Finite Group Databasebeta

← #10827624

Subgroups — #10827624

Order 768.

1228 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5694C211yesmaximal, characteristic
2C2×#4809C211yesmaximal, characteristic, complemented
3C2×#4802C211yesmaximal, characteristic, complemented
4#76619C211yesmaximal, characteristic
5C3×#2026C211yesmaximal, characteristic, complemented
6#71744C211yesmaximal, characteristic, complemented
7#70273C211yesmaximal, characteristic, complemented
8#70268C211yesmaximal, characteristic, complemented
9#69690C211yesmaximal, characteristic, complemented
10#68888C211yesmaximal, characteristic, complemented
11#68884C211yesmaximal, characteristic, complemented
12#68878C211yesmaximal, characteristic, complemented
13#68873C211yesmaximal, characteristic, complemented
14#68685C211yesmaximal, characteristic, complemented
15#68669C211yesmaximal, characteristic
16#23983—31nomaximal, Sylow
17C22×D3×Q8C2211yescharacteristic
18C2×C3×#125C2211yescharacteristic
19C2×#946C2211yescharacteristic
20C22×#216C2211yescharacteristic
21C22×Dic12C2211yescharacteristic
22C22×ΓL(1,𝔽25)C2211yescharacteristic
23#5694—24no—
24#5694—24no—
25C2×#898—21no—
26C2×#897C2211yescharacteristic
27C2×#897C2211yescharacteristic
28C2×#897C2211yescharacteristic
29C2×#894—21no—
30C2×#892—21no—
31C2×#892C2211yescharacteristic
32C2×D3×C4⋊C4C2211yescharacteristic
33C2×#890—21no—
34C2×C4×D12C2211yescharacteristic
35C2×C4×Dic6C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C3×#391C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×(C2×D3)⋊C8C2211yescharacteristic
41C2×(C2×D3)⋊C8C2211yescharacteristic
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×#816C2211yescharacteristic
44C2×#816C2211yescharacteristic
45#4987C2211yescharacteristic
46C2×#810C2211yescharacteristic
47C2×#810C2211yescharacteristic
48C2×#810C2211yescharacteristic
49#4929C2211yescharacteristic
50#4809—24no—
51#4802—24no—
52#4673—21no—
53#4668—21no—
54#4665—21no—
55#4656—21no—
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#336C2211yescharacteristic
59#4551C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#552—31no—
65C2×#451—31no—
66C2×#419—31no—
67#2409—31no—
68#2026—31no—
69#2026D311yescharacteristic, complemented
70#2001—31no—
71#2001—31no—
72#1894—31no—
73#1878—31no—
74#1878—31no—
75#1872—31no—
76#1872—31no—
77#1870—31no—
78#1825—31no—
79C22×C3×Q8C2311yescharacteristic
80C2×D3×Q8—22no—
81C2×D3×Q8—22no—
82C2×D3×Q8—22no—
83C2×D3×Q8—22no—
84C2×D3×Q8—41no—
85C2×D3×Q8—41no—
86C22×D12D411yescharacteristic
87C22×C4×D3—21no—
88C22×C4×D3—21no—
89C22×C4×D3C2311yescharacteristic
90C22×C4×D3C2311yescharacteristic
91C22×Dic6—21no—
92C22×Dic6C2311yescharacteristic
93C22×Dic6C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C3×#125—22no—
97C3×#125—22no—
98C2×C3×C4⋊C4—21no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C42C2311yescharacteristic
104#946—22no—
105#946—41no—
106C2×#216—22no—
107C2×#216—22no—
108C2×#216—41no—
109C2×(C2×D3)⋊C4—21no—
110C2×(C2×D3)⋊C4—21no—
