Finite Group Databasebeta

← #10972843

Subgroups — #10972843

Order 768.

2294 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×Dic3C211yesmaximal, characteristic, complemented
2C2×#5538C211yesmaximal, characteristic
3C3×#2409C211yesmaximal, characteristic, complemented
4#84068C211yesmaximal, characteristic, complemented
5#82777C212yesmaximal, complemented
6#82744C212yesmaximal, complemented
7#82374C211yesmaximal, characteristic, complemented
8#77204C212yesmaximal, complemented
9#77197C212yesmaximal, complemented
10#76812C212yesmaximal, complemented
11#76806C212yesmaximal, complemented
12#76611C212yesmaximal, complemented
13#76547C212yesmaximal, complemented
14#74871C212yesmaximal, complemented
15#74771C212yesmaximal
16#74588C212yesmaximal, complemented
17#74488C212yesmaximal, complemented
18#74028C211yesmaximal, characteristic, complemented
19#73863C211yesmaximal, characteristic, complemented
20#35245—31nomaximal, Sylow
21C23×C3×Q8C2211yescharacteristic
22C2×C3×C22⋊Q8C2212yes—
23C2×C3×C4×D4C2211yescharacteristic
24C2×#946C2212yes—
25C2×Q8×Dic3—28no—
26C2×Q8×Dic3C2212yes—
27C2×Q8×Dic3C2212yes—
28C2×Q8×Dic3C2212yes—
29C2×Q8×Dic3C2212yes—
30C2×#939C2211yescharacteristic
31C2×#935C2211yescharacteristic
32C2×C4×#67C2211yescharacteristic
33C2×C4×#67C2211yescharacteristic
34C2×#926C2211yescharacteristic
35C22×C4⋊Dic3C2212yes—
36C22×C4⋊Dic3C2211yescharacteristic
37C22×C4×Dic3C2212yes—
38C22×C4×Dic3C2211yescharacteristic
39#5538—28no—
40C2×#898C2211yescharacteristic
41C2×#889C2211yescharacteristic
42C2×#886C2211yescharacteristic
43C2×#885C2211yescharacteristic
44C2×#879C2211yescharacteristic
45C2×#878C2211yescharacteristic
46C2×#872C2211yescharacteristic
47C2×C4×Dic6C2211yescharacteristic
48C3×#395C2212yes—
49C3×#393C2212yes—
50C3×#391C2212yes—
51C3×#386C2212yes—
52C3×#385C2212yes—
53C3×#380C2211yescharacteristic
54#5231C2212yes—
55#5230C2212yes—
56#5229C2212yes—
57#5220C2212yes—
58#5213C2212yes—
59#5212C2212yes—
60#5212C2211yescharacteristic
61#5210C2212yes—
62#4990C2214yes—
63#4987C2212yes—
64#4986C2212yes—
65#4984C2212yes—
66#4984C2214yes—
67#4982C2214yes—
68#4980C2214yes—
69#4977C2212yes—
70Dic3×C4⋊C4C2212yes—
71#4961C2214yes—
72#4958C2212yes—
73#4951C2214yes—
74#4951C2214yes—
75#4950C2212yes—
76#4949C2212yes—
77#4946C2212yes—
78#4945C2214yes—
79#4943C2212yes—
80Dic3×C22⋊C4C2212yes—
81#4928C2212yes—
82#4677C2212yes—
83#4670C2214yes—
84#4669C2214yes—
85#4660C2214yes—
86#4659C2212yes—
87#4656C2214yes—
88#4655C2214yes—
89#4654C2214yes—
90#4652C2214yes—
91#4651C2212yes—
92#4648C2212yes—
93#4647C2214yes—
94C2×#529—31no—
95C22×C4×Q8—31no—
96#2853—32no—
97#2853—32no—
98#2634—32no—
99#2632—32no—
100#2604—32no—
101#2604—32no—
102#2591—32no—
103#2583—32no—
104#2581—32no—
105#2536—32no—
106#2487—31no—
107#2487—31no—
