Finite Group Databasebeta

← #14914960

Subgroups — #14914960

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×#10623041C211yesmaximal, characteristic
2C2×#10623054C211yesmaximal, characteristic, complemented
3C2×#10623053C211yesmaximal, characteristic, complemented
4#13071666C214yesmaximal, complemented
5#13071656C212yesmaximal, complemented
6#13071645C212yesmaximal, complemented
7#13071634C212yesmaximal, complemented
8#13071630C214yesmaximal, complemented
9#13071623C212yesmaximal, complemented
10#13071310C212yesmaximal, complemented
11#13071299C212yesmaximal, complemented
12#13071204C211yesmaximal, characteristic, complemented
13C4×#66950C212yesmaximal, complemented
14C4×#66948C212yesmaximal, complemented
15#13071104C211yesmaximal, characteristic, complemented
16C2×#10622598C211yesmaximal, characteristic, complemented
17C11×#2274C211yesmaximal, characteristic, complemented
18C22×#4339C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C2×#66983C2214yes—
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2212yes—
26C22×C4×Dic11C2211yescharacteristic
27#10623054—28no—
28#10623053—28no—
29#10623041C4116yescomplemented
30C2×#66950C2212yes—
31C2×#66950C2212yes—
32C2×#66948C2212yes—
33C2×#66948C2212yes—
34C2×#66946C2211yescharacteristic
35C2×#66946C2211yescharacteristic
36C2×#66945C2212yes—
37C2×C4⋊C4×D11C2212yes—
38C2×#66940C2211yescharacteristic
39C2×#66940C2211yescharacteristic
40C2×(C22⋊D11)⋊C4C2212yes—
41C2×(C22⋊D11)⋊C4C2214yes—
42C2×(C22⋊D11)⋊C4C2212yes—
43C2×C4×D44C2212yes—
44C2×C4×D44C2214yes—
45C2×#66925C2212yes—
46C2×C42×D11C2212yes—
47C2×C4×Dic22C2212yes—
48C4×C11×C4⋊C4C2212yes—
49C4×C11×C4⋊C4C2212yes—
50C4×C11×C4⋊C4C2212yes—
51C4×C11×C4⋊C4C2212yes—
52C4×C11×C22⋊C4C2214yes—
53C2×C11⋊#95C2212yes—
54#10622601C2211yescharacteristic
55#10622601C2211yescharacteristic
56#10622600C2212yes—
57#10622600C2212yes—
58#10622598C2212yes—
59#10622598C2212yes—
60#10622598C2212yes—
61#10622598C2212yes—
62#10622587C2211yescharacteristic
63#10622587C2211yescharacteristic
64#10622571C2212yes—
65#10622571C2212yes—
66#10622571C2214yes—
67#10622553C2214yes—
68#10622553C2214yes—
69#10622552C2214yes—
70#10622552C2212yes—
71C4×(C2×D11)⋊C4C2212yes—
72C4×(C2×D11)⋊C4C2212yes—
73C4×(C2×D11)⋊C4C2214yes—
74C4×(C2×D11)⋊C4C2214yes—
75C4×C4⋊Dic11C2214yes—
76#10622542C2212yes—
77#10622541C2214yes—
78#10622283C2214yes—
79#10622283C2214yes—
80#10622281C2214yes—
81#10622281C2214yes—
82#10622278C2214yes—
83#10622278C2214yes—
84#10622266C2214yes—
85#10622266C2214yes—
86C23×C4×C11C2312yes—
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11C2312yes—
89C22×C22⋊D11C2312yes—
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2312yes—
93C2×#4339—24no—
94C2×#4339—24no—
95C2×#4339—24no—
96C2×#4339—24no—
97C2×#4339C2×C418yescomplemented
98C2×#4339C2×C418yescomplemented
99C22×D44C2311yescharacteristic
100C22×D44C2311yescharacteristic
101C22×D44C2314yes—
102C22×C4×D11C2312yes—
103C22×C4×D11C2312yes—
104C22×C4×D11C2312yes—
105C22×C4×D11C2312yes—
106C22×C4×D11C2314yes—
