Finite Group Databasebeta

← #11069166

Subgroups — #11069166

Order 768.

2484 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5619C212yesmaximal, complemented
2C3×#2856C211yesmaximal, characteristic, complemented
3#83188C211yesmaximal, characteristic, complemented
4#83173C211yesmaximal, characteristic, complemented
5#82716C214yesmaximal, complemented
6#82678C212yesmaximal, complemented
7#82667C212yesmaximal, complemented
8#82641C212yesmaximal, complemented
9C4×#930C211yesmaximal, characteristic, complemented
10#82062C211yesmaximal, characteristic, complemented
11#76441C212yesmaximal, complemented
12#76390C214yesmaximal, complemented
13#76335C212yesmaximal, complemented
14#76325C212yesmaximal, complemented
15#76318C212yesmaximal, complemented
16#74360C211yesmaximal, characteristic, complemented
17#74336C211yesmaximal, characteristic, complemented
18#39352—31nomaximal, Sylow
19C2×C3×#127C2211yescharacteristic
20C2×C3×#121C2212yes—
21C2×C3×#121C2212yes—
22C2×C3×#121C2212yes—
23C22×C3×C42C2211yescharacteristic
24C2×#940C2212yes—
25C2×#939C2214yes—
26C2×#938C2214yes—
27C2×#938C2212yes—
28C2×#938C2212yes—
29C2×D4×Dic3C2212yes—
30C2×D4×Dic3C2212yes—
31C2×#930C2211yescharacteristic
32C2×C4×#67C2212yes—
33C2×#926C2212yes—
34#5619—216no—
35C2×#893C2212yes—
36C2×D3×C4⋊C4C2212yes—
37C2×#890C2212yes—
38C2×#886C2214yes—
39C2×#883C2214yes—
40C2×#883C2214yes—
41C2×C4×D12C2211yescharacteristic
42C3×#390C2212yes—
43C3×#390C2212yes—
44C3×#390C2212yes—
45C3×#384C2211yescharacteristic
46#5223C2214yes—
47#5222C2214yes—
48#5222C2214yes—
49#5221C2212yes—
50#5221C2212yes—
51#5221C2212yes—
52#5220C2214yes—
53#5213C2212yes—
54#5212C2212yes—
55#5212C2211yescharacteristic
56#5212C2211yescharacteristic
57#5212C2211yescharacteristic
58#4989C2214yes—
59#4987C2212yes—
60#4984C2212yes—
61#4982C2214yes—
62#4975C2212yes—
63#4972C2212yes—
64#4972C2212yes—
65#4961C2214yes—
66#4959C2214yes—
67#4956C2214yes—
68#4953C2214yes—
69#4950C2214yes—
70#4949C2214yes—
71#4949C2214yes—
72#4948C2214yes—
73#4942C2214yes—
74#4940C2212yes—
75#4939C2211yescharacteristic
76C4×(C2×D3)⋊C4C2212yes—
77#4936C2212yes—
78#4935C2211yescharacteristic
79#4935C2211yescharacteristic
80C4×C4⋊Dic3C2212yes—
81C4×C4⋊Dic3C2211yescharacteristic
82C4×C4⋊Dic3C2211yescharacteristic
83C4×C4⋊Dic3C2211yescharacteristic
84#4928C2211yescharacteristic
85C2×#540—32no—
86#2856D311yescharacteristic, complemented
87#2706—34no—
88#2671—34no—
89#2624—32no—
90#2552—31no—
91#2541—31no—
92#2537—32no—
93#2501—32no—
94#2454—32no—
95#2445—32no—
96#2422—32no—
97#2416—32no—
98#2366—31no—
99D4×C4⋊C4—31no—
100C4×#121—31no—
101#2285—31no—
