Finite Group Databasebeta

← #10848707

Subgroups — #10848707

Order 768.

1158 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5622C211yesmaximal, characteristic
2C2×#5183C211yesmaximal, characteristic, complemented
3#82811C211yesmaximal, characteristic
4C2×#4792C211yesmaximal, characteristic, complemented
5C3×#2001C211yesmaximal, characteristic
6#72065C211yesmaximal, characteristic, complemented
7#71700C211yesmaximal, characteristic
8#71700C211yesmaximal, characteristic
9#70281C211yesmaximal, characteristic, complemented
10#70239C211yesmaximal, characteristic, complemented
11#70225C211yesmaximal, characteristic, complemented
12#69964C211yesmaximal, characteristic
13Dic3×C22⋊C8C211yesmaximal, characteristic
14#68908C211yesmaximal, characteristic, complemented
15#68803C211yesmaximal, characteristic, complemented
16#25600—31nomaximal, Sylow
17C22×C3×Q16C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×Q8×Dic3C2211yescharacteristic
21C2×#944C2211yescharacteristic
22C2×#944C2211yescharacteristic
23C22×#216C2211yescharacteristic
24C22×#216C2211yescharacteristic
25C2×#924C2211yescharacteristic
26C2×#924C2211yescharacteristic
27C22×C4×Dic3C2211yescharacteristic
28C22×Dic12C2211yescharacteristic
29#5622—24no—
30#5622—24no—
31C2×#889—21no—
32C2×#888C2211yescharacteristic
33C2×#887—21no—
34C2×#887C2211yescharacteristic
35C2×#878—21no—
36C2×#877—21no—
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40#5229C2211yescharacteristic
41C2×#835C2211yescharacteristic
42C2×#835C2211yescharacteristic
43C2×#830C2211yescharacteristic
44#5183—24no—
45C2×#816C2211yescharacteristic
46C2×#816C2211yescharacteristic
47C2×C8×Dic3C2211yescharacteristic
48C2×C8×Dic3C2211yescharacteristic
49#4976—21no—
50#4976—21no—
51#4975C2211yescharacteristic
52#4973C2211yescharacteristic
53C2×#810C2211yescharacteristic
54C2×#810C2211yescharacteristic
55#4942—21no—
56#4942—21no—
57#4792—24no—
58C3×#340C2211yescharacteristic
59#4551C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#533—31no—
65C2×#494—31no—
66C2×#487—31no—
67#2857—31no—
68#2001—31no—
69#2001—31no—
70#2001—31no—
71#2001D311yescharacteristic
72#1990—31no—
73#1956—31no—
74#1878—31no—
75#1878—31no—
76#1878—31no—
77#1878—31no—
78C4×C22⋊C8—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×Dic3D411yescharacteristic
83C23×Dic3D411yescharacteristic
84C22×Dic6—21no—
85C22×Dic6C2311yescharacteristic
86C22×Dic6C2311yescharacteristic
87C2×C3×Q16—22no—
88C2×C3×Q16—22no—
89C2×C3×Q16—41no—
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C3×C22⋊Q8—22no—
93C3×C22⋊Q8—22no—
94C3×C22⋊Q8—41no—
95C3×C22⋊Q8—41no—
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C22⋊C4—21no—
101C2×C3×C22⋊C4—21no—
102C2×#217—21no—
103C2×#217—21no—
104Q8×Dic3—22no—
105Q8×Dic3—22no—
106#944—22no—
107#944—22no—
108#944—22no—
109#944D414yes—
110C2×#216—22no—
111C2×#216—22no—
112C2×#216—22no—
113C2×#216—22no—
114C2×#216—41no—
115C2×#216—41no—
116C2×C4⋊Dic3—21no—
117C2×C4⋊Dic3C2311yescharacteristic
118C2×C4⋊Dic3C2311yescharacteristic
119#924—22no—
120#924—22no—
121#924—41no—
122#924—41no—
123C2×Dic3⋊C4—21no—
124C2×Dic3⋊C4—21no—
125C2×Dic3⋊C4—21no—
126C2×Dic3⋊C4—21no—
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4—21no—
133C2×C4×Dic3—21no—
134C2×C4×Dic3—21no—
135C2×C4×Dic3—22no—
136C2×C4×Dic3—22no—
137C2×C4×Dic3D411yescharacteristic
138C2×C4×Dic3D411yescharacteristic
139C2×C4×Dic3C2311yescharacteristic
140C2×C4×Dic3C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C2×Dic12—22no—
