Finite Group Databasebeta

← #10992702

Subgroups — #10992702

Order 768.

1802 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2285C211yesmaximal, characteristic, complemented
2#82283C212yesmaximal
3#82240C212yesmaximal, complemented
4#82076C211yesmaximal, characteristic, complemented
5C42×#67C211yesmaximal, characteristic
6#74376C211yesmaximal, characteristic, complemented
7#74355C211yesmaximal, characteristic, complemented
8#74320C211yesmaximal, characteristic, complemented
9#74318C211yesmaximal, characteristic, complemented
10#74234C212yesmaximal, complemented
11#74171C212yesmaximal, complemented
12#74020C212yesmaximal
13#73940C212yesmaximal
14#73918C212yesmaximal, complemented
15#73892C212yesmaximal, complemented
16#73791C212yesmaximal, complemented
17#73697C212yesmaximal, complemented
18#73661C212yesmaximal, complemented
19#73647C212yesmaximal, complemented
20#36210—31nomaximal, Sylow
21C2×C3×#117C2212yes—
22C22×C3×C42C2211yescharacteristic
23C2×C4×#67C2211yescharacteristic
24C2×C4×#67C2211yescharacteristic
25C2×C4×#67C2211yescharacteristic
26C2×#924C2212yes—
27C2×#897C2212yes—
28C2×#892C2212yes—
29C2×#890C2212yes—
30C2×#887C2212yes—
31C2×C42×D3C2211yescharacteristic
32C2×#869C2211yescharacteristic
33C3×#384C2211yescharacteristic
34C3×#384C2211yescharacteristic
35C3×#382C2212yes—
36C3×#380C2212yes—
37C3×#380C2212yes—
38C3×C4×C4⋊C4C2212yes—
39C3×C4×C4⋊C4C2212yes—
40#5212C2212yes—
41#5212C2212yes—
42C4×#217C2211yescharacteristic
43C4×#217C2211yescharacteristic
44C4×#217C2211yescharacteristic
45#4987C2212yes—
46#4987C2212yes—
47#4987C2212yes—
48#4987C2212yes—
49#4984C2212yes—
50#4984C2212yes—
51#4984C2212yes—
52#4984C2212yes—
53#4977C2212yes—
54#4977C2212yes—
55Dic3×C4⋊C4C2212yes—
56Dic3×C4⋊C4C2212yes—
57Dic3×C4⋊C4C2212yes—
58Dic3×C4⋊C4C2212yes—
59#4973C2212yes—
60#4973C2212yes—
61#4972C2212yes—
62#4972C2212yes—
63#4972C2212yes—
64#4972C2212yes—
65#4959C2214yes—
66#4952C2214yes—
67#4951C2214yes—
68#4951C2214yes—
69#4940C2214yes—
70C4×(C2×D3)⋊C4C2211yescharacteristic
71C4×(C2×D3)⋊C4C2211yescharacteristic
72C4×(C2×D3)⋊C4C2211yescharacteristic
73#4937C2214yes—
74#4935C2211yescharacteristic
75C4×C4⋊Dic3C2214yes—
76#4933C2214yes—
77C4×Dic3⋊C4C2211yescharacteristic
78C4×Dic3⋊C4C2211yescharacteristic
79C4×Dic3⋊C4C2211yescharacteristic
80C42×Dic3C2211yescharacteristic
81#4929C2212yes—
82#4928C2212yes—
83#4928C2212yes—
84#4675C2214yes—
85#4670C2214yes—
86C3⋊#401C2214yes—
87#4658C2214yes—
88#4658C2214yes—
89#4654C2214yes—
90#4653C2214yes—
91#4647C2214yes—
92#2859—31no—
93#2857—31no—
94#2857—31no—
95#2562—32no—
96#2514—32no—
97#2509—32no—
98#2495—32no—
99#2494—32no—
100#2494—32no—
101#2485—32no—
