Finite Group Databasebeta

← #11634155

Subgroups — #11634155

Order 768.

2310 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5728C211yesmaximal, characteristic, complemented
2C2×#5563C211yesmaximal, characteristic, complemented
3C3×#2547C211yesmaximal, characteristic, complemented
4#83259C211yesmaximal, characteristic, complemented
5#82998C212yesmaximal, complemented
6#82995C212yesmaximal, complemented
7C4×#938C211yesmaximal, characteristic, complemented
8#77597C214yesmaximal, complemented
9#77469C214yesmaximal, complemented
10#76620C212yesmaximal, complemented
11#76491C212yesmaximal, complemented
12#74019C212yesmaximal, complemented
13#73914C212yesmaximal, complemented
14#73900C212yesmaximal, complemented
15#73885C212yesmaximal, complemented
16C4×#895C211yesmaximal, characteristic, complemented
17#73656C211yesmaximal, characteristic, complemented
18#59050—31nomaximal, Sylow
19C2×C3×C4⋊Q8C2211yescharacteristic
20C2×C3×#124C2212yes—
21C2×C3×C4×D4C2211yescharacteristic
22C2×#946C2212yes—
23C2×#946C2212yes—
24C2×#946C2212yes—
25C2×Q8×Dic3C2212yes—
26C2×#938C2212yes—
27C2×#938C2211yescharacteristic
28C2×#930C2212yes—
29C2×C4×#67C2212yes—
30C2×#926C2212yes—
31#5728—28no—
32#5563—28no—
33C2×#897C2212yes—
34C2×#895C2211yescharacteristic
35C2×#892C2212yes—
36C2×#892C2212yes—
37C2×#890C2212yes—
38C2×#887C2212yes—
39C2×#885C2214yes—
40C2×C4×D12C2211yescharacteristic
41C2×C4×D12C2212yes—
42C2×C42×D3C2211yescharacteristic
43C2×#869C2211yescharacteristic
44C3×#397C2214yes—
45C3×#391C2212yes—
46C3×#380C2212yes—
47C3×#380C2212yes—
48C3×C4×C4⋊C4C2211yescharacteristic
49#5221C2211yescharacteristic
50C4×#217C2212yes—
51#4993C2214yes—
52#4988C2211yescharacteristic
53#4988C2212yes—
54#4987C2211yescharacteristic
55#4987C2211yescharacteristic
56#4984C2211yescharacteristic
57#4975C2212yes—
58Dic3×C4⋊C4C2212yes—
59#4972C2212yes—
60#4972C2211yescharacteristic
61#4961C2214yes—
62#4960C2214yes—
63#4957C2214yes—
64#4957C2214yes—
65#4957C2214yes—
66#4956C2212yes—
67#4949C2214yes—
68#4948C2214yes—
69#4945C2214yes—
70#4944C2212yes—
71C4×(C2×D3)⋊C4C2212yes—
72C4×C4⋊Dic3C2212yes—
73C4×C4⋊Dic3C2211yescharacteristic
74#4928C2212yes—
75#4675C2214yes—
76#4672C2214yes—
77#4670C2212yes—
78#4670C2214yes—
79#4669C2214yes—
80#4669C2214yes—
81#4665C2212yes—
82#4655C2214yes—
83#4649C2214yes—
84#4647C2214yes—
85#4646C2214yes—
86C2×#555—31no—
87C2×#533—31no—
88#2730—34no—
89#2547D311yescharacteristic, complemented
90#2542—31no—
91#2540—32no—
92#2490—32no—
93#2448—34no—
94#2441—32no—
95#2426—32no—
96#2415—32no—
97#2414—32no—
98#2369—31no—
99#2362—32no—
100#2354—32no—
101C4×#121—31no—
102C4×#121—31no—
103C22×C3×Q8C2312yes—
