Finite Group Databasebeta

← #10827357

Subgroups — #10827357

Order 768.

1338 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5618C211yesmaximal, characteristic, complemented
2C2×#5172C211yesmaximal, characteristic, complemented
3#82812C211yesmaximal, characteristic, complemented
4C2×#4804C211yesmaximal, characteristic, complemented
5C3×#2000C211yesmaximal, characteristic, complemented
6#72047C211yesmaximal, characteristic, complemented
7#71692C211yesmaximal, characteristic, complemented
8#71684C211yesmaximal, characteristic, complemented
9#70232C211yesmaximal, characteristic, complemented
10#70202C211yesmaximal, characteristic, complemented
11#70172C211yesmaximal, characteristic, complemented
12#69957C211yesmaximal, characteristic, complemented
13#69932C211yesmaximal, characteristic, complemented
14#68899C211yesmaximal, characteristic, complemented
15#68873C211yesmaximal, characteristic, complemented
16#23962—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×#939—21no—
22C2×#938C2211yescharacteristic
23C2×D4×Dic3—21no—
24C2×D4×Dic3C2211yescharacteristic
25C22×#213C2211yescharacteristic
26C2×#930C2211yescharacteristic
27C2×C4×#67C2211yescharacteristic
28C22×C4⋊Dic3C2211yescharacteristic
29C22×D3×C8C2211yescharacteristic
30#5618—24no—
31#5618—24no—
32C2×#892C2211yescharacteristic
33C2×#890C2211yescharacteristic
34C2×#886—21no—
35C2×#879—21no—
36C2×C3×#103C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×C22⋊C8C2211yescharacteristic
39#5229C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#835C2211yescharacteristic
42C2×#832C2211yescharacteristic
43C2×#830C2211yescharacteristic
44#5172—24no—
45C2×#821C2211yescharacteristic
46C2×#821C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic
48#4991—21no—
49#4989—21no—
50#4988C2211yescharacteristic
51#4987C2211yescharacteristic
52C2×#809C2211yescharacteristic
53#4960—21no—
54#4956—21no—
55#4804—24no—
56C3×#340C2211yescharacteristic
57#4551C2211yescharacteristic
58#4551C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#553—31no—
65C2×#449—31no—
66C2×#416—31no—
67#2407—31no—
68#2026—31no—
69#2025—31no—
70#2000D311yescharacteristic, complemented
71#1999—31no—
72#1893—31no—
73#1879—31no—
74#1877—31no—
75#1874—31no—
76#1872—31no—
77#1869—31no—
78#1825—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67—21no—
84C22×#67—21no—
85C22×#67D411yescharacteristic
86C23×Dic3—21no—
87C23×Dic3—21no—
88C2×#239—22no—
89C2×#239—22no—
90C2×#239—22no—
91C2×#239—22no—
92C2×#239—41no—
93C2×#239—41no—
94C22×D12—21no—
95C22×D12C2311yescharacteristic
96C22×C4×D3—21no—
97C22×C4×D3C2311yescharacteristic
98C2×C3×SD16—22no—
99C2×C3×SD16—22no—
100C2×C3×SD16—41no—
101C22×C3×C8C2311yescharacteristic
102C22×C3×C8C2311yescharacteristic
103C3×C22⋊Q8—22no—
104C3×C22⋊Q8—41no—
105C3×#121—22no—
106C3×#121—22no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4—21no—
112C2×#217—21no—
113C2×#217—21no—
114C2×#217D411yescharacteristic
115#939—28no—
116#938—22no—
117#938D414yescomplemented
118D4×Dic3—28no—
119D4×Dic3—22no—
120D4×Dic3—22no—
121C2×#213—22no—
122C2×#213—22no—
123C2×#213—41no—
124#930—22no—
125#930—41no—
126C4×#67—22no—
