Finite Group Databasebeta

← #10830996

Subgroups — #10830996

Order 768.

1412 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#918C211yesmaximal, characteristic, complemented
2C2×C3×#470C211yesmaximal, characteristic, complemented
3C2×#5134C211yesmaximal, characteristic, complemented
4C2×#5128C211yesmaximal, characteristic, complemented
5#82812C211yesmaximal, characteristic
6#82751C211yesmaximal, characteristic, complemented
7#72066C211yesmaximal, characteristic, complemented
8#71700C211yesmaximal, characteristic, complemented
9#71699C211yesmaximal, characteristic, complemented
10#70578C211yesmaximal, characteristic, complemented
11#70574C211yesmaximal, characteristic, complemented
12#70285C211yesmaximal, characteristic, complemented
13#70280C211yesmaximal, characteristic, complemented
14#70267C211yesmaximal, characteristic, complemented
15#70266C211yesmaximal, characteristic, complemented
16#24276—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×D3×Q8C2211yescharacteristic
19C22×C3×Q16C2211yescharacteristic
20C22×C3×M16C2211yescharacteristic
21C2×C3×C22⋊Q8C2211yescharacteristic
22C2×C3×C22⋊Q8C2211yescharacteristic
23C22×#216C2211yescharacteristic
24C22×#215C2211yescharacteristic
25C2×#930C2211yescharacteristic
26C2×C4×#67C2211yescharacteristic
27C2×#924C2211yescharacteristic
28C2×#918—24no—
29C2×#918—24no—
30C2×#918—24no—
31C22×#204C2211yescharacteristic
32C22×ΓL(1,𝔽25)C2211yescharacteristic
33C3×#470—24no—
34C2×C3×#106C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37#5229C2211yescharacteristic
38#5229C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#830C2211yescharacteristic
42#5134—24no—
43#5128—24no—
44C2×#821C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#818C2211yescharacteristic
47C2×#816C2211yescharacteristic
48C2×Dic3⋊C8C2211yescharacteristic
49C2×C8×Dic3C2211yescharacteristic
50#4991—21no—
51#4989—21no—
52#4989—21no—
53#4988C2211yescharacteristic
54#4987C2211yescharacteristic
55#4987C2211yescharacteristic
56#4979—21no—
57#4973C2211yescharacteristic
58C2×#810C2211yescharacteristic
59C2×#809C2211yescharacteristic
60#4960—21no—
61#4956—21no—
62#4956—21no—
63#4947—21no—
64#4529C2211yescharacteristic
65#4529C2211yescharacteristic
66C22×#137—31no—
67C2×#470D311yescharacteristic, complemented
68C2×#468—31no—
69C2×#436—31no—
70#2409—31no—
71#2407—31no—
72#2056—31no—
73#2055—31no—
74#2001—31no—
75#2000—31no—
76#1969—31no—
77#1968—31no—
78#1809—31no—
79#1788—31no—
80#1787—31no—
81C22×C3×Q8C2311yescharacteristic
82C22×C3×Q8C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C22×#67—21no—
85C22×#67D411yescharacteristic
86C2×#239—22no—
87C2×#239—22no—
88C2×#239—22no—
89C2×#239—22no—
90C2×#239—41no—
91C2×#239—41no—
92C2×D3×Q8—22no—
