Finite Group Databasebeta

← #10828172

Subgroups — #10828172

Order 768.

1344 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5831C211yesmaximal, characteristic
2C2×D3×#103C211yesmaximal, characteristic, complemented
3C2×#4777C211yesmaximal, characteristic, complemented
4#73912C211yesmaximal, characteristic, complemented
5C3×#1788C211yesmaximal, characteristic, complemented
6#72135C211yesmaximal, characteristic, complemented
7#70266C211yesmaximal, characteristic, complemented
8#70238C211yesmaximal, characteristic, complemented
9#70237C211yesmaximal, characteristic, complemented
10#70216C211yesmaximal, characteristic, complemented
11#70202C211yesmaximal, characteristic, complemented
12#70178C211yesmaximal, characteristic, complemented
13#69957C211yesmaximal, characteristic, complemented
14#69936C211yesmaximal, characteristic, complemented
15#69526C211yesmaximal, characteristic, complemented
16#24036—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×D3×Q8C2211yescharacteristic
19#5831—24no—
20#5831—24no—
21C2×Q8×Dic3C2211yescharacteristic
22C2×#938—21no—
23C2×#938C2211yescharacteristic
24C2×#936—21no—
25C2×#936C2211yescharacteristic
26C2×C4×#67—21no—
27C2×C4×#67C2211yescharacteristic
28C2×#924—21no—
29C2×#924C2211yescharacteristic
30C22×D3×C8C2211yescharacteristic
31C2×D3×C4⋊C4C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×C22⋊C8C2211yescharacteristic
37C3×#380C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic
42#5212C2211yescharacteristic
43C2×#830C2211yescharacteristic
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×#817C2211yescharacteristic
46C2×#816C2211yescharacteristic
47C2×#816C2211yescharacteristic
48#4987C2211yescharacteristic
49#4984C2211yescharacteristic
50#4972C2211yescharacteristic
51C2×#810C2211yescharacteristic
52C2×#810C2211yescharacteristic
53C2×#808C2211yescharacteristic
54#4956—21no—
55#4949—21no—
56D3×#103—24no—
57#4777—24no—
58#4668—21no—
59#4658—21no—
60#4551C2211yescharacteristic
61#4550C2211yescharacteristic
62#4550C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#548—31no—
65C2×#481—31no—
66C22×#103—31no—
67#2487—31no—
68#2042—31no—
69#2042—31no—
70#2035—31no—
71#2035—31no—
72#1893—31no—
73#1869—31no—
74#1865—31no—
75#1865—31no—
76#1788—31no—
77#1788D311yescharacteristic, complemented
78#1787—31no—
79C2×C3×#41—22no—
80C2×C3×#41—22no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—41no—
84C2×C3×#41—41no—
85C22×C3×Q8C2311yescharacteristic
86C22×C3×D4—21no—
87C22×C3×D4C2311yescharacteristic
88C23×C3×C4—21no—
89C23×C3×C4C2311yescharacteristic
90C22×#67—21no—
91C22×#67D411yescharacteristic
92C2×D3×Q8—22no—
93C2×D3×Q8—22no—
94C2×D3×Q8—22no—
95C2×D3×Q8—41no—
96C2×D3×Q8—41no—
97C2×D3×Q8D414yes—
98C22×C4×D3—21no—
99C22×C4×D3—21no—
100C22×C4×D3C2311yescharacteristic
101C22×Dic6—21no—
102C22×Dic6C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C22×C3×C8C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C22⋊C4—21no—
108C2×#217—21no—
109C2×#217—21no—
110C2×#217—21no—
111C2×#217—21no—
112C2×#217—21no—
