Finite Group Databasebeta

← #11633810

Subgroups — #11633810

Order 768.

2458 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#547C211yesmaximal, characteristic, complemented
2C2×#5728C211yesmaximal, characteristic, complemented
3#84097C212yesmaximal, complemented
4#84089C212yesmaximal, complemented
5#83229C211yesmaximal, characteristic, complemented
6#82878C214yesmaximal, complemented
7#82851C214yesmaximal, complemented
8#82777C212yesmaximal, complemented
9#82753C212yesmaximal, complemented
10#82703C212yesmaximal, complemented
11#82661C212yesmaximal, complemented
12C4×#938C211yesmaximal, characteristic, complemented
13C4×#938C211yesmaximal, characteristic, complemented
14#82384C211yesmaximal, characteristic, complemented
15#82384C211yesmaximal, characteristic, complemented
16#82172C212yesmaximal, complemented
17#82161C212yesmaximal, complemented
18#59034—31nomaximal, Sylow
19C22×C3×#41C2212yes—
20C3×#547—28no—
21C2×C3×C4⋊Q8C2211yescharacteristic
22C2×C3×#123C2214yes—
23C2×C3×C22⋊Q8C2212yes—
24C2×C3×#121C2212yes—
25C2×C3×C4×D4C2211yescharacteristic
26C2×C3×C4×D4C2211yescharacteristic
27C22×C3×C4⋊C4C2212yes—
28C2×#946C2212yes—
29C2×Q8×Dic3C2212yes—
30C2×Q8×Dic3C2212yes—
31C2×#938C2211yescharacteristic
32C2×#938C2211yescharacteristic
33C2×C4×#67C2212yes—
34C2×C4×#67C2212yes—
35#5728—28no—
36C2×#897C2212yes—
37C2×#892C2212yes—
38C2×#890C2212yes—
39C2×#887C2212yes—
40C2×C42×D3C2211yescharacteristic
41C2×#869C2211yescharacteristic
42#5229C2212yes—
43#5223C2214yes—
44#5222C2214yes—
45#5221C2214yes—
46#5221C2212yes—
47#5221C2211yescharacteristic
48#5221C2212yes—
49#5221C2214yes—
50#5221C2211yescharacteristic
51#5213C2214yes—
52#5212C2212yes—
53#5212C2212yes—
54#5212C2212yes—
55#5212C2214yes—
56#5212C2212yes—
57#5210C2214yes—
58C4×#217C2212yes—
59C4×#217C2214yes—
60C4×#217C2212yes—
61#4990C2214yes—
62#4987C2211yescharacteristic
63#4987C2211yescharacteristic
64#4986C2214yes—
65#4984C2212yes—
66#4982C2214yes—
67#4980C2214yes—
68#4978C2214yes—
69#4977C2212yes—
70#4977C2212yes—
71Dic3×C4⋊C4C2212yes—
72#4972C2211yescharacteristic
73#4972C2211yescharacteristic
74#4961C2214yes—
75#4956C2212yes—
76#4956C2212yes—
77#4953C2214yes—
78#4947C2214yes—
79#4947C2214yes—
80#4945C2214yes—
81#4944C2214yes—
82#4944C2212yes—
83#4944C2212yes—
84C4×C4⋊Dic3C2211yescharacteristic
85C4×C4⋊Dic3C2211yescharacteristic
86C2×#547D311yescharacteristic, complemented
87C2×#533—31no—
88#2696—34no—
89#2563—31no—
90#2563—31no—
91#2536—32no—
92#2490—32no—
93#2458—34no—
94#2442—32no—
95#2421—32no—
96#2414—32no—
97#2407—32no—
98#2365—31no—
99#2352—32no—
100#2341—32no—
101C4×#121—31no—
102C4×#121—31no—
103C2×C3×#41—28no—
104C2×C3×#41—28no—
105C2×C3×#41—44no—
106C22×C3×Q8C2312yes—
107C22×C3×D4C2311yescharacteristic
108C22×C3×D4C2314yes—
109C22×C3×D4C2311yescharacteristic
110C23×C3×C4C2312yes—
111C23×C3×C4C2312yes—
112C23×C3×C4C2314yes—
113C22×#67C2312yes—
114C22×#67C2312yes—
115C22×C4×D3C2311yescharacteristic
116C22×C4×D3C2311yescharacteristic
117C22×C4×D3C2311yescharacteristic
118C22×Dic6C2312yes—
119C3×C4⋊Q8D418yescomplemented
