Finite Group Databasebeta

← #10702084

Subgroups — #10702084

Order 768.

1278 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5822C211yesmaximal, characteristic
2C2×C3×#410C211yesmaximal, characteristic, complemented
3C2×#5233C211yesmaximal, characteristic, complemented
4C2×#5006C211yesmaximal, characteristic, complemented
5C2×#5002C211yesmaximal, characteristic, complemented
6#71579C211yesmaximal, characteristic, complemented
7C2×#4531C211yesmaximal, characteristic, complemented
8#11038—31nomaximal, Sylow
9C22×C3×#41C2211yescharacteristic
10C22×#235C2211yescharacteristic
11C2×C3×#117C2211yescharacteristic
12C2×C3×#117C2211yescharacteristic
13C2×#951—21no—
14#5822—22no—
15#5822—22no—
16#5822—22no—
17#5822C414yescomplemented
18C2×#950—22no—
19C2×#949—21no—
20C2×#942—21no—
21C2×#932—21no—
22C2×#926C2211yescharacteristic
23C22×#208C2211yescharacteristic
24C23×C3⋊C8C2211yescharacteristic
25C3×#410—22no—
26C3×#410—22no—
27C2×C3×#99—22no—
28#5233—22no—
29#5233—22no—
30C2×#835—21no—
31C2×#832—21no—
32#5006—22no—
33#5006—22no—
34#5002—22no—
35#5002—22no—
36C2×#810—21no—
37C2×#809—21no—
38C2×#806—22no—
39#4531—22no—
40#4524—22no—
41C2×#575—31no—
42C2×#416—31no—
43C2×#416—31no—
44C2×#410—31no—
45C2×#410D311yescharacteristic, complemented
46C2×H(3,ℤ/4)—31no—
47#1729—31no—
48C2×C3×#41—21no—
49C2×C3×#41—21no—
50C2×C3×#41—21no—
51C2×C3×#41—21no—
52C2×C3×#41—21no—
53C2×C3×#41—21no—
54C2×C3×#41—21no—
55C2×C3×#41—21no—
56C2×C3×#41—21no—
57C2×C3×#41—21no—
58C2×C3×#41C2×C412yes—
59C2×C3×#41D412yes—
60C22×C3×Q8D411yescharacteristic
61C22×C3×D4—21no—
62C22×C3×D4D411yescharacteristic
63C23×C3×C4—21no—
64C23×C3×C4C2311yescharacteristic
65C22×#67—21no—
66C2×#235—21no—
67C2×#235—21no—
68C2×#235—21no—
69C2×#235—21no—
70C2×#235—21no—
71C2×#235—21no—
72C2×#235—21no—
73C2×#235—21no—
74C2×#235—21no—
75C2×#235—21no—
76C2×#235C2×C412yes—
77C2×#235D412yes—
78C22×D12D411yescharacteristic
79C22×C4×D3—21no—
80C22×Dic6D411yescharacteristic
81C3×#117—21no—
82C3×#117—21no—
83C3×#117—21no—
84C3×#117—21no—
85C3×#117—21no—
86C3×#117—21no—
87C3×#117—21no—
88C3×#117D412yes—
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4—21no—
91C2×C3×C22⋊C4—21no—
92C2×C3×C22⋊C4D412yes—
93C2×C3×C42—21no—
94C2×C3×C42—21no—
95C2×#217—21no—
96#951—24no—
97#951—24no—
98#950—28no—
99#950—28no—
100#949—24no—
101#949—24no—
102C2×#216—22no—
103#942—24no—
104#942—24no—
105C2×#215—22no—
106C2×#214—22no—
107#932—24no—
108#932—24no—
109C2×#213—22no—
110#926—21no—
111#926—21no—
112#926—21no—
113#926D412yes—
114C2×C4⋊Dic3—21no—
115C2×C4×Dic3—21no—
116C2×#208—21no—
117C2×#208—21no—
118C2×#208—21no—
119C2×#208—21no—
120C2×#208C2×C412yes—
121C2×#208D412yes—
122C22×C3⋊C8—21no—
