Finite Group Databasebeta

← #10810643

Subgroups — #10810643

Order 768.

1490 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5631C211yesmaximal, characteristic
2#82241C211yesmaximal, characteristic, complemented
3C2×#5002C211yesmaximal, characteristic, complemented
4C2×#4804C211yesmaximal, characteristic, complemented
5C2×#67⋊C8C211yesmaximal, characteristic, complemented
6C3×#1873C211yesmaximal, characteristic, complemented
7#71696C211yesmaximal, characteristic, complemented
8#70267C211yesmaximal, characteristic, complemented
9#70229C211yesmaximal, characteristic, complemented
10#70225C211yesmaximal, characteristic, complemented
11#69960C211yesmaximal, characteristic, complemented
12#68892C211yesmaximal, characteristic, complemented
13#68882C211yesmaximal, characteristic, complemented
14#68879C211yesmaximal, characteristic, complemented
15#68780C211yesmaximal, characteristic, complemented
16#22417—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×#235C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×C3×#117C2211yescharacteristic
21C2×#944C2211yescharacteristic
22C2×C4×#67C2211yescharacteristic
23C23×C3⋊C8C2211yescharacteristic
24C22×D3×C8C2211yescharacteristic
25#5631—24no—
26#5631C418yescomplemented
27C2×#897C2211yescharacteristic
28C2×#894—21no—
29C2×#893C2211yescharacteristic
30C2×#892C2211yescharacteristic
31C2×D3×C4⋊C4—21no—
32C2×#884—21no—
33C2×#883—21no—
34C2×C3×#103C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C2×C3×C22⋊C8C2211yescharacteristic
37C2×#835C2211yescharacteristic
38C2×#835C2211yescharacteristic
39#5212C2211yescharacteristic
40C2×#821C2211yescharacteristic
41C2×#821C2211yescharacteristic
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×#816C2211yescharacteristic
44C2×#816C2211yescharacteristic
45C2×Dic3⋊C8C2211yescharacteristic
46C2×C8×Dic3C2211yescharacteristic
47#5002—24no—
48#4987C2211yescharacteristic
49#4975C2211yescharacteristic
50Dic3×C4⋊C4C2211yescharacteristic
51C2×#810C2211yescharacteristic
52C2×#810C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#809C2211yescharacteristic
55#4957—21no—
56#4944—21no—
57#4940—21no—
58C4×Dic3⋊C4—21no—
59#4804—24no—
60#67⋊C8—24no—
61C3×#340C2211yescharacteristic
62C3×#340C2211yescharacteristic
63#4529C2211yescharacteristic
64#4529C2211yescharacteristic
65C2×#547—31no—
66C2×C8×D4—31no—
67C2×#416—31no—
68C2×#416—31no—
69#2354—31no—
70#1981—31no—
71#1956—31no—
72#1892—31no—
73#1892—31no—
74#1873—31no—
75#1873D311yescharacteristic, complemented
76#1802—31no—
77#1788—31no—
78#1788—31no—
79C4×#102—31no—
80C22×C3×Q8C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67—21no—
83C22×#67D411yescharacteristic
84C2×#239—22no—
85C2×#239—22no—
86C2×#239—22no—
87C2×#239—41no—
88C2×#239—41no—
89C2×#239C2×C414yes—
90C2×#235—22no—
91C2×#235—22no—
92C2×#235—22no—
93C2×#235—41no—
94C2×#235—41no—
95C2×#235C2×C414yes—
96C22×D12—21no—
97C22×D12C2311yescharacteristic
98C22×C4×D3—21no—
99C22×C4×D3—21no—
100C22×C4×D3—21no—
101C22×C4×D3C2311yescharacteristic
102C22×Dic6C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C22×C3×C8C2311yescharacteristic
105C3×C22⋊Q8—22no—
106C3×C22⋊Q8C2×C414yes—
107C3×#117—22no—