127C4×#67—22no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4—21no—
133C2×(C2×D3)⋊C4D411yescharacteristic
134C2×C4⋊Dic3—21no—
135C2×C4⋊Dic3—21no—
136C2×C4⋊Dic3—22no—
137C2×C4⋊Dic3—22no—
138C2×C4⋊Dic3C2311yescharacteristic
139C2×C4⋊Dic3C2311yescharacteristic
140C2×C4⋊Dic3C2311yescharacteristic
141C2×Dic3⋊C4—21no—
142C2×Dic3⋊C4D411yescharacteristic
143C2×C4×Dic3—21no—
144C2×C4×Dic3C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146C22×C3⋊C8C2311yescharacteristic
147C2×D3×C8—22no—
148C2×D3×C8—41no—
149C2×D3×C8—41no—
150#892—22no—
151#892D414yescomplemented
152#890—22no—
153#890—22no—
154#886—28no—
155#879—28no—
156C3×#103—22no—
157C3×#102—41no—
158C3×C22⋊C8—41no—
159#835—22no—
160#835—22no—
161#832—41no—
162C3⋊#95—21no—
163C3⋊#95—21no—
164C3⋊#95—21no—
165#830—41no—
166#821—22no—
167#821—22no—
168(C2×D3)⋊C8—22no—
169#809—22no—
170C22×#41—31no—
171C22×SD16C2×D311yescharacteristic
172C22×D8—31no—
173C23×C8—31no—
174#553—64no—
175#553—64no—
176C2×#126—61no—
177C2×#125—31no—
178C2×#123—61no—
179C2×C22⋊Q8C2×D311yescharacteristic
180C2×#121—31no—
181C2×#121—31no—
182C2×#121—61no—
183C2×#121C2×D311yescharacteristic
184C2×C4×D4—31no—
185C2×C4×D4—31no—
186C2×C4×D4—61no—
187C2×#117—31no—
188C22×C4⋊C4—31no—
189#449—64no—
190#416—64no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103C2×D311yescharacteristic
194C2×#102—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102C2×D311yescharacteristic
199C2×C22⋊C8—31no—
200C2×C22⋊C8—31no—
201C2×C22⋊C8C2×D311yescharacteristic
202#394—61no—
203#392—61no—
204#391—31no—
205#390—31no—
206#386—61no—
207#385—61no—
208#380—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340C2×D311yescharacteristic
215#336—31no—
216#336—31no—
217C24×C3—21no—
218C24×C3C2×D411yescharacteristic
219C23×D3—21no—
220C23×D3C2×D411yescharacteristic
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8#4112yes—
227C2×C3×D4—24no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—42no—
234C2×C3×D4—42no—
235C2×C3×D4C2×D412yes—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2411yescharacteristic
247C2×#67—22no—
248C2×#67—22no—
249C2×#67—24no—
250C2×#67—41no—
251C2×#67—42no—
252C2×#67—42no—
253C2×#67—81no—
254C2×#67—81no—
255C2×#67—81no—
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3—24no—
259C22×Dic3—24no—
260C22×Dic3—21no—
261C22×Dic3—81no—
262C22×Dic3—81no—
263C22×Dic3—81no—
264C22×Dic3—81no—
265C22×Dic3C2×D411yescharacteristic
266C22×Dic3C2×D411yescharacteristic
267C22×Dic3C2×D411yescharacteristic
268#239—28no—
269#239—44no—
270#239—44no—
271#239—44no—
272C2×D12—21no—
273C2×D12—21no—
274C2×D12—21no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12—42no—
278C2×D12—42no—
279C2×D12—42no—
280C2×D12#4112yes—
281C2×C4×D3—21no—
282C2×C4×D3—21no—
283C2×C4×D3—21no—
284C2×C4×D3—21no—
285C2×C4×D3—42no—
286C2×C4×D3—42no—
287C2×C4×D3—42no—
288C2×C4×D3C2×D412yes—
289C2×C4×D3C2×D412yes—
290C3×SD16—44no—
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—42no—
301C3×C4⋊C4C2×D412yes—
302C3×C22⋊C4—24no—
303C3×C22⋊C4—42no—
304#217—24no—
305#217—24no—
306#217—22no—
307#213—44no—
308(C2×D3)⋊C4—22no—
309(C2×D3)⋊C4—24no—
310(C2×D3)⋊C4—42no—
