Finite Group Databasebeta

← #10944024

Subgroups — #10944024

Order 768.

1468 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
1C2×#5522C211yesmaximal, characteristic
2#82811C211yesmaximal, characteristic, complemented
3C2×#5047C211yesmaximal, characteristic
4C2×#4795C211yesmaximal, characteristic, complemented
5C2×#4818C211yesmaximal, characteristic, complemented
6C2×#4733C211yesmaximal, characteristic
7C3×#1873C211yesmaximal, characteristic, complemented
8#71585C211yesmaximal, characteristic, complemented
9#70281C211yesmaximal, characteristic, complemented
10#70276C211yesmaximal, characteristic, complemented
11#69908C211yesmaximal, characteristic, complemented
12#68908C211yesmaximal, characteristic, complemented
13#68904C211yesmaximal, characteristic, complemented
14#68896C211yesmaximal, characteristic, complemented
15#68892C211yesmaximal, characteristic, complemented
16#32907—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×#117C2211yescharacteristic
20C2×#944C2211yescharacteristic
21C22×#216C2211yescharacteristic
22C22×#215C2211yescharacteristic
23C2×#924C2211yescharacteristic
24C22×C4×Dic3C2211yescharacteristic
25C22×Dic12C2211yescharacteristic
26C22×#204C2211yescharacteristic
27#5522—24no—
28#5522—24no—
29C2×#893C2211yescharacteristic
30C2×#893C2211yescharacteristic
31C2×#887C2211yescharacteristic
32C2×#887C2211yescharacteristic
33C2×#67⋊C4—21no—
34C2×#67⋊C4—21no—
35C2×#872—21no—
36C2×C42×D3—21no—
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40#5229C2211yescharacteristic
41C2×#830C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×#816C2211yescharacteristic
44C2×Dic3⋊C8C2211yescharacteristic
45C2×Dic3⋊C8C2211yescharacteristic
46#5047—24no—
47#4976—21no—
48#4976—21no—
49#4975C2211yescharacteristic
50#4973C2211yescharacteristic
51C2×#810C2211yescharacteristic
52C2×#810C2211yescharacteristic
53C2×#810C2211yescharacteristic
54C2×#809C2211yescharacteristic
55#4942—21no—
56#4942—21no—
57#4818—24no—
58#4795—24no—
59#4733—24no—
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62#4550C2211yescharacteristic
63#4550C2211yescharacteristic
64#4529C2211yescharacteristic
65#4529C2211yescharacteristic
66C2×C4×#41—31no—
67C2×#462—31no—
68C2×#461—31no—
69C2×#452—31no—
70C2×#452—31no—
71#2857—31no—
72#1878—31no—
73#1878—31no—
74#1877—31no—
75#1877—31no—
76#1873—31no—
77#1873D311yescharacteristic, complemented
78#1803—31no—
79#1802—31no—
80#1797—31no—
81C22×C3×Q8C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67—21no—
84C23×Dic3D411yescharacteristic
85C23×Dic3D411yescharacteristic
86C2×#235—22no—
87C2×#235—22no—
88C2×#235—22no—
89C2×#235—22no—
90C2×#235—22no—
91C2×#235D414yes—
92C22×D12C2311yescharacteristic
93C22×C4×D3—21no—
94C22×C4×D3—21no—
95C22×C4×D3—21no—
96C22×Dic6C2311yescharacteristic
97C22×Dic6C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C3×C22⋊Q8—22no—
101C3×C22⋊Q8—22no—
102C3×#117—22no—
103C3×#117—22no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C42—21no—
111C2×#217—21no—
112#944—22no—
113#944—22no—
114C2×#216—22no—
115C2×#216—22no—
