Finite Group Databasebeta

← C4×#63947 #11860000

Subgroups — C4×#63947 #11860000

Order 1152.

1055 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#239C211yesmaximal, characteristic, complemented
2C2×#63947C211yesmaximal, characteristic
3C4×#3795C211yesmaximal, characteristic, complemented
4C4×#3756C211yesmaximal, characteristic, complemented
5C3×C4×#215C211yesmaximal, characteristic, complemented
6Dic3×#215C211yesmaximal, characteristic, complemented
7#10591556C211yesmaximal, characteristic, complemented
8#10591537C211yesmaximal, characteristic, complemented
9#10590608C211yesmaximal, characteristic, complemented
10#10590572C211yesmaximal, characteristic, complemented
11#10590479C211yesmaximal, characteristic, complemented
12#10590452C211yesmaximal, characteristic, complemented
13C4×#3716C211yesmaximal, characteristic, complemented
14C4×#3713C211yesmaximal, characteristic, complemented
15C4×D3×C3⋊C8C211yesmaximal, characteristic, complemented
16C4×#950—31nomaximal
17C4×#916—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C3×#893—21no—
26C3×#893C2211yescharacteristic
27C3×#892—21no—
28C3×#892C2211yescharacteristic
29C3×C4×D12—21no—
30C3×C4×D12C2211yescharacteristic
31C3×C4×D12C2211yescharacteristic
32C3×C42×D3—21no—
33C3×C42×D3C2211yescharacteristic
34#63947C418yesdirect product factor
35C4×#625—21no—
36Dic3×D12C2211yescharacteristic
37#63879—21no—
38#63877—21no—
39C4×D3×Dic3—21no—
40#63844C2211yescharacteristic
41#63841C2211yescharacteristic
42C2×#3716C2211yescharacteristic
43C2×#3713C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46#63662C2211yescharacteristic
47#63637C2211yescharacteristic
48#63634C2211yescharacteristic
49C4×C3⋊(C3⋊C8)C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#809C2211yescharacteristic
52C3×#808C2211yescharacteristic
53C3×C4×C3⋊C8C2211yescharacteristic
54#63576C2211yescharacteristic
55#63573C2211yescharacteristic
56#63567C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61Dic3×C3⋊C8C2211yescharacteristic
62C3×C4×#41—31no—
63C2×#950—31no—
64C2×#916—31no—
65C4×#239D311yescharacteristic, complemented
66C4×#237—31no—
67C4×#235—31no—
68C3×C4×SD16—31no—
69#5233—31no—
70Dic3×SD16—31no—
71C4×#216—31no—
72C4×#216—31no—
73C4×#216—31no—
74C4×#216—61no—
75C4×#215—31no—
76C4×#215D311yescharacteristic, complemented
77C4×#214—31no—
78C4×#214—31no—
79C4×#213—31no—
80C4×#213—31no—
81C4×#213—31no—
82#5002—31no—
83#4998—31no—
84C2×C4×C3⋊C8—31no—
85#4860—31no—
86#4852—31no—
87#4804—31no—
88#4790—31no—
89#4772—31no—
90#4756—31no—
91C4×#204—31no—
92C4×D3×C8—31no—
93C2×C32×Q8C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C3×#239—22no—
96C3×#239C2×C414yescomplemented
97C2×C3×D12—21no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3D411yescharacteristic
105C2×C3×C4×D3D411yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×#625—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3795—22no—
111#3795C2×C414yescomplemented
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C42—21no—
115C32×C42C2311yescharacteristic
116#3756C2×C414yescomplemented
