Finite Group Databasebeta

← #10968112

Subgroups — #10968112

Order 768.

2642 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5494C212yesmaximal, complemented
2C2×C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
3#84032C212yesmaximal, complemented
4#82130C212yesmaximal, complemented
5#82081C211yesmaximal, characteristic, complemented
6#82076C211yesmaximal, characteristic, complemented
7C4×#930C212yesmaximal, complemented
8#73604C214yesmaximal, complemented
9#73602C214yesmaximal, complemented
10#73585C212yesmaximal, complemented
11#73512C212yesmaximal, complemented
12#73507C212yesmaximal, complemented
13#73487C212yesmaximal, complemented
14#73379C212yesmaximal, complemented
15#73333C212yesmaximal, complemented
16#35005—31nomaximal, Sylow
17C24×C3×C4C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×C3×C42C2211yescharacteristic
21C22×C3×C42C2211yescharacteristic
22C2×#953C2214yes—
23C2×#930C2212yes—
24C2×#930C2212yes—
25C2×#930C2212yes—
26C2×#930C2212yes—
27C2×#930C2212yes—
28C2×C4×#67C2214yes—
29C2×#924C2212yes—
30#5494—216no—
31C2×#885C2214yes—
32C2×#884C2214yes—
33C2×#883C2214yes—
34C2×#879C2214yes—
35C2×#874C2211yescharacteristic, complemented
36C2×C4×D12C2212yescomplemented
37C2×#869C2211yescharacteristic, complemented
38C3×C4×C22⋊C4C2212yes—
39C3×C4×C22⋊C4C2212yes—
40C3×C4×C22⋊C4C2212yes—
41C3×C4×C22⋊C4C2212yes—
42C2×C3×#95C2211yescharacteristic
43C2×C3×#95C2211yescharacteristic
44#5213C2214yes—
45#5213C2214yes—
46#5213C2214yes—
47#5213C2214yes—
48#5212C2212yes—
49#5212C2212yes—
50#5212C2212yes—
51#5212C2212yes—
52#4961C2214yes—
53#4961C2214yes—
54#4960C2214yes—
55#4953C2214yes—
56#4940C2214yescomplemented
57#4939C2212yescomplemented
58#4939C2212yescomplemented
59#4939C2212yescomplemented
60#4939C2212yescomplemented
61C4×(C2×D3)⋊C4C2214yescomplemented
62#4935C2211yescharacteristic, complemented
63#4935C2211yescharacteristic, complemented
64C4×C4⋊Dic3C2212yescomplemented
65#4929C2212yescomplemented
66#4928C2212yescomplemented
67#4928C2212yescomplemented
68#4928C2212yescomplemented
69#4674C2214yescomplemented
70#4673C2214yescomplemented
71#4672C2214yescomplemented
72#4670C2214yescomplemented
73#4668C2214yescomplemented
74#4665C2214yescomplemented
75#4659C2214yescomplemented
76#4653C2214yescomplemented
77C2×#538—32no—
78#2857—31no—
79#2856—31no—
80#2847—32no—
81#2639—32no—
82#2617—32no—
83#2559—34no—
84#2557—34no—
85#2496—32no—
86#2491—32no—
87#2428—32no—
88#2422—32no—
89#2325—32no—
90C4×#121—32no—
91C2×C4×C22⋊C4D311yescharacteristic, complemented
92C25×C3C2311yescharacteristic
93C23×C3×C4—24no—
94C23×C3×C4—42no—
95C23×C3×C4—42no—
96C23×C3×C4C2312yes—
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2312yes—
