Finite Group Databasebeta

← #10993919

Subgroups — #10993919

Order 768.

3120 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5726C211yesmaximal, characteristic, complemented
2C2×#5631C212yesmaximal, complemented
3C2×C4×#235C211yesmaximal, characteristic, complemented
4C3×#2857C211yesmaximal, characteristic, complemented
5#83239C211yesmaximal, characteristic, complemented
6#82814C212yesmaximal, complemented
7C4×#930C211yesmaximal, characteristic, complemented
8#76625C212yesmaximal, complemented
9#76613C212yesmaximal, complemented
10#76286C212yesmaximal, complemented
11#76208C214yesmaximal, complemented
12D3×#389C212yesmaximal, complemented
13#74369C211yesmaximal, characteristic, complemented
14#74360C211yesmaximal, characteristic, complemented
15#74022C214yesmaximal, complemented
16#73911C212yesmaximal, complemented
17#73887C212yesmaximal, complemented
18#36259—31nomaximal, Sylow
19C22×#239C2212yes—
20C22×#235C2211yescharacteristic
21C2×C3×C4⋊Q8C2211yescharacteristic
22C2×C3×C22⋊Q8C2212yes—
23C22×C3×C42C2211yescharacteristic
24C2×#946C2212yes—
25C2×#944C2212yes—
26C2×#930C2211yescharacteristic
27C2×C4×#67C2212yes—
28C2×C4×#67C2212yes—
29C2×C4×#67C2212yes—
30C2×#926C2211yescharacteristic
31#5726—28no—
32#5631—216no—
33C2×#897C2212yes—
34C2×#895C2212yes—
35C2×#894C2214yes—
36C2×#894C2214yes—
37C2×#893C2212yes—
38C2×D3×C4⋊C4C2212yes—
39C2×D3×C4⋊C4C2214yes—
40C2×D3×C4⋊C4C2212yes—
41C2×#884C2214yes—
42C2×#883C2214yes—
43C4×#235—28no—
44C2×C4×D12C2211yescharacteristic
45C2×C4×D12C2211yescharacteristic
46C2×C4×D12C2211yescharacteristic
47C2×#872C2212yes—
48C2×C42×D3C2212yes—
49C2×C4×Dic6C2211yescharacteristic
50C2×C4×Dic6C2211yescharacteristic
51C3×#391C2212yes—
52C3×#389C2212yes—
53C3×#389C2212yes—
54C3×#384C2211yescharacteristic
55C3×#380C2212yes—
56C3×#380C2212yes—
57#5229C2212yes—
58#5213C2212yes—
59#5212C2211yescharacteristic
60#4994C2214yes—
61#4990C2214yes—
62#4989C2214yes—
63#4988C2212yes—
64#4987C2212yes—
65#4987C2212yes—
66#4984C2212yes—
67#4983C2214yes—
68#4976C2214yes—
69#4972C2212yes—
70#4972C2212yes—
71#4972C2212yes—
72#4959C2214yes—
73#4952C2214yes—
74#4940C2212yes—
75#4939C2211yescharacteristic
76C4×(C2×D3)⋊C4C2212yes—
77C4×C4⋊Dic3C2211yescharacteristic
78#4928C2211yescharacteristic
79#4676C2214yes—
80#4669C2214yes—
81#4665C2214yes—
82#4665C2214yes—
83#4664C2214yes—
84D3×#95C2214yes—
85#4657C2214yes—
86#4647C2214yes—
87C2×#547—31no—
88C2×#547—32no—
89C2×C4×#41—31no—
90#2857D311yescharacteristic, complemented