93C2×D3×Q8—22no—
94C2×D3×Q8—22no—
95C2×D3×Q8—22no—
96C2×D3×Q8—41no—
97C2×D3×Q8—41no—
98C22×D12—21no—
99C22×D12C2311yescharacteristic
100C22×C4×D3—21no—
101C22×C4×D3—21no—
102C22×C4×D3C2311yescharacteristic
103C22×Dic6—21no—
104C22×Dic6C2311yescharacteristic
105C2×C3×Q16—22no—
106C2×C3×Q16—22no—
107C2×C3×Q16D414yescomplemented
108C2×C3×M16—22no—
109C2×C3×M16—22no—
110C2×C3×M16—22no—
111C22×C3×C8C2311yescharacteristic
112C22×C3×C8C2311yescharacteristic
113C3×C22⋊Q8—22no—
114C3×C22⋊Q8—22no—
115C3×C22⋊Q8—41no—
116C3×C22⋊Q8—41no—
117C2×C3×C4⋊C4—21no—
118C2×C3×C4⋊C4—21no—
119C2×C3×C4⋊C4C2311yescharacteristic
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C22⋊C4—21no—
122C2×C3×C22⋊C4—21no—
123C2×#217—21no—
124C2×#217D411yescharacteristic
125C2×#216—22no—
126C2×#216—22no—
127C2×#216—22no—
128C2×#215—22no—
129C2×#215—22no—
130C2×#215—22no—
131#930—22no—
132#930—41no—
133C4×#67—22no—
134C4×#67—22no—
135C2×(C2×D3)⋊C4—21no—
136C2×(C2×D3)⋊C4—21no—
137C2×(C2×D3)⋊C4—21no—
138C2×(C2×D3)⋊C4—21no—
139C2×(C2×D3)⋊C4—21no—
140C2×(C2×D3)⋊C4D411yescharacteristic
141C2×C4⋊Dic3C2311yescharacteristic
142C2×C4⋊Dic3C2311yescharacteristic
143#924—22no—
144#924—41no—
145C2×Dic3⋊C4—21no—
146C2×Dic3⋊C4D411yescharacteristic
147C2×C4×Dic3C2311yescharacteristic
148C22×C3⋊C8C2311yescharacteristic
149C22×C3⋊C8C2311yescharacteristic
150#918—232no—
151C2×#204—22no—
152C2×#204—22no—
153C2×#204D414yescomplemented
154C2×ΓL(1,𝔽25)—22no—
155C2×ΓL(1,𝔽25)—22no—
156C2×ΓL(1,𝔽25)D414yescomplemented
157C3×#106—22no—
158C3×#103—22no—
159C3×#103—22no—
160#835—41no—
161#835—41no—
162C3⋊#95—21no—
163C3⋊#95—21no—
164C3⋊#95—21no—
165C3⋊#95—21no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169C3⋊#95—21no—
170#830—22no—
171#821—22no—
172(C2×D3)⋊C8—22no—
173#818—22no—
174#816—22no—
175Dic3⋊C8—22no—
176C8×Dic3—22no—
177#810—41no—
178#809—41no—
179C22×#41—31no—
180C23×Q8—31no—
181C2×#137—64no—
182C2×#137—64no—
183C2×#137—64no—
184C22×Q16—31no—
185C22×Q16C2×D311yescharacteristic
186C22×SD16—31no—
187C22×SD16—31no—
188C22×M16—31no—
189C22×M16C2×D311yescharacteristic
190C2×C22⋊Q8—31no—
191C2×C22⋊Q8C2×D311yescharacteristic
192C2×C22⋊Q8C2×D311yescharacteristic
193C2×#121—31no—
194C2×C4×D4—31no—
195#470—24no—
196#468—64no—
197#436—64no—
198C2×#107—31no—
199C2×#106C2×D311yescharacteristic
200C2×C4⋊C8—31no—
201C2×#103—31no—
202C2×#103—31no—
203C2×#103—31no—
204C2×#103—31no—
205C2×#103C2×D311yescharacteristic
206C2×#103C2×D311yescharacteristic
207C2×#102—31no—
208C2×#102—31no—
209C2×C22⋊C8—31no—
210C2×C22⋊C8—31no—
211C2×C4×C8—31no—
212#395—61no—
213#394—61no—
214#393—61no—
215#392—61no—
216#391—31no—
217#391—31no—
218#391—31no—
219#390—31no—
220#386—61no—
221#386—61no—
222#385—61no—
223#385—61no—
224#380—31no—
225#380—31no—
