Finite Group Databasebeta

← C4×#63808 #11859995

Subgroups — C4×#63808 #11859995

Order 1152.

1067 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63808C211yesmaximal, characteristic
2C4×#3799C212yesmaximal, complemented
3C4×#3745C211yesmaximal, characteristic, complemented
4C3×C4×Dic12C211yesmaximal, characteristic, complemented
5C3×C4×D3×C8C211yesmaximal, characteristic, complemented
6Dic3×Dic12C211yesmaximal, characteristic, complemented
7#10590792C212yesmaximal, complemented
8#10590763C211yesmaximal, characteristic, complemented
9#10590707C211yesmaximal, characteristic, complemented
10#10590690C212yesmaximal, complemented
11C4×#3717C212yesmaximal, complemented
12C4×#919—31nomaximal
13C4×#904—31nomaximal
14C2×#3799C2212yes—
15C2×#3745C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C2212yes—
17C2×C3×Dic12C2211yescharacteristic
18C2×C3×D3×C8C2211yescharacteristic
19C2×C3×D3×C8C2211yescharacteristic
20C3×C42×D3C2211yescharacteristic
21C3×C4×Dic6C2212yes—
22#63904—22no—
23C4×#626—22no—
24#63894C2212yes—
25C4×#624—22no—
26Dic3×Dic6C2212yes—
27#63841C2212yes—
28#63836—22no—
29C2×#3717C2212yes—
30#63808C418yesdirect product factor
31C32×C4×C8C2211yescharacteristic
32#63648C2212yes—
33#63645C2211yescharacteristic
34C3×#818C2211yescharacteristic
35C3×#816C2212yes—
36C3×C8×Dic3C2211yescharacteristic
37C3×C8×Dic3C2211yescharacteristic
38C3×C4×C3⋊C8C2211yescharacteristic
39#63573C2212yes—
40#63566C2212yes—
41#63564C2212yes—
42C2×#919—31no—
43C2×#904—31no—
44C4×#239—32no—
45C4×#235—32no—
46C3×C4×Q16—31no—
47C2×C3×C4×C8—31no—
48Dic3×Q16—31no—
49#5113—32no—
50#5106—31no—
51C4×#215—32no—
52#4880—31no—
53#4872—31no—
54#4804—32no—
55#4788—32no—
56C4×Dic12—31no—
57C4×Dic12D311yescharacteristic, complemented
58C4×D24—31no—
59C4×D24—31no—
60C4×D24—31no—
61C4×D24—61no—
62C4×#204—32no—
63C4×#204—32no—
64C4×D3×C8D311yescharacteristic, complemented
65C2×C4⋊(C3⋊D3)C2312yes—
66C2×C4×C3⋊D3—22no—
67C2×C3×C4×D3D411yescharacteristic
68C2×C3×C4×D3D411yescharacteristic
69C2×C3×C4×D3C2311yescharacteristic
70C2×C3×Dic6C2312yes—
71C2×#626—22no—
72C2×#624—22no—
73C2×#624—22no—
74#3799—24no—
75#3799C2×C418yescomplemented
76C2×C32×C8C2311yescharacteristic
77C2×C32×C8C2311yescharacteristic
78C32×C42C2311yescharacteristic
79#3752—22no—
80C4⋊(C3⋊Dic3)C2312yes—
81#3745C2×C414yescomplemented
82C3×C4⋊Dic3C2312yes—
83C3×Dic3⋊C4—22no—
84C3×C4×Dic3—22no—
85C3×C4×Dic3D411yescharacteristic
86C3×C4×Dic3D411yescharacteristic
87C3×C4×Dic3C2311yescharacteristic
88C2×C3×C3⋊C8C2311yescharacteristic
89C2×C3×C3⋊C8C2311yescharacteristic
90C3×Dic12C2×C414yescomplemented
91C3×D3×C8—22no—
92C3×D3×C8C2×C414yescomplemented
93Dic3⋊Dic3—22no—
94#3722—22no—
95(C2×D3)⋊Dic3—22no—
96Dic32—22no—
97Dic32—22no—
98#3717C2×C418yescomplemented
99C4×#135—91noSylow
100C2×#239—32no—
101C2×#235—32no—
102C2×C3×Q16—31no—
103C22×C3×C8—31no—
104C22×C3×C8—31no—
105C3×C4×Q8—32no—
106C2×C3×C42—31no—
107Q8×Dic3—32no—
108C2×#215—32no—
109C4×#67—62no—
110C4×#67—62no—
111#926—32no—
112#919—38no—
113C2×Dic12C2×D311yescharacteristic
114#904—38no—
115C2×D24—31no—
116C2×D24—31no—