108#2409—31no—
109#2409D311yescharacteristic, complemented
110#2323—32no—
111#2323—32no—
112#2283—31no—
113C22×C3×Q8—28no—
114C22×C3×Q8—24no—
115C22×C3×Q8C2312yes—
116C22×C3×Q8C2312yes—
117C22×C3×D4C2311yescharacteristic
118C23×C3×C4C2312yes—
119C23×C3×C4C2311yescharacteristic
120C23×C3×C4C2311yescharacteristic
121C22×#67C2311yescharacteristic
122C22×#67C2311yescharacteristic
123C23×Dic3C2311yescharacteristic
124C23×Dic3C2312yes—
125C23×Dic3C2311yescharacteristic
126C22×C4×D3C2311yescharacteristic
127C22×Dic6C2311yescharacteristic
128C3×C22⋊Q8—28no—
129C3×C4×D4—24no—
130C2×C3×C4⋊C4C2312yes—
131C2×C3×C4⋊C4C2314yes—
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C22⋊C4C2312yes—
134C2×C3×C22⋊C4C2314yes—
135C2×C3×C22⋊C4C2311yescharacteristic
136C2×C3×C22⋊C4C2311yescharacteristic
137C2×C3×C42C2311yescharacteristic
138C2×#217C2312yes—
139C2×#217C2311yescharacteristic
140C2×#217C2311yescharacteristic
141C2×#217C2311yescharacteristic
142C2×#217C2311yescharacteristic
143C2×#217C2314yes—
144#946—28no—
145Q8×Dic3—28no—
146Q8×Dic3—28no—
147Q8×Dic3—28no—
148Q8×Dic3—28no—
149#939—24no—
150#935—24no—
151C4×#67—24no—
152C4×#67—24no—
153C2×(C2×D3)⋊C4C2311yescharacteristic
154C2×(C2×D3)⋊C4C2314yes—
155C2×(C2×D3)⋊C4C2311yescharacteristic
156C2×(C2×D3)⋊C4C2311yescharacteristic
157C2×(C2×D3)⋊C4C2311yescharacteristic
158C2×(C2×D3)⋊C4C2314yes—
159#926—24no—
160C2×C4⋊Dic3—24no—
161C2×C4⋊Dic3—28no—
162C2×C4⋊Dic3C2314yes—
163C2×C4⋊Dic3C2311yescharacteristic
164C2×C4⋊Dic3C2314yes—
165C2×C4⋊Dic3C2312yes—
166C2×C4⋊Dic3C2312yes—
167C2×C4⋊Dic3C2312yes—
168C2×C4⋊Dic3C2311yescharacteristic
169C2×C4⋊Dic3C2311yescharacteristic
170C2×C4⋊Dic3C2314yes—
171C2×Dic3⋊C4C2311yescharacteristic
172C2×Dic3⋊C4C2314yes—
173C2×Dic3⋊C4C2311yescharacteristic
174C2×Dic3⋊C4C2311yescharacteristic
175C2×Dic3⋊C4C2311yescharacteristic
176C2×Dic3⋊C4C2311yescharacteristic
177C2×Dic3⋊C4C2311yescharacteristic
178C2×Dic3⋊C4C2314yes—
179C2×C4×Dic3—28no—
180C2×C4×Dic3D418yes—
181C2×C4×Dic3C2314yes—
182C2×C4×Dic3C2314yes—
183C2×C4×Dic3C2311yescharacteristic
184C2×C4×Dic3C2314yes—
185C2×C4×Dic3C2311yescharacteristic
186C2×C4×Dic3C2311yescharacteristic
187C2×C4×Dic3C2311yescharacteristic
188C2×C4×Dic3C2311yescharacteristic
189#898—24no—
190#889—24no—
191#886—24no—
192#885—24no—
193#879—24no—
194#878—24no—
195#872—24no—
196C4×Dic6—24no—
197C3×#95C2314yes—
198C3×#95C2312yes—
199C3×#95C2314yes—
200C3⋊#95C2314yes—
201C3⋊#95C2312yes—
202C3⋊#95C2314yes—
203C3⋊#95C2314yes—
204C3⋊#95C2314yes—
205C3⋊#95C2314yes—
206C3⋊#95C2314yes—
207C3⋊#95C2314yes—
208C3⋊#95C2314yes—
209C3⋊#95C2314yes—
210C23×Q8C2×D311yescharacteristic
211#529—68no—
212C2×#126—31no—
213C2×#126—31no—
214C2×#125—31no—
215C2×#124—31no—
216C2×#123—31no—
217C2×#123—31no—
218C2×C22⋊Q8—32no—
219C2×C22⋊Q8—31no—
