Finite Group Databasebeta

← #10823433

Subgroups — #10823433

Order 768.

1260 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5680C211yesmaximal, characteristic, complemented
2C2×#4817C211yesmaximal, characteristic, complemented
3C2×#4785C211yesmaximal, characteristic, complemented
4#75964C211yesmaximal, characteristic, complemented
5C3×#2042C211yesmaximal, characteristic, complemented
6#71728C211yesmaximal, characteristic, complemented
7#70274C211yesmaximal, characteristic, complemented
8#70272C211yesmaximal, characteristic, complemented
9#70220C211yesmaximal, characteristic, complemented
10#70206C211yesmaximal, characteristic, complemented
11#70204C211yesmaximal, characteristic
12#70152C211yesmaximal, characteristic, complemented
13#69606C211yesmaximal, characteristic, complemented
14#68679C211yesmaximal, characteristic, complemented
15#68600C211yesmaximal, characteristic, complemented
16#23575—31nomaximal, Sylow
17C2×C3×#124C2211yescharacteristic
18C2×#946C2211yescharacteristic
19C2×Q8×Dic3C2211yescharacteristic
20C22×#215C2211yescharacteristic
21C2×#938C2211yescharacteristic
22C2×D4×Dic3C2211yescharacteristic
23C22×#213C2211yescharacteristic
24#5680—24no—
25#5680—24no—
26C2×#895C2211yescharacteristic
27C2×#893—21no—
28C2×#893C2211yescharacteristic
29C2×#883—21no—
30C2×#67⋊C4—21no—
31C2×#879—21no—
32C2×#877—21no—
33C2×C42×D3C2211yescharacteristic
34C2×#870C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C3×#389C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#832C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×#821C2211yescharacteristic
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#815C2211yescharacteristic
47C2×#815C2211yescharacteristic
48#4990—21no—
49#4987C2211yescharacteristic
50Dic3×C4⋊C4C2211yescharacteristic
51C2×#808C2211yescharacteristic
52C2×#807C2211yescharacteristic
53#4939C2211yescharacteristic
54#4817—24no—
55#4785—24no—
56#4666—21no—
57#4665—21no—
58C3×#336C2211yescharacteristic
59#4551C2211yescharacteristic
60#4551C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#529—31no—
65C2×#442—31no—
66C2×#440—31no—
67C4×#121—31no—
68#2059—31no—
69#2042D311yescharacteristic, complemented
70#2035—31no—
71#2033—31no—
72#2025—31no—
73#2012—31no—
74#2000—31no—
75#1999—31no—
76#1763—31no—
77#1762—31no—
78#1749—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C22×#67—21no—
82C23×Dic3—21no—
83C22×D12—21no—
84C22×D12C2311yescharacteristic
85C22×C4×D3—21no—
86C22×C4×D3D411yescharacteristic
87C22×C4×D3D411yescharacteristic
88C22×C4×D3C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C3×#124—22no—
92C3×#124—22no—
93C2×C3×C4⋊C4—21no—
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C22⋊C4—21no—
97C2×C3×C22⋊C4—21no—
98C2×C3×C42C2311yescharacteristic
99C2×#217—21no—
100C2×#217—21no—
101#946—22no—
102#946—22no—
103Q8×Dic3—22no—
104Q8×Dic3D414yescomplemented
105C2×#215—22no—
106C2×#215—22no—
107C2×#215—22no—
108#938—22no—
109#938—22no—
110D4×Dic3—22no—
