Finite Group Databasebeta

← #11784799

Subgroups — #11784799

Order 1152.

1321 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic
2C2×#63664C211yesmaximal, characteristic, complemented
3C2×C3×#837C211yesmaximal, characteristic, complemented
4C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
5C2×#63569C211yesmaximal, characteristic, complemented
6C2×#63568C211yesmaximal, characteristic, complemented
7#10591069C211yesmaximal, characteristic, complemented
8#72138—31nomaximal
9#70380—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C3×D3×#41—22no—
12C3×D3×#41—22no—
13C3×D3×#41—22no—
14C3×D3×#41—22no—
15C2×C3×#239C411yescharacteristic, complemented
16C2×C3×D3×Q8C411yescharacteristic, complemented
17C2×C3×#237—21no—
18C2×C3×#237C411yescharacteristic, complemented
19C2×C3×D3×D4—21no—
20C2×C3×D3×D4C411yescharacteristic, complemented
21C2×C3×#235—21no—
22C2×C3×#235C2211yescharacteristic
23C22×C3×C4×D3—21no—
24C22×C3×C4×D3C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
26C2×#3748C2211yescharacteristic, complemented
27C2×C3×C4×Dic3C2211yescharacteristic, complemented
28C2×C3×#208C2211yescharacteristic, complemented
29C2×(C2×D3)⋊Dic3—21no—
30#63664—22no—
31C3×#837—22no—
32#63579—21no—
33#63569—22no—
34#63568—22no—
35(C2×D3)⋊(C3⋊C8)—21no—
36(C2×D3)⋊(C3⋊C8)—21no—
37C22×C3×#41—31no—
38C2×D3×#41D311yescharacteristic
39C2×C3×#104—31no—
40C2×#837—31no—
41C2×#837—31no—
42C2×#837—31no—
43C2×#837—31no—
44C2×#837—61no—
45C2×#837D311yescharacteristic, complemented
46C4×#217—31no—
47#5207—31no—
48C2×#825—31no—
49#5126—31no—
50C4×(C2×D3)⋊C4—31no—
51C2×#805—31no—
52C23×C3×D3—21no—
53C23×C3×D3D411yescharacteristic
54C32×#41—21no—
55C32×#41—21no—
56C32×#41D412yes—
57C32×#41D412yes—
58C2×C32×Q8C2×C411yescharacteristic
59C2×C32×D4—21no—
60C2×C32×D4C2×C411yescharacteristic
61C22×C32×C4—21no—
62C22×C32×C4C2311yescharacteristic
63C22×C3⋊Dic3—21no—
64C2×C3×#67—21no—
65C2×C3×#67—21no—
66C2×C3×#67—21no—
67C22×C3×Dic3—21no—
68C22×C3×Dic3—21no—
69C22×C3×Dic3D411yescharacteristic
70C3×#239—22no—
71C3×#239—22no—
72C3×D3×Q8—22no—
73C3×D3×Q8—22no—
74C3×#237—24no—
75C3×#237—24no—
76C3×#237—22no—
77C3×#237—22no—
78C3×D3×D4—24no—
79C3×D3×D4—24no—
80C3×D3×D4—22no—
81C3×D3×D4—22no—
82C3×#235—24no—
83C3×#235—24no—
84C3×#235—21no—
85C3×#235—21no—
86C3×#235D412yes—
87C3×#235D412yes—
88C2×C3×D12—21no—
89C2×C3×D12C2×C411yescharacteristic
90C2×C3×C4×D3—24no—
91C2×C3×C4×D3—24no—
92C2×C3×C4×D3—21no—
93C2×C3×C4×D3—21no—
94C2×C3×C4×D3—21no—
95C2×C3×C4×D3—21no—
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2×C411yescharacteristic
100C2×C3×C4×D3C2×C411yescharacteristic
101C2×C3×C4×D3D411yescharacteristic
102C2×C3×C4×D3D411yescharacteristic
103C2×C3×Dic6—21no—
104C2×C3×Dic6C2×C411yescharacteristic
105C4×C3⋊Dic3—21no—
106C4×C3⋊Dic3—21no—
107#3748—21no—
108#3748—21no—
109C2×C3⋊(C3⋊C8)—21no—
110C3×C4×Dic3—21no—
111C3×C4×Dic3—21no—
112C3×#208—21no—
113C3×#208—21no—
114C2×C3×C3⋊C8—21no—
115(C2×D3)⋊Dic3—24no—
116#1789—91noSylow
117C2×C3×#41—21no—
118C2×C3×#41—31no—
119C2×C3×#41—31no—
