Finite Group Databasebeta

← #10800998

Subgroups — #10800998

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×C4×#215C211yesmaximal, characteristic, complemented
3C2×#4810C211yesmaximal, characteristic
4C2×#4711C211yesmaximal, characteristic, complemented
5#73763C211yesmaximal, characteristic, complemented
6C3×#1763C211yesmaximal, characteristic, complemented
7#70267C211yesmaximal, characteristic, complemented
8#70240C211yesmaximal, characteristic, complemented
9#70238C211yesmaximal, characteristic, complemented
10#69830C211yesmaximal, characteristic, complemented
11C4×#809C211yesmaximal, characteristic, complemented
12#68897C211yesmaximal, characteristic, complemented
13#68895C211yesmaximal, characteristic, complemented
14#68880C211yesmaximal, characteristic, complemented
15#68875C211yesmaximal, characteristic, complemented
16#21464—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C2×C3×C4×Q8C2211yescharacteristic
19C2×Q8×Dic3C2211yescharacteristic
20C22×#215C2211yescharacteristic
21C22×D24C2211yescharacteristic
22#5574—24no—
23#5574—24no—
24C2×#895C2211yescharacteristic
25C2×#893—21no—
26C2×#893C2211yescharacteristic
27C2×D3×C4⋊C4—21no—
28C2×D3×C4⋊C4C2211yescharacteristic
29C2×C4×D12—21no—
30C2×C4×D12C2211yescharacteristic
31C2×C4×D12C2211yescharacteristic
32C2×#872—21no—
33C2×#872C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C2×C3×#97C2211yescharacteristic
37C3×C4×C4⋊C4C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#821C2211yescharacteristic
40C2×#821C2211yescharacteristic
41C2×(C2×D3)⋊C8C2211yescharacteristic
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×#817C2211yescharacteristic
44C4×#215—24no—
45#4988C2211yescharacteristic
46#4987C2211yescharacteristic
47#4984C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#808C2211yescharacteristic
52#4940—21no—
53#4939—21no—
54C2×C4×C3⋊C8C2211yescharacteristic
55#4810C418yescomplemented
56#4711—24no—
57#4668—21no—
58#4665—21no—
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61#4550C2211yescharacteristic
62#4550C2211yescharacteristic
63#4529C2211yescharacteristic
64#4529C2211yescharacteristic
65C2×#520—31no—
66C2×#449—31no—
67C2×#442—31no—
68C2×C4×SD16—31no—
69#2324—31no—
70#1880—31no—
71#1879—31no—
72#1874—31no—
73#1865—31no—
74#1864—31no—
75#1853—31no—
76#1788—31no—
77#1763D311yescharacteristic, complemented
78C4×#102—31no—
79#1750—31no—
80C22×C3×Q8C2311yescharacteristic
81C2×#239—22no—
82C2×#239—22no—
83C2×#239—22no—
84C2×#239—22no—
85C2×#239—22no—
86C2×#239C2×C414yescomplemented
87C22×D12—21no—
88C22×D12—21no—
89C22×D12C2311yescharacteristic
90C22×D12C2311yescharacteristic
91C22×C4×D3—21no—
92C22×C4×D3—21no—
93C22×C4×D3—21no—
94C22×C4×D3—21no—
95C22×C4×D3—21no—
96C22×C4×D3C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C3×C4×Q8—22no—
100C3×C4×Q8D414yescomplemented
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C42—21no—
106C2×C3×C42—21no—
107C2×C3×C42C2311yescharacteristic
108Q8×Dic3—22no—
109Q8×Dic3—22no—
110C2×#215—22no—
111C2×#215—22no—
112C2×#215C2×C414yescomplemented
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4D411yescharacteristic
121C2×(C2×D3)⋊C4D411yescharacteristic
122C2×C4⋊Dic3—21no—
123C2×C4⋊Dic3—21no—
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×Dic3⋊C4—21no—
127C2×Dic3⋊C4D411yescharacteristic
128C2×Dic3⋊C4D411yescharacteristic
129C2×C4×Dic3—21no—
130C2×C4×Dic3C2311yescharacteristic
131C22×C3⋊C8C2311yescharacteristic
132C22×C3⋊C8C2311yescharacteristic
133C2×D24—22no—
134C2×D24—22no—
135C2×D24C2×C414yescomplemented
136#895—22no—
137#895C2×C414yescomplemented