102C22×C3×D4C2312yes—
103C22×C3×D4C2312yes—
104C22×C3×D4C2312yes—
105C22×C3×D4C2314yes—
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C22×#67C2314yes—
110C22×#67C2314yes—
111C22×#67C2312yes—
112C23×Dic3C2314yes—
113C22×D12C2311yescharacteristic
114C22×C4×D3C2312yes—
115C22×C4×D3C2314yes—
116C3×#127—24no—
117C3×#121—28no—
118C3×#121—44no—
119C3×#121—44no—
120C2×C3×C4⋊C4C2312yes—
121C2×C3×C4⋊C4C2312yes—
122C2×C3×C4⋊C4C2312yes—
123C2×C3×C22⋊C4C2314yes—
124C2×C3×C22⋊C4C2314yes—
125C2×C3×C22⋊C4C2314yes—
126C2×C3×C42—24no—
127C2×C3×C42C2311yescharacteristic
128C2×C3×C42C2311yescharacteristic
129C2×C3×C42C2311yescharacteristic
130C2×C3×C42C2311yescharacteristic
131C2×#217C2314yes—
132C2×#217C2312yes—
133C2×#217C2312yes—
134C2×#217C2314yes—
135C2×#217C2314yes—
136C2×#217C2314yes—
137C2×#217C2314yes—
138C2×#217C2312yes—
139#940—28no—
140#939—216no—
141#938—216no—
142#938—44no—
143#938—44no—
144D4×Dic3—28no—
145D4×Dic3—44no—
146#930D418yescomplemented
147C4×#67—44no—
148C2×(C2×D3)⋊C4C2312yes—
149C2×(C2×D3)⋊C4C2312yes—
150C2×(C2×D3)⋊C4C2314yes—
151C2×(C2×D3)⋊C4C2312yes—
152C2×(C2×D3)⋊C4C2312yes—
153#926—28no—
154C2×C4⋊Dic3C2311yescharacteristic
155C2×C4⋊Dic3C2312yes—
156C2×C4⋊Dic3C2311yescharacteristic
157C2×C4⋊Dic3C2311yescharacteristic
158C2×C4⋊Dic3C2311yescharacteristic
159C2×C4⋊Dic3C2311yescharacteristic
160C2×C4⋊Dic3C2311yescharacteristic
161C2×C4⋊Dic3C2312yes—
162C2×C4⋊Dic3C2312yes—
163C2×C4⋊Dic3C2314yes—
164C2×C4⋊Dic3C2312yes—
165C2×C4⋊Dic3C2311yescharacteristic
166C2×Dic3⋊C4C2314yes—
167C2×Dic3⋊C4C2312yes—
168C2×Dic3⋊C4C2314yes—
169C2×Dic3⋊C4C2314yes—
170C2×C4×Dic3C2312yes—
171C2×C4×Dic3C2312yes—
172C2×C4×Dic3C2312yes—
173#893—28no—
174D3×C4⋊C4—44no—
175#890—28no—
176#886—216no—
177#883—216no—
178#883—48no—
179C4×D12—24no—
180C3⋊#95C2312yes—
181C3⋊#95C2312yes—
182C3⋊#95C2312yes—
183C3⋊#95C2312yes—
184C3⋊#95C2312yes—
185C3⋊#95C2312yes—
186C3⋊#95C2312yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189#540—616no—
190C2×#127—32no—
191C2×#127C2×D311yescharacteristic
192C2×#125—32no—
193C2×#123—34no—
194C2×#123—34no—
195C2×#123—34no—
196C2×#121—31no—
197C2×#121—34no—
198C2×#121—34no—
199C2×#121—32no—
200C2×#121—32no—
201C2×#121C2×D312yes—
202C2×#121C2×D312yes—
203C2×#121C2×D312yes—
204C2×C4×D4—32no—
205C2×C4×D4—32no—
206C2×C4×D4—32no—
207C2×C4×D4—32no—
208C2×C4×D4—31no—
209C2×#117—32no—
210C22×C4⋊C4—32no—
211C22×C42C2×D311yescharacteristic
212#399—34no—
213#399—34no—
214#398—34no—
215#397—34no—
216#396—34no—
217#394—34no—
218#394—34no—
219#394—34no—
220#394—34no—
221#392—34no—
222#390—32no—
223#390—32no—
224#390—32no—
225#390—31no—
226#390C2×D312yes—
