Finite Group Databasebeta

← #11330843

Subgroups — #11330843

Order 768.

1976 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5639C211yesmaximal, characteristic, complemented
2C2×#5645C211yesmaximal, characteristic, complemented
3C3×#2378C211yesmaximal, characteristic, complemented
4#76656C212yesmaximal, complemented
5#76622C212yesmaximal, complemented
6#76114C212yesmaximal, complemented
7#76000C212yesmaximal, complemented
8#75851C212yesmaximal, complemented
9#75696C212yesmaximal, complemented
10#75687C212yesmaximal, complemented
11#75516C212yesmaximal, complemented
12#75332C212yesmaximal, complemented
13#75171C212yesmaximal, complemented
14#75166C212yesmaximal, complemented
15#75020C212yesmaximal, complemented
16#74137C211yesmaximal, characteristic
17#74074C211yesmaximal, characteristic, complemented
18#74033C211yesmaximal, characteristic, complemented
19#73949C211yesmaximal, characteristic, complemented
20#48783—31nomaximal, Sylow
21C2×C3×C22⋊Q8C2211yescharacteristic
22C2×#946C2212yes—
23C2×#946C2211yescharacteristic
24C2×Q8×Dic3C2211yescharacteristic
25C2×#930C2211yescharacteristic
26C2×C4×#67C2211yescharacteristic
27C2×#926C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29#5645—28no—
30#5639—28no—
31C2×#898C2212yes—
32C2×#894C2212yes—
33C2×#892C2212yes—
34C2×D3×C4⋊C4C2211yescharacteristic
35C2×#890C2212yes—
36C2×#890C2211yescharacteristic
37C2×#889C2212yes—
38C2×#886C2212yes—
39C2×#883C2212yes—
40C2×#67⋊C4C2212yes—
41C2×#879C2212yes—
42C3×#391C2212yes—
43C3×#389C2212yes—
44C3×#388C2212yes—
45C3×#388C2212yes—
46C3×#387C2212yes—
47C3×#387C2212yes—
48C3×#381C2211yescharacteristic
49C3×#380C2211yescharacteristic
50#4994C2212yes—
51#4994C2212yes—
52#4994C2212yes—
53#4994C2212yes—
54#4994C2212yes—
55#4988C2212yes—
56#4987C2212yes—
57#4987C2212yes—
58#4984C2212yes—
59#4984C2212yes—
60#4984C2212yes—
61#4981C2212yes—
62#4961C2212yes—
63#4961C2212yes—
64#4961C2212yes—
65#4960C2212yes—
66#4958C2211yescharacteristic
67#4958C2211yescharacteristic
68#4950C2212yes—
69#4950C2211yescharacteristic
70#4950C2211yescharacteristic
71#4943C2212yes—
72#4940C2212yes—
73#4940C2212yes—
74#4939C2212yes—
75C4×(C2×D3)⋊C4C2212yes—
76C4×(C2×D3)⋊C4C2212yes—
77#4936C2212yes—
78#4935C2212yes—
79#4928C2212yes—
80#4677C2212yes—
81#4677C2212yes—
82#4677C2212yes—
83#4677C2211yescharacteristic
84#4674C2212yes—
85#4674C2212yes—
86#4674C2212yes—
87#4672C2211yescharacteristic
88#4671C2211yescharacteristic
89#4670C2212yes—
