Finite Group Databasebeta

← C4×#63949 #11859998

Subgroups — C4×#63949 #11859998

Order 1152.

1061 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#239C211yesmaximal, characteristic, complemented
2C2×#63949C211yesmaximal, characteristic
3C4×#3799C211yesmaximal, characteristic, complemented
4C4×#3755C211yesmaximal, characteristic, complemented
5C3×C4×#216C211yesmaximal, characteristic, complemented
6Dic3×#216C211yesmaximal, characteristic, complemented
7#10591556C211yesmaximal, characteristic, complemented
8#10591536C211yesmaximal, characteristic, complemented
9#10590610C211yesmaximal, characteristic, complemented
10#10590571C211yesmaximal, characteristic, complemented
11#10590475C211yesmaximal, characteristic, complemented
12#10590456C211yesmaximal, characteristic, complemented
13C4×#3715C211yesmaximal, characteristic, complemented
14C4×#3714C211yesmaximal, characteristic, complemented
15C4×D3×C3⋊C8C211yesmaximal, characteristic, complemented
16C4×#950—31nomaximal
17C4×#919—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C2×#3755C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C3×#893—21no—
26C3×#893C2211yescharacteristic
27C3×#892—21no—
28C3×#892C2211yescharacteristic
29C3×C4×D12—21no—
30C3×C4×D12C2211yescharacteristic
31C3×C42×D3—21no—
32C3×C42×D3C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34#63949C418yesdirect product factor
35#63904—21no—
36C4×#626—21no—
37#63894C2211yescharacteristic
38C4×#624—21no—
39Dic3×Dic6C2211yescharacteristic
40#63841C2211yescharacteristic
41#63836—21no—
42C2×#3715C2211yescharacteristic
43C2×#3714C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46#63662C2211yescharacteristic
47#63636C2211yescharacteristic
48#63635C2211yescharacteristic
49C4×C3⋊(C3⋊C8)C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#807C2211yescharacteristic
53C3×C4×C3⋊C8C2211yescharacteristic
54#63575C2211yescharacteristic
55#63574C2211yescharacteristic
56#63565C2211yescharacteristic
57#63564C2211yescharacteristic
58#63563C2211yescharacteristic
59#63562C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61Dic3×C3⋊C8C2211yescharacteristic
62C3×C4×#41—31no—
63C2×#950—31no—
64C2×#919—31no—
65C4×#239—31no—
66C4×#239D311yescharacteristic, complemented
67C4×#235—31no—
68C3×C4×Q16—31no—
69#5233—31no—
70Dic3×Q16—31no—
71C4×#216—31no—
72C4×#216D311yescharacteristic, complemented
73C4×#215—31no—
74C4×#215—31no—
75C4×#215—31no—
76C4×#215—31no—
77C4×#215—61no—
78C4×#214—31no—
79C4×#214—31no—
80C4×#213—31no—
81C4×#213—31no—
82#5002—31no—
83#4998—31no—
84C2×C4×C3⋊C8—31no—
85#4880—31no—
86#4872—31no—
87#4804—31no—
88#4804—31no—
89#4788—31no—
90#4788—31no—
91C4×D24—31no—
92C4×D3×C8—31no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C3×#239—22no—
97C3×#239C2×C414yescomplemented
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3D411yescharacteristic
104C2×C3×C4×D3D411yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#626—21no—
108C2×#624—21no—
109C2×#624—21no—
110#3799—22no—
111#3799C2×C414yescomplemented
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C42—21no—
115C32×C42C2311yescharacteristic
116#3755C2×C414yescomplemented
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#216C2×C414yescomplemented
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3—21no—
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
137Dic3⋊Dic3—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142#3715C2×C414yescomplemented
143#3714C2×C414yescomplemented
144D3×C3⋊C8—22no—
145D3×C3⋊C8C2×C414yescomplemented
146C4×#135—91noSylow
147C2×C3×#41—31no—
148C2×#239—31no—
149C2×#239C2×D311yescharacteristic
