Finite Group Databasebeta

← #11058608

Subgroups — #11058608

Order 768.

2468 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5580C211yesmaximal, characteristic, complemented
2C2×#5555C211yesmaximal, characteristic, complemented
3C3×#2538C211yesmaximal, characteristic, complemented
4#82815C212yesmaximal, complemented
5#82756C212yesmaximal, complemented
6#82479C211yesmaximal, characteristic, complemented
7C4×#938C211yesmaximal, characteristic, complemented
8#77350C214yesmaximal, complemented
9#77348C214yesmaximal, complemented
10#76435C212yesmaximal, complemented
11#76294C212yesmaximal, complemented
12#76212C212yesmaximal, complemented
13#76102C212yesmaximal, complemented
14#74376C211yesmaximal, characteristic, complemented
15#74360C211yesmaximal, characteristic, complemented
16#73933C212yesmaximal, complemented
17#73901C212yesmaximal, complemented
18#38908—31nomaximal, Sylow
19C22×#237C2212yes—
20C2×C3×C22⋊Q8C2212yes—
21C2×C3×C4×Q8C2211yescharacteristic
22C2×C3×C4×D4C2211yescharacteristic
23C2×#947C2211yescharacteristic
24C2×#946C2211yescharacteristic
25C2×#938C2211yescharacteristic
26C2×#930C2212yes—
27C2×C4×#67C2212yes—
28C22×C4⋊Dic3C2212yes—
29#5580—28no—
30#5555—28no—
31C2×#898C2212yes—
32C2×#897C2212yes—
33C2×#897C2212yes—
34C2×#895C2211yescharacteristic
35C2×#894C2212yes—
36C2×#893C2212yes—
37C2×D3×C4⋊C4C2212yes—
38C2×#890C2211yescharacteristic
39C2×#886C2214yes—
40C2×C4×D12C2212yes—
41C2×C4×D12C2211yescharacteristic
42C2×#872C2212yes—
43C2×C42×D3C2211yescharacteristic
44C2×#869C2211yescharacteristic
45C3×#396C2214yes—
46C3×#390C2212yes—
47C3×#389C2212yes—
48C3×#384C2211yescharacteristic
49C3×#380C2212yes—
50#5229C2212yes—
51#5221C2211yescharacteristic
52C4×#217C2212yes—
53#4994C2214yes—
54#4992C2214yes—
55#4989C2214yes—
56#4987C2212yes—
57#4987C2214yes—
58#4987C2212yes—
59#4987C2212yes—
60#4987C2211yescharacteristic
61#4986C2214yes—
62#4984C2212yes—
63#4984C2212yes—
64#4982C2214yes—
65#4977C2212yes—
66#4973C2212yes—
67#4972C2211yescharacteristic
68#4972C2212yes—
69#4961C2214yes—
70#4960C2214yes—
71#4958C2214yes—
72#4956C2214yes—
73#4956C2214yes—
74#4956C2212yes—
75#4950C2214yes—
76#4944C2212yes—
77#4942C2214yes—
78#4942C2214yes—
79C4×C4⋊Dic3C2211yescharacteristic
80#4929C2212yes—
81#4929C2212yes—
82#4675C2214yes—
83#4665C2214yes—
84#4661C2214yes—
85#4660C2214yes—
86C2×#547—31no—
87C2×#529—31no—
88#2857—31no—
89#2695—34no—
90#2693—34no—
91#2625—32no—
92#2568—31no—
93#2538D311yescharacteristic, complemented
94#2535—32no—
95#2442—32no—
96#2427—32no—
97#2417—32no—
98#2417—32no—
99#2407—32no—
100D4×C4⋊C4—31no—
101#2311—32no—
102C4×#121—31no—
103C22×C3×Q8C2311yescharacteristic
104C22×C3×D4C2311yescharacteristic
105C23×C3×C4C2312yes—
