Finite Group Databasebeta

← #14914953

Subgroups — #14914953

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×#10623035C211yesmaximal, characteristic, complemented
3C2×C4×#4339C211yesmaximal, characteristic, complemented
4#13071663C214yesmaximal, complemented
5#13071653C212yesmaximal, complemented
6#13071642C212yesmaximal, complemented
7#13071632C214yesmaximal, complemented
8#13071631C212yesmaximal, complemented
9#13071620C212yesmaximal, complemented
10#13071307C212yesmaximal, complemented
11#13071296C212yesmaximal, complemented
12#13071209C211yesmaximal, characteristic, complemented
13#13071146C212yesmaximal, complemented
14#13071124C212yesmaximal, complemented
15#13071106C211yesmaximal, characteristic, complemented
16#13070973C211yesmaximal, characteristic, complemented
17C2×C11×#389C211yesmaximal, characteristic, complemented
18C22×#4339C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2212yes—
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C2×#66983C2214yes—
25C2×C4×C22⋊D11C2212yes—
26C2×C4×C22⋊D11C2214yes—
27C2×C4×C22⋊D11C2212yes—
28C2×#66979C2211yescharacteristic
29C2×#66979C2211yescharacteristic
30#10623041C4116yescomplemented
31C2×#66950C2212yes—
32C2×#66950C2212yes—
33C2×#66948C2212yes—
34C2×#66948C2212yes—
35#10623035—28no—
36C2×#66946C2212yes—
37C2×#66946C2214yes—
38C2×#66945C2212yes—
39C2×C4⋊C4×D11C2212yes—
40C2×#66940C2212yes—
41C4×#4339—28no—
42C2×C4×D44C2211yescharacteristic
43C2×C4×D44C2211yescharacteristic
44C2×#66925C2212yes—
45C2×C42×D11C2212yes—
46C2×C4×Dic22C2211yescharacteristic
47C2×C4×Dic22C2211yescharacteristic
48C11×#389C2212yes—
49C11×#389C2212yes—
50C11×#389C2212yes—
51C11×#389C2212yes—
52C2×C11×#95C2212yes—
53#10622826C2212yes—
54#10622826C2212yes—
55#10622826C2214yes—
56C4×C22⋊Dic11C2214yes—
57#10622603C2214yes—
58#10622603C2214yes—
59#10622602C2214yes—
60#10622602C2214yes—
61#10622601C2212yes—
62#10622601C2214yes—
63#10622600C2212yes—
64#10622600C2212yes—
65C4⋊C4×Dic11C2212yes—
66C4⋊C4×Dic11C2214yes—
67C4⋊C4×Dic11C2212yes—
68C4⋊C4×Dic11C2212yes—
69C4⋊C4×Dic11C2212yes—
70#10622587C2212yes—
71#10622586C2214yes—
72#10622552C2211yescharacteristic
73#10622552C2211yescharacteristic
74C4×(C2×D11)⋊C4C2212yes—
75C4×(C2×D11)⋊C4C2212yes—
76#10622542C2211yescharacteristic
77#10622542C2211yescharacteristic
78#10622282C2214yes—
79#10622282C2214yes—
80#10622279C2214yes—
81#10622279C2214yes—
82#10622278C2214yes—
83#10622278C2214yes—
84#10622267C2214yes—
85#10622267C2214yes—
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2312yes—
89C23×C4×C11C2312yes—
90C23×C4×C11C2311yescharacteristic
91C22×C22⋊D11C2312yes—
92C22×C22⋊D11C2312yes—
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
109C2×C11×C4⋊C4—24no—
110C2×C11×C4⋊C4—44no—
111C2×C11×C4⋊C4C2×C418yescomplemented
112C2×C11×C4⋊C4C2312yes—
