Finite Group Databasebeta

← #11864142

Subgroups — #11864142

Order 1152.

1761 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic, complemented
2C2×#64158C211yesmaximal, characteristic, complemented
3C2×#63909C211yesmaximal, characteristic, complemented
4C2×#63825C211yesmaximal, characteristic, complemented
5C3×#5232C211yesmaximal, characteristic, complemented
6#10591588C212yesmaximal, complemented
7#10591584C212yesmaximal, complemented
8#10591452C212yesmaximal, complemented
9#10591448C212yesmaximal, complemented
10#10591087C211yesmaximal, characteristic, complemented
11#10591069C211yesmaximal, characteristic, complemented
12#84082—31nomaximal
13#78884—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
16C3×D3×#41—24no—
17C3×D3×#41—24no—
18C2×C3×#239C2211yescharacteristic, complemented
19C2×C3×D3×Q8C2211yescharacteristic, complemented
20C2×C3×#237—21no—
21C2×C3×#237C2211yescharacteristic, complemented
22C2×C3×D3×D4—21no—
23C2×C3×D3×D4C2211yescharacteristic, complemented
24C2×C3×#235—21no—
25C2×C3×#235C2211yescharacteristic
26C22×C3×C4×D3—21no—
27C22×C3×C4×D3C2211yescharacteristic
28C22×#626—21no—
29#64158—24no—
30C2×#3755C2212yescomplemented
31C2×#3753C2212yescomplemented
32C2×#3748C2211yescharacteristic, complemented
33C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
34C2×C3×#208C2211yescharacteristic, complemented
35C2×#3722—21no—
36#63909—21no—
37#63909—21no—
38#63909C2212yes—
39#63909C2212yescomplemented
40C2×#3717C2212yescomplemented
41#63825—24no—
42C2×#3714C2212yescomplemented
43C3×#835C2212yescomplemented
44C3×#832C2212yescomplemented
45#63565C2212yescomplemented
46#63562C2212yescomplemented
47(C2×D3)⋊(C3⋊C8)C2212yescomplemented
48(C2×D3)⋊(C3⋊C8)C2212yescomplemented
49C22×C3×#41—31no—
50C2×D3×#41D311yescharacteristic, complemented
51C2×#949—31no—
52C2×#949—31no—
53C2×#949—31no—
54C2×#949—61no—
55C2×#930—31no—
56C2×#908—31no—
57C2×#895—31no—
58C3×#417—31no—
59#5238—32no—
60#5238—32no—
61#5232—31no—
62#5232D311yescharacteristic, complemented
63#5227—32no—
64#5217—32no—
65#5207—31no—
66#5126—31no—
67#4966—31no—
68#4810—32no—
69#4806—32no—
70#4781—32no—
71#4773—32no—
72C23×C3⋊D3—21no—
73C23×C3×D3—21no—
74C23×C3×D3D411yescharacteristic
75C32×#41—22no—
76C32×#41D414yescomplemented
77C2×C32×Q8C2311yescharacteristic
78C2×C32×D4—21no—
79C2×C32×D4C2311yescharacteristic
80C22×C32×C4—21no—
81C22×C32×C4C2311yescharacteristic
82C2×C4⋊(C3⋊D3)—22no—
83C2×C4⋊(C3⋊D3)—22no—
84C2×C4⋊(C3⋊D3)—21no—
85C2×C4⋊(C3⋊D3)C2312yes—
86C2×C3×#67—21no—
87C2×C3×#67—21no—
88C2×C3×#67—21no—
89C22×C3×Dic3—21no—
90C22×C3×Dic3—21no—
91C22×C3×Dic3D411yescharacteristic
92C3×#239—22no—
93C3×#239—22no—
94C3×D3×Q8—22no—
95C3×D3×Q8—22no—
96C3×#237—28no—
97C3×#237—22no—
98C3×#237—22no—
99C3×D3×D4—28no—
100C3×D3×D4—22no—
101C3×D3×D4—22no—