116C2×#216—22no—
117C2×#215—22no—
118C2×#215—22no—
119C2×#215—22no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122C2×C4⋊Dic3C2311yescharacteristic
123#924—22no—
124#924—22no—
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×C4×Dic3—21no—
133C2×C4×Dic3—21no—
134C2×C4×Dic3—22no—
135C2×C4×Dic3—22no—
136C2×C4×Dic3D411yescharacteristic
137C2×C4×Dic3D411yescharacteristic
138C2×C4×Dic3C2311yescharacteristic
139C2×C4×Dic3C2311yescharacteristic
140C22×C3⋊C8C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142C2×Dic12—22no—
143C2×Dic12—22no—
144C2×Dic12—22no—
145C2×#204—22no—
146C2×#204—22no—
147C2×#204—22no—
148#893—22no—
149#893—22no—
150#893—22no—
151#893D414yes—
152#887—22no—
153#887—22no—
154#887—22no—
155#887D414yes—
156#67⋊C4—28no—
157#67⋊C4—28no—
158#872—28no—
159C42×D3—28no—
160C3×#103—22no—
161C3×#103—22no—
162C3×C22⋊C8—22no—
163C3⋊#95—21no—
164C3⋊#95—21no—
165C3⋊#95—21no—
166C3⋊#95—21no—
167#830—22no—
168#821—22no—
169#816—22no—
170Dic3⋊C8—22no—
171Dic3⋊C8—22no—
172#810—22no—
173#810—22no—
174#810—22no—
175#809—22no—
176C22×#41—31no—
177C22×Q16—31no—
178C22×Q16—31no—
179C22×SD16—31no—
180C22×SD16—31no—
181C2×C4⋊Q8—31no—
182C2×C22⋊Q8—31no—
183C2×C22⋊Q8C2×D311yescharacteristic
184C4×#41—64no—
185C4×#41—64no—
186C2×C4×Q8—31no—
187C2×C4×Q8—31no—
188C2×C4×D4—31no—
189C2×C4×D4—31no—
190C2×C4×D4—61no—
191C2×C4×D4—61no—
192C2×#117—61no—
193C2×#117C2×D311yescharacteristic
194C22×C42—31no—
195C22×C42—61no—
196#462—64no—
197#461—64no—
198#452—64no—
199#452—64no—
200C2×C4⋊C8—31no—
201C2×C4⋊C8—31no—
202C2×#103—31no—
203C2×#103—31no—
204C2×#103—31no—
205C2×#103—31no—
206C2×#103C2×D311yescharacteristic
207C2×#103C2×D311yescharacteristic
208C2×#102—31no—
209C2×#102—31no—
210C2×C22⋊C8—31no—
211C2×C22⋊C8C2×D311yescharacteristic
212#391—31no—
213#391—31no—
214#389—61no—
215#389—61no—
216#384—31no—
217#380—61no—
218#380—61no—
219#340—31no—
220#340—31no—
221#340C2×D311yescharacteristic
222#340C2×D311yescharacteristic
223#336—31no—
224#336—31no—
225C24×C3C2×D411yescharacteristic
226C23×D3—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8—21no—
231C2×C3×Q8—21no—
232C2×C3×Q8—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×C4—21no—
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2×D412yes—
243C22×C3×C4#4112yes—
244C22×C3×C4C2411yescharacteristic
245C2×#67—24no—
246C2×#67—24no—
247C2×#67—24no—
248C22×Dic3—21no—
249C22×Dic3—22no—
250C22×Dic3—22no—
251C22×Dic3—22no—
252C22×Dic3—22no—
253C22×Dic3—22no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3—41no—
257C22×Dic3C2×D411yescharacteristic
258C22×Dic3C2×D411yescharacteristic
259C22×Dic3C2×D411yescharacteristic
260C22×Dic3C2×D411yescharacteristic
261#235—28no—
262#235—28no—
263#235—28no—
264#235—28no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12C2×D412yes—
269C2×D12C2×D412yes—
270C2×D12#4112yes—
271C2×C4×D3—24no—
272C2×C4×D3—24no—
273C2×C4×D3—24no—
274C2×C4×D3—24no—
275C2×C4×D3—24no—
276C2×C4×D3—42no—
277C2×C4×D3—42no—
278C2×C4×D3—42no—
279C2×C4×D3—42no—
280C2×Dic6—21no—
281C2×Dic6—21no—
282C2×Dic6—21no—
283C2×Dic6—21no—