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C2311yescharacteristic
103C23×C3×C4C2311yescharacteristic
104C22×#67C2314yes—
105C22×#67C2314yes—
106C22×#67C2314yes—
107C22×D12C2312yes—
108C22×D12C2312yes—
109C22×D12C2312yes—
110C22×C4×D3C2314yes—
111C22×Dic6C2312yes—
112C2×C3×C22⋊C4—24no—
113C2×C3×C22⋊C4D418yescomplemented
114C2×C3×C22⋊C4C2312yes—
115C2×C3×C22⋊C4C2312yes—
116C2×C3×C22⋊C4C2312yes—
117C2×C3×C22⋊C4C2312yes—
118C2×C3×C42—42no—
119C2×C3×C42—42no—
120C2×C3×C42C2311yescharacteristic
121C2×C3×C42C2312yes—
122C2×C3×C42C2311yescharacteristic
123C2×C3×C42C2311yescharacteristic
124C2×C3×C42C2311yescharacteristic
125C2×C3×C42C2312yes—
126#953—216no—
127C2×#217C2314yes—
128C2×#217C2314yes—
129C2×#217C2314yes—
130#930—28no—
131#930—28no—
132#930—28no—
133#930—44no—
134#930—44no—
135C4×#67—216no—
136C2×(C2×D3)⋊C4C2314yes—
137C2×(C2×D3)⋊C4C2314yes—
138C2×(C2×D3)⋊C4C2314yes—
139C2×(C2×D3)⋊C4C2314yes—
140C2×(C2×D3)⋊C4C2314yes—
141C2×(C2×D3)⋊C4C2314yes—
142C2×(C2×D3)⋊C4C2314yes—
143C2×(C2×D3)⋊C4C2314yes—
144C2×C4⋊Dic3C2312yes—
145C2×C4⋊Dic3C2312yes—
146C2×C4⋊Dic3C2312yes—
147C2×C4⋊Dic3C2312yes—
148C2×C4⋊Dic3C2312yes—
149C2×C4⋊Dic3C2312yes—
150C2×C4⋊Dic3C2312yes—
151C2×C4⋊Dic3C2312yes—
152#924—28no—
153C2×Dic3⋊C4C2314yes—
154C2×Dic3⋊C4C2314yes—
155C2×C4×Dic3C2314yes—
156#885—216no—
157#884—216no—
158#883—216no—
159#879—216no—
160#874—42no—
161C4×D12—44no—
162#869—42no—
163C3×#95C2312yes—
164C3×#95C2312yes—
165C3×#95C2312yes—
166C3×#95C2312yes—
167C3⋊#95C2314yes—
168C3⋊#95C2314yes—
169C3⋊#95C2314yes—
170C3⋊#95C2314yes—
171C3⋊#95C2314yes—
172C3⋊#95C2314yes—
173C24×C4C2×D311yescharacteristic
174#538—616no—
175C2×C4⋊Q8—31no—
176C2×#127—31no—
177C2×#126—34no—
178C2×#124—34no—
179C2×#123—34no—
180C2×C22⋊Q8—32no—
181C2×#121—32no—
182C2×#121—32no—
183C2×#121—32no—
184C2×#121—32no—
185C2×#121—32no—
186C2×#121—34no—
187C2×#120—34no—
188C2×C4×D4—34no—
189C2×C4×D4—32no—
190C22×C22⋊C4C2×D311yescharacteristic
191C22×C22⋊C4C2×D311yescharacteristic
192C22×C42C2×D311yescharacteristic
193C22×C42C2×D311yescharacteristic
194#400—34no—
195#397—34no—
196#397—34no—
197#394—34no—
198#394—34no—
199#394—34no—
200#393—34no—
201#392—34no—
202#391—32no—
203#390—32no—
204#390—32no—
205#390—32no—
206#390—32no—
207#389—32no—
208#389—32no—
209#389—32no—
210#388—34no—
211#388—34no—
212#387—34no—
213#386—34no—
214#386—34no—
215#386—34no—
216#386—34no—
217#386—34no—
218#385—34no—
219#384—31no—
220#384—31no—
221#380—32no—
222#380—32no—
223#380—32no—
224#380—32no—
225C4×C4⋊C4—32no—
226C4×C22⋊C4—34no—
227C4×C22⋊C4C2×D312yes—
228C4×C22⋊C4C2×D312yes—
229C4×C22⋊C4C2×D312yes—
230C4×C22⋊C4C2×D312yes—
231C2×#95C2×D311yescharacteristic
232C2×#95C2×D311yescharacteristic
233C24×C3—22no—
234C24×C3—22no—
235C24×C3—41no—
