Finite Group Databasebeta

← #10823525

Subgroups — #10823525

Order 768.

1186 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#540C211yesmaximal, characteristic
2C2×C4×#214C211yesmaximal, characteristic, complemented
3C2×#5018C211yesmaximal, characteristic, complemented
4#82235C211yesmaximal, characteristic, complemented
5#71768C211yesmaximal, characteristic, complemented
6#71762C211yesmaximal, characteristic, complemented
7#71744C211yesmaximal, characteristic, complemented
8#71739C211yesmaximal, characteristic, complemented
9#71685C211yesmaximal, characteristic, complemented
10#71685C211yesmaximal, characteristic, complemented
11#71680C211yesmaximal, characteristic, complemented
12#71679C211yesmaximal, characteristic, complemented
13#71609C211yesmaximal, characteristic, complemented
14C4×#832C211yesmaximal, characteristic, complemented
15#71582C211yesmaximal, characteristic, complemented
16#23582—31nomaximal, Sylow
17C3×#540—24no—
18C3×#540—24no—
19C2×C3×#127C2211yescharacteristic
20C2×C3×#125C2211yescharacteristic
21C2×C3×#123—21no—
22C2×C3×#123—21no—
23C2×C3×#121—21no—
24C2×C3×#121—21no—
25C2×C3×#121C2211yescharacteristic
26C2×C3×#121C2211yescharacteristic
27C2×C3×C4×D4C2211yescharacteristic
28C2×C3×C4×D4C2211yescharacteristic
29C2×C3×#117C2211yescharacteristic
30C22×#214C2211yescharacteristic
31C22×#214C2211yescharacteristic
32C2×#924C2211yescharacteristic
33C2×C4×Dic6C2211yescharacteristic
34C2×#832C2211yescharacteristic
35C2×#832C2211yescharacteristic
36C2×#832C2211yescharacteristic
37C2×#832C2211yescharacteristic
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic
40#5212C2211yescharacteristic
41C2×#830C2211yescharacteristic
42C2×#830C2211yescharacteristic
43#5018—24no—
44C4×#214—24no—
45#4978—21no—
46#4976—21no—
47C2×#810C2211yescharacteristic
48C2×#810C2211yescharacteristic
49C2×#808C2211yescharacteristic
50C2×#807C2211yescharacteristic
51#4945—21no—
52#4944—21no—
53C4×C4⋊Dic3C2211yescharacteristic
54#4929C2211yescharacteristic
55#4928C2211yescharacteristic
56C2×#803C2211yescharacteristic
57C2×C4×C3⋊C8C2211yescharacteristic
58#4529C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#540D311yescharacteristic
65C2×#440—31no—
66C2×C4×SD16—31no—
67#2323—31no—
68#2059—31no—
69#2041—31no—
70#2034—31no—
71#2033—31no—
72#2026—31no—
73#2014—31no—
74#2000—31no—
75#2000—31no—
76#1762—31no—
77C4×#102—31no—
78#1750—31no—
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4—21no—
82C22×C3×D4—21no—
83C22×C3×D4C2311yescharacteristic
84C22×C3×D4C2311yescharacteristic
85C23×C3×C4—21no—
86C23×C3×C4—21no—
87C23×C3×C4C2311yescharacteristic
88C22×Dic6C2311yescharacteristic
89C3×#127—22no—
90C3×#127—22no—
91C3×#125—22no—
92C3×#125—22no—
93C3×#123—28no—
94C3×#123—28no—
95C3×#121—28no—
96C3×#121—28no—
97C3×#121—22no—
98C3×#121—22no—
99C3×#121—22no—
100C3×#121—22no—
101C3×C4×D4—22no—
102C3×C4×D4—22no—
103C3×C4×D4D414yes—
104C3×C4×D4D414yes—
105C3×#117—22no—
106C3×#117—22no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4D411yescharacteristic
110C2×C3×C4⋊C4D411yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4D411yescharacteristic
118C2×C3×C22⋊C4D411yescharacteristic
119C2×C3×C42C2311yescharacteristic
120C2×C3×C42C2311yescharacteristic
121C2×#217—21no—
122C2×#217—21no—
123C2×#214—22no—
124C2×#214—22no—
125C2×#214—22no—
126C2×#214—22no—
127C2×#214—22no—
128C2×#214—22no—
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131C2×C4⋊Dic3C2311yescharacteristic
