Finite Group Databasebeta

← C2×#10591005 #11858158

Subgroups — C2×#10591005 #11858158

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×D3×#235C211yesmaximal, characteristic
2C2×C3×D3×M16C211yesmaximal, characteristic, complemented
3C2×#63855C211yesmaximal, characteristic, complemented
4C2×#63652C211yesmaximal, characteristic, complemented
5C2×C3×#825C211yesmaximal, characteristic, complemented
6C2×#63570C211yesmaximal, characteristic, complemented
7C2×#63568C211yesmaximal, characteristic, complemented
8#10591005C218yesmaximal, direct product factor
9C2×#5139—31nomaximal
10C2×#4821—31nomaximal
11C2×#3828C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C2×D3×#67—21no—
15C2×#3804—21no—
16D3×#235—22no—
17D3×#235—22no—
18D3×#235C414yescomplemented
19D3×#235C2214yes—
20C2×D3×D12C411yescharacteristic, complemented
21C2×C4×D32—21no—
22C2×#3799C411yescharacteristic, complemented
23C2×#3798—21no—
24C2×#3795C411yescharacteristic, complemented
25C2×D3×Dic6C411yescharacteristic, complemented
26C2×C32×M16C2211yescharacteristic, complemented
27C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
28C2×C3×C4×Dic3C2211yescharacteristic, complemented
29C2×C3×#208C2211yescharacteristic, complemented
30C3×D3×M16—22no—
31C3×D3×M16C2214yescomplemented
32C2×C3×ΓL(1,𝔽25)—21no—
33C2×C3×D3×C8—21no—
34C2×Dic3⋊Dic3—21no—
35C2×(C2×D3)⋊Dic3—21no—
36#63855—22no—
37#63855C2214yescomplemented
38#63652C2214yescomplemented
39C3×#825C2214yescomplemented
40#63570C2214yescomplemented
41#63568C2214yescomplemented
42C2×D3×#41—31no—
43C22×#235—31no—
44C22×C3×M16—31no—
45C2×#926—31no—
46C2×D3×M16D311yescharacteristic, complemented
47C2×#872—31no—
48C2×C3×#104—31no—
49C2×#837—31no—
50#5139—38no—
51C2×#825—31no—
52C2×#825—31no—
53C2×#825—31no—
54C2×#825—31no—
55C2×#825—61no—
56C2×#825D311yescharacteristic, complemented
57C2×#805—31no—
58#4821—38no—
59C23×C3×D3D411yescharacteristic
60C22×D32—21no—
61C22×C32×C4C2311yescharacteristic
62C2×#638—21no—
63C22×C3⋊Dic3—21no—
64#3828—21no—
65#3828—21no—
66#3828C2×C412yes—
67#3828C2312yes—
68C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
69C2×C4×C3⋊D3—21no—
70C2×#634C2×C411yescharacteristic
71C2×C3×#67—21no—
72C22×C3×Dic3—21no—
73C22×C3×Dic3D411yescharacteristic
74C3×#235—21no—
75C3×#235—21no—
76C3×#235C2×C412yes—
77C3×#235C2312yes—
78C2×C3×D12C2×C411yescharacteristic
79C2×C3×C4×D3—21no—
80C2×C3×C4×D3C2×C411yescharacteristic
81C2×C3×C4×D3C2×C411yescharacteristic
82C2×C3×C4×D3C2×C412yes—
83C2×C3×C4×D3D412yes—
84C2×C3×C4×D3D411yescharacteristic
85C2×C3×C4×D3D411yescharacteristic
86C2×C3×C4×D3D412yes—
87C2×C3×C4×D3C2312yes—
88C2×C3×Dic6C2×C411yescharacteristic
89D3×#67—24no—
90D3×#67—24no—
91C2×#627—21no—
92C2×#626—21no—
