Finite Group Databasebeta

← #10846152

Subgroups — #10846152

Order 768.

1120 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2541C211yesmaximal, characteristic
2C2×#5075C211yesmaximal, characteristic, complemented
3C2×#5042C211yesmaximal, characteristic, complemented
4C2×#5041C211yesmaximal, characteristic, complemented
5#82375C211yesmaximal, characteristic, complemented
6C2×#5011C211yesmaximal, characteristic, complemented
7#71765C211yesmaximal, characteristic, complemented
8#71685C211yesmaximal, characteristic, complemented
9#71685C211yesmaximal, characteristic, complemented
10#71682C211yesmaximal, characteristic, complemented
11#71681C211yesmaximal, characteristic, complemented
12#71680C211yesmaximal, characteristic, complemented
13#71679C211yesmaximal, characteristic, complemented
14#69475C211yesmaximal, characteristic, complemented
15#69468C211yesmaximal, characteristic, complemented
16#25402—31nomaximal, Sylow
17C2×C3×#127—21no—
18C2×C3×#127C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×C3×#121C2211yescharacteristic
22C2×C3×#121C2211yescharacteristic
23C2×C3×C4×D4C2211yescharacteristic
24C22×#214C2211yescharacteristic
25C22×#214C2211yescharacteristic
26C2×#924C2211yescharacteristic
27C2×#924C2211yescharacteristic
28C22×#208C2211yescharacteristic
29C23×C3⋊C8C2211yescharacteristic
30C2×C4×Dic6C2211yescharacteristic
31C3×#392—21no—
32C3×#392—21no—
33C3×#390—21no—
34C3×C4×C4⋊C4C2211yescharacteristic
35#5222—21no—
36C2×#832C2211yescharacteristic
37C2×#832C2211yescharacteristic
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic
42#5212C2211yescharacteristic
43#5212C2211yescharacteristic
44C2×#830C2211yescharacteristic
45C2×#830C2211yescharacteristic
46#5075—24no—
47#5042—24no—
48#5041—24no—
49#5011—24no—
50#4983—21no—
51C2×#810C2211yescharacteristic
52C2×#810C2211yescharacteristic
53C2×#808C2211yescharacteristic
54C2×#807C2211yescharacteristic
55#4944—21no—
56#4944—21no—
57#4936C2211yescharacteristic
58C2×C4⋊(C3⋊C8)C2211yescharacteristic
59C2×#803C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#468—31no—
65C2×#465—31no—
66C2×#460—31no—
67C2×#435—31no—
68#2541D311yescharacteristic
69#2536—31no—
70#2034—31no—
71#2033—31no—
72#2000—31no—
73#2000—31no—
74#1961—31no—
75#1949—31no—
76#1895—31no—
77#1893—31no—
78#1763—31no—
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4—21no—
82C22×C3×D4—21no—
83C22×C3×D4—21no—
84C22×C3×D4—21no—
85C22×C3×D4D411yescharacteristic
86C22×C3×D4C2311yescharacteristic
87C22×C3×D4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C22×Dic6C2311yescharacteristic
91C3×#127—22no—
92C3×#127—22no—
93C3×#127—44no—
94C3×#121—22no—
95C3×#121—22no—
96C3×#121—22no—
97C3×#121—22no—
98C3×#121—41no—
99C3×#121—41no—
100C3×#121—41no—
101C3×#121—41no—
102C3×C4×D4—22no—
103C3×C4×D4—22no—
104C2×C3×C4⋊C4D411yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C22⋊C4—21no—
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4D411yescharacteristic
112C2×C3×C22⋊C4D411yescharacteristic
113C2×C3×C42—21no—
114C2×C3×C42C2311yescharacteristic
115C2×#217—21no—
116C2×#217—21no—
117C2×#217—21no—
118C2×#217—21no—
119C2×#214—22no—
120C2×#214—22no—
121C2×#214—22no—
122C2×#214—22no—
123C2×#214—41no—
124C2×#214—41no—
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×C4⋊Dic3C2311yescharacteristic
128#924—22no—
129#924—22no—
130#924—41no—
131#924—41no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4—21no—
135C2×C4×Dic3—21no—
136C2×#208—22no—
137C2×#208—22no—
