Finite Group Databasebeta

← #11634140

Subgroups — #11634140

Order 768.

2310 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#555C211yesmaximal, characteristic, complemented
2C2×#5728C211yesmaximal, characteristic, complemented
3#83230C211yesmaximal, characteristic, complemented
4#83006C214yesmaximal, complemented
5#82963C214yesmaximal, complemented
6#82703C212yesmaximal, complemented
7#82668C212yesmaximal, complemented
8#82661C212yesmaximal, complemented
9#82646C212yesmaximal, complemented
10C4×#938C211yesmaximal, characteristic, complemented
11C4×#938C211yesmaximal, characteristic, complemented
12#82382C211yesmaximal, characteristic, complemented
13#82379C211yesmaximal, characteristic, complemented
14#82277C212yesmaximal, complemented
15#82249C212yesmaximal, complemented
16#82243C212yesmaximal, complemented
17#82241C212yesmaximal, complemented
18#59050—31nomaximal, Sylow
19C3×#555—28no—
20C2×C3×C4⋊Q8C2211yescharacteristic
21C2×C3×#124C2214yes—
22C2×C3×#121C2212yes—
23C2×C3×#121C2212yes—
24C2×C3×C4×D4C2211yescharacteristic
25C2×C3×C4×D4C2211yescharacteristic
26C2×C3×#117C2212yes—
27C2×C3×#117C2212yes—
28C2×#946C2212yes—
29C2×Q8×Dic3C2212yes—
30C2×#938C2211yescharacteristic
31C2×#938C2211yescharacteristic
32C2×#936C2212yes—
33C2×C4×#67C2212yes—
34C2×C4×#67C2212yes—
35C2×#924C2212yes—
36C2×#924C2212yes—
37#5728—28no—
38C2×#897C2212yes—
39C2×#892C2212yes—
40C2×#890C2212yes—
41C2×#887C2212yes—
42C2×C42×D3C2211yescharacteristic
43C2×#869C2211yescharacteristic
44#5229C2214yes—
45#5223C2214yes—
46#5222C2214yes—
47#5221C2214yes—
48#5221C2212yes—
49#5221C2214yes—
50#5221C2211yescharacteristic
51#5221C2211yescharacteristic
52#5212C2212yes—
53#5212C2212yes—
54C4×#217C2212yes—
55C4×#217C2212yes—
56#4987C2211yescharacteristic
57#4987C2211yescharacteristic
58#4984C2212yes—
59#4984C2212yes—
60#4975C2212yes—
61Dic3×C4⋊C4C2212yes—
62Dic3×C4⋊C4C2212yes—
63#4973C2212yes—
64#4972C2211yescharacteristic
65#4972C2211yescharacteristic
66#4961C2214yes—
67#4957C2214yes—
68#4956C2212yes—
69#4956C2212yes—
70#4953C2214yes—
71#4953C2214yes—
72#4949C2214yes—
73#4949C2214yes—
74#4948C2214yes—
75#4945C2214yes—
76#4944C2214yes—
77#4944C2212yes—
78#4944C2212yes—
79#4944C2214yes—
80#4940C2214yes—
81C4×C4⋊Dic3C2211yescharacteristic
82C4×C4⋊Dic3C2211yescharacteristic
83#4933C2214yes—
84C4×Dic3⋊C4C2214yes—
85#4928C2214yes—
86C2×#555D311yescharacteristic, complemented
87C2×#533—31no—
88#2730—34no—
89#2547—31no—
90#2542—31no—
91#2540—32no—
92#2490—32no—
93#2448—34no—
94#2441—32no—
95#2426—32no—
96#2415—32no—
97#2414—32no—
98#2369—31no—
