Finite Group Databasebeta

← #15620517

Subgroups — #15620517

Order 2816.

4836 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623453C211yesmaximal, characteristic, complemented
2#13081945C212yesmaximal, complemented
3#13078021C214yesmaximal, complemented
4#13078017C214yesmaximal, complemented
5#13078012C218yesmaximal, complemented
6#13078007C218yesmaximal, complemented
7C2×#10622853C211yesmaximal, characteristic, complemented
8C2×#10622619C212yesmaximal, complemented
9C11×#3449C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C22×C11×#41C2211yescharacteristic, complemented
12#10623453—22no—
13#10623453—22no—
14#10623453—24no—
15#10623453—24no—
16#10623453C2214yes—
17#10623453C2214yes—
18C2×#67043—22no—
19C2×#67042—22no—
20C2×#41×D11—24no—
21C2×#67040—21no—
22C2×#67037—21no—
23C2×#67037C2214yes—
24C22×#4339—22no—
25C22×#4339C2212yes—
26C11×#537—22no—
27C11×#536—21no—
28C11×#536C2212yescomplemented
29C11×#535—21no—
30C11×#535C2212yescomplemented
31C11×#534C2214yescomplemented
32C11×#532—22no—
33C11×#525—22no—
34C11×#525C2214yescomplemented
35C2×C11×#117C2211yescharacteristic, complemented
36#10623364—24no—
37#10623363—24no—
38#10623361—22no—
39#10623359—24no—
40#10623356—22no—
41#10623347C2214yescomplemented
42#10623336C2214yescomplemented
43#10623335C2218yescomplemented
44#10623322C2218yescomplemented
45C2×#66979C2212yescomplemented
46#10622853C2214yescomplemented
47#10622853C2214yescomplemented
48C2×#66898C2214yescomplemented
49#10622666C22132yescomplemented
50#10622645C22132yescomplemented
51#10622619C2218yescomplemented
52#10622619C2218yescomplemented
53C2×#66870C2218yescomplemented
54C2×C11×#41—22no—
55C2×C11×#41—22no—
56C2×C11×#41—22no—
57C2×C11×#41—22no—
58C2×C11×#41—22no—
59C2×C11×#41—22no—
60C2×C11×#41—22no—
61C2×C11×#41—22no—
62C2×C11×#41—21no—
63C2×C11×#41—21no—
64C2×C11×#41—21no—
65C2×C11×#41—21no—
66C2×C11×#41D412yescomplemented
67C2×C11×#41D412yescomplemented
68C2×C11×#41C2312yes—
69C2×C11×#41C2312yes—
70C22×Q8×C11D411yescharacteristic, complemented
71C22×Q8×C11C2311yescharacteristic, complemented
72C22×D4×C11D411yescharacteristic, complemented
73C22×D4×C11C2312yes—
74C22×D4×C11C2312yes—
75C22×D4×C11C2311yescharacteristic, complemented
76C23×C4×C11D412yescomplemented
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2312yescomplemented
79C22×C22⋊D11—24no—
80C22×C22⋊D11C2314yes—
81#67043—28no—
82#67043—28no—
83#67043—28no—
84#67043—28no—
85#67042—28no—
86#67042—28no—
87#67042—28no—
88#67042—28no—
89#41×D11—216no—
90#41×D11—216no—
91#41×D11—216no—
92#41×D11—216no—
93#67040—28no—
94#67040—24no—
95#67040—24no—
96C2×#4343—24no—
97C2×Q8×D11—24no—