117C2×D24—61no—
118C2×#204—32no—
119C2×D3×C8C2×D311yescharacteristic
120C2×D3×C8C2×D311yescharacteristic
121#893—32no—
122#893—62no—
123#892—32no—
124#892—62no—
125C4×D12—32no—
126C4×D12—32no—
127C4×D12—32no—
128C4×D12—62no—
129C4×D12—62no—
130#872—62no—
131C42×D3—62no—
132C42×D3—62no—
133C42×D3C2×D311yescharacteristic
134C4×Dic6—32no—
135C4×Dic6C2×D312yes—
136C3×#107—31no—
137C3×#103—32no—
138C3×C4×C8—21no—
139C3×C4×C8—31no—
140C3×C4×C8—31no—
141C3×C4×C8—31no—
142C3×C4×C8C2×D311yescharacteristic
143C3×C4×C8C2×D311yescharacteristic
144#835—32no—
145#821—32no—
146#821—32no—
147#821—32no—
148#821—62no—
149#818—31no—
150#818—31no—
151#818—61no—
152#818C2×D311yescharacteristic
153#817—32no—
154#816—32no—
155#816C2×D312yes—
156C8×Dic3C2×D311yescharacteristic
157C8×Dic3C2×D311yescharacteristic
158#809—32no—
159#808—32no—
160C4×C3⋊C8C2×D311yescharacteristic
161C22×C3⋊D3—22no—
162C22×C3×D3C2×D411yescharacteristic
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2411yescharacteristic
166C2×C3⋊Dic3—22no—
167C4⋊(C3⋊D3)—22no—
168C4⋊(C3⋊D3)C22×C414yes—
169C4×C3⋊D3—44no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3C2×D411yescharacteristic
173C2×C3×Dic3C2×D411yescharacteristic
174C2×C3×Dic3C2×D411yescharacteristic
175C3×C4×D3—22no—
176C3×C4×D3—22no—
177C3×C4×D3C22×C412yes—
178C3×C4×D3#4112yes—
179C3×Dic6—22no—
180C3×Dic6C22×C414yes—
181#626—28no—
182#624—28no—
183#624—44no—
184C32×C8—21no—
185C32×C8C22×C412yes—
186C3×C3⋊C8—21no—
187C3×C3⋊C8C22×C412yes—
188C2×#135—91no—
189C4×#41—92no—
190C4×Q16—31no—
191C4×Q16—91no—
192C4×SD16—92no—
193C4×SD16—92no—
194C4×D8—91no—
195C4×D8—91no—
196#427—91no—
197#416—92no—
198C2×C4×C8—31no—
199C2×C3×Q8—32no—
200C22×C3×C4—31no—
201C22×C3×C4—31no—
202C22×C3×C4—31no—
203C2×#67—62no—
204#239—38no—
205#239—64no—
206#235—38no—
207#235—64no—
208C2×D12—32no—
209C2×D12—32no—
210C2×D12—62no—
211C2×D12—62no—
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×C4×D3—62no—
217C2×C4×D3—62no—
218C2×C4×D3—122no—
219C2×C4×D3D1211yescharacteristic
220C2×C4×D3D1211yescharacteristic
221C2×C4×D3C22×D311yescharacteristic
222C2×Dic6C22×D312yes—
223C3×Q16—34no—
224C2×C3×C8—21no—
225C2×C3×C8—21no—
226C2×C3×C8—31no—
227C2×C3×C8—34no—
228C2×C3×C8—31no—
229C2×C3×C8—62no—
230C2×C3×C8C22×D311yescharacteristic
231C2×C3×C8C22×D311yescharacteristic
232C2×C3×C8C22×D311yescharacteristic
233C2×C3×C8C22×D311yescharacteristic
234C3×C4⋊C4—32no—
235C3×C4⋊C4—62no—
236C3×C42—21no—
237C3×C42—31no—
238C3×C42—31no—
239C3×C42—31no—
240C3×C42—62no—
241C3×C42C22×D311yescharacteristic
242C3×C42C22×D311yescharacteristic
243#217—62no—
244#215—38no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—62no—
249(C2×D3)⋊C4—62no—
250(C2×D3)⋊C4—122no—
251C4⋊Dic3—32no—
252C4⋊Dic3—32no—
253C4⋊Dic3—62no—
254C4⋊Dic3—62no—
255C4⋊Dic3C22×D312yes—
256Dic3⋊C4—22no—
257Dic3⋊C4—62no—
258C4×Dic3—22no—
259C4×Dic3—62no—
260C4×Dic3—62no—
261C4×Dic3—62no—
262C4×Dic3—62no—
263C4×Dic3D1211yescharacteristic
264C4×Dic3D1211yescharacteristic
265C4×Dic3C22×D311yescharacteristic
266C2×C3⋊C8C22×D311yescharacteristic
267C2×C3⋊C8C22×D311yescharacteristic