113C2×#217D411yescharacteristic
114Q8×Dic3—22no—
115Q8×Dic3—22no—
116#938—28no—
117#938—22no—
118#938D414yes—
119#936—28no—
120#936—22no—
121#936—22no—
122C4×#67—28no—
123C4×#67—22no—
124C4×#67—22no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4D411yescharacteristic
127C2×C4⋊Dic3—21no—
128C2×C4⋊Dic3—21no—
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131C2×C4⋊Dic3C2311yescharacteristic
132#924—28no—
133#924—22no—
134#924—22no—
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4—21no—
138C2×Dic3⋊C4D411yescharacteristic
139C2×C4×Dic3—21no—
140C2×C4×Dic3C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C2×D3×C8—22no—
144C2×D3×C8—41no—
145C2×D3×C8—41no—
146D3×C4⋊C4—22no—
147D3×C4⋊C4—22no—
148C3×#103—22no—
149C3×#103—22no—
150C3×#102—22no—
151C3×#102—41no—
152C3×C22⋊C8—41no—
153C3×#95—21no—
154#835—22no—
155#835—22no—
156#832—22no—
157#832—41no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162#830—41no—
163(C2×D3)⋊C8—22no—
164#817—22no—
165#816—22no—
166#816—41no—
167#810—22no—
168#810—41no—
169#808—22no—
170C22×#41C2×D311yescharacteristic
171C23×Q8—31no—
172C23×C8—31no—
173#548—64no—
174#548—64no—
175C2×#124—31no—
176C2×#124—61no—
177C2×C22⋊Q8—31no—
178C2×C22⋊Q8—61no—
179C2×#121—31no—
180C2×#121—61no—
181C2×C4×Q8—31no—
182C2×C4×D4—31no—
183C2×C4×D4—61no—
184C22×C4⋊C4—31no—
185#481—64no—
186C2×#106—31no—
187C2×#106—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—64no—
195C2×#103C2×D311yescharacteristic
196C2×#103C2×D311yescharacteristic
197C2×#102—31no—
198C2×#102—31no—
199C2×#102C2×D311yescharacteristic
200C2×#102C2×D311yescharacteristic
201C2×C22⋊C8—31no—
202C2×C22⋊C8—31no—
203C2×C22⋊C8C2×D311yescharacteristic
204#400—61no—
205#399—61no—
206#389—31no—
207#389—31no—
208#386—61no—
209#385—61no—
210#380—31no—
211#380—31no—
212#380C2×D311yescharacteristic
213#340—31no—
214#340—31no—
215#336—31no—
216#336—31no—
217C24×C3—21no—
218C24×C3C2×D411yescharacteristic
219C23×D3C2×D411yescharacteristic
220C3×#41—44no—
221C3×#41—44no—
222C3×#41—44no—
223C3×#41—44no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8C2×D412yes—
228C2×C3×Q8#4112yes—
229C2×C3×Q8#4112yes—
230C2×C3×D4—24no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—42no—
237C2×C3×D4—42no—
238C2×C3×D4C2×D412yes—
239C22×C3×C4—21no—
240C22×C3×C4—24no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—42no—
250C22×C3×C4—42no—
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2411yescharacteristic
253C2×#67—22no—
254C2×#67—24no—
255C2×#67—22no—
256C2×#67—22no—
257C2×#67—42no—
258C2×#67—42no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3C2×D411yescharacteristic
264C22×Dic3C2×D411yescharacteristic
265C22×Dic3C2×D411yescharacteristic
266D3×Q8—28no—
267D3×Q8—44no—
268D3×Q8—44no—
269D3×Q8—44no—
270C2×C4×D3—21no—
271C2×C4×D3—21no—
272C2×C4×D3—21no—
273C2×C4×D3—21no—
274C2×C4×D3—24no—
275C2×C4×D3—42no—
276C2×C4×D3—42no—
277C2×C4×D3—42no—
278C2×C4×D3—81no—
279C2×C4×D3—81no—
280C2×C4×D3C2×D412yes—
281C2×C4×D3C2×D412yes—
282C2×Dic6—21no—
283C2×Dic6—21no—
284C2×Dic6—21no—
285C2×Dic6—21no—
286C2×Dic6—21no—
