Finite Group Databasebeta

← #10823491

Subgroups — #10823491

Order 768.

1178 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5733C211yesmaximal, characteristic, complemented
2C2×#4757C211yesmaximal, characteristic, complemented
3C2×#4756C211yesmaximal, characteristic, complemented
4#76430C211yesmaximal, characteristic, complemented
5C3×#2023C211yesmaximal, characteristic, complemented
6#71782C211yesmaximal, characteristic, complemented
7#70205C211yesmaximal, characteristic, complemented
8#70204C211yesmaximal, characteristic
9#69659C211yesmaximal, characteristic, complemented
10#68825C211yesmaximal, characteristic, complemented
11#68822C211yesmaximal, characteristic, complemented
12#68782C211yesmaximal, characteristic, complemented
13#68781C211yesmaximal, characteristic, complemented
14#68630C211yesmaximal, characteristic, complemented
15#68601C211yesmaximal, characteristic, complemented
16#23579—31nomaximal, Sylow
17C2×C3×C4⋊Q8C2211yescharacteristic
18C2×#947—21no—
19C2×#946—21no—
20C2×#938C2211yescharacteristic
21C2×D4×Dic3C2211yescharacteristic
22C22×#214C2211yescharacteristic
23C22×#213C2211yescharacteristic
24#5733—24no—
25#5733—24no—
26C2×#898—21no—
27C2×#897C2211yescharacteristic
28C2×#895C2211yescharacteristic
29C2×#894—21no—
30C2×#893C2211yescharacteristic
31C2×#887C2211yescharacteristic
32C2×#875C2211yescharacteristic
33C2×#872C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C3×#390C2211yescharacteristic
37C2×#821C2211yescharacteristic
38C2×#821C2211yescharacteristic
39C2×(C2×D3)⋊C8C2211yescharacteristic
40C2×(C2×D3)⋊C8C2211yescharacteristic
41C2×#816C2211yescharacteristic
42C2×#816C2211yescharacteristic
43C2×#815C2211yescharacteristic
44C2×C8×Dic3C2211yescharacteristic
45#4987C2211yescharacteristic
46Dic3×C4⋊C4C2211yescharacteristic
47C2×#810C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#807C2211yescharacteristic
50C2×#807C2211yescharacteristic
51#4958—21no—
52#4957—21no—
53#4946—21no—
54#4944—21no—
55#4928C2211yescharacteristic
56#4757—24no—
57#4756—24no—
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#542—31no—
65C2×#440—31no—
66C2×C4×D8—31no—
67#2324—31no—
68#2057—31no—
69#2042—31no—
70#2036—31no—
71#2033—31no—
72#2023D311yescharacteristic, complemented
73#2012—31no—
74#2000—31no—
75#1999—31no—
76#1762—31no—
77C4×#103—31no—
78#1750—31no—
79C22×C3×Q8—21no—
80C22×C3×D4C2311yescharacteristic
81C22×#67—21no—
82C23×Dic3—21no—
83C22×D12—21no—
84C22×D12C2311yescharacteristic
85C22×C4×D3—21no—
86C22×C4×D3C2311yescharacteristic
87C22×Dic6C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C3×C4⋊Q8—22no—
91C3×C4⋊Q8—22no—
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4C2311yescharacteristic
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#947—28no—
102#946—28no—
103#938—22no—
104#938—22no—
105D4×Dic3—22no—
106D4×Dic3—22no—
107C2×#214—22no—
108C2×#214—22no—
109C2×#214—22no—
110C2×#213—22no—
111C2×#213—22no—
112C2×#213—22no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4D411yescharacteristic