311(C2×D3)⋊C4—42no—
312(C2×D3)⋊C4—81no—
313(C2×D3)⋊C4—81no—
314C4⋊Dic3—24no—
315C4⋊Dic3—24no—
316C4⋊Dic3—21no—
317C4⋊Dic3—21no—
318C4⋊Dic3—21no—
319C4⋊Dic3—21no—
320C4⋊Dic3C2×D412yes—
321C4⋊Dic3C2×D412yes—
322Dic3⋊C4—24no—
323Dic3⋊C4—22no—
324C4×Dic3—21no—
325C4×Dic3—21no—
326C4×Dic3—24no—
327C2×C3⋊C8—21no—
328C2×C3⋊C8—21no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8—21no—
332C2×C3⋊C8—21no—
333D3×C8—44no—
334C2×#41—62no—
335C2×#41—62no—
336C2×#41—62no—
337C2×#41—62no—
338C2×#41—121no—
339C2×#41—121no—
340C22×Q8C22×D311yescharacteristic
341C22×D4—21no—
342C22×D4—31no—
343C22×D4—31no—
344C22×D4—61no—
345C22×D4—61no—
346C22×D4—61no—
347C22×D4C22×D311yescharacteristic
348C23×C4—31no—
349C23×C4—61no—
350C23×C4—61no—
351C23×C4—61no—
352C23×C4C22×D311yescharacteristic
353C2×SD16—22no—
354C2×SD16—22no—
355C2×SD16—41no—
356C2×D8—62no—
357C2×D8—62no—
358C2×D8—121no—
359C22×C8—31no—
360C22×C8—31no—
361C22×C8—62no—
362C22×C8—121no—
363C22×C8—121no—
364C22×C8C22×D311yescharacteristic
365C22×C8C22×D311yescharacteristic
366#126—68no—
367#125—62no—
368#125—62no—
369#123—68no—
370C22⋊Q8—22no—
371C22⋊Q8—41no—
372#121—22no—
373#121—22no—
374#121—34no—
375#121—62no—
376#121—68no—
377#121—62no—
378#121—121no—
379C4×D4—62no—
380C4×D4—62no—
381C4×D4—62no—
382C4×D4—68no—
383C4×D4—62no—
384#117—34no—
385#117—62no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—31no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—62no—
392C2×C4⋊C4—62no—
393C2×C4⋊C4—61no—
394C2×C4⋊C4—61no—
395C2×C4⋊C4—61no—
396C2×C4⋊C4C22×D311yescharacteristic
397C2×C4⋊C4C22×D311yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—31no—
401C2×C22⋊C4—31no—
402C2×C22⋊C4—61no—
403C2×C22⋊C4—61no—
404C2×C22⋊C4—61no—
405C2×C22⋊C4—61no—
406C2×C22⋊C4—61no—
407C2×C22⋊C4—61no—
408C2×C22⋊C4—61no—
409C2×C42—31no—
410C2×C42—61no—
411#103—22no—
412#103—62no—
413#103—62no—
414#102—41no—
415#102—62no—
416#102—62no—
417#102—62no—
418#102—121no—
419C22⋊C8—41no—
420C22⋊C8—62no—
421C22⋊C8—121no—
422#95—61no—
423#95—61no—
424#95—61no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—22no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3—41no—
437C23×C3—41no—
438C23×C3#13512yes—
439C23×C3C22×D411yescharacteristic
440C22×D3—21no—
441C22×D3—21no—
442C22×D3—21no—
443C22×D3—21no—
444C22×D3—21no—
445C22×D3—21no—
446C22×D3—22no—
447C22×D3—41no—
448C22×D3—41no—
449C22×D3—41no—
450C22×D3—41no—
451C22×D3—41no—
452C22×D3—41no—
453C22×D3#12012yes—
454C3×Q8—22no—
455C3×Q8—22no—
456C3×Q8—41no—
457C3×Q8—41no—
458C3×D4—22no—
459C3×D4—22no—
460C3×D4—48no—
461C3×D4—41no—
462C3×D4—41no—
463C2×C3×C4—22no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—22no—
467C2×C3×C4—21no—
468C2×C3×C4—41no—
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×C4—41no—
479C2×C3×C4C22×D411yescharacteristic
480C2×C3×C4C22×D411yescharacteristic
481C2×C3×C4C2×#4111yescharacteristic
482C2×C3×C4C2×#4111yescharacteristic
483C2×C3×C4H(5,𝔽2)11yescharacteristic
484C2×C3×C4H(5,𝔽2)11yescharacteristic
485#67—44no—
486#67—84no—
487#67—84no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—41no—
499C2×Dic3—41no—
500C2×Dic3—41no—
501C2×Dic3—41no—