132#924—22no—
133#924—22no—
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4—21no—
137C2×C4×Dic3—21no—
138C2×C4×Dic3—21no—
139C22×C3⋊C8C2311yescharacteristic
140C22×C3⋊C8C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C4×Dic6—22no—
144C4×Dic6—22no—
145#832—22no—
146#832—22no—
147#832—22no—
148#832—22no—
149#832—22no—
150#832—22no—
151C3⋊#95—21no—
152C3⋊#95—21no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156#830—22no—
157#830—22no—
158#810—22no—
159#810—22no—
160#808—22no—
161#807—22no—
162#803—22no—
163C4×C3⋊C8—22no—
164C22×SD16—31no—
165C22×SD16—31no—
166#540—24no—
167#540—24no—
168C2×#127C2×D311yescharacteristic
169C2×#125C2×D311yescharacteristic
170C2×#123—21no—
171C2×#123—21no—
172C2×C22⋊Q8—31no—
173C2×#121—21no—
174C2×#121—21no—
175C2×#121C2×D311yescharacteristic
176C2×#121C2×D311yescharacteristic
177C2×C4×Q8—31no—
178C2×C4×D4C2×D311yescharacteristic
179C2×C4×D4C2×D311yescharacteristic
180C2×#117C2×D311yescharacteristic
181#440—64no—
182C4×SD16—64no—
183C2×#107—31no—
184C2×#106—31no—
185C2×#103—31no—
186C2×#103—31no—
187C2×#102—31no—
188C2×#102—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×C22⋊C8—31no—
194C2×C22⋊C8—31no—
195C2×#97—31no—
196C2×C4×C8—31no—
197#391—31no—
198#389—31no—
199#389—61no—
200#388—61no—
201#388—61no—
202#387—61no—
203#380—31no—
204C4×C4⋊C4—31no—
205#340—31no—
206#340—31no—
207#340—31no—
208#340—31no—
209#336—31no—
210#336—31no—
211C24×C3—21no—
212C24×C3—21no—
213C24×C3C2×D411yescharacteristic
214C2×C3×D4—24no—
215C2×C3×D4—24no—
216C2×C3×D4—24no—
217C2×C3×D4—24no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—81no—
229C2×C3×D4—81no—
230C2×C3×D4—81no—
231C2×C3×D4—81no—
232C2×C3×D4—81no—
233C2×C3×D4—81no—
234C2×C3×D4—81no—
235C2×C3×D4—81no—
236C2×C3×D4C2×D412yes—
237C2×C3×D4C2×D412yes—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—24no—
247C22×C3×C4—24no—
248C22×C3×C4—81no—
249C22×C3×C4—81no—
250C22×C3×C4—81no—
251C22×C3×C4—81no—
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2411yescharacteristic
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6—21no—
266C2×Dic6—21no—
267C2×Dic6#4112yes—
268C3×C4⋊C4—24no—
269C3×C4⋊C4—24no—
270C3×C4⋊C4—22no—
271C3×C4⋊C4—22no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4C2×D412yes—
275C3×C4⋊C4C2×D412yes—
276C3×C22⋊C4—24no—
277C3×C22⋊C4—24no—
278C3×C22⋊C4—24no—
279C3×C22⋊C4—24no—
280C3×C22⋊C4—22no—
281C3×C22⋊C4—22no—
282C3×C42—21no—
283C3×C42—21no—
284C3×C42C2×D412yes—
285C3×C42C2×D412yes—
286#217—24no—
287#217—81no—
288#214—28no—
289#214—28no—
290C4⋊Dic3—21no—
291C4⋊Dic3—21no—
292C4⋊Dic3—21no—
293C4⋊Dic3—21no—
294C4⋊Dic3—21no—
295C4⋊Dic3#4112yes—
296Dic3⋊C4—24no—
297Dic3⋊C4—42no—
298Dic3⋊C4—81no—
299C4×Dic3—42no—
300C4×Dic3—81no—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—21no—
303C2×C3⋊C8—21no—
304C2×C3⋊C8—21no—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8#4112yes—
312C2×C3⋊C8#4112yes—
313C22×Q8—31no—
314C22×D4—21no—
315C22×D4—21no—
316C22×D4—21no—
317C22×D4—21no—
318C22×D4C22×D311yescharacteristic
319C22×D4C22×D311yescharacteristic
320C23×C4—21no—
321C23×C4—21no—
322C23×C4C22×D311yescharacteristic
323C2×SD16—62no—
324C2×SD16—62no—
325C2×SD16—62no—
326C2×SD16—62no—
327C2×SD16—62no—
328C2×SD16—62no—
329C22×C8—31no—
330C22×C8—31no—
331C22×C8—31no—
332C22×C8—31no—
333#127—22no—
334#127—22no—
335#125—22no—
336#125—22no—
337#123—28no—
338#123—28no—
339C22⋊Q8—62no—