104C22×C3×D4C2311yescharacteristic
105C23×C3×C4C2312yes—
106C22×#67C2312yes—
107C22×#67C2314yes—
108C22×D12C2311yescharacteristic
109C22×D12C2312yes—
110C22×C4×D3C2312yes—
111C22×C4×D3C2311yescharacteristic
112C22×C4×D3C2311yescharacteristic
113C22×C4×D3C2311yescharacteristic
114C22×Dic6C2312yes—
115C3×C4⋊Q8—24no—
116C3×#124—44no—
117C3×C4×D4—24no—
118C2×C3×C4⋊C4C2311yescharacteristic
119C2×C3×C4⋊C4C2311yescharacteristic
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C4⋊C4C2312yes—
122C2×C3×C4⋊C4C2312yes—
123C2×C3×C22⋊C4C2312yes—
124C2×C3×C22⋊C4C2314yes—
125C2×C3×C22⋊C4C2314yes—
126C2×C3×C42C2312yes—
127C2×C3×C42C2311yescharacteristic
128C2×#217C2312yes—
129C2×#217C2312yes—
130C2×#217C2314yes—
131C2×#217C2312yes—
132#946—28no—
133#946—28no—
134#946—44no—
135Q8×Dic3—28no—
136#938—28no—
137#938—24no—
138#930—28no—
139C4×#67—28no—
140C2×(C2×D3)⋊C4C2312yes—
141C2×(C2×D3)⋊C4C2312yes—
142C2×(C2×D3)⋊C4C2312yes—
143C2×(C2×D3)⋊C4C2314yes—
144C2×(C2×D3)⋊C4C2314yes—
145C2×(C2×D3)⋊C4C2314yes—
146C2×(C2×D3)⋊C4C2312yes—
147C2×(C2×D3)⋊C4C2312yes—
148C2×(C2×D3)⋊C4C2312yes—
149C2×(C2×D3)⋊C4C2314yes—
150#926—28no—
151C2×C4⋊Dic3C2314yes—
152C2×C4⋊Dic3C2311yescharacteristic
153C2×C4⋊Dic3C2311yescharacteristic
154C2×C4⋊Dic3C2312yes—
155C2×C4⋊Dic3C2312yes—
156C2×C4⋊Dic3C2312yes—
157C2×C4⋊Dic3C2311yescharacteristic
158C2×Dic3⋊C4C2314yes—
159C2×Dic3⋊C4C2312yes—
160C2×Dic3⋊C4C2314yes—
161C2×Dic3⋊C4C2314yes—
162C2×Dic3⋊C4C2314yes—
163C2×C4×Dic3C2314yes—
164C2×C4×Dic3C2314yes—
165C2×C4×Dic3C2311yescharacteristic
166C2×C4×Dic3C2312yes—
167C2×C4×Dic3C2311yescharacteristic
168C2×C4×Dic3C2311yescharacteristic
169C2×C4×Dic3C2314yes—
170#897—28no—
171#895—24no—
172#892—28no—
173#892—28no—
174#890—28no—
175#887—28no—
176#885—216no—
177C4×D12—24no—
178C4×D12—44no—
179C42×D3—24no—
180#869D418yescomplemented
181C3×#95C2312yes—
182C3×#95C2314yes—
183C3×#95C2314yes—
184C3⋊#95C2312yes—
185C3⋊#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2312yes—
188C3⋊#95C2312yes—
189C3⋊#95C2312yes—
190C3⋊#95C2312yes—
191#555—68no—
192#533—68no—
193C2×C4⋊Q8—31no—
194C2×C4⋊Q8C2×D311yescharacteristic
195C2×#125—32no—
196C2×#124—34no—
197C2×#124C2×D312yes—
198C2×C22⋊Q8—32no—
199C2×C22⋊Q8—32no—
200C2×C22⋊Q8—32no—
201C2×C22⋊Q8—32no—
202C2×#121—32no—
203C2×#121—31no—
204C2×#121—32no—
205C2×#121—31no—
206C2×C4×Q8—32no—
207C2×C4×Q8—32no—
208C2×C4×D4—32no—
209C2×C4×D4—31no—
210C2×C4×D4—32no—
211C2×C4×D4C2×D311yescharacteristic
212C2×#117—32no—
213C2×#117—32no—
214C2×#117—32no—
215C22×C42—31no—
216#399—34no—
217#399—34no—
218#397—34no—
219#397C2×D314yes—
220#396—34no—
221#394—34no—
222#394—34no—
223#392—34no—
224#391—34no—
225#391C2×D312yes—
226#390—31no—
