Finite Group Databasebeta

← #14916620

Subgroups — #14916620

Order 2816.

2610 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623079C211yesmaximal, characteristic
2#13071785C214yesmaximal, complemented
3#13071703C212yesmaximal, complemented
4#13071677C212yesmaximal, complemented
5#13071567C211yesmaximal, characteristic, complemented
6#13071566C212yesmaximal, complemented
7C4⋊C4×D44C211yesmaximal, characteristic, complemented
8D4×C4⋊Dic11C211yesmaximal, characteristic, complemented
9#13071512C212yesmaximal, complemented
10#13071312C212yesmaximal, complemented
11#13071310C212yesmaximal, complemented
12#13071304C214yesmaximal, complemented
13#13071205C212yesmaximal, complemented
14#13071204C212yesmaximal, complemented
15#13071021C211yesmaximal, characteristic, complemented
16#13071020C211yesmaximal, characteristic, complemented
17C11×#2354C211yesmaximal, characteristic, complemented
18C22×#4339C2212yes—
19C2×C4×D4×C11C2211yescharacteristic
20C2×C11×#117C2212yes—
21C2×#66993C2211yescharacteristic
22C2×#66991C2211yescharacteristic
23C2×D4×Dic11C2212yes—
24C2×C4×C22⋊D11C2212yes—
25C22×C4⋊Dic11C2212yes—
26#10623079C4116yescomplemented
27C2×#66948C2211yescharacteristic
28C2×#66945C2212yes—
29C2×#66945C2212yes—
30C2×C4⋊C4×D11C2212yes—
31C2×#66941C2211yescharacteristic
32C2×#66938C2212yes—
33C2×#66937C2212yes—
34C2×(C22⋊D11)⋊C4C2214yes—
35C2×C4×D44C2212yes—
36C2×C4×D44C2211yescharacteristic
37C2×#66925C2212yes—
38C2×C42×D11C2211yescharacteristic
39C11×#390C2212yes—
40C11×#388C2214yes—
41C11×#384C2211yescharacteristic
42C11×#380C2212yes—
43C4×C11×C4⋊C4C2212yes—
44C4×C11×C4⋊C4C2211yescharacteristic
45#10622825C2212yes—
46#10622603C2214yes—
47#10622601C2212yes—
48#10622600C2211yescharacteristic
49#10622600C2212yes—
50#10622600C2212yes—
51#10622600C2212yes—
52#10622600C2211yescharacteristic
53#10622600C2212yes—
54#10622598C2212yes—
55#10622590C2212yes—
56#10622589C2211yescharacteristic
57#10622589C2211yescharacteristic
58C4⋊C4×Dic11C2212yes—
59C4⋊C4×Dic11C2212yes—
60C4⋊C4×Dic11C2212yes—
61#10622571C2214yes—
62#10622571C2214yes—
63#10622570C2214yes—
64#10622570C2214yes—
65#10622569C2214yes—
66#10622563C2214yes—
67#10622559C2214yes—
68#10622557C2214yes—
69#10622553C2214yes—
70#10622552C2214yes—
71#10622548C2211yescharacteristic
72C4×C4⋊Dic11C2211yescharacteristic
73C4×Dic11⋊C4C2212yes—
74C4×Dic11⋊C4C2214yes—
75#10622542C2214yes—
76#10622541C2212yes—
77#10622281C2214yes—
78#10622281C2214yes—
79#10622280C2212yes—
80#10622278C2214yes—
81#10622263C2212yes—
82#10622260C2214yes—
83#10622259C2214yes—
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11C2312yes—
86C22×C22⋊D11C2312yes—
87C22×C22⋊D11C2312yes—
88C22×C22⋊D11C2312yes—
89C23×Dic11C2314yes—
90C2×#4339—44no—
91C2×#4339—44no—
92C2×#4339C2×C4116yescomplemented
93C22×D44C2311yescharacteristic
94C22×D44C2312yes—
95C22×C4×D11C2311yescharacteristic
96C22×C4×D11C2311yescharacteristic
97C22×C4×D11C2311yescharacteristic
98C22×C4×D11C2312yes—
99C22×C4×D11C2314yes—
100C22×Dic22C2312yes—