106C22×#67C2314yes—
107C22×#67C2312yes—
108C23×Dic3C2314yes—
109C2×#237—28no—
110C2×#237—28no—
111C2×#237—44no—
112C22×D12C2312yes—
113C22×D12C2311yescharacteristic
114C22×C4×D3C2311yescharacteristic
115C22×C4×D3C2311yescharacteristic
116C22×C4×D3C2311yescharacteristic
117C22×C4×D3C2312yes—
118C22×C4×D3C2314yes—
119C22×Dic6C2312yes—
120C3×C22⋊Q8—44no—
121C3×C4×Q8—24no—
122C3×C4×D4—24no—
123C2×C3×C4⋊C4C2312yes—
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2312yes—
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2312yes—
128C2×C3×C4⋊C4C2314yes—
129C2×C3×C4⋊C4C2312yes—
130C2×C3×C22⋊C4C2312yes—
131C2×C3×C22⋊C4C2314yes—
132C2×C3×C22⋊C4C2314yes—
133C2×C3×C42C2312yes—
134C2×C3×C42C2311yescharacteristic
135C2×#217C2312yes—
136C2×#217C2312yes—
137C2×#217C2312yes—
138#947—24no—
139#946—24no—
140#938—24no—
141#930—28no—
142C4×#67—44no—
143C2×(C2×D3)⋊C4C2314yes—
144C2×(C2×D3)⋊C4C2312yes—
145C2×(C2×D3)⋊C4C2312yes—
146C2×(C2×D3)⋊C4C2312yes—
147C2×(C2×D3)⋊C4C2312yes—
148C2×(C2×D3)⋊C4C2312yes—
149C2×(C2×D3)⋊C4C2314yes—
150C2×(C2×D3)⋊C4C2314yes—
151C2×(C2×D3)⋊C4C2312yes—
152C2×C4⋊Dic3—28no—
153C2×C4⋊Dic3C2314yes—
154C2×C4⋊Dic3C2312yes—
155C2×C4⋊Dic3C2311yescharacteristic
156C2×C4⋊Dic3C2311yescharacteristic
157C2×C4⋊Dic3C2312yes—
158C2×C4⋊Dic3C2312yes—
159C2×C4⋊Dic3C2314yes—
160C2×C4⋊Dic3C2311yescharacteristic
161C2×Dic3⋊C4C2312yes—
162C2×Dic3⋊C4C2312yes—
163C2×Dic3⋊C4C2314yes—
164C2×Dic3⋊C4C2312yes—
165C2×C4×Dic3C2312yes—
166C2×C4×Dic3C2311yescharacteristic
167C2×C4×Dic3C2311yescharacteristic
168C2×C4×Dic3C2311yescharacteristic
169#898—28no—
170#897—28no—
171#897—44no—
172#895—24no—
173#894—28no—
174#893—44no—
175D3×C4⋊C4—44no—
176#890—24no—
177#886—216no—
178C4×D12—28no—
179C4×D12D418yescomplemented
180#872—28no—
181C42×D3—24no—
182#869—24no—
183C3×#95C2314yes—
184C3⋊#95C2312yes—
185C3⋊#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2312yes—
189C3⋊#95C2314yes—
190C3⋊#95C2314yes—
191C3⋊#95C2314yes—
192C3⋊#95C2314yes—
193C3⋊#95C2312yes—
194C22×#41—32no—
195#547—68no—
196C2×C4⋊Q8—31no—
197#529—68no—
198C2×#126—32no—
199C2×#125—31no—
200C2×#124—31no—
201C2×#123—32no—
202C2×#123—34no—
203C2×C22⋊Q8—31no—
204C2×C22⋊Q8—32no—
205C2×C22⋊Q8—32no—
206C2×C22⋊Q8C2×D312yes—
207C2×#121—31no—
208C2×#121—32no—
209C2×#121—31no—
210C2×C4×Q8C2×D311yescharacteristic
211C2×C4×D4—32no—
212C2×C4×D4—32no—
213C2×C4×D4—31no—
214C2×C4×D4—32no—
215C2×C4×D4C2×D311yescharacteristic
216C2×#117—32no—
217C22×C4⋊C4—32no—
218C22×C4⋊C4—32no—
219C22×C42—31no—
220#400—34no—
221#400—34no—
222#398—34no—
223#398—34no—
224#397—34no—
225#397—34no—
226#396—34no—
227#396C2×D314yes—
228#394—34no—
229#392—34no—
230#391—32no—
231#391—32no—
232#391—32no—
233#391—32no—
234#390—31no—
235#390C2×D312yes—
