Finite Group Databasebeta

← #10901348

Subgroups — #10901348

Order 768.

1348 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5596C211yesmaximal, characteristic
2C2×#4890C211yesmaximal, characteristic, complemented
3C2×#4759C211yesmaximal, characteristic, complemented
4#74001C211yesmaximal, characteristic, complemented
5C3×#2033C211yesmaximal, characteristic, complemented
6#71679C211yesmaximal, characteristic, complemented
7#70617C211yesmaximal, characteristic, complemented
8#70211C211yesmaximal, characteristic, complemented
9#70177C211yesmaximal, characteristic, complemented
10#70153C211yesmaximal, characteristic, complemented
11#69934C211yesmaximal, characteristic, complemented
12#69908C211yesmaximal, characteristic, complemented
13#69523C211yesmaximal, characteristic, complemented
14#68892C211yesmaximal, characteristic, complemented
15#68826C211yesmaximal, characteristic, complemented
16#29687—31nomaximal, Sylow
17C22×#237—21no—
18C2×C3×#121C2211yescharacteristic
19C2×#940C2211yescharacteristic
20C2×#939—21no—
21C2×D4×Dic3C2211yescharacteristic
22C2×#930C2211yescharacteristic
23C22×C4×Dic3C2211yescharacteristic
24#5596—24no—
25#5596—24no—
26C2×#893C2211yescharacteristic
27C2×#888C2211yescharacteristic
28C2×#888C2211yescharacteristic
29C2×#885—21no—
30C2×#67⋊C4—21no—
31C2×#878—21no—
32C2×C3×#107C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×C3×C22⋊C8C2211yescharacteristic
36C3×#380C2211yescharacteristic
37C2×#832C2211yescharacteristic
38C2×#832C2211yescharacteristic
39#5212C2211yescharacteristic
40C2×#830C2211yescharacteristic
41C2×#821C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×#818C2211yescharacteristic
44C2×Dic3⋊C8C2211yescharacteristic
45C2×Dic3⋊C8C2211yescharacteristic
46#4984C2211yescharacteristic
47#4975C2211yescharacteristic
48#4972C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#807C2211yescharacteristic
52C2×#807C2211yescharacteristic
53#4942—21no—
54#4890—24no—
55#4759—24no—
56#4647—21no—
57#4646—21no—
58C3×#340C2211yescharacteristic
59#4551C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#532—31no—
65C2×#474—31no—
66C2×#474—31no—
67#2857—31no—
68#2057—31no—
69#2057—31no—
70#2041—31no—
71#2041—31no—
72#2033—31no—
73#2033—31no—
74#2033—31no—
75#2033D311yescharacteristic, complemented
76#1802—31no—
77#1802—31no—
78#1797—31no—
79C22×C3×D4—21no—
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67—21no—
83C22×#67—21no—
84C22×#67—21no—
85C23×Dic3—21no—
86C23×Dic3D411yescharacteristic
87C23×Dic3D411yescharacteristic
88C2×#237—28no—
89C2×#237—44no—
90C2×#237—44no—
91C22×D12C2311yescharacteristic
92C22×C4×D3—21no—
93C22×Dic6—21no—
94C22×Dic6—21no—
95C22×C3×C8C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C3×#121—22no—
98C3×#121—22no—
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C22⋊C4—21no—
103C2×C3×C22⋊C4—21no—
104C2×#217—21no—
105C2×#217—21no—
106#940—22no—
107#940—22no—
108#939—28no—
109D4×Dic3—22no—
110D4×Dic3D414yes—