90#4670C2212yes—
91#4668C2212yes—
92#4668C2212yes—
93#4665C2212yes—
94#4665C2212yes—
95#4665C2212yes—
96#4665C2212yes—
97#4661C2212yes—
98#4661C2212yes—
99#4661C2212yes—
100#4659C2212yes—
101#4659C2212yes—
102#4659C2212yes—
103#4659C2211yescharacteristic
104#4653C2212yes—
105#4653C2212yes—
106#4653C2212yes—
107#4653C2212yes—
108#4653C2212yes—
109#4653C2212yes—
110C2×#552—31no—
111C2×#539—31no—
112#2732—32no—
113#2721—32no—
114#2719—32no—
115#2718—32no—
116#2707—32no—
117#2706—32no—
118#2635—31no—
119#2624—31no—
120#2579—31no—
121#2484—31no—
122#2481—32no—
123#2471—32no—
124#2466—32no—
125#2457—32no—
126#2441—32no—
127#2421—32no—
128#2378D311yescharacteristic, complemented
129C22×C3×Q8C2311yescharacteristic
130C23×C3×C4C2311yescharacteristic
131C22×#67C2311yescharacteristic
132C22×#67C2312yes—
133C23×Dic3C2311yescharacteristic
134C23×Dic3C2311yescharacteristic
135C22×D12C2312yes—
136C22×D12C2311yescharacteristic
137C22×C4×D3C2312yes—
138C22×C4×D3C2311yescharacteristic
139C22×C4×D3C2312yes—
140C3×C22⋊Q8D418yescomplemented
141C2×C3×C4⋊C4C2312yes—
142C2×C3×C4⋊C4C2312yes—
143C2×C3×C4⋊C4C2312yes—
144C2×C3×C4⋊C4C2312yes—
145C2×C3×C4⋊C4C2311yescharacteristic
146C2×C3×C22⋊C4C2312yes—
147C2×C3×C22⋊C4C2311yescharacteristic
148C2×C3×C22⋊C4C2311yescharacteristic
149C2×C3×C22⋊C4C2312yes—
150C2×C3×C42C2312yes—
151C2×C3×C42C2312yes—
152C2×#217C2312yes—
153C2×#217C2311yescharacteristic
154#946—24no—
155#946—28no—
156Q8×Dic3—24no—
157#930—24no—
158C4×#67—24no—
159C2×(C2×D3)⋊C4C2312yes—
160C2×(C2×D3)⋊C4C2312yes—
161C2×(C2×D3)⋊C4C2312yes—
162C2×(C2×D3)⋊C4C2312yes—
163C2×(C2×D3)⋊C4C2312yes—
164C2×(C2×D3)⋊C4C2311yescharacteristic
165C2×(C2×D3)⋊C4C2312yes—
166C2×(C2×D3)⋊C4C2312yes—
167C2×(C2×D3)⋊C4C2312yes—
168C2×(C2×D3)⋊C4C2312yes—
169C2×(C2×D3)⋊C4C2312yes—
170C2×(C2×D3)⋊C4C2312yes—
171C2×(C2×D3)⋊C4C2312yes—
172C2×(C2×D3)⋊C4C2312yes—
173C2×(C2×D3)⋊C4C2312yes—
174C2×(C2×D3)⋊C4C2312yes—
175#926—24no—
176C2×C4⋊Dic3C2311yescharacteristic
177C2×C4⋊Dic3C2312yes—
178C2×C4⋊Dic3C2312yes—
179C2×C4⋊Dic3C2311yescharacteristic
180C2×C4⋊Dic3C2311yescharacteristic
181C2×C4⋊Dic3C2312yes—
182C2×C4⋊Dic3C2312yes—
183C2×C4⋊Dic3C2312yes—
184C2×C4⋊Dic3C2312yes—
185C2×C4⋊Dic3C2312yes—
186C2×C4⋊Dic3C2312yes—
187C2×C4⋊Dic3C2312yes—
188C2×C4⋊Dic3C2312yes—
189C2×C4⋊Dic3C2312yes—
190C2×Dic3⋊C4—24no—
191C2×Dic3⋊C4C2312yes—
192C2×Dic3⋊C4C2312yes—
193C2×Dic3⋊C4C2312yes—
194C2×Dic3⋊C4C2312yes—
195C2×Dic3⋊C4C2312yes—
196C2×Dic3⋊C4C2311yescharacteristic
197C2×Dic3⋊C4C2312yes—