226#340—31no—
227#340—31no—
228C24×C3C2×D411yescharacteristic
229C23×D3—21no—
230C23×D3C2×D411yescharacteristic
231C2×C3×Q8—21no—
232C2×C3×Q8—21no—
233C2×C3×Q8—21no—
234C2×C3×Q8—21no—
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C2×C3×Q8—21no—
241C2×C3×Q8C2×D412yes—
242C2×C3×Q8C2×D412yes—
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×C4C2411yescharacteristic
255C2×#67—22no—
256C2×#67—22no—
257C2×#67—41no—
258C2×#67—42no—
259C2×#67—42no—
260C2×#67—81no—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3C2×D411yescharacteristic
265C22×Dic3C2×D411yescharacteristic
266C22×Dic3C2×D411yescharacteristic
267#239—28no—
268#239—44no—
269#239—44no—
270#239—44no—
271D3×Q8—28no—
272D3×Q8—44no—
273D3×Q8—44no—
274D3×Q8—44no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12—21no—
278C2×D12—21no—
279C2×D12—21no—
280C2×D12—42no—
281C2×D12—42no—
282C2×D12—42no—
283C2×D12C2×D412yes—
284C2×C4×D3—21no—
285C2×C4×D3—21no—
286C2×C4×D3—21no—
287C2×C4×D3—21no—
288C2×C4×D3—42no—
289C2×C4×D3—42no—
290C2×C4×D3—42no—
291C2×C4×D3—42no—
292C2×C4×D3—42no—
293C2×C4×D3—42no—
294C2×C4×D3C2×D412yes—
295C2×C4×D3#4112yes—
296C2×Dic6—21no—
297C2×Dic6—21no—
298C2×Dic6—21no—
299C2×Dic6—21no—
300C2×Dic6—21no—
301C2×Dic6—42no—
302C2×Dic6—42no—
303C2×Dic6—42no—
304C2×Dic6C2×D412yes—
305C3×Q16—28no—
306C3×M16—44no—
307C2×C3×C8—21no—
308C2×C3×C8—21no—
309C2×C3×C8—21no—
310C2×C3×C8C2×D412yes—
311C2×C3×C8C2×D412yes—
312C2×C3×C8C2×D412yes—
313C3×C4⋊C4—21no—
314C3×C4⋊C4—21no—
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—42no—
318C3×C4⋊C4—42no—
319C3×C22⋊C4—42no—
320C3×C22⋊C4—42no—
321#217—22no—
322#217—42no—
323#216—28no—
324#215—28no—
325(C2×D3)⋊C4—22no—
326(C2×D3)⋊C4—42no—
327(C2×D3)⋊C4—42no—
328(C2×D3)⋊C4—42no—
329(C2×D3)⋊C4—81no—
330(C2×D3)⋊C4—81no—
331C4⋊Dic3—21no—
332C4⋊Dic3—21no—
333C4⋊Dic3—21no—
334C4⋊Dic3—21no—
335Dic3⋊C4—22no—
336Dic3⋊C4—42no—
337C4×Dic3—21no—
338C4×Dic3—21no—
339C2×C3⋊C8—21no—
340C2×C3⋊C8—21no—
341C2×C3⋊C8—21no—
342C2×C3⋊C8—21no—
343C2×C3⋊C8—21no—
344C2×C3⋊C8C2×D412yes—
345#204—28no—
346ΓL(1,𝔽25)—28no—
347C2×#41—62no—
348C2×#41—62no—
349C2×#41—62no—
350C2×#41—62no—
351C2×#41—121no—
352C2×#41—121no—
353C22×Q8—31no—
354C22×Q8—61no—
355C22×Q8—62no—
356C22×Q8—62no—
357C22×Q8—62no—
358C22×Q8—62no—
359C22×Q8—121no—
360C22×Q8—121no—
361C22×Q8C22×D311yescharacteristic
362C22×Q8C22×D311yescharacteristic
363C22×D4—31no—
364C22×D4—31no—
365C22×D4—61no—
366C22×D4—61no—
367C23×C4—31no—
368C23×C4—61no—
369C23×C4—61no—
370C23×C4C22×D311yescharacteristic
371#137—632no—
372C2×Q16—22no—
373C2×Q16—22no—
374C2×Q16—62no—
375C2×Q16—62no—
376C2×Q16—62no—
377C2×Q16#6714yescomplemented
378C2×SD16—34no—
379C2×SD16—62no—
380C2×SD16—62no—
381C2×SD16—62no—
382C2×SD16—62no—
383C2×SD16—62no—
