Finite Group Databasebeta

← C2×#10591670 #11858160

Subgroups — C2×#10591670 #11858160

Order 1152.

1629 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic
2C2×#63855C211yesmaximal, characteristic, complemented
3C2×D3×#208C211yesmaximal, characteristic, complemented
4C2×#63664C211yesmaximal, characteristic, complemented
5C2×C3×#837C211yesmaximal, characteristic, complemented
6#10591670C218yesmaximal, direct product factor
7C2×#63569C211yesmaximal, characteristic, complemented
8C2×#63568C211yesmaximal, characteristic, complemented
9C2×#5236—31nomaximal
10C2×#4821—31nomaximal
11C2×C32×#41C2211yescharacteristic
12C3×D3×#41—22no—
13C3×D3×#41—22no—
14C3×D3×#41C414yescomplemented
15C3×D3×#41C2214yes—
16C2×C3×#239C411yescharacteristic, complemented
17C2×C3×D3×Q8C411yescharacteristic, complemented
18C2×C3×#237—21no—
19C2×C3×#237C411yescharacteristic, complemented
20C2×C3×D3×D4—21no—
21C2×C3×D3×D4C411yescharacteristic, complemented
22C2×C3×#235—21no—
23C2×C3×#235C2211yescharacteristic
24C22×C3×C4×D3—21no—
25C22×C3×C4×D3C2211yescharacteristic
26C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
27C2×#3748C2211yescharacteristic, complemented
28C2×C3×C4×Dic3C2211yescharacteristic, complemented
29C2×C3×#208C2211yescharacteristic, complemented
30C2×Dic3⋊Dic3—21no—
31C2×(C2×D3)⋊Dic3—21no—
32#63855—22no—
33#63855C2214yescomplemented
34C2×#3711—21no—
35D3×#208—22no—
36D3×#208C2214yescomplemented
37C2×D3×C3⋊C8—21no—
38#63664C2214yescomplemented
39C3×#837C2214yescomplemented
40#63569C2214yescomplemented
41#63568C2214yescomplemented
42C22×C3×#41—31no—
43C2×D3×#41D311yescharacteristic
44C2×#926—31no—
45C22×#208—31no—
46C2×D3×M16—31no—
47C2×#872—31no—
48C2×C3×#104—31no—
49#5236—38no—
50C2×#837—31no—
51C2×#837—31no—
52C2×#837—31no—
53C2×#837—31no—
54C2×#837—61no—
55C2×#837D311yescharacteristic, complemented
56C2×#825—31no—
57C2×#805—31no—
58#4821—38no—
59C23×C3×D3—21no—
60C23×C3×D3D411yescharacteristic
61C32×#41—21no—
62C32×#41—21no—
63C32×#41C2×C412yes—
64C32×#41C2312yes—
65C2×C32×Q8C2×C411yescharacteristic
66C2×C32×D4—21no—
67C2×C32×D4C2×C411yescharacteristic
68C22×C32×C4—21no—
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3—21no—
71C2×C3×#67—21no—
72C2×C3×#67—21no—
73C2×C3×#67—21no—
74C22×C3×Dic3—21no—
75C22×C3×Dic3—21no—
76C22×C3×Dic3D411yescharacteristic
77C3×#239—22no—
78C3×#239C2×C414yescomplemented
79C3×D3×Q8—22no—
80C3×D3×Q8C2×C414yescomplemented
81C3×#237—24no—
82C3×#237—24no—
83C3×#237—22no—
84C3×#237C2×C414yescomplemented
85C3×D3×D4—24no—
86C3×D3×D4—24no—
87C3×D3×D4—22no—
88C3×D3×D4C2×C414yescomplemented
89C3×#235—21no—
90C3×#235—21no—
91C3×#235—24no—
92C3×#235—24no—
93C3×#235C2×C412yes—
94C3×#235C2312yes—
95C2×C3×D12—21no—
96C2×C3×D12C2×C411yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—24no—
