Finite Group Databasebeta

← #11864214

Subgroups — #11864214

Order 1152.

1589 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic, complemented
3C2×#63856C211yesmaximal, characteristic, complemented
4C2×#63827C211yesmaximal, characteristic, complemented
5#10592931C211yesmaximal, characteristic, complemented
6#10591597C212yesmaximal, complemented
7#10591594C212yesmaximal, complemented
8#10591461C212yesmaximal, complemented
9#10591458C212yesmaximal, complemented
10#10591088C211yesmaximal, characteristic, complemented
11#10591069C211yesmaximal, characteristic, complemented
12#84084—31nomaximal
13#83981—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C3×D3×#41—24no—
16C3×D3×#41—24no—
17C2×C3×#239C2211yescharacteristic
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#237—21no—
20C2×C3×#237C2211yescharacteristic
21C2×C3×D3×D4—21no—
22C2×C3×D3×D4C2211yescharacteristic
23C2×C3×#235—21no—
24C2×C3×#235C2211yescharacteristic
25C22×C3×C4×D3—21no—
26C22×C3×C4×D3C2211yescharacteristic
27C22×C3×Dic6C2211yescharacteristic, complemented
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
29C2×#3748C2211yescharacteristic, complemented
30C3×#951—24no—
31C2×C3×#216C2212yescomplemented
32C2×C3×#214C2212yescomplemented
33C2×C3×#208C2211yescharacteristic, complemented
34C2×#3724—21no—
35C2×(C2×D3)⋊Dic3—21no—
36#63856—21no—
37#63856—21no—
38#63856C2212yes—
39#63856C2212yescomplemented
40C2×#3718C2212yescomplemented
41#63827—24no—
42C2×#3715C2212yescomplemented
43#63662C2212yescomplemented
44#63659C2212yescomplemented
45#63566C2212yescomplemented
46#63563C2212yescomplemented
47(C2×D3)⋊(C3⋊C8)C2212yes—
48(C2×D3)⋊(C3⋊C8)C2212yescomplemented
49C22×C3×#41—31no—
50C2×D3×#41D311yescharacteristic
51C2×C3×#137—31no—
52C2×#951—31no—
53C2×#951D311yescharacteristic, complemented
54C2×#946—31no—
55C2×#942—31no—
56C2×#924—31no—
57#5239—32no—
58#5239—32no—
59#5232—31no—
60#5232—31no—
61#5232—31no—
62#5232—61no—
63#5228—32no—
64#5218—32no—
65#5207—31no—
66#5187—32no—
67#5186—32no—
68#5173—32no—
69#5169—32no—
70#5133—31no—
71#5126—31no—
72C23×C3×D3—21no—
73C23×C3×D3D411yescharacteristic
74C32×#41—22no—
75C32×#41D414yes—
76C2×C32×Q8C2311yescharacteristic
77C2×C32×D4—21no—
78C2×C32×D4C2311yescharacteristic
79C22×C32×C4—21no—
80C22×C32×C4C2311yescharacteristic
81C22×C3⋊Dic3—21no—
82C2×C3×#67—21no—
83C2×C3×#67—21no—
84C2×C3×#67—21no—
85C22×C3×Dic3—21no—
86C22×C3×Dic3—21no—
87C22×C3×Dic3D411yescharacteristic
88C3×#239—22no—
89C3×#239—22no—
90C3×D3×Q8—22no—
91C3×D3×Q8—22no—
92C3×#237—28no—
93C3×#237—22no—
94C3×#237—22no—
95C3×D3×D4—28no—
96C3×D3×D4—22no—
97C3×D3×D4—22no—
98C3×#235—28no—
99C3×#235—22no—
100C3×#235D414yes—
101C2×C3×D12—21no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—28no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—22no—
107C2×C3×C4×D3—22no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3D411yescharacteristic
