Finite Group Databasebeta

← #10804165

Subgroups — #10804165

Order 768.

1446 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5606C211yesmaximal, characteristic
2C2×#5126C211yesmaximal, characteristic, complemented
3D3×#407C211yesmaximal, characteristic, complemented
4C3×#1900C211yesmaximal, characteristic, complemented
5#72003C211yesmaximal, characteristic, complemented
6#71683C211yesmaximal, characteristic, complemented
7#70081C212yesmaximal, complemented
8#70080C212yesmaximal, complemented
9#69986C211yesmaximal, characteristic, complemented
10#68993C212yesmaximal, complemented
11#68991C212yesmaximal, complemented
12#21754—31nomaximal, Sylow
13C22×#237C2211yescharacteristic
14C23×C4×D3C2211yescharacteristic
15C22×C3×M16C2211yescharacteristic
16C2×C3×#121C2211yescharacteristic
17C2×#938C2211yescharacteristic
18C2×#937C412yes—
19C2×D4×Dic3C412yes—
20C2×#924C2211yescharacteristic
21C22×#208C2211yescharacteristic
22C2×D3×M16C2212yes—
23#5606—21no—
24#5606—21no—
25#5606—21no—
26#5606—21no—
27#5606—21no—
28#5606—21no—
29#5606—21no—
30#5606—21no—
31C2×#897C2211yescharacteristic
32C2×#892C2211yescharacteristic
33C2×#883C412yes—
34C2×#67⋊C4C412yes—
35C2×C3×#100C2212yescomplemented
36C3×#407C2211yescharacteristic
37C2×#833C2212yescomplemented
38#5207C2211yescharacteristic
39C2×#824C2212yescomplemented
40C2×#824C2212yescomplemented
41#5126—21no—
42#5126—21no—
43#5126C2212yes—
44#5126C2212yes—
45#5126C2212yes—
46C2×(C2×D3)⋊C8—21no—
47C2×(C2×D3)⋊C8—21no—
48#4726—21no—
49#4726—21no—
50D3×C22⋊C8—21no—
51D3×C22⋊C8—21no—
52C3×#343C2212yescomplemented
53#4554C2212yescomplemented
54#4554C2212yescomplemented
55#4530C2212yescomplemented
56C2×#525—31no—
57C2×#407—31no—
58C2×#407—31no—
59#1901—31no—
60#1901—32no—
61#1901—31no—
62#1900—32no—
63#1900—31no—
64#1900D311yescharacteristic, complemented
65#1822—32no—
66#1785—32no—
67C24×D3C2×C411yescharacteristic
68C22×C3×D4C2×C412yes—
69C22×C3×D4C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C22×#67C2×C412yes—
72C22×#67C2×C412yes—
73C23×Dic3C2×C412yes—
74C23×Dic3C2×C411yescharacteristic
75C2×#237—21no—
76C2×#237—21no—
77C2×#237—21no—
78C2×#237—21no—
79C2×#237—42no—
80C2×#237—42no—
81C22×C4×D3—42no—
82C22×C4×D3—42no—
83C22×C4×D3C2×C411yescharacteristic
84C22×C4×D3C2×C411yescharacteristic
85C22×C4×D3D411yescharacteristic
86C22×C4×D3D411yescharacteristic
87C22×C4×D3D411yescharacteristic
88C22×C4×D3D411yescharacteristic
89C22×C4×D3D411yescharacteristic
90C22×C4×D3D411yescharacteristic
91C22×C4×D3D411yescharacteristic
92C22×C4×D3D411yescharacteristic
93C22×C4×D3C2311yescharacteristic
94C22×C4×D3C2311yescharacteristic
95C22×Dic6C2311yescharacteristic
96C2×C3×M16—21no—
97C2×C3×M16—42no—
98C2×C3×M16C2312yes—
99C2×C3×M16C2312yes—
100C22×C3×C8—21no—
101C3×#121—21no—
102C3×#121—21no—
103C3×#121—21no—
104C3×#121—21no—
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C22⋊C4C2×C412yes—
107C2×#217C2×C412yes—