227#390—32no—
228#390—31no—
229#390—34no—
230#390—34no—
231#390—34no—
232#389—31no—
233#389—32no—
234#389—31no—
235#389—32no—
236#389—34no—
237#388—34no—
238#388—32no—
239#388—34no—
240#388—34no—
241#388—34no—
242#388—32no—
243#387—34no—
244#386—32no—
245#386—32no—
246#384—32no—
247#380—31no—
248#380—31no—
249#380C2×D312yes—
250#380C2×D312yes—
251C4×C4⋊C4—32no—
252C4×C4⋊C4—32no—
253C4×C4⋊C4—31no—
254C4×C4⋊C4—34no—
255C4×C4⋊C4C2×D311yescharacteristic
256C4×C22⋊C4—32no—
257C4×C22⋊C4—32no—
258C24×C3C2412yes—
259C23×D3C2412yes—
260C23×D3C2411yescharacteristic
261C2×C3×Q8—24no—
262C2×C3×Q8—24no—
263C2×C3×Q8—24no—
264C2×C3×D4—22no—
265C2×C3×D4—22no—
266C2×C3×D4—22no—
267C22×C3×C4—24no—
268C22×C3×C4—24no—
269C22×C3×C4—24no—
270C22×C3×C4C2412yes—
271C22×C3×C4C2412yes—
272C22×C3×C4C2412yes—
273C22×C3×C4C2414yes—
274C22×C3×C4C2411yescharacteristic
275C22×C3×C4C2411yescharacteristic
276C22×C3×C4C2411yescharacteristic
277C2×#67—24no—
278C2×#67—28no—
279C2×#67—24no—
280C2×#67—42no—
281C2×#67—44no—
282C2×#67—44no—
283C22×Dic3C2411yescharacteristic
284C22×Dic3C2412yes—
285C22×Dic3C2411yescharacteristic
286C22×Dic3C2412yes—
287C22×Dic3C2414yes—
288C22×Dic3C2412yes—
289C22×Dic3C2411yescharacteristic
290C2×D12—24no—
291C2×D12—22no—
292C2×D12—22no—
293C2×D12—22no—
294C2×D12—42no—
295C2×D12—42no—
296C2×C4×D3—22no—
297C2×C4×D3—22no—
298C2×C4×D3—22no—
299C2×C4×D3—22no—
300C2×C4×D3—24no—
301C2×C4×D3—22no—
302C2×C4×D3—24no—
303C2×C4×D3—22no—
304C2×C4×D3—24no—
305C2×C4×D3—41no—
306C2×C4×D3—41no—
307C2×C4×D3#4114yes—
308C2×Dic6—42no—
309C2×Dic6—42no—
310C2×Dic6C2×D418yes—
311C3×C4⋊C4—24no—
312C3×C4⋊C4—24no—
313C3×C4⋊C4—22no—
314C3×C4⋊C4—22no—
315C3×C4⋊C4—22no—
316C3×C22⋊C4—24no—
317C3×C22⋊C4—44no—
318C3×C22⋊C4—44no—
319C3×C42—24no—
320C3×C42C2×D414yes—
321#217—28no—
322#217—24no—
323#217—24no—
324#217—42no—
325(C2×D3)⋊C4—24no—
326(C2×D3)⋊C4—24no—
327(C2×D3)⋊C4—28no—
328(C2×D3)⋊C4—28no—
329(C2×D3)⋊C4—24no—
330(C2×D3)⋊C4—28no—
331(C2×D3)⋊C4—42no—
332(C2×D3)⋊C4—42no—
333(C2×D3)⋊C4—42no—
334(C2×D3)⋊C4—44no—
335C4⋊Dic3—22no—
336C4⋊Dic3—22no—
337C4⋊Dic3—28no—
338C4⋊Dic3—42no—
339C4⋊Dic3C2×D418yes—
340C4⋊Dic3C2×D418yes—
341C4⋊Dic3#4114yes—
342Dic3⋊C4—28no—
343Dic3⋊C4—24no—
344Dic3⋊C4—28no—
345Dic3⋊C4—44no—
346Dic3⋊C4—44no—
347C4×Dic3—22no—
348C4×Dic3—22no—
349C4×Dic3—22no—
350C4×Dic3—24no—
351C4×Dic3—28no—
352C4×Dic3—28no—
353C4×Dic3—44no—
354C22×Q8—32no—
355C22×Q8C22×D312yes—
356C22×D4—32no—
357C22×D4—34no—
358C22×D4—31no—
359C22×D4—32no—
360C22×D4C22×D311yescharacteristic
361C23×C4—31no—
362C23×C4—32no—
363C23×C4—31no—
364C23×C4—31no—
365C23×C4C22×D312yes—
366C4⋊Q8—24no—
367C4⋊Q8—38no—
368#125—68no—
369#124—44no—
