Finite Group Databasebeta

← C4×#64159 #11859970

Subgroups — C4×#64159 #11859970

Order 1152.

1500 conjugacy classes of subgroups.

The subgroup lattice has 405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×#41C211yesmaximal, characteristic, complemented
2C2×#64159C211yesmaximal, characteristic
3C4×#3828C211yesmaximal, characteristic, complemented
4#10592932C211yesmaximal, characteristic, complemented
5C4×#3756C212yesmaximal, complemented
6C4×#3755C212yesmaximal, complemented
7C4×#3754C212yesmaximal, complemented
8C4×#3753C212yesmaximal, complemented
9#10592701C211yesmaximal, characteristic, complemented
10#10592697C211yesmaximal, characteristic, complemented
11C2×C4×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
12C4×#950—34nomaximal
13C2×C32×#41C2211yescharacteristic
14C2×#3828C2211yescharacteristic
15C32×C4×Q8C2212yes—
16C32×C4×D4—22no—
17C32×C4×D4C2212yes—
18C32×#117—21no—
19C32×#117C2211yescharacteristic
20C2×C32×C42—21no—
21C2×C32×C42C2211yescharacteristic
22#64159C418yesdirect product factor
23C2×#3756C2211yescharacteristic
24C2×#3755C2211yescharacteristic
25C2×#3754C2211yescharacteristic
26C2×#3753C2211yescharacteristic
27C4×#638—22no—
28#64135C2211yescharacteristic
29C22×C3⋊(C3⋊C8)C2211yescharacteristic
30C22×C3⋊(C3⋊C8)C2211yescharacteristic
31C4×C4⋊(C3⋊D3)C2212yes—
32#64081—21no—
33C42×C3⋊D3—21no—
34C4×#634C2212yes—
35#63662C2212yes—
36#63659C2212yes—
37#63637C2212yes—
38#63636C2212yes—
39#63635C2212yes—
40#63634C2212yes—
41C4×C3⋊(C3⋊C8)C2212yes—
42C4×C3⋊(C3⋊C8)C2212yes—
43C3×C4×#41D314yescomplemented
44C2×#950—34no—
45C4×#235—34no—
46#5233—34no—
47C4×#216—38no—
48C4×#215—38no—
49C4×#214—38no—
50C4×#213—38no—
51#5002—34no—
52#4998—34no—
53C2×C4×C3⋊C8—34no—
54C32×#41—22no—
55C32×#41C2×C414yescomplemented
56C2×C32×Q8C2311yescharacteristic
57C2×C32×D4—21no—
58C2×C32×D4C2311yescharacteristic
59C22×C32×C4—21no—
60C22×C32×C4—22no—
61C22×C32×C4D412yes—
62C22×C32×C4C2311yescharacteristic
63C2×#638—21no—
64#3828—22no—
65#3828C2×C414yescomplemented
66C2×C4⋊(C3⋊D3)C2311yescharacteristic
67C2×C4×C3⋊D3—21no—
68C2×C4×C3⋊D3—22no—
69C2×#634C2311yescharacteristic
70C32×C4⋊C4—22no—
71C32×C4⋊C4C2312yes—
72C32×C22⋊C4—21no—
73C32×C22⋊C4—22no—
74C32×C42—21no—
75C32×C42—22no—
76C32×C42D411yescharacteristic
77C32×C42D411yescharacteristic
78C32×C42C2312yes—
79#3757—21no—
80#3756C2×C414yescomplemented
81#3755C2×C414yescomplemented
82#3754C2×C414yescomplemented
83#3753C2×C414yescomplemented
84#3752—22no—
85C4⋊(C3⋊Dic3)C2312yes—
86#3750—22no—
87C4×C3⋊Dic3—22no—
88C4×C3⋊Dic3—21no—
89C2×C3⋊(C3⋊C8)—22no—
90C2×C3⋊(C3⋊C8)C2×C414yescomplemented
91C2×C3⋊(C3⋊C8)C2312yes—
92C2×C3⋊(C3⋊C8)C2311yescharacteristic
