Finite Group Databasebeta

← #10799208

Subgroups — #10799208

Order 768.

1434 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#918C211yesmaximal, characteristic
2C2×#4893C211yesmaximal, characteristic, complemented
3#78956C211yesmaximal, characteristic
4D3×#419C211yesmaximal, characteristic, complemented
5C2×#4751C211yesmaximal, characteristic
6C2×D3×#101C211yesmaximal, characteristic, complemented
7#78548C211yesmaximal, characteristic, complemented
8C3×#1979C211yesmaximal, characteristic, complemented
9#72069C211yesmaximal, characteristic, complemented
10#70708C211yesmaximal, characteristic, complemented
11#70336C211yesmaximal, characteristic, complemented
12#70335C211yesmaximal, characteristic, complemented
13#70108C211yesmaximal, characteristic, complemented
14#70107C211yesmaximal, characteristic, complemented
15#69902C211yesmaximal, characteristic, complemented
16#21250—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×D3×Q8C2211yescharacteristic
19C22×C3×Q16C2211yescharacteristic
20C22×#216C2211yescharacteristic
21C22×#215C2211yescharacteristic
22C2×#918—24no—
23C2×#918—21no—
24C2×#918—21no—
25C2×#918—21no—
26C2×#918—21no—
27C2×#918C418yescomplemented
28C2×D3×M16C2211yescharacteristic
29C2×D3×M16C2211yescharacteristic
30C2×D3×M16C2211yescharacteristic
31C22×#204C2211yescharacteristic
32C22×ΓL(1,𝔽25)C2211yescharacteristic
33D3×#117C2211yescharacteristic
34C2×C3×#108C2211yescharacteristic
35C3×#419C2211yescharacteristic
36C3×#419C2211yescharacteristic
37C2×C3×#101C2211yescharacteristic
38C2×C3×#101C2211yescharacteristic
39C3×#405C2211yescharacteristic
40C2×#836C2211yescharacteristic
41C2×#836C2211yescharacteristic
42#5225C2211yescharacteristic
43#5225C2211yescharacteristic
44C2×#824C2211yescharacteristic
45C2×#824C2211yescharacteristic
46#5131C2211yescharacteristic
47C2×#823C2211yescharacteristic
48C2×#823C2211yescharacteristic
49C2×#822C2211yescharacteristic
50C2×#822C2211yescharacteristic
51#5122C2211yescharacteristic
52#5120C2211yescharacteristic
53C2×#819C2211yescharacteristic
54#5101C2211yescharacteristic
55#5004C2211yescharacteristic
56#5001C2211yescharacteristic
57#4997C2211yescharacteristic
58#4893—24no—
59#4804—22no—
60#4803—22no—
61#4802—22no—
62D3×#103—22no—
63#4751—24no—
64D3×#101—24no—
65#4708—21no—
66#4707—21no—
67#4689—21no—
68C4×ΓL(1,𝔽25)—21no—
69C22×#137—31no—
70C2×#430—31no—
71#2896—31no—
72C2×#419—31no—
73C2×#413—31no—
74C22×#101—31no—
75#2873—31no—
76#1979—31no—
77#1979—31no—
78#1979—31no—
79#1979D311yescharacteristic, complemented
80#1977—31no—
81#1977—31no—
82#1977—31no—
83#1977—31no—
84C22×C3×Q8C2311yescharacteristic
85C22×C3×Q8C2311yescharacteristic
86C2×#239—22no—
87C2×#239—21no—
88C2×#239—21no—
89C2×#239—22no—
90C2×#239—21no—
91C2×#239—21no—
92C2×#239—22no—
93C2×#239C2×C414yes—
94C2×D3×Q8—22no—
