Finite Group Databasebeta

← #10993918

Subgroups — #10993918

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×C3×#547C211yesmaximal, characteristic, complemented
2C2×#5824C212yesmaximal, complemented
3C2×C4×#237C211yesmaximal, characteristic, complemented
4#84088C212yesmaximal, complemented
5#83269C211yesmaximal, characteristic, complemented
6#83239C211yesmaximal, characteristic, complemented
7#82846C214yesmaximal, complemented
8#82842C214yesmaximal, complemented
9#82813C212yesmaximal, complemented
10#82757C212yesmaximal, complemented
11#82705C212yesmaximal, complemented
12#82699C212yesmaximal, complemented
13C4×#938C211yesmaximal, characteristic, complemented
14#82376C211yesmaximal, characteristic, complemented
15D4×C4⋊Dic3C211yesmaximal, characteristic, complemented
16#82196C212yesmaximal, complemented
17C2×#4972C212yesmaximal, complemented
18#36259—31nomaximal, Sylow
19C22×C3×#41C2212yes—
20C22×#237C2211yescharacteristic
21C3×#547—28no—
22C2×C3×C4⋊Q8C2211yescharacteristic
23C2×C3×#123C2214yes—
24C2×C3×C22⋊Q8C2212yes—
25C2×C3×#121C2212yes—
26C2×C3×C4×D4C2211yescharacteristic
27C2×C3×C4×D4C2211yescharacteristic
28C22×C3×C4⋊C4C2212yes—
29#5824—216no—
30C2×#946C2212yes—
31C2×#944C2212yes—
32C2×#939C2214yes—
33C2×#938C2211yescharacteristic
34C2×#935C2214yes—
35C2×D4×Dic3C2211yescharacteristic
36C2×D4×Dic3C2212yes—
37C2×#929C2214yes—
38C2×C4×#67C2212yes—
39C2×C4×#67C2212yes—
40C22×C4⋊Dic3C2212yes—
41C2×#924C2212yes—
42C22×Dic3⋊C4C2214yes—
43C22×C4×Dic3C2212yes—
44C4×#237—28no—
45C2×#892C2211yescharacteristic
46C2×#887C2211yescharacteristic
47C2×#67⋊C4C2212yes—
48C2×#877C2212yes—
49C2×C42×D3C2211yescharacteristic
50C2×C4×Dic6C2211yescharacteristic
51#5229C2212yes—
52#5229C2212yes—
53#5221C2211yescharacteristic
54#5221C2212yes—
55#5220C2214yes—
56#5220C2214yes—
57#5212C2212yes—
58#5212C2212yes—
59#5211C2214yes—
60C4×#217C2212yes—
61C2×C3⋊#95C2214yes—
62#4992C2214yes—
63#4987C2212yes—
64#4987C2211yescharacteristic
65#4987C2212yes—
66#4984C2212yes—
67#4983C2214yes—
68#4983C2214yes—
69#4972C2212yes—
70#4972C2212yes—
71#4972C2212yes—
72#4972C2212yes—
73#4972C2214yes—
74#4972C2212yes—
75#4972C2214yes—
76#4972C2211yescharacteristic
77#4961C2214yes—
78#4956C2212yes—
79#4950C2214yes—
80#4948C2214yes—
81#4948C2214yes—
82#4944C2214yes—
83#4944C2214yes—
84#4944C2212yes—
85#4935C2211yescharacteristic
86C4×C4⋊Dic3C2211yescharacteristic
87C2×#547—32no—
88C2×#547D311yescharacteristic, complemented