236C24×C3—41no—
237C24×C3—41no—
238C24×C3—41no—
239C24×C3C2×D414yes—
240C24×C3C2412yes—
241C24×C3C2411yescharacteristic
242C23×D3C2414yes—
243C22×C3×C4—22no—
244C22×C3×C4—22no—
245C22×C3×C4—22no—
246C22×C3×C4—22no—
247C22×C3×C4—24no—
248C22×C3×C4—24no—
249C22×C3×C4—24no—
250C22×C3×C4—24no—
251C22×C3×C4—41no—
252C22×C3×C4—41no—
253C22×C3×C4—41no—
254C22×C3×C4—41no—
255C22×C3×C4—42no—
256C22×C3×C4—42no—
257C22×C3×C4—41no—
258C22×C3×C4—41no—
259C22×C3×C4—41no—
260C22×C3×C4—41no—
261C22×C3×C4—41no—
262C22×C3×C4—41no—
263C22×C3×C4—416no—
264C22×C3×C4C2×D414yes—
265C22×C3×C4C2×D414yes—
266C22×C3×C4#4114yes—
267C22×C3×C4#4114yes—
268C22×C3×C4C2412yes—
269C22×C3×C4C2412yes—
270C22×C3×C4C2412yes—
271C22×C3×C4C2411yescharacteristic
272C22×C3×C4C2411yescharacteristic
273C22×C3×C4C2411yescharacteristic
274C22×C3×C4C2411yescharacteristic
275C22×C3×C4C2411yescharacteristic
276C22×C3×C4C2411yescharacteristic
277C2×#67—28no—
278C2×#67—28no—
279C2×#67—28no—
280C2×#67—28no—
281C2×#67—28no—
282C2×#67—44no—
283C2×#67—44no—
284C2×#67—44no—
285C2×#67—44no—
286C22×Dic3C2414yes—
287C22×Dic3C2414yes—
288C22×Dic3C2414yes—
289C2×D12—24no—
290C2×D12—24no—
291C2×D12—24no—
292C2×D12—24no—
293C2×D12—24no—
294C2×D12—42no—
295C2×D12—42no—
296C2×D12—42no—
297C2×D12—42no—
298C2×C4×D3—28no—
299C2×C4×D3—44no—
300C2×C4×D3—44no—
301C2×Dic6—24no—
302C2×Dic6—42no—
303C2×Dic6—42no—
304C3×C22⋊C4—24no—
305C3×C22⋊C4—24no—
306C3×C22⋊C4C2×D418yes—
307C3×C22⋊C4C2×D418yes—
308C3×C42—22no—
309C3×C42—24no—
310C3×C42—22no—
311C3×C42—41no—
312C3×C42—41no—
313C3×C42—42no—
314#217—28no—
315#217—28no—
316#217—28no—
317(C2×D3)⋊C4—28no—
318(C2×D3)⋊C4—28no—
319(C2×D3)⋊C4—28no—
320(C2×D3)⋊C4—28no—
321(C2×D3)⋊C4—44no—
322(C2×D3)⋊C4—44no—
323(C2×D3)⋊C4—44no—
324(C2×D3)⋊C4—44no—
325C4⋊Dic3—24no—
326C4⋊Dic3—24no—
327C4⋊Dic3—24no—
328C4⋊Dic3—24no—
329C4⋊Dic3—24no—
330C4⋊Dic3—24no—
331C4⋊Dic3—42no—
332C4⋊Dic3—42no—
333Dic3⋊C4—28no—
334Dic3⋊C4—28no—
335C4×Dic3—28no—
336C25C22×D311yescharacteristic
337C22×Q8—32no—
338C22×D4—34no—
339C22×D4—34no—
340C22×D4—34no—
341C22×D4—32no—
342C22×D4—32no—
343C22×D4—32no—
344C23×C4—24no—
345C23×C4—34no—
346C23×C4—42no—
347C23×C4—42no—
348C23×C4C22×D312yes—
349C23×C4C22×D311yescharacteristic
350C23×C4C22×D311yescharacteristic
351C23×C4C22×D311yescharacteristic
352C23×C4C22×D312yes—
353C23×C4C22×D311yescharacteristic
354C23×C4C22×D311yescharacteristic
355C23×C4C22×D311yescharacteristic
356C4⋊Q8—122no—
357#127—122no—
358#126—616no—
359#124—616no—
360#123—616no—
361C22⋊Q8—68no—
362#121—68no—
363#121—68no—
364#121—68no—
365#121—616no—
366#121—124no—
367#121—124no—
368#120—616no—
369C4×D4—616no—
370C4×D4—124no—
371C2×C4⋊C4—32no—
372C2×C4⋊C4—34no—
373C2×C4⋊C4—34no—
374C2×C4⋊C4—32no—
375C2×C4⋊C4—32no—