101C4×D4×C11C2×C418yescomplemented
102C11×#117—44no—
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2312yes—
105C2×C11×C4⋊C4C2312yes—
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2312yes—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C22⋊C4C2314yes—
110C2×C11×C22⋊C4C2314yes—
111C2×C11×C22⋊C4C2312yes—
112C2×C42×C11C2312yes—
113C2×C42×C11C2314yes—
114C2×C42×C11C2311yescharacteristic
115C2×C22⋊Dic11C2314yes—
116C2×C22⋊Dic11C2312yes—
117#66993C2×C418yes—
118#66991C2×C418yescomplemented
119D4×Dic11—44no—
120C4×C22⋊D11C2×C4116yescomplemented
121C2×(C2×D11)⋊C4C2312yes—
122C2×(C2×D11)⋊C4C2312yes—
123C2×(C2×D11)⋊C4C2314yes—
124C2×(C2×D11)⋊C4C2314yes—
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2312yes—
128C2×(C2×D11)⋊C4C2312yes—
129C2×C4⋊Dic11—44no—
130C2×C4⋊Dic11C2312yes—
131C2×C4⋊Dic11C2312yes—
132C2×C4⋊Dic11C2311yescharacteristic
133C2×C4⋊Dic11C2311yescharacteristic
134C2×C4⋊Dic11C2314yes—
135C2×C4⋊Dic11C2312yes—
136C2×C4⋊Dic11C2311yescharacteristic
137C2×Dic11⋊C4C2312yes—
138C2×Dic11⋊C4C2312yes—
139C2×Dic11⋊C4C2312yes—
140C2×Dic11⋊C4C2312yes—
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2312yes—
143C2×C4×Dic11C2312yes—
144C2×C4×Dic11C2314yes—
145C2×C4×Dic11C2314yes—
146C2×C4×Dic11C2311yescharacteristic
147C2×C4×Dic11C2311yescharacteristic
148C2×C4×Dic11C2311yescharacteristic
149#66948C2×C418yescomplemented
150#66945—44no—
151#66945—44no—
152C4⋊C4×D11—44no—
153#66941C2×C418yescomplemented
154#66938C2×C4116yescomplemented
155#66937C2×C4116yescomplemented
156(C22⋊D11)⋊C4—48no—
157C4×D44—44no—
158C4×D44C2×C418yescomplemented
159#66925—44no—
160C42×D11C2×C418yescomplemented
161C11×#95C2314yes—
162C11×#95C2312yes—
163C11⋊#95C2312yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C11⋊#95C2314yes—
167C11⋊#95C2312yes—
168C11⋊#95C2312yes—
169C11⋊#95C2314yes—
170C11⋊#95C2314yes—
171#34368—111nomaximal, Sylow
172C24×C11C2412yes—
173C23×D11C2411yescharacteristic
174C23×D11C2412yes—
175C2×D4×C11—22no—
176C2×D4×C11—22no—
177C2×D4×C11C22×C414yes—
178C22×C4×C11—24no—
179C22×C4×C11—24no—
180C22×C4×C11C22×C418yes—
181C22×C4×C11C2414yes—
182C22×C4×C11C2412yes—
183C22×C4×C11C2412yes—
184C22×C4×C11C2411yescharacteristic
185C22×C4×C11C2412yes—
186C22×C4×C11C2411yescharacteristic
187C22×C4×C11C2411yescharacteristic
188C2×C22⋊D11—24no—
189C2×C22⋊D11—24no—
190C2×C22⋊D11—42no—
191C2×C22⋊D11—42no—
192C2×C22⋊D11—42no—
193C2×C22⋊D11—42no—
194C2×C22⋊D11C22×C418yes—
195C2×C22⋊D11C22×C418yes—
196C2×C22⋊D11C22×C418yes—
197C22×Dic11—44no—
198C22×Dic11—44no—
199C22×Dic11—44no—
200C22×Dic11C2412yes—
201C22×Dic11C2412yes—
202C22×Dic11C2414yes—
203C22×Dic11C2411yescharacteristic
204C22×Dic11C2411yescharacteristic
205C22×Dic11C2412yes—
206C22×Dic11C2411yescharacteristic
207#4339—432no—
208C2×D44—22no—
209C2×D44—22no—
210C2×D44—42no—
211C2×D44—42no—
212C2×D44C22×C414yes—
213C2×D44C22×C418yes—
214C2×C4×D11—22no—
215C2×C4×D11—22no—
216C2×C4×D11—22no—
217C2×C4×D11—24no—
218C2×C4×D11—24no—
219C2×C4×D11—22no—
220C2×C4×D11—22no—
221C2×C4×D11—22no—
