Finite Group Databasebeta

← #10801015

Subgroups — #10801015

Order 768.

1420 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5523C211yesmaximal, characteristic
2#82235C211yesmaximal, characteristic, complemented
3C2×#4733C211yesmaximal, characteristic
4C2×#4710C211yesmaximal, characteristic, complemented
5C2×C4×Dic12C211yesmaximal, characteristic, complemented
6C3×#1750C211yesmaximal, characteristic, complemented
7#69960C211yesmaximal, characteristic
8#69930C211yesmaximal, characteristic, complemented
9#69927C211yesmaximal, characteristic, complemented
10#69813C211yesmaximal, characteristic, complemented
11C4×#821C211yesmaximal, characteristic, complemented
12#68685C211yesmaximal, characteristic, complemented
13#68683C211yesmaximal, characteristic, complemented
14#68672C211yesmaximal, characteristic, complemented
15#68670C211yesmaximal, characteristic, complemented
16#21465—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C2×C3×#117C2211yescharacteristic
19C22×C4⋊Dic3C2211yescharacteristic
20C2×#924C2211yescharacteristic
21C22×Dic12C2211yescharacteristic
22C22×#204C2211yescharacteristic
23#5523—24no—
24#5523—24no—
25C2×#892—21no—
26C2×D3×C4⋊C4—21no—
27C2×#67⋊C4—21no—
28C2×#67⋊C4—21no—
29C2×C4×D12C2211yescharacteristic
30C2×C4×D12C2211yescharacteristic
31C2×C4×Dic6C2211yescharacteristic
32C2×C4×Dic6C2211yescharacteristic
33C2×C4×Dic6C2211yescharacteristic
34C2×C3×C22⋊C8C2211yescharacteristic
35C2×C3×C22⋊C8C2211yescharacteristic
36C2×C3×#97C2211yescharacteristic
37C2×C3×C4×C8C2211yescharacteristic
38#5212C2211yescharacteristic
39C2×#821C2211yescharacteristic
40C2×#821C2211yescharacteristic
41C2×#821C2211yescharacteristic
42C2×#818C2211yescharacteristic
43C2×#818C2211yescharacteristic
44C2×#816C2211yescharacteristic
45C2×#816C2211yescharacteristic
46C2×#816C2211yescharacteristic
47C2×#816C2211yescharacteristic
48C2×#816C2211yescharacteristic
49#4978—21no—
50#4976—21no—
51#4945—21no—
52#4944—21no—
53C4×C4⋊Dic3C2211yescharacteristic
54#4929C2211yescharacteristic
55#4928C2211yescharacteristic
56#4733C418yescomplemented
57#4710—24no—
58C4×Dic12—24no—
59C3×#336C2211yescharacteristic
60C3×#336C2211yescharacteristic
61#4551C2211yescharacteristic
62#4551C2211yescharacteristic
63#4551C2211yescharacteristic
64#4551C2211yescharacteristic
65C2×#520—31no—
66C2×#452—31no—
67C2×#440—31no—
68C2×C4×Q16—31no—
69#2323—31no—
70#1878—31no—
71#1877—31no—
72#1872—31no—
73#1863—31no—
74#1862—31no—
75#1852—31no—
76#1788—31no—
77#1763—31no—
78C4×#102—31no—
79#1750D311yescharacteristic, complemented
80C23×C3×C4C2311yescharacteristic
81C22×#67—21no—
82C23×Dic3—21no—
83C2×#235—22no—
84C2×#235—22no—
85C2×#235—22no—
86C2×#235—22no—
87C2×#235—22no—
88C2×#235C2×C414yes—
89C22×D12C2311yescharacteristic
90C22×C4×D3—21no—
91C22×C4×D3—21no—
92C22×C4×D3—21no—
93C22×Dic6C2311yescharacteristic
94C22×Dic6C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C3×#117—22no—
100C3×#117—22no—
101C2×C3×C4⋊C4D411yescharacteristic
102C2×C3×C4⋊C4D411yescharacteristic
103C2×C3×C22⋊C4D411yescharacteristic
104C2×C3×C22⋊C4D411yescharacteristic