111C2×(C2×D3)⋊C4—21no—
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4D411yescharacteristic
116C2×(C2×D3)⋊C4D411yescharacteristic
117C2×C4⋊Dic3—21no—
118C2×C4⋊Dic3—21no—
119C2×C4⋊Dic3—21no—
120C2×C4⋊Dic3D411yescharacteristic
121C2×C4⋊Dic3C2311yescharacteristic
122C2×C4⋊Dic3C2311yescharacteristic
123C2×Dic3⋊C4—21no—
124C2×Dic3⋊C4—21no—
125C2×Dic3⋊C4—21no—
126C2×C4×Dic3—21no—
127C2×C4×Dic3—21no—
128C22×C3⋊C8C2311yescharacteristic
129C22×C3⋊C8C2311yescharacteristic
130C2×Dic12—22no—
131C2×Dic12—22no—
132C2×Dic12—41no—
133C2×ΓL(1,𝔽25)—22no—
134C2×ΓL(1,𝔽25)—41no—
135C2×ΓL(1,𝔽25)—41no—
136#898—28no—
137#897—22no—
138#897—22no—
139#897—22no—
140#897—22no—
141#897—41no—
142#897D414yes—
143#894—28no—
144#892—28no—
145#892—22no—
146#892D414yes—
147D3×C4⋊C4—22no—
148D3×C4⋊C4—22no—
149#890—28no—
150C4×D12—22no—
151C4×D12—22no—
152C4×Dic6—22no—
153C4×Dic6—22no—
154C3×#103—22no—
155C3×#103—22no—
156C3×#95—21no—
157C3×#95—21no—
158#835—22no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162(C2×D3)⋊C8—22no—
163(C2×D3)⋊C8—41no—
164(C2×D3)⋊C8—41no—
165#816—22no—
166#816—41no—
167#810—22no—
168#810—22no—
169#810—41no—
170C23×Q8—31no—
171C22×Q16—31no—
172C22×Q16—31no—
173C22×M16—31no—
174#552—64no—
175#552—64no—
176C2×#126—61no—
177C2×#125—61no—
178C2×#125C2×D311yescharacteristic
179C2×#123—61no—
180C2×C22⋊Q8—31no—
181C2×C22⋊Q8—31no—
182C2×C22⋊Q8—31no—
183C2×C22⋊Q8—31no—
184C2×C4×Q8—31no—
185C2×C4×D4—31no—
186C2×#117—31no—
187C2×#117—61no—
188C22×C4⋊C4—31no—
189#451—64no—
190#419—64no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103—31no—
196C2×#103—31no—
197C2×#103C2×D311yescharacteristic
198C2×#103C2×D311yescharacteristic
199C2×C22⋊C8—31no—
200C2×C22⋊C8—31no—
201C2×C22⋊C8—31no—
202#395—61no—
203#393—61no—
204#391—31no—
205#391C2×D311yescharacteristic
206#386—61no—
207#385—61no—
208#380—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340C2×D311yescharacteristic
214#340C2×D311yescharacteristic
215#336—31no—
216#336C2×D311yescharacteristic
217C23×D3C2×D411yescharacteristic
218C23×D3C2×D411yescharacteristic
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8#4112yes—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4C2×D411yescharacteristic
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2411yescharacteristic
232C22×Dic3—21no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3—21no—
236C22×Dic3C2×D411yescharacteristic
237C22×Dic3C2×D411yescharacteristic
238D3×Q8—28no—
239D3×Q8—44no—
240D3×Q8—44no—
241D3×Q8—44no—
242C2×D12—22no—
243C2×D12—22no—
244C2×D12—41no—
245C2×C4×D3—21no—
246C2×C4×D3—21no—
247C2×C4×D3—21no—
248C2×C4×D3—21no—
249C2×C4×D3—24no—
250C2×C4×D3—21no—
251C2×C4×D3—21no—
252C2×C4×D3—21no—
253C2×C4×D3—21no—
254C2×C4×D3—21no—
255C2×C4×D3—21no—
256C2×C4×D3—42no—
257C2×C4×D3—42no—
258C2×C4×D3—42no—
259C2×C4×D3—42no—
260C2×C4×D3—42no—
261C2×C4×D3C2×D412yes—
262C2×C4×D3C2×D412yes—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6—21no—
266C2×Dic6—21no—
267C2×Dic6—21no—
268C2×Dic6—21no—
269C2×Dic6—21no—
