Finite Group Databasebeta

← #10848762

Subgroups — #10848762

Order 768.

1178 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5580C211yesmaximal, characteristic
2C2×#5190C211yesmaximal, characteristic, complemented
3C2×#4797C211yesmaximal, characteristic, complemented
4#76664C211yesmaximal, characteristic, complemented
5C3×#1878C211yesmaximal, characteristic, complemented
6#72071C211yesmaximal, characteristic, complemented
7#71632C211yesmaximal, characteristic, complemented
8#70273C211yesmaximal, characteristic, complemented
9#70272C211yesmaximal, characteristic
10#70227C211yesmaximal, characteristic, complemented
11#69687C211yesmaximal, characteristic, complemented
12#68887C211yesmaximal, characteristic
13#68805C211yesmaximal, characteristic, complemented
14#68672C211yesmaximal, characteristic, complemented
15#68600C211yesmaximal, characteristic, complemented
16#25604—31nomaximal, Sylow
17C22×C3×Q16C2211yescharacteristic
18C2×C3×C4×Q8C2211yescharacteristic
19C2×#947C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C2×#944C2211yescharacteristic
23C22×#216C2211yescharacteristic
24C22×#215C2211yescharacteristic
25C22×#204C2211yescharacteristic
26#5580—24no—
27#5580—24no—
28C2×#898—21no—
29C2×#897C2211yescharacteristic
30C2×#895C2211yescharacteristic
31C2×#894—21no—
32C2×#890C2211yescharacteristic
33C2×C4×D12—21no—
34C2×C4×D12C2211yescharacteristic
35C2×#872—21no—
36C2×C42×D3C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C3×#391C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#835C2211yescharacteristic
42#5190—24no—
43C2×#821C2211yescharacteristic
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#816C2211yescharacteristic
47C2×#815C2211yescharacteristic
48C2×#815C2211yescharacteristic
49#4975C2211yescharacteristic
50C2×#810C2211yescharacteristic
51C2×#809C2211yescharacteristic
52#4929C2211yescharacteristic
53#4797—24no—
54#4667—21no—
55#4667—21no—
56#4647—21no—
57#4647—21no—
58C3×#340C2211yescharacteristic
59C3×#336C2211yescharacteristic
60#4551C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#529—31no—
65C2×#497—31no—
66C2×#491—31no—
67#2857—31no—
68#2001—31no—
69#2001—31no—
70#2000—31no—
71#2000—31no—
72#1992—31no—
73#1959—31no—
74#1878—31no—
75#1878D311yescharacteristic, complemented
76#1877—31no—
77#1877—31no—
78#1749—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×D12—21no—
82C22×D12C2311yescharacteristic
83C22×C4×D3—21no—
84C22×C4×D3D411yescharacteristic
85C22×C4×D3D411yescharacteristic
86C22×C4×D3C2311yescharacteristic
87C22×Dic6C2311yescharacteristic
88C2×C3×Q16—22no—
89C2×C3×Q16—22no—
90C2×C3×Q16—41no—
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C3×C4×Q8—22no—
94C3×C4×Q8—22no—
95C2×C3×C4⋊C4—21no—
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C42—21no—
99C2×C3×C42C2311yescharacteristic
100#947—22no—
101#947D414yes—
102#946—22no—
103#946—22no—
104#946—41no—
105#946—41no—
106#944—22no—