111#930—22no—
112#930—22no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4—21no—
115C2×C4⋊Dic3—21no—
116C2×C4⋊Dic3C2311yescharacteristic
117C2×C4⋊Dic3C2311yescharacteristic
118C2×C4⋊Dic3C2311yescharacteristic
119C2×Dic3⋊C4—21no—
120C2×Dic3⋊C4—21no—
121C2×Dic3⋊C4—21no—
122C2×Dic3⋊C4—21no—
123C2×Dic3⋊C4—21no—
124C2×C4×Dic3—22no—
125C2×C4×Dic3—22no—
126C2×C4×Dic3D411yescharacteristic
127C2×C4×Dic3D411yescharacteristic
128C2×C4×Dic3C2311yescharacteristic
129C2×C4×Dic3C2311yescharacteristic
130C22×C3⋊C8C2311yescharacteristic
131C22×C3⋊C8C2311yescharacteristic
132#893—22no—
133#893D414yes—
134#888—22no—
135#888—22no—
136#888—22no—
137#888—22no—
138#885—28no—
139#67⋊C4—28no—
140#878—44no—
141C3×#107—22no—
142C3×#102—22no—
143C3×#102—41no—
144C3×C22⋊C8—41no—
145C3×#95—21no—
146#832—22no—
147#832—41no—
148C3⋊#95—21no—
149C3⋊#95—21no—
150C3⋊#95—21no—
151#830—41no—
152#821—22no—
153#821—41no—
154#818—22no—
155Dic3⋊C8—22no—
156Dic3⋊C8—22no—
157#809—22no—
158#809—41no—
159#807—22no—
160#807—22no—
161C22×#41—61no—
162#532—64no—
163#532—64no—
164C2×C4⋊Q8—31no—
165C2×C4⋊Q8—31no—
166C2×#127—31no—
167C2×#124—61no—
168C2×C22⋊Q8—61no—
169C2×#121—31no—
170C2×#121—61no—
171C2×#121C2×D311yescharacteristic
172C2×C4×D4—31no—
173C2×C4×D4—31no—
174C2×C4×D4—61no—
175C22×C42—31no—
176#474—64no—
177#474—64no—
178C2×#107—31no—
179C2×#107—31no—
180C2×#107—31no—
181C2×#107C2×D311yescharacteristic
182C2×C4⋊C8—31no—
183C2×C4⋊C8—31no—
184C2×#102—31no—
185C2×#102—31no—
186C2×#102—31no—
187C2×#102—31no—
188C2×#102—31no—
189C2×#102—31no—
190C2×#102C2×D311yescharacteristic
191C2×#102C2×D311yescharacteristic
192C2×C22⋊C8—31no—
193C2×C22⋊C8C2×D311yescharacteristic
194#391—61no—
195#389—31no—
196#389—31no—
197#389—61no—
198#384—31no—
199#380—31no—
200#380—61no—
201#380C2×D311yescharacteristic
202#340—31no—
203#340—31no—
204#340—31no—
205#340C2×D311yescharacteristic
206#336—31no—
207#336—31no—
208C24×C3—21no—
209C24×C3C2×D411yescharacteristic
210C23×D3—21no—
211C2×C3×D4—24no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—42no—
218C2×C3×D4—42no—
219C2×C3×D4C2×D412yes—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4C2×D411yescharacteristic
230C22×C3×C4C2411yescharacteristic
231C2×#67—24no—
232C2×#67—24no—
233C2×#67—24no—
234C2×#67—42no—
235C2×#67—42no—
236C2×#67—42no—
237C2×#67—42no—
238C2×#67—42no—
239C2×#67—42no—
240C22×Dic3—22no—
241C22×Dic3—22no—
242C22×Dic3—21no—
243C22×Dic3—24no—
244C22×Dic3—22no—
245C22×Dic3—22no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—41no—
249C22×Dic3—42no—
250C22×Dic3—42no—
251C22×Dic3D814yes—
252C22×Dic3C2×D411yescharacteristic
253C22×Dic3C2×D411yescharacteristic
254C22×Dic3C2×D411yescharacteristic
255C22×Dic3C2×D411yescharacteristic
256#237—432no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12C2×D412yes—
263C2×C4×D3—24no—
264C2×C4×D3—42no—
265C2×C4×D3—42no—
266C2×Dic6—24no—
267C2×Dic6—42no—
268C2×Dic6—42no—
269C2×Dic6—42no—
270C2×Dic6—42no—
271C2×Dic6—42no—