120C3×#123—216no—
121C3×C22⋊Q8—28no—
122C3×#121—28no—
123C3×C4×D4—24no—
124C3×C4×D4—24no—
125C2×C3×C4⋊C4—28no—
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C4⋊C4C2314yes—
129C2×C3×C4⋊C4C2312yes—
130C2×C3×C4⋊C4C2312yes—
131C2×C3×C22⋊C4C2314yes—
132C2×C3×C22⋊C4C2312yes—
133C2×C3×C22⋊C4C2312yes—
134C2×C3×C42C2311yescharacteristic
135C2×#217C2312yes—
136C2×#217C2312yes—
137C2×#217C2312yes—
138C2×#217C2312yes—
139C2×#217C2314yes—
140C2×#217C2314yes—
141C2×#217C2314yes—
142C2×#217C2314yes—
143C2×#217C2312yes—
144C2×#217C2312yes—
145#946—28no—
146Q8×Dic3—28no—
147Q8×Dic3—44no—
148#938—24no—
149#938—24no—
150C4×#67—28no—
151C4×#67—44no—
152C2×(C2×D3)⋊C4C2312yes—
153C2×(C2×D3)⋊C4C2314yes—
154C2×(C2×D3)⋊C4C2312yes—
155C2×C4⋊Dic3C2311yescharacteristic
156C2×C4⋊Dic3C2311yescharacteristic
157C2×C4⋊Dic3C2311yescharacteristic
158C2×C4⋊Dic3C2311yescharacteristic
159C2×C4⋊Dic3C2314yes—
160C2×C4⋊Dic3C2312yes—
161C2×C4⋊Dic3C2312yes—
162C2×C4⋊Dic3C2314yes—
163C2×Dic3⋊C4C2312yes—
164C2×Dic3⋊C4C2314yes—
165C2×Dic3⋊C4C2312yes—
166C2×C4×Dic3C2312yes—
167C2×C4×Dic3C2312yes—
168C2×C4×Dic3C2311yescharacteristic
169C2×C4×Dic3C2314yes—
170C2×C4×Dic3C2311yescharacteristic
171C2×C4×Dic3C2311yescharacteristic
172C2×C4×Dic3C2314yes—
173#897—28no—
174#892—28no—
175#890—28no—
176#887—28no—
177C42×D3—24no—
178#869—24no—
179C3⋊#95C2312yes—
180C3⋊#95C2312yes—
181C3⋊#95C2312yes—
182C3⋊#95C2314yes—
183C3⋊#95C2312yes—
184C3⋊#95C2314yes—
185C3⋊#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2312yes—
189C3⋊#95C2314yes—
190C3⋊#95C2312yes—
191C22×#41C2×D312yes—
192#547—28no—
193#533—68no—
194C2×C4⋊Q8—31no—
195C2×C4⋊Q8C2×D311yescharacteristic
196C2×#125—32no—
197C2×#123C2×D314yes—
198C2×C22⋊Q8—32no—
199C2×C22⋊Q8—32no—
200C2×C22⋊Q8C2×D312yes—
201C2×#121—31no—
202C2×#121—31no—
203C2×#121C2×D312yes—
204C2×C4×Q8—32no—
205C2×C4×Q8—32no—
206C2×C4×Q8—32no—
207C2×C4×D4—32no—
208C2×C4×D4—32no—
209C2×C4×D4C2×D311yescharacteristic
210C2×C4×D4C2×D311yescharacteristic
211C2×#117—32no—
212C22×C4⋊C4C2×D312yes—
213C22×C42—31no—
214#400—34no—
215#398—34no—
216#397—34no—
217#394—34no—
218#394—34no—
219#393—34no—
220#393—34no—
221#392—34no—
222#391—32no—
223#390—32no—
224#390—32no—
225#390—31no—
226#390—34no—
227#390—34no—
228#390—31no—
229#389—32no—
230#389—31no—
231#389—31no—
232#388—34no—
233#388—34no—
234#388—32no—
235#388—32no—
236#388—34no—
237#387—34no—
238#387—34no—
239#386—34no—
240#386—32no—
241#386—32no—
242#385—34no—
243#382—32no—
244#382—32no—
245#380—32no—
246#380—32no—
247#380—32no—
248#380—32no—
249#380—34no—
250#380—31no—
251#380—31no—
252C4×C4⋊C4—32no—
253C4×C4⋊C4—31no—
254C4×C4⋊C4—31no—
255C4×C22⋊C4—34no—
256C4×C22⋊C4—32no—
257C4×C22⋊C4—32no—
258C24×C3C2412yes—
259C24×C3C2412yes—
260C23×D3C2411yescharacteristic
261C3×#41—432no—
262C2×C3×Q8—24no—
263C2×C3×Q8—24no—
264C2×C3×Q8C2×D418yes—
265C2×C3×D4—28no—
266C2×C3×D4—22no—
267C2×C3×D4—22no—
268C2×C3×D4—28no—
269C2×C3×D4—22no—
270C2×C3×D4—22no—
271C2×C3×D4—22no—
272C2×C3×D4—44no—
273C2×C3×D4#4114yes—
274C22×C3×C4—28no—
275C22×C3×C4—24no—
276C22×C3×C4—28no—
277C22×C3×C4—24no—
278C22×C3×C4—24no—
