Finite Group Databasebeta

← #10848729

Subgroups — #10848729

Order 768.

1216 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×#5691C211yesmaximal, characteristic, complemented
2C2×C3×#488C211yesmaximal, characteristic, complemented
3#83008C211yesmaximal, characteristic, complemented
4C2×#5059C211yesmaximal, characteristic, complemented
5#71740C211yesmaximal, characteristic, complemented
6#70281C211yesmaximal, characteristic, complemented
7#70276C211yesmaximal, characteristic, complemented
8#70273C211yesmaximal, characteristic, complemented
9#70272C211yesmaximal, characteristic, complemented
10#70213C211yesmaximal, characteristic, complemented
11#70208C211yesmaximal, characteristic, complemented
12#70205C211yesmaximal, characteristic, complemented
13#70204C211yesmaximal, characteristic
14#69773C211yesmaximal, characteristic, complemented
15C4×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
16#25601—31nomaximal, Sylow
17C2×C3×#125C2211yescharacteristic
18C2×C3×#124C2211yescharacteristic
19C2×#946C2211yescharacteristic
20C22×#216C2211yescharacteristic
21C22×#215C2211yescharacteristic
22C2×#938C2211yescharacteristic
23C22×#214C2211yescharacteristic
24C22×#213C2211yescharacteristic
25#5691—24no—
26#5691—24no—
27C2×#898—21no—
28C2×#897C2211yescharacteristic
29C2×#895C2211yescharacteristic
30C2×#894—21no—
31C2×#893—21no—
32C2×#893C2211yescharacteristic
33C2×#892—21no—
34C2×#887C2211yescharacteristic
35C2×#875C2211yescharacteristic
36C2×C42×D3C2211yescharacteristic
37C3×#488—24no—
38C2×C3×#103C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#102C2211yescharacteristic
41C2×C3×#102C2211yescharacteristic
42C2×C3×C4×C8C2211yescharacteristic
43#5229C2211yescharacteristic
44#5221C2211yescharacteristic
45C2×#821C2211yescharacteristic
46C2×#821C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic
48C2×(C2×D3)⋊C8C2211yescharacteristic
49C2×#816C2211yescharacteristic
50C2×#816C2211yescharacteristic
51#5059—24no—
52#4956—21no—
53#4956—21no—
54#4944—21no—
55#4944—21no—
56#4936C2211yescharacteristic
57C2×C4×C3⋊C8C2211yescharacteristic
58#4550C2211yescharacteristic
59#4550C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#529—31no—
65C2×#495—31no—
66C2×#488D311yescharacteristic, complemented
67#2850—31no—
68#2001—31no—
69#2000—31no—
70#2000—31no—
71#1999—31no—
72#1991—31no—
73#1958—31no—
74#1880—31no—
75#1879—31no—
76#1878—31no—
77#1877—31no—
78C4×C22⋊C8—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C22×#67—21no—
82C22×D12—21no—
83C22×D12C2311yescharacteristic
84C22×C4×D3—21no—
85C22×C4×D3D411yescharacteristic
86C22×C4×D3D411yescharacteristic
87C22×C4×D3C2311yescharacteristic
88C22×Dic6C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C3×#125—22no—
92C3×#125D414yescomplemented
93C3×#124—22no—
94C3×#124—22no—
95C2×C3×C4⋊C4—21no—
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C22⋊C4—21no—
100C2×C3×C22⋊C4—21no—
101C2×C3×C42C2311yescharacteristic
102C2×#217—21no—
103C2×#217—21no—
104C2×#217—21no—
105#946—41no—
106#946—41no—
107C2×#216—22no—
108C2×#216—22no—
109C2×#216—41no—
110C2×#215—22no—
111C2×#215—22no—
112C2×#215—41no—
113#938—41no—
114#938—41no—
115C2×#214—22no—
116C2×#214—22no—
117C2×#214—41no—
118C2×#213—22no—
119C2×#213—22no—
120C2×#213—41no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×C4⋊Dic3—21no—
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×C4×Dic3—21no—
133C2×C4×Dic3D411yescharacteristic
134C2×C4×Dic3D411yescharacteristic
135C2×C4×Dic3C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137C22×C3⋊C8C2311yescharacteristic
138#898—28no—
139#897—22no—
140#897—22no—
141#895—22no—
142#895—22no—
143#894—28no—
144#893—28no—
