Finite Group Databasebeta

← #10845988

Subgroups — #10845988

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×#2540C211yesmaximal, characteristic, complemented
2C2×#5057C211yesmaximal, characteristic, complemented
3C2×#5049C211yesmaximal, characteristic, complemented
4C2×#5039C211yesmaximal, characteristic, complemented
5#82415C211yesmaximal, characteristic, complemented
6C2×#5012C211yesmaximal, characteristic, complemented
7#71725C211yesmaximal, characteristic, complemented
8#71699C211yesmaximal, characteristic, complemented
9#71697C211yesmaximal, characteristic, complemented
10#71694C211yesmaximal, characteristic, complemented
11#71684C211yesmaximal, characteristic, complemented
12#71682C211yesmaximal, characteristic, complemented
13#71679C211yesmaximal, characteristic, complemented
14C4×#809C211yesmaximal, characteristic, complemented
15#69468C211yesmaximal, characteristic, complemented
16#25390—31nomaximal, Sylow
17C2×C3×#124C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×C3×#121C2211yescharacteristic
22C2×C3×C4×D4C2211yescharacteristic
23C22×#215C2211yescharacteristic
24C22×#213C2211yescharacteristic
25C2×#930C2211yescharacteristic
26C2×#930C2211yescharacteristic
27C22×#208C2211yescharacteristic
28C22×#208C2211yescharacteristic
29C2×C4×D12C2211yescharacteristic
30C3×#399—21no—
31C3×#392—21no—
32C3×#390—21no—
33C3×#390—21no—
34C3×C4×C4⋊C4C2211yescharacteristic
35C2×#835C2211yescharacteristic
36C2×#835C2211yescharacteristic
37C2×#835C2211yescharacteristic
38#5223—21no—
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic
42#5212C2211yescharacteristic
43#5212C2211yescharacteristic
44C2×#830C2211yescharacteristic
45C2×#830C2211yescharacteristic
46#5057—24no—
47#5049—24no—
48#5039—24no—
49#5012—24no—
50#4992—21no—
51C2×#809C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#808C2211yescharacteristic
54C2×#807C2211yescharacteristic
55#4956—21no—
56#4956—21no—
57#4936C2211yescharacteristic
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#2540D311yescharacteristic, complemented
69#2535—31no—
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×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4—21no—
82C22×C3×D4D411yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C22×#67—21no—
87C22×#67—21no—
88C22×D12C2311yescharacteristic
89C22×C4×D3—21no—
90C3×#124—22no—
91C3×#124—22no—
92C3×C22⋊Q8—22no—
93C3×C22⋊Q8—22no—
94C3×C22⋊Q8—41no—
95C3×C22⋊Q8—41no—
96C3×#121—22no—
97C3×#121—22no—
98C3×#121—41no—
99C3×#121—41no—
100C3×C4×D4—22no—
101C3×C4×D4—22no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—21no—
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⋊C4—21no—
112C2×C3×C22⋊C4—21no—
113C2×C3×C22⋊C4D411yescharacteristic
114C2×C3×C22⋊C4D411yescharacteristic
115C2×C3×C42—21no—
116C2×C3×C42C2311yescharacteristic
117C2×#217—21no—
118C2×#217—21no—
119C2×#215—22no—
120C2×#215—22no—
121C2×#215—41no—
122C2×#213—22no—
123C2×#213—22no—
124C2×#213—41no—
125#930—22no—
126#930—22no—
127#930—41no—
128#930—41no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134C2×C4⋊Dic3C2311yescharacteristic
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
145C4×D12—22no—
146C4×D12—22no—
147C3×#95—21no—
148#835—22no—
149#835—22no—
150#835—41no—
151#832—22no—
152#832—22no—
153#832—41no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158#830—22no—
159#830—22no—
160#809—22no—
161#809D414yescomplemented
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×#124C2×D311yescharacteristic
171C2×C22⋊Q8C2×D311yescharacteristic
172C2×C22⋊Q8C2×D311yescharacteristic
173C2×#121—31no—
174C2×#121—31no—
175C2×#121C2×D311yescharacteristic
176C2×#121C2×D311yescharacteristic
177C2×C4×D4—31no—
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—21no—
198#397—61no—
199#392—21no—
200#392—61no—
201#390—21no—
202#390—21no—
203#386—61no—
204#386—61no—
205#382—31no—
206#380—31no—