93C2×#626—21no—
94C2×#625—21no—
95C2×#624—21no—
96#3804—24no—
97#3804—24no—
98C2×D3×Dic3—21no—
99C2×D3×Dic3—21no—
100D3×D12—22no—
101D3×D12C2×C414yescomplemented
102C4×D32—24no—
103C4×D32—24no—
104#3799—22no—
105#3799C2×C414yescomplemented
106#3798—24no—
107#3798—24no—
108#3795—22no—
109#3795C2×C414yescomplemented
110D3×Dic6—22no—
111D3×Dic6C2×C414yescomplemented
112C32×M16—21no—
113C32×M16C2312yescomplemented
114C2×C32×C8—21no—
115C4×C3⋊Dic3—21no—
116C4×C3⋊Dic3C2312yescomplemented
117C3×C4×Dic3—21no—
118C3×C4×Dic3C2312yescomplemented
119C3×#208—21no—
120C3×#208C2312yescomplemented
121C2×C3×C3⋊C8—21no—
122C3×ΓL(1,𝔽25)—24no—
123C3×D3×C8—24no—
124Dic3⋊Dic3—24no—
125(C2×D3)⋊Dic3—24no—
126C2×#421—91noSylow
127C2×C3×#41—31no—
128C23×C3×C4—31no—
129C22×#67—61no—
130D3×#41—34no—
131D3×#41—34no—
132D3×#41—62no—
133D3×#41—62no—
134C2×#239—31no—
135C2×D3×Q8—31no—
136C2×#237—31no—
137C2×#237—61no—
138C2×D3×D4—31no—
139C2×D3×D4—61no—
140C2×#235—31no—
141C2×#235—31no—
142C2×#235—34no—
143C2×#235—34no—
144C2×#235—31no—
145C2×#235—31no—
146C2×#235—61no—
147C2×#235—61no—
148C2×#235—62no—
149C2×#235—62no—
150C2×#235—61no—
151C2×#235—61no—
152C2×#235C2×D311yescharacteristic
153C22×D12—31no—
154C22×C4×D3—61no—
155C22×C4×D3—61no—
156C22×C4×D3C2×D311yescharacteristic
157C22×Dic6—31no—
158C2×C3×M16—21no—
159C2×C3×M16—31no—
160C2×C3×M16—34no—
161C2×C3×M16—61no—
162C2×C3×M16—62no—
163C2×C3×M16C2×D311yescharacteristic, complemented
164C2×C3×M16C2×D311yescharacteristic, complemented
165C22×C3×C8—61no—
166C2×C3×C42—31no—
167C2×#217—61no—
168C2×(C2×D3)⋊C4—61no—
169#926—34no—
170#926—62no—
171C2×C4⋊Dic3—61no—
172C2×Dic3⋊C4—61no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3—61no—
176C2×C4×Dic3C2×D311yescharacteristic, complemented
177C2×#208C2×D311yescharacteristic, complemented
178D3×M16—22no—
179D3×M16C2×D314yescomplemented
180C2×ΓL(1,𝔽25)—21no—
181C2×D3×C8—21no—
182#872—34no—
183#872—62no—
184C3×#104—34no—
185#837—34no—
186#825—34no—
187#825—34no—
188#825—34no—
189#825—34no—
190#825—64no—
191#825C2×D314yescomplemented
192#805—34no—
193C23×C32C2×D411yescharacteristic
194C22×C3⋊D3—21no—
195C22×C3×D3—21no—
196C22×C3×D3—42no—
197C22×C3×D3C22⋊C411yescharacteristic
198C22×C3×D3C22⋊C411yescharacteristic
199C22×C3×D3C22⋊C412yes—
200C22×C3×D3C2×D412yes—
201C2×D32—24no—
202C2×D32—44no—
203C2×C32×C4C22×C411yescharacteristic
204C2×C32×C4C22×C411yescharacteristic
205C2×C32×C4C2×D411yescharacteristic
206C2×C32×C4C2×D411yescharacteristic
207C2×C32×C4C2×D411yescharacteristic
208C2×C32×C4C2411yescharacteristic
209#638—22no—
210#638—22no—
211C2×C3⋊Dic3—21no—
212C2×C3⋊Dic3—22no—
213C2×C3⋊Dic3—42no—
214C4⋊(C3⋊D3)—21no—
215C4⋊(C3⋊D3)C22×C412yes—
216C4×C3⋊D3—22no—
217C4×C3⋊D3—22no—