95C2×D3×Q8—21no—
96C2×D3×Q8—21no—
97C2×D3×Q8—22no—
98C2×D3×Q8—21no—
99C2×D3×Q8—21no—
100C2×D3×Q8—22no—
101C2×D3×Q8C2×C414yes—
102C22×D12—21no—
103C22×D12C2311yescharacteristic
104C22×C4×D3—21no—
105C22×C4×D3—21no—
106C22×C4×D3C2311yescharacteristic
107C22×Dic6—21no—
108C22×Dic6C2311yescharacteristic
109C2×C3×Q16—21no—
110C2×C3×Q16—21no—
111C2×C3×Q16—22no—
112C2×C3×Q16C2×C414yescomplemented
113C2×C3×M16C2311yescharacteristic
114C2×C3×M16C2311yescharacteristic
115C2×C3×M16C2311yescharacteristic
116C22×C3×C8C2311yescharacteristic
117C3×#117C2311yescharacteristic
118C2×#216—21no—
119C2×#216—21no—
120C2×#216—22no—
121C2×#216C2×C414yescomplemented
122C2×#215—21no—
123C2×#215—21no—
124C2×#215—22no—
125C2×#215C2×C414yescomplemented
126#926C2311yescharacteristic
127C2×#208C2311yescharacteristic
128C2×#208C2311yescharacteristic
129C2×#208C2311yescharacteristic
130C22×C3⋊C8C2311yescharacteristic
131#918—28no—
132#918—28no—
133#918—28no—
134#918—28no—
135D3×M16—22no—
136D3×M16—22no—
137D3×M16—22no—
138D3×M16—22no—
139D3×M16—22no—
140D3×M16D414yes—
141C2×#204—21no—
142C2×#204—21no—
143C2×#204—22no—
144C2×#204C2×C414yescomplemented
145C2×ΓL(1,𝔽25)—21no—
146C2×ΓL(1,𝔽25)—21no—
147C2×ΓL(1,𝔽25)—21no—
148C2×ΓL(1,𝔽25)C2×C414yes—
149C2×ΓL(1,𝔽25)D414yes—
150C2×ΓL(1,𝔽25)D411yescharacteristic
151C2×ΓL(1,𝔽25)D411yescharacteristic
152C2×ΓL(1,𝔽25)D411yescharacteristic
153C2×ΓL(1,𝔽25)D411yescharacteristic
154C2×D3×C8—21no—
155C2×D3×C8—21no—
156C2×D3×C8—21no—
157#892D412yes—
158D3×C4⋊C4D412yes—
159D3×C22⋊C4—21no—
160#877—21no—
161#872—21no—
162C42×D3—21no—
163C3×#108—22no—
164C3×#103—22no—
165C3×#103—22no—
166C3×#101—22no—
167C3×#101—22no—
168C3×#97—21no—
169C3×C4×C8—21no—
170#836—22no—
171#836—22no—
172#835—22no—
173#835—22no—
174#824—22no—
175#824—22no—
176#823—22no—
177#823—22no—
178#822—22no—
179#822—22no—
180#821—22no—
181#819—22no—
182#816—22no—
183#815—21no—
184#815—21no—
185C8×Dic3—21no—
186C8×Dic3—21no—
187#810—22no—
188#809—22no—
189#803—21no—
190C4×C3⋊C8—21no—
191C22×#41—31no—
192C23×Q8—31no—
193C2×#137—38no—
194C2×#137—61no—
195C2×#137—61no—
196C2×#137—61no—
197C2×#137—61no—
198C2×#137—64no—
199C22×Q16—31no—
200C22×Q16C2×D311yescharacteristic
201C22×SD16—31no—
202C22×SD16—31no—
203C22×M16—31no—
204C22×M16—31no—
205C22×M16—31no—
206C22×M16—31no—
207C2×#117—31no—
208#430—64no—
209C2×#108—31no—
210C2×#108—31no—
211C2×#108—31no—
212C2×#108C2×D311yescharacteristic
213#419—31no—
214#419—31no—
215#419—31no—
216#419—31no—
217#419—62no—
218#419C2×D311yescharacteristic
219#419C2×D311yescharacteristic
220#418—31no—
221#418—31no—
222#417—62no—
223#416—62no—
224C2×#103—62no—
225#413—64no—
226C2×#101—31no—
227C2×#101—31no—
228C2×#101—31no—
229C2×#101—31no—
230C2×#101—64no—
231C2×#101C2×D311yescharacteristic
232C2×#101C2×D311yescharacteristic
