Finite Group Databasebeta

← #10830995

Subgroups — #10830995

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×#4838C211yesmaximal, characteristic, complemented
3C2×#4816C211yesmaximal, characteristic, complemented
4C2×#4812C211yesmaximal, characteristic, complemented
5#76619C211yesmaximal, characteristic, complemented
6#76618C211yesmaximal, characteristic
7C3×#2056C211yesmaximal, characteristic, complemented
8#72071C211yesmaximal, characteristic, complemented
9#70482C211yesmaximal, characteristic, complemented
10#70267C211yesmaximal, characteristic, complemented
11#70266C211yesmaximal, characteristic, complemented
12#69677C211yesmaximal, characteristic, complemented
13#69676C211yesmaximal, characteristic, complemented
14#68887C211yesmaximal, characteristic, complemented
15#68870C211yesmaximal, characteristic, complemented
16#24276—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×D3×Q8C2211yescharacteristic
19C22×C3×Q16C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C22×#216C2211yescharacteristic
23C22×#215C2211yescharacteristic
24C2×#918—24no—
25C2×#918—24no—
26C2×#918—24no—
27C22×#204C2211yescharacteristic
28C22×ΓL(1,𝔽25)C2211yescharacteristic
29C22×ΓL(1,𝔽25)C2211yescharacteristic
30C2×#897C2211yescharacteristic
31C2×#895C2211yescharacteristic
32C2×C4×D12C2211yescharacteristic
33C2×C3×C4⋊C8C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C3×#391C2211yescharacteristic
37C3×#391C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×#821C2211yescharacteristic
41C2×(C2×D3)⋊C8C2211yescharacteristic
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×#816C2211yescharacteristic
44#4987C2211yescharacteristic
45#4987C2211yescharacteristic
46C2×#810C2211yescharacteristic
47C2×#809C2211yescharacteristic
48C2×#808C2211yescharacteristic
49C2×#807C2211yescharacteristic
50#4939C2211yescharacteristic
51#4929C2211yescharacteristic
52C2×C4×C3⋊C8C2211yescharacteristic
53#4838—24no—
54#4816—24no—
55#4812—24no—
56#4673—21no—
57#4672—21no—
58#4671—21no—
59#4668—21no—
60#4668—21no—
61#4665—21no—
62#4665—21no—
63#4656—21no—
64C3×#340C2211yescharacteristic
65#4551C2211yescharacteristic
66C22×#137—31no—
67C2×#470—31no—
68C2×#468—31no—
69C2×#436—31no—
70#2409—31no—
71#2407—31no—
72#2056D311yescharacteristic, complemented
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
83C2×#239—22no—
84C2×#239—22no—
85C2×#239—22no—
86C2×#239—22no—
87C2×#239—41no—
88C2×#239—41no—
89C2×D3×Q8—22no—
90C2×D3×Q8—22no—
91C2×D3×Q8—22no—
92C2×D3×Q8—22no—
93C2×D3×Q8—41no—
94C2×D3×Q8—41no—
95C22×D12—21no—
96C22×D12—21no—
97C22×D12D411yescharacteristic
98C22×D12C2311yescharacteristic
99C22×C4×D3—21no—
100C22×C4×D3—21no—
101C22×C4×D3C2311yescharacteristic
102C22×C4×D3C2311yescharacteristic
103C22×Dic6—21no—
104C22×Dic6C2311yescharacteristic
105C2×C3×Q16—22no—
106C2×C3×Q16—22no—
107C2×C3×Q16—22no—
108C22×C3×C8C2311yescharacteristic
109C22×C3×C8C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C42C2311yescharacteristic
113#946—22no—
114#946—22no—
115#946—41no—
116#946—41no—
117C2×#216—22no—
118C2×#216—22no—
119C2×#216D414yescomplemented
120C2×#215—22no—
121C2×#215—22no—
122C2×#215D414yescomplemented
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4D411yescharacteristic
132C2×(C2×D3)⋊C4D411yescharacteristic
133C2×C4⋊Dic3—21no—
134C2×C4⋊Dic3D411yescharacteristic
135C2×C4⋊Dic3C2311yescharacteristic
136C2×C4⋊Dic3C2311yescharacteristic
137C2×Dic3⋊C4—21no—
138C2×Dic3⋊C4—21no—
139C22×C3⋊C8C2311yescharacteristic
140C22×C3⋊C8C2311yescharacteristic
141#918—232no—
