Finite Group Databasebeta

← #10800999

Subgroups — #10800999

Order 768.

1476 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5574C211yesmaximal, characteristic, complemented
2C2×#5172C211yesmaximal, characteristic
3C2×Dic3×SD16C211yesmaximal, characteristic, complemented
4C2×#4785C211yesmaximal, characteristic, complemented
5#76430C211yesmaximal, characteristic, complemented
6C3×#1880C211yesmaximal, characteristic, complemented
7#71629C211yesmaximal, characteristic, complemented
8#70267C211yesmaximal, characteristic, complemented
9#70220C211yesmaximal, characteristic, complemented
10#70200C211yesmaximal, characteristic, complemented
11#69657C211yesmaximal, characteristic, complemented
12#68875C211yesmaximal, characteristic, complemented
13#68780C211yesmaximal, characteristic, complemented
14#68671C211yesmaximal, characteristic, complemented
15#68601C211yesmaximal, characteristic, complemented
16#21464—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C2×C3×C4×Q8C2211yescharacteristic
20C2×Q8×Dic3C2211yescharacteristic
21C2×#938C2211yescharacteristic
22C2×D4×Dic3C2211yescharacteristic
23C22×#213C2211yescharacteristic
24#5574—24no—
25#5574—24no—
26C2×#893—21no—
27C2×#893C2211yescharacteristic
28C2×D3×C4⋊C4—21no—
29C2×D3×C4⋊C4C2211yescharacteristic
30C2×C4×D12—21no—
31C2×C4×D12C2211yescharacteristic
32C2×#872—21no—
33C2×#872C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C3×#390C2211yescharacteristic
37C2×#835C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#832C2211yescharacteristic
40#5172C418yescomplemented
41Dic3×SD16—24no—
42C2×#821C2211yescharacteristic
43C2×#821C2211yescharacteristic
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#817C2211yescharacteristic
47C2×#815C2211yescharacteristic
48C2×C8×Dic3C2211yescharacteristic
49#4987C2211yescharacteristic
50Dic3×C4⋊C4C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#808C2211yescharacteristic
53#4958—21no—
54#4957—21no—
55#4946—21no—
56#4944—21no—
57#4928C2211yescharacteristic
58#4785—24no—
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61#4551C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64#4524C2211yescharacteristic
65C2×#520—31no—
66C2×#449—31no—
67C2×#442—31no—
68C2×C4×SD16—31no—
69#2324—31no—
70#1880D311yescharacteristic, complemented
71#1879—31no—
72#1874—31no—
73#1865—31no—
74#1864—31no—
75#1853—31no—
76#1788—31no—
77#1763—31no—
78C4×#102—31no—
79#1750—31no—
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C22×#67—21no—
83C23×Dic3—21no—
84C2×#239—22no—
85C2×#239—22no—
86C2×#239—22no—
87C2×#239—22no—
88C2×#239—22no—
89C2×#239C2×C414yescomplemented
90C22×D12—21no—
91C22×D12C2311yescharacteristic
92C22×C4×D3—21no—
93C22×C4×D3—21no—
94C22×C4×D3—21no—
95C22×C4×D3—21no—
96C22×C4×D3C2311yescharacteristic
97C2×C3×SD16—22no—
98C2×C3×SD16—22no—
99C2×C3×SD16C2×C414yescomplemented
100C22×C3×C8C2311yescharacteristic
101C22×C3×C8C2311yescharacteristic
102C3×C4×Q8—22no—
103C3×C4×Q8—22no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C22⋊C4—21no—
108C2×C3×C22⋊C4—21no—
109C2×C3×C42—21no—
110C2×C3×C42C2311yescharacteristic
111C2×#217—21no—