236#389—32no—
237#389—32no—
238#389—32no—
239#389—31no—
240#389C2×D312yes—
241#388—32no—
242#386—34no—
243#386—34no—
244#386—32no—
245#386—34no—
246#386—34no—
247#385—34no—
248#385—34no—
249#384C2×D311yescharacteristic
250#382—32no—
251#380—32no—
252#380—32no—
253#380—32no—
254#380—31no—
255#380—34no—
256#380—34no—
257#380—34no—
258#380C2×D312yes—
259C4×C4⋊C4—31no—
260C4×C22⋊C4—32no—
261C24×C3C2412yes—
262C23×D3C2412yes—
263C23×D3C2411yescharacteristic
264C2×C3×Q8—22no—
265C2×C3×Q8—22no—
266C2×C3×Q8—22no—
267C2×C3×D4—22no—
268C2×C3×D4—22no—
269C2×C3×D4#4114yes—
270C22×C3×C4—24no—
271C22×C3×C4—24no—
272C22×C3×C4—24no—
273C22×C3×C4C2412yes—
274C22×C3×C4C2412yes—
275C22×C3×C4C2414yes—
276C22×C3×C4C2412yes—
277C22×C3×C4C2411yescharacteristic
278C22×C3×C4C2411yescharacteristic
279C22×C3×C4C2411yescharacteristic
280C2×#67—24no—
281C2×#67—28no—
282C2×#67—28no—
283C2×#67—24no—
284C2×#67—42no—
285C2×#67—44no—
286C22×Dic3—28no—
287C22×Dic3—28no—
288C22×Dic3—44no—
289C22×Dic3C2412yes—
290C22×Dic3C2411yescharacteristic
291C22×Dic3C2412yes—
292C22×Dic3C2414yes—
293C22×Dic3C2411yescharacteristic
294C22×Dic3C2411yescharacteristic
295C22×Dic3C2412yes—
296#237—432no—
297C2×D12—22no—
298C2×D12—22no—
299C2×D12—24no—
300C2×D12—24no—
301C2×D12—42no—
302C2×D12C2×D414yes—
303C2×C4×D3—24no—
304C2×C4×D3—24no—
305C2×C4×D3—22no—
306C2×C4×D3—22no—
307C2×C4×D3—22no—
308C2×C4×D3—22no—
309C2×C4×D3—22no—
310C2×C4×D3—22no—
311C2×C4×D3—22no—
312C2×C4×D3—22no—
313C2×C4×D3—41no—
314C2×C4×D3—44no—
315C2×C4×D3—44no—
316C2×C4×D3—44no—
317C2×C4×D3C2×D418yes—
318C2×Dic6—24no—
319C2×Dic6—24no—
320C2×Dic6—24no—
321C3×C4⋊C4—22no—
322C3×C4⋊C4—24no—
323C3×C4⋊C4—22no—
324C3×C4⋊C4—24no—
325C3×C4⋊C4—24no—
326C3×C4⋊C4—42no—
327C3×C4⋊C4—44no—
328C3×C22⋊C4—24no—
329C3×C22⋊C4—44no—
330C3×C22⋊C4—44no—
331C3×C42—24no—
332C3×C42C2×D414yes—
333#217—24no—
334#217—42no—
335#217—42no—
336(C2×D3)⋊C4—24no—
337(C2×D3)⋊C4—24no—
338(C2×D3)⋊C4—24no—
339(C2×D3)⋊C4—28no—
340(C2×D3)⋊C4—24no—
341(C2×D3)⋊C4—44no—
342(C2×D3)⋊C4—44no—
343(C2×D3)⋊C4—42no—
344(C2×D3)⋊C4C2×D418yes—
345C4⋊Dic3—24no—
346C4⋊Dic3—24no—
347C4⋊Dic3—22no—
348C4⋊Dic3—22no—
349C4⋊Dic3—24no—
350C4⋊Dic3—28no—
351C4⋊Dic3—44no—
352C4⋊Dic3C2×D414yes—
353Dic3⋊C4—24no—
354Dic3⋊C4—24no—
355Dic3⋊C4—44no—
356Dic3⋊C4—42no—
357C4×Dic3—22no—
358C4×Dic3—22no—
359C4×Dic3—22no—
360C4×Dic3—24no—
361C2×#41—68no—
362C2×#41—68no—
363C2×#41—124no—
364C22×Q8—32no—
365C22×Q8C22×D311yescharacteristic
366C22×D4—32no—
367C22×D4—34no—
368C22×D4—31no—
369C22×D4—32no—
370C22×D4C22×D311yescharacteristic
371C23×C4—32no—
372C23×C4—34no—
373C23×C4—31no—
374C23×C4—31no—
375C23×C4—31no—
376C23×C4—34no—
377C23×C4C22×D312yes—
378C4⋊Q8—64no—
379#126—68no—
380#125—64no—
381#124—64no—
