Finite Group Databasebeta

← #10848857

Subgroups — #10848857

Order 768.

1116 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5582C211yesmaximal, characteristic
2C2×#5190C211yesmaximal, characteristic, complemented
3C2×#4792C211yesmaximal, characteristic, complemented
4#76641C211yesmaximal, characteristic, complemented
5C3×#1878C211yesmaximal, characteristic, complemented
6#72071C211yesmaximal, characteristic, complemented
7#71632C211yesmaximal, characteristic, complemented
8#70273C211yesmaximal, characteristic, complemented
9#70272C211yesmaximal, characteristic
10#70226C211yesmaximal, characteristic, complemented
11#69687C211yesmaximal, characteristic, complemented
12#68887C211yesmaximal, characteristic
13#68806C211yesmaximal, characteristic, complemented
14#68672C211yesmaximal, characteristic, complemented
15#68601C211yesmaximal, characteristic, complemented
16#25613—31nomaximal, Sylow
17C22×C3×Q16C2211yescharacteristic
18C2×C3×C4×Q8C2211yescharacteristic
19C2×#947C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C2×#944C2211yescharacteristic
23C22×#216C2211yescharacteristic
24C22×#215C2211yescharacteristic
25C22×#204C2211yescharacteristic
26#5582—24no—
27#5582—24no—
28C2×#897C2211yescharacteristic
29C2×#896—21no—
30C2×#895C2211yescharacteristic
31C2×#894—21no—
32C2×#888C2211yescharacteristic
33C2×#876—21no—
34C2×#875—21no—
35C2×C4×D12C2211yescharacteristic
36C2×#872C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C3×#391C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#835C2211yescharacteristic
42#5190—24no—
43C2×#821C2211yescharacteristic
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#816C2211yescharacteristic
47C2×#815C2211yescharacteristic
48C2×C8×Dic3C2211yescharacteristic
49#4977C2211yescharacteristic
50C2×#810C2211yescharacteristic
51C2×#809C2211yescharacteristic
52#4929C2211yescharacteristic
53#4792—24no—
54#4675—21no—
55#4675—21no—
56#4657—21no—
57#4657—21no—
58C3×#340C2211yescharacteristic
59C3×#336C2211yescharacteristic
60#4551C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#542—31no—
65C2×#497—31no—
66C2×#487—31no—
67#2621—31no—
68#2001—31no—
69#2001—31no—
70#2000—31no—
71#2000—31no—
72#1993—31no—
73#1958—31no—
74#1878—31no—
75#1878D311yescharacteristic, complemented
76#1877—31no—
77#1877—31no—
78#1750—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×D12—21no—
82C22×D12C2311yescharacteristic
83C22×C4×D3—21no—
84C22×C4×D3C2311yescharacteristic
85C22×Dic6—21no—
86C22×Dic6C2311yescharacteristic
87C2×C3×Q16—22no—
88C2×C3×Q16—22no—
89C2×C3×Q16—41no—
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C3×C4×Q8—22no—
93C3×C4×Q8—22no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C42—21no—
98C2×C3×C42C2311yescharacteristic
99#947—22no—
100#947D414yes—
101#946—22no—
102#946—22no—
103#946—41no—
104#946—41no—
105#944—22no—
106#944—22no—
107C2×#216—22no—
108C2×#216—22no—
109C2×#216—41no—
110C2×#215—22no—
111C2×#215—22no—
112C2×#215—41no—
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)⋊C4—21no—
120C2×(C2×D3)⋊C4D411yescharacteristic
121C2×(C2×D3)⋊C4D411yescharacteristic
122C2×C4⋊Dic3—21no—
123C2×C4⋊Dic3C2311yescharacteristic
124C2×C4⋊Dic3C2311yescharacteristic
125C2×Dic3⋊C4—21no—
126C2×Dic3⋊C4—21no—
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4D411yescharacteristic
131C2×Dic3⋊C4D411yescharacteristic
132C2×C4×Dic3C2311yescharacteristic
133C22×C3⋊C8C2311yescharacteristic
134C22×C3⋊C8C2311yescharacteristic
135C2×#204—22no—
136C2×#204—22no—
137C2×#204—41no—
138#897—41no—
139#897—41no—
140#896—28no—
141#895—22no—
142#895—22no—
143#894—28no—
144#888—22no—