142C2×#204—22no—
143C2×#204—22no—
144C2×#204—22no—
145C2×ΓL(1,𝔽25)—22no—
146C2×ΓL(1,𝔽25)—22no—
147C2×ΓL(1,𝔽25)—22no—
148C2×ΓL(1,𝔽25)—22no—
149C2×ΓL(1,𝔽25)—22no—
150C2×ΓL(1,𝔽25)D414yescomplemented
151#897—22no—
152#897—41no—
153#895—22no—
154#895—41no—
155C4×D12—22no—
156C4×D12—22no—
157C3×C4⋊C8—22no—
158C3×#103—22no—
159C3×#103—22no—
160C3×#95—21no—
161C3×#95—21no—
162C3×#95—21no—
163C3×#95—21no—
164#835—41no—
165#835—41no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169C3⋊#95—21no—
170#821—22no—
171(C2×D3)⋊C8—22no—
172(C2×D3)⋊C8—22no—
173#816—22no—
174#810—41no—
175#809—41no—
176#808—22no—
177#807—22no—
178C4×C3⋊C8—22no—
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×M16—31no—
190C2×C22⋊Q8—31no—
191C2×C22⋊Q8—31no—
192C2×C22⋊Q8—31no—
193C2×#121—31no—
194C2×C4×D4—31no—
195#470—64no—
196#468—64no—
197#436—64no—
198C2×#107—31no—
199C2×#106—31no—
200C2×C4⋊C8C2×D311yescharacteristic
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#391C2×D311yescharacteristic
218#391C2×D311yescharacteristic
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#340C2×D311yescharacteristic
228C23×D3—21no—
229C23×D3C2×D411yescharacteristic
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×C4C2×D411yescharacteristic
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2411yescharacteristic
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3C2×D411yescharacteristic
254C22×Dic3C2×D411yescharacteristic
255#239—28no—
256#239—44no—
257#239—44no—
258#239—44no—
259D3×Q8—28no—
260D3×Q8—44no—
261D3×Q8—44no—
262D3×Q8—44no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—22no—
268C2×D12—22no—
269C2×D12—21no—
270C2×D12—41no—
271C2×D12—42no—
272C2×D12—42no—
273C2×D12—42no—
274C2×D12—42no—
275C2×D12—42no—
276C2×D12—81no—
277C2×D12C2×D412yes—
278C2×C4×D3—21no—
279C2×C4×D3—21no—
280C2×C4×D3—21no—
281C2×C4×D3—21no—
282C2×C4×D3—21no—
283C2×C4×D3—21no—
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—
306C2×C3×C8—21no—
307C2×C3×C8—21no—
308C2×C3×C8—21no—
309C2×C3×C8—21no—
310C2×C3×C8—21no—
311C2×C3×C8C2×D412yes—
312C3×C4⋊C4—21no—
313C3×C4⋊C4—21no—
314C3×C4⋊C4—21no—
315C3×C4⋊C4—21no—
316C3×C42—21no—
317C3×C42—21no—
318#216—28no—
319#215—28no—
320(C2×D3)⋊C4—22no—
321(C2×D3)⋊C4—22no—
322(C2×D3)⋊C4—42no—
323(C2×D3)⋊C4—42no—
324(C2×D3)⋊C4—42no—
325(C2×D3)⋊C4—42no—
326(C2×D3)⋊C4—42no—
327(C2×D3)⋊C4—42no—
328(C2×D3)⋊C4—81no—
329(C2×D3)⋊C4—81no—
330C4⋊Dic3—22no—
331C4⋊Dic3—21no—
332C4⋊Dic3—21no—
333C4⋊Dic3—21no—
334C4⋊Dic3—21no—
335C4⋊Dic3—42no—
336Dic3⋊C4—42no—
337Dic3⋊C4—42no—
338C2×C3⋊C8—21no—
339C2×C3⋊C8—21no—
340C2×C3⋊C8—21no—
341C2×C3⋊C8C2×D412yes—
342C2×C3⋊C8C2×D412yes—
343C2×C3⋊C8C2×D412yes—
344#204—28no—
345ΓL(1,𝔽25)—28no—
346ΓL(1,𝔽25)—44no—
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—31no—
369C23×C4—61no—
370C23×C4—61no—
371#137—632no—
372C2×Q16—22no—
373C2×Q16—22no—
374C2×Q16—22no—
375C2×Q16—34no—
376C2×Q16—62no—
377C2×Q16—62no—
378C2×SD16—34no—
379C2×SD16—62no—
380C2×SD16—62no—
381C2×SD16—62no—
382C2×SD16—62no—
383C2×SD16—62no—
384C2×M16—34no—
385C2×M16—62no—
386C2×M16—62no—
387C2×M16—62no—
388C2×M16—62no—
389C2×M16—62no—
390C22×C8—31no—
391C22×C8—31no—
392C22×C8C22×D311yescharacteristic
393C22×C8C22×D311yescharacteristic
394C22⋊Q8—62no—
395C22⋊Q8—62no—
396C22⋊Q8—62no—
397C22⋊Q8—121no—
398C22⋊Q8—121no—
399C22⋊Q8—121no—
400#121—62no—
401#121—121no—
402C4×D4—62no—
403C4×D4—62no—
404C2×C4⋊C4—31no—
405C2×C4⋊C4—31no—
406C2×C4⋊C4—31no—
407C2×C4⋊C4—61no—
408C2×C4⋊C4—61no—
409C2×C4⋊C4—61no—
410C2×C4⋊C4C22×D311yescharacteristic