89C2×C4×#41—31no—
90#2857—31no—
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—
104C2×C3×#41—28no—
105C2×C3×#41—28no—
106C2×C3×#41—28no—
107C22×C3×Q8C2312yes—
108C22×C3×D4C2314yes—
109C22×C3×D4C2311yescharacteristic
110C22×C3×D4C2311yescharacteristic
111C23×C3×C4C2314yes—
112C23×C3×C4C2312yes—
113C23×C3×C4C2312yes—
114C22×#67C2312yes—
115C22×#67C2312yes—
116C23×Dic3C2314yes—
117C23×Dic3C2312yes—
118C23×Dic3C2312yes—
119C2×#237—24no—
120C2×#237—24no—
121C2×#237D418yescomplemented
122C22×C4×D3C2311yescharacteristic
123C22×C4×D3C2311yescharacteristic
124C22×C4×D3C2311yescharacteristic
125C22×Dic6C2311yescharacteristic
126C3×C4⋊Q8—24no—
127C3×#123—216no—
128C3×C22⋊Q8—28no—
129C3×#121—28no—
130C3×C4×D4—24no—
131C3×C4×D4D418yescomplemented
132C2×C3×C4⋊C4—28no—
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C4⋊C4C2312yes—
135C2×C3×C4⋊C4C2314yes—
136C2×C3×C4⋊C4C2312yes—
137C2×C3×C4⋊C4C2311yescharacteristic
138C2×C3×C22⋊C4C2314yes—
139C2×C3×C22⋊C4C2312yes—
140C2×C3×C22⋊C4C2312yes—
141C2×C3×C42C2311yescharacteristic
142C2×#217C2312yes—
143C2×#217C2312yes—
144C2×#217C2312yes—
145C2×#217C2314yes—
146C2×#217C2314yes—
147C2×#217C2312yes—
148C2×#217C2314yes—
149#946—28no—
150#944—28no—
151#939—216no—
152#938—24no—
153#935—216no—
154D4×Dic3—24no—
155D4×Dic3—28no—
156#929—216no—
157C4×#67—28no—
158C4×#67—28no—
159C2×(C2×D3)⋊C4C2312yes—
160C2×(C2×D3)⋊C4C2312yes—
161C2×(C2×D3)⋊C4C2314yes—
162C2×C4⋊Dic3—28no—
163C2×C4⋊Dic3C2311yescharacteristic
164C2×C4⋊Dic3C2312yes—
165C2×C4⋊Dic3C2312yes—
166C2×C4⋊Dic3C2314yes—
167C2×C4⋊Dic3C2311yescharacteristic
168C2×C4⋊Dic3C2312yes—
169C2×C4⋊Dic3C2311yescharacteristic
170#924—28no—
171C2×Dic3⋊C4—216no—
172C2×Dic3⋊C4C2312yes—
173C2×Dic3⋊C4C2314yes—
174C2×Dic3⋊C4C2314yes—
175C2×Dic3⋊C4C2312yes—
176C2×Dic3⋊C4C2312yes—
177C2×Dic3⋊C4C2314yes—
178C2×Dic3⋊C4C2314yes—
179C2×C4×Dic3—28no—
180C2×C4×Dic3C2312yes—
181C2×C4×Dic3C2311yescharacteristic
182C2×C4×Dic3C2312yes—
183C2×C4×Dic3C2312yes—
184C2×C4×Dic3C2311yescharacteristic
185C2×C4×Dic3C2312yes—
186C2×C4×Dic3C2311yescharacteristic
187#892—24no—
188#887—24no—
189#67⋊C4—28no—
190#877—28no—
191C42×D3—24no—
192C4×Dic6—24no—
193C3⋊#95C2312yes—
194C3⋊#95C2314yes—
195C3⋊#95C2314yes—
196C3⋊#95C2312yes—
197C3⋊#95C2314yes—
198C3⋊#95C2314yes—
199C3⋊#95C2314yes—
200C3⋊#95C2312yes—
201C3⋊#95C2314yes—
202C22×#41—31no—
203C22×#41C2×D312yes—
204#547—28no—
205#547—616no—
206C2×C4⋊Q8—32no—
207C2×C4⋊Q8C2×D311yescharacteristic
208C2×#123—34no—