218#634—21no—
219#634C22×C412yes—
220C3×#67—22no—
221C3×#67—22no—
222C2×C3×Dic3—21no—
223C2×C3×Dic3—22no—
224C2×C3×Dic3—42no—
225C2×C3×Dic3C22⋊C411yescharacteristic
226C2×C3×Dic3C22⋊C412yes—
227C2×C3×Dic3C22⋊C411yescharacteristic
228C2×C3×Dic3C2×D412yes—
229C3×D12—21no—
230C3×D12C22×C412yes—
231C3×C4×D3—22no—
232C3×C4×D3—22no—
233C3×C4×D3C22⋊C412yes—
234C3×C4×D3C22⋊C412yes—
235C3×C4×D3C22⋊C412yes—
236C3×C4×D3C22⋊C412yes—
237C3×C4×D3C22×C412yes—
238C3×C4×D3C22×C412yes—
239C3×C4×D3C2×D412yes—
240C3×C4×D3C2×D412yes—
241C3×Dic6—21no—
242C3×Dic6C22×C412yes—
243#627—24no—
244#626—24no—
245#626—24no—
246#625—24no—
247#624—24no—
248D3×Dic3—24no—
249D3×Dic3—24no—
250C32×C8—22no—
251C3×C3⋊C8—22no—
252C22×#41—91no—
253C22×M16—31no—
254C2×#117—91no—
255#421—98no—
256C2×#104—31no—
257C2×#104—91no—
258C2×#104—91no—
259C2×#104—91no—
260C24×C3—31no—
261C23×D3—61no—
262C23×D3—61no—
263C23×D3D1211yescharacteristic
264C3×#41—32no—
265C3×#41—32no—
266C3×#41—61no—
267C3×#41—61no—
268C2×C3×Q8—31no—
269C2×C3×D4—31no—
270C2×C3×D4—61no—
271C22×C3×C4—21no—
272C22×C3×C4—31no—
273C22×C3×C4—31no—
274C22×C3×C4—31no—
275C22×C3×C4—32no—
276C22×C3×C4—32no—
277C22×C3×C4—31no—
278C22×C3×C4—31no—
279C22×C3×C4—32no—
280C22×C3×C4—32no—
281C22×C3×C4—61no—
282C22×C3×C4—61no—
283C22×C3×C4C22×D311yescharacteristic
284C22×C3×C4C22×D311yescharacteristic
285C2×#67—21no—
286C2×#67—61no—
287C2×#67—64no—
288C2×#67—64no—
289C2×#67—61no—
290C2×#67—61no—
291C2×#67—61no—
292C2×#67—61no—
293C2×#67—61no—
294C2×#67—121no—
295C22×Dic3—21no—
296C22×Dic3—61no—
297C22×Dic3—61no—
298C22×Dic3—61no—
299C22×Dic3—61no—
300C22×Dic3—121no—
301C22×Dic3D1211yescharacteristic
302#239—34no—
303#239—62no—
304D3×Q8—34no—
305D3×Q8—62no—
306#237—34no—
307#237—64no—
308#237—64no—
309#237—62no—
310D3×D4—34no—
311D3×D4—64no—
312D3×D4—64no—
313D3×D4—62no—
314#235—21no—
315#235—21no—
316#235—32no—
317#235—32no—
318#235—32no—
319#235—32no—
320#235—34no—
321#235—34no—
322#235—62no—
323#235—62no—
324#235—62no—
325#235—64no—
326#235—64no—
327#235—62no—
328#235—64no—
329#235—64no—
330#235—61no—
331#235—61no—
332#235—61no—
333#235—61no—
334#235—64no—
335#235—64no—
336#235—121no—
337#235—121no—
338#235C4×D312yes—
339#235C22×D312yes—
340C2×D12—31no—
341C2×D12—31no—
342C2×D12—34no—
343C2×D12—61no—
344C2×D12—62no—
345C2×D12—61no—
346C2×D12—61no—
347C2×D12C4×D311yescharacteristic
348C2×C4×D3—21no—
349C2×C4×D3—64no—
350C2×C4×D3—64no—
351C2×C4×D3—61no—
352C2×C4×D3—61no—
353C2×C4×D3—61no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×C4×D3—61no—
357C2×C4×D3—64no—
358C2×C4×D3—64no—
359C2×C4×D3—121no—
360C2×C4×D3C4×D311yescharacteristic
361C2×C4×D3C4×D311yescharacteristic
362C2×C4×D3C4×D312yes—
363C2×C4×D3D1212yes—