107C22×Dic22C2311yescharacteristic
108C22×Dic22C2311yescharacteristic
109C11×#117—24no—
110C11×#117D418yescomplemented
111C2×C11×C4⋊C4C2×C418yescomplemented
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2312yes—
115C2×C11×C4⋊C4C2312yes—
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C22⋊C4C2312yes—
119C2×C11×C22⋊C4C2312yes—
120C2×C42×C11C2312yes—
121C2×C42×C11C2314yes—
122C2×C42×C11C2314yes—
123C2×C42×C11C2312yes—
124#66983C2×C4132yescomplemented
125C2×(C2×D11)⋊C4C2312yes—
126C2×(C2×D11)⋊C4C2312yes—
127C2×(C2×D11)⋊C4C2312yes—
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2312yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2312yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2312yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×C4⋊Dic11—24no—
137C2×C4⋊Dic11—44no—
138C2×C4⋊Dic11C2312yes—
139C2×C4⋊Dic11C2314yes—
140C2×C4⋊Dic11C2312yes—
141C2×C4⋊Dic11C2314yes—
142C2×C4⋊Dic11C2314yes—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2312yes—
145C2×Dic11⋊C4C2312yes—
146C2×C4×Dic11—24no—
147C2×C4×Dic11C2314yes—
148C2×C4×Dic11C2311yescharacteristic
149C2×C4×Dic11C2312yes—
150C2×C4×Dic11C2312yes—
151C2×C4×Dic11C2311yescharacteristic
152C2×C4×Dic11C2311yescharacteristic
153C2×C4×Dic11C2311yescharacteristic
154#66950C2×C4116yescomplemented
155#66950C2×C4116yescomplemented
156#66948C2×C4116yescomplemented
157#66948C2×C4116yescomplemented
158#66946—24no—
159#66946—24no—
160#66945—28no—
161C4⋊C4×D11—28no—
162#66940—24no—
163#66940—24no—
164(C22⋊D11)⋊C4—28no—
165(C22⋊D11)⋊C4—28no—
166(C22⋊D11)⋊C4—216no—
167C4×D44—28no—
168C4×D44—48no—
169#66925—28no—
170C42×D11—28no—
171C4×Dic22—28no—
172C11×#95C2314yes—
173C11×#95C2314yes—
174C11⋊#95C2312yes—
175C11⋊#95C2312yes—
176C11⋊#95C2314yes—
177C11⋊#95C2314yes—
178C11⋊#95C2314yes—
179C11⋊#95C2314yes—
180C11⋊#95C2312yes—
181C11⋊#95C2312yes—
182#34267—111nomaximal, Sylow
183C24×C11C2411yescharacteristic
184C23×D11C2412yes—
185C23×D11C2412yes—
186C22×C4×C11—42no—
187C22×C4×C11—42no—
188C22×C4×C11C22×C418yes—
189C22×C4×C11C22×C414yes—
190C22×C4×C11C2×D414yes—
191C22×C4×C11#4114yes—
192C22×C4×C11C2412yes—
193C22×C4×C11C2412yes—
194C22×C4×C11C2414yes—
195C22×C4×C11C2412yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2411yescharacteristic
198C22×C4×C11C2411yescharacteristic
199C2×C22⋊D11—24no—
200C2×C22⋊D11—24no—
201C2×C22⋊D11—24no—
202C2×C22⋊D11—24no—
203C2×C22⋊D11C22×C418yes—
204C2×C22⋊D11C22×C418yes—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—24no—
210C22×Dic11—41no—
211C22×Dic11—41no—
212C22×Dic11—42no—
213C22×Dic11—42no—
214C22×Dic11C2411yescharacteristic
215C22×Dic11C2414yes—
216C22×Dic11C2411yescharacteristic
217C22×Dic11C2412yes—
218C22×Dic11C2412yes—
219C22×Dic11C2411yescharacteristic
220C22×Dic11C2411yescharacteristic
221#4339—232no—
222#4339—232no—
223C2×D44—22no—
224C2×D44—22no—
225C2×D44—22no—
226C2×D44—22no—
227C2×D44—44no—
228C2×D44—44no—
229C2×D44C22×C414yes—
230C2×D44C22×C414yes—
231C2×D44C22×C4116yes—
232C2×C4×D11—24no—
233C2×C4×D11—24no—