138C2×#208—41no—
139C22×C3⋊C8—22no—
140C22×C3⋊C8—22no—
141C22×C3⋊C8—41no—
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146C4×Dic6—22no—
147C4×Dic6—22no—
148C3×#95—21no—
149#832—22no—
150#832—22no—
151#832—22no—
152#832—22no—
153#832—41no—
154#832—41no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159#830—22no—
160#830—22no—
161#810—22no—
162#810D414yescomplemented
163#808—22no—
164#807—22no—
165C4⋊(C3⋊C8)D414yescomplemented
166#803—22no—
167C22×SD16—31no—
168C22×SD16—31no—
169C22×M16—31no—
170C23×C8—31no—
171C2×#127—21no—
172C2×#127C2×D311yescharacteristic
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8—31no—
175C2×#121C2×D311yescharacteristic
176C2×#121C2×D311yescharacteristic
177C2×#121C2×D311yescharacteristic
178C2×#121C2×D311yescharacteristic
179C2×C4×Q8—31no—
180C2×C4×D4C2×D311yescharacteristic
181#468—64no—
182#465—64no—
183#460—64no—
184#435—64no—
185C2×#107—31no—
186C2×#106—31no—
187C2×C4⋊C8—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×#102—31no—
196C2×C22⋊C8—31no—
197C2×C22⋊C8—31no—
198C2×#97—31no—
199#398—61no—
200#394—61no—
201#392—21no—
202#392—21no—
203#390—21no—
204#388—61no—
205#388—61no—
206#382—31no—
207#380—31no—
208#380—31no—
209C4×C4⋊C4C2×D311yescharacteristic
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3C2×D411yescharacteristic
217C24×C3C2×D411yescharacteristic
218C2×C3×D4—22no—
219C2×C3×D4—22no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—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—
232C2×C3×D4—41no—
233C2×C3×D4—42no—
234C2×C3×D4—42no—
235C2×C3×D4—42no—
236C2×C3×D4—42no—
237C2×C3×D4—42no—
238C2×C3×D4—42no—
239C2×C3×D4—42no—
240C2×C3×D4—42no—
241C2×C3×D4—42no—
242C2×C3×D4—42no—
243C2×C3×D4—42no—
244C2×C3×D4—42no—
245C2×C3×D4—81no—
246C2×C3×D4—81no—
247C2×C3×D4—81no—
248C2×C3×D4—81no—
249C2×C3×D4—81no—
250C2×C3×D4—81no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4C2×D411yescharacteristic
266C22×C3×C4C2×D411yescharacteristic
267C22×C3×C4C2×D411yescharacteristic
268C22×C3×C4C2×D411yescharacteristic
269C22×C3×C4C2411yescharacteristic
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—21no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×Dic6—21no—
277C2×Dic6—21no—
278C2×Dic6—21no—
279C2×Dic6C2×D412yes—
280C3×C4⋊C4—22no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4C2×D412yes—
284C3×C4⋊C4#4112yes—
285C3×C22⋊C4—22no—
286C3×C22⋊C4—22no—
287C3×C22⋊C4—42no—
288C3×C22⋊C4—42no—
289C3×C22⋊C4—42no—
290C3×C22⋊C4—42no—
291C3×C42—42no—
292C3×C42C2×D412yes—
293C3×C42#4112yes—
294#217—42no—
295#217—42no—
296#217—42no—
297#217—42no—
298#214—44no—
299#214—44no—
300C4⋊Dic3—21no—
301C4⋊Dic3—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306Dic3⋊C4—42no—
307Dic3⋊C4—42no—
308Dic3⋊C4—42no—
309C4×Dic3—42no—
310#208—44no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—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—
320C2×C3⋊C8—44no—
321C2×C3⋊C8C2×D412yes—
322C2×C3⋊C8C2×D412yes—
323C2×C3⋊C8C2×D412yes—
324C22×Q8—31no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—21no—
328C22×D4—21no—
329C22×D4—21no—
330C22×D4—21no—
331C22×D4#6711yescharacteristic
332C22×D4C22×D311yescharacteristic
333C22×D4C22×D311yescharacteristic
334C23×C4C22×D311yescharacteristic
335C23×C4C22×D311yescharacteristic
336C2×SD16—62no—
337C2×SD16—62no—
338C2×SD16—62no—
339C2×SD16—62no—
340C2×SD16—121no—
341C2×SD16—121no—
342C2×M16—62no—
343C2×M16—62no—
344C2×M16—121no—
345C22×C8—31no—
346C22×C8—31no—
347C22×C8—31no—
348C22×C8—31no—