105C2×C3×C42C2311yescharacteristic
106C2×C3×C42C2311yescharacteristic
107C2×#217—21no—
108C2×#217—21no—
109C2×(C2×D3)⋊C4—21no—
110C2×(C2×D3)⋊C4—21no—
111C2×C4⋊Dic3—21no—
112C2×C4⋊Dic3—22no—
113C2×C4⋊Dic3—22no—
114C2×C4⋊Dic3C2311yescharacteristic
115C2×C4⋊Dic3C2311yescharacteristic
116C2×C4⋊Dic3C2311yescharacteristic
117C2×C4⋊Dic3C2311yescharacteristic
118C2×C4⋊Dic3C2311yescharacteristic
119#924—22no—
120#924C2×C414yescomplemented
121C2×Dic3⋊C4—21no—
122C2×Dic3⋊C4—21no—
123C2×Dic3⋊C4—21no—
124C2×Dic3⋊C4—21no—
125C2×Dic3⋊C4—21no—
126C2×C4×Dic3—21no—
127C2×C4×Dic3—21no—
128C2×C4×Dic3—21no—
129C2×C4×Dic3—21no—
130C2×Dic12—22no—
131C2×Dic12—22no—
132C2×Dic12C2×C414yescomplemented
133C2×#204—22no—
134C2×#204—22no—
135C2×#204C2×C414yescomplemented
136#892—28no—
137D3×C4⋊C4—28no—
138#67⋊C4—28no—
139#67⋊C4—28no—
140C4×D12—22no—
141C4×D12—22no—
142C4×D12—22no—
143C4×D12D414yes—
144C4×Dic6—22no—
145C4×Dic6—22no—
146C4×Dic6—22no—
147C4×Dic6—22no—
148C4×Dic6—22no—
149C4×Dic6D414yes—
150C3×C22⋊C8—22no—
151C3×C22⋊C8C2×C414yescomplemented
152C3×#97—22no—
153C3×C4×C8—22no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159#821—22no—
160#821—22no—
161#821C2×C414yescomplemented
162#818—22no—
163#818—22no—
164#816—22no—
165#816—22no—
166#816—22no—
167#816—22no—
168#816C2×C414yescomplemented
169C22×#41—31no—
170C22×Q16—31no—
171C22×SD16—31no—
172C2×C22⋊Q8—31no—
173#520—64no—
174#520—64no—
175C2×C4×Q8—31no—
176C2×C4×Q8—31no—
177C2×C4×Q8—31no—
178C2×C4×D4—31no—
179C2×C4×D4—31no—
180C2×C4×D4—61no—
181C2×C4×D4—61no—
182C2×#117—61no—
183C2×#117C2×D311yescharacteristic
184C22×C4⋊C4—31no—
185C22×C4⋊C4—61no—
186#452—38no—
187#440—64no—
188C4×Q16—64no—
189C2×#107—31no—
190C2×#107—31no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×C22⋊C8C2×D311yescharacteristic
200C2×C22⋊C8C2×D311yescharacteristic
201C2×#97C2×D311yescharacteristic
202C2×C4×C8C2×D311yescharacteristic
203#391—31no—
204#389—31no—
205#389—61no—
206#388—61no—
207#388—61no—
208#387—61no—
209#380—31no—
210C4×C4⋊C4—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#336C2×D311yescharacteristic
216#336C2×D311yescharacteristic
217C24×C3C2×D411yescharacteristic
218C23×D3—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4C22×C412yes—
224C22×C3×C4C2×D411yescharacteristic
225C22×C3×C4C2×D411yescharacteristic
226C22×C3×C4C2×D411yescharacteristic
227C22×C3×C4C2×D411yescharacteristic
228C22×C3×C4C2×D411yescharacteristic
229C22×C3×C4#4112yes—
230C22×C3×C4C2411yescharacteristic
231C2×#67—24no—
232C2×#67—24no—
233C2×#67—24no—
234C22×Dic3—21no—
235C22×Dic3—21no—
236C22×Dic3—21no—
237C22×Dic3—21no—
238C22×Dic3—21no—
239C22×Dic3—24no—
240C22×Dic3—21no—
241C22×Dic3—21no—
242C22×Dic3—81no—
243C22×Dic3—81no—
244#235—28no—
245#235—28no—
246#235—28no—
247#235—28no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12C22×C412yes—
252C2×D12C2×D412yes—
253C2×D12#4112yes—
254C2×C4×D3—24no—
255C2×C4×D3—24no—
256C2×C4×D3—24no—
257C2×C4×D3—24no—
258C2×C4×D3—24no—
259C2×C4×D3—81no—
260C2×C4×D3—81no—
261C2×C4×D3—81no—
262C2×C4×D3—81no—
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×Dic6C22×C412yes—