227#390C2×D312yes—
228#390C2×D312yes—
229#389—32no—
230#389—32no—
231#389—32no—
232#389—31no—
233#388—32no—
234#386—34no—
235#386—32no—
236#386—34no—
237#385—34no—
238#385—34no—
239#384—32no—
240#384—31no—
241#384—31no—
242#384C2×D311yescharacteristic
243#382—32no—
244#380—31no—
245#380—32no—
246#380—31no—
247#380—31no—
248#380—32no—
249#380—34no—
250C4×C4⋊C4—31no—
251C4×C4⋊C4—31no—
252C4×C4⋊C4—32no—
253C4×C4⋊C4—31no—
254C4×C22⋊C4—32no—
255C24×C3C2414yes—
256C24×C3C2411yescharacteristic
257C23×D3C2412yes—
258C2×C3×D4—28no—
259C2×C3×D4—24no—
260C2×C3×D4—24no—
261C2×C3×D4—24no—
262C2×C3×D4—24no—
263C2×C3×D4—24no—
264C2×C3×D4—24no—
265C2×C3×D4—24no—
266C2×C3×D4—42no—
267C2×C3×D4—44no—
268C2×C3×D4—44no—
269C2×C3×D4—42no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—22no—
274C22×C3×C4—22no—
275C22×C3×C4—22no—
276C22×C3×C4—22no—
277C22×C3×C4—41no—
278C22×C3×C4C2×D414yes—
279C22×C3×C4C2411yescharacteristic
280C22×C3×C4C2414yes—
281C22×C3×C4C2411yescharacteristic
282C22×C3×C4C2411yescharacteristic
283C22×C3×C4C2411yescharacteristic
284C22×C3×C4C2411yescharacteristic
285C22×C3×C4C2411yescharacteristic
286C2×#67—28no—
287C2×#67—28no—
288C2×#67—42no—
289C2×#67—42no—
290C2×#67—44no—
291C2×#67—44no—
292C2×#67—44no—
293C2×#67—44no—
294C2×#67C2×D418yes—
295C22×Dic3—28no—
296C22×Dic3—44no—
297C22×Dic3—44no—
298C22×Dic3C2412yes—
299C22×Dic3C2412yes—
300C22×Dic3C2412yes—
301C22×Dic3C2412yes—
302C22×Dic3C2412yes—
303C22×Dic3C2412yes—
304C22×Dic3C2412yes—
305C2×D12—22no—
306C2×D12—22no—
307C2×D12C2×D414yes—
308C2×C4×D3—24no—
309C2×C4×D3—24no—
310C2×C4×D3—24no—
311C2×C4×D3—28no—
312C2×C4×D3—44no—
313C2×C4×D3—44no—
314C3×C4⋊C4—24no—
315C3×C4⋊C4—24no—
316C3×C4⋊C4—42no—
317C3×C22⋊C4—28no—
318C3×C22⋊C4—28no—
319C3×C22⋊C4—44no—
320C3×C42—22no—
321C3×C42—22no—
322C3×C42—22no—
323C3×C42#4114yes—
324#217—24no—
325#217—24no—
326#217—28no—
327#217—44no—
328#217—42no—
329#217—44no—
330#217—44no—
331#217—44no—
332(C2×D3)⋊C4—28no—
333(C2×D3)⋊C4—24no—
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—42no—
336(C2×D3)⋊C4C2×D418yes—
337C4⋊Dic3—24no—
338C4⋊Dic3—24no—
339C4⋊Dic3—22no—
340C4⋊Dic3—24no—
341C4⋊Dic3—22no—
342C4⋊Dic3—22no—
343C4⋊Dic3—22no—
344C4⋊Dic3—22no—
345C4⋊Dic3—22no—
346C4⋊Dic3—28no—
347C4⋊Dic3—42no—
348C4⋊Dic3C2×D414yes—
349Dic3⋊C4—28no—
350Dic3⋊C4—44no—
351Dic3⋊C4—44no—
352Dic3⋊C4—42no—
353C4×Dic3—24no—
354C4×Dic3—24no—
355C4×Dic3—24no—
356C22×D4—32no—
357C22×D4—34no—
358C22×D4—34no—
359C22×D4—31no—
360C22×D4C22×D312yes—
361C22×D4C22×D312yes—
362C22×D4C22×D314yes—
363C22×D4C22×D312yes—
364C23×C4—34no—
365C23×C4—32no—
366C23×C4—34no—
367C23×C4C22×D311yescharacteristic