91#2854—32no—
92#2546—31no—
93#2538—31no—
94#2486—32no—
95#2429—32no—
96#2425—34no—
97#2416—32no—
98#2415—32no—
99#2413—34no—
100D4×C4⋊C4—31no—
101#2339—32no—
102C4×#121—31no—
103C2×#389—32no—
104C22×C3×Q8C2312yes—
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C22×#67C2312yes—
109C22×#67C2312yes—
110C2×#239—28no—
111C2×#239—28no—
112C2×#239—28no—
113C2×#235—24no—
114C2×#235—24no—
115C2×#235D418yescomplemented
116C22×D12C2314yes—
117C22×D12C2311yescharacteristic
118C22×D12C2311yescharacteristic
119C22×C4×D3C2314yes—
120C22×C4×D3C2312yes—
121C22×C4×D3C2312yes—
122C22×C4×D3C2314yes—
123C22×C4×D3C2312yes—
124C22×C4×D3C2312yes—
125C22×Dic6C2311yescharacteristic
126C3×C4⋊Q8—24no—
127C3×C22⋊Q8—28no—
128C2×C3×C4⋊C4C2312yes—
129C2×C3×C4⋊C4C2312yes—
130C2×C3×C4⋊C4C2314yes—
131C2×C3×C4⋊C4C2312yes—
132C2×C3×C4⋊C4C2312yes—
133C2×C3×C4⋊C4C2312yes—
134C2×C3×C22⋊C4C2314yes—
135C2×C3×C42—24no—
136C2×C3×C42C2311yescharacteristic
137C2×C3×C42C2311yescharacteristic
138C2×C3×C42C2311yescharacteristic
139C2×C3×C42C2311yescharacteristic
140C2×#217C2312yes—
141C2×#217C2312yes—
142#946—28no—
143#944—28no—
144#930—24no—
145C4×#67—28no—
146C4×#67—28no—
147C4×#67—28no—
148C2×(C2×D3)⋊C4C2312yes—
149C2×(C2×D3)⋊C4C2314yes—
150C2×(C2×D3)⋊C4C2312yes—
151C2×(C2×D3)⋊C4C2312yes—
152C2×(C2×D3)⋊C4C2314yes—
153C2×(C2×D3)⋊C4C2314yes—
154C2×(C2×D3)⋊C4C2312yes—
155C2×(C2×D3)⋊C4C2312yes—
156C2×(C2×D3)⋊C4C2314yes—
157C2×(C2×D3)⋊C4C2312yes—
158#926—24no—
159C2×C4⋊Dic3C2314yes—
160C2×C4⋊Dic3C2311yescharacteristic
161C2×C4⋊Dic3C2311yescharacteristic
162C2×C4⋊Dic3C2311yescharacteristic
163C2×C4⋊Dic3C2311yescharacteristic
164C2×C4⋊Dic3C2311yescharacteristic
165C2×Dic3⋊C4C2314yes—
166C2×Dic3⋊C4C2314yes—
167C2×Dic3⋊C4C2314yes—
168C2×Dic3⋊C4C2312yes—
169C2×Dic3⋊C4C2314yes—
170C2×Dic3⋊C4C2312yes—
171C2×Dic3⋊C4C2312yes—
172C2×C4×Dic3C2312yes—
173C2×C4×Dic3C2312yes—
174C2×C4×Dic3C2312yes—
175C2×C4×Dic3C2312yes—
176#897—28no—
177#895—28no—
178#894—216no—
179#894—216no—
180#893—28no—
181D3×C4⋊C4—28no—
182D3×C4⋊C4—216no—
183D3×C4⋊C4—28no—
184#884—216no—
185#883—216no—
186C4×D12—24no—
187C4×D12—24no—
188C4×D12D418yescomplemented
189#872—28no—
190C42×D3—28no—
191C4×Dic6—24no—
192C4×Dic6—24no—
193C3×#95C2314yes—
194C3×#95C2314yes—
195C3⋊#95C2312yes—
196C3⋊#95C2312yes—
197C3⋊#95C2314yes—
198C3⋊#95C2314yes—
199C3⋊#95C2314yes—
200C3⋊#95C2314yes—
201C3⋊#95C2312yes—
202C22×#41—32no—
203C22×#41—31no—
204#547—68no—
205#547—616no—
206C2×C4⋊Q8—32no—