268Dic12C4×D314yescomplemented
269D24—34no—
270D24—34no—
271D24—64no—
272#204—38no—
273D3×C8—22no—
274D3×C8C4×D314yescomplemented
275C22×C32C22×D411yescharacteristic
276C2×C3⋊D3—24no—
277C2×C3⋊D3—42no—
278C2×C3⋊D3—42no—
279C2×C3×D3—21no—
280C2×C3×D3—21no—
281C2×C3×D3C4×D412yes—
282C32×C4—21no—
283C32×C4#13512yescomplemented
284C32×C4C23×C411yescharacteristic
285C32×C4C2×#4111yescharacteristic
286C3⋊Dic3—42no—
287C3×Dic3—24no—
288C3×Dic3—21no—
289C3×Dic3—42no—
290C3×Dic3C4×D412yes—
291C3×Dic3#13512yescomplemented
292C2×#41—92no—
293#135—98no—
294C2×Q16—31no—
295C2×SD16—92no—
296C2×D8—91no—
297C22×C8—31no—
298C22×C8—31no—
299C4×Q8—32no—
300C4×Q8—92no—
301C4×D4—92no—
302C4×D4—92no—
303C4×D4—182no—
304C4×D4—182no—
305#117—92no—
306#117—182no—
307C2×C42—31no—
308C2×C42—182no—
309#107—31no—
310#107—91no—
311#106—92no—
312#103—32no—
313#103—92no—
314#102—92no—
315#102—92no—
316C4×C8—31no—
317C4×C8—31no—
318C4×C8—31no—
319C4×C8D3211yescharacteristic
320C23×C3—31no—
321C22×D3—62no—
322C22×D3—62no—
323C22×D3—122no—
324C22×D3C2×D1211yescharacteristic
325C3×Q8—34no—
326C3×Q8—62no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—31no—
331C2×C3×C4—31no—
332C2×C3×C4—32no—
333C2×C3×C4—32no—
334C2×C3×C4—31no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4C2×D1211yescharacteristic
340C2×C3×C4C2×D1211yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4C23×D311yescharacteristic
344C2×C3×C4C23×D311yescharacteristic
345#67—68no—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—122no—
351C2×Dic3C2×D1211yescharacteristic
352C2×Dic3C2×D1211yescharacteristic
353C2×Dic3C2×D1211yescharacteristic
354D12—34no—
355D12—34no—
356D12—64no—
357D12—68no—
358D12—62no—
359D12—62no—
360D12—122no—
361C4×D3—22no—
362C4×D3—22no—
363C4×D3—68no—
364C4×D3—68no—
365C4×D3—124no—
366C4×D3—124no—
367C4×D3—124no—
368C4×D3—124no—
369C4×D3—244no—
370C4×D3C2×C4×D312yes—
371C4×D3#23512yes—
372Dic6—22no—
373Dic6C2×C4×D314yes—
374C3×C8—21no—
375C3×C8—21no—
376C3×C8—22no—
377C3×C8—32no—
378C3×C8—41no—
379C3×C8—61no—
380C3×C8C2×C4×D312yes—
381C3×C8C2×C4×D312yes—
382C3⋊C8—21no—
383C3⋊C8C2×C4×D312yes—
384C2×C32C2×C4×D411yescharacteristic
385C2×C32C2×#13511yescharacteristic
386C2×C32C2×#13511yescharacteristic
387C3⋊D3—44no—
388C3×D3—22no—
389#41—98no—
390#41—184no—
391C2×Q8—32no—
392C2×D4—92no—
393C2×D4—182no—
394C22×C4—31no—
395C22×C4—31no—
396C22×C4—31no—
397C22×C4—182no—
398C22×C4—182no—
399C22×C4—182no—
400Q16—34no—
401SD16—98no—
402D8—94no—
403C2×C8—31no—
404C2×C8—34no—
405C2×C8—31no—
406C2×C8—62no—
407C2×C8C2×D3211yescharacteristic
408C2×C8C2×D3211yescharacteristic
409C4⋊C4—32no—
410C4⋊C4—62no—
411C4⋊C4—92no—
412C4⋊C4—182no—
413C22⋊C4—182no—
414C22⋊C4—182no—
415C22⋊C4—182no—
416C42—31no—
417C42—31no—
418C42—31no—
419C42—62no—
420C42—182no—
421C42—182no—
422C42C2×D3211yescharacteristic
423C22×C3—21no—
424C22×C3—32no—
425C22×C3—61no—
426C22×C3—61no—
427C22×C3C22×D1211yescharacteristic
428C22×C3C2×D3×D411yescharacteristic
429C2×D3—21no—
430C2×D3—21no—
431C2×D3—64no—
432C2×D3—64no—
433C2×D3—124no—
434C2×D3—122no—
435C2×D3—122no—