220C2×C22⋊Q8C2×D312yes—
221C2×#121—31no—
222C2×C4×Q8—32no—
223C2×C4×Q8—32no—
224C2×C4×Q8—32no—
225C2×C4×Q8—32no—
226C2×C4×Q8—31no—
227C2×C4×Q8—68no—
228C2×C4×D4—31no—
229C2×C4×D4—31no—
230C2×C4×D4C2×D311yescharacteristic
231C2×#117—31no—
232C2×#117—31no—
233C22×C4⋊C4—32no—
234C22×C4⋊C4—31no—
235C22×C42—31no—
236C22×C42—32no—
237#400—32no—
238#400—34no—
239#400—32no—
240#399—32no—
241#399—32no—
242#398—34no—
243#395—32no—
244#395—34no—
245#395C2×D312yes—
246#394—34no—
247#393—32no—
248#393C2×D312yes—
249#391—32no—
250#391C2×D312yes—
251#389—32no—
252#389—34no—
253#389—32no—
254#389—34no—
255#388—34no—
256#388—34no—
257#388—34no—
258#388—34no—
259#388—34no—
260#388—34no—
261#387—34no—
262#387—34no—
263#387—34no—
264#387—34no—
265#386—32no—
266#386—32no—
267#386—32no—
268#386C2×D312yes—
269#385—32no—
270#385—32no—
271#385—32no—
272#385C2×D312yes—
273#383—32no—
274#382—32no—
275#381—32no—
276#380—32no—
277#380—31no—
278#380—32no—
279#380C2×D311yescharacteristic
280C4×C4⋊C4—32no—
281C4×C22⋊C4—32no—
282#376—32no—
283C24×C3C2411yescharacteristic
284C24×C3C2411yescharacteristic
285C23×D3C2411yescharacteristic
286C2×C3×Q8—232no—
287C2×C3×Q8—24no—
288C2×C3×Q8—24no—
289C2×C3×Q8—28no—
290C2×C3×Q8—24no—
291C2×C3×Q8#4118yes—
292C2×C3×D4—22no—
293C2×C3×D4—22no—
294C2×C3×D4—22no—
295C22×C3×C4—24no—
296C22×C3×C4—28no—
297C22×C3×C4—24no—
298C22×C3×C4—22no—
299C22×C3×C4—24no—
300C22×C3×C4C2×D414yes—
301C22×C3×C4C2414yes—
302C22×C3×C4C2411yescharacteristic
303C22×C3×C4C2411yescharacteristic
304C22×C3×C4C2411yescharacteristic
305C22×C3×C4C2411yescharacteristic
306C22×C3×C4C2414yes—
307C22×C3×C4C2411yescharacteristic
308C2×#67—22no—
309C2×#67—22no—
310C2×#67—22no—
311C2×#67—22no—
312C2×#67—42no—
313C22×Dic3—22no—
314C22×Dic3—22no—
315C22×Dic3—24no—
316C22×Dic3—42no—
317C22×Dic3—44no—
318C22×Dic3C2×D414yes—
319C22×Dic3C2×D414yes—
320C22×Dic3C2411yescharacteristic
321C22×Dic3C2414yes—
322C22×Dic3C2414yes—
323C22×Dic3C2411yescharacteristic
324C22×Dic3C2411yescharacteristic
325C22×Dic3C2411yescharacteristic
326C22×Dic3C2411yescharacteristic
327C22×Dic3C2411yescharacteristic
328C22×Dic3C2411yescharacteristic
329C2×C4×D3—22no—
330C2×C4×D3—24no—
331C2×Dic6—22no—
332C2×Dic6—42no—
333C3×C4⋊C4—22no—
334C3×C4⋊C4—24no—
335C3×C4⋊C4—28no—
336C3×C22⋊C4—22no—
337C3×C22⋊C4—24no—
338C3×C22⋊C4—22no—
339C3×C22⋊C4—28no—
340C3×C42—22no—
341#217—22no—
342#217—24no—
343#217—22no—
344#217—22no—
345#217—22no—
346#217—44no—
347(C2×D3)⋊C4—22no—
348(C2×D3)⋊C4—28no—
349(C2×D3)⋊C4—22no—
350(C2×D3)⋊C4—22no—
351(C2×D3)⋊C4—22no—
352(C2×D3)⋊C4—44no—
353C4⋊Dic3—24no—
354C4⋊Dic3—24no—
355C4⋊Dic3—24no—
356C4⋊Dic3—22no—
357C4⋊Dic3—22no—
358C4⋊Dic3—22no—
359C4⋊Dic3—28no—
360C4⋊Dic3—28no—
361C4⋊Dic3—44no—
362Dic3⋊C4—22no—
363Dic3⋊C4—28no—
364Dic3⋊C4—22no—
365Dic3⋊C4—22no—
