Finite Group Databasebeta

← C4×#63810 #11859996

Subgroups — C4×#63810 #11859996

Order 1152.

1081 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63810C211yesmaximal, characteristic
2C4×#3796C212yesmaximal, complemented
3C4×C8×C3⋊D3C211yesmaximal, characteristic, complemented
4C3×C4×Dic12C211yesmaximal, characteristic, complemented
5C3×C4×D24C211yesmaximal, characteristic, complemented
6#10590956C212yesmaximal, complemented
7#10590818C211yesmaximal, characteristic, complemented
8#10590777C211yesmaximal, characteristic, complemented
9#10590742C212yesmaximal, complemented
10#10590714C211yesmaximal, characteristic, complemented
11C4×#3715C212yesmaximal, complemented
12C4×#919—31nomaximal
13C4×#912—31nomaximal
14C2×#3796C2212yes—
15C2×C8×C3⋊D3C2211yescharacteristic
16C2×C8×C3⋊D3C2211yescharacteristic
17C42×C3⋊D3C2211yescharacteristic
18C2×C3×Dic12C2211yescharacteristic
19C2×C3×D24C2211yescharacteristic
20C3×C4×D12C2212yes—
21C3×C4×Dic6C2212yes—
22C4×#626—22no—
23#63898C2212yes—
24#63881—22no—
25#63878—22no—
26C4×D3×Dic3—22no—
27#63849C2212yes—
28#63843C2212yes—
29C2×#3715C2212yes—
30#63810C418yesdirect product factor
31C32×C4×C8C2211yescharacteristic
32C8×C3⋊Dic3C2211yescharacteristic
33C8×C3⋊Dic3C2211yescharacteristic
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#821C2212yes—
36C3×#818C2211yescharacteristic
37C3×#818C2211yescharacteristic
38C3×#816C2212yes—
39#63574C2212yes—
40#63565C2212yes—
41#63562C2212yes—
42C2×#919—31no—
43C2×#912—31no—
44C4×#239—32no—
45C4×#237—32no—
46C3×C4×Q16—31no—
47C3×C4×D8—31no—
48Dic3×Q16—31no—
49Dic3×D8—31no—
50C4×#215—32no—
51C4×#214—32no—
52#4880—31no—
53#4880—31no—
54#4873—31no—
55#4872—31no—
56#4804—32no—
57#4788—32no—
58#4772—32no—
59#4758—32no—
60C4×Dic12D311yescharacteristic, complemented
61C4×D24D311yescharacteristic, complemented
62C4×D3×C8—31no—
63C4×D3×C8—31no—
64C4×D3×C8—61no—
65C2×C4×C3⋊D3D411yescharacteristic
66C2×C4×C3⋊D3D411yescharacteristic
67C2×C4×C3⋊D3C2311yescharacteristic
68C2×C3×D12C2312yes—
69C2×C3×C4×D3—22no—
70C2×C3×Dic6C2312yes—
71C2×#626—22no—
72C2×D3×Dic3—22no—
73C2×D3×Dic3—22no—
74#3796—24no—
75#3796C2×C418yescomplemented
76C2×C32×C8C2311yescharacteristic
77C2×C32×C8C2311yescharacteristic
78C32×C42C2311yescharacteristic
79C4×C3⋊Dic3D411yescharacteristic
80C4×C3⋊Dic3D411yescharacteristic
81C4×C3⋊Dic3C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C8×C3⋊D3—22no—
85C8×C3⋊D3C2×C414yescomplemented
86C3×(C2×D3)⋊C4—22no—
87C3×C4⋊Dic3C2312yes—
88C3×C4⋊Dic3C2312yes—
89C3×Dic3⋊C4—22no—
90C3×C4×Dic3—22no—
91C3×Dic12C2×C414yescomplemented
92C3×D24C2×C414yescomplemented
93Dic3⋊Dic3—22no—
94#3722—22no—
95(C2×D3)⋊Dic3—22no—
96Dic32—22no—
97Dic32—22no—
98#3715C2×C418yescomplemented
99C4×#135—91noSylow
100C2×#239—32no—
101C2×#237—32no—
102C2×C3×Q16—31no—
103C2×C3×D8—31no—
104C3×C4×Q8—32no—
105C3×C4×D4—32no—
106Q8×Dic3—32no—
107C2×#215—32no—
108D4×Dic3—32no—
109C2×#214—32no—
110C4×#67—62no—
111C2×C4×Dic3—62no—
112#919—38no—
113#912—38no—
114C2×Dic12C2×D311yescharacteristic
