Finite Group Databasebeta

← #10966655

Subgroups — #10966655

Order 768.

2726 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×C4×#237C211yesmaximal, characteristic, complemented
2C2×C4×#237C211yesmaximal, characteristic, complemented
3C3×#2535C211yesmaximal, characteristic, complemented
4#82701C212yesmaximal, complemented
5Dic3×#121C212yesmaximal, complemented
6#82388C211yesmaximal, characteristic, complemented
7#82375C211yesmaximal, characteristic, complemented
8#77533C212yesmaximal, complemented
9#77458C212yesmaximal, complemented
10#76692C212yesmaximal, complemented
11#76665C212yesmaximal, complemented
12#74903C214yesmaximal, complemented
13#74657C214yesmaximal, complemented
14#74191C211yesmaximal, characteristic, complemented
15#74147C211yesmaximal, characteristic, complemented
16#74025C212yesmaximal, complemented
17#73866C212yesmaximal, complemented
18#34909—31nomaximal, Sylow
19C22×#237C2211yescharacteristic
20C22×#237C2211yescharacteristic
21C2×C3×#121C2212yes—
22C2×C3×C4×D4C2211yescharacteristic
23C2×C3×C4×D4C2211yescharacteristic
24C2×D4×Dic3C2214yes—
25C2×D4×Dic3C2211yescharacteristic
26C2×D4×Dic3C2211yescharacteristic
27C2×C4×#67C2212yes—
28C2×C4×#67C2212yes—
29C2×#924C2212yes—
30C22×C4×Dic3C2212yes—
31C22×C4×Dic3C2212yes—
32C4×#237—28no—
33C4×#237—28no—
34C2×#892C2211yescharacteristic
35C2×#892C2211yescharacteristic
36C2×#887C2211yescharacteristic
37C2×#887C2211yescharacteristic
38C2×#67⋊C4C2212yes—
39C2×#67⋊C4C2212yes—
40C2×#877C2212yes—
41C2×#877C2212yes—
42C2×C42×D3C2211yescharacteristic
43C2×C4×Dic6C2211yescharacteristic
44C2×C4×Dic6C2211yescharacteristic
45C3×#397C2212yes—
46C3×#392C2212yes—
47C3×#386C2214yes—
48C3×#382C2211yescharacteristic
49C3×#380C2212yes—
50#5223C2214yes—
51#5222C2212yes—
52#5221C2212yes—
53#5220C2214yes—
54#5220C2214yes—
55#5212C2212yes—
56#5210C2214yes—
57#4987C2212yes—
58#4984C2212yes—
59#4983C2212yes—
60Dic3×C4⋊C4C2212yes—
61#4973C2212yes—
62#4972C2212yes—
63#4961C2214yes—
64#4959C2214yes—
65#4951C2214yes—
66#4949C2212yes—
67#4947C2212yes—
68#4946C2214yes—
69#4946C2214yes—
70#4945C2214yes—
71#4944C2214yes—
72Dic3×C22⋊C4C2214yes—
73Dic3×C22⋊C4C2214yes—
74#4936C2211yescharacteristic
75#4675C2214yes—
76#4666C2212yes—
77#4664C2212yes—
78#4659C2212yes—
79#4656C2212yes—
80#4654C2214yes—
81#4653C2214yes—
82#4652C2214yes—
83#4651C2212yes—
84#4649C2214yes—
85#4648C2212yes—
86C2×C4×#41—31no—
87C2×C4×#41—31no—
88#2600—34no—
89#2599—32no—
90#2598—32no—
91#2581—31no—
92#2580—31no—
93#2536—31no—
94#2535D311yescharacteristic, complemented
95#2485—32no—
96#2407—32no—
97#2395—32no—
98#2388—32no—
99C4×C22⋊Q8—32no—
100C4×#121—32no—
101#2290—34no—