366Dic3⋊C4—22no—
367Dic3⋊C4—22no—
368Dic3⋊C4—22no—
369Dic3⋊C4—44no—
370C4×Dic3—22no—
371C4×Dic3—28no—
372C4×Dic3—28no—
373C4×Dic3—44no—
374C4×Dic3C2×D414yes—
375C4×Dic3C2×D414yes—
376C4×Dic3C2×D414yes—
377C4×Dic3C2×D414yes—
378C22×Q8—28no—
379C22×Q8—24no—
380C22×Q8—31no—
381C22×Q8C22×D312yes—
382C22×Q8C22×D312yes—
383C22×D4—31no—
384C22×D4—31no—
385C22×D4C22×D311yescharacteristic
386C23×C4—31no—
387C23×C4—31no—
388C23×C4—32no—
389C23×C4—31no—
390C23×C4C22×D312yes—
391C23×C4C22×D311yescharacteristic
392C23×C4C22×D311yescharacteristic
393#126—64no—
394#126—64no—
395#125—64no—
396#124—64no—
397#123—64no—
398#123—64no—
399C22⋊Q8—28no—
400C22⋊Q8—64no—
401C22⋊Q8—68no—
402#121—64no—
403C4×Q8—64no—
404C4×Q8—68no—
405C4×Q8—68no—
406C4×Q8—68no—
407C4×Q8—68no—
408C4×D4—24no—
409C4×D4—64no—
410C4×D4—64no—
411#117—64no—
412#117—64no—
413C2×C4⋊C4—32no—
414C2×C4⋊C4—34no—
415C2×C4⋊C4—34no—
416C2×C4⋊C4—32no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—31no—
419C2×C4⋊C4—31no—
420C2×C4⋊C4—31no—
421C2×C4⋊C4—31no—
422C2×C4⋊C4—31no—
423C2×C4⋊C4—31no—
424C2×C4⋊C4—31no—
425C2×C4⋊C4—31no—
426C2×C4⋊C4—32no—
427C2×C4⋊C4—34no—
428C2×C4⋊C4—34no—
429C2×C4⋊C4—34no—
430C2×C4⋊C4—68no—
431C2×C4⋊C4—64no—
432C2×C4⋊C4C22×D311yescharacteristic
433C2×C4⋊C4C22×D312yes—
434C2×C4⋊C4C22×D314yes—
435C2×C22⋊C4—31no—
436C2×C22⋊C4—31no—
437C2×C22⋊C4—31no—
438C2×C22⋊C4—31no—
439C2×C22⋊C4—32no—
440C2×C22⋊C4—31no—
441C2×C22⋊C4—31no—
442C2×C22⋊C4—31no—
443C2×C22⋊C4—31no—
444C2×C22⋊C4—34no—
445C2×C22⋊C4—34no—
446C2×C22⋊C4—34no—
447C2×C22⋊C4C22×D311yescharacteristic
448C2×C22⋊C4C22×D311yescharacteristic
449C2×C22⋊C4C22×D314yes—
450C2×C22⋊C4C22×D312yes—
451C2×C42—38no—
452C2×C42—31no—
453C2×C42—31no—
454C2×C42—31no—
455C2×C42—31no—
456C2×C42—31no—
457C2×C42—34no—
458C2×C42—34no—
459C2×C42—34no—
460C2×C42—68no—
461C2×C42C22×D311yescharacteristic
462#95—32no—
463#95—34no—
464#95—34no—
465#95—34no—
466#95—34no—
467#95—34no—
468#95—34no—
469#95—34no—
470#95—34no—
471#95—34no—
472#95C22×D312yes—
473#95C22×D314yes—
474#95C22×D314yes—
475C23×C3—22no—
476C23×C3—22no—
477C23×C3—21no—
478C23×C3—22no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—22no—
482C23×C3C22×D412yes—
483C23×C32−1+412yes—
484C23×C32−1+412yes—
485C23×C3C2511yescharacteristic
486C22×D3—21no—
487C22×D3—22no—
488C22×D3—21no—
489C22×D3—21no—
490C22×D3—22no—
491C3×Q8—216no—
492C3×Q8—216no—
493C3×D4—44no—
494C2×C3×C4—216no—
495C2×C3×C4—24no—
496C2×C3×C4—22no—
497C2×C3×C4—24no—
498C2×C3×C4—28no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—24no—
503C2×C3×C4—22no—
504C2×C3×C4—24no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—24no—
508C2×C3×C4—22no—
509C2×C3×C4—44no—
510C2×C3×C4C22×D412yes—
511C2×C3×C4C22×D412yes—
512C2×C3×C4C2×#4118yes—
513C2×C3×C4C2×#4114yes—
514#67—44no—
515#67—44no—
