Finite Group Databasebeta

← #10848822

Subgroups — #10848822

Order 768.

1158 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5733C211yesmaximal, characteristic, complemented
2C2×#5089C211yesmaximal, characteristic, complemented
3C2×#4696C211yesmaximal, characteristic, complemented
4#74370C211yesmaximal, characteristic, complemented
5C3×#1990C211yesmaximal, characteristic, complemented
6#69753C211yesmaximal, characteristic, complemented
7#69581C211yesmaximal, characteristic, complemented
8#68909C211yesmaximal, characteristic, complemented
9#68908C211yesmaximal, characteristic, complemented
10#68897C211yesmaximal, characteristic, complemented
11#68896C211yesmaximal, characteristic, complemented
12#68888C211yesmaximal, characteristic, complemented
13#68887C211yesmaximal, characteristic, complemented
14#68887C211yesmaximal, characteristic, complemented
15#68886C211yesmaximal, characteristic
16#25610—31nomaximal, Sylow
17C2×C3×C4⋊Q8C2211yescharacteristic
18C2×#947—21no—
19C2×#946—21no—
20C22×Dic12C2211yescharacteristic
21C22×D24C2211yescharacteristic
22C22×#204C2211yescharacteristic
23C22×#204C2211yescharacteristic
24#5733—24no—
25#5733—24no—
26C2×#898—21no—
27C2×#897C2211yescharacteristic
28C2×#897C2211yescharacteristic
29C2×#895C2211yescharacteristic
30C2×#895C2211yescharacteristic
31C2×#894—21no—
32C2×#893C2211yescharacteristic
33C2×#887C2211yescharacteristic
34C2×#875C2211yescharacteristic
35C2×#875C2211yescharacteristic
36C2×#872C2211yescharacteristic
37C2×C3×C4×C8C2211yescharacteristic
38C3×#384C2211yescharacteristic
39C2×(C2×D3)⋊C8C2211yescharacteristic
40C2×(C2×D3)⋊C8C2211yescharacteristic
41#5089—24no—
42#4994—21no—
43#4994—21no—
44#4991—21no—
45#4991—21no—
46#4988C2211yescharacteristic
47#4973C2211yescharacteristic
48C2×#810C2211yescharacteristic
49C2×#810C2211yescharacteristic
50C2×#810C2211yescharacteristic
51C2×#810C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#809C2211yescharacteristic
55C2×#809C2211yescharacteristic
56C2×#803C2211yescharacteristic
57#4696—24no—
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62#4550C2211yescharacteristic
63#4550C2211yescharacteristic
64C2×#542—31no—
65C2×#495—31no—
66C2×#489—31no—
67#2620—31no—
68#2001—31no—
69#2000—31no—
70#2000—31no—
71#1999—31no—
72#1990D311yescharacteristic, complemented
73#1959—31no—
74#1880—31no—
75#1879—31no—
76#1878—31no—
77#1877—31no—
78#1750—31no—
79C22×C3×Q8—21no—
80C22×D12—21no—
81C22×D12—21no—
82C22×D12C2311yescharacteristic
83C22×D12C2311yescharacteristic
84C22×C4×D3—21no—
85C22×C4×D3C2311yescharacteristic
86C22×Dic6C2311yescharacteristic
87C22×Dic6C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C3×C4⋊Q8—22no—
91C3×C4⋊Q8D414yescomplemented
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4—21no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C42C2311yescharacteristic
100#947—28no—
101#946—28no—
102C2×(C2×D3)⋊C4—21no—
103C2×(C2×D3)⋊C4—21no—
104C2×(C2×D3)⋊C4—21no—
105C2×(C2×D3)⋊C4—21no—
106C2×(C2×D3)⋊C4—21no—