102#2283—31no—
103C22×C3×D4C2311yescharacteristic
104C22×C3×D4C2314yes—
105C22×C3×D4C2311yescharacteristic
106C23×C3×C4C2312yes—
107C23×C3×C4C2312yes—
108C22×#67C2312yes—
109C22×#67C2312yes—
110C23×Dic3C2312yes—
111C23×Dic3C2312yes—
112C23×Dic3C2312yes—
113C23×Dic3C2312yes—
114C2×#237—24no—
115C2×#237—28no—
116C2×#237—24no—
117C2×#237—24no—
118C2×#237—24no—
119C22×C4×D3C2311yescharacteristic
120C22×C4×D3C2311yescharacteristic
121C22×C4×D3C2311yescharacteristic
122C22×Dic6C2311yescharacteristic
123C22×Dic6C2311yescharacteristic
124C3×#121—28no—
125C3×C4×D4—24no—
126C3×C4×D4—24no—
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C4⋊C4C2312yes—
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C22⋊C4C2314yes—
131C2×C3×C22⋊C4C2312yes—
132C2×C3×C22⋊C4C2312yes—
133C2×C3×C22⋊C4C2314yes—
134C2×C3×C42C2311yescharacteristic
135C2×#217C2314yes—
136C2×#217C2314yes—
137C2×#217C2312yes—
138C2×#217C2314yes—
139C2×#217C2312yes—
140C2×#217C2314yes—
141D4×Dic3—216no—
142D4×Dic3—24no—
143D4×Dic3—24no—
144C4×#67—28no—
145C4×#67—28no—
146C2×(C2×D3)⋊C4C2312yes—
147C2×(C2×D3)⋊C4C2312yes—
148C2×(C2×D3)⋊C4C2314yes—
149C2×C4⋊Dic3C2314yes—
150C2×C4⋊Dic3C2311yescharacteristic
151C2×C4⋊Dic3C2312yes—
152C2×C4⋊Dic3C2311yescharacteristic
153#924—28no—
154C2×Dic3⋊C4C2314yes—
155C2×Dic3⋊C4C2312yes—
156C2×Dic3⋊C4C2312yes—
157C2×Dic3⋊C4C2312yes—
158C2×Dic3⋊C4C2312yes—
159C2×Dic3⋊C4C2314yes—
160C2×C4×Dic3—28no—
161C2×C4×Dic3—28no—
162C2×C4×Dic3C2314yes—
163C2×C4×Dic3C2312yes—
164C2×C4×Dic3C2312yes—
165C2×C4×Dic3C2312yes—
166C2×C4×Dic3C2312yes—
167C2×C4×Dic3C2312yes—
168C2×C4×Dic3C2312yes—
169C2×C4×Dic3C2311yescharacteristic
170C2×C4×Dic3C2311yescharacteristic
171C2×C4×Dic3C2311yescharacteristic
172#892—24no—
173#892—24no—
174#887—24no—
175#887—24no—
176#67⋊C4—28no—
177#67⋊C4—28no—
178#877—28no—
179#877—28no—
180C42×D3D418yescomplemented
181C4×Dic6—24no—
182C4×Dic6—24no—
183C3×#95C2312yes—
184C3×#95C2314yes—
185C3×#95C2312yes—
186C3⋊#95C2314yes—
187C3⋊#95C2312yes—
188C3⋊#95C2314yes—
189C3⋊#95C2314yes—
190C3⋊#95C2312yes—
191C3⋊#95C2314yes—
192C3⋊#95C2314yes—
193C3⋊#95C2314yes—
194C3⋊#95C2314yes—
195C22×#41—31no—
196C22×#41—31no—
197C2×C22⋊Q8—32no—
198C2×#121C2×D312yes—
199C4×#41—68no—
200C4×#41—68no—
201C2×C4×Q8—31no—
202C2×C4×Q8—31no—
203C2×C4×Q8—31no—
204C2×C4×Q8—31no—
205C2×C4×D4—31no—
206C2×C4×D4—34no—
207C2×C4×D4—31no—
208C2×C4×D4—32no—
209C2×C4×D4—32no—
210C2×C4×D4—32no—
211C2×C4×D4—32no—
212C2×C4×D4C2×D311yescharacteristic
213C2×C4×D4C2×D311yescharacteristic
214C2×#117—31no—
215C2×#117—31no—
216C2×#117—32no—
217C2×#117—32no—
218C22×C42—31no—
219C22×C42—32no—
220C22×C42—32no—
221#400—32no—