108C2×#217C2×C412yes—
109#938—21no—
110#938—21no—
111#938—21no—
112#938—21no—
113#937—22no—
114#937—22no—
115#937—22no—
116#937—22no—
117D4×Dic3—22no—
118D4×Dic3—22no—
119D4×Dic3—22no—
120D4×Dic3—22no—
121C2×(C2×D3)⋊C4C2×C412yes—
122C2×(C2×D3)⋊C4C2×C412yes—
123C2×C4⋊Dic3C2×C412yes—
124C2×C4⋊Dic3C2311yescharacteristic
125#924—21no—
126#924—21no—
127#924—21no—
128#924—21no—
129C2×Dic3⋊C4C2×C412yes—
130C2×C4×Dic3C2×C412yes—
131C2×#208—21no—
132C2×#208—42no—
133C2×#208C2312yes—
134C2×#208C2312yes—
135C22×C3⋊C8—21no—
136D3×M16—42no—
137D3×M16—42no—
138C2×ΓL(1,𝔽25)—22no—
139C2×D3×C8—22no—
140#897—21no—
141#897—21no—
142#897—21no—
143#897—21no—
144#892—21no—
145#892—21no—
146#892—21no—
147#892—21no—
148#883—22no—
149#883—22no—
150#883—22no—
151#883—22no—
152#67⋊C4—22no—
153#67⋊C4—22no—
154#67⋊C4—22no—
155#67⋊C4—22no—
156C3×#100—42no—
157C3×C22⋊C8—21no—
158C3×C22⋊C8—21no—
159#833—42no—
160#830—21no—
161#830—21no—
162#824—42no—
163#824—42no—
164(C2×D3)⋊C8—22no—
165(C2×D3)⋊C8—22no—
166(C2×D3)⋊C8—22no—
167(C2×D3)⋊C8—22no—
168(C2×D3)⋊C8—22no—
169(C2×D3)⋊C8—22no—
170C22×#41—31no—
171C24×C4—31no—
172C22×M16—31no—
173C22×M16—32no—
174C22×M16C2×D311yescharacteristic
175#525—61no—
176#525—61no—
177#525—61no—
178#525—61no—
179#525—61no—
180#525—61no—
181#525—61no—
182#525—61no—
183C2×#123—32no—
184C2×C22⋊Q8—31no—
185C2×C22⋊Q8—31no—
186C2×#121—31no—
187C2×#121C2×D311yescharacteristic
188C2×#120—32no—
189C2×C4×D4—32no—
190C2×C4×D4—32no—
191C2×#117—31no—
192C2×#101—32no—
193C2×#101—32no—
194C2×#100—32no—
195C2×#100C2×D312yescomplemented
196#407—31no—
197#407—32no—
198#407—32no—
199#407—32no—
200#407—61no—
201#407—61no—
202#407—61no—
203#407—61no—
204#407C2×D311yescharacteristic
205C2×C22⋊C8—61no—
206C2×C22⋊C8—61no—
207C2×C22⋊C8—61no—
208C2×C22⋊C8—61no—
209#343—32no—
210#343—32no—
211#343—32no—
212#343C2×D312yescomplemented
213C24×C3C22×C411yescharacteristic
214C24×C3C22×C412yes—
215C23×D3—42no—
216C23×D3—42no—
217C23×D3—42no—
218C23×D3C22⋊C411yescharacteristic
219C23×D3C22⋊C411yescharacteristic
220C23×D3C22⋊C411yescharacteristic
221C23×D3C22⋊C411yescharacteristic
222C23×D3C22×C411yescharacteristic
223C23×D3C22×C411yescharacteristic
224C2×C3×D4—22no—
225C2×C3×D4—22no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—22no—
229C2×C3×D4—22no—
230C2×C3×D4—44no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4C22×C411yescharacteristic
234C22×C3×C4C22×C412yes—
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2411yescharacteristic
240C2×#67—22no—
241C2×#67—22no—
242C2×#67—22no—
243C2×#67—22no—
244C2×#67—44no—
245C2×#67—44no—
246C22×Dic3—22no—
247C22×Dic3—22no—
248C22×Dic3—42no—
249C22×Dic3—44no—
250C22×Dic3C22⋊C411yescharacteristic
251C22×Dic3C22⋊C411yescharacteristic
252C22×Dic3C22⋊C411yescharacteristic
253C22×Dic3C22⋊C411yescharacteristic
254C22×Dic3C22×C412yes—
255C22×Dic3C22×C411yescharacteristic
256C22×Dic3C22×C411yescharacteristic