120C2×C3×#41—31no—
121C2×C3×#41—61no—
122C2×C3×#41—61no—
123C2×C3×#41—62no—
124C2×C3×#41—62no—
125C2×C3×#41—62no—
126C2×C3×#41—62no—
127C2×C3×#41C2×D311yescharacteristic
128C2×C3×#41C2×D311yescharacteristic
129C22×C3×Q8—31no—
130C22×C3×D4—31no—
131C22×C3×D4—61no—
132C23×C3×C4—31no—
133C23×C3×C4—61no—
134D3×#41—22no—
135D3×#41—22no—
136D3×#41—22no—
137D3×#41—22no—
138C2×#239Dic311yescharacteristic, complemented
139C2×D3×Q8Dic311yescharacteristic, complemented
140C2×#237—21no—
141C2×#237Dic311yescharacteristic, complemented
142C2×D3×D4—21no—
143C2×D3×D4Dic311yescharacteristic, complemented
144C2×#235—21no—
145C2×#235C2×D311yescharacteristic
146C22×C4×D3—21no—
147C22×C4×D3C2×D311yescharacteristic
148C2×C3×M16—31no—
149C2×C3×C42—31no—
150C2×#217—61no—
151C2×(C2×D3)⋊C4—61no—
152C2×C4×Dic3—31no—
153C2×C4×Dic3—31no—
154C2×C4×Dic3—61no—
155C2×C4×Dic3C2×D311yescharacteristic, complemented
156C2×#208—31no—
157C2×#208—31no—
158C2×#208—61no—
159C2×#208C2×D311yescharacteristic, complemented
160C3×#104—62no—
161#837—22no—
162#837—62no—
163#837—62no—
164#837—64no—
165#837—62no—
166#837—62no—
167C3⋊#95—61no—
168C3⋊#95—61no—
169#830—61no—
170#830—61no—
171#825—62no—
172(C2×D3)⋊C8—61no—
173(C2×D3)⋊C8—61no—
174#805—62no—
175C23×C32—21no—
176C23×C32C2×D411yescharacteristic
177C22×C3×D3—24no—
178C22×C3×D3—21no—
179C22×C3×D3—21no—
180C22×C3×D3—21no—
181C22×C3×D3—22no—
182C22×C3×D3—41no—
183C22×C3×D3—42no—
184C22×C3×D3—42no—
185C22×C3×D3C22⋊C411yescharacteristic
186C22×C3×D3C22⋊C411yescharacteristic
187C32×Q8—21no—
188C32×Q8C22⋊C412yescomplemented
189C32×D4—22no—
190C32×D4—22no—
191C32×D4—21no—
192C32×D4C22⋊C412yescomplemented
193C2×C32×C4—21no—
194C2×C32×C4—22no—
195C2×C32×C4—22no—
196C2×C32×C4C22×C411yescharacteristic
197C2×C32×C4C2×D411yescharacteristic
198C2×C32×C4C2×D411yescharacteristic
199C2×C32×C4C2×D411yescharacteristic
200C2×C32×C4C2×D411yescharacteristic
201C2×C32×C4C2×D411yescharacteristic
202C2×C3⋊Dic3—22no—
203C2×C3⋊Dic3—41no—
204C2×C3⋊Dic3—41no—
205C3×#67—24no—
206C3×#67—24no—
207C3×#67—22no—
208C3×#67—22no—
209C2×C3×Dic3—24no—
210C2×C3×Dic3—21no—
211C2×C3×Dic3—21no—
212C2×C3×Dic3—21no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3—41no—
215C2×C3×Dic3—41no—
216C2×C3×Dic3C22⋊C411yescharacteristic
217C2×C3×Dic3C22⋊C411yescharacteristic
218C3×D12—24no—
219C3×D12—21no—
220C3×D12C22⋊C412yescomplemented
221C3×C4×D3—24no—
222C3×C4×D3—24no—
223C3×C4×D3—21no—
224C3×C4×D3—21no—
225C3×C4×D3—21no—
226C3×C4×D3—21no—
227C3×C4×D3—21no—
228C3×C4×D3—21no—
229C3×C4×D3—22no—
230C3×C4×D3—22no—
231C3×C4×D3—21no—
232C3×C4×D3—21no—
233C3×Dic6—24no—
234C3×Dic6—21no—
235C3×Dic6C22⋊C412yescomplemented
236C3⋊(C3⋊C8)—41no—
237C3×C3⋊C8—41no—
238C22×#41—31no—
239C2×#104—31no—
240C2×#104—91no—
241C2×#104—91no—
242C2×#104—91no—
243#407—91no—
244C4×C22⋊C4—91no—
245C24×C3—31no—
246C24×C3—61no—
247C23×D3—21no—
248C23×D3#6711yescharacteristic
249C3×#41—21no—
250C3×#41—21no—
251C3×#41—21no—
252C3×#41—21no—
253C3×#41—22no—
254C3×#41—22no—
255C3×#41—32no—
256C3×#41—32no—