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119C4×C3⋊Dic3—21no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#215C2×C414yescomplemented
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3D411yescharacteristic
133C3×C4×Dic3D411yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3724—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142#3716C2×C414yescomplemented
143#3713C2×C414yescomplemented
144D3×C3⋊C8—22no—
145D3×C3⋊C8C2×C414yescomplemented
146C4×#135—91noSylow
147C2×C3×#41—31no—
148C2×#239C2×D311yescharacteristic
149C2×#237—31no—
150C2×#235—31no—
151C2×C3×SD16—31no—
152C3×C4×Q8—21no—
153C3×C4×Q8—31no—
154C3×C4×Q8C2×D311yescharacteristic
155C3×C4×Q8C2×D311yescharacteristic
156C3×C4×D4—31no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C3×C4×D4—61no—
160C3×C4×D4—61no—
161C3×#117—31no—
162C3×#117—61no—
163C2×C3×C42—31no—
164C2×C3×C42—61no—
165#950—38no—
166Q8×Dic3C2×D311yescharacteristic
167C2×#216—31no—
168C2×#216—31no—
169C2×#216—61no—
170C2×#215C2×D311yescharacteristic
171D4×Dic3—31no—
172C2×#214—31no—
173C2×#213—31no—
174C2×#213—31no—
175C4×#67—61no—
176C4×#67—61no—
177C4×#67—61no—
178#926—31no—
179C2×C4×Dic3—61no—
180C22×C3⋊C8—31no—
181C22×C3⋊C8—31no—
182#916—38no—
183C2×#204—31no—
184C2×D3×C8—31no—
185C2×D3×C8—31no—
186#893—21no—
187#893C2×D311yescharacteristic
188#892—21no—
189#892—31no—
190#892C2×D311yescharacteristic
191#887—31no—
192#67⋊C4—61no—
193#877—61no—
194C4×D12—21no—
195C4×D12—31no—
196C4×D12C2×D311yescharacteristic
197C4×D12C2×D311yescharacteristic
198#872—61no—
199C42×D3—21no—
200C42×D3—61no—
201C42×D3C2×D311yescharacteristic
202C4×Dic6—31no—
203C4×Dic6—31no—
204C4×Dic6—31no—
205C4×Dic6—61no—
206C3×#106—31no—
207C3×#103—31no—
208C3×#102—31no—
209C3×C4×C8—31no—
210#835—31no—
211#835—31no—
212#835—61no—
213#835C2×D311yescharacteristic
214#832—31no—
215#832—31no—
216#832—31no—
217#821—31no—
218#817—31no—
219#816—31no—
220C8×Dic3—31no—
221C8×Dic3—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#810—61no—
226#809—31no—
227#809—31no—
228#809C2×D311yescharacteristic
229#808—31no—
230#808C2×D311yescharacteristic
231#807—31no—
232#807—31no—
233#807—31no—
234#807—31no—
235#807—61no—
236C4×C3⋊C8—31no—
237C4×C3⋊C8—31no—
238C4×C3⋊C8—31no—
239C4×C3⋊C8—31no—
240C4×C3⋊C8—61no—
241C4×C3⋊C8C2×D311yescharacteristic
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8C22×C412yes—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254#634—21no—
255#634C22×C412yes—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—24no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12C22×C412yes—
265C3×D12C22×C412yes—
266C3×C4×D3—22no—
267C3×C4×D3—24no—
268C3×C4×D3—22no—
269C3×C4×D3—42no—
270C3×C4×D3—42no—
271C3×C4×D3—42no—
272C3×C4×D3C22×C412yes—
273C3×C4×D3#4112yes—
274#625—24no—
275D3×Dic3—24no—
276D3×Dic3—42no—
277C3⋊(C3⋊C8)—21no—
278C3⋊(C3⋊C8)C22×C412yes—
279C3×C3⋊C8—21no—
280C3×C3⋊C8C22×C412yes—
281C2×#135—91no—
282C4×#41—31no—
283C4×#41—91no—
284C4×Q16—91no—
285C4×Q16—91no—
286C4×SD16—31no—
287C4×SD16—91no—
288C4×SD16—91no—
289C4×SD16—91no—
290C4×D8—91no—
291C4×D8—91no—
292#427—91no—
293#416—91no—
294#416—91no—
295C2×C4×C8—91no—
296C3×#41—34no—