138#893—28no—
139#893—22no—
140#893—22no—
141D3×C4⋊C4—28no—
142D3×C4⋊C4—22no—
143D3×C4⋊C4—22no—
144C4×D12—28no—
145C4×D12—22no—
146C4×D12—22no—
147C4×D12—22no—
148C4×D12D414yescomplemented
149#872—28no—
150#872—22no—
151#872—22no—
152C3×#103—22no—
153C3×#103C2×C414yescomplemented
154C3×#97—22no—
155C3×#95—21no—
156#835—22no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159#821—22no—
160#821—22no—
161(C2×D3)⋊C8—22no—
162(C2×D3)⋊C8C2×C414yescomplemented
163#817—22no—
164#809—22no—
165#809—22no—
166#809C2×C414yescomplemented
167#808—22no—
168C4×C3⋊C8—22no—
169C22×#41—31no—
170C22×SD16—31no—
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×#103C2×D311yescharacteristic
193C2×#103C2×D311yescharacteristic
194C2×#102—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×C22⋊C8—31no—
200C2×C22⋊C8—31no—
201C2×#97C2×D311yescharacteristic
202C2×C4×C8—31no—
203#390—31no—
204#390—61no—
205#389—31no—
206#388—61no—
207#386—61no—
208#385—61no—
209#380—31no—
210C4×C4⋊C4C2×D311yescharacteristic
211#340—31no—
212#340—31no—
213#340C2×D311yescharacteristic
214#340C2×D311yescharacteristic
215#336—31no—
216#336—31no—
217C23×D3—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—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2×D411yescharacteristic
232C22×C3×C4C2411yescharacteristic
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3C2×D411yescharacteristic
236C22×Dic3C2×D411yescharacteristic
237C22×Dic3C2×D411yescharacteristic
238#239—28no—
239#239—28no—
240#239—28no—
241#239—28no—
242C2×D12—24no—
243C2×D12—24no—
244C2×D12—24no—
245C2×D12—21no—
246C2×D12—21no—
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—24no—
254C2×D12—81no—
255C2×D12—81no—
256C2×D12C22×C412yes—
257C2×D12C22×C412yes—
258C2×D12C2×D412yes—
259C2×D12#4112yes—
260C2×C4×D3—24no—
261C2×C4×D3—24no—
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×C4×D3—21no—
266C2×C4×D3—24no—
267C2×C4×D3—24no—
268C2×C4×D3—24no—
269C2×C4×D3—24no—
270C2×C4×D3—42no—
271C2×C4×D3—81no—
272C2×C4×D3—81no—
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—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8C22×C412yes—
287C3×C4⋊C4—24no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—21no—
292C3×C4⋊C4C22×C412yes—
293C3×C4⋊C4C2×D412yes—
294C3×C42—24no—
295C3×C42—81no—
296C3×C42C2×D412yes—
297C3×C42C2×D412yes—
298#215—28no—
299(C2×D3)⋊C4—24no—
300(C2×D3)⋊C4—22no—
301(C2×D3)⋊C4—24no—
302(C2×D3)⋊C4—22no—
303(C2×D3)⋊C4—24no—
304(C2×D3)⋊C4—42no—
305(C2×D3)⋊C4—81no—
306(C2×D3)⋊C4—81no—
307(C2×D3)⋊C4—81no—
308C4⋊Dic3—24no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3—21no—
312C4⋊Dic3—81no—
313C4⋊Dic3C2×D412yes—
314Dic3⋊C4—24no—
315Dic3⋊C4—22no—
316Dic3⋊C4—22no—
317C4×Dic3—24no—
318C4×Dic3—21no—
319C4×Dic3—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8—21no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8C22×C412yes—
326D24—28no—
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—31no—
336C22×D4—61no—
337C22×D4—61no—
338C23×C4—31no—
339C23×C4—61no—
340C23×C4—61no—
341C23×C4—61no—
342C23×C4—61no—
343C23×C4—61no—
344C2×SD16—34no—
345C2×SD16—62no—
346C2×SD16—62no—
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—62no—
358C4×Q8—62no—
359C4×Q8D1214yescomplemented
360C4×D4—34no—
361C4×D4—68no—
362C4×D4—62no—
363C4×D4—68no—
364C4×D4—62no—
365C4×D4—62no—
366C4×D4—62no—
367C4×D4—62no—
368#117—68no—
369#117—62no—
370#117—62no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—31no—
376C2×C4⋊C4—62no—
377C2×C4⋊C4—68no—
378C2×C4⋊C4—61no—
379C2×C4⋊C4—61no—
380C2×C4⋊C4—62no—
381C2×C4⋊C4—61no—
382C2×C4⋊C4C22×D311yescharacteristic