145#893—22no—
146#893—22no—
147#892—28no—
148#887—22no—
149#887—22no—
150#875—22no—
151#875D414yescomplemented
152C42×D3—22no—
153C42×D3—22no—
154C3×#103—22no—
155C3×#103—22no—
156C3×#102—22no—
157C3×#102—22no—
158C3×C4×C8—22no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162C3⋊#95—21no—
163#821—41no—
164#821—41no—
165(C2×D3)⋊C8—22no—
166(C2×D3)⋊C8—22no—
167#816—41no—
168#816—41no—
169C4×C3⋊C8—22no—
170C22×Q16—31no—
171C22×SD16—31no—
172C22×SD16—31no—
173C22×D8—31no—
174#529—64no—
175#529—64no—
176C2×#126—61no—
177C2×#125C2×D311yescharacteristic
178C2×#124—31no—
179C2×#124C2×D311yescharacteristic
180C2×#123—61no—
181C2×C22⋊Q8—31no—
182C2×C22⋊Q8—31no—
183C2×#121—31no—
184C2×#121—31no—
185C2×C4×Q8—31no—
186C2×C4×D4—31no—
187C2×C4×D4—61no—
188C2×#117—61no—
189C22×C42—31no—
190#495—64no—
191#488—24no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103C2×D311yescharacteristic
195C2×#103C2×D311yescharacteristic
196C2×#102—31no—
197C2×#102—31no—
198C2×#102C2×D311yescharacteristic
199C2×#102C2×D311yescharacteristic
200C2×C22⋊C8—31no—
201C2×C22⋊C8—31no—
202C2×C4×C8—31no—
203C2×C4×C8C2×D311yescharacteristic
204#391—31no—
205#390—31no—
206#388—61no—
207#388—61no—
208#386—61no—
209#386—61no—
210#382—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#336—31no—
216#336—31no—
217C24×C3—21no—
218C23×D3—21no—
219C23×D3C2×D411yescharacteristic
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×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
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—42no—
239C2×#67—42no—
240C2×#67—42no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3—21no—
244C22×Dic3C2×D411yescharacteristic
245C22×Dic3C2×D411yescharacteristic
246C22×Dic3C2×D411yescharacteristic
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—24no—
252C2×D12—21no—
253C2×D12—42no—
254C2×D12—42no—
255C2×D12C2×D412yes—
256C2×C4×D3—24no—
257C2×C4×D3—22no—
258C2×C4×D3—22no—
259C2×C4×D3—22no—
260C2×C4×D3—21no—
261C2×C4×D3—21no—
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×C4×D3—21no—
266C2×C4×D3—22no—
267C2×C4×D3—41no—
268C2×C4×D3—41no—
269C2×C4×D3—42no—
270C2×C4×D3—42no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×Dic6C2×D412yes—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C3×C4⋊C4—24no—
284C3×C4⋊C4—24no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4C2×D412yes—
288C3×C4⋊C4C2×D412yes—
289C3×C22⋊C4—42no—
290C3×C22⋊C4—42no—
291C3×C42C2×D412yes—
292C3×C42C2×D412yes—
293#217—42no—
294#217—42no—
295#217—42no—
296#216—44no—
297#215—44no—
298#214—44no—
299#213—44no—
300(C2×D3)⋊C4—24no—
301(C2×D3)⋊C4—24no—
302(C2×D3)⋊C4—24no—
303(C2×D3)⋊C4—24no—
304(C2×D3)⋊C4—24no—
305(C2×D3)⋊C4—42no—
306C4⋊Dic3—24no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311Dic3⋊C4—24no—
312Dic3⋊C4—42no—
313C4×Dic3—24no—
314C4×Dic3—22no—
315C4×Dic3—22no—
316C4×Dic3—21no—
317C4×Dic3—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8#4112yes—
323C2×C3⋊C8#4112yes—
324C22×Q8—31no—
325C22×Q8C22×D311yescharacteristic
326C22×D4—31no—
327C22×D4—61no—
328C22×D4—61no—
329C22×D4C22×D311yescharacteristic
330C23×C4—31no—
331C23×C4—31no—
332C23×C4—31no—
333C23×C4—61no—
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—
343C2×D8—62no—
344C2×D8—62no—
345C2×D8—121no—
346C22×C8—31no—
347C22×C8—31no—
348C22×C8C22×D311yescharacteristic
349C22×C8C22×D311yescharacteristic
350#126—68no—
351#125—22no—
352#125#6714yescomplemented
353#124—22no—
354#124—22no—
355#124—34no—
356#124—62no—
357#123—68no—
358C22⋊Q8—62no—
359C22⋊Q8—62no—
360C22⋊Q8—121no—
361C22⋊Q8—121no—
362#121—62no—
363#121—62no—
364#121—121no—
365#121—121no—
366C4×Q8—62no—
367C4×Q8—62no—
368C4×D4—62no—
369C4×D4—68no—