207C2×C4⋊Q8C2×D311yescharacteristic
208C2×#123—34no—
209C2×#123—34no—
210C2×#123—34no—
211C2×C22⋊Q8—32no—
212C2×C22⋊Q8—32no—
213C2×C22⋊Q8C2×D312yes—
214C2×#121—31no—
215C2×#121—32no—
216C2×#121—34no—
217C4×#41—68no—
218C2×C4×Q8—31no—
219C2×C4×Q8—31no—
220C2×C4×D4—32no—
221C2×C4×D4—32no—
222C2×C4×D4—32no—
223C2×C4×D4—32no—
224C2×C4×D4—31no—
225C2×C4×D4—31no—
226C2×C4×D4—31no—
227C2×#117—31no—
228C2×#117—32no—
229C22×C4⋊C4—32no—
230C22×C4⋊C4—34no—
231C22×C4⋊C4—32no—
232C22×C42—32no—
233C22×C42C2×D311yescharacteristic
234#398—34no—
235#398—34no—
236#397—34no—
237#396—34no—
238#396—34no—
239#394—34no—
240#391—32no—
241#391C2×D312yes—
242#390—32no—
243#390—31no—
244#389—32no—
245#389—32no—
246#389—32no—
247#389—34no—
248#389—32no—
249#389—31no—
250#389—34no—
251#389C2×D312yes—
252#389C2×D312yes—
253#388—34no—
254#388—32no—
255#388—34no—
256#386—32no—
257#386—34no—
258#386—34no—
259#385—34no—
260#384C2×D311yescharacteristic
261#381—34no—
262#380—31no—
263#380—32no—
264#380—32no—
265#380C2×D312yes—
266#380C2×D312yes—
267C4×C4⋊C4—31no—
268C4×C22⋊C4—32no—
269C2×#95—34no—
270C24×C3C2411yescharacteristic
271C23×D3C2412yes—
272C23×D3C2412yes—
273C2×C3×Q8—24no—
274C2×C3×Q8—24no—
275C2×C3×Q8—24no—
276C22×C3×C4—22no—
277C22×C3×C4—22no—
278C22×C3×C4—22no—
279C22×C3×C4—22no—
280C22×C3×C4—22no—
281C22×C3×C4—22no—
282C22×C3×C4—22no—
283C22×C3×C4—41no—
284C22×C3×C4C2×D414yes—
285C22×C3×C4C2411yescharacteristic
286C22×C3×C4C2414yes—
287C22×C3×C4C2414yes—
288C22×C3×C4C2411yescharacteristic
289C22×C3×C4C2411yescharacteristic
290C22×C3×C4C2411yescharacteristic
291C22×C3×C4C2411yescharacteristic
292C22×C3×C4C2411yescharacteristic
293C2×#67—24no—
294C2×#67—24no—
295C2×#67—24no—
296C2×#67—24no—
297C2×#67—42no—
298C2×#67C2×D418yes—
299C22×Dic3C2412yes—
300C22×Dic3C2412yes—
301C22×Dic3C2412yes—
302C22×Dic3C2412yes—
303C22×Dic3C2412yes—
304C22×Dic3C2412yes—
305#239—432no—
306#235—232no—
307C2×D12—28no—
308C2×D12—28no—
309C2×D12—28no—
310C2×D12—22no—
311C2×D12—22no—
312C2×D12—22no—
313C2×D12C2×D414yes—
314C2×D12C2×D414yes—
315C2×D12#4114yes—
316C2×C4×D3—24no—
317C2×C4×D3—24no—
318C2×C4×D3—24no—
319C2×C4×D3—24no—
320C2×C4×D3—24no—
321C2×C4×D3—28no—
322C2×C4×D3—28no—
323C2×C4×D3—28no—
324C2×C4×D3—28no—
325C2×C4×D3—24no—
326C2×C4×D3—24no—
327C2×C4×D3—24no—
328C2×C4×D3—24no—
329C2×C4×D3—28no—
330C2×C4×D3—44no—
331C2×C4×D3—42no—
332C2×C4×D3C2×D418yes—
333C2×C4×D3C2×D418yes—
334C2×Dic6—22no—
335C2×Dic6—22no—
336C2×Dic6C2×D414yes—
337C3×C4⋊C4—28no—
338C3×C4⋊C4—24no—