270C2×Dic6—21no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6—42no—
274C2×Dic6—42no—
275C2×Dic6—42no—
276C2×Dic6C2×D412yes—
277C2×Dic6#4112yes—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C3×C4⋊C4—24no—
285C3×C4⋊C4—24no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4C2×D412yes—
291C3×C4⋊C4C2×D412yes—
292C3×C42—21no—
293C3×C42—21no—
294#216—44no—
295(C2×D3)⋊C4—24no—
296(C2×D3)⋊C4—22no—
297(C2×D3)⋊C4—24no—
298(C2×D3)⋊C4—24no—
299(C2×D3)⋊C4—22no—
300(C2×D3)⋊C4—42no—
301(C2×D3)⋊C4—42no—
302(C2×D3)⋊C4—42no—
303C4⋊Dic3—24no—
304C4⋊Dic3—21no—
305C4⋊Dic3—22no—
306C4⋊Dic3—24no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3—42no—
310C4⋊Dic3C2×D412yes—
311Dic3⋊C4—24no—
312Dic3⋊C4—24no—
313Dic3⋊C4—42no—
314C4×Dic3—24no—
315C4×Dic3—24no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8—21no—
322Dic12—44no—
323ΓL(1,𝔽25)—44no—
324C22×Q8—31no—
325C22×Q8—31no—
326C22×Q8—61no—
327C22×Q8—62no—
328C22×Q8—62no—
329C22×Q8—62no—
330C22×Q8—62no—
331C22×Q8—121no—
332C22×Q8—121no—
333C22×Q8C22×D311yescharacteristic
334C22×D4—31no—
335C23×C4—31no—
336C23×C4—31no—
337C23×C4—61no—
338C23×C4—61no—
339C2×Q16—62no—
340C2×Q16—62no—
341C2×Q16—62no—
342C2×Q16—62no—
343C2×Q16—121no—
344C2×Q16—121no—
345C2×M16—62no—
346C2×M16—121no—
347C2×M16—121no—
348C22×C8—31no—
349C22×C8—31no—
350C22×C8C22×D311yescharacteristic
351C22×C8C22×D311yescharacteristic
352#126—68no—
353#125—22no—
354#125—22no—
355#125—68no—
356#123—68no—
357C22⋊Q8—34no—
358C22⋊Q8—62no—
359C22⋊Q8—62no—
360C22⋊Q8—62no—
361C22⋊Q8—62no—
362C22⋊Q8—62no—
363C22⋊Q8—121no—
364C22⋊Q8—121no—
365C4×Q8—62no—
366C4×Q8—62no—
367C4×D4—62no—
368C4×D4—62no—
369#117—34no—
370#117—62no—
371#117—68no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—31no—
376C2×C4⋊C4—31no—
377C2×C4⋊C4—62no—
378C2×C4⋊C4—61no—
379C2×C4⋊C4—61no—
380C2×C4⋊C4—61no—
381C2×C4⋊C4—61no—
382C2×C4⋊C4—62no—
383C2×C4⋊C4—61no—
384C2×C4⋊C4—61no—
385C2×C4⋊C4C22×D311yescharacteristic
386C2×C4⋊C4C22×D311yescharacteristic
387C2×C4⋊C4C22×D311yescharacteristic
388C2×C22⋊C4—31no—
389C2×C22⋊C4—31no—
390C2×C22⋊C4—61no—
391C2×C22⋊C4—61no—
392C2×C22⋊C4—61no—
393C2×C22⋊C4—61no—
394C2×C22⋊C4—61no—
395C2×C22⋊C4—61no—
396C2×C42—61no—
397C2×C42—61no—
398C2×C42C22×D311yescharacteristic
399#103—22no—
400#103—22no—
401#103—62no—
402#103—62no—
403#103—62no—
404#103—62no—
405#103—121no—
406#103—121no—
407C22⋊C8—62no—
408C22⋊C8—121no—
409C22⋊C8—121no—
410#95—21no—
411#95—21no—
412#95—61no—
413#95—61no—
414#95—61no—
415C23×C3C22×D411yescharacteristic
416C22×D3—21no—
417C22×D3—21no—
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—21no—
421C22×D3—21no—
422C22×D3—21no—
423C22×D3—21no—
424C22×D3—21no—
425C22×D3—21no—
426C22×D3—21no—
427C22×D3—21no—
428C22×D3#12012yes—
429C22×D3#13712yes—
430C3×Q8—22no—
431C3×Q8—22no—
432C3×Q8—41no—
433C3×Q8—41no—
434C2×C3×C4—21no—
435C2×C3×C4—22no—
436C2×C3×C4—21no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4C22×D411yescharacteristic
453C2×C3×C4C22×D411yescharacteristic
454C2×C3×C4C2×#4111yescharacteristic