107C2×(C2×D3)⋊C4—21no—
108C2×(C2×D3)⋊C4—21no—
109C2×(C2×D3)⋊C4—21no—
110C2×(C2×D3)⋊C4—21no—
111C2×(C2×D3)⋊C4—21no—
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4D411yescharacteristic
114C2×(C2×D3)⋊C4D411yescharacteristic
115C2×C4⋊Dic3—21no—
116C2×C4⋊Dic3—21no—
117C2×Dic3⋊C4—21no—
118C2×Dic3⋊C4D411yescharacteristic
119C2×Dic3⋊C4D411yescharacteristic
120C2×C4×Dic3—21no—
121C2×C4×Dic3C2311yescharacteristic
122C22×C3⋊C8C2311yescharacteristic
123C22×C3⋊C8C2311yescharacteristic
124C2×Dic12—22no—
125C2×Dic12—22no—
126C2×Dic12—41no—
127C2×D24—22no—
128C2×D24—22no—
129C2×D24—41no—
130C2×#204—22no—
131C2×#204—22no—
132C2×#204—22no—
133C2×#204—22no—
134C2×#204—41no—
135C2×#204—41no—
136#898—28no—
137#897—22no—
138#897—22no—
139#897—41no—
140#897—41no—
141#895—22no—
142#895—22no—
143#895—41no—
144#895—41no—
145#894—28no—
146#893—22no—
147#893—22no—
148#887—22no—
149#887—22no—
150#875—22no—
151#875—22no—
152#875—22no—
153#875D414yescomplemented
154#872—22no—
155#872—22no—
156C3×C4×C8—22no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159(C2×D3)⋊C8—22no—
160(C2×D3)⋊C8—22no—
161#810—22no—
162#810—22no—
163#810—41no—
164#810—41no—
165#809—22no—
166#809—22no—
167#809—41no—
168#809—41no—
169#803—22no—
170C22×Q16—31no—
171C22×SD16—31no—
172C22×SD16—31no—
173C22×D8—31no—
174#542—64no—
175#542—64no—
176C2×C4⋊Q8C2×D311yescharacteristic
177C2×#126—61no—
178C2×#124—31no—
179C2×#124—31no—
180C2×#124—61no—
181C2×#123—61no—
182C2×C22⋊Q8—31no—
183C2×C22⋊Q8—31no—
184C2×C22⋊Q8—61no—
185C2×#121—31no—
186C2×#121—31no—
187C2×C4×Q8—31no—
188C2×C4×D4—31no—
189C2×#117—31no—
190#495—64no—
191#489—64no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×#102—31no—
200C2×C22⋊C8—31no—
201C2×C22⋊C8—31no—
202C2×#97—31no—
203C2×C4×C8C2×D311yescharacteristic
204#396—61no—
205#396—61no—
206#394—61no—
207#394—61no—
208#391—31no—
209#390—31no—
210#384C2×D311yescharacteristic
211#340C2×D311yescharacteristic
212#340C2×D311yescharacteristic
213#340C2×D311yescharacteristic
214#340C2×D311yescharacteristic
215#336—31no—
216#336—31no—
217C23×D3—21no—
218C23×D3—21no—
219C23×D3C2×D411yescharacteristic
220C2×C3×Q8—24no—
221C2×C3×Q8—81no—
222C2×C3×Q8—81no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4C2×D411yescharacteristic
228C22×C3×C4C2×D411yescharacteristic
229C22×C3×C4C2411yescharacteristic
230C22×Dic3—21no—
231C22×Dic3—21no—
232C22×Dic3C2×D411yescharacteristic
233C22×Dic3C2×D411yescharacteristic
234C22×Dic3C2×D411yescharacteristic
235C2×D12—21no—
236C2×D12—21no—
237C2×D12—21no—
238C2×D12—21no—
239C2×D12—21no—
240C2×D12—21no—
241C2×D12—21no—
242C2×D12—21no—
243C2×D12—21no—
244C2×D12—21no—
245C2×D12—21no—
246C2×D12—24no—
247C2×D12—42no—
248C2×D12—81no—
249C2×D12—81no—
250C2×D12—81no—
251C2×D12—81no—
252C2×D12C2×D412yes—
253C2×C4×D3—21no—
254C2×C4×D3—21no—
255C2×C4×D3—21no—
256C2×C4×D3—21no—
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×C4×D3—24no—
260C2×C4×D3—81no—
261C2×C4×D3—81no—
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6—21no—