112C2×#217—21no—
113Q8×Dic3—22no—
114Q8×Dic3D414yescomplemented
115#938—22no—
116#938C2×C414yescomplemented
117D4×Dic3—22no—
118D4×Dic3—22no—
119C2×#213—22no—
120C2×#213—22no—
121C2×#213C2×C414yescomplemented
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4D411yescharacteristic
126C2×(C2×D3)⋊C4D411yescharacteristic
127C2×C4⋊Dic3—21no—
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4D411yescharacteristic
134C2×Dic3⋊C4D411yescharacteristic
135C2×C4×Dic3—21no—
136C2×C4×Dic3—21no—
137C2×C4×Dic3C2311yescharacteristic
138C22×C3⋊C8C2311yescharacteristic
139C22×C3⋊C8C2311yescharacteristic
140#893—28no—
141#893—22no—
142#893D414yescomplemented
143D3×C4⋊C4—28no—
144D3×C4⋊C4—22no—
145D3×C4⋊C4—22no—
146C4×D12—28no—
147C4×D12—22no—
148C4×D12—22no—
149#872—28no—
150#872—22no—
151#872—22no—
152C3×#103—22no—
153C3×#102—22no—
154#835—22no—
155#835C2×C414yescomplemented
156#832—22no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160#821—22no—
161#821C2×C414yescomplemented
162(C2×D3)⋊C8—22no—
163(C2×D3)⋊C8C2×C414yescomplemented
164#817—22no—
165#815—22no—
166C8×Dic3—22no—
167#809—22no—
168#808—22no—
169C22×#41—31no—
170C22×SD16C2×D311yescharacteristic
171C22×D8—31no—
172C2×#121—31no—
173#520—64no—
174#520—64no—
175C2×C4×Q8—31no—
176C2×C4×Q8C2×D311yescharacteristic
177C2×C4×D4—31no—
178C2×C4×D4—31no—
179C2×C4×D4—31no—
180C2×C4×D4—61no—
181C2×C4×D4—61no—
182C2×#117—31no—
183C2×#117—61no—
184C22×C4⋊C4—31no—
185C22×C4⋊C4—61no—
186#449—38no—
187#442—64no—
188C4×SD16—64no—
189C2×#106—31no—
190C2×#106—31no—
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×#97—31no—
202C2×C4×C8—31no—
203#390—61no—
204#390C2×D311yescharacteristic
205#389—31no—
206#388—61no—
207#386—61no—
208#385—61no—
209#380—31no—
210C4×C4⋊C4—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340C2×D311yescharacteristic
215#336—31no—
216#336C2×D311yescharacteristic
217C24×C3—21no—
218C23×D3—21no—
219C23×D3C2×D411yescharacteristic
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8C22×C412yes—
224C2×C3×Q8C2×D412yes—
225C2×C3×Q8#4112yes—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4C22×C412yes—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2411yescharacteristic
238C2×#67—24no—
239C2×#67—81no—
240C2×#67—81no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3—21no—
244C22×Dic3—42no—
245C22×Dic3—81no—
246C22×Dic3—81no—
247C22×Dic3C2×D411yescharacteristic
248C22×Dic3C2×D411yescharacteristic
249C22×Dic3C2×D411yescharacteristic
250#239—28no—
251#239—28no—
252#239—28no—
253#239—28no—
254C2×D12—24no—
255C2×D12—24no—
256C2×D12—24no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—21no—
260C2×D12C22×C412yes—
261C2×D12C2×D412yes—
262C2×D12#4112yes—
263C2×C4×D3—24no—
264C2×C4×D3—24no—
265C2×C4×D3—21no—
266C2×C4×D3—21no—
267C2×C4×D3—21no—
268C2×C4×D3—21no—
269C2×C4×D3—24no—
270C2×C4×D3—24no—
271C2×C4×D3—24no—
272C2×C4×D3—24no—
273C2×C4×D3—81no—
274C2×C4×D3—81no—
275C2×C4×D3—81no—
276C2×C4×D3—81no—
277C2×C4×D3—81no—
278C2×C4×D3—81no—
279C2×C4×D3C22×C412yes—
280C2×C4×D3#4112yes—
281C3×SD16—28no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8C22×C412yes—