107#944—22no—
108C2×#216—22no—
109C2×#216—22no—
110C2×#216—41no—
111C2×#215—22no—
112C2×#215—22no—
113C2×#215—41no—
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)⋊C4—21no—
121C2×C4⋊Dic3—21no—
122C2×C4⋊Dic3—21no—
123C2×C4⋊Dic3C2311yescharacteristic
124C2×C4⋊Dic3C2311yescharacteristic
125C2×Dic3⋊C4—21no—
126C2×Dic3⋊C4—21no—
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×C4×Dic3D411yescharacteristic
133C2×C4×Dic3D411yescharacteristic
134C2×C4×Dic3C2311yescharacteristic
135C22×C3⋊C8C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137C2×#204—22no—
138C2×#204—22no—
139C2×#204—41no—
140#898—28no—
141#897—41no—
142#897—41no—
143#895—22no—
144#895—22no—
145#894—28no—
146#890—22no—
147#890D414yes—
148C4×D12—28no—
149C4×D12—22no—
150C4×D12—22no—
151#872—28no—
152C42×D3—22no—
153C42×D3—22no—
154C3×#103—22no—
155C3×#103—41no—
156C3×#95—21no—
157C3×#95—21no—
158#835—22no—
159#835—41no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162#821—41no—
163(C2×D3)⋊C8—22no—
164(C2×D3)⋊C8—22no—
165#816—22no—
166#815—22no—
167#815—22no—
168#810—22no—
169#809—41no—
170C22×Q16—31no—
171C22×Q16C2×D311yescharacteristic
172C22×SD16—31no—
173C22×SD16—31no—
174C2×C4⋊Q8—31no—
175#529—64no—
176#529—64no—
177C2×#126—61no—
178C2×#125—31no—
179C2×#124—31no—
180C2×#123—61no—
181C2×C22⋊Q8—31no—
182C2×C22⋊Q8—31no—
183C2×C22⋊Q8—31no—
184C2×#121—31no—
185C2×C4×Q8C2×D311yescharacteristic
186C2×C4×D4—31no—
187C2×C4×D4—61no—
188C2×#117—61no—
189C22×C42—31no—
190#497—64no—
191#491—64no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103—31no—
196C2×#103C2×D311yescharacteristic
197C2×#103C2×D311yescharacteristic
198C2×#102—31no—
199C2×#102—31no—
200C2×C22⋊C8—31no—
201C2×C22⋊C8—31no—
202C2×#97—31no—
203C2×#97—31no—
204#391—31no—
205#391C2×D311yescharacteristic
206#389—61no—
207#389—61no—
208#384—31no—
209#380—61no—
210#380—61no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340C2×D311yescharacteristic
215#336—31no—
216#336C2×D311yescharacteristic
217C23×D3—21no—
218C23×D3C2×D411yescharacteristic
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8C2×D412yes—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2411yescharacteristic
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3—21no—
241C22×Dic3C2×D411yescharacteristic
242C22×Dic3C2×D411yescharacteristic
243C22×Dic3C2×D411yescharacteristic
244C2×D12—21no—
245C2×D12—21no—
246C2×D12—21no—
247C2×D12—21no—
248C2×D12—24no—
249C2×D12—21no—
250C2×D12—42no—
251C2×D12—42no—
252C2×D12C2×D412yes—
253C2×C4×D3—24no—
254C2×C4×D3—22no—
255C2×C4×D3—22no—
256C2×C4×D3—21no—
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×C4×D3—21no—
262C2×C4×D3—22no—
263C2×C4×D3—22no—
264C2×C4×D3—41no—
265C2×C4×D3—41no—
266C2×C4×D3—42no—
267C2×C4×D3—42no—
268C2×Dic6—21no—
269C2×Dic6—21no—
270C2×Dic6—21no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C3×Q16—44no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8#4112yes—