123C22×C3⋊C8—21no—
124C22×C3⋊C8—21no—
125C22×C3⋊C8—21no—
126C22×C3⋊C8—21no—
127C22×C3⋊C8—21no—
128C22×C3⋊C8D412yes—
129C22×C3⋊C8D412yes—
130C3×#99—28no—
131#835—24no—
132#832—24no—
133#810—24no—
134#809—24no—
135#806—28no—
136C22×#41—31no—
137C22×#41C2×D311yescharacteristic
138#575—34no—
139#575—62no—
140#575—62no—
141#575—62no—
142C2×#137—61no—
143C2×#137—61no—
144C2×AGL(1,ℤ/8)—61no—
145C2×AGL(1,ℤ/8)—61no—
146C2×#135—62no—
147C22×M16—31no—
148C23×C8—31no—
149C2×#117—31no—
150C2×#117C2×D311yescharacteristic
151C2×#117C2×D311yescharacteristic
152#416—62no—
153#416—62no—
154#416—62no—
155#416—62no—
156C2×#103—61no—
157C2×#103—61no—
158C2×#102—61no—
159C2×#102—61no—
160#410—22no—
161#410—22no—
162#410—62no—
163#410—62no—
164C2×#99—22no—
165C2×#99—62no—
166H(3,ℤ/4)—62no—
167#336—62no—
168C24×C3—21no—
169C24×C3C2×D411yescharacteristic
170C23×D3—21no—
171C3×#41—22no—
172C3×#41—22no—
173C3×#41—22no—
174C3×#41—22no—
175C3×#41—22no—
176C3×#41—22no—
177C3×#41—22no—
178C3×#41—22no—
179C3×#41—41no—
180C3×#41—41no—
181C3×#41—41no—
182C3×#41—41no—
183C3×#41—41no—
184C3×#41—41no—
185C3×#41—41no—
186C3×#41—41no—
187C2×C3×Q8—21no—
188C2×C3×Q8—21no—
189C2×C3×Q8—21no—
190C2×C3×Q8—21no—
191C2×C3×Q8—21no—
192C2×C3×Q8C22⋊C412yes—
193C2×C3×D4—22no—
194C2×C3×D4—22no—
195C2×C3×D4—21no—
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4—21no—
199C2×C3×D4—21no—
200C2×C3×D4—41no—
201C2×C3×D4—41no—
202C2×C3×D4—41no—
203C2×C3×D4—41no—
204C2×C3×D4C22⋊C412yes—
205C22×C3×C4—21no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—41no—
210C22×C3×C4—41no—
211C22×C3×C4—41no—
212C22×C3×C4—41no—
213C22×C3×C4—41no—
214C22×C3×C4C22×C411yescharacteristic
215C22×C3×C4C2×D411yescharacteristic
216C22×C3×C4C2×D411yescharacteristic
217C22×C3×C4C2×D411yescharacteristic
218C22×C3×C4C2×D411yescharacteristic
219C22×C3×C4C2×D411yescharacteristic
220C22×C3×C4C2×D411yescharacteristic
221C22×C3×C4C2×D411yescharacteristic
222C22×C3×C4C2×D411yescharacteristic
223C22×C3×C4C2×D411yescharacteristic
224C22×C3×C4#4111yescharacteristic
225C22×C3×C4#4111yescharacteristic
226C22×C3×C4#4111yescharacteristic
227C22×C3×C4#4111yescharacteristic
228C2×#67—22no—
229C2×#67—22no—
230C2×#67—41no—
231C2×#67—41no—
232C2×#67—41no—
233C2×#67—41no—
234C22×Dic3—21no—
235C22×Dic3—41no—
236#235—22no—
237#235—22no—
238#235—22no—
239#235—22no—
240#235—22no—
241#235—22no—
242#235—22no—
243#235—22no—
244#235—41no—
245#235—41no—
246#235—41no—
247#235—41no—
248#235—41no—
249#235—41no—
250#235—41no—
251#235—41no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12C22⋊C412yes—
258C2×C4×D3—22no—
259C2×C4×D3—22no—
260C2×C4×D3—41no—
261C2×C4×D3—41no—
262C2×C4×D3—41no—
263C2×C4×D3—41no—
264C2×Dic6—21no—