297C3×#41—62no—
298C2×C3×Q8—21no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C2×C3×D4—61no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C2×#67—61no—
312C2×#67—61no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315#239—22no—
316#239C4×D314yescomplemented
317#237—34no—
318#237—62no—
319#235—34no—
320#235—62no—
321C2×D12—21no—
322C2×D12C22×D311yescharacteristic
323C2×D12C22×D311yescharacteristic
324C2×C4×D3—21no—
325C2×C4×D3—21no—
326C2×C4×D3—21no—
327C2×C4×D3—21no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3#6711yescharacteristic
331C2×C4×D3#6711yescharacteristic
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—61no—
336C3×SD16—34no—
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—41no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C42—21no—
353C3×C42—21no—
354C3×C42—21no—
355C3×C42—31no—
356C3×C42—31no—
357C3×C42—31no—
358C3×C42—41no—
359C3×C42—61no—
360C3×C42—61no—
361C3×C42C22×D311yescharacteristic
362C3×C42C22×D311yescharacteristic
363#217—61no—
364#217—61no—
365#216—34no—
366#216—34no—
367#216—64no—
368#215C4×D314yescomplemented
369#214—34no—
370#213—34no—
371#213—34no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378C4⋊Dic3—21no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—61no—
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—121no—
389C4×Dic3—21no—
390C4×Dic3—21no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—121no—
398C4×Dic3#6711yescharacteristic
399C4×Dic3#6711yescharacteristic
400C4×Dic3C22×D311yescharacteristic
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—34no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8—62no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411#204—34no—
412D3×C8—34no—
413D3×C8—62no—
414C22×C32C22×D411yescharacteristic
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—22no—
418C2×C3×D3—22no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3C4×D412yes—
424C32×C4—22no—
425C32×C4—21no—
426C32×C4—41no—
427C32×C4#13512yescomplemented
428C32×C4C23×C411yescharacteristic
429C32×C4C2×#4111yescharacteristic
430C3⋊Dic3—22no—
431C3⋊Dic3—41no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3C4×D412yes—
436C3×Dic3#13512yescomplemented
437C2×#41—31no—
438C2×#41—91no—
439#135—98no—
440C2×Q16—91no—
441C2×SD16—31no—
442C2×SD16—91no—
443C2×D8—91no—
444C22×C8—91no—
445C22×C8—91no—
446C4×Q8—31no—
447C4×Q8—91no—
448C4×Q8—91no—
449C4×Q8D3211yescharacteristic
450C4×D4—31no—
451C4×D4—31no—
452C4×D4—31no—
453C4×D4—61no—
454C4×D4—61no—
455C4×D4—91no—
456C4×D4—181no—
457C4×D4—181no—
458#117—31no—
459#117—61no—
460#117—91no—
461#117—181no—
462C2×C42—31no—
463C2×C42—61no—
464C2×C42—181no—
465#107—91no—
466#107—91no—
467#106—31no—
468#106—91no—
469#103—31no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—91no—
475#102—91no—
476#102—91no—
477C4×C8—31no—
478C4×C8—91no—
479C4×C8—91no—
480C4×C8—91no—
481C23×C3—31no—
482C23×C3—61no—
483C23×C3—61no—
484C22×D3—21no—
485C22×D3—21no—
486C22×D3C2×#6711yescharacteristic
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—22no—
490C3×Q8—41no—
491C3×Q8C2×C4×D312yes—
492C3×Q8C2×C4×D312yes—
