Finite Group Databasebeta

← #10800210

Subgroups — #10800210

Order 768.

1256 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86018C211yesmaximal, characteristic
2C2×Dic3×M16C211yesmaximal, characteristic, complemented
3C4×#877C211yesmaximal, characteristic, complemented
4C3×#1871C211yesmaximal, characteristic, complemented
5#71984C211yesmaximal, characteristic, complemented
6#71713C211yesmaximal, characteristic, complemented
7#70358C212yesmaximal, complemented
8Dic3×#104C212yesmaximal, complemented
9#69453C211yesmaximal, characteristic, complemented
10#68730C212yesmaximal, complemented
11#68728C212yesmaximal, complemented
12#21382—31nomaximal, Sylow
13C22×C3×M16C2211yescharacteristic
14C3×#525C2211yescharacteristic
15#5832C2211yescharacteristic
16Dic3×#41C2211yescharacteristic
17#5791C2211yescharacteristic
18C22×C4×Dic3C2211yescharacteristic
19C22×#208C2211yescharacteristic
20#5649—21no—
21#5649—21no—
22#5624C411yescharacteristic, complemented
23#5624C411yescharacteristic, complemented
24#5622C411yescharacteristic, complemented
25#5622C411yescharacteristic, complemented
26#5600C411yescharacteristic, complemented
27#5600C411yescharacteristic, complemented
28#5596C411yescharacteristic, complemented
29#5596C411yescharacteristic, complemented
30#5586—21no—
31#5586—21no—
32#5538—21no—
33#5538—21no—
34C4×#237—21no—
35C4×#237—21no—
36#5522C2211yescharacteristic
37#5517C2211yescharacteristic
38C2×#877—21no—
39C2×C3×#104C2212yes—
40C3×C4×C22⋊C4C2211yescharacteristic
41C2×#837C2212yes—
42C4×#217C2211yescharacteristic
43C2×#825C2212yes—
44Dic3×M16—21no—
45Dic3×M16—21no—
46Dic3×M16C2212yes—
47Dic3×M16C2212yes—
48C2×#815—21no—
49C2×C8×Dic3—21no—
50Dic3×C22⋊C4—21no—
51C4×Dic3⋊C4C2212yes—
52C42×Dic3C2212yes—
53C2×#805C2212yes—
54#4649—21no—
55#4648—21no—
56C3×#339C2212yes—
57#4555C2212yes—
58#4532C2212yes—
59#4523C2212yes—
60#3444—31no—
61C2×C4×M16—31no—
62C4×#117—31no—
63#1986—32no—
64#1980—32no—
65#1871—31no—
66#1871—31no—
67#1871—31no—
68#1871D311yescharacteristic, complemented
69C4×#104—32no—
70C4×#104—32no—
71C2×C3×#41C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×Dic3D411yescharacteristic
74C23×Dic3D411yescharacteristic
75C2×#237—21no—
76C2×#237—21no—
77C2×#235C2311yescharacteristic
78C2×C3×M16—21no—
79C2×C3×M16—24no—
80C2×C3×M16C2312yes—
81C22×C3×C8—21no—
82C3×#123—21no—
83C3×C22⋊Q8C2×C411yescharacteristic
84C3×C22⋊Q8C2×C411yescharacteristic
85C3×#121C2×C411yescharacteristic
86C3×#121C2×C411yescharacteristic
87C3×#120—21no—
88C3×C4×D4—21no—
89C3×C4×D4—21no—
90C3×#117C2311yescharacteristic
91C2×C3×C22⋊C4—21no—
92C2×C3×C42C2312yes—
93#953—21no—
94C2×#217—21no—
95#947C2×C411yescharacteristic
96Q8×Dic3C2×C411yescharacteristic
97Q8×Dic3C2×C411yescharacteristic
98#944C2×C411yescharacteristic
99#940C2×C411yescharacteristic
100#939—21no—
101#939—21no—
102#939—21no—
103#939—21no—
104#936C2×C411yescharacteristic
105#935—21no—
106#935—21no—
107D4×Dic3—21no—
108D4×Dic3—21no—
109D4×Dic3—21no—
110D4×Dic3—21no—
111D4×Dic3C2×C411yescharacteristic