101C2×C3×C4×D3—24no—
102C2×C3×C4×D3C2×C411yescharacteristic
103C2×C3×C4×D3C2×C411yescharacteristic
104C2×C3×C4×D3C2×C412yes—
105C2×C3×C4×D3D412yes—
106C2×C3×C4×D3D411yescharacteristic
107C2×C3×C4×D3D412yes—
108C2×C3×C4×D3D411yescharacteristic
109C2×C3×C4×D3C2312yes—
110C2×C3×Dic6—21no—
111C2×C3×Dic6C2×C411yescharacteristic
112C4×C3⋊Dic3—21no—
113C4×C3⋊Dic3C2312yescomplemented
114#3748—21no—
115#3748C2312yescomplemented
116C2×C3⋊(C3⋊C8)—21no—
117C3×C4×Dic3—21no—
118C3×C4×Dic3C2312yescomplemented
119C3×#208—21no—
120C3×#208C2312yescomplemented
121C2×C3×C3⋊C8—21no—
122Dic3⋊Dic3—24no—
123(C2×D3)⋊Dic3—24no—
124#3711—24no—
125D3×C3⋊C8—24no—
126C2×#421—91noSylow
127C2×C3×#41—21no—
128C2×C3×#41—34no—
129C2×C3×#41—34no—
130C2×C3×#41—31no—
131C2×C3×#41—31no—
132C2×C3×#41—31no—
133C2×C3×#41—61no—
134C2×C3×#41—61no—
135C2×C3×#41—62no—
136C2×C3×#41—62no—
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—22no—
145D3×#41—22no—
146D3×#41Dic314yescomplemented
147D3×#41C2×D314yes—
148C2×#239Dic311yescharacteristic, complemented
149C2×D3×Q8Dic311yescharacteristic, complemented
150C2×#237—21no—
151C2×#237Dic311yescharacteristic, complemented
152C2×D3×D4—21no—
153C2×D3×D4Dic311yescharacteristic, complemented
154C2×#235—21no—
155C2×#235C2×D311yescharacteristic
156C22×C4×D3—21no—
157C22×C4×D3C2×D311yescharacteristic
158C2×C3×M16—31no—
159C2×C3×C42—31no—
160C2×#217—61no—
161C2×(C2×D3)⋊C4—61no—
162#926—34no—
163#926—62no—
164C2×C4⋊Dic3—61no—
165C2×Dic3⋊C4—61no—
166C2×C4×Dic3—31no—
167C2×C4×Dic3—31no—
168C2×C4×Dic3—61no—
169C2×C4×Dic3C2×D311yescharacteristic, complemented
170C2×#208—31no—
171C2×#208—31no—
172C2×#208—34no—
173C2×#208—61no—
174C2×#208—61no—
175C2×#208—62no—
176C2×#208C2×D311yescharacteristic, complemented
177C22×C3⋊C8—61no—
178D3×M16—34no—
179D3×M16—62no—
180C2×ΓL(1,𝔽25)—61no—
181C2×D3×C8—61no—
182#872—34no—
183#872—62no—
184C3×#104—34no—
185#837—34no—
186#837—34no—
187#837—34no—
188#837—34no—
189#837—64no—
190#837C2×D314yescomplemented
191#825—34no—
192#805—34no—
193C23×C32—21no—
194C23×C32C2×D411yescharacteristic
195C22×C3×D3—21no—
196C22×C3×D3—24no—
197C22×C3×D3—42no—
198C22×C3×D3—44no—
199C22×C3×D3C22⋊C411yescharacteristic
200C22×C3×D3C22⋊C411yescharacteristic
201C22×C3×D3C22⋊C412yes—
202C22×C3×D3C2×D412yes—
203C32×Q8—21no—
204C32×Q8C22×C412yes—
205C32×D4—22no—
206C32×D4—22no—
207C32×D4—21no—
208C32×D4C22×C412yes—
209C2×C32×C4—21no—
210C2×C32×C4—22no—
211C2×C32×C4—22no—
212C2×C32×C4C22×C411yescharacteristic
213C2×C32×C4C22×C411yescharacteristic
214C2×C32×C4C2×D411yescharacteristic
215C2×C32×C4C2×D411yescharacteristic
216C2×C32×C4C2×D411yescharacteristic
217C2×C32×C4C2411yescharacteristic
218C2×C3⋊Dic3—22no—
219C2×C3⋊Dic3—42no—
220C3×#67—22no—