102#2421—32no—
103#2415—32no—
104#2370—32no—
105#2362—32no—
106#2347—32no—
107C4×C4⋊Q8—31no—
108#2285—31no—
109#2285D311yescharacteristic, complemented
110C42×D4—31no—
111C23×C3×C4C2311yescharacteristic
112C23×C3×C4C2311yescharacteristic
113C23×C3×C4C2311yescharacteristic
114C22×#67C2311yescharacteristic
115C22×C4×D3C2311yescharacteristic
116C22×C4×D3C2311yescharacteristic
117C22×C4×D3C2311yescharacteristic
118C22×Dic6C2312yes—
119C3×#117—28no—
120C2×C3×C4⋊C4C2312yes—
121C2×C3×C4⋊C4C2312yes—
122C2×C3×C4⋊C4C2312yes—
123C2×C3×C4⋊C4C2312yes—
124C2×C3×C4⋊C4C2312yes—
125C2×C3×C4⋊C4C2312yes—
126C2×C3×C22⋊C4C2314yes—
127C2×C3×C42—24no—
128C2×C3×C42C2311yescharacteristic
129C2×C3×C42C2311yescharacteristic
130C2×C3×C42C2311yescharacteristic
131C2×C3×C42C2314yes—
132C2×C3×C42C2311yescharacteristic
133C2×#217C2311yescharacteristic
134C2×#217C2311yescharacteristic
135C2×#217C2311yescharacteristic
136C2×#217C2314yes—
137C4×#67—24no—
138C4×#67—24no—
139C4×#67—24no—
140C2×(C2×D3)⋊C4C2311yescharacteristic
141C2×(C2×D3)⋊C4C2314yes—
142C2×(C2×D3)⋊C4C2311yescharacteristic
143C2×(C2×D3)⋊C4C2311yescharacteristic
144C2×(C2×D3)⋊C4C2314yes—
145C2×C4⋊Dic3C2314yes—
146C2×C4⋊Dic3C2314yes—
147C2×C4⋊Dic3C2312yes—
148C2×C4⋊Dic3C2312yes—
149C2×C4⋊Dic3C2312yes—
150C2×C4⋊Dic3C2312yes—
151C2×C4⋊Dic3C2312yes—
152#924—44no—
153C2×Dic3⋊C4C2311yescharacteristic
154C2×Dic3⋊C4C2314yes—
155C2×Dic3⋊C4C2311yescharacteristic
156C2×Dic3⋊C4C2311yescharacteristic
157C2×Dic3⋊C4C2314yes—
158C2×Dic3⋊C4C2314yes—
159C2×C4×Dic3C2311yescharacteristic
160C2×C4×Dic3C2311yescharacteristic
161C2×C4×Dic3C2311yescharacteristic
162C2×C4×Dic3C2311yescharacteristic
163C2×C4×Dic3C2311yescharacteristic
164C2×C4×Dic3C2311yescharacteristic
165C2×C4×Dic3C2311yescharacteristic
166C2×C4×Dic3C2311yescharacteristic
167C2×C4×Dic3C2314yes—
168C2×C4×Dic3C2314yes—
169C2×C4×Dic3C2311yescharacteristic
170#897—28no—
171#892—44no—
172#890—28no—
173#887—44no—
174C42×D3—24no—
175#869—24no—
176C3×#95C2314yes—
177C3×#95C2314yes—
178C3⋊#95C2314yes—
179C3⋊#95C2311yescharacteristic
180C3⋊#95C2314yes—
181C3⋊#95C2314yes—
182C3⋊#95C2311yescharacteristic
183C3⋊#95C2314yes—
184C3⋊#95C2314yes—
185C3⋊#95C2311yescharacteristic
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2311yescharacteristic
189C3⋊#95C2314yes—
190C3⋊#95C2314yes—
191C3⋊#95C2314yes—
192C3⋊#95C2311yescharacteristic
193C3⋊#95C2311yescharacteristic
194C2×C4⋊Q8—31no—
195C2×#125—32no—
196C2×C22⋊Q8—32no—
197C2×C22⋊Q8—32no—
198C2×C4×Q8—32no—
199C2×C4×D4—31no—
200C2×C4×D4—31no—
201C2×C4×D4—31no—
202C2×#117—32no—
203C2×#117C2×D312yes—
204C22×C42—31no—
205C22×C42C2×D311yescharacteristic
206#401—34no—
207#400—34no—