233C2×#100—31no—
234C2×#100—31no—
235#405—31no—
236#405—31no—
237#405—31no—
238#405—61no—
239#405—61no—
240#405C2×D311yescharacteristic
241C4×M16—61no—
242C4×M16—61no—
243C23×D3—21no—
244C23×D3#4111yescharacteristic
245C2×C3×Q8—21no—
246C2×C3×Q8—21no—
247C2×C3×Q8—21no—
248C2×C3×Q8—21no—
249C2×C3×Q8—21no—
250C2×C3×Q8—21no—
251C2×C3×Q8—21no—
252C2×C3×Q8—21no—
253C2×C3×Q8—21no—
254C2×C3×Q8—21no—
255C2×C3×Q8C22×C412yes—
256C2×C3×Q8C22×C412yes—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4C2411yescharacteristic
260C22×Dic3—21no—
261C22×Dic3#4111yescharacteristic
262#239—24no—
263#239—24no—
264#239—24no—
265#239—24no—
266#239—42no—
267#239—42no—
268#239—42no—
269#239—42no—
270D3×Q8—24no—
271D3×Q8—24no—
272D3×Q8—24no—
273D3×Q8—24no—
274D3×Q8—42no—
275D3×Q8—42no—
276D3×Q8—42no—
277D3×Q8—42no—
278C2×D12—21no—
279C2×D12—21no—
280C2×D12—21no—
281C2×D12—21no—
282C2×D12—24no—
283C2×D12—21no—
284C2×D12—41no—
285C2×D12—41no—
286C2×D12—42no—
287C2×D12C22×C412yes—
288C2×C4×D3—24no—
289C2×C4×D3—24no—
290C2×C4×D3—22no—
291C2×C4×D3—41no—
292C2×C4×D3—41no—
293C2×C4×D3—42no—
294C2×C4×D3—41no—
295C2×C4×D3—41no—
296C2×C4×D3—42no—
297C2×C4×D3C22×C412yes—
298C2×C4×D3C2×D411yescharacteristic
299C2×C4×D3C2×D411yescharacteristic
300C2×C4×D3C2×D412yes—
301C2×C4×D3C2×D411yescharacteristic
302C2×C4×D3C2×D411yescharacteristic
303C2×C4×D3C2×D412yes—
304C2×C4×D3#4112yes—
305C2×Dic6—21no—
306C2×Dic6—21no—
307C2×Dic6—21no—
308C2×Dic6—21no—
309C2×Dic6—21no—
310C2×Dic6—24no—
311C2×Dic6—41no—
312C2×Dic6—41no—
313C2×Dic6—42no—
314C2×Dic6C22×C412yes—
315C3×Q16—24no—
316C3×Q16—24no—
317C3×M16—21no—
318C3×M16—21no—
319C3×M16—21no—
320C3×M16—21no—
321C3×M16—21no—
322C3×M16C2×D412yes—
323C2×C3×C8—21no—
324C2×C3×C8—21no—
325C2×C3×C8—21no—
326C2×C3×C8C22×C412yes—
327C2×C3×C8C2×D411yescharacteristic
328C2×C3×C8C2×D411yescharacteristic
329C2×C3×C8C2×D412yes—
330C3×C4⋊C4C2×D412yes—
331C3×C22⋊C4—21no—
332C3×C42—21no—
333#217—21no—
334#216—24no—
335#216—24no—
336#215—24no—
337#215—24no—
338(C2×D3)⋊C4—22no—
339C4⋊Dic3C2×D412yes—
340Dic3⋊C4—22no—
341C4×Dic3—21no—
342C4×Dic3—22no—
343#208—21no—
344#208—21no—
345#208—21no—
346#208—21no—
347#208—21no—
348#208C2×D412yes—
349C2×C3⋊C8—21no—
350C2×C3⋊C8—21no—
351C2×C3⋊C8—21no—
352C2×C3⋊C8C22×C412yes—
353C2×C3⋊C8C2×D411yescharacteristic
354C2×C3⋊C8C2×D411yescharacteristic
355C2×C3⋊C8C2×D412yes—
356#204—24no—
357#204—24no—
358ΓL(1,𝔽25)—24no—
359ΓL(1,𝔽25)—42no—
360ΓL(1,𝔽25)—42no—
361ΓL(1,𝔽25)C22⋊C414yes—
362ΓL(1,𝔽25)C22⋊C414yes—
363ΓL(1,𝔽25)C22⋊C414yes—
364ΓL(1,𝔽25)C22⋊C414yes—
365D3×C8—24no—
366D3×C8—42no—
367D3×C8—42no—
368C2×#41—34no—
369C2×#41—62no—
370C2×#41—61no—
371C2×#41—61no—
372C2×#41—62no—
373C2×#41—61no—
374C2×#41—61no—
375C2×#41—62no—
376C22×Q8—34no—
377C22×Q8—31no—
378C22×Q8—61no—
379C22×Q8—62no—
380C22×Q8—61no—
381C22×Q8—61no—