113C2×C11×C4⋊C4C2312yes—
114C2×C11×C4⋊C4C2314yes—
115C2×C11×C4⋊C4C2314yes—
116C2×C11×C4⋊C4C2312yes—
117C2×C11×C4⋊C4C2312yes—
118C2×C42×C11—24no—
119C2×C42×C11C2311yescharacteristic
120C2×C42×C11C2311yescharacteristic
121C2×C42×C11C2311yescharacteristic
122C2×C42×C11C2311yescharacteristic
123C2×C22⋊Dic11C2312yes—
124C2×C22⋊Dic11C2312yes—
125#66983C2×C4132yescomplemented
126C4×C22⋊D11—28no—
127C4×C22⋊D11—28no—
128C4×C22⋊D11—216no—
129C2×(C2×D11)⋊C4C2312yes—
130C2×(C2×D11)⋊C4C2312yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2312yes—
133C2×(C2×D11)⋊C4C2312yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2312yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2312yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2314yes—
140#66979—24no—
141#66979D418yescomplemented
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4⋊Dic11C2311yescharacteristic
144C2×C4⋊Dic11C2314yes—
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×Dic11C2312yes—
154C2×C4×Dic11C2314yes—
155C2×C4×Dic11C2314yes—
156C2×C4×Dic11C2312yes—
157#66950C2×C4116yescomplemented
158#66950C2×C4116yescomplemented
159#66948C2×C4116yescomplemented
160#66948C2×C4116yescomplemented
161#66946—28no—
162#66946—48no—
163#66945—28no—
164C4⋊C4×D11—28no—
165#66940—28no—
166C4×D44—24no—
167C4×D44—24no—
168#66925—28no—
169C42×D11—28no—
170C4×Dic22—24no—
171C4×Dic22—24no—
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—22no—
187C22×C4×C11—22no—
188C22×C4×C11—24no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—42no—
192C22×C4×C11—42no—
193C22×C4×C11—41no—
194C22×C4×C11—41no—
195C22×C4×C11—42no—
196C22×C4×C11—42no—
197C22×C4×C11C22×C418yes—
198C22×C4×C11C22×C414yes—
199C22×C4×C11C2×D414yes—
200C22×C4×C11#4114yes—
201C22×C4×C11C2411yescharacteristic
202C22×C4×C11C2414yes—
203C22×C4×C11C2411yescharacteristic
204C22×C4×C11C2414yes—
205C22×C4×C11C2411yescharacteristic
206C22×C4×C11C2411yescharacteristic
207C22×C4×C11C2411yescharacteristic
208C22×C4×C11C2411yescharacteristic
209C2×C22⋊D11—24no—
210C2×C22⋊D11—24no—
211C2×C22⋊D11—24no—
212C2×C22⋊D11—24no—
213C2×C22⋊D11C22×C418yes—
214C2×C22⋊D11C22×C418yes—
215C22×Dic11C2412yes—
216C22×Dic11C2412yes—
217C22×Dic11C2412yes—
218C22×Dic11C2412yes—
219C22×Dic11C2412yes—
220C22×Dic11C2412yes—
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—28no—
235C2×C4×D11—24no—
236C2×C4×D11—24no—
237C2×C4×D11—24no—
238C2×C4×D11—24no—
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—24no—
254C11×C4⋊C4—24no—
255C11×C4⋊C4—28no—
256C11×C4⋊C4—44no—
257C11×C4⋊C4C22×C418yes—
258C11×C4⋊C4C22×C418yes—
259C42×C11—22no—
260C42×C11—22no—
261C42×C11—22no—
262C42×C11—22no—
263C22⋊Dic11—24no—
264C22⋊Dic11C2×D418yes—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—28no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4—24no—