198C2×C4×Dic3C2311yescharacteristic
199C2×C4×Dic3C2312yes—
200C2×C4×Dic3C2312yes—
201C2×C4×Dic3C2312yes—
202#898—28no—
203#894—28no—
204#892—28no—
205D3×C4⋊C4—24no—
206#890—24no—
207#890—28no—
208#889—28no—
209#886—28no—
210#883—28no—
211#67⋊C4—28no—
212#879—28no—
213C3×#95C2311yescharacteristic
214C3×#95C2311yescharacteristic
215C3×#95C2312yes—
216C3×#95C2312yes—
217C3×#95C2312yes—
218C3×#95C2312yes—
219C3×#95C2312yes—
220C3×#95C2312yes—
221C3⋊#95C2312yes—
222C3⋊#95C2312yes—
223C3⋊#95C2312yes—
224C3⋊#95C2312yes—
225C3⋊#95C2312yes—
226C3⋊#95C2312yes—
227C3⋊#95C2312yes—
228C3⋊#95C2312yes—
229C3⋊#95C2312yes—
230C3⋊#95C2312yes—
231C3⋊#95C2312yes—
232C3⋊#95C2312yes—
233C3⋊#95C2312yes—
234C3⋊#95C2312yes—
235#552—68no—
236#539—68no—
237C2×#126—32no—
238C2×#126—32no—
239C2×#125—32no—
240C2×#125—32no—
241C2×#125—31no—
242C2×#123—32no—
243C2×#123—32no—
244C2×#123—32no—
245C2×C22⋊Q8—32no—
246C2×C22⋊Q8—31no—
247C2×C22⋊Q8C2×D311yescharacteristic
248C2×#121—31no—
249C2×C4×Q8—31no—
250C2×C4×D4—31no—
251C2×C4×D4—32no—
252C2×#117—31no—
253C2×#117—32no—
254C22×C4⋊C4—31no—
255C22×C4⋊C4—31no—
256#400—31no—
257#400—32no—
258#400—32no—
259#400—32no—
260#399—32no—
261#399—31no—
262#399—32no—
263#399—32no—
264#398—32no—
265#398—32no—
266#398—32no—
267#398—32no—
268#397—32no—
269#397—32no—
270#397—32no—
271#396—32no—
272#396—32no—
273#396—32no—
274#396—32no—
275#396—32no—
276#394—32no—
277#394—32no—
278#394—32no—
279#394—31no—
280#392—32no—
281#392—31no—
282#391C2×D312yes—
283#390—32no—
284#390—32no—
285#389—32no—
286#389—32no—
287#389—32no—
288#389—32no—
289#389C2×D312yes—
290#388—32no—
291#388—32no—
292#388—32no—
293#388—32no—
294#388C2×D312yes—
295#388C2×D312yes—
296#387—32no—
297#387—32no—
298#387—32no—
299#387—32no—
300#387—32no—
301#387—32no—
302#387C2×D312yes—
303#387C2×D312yes—
304#386—31no—
305#386—31no—
306#386—32no—
307#386—32no—
308#386—32no—
309#386—32no—
310#385—31no—
311#385—31no—
312#385—32no—
313#385—32no—
314#385—32no—
315#384—32no—
316#382—32no—
317#381—32no—
318#381C2×D311yescharacteristic
319#380—32no—
320#380—32no—
321#380C2×D311yescharacteristic
322C4×C22⋊C4—32no—
323C4×C22⋊C4—32no—
324C24×C3C2411yescharacteristic
325C23×D3C2412yes—
326C23×D3C2411yescharacteristic
327C2×C3×Q8—42no—
328C2×C3×Q8C2×D414yes—
329C22×C3×C4—42no—
330C22×C3×C4C2×D414yes—
331C22×C3×C4C2412yes—
332C22×C3×C4C2412yes—
333C22×C3×C4C2412yes—
334C22×C3×C4C2412yes—
335C22×C3×C4C2411yescharacteristic
336C22×C3×C4C2411yescharacteristic