208#400—34no—
209#397—34no—
210#397—34no—
211#394—34no—
212#391—32no—
213#391—32no—
214#391—32no—
215#389—32no—
216#389—32no—
217#389—32no—
218#389—32no—
219#389—32no—
220#389—32no—
221#389—32no—
222#389—32no—
223#389—32no—
224#389—32no—
225#389—34no—
226#388—34no—
227#388—34no—
228#388—34no—
229#388—34no—
230#387—34no—
231#387—34no—
232#387—34no—
233#384—31no—
234#384C2×D311yescharacteristic
235#384C2×D311yescharacteristic
236#383—34no—
237#382—32no—
238#382—32no—
239#382C2×D312yes—
240#380—32no—
241#380—32no—
242#380—32no—
243#380—32no—
244#380—32no—
245#380—32no—
246#380C2×D312yes—
247#380C2×D312yes—
248C4×C4⋊C4—32no—
249C4×C4⋊C4—32no—
250C4×C4⋊C4—32no—
251C4×C4⋊C4—32no—
252C4×C4⋊C4—34no—
253C4×C4⋊C4—31no—
254C4×C4⋊C4—31no—
255C4×C4⋊C4—31no—
256C4×C4⋊C4C2×D312yes—
257C4×C4⋊C4C2×D312yes—
258C4×C22⋊C4—31no—
259C4×C22⋊C4—31no—
260C4×C22⋊C4—31no—
261C4×C22⋊C4—31no—
262C4×C22⋊C4—31no—
263C4×C22⋊C4—31no—
264C43—31no—
265C24×C3C2411yescharacteristic
266C23×D3C2411yescharacteristic
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—22no—
274C22×C3×C4—22no—
275C22×C3×C4#4114yes—
276C22×C3×C4C2411yescharacteristic
277C22×C3×C4C2414yes—
278C22×C3×C4C2414yes—
279C22×C3×C4C2411yescharacteristic
280C22×C3×C4C2411yescharacteristic
281C22×C3×C4C2411yescharacteristic
282C22×C3×C4C2411yescharacteristic
283C22×C3×C4C2411yescharacteristic
284C2×#67—22no—
285C2×#67—22no—
286C2×#67—22no—
287C22×Dic3C2411yescharacteristic
288C22×Dic3C2411yescharacteristic
289C22×Dic3C2411yescharacteristic
290C22×Dic3C2411yescharacteristic
291C22×Dic3C2414yes—
292C22×Dic3C2414yes—
293C22×Dic3C2411yescharacteristic
294C22×Dic3C2411yescharacteristic
295C22×Dic3C2411yescharacteristic
296C2×C4×D3—22no—
297C2×C4×D3—22no—
298C2×C4×D3—22no—
299C2×C4×D3—22no—
300C2×C4×D3—22no—
301C2×C4×D3—22no—
302C2×C4×D3—22no—
303C2×C4×D3—22no—
304C2×C4×D3#4114yes—
305C2×Dic6—24no—
306C2×Dic6—24no—
307C2×Dic6—24no—
308C3×C4⋊C4—24no—
309C3×C4⋊C4—24no—
310C3×C4⋊C4—24no—
311C3×C4⋊C4—24no—
312C3×C4⋊C4—24no—
313C3×C4⋊C4—24no—
314C3×C22⋊C4—28no—
315C3×C42—22no—
316C3×C42—22no—
317C3×C42—22no—
318C3×C42—28no—
319C3×C42#4114yes—
320#217—22no—
321#217—22no—
322#217—22no—
323#217—44no—
324(C2×D3)⋊C4—28no—
325(C2×D3)⋊C4—22no—
326(C2×D3)⋊C4—22no—
327(C2×D3)⋊C4—22no—
328(C2×D3)⋊C4—44no—
329C4⋊Dic3—24no—
330C4⋊Dic3—24no—
331C4⋊Dic3—24no—
332C4⋊Dic3—24no—
333C4⋊Dic3—24no—
334C4⋊Dic3—28no—
335C4⋊Dic3—28no—
336Dic3⋊C4—22no—
337Dic3⋊C4—28no—
338Dic3⋊C4—22no—
339Dic3⋊C4—22no—
340Dic3⋊C4—44no—
341Dic3⋊C4—44no—
342C4×Dic3—22no—
343C4×Dic3—22no—
344C4×Dic3—22no—
345C4×Dic3—22no—
346C4×Dic3—22no—
347C4×Dic3—22no—
348C4×Dic3—22no—
349C4×Dic3—22no—
350C4×Dic3—44no—