279C22×C3×C4—24no—
280C22×C3×C4—24no—
281C22×C3×C4—24no—
282C22×C3×C4—44no—
283C22×C3×C4C2412yes—
284C22×C3×C4C2412yes—
285C22×C3×C4C2411yescharacteristic
286C22×C3×C4C2414yes—
287C22×C3×C4C2411yescharacteristic
288C22×C3×C4C2411yescharacteristic
289C2×#67—24no—
290C2×#67—24no—
291C2×#67—24no—
292C2×#67—42no—
293C2×#67—42no—
294C2×#67—42no—
295C22×Dic3C2412yes—
296C22×Dic3C2412yes—
297C22×Dic3C2412yes—
298C22×Dic3C2412yes—
299C22×Dic3C2411yescharacteristic
300C22×Dic3C2414yes—
301C22×Dic3C2411yescharacteristic
302C22×Dic3C2411yescharacteristic
303C2×C4×D3—22no—
304C2×C4×D3—22no—
305C2×C4×D3—22no—
306C2×C4×D3—22no—
307C2×C4×D3—22no—
308C2×C4×D3—22no—
309C2×C4×D3—41no—
310C2×C4×D3—41no—
311C2×C4×D3#4114yescomplemented
312C2×Dic6—24no—
313C2×Dic6—42no—
314C2×Dic6—42no—
315C3×C4⋊C4—22no—
316C3×C4⋊C4—28no—
317C3×C4⋊C4—22no—
318C3×C4⋊C4C2×D418yes—
319C3×C4⋊C4C2×D418yes—
320C3×C22⋊C4—24no—
321C3×C22⋊C4—24no—
322C3×C22⋊C4—28no—
323C3×C42C2×D414yes—
324#217—24no—
325#217—24no—
326#217—24no—
327#217—42no—
328#217—44no—
329#217—44no—
330#217—42no—
331#217—42no—
332#217—44no—
333#217—44no—
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—28no—
336(C2×D3)⋊C4—42no—
337C4⋊Dic3—24no—
338C4⋊Dic3—24no—
339C4⋊Dic3—28no—
340C4⋊Dic3—22no—
341C4⋊Dic3—22no—
342C4⋊Dic3—22no—
343C4⋊Dic3—22no—
344C4⋊Dic3—44no—
345Dic3⋊C4—28no—
346Dic3⋊C4—24no—
347Dic3⋊C4—42no—
348C4×Dic3—22no—
349C4×Dic3—22no—
350C4×Dic3—22no—
351C4×Dic3—28no—
352C4×Dic3—24no—
353C4×Dic3—24no—
354C4×Dic3—44no—
355C2×#41—28no—
356C2×#41—28no—
357C2×#41—44no—
358C22×Q8—32no—
359C22×Q8C22×D312yes—
360C22×D4—32no—
361C22×D4—32no—
362C22×D4C22×D311yescharacteristic
363C22×D4C22×D314yes—
364C22×D4C22×D311yescharacteristic
365C23×C4—31no—
366C23×C4—31no—
367C23×C4—31no—
368C23×C4C22×D312yes—
369C23×C4C22×D312yes—
370C23×C4C22×D314yes—
371C4⋊Q8—64no—
372C4⋊Q8#6718yescomplemented
373#125—68no—
374#123—216no—
375C22⋊Q8—28no—
376C22⋊Q8—68no—
377C22⋊Q8—68no—
378#121—28no—
379#121—64no—
380#121—64no—
381C4×Q8—68no—
382C4×Q8—68no—
383C4×Q8—124no—
384C4×D4—24no—
385C4×D4—24no—
386C4×D4—68no—
387C4×D4—124no—
388#117—68no—
389C2×C4⋊C4—28no—
390C2×C4⋊C4—32no—
391C2×C4⋊C4—32no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—34no—
394C2×C4⋊C4—34no—
395C2×C4⋊C4—32no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—32no—
400C2×C4⋊C4—34no—
401C2×C4⋊C4C22×D311yescharacteristic
402C2×C4⋊C4C22×D314yes—
403C2×C4⋊C4C22×D311yescharacteristic
404C2×C4⋊C4C22×D312yes—
405C2×C4⋊C4C22×D312yes—
406C2×C22⋊C4—32no—
407C2×C22⋊C4—32no—
408C2×C22⋊C4—32no—
409C2×C22⋊C4—34no—
410C2×C22⋊C4—32no—
411C2×C22⋊C4—32no—
412C2×C22⋊C4—32no—
413C2×C22⋊C4—34no—
414C2×C22⋊C4—32no—
415C2×C22⋊C4—34no—
416C2×C22⋊C4—34no—
417C2×C22⋊C4—34no—
418C2×C22⋊C4—32no—
419C2×C22⋊C4C22×D312yes—
420C2×C22⋊C4C22×D312yes—
421C2×C22⋊C4C22×D314yes—
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×D311yescharacteristic
431#95—32no—
432#95—34no—
433#95—32no—
434#95—32no—
435#95—32no—
436#95—32no—
437#95—32no—
438#95—34no—
439#95—34no—
440#95—34no—
441#95—34no—
442#95—34no—