382#123—616no—
383#123—68no—
384C22⋊Q8—44no—
385C22⋊Q8—68no—
386C22⋊Q8—64no—
387C22⋊Q8—124no—
388#121—64no—
389#121—68no—
390#121—64no—
391C4×Q8—24no—
392C4×D4—24no—
393C4×D4—38no—
394C4×D4—68no—
395C4×D4—124no—
396C4×D4—124no—
397#117—68no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—31no—
400C2×C4⋊C4—32no—
401C2×C4⋊C4—34no—
402C2×C4⋊C4—32no—
403C2×C4⋊C4—32no—
404C2×C4⋊C4—32no—
405C2×C4⋊C4—31no—
406C2×C4⋊C4—32no—
407C2×C4⋊C4—34no—
408C2×C4⋊C4—32no—
409C2×C4⋊C4—34no—
410C2×C4⋊C4—68no—
411C2×C4⋊C4—124no—
412C2×C4⋊C4C22×D312yes—
413C2×C4⋊C4C22×D312yes—
414C2×C4⋊C4C22×D311yescharacteristic
415C2×C4⋊C4C22×D311yescharacteristic
416C2×C4⋊C4C22×D312yes—
417C2×C4⋊C4C22×D314yes—
418C2×C4⋊C4C22×D312yes—
419C2×C22⋊C4—32no—
420C2×C22⋊C4—32no—
421C2×C22⋊C4—32no—
422C2×C22⋊C4—32no—
423C2×C22⋊C4—32no—
424C2×C22⋊C4—32no—
425C2×C22⋊C4—34no—
426C2×C22⋊C4—32no—
427C2×C22⋊C4—32no—
428C2×C22⋊C4—34no—
429C2×C22⋊C4—32no—
430C2×C22⋊C4—34no—
431C2×C22⋊C4C22×D312yes—
432C2×C22⋊C4C22×D314yes—
433C2×C22⋊C4C22×D314yes—
434C2×C42—31no—
435C2×C42—32no—
436C2×C42—31no—
437C2×C42—31no—
438C2×C42—64no—
439C2×C42C22×D312yes—
440C2×C42C22×D311yescharacteristic
441#95—32no—
442#95—32no—
443#95—32no—
444#95—34no—
445#95—34no—
446#95—34no—
447#95—34no—
448#95—34no—
449#95—34no—
450#95—34no—
451#95C22×D314yes—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3C2×#4114yes—
459C23×C3C2511yescharacteristic
460C22×D3—21no—
461C22×D3—22no—
462C22×D3—21no—
463C22×D3—21no—
464C22×D3—21no—
465C22×D3—22no—
466C22×D3—22no—
467C22×D3—21no—
468C22×D3—22no—
469C22×D3—22no—
470C22×D3—22no—
471C22×D3—21no—
472C22×D3C22×D414yes—
473C22×D32−1+412yes—
474C3×Q8—44no—
475C3×D4—28no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—24no—
482C2×C3×C4—22no—
483C2×C3×C4—24no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—24no—
490C2×C3×C4—48no—
491C2×C3×C4C22×D412yes—
492C2×C3×C4C22×D412yes—
493C2×C3×C4C22×D412yes—
494C2×C3×C4C2×#4112yes—
495C2×C3×C4H(5,𝔽2)12yes—
496C2×C3×C4H(5,𝔽2)12yes—
497C2×C3×C42−1+412yes—
498#67—416no—
499#67—48no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—24no—
506C2×Dic3—22no—
507C2×Dic3—21no—
508C2×Dic3—24no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—24no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—22no—
518C2×Dic3—21no—
519C2×Dic3—22no—
520C2×Dic3—416no—
521C2×Dic3C22×D414yes—
522D12—28no—
523D12—48no—
524C4×D3—216no—
525C4×D3—44no—
526C4×D3—44no—
527C4×D3—44no—
528C4×D3—88no—
529Dic6—48no—
530C24—32no—
531C24—31no—
532C24C23×D312yes—
533#41—1232no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—64no—
538C2×Q8—64no—
539C2×Q8—64no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—34no—
543C2×D4—64no—
544C2×D4—64no—
545C2×D4—68no—