382C22×Q8—62no—
383C22×Q8—61no—
384C22×Q8—61no—
385C22×Q8—62no—
386C22×Q8C22×D311yescharacteristic
387C22×Q8C22×D311yescharacteristic
388C22×D4—31no—
389C22×D4—61no—
390C23×C4—31no—
391C23×C4—61no—
392C23×C4—61no—
393#137—68no—
394#137—68no—
395#137—68no—
396#137—68no—
397C2×Q16—21no—
398C2×Q16—21no—
399C2×Q16—22no—
400C2×Q16—34no—
401C2×Q16—61no—
402C2×Q16—61no—
403C2×Q16—62no—
404C2×Q16C4×D314yescomplemented
405C2×SD16—34no—
406C2×SD16—34no—
407C2×SD16—61no—
408C2×SD16—61no—
409C2×SD16—62no—
410C2×SD16—61no—
411C2×SD16—61no—
412C2×SD16—62no—
413C2×M16—34no—
414C2×M16—31no—
415C2×M16—31no—
416C2×M16—31no—
417C2×M16—31no—
418C2×M16—34no—
419C2×M16—31no—
420C2×M16—34no—
421C2×M16—31no—
422C2×M16—31no—
423C2×M16—61no—
424C2×M16—61no—
425C2×M16—61no—
426C2×M16—62no—
427C2×M16—62no—
428C2×M16—62no—
429C2×M16—62no—
430C2×M16—62no—
431C2×M16C22×D311yescharacteristic
432C2×M16C22×D311yescharacteristic
433C2×M16C22×D311yescharacteristic
434C22×C8—31no—
435C22×C8—61no—
436C22×C8—61no—
437C22×C8—61no—
438C22×C8C22×D311yescharacteristic
439#117—31no—
440#117—32no—
441#117—61no—
442#117—61no—
443#117C22×D311yescharacteristic
444C2×C4⋊C4—32no—
445C2×C22⋊C4—61no—
446C2×C42—61no—
447#108—22no—
448#108—62no—
449#108—62no—
450#108—62no—
451#103—22no—
452#103—22no—
453#103—62no—
454#103—62no—
455#103—62no—
456#103—62no—
457#102—62no—
458#102—62no—
459#101—22no—
460#101—22no—
461#101—62no—
462#101—62no—
463#101—62no—
464#101—62no—
465#100—62no—
466#100—62no—
467#97—21no—
468#97—61no—
469#97—61no—
470#97—61no—
471C4×C8—21no—
472C4×C8—61no—
473C4×C8—61no—
474C4×C8—61no—
475C23×C3C2×#4111yescharacteristic
476C22×D3—22no—
477C22×D3—42no—
478C22×D3—41no—
479C22×D3—41no—
480C22×D3—82no—
481C22×D3C4×D412yes—
482C22×D3#12111yescharacteristic
483C22×D3#12111yescharacteristic
484C22×D3#12412yes—
485C3×Q8—22no—
486C3×Q8—22no—
487C3×Q8—22no—
488C3×Q8—22no—
489C3×Q8—41no—
490C3×Q8—41no—
491C3×Q8—41no—
492C3×Q8—41no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4C23×C411yescharacteristic
501C2×C3×C4C22×D411yescharacteristic
502C2×C3×C4C22×D411yescharacteristic
503C2×C3×C4C22×D411yescharacteristic
504C2×C3×C4C22×D411yescharacteristic
505C2×C3×C4C2×#4111yescharacteristic
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—41no—
509C2×Dic3—41no—
510C2×Dic3C4×D412yes—
511C2×Dic3#12111yescharacteristic
512C2×Dic3#12111yescharacteristic
513C2×Dic3#12412yes—
514D12—22no—
515D12—22no—
516D12—44no—
517D12—44no—
518D12—41no—
519D12—41no—
520C4×D3—44no—
521C4×D3—44no—
522C4×D3—44no—
523C4×D3—44no—
524C4×D3—82no—
525C4×D3C2×C22⋊C412yes—
526C4×D3C2×C22⋊C412yes—
527C4×D3C4×D412yes—
528C4×D3C4×D412yes—
529C4×D3#12112yes—
530C4×D3#12112yes—
531C4×D3#12712yes—
532C4×D3#12712yes—
533Dic6—22no—
534Dic6—22no—
535Dic6—41no—
536Dic6—41no—
537Dic6—44no—
538Dic6—44no—