108C3×#117—41no—
109C2×C3×C4⋊C4—21no—
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4—21no—
115C2×C3×C42—21no—
116C2×#217—21no—
117C2×#217D411yescharacteristic
118#944—22no—
119#944C2×C414yes—
120C4×#67C2×C414yes—
121C4×#67D414yes—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4D411yescharacteristic
127C2×C4⋊Dic3—21no—
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4D411yescharacteristic
135C2×C4×Dic3—21no—
136C2×C4×Dic3—21no—
137C2×C4×Dic3C2311yescharacteristic
138C22×C3⋊C8—22no—
139C22×C3⋊C8—22no—
140C22×C3⋊C8—41no—
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C2×D3×C8—22no—
144C2×D3×C8—22no—
145C2×D3×C8—41no—
146#897—22no—
147#897C2×C414yes—
148#894—28no—
149#893—22no—
150#893C2×C414yes—
151#892—22no—
152#892—41no—
153D3×C4⋊C4—28no—
154#884—28no—
155#883—28no—
156C3×#103—22no—
157C3×#103—41no—
158C3×C22⋊C8—22no—
159#835—22no—
160#835—41no—
161C3⋊#95—21no—
162C3⋊#95—21no—
163C3⋊#95—21no—
164#821—22no—
165#821—22no—
166(C2×D3)⋊C8—22no—
167#816—41no—
168#816—41no—
169Dic3⋊C8—22no—
170C8×Dic3—22no—
171#810—22no—
172#810—22no—
173#809—22no—
174#809D414yescomplemented
175C22×#41—31no—
176C22×#41—31no—
177C23×C8—31no—
178C23×C8—31no—
179#547—38no—
180#547—64no—
181C2×C4⋊Q8—31no—
182C2×#123—61no—
183C2×#123—61no—
184C2×C22⋊Q8—31no—
185C2×C22⋊Q8C2×D311yescharacteristic
186C2×#121—61no—
187C2×C4×D4—31no—
188C2×C4×D4—31no—
189C2×#117—31no—
190C2×#117C2×D311yescharacteristic
191C22×C4⋊C4—61no—
192C8×D4—64no—
193C2×C4⋊C8—31no—
194#416—64no—
195#416—64no—
196C2×#103—31no—
197C2×#103—31no—
198C2×#103—31no—
199C2×#103—31no—
200C2×#103—31no—
201C2×#103—31no—
202C2×#103C2×D311yescharacteristic
203C2×#103C2×D311yescharacteristic
204C2×#102—31no—
205C2×#102—31no—
206C2×#102—31no—
207C2×#102—31no—
208C2×C22⋊C8—31no—
209C2×C22⋊C8C2×D311yescharacteristic
210C2×C4×C8—31no—
211#390—61no—
212#388—61no—
213#388—61no—
214#384—31no—
215#380—31no—
216#380—31no—
217C4×C4⋊C4—31no—
218C4×C4⋊C4—61no—
219#340—31no—
220#340—31no—
221#340C2×D311yescharacteristic
222#340C2×D311yescharacteristic
223C24×C3C2×D411yescharacteristic
224C23×D3—21no—
225C23×D3C2×D411yescharacteristic
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8—21no—
231C2×C3×Q8C22×C412yes—
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×C4C22×C412yes—
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2×D412yes—
243C22×C3×C4C2411yescharacteristic
244C2×#67—24no—
245C2×#67—22no—
246C2×#67—22no—
247C2×#67—42no—
248C2×#67—42no—
249C2×#67C22⋊C414yes—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3C2×D411yescharacteristic
254C22×Dic3C2×D411yescharacteristic
255C22×Dic3C2×D411yescharacteristic
256#239—28no—
257#239—44no—
258#239—44no—
259#239—44no—
260#235—28no—
261#235—44no—
262#235—44no—
263#235—44no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—24no—
268C2×D12—42no—
269C2×D12—42no—
270C2×D12C22×C412yes—
271C2×D12C2×D412yes—
272C2×D12#4112yes—
273C2×C4×D3—21no—
274C2×C4×D3—21no—
275C2×C4×D3—21no—
276C2×C4×D3—21no—
277C2×C4×D3—24no—
278C2×C4×D3—24no—
279C2×C4×D3—24no—
280C2×C4×D3—42no—
281C2×C4×D3—42no—
282C2×C4×D3—42no—
283C2×C4×D3—42no—
284C2×C4×D3—42no—
285C2×C4×D3—42no—
286C2×C4×D3C22×C412yes—
287C2×C4×D3C2×D412yes—