384C2×M16—22no—
385C2×M16—22no—
386C2×M16—22no—
387C2×M16—34no—
388C2×M16—62no—
389C2×M16—62no—
390C22×C8—31no—
391C22×C8—31no—
392C22×C8C22×D311yescharacteristic
393C22×C8C22×D311yescharacteristic
394C22⋊Q8—22no—
395C22⋊Q8—22no—
396C22⋊Q8—41no—
397C22⋊Q8—41no—
398C22⋊Q8—62no—
399C22⋊Q8—121no—
400#121—62no—
401#121—121no—
402C4×D4—62no—
403C4×D4—62no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—31no—
407C2×C4⋊C4—31no—
408C2×C4⋊C4—31no—
409C2×C4⋊C4—61no—
410C2×C4⋊C4C22×D311yescharacteristic
411C2×C4⋊C4C22×D311yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—31no—
415C2×C22⋊C4—31no—
416C2×C22⋊C4—61no—
417C2×C22⋊C4—61no—
418C2×C22⋊C4—61no—
419C2×C22⋊C4—61no—
420C2×C22⋊C4—61no—
421C2×C22⋊C4—61no—
422C2×C42—31no—
423#107—62no—
424#106—22no—
425C4⋊C8—62no—
426#103—22no—
427#103—22no—
428#103—62no—
429#103—121no—
430#103—121no—
431#103—121no—
432#102—62no—
433#102—121no—
434C22⋊C8—62no—
435C22⋊C8—62no—
436C4×C8—62no—
437#95—61no—
438#95—61no—
439#95—61no—
440#95—61no—
441#95—61no—
442#95—61no—
443#95—61no—
444#95—61no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—21no—
450C23×C3—21no—
451C23×C3—21no—
452C23×C3C22×D411yescharacteristic
453C22×D3—21no—
454C22×D3—21no—
455C22×D3—21no—
456C22×D3—21no—
457C22×D3—21no—
458C22×D3—21no—
459C22×D3—22no—
460C22×D3—41no—
461C22×D3—41no—
462C22×D3—41no—
463C22×D3—41no—
464C22×D3—41no—
465C22×D3—41no—
466C22×D3#12112yes—
467C3×Q8—22no—
468C3×Q8—22no—
469C3×Q8—22no—
470C3×Q8—22no—
471C3×Q8—41no—
472C3×Q8—41no—
473C3×Q8—41no—
474C3×Q8—41no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—21no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4C22×D411yescharacteristic
495C2×C3×C4C22×D411yescharacteristic
496C2×C3×C4C22×D411yescharacteristic
497C2×C3×C4C2×#4111yescharacteristic
498C2×C3×C4H(5,𝔽2)11yescharacteristic
499C2×C3×C4H(5,𝔽2)11yescharacteristic
500#67—44no—
501#67—84no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—22no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3—41no—
513C2×Dic3—41no—
514C2×Dic3—41no—
515C2×Dic3—41no—
516C2×Dic3—41no—
517C2×Dic3—41no—
518C2×Dic3#12112yes—
519C2×Dic3#13712yescomplemented
520D12—22no—
521D12—22no—
522D12—48no—
523D12—41no—
524D12—41no—
525C4×D3—22no—
526C4×D3—22no—
527C4×D3—22no—
528C4×D3—22no—
529C4×D3—48no—
530C4×D3—48no—
531Dic6—22no—
532Dic6—22no—
533Dic6—48no—
534Dic6—41no—
535Dic6—41no—
536C3×C8—41no—
537C3×C8#12014yes—
538C3⋊C8—22no—
539C3⋊C8—41no—
540C24—31no—
541C24—61no—
542C24D3×D411yescharacteristic
543#41—68no—
544#41—124no—
545#41—124no—
546#41—124no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—32no—
558C2×Q8—61no—
559C2×Q8—68no—
560C2×Q8—61no—
561C2×Q8—61no—
562C2×Q8—61no—
563C2×Q8—61no—
564C2×Q8—122no—
565C2×Q8—122no—
566C2×Q8—122no—
