Finite Group Databasebeta

← C4×#63809 #11860002

Subgroups — C4×#63809 #11860002

Order 1152.

1081 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63809C211yesmaximal, characteristic
2C4×#3796C212yesmaximal, complemented
3C4×C8×C3⋊D3C211yesmaximal, characteristic, complemented
4C3×C4×#204C212yesmaximal, complemented
5#10590956C212yesmaximal, complemented
6#10590790C211yesmaximal, characteristic, complemented
7#10590775C212yesmaximal, complemented
8#10590740C211yesmaximal, characteristic, complemented
9#10590712C211yesmaximal, characteristic, complemented
10C4×#3718C211yesmaximal, characteristic, complemented
11C4×#3713C211yesmaximal, characteristic, complemented
12C4×#916—32nomaximal
13C2×#3796C2212yes—
14C2×C8×C3⋊D3C2211yescharacteristic
15C2×C8×C3⋊D3C2211yescharacteristic
16C42×C3⋊D3C2211yescharacteristic
17C2×C3×#204C2212yes—
18C3×C4×D12C2212yes—
19C3×C4×Dic6C2212yes—
20C4×#626—22no—
21#63898C2212yes—
22#63881—22no—
23#63878—22no—
24C4×D3×Dic3—22no—
25#63849C2212yes—
26#63843C2212yes—
27C2×#3718C2211yescharacteristic
28C2×#3713C2211yescharacteristic
29#63809C418yesdirect product factor
30C32×C4×C8C2211yescharacteristic
31C8×C3⋊Dic3C2211yescharacteristic
32C8×C3⋊Dic3C2211yescharacteristic
33C4×C3⋊(C3⋊C8)C2211yescharacteristic
34C3×#821C2212yes—
35C3×#817C2212yes—
36C3×#816C2212yes—
37#63576C2211yescharacteristic
38#63576C2211yescharacteristic
39#63565C2212yes—
40#63562C2212yes—
41C2×#916—32no—
42C4×#239—32no—
43C4×#237—32no—
44C3×C4×SD16—32no—
45Dic3×SD16—32no—
46C4×#216—32no—
47C4×#213—32no—
48#4860—32no—
49#4852—32no—
50#4804—32no—
51#4790—32no—
52#4772—32no—
53#4756—32no—
54C4×#204D312yescomplemented
55C4×D3×C8—32no—
56C4×D3×C8—61no—
57C2×C4×C3⋊D3D411yescharacteristic
58C2×C4×C3⋊D3D411yescharacteristic
59C2×C4×C3⋊D3C2311yescharacteristic
60C2×C3×D12C2312yes—
61C2×C3×C4×D3—22no—
62C2×C3×Dic6C2312yes—
63C2×#626—22no—
64C2×D3×Dic3—22no—
65C2×D3×Dic3—22no—
66#3796—24no—
67#3796C2×C418yescomplemented
68C2×C32×C8C2311yescharacteristic
69C2×C32×C8C2311yescharacteristic
70C32×C42C2311yescharacteristic
71C4×C3⋊Dic3D411yescharacteristic
72C4×C3⋊Dic3D411yescharacteristic
73C4×C3⋊Dic3C2311yescharacteristic
74C2×C3⋊(C3⋊C8)C2311yescharacteristic
75C2×C3⋊(C3⋊C8)C2311yescharacteristic
76C8×C3⋊D3—22no—
77C8×C3⋊D3C2×C414yescomplemented
78C3×(C2×D3)⋊C4—22no—
79C3×C4⋊Dic3C2312yes—
80C3×C4⋊Dic3C2312yes—
81C3×Dic3⋊C4—22no—
82C3×C4×Dic3—22no—
83C3×#204C2×C418yescomplemented
84Dic3⋊Dic3—22no—
85#3722—22no—
86(C2×D3)⋊Dic3—22no—
87Dic32—22no—
88Dic32—22no—
89#3718C2×C414yescomplemented
90#3713C2×C414yescomplemented
91C4×#135—91noSylow
92C2×#239—32no—