150C2×#235—31no—
151C2×C3×Q16—31no—
152C3×C4×Q8—21no—
153C3×C4×Q8—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8C2×D311yescharacteristic
156C3×C4×Q8C2×D311yescharacteristic
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×Dic3—31no—
167Q8×Dic3C2×D311yescharacteristic
168C2×#216C2×D311yescharacteristic
169C2×#215—31no—
170C2×#215—31no—
171C2×#215—31no—
172C2×#215—61no—
173C2×#214—31no—
174C2×#213—31no—
175C4×#67—61no—
176C4×#67—61no—
177#926—31no—
178C22×C3⋊C8—31no—
179C22×C3⋊C8—31no—
180#919—38no—
181C2×D24—31no—
182C2×D3×C8—31no—
183C2×D3×C8—31no—
184#893—21no—
185#893—31no—
186#893—61no—
187#893C2×D311yescharacteristic
188#892—21no—
189#892—31no—
190#892—61no—
191#892C2×D311yescharacteristic
192C4×D12—21no—
193C4×D12—31no—
194C4×D12—31no—
195C4×D12—31no—
196C4×D12—61no—
197C4×D12—61no—
198C4×D12C2×D311yescharacteristic
199#872—61no—
200C42×D3—21no—
201C42×D3—61no—
202C42×D3—61no—
203C42×D3C2×D311yescharacteristic
204C4×Dic6—31no—
205C4×Dic6C2×D311yescharacteristic
206C3×#107—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×C4×C8—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—61no—
214#835C2×D311yescharacteristic
215#832—31no—
216#832—31no—
217#821—31no—
218#821—31no—
219#818—31no—
220C8×Dic3—31no—
221C8×Dic3—31no—
222#810—31no—
223#810C2×D311yescharacteristic
224#809—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—61no—
229#808—31no—
230#808—31no—
231#808—31no—
232#808—31no—
233#808—61no—
234#807—31no—
235#807C2×D311yescharacteristic
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—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)C22×C412yes—
255C4×C3⋊D3—42no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—24no—
263C3×D12—21no—
264C3×D12C22×C412yes—
265C3×C4×D3—22no—
266C3×C4×D3—24no—
267C3×C4×D3—22no—
268C3×C4×D3—42no—
269C3×C4×D3—42no—
270C3×C4×D3C22×C412yes—
271C3×C4×D3#4112yes—
272C3×Dic6—21no—
273C3×Dic6C22×C412yes—
274#626—24no—
275#624—24no—
276#624—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—31no—
285C4×Q16—91no—
286C4×SD16—91no—
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×Q8—31no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
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—
310C2×#67—61no—
311#239—22no—
312#239—34no—
313#239—62no—
314#239C4×D314yescomplemented
315#235—34no—
316#235—62no—
317C2×D12—21no—
318C2×D12—31no—
319C2×D12—31no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3—21no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—121no—
333C2×C4×D3#6711yescharacteristic
334C2×C4×D3#6711yescharacteristic
335C2×C4×D3C22×D311yescharacteristic
336C2×Dic6C22×D311yescharacteristic
337C3×Q16—34no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—41no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C42—21no—
354C3×C42—21no—
355C3×C42—21no—
356C3×C42—31no—
357C3×C42—31no—
358C3×C42—31no—
359C3×C42—41no—
360C3×C42—61no—
361C3×C42—61no—
362C3×C42—61no—
363C3×C42C22×D311yescharacteristic
364C3×C42C22×D311yescharacteristic
365#217—61no—
366#216C4×D314yescomplemented
367#215—34no—
368#215—34no—
369#215—34no—
370#215—64no—
371#214—34no—
372#213—34no—
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—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—121no—
382C4⋊Dic3—21no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389Dic3⋊C4—21no—
390Dic3⋊C4—61no—
391C4×Dic3—21no—
392C4×Dic3—21no—
393C4×Dic3—21no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
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
411D24—34no—
412D3×C8—34no—
413D3×C8—62no—
414C22×C32C22×D411yescharacteristic
415C2×C3⋊D3—22no—