102C3×#235—28no—
103C3×#235—22no—
104C3×#235D414yescomplemented
105C2×C3×D12—21no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—28no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—22no—
111C2×C3×C4×D3—22no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3D411yescharacteristic
114C2×C3×C4×D3D411yescharacteristic
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×Dic6—21no—
118C2×C3×Dic6C2311yescharacteristic
119C2×#626—22no—
120C2×#626—22no—
121C2×#626—44no—
122#3755—24no—
123#3753—24no—
124#3748—22no—
125C2×C3⋊(C3⋊C8)C2312yes—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2312yes—
128C3×#208—22no—
129C2×C3×C3⋊C8C2312yes—
130#3722—22no—
131#3722—22no—
132#3717—24no—
133#3714—24no—
134#3006—91noSylow
135C2×C3×#41—21no—
136C2×C3×#41—31no—
137C2×C3×#41—31no—
138C2×C3×#41—31no—
139C2×C3×#41—61no—
140C2×C3×#41—61no—
141C2×C3×#41—64no—
142C2×C3×#41—64no—
143C2×C3×#41C2×D311yescharacteristic
144C2×C3×#41C2×D311yescharacteristic
145C22×C3×Q8—31no—
146C22×C3×D4—31no—
147C22×C3×D4—61no—
148C23×C3×C4—31no—
149C23×C3×C4—61no—
150C22×#67—61no—
151D3×#41—24no—
152D3×#41—24no—
153C2×#239C2×D311yescharacteristic, complemented
154C2×D3×Q8C2×D311yescharacteristic, complemented
155C2×#237—21no—
156C2×#237C2×D311yescharacteristic, complemented
157C2×D3×D4—21no—
158C2×D3×D4C2×D311yescharacteristic, complemented
159C2×#235—21no—
160C2×#235C2×D311yescharacteristic
161C22×D12—31no—
162C22×D12—31no—
163C22×D12—61no—
164C22×D12—61no—
165C22×C4×D3—21no—
166C22×C4×D3C2×D311yescharacteristic
167C2×C3×M16—31no—
168C2×C3×C4⋊C4—31no—
169#949—64no—
170#949—68no—
171#949—64no—
172#949—64no—
173C2×#215—32no—
174C2×#215—32no—
175C2×#215—32no—
176C2×#215—62no—
177C2×#213—32no—
178C2×#213—32no—
179C2×#213—32no—
180C2×#213—62no—
181#930—32no—
182#930—32no—
183#930—61no—
184#930—61no—
185C2×(C2×D3)⋊C4—61no—
186C2×(C2×D3)⋊C4—61no—
187C2×C4⋊Dic3C2×D311yescharacteristic, complemented
188C2×#208—31no—
189C2×#208—31no—
190C2×#208—61no—
191C2×#208C2×D311yescharacteristic, complemented
192#908—64no—
193C2×D24—32no—
194C2×#204—32no—
195#895—32no—
196#895—32no—
197#895—61no—
198#895—61no—
199C3×#103—32no—
200C3×#102—32no—
201#835—32no—
202#835C2×D312yescomplemented
203#832—32no—
204#832C2×D312yescomplemented
205#830—32no—
206#830—32no—
207(C2×D3)⋊C8—32no—
208(C2×D3)⋊C8—32no—
209#810—32no—
210#809—32no—
211C23×C32—21no—
212C23×C32C2×D411yescharacteristic
213C22×C3⋊D3—22no—
214C22×C3⋊D3—42no—
215C22×C3⋊D3—42no—
216C22×C3⋊D3—42no—
217C22×C3×D3—24no—
218C22×C3×D3—22no—
219C22×C3×D3—21no—
220C22×C3×D3—22no—
221C22×C3×D3—41no—
222C22×C3×D3—42no—
223C22×C3×D3—42no—
224C22×C3×D3C2×D411yescharacteristic
225C22×C3×D3C2×D411yescharacteristic
226C32×Q8—21no—
227C32×Q8C2×D412yescomplemented
228C32×D4—24no—
229C32×D4—21no—
230C32×D4C2×D412yescomplemented
231C2×C32×C4—21no—