145#888D414yes—
146#876—28no—
147#875—28no—
148C4×D12—22no—
149C4×D12—22no—
150#872—22no—
151#872—22no—
152C3×#103—22no—
153C3×#103—41no—
154C3×#95—21no—
155C3×#95—21no—
156#835—22no—
157#835—41no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162#821—41no—
163(C2×D3)⋊C8—22no—
164(C2×D3)⋊C8—22no—
165#816—22no—
166#815—22no—
167C8×Dic3—22no—
168#810—22no—
169#809—41no—
170C22×Q16—31no—
171C22×Q16C2×D311yescharacteristic
172C22×SD16—31no—
173C22×SD16—31no—
174#542—64no—
175#542—64no—
176C2×C4⋊Q8—31no—
177C2×C4⋊Q8—31no—
178C2×#126—61no—
179C2×#124—31no—
180C2×#124—61no—
181C2×#123—61no—
182C2×C22⋊Q8—31no—
183C2×C22⋊Q8—31no—
184C2×C22⋊Q8—31no—
185C2×C22⋊Q8—61no—
186C2×#121—31no—
187C2×C4×Q8C2×D311yescharacteristic
188C2×C4×D4—31no—
189C2×#117—31no—
190#497—64no—
191#487—64no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103—31no—
196C2×#103C2×D311yescharacteristic
197C2×#103C2×D311yescharacteristic
198C2×#102—31no—
199C2×#102—31no—
200C2×C22⋊C8—31no—
201C2×C22⋊C8—31no—
202C2×#97—31no—
203C2×C4×C8—31no—
204#398—61no—
205#398—61no—
206#397—61no—
207#397—61no—
208#391—31no—
209#391C2×D311yescharacteristic
210#382—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340C2×D311yescharacteristic
215#336—31no—
216#336C2×D311yescharacteristic
217C23×D3—21no—
218C23×D3C2×D411yescharacteristic
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8C2×D412yes—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2411yescharacteristic
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3—21no—
241C22×Dic3C2×D411yescharacteristic
242C22×Dic3C2×D411yescharacteristic
243C22×Dic3C2×D411yescharacteristic
244C2×D12—21no—
245C2×D12—21no—
246C2×D12—21no—
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—24no—
250C2×D12—81no—
251C2×D12—81no—
252C2×D12C2×D412yes—
253C2×C4×D3—21no—
254C2×C4×D3—21no—
255C2×C4×D3—21no—
256C2×C4×D3—21no—
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×C4×D3—24no—
260C2×C4×D3—81no—
261C2×C4×D3—81no—
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6—21no—
266C2×Dic6—21no—
267C2×Dic6—21no—
268C2×Dic6—24no—
269C2×Dic6—81no—
270C2×Dic6—81no—
271C3×Q16—44no—
272C2×C3×C8—21no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8#4112yes—
278C3×C4⋊C4—24no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4C2×D412yes—
283C3×C42—24no—
284C3×C42—21no—
285C3×C42—21no—
286#216—44no—
287#215—44no—
288(C2×D3)⋊C4—24no—
289(C2×D3)⋊C4—24no—
290(C2×D3)⋊C4—24no—
291(C2×D3)⋊C4—22no—
292(C2×D3)⋊C4—22no—
293(C2×D3)⋊C4—24no—
294(C2×D3)⋊C4—24no—
295(C2×D3)⋊C4—42no—
296(C2×D3)⋊C4—42no—
297C4⋊Dic3—21no—
298C4⋊Dic3—21no—
299C4⋊Dic3—21no—
300C4⋊Dic3—42no—
301C4⋊Dic3C2×D412yes—
302Dic3⋊C4—24no—
303Dic3⋊C4—22no—
304Dic3⋊C4—22no—
305Dic3⋊C4—24no—
306Dic3⋊C4—42no—
307Dic3⋊C4—42no—
308Dic3⋊C4—42no—
309C4×Dic3C2×D412yes—
310C4×Dic3C2×D412yes—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8#4112yes—
317#204—44no—
318C22×Q8—31no—
319C22×Q8—61no—
320C22×Q8C22×D311yescharacteristic
321C22×Q8C22×D311yescharacteristic
322C22×D4—31no—
323C22×D4—61no—
324C23×C4—31no—
325C23×C4—61no—
326C2×Q16—22no—
327C2×Q16—22no—
328C2×Q16—41no—
329C2×Q16—62no—
330C2×Q16—62no—
331C2×Q16—121no—
332C2×SD16—62no—
333C2×SD16—62no—
334C2×SD16—62no—
335C2×SD16—62no—
336C2×SD16—121no—
337C2×SD16—121no—
338C22×C8—31no—
339C22×C8—31no—
340C22×C8C22×D311yescharacteristic
341C22×C8C22×D311yescharacteristic
342C4⋊Q8—34no—
343C4⋊Q8—62no—
344C4⋊Q8—62no—
345C4⋊Q8—62no—
346#126—68no—
347#124—34no—
348#124—68no—
349#124—62no—
350#123—68no—
351C22⋊Q8—68no—
352C22⋊Q8—62no—
353C22⋊Q8—62no—
354C22⋊Q8—121no—
355C22⋊Q8—121no—
356C22⋊Q8—121no—