287C2×Dic6—24no—
288C2×Dic6—42no—
289C2×Dic6—42no—
290C2×Dic6C2×D412yes—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8—21no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—21no—
301C3×C22⋊C4—81no—
302#217—24no—
303#217—24no—
304#217—24no—
305#217—24no—
306#217—22no—
307#217—81no—
308(C2×D3)⋊C4—22no—
309(C2×D3)⋊C4—42no—
310C4⋊Dic3—24no—
311C4⋊Dic3—21no—
312C4⋊Dic3—21no—
313C4⋊Dic3—21no—
314C4⋊Dic3—21no—
315C4⋊Dic3—21no—
316C4⋊Dic3—81no—
317C4⋊Dic3C2×D412yes—
318Dic3⋊C4—24no—
319Dic3⋊C4—22no—
320Dic3⋊C4—42no—
321Dic3⋊C4—81no—
322C4×Dic3—24no—
323C4×Dic3—21no—
324C4×Dic3—21no—
325C2×C3⋊C8—21no—
326C2×C3⋊C8—21no—
327C2×C3⋊C8—21no—
328C2×C3⋊C8—21no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331D3×C8—44no—
332C2×#41—22no—
333C2×#41—22no—
334C2×#41—22no—
335C2×#41—22no—
336C2×#41—41no—
337C2×#41—41no—
338C22×Q8—34no—
339C22×Q8—31no—
340C22×Q8—61no—
341C22×Q8—62no—
342C22×Q8—62no—
343C22×Q8—62no—
344C22×Q8—121no—
345C22×Q8—121no—
346C22×Q8C22×D311yescharacteristic
347C22×D4—21no—
348C22×D4—31no—
349C22×D4—61no—
350C22×D4C22×D311yescharacteristic
351C23×C4—21no—
352C23×C4—31no—
353C23×C4—61no—
354C23×C4—61no—
355C23×C4C22×D311yescharacteristic
356C22×C8—31no—
357C22×C8—31no—
358C22×C8—62no—
359C22×C8—121no—
360C22×C8—121no—
361C22×C8C22×D311yescharacteristic
362C22×C8C22×D311yescharacteristic
363#124—62no—
364#124—68no—
365#124—62no—
366C22⋊Q8—62no—
367C22⋊Q8—62no—
368C22⋊Q8—68no—
369#121—34no—
370#121—62no—
371#121—68no—
372C4×Q8—62no—
373C4×Q8—62no—
374C4×D4—62no—
375C4×D4—62no—
376C4×D4—68no—
377C2×C4⋊C4—31no—
378C2×C4⋊C4—31no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—62no—
382C2×C4⋊C4—62no—
383C2×C4⋊C4—61no—
384C2×C4⋊C4—61no—
385C2×C4⋊C4—61no—
386C2×C4⋊C4—61no—
387C2×C4⋊C4—61no—
388C2×C4⋊C4C22×D311yescharacteristic
389C2×C4⋊C4C22×D311yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—31no—
392C2×C22⋊C4—31no—
393C2×C22⋊C4—61no—
394C2×C22⋊C4—61no—
395C2×C22⋊C4—61no—
396C2×C22⋊C4—61no—
397C2×C22⋊C4—61no—
398C2×C22⋊C4—61no—
399C2×C42—31no—
400C2×C42—61no—
401#106—62no—
402#106—62no—
403#103—22no—
404#103—22no—
405#103—62no—
406#103—62no—
407#103—62no—
408#103—62no—
409#103—121no—
410#103—121no—
411#102—22no—
412#102—41no—
413#102—62no—
414#102—121no—
415C22⋊C8—41no—
416C22⋊C8—62no—
417C22⋊C8—121no—
418#95—21no—
419#95—61no—
420#95—61no—
421#95—61no—
422#95—61no—
423C23×C3—21no—
424C23×C3—22no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3—41no—
437C23×C3C22×D411yescharacteristic
438C22×D3—21no—
439C22×D3—21no—
440C22×D3—21no—
441C22×D3—21no—
442C22×D3#12012yes—
443C22×D3#13512yes—
444C22×D3#13712yes—
445C3×Q8—22no—
446C3×Q8—22no—
447C3×Q8—22no—
448C3×Q8#12314yes—
449C3×D4—22no—
450C3×D4—22no—
451C3×D4—48no—
452C3×D4—41no—
453C3×D4—41no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—48no—
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—41no—
471C2×C3×C4C22×D411yescharacteristic
472C2×C3×C4C22×D411yescharacteristic
473C2×C3×C4C2×#4111yescharacteristic
474C2×C3×C4C2×#4111yescharacteristic
475C2×C3×C4H(5,𝔽2)11yescharacteristic