98#67037—28no—
99#67037—24no—
100#67037—24no—
101#67037—28no—
102#67037—216no—
103#67037C23116yes—
104C2×#4341—24no—
105C2×#4341—28no—
106C2×D4×D11—24no—
107C2×D4×D11—28no—
108C2×#4339—24no—
109C2×#4339—24no—
110C2×#4339—28no—
111C2×#4339—28no—
112C2×#4339—22no—
113C2×#4339—24no—
114C2×#4339—28no—
115C2×#4339—28no—
116C2×#4339—22no—
117C2×#4339—22no—
118C2×#4339—22no—
119C2×#4339—22no—
120C2×#4339—22no—
121C2×#4339—22no—
122C2×#4339—22no—
123C2×#4339D414yescomplemented
124C2×#4339D414yescomplemented
125C2×#4339C2314yes—
126C2×#4339C2314yes—
127C22×D44—22no—
128C22×D44D412yescomplemented
129C22×C4×D11—24no—
130C22×C4×D11D414yescomplemented
131C22×Dic22—22no—
132C22×Dic22D412yescomplemented
133C11×C4⋊Q8—22no—
134C11×#127—22no—
135C11×#124—22no—
136C11×#124—22no—
137C11×#123—24no—
138C11×#123C2318yescomplemented
139C11×C22⋊Q8—24no—
140C11×C22⋊Q8—24no—
141C11×#121—24no—
142C11×#121—28no—
143C11×#121—24no—
144C11×#120—24no—
145C11×#120C2318yescomplemented
146C4×D4×C11—28no—
147C11×#117—21no—
148C11×#117—21no—
149C11×#117C2312yescomplemented
150C11×#117C2312yescomplemented
151C2×C11×C4⋊C4—21no—
152C2×C11×C22⋊C4C2312yes—
153C2×C42×C11—21no—
154#67006C23116yescomplemented
155C2×C22⋊Dic11C2314yes—
156#67000—24no—
157#66999—28no—
158#66997—24no—
159#66993—24no—
160#66992—216no—
161#66991—28no—
162#66990—28no—
163#66989—24no—
164#66988—28no—
165#66983—28no—
166#66982C23116yescomplemented
167C4×C22⋊D11—216no—
168#66979—22no—
169#66979—22no—
170#66979C2314yescomplemented
171#66979C2314yescomplemented
172C2×C4⋊Dic11—22no—
173#66977—28no—
174C2×C4×Dic11—22no—
175#66898C23116yescomplemented
176#66870C23132yescomplemented
177#60398—111nomaximal, Sylow
178C24×C11C2×D412yes—
179C24×C11C2412yes—
180C24×C11C2411yescharacteristic
181C23×D11—24no—
182C23×D11C2×D414yes—
183C11×#41—24no—
184C11×#41—24no—
185C11×#41—24no—
186C11×#41—24no—
187C11×#41—24no—
188C11×#41—24no—
189C11×#41—24no—
190C11×#41—24no—
191C11×#41—41no—
192C11×#41—42no—
193C11×#41—42no—
194C11×#41—42no—
195C11×#41—41no—
196C11×#41—42no—
197C11×#41—42no—
198C11×#41—41no—
199C11×#41—41no—
200C11×#41—42no—
201C2×Q8×C11—22no—
202C2×Q8×C11—22no—
203C2×Q8×C11—22no—
204C2×Q8×C11—22no—
205C2×Q8×C11—21no—
206C2×Q8×C11—21no—
207C2×Q8×C11C2×D412yes—
208C2×Q8×C11C2×D412yes—
209C2×D4×C11—24no—
210C2×D4×C11—24no—
211C2×D4×C11—24no—
212C2×D4×C11—24no—
213C2×D4×C11—22no—
214C2×D4×C11—22no—
215C2×D4×C11—28no—
216C2×D4×C11—22no—
217C2×D4×C11—22no—
218C2×D4×C11—22no—
219C2×D4×C11—22no—
220C2×D4×C11—21no—
221C2×D4×C11—21no—
222C2×D4×C11C2×D412yes—
223C2×D4×C11C2×D414yes—
224C2×D4×C11C2×D412yes—
225C2×D4×C11C2414yes—
226C22×C4×C11—22no—