115C2×D24C2×D311yescharacteristic
116C2×D3×C8—31no—
117C2×D3×C8—31no—
118C2×D3×C8—31no—
119C2×D3×C8—31no—
120C2×D3×C8—61no—
121C2×D3×C8—61no—
122#893—32no—
123#893—62no—
124#892—32no—
125#892—32no—
126#892—62no—
127#887—32no—
128#67⋊C4—62no—
129#877—62no—
130C4×D12—62no—
131C4×D12C2×D312yes—
132C42×D3—31no—
133C42×D3—31no—
134C42×D3—61no—
135C42×D3—62no—
136C4×Dic6C2×D312yes—
137C3×#107—31no—
138C3×#107—31no—
139C3×#103—32no—
140C3×#102—32no—
141C3×C4×C8—21no—
142C3×C4×C8C2×D311yescharacteristic
143C3×C4×C8C2×D311yescharacteristic
144#835—32no—
145#832—32no—
146#821C2×D312yes—
147#818C2×D311yescharacteristic
148#818C2×D311yescharacteristic
149#816C2×D312yes—
150C8×Dic3—31no—
151C8×Dic3—31no—
152C8×Dic3—31no—
153C8×Dic3—31no—
154C8×Dic3—61no—
155C8×Dic3—61no—
156#810—32no—
157#809—32no—
158#808—32no—
159#808—32no—
160C4×C3⋊C8—31no—
161C4×C3⋊C8—31no—
162C4×C3⋊C8—61no—
163C22×C3⋊D3C2×D411yescharacteristic
164C22×C3×D3—22no—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2411yescharacteristic
168C2×C3⋊Dic3C2×D411yescharacteristic
169C2×C3⋊Dic3C2×D411yescharacteristic
170C2×C3⋊Dic3C2×D411yescharacteristic
171C4×C3⋊D3—22no—
172C4×C3⋊D3—22no—
173C4×C3⋊D3C22×C412yes—
174C4×C3⋊D3#4112yes—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C3×D12—22no—
179C3×D12C22×C414yes—
180C3×C4×D3—44no—
181C3×Dic6—22no—
182C3×Dic6C22×C414yes—
183#626—28no—
184D3×Dic3—28no—
185D3×Dic3—44no—
186C32×C8—21no—
187C32×C8C22×C412yes—
188C3⋊(C3⋊C8)—21no—
189C3⋊(C3⋊C8)C22×C412yes—
190C2×#135—91no—
191C4×#41—92no—
192C4×Q16—31no—
193C4×Q16—91no—
194C4×SD16—92no—
195C4×SD16—92no—
196C4×D8—31no—
197C4×D8—91no—
198#427—91no—
199#416—92no—
200C2×C4×C8—91no—
201C2×C3×Q8—32no—
202C2×C3×D4—32no—
203C22×C3×C4—62no—
204C2×#67—62no—
205C22×Dic3—62no—
206C22×Dic3—62no—
207#239—38no—
208#239—64no—
209#237—38no—
210#237—64no—
211C2×D12—62no—
212C2×D12C22×D312yes—
213C2×C4×D3—22no—
214C2×C4×D3—31no—
215C2×C4×D3—31no—
216C2×C4×D3—31no—
217C2×C4×D3—31no—
218C2×C4×D3—31no—
219C2×C4×D3—31no—
220C2×C4×D3—61no—
221C2×C4×D3—61no—
222C2×C4×D3—61no—
223C2×C4×D3—62no—
224C2×C4×D3—62no—
225C2×Dic6C22×D312yes—
226C3×Q16—34no—
227C3×D8—34no—
228C2×C3×C8—21no—
229C2×C3×C8—21no—
230C2×C3×C8C22×D311yescharacteristic
231C2×C3×C8C22×D311yescharacteristic
232C2×C3×C8C22×D311yescharacteristic
233C2×C3×C8C22×D311yescharacteristic
234C3×C4⋊C4—32no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—62no—
237C3×C22⋊C4—62no—
238C3×C42—21no—
239C3×C42—62no—
240C3×C42C22×D311yescharacteristic
241C3×C42C22×D311yescharacteristic
242#217—62no—
243#215—38no—
244#214—38no—
245(C2×D3)⋊C4—22no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—62no—
249C4⋊Dic3—62no—
250C4⋊Dic3C22×D312yes—
251C4⋊Dic3C22×D312yes—
252Dic3⋊C4—22no—
253Dic3⋊C4—62no—
254C4×Dic3—22no—
255C4×Dic3—31no—
256C4×Dic3—31no—
257C4×Dic3—31no—
258C4×Dic3—31no—
259C4×Dic3—31no—
260C4×Dic3—31no—
261C4×Dic3—61no—
262C4×Dic3—61no—
263C4×Dic3—61no—
264C4×Dic3—62no—
265C4×Dic3—62no—
266C4×Dic3—62no—
267C4×Dic3—62no—
268C2×C3⋊C8—31no—