370#124—616no—
371C22⋊Q8—68no—
372C22⋊Q8—68no—
373C22⋊Q8—68no—
374C22⋊Q8—124no—
375#121—64no—
376#121—68no—
377#121—68no—
378#121—64no—
379C4×Q8—68no—
380C4×Q8—68no—
381C4×D4—24no—
382C4×D4—68no—
383C4×D4—64no—
384C4×D4—124no—
385#117—68no—
386#117—68no—
387#117—68no—
388C2×C4⋊C4—32no—
389C2×C4⋊C4—32no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—32no—
393C2×C4⋊C4—34no—
394C2×C4⋊C4—34no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—34no—
397C2×C4⋊C4—32no—
398C2×C4⋊C4—34no—
399C2×C4⋊C4—34no—
400C2×C4⋊C4C22×D311yescharacteristic
401C2×C4⋊C4C22×D312yes—
402C2×C4⋊C4C22×D312yes—
403C2×C4⋊C4C22×D311yescharacteristic
404C2×C4⋊C4C22×D311yescharacteristic
405C2×C22⋊C4—34no—
406C2×C22⋊C4—32no—
407C2×C22⋊C4—32no—
408C2×C22⋊C4—34no—
409C2×C22⋊C4—34no—
410C2×C22⋊C4—32no—
411C2×C22⋊C4—32no—
412C2×C22⋊C4—32no—
413C2×C22⋊C4—34no—
414C2×C22⋊C4—32no—
415C2×C22⋊C4—32no—
416C2×C22⋊C4—32no—
417C2×C22⋊C4—34no—
418C2×C22⋊C4—32no—
419C2×C22⋊C4C22×D312yes—
420C2×C22⋊C4C22×D314yes—
421C2×C22⋊C4C22×D314yes—
422C2×C42—34no—
423C2×C42—34no—
424C2×C42—32no—
425C2×C42—31no—
426C2×C42—31no—
427C2×C42—31no—
428C2×C42—34no—
429C2×C42—64no—
430C2×C42C22×D312yes—
431C2×C42C22×D311yescharacteristic
432#95—32no—
433#95—32no—
434#95—32no—
435#95—32no—
436#95—32no—
437#95—34no—
438#95—34no—
439#95C22×D314yes—
440#95C22×D312yes—
441#95C22×D314yes—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3C2511yescharacteristic
450C22×D3—21no—
451C22×D3—21no—
452C22×D3—21no—
453C22×D3—21no—
454C22×D3—21no—
455C22×D3—21no—
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3C2×#4112yes—
464C3×Q8—48no—
465C3×D4—44no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—22no—
469C2×C3×C4—24no—
470C2×C3×C4—22no—
471C2×C3×C4—24no—
472C2×C3×C4—22no—
473C2×C3×C4—24no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—48no—
481C2×C3×C4C22×D412yes—
482C2×C3×C4C22×D412yes—
483C2×C3×C4C22×D412yes—
484C2×C3×C4C2×#4112yes—
485C2×C3×C4C2×#4112yes—
486C2×C3×C4H(5,𝔽2)12yes—
487C2×C3×C42−1+412yes—
488#67—48no—
489#67—88no—
490C2×Dic3—21no—
491C2×Dic3—22no—
492C2×Dic3—21no—
493C2×Dic3—22no—
494C2×Dic3—24no—
495C2×Dic3—24no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—21no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—21no—
505C2×Dic3—22no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3C22×D418yes—
509C2×Dic3C2×#4114yes—
510C2×Dic3C2×#4112yes—
511D12—48no—
512D12—44no—
513C4×D3—28no—
514C4×D3—44no—
515C4×D3—44no—
516C4×D3—48no—
517Dic6—48no—
518C24—31no—
519C24—32no—
520C24C23×D312yes—
521C2×Q8—24no—
522C2×Q8—24no—
523C2×Q8—24no—
524C2×Q8—38no—
525C2×Q8—122no—
526C2×Q8—122no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—64no—