266C2×Dic6—21no—
267C2×Dic6—21no—
268C2×Dic6—21no—
269C2×Dic6—21no—
270C2×Dic6—21no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6C2×D412yes—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8#4112yes—
279C2×C3×C8#4112yes—
280C3×C4⋊C4—24no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—81no—
288C3×C4⋊C4—81no—
289C3×C4⋊C4C2×D412yes—
290C3×C4⋊C4C2×D412yes—
291C3×C42C2×D412yes—
292C3×C42C2×D412yes—
293(C2×D3)⋊C4—24no—
294(C2×D3)⋊C4—24no—
295(C2×D3)⋊C4—24no—
296(C2×D3)⋊C4—22no—
297(C2×D3)⋊C4—22no—
298(C2×D3)⋊C4—24no—
299(C2×D3)⋊C4—24no—
300(C2×D3)⋊C4—42no—
301(C2×D3)⋊C4—42no—
302(C2×D3)⋊C4—42no—
303(C2×D3)⋊C4—42no—
304(C2×D3)⋊C4—81no—
305(C2×D3)⋊C4—81no—
306C4⋊Dic3—24no—
307C4⋊Dic3—42no—
308Dic3⋊C4—24no—
309Dic3⋊C4—22no—
310Dic3⋊C4—22no—
311C4×Dic3—24no—
312C4×Dic3—21no—
313C4×Dic3—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320Dic12—44no—
321D24—44no—
322#204—44no—
323#204—44no—
324C22×Q8—21no—
325C22×Q8—31no—
326C22×Q8—31no—
327C22×D4—31no—
328C22×D4—31no—
329C22×D4—61no—
330C22×D4—61no—
331C23×C4—31no—
332C23×C4—61no—
333C2×Q16—62no—
334C2×Q16—62no—
335C2×Q16—121no—
336C2×SD16—62no—
337C2×SD16—62no—
338C2×SD16—62no—
339C2×SD16—62no—
340C2×SD16—121no—
341C2×SD16—121no—
342C2×D8—62no—
343C2×D8—62no—
344C2×D8—121no—
345C22×C8—31no—
346C22×C8—31no—
347C22×C8C22×D311yescharacteristic
348C22×C8C22×D311yescharacteristic
349C4⋊Q8—22no—
350C4⋊Q8D1214yescomplemented
351#126—68no—
352#124—34no—
353#124—68no—
354#124—62no—
355#124—62no—
356#124—62no—
357#123—68no—
358C22⋊Q8—62no—
359C22⋊Q8—68no—
360C22⋊Q8—62no—
361C22⋊Q8—121no—
362C22⋊Q8—121no—
363#121—62no—
364#121—62no—
365#121—121no—
366#121—121no—
367C4×Q8—62no—
368C4×Q8—62no—
369C4×D4—62no—
370C4×D4—62no—
371#117—62no—
372#117—62no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—31no—
377C2×C4⋊C4—31no—
378C2×C4⋊C4—61no—
379C2×C4⋊C4—61no—
380C2×C4⋊C4—61no—
381C2×C4⋊C4C22×D311yescharacteristic
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×C22⋊C4—61no—
395C2×C22⋊C4—61no—
396C2×C22⋊C4—61no—
397C2×C22⋊C4—61no—
398C2×C42—31no—
399C2×C42—61no—
400C2×C42C22×D311yescharacteristic
401#103—62no—
402#103—62no—
403#103—121no—
404#103—121no—
405#102—62no—
406#102—62no—
407#102—121no—
408#102—121no—
409C22⋊C8—62no—
410C22⋊C8—62no—
411#97—62no—
412C4×C8—22no—
413#95—61no—
414#95—61no—
415C23×C3C22×D411yescharacteristic
416C22×D3—21no—
417C22×D3—22no—
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—21no—
421C22×D3—21no—
422C22×D3—21no—
423C22×D3—21no—
424C22×D3—41no—
425C22×D3—41no—
426C22×D3—41no—
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—
437C3×Q8—84no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4#12012yes—
455C2×C3×C4#12012yes—
456C2×C3×C4C22×D411yescharacteristic
457C2×C3×C4C22×D411yescharacteristic
458C2×C3×C4C2×#4111yescharacteristic
459C2×C3×C4C2×#4111yescharacteristic
460C2×C3×C4H(5,𝔽2)11yescharacteristic
461C2×C3×C4H(5,𝔽2)11yescharacteristic
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—22no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477D12—22no—