411C2×C4⋊C4C22×D311yescharacteristic
412C2×C22⋊C4—31no—
413C2×C22⋊C4—31no—
414C2×C22⋊C4—61no—
415C2×C22⋊C4—61no—
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×C42C22×D311yescharacteristic
423#107—62no—
424#106—62no—
425C4⋊C8—22no—
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—21no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—61no—
442#95—61no—
443#95—61no—
444#95—61no—
445C23×C3C22×D411yescharacteristic
446C22×D3—21no—
447C22×D3—21no—
448C22×D3—21no—
449C22×D3—21no—
450C22×D3—21no—
451C22×D3—21no—
452C22×D3—21no—
453C22×D3—21no—
454C22×D3—21no—
455C22×D3—22no—
456C22×D3—21no—
457C22×D3—21no—
458C22×D3—21no—
459C22×D3—21no—
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—21no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
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#13712yescomplemented
493C2×C3×C4C22×D411yescharacteristic
494C2×C3×C4C22×D411yescharacteristic
495C2×C3×C4C22×D411yescharacteristic
496C2×C3×C4C2×#4111yescharacteristic
497C2×C3×C4H(5,𝔽2)11yescharacteristic
498C2×C3×C4H(5,𝔽2)11yescharacteristic
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—22no—
505C2×Dic3—41no—
506C2×Dic3—41no—
507C2×Dic3—41no—
508C2×Dic3—41no—
509C2×Dic3—41no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3—41no—
513C2×Dic3#12112yes—
514D12—22no—
515D12—22no—
516D12—44no—
517D12—48no—
518D12—41no—
519D12—41no—
520D12—84no—
521C4×D3—22no—
522C4×D3—22no—
523C4×D3—22no—
524C4×D3—22no—
525C4×D3—48no—
526C4×D3—48no—
527C4×D3—41no—
528C4×D3—41no—
529C4×D3—41no—
530C4×D3—41no—
531Dic6—22no—
532Dic6—22no—
533Dic6—48no—
534Dic6—41no—
535Dic6—41no—
536C3×C8—22no—
537C3×C8—41no—
538C3⋊C8—41no—
539C3⋊C8#12014yes—
540C24—31no—
541C24—31no—
542C24—61no—
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×Q8D3×D412yes—
571C2×Q8D3×D412yes—
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—121no—
581C2×D4—122no—
582C2×D4—122no—
583C2×D4—122no—
584C2×D4—122no—
585C2×D4—122no—
586C2×D4—241no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—31no—
592C22×C4—32no—
593C22×C4—32no—
594C22×C4—31no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—122no—
609C22×C4—122no—
610C22×C4—122no—
611C22×C4—122no—
612C22×C4—122no—
613C22×C4—122no—
614C22×C4D3×D411yescharacteristic
615C22×C4D3×D411yescharacteristic
616C22×C4C23×D311yescharacteristic
617Q16—28no—
618Q16—68no—
619SD16—68no—
620SD16—68no—
621M16—68no—
622M16—124no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—32no—
629C2×C8—32no—
630C2×C8—32no—
631C2×C8—61no—
632C2×C8—61no—
633C2×C8—61no—
634C2×C8D3×D412yes—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—62no—
640C4⋊C4—61no—
641C4⋊C4—61no—
642C4⋊C4—61no—
643C4⋊C4—61no—
644C4⋊C4—122no—
645C4⋊C4—122no—
646C4⋊C4—122no—
647C22⋊C4—62no—
648C22⋊C4—62no—
649C22⋊C4—122no—
650C22⋊C4—122no—
651C22⋊C4—122no—
652C22⋊C4—122no—
653C22⋊C4—122no—
654C22⋊C4—122no—
655C22⋊C4—241no—
656C22⋊C4—241no—
657C42—21no—
658C42—21no—
659C22×C3C2×#12111yescharacteristic
660C22×C3D4211yescharacteristic
661C22×C3D4211yescharacteristic
662C22×C3C2×#13711yescharacteristic
663C22×C3#57511yescharacteristic
664C22×C3#57711yescharacteristic
665C22×C3#57811yescharacteristic
666C2×D3—22no—
667C2×D3—22no—
668C2×D3—22no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—42no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—42no—
677C2×D3—41no—
678C2×D3—42no—
679C2×D3—41no—
680C2×D3—41no—
681C2×D3—41no—
682C2×D3—41no—
683C2×D3—81no—
684C2×D3—81no—
685C2×D3—81no—
686C2×D3—81no—
687C3×C4—22no—
688C3×C4—42no—
689C3×C4—42no—
690C3×C4—41no—