227C22×C4×C11—22no—
228C22×C4×C11—22no—
229C22×C4×C11—22no—
230C22×C4×C11—22no—
231C22×C4×C11—24no—
232C22×C4×C11—24no—
233C22×C4×C11—22no—
234C22×C4×C11—22no—
235C22×C4×C11C2×D414yes—
236C22×C4×C11C2×D414yes—
237C22×C4×C11C2×D412yes—
238C22×C4×C11C2×D412yes—
239C22×C4×C11C2×D412yes—
240C22×C4×C11C2×D412yes—
241C22×C4×C11C2×D412yes—
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2412yes—
247C22×C4×C11C2411yescharacteristic
248C22×C4×C11C2411yescharacteristic
249C2×C22⋊D11—28no—
250C2×C22⋊D11—216no—
251C2×C22⋊D11—24no—
252C2×C22⋊D11—24no—
253C2×C22⋊D11—24no—
254C2×C22⋊D11—24no—
255C2×C22⋊D11—216no—
256C2×C22⋊D11—216no—
257C2×C22⋊D11C2×D418yes—
258C2×C22⋊D11C2418yes—
259C22×Dic11—24no—
260C22×Dic11—24no—
261C22×Dic11C2×D414yes—
262#4343—216no—
263#4343—216no—
264Q8×D11—216no—
265Q8×D11—216no—
266#4341—232no—
267#4341—216no—
268#4341—216no—
269#4341—232no—
270D4×D11—232no—
271D4×D11—216no—
272D4×D11—216no—
273D4×D11—232no—
274#4339—216no—
275#4339—216no—
276#4339—216no—
277#4339—216no—
278#4339—216no—
279#4339—24no—
280#4339—24no—
281#4339—24no—
282#4339—24no—
283#4339—24no—
284#4339—24no—
285#4339—24no—
286#4339—24no—
287#4339—24no—
288#4339—24no—
289#4339—216no—
290#4339—24no—
291#4339—24no—
292#4339—24no—
293#4339—24no—
294#4339—24no—
295#4339—24no—
296C2×D44—24no—
297C2×D44—28no—
298C2×D44—28no—
299C2×D44—22no—
300C2×D44—22no—
301C2×D44—22no—
302C2×D44—22no—
303C2×D44C2×D414yes—
304C2×D44C2×D414yes—
305C2×C4×D11—28no—
306C2×C4×D11—216no—
307C2×C4×D11—216no—
308C2×C4×D11—24no—
309C2×C4×D11—24no—
310C2×C4×D11—24no—
311C2×C4×D11—24no—
312C2×C4×D11C2×D418yes—
313C2×C4×D11C2×D418yes—
314C2×Dic22—24no—
315C2×Dic22—28no—
316C2×Dic22—28no—
317C2×Dic22—22no—
318C2×Dic22—22no—
319C2×Dic22—22no—
320C2×Dic22—22no—
321C2×Dic22C2×D414yes—
322C2×Dic22C2×D414yes—
323C11×C4⋊C4—22no—
324C11×C4⋊C4—22no—
325C11×C4⋊C4—28no—
326C11×C22⋊C4—22no—
327C11×C22⋊C4—28no—
328C11×C22⋊C4—28no—
329C11×C22⋊C4C2414yes—
330C42×C11—22no—
331C42×C11—22no—
332C22⋊Dic11—216no—
333C22⋊Dic11—24no—
334C22⋊Dic11C2418yes—
335(C2×D11)⋊C4—216no—
336C4⋊Dic11—24no—
337C4⋊Dic11—24no—
338Dic11⋊C4—216no—
339C4×Dic11—24no—
340C4×Dic11—24no—
341C2×#585—111no—
342#3449—112no—
343#3449D1111yescharacteristic, complemented
344#3028—114no—
345#3027—114no—
346#3026—118no—
347#3025—118no—
348C2×#410—111no—
349C2×#410—112no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11—24no—
353C23×C11—22no—
354C23×C11—81no—
355C23×C11—82no—
356C23×C11—82no—
357C23×C11C22×D412yes—
358C23×C11C22×D412yes—
359C23×C11C22×D414yes—
360C23×C11C22×D411yescharacteristic
361C23×C11C22×D411yescharacteristic
362C23×C11C2511yescharacteristic