209C2×#123—34no—
210C2×#123C2×D314yes—
211C2×C22⋊Q8—32no—
212C2×C22⋊Q8—32no—
213C2×C22⋊Q8C2×D312yes—
214C2×#121—31no—
215C2×#121—34no—
216C2×#121C2×D312yes—
217C4×#41—68no—
218C2×C4×Q8—31no—
219C2×C4×Q8—31no—
220C2×C4×D4—31no—
221C2×C4×D4—32no—
222C2×C4×D4—32no—
223C2×C4×D4—32no—
224C2×C4×D4—32no—
225C2×C4×D4C2×D311yescharacteristic
226C2×C4×D4C2×D311yescharacteristic
227C2×#117—31no—
228C2×#117—32no—
229C22×C4⋊C4—32no—
230C22×C4⋊C4—34no—
231C22×C4⋊C4C2×D312yes—
232C22×C42—32no—
233C22×C42—31no—
234#398—34no—
235#398—34no—
236#397—34no—
237#396—34no—
238#396—34no—
239#394—34no—
240#391—32no—
241#391—32no—
242#390—31no—
243#390—32no—
244#389—32no—
245#389—32no—
246#389—32no—
247#389—32no—
248#389—34no—
249#389—32no—
250#389—34no—
251#389—32no—
252#389—31no—
253#388—34no—
254#388—34no—
255#388—32no—
256#386—34no—
257#386—34no—
258#386—32no—
259#385—34no—
260#384—31no—
261#381—34no—
262#380—32no—
263#380—32no—
264#380—32no—
265#380—32no—
266#380—31no—
267C4×C4⋊C4—31no—
268C4×C22⋊C4—32no—
269C2×#95—34no—
270C24×C3C2412yes—
271C24×C3C2412yes—
272C23×D3C2411yescharacteristic
273C3×#41—432no—
274C2×C3×Q8—24no—
275C2×C3×Q8—24no—
276C2×C3×Q8—24no—
277C2×C3×D4—28no—
278C2×C3×D4—28no—
279C2×C3×D4—28no—
280C2×C3×D4—22no—
281C2×C3×D4—22no—
282C2×C3×D4—22no—
283C2×C3×D4C2×D414yes—
284C2×C3×D4C2×D414yes—
285C2×C3×D4#4114yes—
286C22×C3×C4—24no—
287C22×C3×C4—24no—
288C22×C3×C4—28no—
289C22×C3×C4—28no—
290C22×C3×C4—28no—
291C22×C3×C4—24no—
292C22×C3×C4—24no—
293C22×C3×C4—24no—
294C22×C3×C4C2×D418yes—
295C22×C3×C4C2412yes—
296C22×C3×C4C2414yes—
297C22×C3×C4C2412yes—
298C22×C3×C4C2411yescharacteristic
299C22×C3×C4C2411yescharacteristic
300C22×C3×C4C2411yescharacteristic
301C2×#67—24no—
302C2×#67—24no—
303C2×#67—24no—
304C2×#67—24no—
305C2×#67—42no—
306C2×#67C2×D418yes—
307C22×Dic3—24no—
308C22×Dic3—24no—
309C22×Dic3—24no—
310C22×Dic3—28no—
311C22×Dic3—28no—
312C22×Dic3—24no—
313C22×Dic3—42no—
314C22×Dic3—44no—
315C22×Dic3C2×D418yes—
316C22×Dic3C2411yescharacteristic
317C22×Dic3C2412yes—
318C22×Dic3C2412yes—
319C22×Dic3C2414yes—
320C22×Dic3C2411yescharacteristic
321C22×Dic3C2412yes—
322C22×Dic3C2412yes—
323C22×Dic3C2411yescharacteristic
324#237—232no—
325C2×C4×D3—22no—
326C2×C4×D3—22no—
327C2×C4×D3—22no—
328C2×C4×D3—22no—
329C2×C4×D3—22no—
330C2×C4×D3—22no—
331C2×C4×D3—22no—
332C2×C4×D3—41no—
333C2×C4×D3C2×D414yes—
334C2×Dic6—22no—
335C2×Dic6—22no—
336C2×Dic6C2×D414yes—
337C3×C4⋊C4—22no—
338C3×C4⋊C4—24no—
339C3×C4⋊C4—28no—