222#399—32no—
223#398—32no—
224#397—34no—
225#397C2×D312yes—
226#395—32no—
227#394—32no—
228#394—34no—
229#394—34no—
230#393—32no—
231#392—34no—
232#392C2×D312yes—
233#391—32no—
234#390—32no—
235#389—32no—
236#389—32no—
237#388—34no—
238#388—34no—
239#388—34no—
240#387—34no—
241#387—34no—
242#387—34no—
243#386—34no—
244#386—34no—
245#386C2×D314yes—
246#385—34no—
247#385—34no—
248#385—34no—
249#383—32no—
250#382—31no—
251#382C2×D311yescharacteristic
252#381—32no—
253#380—32no—
254#380—32no—
255#380C2×D312yes—
256C4×C4⋊C4—32no—
257C4×C4⋊C4—34no—
258C4×C22⋊C4—34no—
259C4×C22⋊C4—34no—
260C4×C22⋊C4—32no—
261#376—32no—
262C24×C3C2412yes—
263C24×C3C2412yes—
264C23×D3C2411yescharacteristic
265C2×C3×D4—24no—
266C2×C3×D4—28no—
267C2×C3×D4—28no—
268C2×C3×D4—22no—
269C2×C3×D4—22no—
270C2×C3×D4—22no—
271C2×C3×D4—44no—
272C2×C3×D4#4114yescomplemented
273C22×C3×C4—24no—
274C22×C3×C4—24no—
275C22×C3×C4—24no—
276C22×C3×C4—24no—
277C22×C3×C4—44no—
278C22×C3×C4C2414yes—
279C22×C3×C4C2412yes—
280C22×C3×C4C2412yes—
281C22×C3×C4C2411yescharacteristic
282C22×C3×C4C2411yescharacteristic
283C22×C3×C4C2411yescharacteristic
284C2×#67—24no—
285C2×#67—24no—
286C2×#67—24no—
287C2×#67—24no—
288C2×#67—24no—
289C2×#67—24no—
290C22×Dic3—24no—
291C22×Dic3—24no—
292C22×Dic3—24no—
293C22×Dic3—24no—
294C22×Dic3—24no—
295C22×Dic3—24no—
296C22×Dic3—24no—
297C22×Dic3—28no—
298C22×Dic3—42no—
299C22×Dic3—42no—
300C22×Dic3#4118yescomplemented
301C22×Dic3C2414yes—
302C22×Dic3C2412yes—
303C22×Dic3C2412yes—
304C22×Dic3C2411yescharacteristic
305C22×Dic3C2411yescharacteristic
306C22×Dic3C2412yes—
307C22×Dic3C2412yes—
308C22×Dic3C2411yescharacteristic
309#237—232no—
310#237—232no—
311C2×C4×D3—22no—
312C2×C4×D3—22no—
313C2×C4×D3—24no—
314C2×C4×D3—42no—
315C2×C4×D3C2×D414yes—
316C2×C4×D3C2×D414yes—
317C2×C4×D3C2×D414yes—
318C2×Dic6—22no—
319C2×Dic6—22no—
320C2×Dic6—22no—
321C2×Dic6—24no—
322C2×Dic6#4114yescomplemented
323C3×C4⋊C4—22no—
324C3×C4⋊C4—22no—
325C3×C4⋊C4—24no—
326C3×C22⋊C4—28no—
327C3×C22⋊C4—24no—
328C3×C22⋊C4—24no—
329C3×C22⋊C4—44no—
330C3×C42C2×D414yes—
331#217—28no—
332#217—24no—
333#217—24no—
334#217—28no—
335#217—28no—
336#217—44no—
337(C2×D3)⋊C4—24no—
338(C2×D3)⋊C4—24no—
339(C2×D3)⋊C4—44no—
340C4⋊Dic3—22no—
341C4⋊Dic3—22no—
342C4⋊Dic3—24no—
343C4⋊Dic3—28no—
344Dic3⋊C4—24no—
345Dic3⋊C4—24no—
346Dic3⋊C4—24no—
347Dic3⋊C4—24no—
348Dic3⋊C4—28no—
349Dic3⋊C4—44no—
350C4×Dic3—24no—
351C4×Dic3—24no—
352C4×Dic3—24no—
353C4×Dic3—24no—
354C4×Dic3—24no—
355C4×Dic3—24no—
356C4×Dic3—28no—
357C4×Dic3C2×D414yes—
358C4×Dic3C2×D414yes—
359C4×Dic3C2×D414yes—
360C2×#41—64no—
361C2×#41—64no—
362C2×#41—68no—
363C2×#41—64no—