455C2×C3×C4C2×#4111yescharacteristic
456C2×C3×C4H(5,𝔽2)11yescharacteristic
457C2×C3×C4H(5,𝔽2)11yescharacteristic
458C2×Dic3—21no—
459C2×Dic3—21no—
460C2×Dic3—22no—
461C2×Dic3—22no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—22no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3#12012yes—
476D12—44no—
477C4×D3—22no—
478C4×D3—22no—
479C4×D3—22no—
480C4×D3—22no—
481C4×D3—48no—
482C4×D3—48no—
483C4×D3—41no—
484C4×D3—41no—
485C4×D3—41no—
486C4×D3—41no—
487Dic6—22no—
488Dic6—22no—
489Dic6—22no—
490Dic6—22no—
491Dic6—48no—
492Dic6—41no—
493Dic6—41no—
494Dic6—41no—
495Dic6—41no—
496C3×C8—41no—
497C3×C8—41no—
498C3⋊C8—41no—
499C3⋊C8—41no—
500C24—31no—
501C24—31no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—32no—
508C2×Q8—32no—
509C2×Q8—61no—
510C2×Q8—61no—
511C2×Q8—68no—
512C2×Q8—61no—
513C2×Q8—61no—
514C2×Q8—61no—
515C2×Q8—61no—
516C2×Q8—61no—
517C2×Q8—61no—
518C2×Q8—61no—
519C2×Q8—61no—
520C2×Q8—122no—
521C2×Q8—122no—
522C2×Q8—122no—
523C2×Q8—124no—
524C2×Q8—124no—
525C2×Q8—124no—
526C2×Q8#23912yes—
527C2×D4—62no—
528C2×D4—62no—
529C2×D4—121no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—31no—
535C22×C4—32no—
536C22×C4—32no—
537C22×C4—31no—
538C22×C4—64no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4—61no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—122no—
554C22×C4—122no—
555C22×C4—122no—
556C22×C4—122no—
557C22×C4—122no—
558C22×C4D3×D411yescharacteristic
559C22×C4D3×D411yescharacteristic
560C22×C4C23×D311yescharacteristic
561Q16—124no—
562Q16—124no—
563M16—124no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—61no—
571C2×C8—61no—
572C2×C8—61no—
573C2×C8—61no—
574C2×C8—61no—
575C2×C8—61no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—32no—
583C4⋊C4—62no—
584C4⋊C4—64no—
585C4⋊C4—64no—
586C4⋊C4—64no—
587C4⋊C4—64no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—122no—
592C4⋊C4—122no—
593C4⋊C4D3×D412yes—
594C4⋊C4D3×D412yes—
595C22⋊C4—62no—
596C22⋊C4—62no—
597C22⋊C4—64no—
598C22⋊C4—64no—
599C22⋊C4—64no—
600C22⋊C4—122no—
601C22⋊C4—122no—
602C22⋊C4—122no—
603C42—21no—
604C42—21no—
605C42—64no—
606C42—64no—
607C22×C3C2×#12011yescharacteristic
608C22×C3#54611yescharacteristic
609C22×C3#54611yescharacteristic
610C22×C3C2×#13711yescharacteristic
611C22×C3#57511yescharacteristic
612C22×C3#57811yescharacteristic
613C22×C3#57811yescharacteristic
614C2×D3—22no—
615C2×D3—22no—
616C2×D3—22no—
617C2×D3—22no—
618C2×D3—22no—
619C2×D3—22no—
620C2×D3—41no—
621C2×D3—41no—
622C2×D3—41no—
623C2×D3—41no—
624C2×D3—41no—
625C2×D3—41no—
626C2×D3—41no—
627C2×D3—41no—
628C3×C4—42no—
629C3×C4—42no—
630C3×C4—41no—
631C3×C4—41no—
632C3×C4—42no—
633C3×C4—81no—
634C3×C4#52511yescharacteristic
635C3×C4#53511yescharacteristic
636C3×C4#54611yescharacteristic
637C3×C4#54611yescharacteristic
638Dic3—22no—
639Dic3—42no—
640Dic3—42no—
641Dic3—41no—
642Dic3—42no—
643Dic3—81no—
644C23—32no—
645C23—32no—
646C23—61no—
647C23—61no—
648C23—61no—
649C23—61no—
650C23—61no—
651C23—61no—
652C23—61no—