93C2×#237—32no—
94C2×C3×SD16—32no—
95C3×C4×Q8—32no—
96C3×C4×D4—32no—
97Q8×Dic3—32no—
98C2×#216—32no—
99D4×Dic3—32no—
100C2×#213—32no—
101C4×#67—62no—
102C2×C4×Dic3—62no—
103#916—316no—
104C2×#204C2×D312yes—
105C2×D3×C8—32no—
106C2×D3×C8—32no—
107C2×D3×C8—61no—
108C2×D3×C8—61no—
109#893—32no—
110#893—62no—
111#892—32no—
112#892—32no—
113#892—62no—
114#887—32no—
115#67⋊C4—62no—
116#877—62no—
117C4×D12—62no—
118C4×D12C2×D312yes—
119C42×D3—32no—
120C42×D3—61no—
121C42×D3—62no—
122C4×Dic6C2×D312yes—
123C3×#106—32no—
124C3×#103—32no—
125C3×#102—32no—
126C3×C4×C8—21no—
127C3×C4×C8C2×D312yes—
128#835—32no—
129#832—32no—
130#821C2×D312yes—
131#817C2×D312yes—
132#816C2×D312yes—
133C8×Dic3—32no—
134C8×Dic3—32no—
135C8×Dic3—61no—
136C8×Dic3—61no—
137#810—32no—
138#809—32no—
139#807—32no—
140#807—32no—
141C4×C3⋊C8—32no—
142C4×C3⋊C8—61no—
143C22×C3⋊D3C2×D411yescharacteristic
144C22×C3×D3—22no—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2411yescharacteristic
148C2×C3⋊Dic3C2×D411yescharacteristic
149C2×C3⋊Dic3C2×D411yescharacteristic
150C2×C3⋊Dic3C2×D411yescharacteristic
151C4×C3⋊D3—22no—
152C4×C3⋊D3—22no—
153C4×C3⋊D3C22×C412yes—
154C4×C3⋊D3#4112yes—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C3×D12—22no—
159C3×D12C22×C414yes—
160C3×C4×D3—44no—
161C3×Dic6—22no—
162C3×Dic6C22×C414yes—
163#626—28no—
164D3×Dic3—28no—
165D3×Dic3—44no—
166C32×C8—21no—
167C32×C8C22×C412yes—
168C3⋊(C3⋊C8)—21no—
169C3⋊(C3⋊C8)C22×C412yes—
170C2×#135—91no—
171C4×#41—92no—
172C4×Q16—91no—
173C4×Q16—91no—
174C4×SD16—32no—
175C4×SD16—92no—
176C4×D8—91no—
177C4×D8—91no—
178#427—91no—
179#416—92no—
180C2×C4×C8—91no—
181C2×C3×Q8—32no—
182C2×C3×D4—32no—
183C22×C3×C4—62no—
184C2×#67—62no—
185C22×Dic3—62no—
186C22×Dic3—62no—
187#239—38no—
188#239—64no—
189#237—38no—
190#237—64no—
191C2×D12—62no—
192C2×D12C22×D312yes—
193C2×C4×D3—22no—
194C2×C4×D3—32no—
195C2×C4×D3—32no—
196C2×C4×D3—32no—
197C2×C4×D3—61no—
198C2×C4×D3—61no—
199C2×C4×D3—61no—
200C2×C4×D3—62no—
201C2×C4×D3—62no—
202C2×Dic6C22×D312yes—
203C3×SD16—38no—
204C2×C3×C8—21no—
205C2×C3×C8—21no—
206C2×C3×C8C22×D312yes—
207C2×C3×C8C22×D312yes—
208C3×C4⋊C4—32no—
209C3×C4⋊C4—32no—
210C3×C4⋊C4—62no—
211C3×C22⋊C4—62no—
212C3×C42—21no—
213C3×C42—62no—
214C3×C42C22×D312yes—
215#217—62no—
216#216—38no—
217#213—38no—
218(C2×D3)⋊C4—22no—
219(C2×D3)⋊C4—62no—
220(C2×D3)⋊C4—62no—
221(C2×D3)⋊C4—62no—
222C4⋊Dic3—62no—
223C4⋊Dic3C22×D312yes—
224C4⋊Dic3C22×D312yes—
225Dic3⋊C4—22no—
226Dic3⋊C4—62no—
227C4×Dic3—22no—
228C4×Dic3—32no—
229C4×Dic3—32no—
230C4×Dic3—32no—
231C4×Dic3—61no—
232C4×Dic3—61no—
233C4×Dic3—61no—
234C4×Dic3—62no—
235C4×Dic3—62no—