110C2×C3×C4×D3D411yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×Dic6—21no—
114C2×C3×Dic6—22no—
115C2×C3×Dic6—22no—
116C2×C3×Dic6—21no—
117C2×C3×Dic6C2312yes—
118C2×C3×Dic6C2311yescharacteristic
119C4⋊(C3⋊Dic3)—21no—
120C4⋊(C3⋊Dic3)C2312yes—
121#3748—22no—
122C2×C3⋊(C3⋊C8)C2312yes—
123C3×#216—24no—
124C3×#214—24no—
125C3×#208—22no—
126C2×C3×C3⋊C8C2312yes—
127#3724—22no—
128#3724—22no—
129(C2×D3)⋊Dic3—22no—
130(C2×D3)⋊Dic3—22no—
131#3718—24no—
132#3715—24no—
133#3007—91noSylow
134C2×C3×#41—21no—
135C2×C3×#41—31no—
136C2×C3×#41—31no—
137C2×C3×#41—31no—
138C2×C3×#41—61no—
139C2×C3×#41—61no—
140C2×C3×#41—64no—
141C2×C3×#41—64no—
142C2×C3×#41C2×D311yescharacteristic
143C2×C3×#41C2×D311yescharacteristic
144C22×C3×Q8—31no—
145C22×C3×Q8—31no—
146C22×C3×D4—31no—
147C22×C3×D4—61no—
148C23×C3×C4—31no—
149C23×C3×C4—61no—
150D3×#41—24no—
151D3×#41—24no—
152C2×#239C2×D311yescharacteristic
153C2×D3×Q8C2×D311yescharacteristic
154C2×#237—21no—
155C2×#237C2×D311yescharacteristic
156C2×D3×D4—21no—
157C2×D3×D4C2×D311yescharacteristic
158C2×#235—21no—
159C2×#235C2×D311yescharacteristic
160C22×C4×D3—21no—
161C22×C4×D3C2×D311yescharacteristic
162C22×Dic6C2×D311yescharacteristic, complemented
163C3×#137—64no—
164C2×C3×Q16—32no—
165C2×C3×SD16—32no—
166C2×C3×M16—31no—
167C2×#217—61no—
168#951—24no—
169#951—64no—
170#946—32no—
171#946—32no—
172#946—61no—
173#946—61no—
174C2×#216—32no—
175C2×#216—32no—
176C2×#216C2×D312yescomplemented
177#942—64no—
178C2×#215—32no—
179C2×#214—32no—
180C2×#214C2×D312yescomplemented
181C2×(C2×D3)⋊C4—61no—
182C2×C4⋊Dic3—31no—
183C2×C4⋊Dic3—31no—
184C2×C4⋊Dic3—61no—
185#924—32no—
186#924—32no—
187#924—61no—
188#924—61no—
189C2×Dic3⋊C4—61no—
190C2×Dic3⋊C4—61no—
191C2×#208—31no—
192C2×#208—31no—
193C2×#208—61no—
194C2×#208C2×D311yescharacteristic, complemented
195#835—32no—
196#835—32no—
197#835—32no—
198#835—62no—
199#832—32no—
200#832—32no—
201#832—32no—
202#832—62no—
203#830—32no—
204#830—32no—
205#821—32no—
206(C2×D3)⋊C8—32no—
207(C2×D3)⋊C8—32no—
208#816—32no—
209C23×C32—21no—
210C23×C32C2×D411yescharacteristic
211C22×C3×D3—24no—
212C22×C3×D3—22no—
213C22×C3×D3—21no—
214C22×C3×D3—22no—
215C22×C3×D3—41no—
216C22×C3×D3—42no—
217C22×C3×D3—42no—
218C22×C3×D3C2×D411yescharacteristic
219C22×C3×D3C2×D411yescharacteristic
220C32×Q8—21no—
221C32×Q8C2×D412yes—
222C32×D4—24no—
223C32×D4—21no—
224C32×D4C2×D412yes—
225C2×C32×C4—21no—
226C2×C32×C4—24no—
227C2×C32×C4C2×D411yescharacteristic
228C2×C32×C4C2×D412yes—
229C2×C32×C4C2×D412yes—
230C2×C32×C4C2411yescharacteristic
231C2×C3⋊Dic3—22no—
232C2×C3⋊Dic3—42no—
233C3×#67—24no—
234C3×#67—24no—
235C3×#67—24no—
236C2×C3×Dic3—24no—
237C2×C3×Dic3—22no—
238C2×C3×Dic3—21no—
239C2×C3×Dic3—22no—
240C2×C3×Dic3—42no—
241C2×C3×Dic3C2×D411yescharacteristic
242C2×C3×Dic3C2×D411yescharacteristic
243C3×D12—24no—
244C3×D12—21no—
245C3×D12C2×D412yes—
246C3×C4×D3—24no—
247C3×C4×D3—24no—
248C3×C4×D3—22no—
249C3×C4×D3—24no—
250C3×C4×D3—22no—
251C3×C4×D3—21no—