691C3×C4—81no—
692C3×C4—81no—
693C3×C4C2×#12011yescharacteristic
694C3×C4#53511yescharacteristic
695C3×C4#54611yescharacteristic
696C3×C4#54611yescharacteristic
697Dic3—22no—
698Dic3—42no—
699Dic3—41no—
700Dic3—81no—
701Dic3—81no—
702C23—32no—
703C23—61no—
704C23—61no—
705C23—61no—
706C23—61no—
707C23—61no—
708C23—61no—
709C23—61no—
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—124no—
740D4—128no—
741D4—121no—
742D4—121no—
743D4—244no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—32no—
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—61no—
763C2×C4—61no—
764C2×C4—62no—
765C2×C4—62no—
766C2×C4—62no—
767C2×C4—62no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—62no—
771C2×C4—61no—
772C2×C4—128no—
773C2×C4—128no—
774C2×C4—121no—
775C2×C4—121no—
776C2×C4—121no—
777C2×C4—121no—
778C2×C4—121no—
779C2×C4—121no—
780C2×C4—121no—
781C2×C4—121no—
782C2×C4—121no—
783C2×C4—121no—
784C2×C4—121no—
785C2×C4—121no—
786C2×C4#91812yescomplemented
787C2×C4C2×D3×D411yescharacteristic
788C2×C4C2×D3×D411yescharacteristic
789C2×C4C2×D3×D411yescharacteristic
790C2×C4D3×#4111yescharacteristic
791C2×C4#100911yescharacteristic
792C2×C4#100911yescharacteristic
793C8—22no—
794C8—34no—
795C8—41no—
796C8—121no—
797C2×C3#240811yescharacteristic
798C2×C3#305611yescharacteristic
799C2×C3#306311yescharacteristic
800C2×C3#327511yescharacteristic
801C2×C3#327611yescharacteristic
802C2×C3#327711yescharacteristic
803C2×C3#327811yescharacteristic
804D3—42no—
805D3—81no—
806D3—82no—
807C22—62no—
808C22—62no—
809C22—62no—
810C22—121no—
811C22—121no—
812C22—121no—
813C22—121no—
814C22—121no—
815C22—122no—
816C22—121no—
817C22—121no—
818C22—122no—
819C22—121no—
820C22—121no—
821C22—121no—
822C22—121no—
823C22—122no—
824C22—241no—
825C22—241no—
826C22—241no—
827C22—241no—
828C22D3×#12111yescharacteristic
829C22#560911yescharacteristic
830C22#560911yescharacteristic
831C22C2×#91811yescharacteristic
832C22#576811yescharacteristic
833C22#577811yescharacteristic
834C22#577911yescharacteristic
835C4—22no—
836C4—41no—
837C4—42no—
838C4—42no—
839C4—62no—
840C4—81no—
841C4—81no—
842C4—121no—
843C4—122no—
844C4—241no—
845C4—241no—
846C4D3×#12011yescharacteristic
847C4#565411yescharacteristic
848C4#565411yescharacteristic
849C4#567411yescharacteristic
850C3#2427611yescharacteristic, complemented, Sylow
851C2—122no—
852C2—241no—
853C2—242no—
854C2#7689511yescharacteristic
855C2#8050111yescharacteristic
856C2#8050311yescharacteristic
857C2#8061311yescharacteristic
858C2#8062911yescharacteristic
859C2#8075911yescharacteristic
860C2#8090711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2056C2
socleC23×C3C22×D4
prime radical#76618C2
hypercenter#2056D3
hypocenterC3#24276
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2056

Complements

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

NH ≅ G/Ntype
1. C22×#918C2semidirect
2. C2×#4838C2semidirect
3. C2×#4816C2semidirect
4. C2×#4812C2semidirect
5. #76619C2semidirect
7. C3×#2056C2semidirect
8. #72071C2semidirect
9. #70482C2semidirect
10. #70267C2semidirect
11. #70266C2semidirect
12. #69677C2semidirect
13. #69676C2semidirect
14. #68887C2semidirect
15. #68870C2semidirect
72. #2056D3semidirect
119. C2×#216D4semidirect
122. C2×#215D4semidirect
150. C2×ΓL(1,𝔽25)D4semidirect
492. C2×C3×C4#137semidirect
786. C2×C4#918semidirect
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×#48382
C2×#48162
C2×#48122
#766192
#766182
C3×#20562
#720712
#704822
#702672
#702662
#696772
#696762
#688872
#688702
#242763