Finite Group Databasebeta

← #10845986

Subgroups — #10845986

Order 768.

1084 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2535C211yesmaximal, characteristic, complemented
2C2×#5039C211yesmaximal, characteristic, complemented
3C2×#5042C211yesmaximal, characteristic, complemented
4#82377C211yesmaximal, characteristic, complemented
5C2×#5016C211yesmaximal, characteristic, complemented
6C2×#5012C211yesmaximal, characteristic, complemented
7#71685C211yesmaximal, characteristic, complemented
8#71684C211yesmaximal, characteristic, complemented
9C4×#832C211yesmaximal, characteristic, complemented
10#69551C211yesmaximal, characteristic, complemented
11#69540C211yesmaximal, characteristic, complemented
12#69526C211yesmaximal, characteristic, complemented
13#69523C211yesmaximal, characteristic, complemented
14#69517C211yesmaximal, characteristic, complemented
15#69516C211yesmaximal, characteristic, complemented
16#25390—31nomaximal, Sylow
17C2×C3×#121C2211yescharacteristic
18C2×C3×#121C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C22×#214C2211yescharacteristic
22C22×#213C2211yescharacteristic
23C2×#930C2211yescharacteristic
24C2×#930C2211yescharacteristic
25C2×#924C2211yescharacteristic
26C2×#924C2211yescharacteristic
27C22×#208C2211yescharacteristic
28C22×#208C2211yescharacteristic
29C2×#875C2211yescharacteristic
30C3×#397—21no—
31C3×#392—21no—
32C3×#386—21no—
33C3×#386—21no—
34C3×#382C2211yescharacteristic
35C3×#380C2211yescharacteristic
36C3×#380C2211yescharacteristic
37#5223—21no—
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#830C2211yescharacteristic
41C2×#830C2211yescharacteristic
42#5042—24no—
43#5039—24no—
44#5016—24no—
45#5012—24no—
46#4993—21no—
47C2×#810C2211yescharacteristic
48C2×#810C2211yescharacteristic
49C2×#810C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#808C2211yescharacteristic
54C2×#807C2211yescharacteristic
55#4957—21no—
56#4957—21no—
57C4×C4⋊Dic3C2211yescharacteristic
58C2×C4⋊(C3⋊C8)C2211yescharacteristic
59C2×C4×C3⋊C8C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#469—31no—
65C2×#468—31no—
66C2×#463—31no—
67C2×#436—31no—
68#2540—31no—
69#2535D311yescharacteristic, complemented
70#2035—31no—
71#2033—31no—
72#2000—31no—
73#1999—31no—
74#1958—31no—
75#1949—31no—
76#1895—31no—
77#1894—31no—
78C4×#102—31no—
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4D411yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4—21no—
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C22×#67—21no—
87C22×#67—21no—
88C22×D12C2311yescharacteristic
89C22×Dic6C2311yescharacteristic
90C3×#121—22no—
91C3×#121—22no—
92C3×#121—41no—
93C3×#121—41no—
94C3×C4×D4—22no—
95C3×C4×D4—22no—
96C3×C4×D4—22no—
97C3×C4×D4—22no—
98C2×C3×C4⋊C4D411yescharacteristic
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C22⋊C4—21no—
103C2×C3×C22⋊C4—21no—
104C2×C3×C22⋊C4—21no—
105C2×C3×C22⋊C4—21no—
106C2×C3×C22⋊C4—21no—
107C2×C3×C22⋊C4D411yescharacteristic
108C2×C3×C22⋊C4D411yescharacteristic
109C2×C3×C42C2311yescharacteristic
110C2×#217—21no—
111C2×#217—21no—
112C2×#214—22no—
113C2×#214—22no—
114C2×#214—41no—
115C2×#213—22no—
116C2×#213—22no—
117C2×#213—41no—
118#930—22no—
119#930—22no—
120#930—41no—
121#930—41no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
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×C4×Dic3—21no—
135C2×#208—22no—
136C2×#208—22no—
137C2×#208—22no—
138C2×#208—22no—
139C2×#208—41no—
140C2×#208—41no—
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145#875—22no—
146#875—22no—