288C3×C4⋊C4—24no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—21no—
292C3×C4⋊C4C2×D412yes—
293C3×C22⋊C4—81no—
294C3×C22⋊C4—81no—
295C3×C42—24no—
296C3×C42—21no—
297C3×C42—21no—
298#217—24no—
299#217—42no—
300#213—28no—
301(C2×D3)⋊C4—24no—
302(C2×D3)⋊C4—22no—
303(C2×D3)⋊C4—22no—
304(C2×D3)⋊C4—24no—
305(C2×D3)⋊C4—81no—
306C4⋊Dic3—21no—
307C4⋊Dic3—21no—
308C4⋊Dic3—24no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3C22×C412yes—
312C4⋊Dic3C2×D412yes—
313Dic3⋊C4—24no—
314Dic3⋊C4—22no—
315Dic3⋊C4—22no—
316Dic3⋊C4—81no—
317C4×Dic3—24no—
318C4×Dic3—81no—
319C4×Dic3C2×D412yes—
320C4×Dic3C2×D412yes—
321C2×C3⋊C8—21no—
322C2×C3⋊C8—21no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8—21no—
326C2×C3⋊C8C22×C412yes—
327C2×#41—34no—
328C2×#41—62no—
329C2×#41—62no—
330C2×#41—62no—
331C2×#41—62no—
332C2×#41—62no—
333C22×Q8C22×D311yescharacteristic
334C22×D4—31no—
335C22×D4—61no—
336C22×D4—61no—
337C22×D4C22×D311yescharacteristic
338C23×C4—31no—
339C23×C4—61no—
340C23×C4—61no—
341C23×C4—61no—
342C23×C4—61no—
343C23×C4—61no—
344C2×SD16—22no—
345C2×SD16—22no—
346C2×SD16C4×D314yescomplemented
347C2×D8—34no—
348C2×D8—62no—
349C2×D8—62no—
350C22×C8—31no—
351C22×C8—31no—
352C22×C8C22×D311yescharacteristic
353C22×C8C22×D311yescharacteristic
354#121—34no—
355#121—62no—
356C4×Q8—22no—
357C4×Q8—22no—
358C4×Q8—34no—
359C4×Q8—62no—
360C4×D4—34no—
361C4×D4—62no—
362C4×D4—62no—
363C4×D4—68no—
364C4×D4—62no—
365C4×D4—62no—
366C4×D4—62no—
367C4×D4—68no—
368#117—62no—
369#117—62no—
370#117—68no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—31no—
376C2×C4⋊C4—31no—
377C2×C4⋊C4—62no—
378C2×C4⋊C4—68no—
379C2×C4⋊C4—61no—
380C2×C4⋊C4—61no—
381C2×C4⋊C4—62no—
382C2×C4⋊C4—61no—
383C2×C4⋊C4C22×D311yescharacteristic
384C2×C4⋊C4C22×D311yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—31no—
388C2×C22⋊C4—31no—
389C2×C22⋊C4—61no—
390C2×C22⋊C4—61no—
391C2×C22⋊C4—61no—
392C2×C22⋊C4—61no—
393C2×C22⋊C4—61no—
394C2×C42—21no—
395C2×C42—31no—
396C2×C42—61no—
397C2×C42—61no—
398C2×C42C22×D311yescharacteristic
399#106—62no—
400#106—62no—
401#103—22no—
402#103—34no—
403#103—62no—
404#102—22no—
405#102—34no—
406#102—62no—
407#102—62no—
408#102—62no—
409C22⋊C8—34no—
410C22⋊C8—62no—
411#97—62no—
412C4×C8—62no—
413#95—61no—
414#95—61no—
415#95—61no—
416C23×C3—22no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3C22×D411yescharacteristic
424C22×D3—22no—
425C22×D3—21no—
426C22×D3—22no—
427C22×D3—21no—
428C22×D3—22no—
429C22×D3—21no—
430C22×D3—21no—
431C22×D3—21no—
432C22×D3—21no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C22×D3C4×D412yes—
438C3×Q8—22no—
439C3×Q8—22no—
440C3×Q8—22no—
441C3×Q8C4×D414yes—
442C3×D4—22no—
443C3×D4—22no—
444C3×D4—41no—
445C3×D4—41no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—22no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4C23×C411yescharacteristic
462C2×C3×C4C22×D411yescharacteristic
463C2×C3×C4C22×D411yescharacteristic
464C2×C3×C4C2×#4111yescharacteristic
465C2×C3×C4C2×#4111yescharacteristic
466C2×C3×C4C2×#4111yescharacteristic
467#67—84no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—84no—
484C2×Dic3C4×D412yes—