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×C3C2×#4114yes—
457C23×C3C2511yescharacteristic
458C22×D3—21no—
459C22×D3—21no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3—21no—
463C22×D3—21no—
464C22×D3C2×#4112yes—
465C3×Q8—216no—
466C3×D4—28no—
467C3×D4—416no—
468C3×D4—44no—
469C2×C3×C4—24no—
470C2×C3×C4—24no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—416no—
480C2×C3×C4—48no—
481C2×C3×C4—48no—
482C2×C3×C4C22×D418yes—
483C2×C3×C4C22×D412yes—
484C2×C3×C4C22×D412yes—
485C2×C3×C4C22×D412yes—
486C2×C3×C4C2×#4112yes—
487C2×C3×C4C2×#4112yes—
488C2×C3×C4H(5,𝔽2)12yes—
489C2×C3×C42−1+412yes—
490#67—48no—
491#67—48no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—24no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—21no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—21no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—24no—
510C2×Dic3—24no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3C2×#4112yes—
516C4×D3—28no—
517C4×D3—44no—
518C4×D3—44no—
519Dic6—48no—
520C24—31no—
521C24C23×D312yes—
522C24C23×D312yes—
523#41—432no—
524C2×Q8—24no—
525C2×Q8—24no—
526C2×Q8—64no—
527C2×Q8—122no—
528C2×Q8—122no—
529C2×Q8C2×#6718yes—
530C2×D4—28no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—28no—
537C2×D4—44no—
538C2×D4—64no—
539C2×D4—64no—
540C2×D4—64no—
541C2×D4—122no—
542C2×D4—122no—
543C2×D4—122no—
544C2×D4#23714yes—
545C22×C4—28no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—28no—
552C22×C4—24no—
553C22×C4—31no—
554C22×C4—34no—
555C22×C4—32no—
556C22×C4—32no—
557C22×C4—32no—
558C22×C4—32no—
559C22×C4—31no—
560C22×C4—34no—
561C22×C4—31no—
562C22×C4—44no—
563C22×C4—62no—
564C22×C4—62no—
565C22×C4—62no—
566C22×C4—62no—
567C22×C4—62no—
568C22×C4—62no—
569C22×C4—121no—
570C22×C4—121no—
571C22×C4C23×D312yes—
572C22×C4C23×D312yes—
573C22×C4C23×D311yescharacteristic
574C22×C4C23×D314yes—
575C22×C4C23×D311yescharacteristic
576C22×C4C23×D311yescharacteristic
577C4⋊C4—22no—
578C4⋊C4—28no—
579C4⋊C4—22no—
580C4⋊C4—64no—
581C4⋊C4—62no—
582C4⋊C4—62no—
583C4⋊C4—62no—
584C4⋊C4—62no—
585C4⋊C4—64no—
586C4⋊C4—68no—
587C4⋊C4—68no—
588C4⋊C4—64no—
589C4⋊C4—122no—
590C4⋊C4—124no—
591C4⋊C4C2×#6718yes—
592C4⋊C4C2×#6718yes—
593C22⋊C4—24no—
594C22⋊C4—24no—
595C22⋊C4—28no—
596C22⋊C4—64no—
597C22⋊C4—64no—
598C22⋊C4—64no—
599C22⋊C4—64no—
600C22⋊C4—68no—
601C22⋊C4—122no—
602C22⋊C4—122no—
603C22⋊C4—122no—
604C22⋊C4—122no—
605C22⋊C4—124no—
606C22⋊C4—124no—
607C22⋊C4—124no—
608C22⋊C4—124no—
609C42—64no—
610C42—64no—
611C42—62no—
612C42—62no—
613C42—62no—
614C42—68no—
615C42—124no—
616C42C2×#6714yes—
617C22×C3—24no—
618C22×C3—24no—
619C22×C3—24no—
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×C3—42no—
629C22×C3—42no—
630C22×C3—42no—
631C22×C3C23×D411yescharacteristic
632C22×C3C22×#4111yescharacteristic
633C22×C3C22×#4111yescharacteristic
634C22×C3C2×H(5,𝔽2)11yescharacteristic
635C22×C3C2×2−1+411yescharacteristic
636C22×C3#58511yescharacteristic
637C22×C3#58511yescharacteristic
638C2×D3—22no—
639C2×D3—22no—
640C2×D3—22no—
641C2×D3—41no—
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—41no—
645C3×C4—28no—