272C2×C3×C8—21no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4C2×D412yes—
284C3×C22⋊C4—24no—
285C3×C22⋊C4—42no—
286#217—24no—
287#217—42no—
288(C2×D3)⋊C4—24no—
289(C2×D3)⋊C4—24no—
290C4⋊Dic3—21no—
291C4⋊Dic3—21no—
292C4⋊Dic3—21no—
293C4⋊Dic3—21no—
294C4⋊Dic3—21no—
295C4⋊Dic3—42no—
296C4⋊Dic3C2×D412yes—
297Dic3⋊C4—24no—
298Dic3⋊C4—42no—
299Dic3⋊C4—42no—
300Dic3⋊C4—42no—
301Dic3⋊C4—42no—
302C4×Dic3—21no—
303C4×Dic3—21no—
304C4×Dic3—22no—
305C4×Dic3—22no—
306C4×Dic3C2×D412yes—
307C4×Dic3C2×D412yes—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×#41—68no—
315C2×#41—124no—
316C2×#41—124no—
317C22×Q8—61no—
318C22×Q8—61no—
319C22×D4—21no—
320C22×D4—31no—
321C22×D4—61no—
322C22×D4—61no—
323C22×D4—61no—
324C22×D4C22×D311yescharacteristic
325C23×C4—31no—
326C23×C4—31no—
327C23×C4—61no—
328C23×C4—61no—
329C23×C4C22×D311yescharacteristic
330C22×C8—31no—
331C22×C8—31no—
332C22×C8C22×D311yescharacteristic
333C22×C8C22×D311yescharacteristic
334C4⋊Q8—62no—
335C4⋊Q8—62no—
336C4⋊Q8—62no—
337C4⋊Q8—62no—
338#127—62no—
339#127—62no—
340#124—68no—
341C22⋊Q8—124no—
342#121—22no—
343#121—22no—
344#121—62no—
345#121—62no—
346#121—68no—
347C4×D4—34no—
348C4×D4—34no—
349C4×D4—62no—
350C4×D4—62no—
351C4×D4—68no—
352C2×C4⋊C4—31no—
353C2×C4⋊C4—31no—
354C2×C4⋊C4—31no—
355C2×C4⋊C4—61no—
356C2×C4⋊C4—61no—
357C2×C4⋊C4—61no—
358C2×C4⋊C4—61no—
359C2×C4⋊C4—61no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4C22×D311yescharacteristic
362C2×C4⋊C4C22×D311yescharacteristic
363C2×C4⋊C4C22×D311yescharacteristic
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—61no—
367C2×C22⋊C4—61no—
368C2×C22⋊C4—61no—
369C2×C22⋊C4—61no—
370C2×C42—31no—
371C2×C42—31no—
372C2×C42—31no—
373C2×C42—31no—
374C2×C42—62no—
375C2×C42—62no—
376#107—22no—
377#107—62no—
378#107—62no—
379#107—62no—
380C4⋊C8—62no—
381C4⋊C8—62no—
382#102—22no—
383#102—41no—
384#102—62no—
385#102—62no—
386#102—62no—
387#102—121no—
388#102—121no—
389#102—121no—
390C22⋊C8—41no—
391C22⋊C8—121no—
392#95—21no—
393#95—61no—
394#95—61no—
395#95—61no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—22no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3C2×D812yes—
410C23×C3C22×D411yescharacteristic
411C22×D3—22no—
412C22×D3—41no—
413C22×D3—41no—
414C22×D3—41no—
415C22×D3—41no—
416C22×D3—41no—
417C22×D3—41no—
418C3×D4—22no—
419C3×D4—22no—
420C3×D4—48no—
421C3×D4—41no—
422C3×D4—41no—
423C2×C3×C4—21no—
424C2×C3×C4—22no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
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×C4C22×D411yescharacteristic
440C2×C3×C4C22×D411yescharacteristic
441C2×C3×C4H(5,𝔽2)11yescharacteristic
442C2×C3×C42−1+411yescharacteristic
443C2×C3×C42−1+411yescharacteristic
444C2×C3×C42−1+411yescharacteristic
445#67—48no—
446#67—48no—
447#67—48no—
448C2×Dic3—21no—
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—21no—
453C2×Dic3—21no—
454C2×Dic3—28no—
455C2×Dic3—22no—