99#2362—32no—
100#2354—32no—
101C4×#121—31no—
102C4×#121—31no—
103C22×C3×Q8C2312yes—
104C22×C3×D4C2311yescharacteristic
105C22×C3×D4C2311yescharacteristic
106C22×C3×D4C2314yes—
107C23×C3×C4C2312yes—
108C23×C3×C4C2312yes—
109C22×#67C2312yes—
110C22×#67C2312yes—
111C22×C4×D3C2311yescharacteristic
112C22×C4×D3C2311yescharacteristic
113C22×C4×D3C2311yescharacteristic
114C22×Dic6C2312yes—
115C3×C4⋊Q8D418yescomplemented
116C3×#124—216no—
117C3×#121—28no—
118C3×#121—28no—
119C3×C4×D4—24no—
120C3×C4×D4—24no—
121C3×#117—28no—
122C3×#117—28no—
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2312yes—
126C2×C3×C4⋊C4C2312yes—
127C2×C3×C22⋊C4C2314yes—
128C2×C3×C22⋊C4C2314yes—
129C2×C3×C22⋊C4C2312yes—
130C2×C3×C22⋊C4C2312yes—
131C2×C3×C42C2314yes—
132C2×C3×C42C2311yescharacteristic
133C2×#217C2312yes—
134C2×#217C2312yes—
135C2×#217C2314yes—
136C2×#217C2312yes—
137C2×#217C2312yes—
138C2×#217C2314yes—
139C2×#217C2312yes—
140C2×#217C2312yes—
141C2×#217C2314yes—
142C2×#217C2314yes—
143#946—28no—
144Q8×Dic3—28no—
145#938—24no—
146#938—24no—
147#936—44no—
148C4×#67—28no—
149C4×#67—44no—
150C2×(C2×D3)⋊C4C2312yes—
151C2×(C2×D3)⋊C4C2314yes—
152C2×(C2×D3)⋊C4C2312yes—
153C2×C4⋊Dic3C2314yes—
154C2×C4⋊Dic3C2311yescharacteristic
155C2×C4⋊Dic3C2311yescharacteristic
156C2×C4⋊Dic3C2311yescharacteristic
157C2×C4⋊Dic3C2312yes—
158C2×C4⋊Dic3C2312yes—
159C2×C4⋊Dic3C2314yes—
160C2×C4⋊Dic3C2311yescharacteristic
161#924—28no—
162#924—44no—
163C2×Dic3⋊C4C2312yes—
164C2×Dic3⋊C4C2314yes—
165C2×Dic3⋊C4C2314yes—
166C2×Dic3⋊C4C2312yes—
167C2×Dic3⋊C4C2314yes—
168C2×C4×Dic3C2314yes—
169C2×C4×Dic3C2312yes—
170C2×C4×Dic3C2312yes—
171C2×C4×Dic3C2311yescharacteristic
172C2×C4×Dic3C2311yescharacteristic
173C2×C4×Dic3C2311yescharacteristic
174C2×C4×Dic3C2314yes—
175#897—28no—
176#892—28no—
177#890—28no—
178#887—28no—
179C42×D3—24no—
180#869—24no—
181C3⋊#95C2312yes—
182C3⋊#95C2314yes—
183C3⋊#95C2312yes—
184C3⋊#95C2314yes—
185C3⋊#95C2312yes—
186C3⋊#95C2312yes—
187C3⋊#95C2314yes—
188C3⋊#95C2312yes—
189C3⋊#95C2312yes—
190C3⋊#95C2314yes—
191#555—28no—
192#533—68no—
193C2×C4⋊Q8—31no—
194C2×C4⋊Q8C2×D311yescharacteristic
195C2×#125—32no—
196C2×#124—32no—
197C2×#124C2×D314yes—
198C2×C22⋊Q8—32no—
199C2×C22⋊Q8—32no—
200C2×C22⋊Q8—32no—
201C2×C22⋊Q8—32no—
202C2×#121—31no—
203C2×#121—31no—
204C2×#121C2×D312yes—
205C2×#121C2×D312yes—
206C2×C4×Q8—32no—
207C2×C4×Q8—32no—
208C2×C4×D4—32no—
209C2×C4×D4—32no—
210C2×C4×D4C2×D311yescharacteristic
211C2×C4×D4C2×D311yescharacteristic
212C2×#117—32no—
213C2×#117C2×D312yes—
214C2×#117C2×D312yes—
215C22×C42—31no—
216#399—34no—
