Finite Group Databasebeta

← #11002201

Subgroups — #11002201

Order 768.

2970 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5605C211yesmaximal, characteristic, complemented
2C22×#894C211yesmaximal, characteristic, complemented
3C3×#2618C211yesmaximal, characteristic, complemented
4#82901C212yesmaximal, complemented
5#82893C212yesmaximal, complemented
6#82723C211yesmaximal, characteristic, complemented
7#82199C211yesmaximal, characteristic, complemented
8#77853C214yesmaximal, complemented
9#77430C214yesmaximal, complemented
10#77355C214yesmaximal, complemented
11#77137C214yesmaximal, complemented
12#74884C212yesmaximal, complemented
13#74742C212yesmaximal, complemented
14#74048C211yesmaximal, characteristic, complemented
15#74004C211yesmaximal, characteristic, complemented
16#36721—31nomaximal, Sylow
17C22×D3×D4C2212yes—
18C23×D12C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic, complemented
20C2×C3×#123C2212yescomplemented
21C2×C3×#121C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic, complemented
23C2×#939C2212yes—
24C2×#938C2212yescomplemented
25C2×#937C2212yescomplemented
26C2×#937C2212yescomplemented
27C2×#930C2211yescharacteristic
28C2×#929C2212yescomplemented
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
32C22×Dic3⋊C4C2211yescharacteristic, complemented
33#5605—28no—
34C2×#895C2212yescomplemented
35C2×#894—28no—
36C2×#894C2212yescomplemented
37C2×#894C2214yescomplemented
38C2×#894C2214yescomplemented
39C2×#883C2212yescomplemented
40C2×#882C2212yescomplemented
41C2×#882C2212yescomplemented
42C2×#882C2214yescomplemented
43C3×#398C2212yescomplemented
44C3×#396C2214yescomplemented
45C3×#394C2212yescomplemented
46C3×#386C2212yescomplemented
47C3×#380C2211yescharacteristic, complemented
48#5220C2212yescomplemented
49#5213C2212yescomplemented
50#5212C2211yescharacteristic, complemented
51#4994C2214yescomplemented
52#4993C2214yescomplemented
53#4991C2212yescomplemented
54#4991C2214yescomplemented
55#4990C2214yescomplemented
56#4989C2214yescomplemented
57#4988C2214yescomplemented
58#4987C2212yescomplemented
59#4987C2212yescomplemented
60#4981C2212yescomplemented
61#4960C2214yes—
62#4960C2214yescomplemented
63#4959C2214yescomplemented
64#4958C2212yescomplemented
65#4957C2214yescomplemented
66#4957C2214yescomplemented
67#4956C2214yescomplemented
68#4955C2212yes—
69#4955C2214yescomplemented
70#4952C2214yescomplemented
71Dic3×C22⋊C4C2212yescomplemented
72#4675C2214yescomplemented
73#4671C2214yes—
74#4670C2214yescomplemented
75#4665C2214yescomplemented
76#4665C2214yescomplemented
77#4650C2214yescomplemented
78C2×#534—31no—
79C22×#123—31no—
80#2847—31no—
81#2847—31no—
82#2706—34no—
83#2706—34no—
84#2678—34no—
85#2678—34no—
86#2618—31no—
87#2618D311yescharacteristic, complemented
88#2539—32no—
89#2504—32no—
90#2405—32no—
91#2403—32no—
92#2312—31no—
93C24×D3C2311yescharacteristic
94C24×D3C2311yescharacteristic
95C24×D3C2312yes—
96C22×C3×D4C2312yes—
97C22×C3×D4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C22×#67C2312yes—