221C3×#67—22no—
222C3×#67—24no—
223C3×#67—24no—
224C2×C3×Dic3—21no—
225C2×C3×Dic3—24no—
226C2×C3×Dic3—22no—
227C2×C3×Dic3—42no—
228C2×C3×Dic3C22⋊C411yescharacteristic
229C2×C3×Dic3C22⋊C411yescharacteristic
230C2×C3×Dic3C22⋊C412yes—
231C2×C3×Dic3C2×D412yes—
232C3×D12—24no—
233C3×D12—21no—
234C3×D12C22×C412yes—
235C3×C4×D3—24no—
236C3×C4×D3—22no—
237C3×C4×D3—22no—
238C3×C4×D3—24no—
239C3×C4×D3C22⋊C412yes—
240C3×C4×D3C22⋊C412yes—
241C3×C4×D3C22⋊C412yes—
242C3×C4×D3C22⋊C412yes—
243C3×C4×D3C22×C412yes—
244C3×C4×D3C22×C412yes—
245C3×C4×D3C2×D412yes—
246C3×C4×D3C2×D412yes—
247C3×Dic6—21no—
248C3×Dic6—24no—
249C3×Dic6C22×C412yes—
250C3⋊(C3⋊C8)—22no—
251C3×C3⋊C8—22no—
252C22×#41—31no—
253C22×M16—91no—
254C2×#117—91no—
255#421—98no—
256C2×#104—31no—
257C2×#104—91no—
258C2×#104—91no—
259C2×#104—91no—
260C24×C3—31no—
261C24×C3—61no—
262C23×D3—21no—
263C23×D3#6711yescharacteristic
264C3×#41—21no—
265C3×#41—21no—
266C3×#41—21no—
267C3×#41—21no—
268C3×#41—22no—
269C3×#41—22no—
270C3×#41—34no—
271C3×#41—34no—
272C3×#41—32no—
273C3×#41—32no—
274C3×#41—41no—
275C3×#41—41no—
276C3×#41—64no—
277C3×#41—64no—
278C3×#41—64no—
279C3×#41—64no—
280C3×#41—62no—
281C3×#41—62no—
282C3×#41—61no—
283C3×#41—61no—
284C3×#41C4×D312yes—
285C3×#41C2×Dic312yes—
286C3×#41C22×D312yes—
287C3×#41C22×D312yes—
288C2×C3×Q8—21no—
289C2×C3×Q8—34no—
290C2×C3×Q8—31no—
291C2×C3×Q8—61no—
292C2×C3×Q8—62no—
293C2×C3×Q8C4×D311yescharacteristic
294C2×C3×Q8C2×Dic311yescharacteristic
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—21no—
298C2×C3×D4—34no—
299C2×C3×D4—31no—
300C2×C3×D4—41no—
301C2×C3×D4—61no—
302C2×C3×D4—62no—
303C2×C3×D4—61no—
304C2×C3×D4—64no—
305C2×C3×D4—64no—
306C2×C3×D4—61no—
307C2×C3×D4—61no—
308C2×C3×D4C4×D311yescharacteristic
309C2×C3×D4C2×Dic311yescharacteristic
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—32no—
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C22×C3×C4—32no—
320C22×C3×C4—32no—
321C22×C3×C4—32no—
322C22×C3×C4—41no—
323C22×C3×C4—61no—
324C22×C3×C4—64no—
325C22×C3×C4—64no—
326C22×C3×C4—61no—
327C22×C3×C4—61no—
328C22×C3×C4—61no—
329C22×C3×C4—61no—
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C2×#67—21no—
333C2×#67—21no—
334C2×#67—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—61no—
338C22×Dic3—61no—
339C22×Dic3—121no—
340C22×Dic3#6711yescharacteristic
341#239—22no—
342#239C2×Dic314yescomplemented
343D3×Q8—22no—
344D3×Q8C2×Dic314yescomplemented
345#237—24no—
346#237—24no—
347#237—22no—
348#237C2×Dic314yescomplemented
349D3×D4—24no—
350D3×D4—24no—
351D3×D4—22no—
352D3×D4C2×Dic314yescomplemented
353#235—21no—
354#235—21no—
355#235—24no—
356#235—24no—
357#235C2×Dic312yes—
358#235C22×D312yes—
359C2×D12—21no—
360C2×D12C2×Dic311yescharacteristic
361C2×C4×D3—21no—