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—22no—
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—41no—
431C3×Dic3—22no—
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—31no—
441C2×SD16—91no—
442C2×SD16—91no—
443C2×D8—91no—
444C22×C8—91no—
445C22×C8—91no—
446C4×Q8—31no—
447C4×Q8—31no—
448C4×Q8—91no—
449C4×Q8D3211yescharacteristic
450C4×D4—31no—
451C4×D4—31no—
452C4×D4—61no—
453C4×D4—61no—
454C4×D4—91no—
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—31no—
466#107—91no—
467#106—91no—
468#106—91no—
469#103—31no—
470#103—31no—
471#103—91no—
472#103—91no—
473#102—91no—
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—
483C22×D3—21no—
484C22×D3—61no—
485C22×D3—61no—
486C22×D3—121no—
487C22×D3C2×#6711yescharacteristic
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—22no—
491C3×Q8—32no—
492C3×Q8—41no—
493C3×Q8—61no—
494C3×Q8C2×C4×D312yes—
495C3×Q8C2×C4×D312yes—
496C3×D4—32no—
497C3×D4—64no—
498C3×D4—61no—
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—21no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—32no—
509C2×C3×C4—32no—
510C2×C3×C4—31no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—62no—
514C2×C3×C4—64no—
515C2×C3×C4—61no—
516C2×C3×C4—62no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—122no—
520C2×C3×C4—122no—
521C2×C3×C4D3×D411yescharacteristic
522C2×C3×C4D3×D411yescharacteristic
523C2×C3×C4C2×#6711yescharacteristic
524C2×C3×C4C2×#6711yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527#67—64no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—121no—
534C2×Dic3C2×#6711yescharacteristic
535C2×Dic3C2×#6711yescharacteristic
536C2×Dic3C2×#6711yescharacteristic
537D12—24no—
538D12—21no—
539D12—32no—
540D12—32no—
541D12—62no—
542D12—64no—
543D12—61no—
544D12—61no—
545D12—121no—
546D12C2×C4×D312yes—
547C4×D3—22no—
548C4×D3—24no—
549C4×D3—22no—
550C4×D3—42no—
551C4×D3—42no—
552C4×D3—64no—
553C4×D3—64no—
554C4×D3—122no—
555C4×D3—122no—
556C4×D3—122no—
557C4×D3—122no—
558C4×D3—242no—
559C4×D3C2×C4×D312yes—
560C4×D3#23512yes—
561Dic6—21no—
562Dic6C2×C4×D312yes—
563C3×C8—32no—
564C3×C8—61no—
565C3⋊C8—21no—
566C3⋊C8—32no—
567C3⋊C8—32no—
568C3⋊C8—62no—
569C3⋊C8—61no—
570C3⋊C8—61no—
571C3⋊C8—121no—
572C3⋊C8C2×C4×D312yes—
573C2×C32C2×C4×D411yescharacteristic
574C2×C32C2×#13511yescharacteristic
575C2×C32C2×#13511yescharacteristic
576C3⋊D3—42no—
577C3×D3—22no—
578C3×D3—42no—
579#41—34no—
580#41—62no—
581#41—94no—
582#41—182no—
583C2×Q8—31no—
584C2×Q8C2×D3211yescharacteristic
585C2×D4—31no—
586C2×D4—61no—
587C2×D4—91no—
588C2×D4—181no—
589C22×C4—31no—
590C22×C4—31no—
591C22×C4—31no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—181no—
596C22×C4—181no—
597C22×C4—181no—
598Q16—34no—
599SD16—94no—
600SD16—94no—
601D8—94no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—94no—
605C2×C8—91no—
606C2×C8—91no—
607C2×C8—182no—
608C4⋊C4—21no—
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—91no—
614C4⋊C4—181no—
615C4⋊C4C2×D3211yescharacteristic
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—181no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C42—21no—
623C42—31no—
624C42—31no—
625C42—31no—
626C42—61no—
627C42—61no—
628C42—61no—
629C42—181no—
630C42—181no—
631C42C2×D3211yescharacteristic
632C22×C3—21no—
633C22×C3—32no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—62no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3C2×D3×D411yescharacteristic
640C22×C3C22×#6711yescharacteristic
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—22no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—62no—
647C2×D3—62no—