363C22×D11—24no—
364C22×D11—216no—
365C22×D11—24no—
366C22×D11—84no—
367C22×D11—88no—
368C22×D11C22×D418yes—
369Q8×C11—24no—
370Q8×C11—24no—
371Q8×C11—41no—
372Q8×C11—41no—
373Q8×C11—42no—
374D4×C11—28no—
375D4×C11—28no—
376D4×C11—24no—
377D4×C11—24no—
378D4×C11—42no—
379D4×C11—42no—
380D4×C11—44no—
381D4×C11—41no—
382D4×C11—41no—
383D4×C11—42no—
384D4×C11—88no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—24no—
388C2×C4×C11—24no—
389C2×C4×C11—24no—
390C2×C4×C11—24no—
391C2×C4×C11—24no—
392C2×C4×C11—24no—
393C2×C4×C11—22no—
394C2×C4×C11—42no—
395C2×C4×C11—44no—
396C2×C4×C11—42no—
397C2×C4×C11—82no—
398C2×C4×C11#12011yescharacteristic
399C2×C4×C11#12012yes—
400C2×C4×C11#12012yes—
401C2×C4×C11#12012yes—
402C2×C4×C11#12011yescharacteristic
403C2×C4×C11#12012yes—
404C2×C4×C11#12012yes—
405C2×C4×C11#12011yescharacteristic
406C2×C4×C11#12011yescharacteristic
407C2×C4×C11#12012yes—
408C2×C4×C11C22×D412yes—
409C2×C4×C11C22×D412yes—
410C2×C4×C11C22×D412yes—
411C2×C4×C11C22×D412yes—
412C2×C4×C11C22×D414yes—
413C2×C4×C11C22×D411yescharacteristic
414C2×C4×C11C22×D411yescharacteristic
415C2×C4×C11C22×D411yescharacteristic
416C2×C4×C11C22×D411yescharacteristic
417C22⋊D11—232no—
418C22⋊D11—28no—
419C22⋊D11—28no—
420C22⋊D11—28no—
421C22⋊D11—28no—
422C22⋊D11—816no—
423C2×Dic11—216no—
424C2×Dic11—24no—
425C2×Dic11—24no—
426C2×Dic11—28no—
427C2×Dic11—84no—
428C2×Dic11C22×D418yes—
429D44—216no—
430D44—24no—
431D44—24no—
432D44—24no—
433D44—24no—
434C4×D11—232no—
435C4×D11—28no—
436C4×D11—28no—
437C4×D11—28no—
438C4×D11—28no—
439Dic22—216no—
440Dic22—24no—
441Dic22—24no—
442Dic22—24no—
443Dic22—24no—
444#585—114no—
445#585—114no—
446#585—224no—
447#585—224no—
448#585—222no—
449#585—222no—
450C2×2−1+4—222no—
451C2×2−1+4—221no—
452C2×H(5,𝔽2)—114no—
453C2×H(5,𝔽2)—222no—
454C2×H(5,𝔽2)—221no—
455C22×#41—112no—
456C22×#41—224no—
457C22×#41—222no—
458C22×#41C2×D1111yescharacteristic
459C22×#41C2×D1111yescharacteristic, complemented
460#537—22no—
461#537—224no—
462#536—21no—
463#536—114no—
464#536—222no—
465#536C2×D1112yescomplemented
466#535—21no—
467#535—114no—
468#535—222no—
469#535C2×D1112yescomplemented
470#534—118no—
471#534C2×D1114yescomplemented
472#532—22no—
473#532—224no—
474#525—22no—
475#525—118no—
476#525—224no—
477#525C2×D1114yescomplemented
478C2×#117—112no—
479C2×#117C2×D1111yescharacteristic, complemented
480#458—1132no—
481B(4,𝔽2)—1132no—
482#410—114no—
483#410—114no—
484#410—118no—
485#410—118no—
486C2×#99—114no—
487C2×#99—118no—
488C22×C11—24no—
489C22×C11—41no—
490C22×C11—42no—
491C22×C11—41no—
492C22×C11—41no—
493C22×C11—42no—
494C22×C11—44no—
495C22×C11—44no—