531C2×D4—64no—
532C2×D4—68no—
533C2×D4—64no—
534C2×D4—62no—
535C2×D4—62no—
536C2×D4—62no—
537C2×D4—122no—
538C2×D4—122no—
539C2×D4—122no—
540C2×D4—124no—
541C2×D4—124no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—32no—
546C22×C4—31no—
547C22×C4—34no—
548C22×C4—34no—
549C22×C4—31no—
550C22×C4—32no—
551C22×C4—32no—
552C22×C4—31no—
553C22×C4—62no—
554C22×C4—62no—
555C22×C4—62no—
556C22×C4—62no—
557C22×C4—64no—
558C22×C4—62no—
559C22×C4—64no—
560C22×C4—62no—
561C22×C4—64no—
562C22×C4—121no—
563C22×C4—121no—
564C22×C4C23×D312yes—
565C22×C4C23×D312yes—
566C22×C4C23×D312yes—
567C22×C4C23×D314yes—
568C22×C4C23×D311yescharacteristic
569C22×C4C23×D311yescharacteristic
570C22×C4C23×D311yescharacteristic
571C4⋊C4—22no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—38no—
577C4⋊C4—38no—
578C4⋊C4—34no—
579C4⋊C4—64no—
580C4⋊C4—68no—
581C4⋊C4—68no—
582C4⋊C4—68no—
583C4⋊C4—62no—
584C4⋊C4—62no—
585C4⋊C4—122no—
586C4⋊C4—124no—
587C4⋊C4—124no—
588C22⋊C4—24no—
589C22⋊C4—44no—
590C22⋊C4—44no—
591C22⋊C4—68no—
592C22⋊C4—68no—
593C22⋊C4—64no—
594C22⋊C4—68no—
595C22⋊C4—64no—
596C22⋊C4—68no—
597C22⋊C4—64no—
598C22⋊C4—64no—
599C22⋊C4—64no—
600C22⋊C4—122no—
601C22⋊C4—122no—
602C22⋊C4—124no—
603C22⋊C4—122no—
604C22⋊C4—122no—
605C42—24no—
606C42—68no—
607C42—68no—
608C42—62no—
609C42—62no—
610C42—62no—
611C42—64no—
612C42—124no—
613C42D3×D414yes—
614C22×C3—42no—
615C22×C3—42no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—42no—
620C22×C3—42no—
621C22×C3C23×D411yescharacteristic
622C22×C3C22×#4111yescharacteristic
623C22×C3C22×#4111yescharacteristic
624C22×C3C2×H(5,𝔽2)11yescharacteristic
625C22×C3C2×2−1+411yescharacteristic
626C22×C3#58511yescharacteristic
627C22×C3#58511yescharacteristic
628C2×D3—22no—
629C2×D3—22no—
630C2×D3—22no—
631C2×D3—41no—
632C2×D3—41no—
633C2×D3—41no—
634C2×D3—41no—
635C2×D3—42no—
636C2×D3—42no—
637C2×D3—42no—
638C2×D3—42no—
639C2×D3—42no—
640C2×D3—42no—
641C2×D3—42no—
642C3×C4—22no—
643C3×C4—42no—
644C3×C4—44no—
645C3×C4—42no—
646C3×C4—42no—
647C3×C4#54814yes—
648C3×C4#55014yes—
649Dic3—22no—
650Dic3—24no—
651Dic3—28no—
652Dic3—41no—
653Dic3—42no—
654Dic3—41no—
655Dic3—42no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—32no—
664C23—61no—
665C23—61no—
666C23—61no—
667C23—61no—
668C23—61no—
669C23—61no—
670C23—62no—
671C23—62no—
672C23—62no—
673C23—62no—
674C23—62no—
675C23—62no—
676C23—62no—
677C23C24×D311yescharacteristic
678Q8—48no—
679Q8—128no—
680D4—44no—
681D4—128no—
682D4—128no—
683D4—124no—
684D4—248no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—38no—
700C2×C4—32no—
701C2×C4—34no—
702C2×C4—48no—
703C2×C4—61no—
704C2×C4—62no—
705C2×C4—61no—