485C2×Dic3#12012yes—
486C2×Dic3#12012yes—
487D12—216no—
488D12—22no—
489D12—22no—
490D12—22no—
491D12C4×D414yes—
492C4×D3—216no—
493C4×D3—22no—
494C4×D3—22no—
495C4×D3—22no—
496C4×D3—22no—
497C4×D3—84no—
498C4×D3—84no—
499C4×D3—84no—
500C3×C8—22no—
501C3×C8—41no—
502C3⋊C8—22no—
503C3⋊C8—41no—
504C24—21no—
505C24—31no—
506C24—61no—
507#41—68no—
508#41—68no—
509#41—68no—
510#41—68no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8C2×C4×D312yes—
515C2×Q8D3×D412yes—
516C2×Q8#23712yes—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—32no—
523C2×D4—32no—
524C2×D4—32no—
525C2×D4—64no—
526C2×D4—64no—
527C2×D4—64no—
528C2×D4—64no—
529C2×D4—61no—
530C2×D4—61no—
531C2×D4—61no—
532C2×D4—241no—
533C2×D4—241no—
534C2×D4C2×C4×D312yes—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—31no—
539C22×C4—31no—
540C22×C4—31no—
541C22×C4—32no—
542C22×C4—32no—
543C22×C4—64no—
544C22×C4—64no—
545C22×C4—64no—
546C22×C4—64no—
547C22×C4—64no—
548C22×C4—64no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—122no—
557C22×C4—241no—
558C22×C4—241no—
559C22×C4—241no—
560C22×C4—241no—
561C22×C4—241no—
562C22×C4—241no—
563C22×C4—241no—
564C22×C4—241no—
565C22×C4D3×D411yescharacteristic
566C22×C4D3×D411yescharacteristic
567C22×C4C23×D311yescharacteristic
568SD16—28no—
569D8—68no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—32no—
576C2×C8—61no—
577C2×C8—61no—
578C2×C8—61no—
579C2×C8—61no—
580C2×C8—61no—
581C2×C8C2×C4×D312yes—
582C4⋊C4—24no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—32no—
587C4⋊C4—32no—
588C4⋊C4—62no—
589C4⋊C4—62no—
590C4⋊C4—64no—
591C4⋊C4—64no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—241no—
597C4⋊C4D3×D412yes—
598C22⋊C4—62no—
599C22⋊C4—62no—
600C22⋊C4—64no—
601C22⋊C4—64no—
602C22⋊C4—64no—
603C22⋊C4—81no—
604C22⋊C4—81no—
605C22⋊C4—122no—
606C22⋊C4—241no—
607C42—24no—
608C42—21no—
609C42—21no—
610C42—32no—
611C42—32no—
612C42—64no—
613C42—241no—
614C22×C3—42no—
615C22×C3—42no—
616C22×C3—42no—
617C22×C3—81no—
618C22×C3—81no—
619C22×C3—81no—
620C22×C3—81no—
621C22×C3C2×C4×D411yescharacteristic
622C22×C3C2×#12011yescharacteristic
623C22×C3#52511yescharacteristic
624C22×C3#57611yescharacteristic
625C22×C3#57711yescharacteristic
626C22×C3#57711yescharacteristic
627C22×C3#57711yescharacteristic
628C2×D3—22no—
629C2×D3—22no—
630C2×D3—22no—
631C2×D3—24no—
632C2×D3—41no—
633C2×D3—42no—
634C2×D3—41no—
635C2×D3—42no—
636C2×D3—42no—
637C2×D3—42no—
638C2×D3—41no—
639C2×D3—42no—
640C2×D3—41no—
641C2×D3—42no—
642C3×C4—24no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—42no—
646C3×C4—81no—
647C3×C4C2×C4×D411yescharacteristic
648C3×C4C2×C4×D411yescharacteristic
649C3×C4#52511yescharacteristic
650C3×C4#52511yescharacteristic
651Dic3—22no—
652Dic3—22no—
653Dic3—22no—
654Dic3—42no—
655Dic3—42no—
656Dic3—81no—
657C23—22no—
658C23—32no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—61no—
666C23—61no—
667C23—61no—
668C23—61no—
669C23—62no—
670C23—62no—
671C23—61no—
672C23—62no—
673C23—61no—
674C23—121no—
675C23—121no—
676C23—121no—
677C23—121no—
678C23C2×D3×D411yescharacteristic
679Q8—22no—
680Q8—22no—
681Q8—22no—