362C2×C4×D3—21no—
363C2×C4×D3—21no—
364C2×C4×D3—24no—
365C2×C4×D3—24no—
366C2×C4×D3C2×Dic311yescharacteristic
367C2×C4×D3C2×Dic311yescharacteristic
368C2×C4×D3C2×Dic312yes—
369C2×C4×D3#6712yes—
370C2×C4×D3#6711yescharacteristic
371C2×C4×D3#6711yescharacteristic
372C2×C4×D3#6712yes—
373C2×C4×D3C22×D312yes—
374C2×Dic6—21no—
375C2×Dic6C2×Dic311yescharacteristic
376C3×M16—32no—
377C3×M16—61no—
378C2×C3×C8—61no—
379C3×C42—32no—
380C3×C42—61no—
381#217—64no—
382(C2×D3)⋊C4—64no—
383C4⋊Dic3—64no—
384Dic3⋊C4—64no—
385C4×Dic3—21no—
386C4×Dic3—32no—
387C4×Dic3—32no—
388C4×Dic3—62no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—121no—
392C4×Dic3C22×D312yescomplemented
393#208—21no—
394#208—32no—
395#208—32no—
396#208—62no—
397#208—64no—
398#208—61no—
399#208—61no—
400#208—121no—
401#208C22×D312yescomplemented
402C2×C3⋊C8—21no—
403C2×C3⋊C8—64no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—121no—
407ΓL(1,𝔽25)—64no—
408D3×C8—64no—
409C22×C32—22no—
410C22×C32—22no—
411C22×C32—42no—
412C22×C32C2×C22⋊C411yescharacteristic
413C22×C32C2×C22⋊C411yescharacteristic
414C22×C32C22×D411yescharacteristic
415C2×C3×D3—22no—
416C2×C3×D3—22no—
417C2×C3×D3—22no—
418C2×C3×D3—42no—
419C2×C3×D3—42no—
420C2×C3×D3—48no—
421C2×C3×D3—42no—
422C2×C3×D3C2×C22⋊C412yes—
423C2×C3×D3C2×C22⋊C412yes—
424C32×C4—22no—
425C32×C4C2×C22⋊C411yescharacteristic
426C32×C4C2×C22⋊C411yescharacteristic
427C32×C4C23×C411yescharacteristic
428C32×C4C22×D411yescharacteristic
429C3⋊Dic3—42no—
430C3×Dic3—22no—
431C3×Dic3—42no—
432C3×Dic3C2×C22⋊C412yes—
433C3×Dic3C2×C22⋊C412yes—
434C2×#41—34no—
435C2×#41—34no—
436C2×#41—31no—
437C2×#41—31no—
438C2×#41—31no—
439C2×#41—61no—
440C2×#41—61no—
441C2×#41—62no—
442C2×#41—62no—
443C2×#41D3211yescharacteristic
444C22×Q8—31no—
445C22×D4—31no—
446C22×D4—61no—
447C23×C4—31no—
448C23×C4—61no—
449C2×M16—31no—
450C2×M16—94no—
451C2×M16—91no—
452C2×M16—181no—
453C2×M16—182no—
454C22×C8—181no—
455#117—94no—
456#117—182no—
457C2×C4⋊C4—181no—
458C2×C22⋊C4—181no—
459C2×C42—31no—
460C2×C42—91no—
461#104—34no—
462#104—94no—
463#104—94no—
464#104—94no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—31no—
469C23×C3—31no—
470C23×C3—32no—
471C23×C3—32no—
472C23×C3—41no—
473C23×C3—64no—
474C23×C3—61no—
475C23×C3—122no—
476C23×C3—124no—
477C23×C3D3×D411yescharacteristic
478C23×C3C2×#6711yescharacteristic
479C22×D3—21no—
480C22×D3—24no—
481C22×D3—42no—
482C22×D3—44no—
483C22×D3#21711yescharacteristic
484C22×D3#21711yescharacteristic
485C22×D3#21712yes—
486C22×D3C2×#6712yes—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—22no—
490C3×Q8—32no—
491C3×Q8—41no—
492C3×Q8—64no—
493C3×Q8—61no—
494C3×Q8C2×C4×D312yes—
495C3×Q8C22×Dic312yes—
496C3×D4—22no—
497C3×D4—22no—
498C3×D4—22no—
499C3×D4—22no—