252C3×C4×D3—21no—
253C3×C4×D3—21no—
254C3×C4×D3—21no—
255C3×Dic6—24no—
256C3×Dic6—21no—
257C3×Dic6—22no—
258C3×Dic6—22no—
259C3×Dic6—42no—
260C3×Dic6C2×D412yes—
261C3⋊(C3⋊C8)—22no—
262C3×C3⋊C8—22no—
263C22×#41—31no—
264C2×#137—31no—
265C2×#137—91no—
266C2×C22⋊Q8—91no—
267#452—92no—
268#452—92no—
269#451—92no—
270#450—92no—
271#417—91no—
272#417—91no—
273#407—91no—
274C24×C3—31no—
275C24×C3—61no—
276C23×D3—21no—
277C23×D3#6711yescharacteristic
278C3×#41—22no—
279C3×#41—22no—
280C3×#41—24no—
281C3×#41—34no—
282C3×#41—42no—
283C3×#41—68no—
284C3×#41—62no—
285C3×#41—68no—
286C3×#41—62no—
287C3×#41—62no—
288C3×#41—62no—
289C3×#41—62no—
290C3×#41#6714yes—
291C3×#41#6714yes—
292C2×C3×Q8—21no—
293C2×C3×Q8—31no—
294C2×C3×Q8—32no—
295C2×C3×Q8—61no—
296C2×C3×Q8—62no—
297C2×C3×Q8—62no—
298C2×C3×Q8—61no—
299C2×C3×Q8—62no—
300C2×C3×Q8—62no—
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×D4—21no—
304C2×C3×D4—21no—
305C2×C3×D4—21no—
306C2×C3×D4—31no—
307C2×C3×D4—41no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C2×C3×D4—62no—
311C2×C3×D4—68no—
312C2×C3×D4—61no—
313C2×C3×D4—61no—
314C2×C3×D4—62no—
315C2×C3×D4C22×D311yescharacteristic
316C2×C3×D4C22×D311yescharacteristic
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—41no—
326C22×C3×C4—61no—
327C22×C3×C4—61no—
328C22×C3×C4—68no—
329C22×C3×C4—61no—
330C22×C3×C4—62no—
331C22×C3×C4—61no—
332C22×C3×C4—62no—
333C22×C3×C4—61no—
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C2×#67—21no—
337C2×#67—21no—
338C2×#67—21no—
339C22×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3—61no—
342C22×Dic3—61no—
343C22×Dic3—121no—
344C22×Dic3#6711yescharacteristic
345#239—22no—
346#239—22no—
347D3×Q8—22no—
348D3×Q8—22no—
349#237—28no—
350#237—22no—
351#237—22no—
352D3×D4—28no—
353D3×D4—22no—
354D3×D4—22no—
355#235—28no—
356#235—22no—
357#235#6714yes—
358C2×D12—21no—
359C2×D12C22×D311yescharacteristic
360C2×C4×D3—28no—
361C2×C4×D3—21no—
362C2×C4×D3—21no—
363C2×C4×D3—22no—
364C2×C4×D3—22no—
365C2×C4×D3—21no—
366C2×C4×D3#6711yescharacteristic
367C2×C4×D3#6711yescharacteristic
368C2×C4×D3C22×D311yescharacteristic
369C2×C4×D3C22×D311yescharacteristic
370C2×Dic6—21no—
371C2×Dic6—22no—
372C2×Dic6—22no—
373C2×Dic6—21no—
374C2×Dic6C22×D312yes—
375C2×Dic6C22×D311yescharacteristic
376C3×Q16—64no—
377C3×SD16—64no—
378C3×M16—62no—
379C2×C3×C8—32no—
380#217—62no—
381#217—62no—
382#216—24no—
383#216—64no—
384#216—64no—
385#215—64no—
386#214—24no—
387#214—64no—
388(C2×D3)⋊C4—62no—
389(C2×D3)⋊C4—62no—
390C4⋊Dic3—32no—
391C4⋊Dic3—32no—
392C4⋊Dic3—62no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—121no—
396Dic3⋊C4—62no—
397Dic3⋊C4—62no—
398Dic3⋊C4—62no—
399Dic3⋊C4—62no—
400#208—22no—
401#208—62no—
402#208—62no—
403#208—122no—
404C2×C3⋊C8—32no—
405C2×C3⋊C8—32no—
406C2×C3⋊C8—62no—
407C2×C3⋊C8C22×D312yes—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—22no—
411C22×C32—41no—
412C22×C32—41no—
413C22×C32#12012yes—