682Q8#67⋊C414yes—
683D4—22no—
684D4—22no—
685D4—34no—
686D4—41no—
687D4—41no—
688D4—616no—
689D4—62no—
690D4—62no—
691D4—62no—
692D4—244no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—32no—
704C2×C4—32no—
705C2×C4—32no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—616no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—244no—
732C2×C4—244no—
733C2×C4—244no—
734C2×C4—244no—
735C2×C4C22×C4×D311yescharacteristic
736C2×C4C2×D3×D411yescharacteristic
737C2×C4C2×D3×D411yescharacteristic
738C2×C4C2×#23711yescharacteristic
739C2×C4D3×#4111yescharacteristic
740C2×C4D3×#4111yescharacteristic
741C8—22no—
742C8—41no—
743C8—62no—
744C8—121no—
745C2×C3—82no—
746C2×C3C4×#12011yescharacteristic
747C2×C3#294611yescharacteristic
748C2×C3#295211yescharacteristic
749C2×C3#301011yescharacteristic
750C2×C3#301211yescharacteristic
751C2×C3#311911yescharacteristic
752C2×C3#312511yescharacteristic
753D3—42no—
754D3—44no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—62no—
759C22—62no—
760C22—64no—
761C22—62no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—122no—
767C22—122no—
768C22—121no—
769C22—122no—
770C22—121no—
771C22—122no—
772C22—121no—
773C22—122no—
774C22—121no—
775C22—122no—
776C22C4×D3×D411yescharacteristic
777C22D3×#12011yescharacteristic
778C22#560611yescharacteristic
779C22#576211yescharacteristic
780C22#577011yescharacteristic
781C22#577411yescharacteristic
782C22#577811yescharacteristic
783C4—24no—
784C4—41no—
785C4—41no—
786C4—42no—
787C4—62no—
788C4—62no—
789C4—62no—
790C4—81no—
791C4—122no—
792C4—122no—
793C4—241no—
794C4C2×#67⋊C411yescharacteristic
795C4C4×D3×D411yescharacteristic
796C4#560611yescharacteristic
797C4#565611yescharacteristic
798C3#2146411yescharacteristic, complemented, Sylow
799C2—82no—
800C2—122no—
801C2—124no—
802C2#7465911yescharacteristic
803C2#7965011yescharacteristic
804C2#7977511yescharacteristic
805C2#8004111yescharacteristic
806C2#8008711yescharacteristic
807C2#8036411yescharacteristic
808C2#8057511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1880C2
socleC23×C3C22×D4
prime radicalC2×#5172C2
cosocleC22×C3×C4C24
hypercenter#1880D3
hypocenterC3#21464
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
1. C2×#5574C2semidirect
3. C2×Dic3×SD16C2semidirect
4. C2×#4785C2semidirect
5. #76430C2semidirect
6. C3×#1880C2semidirect
7. #71629C2semidirect
8. #70267C2semidirect
9. #70220C2semidirect
10. #70200C2semidirect
11. #69657C2semidirect
12. #68875C2semidirect
13. #68780C2semidirect
14. #68671C2semidirect
15. #68601C2semidirect
40. #5172C4semidirect
70. #1880D3semidirect
89. C2×#239C2×C4semidirect
99. C2×C3×SD16C2×C4semidirect
114. Q8×Dic3D4semidirect
116. #938C2×C4semidirect
121. C2×#213C2×C4semidirect
142. #893D4semidirect
155. #835C2×C4semidirect
161. #821C2×C4semidirect
163. (C2×D3)⋊C8C2×C4semidirect
346. C2×SD16C4×D3semidirect
798. C3#21464semidirect

Maximal subgroups

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

subgroupindex
C2×#55742
C2×#51722
C2×Dic3×SD162
C2×#47852
#764302
C3×#18802
#716292
#702672
#702202
#702002
#696572
#688752
#687802
#686712
#686012
#214643