281C3×C4⋊C4—24no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4C2×D412yes—
286C3×C42—24no—
287C3×C42—21no—
288C3×C42—21no—
289#216—44no—
290#215—44no—
291(C2×D3)⋊C4—24no—
292(C2×D3)⋊C4—24no—
293(C2×D3)⋊C4—24no—
294(C2×D3)⋊C4—24no—
295(C2×D3)⋊C4—24no—
296(C2×D3)⋊C4—42no—
297(C2×D3)⋊C4—42no—
298C4⋊Dic3—21no—
299C4⋊Dic3—24no—
300C4⋊Dic3—21no—
301C4⋊Dic3—21no—
302C4⋊Dic3—42no—
303C4⋊Dic3C2×D412yes—
304Dic3⋊C4—24no—
305Dic3⋊C4—24no—
306Dic3⋊C4—42no—
307Dic3⋊C4—42no—
308Dic3⋊C4—42no—
309Dic3⋊C4—42no—
310Dic3⋊C4—42no—
311C4×Dic3—22no—
312C4×Dic3—22no—
313C4×Dic3C2×D412yes—
314C4×Dic3C2×D412yes—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8#4112yes—
321#204—44no—
322C22×Q8—31no—
323C22×Q8C22×D311yescharacteristic
324C22×Q8C22×D311yescharacteristic
325C22×D4—31no—
326C22×D4—61no—
327C23×C4—31no—
328C23×C4—31no—
329C23×C4—31no—
330C23×C4—61no—
331C2×Q16—22no—
332C2×Q16—22no—
333C2×Q16—41no—
334C2×Q16—62no—
335C2×Q16—62no—
336C2×Q16—121no—
337C2×SD16—62no—
338C2×SD16—62no—
339C2×SD16—62no—
340C2×SD16—62no—
341C2×SD16—121no—
342C2×SD16—121no—
343C22×C8—31no—
344C22×C8—31no—
345C22×C8C22×D311yescharacteristic
346C22×C8C22×D311yescharacteristic
347C4⋊Q8—62no—
348C4⋊Q8—62no—
349#126—68no—
350#125—34no—
351#125—62no—
352#124—34no—
353#124—62no—
354#123—68no—
355C22⋊Q8—62no—
356C22⋊Q8—62no—
357C22⋊Q8—121no—
358C22⋊Q8—121no—
359C22⋊Q8—121no—
360C22⋊Q8—121no—
361#121—62no—
362#121—62no—
363C4×Q8—22no—
364C4×Q8—22no—
365C4×D4—62no—
366C4×D4—62no—
367C4×D4—68no—
368#117—68no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—31no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4—61no—
374C2×C4⋊C4—61no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4—61no—
378C2×C4⋊C4—61no—
379C2×C4⋊C4—61no—
380C2×C4⋊C4—61no—
381C2×C4⋊C4C22×D311yescharacteristic
382C2×C4⋊C4C22×D311yescharacteristic
383C2×C22⋊C4—61no—
384C2×C22⋊C4—61no—
385C2×C22⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C22⋊C4—61no—
388C2×C22⋊C4—61no—
389C2×C22⋊C4—61no—
390C2×C42—21no—
391C2×C42—31no—
392C2×C42—31no—
393C2×C42—31no—
394C2×C42—62no—
395C2×C42—62no—
396C2×C42C22×D311yescharacteristic
397#103—22no—
398#103—41no—
399#103—62no—
400#103—62no—
401#103—62no—
402#103—121no—
403#102—121no—
404#102—121no—
405C22⋊C8—62no—
406C22⋊C8—62no—
407#97—62no—
408#97—62no—
409#95—21no—
410#95—21no—
411#95—61no—
412#95—61no—
413C23×C3C22×D411yescharacteristic
414C22×D3—21no—
415C22×D3—21no—
416C22×D3—21no—
417C22×D3—21no—
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—22no—
421C22×D3—41no—
422C22×D3—41no—
423C22×D3—41no—
424C22×D3—41no—
425C22×D3—41no—
426C22×D3—41no—
427C22×D3#13712yes—
428C3×Q8—22no—
429C3×Q8—22no—
430C3×Q8—41no—
431C3×Q8—41no—
432C3×Q8—41no—
433C3×Q8—41no—
434C3×Q8—41no—
435C3×Q8—41no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—41no—
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#13712yes—
454C2×C3×C4C22×D411yescharacteristic
