Finite Group Databasebeta

← #11857981

Subgroups — #11857981

Order 1152.

1625 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic
2C2×#63841C211yesmaximal, characteristic, complemented
3C2×D3×#208C211yesmaximal, characteristic, complemented
4#10592931C211yesmaximal, characteristic, complemented
5C3×#5232C211yesmaximal, characteristic, complemented
6#10591557C212yesmaximal, complemented
7#10591556C212yesmaximal, complemented
8#10591421C212yesmaximal, complemented
9#10591420C212yesmaximal, complemented
10#10591088C211yesmaximal, characteristic, complemented
11#10591087C211yesmaximal, characteristic, complemented
12#84072—31nomaximal
13#78881—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C3×D3×#41—24no—
16C3×D3×#41C418yescomplemented
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
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
28C2×#3748C2211yescharacteristic, complemented
29C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
30C2×C3×#208C2211yescharacteristic, complemented
31C2×(C2×D3)⋊Dic3—21no—
32C2×Dic32—21no—
33#63841—21no—
34#63841—21no—
35#63841C2212yes—
36#63841C2212yescomplemented
37C2×#3711C2212yes—
38D3×#208—24no—
39C2×D3×C3⋊C8C2212yescomplemented
40#63662C2212yescomplemented
41#63659C2212yescomplemented
42C3×#835C2212yescomplemented
43C3×#832C2212yescomplemented
44#63566C2212yescomplemented
45#63565C2212yescomplemented
46#63563C2212yescomplemented
47#63562C2212yescomplemented
48C22×C3×#41—31no—
49C2×D3×#41D311yescharacteristic
50C2×#926—31no—
51C22×#208—31no—
52C2×D3×M16—31no—
53C2×#892—31no—
54C3×#417—31no—
55#5233—32no—
56#5233—32no—
57#5232—31no—
58#5232—31no—
59#5232—31no—
60#5232—31no—
61#5232—61no—
62#5232D311yescharacteristic, complemented
63#5225—32no—
64#5215—32no—
65#5133—31no—
66#4966—31no—
67#4804—32no—
68#4802—32no—
69#4772—32no—
70#4770—32no—
71C23×C3×D3—21no—
72C23×C3×D3D411yescharacteristic
73C32×#41—22no—
74C32×#41C2×C414yes—
75C2×C32×Q8C2311yescharacteristic
76C2×C32×D4—21no—
77C2×C32×D4C2311yescharacteristic
78C22×C32×C4—21no—
79C22×C32×C4C2311yescharacteristic
80C22×C3⋊Dic3—21no—
81C2×C3×#67—21no—
82C2×C3×#67—21no—
83C2×C3×#67—21no—
84C22×C3×Dic3—21no—
85C22×C3×Dic3—21no—
86C22×C3×Dic3D411yescharacteristic
87C3×#239—22no—
88C3×#239C2×C414yescomplemented
89C3×D3×Q8—22no—
90C3×D3×Q8C2×C414yescomplemented
91C3×#237—28no—
92C3×#237—22no—
93C3×#237C2×C414yescomplemented
94C3×D3×D4—28no—
95C3×D3×D4—22no—
96C3×D3×D4C2×C414yescomplemented
97C3×#235—22no—
98C3×#235—28no—
99C3×#235C2×C414yes—
100C2×C3×D12—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—28no—
106C2×C3×C4×D3C2×C414yes—
107C2×C3×C4×D3D411yescharacteristic
108C2×C3×C4×D3D411yescharacteristic
109C2×C3×C4×D3D414yes—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6—21no—
113C2×C3×Dic6C2311yescharacteristic
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2312yes—
116#3748—22no—
117C2×C3⋊(C3⋊C8)C2312yes—