270(C2×D11)⋊C4—44no—
271(C2×D11)⋊C4—42no—
272(C2×D11)⋊C4—42no—
273(C2×D11)⋊C4—44no—
274(C2×D11)⋊C4C22×C4116yes—
275(C2×D11)⋊C4C22×C4116yes—
276C4⋊Dic11—22no—
277C4⋊Dic11—22no—
278C4⋊Dic11C22×C4116yes—
279C4⋊Dic11C2×D414yes—
280C4⋊Dic11C2×D414yes—
281Dic11⋊C4—24no—
282Dic11⋊C4—24no—
283Dic11⋊C4—28no—
284C4×Dic11—24no—
285C4×Dic11—24no—
286C4×Dic11—28no—
287C4×Dic11—24no—
288C4×Dic11—44no—
289C4×Dic11—44no—
290C4×Dic11C2×D418yes—
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×#389D1111yescharacteristic, complemented
307#2274—111no—
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—21no—
331C2×C4×C11—21no—
332C2×C4×C11—24no—
333C2×C4×C11—24no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—24no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—24no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—24no—
345C2×C4×C11—48no—
346C2×C4×C11—44no—
347C2×C4×C11—44no—
348C2×C4×C11—84no—
349C2×C4×C11C4×D4116yescomplemented
350C2×C4×C11C23×C418yes—
351C2×C4×C11C23×C412yes—
352C2×C4×C11C23×C412yes—
353C2×C4×C11C22×D412yes—
354C2×C4×C11C22×D412yes—
355C2×C4×C11C2×#4112yes—
356C2×C4×C11C2×#4112yes—
357C2×C4×C11H(5,𝔽2)12yes—
358C2×C4×C112−1+412yes—
359C22⋊D11—216no—
360C22⋊D11—216no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11C23×C414yes—
376C2×Dic11C23×C414yes—
377C2×Dic11C22×D414yes—
378C2×Dic11C22×D414yes—
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—112no—
400C2×C4×Q8—111no—
401C2×C4×Q8—111no—
402C2×C4×D4—112no—
403C2×C4×D4—114no—
404C2×C4×D4—112no—
405C2×C4×D4—112no—
406C2×C4×D4—114no—
407C2×C4×D4—111no—
408C2×C4×D4—111no—
409C2×#117—111no—
410C2×#117—111no—
411C2×#117—112no—
412C2×#117—112no—
413C22×C4⋊C4—112no—
414C22×C4⋊C4C2×D1111yescharacteristic
415C22×C4⋊C4C2×D1112yes—
416C22×C4⋊C4C2×D1111yescharacteristic
417C22×C42—112no—
418C22×C42C2×D1111yescharacteristic
419#391—112no—
420#391—111no—
421#391—111no—
422#390—112no—
423#390—114no—
424#390—111no—
425#390—111no—
426#389—114no—
427#389C2×D1112yes—
428#389C2×D1112yes—
429#389C2×D1112yes—
430#389C2×D1112yes—
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—112no—
447C4×C4⋊C4—112no—
448C4×C4⋊C4—112no—
449C4×C4⋊C4—114no—
450C4×C4⋊C4—112no—
451C4×C22⋊C4—114no—
452C4×C22⋊C4—112no—
453C4×C22⋊C4—112no—
454C4×C22⋊C4—114no—
455C4×C22⋊C4—114no—
456C2×#95C2×D1112yes—
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—22no—
487C4×C11—22no—
488C4×C11—41no—
489C4×C11—44no—
490C4×C11—41no—
491C4×C11C2×C4×D414yes—
492C4×C11C2×C4×D414yes—
493Dic11—24no—
494Dic11—24no—
495Dic11—24no—
496Dic11—24no—
497Dic11—42no—
498Dic11—42no—
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—112no—
515C23×C4—112no—
516C23×C4—114no—
517C23×C4C22×D1111yescharacteristic
518C23×C4C22×D1111yescharacteristic
519C23×C4C22×D1112yes—