349C22×C8—62no—
350C22×C8—62no—
351C22×C8—121no—
352#127—22no—
353#127—22no—
354#127—44no—
355C22⋊Q8—62no—
356C22⋊Q8—62no—
357C22⋊Q8—121no—
358C22⋊Q8—121no—
359#121—22no—
360#121—22no—
361#121—22no—
362#121—22no—
363#121—41no—
364#121—41no—
365#121—41no—
366#121—41no—
367C4×Q8—62no—
368C4×Q8—62no—
369C4×D4—22no—
370C4×D4—22no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—61no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4#6711yescharacteristic
378C2×C4⋊C4C22×D311yescharacteristic
379C2×C4⋊C4C22×D311yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—61no—
385C2×C22⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C22⋊C4—61no—
388C2×C22⋊C4#6711yescharacteristic
389C2×C22⋊C4#6711yescharacteristic
390C2×C42—21no—
391C2×C42—61no—
392C2×C42C22×D311yescharacteristic
393#107—62no—
394#106—62no—
395C4⋊C8—34no—
396#103—34no—
397#103—62no—
398#102—62no—
399#102—62no—
400#102—62no—
401#102—62no—
402#102—121no—
403#102—121no—
404C22⋊C8—62no—
405C22⋊C8—62no—
406#97—62no—
407#95—21no—
408#95—61no—
409#95—61no—
410#95—61no—
411#95—61no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3—41no—
437C23×C3—41no—
438C23×C3—41no—
439C23×C3AGL(1,ℤ/8)12yes—
440C23×C3C22×D411yescharacteristic
441C3×D4—44no—
442C3×D4—41no—
443C3×D4—41no—
444C3×D4—41no—
445C3×D4—41no—
446C3×D4—41no—
447C3×D4—41no—
448C3×D4—41no—
449C3×D4—41no—
450C3×D4—84no—
451C3×D4—84no—
452C3×D4—84no—
453C3×D4—84no—
454C3×D4—84no—
455C3×D4—84no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4#12112yes—
481C2×C3×C4#12112yes—
482C2×C3×C4C22×D411yescharacteristic
483C2×C3×C4C22×D411yescharacteristic
484C2×C3×C4C2×#4111yescharacteristic
485C2×C3×C4C2×#4111yescharacteristic
486C2×C3×C4H(5,𝔽2)11yescharacteristic
487C2×C3×C4H(5,𝔽2)11yescharacteristic
488C2×Dic3—22no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498C2×Dic3—41no—
499C2×Dic3—41no—
500Dic6—22no—
501Dic6—22no—
502Dic6—41no—
503Dic6—41no—
504C3⋊C8—22no—
505C3⋊C8—22no—
506C3⋊C8—22no—
507C3⋊C8—41no—
508C24—21no—
509C24—21no—
510C24C2×#6711yescharacteristic
511C24C2×#6711yescharacteristic
512C2×Q8—32no—
513C2×Q8—61no—
514C2×Q8—61no—
515C2×Q8—61no—
516C2×Q8—61no—
517C2×Q8—61no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—41no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—81no—
546C2×D4—81no—
547C2×D4—81no—
548C2×D4—81no—
549C2×D4—81no—
550C2×D4—81no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4C2×#6711yescharacteristic
570C22×C4C2×#6711yescharacteristic
571C22×C4C2×#6711yescharacteristic
572C22×C4C2×#6711yescharacteristic
573C22×C4C23×D311yescharacteristic
574SD16—124no—
575SD16—124no—
576M16—124no—
577C2×C8—32no—
578C2×C8—32no—
579C2×C8—32no—
580C2×C8—61no—
581C2×C8—61no—
582C2×C8—61no—
583C2×C8—61no—
584C2×C8—61no—
585C2×C8—61no—
586C2×C8—61no—
587C2×C8—61no—
588C2×C8—61no—
589C2×C8—124no—
590C4⋊C4—22no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—122no—
600C4⋊C4—122no—
601C4⋊C4—122no—
602C4⋊C4D3×D412yes—
603C4⋊C4#23712yes—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—122no—
611C22⋊C4—122no—
612C22⋊C4—122no—
613C22⋊C4—122no—
614C42—42no—
615C42—122no—
616C42D3×D412yes—
617C42#23712yes—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—22no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3—81no—
635C22×C3—81no—
636C22×C3—81no—
637C22×C3—81no—
638C22×C3—81no—
639C22×C3—81no—
640C22×C3—81no—
641C22×C3—81no—
642C22×C3—81no—
643C22×C3—81no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3C2×#12111yescharacteristic