102C22×#67C2312yes—
103C22×#67C2314yes—
104C22×#67C2312yes—
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C2×D3×D4—28no—
108C2×D3×D4—44no—
109C2×D3×D4—44no—
110C22×D12—24no—
111C22×D12—44no—
112C22×D12C2314yes—
113C22×D12C2314yes—
114C22×D12C2312yes—
115C22×D12C2311yescharacteristic
116C22×C4×D3—24no—
117C22×C4×D3—44no—
118C22×C4×D3C2312yes—
119C22×C4×D3C2312yes—
120C22×C4×D3C2312yes—
121C3×#123—44no—
122C3×#121—24no—
123C2×C3×C4⋊C4—24no—
124C2×C3×C4⋊C4C2312yes—
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C4⋊C4C2312yes—
127C2×C3×C4⋊C4C2312yes—
128C2×C3×C4⋊C4C2314yes—
129C2×C3×C22⋊C4C2312yes—
130C2×C3×C22⋊C4C2312yes—
131C2×C3×C22⋊C4C2314yes—
132C2×C3×C22⋊C4C2314yes—
133C2×#217C2312yes—
134C2×#217C2312yes—
135C2×#217C2314yes—
136#939—28no—
137#938—44no—
138#937—28no—
139#937—44no—
140#930—24no—
141#929—44no—
142C2×(C2×D3)⋊C4—24no—
143C2×(C2×D3)⋊C4—24no—
144C2×(C2×D3)⋊C4D418yescomplemented
145C2×(C2×D3)⋊C4C2312yes—
146C2×(C2×D3)⋊C4C2312yes—
147C2×(C2×D3)⋊C4C2314yes—
148C2×(C2×D3)⋊C4C2314yes—
149C2×(C2×D3)⋊C4C2314yes—
150C2×(C2×D3)⋊C4C2314yes—
151C2×(C2×D3)⋊C4C2314yes—
152C2×(C2×D3)⋊C4C2314yes—
153C2×(C2×D3)⋊C4C2314yes—
154C2×(C2×D3)⋊C4C2314yes—
155C2×(C2×D3)⋊C4C2314yes—
156C2×(C2×D3)⋊C4C2312yes—
157C2×(C2×D3)⋊C4C2312yes—
158C2×C4⋊Dic3C2311yescharacteristic
159C2×C4⋊Dic3C2312yes—
160C2×Dic3⋊C4—24no—
161C2×Dic3⋊C4C2312yes—
162C2×Dic3⋊C4C2314yes—
163C2×Dic3⋊C4C2314yes—
164C2×C4×Dic3C2314yes—
165#895—44no—
166#894—216no—
167#894—216no—
168#894—28no—
169#883—28no—
170#882—28no—
171#882—44no—
172#882—48no—
173C3×#95C2314yes—
174C3×#95C2312yes—
175C3⋊#95C2314yes—
176C3⋊#95C2314yes—
177C3⋊#95C2314yes—
178C3⋊#95C2314yes—
179C3⋊#95C2312yes—
180C23×D4—32no—
181C23×D4—31no—
182C24×C4—31no—
183#534—68no—
184C2×#123—32no—
185C2×#123—34no—
186C2×#123—34no—
187C2×#123—32no—
188C2×#123—32no—
189C2×#123—68no—
190C2×#123C2×D312yescomplemented
191C2×#121—32no—
192C2×#121—31no—
193C2×#121—32no—
194C2×#121—32no—
195C2×#121C2×D311yescharacteristic
196C2×#120—32no—
197C2×#120—32no—
198C2×#120—32no—
199C2×#120—32no—
200C2×#120—34no—
201C22×C4⋊C4—31no—
202C22×C4⋊C4C2×D311yescharacteristic, complemented
203C22×C22⋊C4—31no—
204C22×C22⋊C4—31no—
205C22×C22⋊C4—31no—
206#399—34no—
207#398—32no—
208#398C2×D312yescomplemented
209#397—34no—
210#397—34no—
211#396—34no—
212#396C2×D314yescomplemented
213#394—32no—
214#394—34no—
215#394—34no—
216#394C2×D312yescomplemented
217#392—34no—
218#392—34no—
219#392—34no—
220#390—34no—
221#390—34no—
222#390—34no—
223#388—34no—
224#388—34no—
225#386—32no—
226#386—32no—
227#386—34no—
228#386—32no—
229#386—34no—
230#386—34no—
231#386C2×D312yescomplemented
232#385—34no—
233#382—34no—
234#380—31no—
235#380—32no—
236#380—32no—
237#380C2×D311yescharacteristic, complemented
238#379—32no—
239#379—34no—
240C4×C22⋊C4—32no—
241C24×C3C2412yes—
242C24×C3C2411yescharacteristic
243C23×D3—22no—
244C23×D3—22no—
245C23×D3—22no—
246C23×D3—24no—
247C23×D3—22no—
248C23×D3—22no—
249C23×D3—24no—
250C23×D3—42no—
251C23×D3—42no—
252C23×D3—42no—