476C2×C3×C4H(5,𝔽2)11yescharacteristic
477#67—44no—
478#67—48no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498C2×Dic3—41no—
499C2×Dic3#12012yes—
500C4×D3—22no—
501C4×D3—22no—
502C4×D3—22no—
503C4×D3—22no—
504C4×D3—48no—
505C4×D3—84no—
506Dic6—22no—
507Dic6—22no—
508Dic6—48no—
509Dic6—41no—
510Dic6—41no—
511C3×C8—41no—
512C3×C8—41no—
513C3⋊C8—41no—
514C3⋊C8—41no—
515C24—21no—
516C24—31no—
517C24D3×D411yescharacteristic
518#41—44no—
519#41—44no—
520#41—44no—
521#41—44no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—32no—
526C2×Q8—64no—
527C2×Q8—61no—
528C2×Q8—68no—
529C2×Q8—61no—
530C2×Q8—61no—
531C2×Q8—61no—
532C2×Q8—61no—
533C2×Q8—122no—
534C2×Q8—122no—
535C2×Q8—124no—
536C2×Q8—124no—
537C2×Q8—124no—
538C2×Q8#23512yes—
539C2×Q8D3×D412yes—
540C2×Q8#23712yes—
541C2×D4—24no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—64no—
550C2×D4—62no—
551C2×D4—62no—
552C2×D4—62no—
553C2×D4—122no—
554C2×D4—122no—
555C2×D4D3×D412yes—
556C22×C4—21no—
557C22×C4—24no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—31no—
567C22×C4—32no—
568C22×C4—32no—
569C22×C4—31no—
570C22×C4—31no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—64no—
574C22×C4—61no—
575C22×C4—61no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—122no—
583C22×C4—122no—
584C22×C4—122no—
585C22×C4—241no—
586C22×C4—241no—
587C22×C4D3×D411yescharacteristic
588C22×C4C23×D311yescharacteristic
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—61no—
596C2×C8—61no—
597C2×C8—61no—
598C2×C8—61no—
599C2×C8—61no—
600C2×C8—61no—
601C2×C8—124no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—32no—
607C4⋊C4—62no—
608C4⋊C4—64no—
609C4⋊C4—64no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—122no—
616C4⋊C4—241no—
617C4⋊C4—241no—
618C22⋊C4—62no—
619C22⋊C4—62no—
620C22⋊C4—64no—
621C22⋊C4—64no—
622C22⋊C4—64no—
623C22⋊C4—64no—
624C22⋊C4—81no—
625C22⋊C4—122no—
626C22⋊C4—241no—
627C42—64no—
628C42—61no—
629C42—61no—
630C22×C3—42no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—42no—
634C22×C3—41no—
635C22×C3—42no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—81no—
641C22×C3—81no—
642C22×C3—81no—
643C22×C3—81no—
644C22×C3C2×#12011yescharacteristic
645C22×C3#54611yescharacteristic
646C22×C3#54611yescharacteristic
647C22×C3C2×#13511yescharacteristic
648C22×C3C2×#13711yescharacteristic
649C22×C3#57711yescharacteristic
650C22×C3#57711yescharacteristic
651C2×D3—22no—
652C2×D3—22no—
653C2×D3—22no—
654C2×D3—22no—
655C2×D3—22no—
656C2×D3—22no—
657C2×D3#45214yes—
658C3×C4—24no—
659C3×C4—41no—
660C3×C4—81no—
661C3×C4—81no—
662C3×C4C2×#12311yescharacteristic
663C3×C4#53411yescharacteristic
664C3×C4#54611yescharacteristic
665C3×C4#54611yescharacteristic
666Dic3—22no—
667Dic3—42no—
668Dic3—41no—
669Dic3—42no—
670Dic3—41no—
671Dic3—81no—
672Dic3—81no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—22no—
680C23—21no—
681C23—32no—
682C23—32no—
683C23—32no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—61no—
691C23—61no—
692C23—61no—
693C23—61no—
694C23C2×D3×D411yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—62no—