368C23×C4C22×D311yescharacteristic
369C23×C4C22×D311yescharacteristic
370#127—24no—
371#127—68no—
372#125—68no—
373#123—616no—
374#123—616no—
375#123—128no—
376#121—28no—
377#121—38no—
378#121—44no—
379#121—44no—
380#121—616no—
381#121—616no—
382#121—124no—
383#121—124no—
384C4×D4—68no—
385C4×D4—68no—
386C4×D4—64no—
387C4×D4—124no—
388C4×D4—124no—
389#117—68no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—32no—
393C2×C4⋊C4—32no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—34no—
399C2×C4⋊C4—34no—
400C2×C4⋊C4—32no—
401C2×C4⋊C4—31no—
402C2×C4⋊C4—34no—
403C2×C4⋊C4—32no—
404C2×C4⋊C4—34no—
405C2×C4⋊C4—32no—
406C2×C4⋊C4—124no—
407C2×C4⋊C4C22×D312yes—
408C2×C4⋊C4C22×D312yes—
409C2×C4⋊C4C22×D312yes—
410C2×C22⋊C4—32no—
411C2×C22⋊C4—32no—
412C2×C22⋊C4—32no—
413C2×C22⋊C4—34no—
414C2×C22⋊C4—34no—
415C2×C22⋊C4—32no—
416C2×C22⋊C4—32no—
417C2×C22⋊C4—32no—
418C2×C22⋊C4—34no—
419C2×C22⋊C4—34no—
420C2×C22⋊C4—34no—
421C2×C22⋊C4—34no—
422C2×C22⋊C4—32no—
423C2×C22⋊C4C22×D314yes—
424C2×C22⋊C4C22×D314yes—
425C2×C22⋊C4C22×D314yes—
426C2×C42—24no—
427C2×C42—32no—
428C2×C42—32no—
429C2×C42—32no—
430C2×C42C22×D311yescharacteristic
431C2×C42C22×D311yescharacteristic
432C2×C42C22×D311yescharacteristic
433C2×C42C22×D311yescharacteristic
434#95—32no—
435#95—32no—
436#95—32no—
437#95—32no—
438#95—32no—
439#95—32no—
440#95—32no—
441#95—34no—
442#95—34no—
443C23×C3—21no—
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—24no—
450C23×C3—24no—
451C23×C3—24no—
452C23×C3—24no—
453C23×C3—24no—
454C23×C3—24no—
455C23×C3—24no—
456C23×C3C22×D412yes—
457C23×C3C2511yescharacteristic
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3C22×D414yes—
465C3×D4—48no—
466C3×D4—48no—
467C3×D4—84no—
468C3×D4—88no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—28no—
476C2×C3×C4—24no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—24no—
480C2×C3×C4—24no—
481C2×C3×C4—21no—
482C2×C3×C4—44no—
483C2×C3×C4—44no—
484C2×C3×C4C22×D412yes—
485C2×C3×C4C22×D412yes—
486C2×C3×C4C2×#4112yes—
487C2×C3×C4C2×#4112yes—
488C2×C3×C4C2×#4112yes—
489C2×C3×C4H(5,𝔽2)12yes—
490C2×C3×C4H(5,𝔽2)12yes—
491C2×C3×C4H(5,𝔽2)12yes—
492C2×C3×C42−1+412yes—
493#67—48no—
494#67—88no—
495#67—88no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3—22no—
516C2×Dic3—88no—
517C2×Dic3C22×D414yes—
518D12—28no—
519C4×D3—48no—
520C4×D3—88no—
521C24—32no—
522C24C23×D314yes—
523C24C23×D311yescharacteristic
524C2×D4—28no—
525C2×D4—24no—
526C2×D4—24no—
527C2×D4—24no—
528C2×D4—24no—
529C2×D4—24no—
530C2×D4—24no—
531C2×D4—24no—
532C2×D4—38no—
533C2×D4—34no—
534C2×D4—42no—
535C2×D4—44no—
536C2×D4—44no—