253C23×D3—42no—
254C23×D3—42no—
255C23×D3—44no—
256C23×D3—44no—
257C23×D3C2×D414yes—
258C23×D3C2412yes—
259C23×D3C2412yes—
260C23×D3C2412yes—
261C2×C3×D4—24no—
262C2×C3×D4—24no—
263C2×C3×D4—24no—
264C2×C3×D4—22no—
265C2×C3×D4—42no—
266C22×C3×C4—22no—
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—42no—
271C22×C3×C4—42no—
272C22×C3×C4C2×D414yes—
273C22×C3×C4C2414yes—
274C22×C3×C4C2412yes—
275C22×C3×C4C2412yes—
276C22×C3×C4C2412yes—
277C22×C3×C4C2411yescharacteristic
278C22×C3×C4C2411yescharacteristic
279C2×#67—24no—
280C2×#67—24no—
281C2×#67—24no—
282C2×#67—24no—
283C2×#67—28no—
284C2×#67—24no—
285C2×#67—42no—
286C2×#67—42no—
287C2×#67—44no—
288C2×#67—44no—
289C2×#67—44no—
290C22×Dic3—22no—
291C22×Dic3—42no—
292C22×Dic3—42no—
293C22×Dic3C2×D414yes—
294C22×Dic3C2414yes—
295C22×Dic3C2412yes—
296C22×Dic3C2412yes—
297C22×Dic3C2412yes—
298D3×D4—432no—
299C2×D12—24no—
300C2×D12—28no—
301C2×D12—28no—
302C2×D12—28no—
303C2×D12—22no—
304C2×D12—44no—
305C2×D12—42no—
306C2×D12—42no—
307C2×D12—416no—
308C2×D12—44no—
309C2×D12—42no—
310C2×D12—44no—
311C2×C4×D3—24no—
312C2×C4×D3—24no—
313C2×C4×D3—24no—
314C2×C4×D3—24no—
315C2×C4×D3—24no—
316C2×C4×D3—42no—
317C2×C4×D3—42no—
318C2×C4×D3—42no—
319C2×C4×D3—42no—
320C2×C4×D3—416no—
321C3×C4⋊C4—24no—
322C3×C4⋊C4—24no—
323C3×C4⋊C4—22no—
324C3×C4⋊C4—42no—
325C3×C4⋊C4—44no—
326C3×C22⋊C4—24no—
327C3×C22⋊C4—24no—
328C3×C22⋊C4—44no—
329C3×C22⋊C4—44no—
330#217—24no—
331#217—24no—
332#217—44no—
333(C2×D3)⋊C4—28no—
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—24no—
336(C2×D3)⋊C4—28no—
337(C2×D3)⋊C4—44no—
338(C2×D3)⋊C4—44no—
339(C2×D3)⋊C4—44no—
340(C2×D3)⋊C4—44no—
341(C2×D3)⋊C4—44no—
342(C2×D3)⋊C4—44no—
343(C2×D3)⋊C4—44no—
344(C2×D3)⋊C4C2×D418yes—
345(C2×D3)⋊C4C2×D418yes—
346C4⋊Dic3—22no—
347C4⋊Dic3—42no—
348Dic3⋊C4—24no—
349Dic3⋊C4—28no—
350Dic3⋊C4—44no—
351C4×Dic3—44no—
352C25—31no—
353C25—31no—
354C25—32no—
355C22×D4—32no—
356C22×D4—34no—
357C22×D4—32no—
358C22×D4—32no—
359C22×D4—34no—
360C22×D4—31no—
361C22×D4—34no—
362C22×D4—32no—
363C22×D4—64no—
364C22×D4—68no—
365C22×D4—124no—
366C22×D4—124no—
367C22×D4—124no—
368C22×D4C22×D312yes—
369C22×D4C22×D311yescharacteristic
370C23×C4—31no—
371C23×C4—31no—
372C23×C4—32no—
373C23×C4—32no—
374C23×C4—32no—
375C23×C4—64no—
376C23×C4—124no—
377C23×C4C22×D311yescharacteristic
378C23×C4C22×D311yescharacteristic
379C23×C4C22×D311yescharacteristic
380#123—44no—
381#123—68no—
382#123—616no—
383#123—616no—
384#123—68no—
385#123—124no—
386#121—24no—
387#121—68no—
388#121—64no—
389#121—124no—
390#121—124no—
391#120—68no—
392#120—68no—
393#120—124no—
394#120—128no—
395#120—124no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—34no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—32no—
400C2×C4⋊C4—32no—
401C2×C4⋊C4—34no—
402C2×C4⋊C4—64no—
403C2×C4⋊C4C22×D312yes—
404C2×C4⋊C4C22×D312yes—
405C2×C4⋊C4C22×D311yescharacteristic
406C2×C4⋊C4C22×D312yes—
407C2×C4⋊C4C22×D314yes—
408C2×C22⋊C4—38no—
409C2×C22⋊C4—32no—
410C2×C22⋊C4—32no—
411C2×C22⋊C4—32no—
412C2×C22⋊C4—32no—