272C2×Dic6C22×C412yes—
273C2×Dic6C2×D412yes—
274C2×Dic6#4112yes—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8C22×C412yes—
286C2×C3×C8C22×C412yes—
287C3×C4⋊C4—22no—
288C3×C4⋊C4—22no—
289C3×C22⋊C4—22no—
290C3×C22⋊C4—22no—
291C3×C42—21no—
292C3×C42—21no—
293C3×C42C2×D412yes—
294C3×C42C2×D412yes—
295#217—24no—
296#217—81no—
297(C2×D3)⋊C4—24no—
298(C2×D3)⋊C4—24no—
299C4⋊Dic3—24no—
300C4⋊Dic3—21no—
301C4⋊Dic3—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
307C4⋊Dic3C22×C412yes—
308C4⋊Dic3C2×D412yes—
309C4⋊Dic3C2×D412yes—
310Dic3⋊C4—24no—
311Dic3⋊C4—24no—
312Dic3⋊C4—24no—
313Dic3⋊C4—42no—
314Dic3⋊C4—81no—
315C4×Dic3—24no—
316C4×Dic3—24no—
317C4×Dic3—42no—
318C4×Dic3—81no—
319Dic12—28no—
320#204—28no—
321C2×#41—34no—
322C2×#41—62no—
323C2×#41—62no—
324C2×#41—62no—
325C2×#41—62no—
326C2×#41—62no—
327C22×Q8—31no—
328C22×Q8—31no—
329C22×D4—31no—
330C22×D4—61no—
331C23×C4—61no—
332C23×C4—61no—
333C23×C4—61no—
334C23×C4—61no—
335C23×C4C22×D311yescharacteristic
336C2×Q16—34no—
337C2×Q16—62no—
338C2×Q16—62no—
339C2×SD16—34no—
340C2×SD16—62no—
341C2×SD16—62no—
342C22×C8C22×D311yescharacteristic
343C22×C8C22×D311yescharacteristic
344C22×C8C22×D311yescharacteristic
345C22×C8C22×D311yescharacteristic
346C22⋊Q8—34no—
347C22⋊Q8—62no—
348C4×Q8—34no—
349C4×Q8—62no—
350C4×Q8—62no—
351C4×Q8—62no—
352C4×Q8—62no—
353C4×Q8—62no—
354C4×D4—34no—
355C4×D4—62no—
356C4×D4—62no—
357C4×D4—68no—
358C4×D4—68no—
359C4×D4—62no—
360#117—22no—
361#117—22no—
362#117—68no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—68no—
369C2×C4⋊C4—62no—
370C2×C4⋊C4—62no—
371C2×C4⋊C4—61no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4—61no—
374C2×C4⋊C4—61no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4D1211yescharacteristic
378C2×C4⋊C4D1211yescharacteristic
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4D1211yescharacteristic
384C2×C22⋊C4D1211yescharacteristic
385C2×C42—61no—
386C2×C42—61no—
387C2×C42—61no—
388C2×C42—61no—
389C2×C42C22×D311yescharacteristic
390C2×C42C22×D311yescharacteristic
391#107—62no—
392#107—62no—
393#103—34no—
394#103—62no—
395#103—62no—
396#103—62no—
397#103—62no—
398#102—34no—
399#102—62no—
400#102—62no—
401C22⋊C8—22no—
402C22⋊C8C4×D314yescomplemented
403#97—22no—
404C4×C8—22no—
405#95—61no—
406#95—61no—
407#95—61no—
408#95—61no—
409#95—61no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3C4×D412yes—
417C23×C3C22×D411yescharacteristic
418C22×D3—22no—
419C22×D3—22no—
420C22×D3—22no—
421C22×D3—41no—
422C22×D3—41no—
423C22×D3—41no—
424C22×D3—41no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4C4×D412yes—
442C2×C3×C4#12012yes—
443C2×C3×C4#12012yes—
444C2×C3×C4C23×C411yescharacteristic
445C2×C3×C4C22×D411yescharacteristic
446C2×C3×C4C22×D411yescharacteristic
447C2×C3×C4C2×#4111yescharacteristic
448C2×C3×C4C2×#4111yescharacteristic
449C2×C3×C4C2×#4111yescharacteristic
450#67—216no—
451C2×Dic3—22no—
452C2×Dic3—22no—
453C2×Dic3—22no—
454C2×Dic3—22no—
455C2×Dic3—22no—
456C2×Dic3—22no—
457C2×Dic3—22no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—41no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—84no—