539C3×C8—22no—
540C3×C8—41no—
541C3×C8—41no—
542C3×C8C2×C22⋊C412yes—
543C3×C8C2×C22⋊C412yes—
544C3⋊C8—22no—
545C3⋊C8—41no—
546C3⋊C8—41no—
547C3⋊C8C2×C22⋊C412yes—
548C3⋊C8C2×C22⋊C412yes—
549C24—31no—
550C24—61no—
551#41—64no—
552#41—64no—
553#41—64no—
554#41—64no—
555#41—122no—
556#41—122no—
557#41—122no—
558#41—122no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—32no—
570C2×Q8—64no—
571C2×Q8—64no—
572C2×Q8—64no—
573C2×Q8—64no—
574C2×Q8—64no—
575C2×Q8—61no—
576C2×Q8—61no—
577C2×Q8—61no—
578C2×Q8—61no—
579C2×Q8—61no—
580C2×Q8—122no—
581C2×Q8—121no—
582C2×Q8—121no—
583C2×Q8—122no—
584C2×Q8—122no—
585C2×Q8—122no—
586C2×Q8—122no—
587C2×Q8C2×C4×D312yes—
588C2×Q8C2×C4×D312yes—
589C2×D4—32no—
590C2×D4—64no—
591C2×D4—61no—
592C2×D4—61no—
593C2×D4—61no—
594C2×D4—61no—
595C2×D4—61no—
596C2×D4—122no—
597C2×D4—121no—
598C2×D4—121no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—31no—
602C22×C4—32no—
603C22×C4—31no—
604C22×C4—31no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—32no—
608C22×C4—32no—
609C22×C4—32no—
610C22×C4—64no—
611C22×C4—64no—
612C22×C4—62no—
613C22×C4—61no—
614C22×C4—122no—
615C22×C4—121no—
616C22×C4—121no—
617C22×C4—122no—
618C22×C4—121no—
619C22×C4—121no—
620C22×C4C23×D311yescharacteristic
621Q16—24no—
622Q16—24no—
623Q16—64no—
624Q16—64no—
625SD16—64no—
626SD16—64no—
627SD16—64no—
628SD16—64no—
629M16—21no—
630M16—21no—
631M16—21no—
632M16—21no—
633M16—21no—
634M16—34no—
635M16—34no—
636M16—34no—
637M16—34no—
638M16—32no—
639M16—64no—
640M16—61no—
641M16—61no—
642M16—61no—
643M16—61no—
644M16—61no—
645M16—122no—
646M16—122no—
647M16D3×D412yes—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—32no—
652C2×C8—31no—
653C2×C8—31no—
654C2×C8—32no—
655C2×C8—64no—
656C2×C8—61no—
657C2×C8—61no—
658C2×C8—61no—
659C2×C8—122no—
660C2×C8—122no—
661C2×C8C2×C4×D312yes—
662C2×C8D3×D411yescharacteristic
663C2×C8D3×D411yescharacteristic
664C2×C8D3×D412yes—
665C4⋊C4—32no—
666C4⋊C4—62no—
667C4⋊C4D3×D412yes—
668C22⋊C4—21no—
669C22⋊C4—62no—
670C22⋊C4—61no—
671C42—21no—
672C42—62no—
673C42—61no—
674C22×C3—22no—
675C22×C3C2×C4×D411yescharacteristic
676C22×C3C2×#12111yescharacteristic
677C22×C3C2×#12411yescharacteristic
678C2×D3—22no—
679C2×D3—22no—
680C2×D3—42no—
681C2×D3—42no—
682C2×D3—42no—
683C2×D3—82no—
684C2×D3—82no—
685C2×D3—82no—
686C2×D3#39012yes—
687C2×D3#39012yes—
688C3×C4—42no—
689C3×C4—42no—
690C3×C4—42no—
691C3×C4C22×C22⋊C411yescharacteristic
692C3×C4C2×C4×D411yescharacteristic
693C3×C4C2×#12111yescharacteristic
694C3×C4C2×#12711yescharacteristic
695Dic3—42no—
696Dic3—42no—
697Dic3#39012yes—
698Dic3#39012yes—
699C23—31no—
700C23—31no—
701C23—32no—
702C23—32no—
703C23—62no—
704C23—122no—
705C23—121no—
706C23—121no—
707C23—242no—
708C23D3×#4111yescharacteristic
709Q8—22no—
710Q8—22no—
711Q8—22no—
712Q8—22no—