217#399—34no—
218#397—34no—
219#397—34no—
220#396—34no—
221#394—34no—
222#394—34no—
223#392—34no—
224#391—34no—
225#391—32no—
226#390—34no—
227#390—32no—
228#390—31no—
229#390—34no—
230#390—31no—
231#390—34no—
232#389—31no—
233#389—32no—
234#389—32no—
235#389—31no—
236#389—34no—
237#388—34no—
238#388—34no—
239#388—34no—
240#388—32no—
241#388—32no—
242#388—34no—
243#387—34no—
244#386—32no—
245#386—32no—
246#384—32no—
247#380—32no—
248#380—32no—
249#380—31no—
250#380—31no—
251C4×C4⋊C4—32no—
252C4×C4⋊C4—32no—
253C4×C4⋊C4—34no—
254C4×C4⋊C4—31no—
255C4×C4⋊C4—31no—
256C4×C22⋊C4—32no—
257C4×C22⋊C4—32no—
258C24×C3C2412yes—
259C24×C3C2412yes—
260C23×D3C2411yescharacteristic
261C2×C3×Q8—42no—
262C2×C3×Q8—42no—
263C2×C3×Q8C2×D418yes—
264C2×C3×D4—22no—
265C2×C3×D4—22no—
266C2×C3×D4—28no—
267C2×C3×D4—22no—
268C2×C3×D4—22no—
269C2×C3×D4—22no—
270C2×C3×D4—22no—
271C2×C3×D4—44no—
272C2×C3×D4—44no—
273C22×C3×C4—24no—
274C22×C3×C4—24no—
275C22×C3×C4—24no—
276C22×C3×C4—24no—
277C22×C3×C4—24no—
278C22×C3×C4—24no—
279C22×C3×C4C2412yes—
280C22×C3×C4C2412yes—
281C22×C3×C4C2411yescharacteristic
282C22×C3×C4C2414yes—
283C22×C3×C4C2411yescharacteristic
284C22×C3×C4C2411yescharacteristic
285C2×#67—24no—
286C2×#67—24no—
287C2×#67—24no—
288C2×#67—42no—
289C2×#67—42no—
290C2×#67—42no—
291C22×Dic3C2412yes—
292C22×Dic3C2412yes—
293C22×Dic3C2411yescharacteristic
294C22×Dic3C2412yes—
295C22×Dic3C2411yescharacteristic
296C22×Dic3C2414yes—
297C22×Dic3C2412yes—
298C22×Dic3C2411yescharacteristic
299C2×C4×D3—22no—
300C2×C4×D3—22no—
301C2×C4×D3—22no—
302C2×C4×D3—22no—
303C2×C4×D3—22no—
304C2×C4×D3—22no—
305C2×C4×D3—41no—
306C2×C4×D3—41no—
307C2×C4×D3#4114yes—
308C2×Dic6—24no—
309C2×Dic6—24no—
310C2×Dic6—24no—
311C3×C4⋊C4—22no—
312C3×C4⋊C4—22no—
313C3×C4⋊C4C2×D418yes—
314C3×C4⋊C4C2×D418yes—
315C3×C22⋊C4—28no—
316C3×C22⋊C4—28no—
317C3×C22⋊C4—24no—
318C3×C22⋊C4—24no—
319C3×C42—28no—
320C3×C42C2×D414yes—
321#217—28no—
322#217—24no—
323#217—24no—
324#217—24no—
325#217—44no—
326#217—42no—
327#217—44no—
328#217—44no—
329#217—42no—
330#217—42no—
331(C2×D3)⋊C4—24no—
332(C2×D3)⋊C4—28no—
333(C2×D3)⋊C4—42no—
334C4⋊Dic3—24no—
335C4⋊Dic3—24no—
336C4⋊Dic3—28no—
337C4⋊Dic3—22no—
338C4⋊Dic3—22no—
339C4⋊Dic3—22no—
340C4⋊Dic3—44no—
341C4⋊Dic3#4114yes—
342Dic3⋊C4—28no—
343Dic3⋊C4—28no—
344Dic3⋊C4—24no—
345Dic3⋊C4—44no—
346Dic3⋊C4—42no—
347C4×Dic3—22no—
348C4×Dic3—22no—
349C4×Dic3—22no—
350C4×Dic3—28no—
351C4×Dic3—24no—
352C4×Dic3—24no—
353C4×Dic3—44no—
354C22×Q8—32no—
355C22×Q8C22×D312yes—
356C22×D4—32no—
357C22×D4—32no—
358C22×D4C22×D311yescharacteristic