413C2×C22⋊C4—34no—
414C2×C22⋊C4—34no—
415C2×C22⋊C4—32no—
416C2×C22⋊C4—32no—
417C2×C22⋊C4—34no—
418C2×C22⋊C4—34no—
419C2×C22⋊C4—34no—
420C2×C22⋊C4—34no—
421C2×C22⋊C4—34no—
422C2×C22⋊C4—34no—
423C2×C22⋊C4—34no—
424C2×C22⋊C4—34no—
425C2×C22⋊C4—64no—
426C2×C22⋊C4—64no—
427C2×C22⋊C4C22×D312yes—
428C2×C22⋊C4C22×D312yes—
429C2×C22⋊C4C22×D314yes—
430C2×C22⋊C4C22×D314yes—
431C2×C42—34no—
432#95—34no—
433#95—34no—
434#95—34no—
435#95—32no—
436#95—34no—
437#95C22×D312yes—
438#95C22×D314yes—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—24no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—24no—
446C23×C3C22×D412yes—
447C23×C3H(5,𝔽2)12yes—
448C23×C3H(5,𝔽2)12yes—
449C23×C3C2511yescharacteristic
450C22×D3—28no—
451C22×D3—22no—
452C22×D3—22no—
453C22×D3—22no—
454C22×D3—24no—
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—24no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—28no—
462C22×D3—22no—
463C22×D3—24no—
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—24no—
467C22×D3—44no—
468C22×D3—44no—
469C22×D3—48no—
470C22×D3—48no—
471C22×D3—48no—
472C22×D3—44no—
473C22×D3—44no—
474C22×D3—84no—
475C22×D3—84no—
476C22×D3—84no—
477C22×D3—84no—
478C22×D3—88no—
479C22×D3—88no—
480C22×D3C22×D414yes—
481C22×D3H(5,𝔽2)14yes—
482C3×D4—48no—
483C3×D4—82no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—24no—
491C2×C3×C4—22no—
492C2×C3×C4—24no—
493C2×C3×C4—24no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—24no—
497C2×C3×C4—44no—
498C2×C3×C4—44no—
499C2×C3×C4—44no—
500C2×C3×C4C22×D412yes—
501C2×C3×C4C22×D412yes—
502#67—48no—
503#67—48no—
504#67—84no—
505#67—88no—
506C2×Dic3—24no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—24no—
511C2×Dic3—24no—
512C2×Dic3—22no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3—24no—
516C2×Dic3—44no—
517C2×Dic3—44no—
518C2×Dic3C22×D414yes—
519D12—416no—
520D12—48no—
521D12—82no—
522D12—88no—
523C4×D3—48no—
524C4×D3—48no—
525C4×D3—48no—
526C24—32no—
527C24—32no—
528C24—34no—
529C24—32no—
530C24—64no—
531C24—64no—
532C24—62no—
533C24—62no—
534C24—62no—
535C24—62no—
536C24—62no—
537C24—122no—
538C24—122no—
539C24—122no—
540C24—122no—
541C24—122no—
542C24—124no—
543C24—124no—
544C24C23×D312yes—
545C24C23×D311yescharacteristic
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—22no—
550C2×D4—42no—
551C2×D4—64no—
552C2×D4—68no—
553C2×D4—68no—
554C2×D4—68no—
555C2×D4—64no—
556C2×D4—64no—
557C2×D4—64no—
558C2×D4—64no—
559C2×D4—64no—
560C2×D4—68no—
561C2×D4—62no—
562C2×D4—122no—
563C2×D4—122no—
564C2×D4—124no—
565C2×D4—124no—
566C2×D4—122no—
567C2×D4—124no—
568C2×D4—1216no—
569C2×D4—122no—
570C2×D4—122no—
571C2×D4—124no—
572C2×D4—124no—
573C2×D4—124no—
574C2×D4—1232no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—32no—
580C22×C4—34no—
581C22×C4—34no—
582C22×C4—32no—
583C22×C4—32no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—64no—
587C22×C4—64no—
588C22×C4—64no—
589C22×C4—62no—
590C22×C4—64no—
591C22×C4—64no—
592C22×C4—122no—
593C22×C4—122no—
594C22×C4—122no—
595C22×C4—122no—
596C22×C4—1216no—