112D4×Dic3C2×C411yescharacteristic
113#930C2×C411yescharacteristic
114#930C2×C411yescharacteristic
115#929—21no—
116C4×#67—21no—
117C4×#67—21no—
118C4×#67—21no—
119C4×#67—21no—
120#926—21no—
121#926C2311yescharacteristic
122#924C2×C411yescharacteristic
123#924C2×C411yescharacteristic
124C2×Dic3⋊C4—22no—
125C2×C4×Dic3—22no—
126C2×C4×Dic3—21no—
127C2×C4×Dic3—22no—
128C2×C4×Dic3C2×C411yescharacteristic
129C2×C4×Dic3C2×C411yescharacteristic
130C2×C4×Dic3C2×C411yescharacteristic
131C2×C4×Dic3C2×C411yescharacteristic
132C2×C4×Dic3D411yescharacteristic
133C2×C4×Dic3D411yescharacteristic
134C2×C4×Dic3D411yescharacteristic
135C2×C4×Dic3D411yescharacteristic
136C2×C4×Dic3D411yescharacteristic
137C2×C4×Dic3D411yescharacteristic
138C2×C4×Dic3C2312yes—
139C2×C4×Dic3C2311yescharacteristic
140C2×C4×Dic3C2311yescharacteristic
141C2×#208—21no—
142C2×#208—24no—
143C2×#208C2312yes—
144C22×C3⋊C8—21no—
145#898—21no—
146#898—21no—
147#893C2×C411yescharacteristic
148#893C2×C411yescharacteristic
149#892—21no—
150#892—21no—
151#890C2×C411yescharacteristic
152#890C2×C411yescharacteristic
153#889—21no—
154#889—21no—
155#888C2×C411yescharacteristic
156#888C2×C411yescharacteristic
157#887—21no—
158#887—21no—
159#887C2×C411yescharacteristic
160#887C2×C411yescharacteristic
161#886—21no—
162#886—21no—
163#885—21no—
164#885—21no—
165#67⋊C4—21no—
166#67⋊C4—21no—
167#67⋊C4—21no—
168#67⋊C4—21no—
169#67⋊C4—21no—
170#67⋊C4—21no—
171#879—21no—
172#879—21no—
173#878—21no—
174#878—21no—
175#878—21no—
176#878—21no—
177#877—28no—
178#877—21no—
179#877—21no—
180#877—21no—
181#877—21no—
182#872—21no—
183C42×D3—21no—
184C4×Dic6—21no—
185C4×Dic6—21no—
186C3×#104—24no—
187C3×#95—21no—
188#837—24no—
189C3⋊#95—21no—
190C3⋊#95—22no—
191#825—24no—
192#815—22no—
193#815—22no—
194C8×Dic3—22no—
195C8×Dic3—22no—
196#805—24no—
197C22×M16—31no—
198C22×M16C2×D311yescharacteristic
199#533—31no—
200#533—31no—
201#533—31no—
202#532—31no—
203#532—31no—
204#532—31no—
205#529—31no—
206#529—31no—
207#529—31no—
208#529—31no—
209#529—61no—
210#529—61no—
211#529—61no—
212#529—61no—
213#525—31no—
214#525—61no—
215#525—61no—
216#525C2×D311yescharacteristic
217C4×#41—31no—
218C4×#41—31no—
219C4×#41—61no—
220C4×#41—61no—
221C2×#117—61no—
222C22×C42—31no—
223C2×#104—32no—
224C2×#104—32no—
225C2×#104—32no—
226C2×#104C2×D312yes—
227C4×M16—32no—
228C4×M16—32no—
229C4×M16—61no—
230C4×M16—61no—
231C2×#97—61no—
232C2×C4×C8—61no—
233C4×C4⋊C4—32no—
234C4×C4⋊C4—61no—
235C4×C22⋊C4—31no—
236C4×C22⋊C4—61no—
237C4×C22⋊C4C2×D311yescharacteristic
238#376—61no—
239C43—32no—
240#339—32no—
241#339—32no—
242#339—32no—
243#339C2×D312yes—
244C24×C3C2×D411yescharacteristic
245C3×#41—22no—
246C3×#41—22no—
247C2×C3×Q8C22×C411yescharacteristic
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4C22×C411yescharacteristic
252C22×C3×C4—22no—
253C22×C3×C4—22no—
254C22×C3×C4—22no—
255C22×C3×C4—21no—
256C22×C3×C4C22×C411yescharacteristic
257C22×C3×C4C22×C411yescharacteristic
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2×D411yescharacteristic