502C2×Dic3—41no—
503C2×Dic3—41no—
504C2×Dic3—41no—
505C2×Dic3—84no—
506C2×Dic3—84no—
507C2×Dic3#12012yes—
508D12—22no—
509D12—22no—
510D12—48no—
511D12—41no—
512D12—41no—
513C4×D3—22no—
514C4×D3—22no—
515C4×D3—22no—
516C4×D3—22no—
517C4×D3—48no—
518C3×C8—41no—
519C3×C8—41no—
520C3⋊C8—41no—
521C3⋊C8—41no—
522C24—21no—
523C24—31no—
524C24—61no—
525C24D3×D411yescharacteristic
526#41—68no—
527#41—124no—
528#41—124no—
529#41—124no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8#23712yes—
536C2×D4—24no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—32no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—62no—
546C2×D4—62no—
547C2×D4—64no—
548C2×D4—61no—
549C2×D4—61no—
550C2×D4—61no—
551C2×D4—61no—
552C2×D4—61no—
553C2×D4—122no—
554C2×D4—122no—
555C2×D4—122no—
556C2×D4—121no—
557C2×D4—122no—
558C2×D4—122no—
559C2×D4—241no—
560C2×D4—241no—
561C2×D4—241no—
562C2×D4D3×D412yes—
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—21no—
572C22×C4—31no—
573C22×C4—32no—
574C22×C4—32no—
575C22×C4—31no—
576C22×C4—31no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—64no—
584C22×C4—64no—
585C22×C4—61no—
586C22×C4—122no—
587C22×C4—122no—
588C22×C4—122no—
589C22×C4—241no—
590C22×C4—241no—
591C22×C4—241no—
592C22×C4—241no—
593C22×C4D3×D411yescharacteristic
594C22×C4C23×D311yescharacteristic
595SD16—44no—
596D8—124no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—61no—
604C2×C8—61no—
605C2×C8—61no—
606C2×C8—61no—
607C2×C8—61no—
608C2×C8—61no—
609C2×C8—124no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—32no—
614C4⋊C4—32no—
615C4⋊C4—42no—
616C4⋊C4—62no—
617C4⋊C4—64no—
618C4⋊C4—64no—
619C4⋊C4—64no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4D3×D412yes—
625C22⋊C4—24no—
626C22⋊C4—42no—
627C22⋊C4—62no—
628C22⋊C4—64no—
629C22⋊C4—62no—
630C22⋊C4—64no—
631C22⋊C4—64no—
632C22⋊C4—122no—
633C22⋊C4—122no—
634C22⋊C4—241no—
635C22⋊C4—241no—
636C42—64no—
637C42—61no—
638C42—61no—
639C22×C3—22no—
640C22×C3—22no—
641C22×C3—22no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—42no—
647C22×C3—42no—
648C22×C3—42no—
649C22×C3—81no—
650C22×C3—81no—
651C22×C3—81no—
652C22×C3—81no—
653C22×C3C2×#12011yescharacteristic
654C22×C3#54611yescharacteristic
655C22×C3#54611yescharacteristic
656C22×C3C2×#13511yescharacteristic
657C22×C3#57511yescharacteristic
658C22×C3#57611yescharacteristic
659C22×C3#57711yescharacteristic
660C2×D3—22no—
661C2×D3—22no—
662C2×D3—22no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—42no—
668C2×D3—42no—
669C2×D3—42no—
670C2×D3—81no—
671C2×D3—81no—
672C2×D3—81no—
673C2×D3—81no—
674C3×C4—42no—
675C3×C4—41no—
676C3×C4—42no—
677C3×C4—81no—
678C3×C4#52511yescharacteristic
679C3×C4#53511yescharacteristic
680C3×C4#54611yescharacteristic
681C3×C4#54611yescharacteristic
682Dic3—22no—
683Dic3—41no—
684Dic3—41no—
685Dic3—42no—
686Dic3—42no—
687Dic3—81no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—22no—
695C23—32no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—61no—
703C23—61no—
704C23—61no—
705C23—61no—
706C23—61no—
707C23—61no—
708C23—62no—
709C23—121no—
710C23—121no—
711C23—121no—
712C23—121no—
713C23—121no—
714C23—121no—