357C22⋊Q8—121no—
358#121—62no—
359#121—62no—
360C4×Q8—22no—
361C4×Q8—22no—
362C4×D4—62no—
363C4×D4—62no—
364#117—62no—
365#117—62no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4—31no—
371C2×C4⋊C4—61no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4—61no—
374C2×C4⋊C4—61no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4C22×D311yescharacteristic
378C2×C4⋊C4C22×D311yescharacteristic
379C2×C22⋊C4—31no—
380C2×C22⋊C4—31no—
381C2×C22⋊C4—61no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4—61no—
384C2×C22⋊C4—61no—
385C2×C22⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C22⋊C4—61no—
388C2×C42—21no—
389C2×C42—31no—
390C2×C42C22×D311yescharacteristic
391#103—22no—
392#103—41no—
393#103—62no—
394#103—62no—
395#103—62no—
396#103—121no—
397#102—121no—
398#102—121no—
399C22⋊C8—62no—
400C22⋊C8—62no—
401#97—62no—
402C4×C8—62no—
403#95—21no—
404#95—21no—
405#95—61no—
406#95—61no—
407#95—61no—
408#95—61no—
409C23×C3C22×D411yescharacteristic
410C22×D3—21no—
411C22×D3—22no—
412C22×D3—21no—
413C22×D3—21no—
414C22×D3—21no—
415C22×D3—21no—
416C22×D3—21no—
417C22×D3—21no—
418C22×D3—41no—
419C22×D3—41no—
420C22×D3—41no—
421C22×D3—41no—
422C22×D3—41no—
423C22×D3—41no—
424C3×Q8—22no—
425C3×Q8—22no—
426C3×Q8—41no—
427C3×Q8—41no—
428C3×Q8—41no—
429C3×Q8—41no—
430C3×Q8—41no—
431C3×Q8—41no—
432C2×C3×C4—21no—
433C2×C3×C4—22no—
434C2×C3×C4—21no—
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×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4C22×D411yescharacteristic
451C2×C3×C4C22×D411yescharacteristic
452C2×C3×C4C2×#4111yescharacteristic
453C2×C3×C4C2×#4111yescharacteristic
454C2×C3×C4H(5,𝔽2)11yescharacteristic
455C2×C3×C4H(5,𝔽2)11yescharacteristic
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—22no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3#12012yes—
473C2×Dic3#12012yes—
474D12—22no—
475D12—22no—
476D12—41no—
477D12—41no—
478D12—84no—
479C4×D3—41no—
480C4×D3—41no—
481C4×D3—41no—
482C4×D3—41no—
483C4×D3—84no—
484Dic6—41no—
485Dic6—41no—
486Dic6—41no—
487Dic6—41no—
488Dic6—84no—
489C3×C8—22no—
490C3×C8—41no—
491C3⋊C8—22no—
492C3⋊C8—41no—
493C24—31no—
494C24—61no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—64no—
507C2×Q8—61no—
508C2×Q8—61no—
509C2×Q8—61no—
510C2×Q8—61no—
511C2×Q8—61no—
512C2×Q8—61no—
513C2×Q8—241no—
514C2×Q8—241no—
515C2×Q8D3×D412yes—
516C2×D4—32no—
517C2×D4—64no—
518C2×D4—61no—
519C2×D4—61no—
520C2×D4—61no—
521C2×D4—61no—
522C2×D4—61no—
523C2×D4—241no—
524C2×D4—241no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—31no—
530C22×C4—31no—
531C22×C4—31no—
532C22×C4—64no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—61no—
538C22×C4—61no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—61no—
542C22×C4—241no—
543C22×C4—241no—
544C22×C4D3×D411yescharacteristic
545C22×C4D3×D411yescharacteristic
546C22×C4C23×D311yescharacteristic
547Q16—44no—
548Q16—124no—
549SD16—124no—
550SD16—124no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—32no—
557C2×C8—61no—
558C2×C8—61no—
559C2×C8—61no—
560C2×C8—61no—
561C2×C8—61no—
562C2×C8#23512yes—
563C4⋊C4—24no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—32no—
568C4⋊C4—62no—
569C4⋊C4—62no—
570C4⋊C4—64no—
571C4⋊C4—64no—
572C4⋊C4—61no—
573C4⋊C4—61no—
574C4⋊C4—61no—
575C4⋊C4—122no—
576C4⋊C4—122no—
577C4⋊C4—122no—
578C4⋊C4—122no—
579C4⋊C4D3×D412yes—
580C22⋊C4—62no—
581C22⋊C4—62no—
582C22⋊C4—64no—
583C22⋊C4—64no—
584C22⋊C4—64no—
585C22⋊C4—64no—
586C22⋊C4—64no—
587C22⋊C4—122no—
588C22⋊C4—122no—
589C42—24no—
590C42—21no—
591C42—21no—
592C42—32no—
593C42—32no—
594C22×C3C2×#12011yescharacteristic
595C22×C3#53211yescharacteristic