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—228no—
535C4×D4—2216no—
536C4×D4—448no—
537#117—118no—
538#117—228no—
539#117—228no—
540#117—224no—
541C2×C4⋊C4—24no—
542C2×C4⋊C4—44no—
543C2×C4⋊C4—111no—
544C2×C4⋊C4—111no—
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—228no—
552C2×C4⋊C4C4×D1118yescomplemented
553C2×C4⋊C4C22×D1112yes—
554C2×C4⋊C4C22×D1112yes—
555C2×C4⋊C4C22×D1114yes—
556C2×C4⋊C4C22×D1114yes—
557C2×C4⋊C4C22×D1112yes—
558C2×C4⋊C4C22×D1112yes—
559C2×C22⋊C4—112no—
560C2×C22⋊C4—114no—
561C2×C22⋊C4—114no—
562C2×C22⋊C4—112no—
563C2×C22⋊C4—112no—
564C2×C22⋊C4—114no—
565C2×C22⋊C4—112no—
566C2×C22⋊C4—112no—
567C2×C22⋊C4—112no—
568C2×C22⋊C4—114no—
569C2×C22⋊C4—114no—
570C2×C22⋊C4—112no—
571C2×C22⋊C4—112no—
572C2×C42—24no—
573C2×C42—112no—
574C2×C42—114no—
575C2×C42—112no—
576C2×C42—112no—
577C2×C42—112no—
578C2×C42—114no—
579C2×C42—114no—
580C2×C42—228no—
581C2×C42C22×D1111yescharacteristic
582C2×C42C22×D1111yescharacteristic
583C2×C42C22×D1111yescharacteristic
584C2×C42C22×D1111yescharacteristic
585#95—112no—
586#95—114no—
587#95—112no—
588#95—114no—
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—22no—
632C22×C4—22no—
633C22×C4—24no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—112no—
643C22×C4—112no—
644C22×C4—112no—
645C22×C4—112no—
646C22×C4—118no—
647C22×C4—118no—
648C22×C4—112no—
649C22×C4—112no—
650C22×C4—224no—
651C22×C4—224no—
652C22×C4—228no—
653C22×C4—224no—
654C22×C4—224no—
655C22×C4—224no—
656C22×C4—224no—
657C22×C4—224no—
658C22×C4—224no—
659C22×C4—442no—
660C22×C4—442no—
661C22×C4—444no—
662C22×C4—444no—
663C22×C4C2×C4×D1118yes—
664C22×C4C2×C4×D1114yes—
665C22×C4D4×D1114yes—
666C22×C4#434314yes—
667C22×C4C23×D1111yescharacteristic
668C22×C4C23×D1114yes—
669C22×C4C23×D1111yescharacteristic
670C22×C4C23×D1114yes—
671C22×C4C23×D1111yescharacteristic
672C22×C4C23×D1111yescharacteristic
673C22×C4C23×D1111yescharacteristic
674C22×C4C23×D1111yescharacteristic
675C4⋊C4—24no—
676C4⋊C4—24no—
677C4⋊C4—28no—
678C4⋊C4—44no—
679C4⋊C4—1116no—
680C4⋊C4—114no—
681C4⋊C4—114no—
682C4⋊C4—228no—
683C4⋊C4—224no—
684C4⋊C4—224no—
685C4⋊C4—222no—
686C4⋊C4—222no—
687C4⋊C4C2×C4×D1118yes—
688C4⋊C4C2×C4×D1118yes—
689C22⋊C4—118no—
690C22⋊C4—1116no—
691C22⋊C4—1116no—
692C22⋊C4—224no—
693C22⋊C4—224no—
694C22⋊C4—228no—
695C22⋊C4—224no—
696C22⋊C4—224no—
697C22⋊C4—224no—
698C22⋊C4—444no—
699C22⋊C4—442no—
700C22⋊C4—442no—
701C22⋊C4—444no—
702C42—22no—
703C42—22no—
704C42—22no—
705C42—22no—
706C42—118no—
707C42—224no—
708C42—224no—
709C42—228no—
710C42—224no—
711C42—444no—
712C42—444no—
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—
733C23C2×D4×D1112yes—
734C23C2×#434312yes—
735C23C24×D1111yescharacteristic
736Q8—228no—
737Q8—228no—
738D4—2216no—
739D4—2216no—
740D4—228no—
741D4—228no—