111D4×Dic3D414yescomplemented
112C2×#213—22no—
113C2×#213—22no—
114C2×#213—22no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×C4⋊Dic3—21no—
122C2×C4⋊Dic3C2311yescharacteristic
123C2×C4⋊Dic3C2311yescharacteristic
124C2×C4⋊Dic3C2311yescharacteristic
125C2×Dic3⋊C4—21no—
126C2×Dic3⋊C4—21no—
127C2×Dic3⋊C4—21no—
128C2×C4×Dic3—21no—
129C2×C4×Dic3—21no—
130C2×C4×Dic3D411yescharacteristic
131C2×C4×Dic3D411yescharacteristic
132C2×C4×Dic3C2311yescharacteristic
133C22×C3⋊C8C2311yescharacteristic
134C22×C3⋊C8C2311yescharacteristic
135#895—22no—
136#895—22no—
137#893—22no—
138#893—22no—
139#893—44no—
140#883—28no—
141#67⋊C4—28no—
142#879—28no—
143#877—28no—
144C42×D3—22no—
145C42×D3—22no—
146#870—22no—
147#870—22no—
148C3×#103—22no—
149C3×#103—22no—
150C3×#102—22no—
151C3×#102—22no—
152C3×#95—21no—
153#835—22no—
154#832—22no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157#821—22no—
158#821—22no—
159(C2×D3)⋊C8—22no—
160(C2×D3)⋊C8—22no—
161#815—22no—
162#815—22no—
163#808—22no—
164#807—22no—
165C22×SD16—31no—
166C22×D8—31no—
167#529—64no—
168#529—64no—
169C2×#126—61no—
170C2×#125—31no—
171C2×#124C2×D311yescharacteristic
172C2×#123—61no—
173C2×C22⋊Q8—31no—
174C2×#121—31no—
175C2×#121—31no—
176C2×C4×Q8—31no—
177C2×C4×D4—31no—
178C2×C4×D4—31no—
179C2×C4×D4—61no—
180C2×C4×D4—61no—
181C2×#117—61no—
182C22×C42—31no—
183#442—64no—
184#440—64no—
185C2×#107—31no—
186C2×#106—31no—
187C2×#103—31no—
188C2×#103C2×D311yescharacteristic
189C2×#103C2×D311yescharacteristic
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102C2×D311yescharacteristic
194C2×#102C2×D311yescharacteristic
195C2×C22⋊C8—31no—
196C2×C22⋊C8—31no—
197C2×#97—31no—
198C2×#97—31no—
199#390—31no—
200#389C2×D311yescharacteristic
201#388—61no—
202#386—61no—
203#380—31no—
204C4×C4⋊C4—31no—
205C4×C22⋊C4—61no—
206#340—31no—
207#340—31no—
208#340—31no—
209#340—31no—
210#336—31no—
211#336C2×D311yescharacteristic
212C24×C3—21no—
213C23×D3—21no—
214C23×D3C2×D411yescharacteristic
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8C2×D412yes—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4C2×D412yes—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2×D411yescharacteristic
232C22×C3×C4C2411yescharacteristic
233C2×#67—24no—
234C2×#67—42no—
235C2×#67—42no—
236C22×Dic3—21no—
237C22×Dic3—21no—
238C22×Dic3—24no—
239C22×Dic3—21no—
240C22×Dic3—42no—
241C22×Dic3—42no—
242C22×Dic3C2×D411yescharacteristic
243C22×Dic3C2×D411yescharacteristic
244C22×Dic3C2×D411yescharacteristic
245C2×D12—21no—
246C2×D12—21no—
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—24no—
250C2×D12—21no—
251C2×D12—42no—
252C2×D12—42no—
253C2×D12#4112yes—
254C2×C4×D3—22no—
255C2×C4×D3—21no—
256C2×C4×D3—21no—
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×C4×D3—22no—
262C2×C4×D3—22no—
263C2×C4×D3—41no—
264C2×C4×D3—41no—
265C2×C4×D3—41no—
266C2×C4×D3—42no—
267C2×C4×D3—42no—
268C2×C4×D3—42no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8—21no—