288C2×Dic6—21no—
289C2×Dic6—21no—
290C2×Dic6—21no—
291C2×Dic6—21no—
292C2×Dic6—21no—
293C2×Dic6C22×C412yes—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8—21no—
297C2×C3×C8—21no—
298C2×C3×C8—21no—
299C2×C3×C8—21no—
300C3×C4⋊C4—24no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4C22×C412yes—
306C3×C4⋊C4C2×D412yes—
307C3×C22⋊C4—24no—
308C3×C22⋊C4—42no—
309C3×C42—42no—
310#217—81no—
311#217C22⋊C414yes—
312(C2×D3)⋊C4—24no—
313(C2×D3)⋊C4—24no—
314(C2×D3)⋊C4—42no—
315(C2×D3)⋊C4—81no—
316(C2×D3)⋊C4C22⋊C414yes—
317C4⋊Dic3—24no—
318C4⋊Dic3—21no—
319C4⋊Dic3—21no—
320C4⋊Dic3—21no—
321C4⋊Dic3—21no—
322Dic3⋊C4—24no—
323Dic3⋊C4—24no—
324Dic3⋊C4—42no—
325Dic3⋊C4—81no—
326Dic3⋊C4C22⋊C414yes—
327C4×Dic3—42no—
328C4×Dic3—42no—
329C4×Dic3C22×C412yes—
330C4×Dic3C2×D412yes—
331C2×C3⋊C8—21no—
332C2×C3⋊C8—21no—
333C2×C3⋊C8—21no—
334C2×C3⋊C8—21no—
335C2×C3⋊C8—21no—
336C2×C3⋊C8—44no—
337C2×C3⋊C8C2×D412yes—
338D3×C8—44no—
339C2×#41—34no—
340C2×#41—34no—
341C2×#41—62no—
342C2×#41—62no—
343C2×#41—62no—
344C2×#41—62no—
345C2×#41—62no—
346C2×#41—62no—
347C2×#41—121no—
348C2×#41—121no—
349C2×#41—121no—
350C2×#41—121no—
351C22×Q8—31no—
352C22×Q8C22×D311yescharacteristic
353C22×D4—31no—
354C22×D4—31no—
355C22×D4—61no—
356C22×D4—61no—
357C23×C4—31no—
358C23×C4—61no—
359C23×C4—61no—
360C23×C4—61no—
361C23×C4C22×D311yescharacteristic
362C22×C8—31no—
363C22×C8—31no—
364C22×C8—62no—
365C22×C8—62no—
366C22×C8—62no—
367C22×C8—62no—
368C22×C8—121no—
369C22×C8—121no—
370C22×C8C22×D311yescharacteristic
371C22×C8C22×D311yescharacteristic
372C4⋊Q8—34no—
373C4⋊Q8—62no—
374#123—68no—
375#123—68no—
376C22⋊Q8—22no—
377C22⋊Q8—34no—
378C22⋊Q8—62no—
379C22⋊Q8C4×D314yes—
380#121—68no—
381C4×D4—34no—
382C4×D4—34no—
383C4×D4—34no—
384C4×D4—62no—
385#117—22no—
386#117—41no—
387#117—62no—
388#117—121no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—68no—
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—31no—
405C2×C22⋊C4—31no—
406C2×C22⋊C4—61no—
407C2×C22⋊C4—61no—
408C2×C22⋊C4—61no—
409C2×C22⋊C4—61no—
410C2×C22⋊C4—61no—
411C2×C42—21no—
412C2×C42—31no—
413C2×C42—61no—
414C2×C42—61no—
415C4⋊C8—62no—
416#103—22no—
417#103—41no—
418#103—62no—
419#103—62no—
420#103—62no—
421#103—121no—
422#103—121no—
423#103—121no—
424#102—34no—
425#102—62no—
426#102—62no—
427#102—62no—
428C22⋊C8—22no—
429C22⋊C8—62no—
430C4×C8—62no—
431#95—61no—
432#95—61no—
433#95—61no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—21no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3C2×C22⋊C412yes—
441C23×C3C22×D411yescharacteristic
442C22×D3—22no—
443C22×D3—21no—
444C22×D3—22no—
445C22×D3—21no—
446C22×D3—22no—
447C22×D3—21no—
448C22×D3—21no—
449C22×D3—21no—
450C22×D3—21no—
451C22×D3—41no—
452C22×D3—41no—
453C22×D3—41no—
454C22×D3—41no—
455C22×D3C2×C22⋊C412yes—
456C3×Q8—22no—
457C3×Q8—22no—
458C3×Q8—41no—
459C3×Q8—41no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4C2×C22⋊C412yes—
479C2×C3×C4C23×C411yescharacteristic
480C2×C3×C4C22×D411yescharacteristic
481C2×C3×C4C22×D411yescharacteristic
482C2×C3×C4C2×#4111yescharacteristic
483C2×C3×C4H(5,𝔽2)11yescharacteristic
484C2×C3×C4H(5,𝔽2)11yescharacteristic
485#67—28no—