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3C2312yes—
120C3×#208—22no—
121C2×C3×C3⋊C8C2312yes—
122(C2×D3)⋊Dic3—22no—
123(C2×D3)⋊Dic3—22no—
124Dic32—22no—
125Dic32—22no—
126#3711—24no—
127D3×C3⋊C8—24no—
128#2896—91noSylow
129C2×C3×#41—21no—
130C2×C3×#41—38no—
131C2×C3×#41—31no—
132C2×C3×#41—31no—
133C2×C3×#41—31no—
134C2×C3×#41—61no—
135C2×C3×#41—61no—
136C2×C3×#41—64no—
137C2×C3×#41C2×D311yescharacteristic
138C2×C3×#41C2×D311yescharacteristic
139C22×C3×Q8—31no—
140C22×C3×D4—31no—
141C22×C3×D4—61no—
142C23×C3×C4—31no—
143C23×C3×C4—61no—
144D3×#41—24no—
145D3×#41Dic318yescomplemented
146C2×#239C2×D311yescharacteristic
147C2×D3×Q8C2×D311yescharacteristic
148C2×#237—21no—
149C2×#237C2×D311yescharacteristic
150C2×D3×D4—21no—
151C2×D3×D4C2×D311yescharacteristic
152C2×#235—21no—
153C2×#235C2×D311yescharacteristic
154C22×C4×D3—21no—
155C22×C4×D3C2×D311yescharacteristic
156C2×C3×M16—31no—
157C2×C3×C4⋊C4—31no—
158C2×#217—61no—
159C2×(C2×D3)⋊C4—61no—
160#926—32no—
161#926—32no—
162#926—61no—
163#926—61no—
164C2×C4⋊Dic3—31no—
165C2×C4⋊Dic3—31no—
166C2×C4⋊Dic3—61no—
167C2×C4⋊Dic3C2×D311yescharacteristic, complemented
168C2×C4×Dic3—61no—
169C2×C4×Dic3—61no—
170C2×#208—31no—
171C2×#208—31no—
172C2×#208—32no—
173C2×#208—61no—
174C2×#208—64no—
175C2×#208C2×D311yescharacteristic, complemented
176C22×C3⋊C8—32no—
177D3×M16—64no—
178C2×ΓL(1,𝔽25)—32no—
179C2×D3×C8—32no—
180#892—32no—
181#892—32no—
182#892—61no—
183#892—61no—
184C3×#103—32no—
185C3×#102—32no—
186#835—32no—
187#835—32no—
188#835—32no—
189#835—32no—
190#835—62no—
191#835C2×D312yescomplemented
192#832—32no—
193#832—32no—
194#832—32no—
195#832—32no—
196#832—62no—
197#832C2×D312yescomplemented
198#821—32no—
199#816—32no—
200#810—32no—
201#809—32no—
202C23×C32—21no—
203C23×C32C2×D411yescharacteristic
204C22×C3×D3—21no—
205C22×C3×D3—24no—
206C22×C3×D3—41no—
207C22×C3×D3—41no—
208C22×C3×D3—42no—
209C22×C3×D3—42no—
210C22×C3×D3C22⋊C414yes—
211C22×C3×D3C2×D411yescharacteristic
212C22×C3×D3C2×D411yescharacteristic
213C32×Q8—21no—
214C32×Q8C22×C412yes—
215C32×D4—24no—
216C32×D4—21no—
217C32×D4C22×C412yes—
218C2×C32×C4—21no—
219C2×C32×C4—24no—
220C2×C32×C4C22×C412yes—
221C2×C32×C4C2×D411yescharacteristic
222C2×C32×C4C2×D412yes—
223C2×C32×C4C2411yescharacteristic
224C2×C3⋊Dic3—22no—
225C2×C3⋊Dic3—42no—
226C3×#67—24no—
227C3×#67—24no—
228C3×#67—24no—
229C2×C3×Dic3—21no—
230C2×C3×Dic3—24no—
231C2×C3×Dic3—22no—
232C2×C3×Dic3—42no—
233C2×C3×Dic3C22⋊C414yes—
234C2×C3×Dic3C2×D411yescharacteristic
235C2×C3×Dic3C2×D411yescharacteristic
236C3×D12—24no—
237C3×D12—21no—
238C3×D12C22×C412yes—
239C3×C4×D3—24no—
240C3×C4×D3—24no—
241C3×C4×D3—24no—
242C3×C4×D3C22⋊C414yes—
243C3×C4×D3C22⋊C414yes—
244C3×C4×D3C22×C412yes—
245C3×C4×D3C22×C412yes—
246C3×C4×D3C2×D412yes—
247C3×C4×D3C2×D412yes—
248C3×Dic6—21no—
249C3×Dic6—24no—
250C3×Dic6C22×C412yes—
251C3⋊(C3⋊C8)—22no—
252C3×C3⋊C8—22no—
253C22×#41—31no—
254C22×M16—91no—