337C22×C3×C4C2412yes—
338C22×C3×C4C2412yes—
339C2×#67—24no—
340C2×#67—22no—
341C2×#67—22no—
342C2×#67—42no—
343C2×#67—42no—
344C2×#67—41no—
345C22×Dic3—22no—
346C22×Dic3—22no—
347C22×Dic3—42no—
348C22×Dic3—42no—
349C22×Dic3C2412yes—
350C22×Dic3C2411yescharacteristic
351C22×Dic3C2412yes—
352C22×Dic3C2412yes—
353C22×Dic3C2411yescharacteristic
354C22×Dic3C2412yes—
355C22×Dic3C2411yescharacteristic
356C22×Dic3C2412yes—
357C2×D12—24no—
358C2×D12—22no—
359C2×D12—42no—
360C2×D12—42no—
361C2×D12—42no—
362C2×C4×D3—24no—
363C2×C4×D3—24no—
364C2×C4×D3—22no—
365C2×C4×D3—24no—
366C2×C4×D3—42no—
367C2×C4×D3—42no—
368C2×C4×D3—42no—
369C2×C4×D3—42no—
370C3×C4⋊C4—42no—
371C3×C4⋊C4—42no—
372C3×C4⋊C4—42no—
373C3×C4⋊C4C2×D418yes—
374C3×C4⋊C4C2×D414yes—
375C3×C22⋊C4—41no—
376C3×C22⋊C4—41no—
377C3×C22⋊C4—42no—
378C3×C22⋊C4C2×D418yes—
379C3×C42—42no—
380C3×C42—42no—
381#217—22no—
382#217—24no—
383(C2×D3)⋊C4—24no—
384(C2×D3)⋊C4—24no—
385(C2×D3)⋊C4—24no—
386(C2×D3)⋊C4—24no—
387(C2×D3)⋊C4—22no—
388(C2×D3)⋊C4—24no—
389(C2×D3)⋊C4—42no—
390(C2×D3)⋊C4—42no—
391(C2×D3)⋊C4—42no—
392(C2×D3)⋊C4—42no—
393(C2×D3)⋊C4—42no—
394(C2×D3)⋊C4—42no—
395(C2×D3)⋊C4—42no—
396(C2×D3)⋊C4—42no—
397(C2×D3)⋊C4—42no—
398(C2×D3)⋊C4—42no—
399C4⋊Dic3—24no—
400C4⋊Dic3—24no—
401C4⋊Dic3—24no—
402C4⋊Dic3—24no—
403C4⋊Dic3—22no—
404C4⋊Dic3—22no—
405C4⋊Dic3—22no—
406C4⋊Dic3—42no—
407C4⋊Dic3—42no—
408C4⋊Dic3—42no—
409C4⋊Dic3—42no—
410C4⋊Dic3—42no—
411C4⋊Dic3—42no—
412C4⋊Dic3—42no—
413Dic3⋊C4—24no—
414Dic3⋊C4—24no—
415Dic3⋊C4—24no—
416Dic3⋊C4—24no—
417Dic3⋊C4—22no—
418Dic3⋊C4—24no—
419Dic3⋊C4—24no—
420C4×Dic3—24no—
421C4×Dic3—24no—
422C4×Dic3—24no—
423C4×Dic3—22no—
424C22×Q8C22×D311yescharacteristic
425C22×D4—31no—
426C22×D4—32no—
427C22×D4—31no—
428C22×D4—32no—
429C23×C4—31no—
430C23×C4—31no—
431C23×C4—32no—
432C23×C4—31no—
433C23×C4—32no—
434C23×C4C22×D311yescharacteristic
435#126—68no—
436#126—68no—
437#125—68no—
438#125—68no—
439#125—64no—
440#123—68no—
441#123—68no—
442#123—68no—
443C22⋊Q8—68no—
444C22⋊Q8—64no—
445C22⋊Q8D1218yescomplemented
446#121—64no—
447C4×Q8—64no—
448C4×D4—64no—
449C4×D4—68no—
450#117—64no—
451#117—68no—
452C2×C4⋊C4—31no—
453C2×C4⋊C4—32no—
454C2×C4⋊C4—32no—
455C2×C4⋊C4—32no—
456C2×C4⋊C4—31no—
457C2×C4⋊C4—32no—
458C2×C4⋊C4—32no—
459C2×C4⋊C4—31no—
460C2×C4⋊C4—32no—
461C2×C4⋊C4—31no—
462C2×C4⋊C4—32no—
463C2×C4⋊C4—32no—
464C2×C4⋊C4—32no—
465C2×C4⋊C4—32no—
466C2×C4⋊C4—32no—
467C2×C4⋊C4—32no—
468C2×C4⋊C4—32no—
469C2×C4⋊C4—32no—
470C2×C4⋊C4—32no—