383C2×C4⋊C4C22×D311yescharacteristic
384C2×C4⋊C4C22×D311yescharacteristic
385C2×C22⋊C4—31no—
386C2×C22⋊C4—31no—
387C2×C22⋊C4—61no—
388C2×C22⋊C4—61no—
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—21no—
396C2×C42—31no—
397C2×C42—61no—
398C2×C42C22×D311yescharacteristic
399#106—62no—
400#106—62no—
401#103—22no—
402#103—62no—
403#103C4×D314yescomplemented
404#102—34no—
405#102—62no—
406#102—62no—
407#102—62no—
408#102—62no—
409C22⋊C8—34no—
410C22⋊C8—62no—
411#97—22no—
412C4×C8—62no—
413#95—21no—
414#95—61no—
415#95—61no—
416C23×C3C22×D411yescharacteristic
417C22×D3—22no—
418C22×D3—21no—
419C22×D3—22no—
420C22×D3—21no—
421C22×D3—22no—
422C22×D3—21no—
423C22×D3—21no—
424C22×D3—21no—
425C22×D3—21no—
426C22×D3—22no—
427C22×D3—41no—
428C22×D3—41no—
429C22×D3—41no—
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—41no—
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—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4#12012yes—
459C2×C3×C4#12012yes—
460C2×C3×C4C23×C411yescharacteristic
461C2×C3×C4C22×D411yescharacteristic
462C2×C3×C4C22×D411yescharacteristic
463C2×C3×C4C2×#4111yescharacteristic
464C2×C3×C4C2×#4111yescharacteristic
465C2×C3×C4C2×#4111yescharacteristic
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—22no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3C4×D412yes—
481D12—216no—
482D12—22no—
483D12—22no—
484D12—22no—
485D12—22no—
486D12—22no—
487D12—41no—
488D12—41no—
489D12—84no—
490D12C4×D414yes—
491C4×D3—216no—
492C4×D3—22no—
493C4×D3—22no—
494C4×D3—22no—
495C4×D3—22no—
496C4×D3—84no—
497C4×D3—84no—
498C4×D3—84no—
499C4×D3—84no—
500C3×C8—22no—
501C3×C8—41no—
502C3⋊C8—22no—
503C3⋊C8—41no—
504C24—31no—
505C24—61no—
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×Q8C2×D1212yes—
516C2×Q8#23512yes—
517C2×D4—32no—
518C2×D4—32no—
519C2×D4—32no—
520C2×D4—32no—
521C2×D4—64no—
522C2×D4—64no—
523C2×D4—64no—
524C2×D4—64no—
525C2×D4—61no—
526C2×D4—61no—
527C2×D4—61no—
528C2×D4—61no—
529C2×D4—61no—
530C2×D4—61no—
531C2×D4—61no—
532C2×D4—61no—
533C2×D4—241no—
534C2×D4—241no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—31no—
540C22×C4—32no—
541C22×C4—32no—
542C22×C4—31no—
543C22×C4—31no—
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—64no—
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—68no—
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—21no—
587C4⋊C4—32no—
588C4⋊C4—64no—
589C4⋊C4—64no—
590C4⋊C4—62no—
591C4⋊C4—62no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—241no—
596C4⋊C4C2×C4×D312yes—
597C4⋊C4C2×D1212yes—
598C22⋊C4—64no—
599C22⋊C4—64no—
600C22⋊C4—62no—
601C22⋊C4—62no—
602C22⋊C4—64no—
603C22⋊C4—122no—
604C22⋊C4—241no—
605C22⋊C4—241no—
606C22⋊C4—241no—
607C42—24no—
608C42—64no—
609C42—61no—
610C42—61no—
611C42—81no—
612C42C2×D1212yes—
613C42D3×D412yes—
614C22×C3C2×C4×D411yescharacteristic
615C22×C3C2×#12011yescharacteristic
616C22×C3#52511yescharacteristic
617C22×C3#57611yescharacteristic
618C22×C3#57711yescharacteristic
619C22×C3#57711yescharacteristic
620C22×C3#57711yescharacteristic
621C2×D3—22no—
622C2×D3—22no—
623C2×D3—22no—
624C2×D3—24no—
625C2×D3—41no—
626C2×D3—42no—
627C2×D3—41no—
628C2×D3—42no—
629C2×D3—42no—
630C2×D3—42no—
631C2×D3—41no—
632C2×D3—42no—
633C2×D3—41no—
634C2×D3—42no—
635C2×D3—42no—
636C2×D3—42no—
637C2×D3—42no—
638C2×D3—81no—
639C2×D3—81no—
640C2×D3—81no—
641C2×D3—81no—
642C3×C4—22no—
643C3×C4—22no—
644C3×C4—24no—
645C3×C4—42no—
646C3×C4—42no—
647C3×C4—81no—
648C3×C4C2×C4×D411yescharacteristic
649C3×C4C2×C4×D411yescharacteristic
650C3×C4#52511yescharacteristic
651C3×C4#52511yescharacteristic