473D12—22no—
474D12—22no—
475D12—22no—
476D12C4×D414yes—
477C4×D3—216no—
478C4×D3—84no—
479C4×D3—84no—
480Dic6—22no—
481Dic6—22no—
482Dic6—22no—
483Dic6—22no—
484Dic6—22no—
485Dic6—41no—
486Dic6—41no—
487Dic6C4×D414yes—
488C3×C8—22no—
489C3×C8—22no—
490C3×C8—41no—
491C3×C8—41no—
492C24—61no—
493C24C2×D1211yescharacteristic
494#41—68no—
495#41—68no—
496#41—68no—
497#41—68no—
498C2×Q8—32no—
499C2×Q8—32no—
500C2×Q8—32no—
501C2×Q8—32no—
502C2×Q8—61no—
503C2×Q8—61no—
504C2×Q8—61no—
505C2×Q8—61no—
506C2×Q8—61no—
507C2×Q8—61no—
508C2×Q8—61no—
509C2×Q8—61no—
510C2×D4—32no—
511C2×D4—32no—
512C2×D4—32no—
513C2×D4—64no—
514C2×D4—64no—
515C2×D4—64no—
516C2×D4—61no—
517C2×D4—61no—
518C2×D4—61no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—64no—
524C22×C4—64no—
525C22×C4—64no—
526C22×C4—61no—
527C22×C4—64no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—64no—
533C22×C4—64no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—241no—
537C22×C4—241no—
538C22×C4—241no—
539C22×C4—241no—
540C22×C4—241no—
541C22×C4—241no—
542C22×C4C2×C4×D312yes—
543C22×C4C2×D1211yescharacteristic
544C22×C4C2×D1211yescharacteristic
545C22×C4C2×D1211yescharacteristic
546C22×C4C2×D1211yescharacteristic
547C22×C4C2×D1211yescharacteristic
548C22×C4#23512yes—
549C22×C4C23×D311yescharacteristic
550Q16—68no—
551SD16—68no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8C2×C4×D312yes—
563C2×C8C2×C4×D312yes—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—32no—
567C4⋊C4—32no—
568C4⋊C4—32no—
569C4⋊C4—64no—
570C4⋊C4—64no—
571C4⋊C4—64no—
572C4⋊C4—64no—
573C4⋊C4—61no—
574C4⋊C4—61no—
575C4⋊C4—61no—
576C4⋊C4—61no—
577C4⋊C4—61no—
578C4⋊C4—61no—
579C4⋊C4—61no—
580C4⋊C4—122no—
581C4⋊C4—241no—
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—64no—
585C22⋊C4—64no—
586C22⋊C4—64no—
587C22⋊C4—241no—
588C42—21no—
589C42—21no—
590C42—64no—
591C42—64no—
592C42—122no—
593C42—241no—
594C42D3×D412yes—
595C42D3×D412yes—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3—22no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3C2×C4×D411yescharacteristic
604C22×C3C2×#12011yescharacteristic
605C22×C3#52511yescharacteristic
606C22×C3#57611yescharacteristic
607C22×C3#57711yescharacteristic
608C22×C3#57811yescharacteristic
609C22×C3#57811yescharacteristic
610C2×D3—24no—
611C2×D3—42no—
612C2×D3—42no—
613C2×D3—42no—
614C2×D3—42no—
615C2×D3—42no—
616C2×D3—42no—
617C3×C4—22no—
618C3×C4—22no—
619C3×C4—22no—
620C3×C4—41no—
621C3×C4—41no—
622C3×C4C2×C4×D411yescharacteristic
623C3×C4C2×C4×D411yescharacteristic
624C3×C4#52511yescharacteristic
625C3×C4#52511yescharacteristic
626Dic3—24no—
627Dic3—42no—
628Dic3—42no—
629Dic3—42no—
630Dic3—42no—
631Dic3—81no—
632Dic3—81no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—62no—
640C23—62no—
641C23—62no—
642C23—121no—
643C23—121no—
644C23—121no—
645C23—121no—
646C23C4×D1212yes—
647C23C22×D1211yescharacteristic
648Q8—34no—
649Q8—62no—
650Q8—62no—
651Q8—62no—
652Q8—62no—
653Q8—62no—
654Q8—121no—
655Q8—121no—
656D4—34no—
657D4—616no—
658D4—62no—
659D4—62no—