261C22×C3×C4C2411yescharacteristic
262C2×#67—21no—
263C2×#67—21no—
264C2×#67—21no—
265C2×#67—21no—
266C2×#67—21no—
267C22×Dic3—24no—
268C22×Dic3—22no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3—42no—
272C22×Dic3C22⋊C411yescharacteristic
273C22×Dic3C22⋊C411yescharacteristic
274C22×Dic3C22⋊C411yescharacteristic
275C22×Dic3C22⋊C411yescharacteristic
276C22×Dic3C22⋊C411yescharacteristic
277C22×Dic3C22⋊C411yescharacteristic
278C22×Dic3C22⋊C411yescharacteristic
279C22×Dic3C22⋊C411yescharacteristic
280C22×Dic3C2×D411yescharacteristic
281C22×Dic3C2×D411yescharacteristic
282C22×Dic3C2×D411yescharacteristic
283C22×Dic3C2×D411yescharacteristic
284#237—44no—
285#237—44no—
286#235—22no—
287#235—22no—
288C2×D12C22×C411yescharacteristic
289C2×C4×D3—21no—
290C2×C4×D3—21no—
291C2×C4×D3—21no—
292C2×Dic6—21no—
293C2×Dic6—21no—
294C2×Dic6C22×C411yescharacteristic
295C3×M16—24no—
296C3×M16—22no—
297C3×M16#4114yescomplemented
298C2×C3×C8—24no—
299C2×C3×C8—22no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4C22×C411yescharacteristic
303C3×C4⋊C4C22×C411yescharacteristic
304C3×C22⋊C4—24no—
305C3×C22⋊C4—21no—
306C3×C22⋊C4—21no—
307C3×C22⋊C4—21no—
308C3×C22⋊C4—21no—
309C3×C22⋊C4—21no—
310C3×C42—21no—
311C3×C42—22no—
312C3×C42—22no—
313#217—24no—
314#217—21no—
315#217—21no—
316#217—21no—
317#217—21no—
318#217—21no—
319#217—21no—
320#217—21no—
321(C2×D3)⋊C4—21no—
322(C2×D3)⋊C4—21no—
323(C2×D3)⋊C4—21no—
324(C2×D3)⋊C4—21no—
325(C2×D3)⋊C4—21no—
326(C2×D3)⋊C4—21no—
327C4⋊Dic3—21no—
328C4⋊Dic3—21no—
329C4⋊Dic3—21no—
330C4⋊Dic3—21no—
331C4⋊Dic3C22×C411yescharacteristic
332C4⋊Dic3C22×C411yescharacteristic
333Dic3⋊C4—28no—
334Dic3⋊C4—21no—
335Dic3⋊C4—21no—
336Dic3⋊C4—21no—
337Dic3⋊C4—21no—
338Dic3⋊C4—21no—
339Dic3⋊C4—21no—
340Dic3⋊C4—21no—
341Dic3⋊C4—21no—
342Dic3⋊C4—21no—
343Dic3⋊C4—21no—
344C4×Dic3—28no—
345C4×Dic3—21no—
346C4×Dic3—21no—
347C4×Dic3—21no—
348C4×Dic3—21no—
349C4×Dic3—21no—
350C4×Dic3—22no—
351C4×Dic3—22no—
352C4×Dic3—44no—
353C4×Dic3C22⋊C411yescharacteristic
354C4×Dic3C22⋊C411yescharacteristic
355C4×Dic3C22⋊C411yescharacteristic
356C4×Dic3C22⋊C411yescharacteristic
357C4×Dic3C22⋊C411yescharacteristic
358C4×Dic3C22⋊C411yescharacteristic
359C4×Dic3C22⋊C411yescharacteristic
360C4×Dic3C22⋊C411yescharacteristic
361C4×Dic3C22×C411yescharacteristic
362C4×Dic3C22×C411yescharacteristic
363C4×Dic3C22×C411yescharacteristic
364C4×Dic3C22×C411yescharacteristic
365C4×Dic3C2×D411yescharacteristic
366C4×Dic3C2×D411yescharacteristic
367C4×Dic3C2×D411yescharacteristic
368C4×Dic3C2×D411yescharacteristic
369#208—24no—
370#208—22no—
371#208#4114yescomplemented
372C2×C3⋊C8—24no—
373C2×C3⋊C8—22no—
374C2×#41—31no—
375C2×#41—61no—
376C2×#41—61no—
377C2×#41C22×D311yescharacteristic
378C23×C4—31no—
379C23×C4—31no—
380C23×C4C22×D311yescharacteristic
381C2×M16—21no—
382C2×M16—24no—
383C2×M16—32no—
384C2×M16—64no—
385C2×M16—61no—
386C2×M16C22×D312yes—
387C22×C8—21no—
388C22×C8—61no—
389C4⋊Q8—31no—
390C4⋊Q8—31no—
391C4⋊Q8—31no—
392#127—31no—
393#126—61no—