222C2×C4×D11—44no—
223C2×C4×D11—44no—
224C2×C4×D11—44no—
225C2×C4×D11C22×C414yes—
226C2×C4×D11C22×C414yes—
227C2×C4×D11C22×C414yes—
228C2×C4×D11C22×C418yes—
229C2×Dic22—42no—
230C2×Dic22—42no—
231C2×Dic22C22×C418yes—
232C11×C4⋊C4—22no—
233C11×C4⋊C4—24no—
234C11×C4⋊C4—22no—
235C11×C4⋊C4—24no—
236C11×C4⋊C4—42no—
237C11×C4⋊C4C22×C414yes—
238C11×C22⋊C4—44no—
239C11×C22⋊C4—44no—
240C11×C22⋊C4C22×C418yes—
241C42×C11—24no—
242C42×C11—44no—
243C42×C11C22×C414yes—
244C22⋊Dic11—44no—
245C22⋊Dic11C22×C418yes—
246(C2×D11)⋊C4—42no—
247(C2×D11)⋊C4—42no—
248(C2×D11)⋊C4—44no—
249(C2×D11)⋊C4—44no—
250(C2×D11)⋊C4—44no—
251(C2×D11)⋊C4—44no—
252(C2×D11)⋊C4C22×C418yes—
253(C2×D11)⋊C4C22×C418yes—
254C4⋊Dic11—24no—
255C4⋊Dic11—24no—
256C4⋊Dic11—22no—
257C4⋊Dic11—22no—
258C4⋊Dic11—42no—
259C4⋊Dic11—44no—
260C4⋊Dic11C22×C414yes—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—42no—
264Dic11⋊C4—42no—
265Dic11⋊C4—44no—
266Dic11⋊C4C22×C418yes—
267C4×Dic11—28no—
268C4×Dic11—24no—
269C4×Dic11—44no—
270C4×Dic11C22×C414yes—
271C4×Dic11C22×C414yes—
272C4×Dic11C22×C414yes—
273C2×#532—111no—
274#2379—114no—
275#2369—112no—
276#2366—112no—
277#2354—111no—
278#2354—112no—
279#2354D1111yescharacteristic, complemented
280D4×C4⋊C4—112no—
281D4×C4⋊C4—111no—
282D4×C4⋊C4—111no—
283#2324—112no—
284#2324—114no—
285#2324—112no—
286#2311—112no—
287#2311—112no—
288#2285—111no—
289#2285—111no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11C23×C414yes—
297C23×C11C2511yescharacteristic
298C22×D11—21no—
299C22×D11—21no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—22no—
303C22×D11—22no—
304C22×D11—21no—
305C22×D11—21no—
306C22×D11—21no—
307C22×D11—21no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11C23×C414yes—
311C22×D11C23×C412yes—
312D4×C11—28no—
313C2×C4×C11—21no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—21no—
317C2×C4×C11—216no—
318C2×C4×C11—24no—
319C2×C4×C11—24no—
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—24no—
327C2×C4×C11C23×C412yes—
328C2×C4×C11C23×C414yes—
329C2×C4×C11C23×C412yes—
330C2×C4×C11C23×C412yes—
331C2×C4×C11H(5,𝔽2)12yes—
332C2×C4×C11H(5,𝔽2)12yes—
333C2×C4×C11H(5,𝔽2)12yes—
334C2×C4×C112−1+412yes—
335C22⋊D11—216no—
336C22⋊D11—48no—
337C22⋊D11—48no—
338C2×Dic11—22no—
339C2×Dic11—21no—
340C2×Dic11—22no—
341C2×Dic11—21no—
342C2×Dic11—21no—
343C2×Dic11—21no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—24no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—24no—
350C2×Dic11—22no—
351C2×Dic11—24no—
352C2×Dic11—22no—
353C2×Dic11—88no—
354C2×Dic11C23×C412yes—
355C2×Dic11C23×C412yes—
356C2×Dic11C23×C414yes—
357C2×Dic11C23×C412yes—
358C2×Dic11H(5,𝔽2)12yes—
359C2×Dic112−1+412yes—
360D44—28no—
361D44—48no—
362C4×D11—216no—
363C4×D11—28no—
364C4×D11—28no—
365C4×D11—28no—
366C4×D11—88no—
367Dic22—48no—
368C22×#41—112no—
369#532—1116no—
370C2×C4⋊Q8—111no—
371C2×#127—111no—
372C2×#124—112no—
373C2×#121—111no—
374C2×#121—111no—
375C2×#121—112no—
376C2×C4×D4—112no—
377C2×C4×D4—112no—
378C2×C4×D4—114no—
379C2×C4×D4—111no—