493C3×D4—32no—
494C3×D4—32no—
495C3×D4—64no—
496C3×D4—61no—
497C3×D4—61no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—32no—
508C2×C3×C4—32no—
509C2×C3×C4—31no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—62no—
513C2×C3×C4—64no—
514C2×C3×C4—62no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—122no—
518C2×C3×C4—122no—
519C2×C3×C4—122no—
520C2×C3×C4D3×D411yescharacteristic
521C2×C3×C4D3×D411yescharacteristic
522C2×C3×C4C2×#6711yescharacteristic
523C2×C3×C4C2×#6711yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526#67—64no—
527#67—64no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—64no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—121no—
536C2×Dic3—121no—
537C2×Dic3—122no—
538C2×Dic3C2×#6711yescharacteristic
539C2×Dic3C2×#6711yescharacteristic
540C2×Dic3C2×#6711yescharacteristic
541D12—24no—
542D12—21no—
543D12—21no—
544D12C2×C4×D312yes—
545D12C2×C4×D312yes—
546C4×D3—22no—
547C4×D3—24no—
548C4×D3—22no—
549C4×D3—42no—
550C4×D3—42no—
551C4×D3—42no—
552C4×D3—64no—
553C4×D3—122no—
554C4×D3C2×C4×D312yes—
555C4×D3#23512yes—
556Dic6—32no—
557Dic6—32no—
558Dic6—62no—
559Dic6—61no—
560Dic6—61no—
561Dic6—121no—
562C3×C8—32no—
563C3×C8—61no—
564C3⋊C8—21no—
565C3⋊C8—32no—
566C3⋊C8—32no—
567C3⋊C8—62no—
568C3⋊C8—61no—
569C3⋊C8—61no—
570C3⋊C8—121no—
571C3⋊C8C2×C4×D312yes—
572C2×C32C2×C4×D411yescharacteristic
573C2×C32C2×#13511yescharacteristic
574C2×C32C2×#13511yescharacteristic
575C3×D3—22no—
576C3×D3—42no—
577C3×D3—42no—
578#41—34no—
579#41—62no—
580#41—94no—
581#41—182no—
582C2×Q8—91no—
583C2×Q8C2×D3211yescharacteristic
584C2×D4—31no—
585C2×D4—31no—
586C2×D4—61no—
587C2×D4—181no—
588C22×C4—31no—
589C22×C4—31no—
590C22×C4—31no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—181no—
596C22×C4—181no—
597Q16—94no—
598SD16—34no—
599SD16—94no—
600D8—94no—
601C2×C8—31no—
602C2×C8—31no—
603C2×C8—94no—
604C2×C8—91no—
605C2×C8—91no—
606C2×C8—182no—
607C4⋊C4—21no—
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—61no—
611C4⋊C4—91no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4C2×D3211yescharacteristic
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—181no—
620C22⋊C4—181no—
621C42—21no—
622C42—31no—
623C42—31no—
624C42—31no—
625C42—61no—
626C42—61no—
627C42—181no—
628C42—181no—
629C42—181no—
630C42C2×D3211yescharacteristic
631C22×C3—21no—
632C22×C3—32no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—62no—
636C22×C3—62no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3C2×D3×D411yescharacteristic
642C22×C3C22×#6711yescharacteristic
643C2×D3—21no—
644C2×D3—21no—
645C2×D3—22no—
646C2×D3—22no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3C4×#6712yes—
652C3×C4—21no—
653C3×C4—22no—
654C3×C4—22no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—22no—
659C3×C4—32no—
660C3×C4—32no—
661C3×C4—41no—
662C3×C4—42no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—61no—
666C3×C4—81no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4#91612yescomplemented
670C3×C4#95012yescomplemented
671C3×C4C22×C4×D311yescharacteristic
672C3×C4C22×C4×D311yescharacteristic
673C3×C4C2×#23511yescharacteristic