340C3×C4⋊C4—24no—
341C3×C4⋊C4C2×D414yes—
342C3×C22⋊C4—24no—
343C3×C22⋊C4—28no—
344C3×C22⋊C4C2×D418yes—
345C3×C42C2×D414yes—
346#217—24no—
347#217—28no—
348#217—28no—
349#217—24no—
350#217—24no—
351#217—24no—
352#217—44no—
353(C2×D3)⋊C4—24no—
354(C2×D3)⋊C4—28no—
355(C2×D3)⋊C4—24no—
356C4⋊Dic3—22no—
357C4⋊Dic3—24no—
358C4⋊Dic3—24no—
359C4⋊Dic3—22no—
360C4⋊Dic3—28no—
361C4⋊Dic3—42no—
362C4⋊Dic3#4114yescomplemented
363Dic3⋊C4—24no—
364Dic3⋊C4—24no—
365Dic3⋊C4—24no—
366Dic3⋊C4—28no—
367Dic3⋊C4—28no—
368Dic3⋊C4—28no—
369Dic3⋊C4—28no—
370C4×Dic3—24no—
371C4×Dic3—22no—
372C4×Dic3—22no—
373C4×Dic3—22no—
374C4×Dic3—24no—
375C4×Dic3—24no—
376C4×Dic3—24no—
377C2×#41—28no—
378C2×#41—28no—
379C2×#41—28no—
380C2×#41—38no—
381C2×#41—64no—
382C2×#41—64no—
383C22×Q8—31no—
384C22×Q8C22×D312yes—
385C22×D4—32no—
386C22×D4—32no—
387C22×D4C22×D311yescharacteristic
388C22×D4C22×D314yes—
389C22×D4C22×D311yescharacteristic
390C23×C4—32no—
391C23×C4—31no—
392C23×C4—34no—
393C23×C4—32no—
394C23×C4—31no—
395C23×C4—31no—
396C23×C4C22×D314yes—
397C23×C4C22×D312yes—
398C23×C4C22×D312yes—
399C4⋊Q8—24no—
400C4⋊Q8—68no—
401#123—216no—
402#123—616no—
403#123—616no—
404C22⋊Q8—28no—
405C22⋊Q8—68no—
406C22⋊Q8—68no—
407#121—28no—
408#121—64no—
409#121—616no—
410C4×Q8—64no—
411C4×Q8—64no—
412C4×D4—24no—
413C4×D4—68no—
414C4×D4—68no—
415C4×D4—64no—
416C4×D4—68no—
417C4×D4—68no—
418C4×D4#6718yescomplemented
419#117—64no—
420#117—68no—
421C2×C4⋊C4—28no—
422C2×C4⋊C4—31no—
423C2×C4⋊C4—32no—
424C2×C4⋊C4—34no—
425C2×C4⋊C4—34no—
426C2×C4⋊C4—34no—
427C2×C4⋊C4—32no—
428C2×C4⋊C4—34no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—32no—
431C2×C4⋊C4—32no—
432C2×C4⋊C4—32no—
433C2×C4⋊C4—34no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4—32no—
436C2×C4⋊C4—68no—
437C2×C4⋊C4—616no—
438C2×C4⋊C4C22×D311yescharacteristic
439C2×C4⋊C4C22×D312yes—
440C2×C4⋊C4C22×D314yes—
441C2×C4⋊C4C22×D312yes—
442C2×C4⋊C4C22×D311yescharacteristic
443C2×C22⋊C4—32no—
444C2×C22⋊C4—34no—
445C2×C22⋊C4—32no—
446C2×C22⋊C4—34no—
447C2×C22⋊C4—32no—
448C2×C22⋊C4—32no—
449C2×C22⋊C4—32no—
450C2×C22⋊C4—32no—
451C2×C22⋊C4—34no—
452C2×C22⋊C4—34no—
453C2×C22⋊C4C22×D312yes—
454C2×C22⋊C4C22×D314yes—
455C2×C22⋊C4C22×D312yes—
456C2×C42—32no—
457C2×C42—31no—
458C2×C42—32no—
459C2×C42—31no—
460C2×C42—32no—
461C2×C42—32no—
462C2×C42—31no—
463C2×C42—68no—
464C2×C42—64no—
465C2×C42C22×D311yescharacteristic
466#95—32no—
467#95—34no—
468#95—34no—
469#95—34no—
470#95—32no—
471#95—32no—