364C2×C4×D3#6711yescharacteristic
365C2×C4×D3#6711yescharacteristic
366C2×C4×D3#6712yes—
367C2×C4×D3C22×D312yes—
368C2×Dic6—31no—
369C2×Dic6—31no—
370C2×Dic6—34no—
371C2×Dic6—61no—
372C2×Dic6—62no—
373C2×Dic6—61no—
374C2×Dic6—61no—
375C2×Dic6C4×D311yescharacteristic
376C3×M16—21no—
377C3×M16—21no—
378C3×M16—22no—
379C3×M16—32no—
380C3×M16—41no—
381C3×M16—64no—
382C3×M16—61no—
383C3×M16C22×D312yescomplemented
384C3×M16C22×D312yescomplemented
385C2×C3×C8—21no—
386C2×C3×C8—21no—
387C2×C3×C8—41no—
388C2×C3×C8—64no—
389C2×C3×C8—61no—
390C3×C42—32no—
391C3×C42—61no—
392#217—64no—
393(C2×D3)⋊C4—64no—
394C4⋊Dic3—64no—
395Dic3⋊C4—64no—
396C4×Dic3—21no—
397C4×Dic3—32no—
398C4×Dic3—32no—
399C4×Dic3—62no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—121no—
403C4×Dic3C22×D312yescomplemented
404#208—21no—
405#208C22×D312yescomplemented
406C2×C3⋊C8—21no—
407ΓL(1,𝔽25)—24no—
408D3×C8—24no—
409C22×C32—22no—
410C22×C32C2×C22⋊C411yescharacteristic
411C22×C32C2×C22⋊C411yescharacteristic
412C22×C32C22×D411yescharacteristic
413C2×C3⋊D3—22no—
414C2×C3⋊D3—42no—
415C2×C3×D3—22no—
416C2×C3×D3—22no—
417C2×C3×D3—22no—
418C2×C3×D3—42no—
419C2×C3×D3—42no—
420C2×C3×D3—42no—
421C2×C3×D3C2×C22⋊C412yes—
422C2×C3×D3C2×C22⋊C412yes—
423D32—48no—
424C32×C4C2×C22⋊C411yescharacteristic
425C32×C4C2×C22⋊C411yescharacteristic
426C32×C4C23×C411yescharacteristic
427C32×C4C22×D411yescharacteristic
428C3⋊Dic3—22no—
429C3⋊Dic3—42no—
430C3×Dic3—22no—
431C3×Dic3—42no—
432C3×Dic3C2×C22⋊C412yes—
433C3×Dic3C2×C22⋊C412yes—
434C2×#41—31no—
435C2×#41—91no—
436C2×#41—91no—
437C2×#41—94no—
438C2×#41—94no—
439C2×#41—91no—
440C2×#41—181no—
441C2×#41—181no—
442C2×#41—182no—
443C2×#41—182no—
444C22×Q8—91no—
445C22×D4—91no—
446C22×D4—181no—
447C23×C4—31no—
448C23×C4—181no—
449C2×M16—31no—
450C2×M16—34no—
451C2×M16—61no—
452C2×M16—62no—
453C2×M16D3211yescharacteristic, complemented
454C22×C8—61no—
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—31no—
467C23×C3—31no—
468C23×C3—32no—
469C23×C3—32no—
470C23×C3—61no—
471C23×C3—122no—
472C23×C3C2×D1211yescharacteristic
473C23×C3D3×D411yescharacteristic
474C22×D3—21no—
475C22×D3—42no—
476C22×D3—64no—
477C22×D3—61no—
478C22×D3—61no—
479C22×D3—64no—
480C22×D3—121no—
481C22×D3—124no—
482C22×D3—124no—
483C22×D3(C2×D3)⋊C411yescharacteristic
484C22×D3(C2×D3)⋊C411yescharacteristic
485C22×D3(C2×D3)⋊C412yes—
486C22×D3C2×D1212yes—
487C3×Q8—32no—
488C3×Q8—61no—
489C3×D4—32no—
490C3×D4—62no—
491C3×D4—62no—
492C3×D4—61no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—32no—
502C2×C3×C4—32no—
503C2×C3×C4—32no—
504C2×C3×C4—32no—
505C2×C3×C4—32no—
506C2×C3×C4—32no—
507C2×C3×C4—32no—
508C2×C3×C4—32no—
509C2×C3×C4—32no—
510C2×C3×C4—32no—
511C2×C3×C4—61no—
512C2×C3×C4—62no—
