Finite Group Databasebeta

← #10972943

Subgroups — #10972943

Order 768.

3602 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#121C211yesmaximal, characteristic, complemented
2C2×#5805C211yesmaximal, characteristic, complemented
3C2×#5791C211yesmaximal, characteristic, complemented
4C22×#926C211yesmaximal, characteristic, complemented
5#84048C214yesmaximal, complemented
6#84044C211yesmaximal, characteristic, complemented
7#82705C214yesmaximal, complemented
8#82704C214yesmaximal, complemented
9#82700C212yesmaximal, complemented
10#82698C212yesmaximal, complemented
11#82677C212yesmaximal, complemented
12#82676C212yesmaximal, complemented
13#82186C211yesmaximal, characteristic, complemented
14#82157C211yesmaximal, characteristic, complemented
15#82106C214yesmaximal, complemented
16#35252—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C23×C3×D4C2212yes—
19C24×C3×C4C2211yescharacteristic
20C22×#235C2211yescharacteristic
21C2×C3×#121—28no—
22C2×C3×#121C2212yes—
23C2×C3×#121C2212yes—
24C2×C3×#121C2212yes—
25C2×C3×#121C2212yes—
26C22×C3×C4⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2212yes—
28C2×#953C2212yes—
29C2×#953C2214yes—
30C22×#217C2212yes—
31#5805—28no—
32C2×#940C2212yescomplemented
33C2×#939C2218yescomplemented
34C2×#938C2214yescomplemented
35C2×#936C2212yescomplemented
36#5791—28no—
37C2×#930C2211yescharacteristic, complemented
38C2×#930C2211yescharacteristic, complemented
39C2×#929C2212yes—
40C2×C4×#67C2212yescomplemented
41C2×C4×#67C2212yescomplemented
42C2×#926—28no—
43C2×#926C2211yescharacteristic
44C2×#926C2211yescharacteristic
45C2×#926C2212yes—
46C2×#926C2211yescharacteristic
47C2×#926C2212yescomplemented
48C2×#926C2212yescomplemented
49C22×C4⋊Dic3C2212yescomplemented
50C2×#924C2211yescharacteristic, complemented
51C2×#924C2211yescharacteristic, complemented
52C22×C4×Dic3C2212yescomplemented
53#5247C2214yes—
54#5223C2218yescomplemented
55#5222C2218yescomplemented
56#5221C2212yescomplemented
57#5221C2212yescomplemented
58#5221C2214yescomplemented
59#5220C2218yescomplemented
60#5213C2214yes—
61#5210C2214yes—
62#4988C2212yescomplemented
63#4987C2214yescomplemented
64#4977C2212yescomplemented
65#4975C2212yescomplemented
66#4973C2212yescomplemented
67#4972C2214yescomplemented
68#4961C2218yescomplemented
69#4957C2218yescomplemented
70#4948C2218yescomplemented
71#4945C2218yescomplemented
72C2×#535—31no—
73C2×#525—31no—
74C22×#121D311yescharacteristic, complemented
75C22×#117—31no—
76#2856—32no—
77#2850—32no—
78#2620—32no—
79#2619—32no—
80#2416—34no—
81#2414—34no—
82#2411—34no—
83#2410—34no—
84#2317—31no—
85#2311—31no—
86#2309—31no—
87C25×C3C2311yescharacteristic
88C25×C3C2312yes—
89C22×C3×D4—28no—
90C22×C3×D4—24no—
91C22×C3×D4—24no—
92C22×C3×D4—24no—
93C22×C3×D4—48no—
94C22×C3×D4C2314yes—
95C22×C3×D4C2312yes—
96C22×C3×D4C2312yes—
97C22×C3×D4C2314yes—
98C23×C3×C4—24no—
99C23×C3×C4—24no—