699Q8—62no—
700Q8—128no—
701Q8—121no—
702Q8—121no—
703Q8#88314yes—
704D4—22no—
705D4—22no—
706D4—48no—
707D4—41no—
708D4—41no—
709D4—124no—
710D4—128no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—32no—
718C2×C4—48no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—62no—
732C2×C4—62no—
733C2×C4—62no—
734C2×C4—62no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—62no—
741C2×C4—61no—
742C2×C4—62no—
743C2×C4—128no—
744C2×C4—121no—
745C2×C4—121no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C4—121no—
749C2×C4—121no—
750C2×C4—121no—
751C2×C4—121no—
752C2×C4—121no—
753C2×C4—121no—
754C2×C4—244no—
755C2×C4C2×#23511yescharacteristic
756C2×C4C2×D3×D411yescharacteristic
757C2×C4C2×D3×D411yescharacteristic
758C2×C4C2×#23711yescharacteristic
759C2×C4#100411yescharacteristic
760C2×C4#100411yescharacteristic
761C8—41no—
762C8—41no—
763C8—121no—
764C8—121no—
765C2×C3—81no—
766C2×C3—82no—
767C2×C3#240511yescharacteristic
768C2×C3C2×#45211yescharacteristic
769C2×C3#301011yescharacteristic
770C2×C3#330111yescharacteristic
771C2×C3#330111yescharacteristic
772C2×C3#331611yescharacteristic
773C2×C3#331611yescharacteristic
774D3—24no—
775C22—34no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—42no—
780C22—42no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—42no—
785C22—41no—
786C22—62no—
787C22—62no—
788C22—62no—
789C22—62no—
790C22—62no—
791C22—62no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22#549011yescharacteristic
797C22D3×#12011yescharacteristic
798C22#559111yescharacteristic
799C22D3×#13511yescharacteristic
800C22#577011yescharacteristic
801C22#577511yescharacteristic
802C22D3×#13711yescharacteristic
803C4—24no—
804C4—41no—
805C4—62no—
806C4—81no—
807C4—81no—
808C4—121no—
809C4—122no—
810C4—122no—
811C4—121no—
812C4—241no—
813C4—241no—
814C4C2×#88311yescharacteristic
815C4#549011yescharacteristic
816C4#558911yescharacteristic
817C4#559111yescharacteristic
818C3#2403611yescharacteristic, complemented, Sylow
819C2—64no—
820C2—81no—
821C2—82no—
822C2#7385311yescharacteristic
823C2#7884811yescharacteristic
824C2#7890011yescharacteristic
825C2#8008611yescharacteristic
826C2#8010311yescharacteristic
827C2D3×#45211yescharacteristic
828C2#8025511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1788C2
socleC23×C3C22×D4
prime radicalC2×#5831C2
hypercenter#1788D3
hypocenterC3#24036
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×D3×#103C2semidirect
3. C2×#4777C2semidirect
4. #73912C2semidirect
5. C3×#1788C2semidirect
6. #72135C2semidirect
7. #70266C2semidirect
8. #70238C2semidirect
9. #70237C2semidirect
10. #70216C2semidirect
11. #70202C2semidirect
12. #70178C2semidirect
13. #69957C2semidirect
14. #69936C2semidirect
15. #69526C2semidirect
77. #1788D3semidirect
818. C3#24036semidirect

Maximal subgroups

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

subgroupindex
C2×#58312
C2×D3×#1032
C2×#47772
#739122
C3×#17882
#721352
#702662
#702382
#702372
#702162
#702022
#701782
#699572
#699362
#695262
#240363