234C2×C4×D11—24no—
235C2×C4×D11—24no—
236C2×C4×D11—24no—
237C2×C4×D11—24no—
238C2×C4×D11—28no—
239C2×C4×D11—24no—
240C2×C4×D11—24no—
241C2×C4×D11—42no—
242C2×C4×D11—42no—
243C2×C4×D11—44no—
244C2×C4×D11—44no—
245C2×C4×D11C22×C418yes—
246C2×C4×D11C22×C418yes—
247C2×Dic22—22no—
248C2×Dic22—22no—
249C2×Dic22—22no—
250C2×Dic22—22no—
251C2×Dic22C22×C414yes—
252C2×Dic22C22×C414yes—
253C11×C4⋊C4—22no—
254C11×C4⋊C4—22no—
255C11×C4⋊C4C22×C418yes—
256C11×C4⋊C4C22×C418yes—
257C11×C4⋊C4C2×D414yes—
258C11×C4⋊C4C2×D414yes—
259C11×C22⋊C4—24no—
260C11×C22⋊C4C2×D418yes—
261C42×C11—24no—
262C42×C11—44no—
263C42×C11—44no—
264C42×C11C2×D418yes—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4—28no—
270(C2×D11)⋊C4—44no—
271(C2×D11)⋊C4—44no—
272(C2×D11)⋊C4—42no—
273(C2×D11)⋊C4—42no—
274(C2×D11)⋊C4C22×C4116yes—
275(C2×D11)⋊C4C22×C4116yes—
276C4⋊Dic11—28no—
277C4⋊Dic11—24no—
278C4⋊Dic11—24no—
279C4⋊Dic11—44no—
280C4⋊Dic11C22×C4116yes—
281Dic11⋊C4—28no—
282Dic11⋊C4—24no—
283Dic11⋊C4—24no—
284C4×Dic11—28no—
285C4×Dic11—22no—
286C4×Dic11—24no—
287C4×Dic11—24no—
288C4×Dic11—22no—
289C4×Dic11—22no—
290C4×Dic11—22no—
291C2×#537—111no—
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#2274D1111yescharacteristic, complemented
308C23×C11—21no—
309C23×C11—21no—
310C23×C11—21no—
311C23×C11—21no—
312C23×C11C23×C412yes—
313C23×C11C22×D412yes—
314C23×C11C2×#4112yes—
315C23×C11C2511yescharacteristic
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11C23×C414yes—
329C22×D11C23×C414yes—
330C2×C4×C11—24no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—24no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—48no—
343C2×C4×C11C4×D4116yescomplemented
344C2×C4×C11C23×C418yes—
345C2×C4×C11C23×C412yes—
346C2×C4×C11C23×C412yes—
347C2×C4×C11C22×D414yes—
348C2×C4×C11C22×D414yes—
349C2×C4×C11C22×D412yes—
350C2×C4×C11C22×D412yes—
351C2×C4×C11C2×#4112yes—
352C2×C4×C11C2×#4112yes—
353C22⋊D11—216no—
354C22⋊D11—216no—
355C2×Dic11—21no—
356C2×Dic11—21no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—21no—
362C2×Dic11—21no—
363C2×Dic11—21no—
364C2×Dic11—21no—
365C2×Dic11—24no—
366C2×Dic11—24no—
367C2×Dic11—21no—
368C2×Dic11—21no—
369C2×Dic11—21no—
370C2×Dic11—21no—
371C2×Dic11—24no—
372C2×Dic11—44no—
373C2×Dic11—44no—
374C2×Dic11—84no—
375C2×Dic11C23×C414yes—
376C2×Dic11C23×C414yes—
377C2×Dic11H(5,𝔽2)12yes—
378C2×Dic112−1+412yes—
379D44—28no—
380D44—28no—
381D44—416no—
382C4×D11—216no—
383C4×D11—216no—
384C4×D11—48no—
385C4×D11—48no—
386C4×D11—88no—
387Dic22—28no—
388Dic22—28no—
389C22×#41—111no—
390C22×#41—111no—
391#537—1116no—
392C2×C22⋊Q8—112no—
393C2×C22⋊Q8—112no—
394C2×#121—114no—
395C2×#121—112no—
396C2×#121—112no—
397#520—228no—
398C4×#41—228no—
399C2×C4×Q8—111no—
400C2×C4×Q8—111no—
401C2×C4×Q8—112no—
402C2×C4×D4—111no—
403C2×C4×D4—111no—
404C2×C4×D4—112no—
405C2×C4×D4—114no—
406C2×C4×D4—112no—
407C2×C4×D4—112no—
408C2×C4×D4—114no—
409C2×#117—112no—
410C2×#117—112no—
411C2×#117C2×D1111yescharacteristic
412C2×#117C2×D1111yescharacteristic
413C22×C4⋊C4—111no—
