Finite Group Databasebeta

← C4×#63807 #11859997

Subgroups — C4×#63807 #11859997

Order 1152.

1055 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63807C211yesmaximal, characteristic
2C4×#3795C212yesmaximal, complemented
3C4×#3746C211yesmaximal, characteristic, complemented
4C3×C4×D24C211yesmaximal, characteristic, complemented
5C3×C4×D3×C8C211yesmaximal, characteristic, complemented
6#10590954C212yesmaximal, complemented
7#10590807C211yesmaximal, characteristic, complemented
8Dic3×D24C211yesmaximal, characteristic, complemented
9#10590744C212yesmaximal, complemented
10#10590707C211yesmaximal, characteristic, complemented
11C4×#3716C212yesmaximal, complemented
12C4×#912—31nomaximal
13C4×#904—31nomaximal
14C2×#3795C2212yes—
15C2×#3746C2211yescharacteristic
16C4×#634C2212yes—
17C2×C3×D24C2211yescharacteristic
18C2×C3×D3×C8C2211yescharacteristic
19C2×C3×D3×C8C2211yescharacteristic
20C3×C4×D12C2212yes—
21C3×C42×D3C2211yescharacteristic
22C4×#625—22no—
23Dic3×D12C2212yes—
24#63879—22no—
25#63877—22no—
26C4×D3×Dic3—22no—
27#63844C2212yes—
28#63841C2212yes—
29C2×#3716C2212yes—
30#63807C418yesdirect product factor
31C32×C4×C8C2211yescharacteristic
32#63645C2211yescharacteristic
33#63643C2212yes—
34C3×#821C2212yes—
35C3×#818C2211yescharacteristic
36C3×C8×Dic3C2211yescharacteristic
37C3×C8×Dic3C2211yescharacteristic
38C3×C4×C3⋊C8C2211yescharacteristic
39#63573C2212yes—
40#63567C2212yes—
41#63563C2212yes—
42C2×#912—31no—
43C2×#904—31no—
44C4×#237—32no—
45C4×#235—32no—
46C3×C4×D8—31no—
47C2×C3×C4×C8—31no—
48Dic3×D8—31no—
49#5113—32no—
50#5106—31no—
51C4×#214—32no—
52#4880—31no—
53#4873—31no—
54#4772—32no—
55#4758—32no—
56C4×Dic12—31no—
57C4×Dic12—31no—
58C4×Dic12—31no—
59C4×Dic12—61no—
60C4×D24—31no—
61C4×D24D311yescharacteristic, complemented
62C4×#204—32no—
63C4×#204—32no—
64C4×D3×C8D311yescharacteristic, complemented
65C2×#634C2312yes—
66C2×C3×D12C2312yes—
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3D411yescharacteristic
69C2×C3×C4×D3D411yescharacteristic
70C2×C3×C4×D3C2311yescharacteristic
71C2×#625—22no—
72C2×D3×Dic3—22no—
73C2×D3×Dic3—22no—
74#3795—24no—
75#3795C2×C418yescomplemented
76C2×C32×C8C2311yescharacteristic
77C2×C32×C8C2311yescharacteristic
78C32×C42C2311yescharacteristic
79C4⋊(C3⋊Dic3)C2312yes—
80#3750—22no—
81C4×C3⋊Dic3—22no—
82#3746C2×C414yescomplemented
83C3×(C2×D3)⋊C4—22no—
84C3×C4⋊Dic3C2312yes—
85C3×C4×Dic3D411yescharacteristic
86C3×C4×Dic3D411yescharacteristic
87C3×C4×Dic3C2311yescharacteristic
88C2×C3×C3⋊C8C2311yescharacteristic
89C2×C3×C3⋊C8C2311yescharacteristic
90C3×D24C2×C414yescomplemented
91C3×D3×C8—22no—
92C3×D3×C8C2×C414yescomplemented
93#3724—22no—
94(C2×D3)⋊Dic3—22no—
95(C2×D3)⋊Dic3—22no—
96Dic32—22no—
97Dic32—22no—
98#3716C2×C418yescomplemented
99C4×#135—91noSylow
100C2×#237—32no—
101C2×#235—32no—
102C2×C3×D8—31no—
103C22×C3×C8—31no—
104C22×C3×C8—31no—
105C3×C4×D4—32no—
106C2×C3×C42—31no—
107D4×Dic3—32no—
108C2×#214—32no—
109C4×#67—62no—
110C4×#67—62no—
111C4×#67—62no—