496C22×C11—44no—
497C22×C11—48no—
498C22×C11—42no—
499C22×C11—82no—
500C22×C11C2×#12011yescharacteristic
501C22×C11C2×#12011yescharacteristic
502C22×C11C2×#12012yes—
503C22×C11C23×D412yes—
504C22×C11C23×D411yescharacteristic
505C2×D11—28no—
506C2×D11—48no—
507C2×D11—48no—
508C2×D11—84no—
509C2×D11—816no—
510C4×C11—24no—
511C4×C11—44no—
512C4×C11—42no—
513C4×C11C2×#12011yescharacteristic
514C4×C11C2×#12011yescharacteristic
515C4×C11C2×#12011yescharacteristic
516C4×C11C2×#12012yes—
517C4×C11C2×#12012yes—
518C4×C11C2×#12011yescharacteristic
519Dic11—28no—
520Dic11—48no—
5212−1+4—228no—
5222−1+4—228no—
5232−1+4—228no—
5242−1+4—228no—
5252−1+4—228no—
5262−1+4—224no—
5272−1+4—224no—
528H(5,𝔽2)—1116no—
529H(5,𝔽2)—2216no—
530H(5,𝔽2)—228no—
531H(5,𝔽2)—228no—
532H(5,𝔽2)—228no—
533H(5,𝔽2)—228no—
534H(5,𝔽2)—228no—
535H(5,𝔽2)—228no—
536H(5,𝔽2)—224no—
537H(5,𝔽2)—224no—
538C2×#41—22no—
539C2×#41—22no—
540C2×#41—22no—
541C2×#41—22no—
542C2×#41—22no—
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—21no—
547C2×#41—21no—
548C2×#41—21no—
549C2×#41—21no—
550C2×#41—114no—
551C2×#41—114no—
552C2×#41—114no—
553C2×#41—114no—
554C2×#41—224no—
555C2×#41—224no—
556C2×#41—228no—
557C2×#41—228no—
558C2×#41—228no—
559C2×#41—2216no—
560C2×#41—2216no—
561C2×#41—224no—
562C2×#41—224no—
563C2×#41—2216no—
564C2×#41—2216no—
565C2×#41—222no—
566C2×#41—222no—
567C2×#41—222no—
568C2×#41—222no—
569C2×#41—222no—
570C2×#41—222no—
571C2×#41—222no—
572C2×#41—222no—
573C2×#41—224no—
574C2×#41—228no—
575C2×#41—228no—
576C2×#41C22⋊D1112yescomplemented
577C2×#41C22⋊D1112yescomplemented
578C2×#41C22×D1112yes—
579C2×#41C22×D1112yes—
580C22×Q8—112no—
581C22×Q8—222no—
582C22×Q8—224no—
583C22×Q8C22⋊D1111yescharacteristic, complemented
584C22×Q8C22×D1111yescharacteristic, complemented
585C22×D4—114no—
586C22×D4—112no—
587C22×D4—222no—
588C22×D4—228no—
589C22×D4—224no—
590C22×D4—224no—
591C22×D4C22⋊D1111yescharacteristic, complemented
592C22×D4C22×D1112yes—
593C22×D4C22×D1112yes—
594C22×D4C22×D1111yescharacteristic, complemented
595C23×C4—114no—
596C23×C4—224no—
597C23×C4C22⋊D1112yescomplemented
598C23×C4C22×D1111yescharacteristic
599C23×C4C22×D1112yescomplemented
600C4⋊Q8—22no—
601C4⋊Q8—224no—
602#127—22no—
603#127—224no—
604#124—22no—
605#124—22no—
606#124—224no—
607#124—224no—
608#123—24no—
609#123—1116no—
610#123—228no—
611#123C22×D1118yescomplemented
612C22⋊Q8—24no—
613C22⋊Q8—24no—
614C22⋊Q8—228no—
615C22⋊Q8—228no—
616#121—24no—
617#121—28no—
618#121—24no—
619#121—228no—
620#121—228no—
621#121—2216no—
622#120—24no—
623#120—1116no—
624#120—228no—
625#120C22×D1118yescomplemented
626C4×D4—28no—