120C2×(C2×D3)⋊C4D411yescharacteristic
121C2×C4⋊Dic3—21no—
122C2×C4⋊Dic3C2311yescharacteristic
123C2×C4⋊Dic3C2311yescharacteristic
124C2×Dic3⋊C4—21no—
125C2×Dic3⋊C4—21no—
126C2×Dic3⋊C4D411yescharacteristic
127C2×Dic3⋊C4D411yescharacteristic
128C2×C4×Dic3—21no—
129C2×C4×Dic3—21no—
130C2×C4×Dic3C2311yescharacteristic
131C22×C3⋊C8C2311yescharacteristic
132C22×C3⋊C8C2311yescharacteristic
133#898—28no—
134#897—22no—
135#897—22no—
136#895—22no—
137#895—22no—
138#894—28no—
139#893—22no—
140#893D414yescomplemented
141#887—22no—
142#887D414yescomplemented
143#875—22no—
144#875—22no—
145#872—22no—
146#872—22no—
147C3×#102—22no—
148C3×#102—22no—
149C3⋊#95—21no—
150C3⋊#95—21no—
151C3⋊#95—21no—
152#821—22no—
153#821—22no—
154(C2×D3)⋊C8—22no—
155(C2×D3)⋊C8—22no—
156#816—22no—
157#816—22no—
158#815—22no—
159C8×Dic3—22no—
160#810—22no—
161#809—22no—
162#807—22no—
163#807—22no—
164C22×SD16—31no—
165C22×D8—31no—
166#542—64no—
167#542—64no—
168C2×C4⋊Q8C2×D311yescharacteristic
169C2×#126—61no—
170C2×#124—31no—
171C2×#124—61no—
172C2×#123—61no—
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8—61no—
175C2×#121—31no—
176C2×#121—31no—
177C2×C4×Q8—31no—
178C2×C4×D4—31no—
179C2×C4×D4—31no—
180C2×#117—31no—
181#440—64no—
182C4×D8—64no—
183C2×#107—31no—
184C2×#107—31no—
185C2×#103—31no—
186C2×#103—31no—
187C2×#103—31no—
188C2×#102—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102C2×D311yescharacteristic
192C2×#102C2×D311yescharacteristic
193C2×C22⋊C8—31no—
194C2×C22⋊C8—31no—
195C2×#97—31no—
196C2×C4×C8—31no—
197#390—61no—
198#390C2×D311yescharacteristic
199#389—31no—
200#388—61no—
201#386—61no—
202#385—61no—
203#380—31no—
204C4×C4⋊C4—31no—
205#340—31no—
206#340—31no—
207#340C2×D311yescharacteristic
208#340C2×D311yescharacteristic
209#336—31no—
210#336C2×D311yescharacteristic
211C24×C3—21no—
212C23×D3—21no—
213C23×D3C2×D411yescharacteristic
214C2×C3×Q8—24no—
215C2×C3×Q8—81no—
216C2×C3×Q8—81no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4#4112yes—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4C2×D411yescharacteristic
227C22×C3×C4C2×D411yescharacteristic
228C22×C3×C4C2411yescharacteristic
229C2×#67—24no—
230C2×#67—81no—
231C2×#67—81no—
232C22×Dic3—21no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3—42no—
236C22×Dic3—81no—
237C22×Dic3—81no—
238C22×Dic3C2×D411yescharacteristic
239C22×Dic3C2×D411yescharacteristic
240C22×Dic3C2×D411yescharacteristic
241C2×D12—21no—
242C2×D12—21no—
243C2×D12—21no—
244C2×D12—21no—
245C2×D12—21no—
246C2×D12—24no—
247C2×D12—81no—
248C2×D12—81no—
249C2×D12C2×D412yes—
250C2×C4×D3—21no—
251C2×C4×D3—21no—
252C2×C4×D3—21no—
253C2×C4×D3—21no—
254C2×C4×D3—21no—
255C2×C4×D3—21no—
256C2×C4×D3—24no—
257C2×C4×D3—81no—
258C2×C4×D3—81no—
259C2×Dic6—21no—
260C2×Dic6—21no—
261C2×Dic6—21no—
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6C2×D412yes—
265C2×C3×C8—21no—
266C2×C3×C8—21no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C3×C4⋊C4—24no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4C2×D412yes—