513C2×C3×C4—62no—
514C2×C3×C4—62no—
515C2×C3×C4—122no—
516C2×C3×C4C2×C4×D311yescharacteristic
517C2×C3×C4C2×C4×D311yescharacteristic
518C2×C3×C4C2×C4×D311yescharacteristic
519C2×C3×C4C2×C4×D311yescharacteristic
520C2×C3×C4C2×D1211yescharacteristic
521C2×C3×C4D3×D411yescharacteristic
522C2×C3×C4D3×D411yescharacteristic
523C2×C3×C4D3×D411yescharacteristic
524C2×C3×C4C2×#6711yescharacteristic
525C2×C3×C4C2×#6711yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528#67—22no—
529#67—22no—
530#67—64no—
531#67—64no—
532#67—62no—
533#67—62no—
534#67—62no—
535#67—62no—
536#67—64no—
537#67—64no—
538#67—122no—
539#67—122no—
540C2×Dic3—21no—
541C2×Dic3—22no—
542C2×Dic3—42no—
543C2×Dic3—64no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—64no—
547C2×Dic3—62no—
548C2×Dic3—62no—
549C2×Dic3—122no—
550C2×Dic3—121no—
551C2×Dic3—122no—
552C2×Dic3—122no—
553C2×Dic3—124no—
554C2×Dic3(C2×D3)⋊C411yescharacteristic
555C2×Dic3(C2×D3)⋊C411yescharacteristic
556C2×Dic3(C2×D3)⋊C412yes—
557C2×Dic3C2×D1212yes—
558D12—21no—
559D12—32no—
560D12—32no—
561D12—62no—
562D12—64no—
563D12—64no—
564D12—61no—
565D12—61no—
566D12—121no—
567D12C2×C4×D312yes—
568C4×D3—22no—
569C4×D3—22no—
570C4×D3—64no—
571C4×D3—64no—
572C4×D3—64no—
573C4×D3—62no—
574C4×D3—62no—
575C4×D3—62no—
576C4×D3—62no—
577C4×D3—64no—
578C4×D3—122no—
579C4×D3—122no—
580C4×D3(C2×D3)⋊C412yes—
581C4×D3(C2×D3)⋊C412yes—
582C4×D3(C2×D3)⋊C412yes—
583C4×D3(C2×D3)⋊C412yes—
584C4×D3C2×C4×D312yes—
585C4×D3C2×C4×D312yes—
586C4×D3C2×#6712yes—
587C4×D3C2×#6712yes—
588Dic6—21no—
589Dic6—32no—
590Dic6—32no—
591Dic6—62no—
592Dic6—64no—
593Dic6—61no—
594Dic6—61no—
595Dic6—64no—
596Dic6—121no—
597Dic6C2×C4×D312yes—
598C3×C8—22no—
599C3×C8—22no—
600C3×C8—42no—
601C3×C8—62no—
602C3⋊C8—22no—
603C2×C32—21no—
604C2×C32—21no—
605C2×C32#42112yescomplemented
606C2×C32C22×C22⋊C411yescharacteristic
607C3⋊D3—42no—
608C3×D3—22no—
609C3×D3—22no—
610C3×D3—42no—
611C24—31no—
612C24—181no—
613#41—32no—
614#41—32no—
615#41—61no—
616#41—61no—
617#41—94no—
618#41—94no—
619#41—92no—
620#41—92no—
621#41—184no—
622#41—184no—
623#41—184no—
624#41—184no—
625#41—182no—
626#41—182no—
627#41—181no—
628#41—181no—
629C2×Q8—31no—
630C2×Q8—94no—
631C2×Q8—91no—
632C2×Q8—181no—
633C2×Q8—182no—
634C2×D4—31no—
635C2×D4—61no—
636C2×D4—94no—
637C2×D4—91no—
638C2×D4—182no—
639C2×D4—181no—
640C2×D4—181no—
641C2×D4—184no—
642C2×D4—184no—
643C2×D4—181no—
644C2×D4—181no—
645C22×C4—31no—
646C22×C4—32no—
647C22×C4—31no—
648C22×C4—31no—
649C22×C4—32no—
650C22×C4—32no—
651C22×C4—32no—
652C22×C4—31no—
653C22×C4—31no—
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—181no—
657C22×C4—184no—
658C22×C4—184no—
659C22×C4—181no—
660C22×C4—181no—
661C22×C4—181no—