100C23×C3×C4D418yescomplemented
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C2311yescharacteristic
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2312yes—
107C23×C3×C4C2311yescharacteristic
108C22×#67C2312yes—
109C22×#67C2312yes—
110C22×#67C2318yes—
111C22×#67C2312yes—
112C23×Dic3C2314yes—
113C2×#235—24no—
114C2×#235—24no—
115C2×#235—24no—
116C22×D12C2311yescharacteristic
117C22×C4×D3C2312yes—
118C22×Dic6C2311yescharacteristic
119C3×#121—28no—
120C3×#121—28no—
121C3×#121—28no—
122C3×#121—28no—
123C2×C3×C4⋊C4—24no—
124C2×C3×C4⋊C4C2312yes—
125C2×C3×C4⋊C4C2312yes—
126C2×C3×C22⋊C4—28no—
127C2×C3×C22⋊C4C2314yes—
128C2×C3×C22⋊C4C2314yes—
129#953—28no—
130#953—216no—
131C2×#217—28no—
132C2×#217C2318yes—
133C2×#217C2312yes—
134C2×#217C2312yes—
135C2×#217C2312yes—
136C2×#217C2312yes—
137C2×#217C2314yes—
138C2×#217C2318yes—
139C2×#217C2318yes—
140C2×#217C2312yes—
141#940—28no—
142#939—416no—
143#938—216no—
144#936—28no—
145#930—24no—
146#930—24no—
147#929—28no—
148C4×#67—28no—
149C4×#67—28no—
150C2×(C2×D3)⋊C4C2312yes—
151C2×(C2×D3)⋊C4C2312yes—
152C2×(C2×D3)⋊C4C2318yes—
153#926—24no—
154#926—24no—
155#926—28no—
156#926—28no—
157#926—28no—
158#926D418yescomplemented
159C2×C4⋊Dic3—28no—
160C2×C4⋊Dic3C2314yes—
161C2×C4⋊Dic3C2311yescharacteristic
162C2×C4⋊Dic3C2311yescharacteristic
163C2×C4⋊Dic3C2312yes—
164C2×C4⋊Dic3C2312yes—
165#924—24no—
166#924—24no—
167C2×Dic3⋊C4C2312yes—
168C2×Dic3⋊C4C2312yes—
169C2×Dic3⋊C4C2318yes—
170C2×C4×Dic3—28no—
171C2×C4×Dic3C2314yes—
172C2×C4×Dic3C2312yes—
173C2×C4×Dic3C2312yes—
174C2×C4×Dic3C2312yes—
175C3⋊#95C2318yes—
176C3⋊#95C2318yes—
177C22×#41—31no—
178C23×D4C2×D311yescharacteristic
179C23×D4C2×D312yes—
180C24×C4C2×D311yescharacteristic
181#535—68no—
182C2×#127—32no—
183C2×#124—32no—
184#525—68no—
185C2×#123—32no—
186C2×C22⋊Q8—31no—
187C2×C22⋊Q8—31no—
188C2×#121—28no—
189C2×#121—34no—
190C2×#121—31no—
191C2×#121—31no—
192C2×#121—38no—
193C2×#121C2×D312yes—
194C2×#121C2×D312yes—
195C2×#121C2×D312yes—
196C2×#121C2×D312yes—
197C2×#120—32no—
198C2×#120—34no—
199C2×C4×D4—32no—
200C2×C4×D4—32no—
201C2×#117—31no—
202C2×#117—31no—
203C2×#117—31no—
204C2×#117—32no—
205C2×#117—32no—
206C2×#117—32no—
207C2×#117—68no—
208C22×C4⋊C4—32no—
209C22×C4⋊C4C2×D311yescharacteristic
210C22×C22⋊C4—32no—
211C22×C22⋊C4C2×D312yes—
212C22×C42—32no—
213#396—38no—
214#394—38no—
215#394—38no—
216#392—38no—
217#391—32no—
218#390—32no—
219#390—32no—
220#390—34no—
221#390—32no—
222#390—38no—
223#389—34no—
224#388—38no—
225#386—38no—
226#386—34no—
227#385—34no—
228#384—32no—
229#382—32no—
230#380—34no—
231#379—34no—
232C24×C3—22no—
233C24×C3—22no—
234C24×C3—24no—
235C24×C3—24no—
236C24×C3—24no—
237C24×C3—24no—
238C24×C3—42no—
239C24×C3—44no—
240C24×C3—44no—
241C24×C3C2×D414yes—
242C24×C3C2414yes—
243C24×C3C2411yescharacteristic
244C24×C3C2411yescharacteristic
245C24×C3C2411yescharacteristic