478D12—22no—
479D12—41no—
480D12—41no—
481D12—41no—
482D12—41no—
483D12—41no—
484D12—41no—
485D12—84no—
486D12—84no—
487C4×D3—41no—
488C4×D3—41no—
489C4×D3—41no—
490C4×D3—41no—
491C4×D3—84no—
492Dic6—22no—
493Dic6—22no—
494Dic6—41no—
495Dic6—41no—
496Dic6—41no—
497Dic6—41no—
498Dic6—41no—
499Dic6—41no—
500C3×C8—22no—
501C3×C8—22no—
502C3⋊C8—41no—
503C3⋊C8—41no—
504C24—31no—
505C24—61no—
506C24—61no—
507C2×Q8—24no—
508C2×Q8—32no—
509C2×Q8—61no—
510C2×Q8—61no—
511C2×Q8—61no—
512C2×Q8—61no—
513C2×Q8—61no—
514C2×Q8—61no—
515C2×Q8—61no—
516C2×Q8—61no—
517C2×Q8—61no—
518C2×Q8—61no—
519C2×Q8—61no—
520C2×Q8—81no—
521C2×Q8—81no—
522C2×D4—32no—
523C2×D4—64no—
524C2×D4—61no—
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—61no—
534C2×D4—61no—
535C2×D4—122no—
536C2×D4—241no—
537C2×D4—241no—
538C2×D4—241no—
539C2×D4—241no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—31no—
547C22×C4—64no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—241no—
557C22×C4—241no—
558C22×C4D3×D411yescharacteristic
559C22×C4D3×D411yescharacteristic
560C22×C4C23×D311yescharacteristic
561Q16—124no—
562SD16—124no—
563SD16—124no—
564D8—124no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—61no—
570C2×C8—61no—
571C2×C8—61no—
572C2×C8—61no—
573C2×C8—61no—
574C2×C8—61no—
575C2×C8#23912yes—
576C2×C8#23912yes—
577C4⋊C4—24no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—64no—
585C4⋊C4—64no—
586C4⋊C4—62no—
587C4⋊C4—62no—
588C4⋊C4—81no—
589C4⋊C4—81no—
590C4⋊C4—122no—
591C4⋊C4C2×D1212yes—
592C4⋊C4C2×D1212yes—
593C22⋊C4—64no—
594C22⋊C4—64no—
595C22⋊C4—64no—
596C22⋊C4—62no—
597C22⋊C4—62no—
598C22⋊C4—64no—
599C22⋊C4—64no—
600C22⋊C4—122no—
601C22⋊C4—122no—
602C22⋊C4—122no—
603C22⋊C4—122no—
604C22⋊C4—241no—
605C22⋊C4—241no—
606C42—64no—
607C42—61no—
608C42—61no—
609C42C2×D1212yes—
610C42D3×D412yes—
611C22×C3C2×#12011yescharacteristic
612C22×C3#53211yescharacteristic
613C22×C3#53511yescharacteristic
614C22×C3#57611yescharacteristic
615C22×C3#57711yescharacteristic
616C22×C3#57711yescharacteristic
617C22×C3#57811yescharacteristic
618C2×D3—41no—
619C2×D3—41no—
620C2×D3—41no—
621C2×D3—42no—
622C2×D3—41no—
623C2×D3—41no—
624C2×D3—42no—
625C2×D3—41no—
626C2×D3—41no—
627C2×D3—42no—
628C2×D3—81no—
629C2×D3—81no—
630C2×D3—81no—
631C2×D3—81no—
632C2×D3—81no—
633C2×D3—81no—
634C2×D3—81no—
635C2×D3—81no—
636C2×D3—81no—
637C2×D3—81no—
638C2×D3—81no—
639C3×C4—22no—
640C3×C4—22no—
641C3×C4—42no—
642C3×C4—42no—
643C3×C4—81no—
644C3×C4—81no—
645C3×C4#54611yescharacteristic
646C3×C4#54611yescharacteristic
647C3×C4#55011yescharacteristic
648C3×C4#55011yescharacteristic
649Dic3—42no—
650Dic3—41no—
651Dic3—41no—
652Dic3—41no—
653Dic3—81no—
654C23—61no—
655C23—61no—
656C23—62no—
657C23—61no—
658C23—61no—
659C23—61no—
660C23—61no—
661C23—61no—
662C23—121no—
663C23—121no—
664C23—121no—
665C23—121no—
666C23—121no—
667C23—121no—
668C23—121no—
669C23—121no—
670C23—121no—
671C23—121no—
672C23—121no—
673C23—121no—