284C2×Dic6—21no—
285C2×Dic6—21no—
286C2×Dic6—21no—
287C2×Dic6—21no—
288C2×Dic6—21no—
289C2×Dic6C2×D412yes—
290C2×Dic6C2×D412yes—
291C2×Dic6#4112yes—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8—21no—
297C2×C3×C8—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—42no—
303C3×C4⋊C4C2×D412yes—
304C3×C4⋊C4C2×D412yes—
305C3×C22⋊C4—24no—
306C3×C22⋊C4—42no—
307C3×C42—24no—
308#217—42no—
309#216—44no—
310#215—44no—
311(C2×D3)⋊C4—24no—
312(C2×D3)⋊C4—24no—
313C4⋊Dic3—21no—
314C4⋊Dic3—21no—
315Dic3⋊C4—24no—
316Dic3⋊C4—24no—
317Dic3⋊C4—42no—
318Dic3⋊C4—42no—
319Dic3⋊C4—42no—
320Dic3⋊C4—42no—
321Dic3⋊C4—42no—
322C4×Dic3—24no—
323C4×Dic3—21no—
324C4×Dic3—21no—
325C4×Dic3—22no—
326C4×Dic3—24no—
327C4×Dic3—22no—
328C4×Dic3C2×D412yes—
329C4×Dic3C2×D412yes—
330C2×C3⋊C8—21no—
331C2×C3⋊C8—21no—
332C2×C3⋊C8—21no—
333C2×C3⋊C8—21no—
334C2×C3⋊C8—21no—
335C2×C3⋊C8—21no—
336Dic12—44no—
337#204—44no—
338C2×#41—34no—
339C2×#41—62no—
340C2×#41—62no—
341C2×#41—62no—
342C2×#41—62no—
343C2×#41—62no—
344C22×Q8—31no—
345C22×Q8—31no—
346C22×Q8C22×D311yescharacteristic
347C22×D4—31no—
348C22×D4—61no—
349C23×C4—31no—
350C23×C4—31no—
351C23×C4—61no—
352C23×C4—61no—
353C23×C4—61no—
354C23×C4C22×D311yescharacteristic
355C2×Q16—62no—
356C2×Q16—62no—
357C2×Q16—62no—
358C2×Q16—62no—
359C2×Q16—62no—
360C2×Q16—62no—
361C2×SD16—62no—
362C2×SD16—62no—
363C2×SD16—62no—
364C2×SD16—62no—
365C2×SD16—62no—
366C2×SD16—62no—
367C22×C8—31no—
368C22×C8—31no—
369C22×C8C22×D311yescharacteristic
370C22×C8C22×D311yescharacteristic
371C4⋊Q8—62no—
372C4⋊Q8—62no—
373C22⋊Q8—22no—
374C22⋊Q8—22no—
375C22⋊Q8—62no—
376C22⋊Q8—62no—
377C4×Q8—34no—
378C4×Q8—62no—
379C4×Q8—62no—
380C4×Q8—62no—
381C4×D4—34no—
382C4×D4—62no—
383C4×D4—68no—
384C4×D4—68no—
385C4×D4—62no—
386C4×D4—62no—
387#117—22no—
388#117—22no—
389#117—68no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—61no—
393C2×C4⋊C4—61no—
394C2×C4⋊C4—61no—
395C2×C4⋊C4—61no—
396C2×C4⋊C4—61no—
397C2×C4⋊C4—61no—
398C2×C4⋊C4—61no—
399C2×C4⋊C4C22×D311yescharacteristic
400C2×C4⋊C4C22×D311yescharacteristic
401C2×C4⋊C4C22×D311yescharacteristic
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—61no—
405C2×C22⋊C4—61no—
406C2×C22⋊C4—61no—
407C2×C42—21no—
408C2×C42—31no—
409C2×C42—31no—
410C2×C42—31no—
411C2×C42—31no—
412C2×C42—68no—
413C2×C42—62no—
414C2×C42—62no—
415C2×C42—61no—
416C2×C42—61no—
417C4⋊C8—62no—
418C4⋊C8—62no—
419#103—22no—
420#103—22no—
421#103—62no—
422#103—62no—
423#103—62no—
424#103—62no—
425#102—62no—
426#102—62no—
427C22⋊C8—22no—
428C22⋊C8—62no—
429#95—61no—
430#95—61no—
431#95—61no—
432#95—61no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—21no—
438C23×C3—21no—
439C23×C3#12112yes—
440C23×C3C22×D411yescharacteristic
441C22×D3—22no—
442C22×D3—22no—
443C22×D3—22no—
444C22×D3—41no—
445C22×D3—41no—
446C22×D3—41no—
447C22×D3—41no—
448C3×Q8—41no—
449C3×Q8—41no—
450C3×Q8—41no—
451C3×Q8—41no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4#12112yes—
471C2×C3×C4C22×D411yescharacteristic
472C2×C3×C4C22×D411yescharacteristic
473C2×C3×C4C22×D411yescharacteristic
474C2×C3×C4C2×#4111yescharacteristic