742D4—4416no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—24no—
758C2×C4—48no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—84no—
762C2×C4—114no—
763C2×C4—114no—
764C2×C4—114no—
765C2×C4—114no—
766C2×C4—222no—
767C2×C4—222no—
768C2×C4—222no—
769C2×C4—222no—
770C2×C4—222no—
771C2×C4—222no—
772C2×C4—222no—
773C2×C4—222no—
774C2×C4—2216no—
775C2×C4—2216no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—448no—
783C2×C4—448no—
784C2×C4—888no—
785C2×C4#66946116yescomplemented
786C2×C4C22×C4×D1118yes—
787C2×C4C22×C4×D1112yes—
788C2×C4C22×C4×D1112yes—
789C2×C4C2×D4×D1112yes—
790C2×C4C2×D4×D1112yes—
791C2×C4#6703712yes—
792C2×C4C2×#434312yes—
793C2×C4C2×#434312yes—
794C2×C4#6704012yes—
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×#6694614yes—
816C22C23×C4×D1111yescharacteristic
817C22C22×D4×D1111yescharacteristic
818C22C2×#6703711yescharacteristic
819C22C22×#434311yescharacteristic
820C22C2×#6704011yescharacteristic
821C22#1062345311yescharacteristic
822C22#1062345311yescharacteristic
823C4—22no—
824C4—22no—
825C4—28no—
826C4—41no—
827C4—44no—
828C4—41no—
829C4—224no—
830C4—224no—
831C4—224no—
832C4—224no—
833C4—442no—
834C4—442no—
835C4C2×#6694614yes—
836C4C2×#6694614yes—
837C2—24no—
838C2—444no—
839C2—444no—
840C2C22×#6694611yescharacteristic
841C2C4×#6703711yescharacteristic
842C2C4×#6704011yescharacteristic
843C2#1308228111yescharacteristic
844C2#1308229211yescharacteristic
845C2#1308252911yescharacteristic
846C2#1308254011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C11×#389C2
socle, cosocleC23×C11C25
prime radicalC2×#10623041C2
hypercenterC2×#389D11
hypocenterC11#34267
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×#10623035C2semidirect
3. C2×C4×#4339C2semidirect
4. #13071663C2semidirect
5. #13071653C2semidirect
6. #13071642C2semidirect
7. #13071632C2semidirect
8. #13071631C2semidirect
9. #13071620C2semidirect
10. #13071307C2semidirect
11. #13071296C2semidirect
12. #13071209C2semidirect
13. #13071146C2semidirect
14. #13071124C2semidirect
15. #13071106C2semidirect
16. #13070973C2semidirect
17. C2×C11×#389C2semidirect
30. #10623041C4semidirect
97. C2×#4339C2×C4semidirect
98. C2×#4339C2×C4semidirect
111. C2×C11×C4⋊C4C2×C4semidirect
125. #66983C2×C4semidirect
141. #66979D4semidirect
157. #66950C2×C4semidirect
158. #66950C2×C4semidirect
159. #66948C2×C4semidirect
160. #66948C2×C4semidirect
306. C2×#389D11semidirect
349. C2×C4×C11C4×D4semidirect
552. C2×C4⋊C4C4×D11semidirect
713. C11#34267semidirect
785. C2×C4#66946semidirect

Maximal subgroups

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

subgroupindex
C2×#106230412
C2×#106230352
C2×C4×#43392
#130716632
#130716532
#130716422
#130716322
#130716312
#130716202
#130713072
#130712962
#130712092
#130711462
#130711242
#130711062
#130709732
C2×C11×#3892
#3426711