340C22⋊Q8—62no—
341#121—28no—
342#121—28no—
343#121—22no—
344#121—22no—
345#121—22no—
346#121—22no—
347C4×Q8—62no—
348C4×Q8—62no—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4#6714yes—
352C4×D4#6714yes—
353#117—22no—
354#117—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—31no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4#6711yescharacteristic
364C2×C4⋊C4#6711yescharacteristic
365C2×C4⋊C4C22×D311yescharacteristic
366C2×C4⋊C4C22×D311yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—61no—
372C2×C22⋊C4—61no—
373C2×C22⋊C4#6711yescharacteristic
374C2×C22⋊C4#6711yescharacteristic
375C2×C42—61no—
376C2×C42—61no—
377C2×C42C22×D311yescharacteristic
378C2×C42C22×D311yescharacteristic
379#107—62no—
380#106—62no—
381#103—62no—
382#103—62no—
383#102—62no—
384#102—62no—
385#102—62no—
386#102—62no—
387#102—62no—
388#102—62no—
389C22⋊C8—62no—
390C22⋊C8—62no—
391#97—62no—
392C4×C8—62no—
393#95—61no—
394#95—61no—
395#95—61no—
396#95—61no—
397#95—61no—
398C23×C3—21no—
399C23×C3—22no—
400C23×C3—22no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3C22×D411yescharacteristic
420C3×D4—22no—
421C3×D4—22no—
422C3×D4—22no—
423C3×D4—22no—
424C3×D4—41no—
425C3×D4—41no—
426C3×D4—41no—
427C3×D4—41no—
428C3×D4—84no—
429C3×D4—84no—
430C3×D4—84no—
431C3×D4—84no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—84no—
456C2×C3×C4—84no—
457C2×C3×C4#12012yes—
458C2×C3×C4#12012yes—
459C2×C3×C4C22×D411yescharacteristic
460C2×C3×C4C22×D411yescharacteristic
461C2×C3×C4C2×#4111yescharacteristic
462C2×C3×C4C2×#4111yescharacteristic
463C2×C3×C4C2×#4111yescharacteristic
464C2×C3×C4C2×#4111yescharacteristic
465C2×Dic3—22no—
466C2×Dic3—22no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477Dic6—22no—
478Dic6—22no—
479Dic6—41no—
480Dic6—41no—
481C3⋊C8—22no—
482C3⋊C8—22no—
483C3⋊C8—41no—
484C3⋊C8—41no—
485C24—21no—
486C24—21no—
487C24C2×#6711yescharacteristic
488C2×Q8—32no—
489C2×Q8—61no—
490C2×Q8—61no—
491C2×Q8—61no—
492C2×Q8—61no—
493C2×Q8—61no—
494C2×D4—24no—
495C2×D4—24no—
496C2×D4—24no—
497C2×D4—24no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—81no—
509C2×D4—81no—
510C2×D4—81no—
511C2×D4—81no—
512C2×D4—81no—
513C2×D4—81no—
514C2×D4—81no—
515C2×D4—81no—
516C2×D4C2×#6712yes—
517C2×D4C2×#6712yes—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—81no—
535C22×C4—81no—
536C22×C4C2×#6711yescharacteristic
537C22×C4C2×#6711yescharacteristic
538C22×C4C2×#6711yescharacteristic
539C22×C4C2×#6711yescharacteristic
540C22×C4C2×#6711yescharacteristic
541C22×C4C23×D311yescharacteristic
542SD16—68no—
543SD16—68no—
544C2×C8—32no—
545C2×C8—32no—
546C2×C8—61no—
547C2×C8—61no—
548C2×C8—61no—
549C2×C8—61no—
550C2×C8—61no—
551C2×C8—61no—
552C2×C8—61no—
553C2×C8—61no—
554C2×C8—61no—
555C2×C8—61no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—32no—
563C4⋊C4—64no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—61no—
567C4⋊C4—61no—
568C4⋊C4—61no—
569C4⋊C4—122no—
570C4⋊C4—241no—
571C4⋊C4C2×#6712yes—
572C4⋊C4C2×#6712yes—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—22no—
578C22⋊C4—22no—
579C22⋊C4—64no—
580C22⋊C4—241no—
581C42—21no—
582C42—21no—
583C42—122no—
584C42—241no—
585C42C2×#6712yes—
586C42C2×#6712yes—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—42no—
591C22×C3—42no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—42no—
595C22×C3—41no—
596C22×C3—42no—
597C22×C3—42no—
598C22×C3—41no—
599C22×C3—42no—
600C22×C3—81no—