265C2×Dic6—21no—
266C2×Dic6—21no—
267C2×Dic6—21no—
268C2×Dic6—21no—
269C2×Dic6C22⋊C412yes—
270C3×C4⋊C4—22no—
271C3×C4⋊C4—41no—
272C3×C4⋊C4—41no—
273C3×C4⋊C4—41no—
274C3×C22⋊C4—22no—
275C3×C22⋊C4—22no—
276C3×C22⋊C4—22no—
277C3×C22⋊C4—41no—
278C3×C42—22no—
279C3×C42—41no—
280C3×C42—41no—
281C3×C42—41no—
282#217—22no—
283#217—41no—
284#216—28no—
285#215—28no—
286#214—28no—
287#213—28no—
288C4⋊Dic3—22no—
289C4⋊Dic3—41no—
290C4×Dic3—22no—
291C4×Dic3—41no—
292#208—22no—
293#208—22no—
294#208—22no—
295#208—22no—
296C2×C3⋊C8—22no—
297C2×C3⋊C8—22no—
298C2×C3⋊C8—22no—
299C2×C3⋊C8—22no—
300C2×C3⋊C8—22no—
301C2×C3⋊C8—41no—
302C2×C3⋊C8—41no—
303C2×C3⋊C8—41no—
304C2×C3⋊C8—41no—
305C2×C3⋊C8C22⋊C414yes—
306C2×#41—21no—
307C2×#41—21no—
308C2×#41—21no—
309C2×#41—21no—
310C2×#41—21no—
311C2×#41—21no—
312C2×#41—21no—
313C2×#41—21no—
314C2×#41—21no—
315C2×#41—21no—
316C2×#41—32no—
317C2×#41—32no—
318C2×#41—61no—
319C2×#41—61no—
320C2×#41—61no—
321C2×#41—61no—
322C2×#41—61no—
323C2×#41—61no—
324C2×#41—61no—
325C2×#41—61no—
326C2×#41—61no—
327C2×#41—61no—
328C2×#41C4×D312yes—
329C2×#41#6712yes—
330C22×Q8—31no—
331C22×Q8D1211yescharacteristic
332C22×D4—21no—
333C22×D4—31no—
334C22×D4—61no—
335C22×D4D1211yescharacteristic
336C23×C4—21no—
337C23×C4—61no—
338C23×C4C22×D311yescharacteristic
339#137—64no—
340#137—64no—
341#137—64no—
342#137—64no—
343AGL(1,ℤ/8)—64no—
344AGL(1,ℤ/8)—64no—
345AGL(1,ℤ/8)—64no—
346AGL(1,ℤ/8)—64no—
347#135—68no—
348#135—68no—
349C2×Q16—62no—
350C2×SD16—62no—
351C2×SD16—62no—
352C2×D8—62no—
353C2×M16—32no—
354C2×M16—32no—
355C2×M16—61no—
356C2×M16—61no—
357C2×M16—61no—
358C2×M16—61no—
359C22×C8—32no—
360C22×C8—32no—
361C22×C8—61no—
362C22×C8—61no—
363C22×C8—61no—
364C22×C8—61no—
365C22×C8—61no—
366C22×C8—61no—
367#117—21no—
368#117—21no—
369#117—21no—
370#117—21no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—32no—
375#117—61no—
376#117—61no—
377#117—61no—
378#117#6712yes—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—61no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—61no—
384C2×C22⋊C4#6712yes—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—61no—
388#103—64no—
389#103—64no—
390#102—64no—
391#102—64no—
392#99—28no—
393#99—68no—
394C23×C3—22no—
395C23×C3—42no—
396C23×C3—41no—
397C23×C3—41no—
398C23×C3—82no—
399C23×C3C4×D411yescharacteristic
400C23×C3#12011yescharacteristic
401C23×C3#12011yescharacteristic
402C23×C3#12111yescharacteristic
403C23×C3#12111yescharacteristic
404C23×C3#12111yescharacteristic
405C23×C3#12711yescharacteristic
406C22×D3—22no—
407C22×D3—41no—
408C22×D3—41no—
409C22×D3—82no—
410C3×Q8—22no—
411C3×Q8—22no—
412C3×Q8—41no—
413C3×Q8—41no—
414C3×D4—22no—
415C3×D4—22no—
416C3×D4—42no—