597C22×C4—122no—
598C22×C4—122no—
599C22×C4D3×D414yes—
600C22×C4C23×D314yes—
601C22×C4C23×D312yes—
602C22×C4C23×D312yes—
603C22×C4C23×D312yes—
604C22×C4C23×D311yescharacteristic
605C22×C4C23×D311yescharacteristic
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—22no—
609C4⋊C4—42no—
610C4⋊C4—44no—
611C4⋊C4—68no—
612C4⋊C4—64no—
613C4⋊C4—62no—
614C4⋊C4—122no—
615C4⋊C4—124no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—38no—
619C22⋊C4—38no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—68no—
623C22⋊C4—64no—
624C22⋊C4—68no—
625C22⋊C4—64no—
626C22⋊C4—64no—
627C22⋊C4—64no—
628C22⋊C4—124no—
629C22⋊C4—124no—
630C22⋊C4—124no—
631C22⋊C4—124no—
632C22⋊C4—124no—
633C22⋊C4—124no—
634C22⋊C4—124no—
635C22⋊C4—124no—
636C42—124no—
637C22×C3—22no—
638C22×C3—22no—
639C22×C3—24no—
640C22×C3—24no—
641C22×C3—42no—
642C22×C3—42no—
643C22×C3—42no—
644C22×C3—44no—
645C22×C3—44no—
646C22×C3#53514yes—
647C22×C3C23×D411yescharacteristic
648C22×C3C2×H(5,𝔽2)11yescharacteristic
649C22×C3C2×H(5,𝔽2)11yescharacteristic
650C22×C3C2×H(5,𝔽2)12yes—
651C22×C3#58512yes—
652C2×D3—24no—
653C2×D3—24no—
654C2×D3—24no—
655C2×D3—24no—
656C2×D3—24no—
657C2×D3—24no—
658C2×D3—416no—
659C2×D3—42no—
660C2×D3—42no—
661C2×D3—42no—
662C2×D3—42no—
663C2×D3—44no—
664C2×D3—44no—
665C2×D3—42no—
666C2×D3—42no—
667C2×D3—42no—
668C2×D3—44no—
669C2×D3—44no—
670C2×D3—88no—
671C2×D3—816no—
672C3×C4—22no—
673C3×C4—22no—
674C3×C4—42no—
675C3×C4—42no—
676C3×C4—42no—
677C3×C4—44no—
678Dic3—24no—
679Dic3—42no—
680Dic3—42no—
681Dic3—44no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—24no—
688C23—24no—
689C23—34no—
690C23—34no—
691C23—68no—
692C23—62no—
693C23—62no—
694C23—62no—
695C23—62no—
696C23—62no—
697C23—64no—
698C23—62no—
699C23—64no—
700C23—62no—
701C23—62no—
702C23—68no—
703C23—62no—
704C23—62no—
705C23—62no—
706C23—64no—
707C23—64no—
708C23—124no—
709C23—124no—
710C23—128no—
711C23—128no—
712C23—124no—
713C23—128no—
714C23—124no—
715C23—244no—
716C23—244no—
717C23—244no—
718C23—244no—
719C23—248no—
720C23—248no—
721C23C2×D3×D412yes—
722C23#100412yes—
723C23#100912yes—
724C23C24×D311yescharacteristic
725D4—48no—
726D4—82no—
727D4—1216no—
728D4—128no—
729D4—128no—
730D4—128no—
731D4—242no—
732D4—248no—
733D4—244no—
734D4—248no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—34no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—64no—
753C2×C4—62no—
754C2×C4—62no—
755C2×C4—62no—
756C2×C4—64no—
757C2×C4—62no—
758C2×C4—64no—
759C2×C4—62no—
760C2×C4—62no—
761C2×C4—64no—
762C2×C4—128no—
763C2×C4—128no—
764C2×C4—128no—
765C2×C4—124no—
766C2×C4—124no—
767C2×C4C2×D3×D412yes—
768C2×C4C2×D3×D412yes—
769C2×C3—24no—
770C2×C3—82no—
771C2×C3C2×#53511yescharacteristic
772C2×C3#348411yescharacteristic
773C2×C3#348511yescharacteristic
774C2×C3#353412yes—
775C2×C3#353412yes—
776D3—44no—
777D3—44no—
778D3—82no—
779C22—22no—
780C22—22no—
781C22—24no—
782C22—24no—
783C22—42no—
784C22—42no—
785C22—44no—
786C22—42no—
787C22—44no—
788C22—64no—
789C22—64no—
790C22—64no—
791C22—64no—
792C22—64no—