376C2×C4⋊C4—32no—
377C2×C4⋊C4—32no—
378C2×C4⋊C4—32no—
379C2×C4⋊C4—32no—
380C2×C4⋊C4—32no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—34no—
383C2×C22⋊C4—34no—
384C2×C22⋊C4—34no—
385C2×C22⋊C4—34no—
386C2×C22⋊C4—34no—
387C2×C22⋊C4—34no—
388C2×C22⋊C4—34no—
389C2×C22⋊C4—34no—
390C2×C22⋊C4—34no—
391C2×C22⋊C4—34no—
392C2×C22⋊C4—34no—
393C2×C22⋊C4D1218yescomplemented
394C2×C22⋊C4C22×D312yes—
395C2×C22⋊C4C22×D312yes—
396C2×C22⋊C4C22×D312yes—
397C2×C22⋊C4C22×D312yes—
398C2×C42—34no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42C22×D312yes—
402C2×C42C22×D311yescharacteristic
403C2×C42C22×D311yescharacteristic
404C2×C42C22×D312yes—
405C2×C42C22×D311yescharacteristic
406C2×C42C22×D311yescharacteristic
407#95—34no—
408#95—34no—
409#95—34no—
410#95—34no—
411#95—34no—
412#95—34no—
413#95C22×D312yes—
414#95C22×D312yes—
415#95C22×D312yes—
416#95C22×D312yes—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—28no—
422C23×C3—22no—
423C23×C3—22no—
424C23×C3—22no—
425C23×C3—22no—
426C23×C3—22no—
427C23×C3—22no—
428C23×C3—44no—
429C23×C3—44no—
430C23×C3—44no—
431C23×C3—44no—
432C23×C3—44no—
433C23×C3—44no—
434C23×C3C22×D414yes—
435C23×C3C22×D412yes—
436C23×C3C2×#4112yes—
437C23×C3C2×#4112yes—
438C23×C3C2511yescharacteristic
439C22×D3—24no—
440C22×D3—24no—
441C22×D3—24no—
442C22×D3—24no—
443C22×D3—24no—
444C22×D3—24no—
445C22×D3—24no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—22no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—22no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—28no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—44no—
466C2×C3×C4—44no—
467C2×C3×C4—44no—
468C2×C3×C4—48no—
469C2×C3×C4—44no—
470C2×C3×C4—44no—
471C2×C3×C4—48no—
472C2×C3×C4C22×D414yes—
473C2×C3×C4C22×D412yes—
474C2×C3×C4C22×D412yes—
475C2×C3×C4C2×#4112yes—
476C2×C3×C4C2×#4112yes—
477C2×C3×C4C2×#4112yes—
478C2×C3×C4C2×#4112yes—
479C2×C3×C4H(5,𝔽2)12yes—
480C2×C3×C4H(5,𝔽2)12yes—
481#67—416no—
482#67—88no—
483#67—88no—
484C2×Dic3—24no—
485C2×Dic3—24no—
486C2×Dic3—24no—
487C2×Dic3—24no—
488C2×Dic3—24no—
489C2×Dic3—24no—
490C2×Dic3—24no—
491C2×Dic3—24no—
492C2×Dic3—24no—
493D12—48no—
494D12—84no—
495D12—84no—
496C4×D3—88no—
497Dic6—84no—
498C24—22no—
499C24—22no—
500C24—34no—
501C24—41no—
502C24—41no—
503C24—41no—
504C24—41no—
505C24C2×D1214yes—
506C24C23×D312yes—
507C24C23×D311yescharacteristic
508C2×Q8—64no—
509C2×Q8—122no—
510C2×Q8—122no—
511C2×D4—68no—
512C2×D4—68no—
513C2×D4—68no—
514C2×D4—68no—
515C2×D4—68no—
516C2×D4—64no—
517C2×D4—64no—
518C2×D4—64no—
519C2×D4—64no—
520C2×D4—64no—
521C2×D4—122no—
522C2×D4—122no—
523C2×D4—122no—
524C2×D4—122no—
525C2×D4—124no—
526C2×D4—124no—
527C2×D4—124no—
528C2×D4—124no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—34no—