339C3×C4⋊C4—24no—
340C3×C4⋊C4—24no—
341C3×C4⋊C4—24no—
342C3×C4⋊C4—42no—
343C3×C22⋊C4—28no—
344C3×C42—22no—
345C3×C42—22no—
346C3×C42—22no—
347C3×C42C2×D414yes—
348#217—24no—
349#217—24no—
350(C2×D3)⋊C4—24no—
351(C2×D3)⋊C4—28no—
352(C2×D3)⋊C4—24no—
353(C2×D3)⋊C4—24no—
354(C2×D3)⋊C4—24no—
355(C2×D3)⋊C4—28no—
356(C2×D3)⋊C4—28no—
357(C2×D3)⋊C4—24no—
358(C2×D3)⋊C4—44no—
359(C2×D3)⋊C4C2×D418yes—
360C4⋊Dic3—22no—
361C4⋊Dic3—22no—
362C4⋊Dic3—22no—
363C4⋊Dic3—28no—
364C4⋊Dic3C2×D414yes—
365C4⋊Dic3#4114yescomplemented
366Dic3⋊C4—24no—
367Dic3⋊C4—24no—
368Dic3⋊C4—24no—
369Dic3⋊C4—28no—
370Dic3⋊C4—28no—
371Dic3⋊C4—28no—
372Dic3⋊C4—28no—
373C4×Dic3—24no—
374C4×Dic3—24no—
375C4×Dic3—24no—
376C4×Dic3—24no—
377C2×#41—38no—
378C2×#41—64no—
379C2×#41—64no—
380C2×#41—68no—
381C2×#41—68no—
382C2×#41—68no—
383C22×Q8—31no—
384C22×Q8C22×D312yes—
385C22×D4—32no—
386C22×D4—32no—
387C22×D4—31no—
388C22×D4—31no—
389C22×D4—34no—
390C23×C4—32no—
391C23×C4—32no—
392C23×C4—34no—
393C23×C4—32no—
394C23×C4—34no—
395C23×C4—32no—
396C23×C4C22×D311yescharacteristic
397C23×C4C22×D311yescharacteristic
398C23×C4C22×D311yescharacteristic
399C4⋊Q8—24no—
400C4⋊Q8—68no—
401#123—616no—
402#123—616no—
403#123—616no—
404C22⋊Q8—28no—
405C22⋊Q8—68no—
406C22⋊Q8—68no—
407#121—616no—
408#121—68no—
409#121—64no—
410C4×Q8—64no—
411C4×Q8—64no—
412C4×D4—38no—
413C4×D4—64no—
414C4×D4—68no—
415C4×D4—68no—
416C4×D4—68no—
417C4×D4—68no—
418C4×D4—64no—
419#117—68no—
420#117—64no—
421C2×C4⋊C4—31no—
422C2×C4⋊C4—31no—
423C2×C4⋊C4—31no—
424C2×C4⋊C4—32no—
425C2×C4⋊C4—34no—
426C2×C4⋊C4—34no—
427C2×C4⋊C4—34no—
428C2×C4⋊C4—34no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—32no—
431C2×C4⋊C4—32no—
432C2×C4⋊C4—34no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—68no—
435C2×C4⋊C4—68no—
436C2×C4⋊C4—616no—
437C2×C4⋊C4C22×D312yes—
438C2×C4⋊C4C22×D314yes—
439C2×C4⋊C4C22×D312yes—
440C2×C4⋊C4C22×D312yes—
441C2×C4⋊C4C22×D312yes—
442C2×C4⋊C4C22×D312yes—
443C2×C22⋊C4—32no—
444C2×C22⋊C4—32no—
445C2×C22⋊C4—32no—
446C2×C22⋊C4—32no—
447C2×C22⋊C4—34no—
448C2×C22⋊C4—32no—
449C2×C22⋊C4—32no—
450C2×C22⋊C4—34no—
451C2×C22⋊C4—34no—
452C2×C22⋊C4—32no—
453C2×C22⋊C4—32no—
454C2×C22⋊C4—34no—
455C2×C22⋊C4C22×D314yes—
456C2×C42—24no—
457C2×C42—32no—
458C2×C42—32no—
459C2×C42—32no—
460C2×C42—32no—
461C2×C42—68no—
462C2×C42C22×D311yescharacteristic
463C2×C42C22×D311yescharacteristic
464C2×C42C22×D311yescharacteristic
465C2×C42C22×D311yescharacteristic
466#95—32no—
467#95—34no—
468#95—34no—