472#95—34no—
473#95—34no—
474#95—34no—
475C23×C3—22no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3C22×D414yes—
487C23×C3C22×D414yes—
488C23×C3C2×#4114yes—
489C23×C3C2511yescharacteristic
490C22×D3—21no—
491C22×D3—21no—
492C22×D3—21no—
493C22×D3—21no—
494C22×D3—21no—
495C22×D3—21no—
496C22×D3C22×D412yes—
497C3×Q8—48no—
498C3×D4—416no—
499C3×D4—44no—
500C3×D4#121116yescomplemented
501C2×C3×C4—22no—
502C2×C3×C4—21no—
503C2×C3×C4—22no—
504C2×C3×C4—21no—
505C2×C3×C4—216no—
506C2×C3×C4—22no—
507C2×C3×C4—24no—
508C2×C3×C4—22no—
509C2×C3×C4—24no—
510C2×C3×C4—22no—
511C2×C3×C4—24no—
512C2×C3×C4—416no—
513C2×C3×C4—48no—
514C2×C3×C4C22×D412yes—
515C2×C3×C4C22×D414yes—
516C2×C3×C4C22×D412yes—
517C2×C3×C4C22×D412yes—
518C2×C3×C4C22×D412yes—
519C2×C3×C4C2×#4112yes—
520C2×C3×C4C2×#4112yes—
521C2×C3×C42−1+412yes—
522#67—216no—
523#67—48no—
524C2×Dic3—216no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—22no—
528C2×Dic3—22no—
529C2×Dic3—22no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—22no—
533C2×Dic3—21no—
534C2×Dic3—22no—
535C2×Dic3—22no—
536C2×Dic3—24no—
537C2×Dic3—24no—
538C2×Dic3—21no—
539C2×Dic3—22no—
540C2×Dic3—22no—
541C2×Dic3—21no—
542C2×Dic3—22no—
543C2×Dic3—24no—
544C2×Dic3—22no—
545C2×Dic3—416no—
546C2×Dic3—48no—
547C2×Dic3C22×D414yes—
548C2×Dic3C22×D412yes—
549C2×Dic3C2×#4114yes—
550C2×Dic32−1+412yes—
551C4×D3—28no—
552C4×D3—44no—
553C4×D3—44no—
554Dic6—28no—
555C24—31no—
556C24C23×D312yes—
557C24C23×D312yes—
558#41—432no—
559#41—632no—
560C2×Q8—24no—
561C2×Q8—24no—
562C2×Q8—24no—
563C2×Q8—34no—
564C2×Q8—62no—
565C2×Q8—62no—
566C2×D4—28no—
567C2×D4—28no—
568C2×D4—28no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—38no—
573C2×D4—64no—
574C2×D4—64no—
575C2×D4—64no—
576C2×D4—64no—
577C2×D4—122no—
578C2×D4D3×D414yes—
579C2×D4#23714yes—
580C2×D4C2×#6714yes—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—28no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—38no—
590C22×C4—31no—
591C22×C4—32no—
592C22×C4—31no—
593C22×C4—32no—
594C22×C4—34no—
595C22×C4—31no—
596C22×C4—32no—
597C22×C4—32no—
598C22×C4—34no—
599C22×C4—62no—
600C22×C4—68no—
601C22×C4—64no—
602C22×C4—64no—
603C22×C4—64no—
604C22×C4—62no—
605C22×C4—62no—
606C22×C4—68no—
607C22×C4—64no—
608C22×C4—62no—
609C22×C4—62no—
610C22×C4—62no—
611C22×C4—62no—
612C22×C4—121no—
613C22×C4—122no—
614C22×C4—124no—
615C22×C4C2×#6718yes—
616C22×C4C23×D312yes—
617C22×C4C23×D314yes—
618C22×C4C23×D312yes—