207#380—31no—
208C4×C4⋊C4C2×D311yescharacteristic
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×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×D4—22no—
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—41no—
231C2×C3×D4—41no—
232C2×C3×D4—42no—
233C2×C3×D4—42no—
234C2×C3×D4—42no—
235C2×C3×D4—42no—
236C2×C3×D4—81no—
237C2×C3×D4—81no—
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—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2411yescharacteristic
258C2×#67—42no—
259C2×#67—42no—
260C2×#67—42no—
261C2×#67—42no—
262C2×#67—81no—
263C2×#67—81no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3—21no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12—21no—
272C2×D12C2×D412yes—
273C2×C4×D3—42no—
274C2×C4×D3—81no—
275C2×C4×D3—81no—
276C3×C4⋊C4—22no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—42no—
280C3×C4⋊C4—42no—
281C3×C4⋊C4C2×D412yes—
282C3×C4⋊C4#4112yes—
283C3×C22⋊C4—22no—
284C3×C22⋊C4—22no—
285C3×C22⋊C4—42no—
286C3×C22⋊C4—42no—
287C3×C22⋊C4—42no—
288C3×C22⋊C4—42no—
289C3×C22⋊C4—42no—
290C3×C22⋊C4—42no—
291C3×C42—81no—
292C3×C42C2×D412yes—
293C3×C42#4112yes—
294#217—81no—
295#217—81no—
296#215—44no—
297#213—44no—
298(C2×D3)⋊C4—42no—
299(C2×D3)⋊C4—42no—
300(C2×D3)⋊C4—42no—
301C4⋊Dic3—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
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×Q8C22×D311yescharacteristic
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—31no—
325C22×D4—61no—
326C22×D4—61no—
327C22×D4#6711yescharacteristic
328C22×D4C22×D311yescharacteristic
329C23×C4—61no—
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—22no—
349#124—22no—
350C22⋊Q8—22no—
351C22⋊Q8—22no—
352C22⋊Q8—41no—
353C22⋊Q8—41no—
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—62no—
365C4×D4—62no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4—31no—
371C2×C4⋊C4#6711yescharacteristic
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—21no—
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—21no—
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—61no—
405#95—61no—
406#95—61no—
407#95—61no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
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—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3C22×D411yescharacteristic
430C22×D3—22no—
431C22×D3—41no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C3×Q8—41no—
438C3×Q8—41no—
439C3×Q8—41no—
440C3×Q8—41no—
441C3×D4—44no—
442C3×D4—41no—
443C3×D4—41no—
444C3×D4—41no—
445C3×D4—41no—
446C3×D4—84no—
447C3×D4—84no—
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—21no—
455C2×C3×C4—21no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
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—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4#12112yes—
476C2×C3×C4#12112yes—
477C2×C3×C4C22×D411yescharacteristic
478C2×C3×C4C22×D411yescharacteristic
479C2×C3×C4C2×#4111yescharacteristic
480C2×C3×C4C2×#4111yescharacteristic
481C2×C3×C4H(5,𝔽2)11yescharacteristic
482C2×C3×C4H(5,𝔽2)11yescharacteristic
483#67—84no—
484#67—84no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494D12—22no—
495D12—22no—
496D12—41no—
497D12—41no—
498C4×D3—84no—
499C3⋊C8—22no—
500C3⋊C8—22no—
501C3⋊C8—22no—
502C3⋊C8—41no—
503C24—21no—
504C24—61no—
505C24C2×#6711yescharacteristic
506C24C2×#6711yescharacteristic
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×D4—22no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—32no—
521C2×D4—41no—
522C2×D4—41no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—61no—
528C2×D4—61no—
529C2×D4—61no—
530C2×D4—61no—
531C2×D4—61no—
532C2×D4—81no—
533C2×D4—81no—
534C2×D4—122no—
535C2×D4—122no—
536C2×D4—122no—
537C2×D4—122no—
538C2×D4—241no—
539C2×D4—241no—
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—61no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—122no—
559C22×C4—241no—
560C22×C4—241no—