257C22×Dic3C22×C412yes—
258#237—42no—
259#237—42no—
260#237—42no—
261#237—42no—
262#237—44no—
263#237—44no—
264C2×C4×D3—22no—
265C2×C4×D3—22no—
266C2×C4×D3—22no—
267C2×C4×D3—22no—
268C2×C4×D3—42no—
269C2×C4×D3—42no—
270C2×C4×D3—42no—
271C2×C4×D3—42no—
272C2×C4×D3—41no—
273C2×C4×D3—41no—
274C2×C4×D3—41no—
275C2×C4×D3—41no—
276C2×C4×D3—41no—
277C2×C4×D3—41no—
278C2×C4×D3—41no—
279C2×C4×D3—41no—
280C2×C4×D3—42no—
281C2×C4×D3—42no—
282C2×C4×D3C22⋊C411yescharacteristic
283C2×C4×D3C22⋊C411yescharacteristic
284C2×C4×D3C22⋊C411yescharacteristic
285C2×C4×D3C22⋊C411yescharacteristic
286C2×C4×D3C22⋊C411yescharacteristic
287C2×C4×D3C22⋊C411yescharacteristic
288C2×C4×D3C22⋊C411yescharacteristic
289C2×C4×D3C22⋊C411yescharacteristic
290C2×C4×D3C2×D411yescharacteristic
291C2×C4×D3C2×D411yescharacteristic
292C2×C4×D3C2×D411yescharacteristic
293C2×C4×D3C2×D411yescharacteristic
294C2×C4×D3C2×D411yescharacteristic
295C2×C4×D3C2×D411yescharacteristic
296C2×C4×D3C2×D411yescharacteristic
297C2×C4×D3C2×D411yescharacteristic
298C2×Dic6—21no—
299C2×Dic6—21no—
300C2×Dic6—22no—
301C2×Dic6—22no—
302C3×M16—22no—
303C3×M16—22no—
304C3×M16—22no—
305C3×M16—22no—
306C3×M16—42no—
307C2×C3×C8—22no—
308C2×C3×C8—22no—
309C2×C3×C8—42no—
310C3×C4⋊C4—21no—
311C3×C4⋊C4—21no—
312C3×C22⋊C4—22no—
313C3×C22⋊C4—22no—
314#217—22no—
315#217—22no—
316#217—22no—
317#217—22no—
318(C2×D3)⋊C4—22no—
319(C2×D3)⋊C4—22no—
320(C2×D3)⋊C4—22no—
321(C2×D3)⋊C4—22no—
322C4⋊Dic3—21no—
323C4⋊Dic3—21no—
324C4⋊Dic3—22no—
325C4⋊Dic3—22no—
326Dic3⋊C4—22no—
327Dic3⋊C4—22no—
328C4×Dic3—22no—
329C4×Dic3—22no—
330#208—22no—
331#208—22no—
332#208—22no—
333#208—22no—
334#208—42no—
335C2×C3⋊C8—22no—
336C2×C3⋊C8—22no—
337C2×C3⋊C8—42no—
338ΓL(1,𝔽25)—44no—
339D3×C8—44no—
340C25—31no—
341C2×#41—61no—
342C2×#41—61no—
343C2×#41—61no—
344C2×#41—61no—
345C2×#41—122no—
346C2×#41—122no—
347C22×Q8—31no—
348C22×D4—32no—
349C22×D4—32no—
350C22×D4C4×D312yes—
351C22×D4C22×D311yescharacteristic
352C23×C4—31no—
353C23×C4—31no—
354C23×C4—31no—
355C23×C4—31no—
356C23×C4—31no—
357C23×C4—31no—
358C23×C4—31no—
359C23×C4—31no—
360C23×C4—31no—
361C23×C4—31no—
362C23×C4—31no—
363C23×C4—31no—
364C23×C4—31no—
365C23×C4—32no—
366C23×C4—122no—
367C23×C4—122no—
368C23×C4C22×D311yescharacteristic
369C2×M16—21no—
370C2×M16—32no—
371C2×M16—32no—
372C2×M16—42no—
373C2×M16—62no—
374C2×M16—61no—
375C2×M16—122no—
376C2×M16—122no—
377C2×M16—122no—
378C2×M16C22×D312yes—
379C2×M16C22×D312yes—
380C22×C8—21no—
381C22×C8—62no—
382C22×C8—61no—
383#123—62no—
384#123—62no—
385#123—62no—
386#123—62no—
387C22⋊Q8—61no—
388C22⋊Q8—61no—
389C22⋊Q8—61no—
390C22⋊Q8—61no—
391C22⋊Q8—61no—
392C22⋊Q8—61no—
393C22⋊Q8—61no—
394C22⋊Q8—61no—
395#121—21no—
396#121—21no—
397#121—21no—
398#121—21no—
399#121—61no—
400#121—61no—
401#121—61no—
402#121—61no—
403#120—62no—
404#120—62no—
405#120—62no—
406#120—62no—
407C4×D4—62no—
408C4×D4—62no—
409C4×D4—62no—