246C23×D3C2412yes—
247C2×C3×D4—28no—
248C2×C3×D4—28no—
249C2×C3×D4—216no—
250C2×C3×D4—24no—
251C2×C3×D4—24no—
252C2×C3×D4—24no—
253C2×C3×D4—24no—
254C2×C3×D4—24no—
255C2×C3×D4—24no—
256C2×C3×D4—48no—
257C2×C3×D4—432no—
258C2×C3×D4—416no—
259C22×C3×C4—22no—
260C22×C3×C4—22no—
261C22×C3×C4—232no—
262C22×C3×C4—22no—
263C22×C3×C4—22no—
264C22×C3×C4—22no—
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—24no—
271C22×C3×C4—44no—
272C22×C3×C4C2×D414yes—
273C22×C3×C4C2×D414yes—
274C22×C3×C4C2×D414yes—
275C22×C3×C4C2×D414yes—
276C22×C3×C4C2×D414yes—
277C22×C3×C4C2×D414yes—
278C22×C3×C4C2×D414yes—
279C22×C3×C4#4114yes—
280C22×C3×C4C2414yes—
281C22×C3×C4C2411yescharacteristic
282C22×C3×C4C2411yescharacteristic
283C22×C3×C4C2411yescharacteristic
284C22×C3×C4C2411yescharacteristic
285C2×#67—24no—
286C2×#67—24no—
287C2×#67—24no—
288C2×#67—24no—
289C2×#67—24no—
290C2×#67—28no—
291C2×#67—216no—
292C2×#67—44no—
293C2×#67—48no—
294C2×#67—48no—
295C22×Dic3—28no—
296C22×Dic3—28no—
297C22×Dic3—44no—
298C22×Dic3C2412yes—
299C22×Dic3C2412yes—
300C22×Dic3C2414yes—
301C22×Dic3C2412yes—
302C22×Dic3C2414yes—
303#235—416no—
304C2×D12—22no—
305C2×D12—22no—
306C2×D12—22no—
307C2×C4×D3—24no—
308C2×C4×D3—24no—
309C2×C4×D3—24no—
310C2×Dic6—22no—
311C2×Dic6—22no—
312C2×Dic6—22no—
313C3×C4⋊C4—24no—
314C3×C4⋊C4—24no—
315C3×C22⋊C4—28no—
316C3×C22⋊C4—28no—
317#217—24no—
318#217—24no—
319#217—24no—
320#217—24no—
321#217—28no—
322#217—216no—
323#217—48no—
324#217—48no—
325#217C2×D418yes—
326(C2×D3)⋊C4—24no—
327(C2×D3)⋊C4—24no—
328(C2×D3)⋊C4—48no—
329C4⋊Dic3—22no—
330C4⋊Dic3—22no—
331C4⋊Dic3—24no—
332C4⋊Dic3—28no—
333C4⋊Dic3C2×D418yescomplemented
334Dic3⋊C4—24no—
335Dic3⋊C4—24no—
336Dic3⋊C4—48no—
337C4×Dic3—24no—
338C4×Dic3—24no—
339C4×Dic3—28no—
340C4×Dic3C2×D418yescomplemented
341C25C22×D311yescharacteristic
342C25C22×D312yes—
343C2×#41—64no—
344C2×#41—64no—
345C2×#41—64no—
346C22×Q8—31no—
347C22×D4—28no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—24no—
351C22×D4—32no—
352C22×D4—32no—
353C22×D4—32no—
354C22×D4—38no—
355C22×D4—31no—
356C22×D4—48no—
357C22×D4C22×D314yes—
358C22×D4C22×D312yes—
359C22×D4C22×D312yes—
360C22×D4C22×D314yes—
361C23×C4—24no—
362C23×C4—24no—
363C23×C4—34no—
364C23×C4—32no—
365C23×C4#6718yescomplemented
366C23×C4C22×D311yescharacteristic
367C23×C4C22×D311yescharacteristic
368C23×C4C22×D311yescharacteristic
369C23×C4C22×D311yescharacteristic
370C23×C4C22×D311yescharacteristic
371C23×C4C22×D312yes—
372C23×C4C22×D311yescharacteristic
373#127—68no—
374#124—68no—
375#123—68no—
376C22⋊Q8—64no—
377C22⋊Q8—64no—
378#121—28no—
379#121—28no—
380#121—28no—
381#121—28no—
382#121—616no—
383#121—64no—
384#121—64no—
385#121—1216no—
386#120—616no—
387#120—68no—
388C4×D4—68no—
389C4×D4—68no—
390#117—38no—
391#117—68no—
392#117—68no—
393#117—68no—
394#117—64no—
395#117—64no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—32no—