255C2×#117—91no—
256#419—92no—
257#418—92no—
258#417—31no—
259#417—91no—
260#417—91no—
261#417—91no—
262#416—92no—
263#416—92no—
264C24×C3—31no—
265C24×C3—61no—
266C23×D3—21no—
267C23×D3#6711yescharacteristic
268C3×#41—22no—
269C3×#41—22no—
270C3×#41—24no—
271C3×#41—34no—
272C3×#41—34no—
273C3×#41—34no—
274C3×#41—42no—
275C3×#41—68no—
276C3×#41—68no—
277C3×#41—62no—
278C3×#41—62no—
279C3×#41—62no—
280C3×#41C4×D314yes—
281C3×#41C2×Dic314yes—
282C2×C3×Q8—21no—
283C2×C3×Q8—34no—
284C2×C3×Q8—31no—
285C2×C3×Q8—61no—
286C2×C3×Q8—62no—
287C2×C3×Q8C22×D311yescharacteristic
288C2×C3×Q8C22×D311yescharacteristic
289C2×C3×D4—21no—
290C2×C3×D4—21no—
291C2×C3×D4—21no—
292C2×C3×D4—34no—
293C2×C3×D4—31no—
294C2×C3×D4—41no—
295C2×C3×D4—61no—
296C2×C3×D4—62no—
297C2×C3×D4—61no—
298C2×C3×D4—68no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C2×C3×D4C22×D311yescharacteristic
302C2×C3×D4C22×D311yescharacteristic
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—31no—
307C22×C3×C4—34no—
308C22×C3×C4—34no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—41no—
314C22×C3×C4—61no—
315C22×C3×C4—68no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C22×D311yescharacteristic
322C2×#67—21no—
323C2×#67—21no—
324C2×#67—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—61no—
328C22×Dic3—61no—
329C22×Dic3—121no—
330C22×Dic3#6711yescharacteristic
331#239—22no—
332#239C2×Dic314yescomplemented
333D3×Q8—22no—
334D3×Q8C2×Dic314yescomplemented
335#237—28no—
336#237—22no—
337#237C2×Dic314yescomplemented
338D3×D4—28no—
339D3×D4—22no—
340D3×D4C2×Dic314yescomplemented
341#235—22no—
342#235—28no—
343#235C2×Dic314yes—
344C2×D12—21no—
345C2×D12C22×D311yescharacteristic
346C2×C4×D3—21no—
347C2×C4×D3—21no—
348C2×C4×D3—21no—
349C2×C4×D3—28no—
350C2×C4×D3C2×Dic314yes—
351C2×C4×D3#6711yescharacteristic
352C2×C4×D3#6711yescharacteristic
353C2×C4×D3#6714yes—
354C2×C4×D3C22×D311yescharacteristic
355C2×C4×D3C22×D311yescharacteristic
356C2×Dic6—21no—
357C2×Dic6C22×D311yescharacteristic
358C3×M16—62no—
359C2×C3×C8—32no—
360C3×C4⋊C4—32no—
361C3×C4⋊C4—61no—
362#217—62no—
363#217—62no—
364(C2×D3)⋊C4—62no—
365(C2×D3)⋊C4—62no—
366C4⋊Dic3—21no—
367C4⋊Dic3—32no—
368C4⋊Dic3—32no—
369C4⋊Dic3—62no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—121no—
373C4⋊Dic3C22×D312yes—
374C4×Dic3—62no—
375C4×Dic3—62no—
376C4×Dic3—62no—
377C4×Dic3—62no—
378#208—22no—
379#208—64no—
380#208—62no—
381#208—62no—
382#208—122no—
383C2×C3⋊C8—32no—
384C2×C3⋊C8—32no—
385C2×C3⋊C8—62no—
386C2×C3⋊C8—64no—
387C2×C3⋊C8C22×D312yes—
388ΓL(1,𝔽25)—64no—
389D3×C8—64no—
390C22×C32—21no—
391C22×C32—21no—
392C22×C32—22no—
393C22×C32—41no—
394C22×C32—41no—
395C22×C32C2×C22⋊C412yes—
396C22×C32C22×D411yescharacteristic
397C2×C3×D3—21no—
398C2×C3×D3—21no—
399C2×C3×D3—21no—
400C2×C3×D3—21no—
401C2×C3×D3—22no—
402C2×C3×D3—44no—
403C2×C3×D3—48no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C2×C3×D3C2×C22⋊C412yes—