601C22×C3—81no—
602C22×C3—81no—
603C22×C3—81no—
604C22×C3—81no—
605C22×C3—81no—
606C22×C3—81no—
607C22×C3—81no—
608C22×C3C2×#12011yescharacteristic
609C22×C3#52511yescharacteristic
610C22×C3#53211yescharacteristic
611C22×C3#57611yescharacteristic
612C22×C3#57711yescharacteristic
613C22×C3#57711yescharacteristic
614C22×C3#57711yescharacteristic
615C3×C4—22no—
616C3×C4—22no—
617C3×C4—41no—
618C3×C4—41no—
619C3×C4—42no—
620C3×C4—41no—
621C3×C4—42no—
622C3×C4#52511yescharacteristic
623C3×C4#52511yescharacteristic
624C3×C4#53211yescharacteristic
625C3×C4#53211yescharacteristic
626Dic3—42no—
627Dic3—42no—
628Dic3—81no—
629Dic3—81no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—22no—
638C23—22no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23C22×#6711yescharacteristic
652Q8—62no—
653Q8—62no—
654Q8—121no—
655Q8—121no—
656D4—22no—
657D4—22no—
658D4—22no—
659D4—22no—
660D4—41no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—84no—
665D4—84no—
666D4—84no—
667D4—84no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—84no—
694C2×C4—84no—
695C2×C4—121no—
696C2×C4—121no—
697C2×C4—121no—
698C2×C4—121no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4#95312yes—
706C2×C4#95312yes—
707C2×C4D3×#4111yescharacteristic
708C2×C4D3×#4111yescharacteristic
709C2×C4D3×#4111yescharacteristic
710C2×C4D3×#4111yescharacteristic
711C2×C4C22×#6711yescharacteristic
712C2×C4C22×#6711yescharacteristic
713C8—62no—
714C8—62no—
715C8—121no—
716C8—121no—
717C2×C3—81no—
718C2×C3—82no—
719C2×C3—82no—
720C2×C3#238811yescharacteristic
721C2×C3#300911yescharacteristic
722C2×C3#301211yescharacteristic
723C2×C3#311911yescharacteristic
724C2×C3#312611yescharacteristic
725C2×C3#317411yescharacteristic
726C2×C3#317911yescharacteristic
727C22—41no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—41no—
732C22—42no—
733C22—42no—
734C22—41no—
735C22—42no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22#582811yescharacteristic
749C22#583211yescharacteristic
750C22#583511yescharacteristic
751C22#583611yescharacteristic
752C22#583611yescharacteristic
753C22#583611yescharacteristic
754C22C2×#95311yescharacteristic
755C4—22no—
756C4—22no—
757C4—41no—
758C4—41no—
759C4—42no—
760C4—41no—
761C4—42no—
762C4—122no—
763C4—122no—
764C4—241no—
765C4—241no—
766C4#582811yescharacteristic
767C4#582811yescharacteristic
768C4#583211yescharacteristic
769C4#583211yescharacteristic
770C3#2358211yescharacteristic, complemented, Sylow
771C2—81no—
772C2—82no—
773C2—82no—
774C2#8343111yescharacteristic
775C2#8343311yescharacteristic
776C2#8343411yescharacteristic
777C2#8343911yescharacteristic
778C2#8409511yescharacteristic
779C2#8410211yescharacteristic
780C2#8410511yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
Fitting, prime radicalC2×C3×#540C2
socleC23×C3C22×D4
hypercenterC2×#540D3
hypocenterC3#23582
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
2. C2×C4×#214C2semidirect
3. C2×#5018C2semidirect
4. #82235C2semidirect
5. #71768C2semidirect
6. #71762C2semidirect
7. #71744C2semidirect
8. #71739C2semidirect
9. #71685C2semidirect
10. #71685C2semidirect
11. #71680C2semidirect
12. #71679C2semidirect
13. #71609C2semidirect
14. C4×#832C2semidirect
15. #71582C2semidirect
770. C3#23582semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5402
C2×C4×#2142
C2×#50182
#822352
#717682
#717622
#717442
#717392
#716852
#716802
#716792
#716092
C4×#8322
#715822
#235823