455C2×C3×C4C22×D411yescharacteristic
456C2×C3×C4C2×#4111yescharacteristic
457C2×C3×C4C2×#4111yescharacteristic
458C2×C3×C4H(5,𝔽2)11yescharacteristic
459C2×C3×C4H(5,𝔽2)11yescharacteristic
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—22no—
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3#12012yes—
477C2×Dic3#12012yes—
478D12—22no—
479D12—22no—
480D12—48no—
481D12—41no—
482D12—41no—
483C4×D3—44no—
484C4×D3—44no—
485C4×D3—48no—
486C4×D3—41no—
487C4×D3—41no—
488C4×D3—41no—
489C4×D3—41no—
490Dic6—41no—
491Dic6—41no—
492Dic6—41no—
493Dic6—41no—
494C3×C8—22no—
495C3×C8—41no—
496C3⋊C8—22no—
497C3⋊C8—41no—
498C24—31no—
499C24—61no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—61no—
512C2×Q8—61no—
513C2×Q8—61no—
514C2×Q8—61no—
515C2×Q8—61no—
516C2×Q8—61no—
517C2×Q8D3×D412yes—
518C2×D4—32no—
519C2×D4—64no—
520C2×D4—61no—
521C2×D4—61no—
522C2×D4—61no—
523C2×D4—61no—
524C2×D4—61no—
525C2×D4—122no—
526C2×D4—122no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—31no—
532C22×C4—31no—
533C22×C4—31no—
534C22×C4—62no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—64no—
538C22×C4—61no—
539C22×C4—62no—
540C22×C4—61no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4—61no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—121no—
549C22×C4—121no—
550C22×C4—122no—
551C22×C4—122no—
552C22×C4D3×D411yescharacteristic
553C22×C4D3×D411yescharacteristic
554C22×C4C23×D311yescharacteristic
555Q16—44no—
556Q16—124no—
557SD16—124no—
558SD16—124no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—32no—
565C2×C8—61no—
566C2×C8—61no—
567C2×C8—61no—
568C2×C8—61no—
569C2×C8—61no—
570C2×C8#23512yes—
571C4⋊C4—24no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—32no—
576C4⋊C4—64no—
577C4⋊C4—64no—
578C4⋊C4—64no—
579C4⋊C4—61no—
580C4⋊C4—61no—
581C4⋊C4—61no—
582C4⋊C4—122no—
583C4⋊C4—122no—
584C4⋊C4—122no—
585C4⋊C4—122no—
586C4⋊C4—122no—
587C4⋊C4—122no—
588C4⋊C4D3×D412yes—
589C22⋊C4—64no—
590C22⋊C4—64no—
591C22⋊C4—64no—
592C22⋊C4—64no—
593C22⋊C4—64no—
594C22⋊C4—122no—
595C22⋊C4—122no—
596C42—24no—
597C42—21no—
598C42—21no—
599C42—32no—
600C42—32no—
601C42—62no—
602C42—62no—
603C22×C3C2×#12011yescharacteristic
604C22×C3#53211yescharacteristic
605C22×C3#53511yescharacteristic
606C22×C3C2×#13711yescharacteristic
607C22×C3C2×#13711yescharacteristic
608C22×C3#57511yescharacteristic
609C22×C3#57511yescharacteristic
610C2×D3—22no—
611C2×D3—22no—
612C2×D3—22no—
613C2×D3—41no—
614C2×D3—41no—
615C2×D3—41no—
616C2×D3—41no—
617C2×D3—42no—
618C2×D3—42no—
619C2×D3—42no—
620C2×D3—81no—
621C2×D3—81no—
622C2×D3—81no—
623C2×D3—81no—
624C3×C4—22no—
625C3×C4—42no—
626C3×C4—41no—
627C3×C4—42no—
628C3×C4—81no—
629C3×C4—81no—
630C3×C4#54611yescharacteristic
631C3×C4#54611yescharacteristic
632C3×C4#55011yescharacteristic
633C3×C4#55011yescharacteristic
634Dic3—22no—
635Dic3—22no—
636Dic3—41no—
637Dic3—42no—
638Dic3—81no—
639Dic3—81no—
640C23—32no—
641C23—61no—
642C23—61no—