414C22×C4⋊C4—112no—
415C22×C4⋊C4—112no—
416C22×C4⋊C4C2×D1111yescharacteristic
417C22×C42—111no—
418C22×C42—112no—
419#391—111no—
420#391—111no—
421#391—112no—
422#390—111no—
423#390—111no—
424#390—112no—
425#390—114no—
426#389—112no—
427#389—112no—
428#389—112no—
429#389—112no—
430#389—114no—
431#388—114no—
432#388—114no—
433#388—114no—
434#388—114no—
435#387—114no—
436#387—114no—
437#386—114no—
438#386—112no—
439#386—112no—
440#386—114no—
441#386—114no—
442#385—114no—
443#385—114no—
444#380—112no—
445#380—112no—
446C4×C4⋊C4—114no—
447C4×C4⋊C4C2×D1112yes—
448C4×C4⋊C4C2×D1112yes—
449C4×C4⋊C4C2×D1112yes—
450C4×C4⋊C4C2×D1112yes—
451C4×C22⋊C4—112no—
452C4×C22⋊C4—114no—
453C4×C22⋊C4—112no—
454C4×C22⋊C4—114no—
455C4×C22⋊C4C2×D1114yes—
456C2×#95—112no—
457C22×C11—22no—
458C22×C11—22no—
459C22×C11—22no—
460C22×C11—22no—
461C22×C11—22no—
462C22×C11—22no—
463C22×C11C2×C4×D414yes—
464C22×C11C24×C411yescharacteristic
465C22×C11C23×D411yescharacteristic
466C22×C11C22×#4111yescharacteristic
467C22×C11C2×H(5,𝔽2)11yescharacteristic
468C22×C11C2×2−1+411yescharacteristic
469C22×C11#58511yescharacteristic
470C22×C11#58511yescharacteristic
471C2×D11—24no—
472C2×D11—24no—
473C2×D11—24no—
474C2×D11—24no—
475C2×D11—24no—
476C2×D11—24no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—42no—
483C2×D11—42no—
484C2×D11—42no—
485C4×C11—28no—
486C4×C11—24no—
487C4×C11—24no—
488C4×C11—42no—
489C4×C11—42no—
490C4×C11C2×C4×D414yes—
491C4×C11C2×C4×D414yes—
492Dic11—24no—
493Dic11—24no—
494Dic11—22no—
495Dic11—22no—
496Dic11—44no—
497Dic11—41no—
498Dic11—41no—
499C2×#41—118no—
500C2×#41—118no—
501C2×#41—224no—
502C2×#41—224no—
503C2×#41—224no—
504C2×#41—224no—
505C22×Q8—111no—
506C22×Q8—111no—
507C22×D4—112no—
508C22×D4—112no—
509C22×D4—111no—
510C22×D4—111no—
511C22×D4—114no—
512C23×C4—112no—
513C23×C4—112no—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4—112no—
517C23×C4—112no—
518C23×C4—112no—
519C23×C4—114no—
520C23×C4C22×D1112yes—
521C23×C4C22×D1111yescharacteristic
522C22⋊Q8—1116no—
523C22⋊Q8—1116no—
524#121—1132no—
525#121—1116no—
526#121—1116no—
527C4×Q8—224no—
528C4×Q8—224no—
529C4×Q8—228no—
530C4×D4—224no—
531C4×D4—224no—
532C4×D4—228no—
533C4×D4—228no—
534C4×D4—2216no—
535C4×D4—228no—
536C4×D4—448no—
537#117—24no—
538#117—228no—
539#117—228no—
540#117D4418yescomplemented
541C2×C4⋊C4—114no—
542C2×C4⋊C4—112no—
543C2×C4⋊C4—112no—
544C2×C4⋊C4—114no—
545C2×C4⋊C4—114no—
546C2×C4⋊C4—112no—
547C2×C4⋊C4—112no—
548C2×C4⋊C4—114no—
549C2×C4⋊C4—224no—
550C2×C4⋊C4—228no—
551C2×C4⋊C4—444no—
552C2×C4⋊C4C4×D1118yescomplemented
553C2×C4⋊C4C22×D1111yescharacteristic
554C2×C4⋊C4C22×D1111yescharacteristic
555C2×C4⋊C4C22×D1112yes—
556C2×C4⋊C4C22×D1112yes—
557C2×C4⋊C4C22×D1111yescharacteristic
558C2×C4⋊C4C22×D1111yescharacteristic
559C2×C22⋊C4—114no—
560C2×C22⋊C4—114no—
561C2×C22⋊C4—112no—
562C2×C22⋊C4—114no—
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×D1112yes—
571C2×C22⋊C4C22×D1112yes—
572C2×C42—111no—
573C2×C42—114no—
574C2×C42—112no—
575C2×C42—111no—