370C4×D4—62no—
371#117—68no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—31no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4—61no—
378C2×C4⋊C4—61no—
379C2×C4⋊C4C22×D311yescharacteristic
380C2×C4⋊C4C22×D311yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
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×C22⋊C4—61no—
391C2×C22⋊C4—61no—
392C2×C42—31no—
393C2×C42—31no—
394C2×C42—31no—
395C2×C42—61no—
396C2×C42—62no—
397C2×C42—62no—
398C2×C42C22×D311yescharacteristic
399#103—22no—
400#103—22no—
401#103—121no—
402#103—121no—
403#102—22no—
404#102—22no—
405#102—121no—
406#102—121no—
407C22⋊C8—62no—
408C22⋊C8—62no—
409C4×C8—22no—
410C4×C8—62no—
411#95—61no—
412#95—61no—
413#95—61no—
414#95—61no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3C22×D411yescharacteristic
423C22×D3—21no—
424C22×D3—21no—
425C22×D3—21no—
426C22×D3—21no—
427C22×D3—21no—
428C22×D3—21no—
429C22×D3—22no—
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3#13512yes—
437C3×Q8—41no—
438C3×Q8—41no—
439C3×Q8—41no—
440C3×Q8—41no—
441C3×D4—41no—
442C3×D4—41no—
443C3×D4—41no—
444C3×D4—41no—
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×C4C22×D411yescharacteristic
461C2×C3×C4C22×D411yescharacteristic
462C2×C3×C4C2×#4111yescharacteristic
463C2×C3×C4C2×#4111yescharacteristic
464C2×C3×C4H(5,𝔽2)11yescharacteristic
465C2×C3×C4H(5,𝔽2)11yescharacteristic
466#67—84no—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—22no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3#13512yes—
485D12—22no—
486D12—22no—
487D12—48no—
488D12—41no—
489D12—41no—
490C4×D3—44no—
491C4×D3—48no—
492C4×D3—44no—
493C4×D3—41no—
494C4×D3—41no—
495C4×D3—41no—
496C4×D3—41no—
497Dic6—22no—
498Dic6—22no—
499Dic6—41no—
500Dic6—41no—
501C3×C8—41no—
502C3×C8—41no—
503C3⋊C8—22no—
504C3⋊C8—22no—
505C24—21no—
506C24—31no—
507C24—61no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—32no—
515C2×Q8—61no—
516C2×Q8—61no—
517C2×Q8—61no—
518C2×Q8—61no—
519C2×Q8—61no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—32no—
527C2×D4—64no—
528C2×D4—61no—
529C2×D4—61no—
530C2×D4—61no—
531C2×D4—61no—
532C2×D4—61no—
533C2×D4—122no—
534C2×D4—122no—
535C2×D4—122no—
536C2×D4—122no—
537C2×D4—122no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—31no—
542C22×C4—31no—
543C22×C4—31no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—64no—
547C22×C4—61no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—121no—
559C22×C4—121no—
560C22×C4—122no—
561C22×C4—122no—
562C22×C4D3×D411yescharacteristic
563C22×C4D3×D411yescharacteristic
564C22×C4C23×D311yescharacteristic
565Q16—124no—
566SD16—124no—
567SD16—124no—
568D8—124no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—32no—
576C2×C8—32no—
577C2×C8—61no—
578C2×C8—61no—
579C2×C8—61no—
580C2×C8—61no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—64no—
586C4⋊C4—64no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—122no—
592C4⋊C4C2×#6712yes—
593C4⋊C4C2×#6712yes—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—64no—
597C22⋊C4—64no—
598C22⋊C4—64no—
599C22⋊C4—64no—
600C22⋊C4—64no—
601C22⋊C4—122no—
602C22⋊C4—122no—
603C22⋊C4—122no—
604C22⋊C4—122no—
605C42—64no—
606C42—62no—
607C42—62no—
608C42—61no—
609C42—61no—
610C42D3×D412yes—
611C42C2×#6712yes—
612C22×C3—81no—
613C22×C3—81no—
614C22×C3—81no—
615C22×C3—81no—
616C22×C3—81no—
617C22×C3—81no—
618C22×C3—81no—
619C22×C3C2×#12011yescharacteristic
620C22×C3#53211yescharacteristic
621C22×C3#53511yescharacteristic
622C22×C3C2×#13511yescharacteristic
623C22×C3C2×#13511yescharacteristic
624C22×C3#57511yescharacteristic
625C22×C3#57511yescharacteristic
626C2×D3—22no—
627C2×D3—22no—
628C2×D3—22no—
629C2×D3—41no—
630C2×D3—41no—