380C2×C4×D4—112no—
381C2×C4×D4C2×D1111yescharacteristic
382C2×#117—112no—
383C2×#117—112no—
384C2×#117—112no—
385C2×#117C2×D1112yes—
386C22×C4⋊C4—112no—
387C22×C4⋊C4—112no—
388C22×C42—111no—
389#391—114no—
390#391—114no—
391#390—112no—
392#390—114no—
393#390—114no—
394#390—114no—
395#390C2×D1112yes—
396#389—112no—
397#389—112no—
398#389—114no—
399#388—114no—
400#388—114no—
401#388—114no—
402#388C2×D1114yes—
403#386—114no—
404#386—114no—
405#386—114no—
406#386—114no—
407#385—114no—
408#385—114no—
409#385—114no—
410#385—114no—
411#384—111no—
412#384—111no—
413#384—111no—
414#384C2×D1111yescharacteristic
415#382—112no—
416#382—112no—
417#380—112no—
418#380—112no—
419#380—111no—
420#380—111no—
421#380—112no—
422#380—112no—
423#380—112no—
424#380—112no—
425#380C2×D1112yes—
426C4×C4⋊C4—112no—
427C4×C4⋊C4—112no—
428C4×C4⋊C4—112no—
429C4×C4⋊C4—114no—
430C4×C4⋊C4—111no—
431C4×C4⋊C4—112no—
432C4×C4⋊C4C2×D1112yes—
433C4×C4⋊C4C2×D1111yescharacteristic
434C22×C11—24no—
435C22×C11—24no—
436C22×C11—24no—
437C22×C11—42no—
438C22×C11—42no—
439C22×C11—42no—
440C22×C11—42no—
441C22×C11C24×C411yescharacteristic
442C22×C11C2×H(5,𝔽2)11yescharacteristic
443C22×C11C2×H(5,𝔽2)11yescharacteristic
444C22×C11C2×H(5,𝔽2)11yescharacteristic
445C22×C11C2×H(5,𝔽2)11yescharacteristic
446C22×C11C2×2−1+411yescharacteristic
447C22×C11C2×2−1+411yescharacteristic
448C2×D11—22no—
449C2×D11—24no—
450C2×D11—22no—
451C2×D11—22no—
452C2×D11—24no—
453C2×D11—24no—
454C2×D11—41no—
455C2×D11—42no—
456C2×D11—41no—
457C2×D11—42no—
458C2×D11—41no—
459C2×D11—42no—
460C2×D11—42no—
461C2×D11—41no—
462C4×C11—24no—
463C4×C11—22no—
464C4×C11—44no—
465C4×C11—42no—
466C4×C11—42no—
467C4×C11#51814yes—
468C4×C11#52014yes—
469Dic11—22no—
470Dic11—24no—
471Dic11—22no—
472Dic11—42no—
473Dic11—44no—
474Dic11—42no—
475Dic11#52014yes—
476C2×#41—1116no—
477C2×#41—444no—
478C2×#41—444no—
479C22×Q8—112no—
480C22×D4—112no—
481C22×D4—112no—
482C22×D4—112no—
483C22×D4—111no—
484C22×D4—112no—
485C22×D4C22×D1111yescharacteristic
486C23×C4—112no—
487C23×C4—111no—
488C23×C4—111no—
489C23×C4—111no—
490C23×C4—114no—
491C23×C4—114no—
492C23×C4C22×D1112yes—
493C4⋊Q8—118no—
494#127—118no—
495#124—1116no—
496#121—118no—
497#121—118no—
498#121—1116no—
499C4×D4—1116no—
500C4×D4—118no—
501C4×D4—444no—
502C4×D4—448no—
503C4×D4—444no—
504C4×D4C4×D1118yescomplemented
505#117—44no—
506#117—444no—
507#117—444no—
508#117—444no—
509C2×C4⋊C4—112no—
510C2×C4⋊C4—111no—
511C2×C4⋊C4—111no—
512C2×C4⋊C4—112no—
513C2×C4⋊C4—111no—
514C2×C4⋊C4—112no—
515C2×C4⋊C4—112no—
516C2×C4⋊C4—112no—
517C2×C4⋊C4—114no—
518C2×C4⋊C4—114no—
519C2×C4⋊C4—112no—
520C2×C4⋊C4—112no—
521C2×C4⋊C4—112no—
522C2×C4⋊C4—444no—
523C2×C4⋊C4—444no—
524C2×C4⋊C4C22×D1111yescharacteristic
525C2×C4⋊C4C22×D1112yes—
526C2×C4⋊C4C22×D1111yescharacteristic
527C2×C4⋊C4C22×D1112yes—
528C2×C4⋊C4C22×D1112yes—
529C2×C4⋊C4C22×D1111yescharacteristic
530C2×C22⋊C4—112no—
531C2×C22⋊C4—112no—
532C2×C22⋊C4—112no—
533C2×C22⋊C4—114no—
534C2×C22⋊C4—112no—
535C2×C22⋊C4—114no—