407C2×C3×D3C2×C22⋊C412yes—
408C32×C4—22no—
409C32×C4C2×C22⋊C412yes—
410C32×C4C23×C411yescharacteristic
411C32×C4C22×D411yescharacteristic
412C3⋊Dic3—42no—
413C3×Dic3—22no—
414C3×Dic3—42no—
415C3×Dic3C2×C22⋊C412yes—
416C3×Dic3C2×C22⋊C412yes—
417C2×#41—38no—
418C2×#41—31no—
419C2×#41—31no—
420C2×#41—31no—
421C2×#41—61no—
422C2×#41—61no—
423C2×#41—64no—
424C2×#41D3211yescharacteristic
425C22×Q8—31no—
426C22×D4—31no—
427C22×D4—61no—
428C23×C4—31no—
429C23×C4—61no—
430C2×M16—31no—
431C2×M16—92no—
432C2×M16—91no—
433C2×M16—184no—
434C22×C8—92no—
435#117—92no—
436#117—92no—
437#117—181no—
438#117—181no—
439C2×C4⋊C4—31no—
440C2×C4⋊C4—91no—
441C2×C22⋊C4—181no—
442C2×C42—181no—
443#103—32no—
444#103—92no—
445#103—92no—
446#103—92no—
447#102—32no—
448#102—92no—
449#102—92no—
450#102—92no—
451C23×C3—21no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—31no—
455C23×C3—31no—
456C23×C3—34no—
457C23×C3—41no—
458C23×C3—64no—
459C23×C3—61no—
460C23×C3—121no—
461C23×C3—121no—
462C23×C3—122no—
463C23×C3—122no—
464C23×C3D3×D411yescharacteristic
465C23×C3C2×#6711yescharacteristic
466C22×D3—21no—
467C22×D3—24no—
468C22×D3—41no—
469C22×D3—41no—
470C22×D3—42no—
471C22×D3—42no—
472C22×D3#21714yes—
473C22×D3C2×#6711yescharacteristic
474C22×D3C2×#6711yescharacteristic
475C3×Q8—21no—
476C3×Q8—21no—
477C3×Q8—22no—
478C3×Q8—32no—
479C3×Q8—41no—
480C3×Q8—64no—
481C3×Q8—61no—
482C3×Q8C2×C4×D312yes—
483C3×Q8C22×Dic312yes—
484C3×D4—24no—
485C3×D4—24no—
486C3×D4—21no—
487C3×D4—21no—
488C3×D4—22no—
489C3×D4—32no—
490C3×D4—41no—
491C3×D4—44no—
492C3×D4—64no—
493C3×D4—64no—
494C3×D4—64no—
495C3×D4—64no—
496C3×D4—61no—
497C3×D4C2×C4×D312yes—
498C3×D4C22×Dic312yes—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—24no—
502C2×C3×C4—24no—
503C2×C3×C4—21no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—21no—
507C2×C3×C4—34no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—34no—
511C2×C3×C4—34no—
512C2×C3×C4—32no—
513C2×C3×C4—32no—
514C2×C3×C4—32no—
515C2×C3×C4—32no—
516C2×C3×C4—44no—
517C2×C3×C4—41no—
518C2×C3×C4—64no—
519C2×C3×C4—64no—
520C2×C3×C4—64no—
521C2×C3×C4—61no—
522C2×C3×C4—64no—
523C2×C3×C4—62no—
524C2×C3×C4—122no—
525C2×C3×C4C2×C4×D312yes—
526C2×C3×C4D3×D411yescharacteristic
527C2×C3×C4D3×D412yes—
528C2×C3×C4C22×Dic312yes—
529C2×C3×C4C2×#6711yescharacteristic
530C2×C3×C4C2×#6712yes—
531C2×C3×C4C23×D311yescharacteristic
532C2×C3×C4C23×D311yescharacteristic
533#67—24no—
534#67—24no—
535#67—24no—
536C2×Dic3—21no—
537C2×Dic3—24no—
538C2×Dic3—22no—
539C2×Dic3—42no—
540C2×Dic3—62no—
541C2×Dic3—62no—
542C2×Dic3—122no—
543C2×Dic3—122no—
544C2×Dic3—122no—
545C2×Dic3—242no—
546C2×Dic3#21714yes—
547C2×Dic3C2×#6711yescharacteristic
548C2×Dic3C2×#6711yescharacteristic
549D12—24no—
550D12—21no—
551D12C22×Dic312yes—
552C4×D3—24no—
553C4×D3—24no—
554C4×D3—24no—
555C4×D3#21714yes—
556C4×D3#21714yes—
557C4×D3C22×Dic312yes—
558C4×D3C22×Dic312yes—
559C4×D3C2×#6712yes—