410C4×D4—62no—
411C4×D4—62no—
412C4×D4—62no—
413C4×D4—62no—
414C4×D4—62no—
415#117—61no—
416#117—61no—
417#117—61no—
418#117—61no—
419C2×C4⋊C4—32no—
420C2×C4⋊C4—32no—
421C2×C4⋊C4—31no—
422C2×C4⋊C4C22×D311yescharacteristic
423C2×C22⋊C4—32no—
424C2×C22⋊C4—32no—
425C2×C22⋊C4—32no—
426C2×C22⋊C4—32no—
427C2×C22⋊C4C4×D312yes—
428C2×C42—32no—
429#101—122no—
430#101—122no—
431#100—42no—
432#100—122no—
433C22⋊C8—21no—
434C22⋊C8—21no—
435C22⋊C8—62no—
436C22⋊C8—62no—
437C22⋊C8—62no—
438C22⋊C8—62no—
439C22⋊C8—62no—
440C22⋊C8—62no—
441C22⋊C8—61no—
442C22⋊C8—61no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—24no—
447C23×C3—41no—
448C23×C3—42no—
449C23×C3—42no—
450C23×C3C2×C22⋊C411yescharacteristic
451C23×C3C2×C22⋊C411yescharacteristic
452C23×C3C23×C411yescharacteristic
453C22×D3—22no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—41no—
461C22×D3—41no—
462C22×D3—41no—
463C22×D3—41no—
464C22×D3—41no—
465C22×D3—41no—
466C22×D3—41no—
467C22×D3—41no—
468C22×D3—41no—
469C22×D3—41no—
470C22×D3—41no—
471C22×D3—416no—
472C22×D3C2×C22⋊C411yescharacteristic
473C22×D3C2×C22⋊C411yescharacteristic
474C22×D3C2×C22⋊C411yescharacteristic
475C22×D3C2×C22⋊C411yescharacteristic
476C3×D4—44no—
477C3×D4—44no—
478C3×D4—41no—
479C3×D4—41no—
480C3×D4—42no—
481C2×C3×C4—22no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—42no—
490C2×C3×C4C2×C22⋊C411yescharacteristic
491C2×C3×C4C2×C22⋊C411yescharacteristic
492C2×C3×C4C22×D411yescharacteristic
493C2×C3×C4C22×D411yescharacteristic
494C2×C3×C4H(5,𝔽2)12yes—
495C2×C3×C4H(5,𝔽2)12yes—
496#67—44no—
497#67—44no—
498#67—44no—
499#67—44no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—24no—
505C2×Dic3—41no—
506C2×Dic3—41no—
507C2×Dic3—41no—
508C2×Dic3—41no—
509C2×Dic3—44no—
510C2×Dic3—44no—
511C2×Dic3—42no—
512C2×Dic3C2×C22⋊C411yescharacteristic
513C2×Dic3C2×C22⋊C411yescharacteristic
514C2×Dic3C2×C22⋊C411yescharacteristic
515C2×Dic3C2×C22⋊C411yescharacteristic
516C4×D3—22no—
517C4×D3—22no—
518C4×D3—21no—
519C4×D3—21no—
520C4×D3—21no—
521C4×D3—21no—
522C4×D3—21no—
523C4×D3—21no—
524C4×D3—21no—
525C4×D3—21no—
526C4×D3—22no—
527C4×D3—22no—
528C4×D3—41no—
529C4×D3—41no—
530C4×D3—41no—
531C4×D3—41no—
532C4×D3—41no—
533C4×D3—41no—
534C4×D3—41no—
535C4×D3—41no—
536Dic6—41no—
537Dic6—41no—
538Dic6—42no—
539C3×C8—42no—
540C3×C8—42no—
541C3⋊C8—42no—
542C3⋊C8—42no—
543C24—31no—
544C24—31no—
545C24—31no—
546C24—31no—
547C24—31no—
548C24—31no—
549C24—122no—
550C24—122no—
551C24—122no—
552C24C2×C4×D311yescharacteristic
553C24C2×C4×D312yes—
554#41—122no—
555#41—122no—
556#41—122no—
557#41—122no—
558#41—124no—
559#41—124no—
560C2×Q8—61no—
561C2×Q8—61no—
562C2×Q8—62no—
563C2×Q8—62no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—44no—
571C2×D4—62no—
572C2×D4—62no—
573C2×D4—62no—
574C2×D4—62no—
575C2×D4—124no—
576C2×D4—124no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—31no—
580C22×C4—31no—
581C22×C4—31no—