436C2×D3—122no—
437C2×D3—122no—
438C2×D3—242no—
439C2×D3—242no—
440C2×D3C4×D1212yes—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—22no—
446C3×C4—32no—
447C3×C4—32no—
448C3×C4—41no—
449C3×C4—64no—
450C3×C4—61no—
451C3×C4—122no—
452C3×C4#90412yescomplemented
453C3×C4#91912yescomplemented
454C3×C4C22×C4×D311yescharacteristic
455C3×C4C22×C4×D311yescharacteristic
456C3×C4C2×#23511yescharacteristic
457C3×C4D3×#4111yescharacteristic
458Dic3—21no—
459Dic3—24no—
460Dic3—42no—
461Dic3—122no—
462Dic3—122no—
463Dic3—242no—
464Dic3C4×D1212yes—
465Dic3#90412yescomplemented
466C32C4×#13511yescharacteristic, complemented, Sylow
467C23—31no—
468C23—182no—
469Q8—34no—
470Q8—62no—
471D4—94no—
472D4—188no—
473D4—182no—
474C2×C4—31no—
475C2×C4—31no—
476C2×C4—32no—
477C2×C4—32no—
478C2×C4—31no—
479C2×C4—62no—
480C2×C4—62no—
481C2×C4—62no—
482C2×C4—62no—
483C2×C4—188no—
484C2×C4—182no—
485C2×C4—364no—
486C2×C4—364no—
487C2×C4D3×D1211yescharacteristic
488C2×C4D3×D1211yescharacteristic
489C2×C4C22×D3211yescharacteristic
490C8—21no—
491C8—32no—
492C8—61no—
493C8C4×D3212yes—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—62no—
498C2×C3C2×C4×D1211yescharacteristic
499C2×C3C4×D3×D411yescharacteristic
500C2×C3C2×#90411yescharacteristic
501C2×C3C2×#90411yescharacteristic
502C2×C3C2×#91911yescharacteristic
503C2×C3D3×#13511yescharacteristic
504D3—22no—
505D3—124no—
506D3—124no—
507D3—244no—
508C22—32no—
509C22—61no—
510C22—61no—
511C22—184no—
512C22—362no—
513C22—362no—
514C22C2×D3×D1211yescharacteristic
515C4—21no—
516C4—32no—
517C4—32no—
518C4—61no—
519C4—64no—
520C4—122no—
521C4—362no—
522C4#6380812yesdirect product factor
523C4C2×C4×D3211yescharacteristic
524C4D3×#23511yescharacteristic
525C3—21no—
526C3C4×#90411yescharacteristic, complemented
527C3C4×#91911yescharacteristic, complemented
528C2—62no—
529C2—364no—
530C2C4×D3×D1211yescharacteristic
531C2D3×#90411yescharacteristic
532C2C2×#6380811yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×#63808C2
cosocleC2×C32×C4C24
hypercenterC4×C8D32
hypocenterC32C4×#135
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. C4×#3799C2semidirect
3. C4×#3745C2semidirect
4. C3×C4×Dic12C2semidirect
5. C3×C4×D3×C8C2semidirect
6. Dic3×Dic12C2semidirect
7. #10590792C2semidirect
8. #10590763C2semidirect
9. #10590707C2semidirect
10. #10590690C2semidirect
11. C4×#3717C2semidirect
30. #63808C4direct (N × H)
57. C4×Dic12D3semidirect
64. C4×D3×C8D3semidirect
75. #3799C2×C4semidirect
81. #3745C2×C4semidirect
90. C3×Dic12C2×C4semidirect
92. C3×D3×C8C2×C4semidirect
98. #3717C2×C4semidirect
268. Dic12C4×D3semidirect
274. D3×C8C4×D3semidirect
283. C32×C4#135semidirect
291. C3×Dic3#135semidirect
452. C3×C4#904semidirect
453. C3×C4#919semidirect
465. Dic3#904semidirect
466. C32C4×#135semidirect
522. C4#63808direct (N × H)
526. C3C4×#904semidirect
527. C3C4×#919semidirect

Maximal subgroups

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

subgroupindex
C2×#638082
C4×#37992
C4×#37452
C3×C4×Dic122
C3×C4×D3×C82
Dic3×Dic122
#105907922
#105907632
#105907072
#105906902
C4×#37172
C4×#9193
C4×#9043