232C2×C32×C4—24no—
233C2×C32×C4C2×D412yes—
234C2×C32×C4C2×D411yescharacteristic
235C2×C32×C4C2×D412yes—
236C2×C32×C4C2411yescharacteristic
237C4⋊(C3⋊D3)—22no—
238C4⋊(C3⋊D3)—22no—
239C4⋊(C3⋊D3)—42no—
240C3×#67—24no—
241C3×#67—24no—
242C3×#67—24no—
243C2×C3×Dic3—24no—
244C2×C3×Dic3—22no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—22no—
247C2×C3×Dic3—42no—
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C3×D12—24no—
251C3×D12—21no—
252C3×D12C2×D412yescomplemented
253C3×C4×D3—24no—
254C3×C4×D3—24no—
255C3×C4×D3—22no—
256C3×C4×D3—24no—
257C3×C4×D3—22no—
258C3×C4×D3—21no—
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×Dic6—24no—
263C3×Dic6—21no—
264C3×Dic6C2×D412yescomplemented
265#626—44no—
266#626—44no—
267C3⋊(C3⋊C8)—22no—
268C3×C3⋊C8—22no—
269C22×#41—31no—
270C2×AGL(1,ℤ/8)—91no—
271C2×AGL(1,ℤ/8)—91no—
272C2×#121—91no—
273#449—92no—
274#449—92no—
275#448—92no—
276#447—92no—
277#417—31no—
278#417—91no—
279#407—91no—
280C24×C3—31no—
281C24×C3—61no—
282C23×D3—21no—
283C23×D3—61no—
284C23×D3—61no—
285C23×D3—121no—
286C23×D3#6711yescharacteristic
287C3×#41—22no—
288C3×#41—22no—
289C3×#41—24no—
290C3×#41—34no—
291C3×#41—42no—
292C3×#41—68no—
293C3×#41—62no—
294C3×#41—68no—
295C3×#41—62no—
296C3×#41—62no—
297C3×#41—62no—
298C3×#41—62no—
299C3×#41D1214yescomplemented
300C3×#41#6714yescomplemented
301C2×C3×Q8—21no—
302C2×C3×Q8—31no—
303C2×C3×Q8—61no—
304C2×C3×Q8—62no—
305C2×C3×Q8—62no—
306C2×C3×Q8C22×D311yescharacteristic
307C2×C3×Q8C22×D311yescharacteristic
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4—21no—
311C2×C3×D4—31no—
312C2×C3×D4—41no—
313C2×C3×D4—61no—
314C2×C3×D4—61no—
315C2×C3×D4—62no—
316C2×C3×D4—68no—
317C2×C3×D4—61no—
318C2×C3×D4—61no—
319C2×C3×D4—62no—
320C2×C3×D4C22×D311yescharacteristic
321C2×C3×D4C22×D311yescharacteristic
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—41no—
331C22×C3×C4—61no—
332C22×C3×C4—61no—
333C22×C3×C4—68no—
334C22×C3×C4—61no—
335C22×C3×C4—62no—
336C22×C3×C4—62no—
337C22×C3×C4—61no—
338C22×C3×C4—61no—
339C22×C3×C4C22×D311yescharacteristic
340C22×C3×C4C22×D311yescharacteristic
341C2×#67—21no—
342C2×#67—21no—
343C2×#67—21no—
344C2×#67—62no—
345C2×#67—62no—
346C2×#67—124no—
347C22×Dic3—21no—
348C22×Dic3—21no—
349C22×Dic3#6711yescharacteristic
350#239—22no—
351#239—22no—
352D3×Q8—22no—
353D3×Q8—22no—
354#237—28no—
355#237—22no—
356#237—22no—
357D3×D4—28no—
358D3×D4—22no—
359D3×D4—22no—
360#235—28no—
361#235—22no—
362#235#6714yescomplemented
363C2×D12—21no—
364C2×D12—32no—
365C2×D12—32no—
366C2×D12—62no—
367C2×D12—64no—
368C2×D12—62no—
369C2×D12—62no—
370C2×D12—62no—
371C2×D12—62no—
372C2×D12—62no—
373C2×D12—62no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—122no—
377C2×D12—121no—
378C2×D12—124no—
379C2×D12C22×D311yescharacteristic
380C2×C4×D3—28no—