359C22×D4C22×D311yescharacteristic
360C22×D4C22×D314yes—
361C23×C4—31no—
362C23×C4—31no—
363C23×C4—31no—
364C23×C4C22×D312yes—
365C23×C4C22×D312yes—
366C4⋊Q8—64no—
367C4⋊Q8#6718yescomplemented
368#125—68no—
369#124—216no—
370#124—124no—
371C22⋊Q8—68no—
372C22⋊Q8—68no—
373C22⋊Q8—68no—
374C22⋊Q8—124no—
375#121—28no—
376#121—28no—
377#121—64no—
378#121—64no—
379C4×Q8—68no—
380C4×Q8—68no—
381C4×D4—24no—
382C4×D4—24no—
383C4×D4—68no—
384C4×D4—124no—
385#117—28no—
386#117—28no—
387#117—68no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—32no—
390C2×C4⋊C4—32no—
391C2×C4⋊C4—34no—
392C2×C4⋊C4—34no—
393C2×C4⋊C4—32no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—34no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—32no—
399C2×C4⋊C4—34no—
400C2×C4⋊C4—34no—
401C2×C4⋊C4C22×D311yescharacteristic
402C2×C4⋊C4C22×D311yescharacteristic
403C2×C4⋊C4C22×D312yes—
404C2×C4⋊C4C22×D312yes—
405C2×C22⋊C4—32no—
406C2×C22⋊C4—32no—
407C2×C22⋊C4—32no—
408C2×C22⋊C4—34no—
409C2×C22⋊C4—34no—
410C2×C22⋊C4—32no—
411C2×C22⋊C4—32no—
412C2×C22⋊C4—34no—
413C2×C22⋊C4—34no—
414C2×C22⋊C4—34no—
415C2×C22⋊C4—32no—
416C2×C22⋊C4—32no—
417C2×C22⋊C4—32no—
418C2×C22⋊C4C22×D314yes—
419C2×C22⋊C4C22×D314yes—
420C2×C22⋊C4C22×D312yes—
421C2×C22⋊C4C22×D312yes—
422C2×C42—34no—
423C2×C42—32no—
424C2×C42—32no—
425C2×C42—31no—
426C2×C42—31no—
427C2×C42—31no—
428C2×C42—34no—
429C2×C42—64no—
430C2×C42C22×D314yes—
431C2×C42C22×D311yescharacteristic
432#95—32no—
433#95—32no—
434#95—32no—
435#95—32no—
436#95—34no—
437#95—32no—
438#95—32no—
439#95—34no—
440#95—34no—
441#95—34no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3C2511yescharacteristic
457C22×D3—21no—
458C22×D3—21no—
459C22×D3—21no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3—21no—
463C22×D3C2×#4112yes—
464C3×Q8—48no—
465C3×D4—44no—
466C3×D4—44no—
467C3×D4—88no—
468C2×C3×C4—24no—
469C2×C3×C4—24no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—48no—
479C2×C3×C4—48no—
480C2×C3×C4C22×D418yes—
481C2×C3×C4C22×D412yes—
482C2×C3×C4C22×D412yes—
483C2×C3×C4C22×D412yes—
484C2×C3×C4C2×#4112yes—
485C2×C3×C4C2×#4112yes—
486C2×C3×C4H(5,𝔽2)12yes—
487C2×C3×C42−1+412yes—
488#67—48no—
489#67—48no—
490C2×Dic3—21no—
491C2×Dic3—22no—
492C2×Dic3—21no—
493C2×Dic3—22no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—24no—
497C2×Dic3—22no—
498C2×Dic3—24no—
499C2×Dic3—22no—
500C2×Dic3—21no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—21no—
505C2×Dic3—24no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3C2×#4114yes—
513C2×Dic3C2×#4112yes—
514C4×D3—28no—
515C4×D3—44no—