414C22×C32C22×D411yescharacteristic
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—22no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—44no—
422C2×C3×D3—48no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3#13712yescomplemented
426C32×C4—22no—
427C32×C4#12012yes—
428C32×C4C22×D411yescharacteristic
429C32×C4C22×D411yescharacteristic
430C3⋊Dic3—42no—
431C3×Dic3—21no—
432C3×Dic3—22no—
433C3×Dic3—21no—
434C3×Dic3—42no—
435C2×#41—31no—
436C2×#41—31no—
437C2×#41—31no—
438C2×#41—61no—
439C2×#41—61no—
440C2×#41—64no—
441C2×#41—64no—
442C2×#41D3211yescharacteristic
443C22×Q8—31no—
444C22×Q8—31no—
445C22×D4—31no—
446C22×D4—61no—
447C23×C4—31no—
448C23×C4—61no—
449#137—64no—
450#137—184no—
451C2×Q16—32no—
452C2×Q16—92no—
453C2×SD16—32no—
454C2×SD16—92no—
455C2×M16—31no—
456C2×M16—91no—
457C22⋊Q8—92no—
458C22⋊Q8—92no—
459C22⋊Q8—181no—
460C22⋊Q8—181no—
461C2×C4⋊C4—91no—
462C2×C4⋊C4—181no—
463C2×C22⋊C4—181no—
464#103—92no—
465#103—92no—
466#102—92no—
467#102—92no—
468C22⋊C8—92no—
469C22⋊C8—92no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—31no—
474C23×C3—31no—
475C23×C3—41no—
476C23×C3—62no—
477C23×C3—64no—
478C23×C3—62no—
479C23×C3—61no—
480C23×C3—121no—
481C23×C3—122no—
482C23×C3—122no—
483C23×C3D3×D411yescharacteristic
484C23×C3C2×#6711yescharacteristic
485C22×D3—24no—
486C22×D3—22no—
487C22×D3—21no—
488C22×D3—22no—
489C22×D3—41no—
490C22×D3—42no—
491C22×D3—42no—
492C22×D3C2×#6711yescharacteristic
493C22×D3C2×#6711yescharacteristic
494C3×Q8—21no—
495C3×Q8—21no—
496C3×Q8—22no—
497C3×Q8—32no—
498C3×Q8—41no—
499C3×Q8—64no—
500C3×Q8—61no—
501C3×Q8—62no—
502C3×Q8—62no—
503C3×Q8—122no—
504C3×Q8C2×#6712yes—
505C3×Q8C2×#6712yes—
506C3×D4—24no—
507C3×D4—24no—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—22no—
511C3×D4—32no—
512C3×D4—41no—
513C3×D4—44no—
514C3×D4—64no—
515C3×D4—64no—
516C3×D4—64no—
517C3×D4—64no—
518C3×D4—61no—
519C3×D4C2×#6712yes—
520C3×D4C2×#6712yes—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—24no—
524C2×C3×C4—24no—
525C2×C3×C4—21no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—21no—
529C2×C3×C4—31no—
530C2×C3×C4—31no—
531C2×C3×C4—44no—
532C2×C3×C4—41no—
533C2×C3×C4—64no—
534C2×C3×C4—64no—
535C2×C3×C4—64no—
536C2×C3×C4—62no—
537C2×C3×C4—61no—
538C2×C3×C4—62no—
539C2×C3×C4—62no—
540C2×C3×C4—64no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—62no—
546C2×C3×C4—122no—
547C2×C3×C4D3×D411yescharacteristic
548C2×C3×C4D3×D412yes—
549C2×C3×C4C2×#6712yes—
550C2×C3×C4C2×#6712yes—
551C2×C3×C4C2×#6711yescharacteristic
552C2×C3×C4C2×#6712yes—
553C2×C3×C4C23×D311yescharacteristic
554C2×C3×C4C23×D311yescharacteristic
555#67—24no—
556#67—24no—
557#67—24no—
558C2×Dic3—24no—
559C2×Dic3—22no—
560C2×Dic3—21no—
561C2×Dic3—22no—
562C2×Dic3—42no—
563C2×Dic3—62no—
564C2×Dic3—62no—
565C2×Dic3—122no—
566C2×Dic3—122no—
567C2×Dic3—122no—
568C2×Dic3—242no—
569C2×Dic3C2×#6711yescharacteristic
570C2×Dic3C2×#6711yescharacteristic
571D12—24no—