381C2×C4×D3—21no—
382C2×C4×D3—21no—
383C2×C4×D3—22no—
384C2×C4×D3—22no—
385C2×C4×D3—21no—
386C2×C4×D3#6711yescharacteristic
387C2×C4×D3#6711yescharacteristic
388C2×C4×D3C22×D311yescharacteristic
389C2×C4×D3C22×D311yescharacteristic
390C2×Dic6—21no—
391C2×Dic6C22×D311yescharacteristic
392C3×M16—62no—
393C2×C3×C8—32no—
394C3×C4⋊C4—32no—
395C3×C4⋊C4—61no—
396#215—64no—
397#215—68no—
398#215—64no—
399#215—64no—
400#213—64no—
401#213—68no—
402#213—64no—
403#213—64no—
404(C2×D3)⋊C4—62no—
405(C2×D3)⋊C4—62no—
406(C2×D3)⋊C4—62no—
407(C2×D3)⋊C4—62no—
408C4⋊Dic3—21no—
409C4⋊Dic3C22×D312yes—
410#208—22no—
411#208—64no—
412#208—62no—
413#208—62no—
414C2×C3⋊C8—32no—
415C2×C3⋊C8—32no—
416C2×C3⋊C8—62no—
417C2×C3⋊C8C22×D312yes—
418D24—64no—
419#204—64no—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32—22no—
423C22×C32—41no—
424C22×C32—41no—
425C22×C32#12012yes—
426C22×C32C22×D411yescharacteristic
427C2×C3⋊D3—42no—
428C2×C3⋊D3—42no—
429C2×C3⋊D3—42no—
430C2×C3⋊D3—84no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—22no—
435C2×C3×D3—21no—
436C2×C3×D3—21no—
437C2×C3×D3—44no—
438C2×C3×D3—48no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C2×C3×D3AGL(1,ℤ/8)12yescomplemented
442C32×C4—22no—
443C32×C4#12012yes—
444C32×C4C22×D411yescharacteristic
445C32×C4C22×D411yescharacteristic
446C3×Dic3—21no—
447C3×Dic3—22no—
448C3×Dic3—21no—
449C3×Dic3—42no—
450C2×#41—31no—
451C2×#41—31no—
452C2×#41—31no—
453C2×#41—61no—
454C2×#41—61no—
455C2×#41—64no—
456C2×#41—64no—
457C2×#41D3211yescharacteristic
458C22×Q8—31no—
459C22×D4—31no—
460C22×D4—61no—
461C22×D4—91no—
462C22×D4—181no—
463C23×C4—31no—
464C23×C4—61no—
465AGL(1,ℤ/8)—184no—
466AGL(1,ℤ/8)—184no—
467C2×SD16—92no—
468C2×SD16—92no—
469C2×D8—92no—
470C2×D8—92no—
471C2×M16—31no—
472C2×M16—91no—
473#121—92no—
474#121—92no—
475#121—181no—
476#121—181no—
477C2×C4⋊C4—31no—
478C2×C22⋊C4—181no—
479#103—32no—
480#103—92no—
481#102—32no—
482#102—92no—
483C22⋊C8—92no—
484C22⋊C8—92no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—31no—
489C23×C3—31no—
490C23×C3—41no—
491C23×C3—62no—
492C23×C3—64no—
493C23×C3—62no—
494C23×C3—61no—
495C23×C3—121no—
496C23×C3—122no—
497C23×C3—122no—
498C23×C3D3×D411yescharacteristic
499C23×C3C2×#6711yescharacteristic
500C22×D3—24no—
501C22×D3—22no—
502C22×D3—21no—
503C22×D3—22no—
504C22×D3—41no—
505C22×D3—42no—
506C22×D3—42no—
507C22×D3—62no—
508C22×D3—62no—
509C22×D3—122no—
510C22×D3—124no—
511C22×D3—122no—
512C22×D3—122no—
513C22×D3—122no—
514C22×D3—122no—
515C22×D3—122no—
516C22×D3—122no—
517C22×D3—242no—
518C22×D3—242no—
519C22×D3C2×#6711yescharacteristic
520C22×D3C2×#6711yescharacteristic
521C3×Q8—21no—
522C3×Q8—21no—
523C3×Q8—22no—
524C3×Q8—32no—
525C3×Q8—41no—
526C3×Q8—64no—
527C3×Q8—61no—
528C3×Q8C2×D1212yescomplemented
529C3×Q8C2×#6712yescomplemented