471C2×C4⋊C4—32no—
472C2×C4⋊C4—32no—
473C2×C4⋊C4—64no—
474C2×C4⋊C4—64no—
475C2×C4⋊C4C22×D312yes—
476C2×C4⋊C4C22×D312yes—
477C2×C4⋊C4C22×D312yes—
478C2×C4⋊C4C22×D311yescharacteristic
479C2×C4⋊C4C22×D312yes—
480C2×C22⋊C4—32no—
481C2×C22⋊C4—31no—
482C2×C22⋊C4—31no—
483C2×C22⋊C4—32no—
484C2×C22⋊C4—32no—
485C2×C22⋊C4—32no—
486C2×C22⋊C4—32no—
487C2×C22⋊C4—32no—
488C2×C22⋊C4—32no—
489C2×C22⋊C4—32no—
490C2×C22⋊C4—32no—
491C2×C22⋊C4—32no—
492C2×C22⋊C4—32no—
493C2×C22⋊C4—32no—
494C2×C22⋊C4—32no—
495C2×C22⋊C4—32no—
496C2×C22⋊C4—32no—
497C2×C22⋊C4—32no—
498C2×C22⋊C4C22×D311yescharacteristic
499C2×C22⋊C4C22×D311yescharacteristic
500C2×C22⋊C4C22×D312yes—
501C2×C22⋊C4C22×D312yes—
502C2×C42—32no—
503C2×C42—32no—
504C2×C42—31no—
505C2×C42—32no—
506C2×C42C22×D312yes—
507C2×C42C22×D312yes—
508#95—32no—
509#95—32no—
510#95—32no—
511#95—32no—
512#95—32no—
513#95—32no—
514#95—32no—
515#95—32no—
516#95—32no—
517#95—32no—
518#95—32no—
519#95—32no—
520#95—32no—
521#95—32no—
522#95C22×D312yes—
523#95C22×D312yes—
524#95C22×D311yescharacteristic
525#95C22×D311yescharacteristic
526#95C22×D312yes—
527#95C22×D312yes—
528#95C22×D312yes—
529#95C22×D312yes—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—22no—
533C23×C3—22no—
534C23×C3C22×D412yes—
535C23×C3C2511yescharacteristic
536C22×D3—21no—
537C22×D3—22no—
538C22×D3—22no—
539C22×D3—21no—
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—22no—
543C22×D3—22no—
544C22×D3—22no—
545C22×D3—22no—
546C22×D3—22no—
547C22×D32−1+412yes—
548C3×Q8—44no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—44no—
568C2×C3×C4C22×D412yes—
569C2×C3×C4C22×D414yes—
570C2×C3×C4C22×D414yes—
571C2×C3×C4C22×D412yes—
572#67—44no—
573#67—48no—
574C2×Dic3—21no—
575C2×Dic3—22no—
576C2×Dic3—21no—
577C2×Dic3—22no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—21no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—21no—
584C2×Dic3—22no—
585C2×Dic3—22no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—22no—
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—21no—
595C2×Dic3—22no—
596C2×Dic3—44no—
597C2×Dic3—82no—
598D12—82no—
599D12—84no—
600C4×D3—48no—
601C4×D3—44no—
602C4×D3—84no—
603C24—31no—
604C24—32no—
605C24C23×D311yescharacteristic
606C2×Q8—42no—
607C2×Q8C2×D1214yes—
608C2×D4—64no—
609C2×D4—62no—
610C2×D4—64no—
611C2×D4—62no—
612C2×D4—62no—
613C2×D4—122no—
614C2×D4—122no—
615C2×D4—122no—
616C2×D4—121no—
617C2×D4—122no—
618C2×D4—122no—
619C22×C4—32no—
620C22×C4—31no—
621C22×C4—32no—