560C4×D3C2×#6712yes—
561Dic6—21no—
562Dic6—24no—
563Dic6C22×Dic312yes—
564C3×C8—62no—
565C3⋊C8—22no—
566C3⋊C8—62no—
567C3⋊C8—62no—
568C3⋊C8—122no—
569C2×C32—22no—
570C2×C32—42no—
571C2×C32C22×C22⋊C411yescharacteristic
572C2×C32#57511yescharacteristic
573C2×C32#57511yescharacteristic
574C3×D3—22no—
575C3×D3—22no—
576C3×D3—42no—
577C24—31no—
578C24—61no—
579#41—22no—
580#41—34no—
581#41—34no—
582#41—34no—
583#41—68no—
584#41—68no—
585#41—62no—
586#41—62no—
587#41—62no—
588#41D3×Dic314yes—
589C2×Q8—34no—
590C2×Q8—31no—
591C2×Q8—61no—
592C2×Q8—62no—
593C2×Q8C2×D3211yescharacteristic
594C2×D4—21no—
595C2×D4—34no—
596C2×D4—31no—
597C2×D4—61no—
598C2×D4—62no—
599C2×D4—61no—
600C2×D4—68no—
601C2×D4—61no—
602C2×D4—61no—
603C2×D4C2×D3211yescharacteristic
604C22×C4—21no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—34no—
609C22×C4—31no—
610C22×C4—31no—
611C22×C4—34no—
612C22×C4—61no—
613C22×C4—68no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—181no—
619C22×C4C2×D3211yescharacteristic
620M16—62no—
621M16—184no—
622M16—182no—
623C2×C8—32no—
624C2×C8—92no—
625C2×C8—184no—
626C4⋊C4—32no—
627C4⋊C4—61no—
628C4⋊C4—92no—
629C4⋊C4—181no—
630C22⋊C4—182no—
631C22⋊C4—182no—
632C42—182no—
633C42—182no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—22no—
639C22×C3—22no—
640C22×C3—21no—
641C22×C3—22no—
642C22×C3—32no—
643C22×C3—32no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—42no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—62no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3—124no—
659C22×C3—128no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3D3×C22⋊C412yes—
663C22×C3C2×#21712yes—
664C22×C3C2×D3×D411yescharacteristic
665C22×C3C22×#6711yescharacteristic
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—21no—
669C2×D3—21no—
670C2×D3—22no—
671C2×D3—44no—
672C2×D3—48no—
673C2×D3—41no—
674C2×D3—41no—
675C2×D3C2×#21712yes—
676C2×D3C2×#21712yes—
677C3×C4—22no—
678C3×C4—22no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—22no—
682C3×C4—32no—
683C3×C4—32no—
684C3×C4—42no—
685C3×C4—62no—
686C3×C4—122no—
687C3×C4D3×C22⋊C412yes—
688C3×C4C2×#21712yes—
689C3×C4C22×C4×D311yescharacteristic
690C3×C4C2×D3×D411yescharacteristic
691C3×C4C23×Dic311yescharacteristic
692C3×C4C22×#6711yescharacteristic
693Dic3—22no—
694Dic3—42no—
695Dic3—122no—
696Dic3—122no—
697Dic3—242no—
698Dic3C2×#21712yes—
699Dic3C2×#21712yes—
700C32#289611yescharacteristic, complemented, Sylow
701C23—21no—
702C23—31no—
703C23—31no—
704C23—34no—
705C23—64no—
706C23—61no—
707C23—121no—
708C23—121no—
709C23—122no—
710C23—122no—
711C23D3×#6711yescharacteristic
712Q8—21no—
713Q8—32no—
714Q8—64no—
715Q8—61no—
716Q8C2×D3×Dic312yes—
717D4—24no—
718D4—21no—
719D4—32no—
720D4—64no—
721D4—64no—
722D4—64no—
723D4—64no—
724D4—61no—
725D4C2×D3×Dic312yes—
726C2×C4—21no—
727C2×C4—24no—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—34no—
731C2×C4—32no—
732C2×C4—32no—