236C4×Dic3—62no—
237C4×Dic3—62no—
238C2×C3⋊C8—32no—
239C2×C3⋊C8—32no—
240C2×C3⋊C8—61no—
241C2×C3⋊C8—61no—
242#204C4×D318yescomplemented
243D3×C8—38no—
244D3×C8—64no—
245D3×C8—64no—
246D3×C8—64no—
247C22×C32C22×D411yescharacteristic
248C2×C3⋊D3—21no—
249C2×C3⋊D3—21no—
250C2×C3⋊D3C4×D412yes—
251C2×C3×D3—24no—
252C2×C3×D3—42no—
253C2×C3×D3—42no—
254C32×C4—21no—
255C32×C4#13512yescomplemented
256C32×C4C23×C411yescharacteristic
257C32×C4C2×#4111yescharacteristic
258C3⋊Dic3—21no—
259C3⋊Dic3C4×D412yes—
260C3⋊Dic3#13512yescomplemented
261C3×Dic3—24no—
262C3×Dic3—42no—
263C3×Dic3—42no—
264C2×#41—92no—
265#135—98no—
266C2×Q16—91no—
267C2×SD16—32no—
268C2×D8—91no—
269C22×C8—91no—
270C22×C8—91no—
271C4×Q8—32no—
272C4×Q8—92no—
273C4×D4—32no—
274C4×D4—92no—
275C4×D4—182no—
276C4×D4—182no—
277#117—92no—
278#117—182no—
279C2×C42—91no—
280C2×C42—182no—
281#107—91no—
282#107—91no—
283#106—32no—
284#103—32no—
285#103—92no—
286#102—32no—
287#102—92no—
288C4×C8—91no—
289C4×C8—91no—
290C4×C8—91no—
291C4×C8D3211yescharacteristic
292C23×C3—62no—
293C22×D3—22no—
294C22×D3—32no—
295C22×D3—61no—
296C3×Q8—34no—
297C3×Q8—62no—
298C3×D4—34no—
299C3×D4—62no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—62no—
304C2×C3×C4—62no—
305C2×C3×C4—62no—
306C2×C3×C4—124no—
307C2×C3×C4D3×D412yes—
308C2×C3×C4D3×D412yes—
309C2×C3×C4C23×D312yes—
310#67—68no—
311C2×Dic3—22no—
312C2×Dic3—22no—
313C2×Dic3—22no—
314C2×Dic3—32no—
315C2×Dic3—32no—
316C2×Dic3—32no—
317C2×Dic3—61no—
318C2×Dic3—61no—
319C2×Dic3—61no—
320C2×Dic3—68no—
321C2×Dic3—124no—
322D12—22no—
323D12—68no—
324D12C2×C4×D314yes—
325C4×D3—34no—
326C4×D3—34no—
327C4×D3—44no—
328C4×D3—62no—
329C4×D3—62no—
330C4×D3—64no—
331C4×D3—68no—
332C4×D3—64no—
333C4×D3—64no—
334C4×D3—64no—
335C4×D3—124no—
336Dic6—22no—
337Dic6C2×C4×D314yes—
338C3×C8—22no—
339C3×C8—22no—
340C3×C8—22no—
341C3×C8C2×C4×D314yes—
342C3⋊C8—34no—
343C3⋊C8—62no—
344C3⋊C8—62no—
345C3⋊C8—62no—
346C2×C32C2×C4×D411yescharacteristic
347C2×C32C2×#13511yescharacteristic
348C2×C32C2×#13511yescharacteristic
349C3⋊D3—22no—
350C3×D3—44no—
351#41—98no—
352#41—184no—
353C2×Q8—32no—
354C2×D4—32no—
355C2×D4—182no—
356C22×C4—62no—
357C22×C4—91no—
358C22×C4—91no—
359C22×C4—91no—
360C22×C4—182no—
361C22×C4—182no—
362Q16—94no—
363SD16—38no—
364D8—94no—
365C2×C8—91no—
366C2×C8—94no—
367C2×C8—91no—
368C2×C8—182no—
369C2×C8C2×D3211yescharacteristic
370C2×C8C2×D3211yescharacteristic
371C4⋊C4—32no—
372C4⋊C4—32no—
373C4⋊C4—62no—
374C4⋊C4—182no—
375C22⋊C4—62no—
376C22⋊C4—182no—
377C22⋊C4—182no—
378C42—62no—
379C42—91no—
380C42—91no—
381C42—91no—
382C42—182no—
383C42—182no—