715C23#91612yes—
716C23C2×D3×D411yescharacteristic
717Q8—22no—
718Q8—22no—
719Q8—41no—
720Q8—41no—
721D4—22no—
722D4—22no—
723D4—48no—
724D4—41no—
725D4—41no—
726D4—62no—
727D4—62no—
728D4—128no—
729D4—124no—
730D4—121no—
731D4—121no—
732D4—244no—
733D4—244no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—32no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—62no—
754C2×C4—62no—
755C2×C4—62no—
756C2×C4—62no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—62no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—62no—
765C2×C4—128no—
766C2×C4—121no—
767C2×C4—121no—
768C2×C4—121no—
769C2×C4—121no—
770C2×C4—121no—
771C2×C4—121no—
772C2×C4—121no—
773C2×C4—244no—
774C2×C4—244no—
775C2×C4C2×D3×D411yescharacteristic
776C2×C4C2×D3×D411yescharacteristic
777C2×C4C2×#23711yescharacteristic
778C2×C4#100411yescharacteristic
779C2×C4#100411yescharacteristic
780C2×C4D3×#4111yescharacteristic
781C8—41no—
782C8—41no—
783C8—121no—
784C8—121no—
785C2×C3—42no—
786C2×C3—82no—
787C2×C3#240411yescharacteristic
788C2×C3#300211yescharacteristic
789C2×C3#301211yescharacteristic
790C2×C3#329711yescharacteristic
791C2×C3#330111yescharacteristic
792C2×C3#330711yescharacteristic
793C2×C3#330911yescharacteristic
794D3—42no—
795D3—82no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—62no—
807C22—62no—
808C22—62no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—121no—
814C22—121no—
815C22—121no—
816C22—121no—
817C22—122no—
818C22—122no—
819C22—122no—
820C22—241no—
821C22—241no—
822C22—241no—
823C22—241no—
824C22D3×#12011yescharacteristic
825C22#559111yescharacteristic
826C22#561011yescharacteristic
827C22C2×#91611yescharacteristic
828C22#576911yescharacteristic
829C22#577311yescharacteristic
830C22#577811yescharacteristic
831C4—42no—
832C4—41no—
833C4—42no—
834C4—62no—
835C4—81no—
836C4—121no—
837C4—121no—
838C4—122no—
839C4—122no—
840C4—241no—
841C4#559111yescharacteristic
842C4#560611yescharacteristic
843C4#561011yescharacteristic
844C4#571511yescharacteristic
845C3#2396211yescharacteristic, complemented, Sylow
846C2—42no—
847C2—82no—
848C2—122no—
849C2—242no—
850C2#7675411yescharacteristic
851C2#8005011yescharacteristic
852C2#8011111yescharacteristic
853C2#8014511yescharacteristic
854C2#8023111yescharacteristic
855C2#8068111yescharacteristic
856C2#8081911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2000C2
socleC23×C3C22×D4
hypercenter#2000D3
hypocenterC3#23962
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
1. C2×#5618C2semidirect
2. C2×#5172C2semidirect
3. #82812C2semidirect
4. C2×#4804C2semidirect
5. C3×#2000C2semidirect
6. #72047C2semidirect
7. #71692C2semidirect
8. #71684C2semidirect
9. #70232C2semidirect
10. #70202C2semidirect
11. #70172C2semidirect
12. #69957C2semidirect
13. #69932C2semidirect
14. #68899C2semidirect
15. #68873C2semidirect
70. #2000D3semidirect
117. #938D4semidirect
151. #892D4semidirect
845. C3#23962semidirect

Maximal subgroups

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

subgroupindex
C2×#56182
C2×#51722
#828122
C2×#48042
C3×#20002
#720472
#716922
#716842
#702322
#702022
#701722
#699572
#699322
#688992
#688732
#239623