22×C4—114no—
602C22×C4—111no—
603C22×C4—224no—
604C22×C4—224no—
605C22×C4—224no—
606C22×C4—224no—
607C22×C4—228no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4—224no—
613C22×C4—444no—
614C22×C4—444no—
615C22×C4—442no—
616C22×C4—442no—
617C22×C4—444no—
618C22×C4—444no—
619C22×C4—441no—
620C22×C4—441no—
621C22×C4—442no—
622C22×C4—442no—
623C22×C4C2×C4×D1118yes—
624C22×C4C2×C4×D1114yes—
625C22×C4D4×D1114yes—
626C22×C4Q8×D1114yes—
627C22×C4C23×D1112yes—
628C22×C4C23×D1112yes—
629C22×C4C23×D1112yes—
630C22×C4C23×D1112yes—
631C22×C4C23×D1114yes—
632C22×C4C23×D1111yescharacteristic
633C22×C4C23×D1111yescharacteristic
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—44no—
639C4⋊C4—44no—
640C4⋊C4—114no—
641C4⋊C4—1116no—
642C4⋊C4—114no—
643C4⋊C4—228no—
644C4⋊C4—224no—
645C4⋊C4—228no—
646C4⋊C4—224no—
647C4⋊C4—224no—
648C4⋊C4—224no—
649C4⋊C4—224no—
650C4⋊C4—224no—
651C4⋊C4—444no—
652C4⋊C4—444no—
653C4⋊C4—442no—
654C4⋊C4—444no—
655C4⋊C4—442no—
656C4⋊C4C2×C4×D1118yes—
657C4⋊C4C2×C4×D1118yes—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—118no—
661C22⋊C4—1116no—
662C22⋊C4—228no—
663C22⋊C4—224no—
664C22⋊C4—224no—
665C42—24no—
666C42—24no—
667C42—1116no—
668C42—118no—
669C42—224no—
670C42—224no—
671C42—228no—
672C42—222no—
673C42—222no—
674C42—222no—
675C42—222no—
676C11#3425011yescharacteristic, complemented, Sylow
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—114no—
682C23—114no—
683C23—114no—
684C23—222no—
685C23—222no—
686C23—222no—
687C23—222no—
688C23C22×C4×D1112yes—
689C23C2×D4×D1112yes—
690C23C2×Q8×D1112yes—
691C23C24×D1111yescharacteristic
692Q8—1116no—
693D4—1132no—
694D4—1116no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—48no—
710C2×C4—114no—
711C2×C4—114no—
712C2×C4—114no—
713C2×C4—1132no—
714C2×C4—114no—
715C2×C4—114no—
716C2×C4—112no—
717C2×C4—112no—
718C2×C4—221no—
719C2×C4—221no—
720C2×C4—222no—
721C2×C4—222no—
722C2×C4—221no—
723C2×C4—222no—
724C2×C4—222no—
725C2×C4—221no—
726C2×C4—221no—
727C2×C4—221no—
728C2×C4—224no—
729C2×C4—224no—
730C2×C4—221no—
731C2×C4—221no—
732C2×C4—221no—
733C2×C4—221no—
734C2×C4—224no—
735C2×C4—4416no—
736C2×C4—448no—
737C2×C4—448no—
738C2×C4—444no—
739C2×C4—444no—
740C2×C4—888no—
741C2×C4—884no—
742C2×C4C4⋊C4×D11116yescomplemented
743C2×C4C22×C4×D1118yes—
744C2×C4C22×C4×D1112yes—
745C2×C4C22×C4×D1112yes—
746C2×C4C2×D4×D1112yes—
747C2×C4C2×D4×D1112yes—
748C2×C4C2×Q8×D1112yes—
749C2×C4C2×Q8×D1112yes—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—118no—
757C22—224no—
758C22—224no—
759C22—224no—
760C22—224no—
761C22—224no—
762C22—224no—
763C22C2×C4⋊C4×D1114yes—
764C22C23×C4×D1111yescharacteristic
765C22C22×D4×D1111yescharacteristic
766C22C22×Q8×D1111yescharacteristic
767C22D11×H(5,𝔽2)11yescharacteristic
768C22#1062345511yescharacteristic
769C22D11×2−1+411yescharacteristic
770C22#1062345711yescharacteristic
771C4—28no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—42no—
776C4—118no—
777C4—222no—
778C4—222no—
779C4—224no—
780C4—224no—
781C4—441no—
782C4—444no—
783C4—441no—
784C4C2×C4⋊C4×D1114yes—
785C4C2×C4⋊C4×D1114yes—
786C2—24no—
787C2—228no—
788C2C22×C4⋊C4×D1111yescharacteristic
789C2#1308182011yescharacteristic
790C2#1308182511yescharacteristic
791C2#1308228011yescharacteristic
792C2#1308229111yescharacteristic
793C2#1308243111yescharacteristic
794C2#1308243911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2316C2
socle, cosocleC23×C11C25
prime radicalC22×#4339C22
hypercenter#2316D11
hypocenterC11#34250
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2316

Complements

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

NH ≅ G/Ntype
4. #13071535C2semidirect
5. #13071530C2semidirect
6. #13071525C2semidirect
7. #13071520C2semidirect
8. #13071517C2semidirect
9. #13071512C2semidirect
10. #13071238C2semidirect
11. #13071236C2semidirect
12. #13071231C2semidirect
13. #13071098C2semidirect
14. #13071097C2semidirect
15. C2×#10622598C2semidirect
16. D11×#389C2semidirect
17. C11×#2316C2semidirect
29. #10623035C4semidirect
104. C2×C11×C4⋊C4C2×C4semidirect
118. C4×C22⋊D11C2×C4semidirect
123. #66979C2×C4semidirect
154. #66946C2×C4semidirect
156. #66945C2×C4semidirect
159. C4⋊C4×D11C2×C4semidirect
162. #66940C2×C4semidirect
216. #4339C4⋊C4semidirect
292. #2316D11semidirect
327. C2×C4×C11C2×C4⋊C4semidirect
335. C22⋊D11C2×C4⋊C4semidirect
363. D44C2×C4⋊C4semidirect
368. C4×D11C2×C4⋊C4semidirect
369. Dic22C2×C4⋊C4semidirect
529. C2×C4⋊C4C4×D11semidirect
676. C11#34250semidirect
742. C2×C4C4⋊C4×D11semidirect

Maximal subgroups

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

subgroupindex
C2×#106230352
C2×#106230542
C2×#106230532
#130715352
#130715302
#130715252
#130715202
#130715172
#130715122
#130712382
#130712362
#130712312
#130710982
#130710972
C2×#106225982
D11×#3892
C11×#23162
#3425011