272C2×C3×C8—21no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—42no—
279C3×C4⋊C4#4112yes—
280C3×C22⋊C4—24no—
281C3×C22⋊C4—24no—
282C3×C42—21no—
283C3×C42—21no—
284#217—24no—
285#217—24no—
286#215—28no—
287#213—28no—
288(C2×D3)⋊C4—24no—
289(C2×D3)⋊C4—24no—
290(C2×D3)⋊C4—42no—
291(C2×D3)⋊C4—42no—
292(C2×D3)⋊C4—42no—
293(C2×D3)⋊C4—42no—
294C4⋊Dic3—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3—24no—
297C4⋊Dic3—21no—
298C4⋊Dic3—21no—
299C4⋊Dic3C2×D412yes—
300C4⋊Dic3C2×D412yes—
301Dic3⋊C4—24no—
302Dic3⋊C4—24no—
303Dic3⋊C4—24no—
304C4×Dic3—22no—
305C4×Dic3—22no—
306C4×Dic3—24no—
307C4×Dic3—42no—
308C4×Dic3C2×D412yes—
309C4×Dic3C2×D412yes—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8#4112yes—
315C2×C3⋊C8#4112yes—
316C22×Q8C22×D311yescharacteristic
317C22×D4—31no—
318C22×D4—61no—
319C22×D4—61no—
320C22×D4C22×D311yescharacteristic
321C23×C4—31no—
322C23×C4—31no—
323C23×C4—31no—
324C23×C4—61no—
325C23×C4—61no—
326C2×SD16—62no—
327C2×SD16—62no—
328C2×SD16—62no—
329C2×D8—62no—
330C2×D8—62no—
331C2×D8—62no—
332C22×C8—31no—
333C22×C8—31no—
334C22×C8C22×D311yescharacteristic
335C22×C8C22×D311yescharacteristic
336#126—68no—
337#125—62no—
338#125—62no—
339#124—22no—
340#124—22no—
341#123—68no—
342C22⋊Q8—62no—
343C22⋊Q8—62no—
344#121—62no—
345#121—62no—
346#121—62no—
347#121—62no—
348C4×Q8—34no—
349C4×Q8—62no—
350C4×D4—34no—
351C4×D4—62no—
352C4×D4—62no—
353C4×D4—62no—
354C4×D4—68no—
355C4×D4—124no—
356#117—68no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4C22×D311yescharacteristic
366C2×C4⋊C4C22×D311yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—61no—
370C2×C22⋊C4—61no—
371C2×C22⋊C4—61no—
372C2×C22⋊C4—61no—
373C2×C22⋊C4—61no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
377C2×C42—31no—
378C2×C42—31no—
379C2×C42—31no—
380C2×C42—62no—
381C2×C42—62no—
382C2×C42—61no—
383C2×C42—61no—
384C2×C42C22×D311yescharacteristic
385#107—62no—
386#106—62no—
387#103—22no—
388#103—22no—
389#103—62no—
390#102—22no—
391#102—22no—
392#102—62no—
393#102—62no—
394#102—62no—
395C22⋊C8—62no—
396C22⋊C8—62no—
397#97—62no—
398#97—62no—
399#95—21no—
400#95—61no—
401#95—61no—
402C23×C3—22no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3C22×D411yescharacteristic
410C22×D3—21no—
411C22×D3—21no—
412C22×D3—21no—
413C22×D3—21no—
414C22×D3—21no—
415C22×D3—21no—
416C22×D3—22no—
417C22×D3—41no—
418C22×D3—41no—
419C22×D3—41no—
420C22×D3—41no—
421C22×D3—41no—
422C22×D3—41no—
423C22×D3AGL(1,ℤ/8)12yes—
424C3×Q8—22no—
425C3×Q8—22no—
426C3×Q8—41no—
427C3×Q8—41no—
428C3×D4—22no—
429C3×D4—22no—
430C3×D4—41no—
431C3×D4—41no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4C22×D411yescharacteristic
448C2×C3×C4C22×D411yescharacteristic
449C2×C3×C4C2×#4111yescharacteristic
450C2×C3×C4C2×#4111yescharacteristic
451C2×C3×C4C2×#4111yescharacteristic
452C2×C3×C4C2×#4111yescharacteristic
453#67—48no—
454C2×Dic3—21no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—22no—