269C2×C3⋊C8—31no—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—61no—
273C2×C3⋊C8—61no—
274Dic12C4×D314yescomplemented
275D24C4×D314yescomplemented
276D3×C8—34no—
277D3×C8—34no—
278D3×C8—64no—
279D3×C8—62no—
280D3×C8—62no—
281D3×C8—64no—
282C22×C32C22×D411yescharacteristic
283C2×C3⋊D3—21no—
284C2×C3⋊D3—21no—
285C2×C3⋊D3C4×D412yes—
286C2×C3×D3—24no—
287C2×C3×D3—42no—
288C2×C3×D3—42no—
289C32×C4—21no—
290C32×C4#13512yescomplemented
291C32×C4C23×C411yescharacteristic
292C32×C4C2×#4111yescharacteristic
293C3⋊Dic3—21no—
294C3⋊Dic3C4×D412yes—
295C3⋊Dic3#13512yescomplemented
296C3×Dic3—24no—
297C3×Dic3—42no—
298C3×Dic3—42no—
299C2×#41—92no—
300#135—98no—
301C2×Q16—31no—
302C2×SD16—92no—
303C2×D8—31no—
304C22×C8—91no—
305C22×C8—91no—
306C4×Q8—32no—
307C4×Q8—92no—
308C4×D4—32no—
309C4×D4—92no—
310C4×D4—182no—
311C4×D4—182no—
312#117—92no—
313#117—182no—
314C2×C42—91no—
315C2×C42—182no—
316#107—31no—
317#107—31no—
318#106—92no—
319#103—32no—
320#103—92no—
321#102—32no—
322#102—92no—
323C4×C8—91no—
324C4×C8—91no—
325C4×C8—91no—
326C4×C8D3211yescharacteristic
327C23×C3—62no—
328C22×D3—22no—
329C22×D3—31no—
330C22×D3—31no—
331C22×D3—61no—
332C3×Q8—34no—
333C3×Q8—62no—
334C3×D4—34no—
335C3×D4—62no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—62no—
340C2×C3×C4—62no—
341C2×C3×C4—62no—
342C2×C3×C4—124no—
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349#67—68no—
350C2×Dic3—22no—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—31no—
354C2×Dic3—31no—
355C2×Dic3—31no—
356C2×Dic3—31no—
357C2×Dic3—31no—
358C2×Dic3—31no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—68no—
363C2×Dic3—124no—
364D12—22no—
365D12—68no—
366D12C2×C4×D314yes—
367C4×D3—32no—
368C4×D3—32no—
369C4×D3—32no—
370C4×D3—32no—
371C4×D3—44no—
372C4×D3—62no—
373C4×D3—62no—
374C4×D3—62no—
375C4×D3—62no—
376C4×D3—68no—
377C4×D3—64no—
378C4×D3—64no—
379C4×D3—62no—
380C4×D3—62no—
381C4×D3—124no—
382Dic6—22no—
383Dic6C2×C4×D314yes—
384C3×C8—22no—
385C3×C8—21no—
386C3×C8—21no—
387C3×C8—22no—
388C3×C8C2×C4×D312yes—
389C3×C8C2×C4×D312yes—
390C3⋊C8—32no—
391C3⋊C8—32no—
392C3⋊C8—62no—
393C3⋊C8—62no—
394C3⋊C8—61no—
395C3⋊C8—61no—
396C2×C32C2×C4×D411yescharacteristic
397C2×C32C2×#13511yescharacteristic
398C2×C32C2×#13511yescharacteristic
399C3⋊D3—22no—
400C3×D3—44no—
401#41—98no—
402#41—184no—
403C2×Q8—32no—
404C2×D4—32no—
405C2×D4—182no—
406C22×C4—62no—
407C22×C4—91no—
408C22×C4—91no—
409C22×C4—91no—
410C22×C4—182no—
411C22×C4—182no—
412Q16—34no—
413SD16—98no—
414D8—34no—
415C2×C8—91no—
416C2×C8—94no—
417C2×C8—91no—
418C2×C8—182no—
419C2×C8C2×D3211yescharacteristic
420C2×C8C2×D3211yescharacteristic
421C4⋊C4—32no—
422C4⋊C4—32no—
423C4⋊C4—62no—
424C4⋊C4—182no—
425C22⋊C4—62no—
426C22⋊C4—182no—
427C22⋊C4—182no—
428C42—62no—
429C42—91no—
430C42—91no—
431C42—91no—
432C42—182no—
433C42—182no—
434C42C2×D3211yescharacteristic
435C22×C3—21no—
436C22×C3—64no—
437C22×C3—122no—
438C22×C3—122no—
439C22×C3C2×D3×D411yescharacteristic
440C22×C3C2×D3×D411yescharacteristic
441C2×D3—24no—
442C2×D3—32no—
443C2×D3—32no—
444C2×D3—42no—