144C2×Dic12—22no—
145C2×Dic12—41no—
146#889—28no—
147#888—22no—
148#888D414yes—
149#887—28no—
150#887—22no—
151#887—22no—
152#878—28no—
153#877—28no—
154C3×#103—22no—
155C3×#103—41no—
156C3×C22⋊C8—22no—
157#835—22no—
158#835—41no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162C3⋊#95—21no—
163#830—22no—
164#816—22no—
165#816—41no—
166C8×Dic3—22no—
167C8×Dic3—22no—
168#810—22no—
169#810—41no—
170C22×Q16—31no—
171C22×Q16—31no—
172C22×Q16—31no—
173C22×Q16C2×D311yescharacteristic
174#533—64no—
175#533—64no—
176C2×C4⋊Q8—31no—
177C2×C4⋊Q8—31no—
178C2×C4⋊Q8—31no—
179C2×#125—61no—
180C2×C22⋊Q8—31no—
181C2×C22⋊Q8—31no—
182C2×C22⋊Q8—61no—
183C2×C22⋊Q8C2×D311yescharacteristic
184C2×C22⋊Q8C2×D311yescharacteristic
185C2×C4×Q8—31no—
186C2×C4×Q8—31no—
187C2×C4×Q8—61no—
188C2×#117—61no—
189C22×C42—31no—
190#494—64no—
191#487—64no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103—31no—
196C2×#103—31no—
197C2×#103—31no—
198C2×#103C2×D311yescharacteristic
199C2×#103C2×D311yescharacteristic
200C2×C22⋊C8—31no—
201C2×C22⋊C8C2×D311yescharacteristic
202C2×C4×C8—31no—
203C2×C4×C8—31no—
204#391—31no—
205#391—31no—
206#389—61no—
207#389—61no—
208#384—31no—
209#380—61no—
210#380—61no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340C2×D311yescharacteristic
215#336—31no—
216#336—31no—
217C24×C3C2×D411yescharacteristic
218C2×C3×Q8—21no—
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×Q8C2×D412yes—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2411yescharacteristic
242C22×Dic3—22no—
243C22×Dic3—22no—
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3—22no—
247C22×Dic3—22no—
248C22×Dic3—22no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251C22×Dic3Q1614yescomplemented
252C22×Dic3C2×D411yescharacteristic
253C22×Dic3C2×D411yescharacteristic
254C22×Dic3C2×D411yescharacteristic
255C22×Dic3C2×D411yescharacteristic
256C2×Dic6—21no—
257C2×Dic6—21no—
258C2×Dic6—21no—
259C2×Dic6—21no—
260C2×Dic6—21no—
261C2×Dic6—24no—
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6—21no—
266C2×Dic6—21no—
267C2×Dic6—21no—
268C2×Dic6—42no—
269C2×Dic6—42no—
270C2×Dic6C2×D412yes—
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⋊C4—42no—
283C3×C4⋊C4C2×D412yes—
284C3×C22⋊C4—24no—
285C3×C22⋊C4—42no—
286#217—24no—
287#217—42no—
288#216—44no—
289#216—44no—
290C4⋊Dic3—24no—
291C4⋊Dic3—21no—
292C4⋊Dic3—21no—
293C4⋊Dic3—21no—
294C4⋊Dic3C2×D412yes—
295Dic3⋊C4—24no—
296Dic3⋊C4—24no—
297Dic3⋊C4—24no—
298Dic3⋊C4—24no—
299Dic3⋊C4—24no—
300Dic3⋊C4—42no—
301Dic3⋊C4—42no—
302Dic3⋊C4—42no—
303Dic3⋊C4—42no—
304Dic3⋊C4—42no—
305C4×Dic3—24no—
306C4×Dic3—24no—
307C4×Dic3—21no—
308C4×Dic3—21no—
309C4×Dic3—22no—
310C4×Dic3—22no—
311C4×Dic3C2×D412yes—
312C4×Dic3C2×D412yes—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8#4112yes—
319Dic12—44no—
320C22×Q8—31no—
321C22×Q8—31no—
322C22×Q8—61no—
323C22×Q8C22×D311yescharacteristic
324C22×Q8C22×D311yescharacteristic
325C23×C4—31no—
326C23×C4—31no—
327C23×C4C22×D311yescharacteristic
328C2×Q16—22no—
329C2×Q16—22no—
330C2×Q16—41no—
331C2×Q16—62no—
332C2×Q16—62no—
333C2×Q16—62no—
334C2×Q16—62no—
335C2×Q16—62no—
336C2×Q16—62no—
337C2×Q16—121no—
338C2×Q16—121no—
339C2×Q16—121no—
340C22×C8—31no—
341C22×C8—31no—
342C22×C8C22×D311yescharacteristic
343C22×C8C22×D311yescharacteristic
344C4⋊Q8—34no—
345C4⋊Q8—34no—
346C4⋊Q8—62no—
347C4⋊Q8—62no—
348C4⋊Q8—62no—
349C4⋊Q8—62no—
350#125—68no—
351C22⋊Q8—22no—
352C22⋊Q8—22no—
353C22⋊Q8—41no—
354C22⋊Q8—41no—