112#926—32no—
113C2×C4×Dic3—62no—
114#912—38no—
115C2×Dic12—31no—
116C2×Dic12—31no—
117C2×Dic12—61no—
118#904—38no—
119C2×D24C2×D311yescharacteristic
120C2×#204—32no—
121C2×D3×C8C2×D311yescharacteristic
122C2×D3×C8C2×D311yescharacteristic
123#892—32no—
124#887—32no—
125#67⋊C4—62no—
126#877—62no—
127C4×D12—32no—
128C4×D12C2×D312yes—
129#872—62no—
130C42×D3—62no—
131C42×D3C2×D311yescharacteristic
132C4×Dic6—32no—
133C4×Dic6—32no—
134C4×Dic6—32no—
135C4×Dic6—62no—
136C3×#107—31no—
137C3×#102—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#832—32no—
145#821—32no—
146#821C2×D312yes—
147#818—31no—
148#818—31no—
149#818—61no—
150#818C2×D311yescharacteristic
151#817—32no—
152#816—32no—
153#816—32no—
154#816—32no—
155#816—62no—
156C8×Dic3C2×D311yescharacteristic
157C8×Dic3C2×D311yescharacteristic
158#810—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—
167C2×C3⋊Dic3—22no—
168#634—22no—
169#634C22×C414yes—
170C2×C3×Dic3—22no—
171C2×C3×Dic3C2×D411yescharacteristic
172C2×C3×Dic3C2×D411yescharacteristic
173C2×C3×Dic3C2×D411yescharacteristic
174C3×D12—22no—
175C3×D12C22×C414yes—
176C3×C4×D3—22no—
177C3×C4×D3—22no—
178C3×C4×D3—44no—
179C3×C4×D3C22×C412yes—
180C3×C4×D3#4112yes—
181#625—28no—
182D3×Dic3—28no—
183D3×Dic3—44no—
184C32×C8—21no—
185C32×C8C22×C412yes—
186C3×C3⋊C8—21no—
187C3×C3⋊C8C22×C412yes—
188C2×#135—91no—
189C4×#41—92no—
190C4×Q16—91no—
191C4×Q16—91no—
192C4×SD16—92no—
193C4×SD16—92no—
194C4×D8—31no—
195C4×D8—91no—
196#427—91no—
197#416—92no—
198C2×C4×C8—31no—
199C2×C3×D4—32no—
200C22×C3×C4—31no—
201C22×C3×C4—31no—
202C22×C3×C4—31no—
203C22×C3×C4—62no—
204C2×#67—62no—
205C2×#67—62no—
206C22×Dic3—62no—
207C22×Dic3—62no—
208#237—38no—
209#237—64no—
210#235—38no—
211#235—64no—
212C2×D12C22×D312yes—
213C2×C4×D3—22no—
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×C4×D3D1211yescharacteristic
217C2×C4×D3D1211yescharacteristic
218C2×C4×D3C22×D311yescharacteristic
219C2×Dic6—32no—
220C2×Dic6—32no—
221C2×Dic6—62no—
222C3×D8—34no—
223C2×C3×C8—21no—
224C2×C3×C8—21no—
225C2×C3×C8—31no—
226C2×C3×C8—34no—
227C2×C3×C8—31no—
228C2×C3×C8—62no—
229C2×C3×C8C22×D311yescharacteristic
230C2×C3×C8C22×D311yescharacteristic
231C2×C3×C8C22×D311yescharacteristic
232C2×C3×C8C22×D311yescharacteristic
233C3×C4⋊C4—32no—
234C3×C22⋊C4—62no—
235C3×C42—21no—
236C3×C42—31no—
237C3×C42—31no—
238C3×C42—31no—
239C3×C42C22×D311yescharacteristic
240C3×C42C22×D311yescharacteristic
241#217—62no—
242#217—62no—
243#214—38no—
244(C2×D3)⋊C4—22no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—62no—
247C4⋊Dic3—32no—
248C4⋊Dic3—32no—
249C4⋊Dic3—62no—
250C4⋊Dic3C22×D312yes—
251Dic3⋊C4—62no—
252Dic3⋊C4—62no—
253Dic3⋊C4—62no—
254Dic3⋊C4—62no—
255Dic3⋊C4—122no—
256C4×Dic3—62no—
257C4×Dic3—62no—
258C4×Dic3—62no—
259C4×Dic3—62no—
260C4×Dic3—62no—
261C4×Dic3—62no—
262C4×Dic3—122no—
263C4×Dic3D1211yescharacteristic
264C4×Dic3D1211yescharacteristic
265C4×Dic3C22×D311yescharacteristic
266C2×C3⋊C8C22×D311yescharacteristic
267C2×C3⋊C8C22×D311yescharacteristic