567C2×Q8—124no—
568C2×Q8—124no—
569C2×Q8—124no—
570C2×Q8C2×#6712yes—
571C2×Q8C2×#6712yes—
572C2×D4—32no—
573C2×D4—62no—
574C2×D4—62no—
575C2×D4—61no—
576C2×D4—61no—
577C2×D4—61no—
578C2×D4—61no—
579C2×D4—61no—
580C2×D4—122no—
581C2×D4—122no—
582C2×D4—122no—
583C2×D4—121no—
584C2×D4—122no—
585C2×D4—122no—
586C2×D4—241no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—31no—
598C22×C4—31no—
599C22×C4—32no—
600C22×C4—32no—
601C22×C4—31no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—122no—
610C22×C4—122no—
611C22×C4—122no—
612C22×C4—122no—
613C22×C4—122no—
614C22×C4—122no—
615C22×C4D3×D411yescharacteristic
616C22×C4C23×D311yescharacteristic
617Q16—28no—
618Q16—68no—
619SD16—68no—
620SD16—68no—
621M16—44no—
622M16—68no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—32no—
627C2×C8—61no—
628C2×C8—61no—
629C2×C8—61no—
630C2×C8—61no—
631C2×C8—61no—
632C2×C8D3×D412yes—
633C2×C8D3×D412yes—
634C2×C8C2×#6712yes—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—42no—
640C4⋊C4—42no—
641C4⋊C4—62no—
642C4⋊C4—61no—
643C4⋊C4—61no—
644C4⋊C4—61no—
645C4⋊C4—61no—
646C4⋊C4—122no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—62no—
650C22⋊C4—62no—
651C22⋊C4—122no—
652C22⋊C4—122no—
653C22⋊C4—122no—
654C22⋊C4—122no—
655C22⋊C4—241no—
656C22⋊C4—241no—
657C42—61no—
658C42—61no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3C2×#12111yescharacteristic
667C22×C3D4211yescharacteristic
668C22×C3D4211yescharacteristic
669C22×C3C2×#13711yescharacteristic
670C22×C3#57511yescharacteristic
671C22×C3#57711yescharacteristic
672C22×C3#57811yescharacteristic
673C2×D3—22no—
674C2×D3—22no—
675C2×D3—22no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—42no—
681C2×D3—42no—
682C2×D3—42no—
683C2×D3—81no—
684C2×D3—81no—
685C2×D3—81no—
686C2×D3—81no—
687C3×C4—42no—
688C3×C4—42no—
689C3×C4—41no—
690C3×C4—81no—
691C3×C4—81no—
692C3×C4C2×#12011yescharacteristic
693C3×C4#53511yescharacteristic
694C3×C4#54611yescharacteristic
695C3×C4#54611yescharacteristic
696Dic3—22no—
697Dic3—22no—
698Dic3—42no—
699Dic3—41no—
700Dic3—81no—
701Dic3—81no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—32no—
710C23—61no—
711C23—61no—
712C23—61no—
713C23—61no—
714C23—61no—
715C23—61no—
716C23—62no—
717C23—121no—
718C23—121no—
719C23—121no—
720C23—121no—
721C23—121no—
722C23—121no—
723C23C2×D3×D411yescharacteristic
724Q8—22no—
725Q8—22no—
726Q8—22no—
727Q8—22no—
728Q8—41no—
729Q8—41no—
730Q8—41no—
731Q8—41no—
732Q8—62no—
733Q8—62no—
734Q8—128no—
735Q8—121no—
736Q8—121no—
737D4—62no—
738D4—62no—
739D4—128no—
740D4—124no—
741D4—121no—
742D4—121no—
743D4—244no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—32no—
750C2×C4—32no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—62no—
770C2×C4—62no—