257C3×#41—41no—
258C3×#41—41no—
259C3×#41—64no—
260C3×#41—64no—
261C3×#41—62no—
262C3×#41—64no—
263C3×#41—64no—
264C3×#41—62no—
265C3×#41—62no—
266C3×#41—62no—
267C3×#41—61no—
268C3×#41—61no—
269C3×#41D1212yes—
270C3×#41#6712yes—
271C3×#41#6712yes—
272C3×#41#6712yes—
273C2×C3×Q8—21no—
274C2×C3×Q8—31no—
275C2×C3×Q8—61no—
276C2×C3×Q8—62no—
277C2×C3×Q8—62no—
278C2×C3×Q8C4×D311yescharacteristic
279C2×C3×Q8C2×Dic311yescharacteristic
280C2×C3×D4—21no—
281C2×C3×D4—21no—
282C2×C3×D4—21no—
283C2×C3×D4—31no—
284C2×C3×D4—41no—
285C2×C3×D4—61no—
286C2×C3×D4—61no—
287C2×C3×D4—62no—
288C2×C3×D4—64no—
289C2×C3×D4—64no—
290C2×C3×D4—61no—
291C2×C3×D4—61no—
292C2×C3×D4—62no—
293C2×C3×D4C4×D311yescharacteristic
294C2×C3×D4C2×Dic311yescharacteristic
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—41no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C22×C3×C4—64no—
307C22×C3×C4—64no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C22×C3×C4C22×D311yescharacteristic
316C22×C3×C4C22×D311yescharacteristic
317C2×#67—21no—
318C2×#67—21no—
319C2×#67—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3—121no—
325C22×Dic3#6711yescharacteristic
326#239—22no—
327#239—22no—
328D3×Q8—22no—
329D3×Q8—22no—
330#237—24no—
331#237—24no—
332#237—22no—
333#237—22no—
334D3×D4—24no—
335D3×D4—24no—
336D3×D4—22no—
337D3×D4—22no—
338#235—24no—
339#235—24no—
340#235—21no—
341#235—21no—
342#235#6712yes—
343#235#6712yes—
344C2×D12—21no—
345C2×D12C2×Dic311yescharacteristic
346C2×C4×D3—24no—
347C2×C4×D3—24no—
348C2×C4×D3—21no—
349C2×C4×D3—21no—
350C2×C4×D3—21no—
351C2×C4×D3—21no—
352C2×C4×D3—21no—
353C2×C4×D3—21no—
354C2×C4×D3—21no—
355C2×C4×D3C2×Dic311yescharacteristic
356C2×C4×D3C2×Dic311yescharacteristic
357C2×C4×D3#6711yescharacteristic
358C2×C4×D3#6711yescharacteristic
359C2×Dic6—21no—
360C2×Dic6C2×Dic311yescharacteristic
361C3×M16—61no—
362C3×M16—61no—
363C2×C3×C8—61no—
364C3×C42—61no—
365C3×C42—61no—
366#217—64no—
367(C2×D3)⋊C4—64no—
368C4×Dic3—21no—
369C4×Dic3—21no—
370C4×Dic3—62no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3—121no—
376#208—21no—
377#208—21no—
378#208—62no—
379#208—61no—
380#208—61no—
381#208—61no—
382#208—61no—
383#208—121no—
384C2×C3⋊C8—21no—
385C2×C3⋊C8—61no—
386C2×C3⋊C8—61no—
387C2×C3⋊C8—121no—
388C22×C32—21no—
389C22×C32—21no—
390C22×C32—22no—
391C22×C32—41no—
392C22×C32—41no—
393C22×C32C2×C22⋊C411yescharacteristic
394C22×C32#12011yescharacteristic
395C22×C32#12011yescharacteristic
396C2×C3×D3—21no—
397C2×C3×D3—21no—
398C2×C3×D3—21no—
399C2×C3×D3—22no—
400C2×C3×D3—21no—
401C2×C3×D3—21no—
402C2×C3×D3—42no—
403C2×C3×D3—42no—
404C2×C3×D3—48no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407C2×C3×D3#10412yescomplemented
408C32×C4—22no—
409C32×C4C2×C22⋊C411yescharacteristic
410C32×C4C2×C22⋊C411yescharacteristic
411C32×C4#12011yescharacteristic
412C32×C4#12011yescharacteristic
413C3⋊Dic3—42no—
414C3×Dic3—21no—
415C3×Dic3—22no—
416C3×Dic3—21no—
417C3×Dic3—42no—
418C2×#41—31no—
419C2×#41—31no—
420C2×#41—31no—
421C2×#41—61no—
422C2×#41—61no—