355C22⋊Q8—68no—
356C22⋊Q8—62no—
357C22⋊Q8—62no—
358C22⋊Q8—121no—
359C22⋊Q8—121no—
360C4×Q8—62no—
361C4×Q8—68no—
362C4×Q8—62no—
363C4×Q8—62no—
364C4×Q8—62no—
365#117—68no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4—61no—
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⋊C4—61no—
378C2×C4⋊C4—61no—
379C2×C4⋊C4—61no—
380C2×C4⋊C4—61no—
381C2×C4⋊C4C22×D311yescharacteristic
382C2×C4⋊C4C22×D311yescharacteristic
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C42—31no—
388C2×C42—31no—
389C2×C42—31no—
390C2×C42—31no—
391C2×C42—62no—
392C2×C42—62no—
393C2×C42—61no—
394C2×C42—61no—
395#103—22no—
396#103—41no—
397#103—62no—
398#103—62no—
399#103—62no—
400#103—121no—
401#103—121no—
402#103—121no—
403C22⋊C8—22no—
404C22⋊C8—62no—
405C4×C8—62no—
406C4×C8—62no—
407#95—61no—
408#95—61no—
409#95—61no—
410#95—61no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3C2×Q1612yes—
418C23×C3C22×D411yescharacteristic
419C3×Q8—22no—
420C3×Q8—22no—
421C3×Q8—41no—
422C3×Q8—41no—
423C3×Q8—41no—
424C3×Q8—41no—
425C3×Q8—41no—
426C3×Q8—41no—
427C2×C3×C4—21no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
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×C4—41no—
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×C4C22×D411yescharacteristic
447C2×C3×C4C22×D411yescharacteristic
448C2×C3×C4C2×#4111yescharacteristic
449C2×C3×C4C2×#4111yescharacteristic
450C2×C3×C4H(5,𝔽2)11yescharacteristic
451C2×C3×C4H(5,𝔽2)11yescharacteristic
452C2×Dic3—21no—
453C2×Dic3—21no—
454C2×Dic3—28no—
455C2×Dic3—21no—
456C2×Dic3—22no—
457C2×Dic3—22no—
458C2×Dic3—21no—
459C2×Dic3—21no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—41no—
464C2×Dic3—44no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3#12012yes—
472C2×Dic3#12012yes—
473C2×Dic3C2×Q1612yes—
474C2×Dic3C2×Q1612yes—
475C2×Dic3#13512yes—
476C2×Dic3#13712yes—
477C2×Dic3#13712yes—
478Dic6—22no—
479Dic6—22no—
480Dic6—41no—
481Dic6—41no—
482Dic6—48no—
483Dic6—41no—
484Dic6—41no—
485Dic6—41no—
486Dic6—41no—
487C3×C8—22no—
488C3×C8—41no—
489C3⋊C8—22no—
490C3⋊C8—41no—
491C24D3×D411yescharacteristic
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
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—32no—
504C2×Q8—64no—
505C2×Q8—61no—
506C2×Q8—61no—
507C2×Q8—61no—
508C2×Q8—61no—
509C2×Q8—61no—
510C2×Q8—61no—
511C2×Q8—61no—
512C2×Q8—61no—
513C2×Q8—61no—
514C2×Q8—61no—
515C2×Q8—61no—
516C2×Q8—122no—
517C2×Q8—122no—
518C2×Q8D3×D412yes—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—31no—
530C22×C4—31no—
531C22×C4—34no—
532C22×C4—31no—
533C22×C4—31no—
534C22×C4—62no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4—62no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4D3×D411yescharacteristic
544C22×C4C23×D311yescharacteristic
545Q16—44no—
546Q16—124no—
547Q16—124no—
548Q16—124no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—32no—
555C2×C8—61no—
556C2×C8—61no—
557C2×C8—61no—
558C2×C8—61no—
559C2×C8—61no—
560C2×C8#23712yes—
561C4⋊C4—24no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—32no—
566C4⋊C4—42no—
567C4⋊C4—64no—
568C4⋊C4—64no—
569C4⋊C4—64no—
570C4⋊C4—64no—
571C4⋊C4—64no—
572C4⋊C4—64no—
573C4⋊C4—61no—
574C4⋊C4—61no—
575C4⋊C4—61no—
576C4⋊C4—122no—
577C4⋊C4—122no—
578C4⋊C4—122no—
579C4⋊C4—122no—
580C4⋊C4—122no—
581C4⋊C4D3×D412yes—
582C22⋊C4—24no—
583C22⋊C4—42no—
584C22⋊C4—64no—
585C22⋊C4—122no—
586C42—32no—
587C42—32no—
588C42—62no—
589C42—62no—
590C42—64no—
591C42—64no—
592C42—61no—