475C2×C3×C4C2×#4111yescharacteristic
476C2×C3×C4C2×#4111yescharacteristic
477#67—216no—
478C2×Dic3—21no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—44no—
489C2×Dic3—44no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496C2×Dic3#12012yes—
497C2×Dic3#12012yes—
498C2×Dic3#13512yes—
499C2×Dic3#13712yes—
500C2×Dic3#13712yes—
501D12—22no—
502D12—22no—
503D12—22no—
504D12#12114yes—
505C4×D3—216no—
506C4×D3—48no—
507C4×D3—48no—
508Dic6—22no—
509Dic6—22no—
510Dic6—22no—
511Dic6—41no—
512Dic6—41no—
513Dic6—41no—
514Dic6—41no—
515Dic6#12114yes—
516C3×C8—41no—
517C3×C8—41no—
518C3⋊C8—41no—
519C3⋊C8—41no—
520C24—61no—
521C24D3×D411yescharacteristic
522#41—68no—
523#41—68no—
524#41—68no—
525#41—68no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—32no—
533C2×Q8—32no—
534C2×Q8—32no—
535C2×Q8—61no—
536C2×Q8—61no—
537C2×Q8—61no—
538C2×Q8—61no—
539C2×Q8—61no—
540C2×Q8—61no—
541C2×Q8—61no—
542C2×Q8—61no—
543C2×Q8—61no—
544C2×D4—32no—
545C2×D4—32no—
546C2×D4—32no—
547C2×D4—64no—
548C2×D4—64no—
549C2×D4—64no—
550C2×D4—61no—
551C2×D4—61no—
552C2×D4—61no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—31no—
562C22×C4—31no—
563C22×C4—31no—
564C22×C4—31no—
565C22×C4—64no—
566C22×C4—64no—
567C22×C4—64no—
568C22×C4—64no—
569C22×C4—62no—
570C22×C4—62no—
571C22×C4—62no—
572C22×C4—62no—
573C22×C4—62no—
574C22×C4—61no—
575C22×C4—64no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—122no—
579C22×C4—122no—
580C22×C4—122no—
581C22×C4—122no—
582C22×C4—121no—
583C22×C4#23512yes—
584C22×C4D3×D411yescharacteristic
585C22×C4D3×D412yes—
586C22×C4C23×D311yescharacteristic
587Q16—124no—
588Q16—124no—
589SD16—124no—
590SD16—124no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—61no—
598C2×C8—61no—
599C2×C8—61no—
600C2×C8—61no—
601C2×C8—61no—
602C2×C8—61no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—42no—
608C4⋊C4—64no—
609C4⋊C4—64no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—122no—
613C4⋊C4—122no—
614C4⋊C4—122no—
615C4⋊C4—122no—
616C4⋊C4—122no—
617C4⋊C4D3×D412yes—
618C4⋊C4D3×D412yes—
619C22⋊C4—24no—
620C22⋊C4—42no—
621C22⋊C4—64no—
622C22⋊C4—64no—
623C22⋊C4—122no—
624C42—24no—
625C42—32no—
626C42—32no—
627C42—62no—
628C42—62no—
629C42—64no—
630C42—64no—
631C42—61no—
632C42—61no—
633C22×C3—22no—
634C22×C3—22no—
635C22×C3—22no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3C2×#12011yescharacteristic
641C22×C3C2×#12111yescharacteristic
642C22×C3#52511yescharacteristic
643C22×C3C2×#13511yescharacteristic
644C22×C3C2×#13711yescharacteristic
645C22×C3C2×#13711yescharacteristic
646C22×C3#57511yescharacteristic
647C2×D3—24no—
648C2×D3—42no—
649C2×D3—42no—
650C2×D3—42no—
651C2×D3—42no—
652C2×D3—42no—
653C2×D3—42no—
654C3×C4—22no—
655C3×C4—42no—
656C3×C4—42no—
657C3×C4—81no—
658C3×C4—81no—
659C3×C4C2×#12111yescharacteristic
660C3×C4C2×#12111yescharacteristic
661C3×C4#52511yescharacteristic
662C3×C4#52511yescharacteristic
663Dic3—24no—
664Dic3—22no—
665Dic3—22no—
666Dic3—41no—
667Dic3—81no—
668Dic3—81no—
669Dic3#45214yescomplemented
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—62no—