147C3×#95—21no—
148C3×#95—21no—
149C3×#95—21no—
150C3×#95—21no—
151#832—22no—
152#832D414yescomplemented
153C3⋊#95—21no—
154#830—22no—
155#830—22no—
156#810—22no—
157#810—22no—
158#810—41no—
159#809—22no—
160#809—22no—
161#809—41no—
162#808—22no—
163#807—22no—
164C4⋊(C3⋊C8)D414yescomplemented
165C4×C3⋊C8—22no—
166C22×SD16—31no—
167C22×D8—31no—
168C22×M16—31no—
169C22×M16—31no—
170C2×#124—31no—
171C2×C22⋊Q8—31no—
172C2×C22⋊Q8—31no—
173C2×#121—31no—
174C2×#121—31no—
175C2×#121C2×D311yescharacteristic
176C2×#121C2×D311yescharacteristic
177C2×C4×D4C2×D311yescharacteristic
178C2×C4×D4C2×D311yescharacteristic
179#469—64no—
180#468—64no—
181#463—64no—
182#436—64no—
183C2×#107—31no—
184C2×#106—31no—
185C2×C4⋊C8—31no—
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×C22⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×C4×C8—31no—
197#399—61no—
198#397—21no—
199#392—21no—
200#392—61no—
201#390—61no—
202#390—61no—
203#386—21no—
204#386—21no—
205#382C2×D311yescharacteristic
206#380C2×D311yescharacteristic
207#380C2×D311yescharacteristic
208C4×C4⋊C4—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213C24×C3—21no—
214C24×C3C2×D411yescharacteristic
215C24×C3C2×D411yescharacteristic
216C23×D3—21no—
217C2×C3×D4—22no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—41no—
224C2×C3×D4—41no—
225C2×C3×D4—42no—
226C2×C3×D4—42no—
227C2×C3×D4—42no—
228C2×C3×D4—42no—
229C2×C3×D4—81no—
230C2×C3×D4—81no—
231C2×C3×D4C2×D412yes—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—42no—
248C22×C3×C4—81no—
249C22×C3×C4—81no—
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2411yescharacteristic
255C2×#67—42no—
256C2×#67—42no—
257C2×#67—42no—
258C2×#67—42no—
259C2×#67—81no—
260C2×#67—81no—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12—21no—
270C2×Dic6—21no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C3×C4⋊C4—22no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C22⋊C4—22no—
284C3×C22⋊C4—22no—
285C3×C22⋊C4—42no—
286C3×C22⋊C4—42no—
287C3×C22⋊C4—42no—
288C3×C22⋊C4—81no—
289C3×C22⋊C4—81no—
290C3×C42C2×D412yes—
291C3×C42#4112yes—
292#217—42no—
293#217—42no—
294#214—44no—
295#213—44no—
296(C2×D3)⋊C4—42no—
297(C2×D3)⋊C4—42no—
298(C2×D3)⋊C4—42no—
299(C2×D3)⋊C4—42no—
300C4⋊Dic3—21no—
301C4⋊Dic3—21no—
302C4⋊Dic3C2×D412yes—
303C4⋊Dic3#4112yes—
304Dic3⋊C4—42no—
305Dic3⋊C4—42no—
306C4×Dic3—81no—
307#208—44no—
308#208—44no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
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⋊C8C2×D412yes—
319C2×C3⋊C8C2×D412yes—
320C2×C3⋊C8C2×D412yes—
321C22×Q8—31no—
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—31no—
325C22×D4—61no—
326C22×D4—61no—
327C22×D4#6711yescharacteristic
328C22×D4C22×D311yescharacteristic
329C23×C4—21no—
330C23×C4C22×D311yescharacteristic
331C23×C4C22×D311yescharacteristic
332C2×SD16—62no—
333C2×SD16—62no—
334C2×SD16—121no—
335C2×D8—62no—
336C2×D8—62no—
337C2×D8—121no—
338C2×M16—62no—
339C2×M16—62no—
340C2×M16—62no—
341C2×M16—62no—
342C2×M16—121no—
343C2×M16—121no—
344C22×C8—31no—
345C22×C8—31no—
346C22×C8—31no—
347C22×C8—31no—
348#124—62no—
349#124—62no—
350C22⋊Q8—62no—
351C22⋊Q8—62no—
352C22⋊Q8—121no—
353C22⋊Q8—121no—
354#121—22no—
355#121—22no—
356#121—41no—
357#121—41no—
358#121—62no—
359#121—62no—
360#121—121no—
361#121—121no—
362C4×D4—22no—
363C4×D4—22no—
364C4×D4—22no—
365C4×D4—22no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—61no—
369C2×C4⋊C4—61no—
370C2×C4⋊C4#6711yescharacteristic
371C2×C4⋊C4C22×D311yescharacteristic
372C2×C4⋊C4C22×D311yescharacteristic