793C22—64no—
794C22—1216no—
795C22—122no—
796C22—122no—
797C22—124no—
798C22—122no—
799C22—122no—
800C22—124no—
801C22—122no—
802C22—122no—
803C22—124no—
804C22—122no—
805C22—124no—
806C22—248no—
807C22—2416no—
808C22#560714yes—
809C22C22×D3×D411yescharacteristic
810C22C2×#100411yescharacteristic
811C22C2×#100911yescharacteristic
812C22D3×H(5,𝔽2)12yes—
813C22#596812yes—
814C4—22no—
815C4—22no—
816C4—42no—
817C4—44no—
818C4—42no—
819C4—42no—
820C4—64no—
821C4—122no—
822C4—122no—
823C4—124no—
824C3#3672111yescharacteristic, complemented, Sylow
825C2—24no—
826C2—82no—
827C2—124no—
828C2—124no—
829C2—242no—
830C2C2×#560711yescharacteristic
831C2#8630811yescharacteristic
832C2#8635411yescharacteristic
833C2#8638312yes—
834C2#8645912yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2618C2
hypercenter#2618D3
hypocenterC3#36721
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2618

Complements

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

NH ≅ G/Ntype
1. C2×#5605C2semidirect
2. C22×#894C2semidirect
3. C3×#2618C2semidirect
4. #82901C2semidirect
5. #82893C2semidirect
6. #82723C2semidirect
7. #82199C2semidirect
8. #77853C2semidirect
9. #77430C2semidirect
10. #77355C2semidirect
11. #77137C2semidirect
12. #74884C2semidirect
13. #74742C2semidirect
14. #74048C2semidirect
15. #74004C2semidirect
19. C23×C4×D3C22semidirect
20. C2×C3×#123C22semidirect
22. C22×C3×C4⋊C4C22semidirect
24. C2×#938C22semidirect
25. C2×#937C22semidirect
26. C2×#937C22semidirect
28. C2×#929C22semidirect
31. C22×(C2×D3)⋊C4C22semidirect
32. C22×Dic3⋊C4C22semidirect
34. C2×#895C22semidirect
36. C2×#894C22semidirect
37. C2×#894C22semidirect
38. C2×#894C22semidirect
39. C2×#883C22semidirect
40. C2×#882C22semidirect
41. C2×#882C22semidirect
42. C2×#882C22semidirect
43. C3×#398C22semidirect
44. C3×#396C22semidirect
45. C3×#394C22semidirect
46. C3×#386C22semidirect
47. C3×#380C22semidirect
48. #5220C22semidirect
49. #5213C22semidirect
50. #5212C22semidirect
51. #4994C22semidirect
52. #4993C22semidirect
53. #4991C22semidirect
54. #4991C22semidirect
55. #4990C22semidirect
56. #4989C22semidirect
57. #4988C22semidirect
58. #4987C22semidirect
59. #4987C22semidirect
60. #4981C22semidirect
62. #4960C22semidirect
63. #4959C22semidirect
64. #4958C22semidirect
65. #4957C22semidirect
66. #4957C22semidirect
67. #4956C22semidirect
69. #4955C22semidirect
70. #4952C22semidirect
71. Dic3×C22⋊C4C22semidirect
72. #4675C22semidirect
74. #4670C22semidirect
75. #4665C22semidirect
76. #4665C22semidirect
77. #4650C22semidirect
87. #2618D3semidirect
144. C2×(C2×D3)⋊C4D4semidirect
190. C2×#123C2×D3semidirect
202. C22×C4⋊C4C2×D3semidirect
208. #398C2×D3semidirect
212. #396C2×D3semidirect
216. #394C2×D3semidirect
231. #386C2×D3semidirect
237. #380C2×D3semidirect
824. C3#36721semidirect

Maximal subgroups

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

subgroupindex
C2×#56052
C22×#8942
C3×#26182
#829012
#828932
#827232
#821992
#778532
#774302
#773552
#771372
#748842
#747422
#740482
#740042
#367213