500C3×D4—21no—
501C3×D4—21no—
502C3×D4—22no—
503C3×D4—32no—
504C3×D4—41no—
505C3×D4—42no—
506C3×D4—42no—
507C3×D4—64no—
508C3×D4—64no—
509C3×D4—64no—
510C3×D4—62no—
511C3×D4—62no—
512C3×D4—61no—
513C3×D4C2×C4×D312yes—
514C3×D4C22×Dic312yes—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—31no—
528C2×C3×C4—31no—
529C2×C3×C4—32no—
530C2×C3×C4—32no—
531C2×C3×C4—32no—
532C2×C3×C4—32no—
533C2×C3×C4—32no—
534C2×C3×C4—32no—
535C2×C3×C4—32no—
536C2×C3×C4—32no—
537C2×C3×C4—32no—
538C2×C3×C4—32no—
539C2×C3×C4—42no—
540C2×C3×C4—42no—
541C2×C3×C4—41no—
542C2×C3×C4—64no—
543C2×C3×C4—64no—
544C2×C3×C4—64no—
545C2×C3×C4—61no—
546C2×C3×C4—62no—
547C2×C3×C4—62no—
548C2×C3×C4—62no—
549C2×C3×C4—122no—
550C2×C3×C4C2×C4×D311yescharacteristic
551C2×C3×C4C2×C4×D311yescharacteristic
552C2×C3×C4D3×D411yescharacteristic
553C2×C3×C4D3×D411yescharacteristic
554C2×C3×C4D3×D411yescharacteristic
555C2×C3×C4C22×Dic311yescharacteristic
556C2×C3×C4C22×Dic311yescharacteristic
557C2×C3×C4C2×#6711yescharacteristic
558C2×C3×C4C2×#6711yescharacteristic
559C2×C3×C4C2×#6711yescharacteristic
560C2×C3×C4C23×D311yescharacteristic
561C2×C3×C4C23×D311yescharacteristic
562#67—22no—
563#67—22no—
564#67—24no—
565#67—24no—
566C2×Dic3—21no—
567C2×Dic3—24no—
568C2×Dic3—22no—
569C2×Dic3—42no—
570C2×Dic3—62no—
571C2×Dic3—62no—
572C2×Dic3—122no—
573C2×Dic3—122no—
574C2×Dic3—122no—
575C2×Dic3—124no—
576C2×Dic3#21711yescharacteristic
577C2×Dic3#21711yescharacteristic
578C2×Dic3#21712yes—
579C2×Dic3C2×#6712yes—
580D12—24no—
581D12—21no—
582D12C22×Dic312yes—
583C4×D3—24no—
584C4×D3—22no—
585C4×D3—22no—
586C4×D3—24no—
587C4×D3#21712yes—
588C4×D3#21712yes—
589C4×D3#21712yes—
590C4×D3#21712yes—
591C4×D3C22×Dic312yes—
592C4×D3C22×Dic312yes—
593C4×D3C2×#6712yes—
594C4×D3C2×#6712yes—
595Dic6—21no—
596Dic6—24no—
597Dic6C22×Dic312yes—
598C3×C8—62no—
599C3⋊C8—22no—
600C3⋊C8—62no—
601C3⋊C8—62no—
602C3⋊C8—122no—
603C2×C32—21no—
604C2×C32—21no—
605C2×C32—42no—
606C2×C32#42112yescomplemented
607C2×C32C22×C22⋊C411yescharacteristic
608C3×D3—22no—
609C3×D3—22no—
610C3×D3—42no—
611C24—31no—
612C24—61no—
613#41—21no—
614#41—21no—
615#41—34no—
616#41—34no—
617#41—32no—
618#41—32no—
619#41—64no—
620#41—64no—
621#41—64no—
622#41—64no—
623#41—62no—
624#41—62no—
625#41—61no—
626#41—61no—
627#41D3×Dic312yes—
628#41C2×D3212yes—
629C2×Q8—34no—
630C2×Q8—31no—
631C2×Q8—61no—
632C2×Q8—62no—
633C2×Q8D3×Dic311yescharacteristic
634C2×D4—21no—
635C2×D4—34no—
636C2×D4—31no—
637C2×D4—61no—
638C2×D4—62no—
639C2×D4—61no—
640C2×D4—64no—
641C2×D4—64no—
642C2×D4—61no—
643C2×D4—61no—
644C2×D4D3×Dic311yescharacteristic
645C22×C4—21no—
646C22×C4—31no—
647C22×C4—32no—
648C22×C4—31no—
649C22×C4—31no—
650C22×C4—32no—
651C22×C4—32no—
652C22×C4—32no—
653C22×C4—31no—
654C22×C4—31no—