677C23—62no—
678C23—62no—
679C23—121no—
680C23—121no—
681C23—121no—
682C23—121no—
683C23#88412yes—
684C23C2×D3×D411yescharacteristic
685Q8—34no—
686Q8—41no—
687Q8—41no—
688Q8—41no—
689Q8—41no—
690Q8—62no—
691Q8—62no—
692Q8—62no—
693Q8—121no—
694Q8—121no—
695Q8—121no—
696Q8—121no—
697D4—34no—
698D4—616no—
699D4—62no—
700D4—62no—
701D4—62no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—32no—
711C2×C4—32no—
712C2×C4—32no—
713C2×C4—32no—
714C2×C4—32no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—616no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—62no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—128no—
737C2×C4—124no—
738C2×C4—128no—
739C2×C4—124no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4—121no—
743C2×C4—121no—
744C2×C4—121no—
745C2×C4—121no—
746C2×C4#88412yes—
747C2×C4C2×#23511yescharacteristic
748C2×C4C2×D3×D411yescharacteristic
749C2×C4C2×D3×D411yescharacteristic
750C2×C4C2×D3×D411yescharacteristic
751C2×C4D3×#4111yescharacteristic
752C2×C4D3×#4111yescharacteristic
753C8—41no—
754C8—41no—
755C8—121no—
756C8—121no—
757C2×C3—42no—
758C2×C3#284711yescharacteristic
759C2×C3C2×#45211yescharacteristic
760C2×C3#300711yescharacteristic
761C2×C3#303511yescharacteristic
762C2×C3#303911yescharacteristic
763C2×C3#310711yescharacteristic
764C2×C3#311611yescharacteristic
765D3—44no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—64no—
774C22—122no—
775C22—122no—
776C22—122no—
777C22—122no—
778C22—122no—
779C22—122no—
780C22C2×#88411yescharacteristic
781C22D3×#12011yescharacteristic
782C22#565611yescharacteristic
783C22D3×#13511yescharacteristic
784C22#576811yescharacteristic
785C22D3×#13711yescharacteristic
786C22D3×#13711yescharacteristic
787C4—22no—
788C4—34no—
789C4—42no—
790C4—42no—
791C4—62no—
792C4—62no—
793C4—64no—
794C4—81no—
795C4—81no—
796C4—121no—
797C4—241no—
798C4—241no—
799C4#554711yescharacteristic
800C4#554711yescharacteristic
801C4D3×#12111yescharacteristic
802C4D3×#12111yescharacteristic
803C3#3290711yescharacteristic, complemented, Sylow
804C2—42no—
805C2—124no—
806C2#7493511yescharacteristic
807C2#7886111yescharacteristic
808C2#7897411yescharacteristic
809C2D3×#45211yescharacteristic
810C2#8022811yescharacteristic
811C2#8149311yescharacteristic
812C2#8149511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1873C2
socleC23×C3C22×D4
prime radicalC22×#235C22
hypercenter#1873D3
hypocenterC3#32907
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
2. #82811C2semidirect
4. C2×#4795C2semidirect
5. C2×#4818C2semidirect
7. C3×#1873C2semidirect
8. #71585C2semidirect
9. #70281C2semidirect
10. #70276C2semidirect
11. #69908C2semidirect
12. #68908C2semidirect
13. #68904C2semidirect
14. #68896C2semidirect
15. #68892C2semidirect
77. #1873D3semidirect
669. Dic3#452semidirect
803. C3#32907semidirect

Maximal subgroups

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

subgroupindex
C2×#55222
#828112
C2×#50472
C2×#47952
C2×#48182
C2×#47332
C3×#18732
#715852
#702812
#702762
#699082
#689082
#689042
#688962
#688922
#329073