394#126—61no—
395#126—61no—
396#126—61no—
397#125—31no—
398#125—31no—
399#125—61no—
400#125—61no—
401#124—31no—
402#124—31no—
403#124—61no—
404#124—61no—
405#123—21no—
406#123—61no—
407#123—61no—
408#123—61no—
409#123—61no—
410#123—61no—
411C22⋊Q8—31no—
412C22⋊Q8—31no—
413C22⋊Q8—61no—
414C22⋊Q8—61no—
415C22⋊Q8—61no—
416C22⋊Q8—61no—
417C22⋊Q8C4×D311yescharacteristic
418C22⋊Q8C4×D311yescharacteristic
419#121—31no—
420#121—31no—
421#121—61no—
422#121—61no—
423#121—61no—
424#121—61no—
425#121C4×D311yescharacteristic
426#121C4×D311yescharacteristic
427#120—21no—
428#120—61no—
429C4×Q8—31no—
430C4×Q8—31no—
431C4×Q8—31no—
432C4×Q8—31no—
433C4×Q8—61no—
434C4×Q8—61no—
435C4×Q8—61no—
436C4×Q8—61no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4—31no—
440C4×D4—31no—
441C4×D4—31no—
442C4×D4—31no—
443C4×D4—61no—
444C4×D4—61no—
445C4×D4—61no—
446C4×D4—61no—
447C4×D4—61no—
448C4×D4—61no—
449C4×D4—61no—
450C4×D4—61no—
451C4×D4—61no—
452C4×D4—61no—
453C4×D4—61no—
454C4×D4—61no—
455C4×D4—61no—
456C4×D4—61no—
457#117—31no—
458#117—61no—
459#117—61no—
460#117—61no—
461#117—61no—
462#117—61no—
463#117—61no—
464#117—61no—
465#117—61no—
466#117—68no—
467#117C22×D311yescharacteristic
468C2×C4⋊C4—62no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—61no—
471C2×C42—31no—
472C2×C42—31no—
473C2×C42—31no—
474C2×C42—31no—
475C2×C42—31no—
476C2×C42—31no—
477C2×C42—31no—
478C2×C42—31no—
479C2×C42—31no—
480C2×C42—31no—
481C2×C42—31no—
482C2×C42—31no—
483C2×C42—32no—
484C2×C42—61no—
485C2×C42—61no—
486C2×C42—62no—
487C2×C42—62no—
488C2×C42C22×D312yes—
489#104—24no—
490#104—64no—
491#104—64no—
492#104—64no—
493#97—62no—
494#97—62no—
495C4×C8—62no—
496C4×C8—62no—
497#95—21no—
498#95—62no—
499#95—61no—
500C23×C3—22no—
501C23×C3—22no—
502C23×C3—21no—
503C23×C3—41no—
504C23×C3C2×C22⋊C411yescharacteristic
505C23×C3C2×C22⋊C411yescharacteristic
506C23×C3C22×D411yescharacteristic
507C22×D3—21no—
508C3×Q8—22no—
509C3×D4—22no—
510C3×D4—42no—
511C3×D4—42no—
512C3×D4—42no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—24no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—42no—
525C2×C3×C4—42no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4C2×C22⋊C411yescharacteristic
529C2×C3×C4C2×C22⋊C411yescharacteristic
530C2×C3×C4C23×C411yescharacteristic
531C2×C3×C4C22×D411yescharacteristic
532C2×C3×C4C2×#4112yes—
533C2×C3×C4C2×#4112yes—
534#67—42no—
535#67—42no—
536#67—42no—
537#67—42no—
538#67—42no—
539C2×Dic3—22no—
540C2×Dic3—22no—
541C2×Dic3—22no—
542C2×Dic3—22no—
543C2×Dic3—22no—
544C2×Dic3—22no—
545C2×Dic3—22no—
546C2×Dic3—22no—
547C2×Dic3—24no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—41no—
552C2×Dic3—41no—
553C2×Dic3—41no—
554C2×Dic3—42no—
555C2×Dic3—42no—
556C2×Dic3—42no—
557C2×Dic3—42no—
558C2×Dic3#10414yescomplemented
559C2×Dic3C2×C22⋊C411yescharacteristic
560C2×Dic3C2×C22⋊C411yescharacteristic
561C2×Dic3C2×C22⋊C411yescharacteristic
562C2×Dic3C2×C22⋊C411yescharacteristic
563C2×Dic3C2×C22⋊C411yescharacteristic
564C2×Dic3C2×C22⋊C411yescharacteristic