652Dic3—22no—
653Dic3—41no—
654Dic3—41no—
655Dic3—42no—
656Dic3—81no—
657C23—32no—
658C23—62no—
659C23—61no—
660C23—61no—
661C23—61no—
662C23—61no—
663C23—61no—
664C23—62no—
665C23—62no—
666C23—61no—
667C23—62no—
668C23—121no—
669C23—121no—
670C23—121no—
671C23—121no—
672C23—121no—
673C23—121no—
674C23—121no—
675C23—121no—
676C23—121no—
677C23—121no—
678C23C2×D3×D411yescharacteristic
679Q8—22no—
680Q8—22no—
681Q8—22no—
682Q8C4×D1214yes—
683D4—34no—
684D4—616no—
685D4—62no—
686D4—62no—
687D4—62no—
688D4—62no—
689D4—62no—
690D4—121no—
691D4—121no—
692D4—244no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—32no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—616no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—61no—
718C2×C4—62no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—244no—
730C2×C4—244no—
731C2×C4—244no—
732C2×C4—244no—
733C2×C4#88212yes—
734C2×C4#88212yes—
735C2×C4C22×C4×D311yescharacteristic
736C2×C4C22×D1211yescharacteristic
737C2×C4C2×#23511yescharacteristic
738C2×C4C2×D3×D411yescharacteristic
739C2×C4D3×#4111yescharacteristic
740C2×C4D3×#4111yescharacteristic
741C8—22no—
742C8—41no—
743C8—62no—
744C8—121no—
745C2×C3C4×#12011yescharacteristic
746C2×C3#294611yescharacteristic
747C2×C3#295211yescharacteristic
748C2×C3#301011yescharacteristic
749C2×C3#301211yescharacteristic
750C2×C3#311911yescharacteristic
751C2×C3#312511yescharacteristic
752D3—42no—
753D3—44no—
754D3—82no—
755C22—64no—
756C22—62no—
757C22—62no—
758C22—62no—
759C22—121no—
760C22—122no—
761C22—121no—
762C22—122no—
763C22—122no—
764C22—121no—
765C22—122no—
766C22—122no—
767C22—121no—
768C22—122no—
769C22—122no—
770C22—122no—
771C22—122no—
772C22—241no—
773C22—241no—
774C22—241no—
775C22—241no—
776C22C2×#88211yescharacteristic
777C22C4×D3×D411yescharacteristic
778C22#554711yescharacteristic
779C22#577411yescharacteristic
780C22#577811yescharacteristic
781C22#577811yescharacteristic
782C22#577811yescharacteristic
783C4—22no—
784C4—24no—
785C4—22no—
786C4—42no—
787C4—42no—
788C4—62no—
789C4—81no—
790C4—121no—
791C4—122no—
792C4—121no—
793C4—241no—
794C4C2×C4×D1211yescharacteristic
795C4#552411yescharacteristic
796C4C4×D3×D411yescharacteristic
797C4#554711yescharacteristic
798C3#2146411yescharacteristic, complemented, Sylow
799C2—122no—
800C2—124no—
801C2—242no—
802C2C4×#88211yescharacteristic
803C2#7888611yescharacteristic
804C2#7896011yescharacteristic
805C2#7977511yescharacteristic
806C2#7981211yescharacteristic
807C2#7983211yescharacteristic
808C2#7985011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1763C2
socleC23×C3C22×D4
prime radicalC2×#4810C2
cosocleC22×C3×C4C24
hypercenter#1763D3
hypocenterC3#21464
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
1. C2×#5574C2semidirect
2. C2×C4×#215C2semidirect
4. C2×#4711C2semidirect
5. #73763C2semidirect
6. C3×#1763C2semidirect
7. #70267C2semidirect
8. #70240C2semidirect
9. #70238C2semidirect
10. #69830C2semidirect
11. C4×#809C2semidirect
12. #68897C2semidirect
13. #68895C2semidirect
14. #68880C2semidirect
15. #68875C2semidirect
55. #4810C4semidirect
77. #1763D3semidirect
86. C2×#239C2×C4semidirect
100. C3×C4×Q8D4semidirect
112. C2×#215C2×C4semidirect
135. C2×D24C2×C4semidirect
137. #895C2×C4semidirect
148. C4×D12D4semidirect
153. C3×#103C2×C4semidirect
162. (C2×D3)⋊C8C2×C4semidirect
166. #809C2×C4semidirect
359. C4×Q8D12semidirect
403. #103C4×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×C4×#2152
C2×#48102
C2×#47112
#737632
C3×#17632
#702672
#702402
#702382
#698302
C4×#8092
#688972
#688952
#688802
#688752
#214643