706C2×C4—62no—
707C2×C4—64no—
708C2×C4—64no—
709C2×C4—68no—
710C2×C4—62no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—62no—
714C2×C4—61no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—61no—
718C2×C4—62no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—62no—
722C2×C4—124no—
723C2×C4—124no—
724C2×C4—128no—
725C2×C4C2×D3×D412yes—
726C2×C4C2×D3×D412yes—
727C2×C4C2×D3×D412yes—
728C2×C4#100412yes—
729C2×C4D3×#4112yes—
730C2×C4D3×#4112yes—
731C2×C4#101012yes—
732C2×C3—82no—
733C2×C3C2×#54811yescharacteristic
734C2×C3C2×#55011yescharacteristic
735C2×C3#347511yescharacteristic
736C2×C3#348511yescharacteristic
737C2×C3#350611yescharacteristic
738C2×C3#351811yescharacteristic
739C2×C3#354711yescharacteristic
740D3—42no—
741D3—82no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—62no—
750C22—62no—
751C22—62no—
752C22—121no—
753C22—121no—
754C22—121no—
755C22—121no—
756C22—122no—
757C22—122no—
758C22—122no—
759C22—122no—
760C22—122no—
761C22—122no—
762C22—122no—
763C22C22×D3×D411yescharacteristic
764C22C2×#100411yescharacteristic
765C22C2×D3×#4111yescharacteristic
766C22C2×D3×#4111yescharacteristic
767C22C2×#101011yescharacteristic
768C22#596811yescharacteristic
769C22#596811yescharacteristic
770C4—22no—
771C4—42no—
772C4—44no—
773C4—42no—
774C4—42no—
775C4—62no—
776C4—68no—
777C4—64no—
778C4—121no—
779C4—122no—
780C4—121no—
781C4—122no—
782C4#559914yes—
783C4#567714yes—
784C3#5905011yescharacteristic, complemented, Sylow
785C2—82no—
786C2—122no—
787C2—242no—
788C2C2×#559911yescharacteristic
789C2C2×#567711yescharacteristic
790C2#8635411yescharacteristic
791C2#8670311yescharacteristic
792C2#8670811yescharacteristic
793C2#8697911yescharacteristic
794C2#8698911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2547C2
hypercenter#2547D3
hypocenterC3#59050
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2547

Complements

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

NH ≅ G/Ntype
1. C2×#5728C2semidirect
2. C2×#5563C2semidirect
3. C3×#2547C2semidirect
4. #83259C2semidirect
5. #82998C2semidirect
6. #82995C2semidirect
7. C4×#938C2semidirect
8. #77597C2semidirect
9. #77469C2semidirect
10. #76620C2semidirect
11. #76491C2semidirect
12. #74019C2semidirect
13. #73914C2semidirect
14. #73900C2semidirect
15. #73885C2semidirect
16. C4×#895C2semidirect
17. #73656C2semidirect
89. #2547D3semidirect
180. #869D4semidirect
784. C3#59050semidirect

Maximal subgroups

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

subgroupindex
C2×#57282
C2×#55632
C3×#25472
#832592
#829982
#829952
C4×#9382
#775972
#774692
#766202
#764912
#740192
#739142
#739002
#738852
C4×#8952
#736562
#590503