674C23—121no—
675C23C2×D3×D411yescharacteristic
676Q8—62no—
677Q8—62no—
678Q8—84no—
679Q8—121no—
680Q8—121no—
681Q8—121no—
682Q8—121no—
683Q8—121no—
684Q8—121no—
685D4—62no—
686D4—62no—
687D4—121no—
688D4—121no—
689D4—121no—
690D4—121no—
691D4—121no—
692D4—121no—
693D4—244no—
694D4—244no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—62no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—121no—
722C2×C4—121no—
723C2×C4—121no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—244no—
731C2×C4#88212yes—
732C2×C4#88212yes—
733C2×C4C22×D1211yescharacteristic
734C2×C4C2×D3×D411yescharacteristic
735C2×C4C2×#23911yescharacteristic
736C2×C4C2×#23911yescharacteristic
737C2×C4#100911yescharacteristic
738C2×C4#100911yescharacteristic
739C8—22no—
740C8—22no—
741C8—121no—
742C8—121no—
743C2×C3#243111yescharacteristic
744C2×C3#301211yescharacteristic
745C2×C3#301311yescharacteristic
746C2×C3#317311yescharacteristic
747C2×C3#317511yescharacteristic
748C2×C3#322411yescharacteristic
749C2×C3#322511yescharacteristic
750D3—81no—
751D3—82no—
752D3—161no—
753C22—121no—
754C22—121no—
755C22—122no—
756C22—122no—
757C22—121no—
758C22—121no—
759C22—121no—
760C22—121no—
761C22—122no—
762C22—121no—
763C22—241no—
764C22—241no—
765C22—241no—
766C22—241no—
767C22—241no—
768C22—241no—
769C22—241no—
770C22—241no—
771C22—241no—
772C22—241no—
773C22—241no—
774C22C2×#88211yescharacteristic
775C22#567411yescharacteristic
776C22#572511yescharacteristic
777C22#575711yescharacteristic
778C22#576211yescharacteristic
779C22#576211yescharacteristic
780C22#576611yescharacteristic
781C4—22no—
782C4—22no—
783C4—42no—
784C4—42no—
785C4—81no—
786C4—81no—
787C4—121no—
788C4—122no—
789C4—121no—
790C4—121no—
791C4—241no—
792C4#557711yescharacteristic
793C4#557711yescharacteristic
794C4#563011yescharacteristic
795C4#563011yescharacteristic
796C3#2561011yescharacteristic, complemented, Sylow
797C2—241no—
798C2—242no—
799C2—481no—
800C2#7662611yescharacteristic
801C2#7874711yescharacteristic
802C2#7879511yescharacteristic
803C2#8157011yescharacteristic
804C2#8160611yescharacteristic
805C2#8188711yescharacteristic
806C2#8193511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1990C2
socleC23×C3C22×D4
prime radical#68886C2
hypercenter#1990D3
hypocenterC3#25610
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
1. C2×#5733C2semidirect
2. C2×#5089C2semidirect
3. C2×#4696C2semidirect
4. #74370C2semidirect
5. C3×#1990C2semidirect
6. #69753C2semidirect
7. #69581C2semidirect
8. #68909C2semidirect
9. #68908C2semidirect
10. #68897C2semidirect
11. #68896C2semidirect
12. #68888C2semidirect
13. #68887C2semidirect
14. #68887C2semidirect
72. #1990D3semidirect
91. C3×C4⋊Q8D4semidirect
153. #875D4semidirect
350. C4⋊Q8D12semidirect
796. C3#25610semidirect

Maximal subgroups

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

subgroupindex
C2×#57332
C2×#50892
C2×#46962
#743702
C3×#19902
#697532
#695812
#689092
#689082
#688972
#688962
#688882
#688872
#688862
#256103