417C3×D4—42no—
418C3×D4—42no—
419C3×D4—42no—
420C3×D4—41no—
421C3×D4—41no—
422C2×C3×C4—22no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—42no—
426C2×C3×C4—42no—
427C2×C3×C4—42no—
428C2×C3×C4—42no—
429C2×C3×C4—44no—
430C2×C3×C4—42no—
431C2×C3×C4—42no—
432C2×C3×C4—82no—
433C2×C3×C4C2×C22⋊C411yescharacteristic
434C2×C3×C4C2×C22⋊C411yescharacteristic
435C2×C3×C4C2×C22⋊C411yescharacteristic
436C2×C3×C4C4×D411yescharacteristic
437C2×C3×C4C4×D411yescharacteristic
438C2×C3×C4C4×D411yescharacteristic
439C2×C3×C4#12011yescharacteristic
440C2×C3×C4#12011yescharacteristic
441C2×C3×C4#12011yescharacteristic
442C2×C3×C4#12011yescharacteristic
443C2×C3×C4#12011yescharacteristic
444C2×C3×C4#12011yescharacteristic
445C2×C3×C4#12111yescharacteristic
446C2×C3×C4#12111yescharacteristic
447C2×C3×C4#12111yescharacteristic
448C2×C3×C4#12111yescharacteristic
449C2×C3×C4#12111yescharacteristic
450C2×C3×C4#12111yescharacteristic
451C2×C3×C4#12111yescharacteristic
452C2×C3×C4#12111yescharacteristic
453C2×C3×C4#12111yescharacteristic
454C2×C3×C4#12311yescharacteristic
455C2×C3×C4#12311yescharacteristic
456C2×C3×C4#12311yescharacteristic
457C2×C3×C4#12311yescharacteristic
458C2×C3×C4#12411yescharacteristic
459C2×C3×C4#12411yescharacteristic
460C2×C3×C4#12711yescharacteristic
461#67—42no—
462#67—42no—
463#67—42no—
464#67—42no—
465C2×Dic3—22no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—42no—
469C2×Dic3—82no—
470D12—22no—
471D12—22no—
472D12—41no—
473D12—41no—
474C4×D3—42no—
475C4×D3—42no—
476C4×D3—42no—
477C4×D3—42no—
478Dic6—22no—
479Dic6—22no—
480Dic6—41no—
481Dic6—41no—
482C3⋊C8—24no—
483C3⋊C8—42no—
484C24—21no—
485C24—61no—
486C24C2×#6711yescharacteristic
487#41—22no—
488#41—22no—
489#41—22no—
490#41—22no—
491#41—22no—
492#41—22no—
493#41—22no—
494#41—22no—
495#41—41no—
496#41—41no—
497#41—41no—
498#41—41no—
499#41—41no—
500#41—41no—
501#41—41no—
502#41—41no—
503#41—62no—
504#41—62no—
505#41—62no—
506#41—62no—
507#41—62no—
508#41—62no—
509#41—62no—
510#41—62no—
511#41—121no—
512#41—121no—
513#41—121no—
514#41—121no—
515#41—121no—
516#41—121no—
517#41—121no—
518#41—121no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—32no—
525C2×Q8—61no—
526C2×Q8—61no—
527C2×Q8—61no—
528C2×Q8—61no—
529C2×Q8—61no—
530C2×Q8(C2×D3)⋊C412yes—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—32no—
539C2×D4—41no—
540C2×D4—41no—
541C2×D4—41no—
542C2×D4—41no—
543C2×D4—62no—
544C2×D4—62no—
545C2×D4—61no—
546C2×D4—61no—
547C2×D4—61no—
548C2×D4—61no—
549C2×D4—61no—
550C2×D4—121no—
551C2×D4—121no—
552C2×D4—121no—
553C2×D4—121no—
554C2×D4(C2×D3)⋊C412yes—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—61no—
565C22×C4—62no—
566C22×C4—62no—