771C2×C4—62no—
772C2×C4—62no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—62no—
777C2×C4—128no—
778C2×C4—128no—
779C2×C4—121no—
780C2×C4—121no—
781C2×C4—121no—
782C2×C4—121no—
783C2×C4—121no—
784C2×C4—121no—
785C2×C4—121no—
786C2×C4—121no—
787C2×C4C2×D3×D411yescharacteristic
788C2×C4C2×D3×D411yescharacteristic
789C2×C4#100411yescharacteristic
790C2×C4D3×#4111yescharacteristic
791C2×C4#100911yescharacteristic
792C2×C4C22×#6711yescharacteristic
793C8—41no—
794C8—62no—
795C8—121no—
796C8#93714yes—
797C2×C3—81no—
798C2×C3#240811yescharacteristic
799C2×C3#305611yescharacteristic
800C2×C3#306311yescharacteristic
801C2×C3#327511yescharacteristic
802C2×C3#327611yescharacteristic
803C2×C3#327711yescharacteristic
804C2×C3#327811yescharacteristic
805D3—42no—
806D3—82no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—62no—
815C22—62no—
816C22—62no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22—121no—
821C22—122no—
822C22—122no—
823C22—122no—
824C22—241no—
825C22—241no—
826C22—241no—
827C22—241no—
828C22D3×#12111yescharacteristic
829C22#560911yescharacteristic
830C22D3×#13711yescharacteristic
831C22#577711yescharacteristic
832C22#577811yescharacteristic
833C22#577911yescharacteristic
834C22D4×#6711yescharacteristic
835C4—41no—
836C4—42no—
837C4—42no—
838C4—62no—
839C4—62no—
840C4—81no—
841C4—81no—
842C4—121no—
843C4—122no—
844C4—241no—
845C4—241no—
846C4#560711yescharacteristic
847C4#561211yescharacteristic
848C4C2×#93711yescharacteristic
849C4#582911yescharacteristic
850C3#2427611yescharacteristic, complemented, Sylow
851C2—81no—
852C2—122no—
853C2—242no—
854C2#8090411yescharacteristic
855C2#8090711yescharacteristic
856C2#8092211yescharacteristic
857C2#8092311yescharacteristic
858C2#8264011yescharacteristic
859C2#8399411yescharacteristic
860C2#8399711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#470C2
socleC23×C3C22×D4
prime radical#82812C2
hypercenterC2×#470D3
hypocenterC3#24276
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
1. C22×#918C2semidirect
2. C2×C3×#470C2semidirect
3. C2×#5134C2semidirect
4. C2×#5128C2semidirect
6. #82751C2semidirect
7. #72066C2semidirect
8. #71700C2semidirect
9. #71699C2semidirect
10. #70578C2semidirect
11. #70574C2semidirect
12. #70285C2semidirect
13. #70280C2semidirect
14. #70267C2semidirect
15. #70266C2semidirect
67. C2×#470D3semidirect
107. C2×C3×Q16D4semidirect
153. C2×#204D4semidirect
156. C2×ΓL(1,𝔽25)D4semidirect
377. C2×Q16#67semidirect
519. C2×Dic3#137semidirect
850. C3#24276semidirect

Maximal subgroups

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

subgroupindex
C22×#9182
C2×C3×#4702
C2×#51342
C2×#51282
#828122
#827512
#720662
#717002
#716992
#705782
#705742
#702852
#702802
#702672
#702662
#242763