423C2×#41—62no—
424C2×#41—62no—
425C2×#41—62no—
426C2×#41—62no—
427C2×#41D3211yescharacteristic
428C22×Q8—31no—
429C22×D4—31no—
430C22×D4—61no—
431C23×C4—31no—
432C23×C4—61no—
433C2×M16—31no—
434C2×M16—91no—
435C2×C22⋊C4—181no—
436C2×C42—31no—
437C2×C42—91no—
438#104—62no—
439#104—182no—
440#104—182no—
441#104—182no—
442C22⋊C8—181no—
443C22⋊C8—181no—
444#95—181no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3—31no—
449C23×C3—31no—
450C23×C3—41no—
451C23×C3—62no—
452C23×C3—64no—
453C23×C3—61no—
454C23×C3—61no—
455C23×C3—61no—
456C23×C3—121no—
457C23×C3—122no—
458C23×C3—122no—
459C23×C3D3×D411yescharacteristic
460C23×C3C2×#6711yescharacteristic
461C22×D3—24no—
462C22×D3—21no—
463C22×D3—21no—
464C22×D3—21no—
465C22×D3—22no—
466C22×D3—41no—
467C22×D3—42no—
468C22×D3—42no—
469C22×D3#21711yescharacteristic
470C22×D3#21711yescharacteristic
471C3×Q8—21no—
472C3×Q8—21no—
473C3×Q8—22no—
474C3×Q8—32no—
475C3×Q8—41no—
476C3×Q8—64no—
477C3×Q8—61no—
478C3×Q8(C2×D3)⋊C412yescomplemented
479C3×Q8#21712yescomplemented
480C3×D4—22no—
481C3×D4—22no—
482C3×D4—22no—
483C3×D4—22no—
484C3×D4—21no—
485C3×D4—21no—
486C3×D4—22no—
487C3×D4—32no—
488C3×D4—41no—
489C3×D4—42no—
490C3×D4—42no—
491C3×D4—64no—
492C3×D4—64no—
493C3×D4—64no—
494C3×D4—62no—
495C3×D4—62no—
496C3×D4—61no—
497C3×D4(C2×D3)⋊C412yescomplemented
498C3×D4#21712yescomplemented
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—42no—
514C2×C3×C4—42no—
515C2×C3×C4—41no—
516C2×C3×C4—64no—
517C2×C3×C4—64no—
518C2×C3×C4—64no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—62no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—62no—
532C2×C3×C4—62no—
533C2×C3×C4—121no—
534C2×C3×C4—121no—
535C2×C3×C4C2×C4×D311yescharacteristic
536C2×C3×C4C2×D1211yescharacteristic
537C2×C3×C4D3×D411yescharacteristic
538C2×C3×C4D3×D411yescharacteristic
539C2×C3×C4D3×D411yescharacteristic
540C2×C3×C4C22×Dic311yescharacteristic
541C2×C3×C4C2×#6711yescharacteristic
542C2×C3×C4C2×#6711yescharacteristic
543C2×C3×C4C2×#6711yescharacteristic
544C2×C3×C4C2×#6711yescharacteristic
545C2×C3×C4C2×#6711yescharacteristic
546C2×C3×C4C2×#6711yescharacteristic
547#67—24no—
548#67—24no—
549#67—22no—
550#67—22no—
551C2×Dic3—24no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—22no—
556C2×Dic3—41no—
557C2×Dic3—41no—
558C2×Dic3—62no—
559C2×Dic3—62no—
560C2×Dic3—122no—
561C2×Dic3—122no—
562C2×Dic3—121no—
563C2×Dic3—121no—
564C2×Dic3—122no—
565C2×Dic3—121no—
566C2×Dic3—121no—
567C2×Dic3#21711yescharacteristic
568C2×Dic3#21711yescharacteristic
569D12—24no—
570D12—21no—
571D12#21712yescomplemented
572C4×D3—24no—
573C4×D3—24no—
574C4×D3—21no—
575C4×D3—21no—
576C4×D3—21no—
577C4×D3—21no—
578C4×D3—21no—
579C4×D3—21no—
580C4×D3—22no—
581C4×D3—22no—
582C4×D3—21no—
583C4×D3—21no—
584Dic6—24no—
585Dic6—21no—
586Dic6#21712yescomplemented
587C3×C8—121no—
588C3⋊C8—41no—
589C3⋊C8—122no—
590C3⋊C8—121no—
591C3⋊C8—121no—
592C2×C32—21no—
593C2×C32—21no—
594C2×C32—42no—
595C2×C32#37911yescharacteristic
596C2×C32C2×#10411yescharacteristic