653C23—61no—
654C23—61no—
655C23—61no—
656C23—61no—
657C23—61no—
658C23C2×D3×D411yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—41no—
662Q8—41no—
663Q8—62no—
664Q8—62no—
665Q8—62no—
666Q8—62no—
667Q8—128no—
668Q8—121no—
669Q8—121no—
670Q8—121no—
671Q8—121no—
672D4—124no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—32no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—62no—
698C2×C4—62no—
699C2×C4—61no—
700C2×C4—62no—
701C2×C4—62no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—128no—
705C2×C4—128no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—121no—
713C2×C4—121no—
714C2×C4—121no—
715C2×C4—121no—
716C2×C4—121no—
717C2×C4—121no—
718C2×C4—121no—
719C2×C4C2×D3×D411yescharacteristic
720C2×C4C2×D3×D411yescharacteristic
721C2×C4C2×#23911yescharacteristic
722C2×C4D3×#4111yescharacteristic
723C2×C4#100911yescharacteristic
724C2×C4#100911yescharacteristic
725C8—41no—
726C8—41no—
727C8—121no—
728C8—121no—
729C2×C3#240411yescharacteristic
730C2×C3#300711yescharacteristic
731C2×C3#301111yescharacteristic
732C2×C3#331211yescharacteristic
733C2×C3#331211yescharacteristic
734C2×C3#332711yescharacteristic
735C2×C3#332711yescharacteristic
736D3—42no—
737D3—42no—
738C22—62no—
739C22—62no—
740C22—62no—
741C22—62no—
742C22—62no—
743C22—62no—
744C22—121no—
745C22—121no—
746C22—121no—
747C22—121no—
748C22—121no—
749C22—121no—
750C22—121no—
751C22—121no—
752C22D3×#12011yescharacteristic
753C22#563011yescharacteristic
754C22#567611yescharacteristic
755C22#576811yescharacteristic
756C22#577111yescharacteristic
757C22D3×#13711yescharacteristic
758C22#577911yescharacteristic
759C4—42no—
760C4—41no—
761C4—42no—
762C4—41no—
763C4—42no—
764C4—62no—
765C4—81no—
766C4—121no—
767C4—122no—
768C4—122no—
769C4—122no—
770C4—241no—
771C4#562711yescharacteristic
772C4#563011yescharacteristic
773C4#567411yescharacteristic
774C4#567611yescharacteristic
775C3#2398311yescharacteristic, complemented, Sylow
776C2—122no—
777C2—122no—
778C2#7686311yescharacteristic
779C2#8022811yescharacteristic
780C2#8023011yescharacteristic
781C2#8124811yescharacteristic
782C2#8125211yescharacteristic
783C2#8165911yescharacteristic
784C2#8174911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2026C2
socleC23×C3C22×D4
prime radicalC22×D12D4
hypercenter#2026D3
hypocenterC3#23983
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2026

Complements

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

NH ≅ G/Ntype
2. C2×#4809C2semidirect
3. C2×#4802C2semidirect
5. C3×#2026C2semidirect
6. #71744C2semidirect
7. #70273C2semidirect
8. #70268C2semidirect
9. #69690C2semidirect
10. #68888C2semidirect
11. #68884C2semidirect
12. #68878C2semidirect
13. #68873C2semidirect
14. #68685C2semidirect
69. #2026D3semidirect
775. C3#23983semidirect

Maximal subgroups

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

subgroupindex
C2×#56942
C2×#48092
C2×#48022
#766192
C3×#20262
#717442
#702732
#702682
#696902
#688882
#688842
#688782
#688732
#686852
#686692
#239833