546C2×D4—64no—
547C2×D4—64no—
548C2×D4—68no—
549C2×D4—62no—
550C2×D4—62no—
551C2×D4—122no—
552C2×D4—122no—
553C2×D4—124no—
554C2×D4#23914yes—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—32no—
559C22×C4—38no—
560C22×C4—32no—
561C22×C4—31no—
562C22×C4—32no—
563C22×C4—34no—
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—62no—
567C22×C4—68no—
568C22×C4—64no—
569C22×C4—64no—
570C22×C4—68no—
571C22×C4—62no—
572C22×C4—62no—
573C22×C4—62no—
574C22×C4—62no—
575C22×C4—62no—
576C22×C4—62no—
577C22×C4—62no—
578C22×C4—121no—
579C22×C4—124no—
580C22×C4—124no—
581C22×C4—124no—
582C22×C4—124no—
583C22×C4C23×D312yes—
584C22×C4C23×D312yes—
585C22×C4C23×D314yes—
586C22×C4C23×D312yes—
587C22×C4C23×D311yescharacteristic
588C22×C4C23×D311yescharacteristic
589C22×C4C23×D311yescharacteristic
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—34no—
596C4⋊C4—44no—
597C4⋊C4—42no—
598C4⋊C4—68no—
599C4⋊C4—64no—
600C4⋊C4—64no—
601C4⋊C4—64no—
602C4⋊C4—64no—
603C4⋊C4—64no—
604C4⋊C4—62no—
605C4⋊C4—62no—
606C4⋊C4—124no—
607C4⋊C4—122no—
608C4⋊C4—124no—
609C22⋊C4—24no—
610C22⋊C4—38no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—64no—
614C22⋊C4—64no—
615C22⋊C4—64no—
616C22⋊C4—64no—
617C22⋊C4—68no—
618C22⋊C4—64no—
619C22⋊C4—124no—
620C22⋊C4—122no—
621C22⋊C4—124no—
622C22⋊C4—122no—
623C22⋊C4—122no—
624C42—24no—
625C42—62no—
626C42—62no—
627C42—62no—
628C42—64no—
629C42D3×D414yes—
630C22×C3—24no—
631C22×C3—24no—
632C22×C3—24no—
633C22×C3—42no—
634C22×C3—42no—
635C22×C3—42no—
636C22×C3—42no—
637C22×C3C23×D411yescharacteristic
638C22×C3C22×#4111yescharacteristic
639C22×C3C2×H(5,𝔽2)11yescharacteristic
640C22×C3C2×H(5,𝔽2)11yescharacteristic
641C22×C3C2×2−1+411yescharacteristic
642C22×C3C2×2−1+411yescharacteristic
643C22×C3#58511yescharacteristic
644C2×D3—24no—
645C2×D3—24no—
646C2×D3—22no—
647C2×D3—24no—
648C2×D3—22no—
649C2×D3—22no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—42no—
654C2×D3—42no—
655C2×D3—42no—
656C2×D3—41no—
657C2×D3—42no—
658C3×C4—22no—
659C3×C4—42no—
660C3×C4—42no—
661C3×C4—42no—
662C3×C4—44no—
663C3×C4#53714yes—
664C3×C4#54614yes—
665Dic3—24no—
666Dic3—41no—
667Dic3—44no—
668Dic3—41no—
669Dic3—41no—
670Dic3—42no—
671Dic3—42no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—34no—
679C23—32no—
680C23—61no—
681C23—61no—
682C23—62no—
683C23—62no—
684C23—61no—
685C23—61no—
686C23—62no—
687C23—61no—
688C23—62no—
689C23—62no—
690C23—61no—
691C23—62no—
692C23C2×#23914yes—
693C23C24×D311yescharacteristic
694Q8—44no—
695Q8—128no—
696D4—28no—
697D4—68no—
698D4—128no—
699D4—1216no—
700D4—128no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—34no—
716C2×C4—48no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—616no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—64no—