597C2×C32#42111yescharacteristic
598C3×D3—22no—
599C3×D3—41no—
600C3×D3—42no—
601C24—31no—
602C24—61no—
603#41—21no—
604#41—21no—
605#41—32no—
606#41—32no—
607#41—64no—
608#41—64no—
609#41—62no—
610#41—64no—
611#41—64no—
612#41—62no—
613#41—62no—
614#41—62no—
615#41—61no—
616#41—61no—
617#41#62512yes—
618#41#62612yes—
619C2×Q8—31no—
620C2×Q8—61no—
621C2×Q8—62no—
622C2×Q8—62no—
623C2×Q8D3×Dic311yescharacteristic
624C2×D4—21no—
625C2×D4—31no—
626C2×D4—61no—
627C2×D4—61no—
628C2×D4—62no—
629C2×D4—64no—
630C2×D4—64no—
631C2×D4—61no—
632C2×D4—61no—
633C2×D4—62no—
634C2×D4D3×Dic311yescharacteristic
635C22×C4—21no—
636C22×C4—31no—
637C22×C4—31no—
638C22×C4—31no—
639C22×C4—31no—
640C22×C4—31no—
641C22×C4—61no—
642C22×C4—61no—
643C22×C4—64no—
644C22×C4—64no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—61no—
651C22×C4—61no—
652C22×C4—181no—
653C22×C4C2×D3211yescharacteristic
654M16—61no—
655M16—61no—
656M16—181no—
657M16—181no—
658C2×C8—61no—
659C2×C8—181no—
660C22⋊C4—184no—
661C42—61no—
662C42—61no—
663C42—181no—
664C42—181no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—22no—
670C22×C3—22no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—32no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—42no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—61no—
683C22×C3—61no—
684C22×C3—62no—
685C22×C3—61no—
686C22×C3—61no—
687C22×C3—61no—
688C22×C3—81no—
689C22×C3—81no—
690C22×C3—122no—
691C22×C3—122no—
692C22×C3—128no—
693C22×C3—121no—
694C22×C3—121no—
695C22×C3D3×C22⋊C411yescharacteristic
696C22×C3#88211yescharacteristic
697C22×C3#93711yescharacteristic
698C22×C3C2×#21711yescharacteristic
699C22×C3#95311yescharacteristic
700C22×C3#95311yescharacteristic
701C2×D3—21no—
702C2×D3—21no—
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—22no—
707C2×D3—42no—
708C2×D3—42no—
709C2×D3—48no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3#83712yescomplemented
713C3×C4—22no—
714C3×C4—22no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—42no—
720C3×C4—61no—
721C3×C4—61no—
722C3×C4—62no—
723C3×C4—122no—
724C3×C4D3×C22⋊C411yescharacteristic
725C3×C4#88211yescharacteristic
726C3×C4C2×(C2×D3)⋊C411yescharacteristic
727C3×C4#93711yescharacteristic
728C3×C4C2×#21711yescharacteristic
729C3×C4C2×#21711yescharacteristic
730C3×C4#95311yescharacteristic
731C3×C4#95311yescharacteristic
732Dic3—21no—
733Dic3—22no—
734Dic3—21no—
735Dic3—42no—
736Dic3—122no—
737Dic3—122no—
738Dic3—124no—
739C32#178911yescharacteristic, complemented, Sylow
740C23—21no—
741C23—31no—
742C23—31no—
743C23—62no—
744C23—64no—
745C23—61no—
746C23—61no—
747C23—61no—
748C23—121no—
749C23—122no—
750C23—122no—
751C23D3×#6711yescharacteristic
752Q8—21no—
753Q8—32no—
754Q8—64no—
755Q8—61no—
756Q8(C2×D3)⋊Dic312yescomplemented
757D4—22no—
758D4—22no—
759D4—21no—
760D4—32no—
761D4—64no—
762D4—64no—
763D4—64no—
764D4—62no—
765D4—62no—
766D4—61no—
767D4(C2×D3)⋊Dic312yescomplemented
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—31no—
772C2×C4—31no—
773C2×C4—64no—
774C2×C4—64no—