733C2×C4—32no—
734C2×C4—32no—
735C2×C4—34no—
736C2×C4—34no—
737C2×C4—64no—
738C2×C4—64no—
739C2×C4—64no—
740C2×C4—61no—
741C2×C4—64no—
742C2×C4—62no—
743C2×C4—122no—
744C2×C4—182no—
745C2×C4—362no—
746C2×C4C2×D3×Dic312yes—
747C2×C4D3×#6712yes—
748C2×C4D3×#6711yescharacteristic
749C2×C4C22×D3211yescharacteristic
750C8—62no—
751C8—182no—
752C2×C3—22no—
753C2×C3—22no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—42no—
758C2×C3—42no—
759C2×C3—42no—
760C2×C3—62no—
761C2×C3—62no—
762C2×C3—82no—
763C2×C3—122no—
764C2×C3C2×D3×C22⋊C411yescharacteristic
765C2×C3#577311yescharacteristic
766C2×C3#577711yescharacteristic
767C2×C3#582211yescharacteristic
768C2×C3#582211yescharacteristic
769C2×C3C22×#21711yescharacteristic
770D3—22no—
771D3—22no—
772D3—42no—
773C22—21no—
774C22—21no—
775C22—22no—
776C22—32no—
777C22—32no—
778C22—41no—
779C22—41no—
780C22—61no—
781C22—61no—
782C22—61no—
783C22—61no—
784C22—62no—
785C22—124no—
786C22—128no—
787C22—121no—
788C22—121no—
789C22D3×#21712yes—
790C22C2×D3×#6711yescharacteristic
791C4—22no—
792C4—32no—
793C4—32no—
794C4—62no—
795C4—122no—
796C4—362no—
797C4D3×#21712yes—
798C4C22×D3×Dic311yescharacteristic
799C4C2×D3×#6711yescharacteristic
800C3—21no—
801C3#7888111yescharacteristic, complemented
802C3#8407211yescharacteristic, complemented
803C2—22no—
804C2—42no—
805C2—62no—
806C2—62no—
807C2—122no—
808C2#1059546911yescharacteristic
809C2#1059547011yescharacteristic
810C2C2×D3×#21711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×#41C2
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32#2896
LCSG ▷ 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×#63841C2semidirect
3. C2×D3×#208C2semidirect
4. #10592931C2semidirect
5. C3×#5232C2semidirect
6. #10591557C2semidirect
7. #10591556C2semidirect
8. #10591421C2semidirect
9. #10591420C2semidirect
10. #10591088C2semidirect
11. #10591087C2semidirect
16. C3×D3×#41C4semidirect
27. C2×C4⋊(C3⋊Dic3)C22semidirect
28. C2×#3748C22semidirect
29. C2×C3×C4⋊Dic3C22semidirect
30. C2×C3×#208C22semidirect
36. #63841C22semidirect
39. C2×D3×C3⋊C8C22semidirect
40. #63662C22semidirect
41. #63659C22semidirect
42. C3×#835C22semidirect
43. C3×#832C22semidirect
44. #63566C22semidirect
45. #63565C22semidirect
46. #63563C22semidirect
47. #63562C22semidirect
62. #5232D3semidirect
88. C3×#239C2×C4semidirect
90. C3×D3×Q8C2×C4semidirect
93. C3×#237C2×C4semidirect
96. C3×D3×D4C2×C4semidirect
145. D3×#41Dic3semidirect
167. C2×C4⋊Dic3C2×D3semidirect
175. C2×#208C2×D3semidirect
191. #835C2×D3semidirect
197. #832C2×D3semidirect
332. #239C2×Dic3semidirect
334. D3×Q8C2×Dic3semidirect
337. #237C2×Dic3semidirect
340. D3×D4C2×Dic3semidirect
700. C32#2896semidirect
801. C3#78881semidirect
802. C3#84072semidirect

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×#638412
C2×D3×#2082
#105929312
C3×#52322
#105915572
#105915562
#105914212
#105914202
#105910882
#105910872
#840723
#788813