516C2×Dic3—28no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—24no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—22no—
528C2×Dic3—24no—
529C2×Dic3—24no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—24no—
533C2×Dic3—24no—
534C2×Dic3—22no—
535C2×Dic3—24no—
536C2×Dic3—44no—
537C2×Dic3—48no—
538C2×Dic3C22×D412yes—
539C2×Dic3C22×D412yes—
540C2×Dic3C22×D412yes—
541C2×Dic3C22×D412yes—
542C4×D3—44no—
543Dic6—44no—
544C24—31no—
545C24C23×D311yescharacteristic
546C24C23×D311yescharacteristic
547C2×Q8—232no—
548C2×Q8—24no—
549C2×Q8—24no—
550C2×Q8—28no—
551C2×Q8—24no—
552C2×Q8—62no—
553C2×Q8—122no—
554C2×Q8#23718yes—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—62no—
559C2×D4—62no—
560C2×D4—62no—
561C2×D4—62no—
562C2×D4—122no—
563C22×C4—24no—
564C22×C4—28no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—24no—
568C22×C4—34no—
569C22×C4—31no—
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—34no—
574C22×C4—34no—
575C22×C4—31no—
576C22×C4—34no—
577C22×C4—31no—
578C22×C4—31no—
579C22×C4—62no—
580C22×C4—62no—
581C22×C4—64no—
582C22×C4—62no—
583C22×C4—64no—
584C22×C4—122no—
585C22×C4—124no—
586C22×C4D3×D414yes—
587C22×C4C23×D314yes—
588C22×C4C23×D311yescharacteristic
589C22×C4C23×D311yescharacteristic
590C22×C4C23×D311yescharacteristic
591C22×C4C23×D311yescharacteristic
592C22×C4C23×D314yes—
593C22×C4C23×D311yescharacteristic
594C4⋊C4—22no—
595C4⋊C4—24no—
596C4⋊C4—28no—
597C4⋊C4—68no—
598C4⋊C4—68no—
599C4⋊C4—62no—
600C4⋊C4—62no—
601C4⋊C4—62no—
602C4⋊C4—62no—
603C4⋊C4—62no—
604C4⋊C4—62no—
605C4⋊C4—62no—
606C4⋊C4—62no—
607C4⋊C4—64no—
608C4⋊C4—64no—
609C4⋊C4—62no—
610C4⋊C4—68no—
611C4⋊C4—64no—
612C4⋊C4—124no—
613C4⋊C4—124no—
614C22⋊C4—22no—
615C22⋊C4—24no—
616C22⋊C4—22no—
617C22⋊C4—28no—
618C22⋊C4—62no—
619C22⋊C4—62no—
620C22⋊C4—62no—
621C22⋊C4—62no—
622C22⋊C4—62no—
623C22⋊C4—62no—
624C22⋊C4—62no—
625C22⋊C4—64no—
626C22⋊C4—62no—
627C22⋊C4—68no—
628C22⋊C4—124no—
629C22⋊C4—124no—
630C42—22no—
631C42—34no—
632C42—34no—
633C42—34no—
634C42—34no—
635C42—68no—
636C42—68no—
637C42—62no—
638C42—124no—
639C22×C3—22no—
640C22×C3—22no—
641C22×C3—24no—
642C22×C3—24no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—42no—
647C22×C3—42no—
648C22×C3#53614yes—
649C22×C3C23×D411yescharacteristic
650C22×C3C22×#4112yes—
651C22×C3C2×2−1+411yescharacteristic
652C22×C3C2×2−1+411yescharacteristic
653C22×C3#58512yes—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—42no—
658C2×D3—42no—
659C3×C4—22no—
660C3×C4—28no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—44no—
665C3×C4#52514yes—
666Dic3—22no—
667Dic3—22no—
668Dic3—22no—
669Dic3—22no—
670Dic3—41no—
671Dic3—41no—
672Dic3—41no—
673Dic3—44no—
674Dic3—44no—
675C23—22no—
676C23—22no—
677C23—21no—
678C23—22no—
679C23—21no—
680C23—21no—
681C23—22no—