622C22×C4—32no—
623C22×C4—32no—
624C22×C4—31no—
625C22×C4—31no—
626C22×C4—32no—
627C22×C4—42no—
628C22×C4—64no—
629C22×C4—62no—
630C22×C4—62no—
631C22×C4—64no—
632C22×C4—62no—
633C22×C4—64no—
634C22×C4—122no—
635C22×C4—122no—
636C22×C4—122no—
637C22×C4—122no—
638C22×C4—122no—
639C22×C4—122no—
640C22×C4C2×D1214yes—
641C22×C4C23×D312yes—
642C22×C4C23×D312yes—
643C22×C4C23×D312yes—
644C22×C4C23×D312yes—
645C22×C4C23×D311yescharacteristic
646C22×C4C23×D311yescharacteristic
647C22×C4C23×D312yes—
648C22×C4C23×D312yes—
649C4⋊C4—42no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—62no—
653C4⋊C4—64no—
654C4⋊C4—64no—
655C4⋊C4—64no—
656C4⋊C4—62no—
657C4⋊C4—64no—
658C4⋊C4—64no—
659C4⋊C4—62no—
660C4⋊C4—64no—
661C4⋊C4—62no—
662C4⋊C4—64no—
663C4⋊C4—64no—
664C4⋊C4—64no—
665C4⋊C4—64no—
666C4⋊C4—122no—
667C4⋊C4—122no—
668C4⋊C4—122no—
669C4⋊C4—122no—
670C4⋊C4—122no—
671C4⋊C4—122no—
672C4⋊C4—122no—
673C4⋊C4C2×D1214yes—
674C4⋊C4C2×D1218yes—
675C22⋊C4—41no—
676C22⋊C4—42no—
677C22⋊C4—41no—
678C22⋊C4—64no—
679C22⋊C4—62no—
680C22⋊C4—62no—
681C22⋊C4—64no—
682C22⋊C4—64no—
683C22⋊C4—64no—
684C22⋊C4—64no—
685C22⋊C4—64no—
686C22⋊C4—122no—
687C22⋊C4—122no—
688C22⋊C4—122no—
689C22⋊C4—122no—
690C22⋊C4—122no—
691C22⋊C4—122no—
692C22⋊C4—122no—
693C22⋊C4—122no—
694C22⋊C4—122no—
695C22⋊C4—122no—
696C22⋊C4C2×D1218yes—
697C42—42no—
698C42—42no—
699C42—64no—
700C42—64no—
701C42—62no—
702C42—64no—
703C22×C3—22no—
704C22×C3—22no—
705C22×C3—22no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3C23×D411yescharacteristic
709C22×C3C2×2−1+411yescharacteristic
710C22×C3#58512yes—
711C22×C3#58511yescharacteristic
712C22×C3#58512yes—
713C2×D3—22no—
714C2×D3—24no—
715C2×D3—41no—
716C2×D3—41no—
717C2×D3—42no—
718C2×D3—42no—
719C2×D3—42no—
720C2×D3—42no—
721C2×D3—42no—
722C2×D3—42no—
723C2×D3—42no—
724C2×D3—42no—
725C3×C4—22no—
726C3×C4—24no—
727C3×C4—22no—
728C3×C4—24no—
729C3×C4—42no—
730C3×C4—42no—
731C3×C4—42no—
732C3×C4—42no—
733Dic3—41no—
734Dic3—42no—
735Dic3—41no—
736Dic3—42no—
737Dic3—42no—
738Dic3—42no—
739Dic3—42no—
740Dic3—41no—
741C23—21no—
742C23—22no—
743C23—21no—
744C23—22no—
745C23—32no—
746C23—61no—
747C23—62no—
748C23—61no—
749C23—62no—
750C23—62no—
751C23—62no—
752C23—62no—
753C23—62no—
754C23—62no—
755C23—62no—
756C23—62no—
757C23C22×D1212yes—
758C23C24×D311yescharacteristic
759Q8—44no—
760D4—124no—
761D4—128no—
762D4—242no—
763D4—244no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—44no—