456C2×Dic3—44no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3—48no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—41no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3#12012yes—
467C2×Dic3#12012yes—
468C2×Dic3C2×D812yes—
469C2×Dic3C2×D812yes—
470C2×Dic3AGL(1,ℤ/8)12yes—
471C2×Dic3#13712yes—
472D12—22no—
473D12—22no—
474D12—41no—
475D12—41no—
476C4×D3—48no—
477Dic6—48no—
478Dic6—84no—
479C3×C8—41no—
480C3×C8—41no—
481C3⋊C8—41no—
482C3⋊C8—41no—
483C24—21no—
484C24—61no—
485C24D3×D411yescharacteristic
486#41—1232no—
487C2×Q8—64no—
488C2×Q8—122no—
489C2×Q8—122no—
490C2×Q8—122no—
491C2×Q8—122no—
492C2×Q8—122no—
493C2×D4—24no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—32no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—64no—
503C2×D4—64no—
504C2×D4—64no—
505C2×D4—61no—
506C2×D4—61no—
507C2×D4—61no—
508C2×D4—61no—
509C2×D4—61no—
510C2×D4—122no—
511C2×D4—122no—
512C2×D4—122no—
513C2×D4—122no—
514C2×D4—122no—
515C2×D4—122no—
516C2×D4D3×D412yes—
517C22×C4—21no—
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—31no—
527C22×C4—34no—
528C22×C4—31no—
529C22×C4—31no—
530C22×C4—31no—
531C22×C4—64no—
532C22×C4—62no—
533C22×C4—62no—
534C22×C4—62no—
535C22×C4—64no—
536C22×C4—62no—
537C22×C4—61no—
538C22×C4—61no—
539C22×C4—61no—
540C22×C4—122no—
541C22×C4—122no—
542C22×C4—122no—
543C22×C4—122no—
544C22×C4—121no—
545C22×C4D3×D411yescharacteristic
546C22×C4C23×D311yescharacteristic
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—61no—
554C2×C8—61no—
555C2×C8—61no—
556C2×C8—61no—
557C2×C8—61no—
558C2×C8—61no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—32no—
565C4⋊C4—64no—
566C4⋊C4—61no—
567C4⋊C4—61no—
568C4⋊C4—61no—
569C4⋊C4—61no—
570C4⋊C4—61no—
571C4⋊C4—122no—
572C4⋊C4—122no—
573C4⋊C4—122no—
574C4⋊C4—122no—
575C4⋊C4—122no—
576C4⋊C4D3×D412yes—
577C22⋊C4—24no—
578C22⋊C4—42no—
579C22⋊C4—64no—
580C22⋊C4—64no—
581C22⋊C4—64no—
582C22⋊C4—122no—
583C42—32no—
584C42—32no—
585C42—62no—
586C42—62no—
587C42—61no—
588C42—61no—
589C22×C3—22no—
590C22×C3—22no—
591C22×C3—22no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3—42no—
597C22×C3—42no—
598C22×C3—42no—
599C22×C3—81no—
600C22×C3—81no—
601C22×C3—81no—
602C22×C3—81no—
603C22×C3C2×#12011yescharacteristic
604C22×C3#53611yescharacteristic
605C22×C3#53711yescharacteristic
606C22×C3C22×D811yescharacteristic
607C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
608C22×C3C2×#13711yescharacteristic
609C22×C3#57511yescharacteristic
610C2×D3—42no—
611C2×D3—42no—
612C2×D3—42no—
613C2×D3—81no—
614C2×D3—81no—
615C2×D3—81no—
616C2×D3—81no—
617C3×C4—41no—
618C3×C4—42no—
619C3×C4—81no—
620C3×C4—81no—
621C3×C4#53611yescharacteristic
622C3×C4#53611yescharacteristic
623C3×C4#53711yescharacteristic
624C3×C4#53711yescharacteristic
625Dic3—22no—
626Dic3—22no—
627Dic3—22no—
628Dic3—42no—
629Dic3—81no—
630Dic3—81no—
631Dic3#44714yes—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—22no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—62no—
646C23—121no—
647C23—121no—
648C23—121no—