576C2×C42—111no—
577C2×C42—112no—
578C2×C42—111no—
579C2×C42—224no—
580C2×C42—228no—
581C2×C42C22×D1112yes—
582C2×C42C22×D1114yes—
583C2×C42C22×D1114yes—
584C2×C42C22×D1112yes—
585#95—114no—
586#95—114no—
587#95—112no—
588#95—112no—
589#95—114no—
590#95—112no—
591#95—112no—
592#95—114no—
593#95C22×D1114yes—
594#95C22×D1114yes—
595C2×C11—24no—
596C2×C11C22×C4×D411yescharacteristic
597C2×C11C4×H(5,𝔽2)11yescharacteristic
598C2×C11C4×2−1+411yescharacteristic
599C2×C11#348811yescharacteristic
600C2×C11#348911yescharacteristic
601C2×C11#351111yescharacteristic
602C2×C11#351211yescharacteristic
603D11—44no—
604D11—44no—
605C24—112no—
606C24—112no—
607C24C23×D1111yescharacteristic
608#41—2232no—
609#41—2232no—
610C2×Q8—114no—
611C2×Q8—114no—
612C2×Q8—222no—
613C2×Q8—222no—
614C2×Q8—222no—
615C2×Q8—222no—
616C2×D4—118no—
617C2×D4—118no—
618C2×D4—114no—
619C2×D4—114no—
620C2×D4—1116no—
621C2×D4—224no—
622C2×D4—224no—
623C2×D4—224no—
624C2×D4—224no—
625C2×D4—222no—
626C2×D4—222no—
627C2×D4—222no—
628C2×D4—222no—
629C2×D4—444no—
630C2×D4—444no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—111no—
634C22×C4—112no—
635C22×C4—112no—
636C22×C4—111no—
637C22×C4—118no—
638C22×C4—118no—
639C22×C4—111no—
640C22×C4—114no—
641C22×C4—111no—
642C22×C4—224no—
643C22×C4—224no—
644C22×C4—222no—
645C22×C4—222no—
646C22×C4—224no—
647C22×C4—224no—
648C22×C4—224no—
649C22×C4—224no—
650C22×C4—222no—
651C22×C4—222no—
652C22×C4—224no—
653C22×C4—224no—
654C22×C4—224no—
655C22×C4—228no—
656C22×C4—442no—
657C22×C4—442no—
658C22×C4—444no—
659C22×C4—444no—
660C22×C4—441no—
661C22×C4—441no—
662C22×C4—442no—
663C22×C4—442no—
664C22×C4C2×C4×D1118yes—
665C22×C4C2×C4×D1114yes—
666C22×C4C2×D4414yes—
667C22×C4#433914yes—
668C22×C4C23×D1112yes—
669C22×C4C23×D1112yes—
670C22×C4C23×D1114yes—
671C22×C4C23×D1112yes—
672C22×C4C23×D1112yes—
673C22×C4C23×D1111yescharacteristic
674C22×C4C23×D1111yescharacteristic
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—1116no—
678C4⋊C4—228no—
679C4⋊C4—224no—
680C4⋊C4—228no—
681C4⋊C4—224no—
682C4⋊C4—224no—
683C4⋊C4—224no—
684C4⋊C4—444no—
685C4⋊C4C2×C4×D1118yes—
686C4⋊C4C2×C4×D1118yes—
687C4⋊C4C2×D4414yes—
688C4⋊C4C2×D4414yes—
689C22⋊C4—24no—
690C22⋊C4—1116no—
691C22⋊C4—1116no—
692C22⋊C4—224no—
693C22⋊C4—224no—
694C22⋊C4—224no—
695C22⋊C4—224no—
696C22⋊C4—228no—
697C22⋊C4—444no—
698C22⋊C4—442no—
699C22⋊C4—442no—
700C22⋊C4—444no—
701C22⋊C4C2×D4418yes—
702C42—24no—
703C42—44no—
704C42—44no—
705C42—222no—
706C42—222no—
707C42—224no—
708C42—224no—
709C42—222no—
710C42—222no—
711C42—228no—
712C42C2×D4418yes—
713C11#3426711yescharacteristic, complemented, Sylow
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—114no—
719C23—114no—
720C23—222no—
721C23—222no—
722C23—222no—
723C23—222no—
724C23—222no—
725C23—222no—
726C23—222no—
727C23—222no—
728C23—222no—
729C23—222no—
730C23—222no—
731C23—222no—
732C23C22×C4×D1112yes—
733C23C22×D4412yes—
734C23C2×#433912yes—
735C23C24×D1111yescharacteristic
736Q8—228no—
737Q8—228no—
738D4—2216no—
739D4—2216no—