662C22×C4—181no—
663C22×C4C2×D3211yescharacteristic
664M16—21no—
665M16—32no—
666M16—64no—
667M16—61no—
668M16C2×D3212yescomplemented
669C2×C8—21no—
670C2×C8—64no—
671C2×C8—61no—
672C4⋊C4—184no—
673C22⋊C4—184no—
674C42—32no—
675C42—61no—
676C42—92no—
677C42—181no—
678C22×C3—22no—
679C22×C3—22no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—32no—
684C22×C3—32no—
685C22×C3—42no—
686C22×C3—62no—
687C22×C3—62no—
688C22×C3—62no—
689C22×C3—122no—
690C22×C3—122no—
691C22×C3—122no—
692C22×C3D3×C22⋊C411yescharacteristic
693C22×C3D3×C22⋊C411yescharacteristic
694C22×C3C2×(C2×D3)⋊C411yescharacteristic
695C22×C3C2×(C2×D3)⋊C411yescharacteristic
696C22×C3C22×D1211yescharacteristic
697C22×C3C2×D3×D411yescharacteristic
698C2×D3—22no—
699C2×D3—22no—
700C2×D3—22no—
701C2×D3—42no—
702C2×D3—42no—
703C2×D3—42no—
704C2×D3—62no—
705C2×D3—62no—
706C2×D3—122no—
707C2×D3—128no—
708C2×D3—128no—
709C2×D3—122no—
710C2×D3—122no—
711C2×D3—242no—
712C2×D3C2×(C2×D3)⋊C412yes—
713C2×D3C2×(C2×D3)⋊C412yes—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—32no—
719C3×C4—32no—
720C3×C4—62no—
721C3×C4—122no—
722C3×C4D3×C22⋊C411yescharacteristic
723C3×C4D3×C22⋊C411yescharacteristic
724C3×C4C2×(C2×D3)⋊C411yescharacteristic
725C3×C4C2×(C2×D3)⋊C411yescharacteristic
726C3×C4C22×C4×D311yescharacteristic
727C3×C4C22×C4×D311yescharacteristic
728C3×C4C2×D3×D411yescharacteristic
729C3×C4C22×#6711yescharacteristic
730Dic3—22no—
731Dic3—42no—
732Dic3—62no—
733Dic3—62no—
734Dic3—122no—
735Dic3—122no—
736Dic3—122no—
737Dic3—124no—
738Dic3C2×(C2×D3)⋊C412yes—
739Dic3C2×(C2×D3)⋊C412yes—
740C32C2×#42111yescharacteristic, complemented, Sylow
741C23—31no—
742C23—31no—
743C23—32no—
744C23—32no—
745C23—61no—
746C23—122no—
747C23—184no—
748C23—181no—
749C23—364no—
750C23D3×D1211yescharacteristic
751Q8—32no—
752Q8—61no—
753Q8—92no—
754Q8—184no—
755Q8—181no—
756D4—32no—
757D4—62no—
758D4—62no—
759D4—61no—
760D4—92no—
761D4—184no—
762D4—184no—
763D4—184no—
764D4—182no—
765D4—182no—
766D4—181no—
767C2×C4—32no—
768C2×C4—31no—
769C2×C4—31no—
770C2×C4—32no—
771C2×C4—32no—
772C2×C4—32no—
773C2×C4—32no—
774C2×C4—32no—
775C2×C4—32no—
776C2×C4—32no—
777C2×C4—32no—
778C2×C4—32no—
779C2×C4—61no—
780C2×C4—62no—
781C2×C4—62no—
782C2×C4—62no—
783C2×C4—122no—
784C2×C4—184no—
785C2×C4—184no—
786C2×C4—184no—
787C2×C4—181no—
788C2×C4—182no—
789C2×C4—182no—
790C2×C4—182no—
791C2×C4—362no—
792C2×C4C4×D3211yescharacteristic
793C2×C4C4×D3211yescharacteristic
794C2×C4D3×D1211yescharacteristic
795C2×C4D3×#6711yescharacteristic
796C2×C4D3×#6711yescharacteristic
797C2×C4C22×D3211yescharacteristic
798C8—22no—
799C8—62no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—22no—
805C2×C3—21no—
806C2×C3—41no—
807C2×C3—41no—