537C2×D4—42no—
538C2×D4—68no—
539C2×D4—68no—
540C2×D4—62no—
541C2×D4—62no—
542C2×D4—122no—
543C2×D4—122no—
544C2×D4—124no—
545C2×D4—124no—
546C2×D4—124no—
547C2×D4—124no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—32no—
556C22×C4—32no—
557C22×C4—32no—
558C22×C4—32no—
559C22×C4—32no—
560C22×C4—32no—
561C22×C4—32no—
562C22×C4—41no—
563C22×C4—68no—
564C22×C4—68no—
565C22×C4—64no—
566C22×C4—64no—
567C22×C4—64no—
568C22×C4—124no—
569C22×C4—124no—
570C22×C4—124no—
571C22×C4—124no—
572C22×C4D3×D414yes—
573C22×C4C23×D311yescharacteristic
574C22×C4C23×D314yes—
575C22×C4C23×D311yescharacteristic
576C22×C4C23×D311yescharacteristic
577C22×C4C23×D311yescharacteristic
578C22×C4C23×D311yescharacteristic
579C22×C4C23×D311yescharacteristic
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—34no—
583C4⋊C4—42no—
584C4⋊C4—68no—
585C4⋊C4—68no—
586C4⋊C4—64no—
587C4⋊C4—64no—
588C4⋊C4—62no—
589C4⋊C4—62no—
590C4⋊C4—62no—
591C4⋊C4—64no—
592C4⋊C4—62no—
593C4⋊C4—62no—
594C4⋊C4—62no—
595C4⋊C4—124no—
596C4⋊C4—122no—
597C4⋊C4—124no—
598C4⋊C4—122no—
599C22⋊C4—28no—
600C22⋊C4—28no—
601C22⋊C4—38no—
602C22⋊C4—44no—
603C22⋊C4—68no—
604C22⋊C4—68no—
605C22⋊C4—64no—
606C22⋊C4—64no—
607C22⋊C4—64no—
608C22⋊C4—64no—
609C22⋊C4—122no—
610C22⋊C4—122no—
611C22⋊C4—124no—
612C22⋊C4—124no—
613C22⋊C4—124no—
614C22⋊C4—124no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—64no—
619C42—64no—
620C42—64no—
621C42#23714yes—
622C22×C3—22no—
623C22×C3—22no—
624C22×C3—22no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—44no—
630C22×C3—44no—
631C22×C3—44no—
632C22×C3—44no—
633C22×C3—44no—
634C22×C3—44no—
635C22×C3—44no—
636C22×C3C23×D411yescharacteristic
637C22×C3C22×#4111yescharacteristic
638C22×C3C2×H(5,𝔽2)11yescharacteristic
639C22×C3C2×H(5,𝔽2)11yescharacteristic
640C22×C3C2×H(5,𝔽2)11yescharacteristic
641C22×C3C2×2−1+411yescharacteristic
642C22×C3#58511yescharacteristic
643C2×D3—24no—
644C2×D3—24no—
645C2×D3—24no—
646C2×D3—42no—
647C2×D3—42no—
648C2×D3—42no—
649C2×D3—42no—
650C3×C4—22no—
651C3×C4—22no—
652C3×C4—22no—
653C3×C4—41no—
654C3×C4—44no—
655C3×C4#54014yescomplemented
656C3×C4#54714yes—
657Dic3—24no—
658Dic3—42no—
659Dic3—42no—
660Dic3—42no—
661Dic3—42no—
662Dic3—42no—
663Dic3—42no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—34no—
678C23—62no—
679C23—62no—
680C23—62no—
681C23—62no—
682C23—62no—
683C23—62no—
684C23C2×D3×D412yes—
685C23C24×D311yescharacteristic
686D4—48no—
687D4—48no—
688D4—68no—
689D4—84no—
690D4—88no—
691D4—128no—
692D4—248no—
693D4—248no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—28no—
701C2×C4—24no—
702C2×C4—21no—
703C2×C4—24no—
704C2×C4—21no—