647C22×C3D4211yescharacteristic
648C22×C3#54611yescharacteristic
649C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
650C22×C3#57511yescharacteristic
651C22×C3#57711yescharacteristic
652C22×C3#57711yescharacteristic
653C3×C4—22no—
654C3×C4—22no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—42no—
658C3×C4—42no—
659C3×C4#53211yescharacteristic
660C3×C4#54011yescharacteristic
661C3×C4D4211yescharacteristic
662C3×C4#55011yescharacteristic
663Dic3—42no—
664Dic3—81no—
665Dic3—81no—
666Dic3—81no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23#93212yes—
695C23C22×#6711yescharacteristic
696Q8—62no—
697Q8—62no—
698Q8—121no—
699Q8—121no—
700D4—44no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—84no—
710D4—84no—
711D4—84no—
712D4—84no—
713D4—84no—
714D4—84no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—22no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—62no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4—121no—
743C2×C4—121no—
744C2×C4—121no—
745C2×C4—121no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C4—121no—
749C2×C4—121no—
750C2×C4—121no—
751C2×C4#93912yes—
752C2×C4#93912yes—
753C2×C4C2×D3×D411yescharacteristic
754C2×C4C2×D3×D411yescharacteristic
755C2×C4C2×#23711yescharacteristic
756C2×C4C2×#23711yescharacteristic
757C2×C4#100411yescharacteristic
758C2×C4#100411yescharacteristic
759C8—62no—
760C8—62no—
761C8—62no—
762C8—121no—
763C2×C3—42no—
764C2×C3—81no—
765C2×C3—161no—
766C2×C3—161no—
767C2×C3#242811yescharacteristic
768C2×C3#305511yescharacteristic
769C2×C3#305711yescharacteristic
770C2×C3#326511yescharacteristic
771C2×C3#327111yescharacteristic
772C2×C3#331011yescharacteristic
773C2×C3#331711yescharacteristic
774C22—22no—
775C22—22no—
776C22—22no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22C2×#93211yescharacteristic
803C22D4×#6711yescharacteristic
804C22C2×#93911yescharacteristic
805C22#580611yescharacteristic
806C22#582211yescharacteristic
807C22#583611yescharacteristic
808C22#583611yescharacteristic
809C4—22no—
810C4—22no—
811C4—42no—
812C4—42no—
813C4—41no—
814C4—41no—
815C4—122no—
816C4—241no—
817C4—241no—
818C4—241no—
819C4#571611yescharacteristic
820C4#571711yescharacteristic
821C4#571811yescharacteristic
822C4#571911yescharacteristic
823C3#2540211yescharacteristic, complemented, Sylow
824C2—42no—
825C2—81no—
826C2—161no—
827C2—161no—
828C2#8262111yescharacteristic
829C2#8318611yescharacteristic
830C2#8337711yescharacteristic
831C2#8348411yescharacteristic
832C2#8349111yescharacteristic
833C2#8357311yescharacteristic
834C2#8358311yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
Fitting, prime radicalC3×#2541C2
socleC23×C3C22×D4
hypercenter#2541D3
hypocenterC3#25402
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2541

Complements

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

NH ≅ G/Ntype
2. C2×#5075C2semidirect
3. C2×#5042C2semidirect
4. C2×#5041C2semidirect
5. #82375C2semidirect
6. C2×#5011C2semidirect
7. #71765C2semidirect
8. #71685C2semidirect
9. #71685C2semidirect
10. #71682C2semidirect
11. #71681C2semidirect
12. #71680C2semidirect
13. #71679C2semidirect
14. #69475C2semidirect
15. #69468C2semidirect
162. #810D4semidirect
165. C4⋊(C3⋊C8)D4semidirect
823. C3#25402semidirect

Maximal subgroups

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

subgroupindex
C3×#25412
C2×#50752
C2×#50422
C2×#50412
#823752
C2×#50112
#717652
#716852
#716822
#716812
#716802
#716792
#694752
#694682
#254023