783C2×C4—61no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—61no—
789C2×C4—62no—
790C2×C4—61no—
791C2×C4—62no—
792C2×C4—61no—
793C2×C4—62no—
794C2×C4—62no—
795C2×C4—62no—
796C2×C4—62no—
797C2×C4—61no—
798C2×C4—62no—
799C2×C4—62no—
800C2×C4—62no—
801C2×C4—62no—
802C2×C4—62no—
803C2×C4—62no—
804C2×C4—62no—
805C2×C4—128no—
806C2×C4—124no—
807C2×C4—124no—
808C2×C4—244no—
809C2×C4—242no—
810C2×C4C22×D1212yes—
811C2×C4C22×D1214yes—
812C2×C4C22×D1214yes—
813C2×C4C22×D1212yes—
814C2×C3—42no—
815C2×C3#348511yescharacteristic
816C2×C3#348711yescharacteristic
817C2×C3#348911yescharacteristic
818C2×C3#356412yes—
819C2×C3#356712yes—
820D3—42no—
821D3—82no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—42no—
826C22—42no—
827C22—64no—
828C22—62no—
829C22—122no—
830C22—121no—
831C22—121no—
832C22—122no—
833C22—122no—
834C22—122no—
835C22—122no—
836C22—122no—
837C22—122no—
838C22—122no—
839C22C23×D1211yescharacteristic
840C22#596611yescharacteristic
841C22#596612yes—
842C22D3×2−1+411yescharacteristic
843C22#596812yes—
844C4—22no—
845C4—22no—
846C4—24no—
847C4—24no—
848C4—42no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—121no—
853C4—122no—
854C4—122no—
855C4—122no—
856C4—121no—
857C4—122no—
858C4—122no—
859C4—121no—
860C3#4878311yescharacteristic, complemented, Sylow
861C2—42no—
862C2—122no—
863C2—242no—
864C2#8585811yescharacteristic
865C2#8587411yescharacteristic
866C2#8590111yescharacteristic
867C2#8710612yes—
868C2#8713812yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2378C2
prime radical#74137C2
hypercenter#2378D3
hypocenterC3#48783
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2378

Complements

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

NH ≅ G/Ntype
1. C2×#5639C2semidirect
2. C2×#5645C2semidirect
3. C3×#2378C2semidirect
4. #76656C2semidirect
5. #76622C2semidirect
6. #76114C2semidirect
7. #76000C2semidirect
8. #75851C2semidirect
9. #75696C2semidirect
10. #75687C2semidirect
11. #75516C2semidirect
12. #75332C2semidirect
13. #75171C2semidirect
14. #75166C2semidirect
15. #75020C2semidirect
17. #74074C2semidirect
18. #74033C2semidirect
19. #73949C2semidirect
128. #2378D3semidirect
140. C3×C22⋊Q8D4semidirect
445. C22⋊Q8D12semidirect
860. C3#48783semidirect

Maximal subgroups

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

subgroupindex
C2×#56392
C2×#56452
C3×#23782
#766562
#766222
#761142
#760002
#758512
#756962
#756872
#755162
#753322
#751712
#751662
#750202
#741372
#740742
#740332
#739492
#487833