351C4×Dic3—44no—
352C4×Dic3#4114yes—
353C22×Q8—32no—
354C22×D4—31no—
355C23×C4—31no—
356C23×C4—31no—
357C23×C4—31no—
358C23×C4C22×D311yescharacteristic
359C23×C4C22×D311yescharacteristic
360C23×C4C22×D311yescharacteristic
361C4⋊Q8—64no—
362#125—68no—
363C22⋊Q8—68no—
364C22⋊Q8—124no—
365C4×Q8—124no—
366C4×D4—64no—
367C4×D4—64no—
368C4×D4—64no—
369#117—28no—
370#117—124no—
371C2×C4⋊C4—32no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—34no—
376C2×C4⋊C4—32no—
377C2×C4⋊C4—34no—
378C2×C4⋊C4—34no—
379C2×C4⋊C4—32no—
380C2×C4⋊C4—32no—
381C2×C4⋊C4—32no—
382C2×C4⋊C4—34no—
383C2×C4⋊C4—34no—
384C2×C4⋊C4C22×D312yes—
385C2×C4⋊C4C22×D312yes—
386C2×C4⋊C4C22×D312yes—
387C2×C4⋊C4C22×D312yes—
388C2×C4⋊C4C22×D312yes—
389C2×C4⋊C4C22×D312yes—
390C2×C22⋊C4—31no—
391C2×C22⋊C4—31no—
392C2×C22⋊C4—31no—
393C2×C22⋊C4—31no—
394C2×C22⋊C4—31no—
395C2×C22⋊C4—31no—
396C2×C22⋊C4—34no—
397C2×C22⋊C4—34no—
398C2×C22⋊C4—34no—
399C2×C22⋊C4C22×D314yes—
400C2×C42—24no—
401C2×C42—31no—
402C2×C42—31no—
403C2×C42—31no—
404C2×C42—31no—
405C2×C42—31no—
406C2×C42—31no—
407C2×C42—31no—
408C2×C42—31no—
409C2×C42—31no—
410C2×C42—34no—
411C2×C42—34no—
412C2×C42—64no—
413C2×C42C22×D314yes—
414C2×C42C22×D311yescharacteristic
415C2×C42C22×D311yescharacteristic
416C2×C42C22×D311yescharacteristic
417C2×C42C22×D311yescharacteristic
418#95—31no—
419#95—31no—
420#95—31no—
421#95—31no—
422#95—31no—
423#95—31no—
424#95—34no—
425#95—34no—
426#95—34no—
427#95—34no—
428#95—34no—
429#95—34no—
430#95—34no—
431#95—34no—
432#95—34no—
433#95—34no—
434#95C22×D314yes—
435#95C22×D314yes—
436C23×C3—21no—
437C23×C3—21no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—21no—
441C23×C3—21no—
442C23×C3C2×#4112yes—
443C23×C3C2511yescharacteristic
444C22×D3—21no—
445C22×D3—21no—
446C22×D3—21no—
447C22×D3—21no—
448C22×D3—21no—
449C22×D3—21no—
450C22×D3C2×#4112yes—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—28no—
454C2×C3×C4—24no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—24no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—24no—
461C2×C3×C4—24no—
462C2×C3×C4—24no—
463C2×C3×C4—21no—
464C2×C3×C4—24no—
465C2×C3×C4—21no—
466C2×C3×C4—44no—
467C2×C3×C4—44no—
468C2×C3×C4C2×#4112yes—
469C2×C3×C4C2×#4112yes—
470C2×C3×C4C2×#4112yes—
471C2×C3×C4C2×#4112yes—
472C2×C3×C4C2×#4112yes—
473C2×C3×C4C2×#4112yes—
474C2×C3×C4C2×#4112yes—
475C2×C3×C4H(5,𝔽2)12yes—
476C2×C3×C42−1+412yes—
477C2×C3×C42−1+412yes—
478#67—28no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—24no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—24no—
493C2×Dic3—24no—
494C2×Dic3—21no—
495C2×Dic3—24no—
496C2×Dic3—24no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—24no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3C2×#4112yes—