619C22×C4C23×D311yescharacteristic
620C22×C4C23×D311yescharacteristic
621C22×C4C23×D311yescharacteristic
622C4⋊C4—22no—
623C4⋊C4—24no—
624C4⋊C4—28no—
625C4⋊C4—24no—
626C4⋊C4—34no—
627C4⋊C4—64no—
628C4⋊C4—68no—
629C4⋊C4—68no—
630C4⋊C4—68no—
631C4⋊C4—68no—
632C4⋊C4—68no—
633C4⋊C4—64no—
634C4⋊C4—64no—
635C4⋊C4—62no—
636C4⋊C4—64no—
637C4⋊C4—64no—
638C4⋊C4—62no—
639C4⋊C4—122no—
640C4⋊C4C2×#6714yes—
641C22⋊C4—24no—
642C22⋊C4—28no—
643C22⋊C4—64no—
644C22⋊C4—68no—
645C22⋊C4—64no—
646C22⋊C4—68no—
647C22⋊C4—64no—
648C22⋊C4—64no—
649C22⋊C4—68no—
650C22⋊C4—64no—
651C22⋊C4—64no—
652C22⋊C4—124no—
653C22⋊C4C2×#6718yes—
654C42—64no—
655C42—62no—
656C42—64no—
657C42—62no—
658C42—64no—
659C42—62no—
660C42—64no—
661C42C2×#6714yes—
662C22×C3—24no—
663C22×C3—24no—
664C22×C3—24no—
665C22×C3—24no—
666C22×C3—24no—
667C22×C3—24no—
668C22×C3—42no—
669C22×C3—42no—
670C22×C3—42no—
671C22×C3—42no—
672C22×C3—42no—
673C22×C3—42no—
674C22×C3—42no—
675C22×C3C2×#12118yes—
676C22×C3C23×D411yescharacteristic
677C22×C3C23×D411yescharacteristic
678C22×C3C22×#4111yescharacteristic
679C22×C3C22×#4111yescharacteristic
680C22×C3C2×2−1+411yescharacteristic
681C22×C3C2×2−1+411yescharacteristic
682C22×C3#58511yescharacteristic
683C2×D3—22no—
684C2×D3—22no—
685C2×D3—22no—
686C2×D3—41no—
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—41no—
690C3×C4—24no—
691C3×C4—22no—
692C3×C4—42no—
693C3×C4—44no—
694C3×C4C2×#12114yes—
695C3×C4#54714yescomplemented
696Dic3—24no—
697Dic3—22no—
698Dic3—24no—
699Dic3—22no—
700Dic3—41no—
701Dic3—44no—
702Dic3—42no—
703Dic3—42no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—32no—
716C23—61no—
717C23—61no—
718C23—61no—
719C23—61no—
720C23—61no—
721C23—61no—
722C23C2×D3×D414yes—
723C23C2×#23714yes—
724C23C22×#6714yes—
725C23C24×D311yescharacteristic
726Q8—48no—
727Q8—68no—
728D4—416no—
729D4—44no—
730D4—616no—
731D4—128no—
732D4#938116yescomplemented
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—216no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—32no—
745C2×C4—34no—
746C2×C4—34no—
747C2×C4—32no—
748C2×C4—416no—
749C2×C4—48no—
750C2×C4—62no—
751C2×C4—61no—
752C2×C4—62no—
753C2×C4—61no—
754C2×C4—62no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—62no—
758C2×C4—616no—
759C2×C4—68no—
760C2×C4—62no—
761C2×C4—64no—
762C2×C4—61no—
763C2×C4—64no—
764C2×C4—62no—
765C2×C4—61no—
766C2×C4—62no—
767C2×C4—62no—
768C2×C4—62no—
769C2×C4—64no—
770C2×C4—61no—
771C2×C4—62no—
772C2×C4—124no—
773C2×C4—1216no—