572D12—21no—
573D12C2×#6712yes—
574C4×D3—24no—
575C4×D3—24no—
576C4×D3—22no—
577C4×D3—24no—
578C4×D3—22no—
579C4×D3—21no—
580C4×D3—21no—
581C4×D3—21no—
582C4×D3—21no—
583Dic6—24no—
584Dic6—21no—
585Dic6—22no—
586Dic6—22no—
587Dic6—42no—
588Dic6C2×#6712yes—
589C3×C8—62no—
590C3⋊C8—22no—
591C3⋊C8—62no—
592C3⋊C8—62no—
593C3⋊C8—122no—
594C2×C32—22no—
595C2×C32—42no—
596C2×C32C2×#12011yescharacteristic
597C2×C32C2×#13711yescharacteristic
598C2×C32#57511yescharacteristic
599C3×D3—22no—
600C3×D3—41no—
601C3×D3—42no—
602C24—31no—
603C24—61no—
604#41—22no—
605#41—34no—
606#41—68no—
607#41—62no—
608#41—68no—
609#41—62no—
610#41—62no—
611#41—62no—
612#41—62no—
613#41#62514yes—
614C2×Q8—31no—
615C2×Q8—32no—
616C2×Q8—61no—
617C2×Q8—62no—
618C2×Q8—62no—
619C2×Q8—61no—
620C2×Q8—62no—
621C2×Q8—62no—
622C2×Q8C2×D3211yescharacteristic
623C2×D4—21no—
624C2×D4—31no—
625C2×D4—61no—
626C2×D4—61no—
627C2×D4—62no—
628C2×D4—68no—
629C2×D4—61no—
630C2×D4—61no—
631C2×D4—62no—
632C2×D4C2×D3211yescharacteristic
633C22×C4—21no—
634C22×C4—31no—
635C22×C4—31no—
636C22×C4—31no—
637C22×C4—31no—
638C22×C4—31no—
639C22×C4—61no—
640C22×C4—61no—
641C22×C4—68no—
642C22×C4—61no—
643C22×C4—62no—
644C22×C4—62no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—181no—
648C22×C4C2×D3211yescharacteristic
649Q16—64no—
650Q16—184no—
651SD16—64no—
652SD16—184no—
653M16—62no—
654M16—182no—
655C2×C8—32no—
656C2×C8—92no—
657C4⋊C4—92no—
658C4⋊C4—182no—
659C4⋊C4—182no—
660C4⋊C4—181no—
661C22⋊C4—182no—
662C22⋊C4—182no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—22no—
668C22×C3—22no—
669C22×C3—21no—
670C22×C3—22no—
671C22×C3—32no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—42no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—61no—
680C22×C3—61no—
681C22×C3—61no—
682C22×C3—61no—
683C22×C3—62no—
684C22×C3—61no—
685C22×C3—81no—
686C22×C3—81no—
687C22×C3—124no—
688C22×C3—128no—
689C22×C3—121no—
690C22×C3—121no—
691C22×C3#93712yes—
692C22×C3#95312yes—
693C22×C3C2×D3×D411yescharacteristic
694C22×C3C22×#6711yescharacteristic
695C2×D3—21no—
696C2×D3—21no—
697C2×D3—21no—
698C2×D3—21no—
699C2×D3—21no—
700C2×D3—22no—
701C2×D3—44no—
702C2×D3—48no—
703C2×D3—41no—
704C2×D3—41no—
705C2×D3#95112yescomplemented
706C3×C4—22no—
707C3×C4—22no—
708C3×C4—21no—
709C3×C4—21no—
710C3×C4—22no—
711C3×C4—42no—
712C3×C4—61no—
713C3×C4—61no—
714C3×C4—62no—
715C3×C4—122no—
716C3×C4#93712yes—
717C3×C4#95312yes—
718C3×C4C2×D3×D411yescharacteristic
719C3×C4C22×#6711yescharacteristic
720C3×C4C22×#6711yescharacteristic
721C3×C4C22×#6711yescharacteristic
722Dic3—21no—
723Dic3—22no—
724Dic3—21no—
725Dic3—42no—
726Dic3—122no—
727Dic3—122no—
728Dic3—242no—
729C32#300711yescharacteristic, complemented, Sylow
730C23—21no—
731C23—31no—
732C23—31no—
733C23—62no—
734C23—64no—
735C23—61no—
736C23—62no—
737C23—121no—
738C23—122no—
739C23—122no—
740C23D3×#6711yescharacteristic
741Q8—21no—
742Q8—32no—
743Q8—64no—
744Q8—61no—