460C2×Dic3—22no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—48no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3#12012yes—
472C2×Dic3#12012yes—
473D12—22no—
474D12—22no—
475D12—48no—
476D12—41no—
477D12—41no—
478C4×D3—44no—
479C4×D3—44no—
480C4×D3—41no—
481C4×D3—41no—
482C4×D3—41no—
483C4×D3—41no—
484C4×D3—84no—
485C3×C8—41no—
486C3×C8—41no—
487C3⋊C8—22no—
488C3⋊C8—22no—
489C24—21no—
490C24—31no—
491C24—61no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8D3×D412yes—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—32no—
504C2×D4—64no—
505C2×D4—64no—
506C2×D4—61no—
507C2×D4—61no—
508C2×D4—61no—
509C2×D4—61no—
510C2×D4—61no—
511C2×D4—122no—
512C2×D4—122no—
513C2×D4—122no—
514C2×D4—122no—
515C2×D4D3×D412yes—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—31no—
520C22×C4—31no—
521C22×C4—31no—
522C22×C4—62no—
523C22×C4—62no—
524C22×C4—62no—
525C22×C4—64no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—121no—
536C22×C4—121no—
537C22×C4—121no—
538C22×C4—122no—
539C22×C4—122no—
540C22×C4—122no—
541C22×C4—122no—
542C22×C4—122no—
543C22×C4D3×D411yescharacteristic
544C22×C4D3×D411yescharacteristic
545C22×C4C23×D311yescharacteristic
546SD16—68no—
547D8—68no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—32no—
555C2×C8—32no—
556C2×C8—61no—
557C2×C8—61no—
558C2×C8—61no—
559C2×C8—61no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—32no—
564C4⋊C4—32no—
565C4⋊C4—42no—
566C4⋊C4—64no—
567C4⋊C4—64no—
568C4⋊C4—64no—
569C4⋊C4—64no—
570C4⋊C4—61no—
571C4⋊C4—61no—
572C4⋊C4—61no—
573C4⋊C4—61no—
574C4⋊C4#23712yes—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—64no—
578C22⋊C4—64no—
579C22⋊C4—64no—
580C22⋊C4—64no—
581C22⋊C4—122no—
582C22⋊C4—122no—
583C22⋊C4—122no—
584C22⋊C4—122no—
585C42—21no—
586C42—21no—
587C42—32no—
588C42—32no—
589C42—62no—
590C42—62no—
591C42—64no—
592C42—122no—
593C22×C3—42no—
594C22×C3—42no—
595C22×C3—42no—
596C22×C3—81no—
597C22×C3—81no—
598C22×C3—81no—
599C22×C3—81no—
600C22×C3C2×#12011yescharacteristic
601C22×C3#52511yescharacteristic
602C22×C3#53211yescharacteristic
603C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
604C22×C3#57511yescharacteristic
605C22×C3#57511yescharacteristic
606C22×C3#57511yescharacteristic
607C2×D3—22no—
608C2×D3—22no—
609C2×D3—22no—
610C2×D3—41no—
611C2×D3—41no—
612C2×D3—41no—
613C2×D3—41no—
614C2×D3—42no—
615C2×D3—42no—
616C2×D3—42no—
617C2×D3—81no—
618C2×D3—81no—
619C2×D3—81no—
620C2×D3—81no—
621C3×C4—42no—
622C3×C4—42no—
623C3×C4—41no—
624C3×C4—41no—
625C3×C4—81no—
626C3×C4#52511yescharacteristic
627C3×C4#52511yescharacteristic
628C3×C4#53211yescharacteristic
629C3×C4#53211yescharacteristic
630Dic3—22no—
631Dic3—22no—
632Dic3—41no—
633Dic3—42no—
634Dic3—42no—
635Dic3—81no—
636C23—22no—
637C23—32no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—61no—
645C23—61no—
646C23—61no—
647C23—61no—
648C23—61no—
649C23—61no—
650C23—62no—
651C23—121no—
652C23—121no—
653C23—121no—
654C23—121no—
655C23—121no—
656C23—121no—