536C2×C22⋊C4—112no—
537C2×C22⋊C4—114no—
538C2×C22⋊C4—114no—
539C2×C22⋊C4—114no—
540C2×C22⋊C4C22×D1114yes—
541C2×C22⋊C4C22×D1114yes—
542C2×C22⋊C4C22×D1112yes—
543C2×C42—111no—
544C2×C42—111no—
545C2×C42—111no—
546C2×C42—118no—
547C2×C42—114no—
548C2×C42—112no—
549C2×C42—114no—
550C2×C42C22×D1112yes—
551C2×C42C22×D1114yes—
552C2×C42C22×D1111yescharacteristic
553#95—114no—
554#95—112no—
555#95—112no—
556#95—114no—
557#95—112no—
558#95—114no—
559#95—114no—
560#95—114no—
561#95C22×D1112yes—
562#95C22×D1114yes—
563C2×C11—44no—
564C2×C11C2×#51811yescharacteristic
565C2×C11C2×#52011yescharacteristic
566C2×C11C2×#52011yescharacteristic
567C2×C11#354811yescharacteristic
568C2×C11#354811yescharacteristic
569C2×C11#354911yescharacteristic
570C2×C11#355011yescharacteristic
571D11—42no—
572D11—44no—
573C24—112no—
574C24—111no—
575C24C23×D1112yes—
576#41—4432no—
577C2×Q8—118no—
578C2×Q8—442no—
579C2×Q8—442no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—118no—
583C2×D4—118no—
584C2×D4—118no—
585C2×D4—114no—
586C2×D4—118no—
587C2×D4—224no—
588C2×D4—224no—
589C2×D4—222no—
590C2×D4—222no—
591C2×D4—442no—
592C2×D4—442no—
593C2×D4—442no—
594C2×D4—442no—
595C2×D4—442no—
596C2×D4—442no—
597C2×D4C2×C4×D1114yes—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—111no—
601C22×C4—111no—
602C22×C4—111no—
603C22×C4—112no—
604C22×C4—114no—
605C22×C4—114no—
606C22×C4—114no—
607C22×C4—118no—
608C22×C4—112no—
609C22×C4—112no—
610C22×C4—114no—
611C22×C4—222no—
612C22×C4—222no—
613C22×C4—224no—
614C22×C4—222no—
615C22×C4—224no—
616C22×C4—222no—
617C22×C4—222no—
618C22×C4—222no—
619C22×C4—444no—
620C22×C4—444no—
621C22×C4—444no—
622C22×C4—444no—
623C22×C4—444no—
624C22×C4—444no—
625C22×C4C2×C4×D1118yes—
626C22×C4C23×D1114yes—
627C22×C4C23×D1112yes—
628C22×C4C23×D1112yes—
629C22×C4C23×D1111yescharacteristic
630C22×C4C23×D1112yes—
631C22×C4C23×D1111yescharacteristic
632C22×C4C23×D1111yescharacteristic
633C4⋊C4—22no—
634C4⋊C4—24no—
635C4⋊C4—22no—
636C4⋊C4—24no—
637C4⋊C4—42no—
638C4⋊C4—118no—
639C4⋊C4—114no—
640C4⋊C4—224no—
641C4⋊C4—224no—
642C4⋊C4—222no—
643C4⋊C4—224no—
644C4⋊C4—222no—
645C4⋊C4—224no—
646C4⋊C4—444no—
647C4⋊C4—444no—
648C4⋊C4—442no—
649C4⋊C4—442no—
650C4⋊C4—442no—
651C4⋊C4C2×C4×D1114yes—
652C22⋊C4—44no—
653C22⋊C4—44no—
654C22⋊C4—118no—
655C22⋊C4—118no—
656C22⋊C4—118no—
657C22⋊C4—444no—
658C22⋊C4—442no—
659C22⋊C4—442no—
660C22⋊C4—444no—
661C22⋊C4—444no—
662C22⋊C4—444no—
663C22⋊C4—444no—
664C22⋊C4C2×C4×D1118yes—
665C42—24no—
666C42—44no—
667C42—114no—
668C42—114no—
669C42—114no—
670C42—228no—
671C42—224no—
672C42—444no—
673C42C2×C4×D1114yes—
674C11#3436811yescharacteristic, complemented, Sylow
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—114no—
682C23—112no—
683C23—222no—
684C23—221no—
685C23—221no—
686C23—222no—
687C23—222no—
688C23—221no—
689C23—221no—
690C23—222no—
691C23—221no—
692C23—222no—
693C23—221no—
694C23—222no—
695C23C22×C4×D1114yes—
696C23C24×D1111yescharacteristic
697Q8—448no—
698D4—28no—
699D4—2216no—
700D4—228no—
701D4—448no—