364C2×#41—64no—
365C22×Q8—31no—
366C22×Q8—31no—
367C22×D4—32no—
368C22×D4—32no—
369C22×D4C22×D311yescharacteristic
370C22×D4C22×D314yes—
371C22×D4C22×D311yescharacteristic
372C23×C4—32no—
373C23×C4—31no—
374C23×C4—31no—
375C23×C4—31no—
376C23×C4—32no—
377C23×C4—32no—
378C23×C4—32no—
379C23×C4C22×D312yes—
380C23×C4C22×D312yes—
381C22⋊Q8—68no—
382#121—28no—
383C4×Q8—64no—
384C4×Q8—64no—
385C4×Q8—64no—
386C4×Q8—64no—
387C4×D4—24no—
388C4×D4—24no—
389C4×D4—64no—
390C4×D4—64no—
391C4×D4—68no—
392C4×D4—68no—
393C4×D4—68no—
394C4×D4—68no—
395C4×D4—616no—
396#117—68no—
397#117—68no—
398#117—64no—
399#117—64no—
400C2×C4⋊C4—31no—
401C2×C4⋊C4—32no—
402C2×C4⋊C4—32no—
403C2×C4⋊C4—32no—
404C2×C4⋊C4—32no—
405C2×C4⋊C4—31no—
406C2×C4⋊C4—34no—
407C2×C4⋊C4—32no—
408C2×C4⋊C4—34no—
409C2×C4⋊C4—34no—
410C2×C4⋊C4C22×D311yescharacteristic
411C2×C4⋊C4C22×D311yescharacteristic
412C2×C4⋊C4C22×D312yes—
413C2×C22⋊C4—32no—
414C2×C22⋊C4—32no—
415C2×C22⋊C4—34no—
416C2×C22⋊C4—34no—
417C2×C22⋊C4—34no—
418C2×C22⋊C4—32no—
419C2×C22⋊C4—32no—
420C2×C22⋊C4—34no—
421C2×C22⋊C4—34no—
422C2×C22⋊C4C22×D312yes—
423C2×C22⋊C4C22×D312yes—
424C2×C22⋊C4C22×D314yes—
425C2×C22⋊C4C22×D314yes—
426C2×C42—31no—
427C2×C42—31no—
428C2×C42—31no—
429C2×C42—38no—
430C2×C42—32no—
431C2×C42—32no—
432C2×C42—32no—
433C2×C42—32no—
434C2×C42—32no—
435C2×C42—32no—
436C2×C42—34no—
437C2×C42—68no—
438C2×C42—68no—
439C2×C42C22×D311yescharacteristic
440#95—34no—
441#95—32no—
442#95—34no—
443#95—32no—
444#95—34no—
445#95—34no—
446#95—34no—
447#95—34no—
448#95—34no—
449#95C22×D312yes—
450#95C22×D312yes—
451#95C22×D314yes—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—24no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—24no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3C2×#4114yes—
463C23×C3C2×#4114yes—
464C23×C3C2511yescharacteristic
465C22×D3—21no—
466C22×D3—22no—
467C22×D3—21no—
468C22×D3—22no—
469C22×D3C22×D412yes—
470C3×D4—28no—
471C3×D4—28no—
472C3×D4—416no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—24no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—24no—
481C2×C3×C4—24no—
482C2×C3×C4—24no—
483C2×C3×C4—48no—
484C2×C3×C4—48no—
485C2×C3×C4C22×D412yes—
486C2×C3×C4C22×D412yes—
487C2×C3×C4C22×D412yes—
488C2×C3×C4C2×#4112yes—
489C2×C3×C4C2×#4112yes—
490#67—216no—
491#67—216no—
492C2×Dic3—216no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—22no—
500C2×Dic3—216no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—24no—
504C2×Dic3—24no—
505C2×Dic3—24no—
506C2×Dic3—22no—
507C2×Dic3—24no—
508C2×Dic3—22no—
509C2×Dic3—48no—
510C2×Dic3—48no—
511C2×Dic3C22×D412yes—
512C2×Dic3C22×D412yes—
513C2×Dic3C22×D412yes—