627C4×D4—2216no—
628#117—21no—
629#117—21no—
630#117—114no—
631#117—114no—
632#117—222no—
633#117—222no—
634#117C22×D1112yescomplemented
635#117C22×D1112yescomplemented
636C2×C4⋊C4—21no—
637C2×C4⋊C4—222no—
638C2×C22⋊C4—114no—
639C2×C22⋊C4C22×D1112yes—
640C2×C42—21no—
641C2×C42—222no—
642#99—1116no—
643#99—1132no—
644C2×C11—22no—
645C2×C11—21no—
646C2×C11—21no—
647C2×C11—22no—
648C2×C11—21no—
649C2×C11—44no—
650C2×C11—82no—
651C2×C11C22×#12011yescharacteristic
652D11—48no—
653C24—114no—
654C24—224no—
655C24C2×C22⋊D1112yes—
656C24C23×D1112yes—
657C24C23×D1111yescharacteristic
658#41—24no—
659#41—24no—
660#41—24no—
661#41—24no—
662#41—24no—
663#41—24no—
664#41—24no—
665#41—24no—
666#41—41no—
667#41—41no—
668#41—42no—
669#41—42no—
670#41—42no—
671#41—42no—
672#41—42no—
673#41—41no—
674#41—41no—
675#41—42no—
676#41—2216no—
677#41—2216no—
678#41—2216no—
679#41—2216no—
680#41—2216no—
681#41—2232no—
682#41—2232no—
683#41—2216no—
684#41—2216no—
685#41—2216no—
686#41—2216no—
687#41—224no—
688#41—224no—
689#41—224no—
690#41—224no—
691#41—224no—
692#41—224no—
693#41—224no—
694#41—224no—
695#41—224no—
696#41—224no—
697#41—224no—
698#41—224no—
699#41—224no—
700#41—224no—
701#41—224no—
702#41—224no—
703#41—2216no—
704C2×Q8—22no—
705C2×Q8—22no—
706C2×Q8—22no—
707C2×Q8—22no—
708C2×Q8—21no—
709C2×Q8—21no—
710C2×Q8—114no—
711C2×Q8—114no—
712C2×Q8—224no—
713C2×Q8—228no—
714C2×Q8—228no—
715C2×Q8—2216no—
716C2×Q8—2216no—
717C2×Q8—222no—
718C2×Q8—222no—
719C2×Q8—222no—
720C2×Q8—222no—
721C2×Q8C2×C22⋊D1112yes—
722C2×Q8C2×C22⋊D1112yes—
723C2×D4—24no—
724C2×D4—24no—
725C2×D4—24no—
726C2×D4—24no—
727C2×D4—22no—
728C2×D4—22no—
729C2×D4—28no—
730C2×D4—22no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—118no—
737C2×D4—118no—
738C2×D4—114no—
739C2×D4—114no—
740C2×D4—224no—
741C2×D4—228no—
742C2×D4—228no—
743C2×D4—2232no—
744C2×D4—2232no—
745C2×D4—2216no—
746C2×D4—2216no—
747C2×D4—228no—
748C2×D4—2216no—
749C2×D4—224no—
750C2×D4—224no—
751C2×D4—224no—
752C2×D4—224no—
753C2×D4—2216no—
754C2×D4—2216no—
755C2×D4—222no—
756C2×D4—222no—
757C2×D4—222no—
758C2×D4—222no—
759C2×D4C2×C22⋊D1114yes—
760C2×D4C2×C22⋊D1112yes—
761C2×D4C2×C22⋊D1112yes—
762C2×D4C23×D1114yes—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—114no—
773C22×C4—118no—
774C22×C4—118no—
775C22×C4—228no—
776C22×C4—2216no—
777C22×C4—2216no—
778C22×C4—224no—
779C22×C4—224no—
780C22×C4—224no—
781C22×C4—224no—
782C22×C4—224no—
783C22×C4—224no—
784C22×C4D4×D1112yes—
785C22×C4D4×D1112yes—
786C22×C4D4×D1112yes—
787C22×C4D4×D1112yes—
788C22×C4C2×C22⋊D1114yes—
789C22×C4C2×C22⋊D1114yes—
790C22×C4C2×C22⋊D1112yes—
791C22×C4C2×C22⋊D1111yescharacteristic