398C2×C4⋊C4—32no—
399C2×C4⋊C4—34no—
400C2×C4⋊C4—31no—
401C2×C4⋊C4—31no—
402C2×C4⋊C4—32no—
403C2×C4⋊C4—32no—
404C2×C4⋊C4—38no—
405C2×C4⋊C4—68no—
406C2×C4⋊C4C22×D312yes—
407C2×C4⋊C4C22×D312yes—
408C2×C22⋊C4—28no—
409C2×C22⋊C4—32no—
410C2×C22⋊C4—32no—
411C2×C22⋊C4—34no—
412C2×C22⋊C4—32no—
413C2×C22⋊C4—32no—
414C2×C22⋊C4—32no—
415C2×C22⋊C4—38no—
416C2×C22⋊C4—32no—
417C2×C22⋊C4—32no—
418C2×C22⋊C4—38no—
419C2×C22⋊C4—38no—
420C2×C22⋊C4—38no—
421C2×C22⋊C4—68no—
422C2×C22⋊C4C22×D314yes—
423C2×C22⋊C4C22×D314yes—
424C2×C42—32no—
425C2×C42—34no—
426C2×C42—32no—
427C2×C42—32no—
428C2×C42—68no—
429#95—38no—
430#95—38no—
431C23×C3—21no—
432C23×C3—21no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—28no—
437C23×C3—28no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—24no—
443C23×C3—24no—
444C23×C3—24no—
445C23×C3—28no—
446C23×C3—28no—
447C23×C3—44no—
448C23×C3—48no—
449C23×C3—48no—
450C23×C3—48no—
451C23×C3—48no—
452C23×C3—48no—
453C23×C3—88no—
454C23×C3—88no—
455C23×C3C22×D412yes—
456C23×C3C22×D412yes—
457C23×C3C22×D412yes—
458C23×C3C22×D412yes—
459C23×C3C2×#4112yes—
460C23×C3H(5,𝔽2)14yes—
461C23×C3C2511yescharacteristic
462C22×D3—22no—
463C22×D3—22no—
464C22×D3—22no—
465C22×D3—24no—
466C22×D3—24no—
467C3×D4—416no—
468C3×D4—416no—
469C3×D4—48no—
470C3×D4—48no—
471C2×C3×C4—28no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—28no—
477C2×C3×C4—28no—
478C2×C3×C4—28no—
479C2×C3×C4—28no—
480C2×C3×C4—24no—
481C2×C3×C4—28no—
482C2×C3×C4—48no—
483C2×C3×C4#121116yescomplemented
484C2×C3×C4C22×D412yes—
485C2×C3×C4C22×D412yes—
486C2×C3×C4C22×D412yes—
487C2×C3×C4C22×D412yes—
488C2×C3×C4C22×D412yes—
489C2×C3×C4C22×D412yes—
490C2×C3×C4C2×#4112yes—
491C2×C3×C4C2×#4112yes—
492#67—48no—
493#67—48no—
494#67—48no—
495#67—816no—
496C2×Dic3—24no—
497C2×Dic3—24no—
498C2×Dic3—24no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—24no—
505C2×Dic3—24no—
506C2×Dic3—24no—
507C2×Dic3—24no—
508C2×Dic3—416no—
509C2×Dic3C22×D418yes—
510D12—44no—
511C4×D3—48no—
512Dic6—44no—
513C24—22no—
514C24—22no—
515C24—24no—
516C24—24no—
517C24—24no—
518C24—24no—
519C24—32no—
520C24—42no—
521C24—44no—
522C24—44no—
523C24C2×#6714yes—
524C24C23×D314yes—
525C24C23×D311yescharacteristic
526C24C23×D311yescharacteristic
527C24C23×D311yescharacteristic
528#41—1216no—
529C2×Q8—62no—
530C2×Q8—62no—
531C2×Q8—62no—
532C2×D4—216no—
533C2×D4—28no—
534C2×D4—28no—
535C2×D4—24no—
536C2×D4—24no—
537C2×D4—24no—
538C2×D4—24no—
539C2×D4—24no—
540C2×D4—24no—
541C2×D4—48no—
542C2×D4—432no—
543C2×D4—416no—
544C2×D4—616no—
545C2×D4—64no—
546C2×D4—64no—
547C2×D4—68no—
548C2×D4—64no—
549C2×D4—64no—
550C2×D4—64no—
551C2×D4—62no—
552C2×D4—62no—
553C2×D4—62no—
554C2×D4—124no—
555C2×D4—128no—
556C2×D4—128no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—232no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—34no—
570C22×C4—32no—
571C22×C4—32no—