268Dic12—34no—
269Dic12—34no—
270Dic12—64no—
271D24C4×D314yescomplemented
272#204—38no—
273D3×C8—22no—
274D3×C8C4×D314yescomplemented
275C22×C32C22×D411yescharacteristic
276C2×C3×D3—21no—
277C2×C3×D3—21no—
278C2×C3×D3—24no—
279C2×C3×D3—42no—
280C2×C3×D3—42no—
281C2×C3×D3C4×D412yes—
282C32×C4—21no—
283C32×C4#13512yescomplemented
284C32×C4C23×C411yescharacteristic
285C32×C4C2×#4111yescharacteristic
286C3⋊Dic3—24no—
287C3⋊Dic3—42no—
288C3×Dic3—21no—
289C3×Dic3—42no—
290C3×Dic3C4×D412yes—
291C3×Dic3#13512yescomplemented
292C2×#41—92no—
293#135—98no—
294C2×Q16—91no—
295C2×SD16—92no—
296C2×D8—31no—
297C22×C8—31no—
298C22×C8—31no—
299C4×Q8—92no—
300C4×Q8—92no—
301C4×D4—32no—
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—92no—
313#103—92no—
314#102—32no—
315#102—92no—
316C4×C8—31no—
317C4×C8—31no—
318C4×C8—31no—
319C4×C8D3211yescharacteristic
320C23×C3—31no—
321C23×C3—62no—
322C22×D3—22no—
323C22×D3C2×D1211yescharacteristic
324C3×D4—34no—
325C3×D4—62no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—31no—
330C2×C3×C4—31no—
331C2×C3×C4—32no—
332C2×C3×C4—32no—
333C2×C3×C4—31no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4—124no—
338C2×C3×C4C2×D1211yescharacteristic
339C2×C3×C4C2×D1211yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343C2×C3×C4C23×D311yescharacteristic
344#67—68no—
345#67—68no—
346C2×Dic3—22no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—68no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—122no—
353C2×Dic3—122no—
354C2×Dic3—124no—
355C2×Dic3C2×D1211yescharacteristic
356C2×Dic3C2×D1211yescharacteristic
357C2×Dic3C2×D1211yescharacteristic
358D12—22no—
359D12C2×C4×D314yes—
360C4×D3—22no—
361C4×D3—22no—
362C4×D3—44no—
363C4×D3—68no—
364C4×D3—124no—
365C4×D3C2×C4×D312yes—
366C4×D3#23512yes—
367Dic6—34no—
368Dic6—34no—
369Dic6—64no—
370Dic6—62no—
371Dic6—62no—
372Dic6—122no—
373C3×C8—21no—
374C3×C8—21no—
375C3×C8—22no—
376C3×C8—32no—
377C3×C8—41no—
378C3×C8—61no—
379C3×C8C2×C4×D312yes—
380C3×C8C2×C4×D312yes—
381C3⋊C8—21no—
382C3⋊C8C2×C4×D312yes—
383C2×C32C2×C4×D411yescharacteristic
384C2×C32C2×#13511yescharacteristic
385C2×C32C2×#13511yescharacteristic
386C3×D3—22no—
387C3×D3—44no—
388#41—98no—
389#41—184no—
390C2×Q8—92no—
391C2×D4—32no—
392C2×D4—182no—
393C22×C4—31no—
394C22×C4—31no—
395C22×C4—31no—
396C22×C4—62no—
397C22×C4—182no—
398C22×C4—182no—
399Q16—94no—
400SD16—98no—
401D8—34no—
402C2×C8—31no—
403C2×C8—34no—
404C2×C8—31no—
405C2×C8—62no—
406C2×C8C2×D3211yescharacteristic
407C2×C8C2×D3211yescharacteristic
408C4⋊C4—32no—
409C4⋊C4—92no—
410C4⋊C4—182no—
411C4⋊C4—182no—
412C22⋊C4—62no—
413C22⋊C4—182no—
414C22⋊C4—182no—
415C42—31no—
416C42—31no—
417C42—31no—
418C42—182no—
419C42—182no—
420C42—182no—
421C42C2×D3211yescharacteristic
422C22×C3—21no—
423C22×C3—32no—
424C22×C3—61no—
425C22×C3—61no—
426C22×C3—64no—
427C22×C3—122no—
428C22×C3—122no—
429C22×C3C22×D1211yescharacteristic
430C22×C3C2×D3×D411yescharacteristic
431C2×D3—21no—
432C2×D3—21no—