469#95—32no—
470#95—32no—
471#95—34no—
472#95—34no—
473#95C22×D314yes—
474#95C22×D314yes—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3C22×D412yes—
482C23×C3C2511yescharacteristic
483C22×D3—22no—
484C22×D3—22no—
485C22×D3—22no—
486C22×D3—22no—
487C22×D3—22no—
488C22×D3—22no—
489C22×D3—22no—
490C22×D3—22no—
491C22×D3—22no—
492C22×D3—22no—
493C22×D3—22no—
494C22×D3C22×D414yes—
495C22×D3C22×D414yes—
496C22×D3C2×#4114yes—
497C3×Q8—48no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—28no—
505C2×C3×C4—21no—
506C2×C3×C4—24no—
507C2×C3×C4—24no—
508C2×C3×C4—24no—
509C2×C3×C4—24no—
510C2×C3×C4—21no—
511C2×C3×C4—24no—
512C2×C3×C4—21no—
513C2×C3×C4—24no—
514C2×C3×C4—44no—
515C2×C3×C4—44no—
516C2×C3×C4C22×D412yes—
517C2×C3×C4C22×D412yes—
518C2×C3×C4C22×D412yes—
519C2×C3×C4C22×D412yes—
520C2×C3×C4C22×D412yes—
521C2×C3×C4C2×#4112yes—
522C2×C3×C4C2×#4112yes—
523C2×C3×C42−1+412yes—
524C2×C3×C42−1+412yes—
525#67—216no—
526#67—48no—
527C2×Dic3—22no—
528C2×Dic3—22no—
529C2×Dic3—22no—
530C2×Dic3—22no—
531C2×Dic3—22no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—22no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3—22no—
540C2×Dic3—22no—
541C2×Dic3—22no—
542C2×Dic3C22×D414yes—
543C2×Dic3C22×D414yes—
544C2×Dic3C2×#4114yes—
545D12—416no—
546D12—44no—
547D12#121116yescomplemented
548C4×D3—216no—
549C4×D3—216no—
550C4×D3—416no—
551C4×D3—48no—
552C4×D3—416no—
553C4×D3—48no—
554Dic6—28no—
555C24—32no—
556C24—32no—
557C24C23×D311yescharacteristic
558#41—632no—
559#41—1232no—
560C2×Q8—24no—
561C2×Q8—24no—
562C2×Q8—24no—
563C2×Q8—34no—
564C2×Q8—62no—
565C2×Q8—62no—
566C2×D4—38no—
567C2×D4—34no—
568C2×D4—34no—
569C2×D4—34no—
570C2×D4—68no—
571C2×D4—68no—
572C2×D4—68no—
573C2×D4—64no—
574C2×D4—64no—
575C2×D4—64no—
576C2×D4—64no—
577C2×D4—62no—
578C2×D4—62no—
579C2×D4—62no—
580C2×D4—122no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—32no—
589C22×C4—32no—
590C22×C4—32no—
591C22×C4—38no—
592C22×C4—38no—
593C22×C4—32no—
594C22×C4—32no—
595C22×C4—32no—
596C22×C4—41no—
597C22×C4—68no—
598C22×C4—64no—
599C22×C4—64no—
600C22×C4—64no—
601C22×C4—68no—
602C22×C4—68no—
603C22×C4—68no—
604C22×C4—68no—
605C22×C4—64no—
606C22×C4—64no—
607C22×C4—64no—
608C22×C4—64no—
609C22×C4—64no—
610C22×C4—64no—
611C22×C4—122no—
612C22×C4—124no—
613C22×C4D3×D414yes—
614C22×C4C23×D311yescharacteristic
615C22×C4C23×D314yes—
616C22×C4C23×D314yes—
617C22×C4C23×D311yescharacteristic
618C22×C4C23×D311yescharacteristic
619C22×C4C23×D311yescharacteristic