582C22×C4—31no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—31no—
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—31no—
590C22×C4—31no—
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—31no—
594C22×C4—31no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—31no—
598C22×C4—31no—
599C22×C4—31no—
600C22×C4—31no—
601C22×C4—32no—
602C22×C4—32no—
603C22×C4—62no—
604C22×C4—62no—
605C22×C4—62no—
606C22×C4—62no—
607C22×C4—62no—
608C22×C4—62no—
609C22×C4—121no—
610C22×C4—121no—
611C22×C4—121no—
612C22×C4—121no—
613C22×C4—121no—
614C22×C4—121no—
615C22×C4—121no—
616C22×C4—121no—
617C22×C4—122no—
618C22×C4—122no—
619C22×C4—122no—
620C22×C4—122no—
621C22×C4—122no—
622C22×C4—122no—
623C22×C4—122no—
624C22×C4—124no—
625C22×C4C2×C4×D311yescharacteristic
626C22×C4C2×C4×D312yes—
627C22×C4D3×D411yescharacteristic
628C22×C4D3×D411yescharacteristic
629C22×C4D3×D411yescharacteristic
630C22×C4D3×D411yescharacteristic
631C22×C4C23×D311yescharacteristic
632M16—22no—
633M16—22no—
634M16—22no—
635M16—22no—
636M16—42no—
637M16—62no—
638M16—62no—
639M16—62no—
640M16—62no—
641M16—124no—
642M16—122no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—42no—
646C2×C8—62no—
647C2×C8—62no—
648C2×C8—124no—
649C2×C8—122no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—62no—
653C4⋊C4—62no—
654C4⋊C4—62no—
655C4⋊C4—62no—
656C4⋊C4—61no—
657C4⋊C4—61no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—62no—
661C22⋊C4—62no—
662C22⋊C4—62no—
663C22⋊C4—62no—
664C22⋊C4—62no—
665C22⋊C4—62no—
666C22⋊C4—62no—
667C22⋊C4—62no—
668C42—62no—
669C42—62no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—44no—
678C22×C3—42no—
679C22×C3—42no—
680C22×C3—42no—
681C22×C3—84no—
682C22×C3#41312yes—
683C22×C3C22×C22⋊C411yescharacteristic
684C22×C3#51812yes—
685C2×D3—21no—
686C2×D3—21no—
687C2×D3—21no—
688C2×D3—21no—
689C2×D3—21no—
690C2×D3—21no—
691C2×D3—21no—
692C2×D3—21no—
693C2×D3—21no—
694C2×D3—21no—
695C2×D3—21no—
696C2×D3—44no—
697C2×D3—44no—
698C2×D3—44no—
699C2×D3—44no—
700C2×D3—44no—
701C2×D3—44no—
702C2×D3#41312yes—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—42no—
706C3×C4#53411yescharacteristic
707C3×C4#53411yescharacteristic
708C3×C4#53412yes—
709Dic3—21no—
710Dic3—21no—
711Dic3—21no—
712Dic3—21no—
713Dic3—42no—
714Dic3—42no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—24no—
719C23—31no—
720C23—31no—
721C23—31no—
722C23—31no—
723C23—41no—
724C23—42no—
725C23—42no—
726C23—62no—
727C23—62no—
728C23—62no—
729C23—62no—
730C23—62no—
731C23—62no—
732C23—62no—
733C23—121no—
734C23—121no—
735C23—121no—
736C23—121no—
737C23—121no—
738C23—121no—
739C23—121no—
740C23—121no—
741C23—121no—
742C23—121no—
743C23—121no—
744C23—1216no—
745C23D3×C22⋊C411yescharacteristic
746C23D3×C22⋊C411yescharacteristic
747C23C22×C4×D311yescharacteristic
748Q8—121no—
749Q8—121no—
750Q8—122no—
751D4—44no—
752D4—44no—
753D4—41no—
754D4—41no—
755D4—42no—
756D4—124no—