775C2×C4—64no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—62no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—62no—
789C2×C4—62no—
790C2×C4—121no—
791C2×C4—121no—
792C2×C4—182no—
793C2×C4—361no—
794C2×C4—361no—
795C2×C4C2×D3×Dic311yescharacteristic
796C2×C4C2×#62511yescharacteristic
797C2×C4C2×#62611yescharacteristic
798C2×C4D3×#6711yescharacteristic
799C2×C4D3×#6711yescharacteristic
800C2×C4D3×#6711yescharacteristic
801C8—121no—
802C8—361no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—41no—
811C2×C3—41no—
812C2×C3—42no—
813C2×C3—42no—
814C2×C3—62no—
815C2×C3—82no—
816C2×C3—121no—
817C2×C3—122no—
818C2×C3D3×#10411yescharacteristic
819C2×C3#482111yescharacteristic
820C2×C3#495511yescharacteristic
821C2×C3C2×#83711yescharacteristic
822C2×C3#523611yescharacteristic
823C2×C3#524711yescharacteristic
824D3—22no—
825D3—41no—
826D3—42no—
827C22—21no—
828C22—21no—
829C22—22no—
830C22—32no—
831C22—41no—
832C22—41no—
833C22—61no—
834C22—61no—
835C22—61no—
836C22—61no—
837C22—62no—
838C22—61no—
839C22—122no—
840C22—122no—
841C22—128no—
842C22—121no—
843C22—121no—
844C22D3×#21711yescharacteristic
845C22#6397611yescharacteristic
846C22#6397711yescharacteristic
847C4—22no—
848C4—61no—
849C4—61no—
850C4—62no—
851C4—122no—
852C4—362no—
853C4C2×(C2×D3)⋊Dic311yescharacteristic
854C4D3×#21711yescharacteristic
855C4#6397611yescharacteristic
856C4#6397711yescharacteristic
857C3—21no—
858C3#7038011yescharacteristic, complemented
859C3#7213811yescharacteristic, complemented
860C2—21no—
861C2—21no—
862C2—42no—
863C2—62no—
864C2—121no—
865C2—122no—
866C2D3×#83711yescharacteristic
867C2#1059167011yescharacteristic
868C2#1059170611yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×D3×#41C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1789
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#63664C2semidirect
3. C2×C3×#837C2semidirect
4. C4×(C2×D3)⋊Dic3C2semidirect
5. C2×#63569C2semidirect
6. C2×#63568C2semidirect
7. #10591069C2semidirect
15. C2×C3×#239C4semidirect
16. C2×C3×D3×Q8C4semidirect
18. C2×C3×#237C4semidirect
20. C2×C3×D3×D4C4semidirect
25. C2×C4×C3⋊Dic3C22semidirect
26. C2×#3748C22semidirect
27. C2×C3×C4×Dic3C22semidirect
28. C2×C3×#208C22semidirect
45. C2×#837D3semidirect
138. C2×#239Dic3semidirect
139. C2×D3×Q8Dic3semidirect
141. C2×#237Dic3semidirect
143. C2×D3×D4Dic3semidirect
155. C2×C4×Dic3C2×D3semidirect
159. C2×#208C2×D3semidirect
188. C32×Q8C22⋊C4semidirect
192. C32×D4C22⋊C4semidirect
220. C3×D12C22⋊C4semidirect
235. C3×Dic6C22⋊C4semidirect
407. C2×C3×D3#104semidirect
478. C3×Q8(C2×D3)⋊C4semidirect
479. C3×Q8#217semidirect
497. C3×D4(C2×D3)⋊C4semidirect
498. C3×D4#217semidirect
571. D12#217semidirect
586. Dic6#217semidirect
712. C2×D3#837semidirect
739. C32#1789semidirect
756. Q8(C2×D3)⋊Dic3semidirect
767. D4(C2×D3)⋊Dic3semidirect
858. C3#70380semidirect
859. C3#72138semidirect

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×#636642
C2×C3×#8372
C4×(C2×D3)⋊Dic32
C2×#635692
C2×#635682
#105910692
#721383
#703803