565C2×Dic3C2×C22⋊C411yescharacteristic
566C2×Dic3C2×C22⋊C411yescharacteristic
567D12—22no—
568C4×D3—41no—
569C4×D3—41no—
570C4×D3—42no—
571C4×D3—42no—
572Dic6—22no—
573Dic6—42no—
574Dic6—42no—
575C3×C8—24no—
576C3⋊C8—24no—
577C24D3×D411yescharacteristic
578#41—22no—
579#41—22no—
580#41—62no—
581#41—62no—
582#41—124no—
583#41—124no—
584C2×Q8—31no—
585C2×Q8—61no—
586C2×Q8—61no—
587C2×Q8C2×C4×D311yescharacteristic
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—31no—
592C2×D4—61no—
593C2×D4—61no—
594C2×D4—61no—
595C2×D4—61no—
596C2×D4—61no—
597C2×D4C2×C4×D311yescharacteristic
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—31no—
603C22×C4—31no—
604C22×C4—31no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—31no—
610C22×C4—31no—
611C22×C4—31no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—64no—
617C22×C4—61no—
618C22×C4—61no—
619C22×C4—62no—
620C22×C4—61no—
621C22×C4—122no—
622C22×C4C2×C4×D311yescharacteristic
623C22×C4C2×C4×D311yescharacteristic
624C22×C4D3×D411yescharacteristic
625C22×C4D3×D411yescharacteristic
626C22×C4D3×D411yescharacteristic
627C22×C4C23×D311yescharacteristic
628M16—24no—
629M16—22no—
630M16—34no—
631M16—64no—
632M16—62no—
633M16#23714yescomplemented
634C2×C8—24no—
635C2×C8—22no—
636C2×C8—64no—
637C2×C8—62no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—31no—
641C4⋊C4—31no—
642C4⋊C4—61no—
643C4⋊C4—61no—
644C4⋊C4—61no—
645C4⋊C4—61no—
646C4⋊C4—61no—
647C4⋊C4—61no—
648C4⋊C4—61no—
649C4⋊C4—61no—
650C4⋊C4—61no—
651C4⋊C4—61no—
652C4⋊C4—61no—
653C4⋊C4—61no—
654C4⋊C4—68no—
655C4⋊C4—61no—
656C4⋊C4—61no—
657C4⋊C4C2×C4×D311yescharacteristic
658C4⋊C4C2×C4×D311yescharacteristic
659C22⋊C4—24no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—61no—
666C22⋊C4—61no—
667C22⋊C4—61no—
668C22⋊C4—61no—
669C22⋊C4—61no—
670C22⋊C4—61no—
671C22⋊C4—61no—
672C22⋊C4—61no—
673C22⋊C4—64no—
674C22⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—61no—
677C22⋊C4—61no—
678C22⋊C4—61no—
679C42—21no—
680C42—22no—
681C42—22no—
682C42—31no—
683C42—31no—
684C42—31no—
685C42—31no—
686C42—31no—
687C42—31no—
688C42—31no—
689C42—31no—
690C42—31no—
691C42—31no—
692C42—31no—
693C42—31no—
694C42—31no—
695C42—31no—
696C42—31no—
697C42—31no—
698C42—61no—
699C42—61no—
700C42—61no—
701C42—61no—
702C42—68no—
703C42—61no—
704C42—62no—
705C42—62no—
706C42—124no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—44no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3C2×#10412yes—
719C22×C3C22×C22⋊C411yescharacteristic
720C22×C3#53212yes—
721C2×D3—41no—
722C2×D3—41no—
723C2×D3—41no—
724C3×C4—21no—
725C3×C4—21no—
726C3×C4—44no—
727C3×C4—41no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4C4×#4112yes—
731C3×C4#52511yescharacteristic
732C3×C4#52511yescharacteristic
733Dic3—21no—
734Dic3—21no—
735Dic3—21no—
736Dic3—21no—
737Dic3—21no—
738Dic3—44no—
739Dic3—41no—
740Dic3—41no—
741Dic3—41no—
742Dic3C2×#10412yes—
743Dic3C2×#10412yes—
744Dic3#42112yes—
745C23—22no—
746C23—22no—
747C23—21no—
748C23—41no—
749C23—61no—