593C42—61no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3C2×#12011yescharacteristic
602C22×C3#53211yescharacteristic
603C22×C3#53511yescharacteristic
604C22×C3C22×Q1611yescharacteristic
605C22×C3C2×#13511yescharacteristic
606C22×C3C2×#13711yescharacteristic
607C22×C3C2×#13711yescharacteristic
608C3×C4—41no—
609C3×C4—42no—
610C3×C4—42no—
611C3×C4—81no—
612C3×C4—81no—
613C3×C4#54611yescharacteristic
614C3×C4#54611yescharacteristic
615C3×C4#55011yescharacteristic
616C3×C4#55011yescharacteristic
617Dic3—22no—
618Dic3—42no—
619Dic3—42no—
620Dic3—41no—
621Dic3—81no—
622Dic3—81no—
623Dic3#45114yes—
624Dic3#45214yes—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23D3×Q1612yes—
632C23C2×D3×D411yescharacteristic
633Q8—22no—
634Q8—22no—
635Q8—41no—
636Q8—41no—
637Q8—41no—
638Q8—41no—
639Q8—41no—
640Q8—41no—
641Q8—62no—
642Q8—62no—
643Q8—128no—
644Q8—121no—
645Q8—121no—
646Q8—121no—
647Q8—121no—
648Q8—121no—
649Q8—121no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—32no—
656C2×C4—32no—
657C2×C4—32no—
658C2×C4—32no—
659C2×C4—32no—
660C2×C4—32no—
661C2×C4—32no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—68no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—124no—
685C2×C4—121no—
686C2×C4—121no—
687C2×C4—121no—
688C2×C4—121no—
689C2×C4—121no—
690C2×C4—121no—
691C2×C4—121no—
692C2×C4—121no—
693C2×C4—121no—
694C2×C4—121no—
695C2×C4C2×D3×D411yescharacteristic
696C2×C4C2×D3×D411yescharacteristic
697C2×C4C2×#23711yescharacteristic
698C2×C4#100411yescharacteristic
699C2×C4#100411yescharacteristic
700C2×C4D3×#4111yescharacteristic
701C8—22no—
702C8—41no—
703C8—62no—
704C8—121no—
705C2×C3—42no—
706C2×C3#243111yescharacteristic
707C2×C3C2×#45111yescharacteristic
708C2×C3C2×#45211yescharacteristic
709C2×C3#317011yescharacteristic
710C2×C3#318511yescharacteristic
711C2×C3#320911yescharacteristic
712C2×C3#321011yescharacteristic
713C22—22no—
714C22—22no—
715C22—22no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22D3×#12011yescharacteristic
721C22#559211yescharacteristic
722C22#559611yescharacteristic
723C22C2×D3×Q1611yescharacteristic
724C22D3×#13511yescharacteristic
725C22D3×#13711yescharacteristic
726C22D3×#13711yescharacteristic
727C4—34no—
728C4—34no—
729C4—42no—
730C4—41no—
731C4—42no—
732C4—62no—
733C4—81no—
734C4—81no—
735C4—121no—
736C4—122no—
737C4—122no—
738C4—241no—
739C4—241no—
740C4#559111yescharacteristic
741C4#559911yescharacteristic
742C4#561011yescharacteristic
743C4#571811yescharacteristic
744C3#2560011yescharacteristic, complemented, Sylow
745C2—42no—
746C2#7667211yescharacteristic
747C2#8017811yescharacteristic
748C2D3×#45111yescharacteristic
749C2#8022011yescharacteristic
750C2D3×#45211yescharacteristic
751C2#8074111yescharacteristic
752C2#8089311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2001C2
socleC23×C3C22×D4
prime radicalC24×C3C2×D4
hypercenter#2001D3
hypocenterC3#25600
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2001

Complements

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

NH ≅ G/Ntype
2. C2×#5183C2semidirect
4. C2×#4792C2semidirect
6. #72065C2semidirect
9. #70281C2semidirect
10. #70239C2semidirect
11. #70225C2semidirect
14. #68908C2semidirect
15. #68803C2semidirect
251. C22×Dic3Q16semidirect
744. C3#25600semidirect

Maximal subgroups

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

subgroupindex
C2×#56222
C2×#51832
#828112
C2×#47922
C3×#20012
#720652
#717002
#702812
#702392
#702252
#699642
Dic3×C22⋊C82
#689082
#688032
#256003