649C23—121no—
650C23—121no—
651C23—121no—
652C23D3×D812yes—
653C23C2×D3×D411yescharacteristic
654Q8—128no—
655Q8—244no—
656D4—22no—
657D4—22no—
658D4—48no—
659D4—41no—
660D4—41no—
661D4—62no—
662D4—62no—
663D4—128no—
664D4—128no—
665D4—128no—
666D4—121no—
667D4—121no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—32no—
673C2×C4—32no—
674C2×C4—32no—
675C2×C4—32no—
676C2×C4—32no—
677C2×C4—32no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—68no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—62no—
698C2×C4—128no—
699C2×C4—128no—
700C2×C4—124no—
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×C4C2×D3×D411yescharacteristic
710C2×C4C2×D3×D411yescharacteristic
711C2×C4#100411yescharacteristic
712C2×C4#101011yescharacteristic
713C2×C4#101011yescharacteristic
714C2×C4#101011yescharacteristic
715C8—41no—
716C8—41no—
717C8—121no—
718C8—121no—
719C2×C3—42no—
720C2×C3—82no—
721C2×C3#261611yescharacteristic
722C2×C3C2×#44711yescharacteristic
723C2×C3#300711yescharacteristic
724C2×C3#322611yescharacteristic
725C2×C3#323511yescharacteristic
726C2×C3#324511yescharacteristic
727C2×C3#325411yescharacteristic
728D3—82no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—122no—
744C22—122no—
745C22—122no—
746C22—241no—
747C22—241no—
748C22—241no—
749C22—241no—
750C22D3×#12011yescharacteristic
751C22#559711yescharacteristic
752C22#564811yescharacteristic
753C22C2×D3×D811yescharacteristic
754C22#576811yescharacteristic
755C22D3×AGL(1,ℤ/8)11yescharacteristic
756C22D3×#13711yescharacteristic
757C4—34no—
758C4—42no—
759C4—41no—
760C4—62no—
761C4—62no—
762C4—62no—
763C4—81no—
764C4—81no—
765C4—122no—
766C4—241no—
767C4—241no—
768C4#559711yescharacteristic
769C4#560811yescharacteristic
770C4#564811yescharacteristic
771C4#567511yescharacteristic
772C3#2968711yescharacteristic, complemented, Sylow
773C2—42no—
774C2—82no—
775C2—242no—
776C2#7697011yescharacteristic
777C2D3×#44711yescharacteristic
778C2#8022811yescharacteristic
779C2#8070211yescharacteristic
780C2#8079411yescharacteristic
781C2#8127411yescharacteristic
782C2#8135811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2033C2
socleC23×C3C22×D4
prime radicalC2×#5596C2
hypercenter#2033D3
hypocenterC3#29687
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2033

Complements

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

NH ≅ G/Ntype
2. C2×#4890C2semidirect
3. C2×#4759C2semidirect
4. #74001C2semidirect
5. C3×#2033C2semidirect
6. #71679C2semidirect
7. #70617C2semidirect
8. #70211C2semidirect
9. #70177C2semidirect
10. #70153C2semidirect
11. #69934C2semidirect
12. #69908C2semidirect
13. #69523C2semidirect
14. #68892C2semidirect
15. #68826C2semidirect
75. #2033D3semidirect
772. C3#29687semidirect

Maximal subgroups

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

subgroupindex
C2×#55962
C2×#48902
C2×#47592
#740012
C3×#20332
#716792
#706172
#702112
#701772
#701532
#699342
#699082
#695232
#688922
#688262
#296873