530C3×D4—24no—
531C3×D4—24no—
532C3×D4—21no—
533C3×D4—21no—
534C3×D4—22no—
535C3×D4—32no—
536C3×D4—41no—
537C3×D4—44no—
538C3×D4—64no—
539C3×D4—64no—
540C3×D4—64no—
541C3×D4—64no—
542C3×D4—61no—
543C3×D4C2×D1212yescomplemented
544C3×D4C2×#6712yescomplemented
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—24no—
548C2×C3×C4—24no—
549C2×C3×C4—21no—
550C2×C3×C4—22no—
551C2×C3×C4—21no—
552C2×C3×C4—22no—
553C2×C3×C4—31no—
554C2×C3×C4—31no—
555C2×C3×C4—44no—
556C2×C3×C4—41no—
557C2×C3×C4—64no—
558C2×C3×C4—64no—
559C2×C3×C4—64no—
560C2×C3×C4—62no—
561C2×C3×C4—61no—
562C2×C3×C4—62no—
563C2×C3×C4—62no—
564C2×C3×C4—64no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—62no—
570C2×C3×C4—122no—
571C2×C3×C4C2×D1212yes—
572C2×C3×C4D3×D411yescharacteristic
573C2×C3×C4D3×D412yes—
574C2×C3×C4C2×#6712yes—
575C2×C3×C4C2×#6711yescharacteristic
576C2×C3×C4C2×#6712yes—
577C2×C3×C4C23×D311yescharacteristic
578C2×C3×C4C23×D311yescharacteristic
579#67—24no—
580#67—24no—
581#67—24no—
582#67—124no—
583#67—124no—
584C2×Dic3—24no—
585C2×Dic3—22no—
586C2×Dic3—21no—
587C2×Dic3—22no—
588C2×Dic3—42no—
589C2×Dic3C2×#6711yescharacteristic
590C2×Dic3C2×#6711yescharacteristic
591D12—24no—
592D12—21no—
593D12—64no—
594D12—62no—
595D12—62no—
596D12—62no—
597D12—62no—
598D12—122no—
599D12—124no—
600D12—124no—
601D12—124no—
602D12—122no—
603D12—122no—
604D12C2×#6712yescomplemented
605C4×D3—24no—
606C4×D3—24no—
607C4×D3—22no—
608C4×D3—24no—
609C4×D3—22no—
610C4×D3—21no—
611C4×D3—21no—
612C4×D3—21no—
613C4×D3—21no—
614Dic6—24no—
615Dic6—21no—
616Dic6C2×#6712yescomplemented
617C3×C8—62no—
618C3⋊C8—22no—
619C3⋊C8—64no—
620C3⋊C8—62no—
621C3⋊C8—62no—
622C2×C32—22no—
623C2×C32—42no—
624C2×C32C2×#12011yescharacteristic
625C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
626C2×C32#57511yescharacteristic
627C3⋊D3—82no—
628C3×D3—22no—
629C3×D3—41no—
630C3×D3—42no—
631C24—31no—
632C24—61no—
633C24—181no—
634#41—22no—
635#41—34no—
636#41—68no—
637#41—62no—
638#41—68no—
639#41—62no—
640#41—62no—
641#41—62no—
642#41—62no—
643#41#62614yescomplemented
644C2×Q8—31no—
645C2×Q8—61no—
646C2×Q8—62no—
647C2×Q8—62no—
648C2×Q8C2×D3211yescharacteristic
649C2×D4—21no—
650C2×D4—31no—
651C2×D4—61no—
652C2×D4—61no—
653C2×D4—62no—
654C2×D4—68no—
655C2×D4—61no—
656C2×D4—61no—
657C2×D4—62no—
658C2×D4—92no—
659C2×D4—182no—
660C2×D4—182no—
661C2×D4—182no—
662C2×D4—182no—
663C2×D4—181no—
664C2×D4—364no—
665C2×D4C2×D3211yescharacteristic
666C22×C4—21no—
667C22×C4—31no—
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—31no—
671C22×C4—31no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—68no—
675C22×C4—61no—
676C22×C4—62no—
677C22×C4—62no—
678C22×C4—61no—
679C22×C4—61no—
680C22×C4C2×D3211yescharacteristic
681SD16—184no—
682SD16—184no—
683D8—184no—
684D8—184no—
685M16—62no—