757D4—124no—
758D4—124no—
759D4—124no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—31no—
769C2×C4—31no—
770C2×C4—31no—
771C2×C4—31no—
772C2×C4—42no—
773C2×C4—62no—
774C2×C4—62no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4—64no—
790C2×C4—121no—
791C2×C4—121no—
792C2×C4—121no—
793C2×C4—121no—
794C2×C4—121no—
795C2×C4—121no—
796C2×C4—121no—
797C2×C4—121no—
798C2×C4—121no—
799C2×C4—121no—
800C2×C4—121no—
801C2×C4—121no—
802C2×C4—124no—
803C2×C4—124no—
804C2×C4—122no—
805C2×C4D3×C22⋊C411yescharacteristic
806C2×C4D3×C22⋊C411yescharacteristic
807C2×C4C2×D3×D411yescharacteristic
808C2×C4C2×D3×D411yescharacteristic
809C2×C4#100412yes—
810C2×C4#100912yes—
811C8—42no—
812C8—42no—
813C8—122no—
814C8—122no—
815C2×C3—22no—
816C2×C3—22no—
817C2×C3—41no—
818C2×C3—82no—
819C2×C3#230811yescharacteristic
820C2×C3C2×#41311yescharacteristic
821C2×C3C2×#41311yescharacteristic
822D3—22no—
823D3—41no—
824D3—41no—
825D3—41no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—32no—
834C22—44no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—61no—
839C22—61no—
840C22—61no—
841C22—61no—
842C22—61no—
843C22—61no—
844C22—61no—
845C22—61no—
846C22—61no—
847C22—61no—
848C22—61no—
849C22—84no—
850C22—124no—
851C22—124no—
852C22—124no—
853C22—124no—
854C22—124no—
855C22—124no—
856C22#474512yes—
857C22C2×D3×C22⋊C411yescharacteristic
858C22#554512yes—
859C4—21no—
860C4—21no—
861C4—42no—
862C4—61no—
863C4—61no—
864C4—61no—
865C4—61no—
866C4—122no—
867C4—122no—
868C4#558911yescharacteristic
869C4#560512yes—
870C4#565311yescharacteristic
871C3#2175411yescharacteristic, complemented, Sylow
872C2—22no—
873C2—22no—
874C2—41no—
875C2—62no—
876C2—82no—
877C2—121no—
878C2—121no—
879C2—121no—
880C2#7487411yescharacteristic
881C2C2×#474511yescharacteristic
882C2D3×#41311yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊C4
commutatorC23×C3C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1900C2
socleC22×C3C22×C22⋊C4
prime radicalC2×#5606C2
cosocleC22×C3×C4C24
hypercenter#1900D3
hypocenterC3#21754
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1900

Complements

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

NH ≅ G/Ntype
2. C2×#5126C2semidirect
3. D3×#407C2semidirect
4. C3×#1900C2semidirect
5. #72003C2semidirect
6. #71683C2semidirect
7. #70081C2semidirect
8. #70080C2semidirect
9. #69986C2semidirect
10. #68993C2semidirect
11. #68991C2semidirect
35. C2×C3×#100C22semidirect
37. C2×#833C22semidirect
39. C2×#824C22semidirect
40. C2×#824C22semidirect
52. C3×#343C22semidirect
53. #4554C22semidirect
54. #4554C22semidirect
55. #4530C22semidirect
64. #1900D3semidirect
195. C2×#100C2×D3semidirect
212. #343C2×D3semidirect
871. C3#21754semidirect

Maximal subgroups

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

subgroupindex
C2×#56062
C2×#51262
D3×#4072
C3×#19002
#720032
#716832
#700812
#700802
#699862
#689932
#689912
#217543