538C22×C4—34no—
539C22×C4—34no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—416no—
553C22×C4—68no—
554C22×C4—124no—
555C22×C4—124no—
556C22×C4C2×D1214yes—
557C22×C4C2×D1214yes—
558C22×C4#23514yes—
559C22×C4#23514yes—
560C22×C4C23×D312yes—
561C22×C4C23×D312yes—
562C22×C4C23×D312yes—
563C22×C4C23×D311yescharacteristic
564C22×C4C23×D311yescharacteristic
565C22×C4C23×D311yescharacteristic
566C22×C4C23×D311yescharacteristic
567C22×C4C23×D311yescharacteristic
568C22×C4C23×D311yescharacteristic
569C4⋊C4—68no—
570C4⋊C4—68no—
571C4⋊C4—64no—
572C4⋊C4—64no—
573C4⋊C4—64no—
574C4⋊C4—64no—
575C4⋊C4—64no—
576C4⋊C4—64no—
577C4⋊C4—122no—
578C4⋊C4—122no—
579C22⋊C4—24no—
580C22⋊C4—24no—
581C22⋊C4—68no—
582C22⋊C4—68no—
583C22⋊C4—68no—
584C22⋊C4—68no—
585C22⋊C4—68no—
586C22⋊C4—68no—
587C22⋊C4—68no—
588C22⋊C4—124no—
589C22⋊C4—124no—
590C22⋊C4—124no—
591C22⋊C4—124no—
592C22⋊C4C2×D1218yes—
593C22⋊C4C2×D1218yes—
594C42—24no—
595C42—22no—
596C42—22no—
597C42—41no—
598C42—42no—
599C42—41no—
600C42—68no—
601C22×C3—22no—
602C22×C3—22no—
603C22×C3—22no—
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—24no—
608C22×C3—24no—
609C22×C3—24no—
610C22×C3—416no—
611C22×C3—42no—
612C22×C3—42no—
613C22×C3—42no—
614C22×C3—42no—
615C22×C3#53214yes—
616C22×C3C23×D411yescharacteristic
617C22×C3C22×#4111yescharacteristic
618C22×C3C22×#4111yescharacteristic
619C22×C3C2×H(5,𝔽2)11yescharacteristic
620C22×C3C2×H(5,𝔽2)11yescharacteristic
621C22×C3#58511yescharacteristic
622C22×C3#58511yescharacteristic
623C2×D3—44no—
624C2×D3—44no—
625C2×D3—44no—
626C2×D3—44no—
627C2×D3—44no—
628C2×D3—44no—
629C2×D3—44no—
630C3×C4—22no—
631C3×C4—22no—
632C3×C4—24no—
633C3×C4—22no—
634C3×C4—22no—
635C3×C4—22no—
636C3×C4—42no—
637C3×C4—42no—
638C3×C4#53814yescomplemented
639Dic3—44no—
640Dic3—44no—
641Dic3—44no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—28no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—64no—
660C23—64no—
661C23—64no—
662C23—64no—
663C23—64no—
664C23—64no—
665C23—64no—
666C23C22×D1214yes—
667C23C22×D1212yes—
668C23C2×#23512yes—
669C23C2×#23512yes—
670C23C24×D311yescharacteristic
671Q8—244no—
672D4—1216no—
673D4—128no—
674D4—244no—
675D4—244no—
676D4—248no—
677D4—248no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—28no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—48no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—48no—
704C2×C4—64no—
705C2×C4—64no—
706C2×C4—64no—
707C2×C4—64no—
708C2×C4—64no—
709C2×C4—64no—
710C2×C4—64no—
711C2×C4—64no—
712C2×C4—64no—
713C2×C4—248no—
714C2×C4C22×D1214yes—
715C2×C4C22×D1212yes—
716C2×C4C22×D1212yes—
717C2×C4C2×#23512yes—
718C2×C4C2×#23512yes—
719C2×C4C2×#23512yes—
720C2×C4C2×#23512yes—
721C2×C4#100412yes—