567C22×C4—121no—
568C22×C4—121no—
569C22×C4—121no—
570C22×C4—121no—
571C22×C4—121no—
572C22×C4C2×C4×D311yescharacteristic
573C22×C4C2×D1211yescharacteristic
574C22×C4#23511yescharacteristic
575C22×C4#23511yescharacteristic
576C22×C4D3×D411yescharacteristic
577C22×C4D3×D411yescharacteristic
578C22×C4D3×D411yescharacteristic
579C22×C4D3×D411yescharacteristic
580C22×C4D3×D411yescharacteristic
581C22×C4D3×D411yescharacteristic
582C22×C4#23711yescharacteristic
583C22×C4#23711yescharacteristic
584C22×C4C2×#6711yescharacteristic
585C22×C4C2×#6711yescharacteristic
586Q16—68no—
587SD16—68no—
588SD16—68no—
589D8—68no—
590M16—62no—
591M16—62no—
592M16—62no—
593M16—62no—
594C2×C8—34no—
595C2×C8—62no—
596C2×C8—62no—
597C2×C8—62no—
598C2×C8—62no—
599C2×C8—62no—
600C2×C8—121no—
601C2×C8—121no—
602C2×C8—121no—
603C2×C8—121no—
604C4⋊C4—22no—
605C4⋊C4—41no—
606C4⋊C4—41no—
607C4⋊C4—41no—
608C4⋊C4—62no—
609C4⋊C4—121no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—41no—
614C22⋊C4—62no—
615C22⋊C4—121no—
616C42—22no—
617C42—41no—
618C42—41no—
619C42—41no—
620C42—62no—
621C42—121no—
622C22×C3—22no—
623C22×C3—22no—
624C22×C3—22no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—42no—
630C22×C3—82no—
631C22×C3—82no—
632C22×C3—82no—
633C22×C3#38611yescharacteristic
634C22×C3#38611yescharacteristic
635C22×C3#39011yescharacteristic
636C22×C3#39211yescharacteristic
637C22×C3#39211yescharacteristic
638C22×C3#39211yescharacteristic
639C22×C3#39411yescharacteristic
640C2×D3—42no—
641C2×D3—82no—
642C2×D3—82no—
643C2×D3—82no—
644C3×C4—42no—
645C3×C4—82no—
646C3×C4—82no—
647C3×C4#37911yescharacteristic
648C3×C4#38611yescharacteristic
649C3×C4#38611yescharacteristic
650C3×C4#39011yescharacteristic
651C3×C4#39211yescharacteristic
652C3×C4#39411yescharacteristic
653C3×C4#39411yescharacteristic
654C3×C4#39411yescharacteristic
655Dic3—42no—
656Dic3—82no—
657C23—22no—
658C23—42no—
659C23—41no—
660C23—41no—
661C23—62no—
662C23—82no—
663C23—121no—
664C23—121no—
665C23—242no—
666C23C4×#6711yescharacteristic
667C23#93011yescharacteristic
668C23#93711yescharacteristic
669C23#93811yescharacteristic
670C23#93911yescharacteristic
671C23#94011yescharacteristic
672C23#95311yescharacteristic
673Q8—22no—
674Q8—22no—
675Q8—41no—
676Q8—41no—
677Q8—62no—
678Q8—62no—
679Q8—121no—
680Q8—121no—
681D4—22no—
682D4—22no—
683D4—42no—
684D4—42no—
685D4—42no—
686D4—42no—
687D4—41no—
688D4—41no—
689D4—62no—
690D4—62no—
691D4—122no—
692D4—122no—
693D4—122no—
694D4—122no—
695D4—121no—
696D4—121no—
697C2×C4—22no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—44no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—62no—