774C2×C4—128no—
775C2×C4—124no—
776C2×C4C2×D3×D412yes—
777C2×C4C2×#23712yes—
778C2×C4D3×#4112yes—
779C2×C4#101012yes—
780C2×C4C22×#6714yes—
781C2×C4C22×#6712yes—
782C2×C4C22×#6712yes—
783C2×C4C22×#6712yes—
784C2×C3—28no—
785C2×C3—82no—
786C2×C3C22×#12111yescharacteristic
787C2×C3C2×#54711yescharacteristic
788C2×C3D4×#4111yescharacteristic
789C2×C3#348211yescharacteristic
790C2×C3#348911yescharacteristic
791C2×C3#349911yescharacteristic
792C2×C3#351511yescharacteristic
793D3—42no—
794C22—24no—
795C22—24no—
796C22—24no—
797C22—24no—
798C22—24no—
799C22—24no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—62no—
808C22—62no—
809C22—62no—
810C22—121no—
811C22—121no—
812C22—121no—
813C22—121no—
814C22C2×#93818yes—
815C22C22×D3×D411yescharacteristic
816C22C22×#23711yescharacteristic
817C22C2×D3×#4111yescharacteristic
818C22C2×#101011yescharacteristic
819C22D3×2−1+411yescharacteristic
820C22#596811yescharacteristic
821C22C23×#6711yescharacteristic
822C4—24no—
823C4—22no—
824C4—42no—
825C4—44no—
826C4—64no—
827C4—62no—
828C4—64no—
829C4—62no—
830C4—124no—
831C4—122no—
832C4—121no—
833C4—122no—
834C4C2×#93814yes—
835C4#582414yescomplemented
836C3#3625911yescharacteristic, complemented, Sylow
837C2—28no—
838C2—82no—
839C2—122no—
840C2#8667411yescharacteristic
841C2#8667611yescharacteristic
842C2#8667911yescharacteristic
843C2#8668311yescharacteristic
844C2C22×#93811yescharacteristic
845C2C2×#582411yescharacteristic
846C2#8729511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×#547C2
hypercenterC2×#547D3
hypocenterC3#36259
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×C3×#547C2semidirect
2. C2×#5824C2semidirect
3. C2×C4×#237C2semidirect
4. #84088C2semidirect
5. #83269C2semidirect
6. #83239C2semidirect
7. #82846C2semidirect
8. #82842C2semidirect
9. #82813C2semidirect
10. #82757C2semidirect
11. #82705C2semidirect
12. #82699C2semidirect
13. C4×#938C2semidirect
14. #82376C2semidirect
15. D4×C4⋊Dic3C2semidirect
16. #82196C2semidirect
17. C2×#4972C2semidirect
88. C2×#547D3semidirect
121. C2×#237D4semidirect
131. C3×C4×D4D4semidirect
362. C4⋊Dic3#41semidirect
418. C4×D4#67semidirect
500. C3×D4#121semidirect
695. C3×C4#547semidirect
732. D4#938semidirect
835. C4#5824semidirect
836. C3#36259semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5472
C2×#58242
C2×C4×#2372
#840882
#832692
#832392
#828462
#828422
#828132
#827572
#827052
#826992
C4×#9382
#823762
D4×C4⋊Dic32
#821962
C2×#49722
#362593