433C2×D3—24no—
434C2×D3—42no—
435C2×D3—42no—
436C2×D3C4×D1212yes—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—22no—
442C3×C4—32no—
443C3×C4—32no—
444C3×C4—41no—
445C3×C4—61no—
446C3×C4—122no—
447C3×C4#90412yescomplemented
448C3×C4#91212yescomplemented
449C3×C4C22×C4×D311yescharacteristic
450C3×C4C22×C4×D311yescharacteristic
451C3×C4C2×#23511yescharacteristic
452C3×C4D3×#4111yescharacteristic
453Dic3—21no—
454Dic3—42no—
455Dic3—64no—
456Dic3—64no—
457Dic3—124no—
458Dic3—122no—
459Dic3—122no—
460Dic3—242no—
461Dic3C4×D1212yes—
462Dic3#90412yescomplemented
463C32C4×#13511yescharacteristic, complemented, Sylow
464C23—31no—
465C23—62no—
466Q8—94no—
467Q8—182no—
468D4—34no—
469D4—62no—
470D4—188no—
471C2×C4—31no—
472C2×C4—31no—
473C2×C4—32no—
474C2×C4—32no—
475C2×C4—31no—
476C2×C4—62no—
477C2×C4—62no—
478C2×C4—62no—
479C2×C4—124no—
480C2×C4—188no—
481C2×C4—182no—
482C2×C4—182no—
483C2×C4—364no—
484C2×C4D3×D1211yescharacteristic
485C2×C4D3×D1211yescharacteristic
486C2×C4C22×D3211yescharacteristic
487C8—21no—
488C8—32no—
489C8—61no—
490C8C4×D3212yes—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—62no—
495C2×C3—124no—
496C2×C3C2×C4×D1211yescharacteristic
497C2×C3C4×D3×D411yescharacteristic
498C2×C3C2×#90411yescharacteristic
499C2×C3C2×#90411yescharacteristic
500C2×C3C2×#91211yescharacteristic
501C2×C3D3×#13511yescharacteristic
502D3—22no—
503D3—44no—
504C22—32no—
505C22—61no—
506C22—61no—
507C22—64no—
508C22—122no—
509C22—122no—
510C22C2×D3×D1211yescharacteristic
511C4—21no—
512C4—32no—
513C4—32no—
514C4—61no—
515C4—122no—
516C4—184no—
517C4—362no—
518C4#6380712yesdirect product factor
519C4C2×C4×D3211yescharacteristic
520C4D3×#23511yescharacteristic
521C3—21no—
522C3C4×#90411yescharacteristic, complemented
523C3C4×#91211yescharacteristic, complemented
524C2—62no—
525C2—124no—
526C2C4×D3×D1211yescharacteristic
527C2D3×#90411yescharacteristic
528C2C2×#6380711yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×#63807C2
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×#3795C2semidirect
3. C4×#3746C2semidirect
4. C3×C4×D24C2semidirect
5. C3×C4×D3×C8C2semidirect
6. #10590954C2semidirect
7. #10590807C2semidirect
8. Dic3×D24C2semidirect
9. #10590744C2semidirect
10. #10590707C2semidirect
11. C4×#3716C2semidirect
30. #63807C4direct (N × H)
61. C4×D24D3semidirect
64. C4×D3×C8D3semidirect
75. #3795C2×C4semidirect
82. #3746C2×C4semidirect
90. C3×D24C2×C4semidirect
92. C3×D3×C8C2×C4semidirect
98. #3716C2×C4semidirect
271. D24C4×D3semidirect
274. D3×C8C4×D3semidirect
283. C32×C4#135semidirect
291. C3×Dic3#135semidirect
447. C3×C4#904semidirect
448. C3×C4#912semidirect
462. Dic3#904semidirect
463. C32C4×#135semidirect
518. C4#63807direct (N × H)
522. C3C4×#904semidirect
523. C3C4×#912semidirect

Maximal subgroups

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

subgroupindex
C2×#638072
C4×#37952
C4×#37462
C3×C4×D242
C3×C4×D3×C82
#105909542
#105908072
Dic3×D242
#105907442
#105907072
C4×#37162
C4×#9123
C4×#9043