792C22×C4C2×C22⋊D1111yescharacteristic
793C22×C4C2×C22⋊D1111yescharacteristic
794C22×C4C2×C22⋊D1111yescharacteristic
795C22×C4C23×D1112yes—
796C22×C4C23×D1111yescharacteristic
797C22×C4C23×D1111yescharacteristic
798C4⋊C4—22no—
799C4⋊C4—22no—
800C4⋊C4—28no—
801C4⋊C4—2216no—
802C4⋊C4—224no—
803C4⋊C4—224no—
804C22⋊C4—22no—
805C22⋊C4—28no—
806C22⋊C4—28no—
807C22⋊C4—118no—
808C22⋊C4—2216no—
809C22⋊C4—2216no—
810C22⋊C4—224no—
811C22⋊C4C23×D1114yes—
812C42—22no—
813C42—22no—
814C42—224no—
815C42—224no—
816C11#6039811yescharacteristic, complemented, Sylow
817C23—22no—
818C23—22no—
819C23—24no—
820C23—22no—
821C23—81no—
822C23—82no—
823C23—82no—
824C23—118no—
825C23—2216no—
826C23—224no—
827C23—224no—
828C23—884no—
829C23—888no—
830C23C2×D4×D1112yes—
831C23C2×D4×D1112yes—
832C23C22×C22⋊D1114yes—
833C23C22×C22⋊D1111yescharacteristic
834C23C22×C22⋊D1111yescharacteristic
835C23C24×D1111yescharacteristic
836Q8—24no—
837Q8—24no—
838Q8—41no—
839Q8—41no—
840Q8—42no—
841Q8—2216no—
842Q8—224no—
843Q8—224no—
844Q8—224no—
845Q8—224no—
846D4—28no—
847D4—28no—
848D4—24no—
849D4—24no—
850D4—42no—
851D4—42no—
852D4—44no—
853D4—41no—
854D4—41no—
855D4—42no—
856D4—88no—
857D4—2216no—
858D4—2232no—
859D4—228no—
860D4—228no—
861D4—228no—
862D4—228no—
863D4—224no—
864D4—224no—
865D4—224no—
866D4—224no—
867D4—8816no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—22no—
877C2×C4—42no—
878C2×C4—44no—
879C2×C4—42no—
880C2×C4—82no—
881C2×C4—118no—
882C2×C4—2232no—
883C2×C4—2216no—
884C2×C4—224no—
885C2×C4—224no—
886C2×C4—228no—
887C2×C4—228no—
888C2×C4—228no—
889C2×C4—228no—
890C2×C4—228no—
891C2×C4—884no—
892C2×C4#6699011yescharacteristic
893C2×C4#6699011yescharacteristic
894C2×C4#6699012yes—
895C2×C4#6699012yes—
896C2×C4#6699012yes—
897C2×C4#6699012yes—
898C2×C4#6699012yes—
899C2×C4#6699011yescharacteristic
900C2×C4#6699011yescharacteristic
901C2×C4#6699012yes—
902C2×C4C2×D4×D1112yes—
903C2×C4C2×D4×D1112yes—
904C2×C4C2×D4×D1112yes—
905C2×C4C2×D4×D1112yes—
906C2×C4C22×C22⋊D1114yes—
907C2×C4C22×C22⋊D1111yescharacteristic
908C2×C4C22×C22⋊D1111yescharacteristic
909C2×C4C22×C22⋊D1111yescharacteristic
910C2×C4C22×C22⋊D1111yescharacteristic
911C22—24no—
912C22—41no—
913C22—42no—
914C22—41no—
915C22—41no—
916C22—42no—
917C22—44no—
918C22—44no—
919C22—44no—
920C22—48no—
921C22—42no—
922C22—82no—
923C22—228no—
924C22—448no—
925C22—448no—
926C22—884no—
927C22—8816no—
928C22C2×#6699011yescharacteristic
929C22C2×#6699011yescharacteristic
930C22C2×#6699012yes—
931C22C22×D4×D1112yes—
932C22C23×C22⋊D1111yescharacteristic
933C4—24no—
934C4—44no—
935C4—42no—
936C4—228no—
937C4—448no—