384C42C2×D3211yescharacteristic
385C22×C3—21no—
386C22×C3—64no—
387C22×C3—122no—
388C22×C3—122no—
389C22×C3C2×D3×D412yes—
390C2×D3—24no—
391C2×D3—34no—
392C2×D3—42no—
393C2×D3—42no—
394C2×D3—62no—
395C2×D3—62no—
396C2×D3—62no—
397C2×D3—62no—
398C2×D3—62no—
399C3×C4—22no—
400C3×C4—22no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—22no—
404C3×C4—64no—
405C3×C4—122no—
406C3×C4—122no—
407C3×C4#91614yescomplemented
408C3×C4C22×C4×D312yes—
409C3×C4D3×#4112yes—
410Dic3—24no—
411Dic3—34no—
412Dic3—34no—
413Dic3—42no—
414Dic3—42no—
415Dic3—62no—
416Dic3—62no—
417Dic3—62no—
418Dic3—62no—
419C32C4×#13511yescharacteristic, complemented, Sylow
420C23—62no—
421C23—91no—
422Q8—34no—
423Q8—62no—
424D4—34no—
425D4—62no—
426D4—188no—
427C2×C4—62no—
428C2×C4—62no—
429C2×C4—62no—
430C2×C4—91no—
431C2×C4—91no—
432C2×C4—92no—
433C2×C4—92no—
434C2×C4—91no—
435C2×C4—124no—
436C2×C4—182no—
437C2×C4—188no—
438C2×C4—182no—
439C2×C4—364no—
440C2×C4#380211yescharacteristic
441C2×C4#380211yescharacteristic
442C2×C4C22×D3211yescharacteristic
443C8—21no—
444C8—92no—
445C8—181no—
446C8C4×D3212yes—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—124no—
451C2×C3C4×D3×D412yes—
452C2×C3C2×#91612yes—
453C2×C3D3×#13512yes—
454D3—44no—
455D3—64no—
456D3—64no—
457C22—64no—
458C22—92no—
459C22—122no—
460C22—122no—
461C22—181no—
462C22—181no—
463C22C2×#380211yescharacteristic
464C4—21no—
465C4—64no—
466C4—92no—
467C4—92no—
468C4—122no—
469C4—122no—
470C4—181no—
471C4#6380912yesdirect product factor
472C4C2×C4×D3211yescharacteristic
473C4#6430611yescharacteristic
474C3—21no—
475C3C4×#91612yescomplemented
476C2—124no—
477C2—182no—
478C2C4×#380211yescharacteristic
479C2#1059468411yescharacteristic
480C2C2×#6380911yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×#63809C2
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×#204C2semidirect
5. #10590956C2semidirect
6. #10590790C2semidirect
7. #10590775C2semidirect
8. #10590740C2semidirect
9. #10590712C2semidirect
10. C4×#3718C2semidirect
11. C4×#3713C2semidirect
29. #63809C4direct (N × H)
54. C4×#204D3semidirect
67. #3796C2×C4semidirect
77. C8×C3⋊D3C2×C4semidirect
83. C3×#204C2×C4semidirect
89. #3718C2×C4semidirect
90. #3713C2×C4semidirect
242. #204C4×D3semidirect
255. C32×C4#135semidirect
260. C3⋊Dic3#135semidirect
407. C3×C4#916semidirect
419. C32C4×#135semidirect
471. C4#63809direct (N × H)
475. C3C4×#916semidirect

Maximal subgroups

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

subgroupindex
C2×#638092
C4×#37962
C4×C8×C3⋊D32
C3×C4×#2042
#105909562
#105907902
#105907752
#105907402
#105907122
C4×#37182
C4×#37132
C4×#9163