631C2×D3—41no—
632C2×D3—41no—
633C2×D3—42no—
634C2×D3—42no—
635C2×D3—42no—
636C2×D3—81no—
637C2×D3—81no—
638C2×D3—81no—
639C2×D3—81no—
640C3×C4—22no—
641C3×C4—22no—
642C3×C4—42no—
643C3×C4—42no—
644C3×C4—81no—
645C3×C4#54611yescharacteristic
646C3×C4#54611yescharacteristic
647C3×C4#55011yescharacteristic
648C3×C4#55011yescharacteristic
649Dic3—22no—
650Dic3—42no—
651Dic3—41no—
652Dic3—41no—
653Dic3—81no—
654Dic3—81no—
655C23—32no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—61no—
664C23—61no—
665C23—61no—
666C23—61no—
667C23—61no—
668C23—61no—
669C23—62no—
670C23—121no—
671C23—121no—
672C23—121no—
673C23—121no—
674C23—121no—
675C23—121no—
676C23C2×D3×D411yescharacteristic
677Q8—41no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681Q8—62no—
682Q8—62no—
683Q8—121no—
684Q8—121no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—62no—
690D4—62no—
691D4—128no—
692D4—121no—
693D4—121no—
694D4—244no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—32no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—62no—
718C2×C4—124no—
719C2×C4—124no—
720C2×C4—128no—
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—121no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4#93712yes—
734C2×C4#93712yes—
735C2×C4C2×D3×D411yescharacteristic
736C2×C4D3×#4111yescharacteristic
737C2×C4D3×#4111yescharacteristic
738C2×C4#100911yescharacteristic
739C2×C4#100911yescharacteristic
740C2×C4C22×#6711yescharacteristic
741C8—41no—
742C8—41no—
743C8—62no—
744C8—62no—
745C2×C3—161no—
746C2×C3#243111yescharacteristic
747C2×C3#300211yescharacteristic
748C2×C3#300211yescharacteristic
749C2×C3#316811yescharacteristic
750C2×C3#318311yescharacteristic
751C2×C3#321111yescharacteristic
752C2×C3#321211yescharacteristic
753D3—42no—
754D3—82no—
755C22—62no—
756C22—62no—
757C22—62no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—121no—
766C22—121no—
767C22—121no—
768C22—121no—
769C22—122no—
770C22—122no—
771C22—122no—
772C22—241no—
773C22—241no—
774C22—241no—
775C22—241no—
776C22#566811yescharacteristic
777C22#567411yescharacteristic
778C22D3×#13511yescharacteristic
779C22D3×#13511yescharacteristic
780C22#576811yescharacteristic
781C22#576811yescharacteristic
782C22C2×#93711yescharacteristic
783C4—22no—
784C4—22no—
785C4—42no—
786C4—42no—
787C4—62no—
788C4—81no—
789C4—121no—
790C4—122no—
791C4—121no—
792C4—241no—
793C4—241no—
794C4#567611yescharacteristic
795C4#567611yescharacteristic
796C4#583411yescharacteristic
797C4#583411yescharacteristic
798C3#2560111yescharacteristic, complemented, Sylow
799C2—122no—
800C2—161no—
801C2—242no—
802C2#8162811yescharacteristic
803C2#8163111yescharacteristic
804C2#8164211yescharacteristic
805C2#8164311yescharacteristic
806C2#8295811yescharacteristic
807C2#8391111yescharacteristic
808C2#8391111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#488C2
socleC23×C3C22×D4
prime radical#70204C2
hypercenterC2×#488D3
hypocenterC3#25601
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
1. C2×#5691C2semidirect
2. C2×C3×#488C2semidirect
3. #83008C2semidirect
4. C2×#5059C2semidirect
5. #71740C2semidirect
6. #70281C2semidirect
7. #70276C2semidirect
8. #70273C2semidirect
9. #70272C2semidirect
10. #70213C2semidirect
11. #70208C2semidirect
12. #70205C2semidirect
14. #69773C2semidirect
15. C4×(C2×D3)⋊C8C2semidirect
66. C2×#488D3semidirect
92. C3×#125D4semidirect
151. #875D4semidirect
352. #125#67semidirect
798. C3#25601semidirect

Maximal subgroups

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

subgroupindex
C2×#56912
C2×C3×#4882
#830082
C2×#50592
#717402
#702812
#702762
#702732
#702722
#702132
#702082
#702052
#702042
#697732
C4×(C2×D3)⋊C82
#256013