713Q8—41no—
714Q8—41no—
715Q8—41no—
716Q8—41no—
717Q8—62no—
718Q8—62no—
719Q8—124no—
720Q8—124no—
721Q8—121no—
722Q8—121no—
723D4—62no—
724D4—62no—
725D4—124no—
726D4—124no—
727D4—121no—
728D4—121no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—32no—
733C2×C4—32no—
734C2×C4—31no—
735C2×C4—31no—
736C2×C4—32no—
737C2×C4—32no—
738C2×C4—32no—
739C2×C4—32no—
740C2×C4—32no—
741C2×C4—32no—
742C2×C4—32no—
743C2×C4—32no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—62no—
749C2×C4—62no—
750C2×C4—124no—
751C2×C4—124no—
752C2×C4—124no—
753C2×C4—124no—
754C2×C4—121no—
755C2×C4—121no—
756C2×C4—242no—
757C2×C4C22×C4×D311yescharacteristic
758C2×C4C2×D3×D411yescharacteristic
759C2×C4C2×D3×D411yescharacteristic
760C2×C4C2×D3×D411yescharacteristic
761C2×C4C2×D3×D411yescharacteristic
762C2×C4D3×#4111yescharacteristic
763C8—22no—
764C8—32no—
765C8—32no—
766C8—41no—
767C8—41no—
768C8—62no—
769C8—121no—
770C8—121no—
771C8D3×C22⋊C412yes—
772C8D3×C22⋊C412yes—
773C2×C3—21no—
774C2×C3—21no—
775C2×C3C2×#39011yescharacteristic
776C2×C3#306912yes—
777D3—22no—
778D3—22no—
779D3—82no—
780C22—22no—
781C22—32no—
782C22—32no—
783C22—62no—
784C22—62no—
785C22—122no—
786C22—122no—
787C22—122no—
788C22—242no—
789C22—242no—
790C22—242no—
791C22C4×D3×D411yescharacteristic
792C22D3×#12111yescharacteristic
793C22D3×#12411yescharacteristic
794C4—32no—
795C4—32no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—122no—
800C4—122no—
801C4C2×D3×C22⋊C411yescharacteristic
802C4C4×D3×D411yescharacteristic
803C4D3×#12111yescharacteristic
804C4D3×#12711yescharacteristic
805C3#2125011yescharacteristic, complemented, Sylow
806C2—21no—
807C2—21no—
808C2—62no—
809C2—62no—
810C2—242no—
811C2D3×#39011yescharacteristic
812C2#8094412yes—
subgroupG/H
centerC22D3×#121
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1979C2
socleC22×C3C2×#121
prime radicalC22×#239C22
cosocleC22×C3×C4C24
hypercenter#1979D3
hypocenterC3#21250
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1979

Complements

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

NH ≅ G/Ntype
2. C2×#4893C2semidirect
4. D3×#419C2semidirect
6. C2×D3×#101C2semidirect
7. #78548C2semidirect
8. C3×#1979C2semidirect
9. #72069C2semidirect
10. #70708C2semidirect
11. #70336C2semidirect
12. #70335C2semidirect
13. #70108C2semidirect
14. #70107C2semidirect
15. #69902C2semidirect
27. C2×#918C4semidirect
79. #1979D3semidirect
112. C2×C3×Q16C2×C4semidirect
121. C2×#216C2×C4semidirect
125. C2×#215C2×C4semidirect
144. C2×#204C2×C4semidirect
404. C2×Q16C4×D3semidirect
805. C3#21250semidirect

Maximal subgroups

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

subgroupindex
C22×#9182
C2×#48932
#789562
D3×#4192
C2×#47512
C2×D3×#1012
#785482
C3×#19792
#720692
#707082
#703362
#703352
#701082
#701072
#699022
#212503