686M16—182no—
687C2×C8—32no—
688C2×C8—92no—
689C4⋊C4—32no—
690C4⋊C4—61no—
691C22⋊C4—182no—
692C22⋊C4—182no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—22no—
698C22×C3—22no—
699C22×C3—21no—
700C22×C3—22no—
701C22×C3—32no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—42no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—61no—
710C22×C3—61no—
711C22×C3—62no—
712C22×C3—61no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—81no—
716C22×C3—81no—
717C22×C3—124no—
718C22×C3—128no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3#88212yes—
722C22×C3#95312yes—
723C22×C3C2×D3×D411yescharacteristic
724C22×C3C22×#6711yescharacteristic
725C2×D3—21no—
726C2×D3—21no—
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—21no—
730C2×D3—22no—
731C2×D3—44no—
732C2×D3—48no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—124no—
736C2×D3—122no—
737C2×D3—122no—
738C2×D3—122no—
739C2×D3—122no—
740C2×D3—122no—
741C2×D3—122no—
742C2×D3—242no—
743C2×D3—242no—
744C2×D3—244no—
745C2×D3—244no—
746C2×D3—248no—
747C2×D3#94912yescomplemented
748C3×C4—22no—
749C3×C4—22no—
750C3×C4—21no—
751C3×C4—21no—
752C3×C4—22no—
753C3×C4—42no—
754C3×C4—61no—
755C3×C4—61no—
756C3×C4—62no—
757C3×C4—122no—
758C3×C4#88212yes—
759C3×C4#95312yes—
760C3×C4C22×D1211yescharacteristic
761C3×C4C2×D3×D411yescharacteristic
762C3×C4C22×#6711yescharacteristic
763C3×C4C22×#6711yescharacteristic
764Dic3—21no—
765Dic3—22no—
766Dic3—21no—
767Dic3—42no—
768C32#300611yescharacteristic, complemented, Sylow
769C23—21no—
770C23—31no—
771C23—31no—
772C23—62no—
773C23—64no—
774C23—61no—
775C23—62no—
776C23—121no—
777C23—122no—
778C23—122no—
779C23—182no—
780C23—362no—
781C23—362no—
782C23—362no—
783C23D3×#6711yescharacteristic
784Q8—21no—
785Q8—32no—
786Q8—64no—
787Q8—61no—
788Q8C2×#62612yescomplemented
789D4—24no—
790D4—21no—
791D4—32no—
792D4—64no—
793D4—64no—
794D4—64no—
795D4—64no—
796D4—61no—
797D4—182no—
798D4—182no—
799D4—364no—
800D4—364no—
801D4—362no—
802D4C2×#62612yescomplemented
803C2×C4—21no—
804C2×C4—24no—
805C2×C4—31no—
806C2×C4—31no—
807C2×C4—64no—
808C2×C4—64no—
809C2×C4—64no—
810C2×C4—61no—
811C2×C4—62no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—62no—
817C2×C4—62no—
818C2×C4—64no—
819C2×C4—62no—
820C2×C4—122no—
821C2×C4C2×#62612yes—
822C2×C4D3×#6712yes—
823C2×C4D3×#6711yescharacteristic
824C2×C4C22×D3211yescharacteristic
825C8—62no—
826C8—182no—
827C2×C3—22no—
828C2×C3—22no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—42no—
833C2×C3—42no—
834C2×C3—42no—
835C2×C3—62no—
836C2×C3—82no—
837C2×C3—121no—
838C2×C3—122no—
839C2×C3C2×#88211yescharacteristic
840C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
841C2×C3#577711yescharacteristic
842C2×C3C2×#94911yescharacteristic
843C2×C3#582211yescharacteristic
844C2×C3C2×#95311yescharacteristic