808C2×C3—62no—
809C2×C3—62no—
810C2×C3—122no—
811C2×C3#482112yescomplemented
812C2×C3#513912yescomplemented
813C2×C3C2×D3×C22⋊C411yescharacteristic
814C2×C3C22×(C2×D3)⋊C411yescharacteristic
815D3—22no—
816D3—22no—
817D3—42no—
818D3—122no—
819D3—122no—
820D3—242no—
821C22—22no—
822C22—32no—
823C22—32no—
824C22—62no—
825C22—62no—
826C22—62no—
827C22—122no—
828C22—122no—
829C22—122no—
830C22—182no—
831C22—368no—
832C22—362no—
833C22D3×(C2×D3)⋊C411yescharacteristic
834C22D3×(C2×D3)⋊C411yescharacteristic
835C22C2×D3×D1211yescharacteristic
836C4—32no—
837C4—32no—
838C4—62no—
839C4—122no—
840C4—182no—
841C4—362no—
842C4D3×(C2×D3)⋊C411yescharacteristic
843C4D3×(C2×D3)⋊C411yescharacteristic
844C4C2×C4×D3211yescharacteristic
845C4C2×D3×#6711yescharacteristic
846C3—21no—
847C3C2×#482111yescharacteristic, complemented
848C3C2×#513911yescharacteristic, complemented
849C2—21no—
850C2—21no—
851C2—62no—
852C2—62no—
853C2—122no—
854C2—362no—
855C2#1059100512yesdirect product factor
856C2C2×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radicalC2×D3×#235C2
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32C2×#421
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×M16C2semidirect
3. C2×#63855C2semidirect
4. C2×#63652C2semidirect
5. C2×C3×#825C2semidirect
6. C2×#63570C2semidirect
7. C2×#63568C2semidirect
8. #10591005C2direct (N × H)
18. D3×#235C4semidirect
20. C2×D3×D12C4semidirect
22. C2×#3799C4semidirect
24. C2×#3795C4semidirect
25. C2×D3×Dic6C4semidirect
26. C2×C32×M16C22semidirect
27. C2×C4×C3⋊Dic3C22semidirect
28. C2×C3×C4×Dic3C22semidirect
29. C2×C3×#208C22semidirect
31. C3×D3×M16C22semidirect
37. #63855C22semidirect
38. #63652C22semidirect
39. C3×#825C22semidirect
40. #63570C22semidirect
41. #63568C22semidirect
46. C2×D3×M16D3semidirect
56. C2×#825D3semidirect
101. D3×D12C2×C4semidirect
105. #3799C2×C4semidirect
109. #3795C2×C4semidirect
111. D3×Dic6C2×C4semidirect
113. C32×M16C23semidirect
116. C4×C3⋊Dic3C23semidirect
118. C3×C4×Dic3C23semidirect
120. C3×#208C23semidirect
163. C2×C3×M16C2×D3semidirect
164. C2×C3×M16C2×D3semidirect
176. C2×C4×Dic3C2×D3semidirect
177. C2×#208C2×D3semidirect
179. D3×M16C2×D3semidirect
191. #825C2×D3semidirect
383. C3×M16C22×D3semidirect
384. C3×M16C22×D3semidirect
403. C4×Dic3C22×D3semidirect
405. #208C22×D3semidirect
453. C2×M16D32semidirect
605. C2×C32#421semidirect
668. M16C2×D32semidirect
740. C32C2×#421semidirect
811. C2×C3#4821semidirect
812. C2×C3#5139semidirect
847. C3C2×#4821semidirect
848. C3C2×#5139semidirect
855. C2#10591005direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D3×#2352
C2×C3×D3×M162
C2×#638552
C2×#636522
C2×C3×#8252
C2×#635702
C2×#635682
#105910052
C2×#51393
C2×#48213