702D4—448no—
703D4—448no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—216no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—112no—
719C2×C4—112no—
720C2×C4—112no—
721C2×C4—112no—
722C2×C4—112no—
723C2×C4—114no—
724C2×C4—228no—
725C2×C4—222no—
726C2×C4—221no—
727C2×C4—221no—
728C2×C4—222no—
729C2×C4—221no—
730C2×C4—221no—
731C2×C4—228no—
732C2×C4—228no—
733C2×C4—2216no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—224no—
738C2×C4—224no—
739C2×C4—222no—
740C2×C4—224no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—888no—
744C2×C4—888no—
745C2×C4C22×C4×D1112yes—
746C2×C4C22×C4×D1114yes—
747C2×C4C22×C4×D1112yes—
748C2×C4C22×C4×D1112yes—
749C2×C4#6703712yes—
750C2×C4#6704212yes—
751C2×C4#6704212yes—
752C2×C4#6704312yes—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—222no—
761C22—224no—
762C22—222no—
763C22—224no—
764C22—222no—
765C22—224no—
766C22—442no—
767C22—441no—
768C22—442no—
769C22—441no—
770C22—442no—
771C22—441no—
772C22—442no—
773C22—441no—
774C22C23×C4×D1111yescharacteristic
775C22C2×#6703711yescharacteristic
776C22C2×#6704211yescharacteristic
777C22C2×#6704211yescharacteristic
778C22C2×#6704311yescharacteristic
779C22D11×H(5,𝔽2)11yescharacteristic
780C22D11×2−1+411yescharacteristic
781C4—24no—
782C4—22no—
783C4—44no—
784C4—42no—
785C4—42no—
786C4—114no—
787C4—222no—
788C4—224no—
789C4—222no—
790C4—442no—
791C4—442no—
792C4—444no—
793C4#1062305414yes—
794C4#1062307614yes—
795C2—44no—
796C2—442no—
797C2—444no—
798C2C2×#1062307611yescharacteristic
799C2D11×#52011yescharacteristic
800C2C2×#1062305411yescharacteristic
801C2#1308300911yescharacteristic
802C2#1308301311yescharacteristic
803C2#1308301711yescharacteristic
804C2#1308302911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2354C2
socle, cosocleC23×C11C25
prime radicalC2×#10623079C2
hypercenter#2354D11
hypocenterC11#34368
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. #13071785C2semidirect
3. #13071703C2semidirect
4. #13071677C2semidirect
5. #13071567C2semidirect
6. #13071566C2semidirect
7. C4⋊C4×D44C2semidirect
8. D4×C4⋊Dic11C2semidirect
9. #13071512C2semidirect
10. #13071312C2semidirect
11. #13071310C2semidirect
12. #13071304C2semidirect
13. #13071205C2semidirect
14. #13071204C2semidirect
15. #13071021C2semidirect
16. #13071020C2semidirect
17. C11×#2354C2semidirect
26. #10623079C4semidirect
92. C2×#4339C2×C4semidirect
101. C4×D4×C11C2×C4semidirect
118. #66991C2×C4semidirect
120. C4×C22⋊D11C2×C4semidirect
149. #66948C2×C4semidirect
153. #66941C2×C4semidirect
154. #66938C2×C4semidirect
155. #66937C2×C4semidirect
158. C4×D44C2×C4semidirect
160. C42×D11C2×C4semidirect
279. #2354D11semidirect
504. C4×D4C4×D11semidirect
674. C11#34368semidirect

Maximal subgroups

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

subgroupindex
C2×#106230792
#130717852
#130717032
#130716772
#130715672
#130715662
C4⋊C4×D442
D4×C4⋊Dic112
#130715122
#130713122
#130713102
#130713042
#130712052
#130712042
#130710212
#130710202
C11×#23542
#3436811