277C3×C4⋊C4C2×D412yes—
278C3×C22⋊C4—81no—
279C3×C22⋊C4—81no—
280C3×C42—21no—
281C3×C42—21no—
282#217—24no—
283#217—42no—
284#214—28no—
285#213—28no—
286(C2×D3)⋊C4—24no—
287(C2×D3)⋊C4—24no—
288(C2×D3)⋊C4—24no—
289(C2×D3)⋊C4—24no—
290(C2×D3)⋊C4—22no—
291(C2×D3)⋊C4—22no—
292(C2×D3)⋊C4—24no—
293(C2×D3)⋊C4—81no—
294C4⋊Dic3—24no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3—21no—
298C4⋊Dic3#4112yes—
299Dic3⋊C4—22no—
300Dic3⋊C4—22no—
301Dic3⋊C4—24no—
302Dic3⋊C4—81no—
303C4×Dic3—24no—
304C4×Dic3—81no—
305C4×Dic3C2×D412yes—
306C4×Dic3C2×D412yes—
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—21no—
314C22×Q8—31no—
315C22×D4—31no—
316C22×D4—61no—
317C22×D4—61no—
318C22×D4C22×D311yescharacteristic
319C23×C4—31no—
320C23×C4—61no—
321C23×C4—61no—
322C2×SD16—62no—
323C2×SD16—62no—
324C2×SD16—62no—
325C2×D8—62no—
326C2×D8—62no—
327C2×D8—62no—
328C22×C8—31no—
329C22×C8—31no—
330C22×C8C22×D311yescharacteristic
331C22×C8C22×D311yescharacteristic
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334#126—68no—
335#124—62no—
336#124—62no—
337#124—68no—
338#123—68no—
339C22⋊Q8—62no—
340C22⋊Q8—68no—
341C22⋊Q8—62no—
342#121—62no—
343#121—62no—
344#121—62no—
345#121—62no—
346C4×Q8—34no—
347C4×Q8—62no—
348C4×D4—34no—
349C4×D4—62no—
350C4×D4—62no—
351C4×D4—62no—
352#117—62no—
353#117—62no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—31no—
356C2×C4⋊C4—31no—
357C2×C4⋊C4—31no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—61no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4C22×D311yescharacteristic
363C2×C4⋊C4C22×D311yescharacteristic
364C2×C4⋊C4C22×D311yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—31no—
368C2×C22⋊C4—31no—
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—61no—
379C2×C42—61no—
380C2×C42C22×D311yescharacteristic
381#107—62no—
382#107—62no—
383#103—62no—
384#103—62no—
385#103—62no—
386#102—22no—
387#102—22no—
388#102—62no—
389#102—62no—
390#102—62no—
391C22⋊C8—62no—
392C22⋊C8—62no—
393#97—62no—
394C4×C8—62no—
395#95—61no—
396#95—61no—
397#95—61no—
398C23×C3—22no—
399C23×C3—41no—
400C23×C3—41no—
401C23×C3—41no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3C22×D411yescharacteristic
406C22×D3—21no—
407C22×D3—22no—
408C22×D3—21no—
409C22×D3—21no—
410C22×D3—21no—
411C22×D3—21no—
412C22×D3—21no—
413C22×D3—21no—
414C22×D3—41no—
415C22×D3—41no—
416C22×D3—41no—
417C22×D3—41no—
418C22×D3—41no—
419C22×D3—41no—
420C3×Q8—84no—
421C3×D4—22no—
422C3×D4—22no—
423C3×D4—41no—
424C3×D4—41no—
425C2×C3×C4—22no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—22no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4C22×D411yescharacteristic
441C2×C3×C4C22×D411yescharacteristic
442C2×C3×C4C2×#4111yescharacteristic
443C2×C3×C4C2×#4111yescharacteristic
444C2×C3×C4C2×#4111yescharacteristic
445C2×C3×C4C2×#4111yescharacteristic
446#67—84no—
447C2×Dic3—21no—
448C2×Dic3—21no—
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—22no—
452C2×Dic3—21no—