504C2×Dic3C2×#4112yes—
505C2×Dic3C2×#4112yes—
506C4×D3—28no—
507C4×D3—44no—
508C4×D3—44no—
509Dic6—48no—
510C24—31no—
511C24C23×D311yescharacteristic
512C2×Q8—64no—
513C2×Q8—64no—
514C2×Q8—64no—
515C2×D4—62no—
516C2×D4—62no—
517C2×D4—62no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—31no—
527C22×C4—31no—
528C22×C4—31no—
529C22×C4—34no—
530C22×C4—31no—
531C22×C4—31no—
532C22×C4—31no—
533C22×C4—31no—
534C22×C4—34no—
535C22×C4—34no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4—62no—
539C22×C4—62no—
540C22×C4—62no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4#23714yes—
545C22×C4C23×D311yescharacteristic
546C22×C4C23×D314yes—
547C22×C4C23×D314yes—
548C22×C4C23×D311yescharacteristic
549C22×C4C23×D311yescharacteristic
550C22×C4C23×D311yescharacteristic
551C22×C4C23×D311yescharacteristic
552C22×C4C23×D311yescharacteristic
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—62no—
560C4⋊C4—62no—
561C4⋊C4—68no—
562C4⋊C4—68no—
563C4⋊C4—68no—
564C4⋊C4—64no—
565C4⋊C4—64no—
566C4⋊C4—62no—
567C4⋊C4—64no—
568C4⋊C4—64no—
569C4⋊C4—64no—
570C4⋊C4—124no—
571C4⋊C4—124no—
572C22⋊C4—28no—
573C22⋊C4—62no—
574C22⋊C4—62no—
575C22⋊C4—68no—
576C22⋊C4—62no—
577C22⋊C4—62no—
578C22⋊C4—62no—
579C22⋊C4—62no—
580C22⋊C4—124no—
581C22⋊C4—124no—
582C42—22no—
583C42—22no—
584C42—22no—
585C42—28no—
586C42—34no—
587C42—62no—
588C42—62no—
589C42—62no—
590C42—62no—
591C42—62no—
592C42—62no—
593C42—62no—
594C42—62no—
595C42—124no—
596C42—124no—
597C42#23514yes—
598C22×C3—22no—
599C22×C3—22no—
600C22×C3—22no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3C22×#4111yescharacteristic
606C22×C3C22×#4111yescharacteristic
607C22×C3C22×#4111yescharacteristic
608C22×C3C22×#4111yescharacteristic
609C22×C3C2×H(5,𝔽2)11yescharacteristic
610C22×C3C2×2−1+411yescharacteristic
611C22×C3C2×2−1+411yescharacteristic
612C2×D3—22no—
613C2×D3—22no—
614C2×D3—22no—
615C2×D3—41no—
616C2×D3—41no—
617C2×D3—41no—
618C2×D3—41no—
619C3×C4—22no—
620C3×C4—44no—
621C3×C4—41no—
622C3×C4—41no—
623C3×C4—44no—
624C3×C4#55214yes—
625C3×C4#55314yes—
626C3×C4#55614yes—
627Dic3—22no—
628Dic3—22no—
629Dic3—22no—
630Dic3—41no—
631Dic3—44no—
632Dic3—41no—
633Dic3—41no—
634Dic3—41no—
635Dic3—44no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—32no—
643C23—61no—
644C23—61no—
645C23—61no—
646C23—61no—
647C23—61no—
648C23—61no—
649C23C2×#23712yes—
650C23C24×D311yescharacteristic
651Q8—128no—
652D4—68no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—28no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—21no—
666C2×C4—24no—
667C2×C4—21no—
668C2×C4—32no—
669C2×C4—32no—