514C2×Dic3C2×#4114yes—
515C2×Dic3C2×#4114yes—
516C2×Dic3C2×#4114yes—
517C4×D3—28no—
518C4×D3—28no—
519C4×D3—44no—
520Dic6—28no—
521Dic6—28no—
522C24—31no—
523C24C23×D312yes—
524C24C23×D312yes—
525#41—632no—
526#41—632no—
527C2×Q8—34no—
528C2×Q8—64no—
529C2×Q8—62no—
530C2×Q8—62no—
531C2×Q8—62no—
532C2×D4—24no—
533C2×D4—28no—
534C2×D4—28no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—44no—
539C2×D4—64no—
540C2×D4—64no—
541C2×D4—64no—
542C2×D4—64no—
543C2×D4—64no—
544C2×D4—64no—
545C2×D4#23714yescomplemented
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—31no—
551C22×C4—38no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—32no—
555C22×C4—32no—
556C22×C4—34no—
557C22×C4—34no—
558C22×C4—34no—
559C22×C4—34no—
560C22×C4—32no—
561C22×C4—32no—
562C22×C4—44no—
563C22×C4—64no—
564C22×C4—64no—
565C22×C4—64no—
566C22×C4—64no—
567C22×C4—64no—
568C22×C4—64no—
569C22×C4—64no—
570C22×C4—68no—
571C22×C4—64no—
572C22×C4—62no—
573C22×C4—62no—
574C22×C4—122no—
575C22×C4—122no—
576C22×C4—122no—
577C22×C4C23×D314yes—
578C22×C4C23×D312yes—
579C22×C4C23×D312yes—
580C22×C4C23×D311yescharacteristic
581C22×C4C23×D311yescharacteristic
582C22×C4C23×D311yescharacteristic
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—24no—
586C4⋊C4—64no—
587C4⋊C4—64no—
588C4⋊C4—68no—
589C4⋊C4—68no—
590C4⋊C4—64no—
591C4⋊C4—64no—
592C4⋊C4—62no—
593C4⋊C4—62no—
594C4⋊C4—64no—
595C4⋊C4—124no—
596C22⋊C4—28no—
597C22⋊C4—24no—
598C22⋊C4—24no—
599C22⋊C4—44no—
600C22⋊C4—64no—
601C22⋊C4—64no—
602C22⋊C4—64no—
603C22⋊C4—64no—
604C22⋊C4—68no—
605C22⋊C4—68no—
606C22⋊C4—68no—
607C22⋊C4—124no—
608C22⋊C4—124no—
609C42—34no—
610C42—34no—
611C42—34no—
612C42—64no—
613C42—64no—
614C42—64no—
615C42—64no—
616C42—68no—
617C42—64no—
618C42—64no—
619C42D3×D414yes—
620C22×C3—24no—
621C22×C3—24no—
622C22×C3—24no—
623C22×C3—28no—
624C22×C3—24no—
625C22×C3—42no—
626C22×C3—42no—
627C22×C3—42no—
628C22×C3—42no—
629C22×C3—42no—
630C22×C3—42no—
631C22×C3—44no—
632C22×C3C23×D411yescharacteristic
633C22×C3C22×#4111yescharacteristic
634C22×C3C22×#4112yes—
635C22×C3C22×#4111yescharacteristic
636C22×C3#58512yes—
637C2×D3—22no—
638C2×D3—22no—
639C2×D3—22no—
640C2×D3—42no—
641C2×D3—42no—
642C3×C4—22no—
643C3×C4—22no—
644C3×C4—42no—
645C3×C4—42no—
646C3×C4—44no—
647C3×C4#52514yes—
648Dic3—24no—
649Dic3—24no—
650Dic3—22no—
651Dic3—22no—
652Dic3—42no—
653Dic3—42no—
654Dic3—44no—
655Dic3#52514yes—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—24no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—24no—
665C23—22no—
666C23—32no—
667C23—61no—
668C23—62no—
669C23—61no—
670C23—62no—
671C23C2×#23714yes—
672C23D3×#4114yes—