655C22×C4—61no—
656C22×C4—64no—
657C22×C4—64no—
658C22×C4—61no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—61no—
662C22×C4—181no—
663C22×C4C2×D3211yescharacteristic
664M16—32no—
665M16—61no—
666M16—92no—
667M16—184no—
668M16—181no—
669C2×C8—61no—
670C2×C8—184no—
671C2×C8—181no—
672C4⋊C4—184no—
673C22⋊C4—184no—
674C42—32no—
675C42—61no—
676C42—92no—
677C42—181no—
678C22×C3—22no—
679C22×C3—22no—
680C22×C3—22no—
681C22×C3—22no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—32no—
686C22×C3—32no—
687C22×C3—42no—
688C22×C3—42no—
689C22×C3—42no—
690C22×C3—42no—
691C22×C3—62no—
692C22×C3—62no—
693C22×C3—62no—
694C22×C3—82no—
695C22×C3—122no—
696C22×C3—122no—
697C22×C3—128no—
698C22×C3—122no—
699C22×C3D3×C22⋊C411yescharacteristic
700C22×C3D3×C22⋊C411yescharacteristic
701C22×C3C2×#21711yescharacteristic
702C22×C3C2×#21711yescharacteristic
703C22×C3C2×D3×D411yescharacteristic
704C22×C3C22×#6711yescharacteristic
705C2×D3—22no—
706C2×D3—22no—
707C2×D3—22no—
708C2×D3—42no—
709C2×D3—42no—
710C2×D3—48no—
711C2×D3—42no—
712C2×D3C2×#21712yes—
713C2×D3C2×#21712yes—
714C3×C4—22no—
715C3×C4—22no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—32no—
721C3×C4—32no—
722C3×C4—42no—
723C3×C4—62no—
724C3×C4—122no—
725C3×C4D3×C22⋊C411yescharacteristic
726C3×C4D3×C22⋊C411yescharacteristic
727C3×C4C2×#21711yescharacteristic
728C3×C4C2×#21711yescharacteristic
729C3×C4C22×C4×D311yescharacteristic
730C3×C4C2×D3×D411yescharacteristic
731C3×C4C23×Dic311yescharacteristic
732C3×C4C22×#6711yescharacteristic
733Dic3—22no—
734Dic3—42no—
735Dic3—122no—
736Dic3—122no—
737Dic3—124no—
738Dic3C2×#21712yes—
739Dic3C2×#21712yes—
740C32C2×#42111yescharacteristic, complemented, Sylow
741C23—21no—
742C23—31no—
743C23—31no—
744C23—32no—
745C23—32no—
746C23—64no—
747C23—61no—
748C23—122no—
749C23—124no—
750C23D3×#6711yescharacteristic
751Q8—21no—
752Q8—32no—
753Q8—64no—
754Q8—61no—
755Q8C2×D3×Dic312yes—
756D4—22no—
757D4—22no—
758D4—21no—
759D4—32no—
760D4—64no—
761D4—64no—
762D4—64no—
763D4—62no—
764D4—62no—
765D4—61no—
766D4C2×D3×Dic312yes—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—32no—
771C2×C4—31no—
772C2×C4—31no—
773C2×C4—32no—
774C2×C4—32no—
775C2×C4—32no—
776C2×C4—32no—
777C2×C4—32no—
778C2×C4—32no—
779C2×C4—32no—
780C2×C4—32no—
781C2×C4—32no—
782C2×C4—64no—
783C2×C4—64no—
784C2×C4—64no—
785C2×C4—61no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4—122no—
790C2×C4—182no—
791C2×C4—362no—
792C2×C4C2×D3×Dic311yescharacteristic
793C2×C4C2×D3×Dic311yescharacteristic
794C2×C4D3×#6711yescharacteristic
795C2×C4D3×#6711yescharacteristic
796C2×C4D3×#6711yescharacteristic
797C2×C4C22×D3211yescharacteristic
798C8—62no—
799C8—182no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—22no—