453C2×Dic3—22no—
454C2×Dic3—21no—
455C2×Dic3—21no—
456C2×Dic3—41no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—84no—
464C2×Dic3#12012yes—
465C2×Dic3#12012yes—
466D12—22no—
467D12—22no—
468D12—41no—
469D12—41no—
470D12—84no—
471C4×D3—41no—
472C4×D3—41no—
473C4×D3—41no—
474C4×D3—41no—
475C4×D3—84no—
476Dic6—22no—
477Dic6—22no—
478Dic6—41no—
479Dic6—41no—
480C3×C8—41no—
481C3×C8—41no—
482C3⋊C8—22no—
483C3⋊C8—22no—
484C24—21no—
485C24—31no—
486C24—61no—
487C2×Q8—24no—
488C2×Q8—32no—
489C2×Q8—61no—
490C2×Q8—61no—
491C2×Q8—61no—
492C2×Q8—61no—
493C2×Q8—61no—
494C2×Q8—81no—
495C2×Q8—81no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—32no—
502C2×D4—64no—
503C2×D4—64no—
504C2×D4—61no—
505C2×D4—61no—
506C2×D4—61no—
507C2×D4—61no—
508C2×D4—61no—
509C2×D4—241no—
510C2×D4—241no—
511C2×D4—241no—
512C2×D4—241no—
513C2×D4#23912yes—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—31no—
518C22×C4—31no—
519C22×C4—31no—
520C22×C4—64no—
521C22×C4—61no—
522C22×C4—61no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—122no—
531C22×C4—241no—
532C22×C4—241no—
533C22×C4—241no—
534C22×C4—241no—
535C22×C4D3×D411yescharacteristic
536C22×C4D3×D411yescharacteristic
537C22×C4C23×D311yescharacteristic
538SD16—68no—
539D8—68no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—32no—
547C2×C8—32no—
548C2×C8—61no—
549C2×C8—61no—
550C2×C8—61no—
551C2×C8—61no—
552C4⋊C4—24no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—32no—
558C4⋊C4—62no—
559C4⋊C4—62no—
560C4⋊C4—64no—
561C4⋊C4—64no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—241no—
566C4⋊C4D3×D412yes—
567C4⋊C4D3×D412yes—
568C22⋊C4—62no—
569C22⋊C4—62no—
570C22⋊C4—64no—
571C22⋊C4—64no—
572C22⋊C4—64no—
573C22⋊C4—64no—
574C22⋊C4—64no—
575C22⋊C4—64no—
576C22⋊C4—81no—
577C22⋊C4—81no—
578C22⋊C4—122no—
579C22⋊C4—241no—
580C42—21no—
581C42—21no—
582C42—32no—
583C42—32no—
584C42—64no—
585C42—241no—
586C22×C3—42no—
587C22×C3—42no—
588C22×C3—42no—
589C22×C3—81no—
590C22×C3—81no—
591C22×C3—81no—
592C22×C3—81no—
593C22×C3C2×#12011yescharacteristic
594C22×C3#52511yescharacteristic
595C22×C3#53211yescharacteristic
596C22×C3#57611yescharacteristic
597C22×C3#57611yescharacteristic
598C22×C3#57711yescharacteristic
599C22×C3#57811yescharacteristic
600C2×D3—41no—
601C2×D3—41no—
602C2×D3—41no—
603C2×D3—42no—
604C2×D3—41no—
605C2×D3—41no—
606C2×D3—42no—
607C2×D3—41no—
608C2×D3—41no—
609C2×D3—42no—
610C2×D3—81no—
611C2×D3—81no—
612C2×D3—81no—
613C2×D3—81no—
614C3×C4—42no—
615C3×C4—42no—
616C3×C4—41no—
617C3×C4—41no—
618C3×C4—81no—
619C3×C4#52511yescharacteristic
620C3×C4#52511yescharacteristic
621C3×C4#53211yescharacteristic
622C3×C4#53211yescharacteristic
623Dic3—22no—
624Dic3—22no—
625Dic3—42no—
626Dic3—42no—
627Dic3—41no—
628Dic3—81no—
629C23—22no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—61no—
637C23—61no—
638C23—61no—
639C23—61no—
640C23—61no—
641C23—62no—
642C23—61no—
643C23—61no—
644C23—121no—
645C23—121no—
646C23—121no—
647C23—121no—
648C23—121no—
649C23—121no—