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—42no—
586C4⋊C4—42no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4D3×D412yes—
594C4⋊C4#23712yes—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—42no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—122no—
604C22⋊C4—122no—
605C22⋊C4—122no—
606C22⋊C4—241no—
607C22⋊C4—241no—
608C42—81no—
609C42D3×D412yes—
610C42#23712yes—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—81no—
626C22×C3—81no—
627C22×C3—81no—
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—42no—
640C2×D3—42no—
641C2×D3—42no—
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—42no—
651C3×C4—42no—
652C3×C4—81no—
653C3×C4#53211yescharacteristic
654C3×C4#54011yescharacteristic
655C3×C4D4211yescharacteristic
656C3×C4#55011yescharacteristic
657Dic3—81no—
658Dic3—81no—
659Dic3—81no—
660C23—21no—
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—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—62no—
682C23—121no—
683C23—121no—
684C23—121no—
685C23—121no—
686C23—121no—
687C23—121no—
688C23C22×#6711yescharacteristic
689Q8—41no—
690Q8—41no—
691Q8—41no—
692Q8—41no—
693D4—44no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—62no—
699D4—62no—
700D4—84no—
701D4—84no—
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—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
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—121no—
734C2×C4—121no—
735C2×C4—121no—
736C2×C4—121no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4—244no—
743C2×C4#93912yes—
744C2×C4#93912yes—
745C2×C4C2×D3×D411yescharacteristic
746C2×C4C2×D3×D411yescharacteristic
747C2×C4C2×#23711yescharacteristic
748C2×C4C2×#23711yescharacteristic
749C2×C4#100411yescharacteristic
750C2×C4#100411yescharacteristic
751C8—62no—
752C8—62no—
753C8—62no—
754C8—121no—
755C2×C3—81no—
756C2×C3—81no—
757C2×C3—161no—
758C2×C3#242811yescharacteristic
759C2×C3#305411yescharacteristic
760C2×C3#306211yescharacteristic
761C2×C3#327311yescharacteristic
762C2×C3#327511yescharacteristic
763C2×C3#332211yescharacteristic
764C2×C3#332611yescharacteristic
765D3—82no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—122no—
788C22—122no—
789C22—122no—
790C22—241no—
791C22—241no—
792C22—241no—
793C22—241no—
794C22D4×#6711yescharacteristic
795C22C2×#93911yescharacteristic
796C22#580611yescharacteristic
797C22#582211yescharacteristic
798C22#582211yescharacteristic
799C22#583511yescharacteristic
800C22#583711yescharacteristic
801C4—22no—
802C4—22no—
803C4—42no—
804C4—42no—
805C4—41no—
806C4—41no—
807C4—81no—
808C4—241no—
809C4—241no—
810C4—241no—
811C4#571611yescharacteristic
812C4#571711yescharacteristic
813C4#571811yescharacteristic
814C4#571911yescharacteristic
815C3#2539011yescharacteristic, complemented, Sylow
816C2—81no—
817C2—81no—
818C2—161no—
819C2—242no—
820C2#8292311yescharacteristic
821C2#8318611yescharacteristic
822C2#8342211yescharacteristic
823C2#8350011yescharacteristic
824C2#8350411yescharacteristic
825C2#8354011yescharacteristic
826C2#8354411yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2540C2
socleC23×C3C22×D4
hypercenter#2540D3
hypocenterC3#25390
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2540

Complements

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

NH ≅ G/Ntype
1. C3×#2540C2semidirect
2. C2×#5057C2semidirect
3. C2×#5049C2semidirect
4. C2×#5039C2semidirect
5. #82415C2semidirect
6. C2×#5012C2semidirect
7. #71725C2semidirect
8. #71699C2semidirect
9. #71697C2semidirect
10. #71694C2semidirect
11. #71684C2semidirect
12. #71682C2semidirect
13. #71679C2semidirect
14. C4×#809C2semidirect
15. #69468C2semidirect
68. #2540D3semidirect
161. #809D4semidirect
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×#25402
C2×#50572
C2×#50492
C2×#50392
#824152
C2×#50122
#717252
#716992
#716972
#716942
#716842
#716822
#716792
C4×#8092
#694682
#253903