670C2×C4—32no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—68no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—64no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—64no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—64no—
691C2×C4—64no—
692C2×C4—61no—
693C2×C4—64no—
694C2×C4—64no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—124no—
699C2×C4—124no—
700C2×C4C2×#23512yes—
701C2×C4C2×#23512yes—
702C2×C4C2×#23512yes—
703C2×C4C2×#23712yes—
704C2×C4C2×#23712yes—
705C2×C4#100712yes—
706C2×C4D3×#4112yes—
707C2×C4D3×#4112yes—
708C2×C4#100912yes—
709C2×C4#101012yes—
710C2×C3—42no—
711C2×C3#344411yescharacteristic
712C2×C3C2×#55211yescharacteristic
713C2×C3C2×#55311yescharacteristic
714C2×C3C2×#55611yescharacteristic
715C2×C3#350911yescharacteristic
716C2×C3#351111yescharacteristic
717C2×C3#351111yescharacteristic
718D3—42no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—62no—
727C22—62no—
728C22—62no—
729C22—121no—
730C22—121no—
731C22—121no—
732C22—121no—
733C22C22×#23511yescharacteristic
734C22C22×#23711yescharacteristic
735C22C2×#100711yescharacteristic
736C22C2×D3×#4111yescharacteristic
737C22C2×D3×#4111yescharacteristic
738C22C2×#100911yescharacteristic
739C22C2×#101011yescharacteristic
740C4—22no—
741C4—44no—
742C4—44no—
743C4—41no—
744C4—41no—
745C4—62no—
746C4—62no—
747C4—62no—
748C4—121no—
749C4—121no—
750C4—121no—
751C4—124no—
752C4—121no—
753C4—124no—
754C4#551314yes—
755C4#553014yes—
756C4#553314yes—
757C3#3621011yescharacteristic, complemented, Sylow
758C2—42no—
759C2—122no—
760C2C2×#551311yescharacteristic
761C2C2×#553011yescharacteristic
762C2C2×#553311yescharacteristic
763C2#8621911yescharacteristic
764C2#8622511yescharacteristic
765C2#8626411yescharacteristic
766C2#8628311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2285C2
prime radicalC22×#67C23
hypercenter#2285D3
hypocenterC3#36210
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2285

Complements

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

NH ≅ G/Ntype
1. C3×#2285C2semidirect
3. #82240C2semidirect
4. #82076C2semidirect
6. #74376C2semidirect
7. #74355C2semidirect
8. #74320C2semidirect
9. #74318C2semidirect
10. #74234C2semidirect
11. #74171C2semidirect
14. #73918C2semidirect
15. #73892C2semidirect
16. #73791C2semidirect
17. #73697C2semidirect
18. #73661C2semidirect
19. #73647C2semidirect
109. #2285D3semidirect
757. C3#36210semidirect

Maximal subgroups

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

subgroupindex
C3×#22852
#822832
#822402
#820762
C42×#672
#743762
#743552
#743202
#743182
#742342
#741712
#740202
#739402
#739182
#738922
#737912
#736972
#736612
#736472
#362103