572C22×C4—34no—
573C22×C4—32no—
574C22×C4—44no—
575C22×C4—68no—
576C22×C4—68no—
577C22×C4—64no—
578C22×C4—64no—
579C22×C4—64no—
580C22×C4—124no—
581C22×C4D3×D414yes—
582C22×C4#23714yes—
583C22×C4C2×#6714yes—
584C22×C4C2×#6714yes—
585C22×C4C2×#6714yes—
586C22×C4C2×#6714yes—
587C22×C4C2×#6714yes—
588C22×C4C2×#6714yes—
589C22×C4C23×D314yes—
590C22×C4C23×D311yescharacteristic
591C22×C4C23×D311yescharacteristic
592C22×C4C23×D311yescharacteristic
593C22×C4C23×D311yescharacteristic
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—38no—
597C4⋊C4—68no—
598C4⋊C4—64no—
599C4⋊C4—62no—
600C4⋊C4—62no—
601C4⋊C4—64no—
602C4⋊C4—64no—
603C4⋊C4—128no—
604C22⋊C4—28no—
605C22⋊C4—28no—
606C22⋊C4—38no—
607C22⋊C4—68no—
608C22⋊C4—616no—
609C22⋊C4—64no—
610C22⋊C4—64no—
611C22⋊C4—64no—
612C22⋊C4—64no—
613C22⋊C4—64no—
614C22⋊C4—64no—
615C22⋊C4—128no—
616C22⋊C4—128no—
617C22⋊C4—128no—
618C42—38no—
619C42—68no—
620C42—64no—
621C42—64no—
622C22×C3—22no—
623C22×C3—22no—
624C22×C3—22no—
625C22×C3—22no—
626C22×C3—24no—
627C22×C3—24no—
628C22×C3—24no—
629C22×C3—24no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—22no—
633C22×C3—416no—
634C22×C3—42no—
635C22×C3—42no—
636C22×C3—44no—
637C22×C3—44no—
638C22×C3—44no—
639C22×C3—48no—
640C22×C3—48no—
641C22×C3—816no—
642C22×C3C2×#12114yes—
643C22×C3#53514yescomplemented
644C22×C3C23×D411yescharacteristic
645C22×C3C23×D411yescharacteristic
646C22×C3C22×#4111yescharacteristic
647C22×C3C2×H(5,𝔽2)12yes—
648C22×C3#58512yes—
649C2×D3—42no—
650C2×D3—42no—
651C2×D3—42no—
652C2×D3—44no—
653C2×D3—44no—
654C3×C4—22no—
655C3×C4—22no—
656C3×C4—44no—
657C3×C4C2×#12114yes—
658C3×C4C2×#12114yes—
659Dic3—28no—
660Dic3—42no—
661Dic3—42no—
662Dic3—42no—
663Dic3—44no—
664C23—21no—
665C23—21no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—21no—
670C23—21no—
671C23—22no—
672C23—22no—
673C23—28no—
674C23—28no—
675C23—24no—
676C23—24no—
677C23—28no—
678C23—28no—
679C23—24no—
680C23—44no—
681C23—48no—
682C23—48no—
683C23—48no—
684C23—48no—
685C23—48no—
686C23—62no—
687C23—62no—
688C23—64no—
689C23—64no—
690C23—62no—
691C23—88no—
692C23—88no—
693C23C2×D3×D412yes—
694C23C2×#23712yes—
695C23#100414yes—
696C23C22×#6712yes—
697C23C22×#6712yes—
698C23C22×#6712yes—
699C23C24×D311yescharacteristic
700Q8—124no—
701D4—416no—
702D4—416no—
703D4—48no—
704D4—48no—
705D4—128no—
706D4—128no—
707D4—128no—
708D4—124no—
709D4—2416no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—28no—
715C2×C4—28no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—24no—
721C2×C4—38no—
722C2×C4—48no—
723C2×C4—64no—
724C2×C4—64no—
725C2×C4—64no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—64no—
729C2×C4—64no—
730C2×C4—64no—
731C2×C4—64no—
732C2×C4—62no—
733C2×C4—62no—
734C2×C4—62no—
735C2×C4—1216no—
736C2×C4—128no—
737C2×C4#939116yescomplemented
738C2×C4C2×D3×D412yes—
739C2×C4C2×D3×D412yes—
740C2×C4C2×#23712yes—