620C22×C4C23×D311yescharacteristic
621C22×C4C23×D311yescharacteristic
622C4⋊C4—24no—
623C4⋊C4—28no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—34no—
628C4⋊C4—34no—
629C4⋊C4—42no—
630C4⋊C4—68no—
631C4⋊C4—68no—
632C4⋊C4—68no—
633C4⋊C4—68no—
634C4⋊C4—64no—
635C4⋊C4—68no—
636C4⋊C4—64no—
637C4⋊C4—62no—
638C4⋊C4—64no—
639C4⋊C4—62no—
640C4⋊C4—62no—
641C22⋊C4—28no—
642C22⋊C4—38no—
643C22⋊C4—68no—
644C22⋊C4—68no—
645C22⋊C4—64no—
646C22⋊C4—64no—
647C22⋊C4—68no—
648C22⋊C4—64no—
649C22⋊C4—64no—
650C22⋊C4—64no—
651C22⋊C4—64no—
652C22⋊C4—64no—
653C22⋊C4—124no—
654C42—22no—
655C42—22no—
656C42—22no—
657C42—64no—
658C42—64no—
659C42—64no—
660C42—64no—
661C42D3×D414yes—
662C22×C3—22no—
663C22×C3—22no—
664C22×C3—22no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3C23×D411yescharacteristic
670C22×C3C23×D411yescharacteristic
671C22×C3C22×#4111yescharacteristic
672C22×C3C22×#4111yescharacteristic
673C22×C3C2×2−1+411yescharacteristic
674C22×C3C2×2−1+411yescharacteristic
675C22×C3#58511yescharacteristic
676C2×D3—24no—
677C2×D3—24no—
678C2×D3—24no—
679C2×D3—24no—
680C2×D3—24no—
681C2×D3—24no—
682C2×D3—42no—
683C2×D3—42no—
684C2×D3—42no—
685C2×D3—42no—
686C2×D3—42no—
687C2×D3—42no—
688C2×D3—42no—
689C2×D3C2×#12118yes—
690C3×C4—22no—
691C3×C4—22no—
692C3×C4—22no—
693C3×C4—44no—
694C3×C4—41no—
695C3×C4—44no—
696C3×C4C2×#12114yes—
697C3×C4#54714yescomplemented
698Dic3—24no—
699Dic3—24no—
700Dic3—24no—
701Dic3—42no—
702Dic3—42no—
703Dic3—42no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—34no—
711C23—34no—
712C23—34no—
713C23—62no—
714C23—62no—
715C23—62no—
716C23—62no—
717C23—62no—
718C23—62no—
719C23—62no—
720C23—62no—
721C23—62no—
722C23—62no—
723C23—62no—
724C23C2×D3×D412yes—
725C23C24×D311yescharacteristic
726Q8—48no—
727Q8—68no—
728D4—316no—
729D4—616no—
730D4—1216no—
731D4—128no—
732D4—124no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—28no—
740C2×C4—21no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—34no—
750C2×C4—34no—
751C2×C4—34no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—616no—
755C2×C4—62no—
756C2×C4—62no—
757C2×C4—62no—
758C2×C4—62no—
759C2×C4—62no—
760C2×C4—62no—
761C2×C4—616no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—62no—
765C2×C4—62no—
766C2×C4—62no—
767C2×C4—62no—
768C2×C4—62no—
769C2×C4—62no—
770C2×C4—62no—
771C2×C4—128no—
772C2×C4—1216no—
773C2×C4—1216no—
774C2×C4—128no—
775C2×C4C2×D3×D412yes—
776C2×C4C2×D3×D412yes—
777C2×C4C2×D3×D412yes—
778C2×C4C2×D3×D412yes—