674C3×C4D3×#4111yescharacteristic
675Dic3—21no—
676Dic3—41no—
677Dic3—41no—
678Dic3—62no—
679Dic3—62no—
680Dic3—122no—
681Dic3—121no—
682Dic3—121no—
683Dic3—241no—
684Dic3C4×#6712yes—
685Dic3#95012yescomplemented
686C32C4×#13511yescharacteristic, complemented, Sylow
687C23—31no—
688C23—61no—
689C23—61no—
690Q8—21no—
691Q8—92no—
692Q8—181no—
693Q8C4×D3212yes—
694D4—32no—
695D4—32no—
696D4—64no—
697D4—61no—
698D4—61no—
699D4—184no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—32no—
705C2×C4—32no—
706C2×C4—31no—
707C2×C4—62no—
708C2×C4—64no—
709C2×C4—62no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4—122no—
715C2×C4—184no—
716C2×C4—181no—
717C2×C4—181no—
718C2×C4—362no—
719C2×C4D3×#6711yescharacteristic
720C2×C4D3×#6711yescharacteristic
721C2×C4C22×D3211yescharacteristic
722C8—32no—
723C8—61no—
724C8—92no—
725C8—181no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—62no—
730C2×C3—122no—
731C2×C3—122no—
732C2×C3C4×D3×D411yescharacteristic
733C2×C3C2×#91611yescharacteristic
734C2×C3D3×#13511yescharacteristic
735C2×C3C2×C4×#6711yescharacteristic
736C2×C3C2×#95011yescharacteristic
737C2×C3C2×#95011yescharacteristic
738D3—22no—
739D3—42no—
740D3—42no—
741C22—32no—
742C22—61no—
743C22—61no—
744C22—62no—
745C22—62no—
746C22—121no—
747C22—121no—
748C22—121no—
749C22—121no—
750C22C2×D3×#6711yescharacteristic
751C4—21no—
752C4—22no—
753C4—32no—
754C4—32no—
755C4—41no—
756C4—61no—
757C4—121no—
758C4—121no—
759C4—182no—
760C4—361no—
761C4#6394712yesdirect product factor
762C4C2×C4×D3211yescharacteristic
763C4D3×#23511yescharacteristic
764C3—21no—
765C3C4×#91611yescharacteristic, complemented
766C3C4×#95011yescharacteristic, complemented
767C2—62no—
768C2—122no—
769C2—122no—
770C2C4×D3×#6711yescharacteristic
771C2C2×#6394711yescharacteristic
772C2D3×#95011yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×#63947C2
cosocleC2×C32×C4C24
hypercenterC4×Q8D32
hypocenterC32C4×#135
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×C4×#239C2semidirect
3. C4×#3795C2semidirect
4. C4×#3756C2semidirect
5. C3×C4×#215C2semidirect
6. Dic3×#215C2semidirect
7. #10591556C2semidirect
8. #10591537C2semidirect
9. #10590608C2semidirect
10. #10590572C2semidirect
11. #10590479C2semidirect
12. #10590452C2semidirect
13. C4×#3716C2semidirect
14. C4×#3713C2semidirect
15. C4×D3×C3⋊C8C2semidirect
34. #63947C4direct (N × H)
65. C4×#239D3semidirect
76. C4×#215D3semidirect
96. C3×#239C2×C4semidirect
111. #3795C2×C4semidirect
116. #3756C2×C4semidirect
122. C3×#215C2×C4semidirect
142. #3716C2×C4semidirect
143. #3713C2×C4semidirect
145. D3×C3⋊C8C2×C4semidirect
316. #239C4×D3semidirect
368. #215C4×D3semidirect
427. C32×C4#135semidirect
436. C3×Dic3#135semidirect
669. C3×C4#916semidirect
670. C3×C4#950semidirect
685. Dic3#950semidirect
686. C32C4×#135semidirect
761. C4#63947direct (N × H)
765. C3C4×#916semidirect
766. C3C4×#950semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2392
C2×#639472
C4×#37952
C4×#37562
C3×C4×#2152
Dic3×#2152
#105915562
#105915372
#105906082
#105905722
#105904792
#105904522
C4×#37162
C4×#37132
C4×D3×C3⋊C82
C4×#9503
C4×#9163