486#67—48no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—22no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498C2×Dic3—41no—
499C2×Dic3—41no—
500C2×Dic3C2×C22⋊C412yes—
501C2×Dic3C2×C22⋊C412yes—
502C2×Dic3C2×C22⋊C412yes—
503C2×Dic3#13512yes—
504C2×Dic3#13512yes—
505D12—22no—
506D12—22no—
507D12—22no—
508D12—48no—
509D12C4×D414yes—
510C4×D3—22no—
511C4×D3—22no—
512C4×D3—22no—
513C4×D3—22no—
514C4×D3—48no—
515C4×D3—48no—
516C4×D3—48no—
517Dic6—22no—
518Dic6—22no—
519Dic6—41no—
520Dic6—41no—
521C3×C8—41no—
522C3×C8—41no—
523C3⋊C8—22no—
524C3⋊C8—41no—
525C24—31no—
526C24—61no—
527C24D3×D411yescharacteristic
528#41—68no—
529#41—68no—
530#41—124no—
531#41—124no—
532#41—124no—
533#41—124no—
534#41—124no—
535#41—124no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—32no—
542C2×Q8—61no—
543C2×Q8—61no—
544C2×Q8—61no—
545C2×Q8—61no—
546C2×Q8—61no—
547C2×Q8C2×C4×D312yes—
548C2×D4—34no—
549C2×D4—32no—
550C2×D4—32no—
551C2×D4—32no—
552C2×D4—64no—
553C2×D4—62no—
554C2×D4—62no—
555C2×D4—64no—
556C2×D4—61no—
557C2×D4—61no—
558C2×D4—61no—
559C2×D4—122no—
560C2×D4—122no—
561C2×D4—122no—
562C2×D4—122no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—32no—
575C22×C4—32no—
576C22×C4—64no—
577C22×C4—64no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—64no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—122no—
587C22×C4—122no—
588C22×C4—122no—
589C22×C4—122no—
590C22×C4—122no—
591C22×C4—122no—
592C22×C4C2×C4×D312yes—
593C22×C4D3×D411yescharacteristic
594C22×C4D3×D412yes—
595C22×C4C23×D311yescharacteristic
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—32no—
603C2×C8—61no—
604C2×C8—61no—
605C2×C8—61no—
606C2×C8—61no—
607C2×C8—61no—
608C2×C8—124no—
609C2×C8—124no—
610C4⋊C4—24no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—34no—
616C4⋊C4—64no—
617C4⋊C4—64no—
618C4⋊C4—64no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—122no—
624C4⋊C4—241no—
625C4⋊C4C2×C4×D312yes—
626C4⋊C4D3×D412yes—
627C22⋊C4—24no—
628C22⋊C4—34no—
629C22⋊C4—34no—
630C22⋊C4—42no—
631C22⋊C4—64no—
632C22⋊C4—64no—
633C22⋊C4—122no—
634C22⋊C4—241no—
635C22⋊C4—241no—
636C42—32no—
637C42—32no—
638C42—42no—
639C42—122no—
640C42—122no—
641C22×C3—22no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3C22×C22⋊C411yescharacteristic
649C22×C3D4211yescharacteristic
650C22×C3#54611yescharacteristic
651C22×C3C2×#13511yescharacteristic
652C22×C3C2×#13511yescharacteristic
653C22×C3#57711yescharacteristic
654C22×C3#57811yescharacteristic
655C2×D3—22no—
656C2×D3—24no—
657C2×D3—22no—
658C2×D3—22no—
659C2×D3—42no—
660C2×D3—42no—
661C2×D3—41no—
662C2×D3—42no—
663C2×D3—41no—
664C2×D3—42no—
665C2×D3—41no—
666C2×D3—42no—
667C2×D3—41no—
668C2×D3—42no—
669C3×C4—22no—
670C3×C4—42no—
671C3×C4—42no—
672C3×C4—42no—
673C3×C4—81no—
674C3×C4C2×C4×D411yescharacteristic
675C3×C4#51811yescharacteristic
676C3×C4D4211yescharacteristic
677C3×C4#54611yescharacteristic
678Dic3—22no—
679Dic3—22no—
680Dic3—42no—
681Dic3—81no—
682Dic3—81no—
683Dic3#41614yescomplemented
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—32no—
691C23—61no—
692C23—62no—
693C23—62no—
694C23—61no—
695C23—61no—
696C23—61no—
697C23—61no—
698C23—61no—
699C23—62no—
700C23—121no—