660D4—62no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—616no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—62no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—121no—
686C2×C4—121no—
687C2×C4—121no—
688C2×C4—121no—
689C2×C4—121no—
690C2×C4—121no—
691C2×C4—121no—
692C2×C4—121no—
693C2×C4—121no—
694C2×C4—121no—
695C2×C4—121no—
696C2×C4—121no—
697C2×C4—121no—
698C2×C4—121no—
699C2×C4—244no—
700C2×C4—244no—
701C2×C4—244no—
702C2×C4C4×D1212yes—
703C2×C4#88212yes—
704C2×C4#88212yes—
705C2×C4C22×C4×D311yescharacteristic
706C2×C4C2×#23511yescharacteristic
707C2×C4C2×D3×D411yescharacteristic
708C2×C4C2×D3×D411yescharacteristic
709C2×C4D3×#4111yescharacteristic
710C2×C4D3×#4111yescharacteristic
711C8—22no—
712C8—22no—
713C8—41no—
714C8—41no—
715C2×C3—42no—
716C2×C3C4×#12011yescharacteristic
717C2×C3#294711yescharacteristic
718C2×C3#295111yescharacteristic
719C2×C3#301111yescharacteristic
720C2×C3#301211yescharacteristic
721C2×C3#312011yescharacteristic
722C2×C3#312411yescharacteristic
723D3—44no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—64no—
732C22—122no—
733C22—122no—
734C22—122no—
735C22—122no—
736C22—122no—
737C22—122no—
738C22C2×C4×D1211yescharacteristic
739C22C2×#88211yescharacteristic
740C22#552411yescharacteristic
741C22#575111yescharacteristic
742C22#575211yescharacteristic
743C22#575311yescharacteristic
744C22#575311yescharacteristic
745C4—22no—
746C4—22no—
747C4—22no—
748C4—41no—
749C4—41no—
750C4—64no—
751C4—122no—
752C4—122no—
753C4—122no—
754C4—122no—
755C4—241no—
756C4—241no—
757C4C4×D3×D411yescharacteristic
758C4C4×D3×D411yescharacteristic
759C4#554711yescharacteristic
760C4#554711yescharacteristic
761C3#2146511yescharacteristic, complemented, Sylow
762C2—42no—
763C2—124no—
764C2C4×#88211yescharacteristic
765C2#7856211yescharacteristic
766C2#7857111yescharacteristic
767C2#7867211yescharacteristic
768C2#7867911yescharacteristic
769C2#7938511yescharacteristic
770C2#7938811yescharacteristic
subgroupG/H
centerC23C22×D12
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1750C2
socleC23×C3C22×D4
prime radicalC22×#235C22
cosocleC22×C3×C4C24
hypercenter#1750D3
hypocenterC3#21465
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#117 ◁ #1750

Complements

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

NH ≅ G/Ntype
2. #82235C2semidirect
4. C2×#4710C2semidirect
5. C2×C4×Dic12C2semidirect
6. C3×#1750C2semidirect
8. #69930C2semidirect
9. #69927C2semidirect
10. #69813C2semidirect
11. C4×#821C2semidirect
12. #68685C2semidirect
13. #68683C2semidirect
14. #68672C2semidirect
15. #68670C2semidirect
56. #4733C4semidirect
79. #1750D3semidirect
120. #924C2×C4semidirect
132. C2×Dic12C2×C4semidirect
135. C2×#204C2×C4semidirect
151. C3×C22⋊C8C2×C4semidirect
161. #821C2×C4semidirect
168. #816C2×C4semidirect
402. C22⋊C8C4×D3semidirect
761. C3#21465semidirect

Maximal subgroups

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

subgroupindex
C2×#55232
#822352
C2×#47332
C2×#47102
C2×C4×Dic122
C3×#17502
#699602
#699302
#699272
#698132
C4×#8212
#686852
#686832
#686722
#686702
#214653