845D3—22no—
846D3—41no—
847D3—42no—
848D3—244no—
849D3—242no—
850D3—242no—
851C22—21no—
852C22—21no—
853C22—22no—
854C22—32no—
855C22—41no—
856C22—41no—
857C22—61no—
858C22—61no—
859C22—61no—
860C22—61no—
861C22—62no—
862C22—61no—
863C22—124no—
864C22—128no—
865C22—121no—
866C22—121no—
867C22—362no—
868C22—362no—
869C22—362no—
870C22—724no—
871C22#6397712yes—
872C22C2×D3×#6711yescharacteristic
873C4—22no—
874C4—61no—
875C4—61no—
876C4—62no—
877C4—122no—
878C4#6397712yes—
879C4C22×#62611yescharacteristic
880C4C2×D3×#6711yescharacteristic
881C3—21no—
882C3#7888411yescharacteristic, complemented
883C3#8408211yescharacteristic, complemented
884C2—22no—
885C2—42no—
886C2—62no—
887C2—121no—
888C2—122no—
889C2—722no—
890C2D3×#94911yescharacteristic
891C2#1059547011yescharacteristic
892C2C2×#6397711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3006
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
1. C2×C3×D3×#41C2semidirect
2. C2×#64158C2semidirect
3. C2×#63909C2semidirect
4. C2×#63825C2semidirect
5. C3×#5232C2semidirect
6. #10591588C2semidirect
7. #10591584C2semidirect
8. #10591452C2semidirect
9. #10591448C2semidirect
10. #10591087C2semidirect
11. #10591069C2semidirect
15. C22×C4⋊(C3⋊D3)C22semidirect
18. C2×C3×#239C22semidirect
19. C2×C3×D3×Q8C22semidirect
21. C2×C3×#237C22semidirect
23. C2×C3×D3×D4C22semidirect
30. C2×#3755C22semidirect
31. C2×#3753C22semidirect
32. C2×#3748C22semidirect
33. C2×C3×C4⋊Dic3C22semidirect
34. C2×C3×#208C22semidirect
39. #63909C22semidirect
40. C2×#3717C22semidirect
42. C2×#3714C22semidirect
43. C3×#835C22semidirect
44. C3×#832C22semidirect
45. #63565C22semidirect
46. #63562C22semidirect
47. (C2×D3)⋊(C3⋊C8)C22semidirect
48. (C2×D3)⋊(C3⋊C8)C22semidirect
50. C2×D3×#41D3semidirect
62. #5232D3semidirect
76. C32×#41D4semidirect
104. C3×#235D4semidirect
153. C2×#239C2×D3semidirect
154. C2×D3×Q8C2×D3semidirect
156. C2×#237C2×D3semidirect
158. C2×D3×D4C2×D3semidirect
187. C2×C4⋊Dic3C2×D3semidirect
191. C2×#208C2×D3semidirect
202. #835C2×D3semidirect
204. #832C2×D3semidirect
227. C32×Q8C2×D4semidirect
230. C32×D4C2×D4semidirect
252. C3×D12C2×D4semidirect
264. C3×Dic6C2×D4semidirect
299. C3×#41D12semidirect
300. C3×#41#67semidirect
362. #235#67semidirect
441. C2×C3×D3AGL(1,ℤ/8)semidirect
528. C3×Q8C2×D12semidirect
529. C3×Q8C2×#67semidirect
543. C3×D4C2×D12semidirect
544. C3×D4C2×#67semidirect
604. D12C2×#67semidirect
616. Dic6C2×#67semidirect
643. #41#626semidirect
747. C2×D3#949semidirect
768. C32#3006semidirect
788. Q8C2×#626semidirect
802. D4C2×#626semidirect
882. C3#78884semidirect
883. C3#84082semidirect

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×#641582
C2×#639092
C2×#638252
C3×#52322
#105915882
#105915842
#105914522
#105914482
#105910872
#105910692
#840823
#788843