646C3×C4—22no—
647C3×C4—42no—
648C3×C4—42no—
649C3×C4#54614yes—
650C3×C4#54814yes—
651Dic3—22no—
652Dic3—41no—
653Dic3—42no—
654Dic3—44no—
655Dic3—41no—
656Dic3—42no—
657Dic3—42no—
658Dic3—42no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—32no—
673C23—61no—
674C23—61no—
675C23—61no—
676C23—61no—
677C23—61no—
678C23—61no—
679C23C2×#23714yes—
680C23C24×D311yescharacteristic
681Q8—216no—
682Q8—128no—
683D4—28no—
684D4—416no—
685D4—44no—
686D4—128no—
687D4—128no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—32no—
699C2×C4—416no—
700C2×C4—48no—
701C2×C4—48no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—68no—
705C2×C4—61no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—62no—
709C2×C4—62no—
710C2×C4—61no—
711C2×C4—62no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—64no—
722C2×C4—64no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—64no—
726C2×C4—124no—
727C2×C4—124no—
728C2×C4C2×#23712yes—
729C2×C4#100412yes—
730C2×C4D3×#4112yes—
731C2×C4#101012yes—
732C2×C4C22×#6712yes—
733C2×C4C22×#6718yes—
734C2×C4C22×#6712yes—
735C2×C4C22×#6712yes—
736C2×C3—44no—
737C2×C3—82no—
738C2×C3C2×#54611yescharacteristic
739C2×C3C2×#54811yescharacteristic
740C2×C3#347511yescharacteristic
741C2×C3#348711yescharacteristic
742C2×C3#350611yescharacteristic
743C2×C3#351511yescharacteristic
744C2×C3#354711yescharacteristic
745D3—42no—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—62no—
761C22—62no—
762C22—62no—
763C22—121no—
764C22—121no—
765C22—121no—
766C22—121no—
767C22C22×#23711yescharacteristic
768C22C2×#100411yescharacteristic
769C22C2×D3×#4111yescharacteristic
770C22C2×#101011yescharacteristic
771C22#596811yescharacteristic
772C22#596811yescharacteristic
773C22C23×#6711yescharacteristic
774C4—28no—
775C4—22no—
776C4—42no—
777C4—42no—
778C4—62no—
779C4—122no—
780C4—122no—
781C4—122no—
782C4—122no—
783C4—121no—
784C4—121no—
785C4—124no—
786C4#580614yes—
787C4#583114yes—
788C3#5903411yescharacteristic, complemented, Sylow
789C2—44no—
790C2—82no—
791C2—122no—
792C2#8667511yescharacteristic
793C2#8668311yescharacteristic
794C2#8670311yescharacteristic
795C2#8670811yescharacteristic
796C2C2×#580611yescharacteristic
797C2C2×#583111yescharacteristic
798C2#8729011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×#547C2
hypercenterC2×#547D3
hypocenterC3#59034
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×C3×#547C2semidirect
2. C2×#5728C2semidirect
3. #84097C2semidirect
4. #84089C2semidirect
5. #83229C2semidirect
6. #82878C2semidirect
7. #82851C2semidirect
8. #82777C2semidirect
9. #82753C2semidirect
10. #82703C2semidirect
11. #82661C2semidirect
12. C4×#938C2semidirect
13. C4×#938C2semidirect
14. #82384C2semidirect
15. #82384C2semidirect
16. #82172C2semidirect
17. #82161C2semidirect
86. C2×#547D3semidirect
119. C3×C4⋊Q8D4semidirect
311. C2×C4×D3#41semidirect
372. C4⋊Q8#67semidirect
788. C3#59034semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5472
C2×#57282
#840972
#840892
#832292
#828782
#828512
#827772
#827532
#827032
#826612
C4×#9382
#823842
#821722
#821612
#590343