938C4C2×#6699011yescharacteristic
939C4C2×#6699011yescharacteristic
940C4C2×#6699011yescharacteristic
941C4C2×#6699012yes—
942C4C2×#6699012yes—
943C4C2×#6699011yescharacteristic
944C2—21no—
945C2—22no—
946C2—21no—
947C2—21no—
948C2—22no—
949C2—44no—
950C2—82no—
951C2—448no—
952C2C22×#6699011yescharacteristic
subgroupG/H
centerC4C2×#66990
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#3449C2
socleC2×C11C22×#120
hypercenter#3449D11
hypocenterC11#60398
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#10623453C2semidirect
2. #13081945C2semidirect
3. #13078021C2semidirect
4. #13078017C2semidirect
5. #13078012C2semidirect
6. #13078007C2semidirect
7. C2×#10622853C2semidirect
8. C2×#10622619C2semidirect
9. C11×#3449C2semidirect
11. C22×C11×#41C22semidirect
28. C11×#536C22semidirect
30. C11×#535C22semidirect
31. C11×#534C22semidirect
34. C11×#525C22semidirect
35. C2×C11×#117C22semidirect
41. #10623347C22semidirect
42. #10623336C22semidirect
43. #10623335C22semidirect
44. #10623322C22semidirect
45. C2×#66979C22semidirect
46. #10622853C22semidirect
47. #10622853C22semidirect
48. C2×#66898C22semidirect
49. #10622666C22semidirect
50. #10622645C22semidirect
51. #10622619C22semidirect
52. #10622619C22semidirect
53. C2×#66870C22semidirect
66. C2×C11×#41D4semidirect
67. C2×C11×#41D4semidirect
70. C22×Q8×C11D4semidirect
71. C22×Q8×C11C23semidirect
72. C22×D4×C11D4semidirect
75. C22×D4×C11C23semidirect
76. C23×C4×C11D4semidirect
78. C23×C4×C11C23semidirect
123. C2×#4339D4semidirect
124. C2×#4339D4semidirect
128. C22×D44D4semidirect
130. C22×C4×D11D4semidirect
132. C22×Dic22D4semidirect
138. C11×#123C23semidirect
145. C11×#120C23semidirect
149. C11×#117C23semidirect
150. C11×#117C23semidirect
154. #67006C23semidirect
166. #66982C23semidirect
170. #66979C23semidirect
171. #66979C23semidirect
175. #66898C23semidirect
176. #66870C23semidirect
343. #3449D11semidirect
459. C22×#41C2×D11semidirect
465. #536C2×D11semidirect
469. #535C2×D11semidirect
471. #534C2×D11semidirect
477. #525C2×D11semidirect
479. C2×#117C2×D11semidirect
576. C2×#41C22⋊D11semidirect
577. C2×#41C22⋊D11semidirect
583. C22×Q8C22⋊D11semidirect
584. C22×Q8C22×D11semidirect
591. C22×D4C22⋊D11semidirect
594. C22×D4C22×D11semidirect
597. C23×C4C22⋊D11semidirect
599. C23×C4C22×D11semidirect
611. #123C22×D11semidirect
625. #120C22×D11semidirect
634. #117C22×D11semidirect
635. #117C22×D11semidirect
816. C11#60398semidirect

Maximal subgroups

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

subgroupindex
C2×#106234532
#130819452
#130780212
#130780172
#130780122
#130780072
C2×#106228532
C2×#106226192
C11×#34492
#6039811