701C23—121no—
702C23—121no—
703C23—121no—
704C23D3×C22⋊C412yes—
705C23C2×D3×D411yescharacteristic
706Q8—22no—
707Q8—22no—
708Q8—41no—
709Q8—41no—
710Q8—62no—
711Q8—62no—
712Q8—121no—
713Q8—121no—
714D4—34no—
715D4—68no—
716D4—62no—
717D4—62no—
718D4—62no—
719D4—128no—
720D4—128no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—32no—
731C2×C4—32no—
732C2×C4—32no—
733C2×C4—32no—
734C2×C4—32no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—62no—
749C2×C4—62no—
750C2×C4—62no—
751C2×C4—62no—
752C2×C4—62no—
753C2×C4—128no—
754C2×C4—128no—
755C2×C4—128no—
756C2×C4—121no—
757C2×C4—121no—
758C2×C4—121no—
759C2×C4—121no—
760C2×C4—121no—
761C2×C4—121no—
762C2×C4—121no—
763C2×C4—121no—
764C2×C4D3×C22⋊C412yes—
765C2×C4C22×C4×D311yescharacteristic
766C2×C4C2×D3×D411yescharacteristic
767C2×C4C2×D3×D411yescharacteristic
768C2×C4#100411yescharacteristic
769C2×C4D3×#4111yescharacteristic
770C2×C4#100911yescharacteristic
771C8—41no—
772C8—41no—
773C8—62no—
774C8—121no—
775C2×C3—42no—
776C2×C3D4×C22⋊C411yescharacteristic
777C2×C3C2×#41611yescharacteristic
778C2×C3#289811yescharacteristic
779C2×C3#328311yescharacteristic
780C2×C3#328411yescharacteristic
781C2×C3#330211yescharacteristic
782C2×C3#330311yescharacteristic
783D3—42no—
784D3—44no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—62no—
793C22—62no—
794C22—64no—
795C22—62no—
796C22—122no—
797C22—121no—
798C22—122no—
799C22—121no—
800C22—122no—
801C22—121no—
802C22—122no—
803C22—121no—
804C22—122no—
805C22—122no—
806C22C2×D3×C22⋊C411yescharacteristic
807C22#559011yescharacteristic
808C22#565411yescharacteristic
809C22D3×#13511yescharacteristic
810C22D3×#13511yescharacteristic
811C22#577811yescharacteristic
812C22#577911yescharacteristic
813C4—22no—
814C4—34no—
815C4—42no—
816C4—42no—
817C4—42no—
818C4—62no—
819C4—62no—
820C4—81no—
821C4—122no—
822C4—241no—
823C4—241no—
824C4C4×D3×D411yescharacteristic
825C4#554511yescharacteristic
826C4#560911yescharacteristic
827C4#561011yescharacteristic
828C3#2241711yescharacteristic, complemented, Sylow
829C2—42no—
830C2—122no—
831C2—124no—
832C2#7487811yescharacteristic
833C2D3×#41611yescharacteristic
834C2#7895711yescharacteristic
835C2#8026911yescharacteristic
836C2#8027011yescharacteristic
837C2#8154411yescharacteristic
838C2#8154511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1873C2
socleC23×C3C22×D4
prime radicalC2×#5631C2
cosocleC22×C3×C4C24
hypercenter#1873D3
hypocenterC3#22417
LCSG ▷ C2×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. #82241C2semidirect
3. C2×#5002C2semidirect
4. C2×#4804C2semidirect
5. C2×#67⋊C8C2semidirect
6. C3×#1873C2semidirect
7. #71696C2semidirect
8. #70267C2semidirect
9. #70229C2semidirect
10. #70225C2semidirect
11. #69960C2semidirect
12. #68892C2semidirect
13. #68882C2semidirect
14. #68879C2semidirect
15. #68780C2semidirect
26. #5631C4semidirect
75. #1873D3semidirect
174. #809D4semidirect
683. Dic3#416semidirect
828. C3#22417semidirect

Maximal subgroups

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

subgroupindex
C2×#56312
#822412
C2×#50022
C2×#48042
C2×#67⋊C82
C3×#18732
#716962
#702672
#702292
#702252
#699602
#688922
#688822
#688792
#687802
#224173