724C2×C4—62no—
725C2×C4—62no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—62no—
729C2×C4—64no—
730C2×C4—64no—
731C2×C4—62no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—62no—
736C2×C4—61no—
737C2×C4—62no—
738C2×C4—124no—
739C2×C4—1216no—
740C2×C4—124no—
741C2×C4—124no—
742C2×C4—248no—
743C2×C4C2×D3×D412yes—
744C2×C4C2×D3×D412yes—
745C2×C4C2×D3×D412yes—
746C2×C4#100412yes—
747C2×C4C2×#23912yes—
748C2×C4#100912yes—
749C2×C4#101012yes—
750C2×C3—44no—
751C2×C3C2×#53711yescharacteristic
752C2×C3C2×#54611yescharacteristic
753C2×C3#348911yescharacteristic
754C2×C3#351511yescharacteristic
755C2×C3#352011yescharacteristic
756C2×C3#354611yescharacteristic
757C2×C3#355211yescharacteristic
758D3—44no—
759D3—42no—
760C22—24no—
761C22—24no—
762C22—24no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—62no—
768C22—64no—
769C22—64no—
770C22—64no—
771C22—62no—
772C22—62no—
773C22—122no—
774C22—121no—
775C22—121no—
776C22—122no—
777C22—121no—
778C22—121no—
779C22—122no—
780C22—122no—
781C22C22×D3×D411yescharacteristic
782C22C2×#100411yescharacteristic
783C22C22×#23911yescharacteristic
784C22C2×#100911yescharacteristic
785C22C2×#101011yescharacteristic
786C22#596611yescharacteristic
787C22D3×2−1+411yescharacteristic
788C4—22no—
789C4—44no—
790C4—42no—
791C4—42no—
792C4—42no—
793C4—64no—
794C4—122no—
795C4—121no—
796C4—121no—
797C4—124no—
798C4—121no—
799C4—122no—
800C4#560814yes—
801C4#563014yes—
802C3#3890811yescharacteristic, complemented, Sylow
803C2—44no—
804C2—122no—
805C2—124no—
806C2C2×#560811yescharacteristic
807C2C2×#563011yescharacteristic
808C2#8638011yescharacteristic
809C2#8675111yescharacteristic
810C2#8678811yescharacteristic
811C2#8693011yescharacteristic
812C2#8701011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2538C2
hypercenter#2538D3
hypocenterC3#38908
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2538

Complements

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

NH ≅ G/Ntype
1. C2×#5580C2semidirect
2. C2×#5555C2semidirect
3. C3×#2538C2semidirect
4. #82815C2semidirect
5. #82756C2semidirect
6. #82479C2semidirect
7. C4×#938C2semidirect
8. #77350C2semidirect
9. #77348C2semidirect
10. #76435C2semidirect
11. #76294C2semidirect
12. #76212C2semidirect
13. #76102C2semidirect
14. #74376C2semidirect
15. #74360C2semidirect
16. #73933C2semidirect
17. #73901C2semidirect
93. #2538D3semidirect
179. C4×D12D4semidirect
802. C3#38908semidirect

Maximal subgroups

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

subgroupindex
C2×#55802
C2×#55552
C3×#25382
#828152
#827562
#824792
C4×#9382
#773502
#773482
#764352
#762942
#762122
#761022
#743762
#743602
#739332
#739012
#389083