779C2×C4C2×D3×D412yes—
780C2×C4#100712yes—
781C2×C4#100712yes—
782C2×C4D3×#4112yes—
783C2×C4D3×#4112yes—
784C2×C3—42no—
785C2×C3C22×#12111yescharacteristic
786C2×C3C2×#54711yescharacteristic
787C2×C3D4×#4111yescharacteristic
788C2×C3#348211yescharacteristic
789C2×C3#348911yescharacteristic
790C2×C3#349911yescharacteristic
791C2×C3#351511yescharacteristic
792D3—28no—
793D3—82no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—38no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—64no—
803C22—64no—
804C22—64no—
805C22—64no—
806C22—64no—
807C22—64no—
808C22—122no—
809C22—122no—
810C22—122no—
811C22—122no—
812C22—122no—
813C22—122no—
814C22—122no—
815C22C22×D3×D411yescharacteristic
816C22C22×D3×D411yescharacteristic
817C22C2×#100711yescharacteristic
818C22C2×#100711yescharacteristic
819C22C2×D3×#4111yescharacteristic
820C22C2×D3×#4111yescharacteristic
821C22#596411yescharacteristic
822C4—22no—
823C4—22no—
824C4—22no—
825C4—44no—
826C4—41no—
827C4—44no—
828C4—64no—
829C4—64no—
830C4—64no—
831C4—122no—
832C4—122no—
833C4—122no—
834C4D3×#12114yes—
835C4#563114yescomplemented
836C3#3625911yescharacteristic, complemented, Sylow
837C2—42no—
838C2—68no—
839C2—242no—
840C2C2×D3×#12111yescharacteristic
841C2C2×#563111yescharacteristic
842C2#8598511yescharacteristic
843C2#8621411yescharacteristic
844C2#8623811yescharacteristic
845C2#8627811yescharacteristic
846C2#8628411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2857C2
hypercenter#2857D3
hypocenterC3#36259
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2857

Complements

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

NH ≅ G/Ntype
1. C2×#5726C2semidirect
2. C2×#5631C2semidirect
3. C2×C4×#235C2semidirect
4. C3×#2857C2semidirect
5. #83239C2semidirect
6. #82814C2semidirect
7. C4×#930C2semidirect
8. #76625C2semidirect
9. #76613C2semidirect
10. #76286C2semidirect
11. #76208C2semidirect
12. D3×#389C2semidirect
13. #74369C2semidirect
14. #74360C2semidirect
15. #74022C2semidirect
16. #73911C2semidirect
17. #73887C2semidirect
90. #2857D3semidirect
115. C2×#235D4semidirect
188. C4×D12D4semidirect
365. C4⋊Dic3#41semidirect
547. D12#121semidirect
697. C3×C4#547semidirect
835. C4#5631semidirect
836. C3#36259semidirect

Maximal subgroups

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

subgroupindex
C2×#57262
C2×#56312
C2×C4×#2352
C3×#28572
#832392
#828142
C4×#9302
#766252
#766132
#762862
#762082
D3×#3892
#743692
#743602
#740222
#739112
#738872
#362593