741C2×C4C2×#23712yes—
742C2×C4C22×#6712yes—
743C2×C4C22×#6712yes—
744C2×C4C22×#6712yes—
745C2×C4C22×#6712yes—
746C2×C3—24no—
747C2×C3—24no—
748C2×C3—42no—
749C2×C3—84no—
750C2×C3C22×#12111yescharacteristic
751C2×C3C2×#53511yescharacteristic
752C2×C3#344911yescharacteristic
753C2×C3#348812yes—
754C2×C3#349412yes—
755D3—82no—
756C22—24no—
757C22—24no—
758C22—24no—
759C22—24no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—416no—
768C22—42no—
769C22—42no—
770C22—48no—
771C22—48no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—816no—
776C22—124no—
777C22—124no—
778C22—122no—
779C22—122no—
780C22—122no—
781C22C2×#93914yes—
782C22#580514yescomplemented
783C22C22×D3×D411yescharacteristic
784C22C22×#23711yescharacteristic
785C22C2×#100412yes—
786C22#596412yes—
787C22C23×#6711yescharacteristic
788C4—22no—
789C4—22no—
790C4—44no—
791C4—68no—
792C4—124no—
793C4—122no—
794C4—122no—
795C4—122no—
796C4C2×#93914yes—
797C4C2×#93914yes—
798C3#3525211yescharacteristic, complemented, Sylow
799C2—24no—
800C2—24no—
801C2—42no—
802C2—84no—
803C2—242no—
804C2#8593612yes—
805C2#8594912yes—
806C2C22×#93911yescharacteristic
807C2C2×#580511yescharacteristic
808C2#8726811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC22×C3×#121C2
hypercenterC22×#121D3
hypocenterC3#35252
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×C3×#121C2semidirect
2. C2×#5805C2semidirect
3. C2×#5791C2semidirect
4. C22×#926C2semidirect
5. #84048C2semidirect
6. #84044C2semidirect
7. #82705C2semidirect
8. #82704C2semidirect
9. #82700C2semidirect
10. #82698C2semidirect
11. #82677C2semidirect
12. #82676C2semidirect
13. #82186C2semidirect
14. #82157C2semidirect
15. #82106C2semidirect
32. C2×#940C22semidirect
33. C2×#939C22semidirect
34. C2×#938C22semidirect
35. C2×#936C22semidirect
37. C2×#930C22semidirect
38. C2×#930C22semidirect
40. C2×C4×#67C22semidirect
41. C2×C4×#67C22semidirect
47. C2×#926C22semidirect
48. C2×#926C22semidirect
49. C22×C4⋊Dic3C22semidirect
50. C2×#924C22semidirect
51. C2×#924C22semidirect
52. C22×C4×Dic3C22semidirect
54. #5223C22semidirect
55. #5222C22semidirect
56. #5221C22semidirect
57. #5221C22semidirect
58. #5221C22semidirect
59. #5220C22semidirect
62. #4988C22semidirect
63. #4987C22semidirect
64. #4977C22semidirect
65. #4975C22semidirect
66. #4973C22semidirect
67. #4972C22semidirect
68. #4961C22semidirect
69. #4957C22semidirect
70. #4948C22semidirect
71. #4945C22semidirect
74. C22×#121D3semidirect
100. C23×C3×C4D4semidirect
158. #926D4semidirect
333. C4⋊Dic3C2×D4semidirect
340. C4×Dic3C2×D4semidirect
365. C23×C4#67semidirect
483. C2×C3×C4#121semidirect
643. C22×C3#535semidirect
737. C2×C4#939semidirect
782. C22#5805semidirect
798. C3#35252semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#1212
C2×#58052
C2×#57912
C22×#9262
#840482
#840442
#827052
#827042
#827002
#826982
#826772
#826762
#821862
#821572
#821062
#352523