708C2×C4—82no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—122no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4—122no—
715C2×C4—122no—
716C2×C4—242no—
717C2×C4D3×C22⋊C411yescharacteristic
718C2×C4D3×C22⋊C411yescharacteristic
719C2×C4#67⋊C411yescharacteristic
720C2×C4#67⋊C411yescharacteristic
721C2×C4#88211yescharacteristic
722C2×C4#88211yescharacteristic
723C2×C4#88211yescharacteristic
724C2×C4#88311yescharacteristic
725C2×C4#88311yescharacteristic
726C2×C4#88411yescharacteristic
727C2×C4#88411yescharacteristic
728C2×C4#88411yescharacteristic
729C2×C4#88411yescharacteristic
730C2×C4#88511yescharacteristic
731C2×C4#88511yescharacteristic
732C2×C4#88611yescharacteristic
733C2×C4C2×(C2×D3)⋊C411yescharacteristic
734C2×C4C4×#6711yescharacteristic
735C2×C4#92911yescharacteristic
736C2×C4#93011yescharacteristic
737C2×C4#93711yescharacteristic
738C2×C4#93711yescharacteristic
739C2×C4#93711yescharacteristic
740C2×C4#93811yescharacteristic
741C2×C4#93911yescharacteristic
742C2×C4#93911yescharacteristic
743C2×C4#93911yescharacteristic
744C2×C4#94011yescharacteristic
745C8—64no—
746C8—122no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—82no—
754C2×C3#143811yescharacteristic
755C2×C3#205312yes—
756D3—82no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—42no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—122no—
769C22—242no—
770C22—242no—
771C22—242no—
772C22#495611yescharacteristic
773C22#495711yescharacteristic
774C22#496011yescharacteristic
775C22#496111yescharacteristic
776C22#521311yescharacteristic
777C22#522311yescharacteristic
778C22#522311yescharacteristic
779C4—42no—
780C4—82no—
781C4—82no—
782C4—122no—
783C4—242no—
784C4#495511yescharacteristic
785C4#495611yescharacteristic
786C4#495711yescharacteristic
787C4#495811yescharacteristic
788C4#495911yescharacteristic
789C4#495911yescharacteristic
790C4#496011yescharacteristic
791C4#496111yescharacteristic
792C3#1103811yescharacteristic, complemented, Sylow
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—82no—
800C2—242no—
801C2#7004312yes—
802C2#7155011yescharacteristic
subgroupG/H
centerC2×C4#885
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC2×C3×#410C2
socleC22×C3#394
prime radicalC2×#5822C2
cosocleC23×C3×C4C23
hypercenterC2×#410D3
hypocenterC3#11038
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. C2×C3×#410C2semidirect
3. C2×#5233C2semidirect
4. C2×#5006C2semidirect
5. C2×#5002C2semidirect
6. #71579C2semidirect
7. C2×#4531C2semidirect
17. #5822C4semidirect
45. C2×#410D3semidirect
792. C3#11038semidirect

Maximal subgroups

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

subgroupindex
C2×#58222
C2×C3×#4102
C2×#52332
C2×#50062
C2×#50022
#715792
C2×#45312
#110383