516C4×D3—44no—
517Dic6—48no—
518C24—31no—
519C24C23×D312yes—
520C24C23×D312yes—
521C2×Q8—42no—
522C2×Q8—42no—
523C2×Q8—64no—
524C2×Q8—64no—
525C2×Q8—64no—
526C2×Q8C2×#6718yes—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—28no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—64no—
537C2×D4—64no—
538C2×D4—64no—
539C2×D4—122no—
540C2×D4—122no—
541C2×D4—122no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—32no—
549C22×C4—31no—
550C22×C4—34no—
551C22×C4—32no—
552C22×C4—32no—
553C22×C4—31no—
554C22×C4—32no—
555C22×C4—31no—
556C22×C4—34no—
557C22×C4—62no—
558C22×C4—62no—
559C22×C4—62no—
560C22×C4—62no—
561C22×C4—62no—
562C22×C4—62no—
563C22×C4—121no—
564C22×C4—121no—
565C22×C4C23×D312yes—
566C22×C4C23×D312yes—
567C22×C4C23×D311yescharacteristic
568C22×C4C23×D314yes—
569C22×C4C23×D311yescharacteristic
570C22×C4C23×D311yescharacteristic
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—34no—
574C4⋊C4—64no—
575C4⋊C4—68no—
576C4⋊C4—62no—
577C4⋊C4—62no—
578C4⋊C4—62no—
579C4⋊C4—64no—
580C4⋊C4—68no—
581C4⋊C4—68no—
582C4⋊C4—64no—
583C4⋊C4—122no—
584C4⋊C4—124no—
585C4⋊C4—124no—
586C4⋊C4C2×#6718yes—
587C4⋊C4C2×#6718yes—
588C22⋊C4—28no—
589C22⋊C4—28no—
590C22⋊C4—24no—
591C22⋊C4—24no—
592C22⋊C4—64no—
593C22⋊C4—64no—
594C22⋊C4—64no—
595C22⋊C4—64no—
596C22⋊C4—68no—
597C22⋊C4—68no—
598C22⋊C4—122no—
599C22⋊C4—122no—
600C22⋊C4—124no—
601C22⋊C4—124no—
602C22⋊C4—124no—
603C22⋊C4—122no—
604C22⋊C4—122no—
605C42—28no—
606C42—64no—
607C42—64no—
608C42—62no—
609C42—62no—
610C42—62no—
611C42—68no—
612C42—124no—
613C42C2×#6714yes—
614C22×C3—42no—
615C22×C3—42no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—42no—
620C22×C3—42no—
621C22×C3—42no—
622C22×C3—42no—
623C22×C3—42no—
624C22×C3—42no—
625C22×C3—42no—
626C22×C3—42no—
627C22×C3—42no—
628C22×C3C23×D411yescharacteristic
629C22×C3C22×#4111yescharacteristic
630C22×C3C22×#4111yescharacteristic
631C22×C3C2×H(5,𝔽2)11yescharacteristic
632C22×C3C2×2−1+411yescharacteristic
633C22×C3#58511yescharacteristic
634C22×C3#58511yescharacteristic
635C2×D3—22no—
636C2×D3—22no—
637C2×D3—22no—
638C2×D3—41no—
639C2×D3—41no—
640C2×D3—41no—
641C2×D3—41no—
642C3×C4—22no—
643C3×C4—28no—
644C3×C4—42no—
645C3×C4—42no—
646C3×C4#54814yes—
647C3×C4#55014yes—
648Dic3—22no—
649Dic3—24no—
650Dic3—44no—
651Dic3—41no—
652Dic3—41no—
653Dic3—42no—
654Dic3—42no—
655Dic3—42no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—32no—
671C23—61no—
672C23—61no—
673C23—61no—
674C23—61no—
675C23—61no—
676C23—61no—
677C23C24×D311yescharacteristic
678Q8—48no—
679Q8—128no—
680D4—44no—
681D4—44no—
682D4—88no—