673C23C24×D311yescharacteristic
674Q8—68no—
675Q8—68no—
676D4—28no—
677D4—28no—
678D4—416no—
679D4—616no—
680D4—616no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—32no—
692C2×C4—34no—
693C2×C4—32no—
694C2×C4—32no—
695C2×C4—34no—
696C2×C4—34no—
697C2×C4—48no—
698C2×C4—48no—
699C2×C4—68no—
700C2×C4—616no—
701C2×C4—616no—
702C2×C4—62no—
703C2×C4—62no—
704C2×C4—61no—
705C2×C4—62no—
706C2×C4—61no—
707C2×C4—62no—
708C2×C4—62no—
709C2×C4—68no—
710C2×C4—62no—
711C2×C4—62no—
712C2×C4—64no—
713C2×C4—64no—
714C2×C4—64no—
715C2×C4—64no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—124no—
719C2×C4—128no—
720C2×C4—128no—
721C2×C4C2×D3×D412yes—
722C2×C4C2×D3×D412yes—
723C2×C4C2×D3×D412yes—
724C2×C4C2×#23712yes—
725C2×C4D3×#4112yes—
726C2×C3—44no—
727C2×C3—44no—
728C2×C3C2×#52511yescharacteristic
729C2×C3C2×#52511yescharacteristic
730C2×C3#344911yescharacteristic
731C2×C3#347512yes—
732C2×C3#348012yes—
733D3—42no—
734C22—24no—
735C22—24no—
736C22—24no—
737C22—28no—
738C22—24no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—62no—
747C22—62no—
748C22—62no—
749C22—122no—
750C22—122no—
751C22C22×D3×D411yescharacteristic
752C22C22×#23711yescharacteristic
753C22C2×D3×#4112yes—
754C22C2×D3×#4111yescharacteristic
755C22#596612yes—
756C4—22no—
757C4—22no—
758C4—34no—
759C4—42no—
760C4—44no—
761C4—42no—
762C4—64no—
763C4—62no—
764C4—62no—
765C4—64no—
766C4—122no—
767C4—122no—
768C4—124no—
769C4#560614yes—
770C3#3490911yescharacteristic, complemented, Sylow
771C2—44no—
772C2—44no—
773C2—122no—
774C2C2×#560611yescharacteristic
775C2D3×#52511yescharacteristic
776C2#8631311yescharacteristic
777C2#8662712yes—
778C2#8687512yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2535C2
hypercenter#2535D3
hypocenterC3#34909
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2535

Complements

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

NH ≅ G/Ntype
1. C2×C4×#237C2semidirect
2. C2×C4×#237C2semidirect
3. C3×#2535C2semidirect
4. #82701C2semidirect
5. Dic3×#121C2semidirect
6. #82388C2semidirect
7. #82375C2semidirect
8. #77533C2semidirect
9. #77458C2semidirect
10. #76692C2semidirect
11. #76665C2semidirect
12. #74903C2semidirect
13. #74657C2semidirect
14. #74191C2semidirect
15. #74147C2semidirect
16. #74025C2semidirect
17. #73866C2semidirect
94. #2535D3semidirect
180. C42×D3D4semidirect
272. C2×C3×D4#41semidirect
300. C22×Dic3#41semidirect
322. C2×Dic6#41semidirect
545. C2×D4#237semidirect
770. C3#34909semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#2372
C3×#25352
#827012
Dic3×#1212
#823882
#823752
#775332
#774582
#766922
#766652
#749032
#746572
#741912
#741472
#740252
#738662
#349093