722C2×C4#100412yes—
723C2×C3—24no—
724C2×C3—44no—
725C2×C3C2×#53211yescharacteristic
726C2×C3C2×#53811yescharacteristic
727C2×C3#345511yescharacteristic
728C2×C3#349611yescharacteristic
729C2×C3#349611yescharacteristic
730C2×C3#350511yescharacteristic
731C2×C3#350611yescharacteristic
732D3—84no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—24no—
740C22—24no—
741C22—24no—
742C22—416no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—124no—
748C22—124no—
749C22—124no—
750C22—124no—
751C22—124no—
752C22—124no—
753C22—124no—
754C22#547714yes—
755C22C23×D1211yescharacteristic
756C22C22×#23511yescharacteristic
757C22C22×#23511yescharacteristic
758C22C2×#100411yescharacteristic
759C22C2×#100411yescharacteristic
760C22#596411yescharacteristic
761C22#596411yescharacteristic
762C4—24no—
763C4—22no—
764C4—22no—
765C4—22no—
766C4—22no—
767C4—22no—
768C4—42no—
769C4—42no—
770C4—124no—
771C4—124no—
772C4—124no—
773C4#549414yescomplemented
774C3#3500511yescharacteristic, complemented, Sylow
775C2—24no—
776C2—44no—
777C2—244no—
778C2C2×#547711yescharacteristic
779C2C2×#549411yescharacteristic
780C2#8573811yescharacteristic
781C2#8578611yescharacteristic
782C2#8578611yescharacteristic
783C2#8578711yescharacteristic
784C2#8578811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×C4×C22⋊C4C2
hypercenterC2×C4×C22⋊C4D3
hypocenterC3#35005
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#5494C2semidirect
2. C2×C3×C4×C22⋊C4C2semidirect
3. #84032C2semidirect
4. #82130C2semidirect
5. #82081C2semidirect
6. #82076C2semidirect
7. C4×#930C2semidirect
8. #73604C2semidirect
9. #73602C2semidirect
10. #73585C2semidirect
11. #73512C2semidirect
12. #73507C2semidirect
13. #73487C2semidirect
14. #73379C2semidirect
15. #73333C2semidirect
35. C2×#874C22semidirect
36. C2×C4×D12C22semidirect
37. C2×#869C22semidirect
56. #4940C22semidirect
57. #4939C22semidirect
58. #4939C22semidirect
59. #4939C22semidirect
60. #4939C22semidirect
61. C4×(C2×D3)⋊C4C22semidirect
62. #4935C22semidirect
63. #4935C22semidirect
64. C4×C4⋊Dic3C22semidirect
65. #4929C22semidirect
66. #4928C22semidirect
67. #4928C22semidirect
68. #4928C22semidirect
69. #4674C22semidirect
70. #4673C22semidirect
71. #4672C22semidirect
72. #4670C22semidirect
73. #4668C22semidirect
74. #4665C22semidirect
75. #4659C22semidirect
76. #4653C22semidirect
91. C2×C4×C22⋊C4D3semidirect
113. C2×C3×C22⋊C4D4semidirect
393. C2×C22⋊C4D12semidirect
638. C3×C4#538semidirect
773. C4#5494semidirect
774. C3#35005semidirect

Maximal subgroups

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

subgroupindex
C2×#54942
C2×C3×C4×C22⋊C42
#840322
#821302
#820812
#820762
C4×#9302
#736042
#736022
#735852
#735122
#735072
#734872
#733792
#733332
#350053