683D4—128no—
684D4—128no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—32no—
696C2×C4—34no—
697C2×C4—48no—
698C2×C4—48no—
699C2×C4—62no—
700C2×C4—61no—
701C2×C4—62no—
702C2×C4—61no—
703C2×C4—68no—
704C2×C4—62no—
705C2×C4—61no—
706C2×C4—62no—
707C2×C4—64no—
708C2×C4—62no—
709C2×C4—62no—
710C2×C4—64no—
711C2×C4—62no—
712C2×C4—61no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—64no—
722C2×C4—124no—
723C2×C4—124no—
724C2×C4D3×#4112yes—
725C2×C4D3×#4112yes—
726C2×C4#100912yes—
727C2×C4#101012yes—
728C2×C4C22×#6718yes—
729C2×C4C22×#6712yes—
730C2×C4C22×#6712yes—
731C2×C4C22×#6712yes—
732C2×C3—82no—
733C2×C3—82no—
734C2×C3C2×#54811yescharacteristic
735C2×C3C2×#55011yescharacteristic
736C2×C3#347511yescharacteristic
737C2×C3#348511yescharacteristic
738C2×C3#350611yescharacteristic
739C2×C3#351811yescharacteristic
740C2×C3#354711yescharacteristic
741D3—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—62no—
757C22—62no—
758C22—62no—
759C22—121no—
760C22—121no—
761C22—121no—
762C22—121no—
763C22C2×D3×#4111yescharacteristic
764C22C2×D3×#4111yescharacteristic
765C22C2×#100911yescharacteristic
766C22C2×#101011yescharacteristic
767C22#596611yescharacteristic
768C22#596611yescharacteristic
769C22C23×#6711yescharacteristic
770C4—22no—
771C4—28no—
772C4—42no—
773C4—42no—
774C4—64no—
775C4—62no—
776C4—122no—
777C4—122no—
778C4—122no—
779C4—121no—
780C4—124no—
781C4—121no—
782C4#583114yes—
783C4#583414yes—
784C3#5905011yescharacteristic, complemented, Sylow
785C2—82no—
786C2—82no—
787C2—122no—
788C2#8695811yescharacteristic
789C2#8696311yescharacteristic
790C2#8697311yescharacteristic
791C2#8697711yescharacteristic
792C2C2×#583111yescharacteristic
793C2C2×#583411yescharacteristic
794C2#8728011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×#555C2
hypercenterC2×#555D3
hypocenterC3#59050
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. C2×C3×#555C2semidirect
2. C2×#5728C2semidirect
3. #83230C2semidirect
4. #83006C2semidirect
5. #82963C2semidirect
6. #82703C2semidirect
7. #82668C2semidirect
8. #82661C2semidirect
9. #82646C2semidirect
10. C4×#938C2semidirect
11. C4×#938C2semidirect
12. #82382C2semidirect
13. #82379C2semidirect
14. #82277C2semidirect
15. #82249C2semidirect
16. #82243C2semidirect
17. #82241C2semidirect
86. C2×#555D3semidirect
115. C3×C4⋊Q8D4semidirect
367. C4⋊Q8#67semidirect
784. C3#59050semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5552
C2×#57282
#832302
#830062
#829632
#827032
#826682
#826612
#826462
C4×#9382
#823822
#823792
#822772
#822492
#822432
#822412
#590503