740D4—228no—
741D4—228no—
742D4—4416no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—48no—
756C2×C4—114no—
757C2×C4—114no—
758C2×C4—112no—
759C2×C4—112no—
760C2×C4—221no—
761C2×C4—221no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—221no—
767C2×C4—221no—
768C2×C4—2216no—
769C2×C4—2216no—
770C2×C4—221no—
771C2×C4—221no—
772C2×C4—224no—
773C2×C4—224no—
774C2×C4—221no—
775C2×C4—221no—
776C2×C4—221no—
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×C4C4×D44116yescomplemented
786C2×C4C22×C4×D1118yes—
787C2×C4C22×C4×D1112yes—
788C2×C4C22×C4×D1112yes—
789C2×C4C22×D4414yes—
790C2×C4C22×D4414yes—
791C2×C4C22×D4412yes—
792C2×C4C22×D4412yes—
793C2×C4C2×#433912yes—
794C2×C4C2×#433912yes—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—224no—
802C22—224no—
803C22—224no—
804C22—224no—
805C22—224no—
806C22—224no—
807C22—442no—
808C22—442no—
809C22—442no—
810C22—442no—
811C22—442no—
812C22—442no—
813C22—442no—
814C22—442no—
815C22C2×C4×D4414yes—
816C22C23×C4×D1111yescharacteristic
817C22C23×D4411yescharacteristic
818C22C22×#433911yescharacteristic
819C22D11×H(5,𝔽2)11yescharacteristic
820C22#1062345511yescharacteristic
821C22D11×2−1+411yescharacteristic
822C22#1062345711yescharacteristic
823C4—24no—
824C4—24no—
825C4—28no—
826C4—42no—
827C4—42no—
828C4—222no—
829C4—222no—
830C4—224no—
831C4—224no—
832C4—441no—
833C4—444no—
834C4—441no—
835C4C2×C4×D4414yes—
836C4C2×C4×D4414yes—
837C2—24no—
838C2—444no—
839C2—444no—
840C2C22×C4×D4411yescharacteristic
841C2#1308182011yescharacteristic
842C2#1308182511yescharacteristic
843C2#1308228611yescharacteristic
844C2#1308229711yescharacteristic
845C2#1308251911yescharacteristic
846C2#1308253311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2274C2
socle, cosocleC23×C11C25
prime radicalC2×#10623041C2
hypercenter#2274D11
hypocenterC11#34267
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×#10623053C2semidirect
4. #13071666C2semidirect
5. #13071656C2semidirect
6. #13071645C2semidirect
7. #13071634C2semidirect
8. #13071630C2semidirect
9. #13071623C2semidirect
10. #13071310C2semidirect
11. #13071299C2semidirect
12. #13071204C2semidirect
13. C4×#66950C2semidirect
14. C4×#66948C2semidirect
15. #13071104C2semidirect
16. C2×#10622598C2semidirect
17. C11×#2274C2semidirect
29. #10623041C4semidirect
97. C2×#4339C2×C4semidirect
98. C2×#4339C2×C4semidirect
110. C11×#117D4semidirect
111. C2×C11×C4⋊C4C2×C4semidirect
124. #66983C2×C4semidirect
154. #66950C2×C4semidirect
155. #66950C2×C4semidirect
156. #66948C2×C4semidirect
157. #66948C2×C4semidirect
307. #2274D11semidirect
343. C2×C4×C11C4×D4semidirect
540. #117D44semidirect
552. C2×C4⋊C4C4×D11semidirect
713. C11#34267semidirect
785. C2×C4C4×D44semidirect

Maximal subgroups

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

subgroupindex
C2×#106230412
C2×#106230542
C2×#106230532
#130716662
#130716562
#130716452
#130716342
#130716302
#130716232
#130713102
#130712992
#130712042
C4×#669502
C4×#669482
#130711042
C2×#106225982
C11×#22742
#3426711