643C23—61no—
644C23—61no—
645C23—61no—
646C23—61no—
647C23—62no—
648C23—121no—
649C23—121no—
650C23—121no—
651C23—121no—
652C23—121no—
653C23—121no—
654C23C2×D3×D411yescharacteristic
655Q8—22no—
656Q8—22no—
657Q8—41no—
658Q8—41no—
659Q8—41no—
660Q8—41no—
661Q8—41no—
662Q8—41no—
663Q8—121no—
664Q8—121no—
665Q8—121no—
666Q8—121no—
667D4—62no—
668D4—62no—
669D4—128no—
670D4—121no—
671D4—121no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—32no—
680C2×C4—32no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—62no—
698C2×C4—61no—
699C2×C4—124no—
700C2×C4—128no—
701C2×C4—124no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—121no—
713C2×C4—121no—
714C2×C4#91812yes—
715C2×C4C2×#23511yescharacteristic
716C2×C4C2×D3×D411yescharacteristic
717C2×C4C2×D3×D411yescharacteristic
718C2×C4#100411yescharacteristic
719C2×C4D3×#4111yescharacteristic
720C2×C4#100911yescharacteristic
721C8—22no—
722C8—41no—
723C8—62no—
724C8—121no—
725C2×C3#243111yescharacteristic
726C2×C3#300711yescharacteristic
727C2×C3#300711yescharacteristic
728C2×C3#317211yescharacteristic
729C2×C3#318111yescharacteristic
730C2×C3#321811yescharacteristic
731C2×C3#321911yescharacteristic
732D3—42no—
733D3—82no—
734C22—62no—
735C22—62no—
736C22—62no—
737C22—121no—
738C22—121no—
739C22—121no—
740C22—121no—
741C22—122no—
742C22—122no—
743C22—122no—
744C22—241no—
745C22—241no—
746C22—241no—
747C22—241no—
748C22#554811yescharacteristic
749C22D3×#12011yescharacteristic
750C22#560711yescharacteristic
751C22C2×#91811yescharacteristic
752C22#576811yescharacteristic
753C22D3×#13711yescharacteristic
754C22#577711yescharacteristic
755C4—22no—
756C4—41no—
757C4—42no—
758C4—42no—
759C4—62no—
760C4—62no—
761C4—81no—
762C4—81no—
763C4—122no—
764C4—121no—
765C4—241no—
766C4—241no—
767C4#549011yescharacteristic
768C4#555311yescharacteristic
769C4#559911yescharacteristic
770C4#565411yescharacteristic
771C3#2560411yescharacteristic, complemented, Sylow
772C2—122no—
773C2—242no—
774C2#7470011yescharacteristic
775C2#7972611yescharacteristic
776C2#7983711yescharacteristic
777C2#8018411yescharacteristic
778C2#8022811yescharacteristic
779C2#8048311yescharacteristic
780C2#8060711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1878C2
socleC23×C3C22×D4
prime radicalC2×#895C22
hypercenter#1878D3
hypocenterC3#25604
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
2. C2×#5190C2semidirect
3. C2×#4797C2semidirect
4. #76664C2semidirect
5. C3×#1878C2semidirect
6. #72071C2semidirect
7. #71632C2semidirect
8. #70273C2semidirect
10. #70227C2semidirect
11. #69687C2semidirect
13. #68805C2semidirect
14. #68672C2semidirect
15. #68600C2semidirect
75. #1878D3semidirect
771. C3#25604semidirect

Maximal subgroups

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

subgroupindex
C2×#55802
C2×#51902
C2×#47972
#766642
C3×#18782
#720712
#716322
#702732
#702722
#702272
#696872
#688872
#688052
#686722
#686002
#256043