445C2×D3—42no—
446C2×D3—62no—
447C2×D3—62no—
448C2×D3—62no—
449C2×D3—61no—
450C2×D3—61no—
451C2×D3—61no—
452C2×D3—61no—
453C3×C4—22no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—22no—
459C3×C4—64no—
460C3×C4—122no—
461C3×C4—122no—
462C3×C4#91212yescomplemented
463C3×C4#91912yescomplemented
464C3×C4C22×C4×D311yescharacteristic
465C3×C4C22×C4×D311yescharacteristic
466C3×C4D3×#4111yescharacteristic
467C3×C4D3×#4111yescharacteristic
468Dic3—24no—
469Dic3—32no—
470Dic3—32no—
471Dic3—32no—
472Dic3—32no—
473Dic3—42no—
474Dic3—42no—
475Dic3—62no—
476Dic3—62no—
477Dic3—62no—
478Dic3—61no—
479Dic3—61no—
480C32C4×#13511yescharacteristic, complemented, Sylow
481C23—62no—
482C23—91no—
483Q8—34no—
484Q8—62no—
485D4—34no—
486D4—62no—
487D4—188no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—91no—
492C2×C4—91no—
493C2×C4—92no—
494C2×C4—92no—
495C2×C4—91no—
496C2×C4—124no—
497C2×C4—182no—
498C2×C4—188no—
499C2×C4—182no—
500C2×C4—364no—
501C2×C4#380211yescharacteristic
502C2×C4#380211yescharacteristic
503C2×C4C22×D3211yescharacteristic
504C8—21no—
505C8—92no—
506C8—181no—
507C8C4×D3212yes—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—124no—
512C2×C3C4×D3×D411yescharacteristic
513C2×C3C4×D3×D411yescharacteristic
514C2×C3C2×#91211yescharacteristic
515C2×C3C2×#91911yescharacteristic
516C2×C3D3×#13511yescharacteristic
517C2×C3D3×#13511yescharacteristic
518D3—44no—
519D3—64no—
520D3—62no—
521D3—62no—
522C22—64no—
523C22—92no—
524C22—122no—
525C22—122no—
526C22—181no—
527C22—181no—
528C22C2×#380211yescharacteristic
529C4—21no—
530C4—64no—
531C4—92no—
532C4—92no—
533C4—122no—
534C4—122no—
535C4—181no—
536C4#6381012yesdirect product factor
537C4C2×C4×D3211yescharacteristic
538C4#6430611yescharacteristic
539C3—21no—
540C3C4×#91211yescharacteristic, complemented
541C3C4×#91911yescharacteristic, complemented
542C2—124no—
543C2—182no—
544C2C4×#380211yescharacteristic
545C2#1059468411yescharacteristic
546C2C2×#6381011yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×#63810C2
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×#3796C2semidirect
3. C4×C8×C3⋊D3C2semidirect
4. C3×C4×Dic12C2semidirect
5. C3×C4×D24C2semidirect
6. #10590956C2semidirect
7. #10590818C2semidirect
8. #10590777C2semidirect
9. #10590742C2semidirect
10. #10590714C2semidirect
11. C4×#3715C2semidirect
30. #63810C4direct (N × H)
60. C4×Dic12D3semidirect
61. C4×D24D3semidirect
75. #3796C2×C4semidirect
85. C8×C3⋊D3C2×C4semidirect
91. C3×Dic12C2×C4semidirect
92. C3×D24C2×C4semidirect
98. #3715C2×C4semidirect
274. Dic12C4×D3semidirect
275. D24C4×D3semidirect
290. C32×C4#135semidirect
295. C3⋊Dic3#135semidirect
462. C3×C4#912semidirect
463. C3×C4#919semidirect
480. C32C4×#135semidirect
536. C4#63810direct (N × H)
540. C3C4×#912semidirect
541. C3C4×#919semidirect

Maximal subgroups

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

subgroupindex
C2×#638102
C4×#37962
C4×C8×C3⋊D32
C3×C4×Dic122
C3×C4×D242
#105909562
#105908182
#105907772
#105907422
#105907142
C4×#37152
C4×#9193
C4×#9123