705C2×C4—24no—
706C2×C4—21no—
707C2×C4—34no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—62no—
711C2×C4—62no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—62no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—62no—
730C2×C4—128no—
731C2×C4—248no—
732C2×C4—248no—
733C2×C4C2×D3×D412yes—
734C2×C4C2×D3×D412yes—
735C2×C4C2×#23712yes—
736C2×C4C2×#23712yes—
737C2×C4C2×#23712yes—
738C2×C4#100412yes—
739C2×C4#100412yes—
740C2×C4#100912yes—
741C2×C4#101012yes—
742C2×C3—42no—
743C2×C3—84no—
744C2×C3C2×#54011yescharacteristic
745C2×C3C2×#54711yescharacteristic
746C2×C3#349411yescharacteristic
747C2×C3#349611yescharacteristic
748C2×C3#349811yescharacteristic
749C2×C3#354811yescharacteristic
750C2×C3#355411yescharacteristic
751D3—44no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—64no—
767C22—64no—
768C22—64no—
769C22—122no—
770C22—122no—
771C22—122no—
772C22—122no—
773C22C22×D3×D411yescharacteristic
774C22C22×#23711yescharacteristic
775C22C2×#100411yescharacteristic
776C22C2×#100411yescharacteristic
777C22C2×#100911yescharacteristic
778C22C2×#101011yescharacteristic
779C22#596411yescharacteristic
780C4—22no—
781C4—22no—
782C4—22no—
783C4—41no—
784C4—44no—
785C4—64no—
786C4—122no—
787C4—122no—
788C4—122no—
789C4—122no—
790C4—122no—
791C4—122no—
792C4#561114yes—
793C4#561914yescomplemented
794C3#3935211yescharacteristic, complemented, Sylow
795C2—42no—
796C2—84no—
797C2—124no—
798C2C2×#561911yescharacteristic
799C2C2×#561111yescharacteristic
800C2#8593611yescharacteristic
801C2#8619511yescharacteristic
802C2#8623211yescharacteristic
803C2#8624111yescharacteristic
804C2#8625111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2856C2
hypercenter#2856D3
hypocenterC3#39352
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2856

Complements

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

NH ≅ G/Ntype
1. C2×#5619C2semidirect
2. C3×#2856C2semidirect
3. #83188C2semidirect
4. #83173C2semidirect
5. #82716C2semidirect
6. #82678C2semidirect
7. #82667C2semidirect
8. #82641C2semidirect
9. C4×#930C2semidirect
10. #82062C2semidirect
11. #76441C2semidirect
12. #76390C2semidirect
13. #76335C2semidirect
14. #76325C2semidirect
15. #76318C2semidirect
16. #74360C2semidirect
17. #74336C2semidirect
86. #2856D3semidirect
146. #930D4semidirect
655. C3×C4#540semidirect
793. C4#5619semidirect
794. C3#39352semidirect

Maximal subgroups

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

subgroupindex
C2×#56192
C3×#28562
#831882
#831732
#827162
#826782
#826672
#826412
C4×#9302
#820622
#764412
#763902
#763352
#763252
#763182
#743602
#743362
#393523