596C22×C3#53511yescharacteristic
597C22×C3#57711yescharacteristic
598C22×C3#57711yescharacteristic
599C22×C3#57811yescharacteristic
600C22×C3#57811yescharacteristic
601C2×D3—41no—
602C2×D3—41no—
603C2×D3—41no—
604C2×D3—42no—
605C2×D3—41no—
606C2×D3—41no—
607C2×D3—42no—
608C2×D3—41no—
609C2×D3—41no—
610C2×D3—42no—
611C2×D3—81no—
612C2×D3—81no—
613C2×D3—81no—
614C2×D3—81no—
615C3×C4—42no—
616C3×C4—42no—
617C3×C4—41no—
618C3×C4—41no—
619C3×C4—81no—
620C3×C4—81no—
621C3×C4#54611yescharacteristic
622C3×C4#54611yescharacteristic
623C3×C4#55011yescharacteristic
624C3×C4#55011yescharacteristic
625Dic3—22no—
626Dic3—22no—
627Dic3—41no—
628Dic3—42no—
629Dic3—81no—
630Dic3—81no—
631C23—61no—
632C23—61no—
633C23—61no—
634C23—61no—
635C23—61no—
636C23—62no—
637C23—61no—
638C23—61no—
639C23—121no—
640C23—121no—
641C23—121no—
642C23—121no—
643C23—121no—
644C23—121no—
645C23C2×D3×D411yescharacteristic
646Q8—22no—
647Q8—22no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653Q8—41no—
654Q8—121no—
655Q8—121no—
656Q8—121no—
657Q8—121no—
658Q8—244no—
659D4—62no—
660D4—62no—
661D4—121no—
662D4—121no—
663D4—244no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—32no—
673C2×C4—32no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—62no—
690C2×C4—61no—
691C2×C4—61no—
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—121no—
704C2×C4—244no—
705C2×C4C2×#23511yescharacteristic
706C2×C4C2×D3×D411yescharacteristic
707C2×C4C2×D3×D411yescharacteristic
708C2×C4#100411yescharacteristic
709C2×C4D3×#4111yescharacteristic
710C2×C4#100911yescharacteristic
711C8—22no—
712C8—41no—
713C8—62no—
714C8—121no—
715C2×C3#243111yescharacteristic
716C2×C3#300911yescharacteristic
717C2×C3#301111yescharacteristic
718C2×C3#317811yescharacteristic
719C2×C3#317811yescharacteristic
720C2×C3#322511yescharacteristic
721C2×C3#322511yescharacteristic
722D3—81no—
723D3—82no—
724C22—121no—
725C22—122no—
726C22—122no—
727C22—121no—
728C22—121no—
729C22—121no—
730C22—121no—
731C22—122no—
732C22—121no—
733C22—121no—
734C22—241no—
735C22—241no—
736C22—241no—
737C22—241no—
738C22#554811yescharacteristic
739C22D3×#12011yescharacteristic
740C22#560711yescharacteristic
741C22#576611yescharacteristic
742C22#577011yescharacteristic
743C22#577811yescharacteristic
744C22#577911yescharacteristic
745C4—41no—
746C4—41no—
747C4—42no—
748C4—42no—
749C4—62no—
750C4—62no—
751C4—81no—
752C4—81no—
753C4—122no—
754C4—121no—
755C4—241no—
756C4—241no—
757C4#549011yescharacteristic
758C4#555311yescharacteristic
759C4#559911yescharacteristic
760C4#565411yescharacteristic
761C3#2561311yescharacteristic, complemented, Sylow
762C2—241no—
763C2—242no—
764C2#7470011yescharacteristic
765C2#7972911yescharacteristic
766C2#7982511yescharacteristic
767C2#8018511yescharacteristic
768C2#8022911yescharacteristic
769C2#8048511yescharacteristic
770C2#8061111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1878C2
socleC23×C3C22×D4
prime radicalC2×#895C22
hypercenter#1878D3
hypocenterC3#25613
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
2. C2×#5190C2semidirect
3. C2×#4792C2semidirect
4. #76641C2semidirect
5. C3×#1878C2semidirect
6. #72071C2semidirect
7. #71632C2semidirect
8. #70273C2semidirect
10. #70226C2semidirect
11. #69687C2semidirect
13. #68806C2semidirect
14. #68672C2semidirect
15. #68601C2semidirect
75. #1878D3semidirect
761. C3#25613semidirect

Maximal subgroups

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

subgroupindex
C2×#55822
C2×#51902
C2×#47922
#766412
C3×#18782
#720712
#716322
#702732
#702722
#702262
#696872
#688872
#688062
#686722
#686012
#256133