682C23—61no—
683C23—62no—
684C23—61no—
685C23—61no—
686C23—62no—
687C23C2×D3×D412yes—
688C23#100712yes—
689C23#101012yes—
690C23C24×D311yescharacteristic
691Q8—216no—
692Q8—216no—
693Q8—124no—
694D4—44no—
695D4—124no—
696D4—124no—
697C2×C4—216no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—28no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—24no—
709C2×C4—21no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—32no—
713C2×C4—32no—
714C2×C4—32no—
715C2×C4—32no—
716C2×C4—44no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—68no—
724C2×C4—64no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—64no—
729C2×C4—62no—
730C2×C4—64no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—64no—
734C2×C4—64no—
735C2×C4—64no—
736C2×C4—62no—
737C2×C4—124no—
738C2×C4—128no—
739C2×C4—124no—
740C2×C4C2×D3×D412yes—
741C2×C4C2×D3×D412yes—
742C2×C4C2×#23718yes—
743C2×C4C2×#23714yes—
744C2×C3—24no—
745C2×C3—81no—
746C2×C3C2×#52511yescharacteristic
747C2×C3C2×#53611yescharacteristic
748C2×C3#344911yescharacteristic
749C2×C3#351612yes—
750C2×C3#351612yes—
751D3—81no—
752C22—22no—
753C22—22no—
754C22—24no—
755C22—24no—
756C22—41no—
757C22—41no—
758C22—42no—
759C22—41no—
760C22—42no—
761C22—121no—
762C22—121no—
763C22—122no—
764C22—121no—
765C22—122no—
766C22#562814yes—
767C22C22×D3×D411yescharacteristic
768C22C22×#23712yes—
769C22C2×#100711yescharacteristic
770C22C2×#101011yescharacteristic
771C22#596812yes—
772C4—22no—
773C4—28no—
774C4—41no—
775C4—41no—
776C4—44no—
777C4—41no—
778C4—62no—
779C4—62no—
780C4—62no—
781C4—62no—
782C4—124no—
783C4—121no—
784C4—121no—
785C4—121no—
786C4—124no—
787C4#558614yes—
788C3#3524511yescharacteristic, complemented, Sylow
789C2—24no—
790C2—81no—
791C2—241no—
792C2C2×#558611yescharacteristic
793C2C2×#562811yescharacteristic
794C2#8633811yescharacteristic
795C2#8671812yes—
796C2#8674912yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2409C2
prime radicalC2×#939C22
hypercenter#2409D3
hypocenterC3#35245
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2409

Complements

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

NH ≅ G/Ntype
1. C22×Q8×Dic3C2semidirect
3. C3×#2409C2semidirect
4. #84068C2semidirect
5. #82777C2semidirect
6. #82744C2semidirect
7. #82374C2semidirect
8. #77204C2semidirect
9. #77197C2semidirect
10. #76812C2semidirect
11. #76806C2semidirect
12. #76611C2semidirect
13. #76547C2semidirect
14. #74871C2semidirect
16. #74588C2semidirect
17. #74488C2semidirect
18. #74028C2semidirect
19. #73863C2semidirect
109. #2409D3semidirect
788. C3#35245semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×Dic32
C2×#55382
C3×#24092
#840682
#827772
#827442
#823742
#772042
#771972
#768122
#768062
#766112
#765472
#748712
#747712
#745882
#744882
#740282
#738632
#352453