750C23D3×C22⋊C411yescharacteristic
751C23D3×C22⋊C411yescharacteristic
752C23C2×D3×D411yescharacteristic
753Q8—22no—
754Q8—62no—
755Q8—122no—
756Q8—122no—
757D4—22no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—62no—
762D4—122no—
763D4—122no—
764D4—122no—
765D4—122no—
766D4—122no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—24no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—31no—
779C2×C4—31no—
780C2×C4—31no—
781C2×C4—34no—
782C2×C4—31no—
783C2×C4—31no—
784C2×C4—31no—
785C2×C4—31no—
786C2×C4—31no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—62no—
792C2×C4—62no—
793C2×C4—62no—
794C2×C4—62no—
795C2×C4—62no—
796C2×C4—62no—
797C2×C4—62no—
798C2×C4—62no—
799C2×C4—64no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—122no—
804C2×C4—122no—
805C2×C4—122no—
806C2×C4—122no—
807C2×C4—121no—
808C2×C4—121no—
809C2×C4—121no—
810C2×C4—122no—
811C2×C4—122no—
812C2×C4—121no—
813C2×C4—121no—
814C2×C4D3×C22⋊C411yescharacteristic
815C2×C4D3×C22⋊C411yescharacteristic
816C2×C4C22×C4×D311yescharacteristic
817C2×C4C2×D3×D411yescharacteristic
818C2×C4C2×#23712yes—
819C2×C4D3×#4112yes—
820C8—24no—
821C8—64no—
822C2×C3—22no—
823C2×C3—22no—
824C2×C3—41no—
825C2×C3—81no—
826C2×C3#229711yescharacteristic
827C2×C3C22×#10411yescharacteristic
828C2×C3C2×#42111yescharacteristic
829D3—81no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—44no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—121no—
842C22—121no—
843C22—121no—
844C22D3×#10412yes—
845C22C2×D3×C22⋊C411yescharacteristic
846C22#559612yes—
847C4—21no—
848C4—21no—
849C4—32no—
850C4—32no—
851C4—32no—
852C4—44no—
853C4—41no—
854C4—41no—
855C4—41no—
856C4—61no—
857C4—61no—
858C4—61no—
859C4—61no—
860C4—61no—
861C4—124no—
862C4—121no—
863C4—121no—
864C4—121no—
865C4C4×#23712yes—
866C4#558611yescharacteristic
867C4#565611yescharacteristic
868C3#2138211yescharacteristic, complemented, Sylow
869C2—22no—
870C2—22no—
871C2—41no—
872C2—81no—
873C2—241no—
874C2#7465811yescharacteristic
875C2C2×D3×#10411yescharacteristic
876C2D3×#42111yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1871C2
socleC22×C3C22×C22⋊C4
prime radical#86018C2
cosocleC22×C3×C4C24
hypercenter#1871D3
hypocenterC3#21382
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
2. C2×Dic3×M16C2semidirect
3. C4×#877C2semidirect
4. C3×#1871C2semidirect
5. #71984C2semidirect
6. #71713C2semidirect
7. #70358C2semidirect
8. Dic3×#104C2semidirect
9. #69453C2semidirect
10. #68730C2semidirect
11. #68728C2semidirect
22. #5624C4semidirect
23. #5624C4semidirect
24. #5622C4semidirect
25. #5622C4semidirect
26. #5600C4semidirect
27. #5600C4semidirect
28. #5596C4semidirect
29. #5596C4semidirect
68. #1871D3semidirect
297. C3×M16#41semidirect
371. #208#41semidirect
558. C2×Dic3#104semidirect
633. M16#237semidirect
868. C3#21382semidirect

Maximal subgroups

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

subgroupindex
#860182
C2×Dic3×M162
C4×#8772
C3×#18712
#719842
#717132
#703582
Dic3×#1042
#694532
#687302
#687282
#213823