648C2×D3—122no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—241no—
654C2×D3—241no—
655C2×D3C4×#6712yes—
656C3×C4—21no—
657C3×C4—22no—
658C3×C4—22no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—22no—
663C3×C4—32no—
664C3×C4—32no—
665C3×C4—41no—
666C3×C4—42no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—61no—
670C3×C4—62no—
671C3×C4—81no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4#91912yescomplemented
675C3×C4#95012yescomplemented
676C3×C4C22×C4×D311yescharacteristic
677C3×C4C22×C4×D311yescharacteristic
678C3×C4C2×#23511yescharacteristic
679C3×C4D3×#4111yescharacteristic
680Dic3—22no—
681Dic3—21no—
682Dic3—41no—
683Dic3—41no—
684Dic3—121no—
685Dic3—121no—
686Dic3—241no—
687Dic3C4×#6712yes—
688Dic3#95012yescomplemented
689C32C4×#13511yescharacteristic, complemented, Sylow
690C23—31no—
691C23—61no—
692C23—181no—
693Q8—21no—
694Q8—32no—
695Q8—61no—
696Q8C4×D3212yes—
697D4—32no—
698D4—64no—
699D4—61no—
700D4—92no—
701D4—184no—
702D4—181no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—31no—
706C2×C4—31no—
707C2×C4—32no—
708C2×C4—32no—
709C2×C4—31no—
710C2×C4—62no—
711C2×C4—64no—
712C2×C4—61no—
713C2×C4—62no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—122no—
717C2×C4—122no—
718C2×C4—184no—
719C2×C4—181no—
720C2×C4—362no—
721C2×C4—362no—
722C2×C4D3×#6711yescharacteristic
723C2×C4D3×#6711yescharacteristic
724C2×C4C22×D3211yescharacteristic
725C8—32no—
726C8—61no—
727C8—92no—
728C8—181no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—62no—
733C2×C3—122no—
734C2×C3C4×D3×D411yescharacteristic
735C2×C3C2×#91911yescharacteristic
736C2×C3D3×#13511yescharacteristic
737C2×C3C2×C4×#6711yescharacteristic
738C2×C3C2×#95011yescharacteristic
739C2×C3C2×#95011yescharacteristic
740D3—22no—
741D3—42no—
742D3—122no—
743D3—122no—
744D3—242no—
745C22—32no—
746C22—61no—
747C22—61no—
748C22—62no—
749C22—121no—
750C22—121no—
751C22—182no—
752C22—361no—
753C22—361no—
754C22C2×D3×#6711yescharacteristic
755C4—21no—
756C4—22no—
757C4—32no—
758C4—32no—
759C4—41no—
760C4—61no—
761C4—62no—
762C4—121no—
763C4—121no—
764C4—361no—
765C4#6394912yesdirect product factor
766C4C2×C4×D3211yescharacteristic
767C4D3×#23511yescharacteristic
768C3—21no—
769C3C4×#91911yescharacteristic, complemented
770C3C4×#95011yescharacteristic, complemented
771C2—62no—
772C2—122no—
773C2—362no—
774C2C4×D3×#6711yescharacteristic
775C2C2×#6394911yescharacteristic
776C2D3×#95011yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×#63949C2
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×#3799C2semidirect
4. C4×#3755C2semidirect
5. C3×C4×#216C2semidirect
6. Dic3×#216C2semidirect
7. #10591556C2semidirect
8. #10591536C2semidirect
9. #10590610C2semidirect
10. #10590571C2semidirect
11. #10590475C2semidirect
12. #10590456C2semidirect
13. C4×#3715C2semidirect
14. C4×#3714C2semidirect
15. C4×D3×C3⋊C8C2semidirect
34. #63949C4direct (N × H)
66. C4×#239D3semidirect
72. C4×#216D3semidirect
97. C3×#239C2×C4semidirect
111. #3799C2×C4semidirect
116. #3755C2×C4semidirect
121. C3×#216C2×C4semidirect
142. #3715C2×C4semidirect
143. #3714C2×C4semidirect
145. D3×C3⋊C8C2×C4semidirect
314. #239C4×D3semidirect
366. #216C4×D3semidirect
427. C32×C4#135semidirect
436. C3×Dic3#135semidirect
674. C3×C4#919semidirect
675. C3×C4#950semidirect
688. Dic3#950semidirect
689. C32C4×#135semidirect
765. C4#63949direct (N × H)
769. C3C4×#919semidirect
770. 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×#639492
C4×#37992
C4×#37552
C3×C4×#2162
Dic3×#2162
#105915562
#105915362
#105906102
#105905712
#105904752
#105904562
C4×#37152
C4×#37142
C4×D3×C3⋊C82
C4×#9503
C4×#9193