373C2×C4⋊C4C22×D311yescharacteristic
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4—61no—
384C2×C22⋊C4—61no—
385C2×C22⋊C4#6711yescharacteristic
386C2×C22⋊C4#6711yescharacteristic
387C2×C42—61no—
388C2×C42C22×D311yescharacteristic
389#107—62no—
390#106—62no—
391C4⋊C8—34no—
392#103—62no—
393#103—62no—
394#103—121no—
395#102—34no—
396#102—62no—
397#102—62no—
398#102—62no—
399#102—121no—
400C22⋊C8—62no—
401C22⋊C8—62no—
402C4×C8—62no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—61no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—22no—
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—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3C22×D411yescharacteristic
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C3×D4—22no—
438C3×D4—22no—
439C3×D4—44no—
440C3×D4—41no—
441C3×D4—41no—
442C3×D4—84no—
443C3×D4—84no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—84no—
472C2×C3×C4#12112yes—
473C2×C3×C4#12112yes—
474C2×C3×C4C22×D411yescharacteristic
475C2×C3×C4C22×D411yescharacteristic
476C2×C3×C4C2×#4111yescharacteristic
477C2×C3×C4C2×#4111yescharacteristic
478C2×C3×C4H(5,𝔽2)11yescharacteristic
479C2×C3×C4H(5,𝔽2)11yescharacteristic
480#67—84no—
481#67—84no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491D12—41no—
492D12—41no—
493D12—41no—
494D12—41no—
495Dic6—41no—
496Dic6—41no—
497Dic6—41no—
498Dic6—41no—
499C3⋊C8—22no—
500C3⋊C8—22no—
501C3⋊C8—22no—
502C3⋊C8—41no—
503C24—21no—
504C24—61no—
505C24C2×#6711yescharacteristic
506C24C2×#6711yescharacteristic
507C2×Q8—61no—
508C2×Q8—61no—
509C2×Q8—61no—
510C2×Q8—61no—
511C2×Q8—61no—
512C2×Q8—61no—
513C2×D4—22no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—41no—
520C2×D4—41no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—61no—
526C2×D4—61no—
527C2×D4—61no—
528C2×D4—61no—
529C2×D4—61no—
530C2×D4—61no—
531C2×D4—81no—
532C2×D4—81no—
533C2×D4—122no—
534C2×D4—122no—
535C2×D4—122no—
536C2×D4—122no—
537C2×D4—241no—
538C2×D4—241no—
539C2×D4D3×D412yes—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—42no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4—81no—
560C22×C4—81no—
561C22×C4C2×#6711yescharacteristic
562C22×C4C2×#6711yescharacteristic
563C22×C4C2×#6711yescharacteristic
564C22×C4C2×#6711yescharacteristic
565C22×C4C23×D311yescharacteristic
566SD16—124no—
567D8—124no—
568M16—124no—
569M16—124no—
570C2×C8—32no—
571C2×C8—32no—
572C2×C8—32no—
573C2×C8—61no—
574C2×C8—61no—
575C2×C8—61no—
576C2×C8—61no—
577C2×C8—61no—
578C2×C8—61no—
579C2×C8—61no—
580C2×C8—61no—
581C2×C8—61no—
582C4⋊C4—22no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—32no—
590C4⋊C4—32no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—122no—
594C4⋊C4—122no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—42no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—81no—
601C22⋊C4—81no—
602C22⋊C4—122no—
603C22⋊C4—122no—
604C22⋊C4—122no—
605C22⋊C4—122no—
606C22⋊C4—122no—
607C22⋊C4—122no—
608C42—241no—
609C42D3×D412yes—
610C42#23712yes—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—42no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—42no—
617C22×C3—41no—
618C22×C3—42no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—81no—
629C22×C3—81no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3C2×#12111yescharacteristic
633C22×C3D4211yescharacteristic
634C22×C3#54611yescharacteristic
635C22×C3#57511yescharacteristic
636C22×C3#57511yescharacteristic
637C22×C3#57611yescharacteristic
638C22×C3#57711yescharacteristic
639C2×D3—81no—