806C2×C3—41no—
807C2×C3—41no—
808C2×C3—42no—
809C2×C3—42no—
810C2×C3—62no—
811C2×C3—62no—
812C2×C3—82no—
813C2×C3—122no—
814C2×C3#482112yescomplemented
815C2×C3#523612yescomplemented
816C2×C3C2×D3×C22⋊C411yescharacteristic
817C2×C3C22×#21711yescharacteristic
818D3—22no—
819D3—22no—
820D3—42no—
821C22—22no—
822C22—22no—
823C22—32no—
824C22—32no—
825C22—42no—
826C22—62no—
827C22—62no—
828C22—62no—
829C22—122no—
830C22—122no—
831C22—128no—
832C22—122no—
833C22D3×#21711yescharacteristic
834C22D3×#21711yescharacteristic
835C22C2×D3×#6711yescharacteristic
836C4—22no—
837C4—32no—
838C4—32no—
839C4—62no—
840C4—122no—
841C4—362no—
842C4D3×#21711yescharacteristic
843C4D3×#21711yescharacteristic
844C4C22×D3×Dic311yescharacteristic
845C4C2×D3×#6711yescharacteristic
846C3—21no—
847C3C2×#482111yescharacteristic, complemented
848C3C2×#523611yescharacteristic, complemented
849C2—21no—
850C2—21no—
851C2—42no—
852C2—62no—
853C2—62no—
854C2—122no—
855C2#1059167012yesdirect product factor
856C2C2×D3×#21711yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×D3×#41C2
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32C2×#421
LCSG ▷ 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×#63855C2semidirect
3. C2×D3×#208C2semidirect
4. C2×#63664C2semidirect
5. C2×C3×#837C2semidirect
6. #10591670C2direct (N × H)
7. C2×#63569C2semidirect
8. C2×#63568C2semidirect
14. C3×D3×#41C4semidirect
16. C2×C3×#239C4semidirect
17. C2×C3×D3×Q8C4semidirect
19. C2×C3×#237C4semidirect
21. C2×C3×D3×D4C4semidirect
26. C2×C4×C3⋊Dic3C22semidirect
27. C2×#3748C22semidirect
28. C2×C3×C4×Dic3C22semidirect
29. C2×C3×#208C22semidirect
33. #63855C22semidirect
36. D3×#208C22semidirect
38. #63664C22semidirect
39. C3×#837C22semidirect
40. #63569C22semidirect
41. #63568C22semidirect
55. C2×#837D3semidirect
78. C3×#239C2×C4semidirect
80. C3×D3×Q8C2×C4semidirect
84. C3×#237C2×C4semidirect
88. C3×D3×D4C2×C4semidirect
113. C4×C3⋊Dic3C23semidirect
115. #3748C23semidirect
118. C3×C4×Dic3C23semidirect
120. C3×#208C23semidirect
146. D3×#41Dic3semidirect
148. C2×#239Dic3semidirect
149. C2×D3×Q8Dic3semidirect
151. C2×#237Dic3semidirect
153. C2×D3×D4Dic3semidirect
169. C2×C4×Dic3C2×D3semidirect
176. C2×#208C2×D3semidirect
190. #837C2×D3semidirect
342. #239C2×Dic3semidirect
344. D3×Q8C2×Dic3semidirect
348. #237C2×Dic3semidirect
352. D3×D4C2×Dic3semidirect
392. C4×Dic3C22×D3semidirect
401. #208C22×D3semidirect
606. C2×C32#421semidirect
740. C32C2×#421semidirect
814. C2×C3#4821semidirect
815. C2×C3#5236semidirect
847. C3C2×#4821semidirect
848. C3C2×#5236semidirect
855. C2#10591670direct (N × H)

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×#638552
C2×D3×#2082
C2×#636642
C2×C3×#8372
#105916702
C2×#635692
C2×#635682
C2×#52363
C2×#48213