745Q8—62no—
746Q8—62no—
747Q8—122no—
748Q8C2×#62512yes—
749D4—24no—
750D4—21no—
751D4—32no—
752D4—64no—
753D4—64no—
754D4—64no—
755D4—64no—
756D4—61no—
757D4C2×#62512yes—
758C2×C4—21no—
759C2×C4—24no—
760C2×C4—31no—
761C2×C4—31no—
762C2×C4—64no—
763C2×C4—64no—
764C2×C4—64no—
765C2×C4—61no—
766C2×C4—62no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—62no—
772C2×C4—62no—
773C2×C4—64no—
774C2×C4—62no—
775C2×C4—122no—
776C2×C4—182no—
777C2×C4—362no—
778C2×C4C2×#62512yes—
779C2×C4D3×#6712yes—
780C2×C4D3×#6711yescharacteristic
781C2×C4C22×D3211yescharacteristic
782C8—62no—
783C8—182no—
784C2×C3—22no—
785C2×C3—22no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—42no—
790C2×C3—42no—
791C2×C3—42no—
792C2×C3—62no—
793C2×C3—82no—
794C2×C3—121no—
795C2×C3—122no—
796C2×C3D3×#13711yescharacteristic
797C2×C3#577711yescharacteristic
798C2×C3C2×#93711yescharacteristic
799C2×C3#582211yescharacteristic
800C2×C3C2×#95111yescharacteristic
801C2×C3C2×#95311yescharacteristic
802D3—22no—
803D3—41no—
804D3—42no—
805C22—21no—
806C22—21no—
807C22—22no—
808C22—32no—
809C22—41no—
810C22—41no—
811C22—61no—
812C22—61no—
813C22—61no—
814C22—61no—
815C22—62no—
816C22—61no—
817C22—124no—
818C22—128no—
819C22—121no—
820C22—121no—
821C22#6397612yes—
822C22C2×D3×#6711yescharacteristic
823C4—22no—
824C4—61no—
825C4—61no—
826C4—62no—
827C4—122no—
828C4—362no—
829C4#6397612yes—
830C4C22×#62511yescharacteristic
831C4C2×D3×#6711yescharacteristic
832C3—21no—
833C3#8398111yescharacteristic, complemented
834C3#8408411yescharacteristic, complemented
835C2—22no—
836C2—42no—
837C2—62no—
838C2—121no—
839C2—122no—
840C2D3×#95111yescharacteristic
841C2#1059547011yescharacteristic
842C2C2×#6397611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×#41C2
hypercenterC2×#41D32
hypocenterC32#3007
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×C3×#951C2semidirect
3. C2×#63856C2semidirect
4. C2×#63827C2semidirect
5. #10592931C2semidirect
6. #10591597C2semidirect
7. #10591594C2semidirect
8. #10591461C2semidirect
9. #10591458C2semidirect
10. #10591088C2semidirect
11. #10591069C2semidirect
27. C22×C3×Dic6C22semidirect
28. C2×C4⋊(C3⋊Dic3)C22semidirect
29. C2×#3748C22semidirect
31. C2×C3×#216C22semidirect
32. C2×C3×#214C22semidirect
33. C2×C3×#208C22semidirect
39. #63856C22semidirect
40. C2×#3718C22semidirect
42. C2×#3715C22semidirect
43. #63662C22semidirect
44. #63659C22semidirect
45. #63566C22semidirect
46. #63563C22semidirect
48. (C2×D3)⋊(C3⋊C8)C22semidirect
53. C2×#951D3semidirect
162. C22×Dic6C2×D3semidirect
176. C2×#216C2×D3semidirect
180. C2×#214C2×D3semidirect
194. C2×#208C2×D3semidirect
425. C2×C3×D3#137semidirect
705. C2×D3#951semidirect
729. C32#3007semidirect
833. C3#83981semidirect
834. C3#84084semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×#412
C2×C3×#9512
C2×#638562
C2×#638272
#105929312
#105915972
#105915942
#105914612
#105914582
#105910882
#105910692
#840843
#839813