657C23C2×D3×D411yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—41no—
661Q8—41no—
662D4—22no—
663D4—22no—
664D4—41no—
665D4—41no—
666D4—62no—
667D4—62no—
668D4—128no—
669D4—128no—
670D4—121no—
671D4—121no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—32no—
681C2×C4—32no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—61no—
698C2×C4—124no—
699C2×C4—124no—
700C2×C4—128no—
701C2×C4—121no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—244no—
713C2×C4C2×D3×D411yescharacteristic
714C2×C4C2×D3×D411yescharacteristic
715C2×C4C2×#23711yescharacteristic
716C2×C4D3×#4111yescharacteristic
717C2×C4D3×#4111yescharacteristic
718C2×C4D3×#4111yescharacteristic
719C8—41no—
720C8—41no—
721C8—62no—
722C8—62no—
723C2×C3—82no—
724C2×C3#238811yescharacteristic
725C2×C3#300511yescharacteristic
726C2×C3#300611yescharacteristic
727C2×C3#311111yescharacteristic
728C2×C3#311411yescharacteristic
729C2×C3#318011yescharacteristic
730C2×C3#318311yescharacteristic
731D3—42no—
732D3—82no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—62no—
737C22—62no—
738C22—62no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—121no—
744C22—121no—
745C22—121no—
746C22—121no—
747C22—122no—
748C22—122no—
749C22—122no—
750C22—241no—
751C22—241no—
752C22—241no—
753C22—241no—
754C22D3×#12011yescharacteristic
755C22#560611yescharacteristic
756C22#566811yescharacteristic
757C22#576811yescharacteristic
758C22#576811yescharacteristic
759C22D3×AGL(1,ℤ/8)11yescharacteristic
760C22#577711yescharacteristic
761C4—42no—
762C4—41no—
763C4—42no—
764C4—41no—
765C4—62no—
766C4—62no—
767C4—81no—
768C4—121no—
769C4—122no—
770C4—122no—
771C4—241no—
772C4#559611yescharacteristic
773C4#559611yescharacteristic
774C4#565611yescharacteristic
775C4#565611yescharacteristic
776C3#2357511yescharacteristic, complemented, Sylow
777C2—82no—
778C2—122no—
779C2—242no—
780C2#7688911yescharacteristic
781C2#8008411yescharacteristic
782C2#8022711yescharacteristic
783C2#8050711yescharacteristic
784C2#8057011yescharacteristic
785C2#8163111yescharacteristic
786C2#8166811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2042C2
socleC23×C3C22×D4
prime radical#70204C2
hypercenter#2042D3
hypocenterC3#23575
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2042

Complements

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

NH ≅ G/Ntype
1. C2×#5680C2semidirect
2. C2×#4817C2semidirect
3. C2×#4785C2semidirect
4. #75964C2semidirect
5. C3×#2042C2semidirect
6. #71728C2semidirect
7. #70274C2semidirect
8. #70272C2semidirect
9. #70220C2semidirect
10. #70206C2semidirect
12. #70152C2semidirect
13. #69606C2semidirect
14. #68679C2semidirect
15. #68600C2semidirect
69. #2042D3semidirect
104. Q8×Dic3D4semidirect
111. D4×Dic3D4semidirect
776. C3#23575semidirect

Maximal subgroups

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

subgroupindex
C2×#56802
C2×#48172
C2×#47852
#759642
C3×#20422
#717282
#702742
#702722
#702202
#702062
#702042
#701522
#696062
#686792
#686002
#235753