640C2×D3—81no—
641C2×D3—81no—
642C2×D3—81no—
643C2×D3—81no—
644C2×D3—81no—
645C2×D3—81no—
646C3×C4—22no—
647C3×C4—22no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4—81no—
651C3×C4—81no—
652C3×C4—81no—
653C3×C4#53211yescharacteristic
654C3×C4#54011yescharacteristic
655C3×C4D4211yescharacteristic
656C3×C4#55011yescharacteristic
657Dic3—42no—
658Dic3—42no—
659Dic3—81no—
660C23—22no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—121no—
682C23—121no—
683C23—121no—
684C23—121no—
685C23—121no—
686C23—121no—
687C23—121no—
688C23C22×#6711yescharacteristic
689Q8—121no—
690Q8—121no—
691Q8—121no—
692Q8—121no—
693D4—22no—
694D4—22no—
695D4—44no—
696D4—41no—
697D4—41no—
698D4—84no—
699D4—84no—
700D4—121no—
701D4—121no—
702D4—121no—
703D4—121no—
704D4—244no—
705D4—244no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—62no—
734C2×C4—62no—
735C2×C4—84no—
736C2×C4—121no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4—121no—
743C2×C4#93912yes—
744C2×C4#93912yes—
745C2×C4C2×D3×D411yescharacteristic
746C2×C4C2×D3×D411yescharacteristic
747C2×C4C2×#23711yescharacteristic
748C2×C4#100411yescharacteristic
749C2×C4D3×#4111yescharacteristic
750C2×C4#100911yescharacteristic
751C8—62no—
752C8—62no—
753C8—62no—
754C8—121no—
755C2×C3—81no—
756C2×C3—81no—
757C2×C3—82no—
758C2×C3#242811yescharacteristic
759C2×C3#305411yescharacteristic
760C2×C3#306211yescharacteristic
761C2×C3#327311yescharacteristic
762C2×C3#327511yescharacteristic
763C2×C3#332211yescharacteristic
764C2×C3#332611yescharacteristic
765D3—161no—
766C22—41no—
767C22—42no—
768C22—41no—
769C22—41no—
770C22—42no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—41no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—241no—
788C22—241no—
789C22—241no—
790C22—241no—
791C22—241no—
792C22—241no—
793C22—241no—
794C22D4×#6711yescharacteristic
795C22C2×#93911yescharacteristic
796C22#582211yescharacteristic
797C22#582211yescharacteristic
798C22#582911yescharacteristic
799C22#583511yescharacteristic
800C22#583611yescharacteristic
801C4—22no—
802C4—22no—
803C4—41no—
804C4—41no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4—122no—
809C4—122no—
810C4—241no—
811C4#559611yescharacteristic
812C4#559911yescharacteristic
813C4#560911yescharacteristic
814C4#561911yescharacteristic
815C3#2539011yescharacteristic, complemented, Sylow
816C2—81no—
817C2—81no—
818C2—82no—
819C2—481no—
820C2#8264911yescharacteristic
821C2#8292311yescharacteristic
822C2#8337911yescharacteristic
823C2#8350411yescharacteristic
824C2#8350811yescharacteristic
825C2#8361711yescharacteristic
826C2#8362111yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2535C2
socleC23×C3C22×D4
hypercenter#2535D3
hypocenterC3#25390
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2535

Complements

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

NH ≅ G/Ntype
1. C3×#2535C2semidirect
2. C2×#5039C2semidirect
3. C2×#5042C2semidirect
4. #82377C2semidirect
5. C2×#5016C2semidirect
6. C2×#5012C2semidirect
7. #71685C2semidirect
8. #71684C2semidirect
9. C4×#832C2semidirect
10. #69551C2semidirect
11. #69540C2semidirect
12. #69526C2semidirect
13. #69523C2semidirect
14. #69517C2semidirect
15. #69516C2semidirect
69. #2535D3semidirect
152. #832D4semidirect
164. C4⋊(C3⋊C8)D4semidirect
815. C3#25390semidirect

Maximal subgroups

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

subgroupindex
C3×#25352
C2×#50392
C2×#50422
#823772
C2×#50162
C2×#50122
#716852
#716842
C4×#8322
#695512
#695402
#695262
#695232
#695172
#695162
#253903