650C23C2×D3×D411yescharacteristic
651Q8—62no—
652Q8—62no—
653Q8—84no—
654Q8—121no—
655Q8—121no—
656D4—22no—
657D4—22no—
658D4—41no—
659D4—41no—
660D4—62no—
661D4—62no—
662D4—121no—
663D4—121no—
664D4—244no—
665D4—244no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—32no—
675C2×C4—32no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—62no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—62no—
692C2×C4—121no—
693C2×C4—121no—
694C2×C4—121no—
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—244no—
704C2×C4—244no—
705C2×C4C2×D3×D411yescharacteristic
706C2×C4C2×D3×D411yescharacteristic
707C2×C4C2×#23911yescharacteristic
708C2×C4D3×#4111yescharacteristic
709C2×C4D3×#4111yescharacteristic
710C2×C4D3×#4111yescharacteristic
711C8—41no—
712C8—41no—
713C8—62no—
714C8—62no—
715C2×C3—82no—
716C2×C3#238811yescharacteristic
717C2×C3#300811yescharacteristic
718C2×C3#301311yescharacteristic
719C2×C3#311811yescharacteristic
720C2×C3#312411yescharacteristic
721C2×C3#317511yescharacteristic
722C2×C3#317911yescharacteristic
723D3—81no—
724D3—82no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—121no—
733C22—121no—
734C22—122no—
735C22—121no—
736C22—121no—
737C22—121no—
738C22—121no—
739C22—122no—
740C22—121no—
741C22—122no—
742C22—241no—
743C22—241no—
744C22—241no—
745C22—241no—
746C22D3×#12011yescharacteristic
747C22#562711yescharacteristic
748C22#566811yescharacteristic
749C22#575711yescharacteristic
750C22#576211yescharacteristic
751C22#577411yescharacteristic
752C22#577911yescharacteristic
753C4—41no—
754C4—42no—
755C4—42no—
756C4—41no—
757C4—62no—
758C4—62no—
759C4—81no—
760C4—122no—
761C4—121no—
762C4—122no—
763C4—241no—
764C4#562711yescharacteristic
765C4#562711yescharacteristic
766C4#566811yescharacteristic
767C4#566811yescharacteristic
768C3#2357911yescharacteristic, complemented, Sylow
769C2—82no—
770C2—241no—
771C2—242no—
772C2#7677711yescharacteristic
773C2#8000411yescharacteristic
774C2#8004211yescharacteristic
775C2#8095311yescharacteristic
776C2#8104811yescharacteristic
777C2#8155811yescharacteristic
778C2#8166711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2023C2
socleC23×C3C22×D4
prime radical#70204C2
hypercenter#2023D3
hypocenterC3#23579
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2023

Complements

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

NH ≅ G/Ntype
1. C2×#5733C2semidirect
2. C2×#4757C2semidirect
3. C2×#4756C2semidirect
4. #76430C2semidirect
5. C3×#2023C2semidirect
6. #71782C2semidirect
7. #70205C2semidirect
9. #69659C2semidirect
10. #68825C2semidirect
11. #68822C2semidirect
12. #68782C2semidirect
13. #68781C2semidirect
14. #68630C2semidirect
15. #68601C2semidirect
72. #2023D3semidirect
140. #893D4semidirect
142. #887D4semidirect
768. C3#23579semidirect

Maximal subgroups

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

subgroupindex
C2×#57332
C2×#47572
C2×#47562
#764302
C3×#20232
#717822
#702052
#702042
#696592
#688252
#688222
#687822
#687812
#686302
#686012
#235793