93C2×C3⋊(C3⋊C8)C2311yescharacteristic
94C4×#135—91noSylow
95C2×C3×#41C2×D314yes—
96C2×#235—34no—
97C3×C4×Q8C2×D318yes—
98C3×C4×D4—28no—
99C3×C4×D4C2×D318yes—
100C3×#117—24no—
101C3×#117C2×D314yes—
102C2×C3×C42—24no—
103C2×C3×C42C2×D314yes—
104#950—332no—
105C2×#216—34no—
106C2×#215—34no—
107C2×#214—34no—
108C2×#213—34no—
109C4×#67—68no—
110#926—34no—
111C22×C3⋊C8—34no—
112C22×C3⋊C8—34no—
113C4×D12—38no—
114#872—64no—
115C42×D3—64no—
116C4×Dic6—38no—
117#835—38no—
118#832—38no—
119#810—38no—
120#809—38no—
121#808—38no—
122#807—38no—
123C4×C3⋊C8—38no—
124C4×C3⋊C8—38no—
125C23×C32—21no—
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—21no—
128C32×Q8—21no—
129C32×Q8C22×C412yes—
130C32×D4—24no—
131C32×D4—21no—
132C32×D4C22×C412yes—
133C2×C32×C4—21no—
134C2×C32×C4—24no—
135C2×C32×C4—24no—
136C2×C32×C4—22no—
137C2×C32×C4—44no—
138C2×C32×C4C22×C412yes—
139C2×C32×C4C2×D412yes—
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D412yes—
142C2×C32×C4#4112yes—
143C2×C32×C4C2411yescharacteristic
144#638—24no—
145C2×C3⋊Dic3—21no—
146C2×C3⋊Dic3—22no—
147C4⋊(C3⋊D3)—21no—
148C4⋊(C3⋊D3)C22×C412yes—
149C4×C3⋊D3—24no—
150C4×C3⋊D3—44no—
151#634—21no—
152#634C22×C412yes—
153C3⋊(C3⋊C8)—22no—
154C3⋊(C3⋊C8)C22×C412yes—
155C3⋊(C3⋊C8)C22×C412yes—
156C2×#135—91no—
157C4×#41—91no—
158C4×#41C3⋊D311yescharacteristic, complemented
159C4×Q16—92no—
160C4×SD16—92no—
161C4×SD16—92no—
162C4×D8—92no—
163#427—91no—
164#416—91no—
165#416—91no—
166C2×C4×C8—91no—
167C3×#41—28no—
168C3×#41C4×D3116yescomplemented
169C2×C3×Q8C22×D314yes—
170C2×C3×D4—24no—
171C2×C3×D4C22×D314yes—
172C22×C3×C4—24no—
173C22×C3×C4—28no—
174C22×C3×C4#6718yes—
175C22×C3×C4C22×D314yes—
176C2×#67—64no—
177#235—316no—
178#235—68no—
179C2×D12—34no—
180C2×C4×D3—64no—
181C2×C4×D3—68no—
182C2×Dic6—34no—
183C3×C4⋊C4—28no—
184C3×C4⋊C4C22×D318yes—
185C3×C22⋊C4—24no—
186C3×C22⋊C4—28no—
187C3×C42—24no—
188C3×C42—28no—
189C3×C42#6714yes—
190C3×C42#6714yes—
191C3×C42C22×D318yes—
192#217—64no—
193#216—316no—
194#215—316no—
195#214—316no—
196#213—316no—
197(C2×D3)⋊C4—68no—
198C4⋊Dic3—38no—
199Dic3⋊C4—68no—
200C4×Dic3—68no—
201C4×Dic3—64no—
202C2×C3⋊C8—316no—
203C2×C3⋊C8—34no—
204C2×C3⋊C8—34no—
205C2×C3⋊C8—38no—
206C2×C3⋊C8—68no—
207C22×C32—22no—
208C22×C32—22no—
209C22×C32—42no—
210C22×C32C4×D412yes—
211C22×C32C22×D411yescharacteristic
212C2×C3⋊D3—22no—
213C2×C3⋊D3—42no—
214C32×C4—22no—
215C32×C4—22no—
216C32×C4—42no—
217C32×C4C4×D412yes—
218C32×C4#13514yescomplemented
219C32×C4C23×C411yescharacteristic
220C32×C4C2×#4111yescharacteristic
221C3⋊Dic3—22no—
222C3⋊Dic3—42no—
223C2×#41—91no—
224C2×#41C2×C3⋊D311yescharacteristic
225#135—98no—
226C2×Q16—91no—
227C2×SD16—91no—
228C2×SD16—91no—
229C2×D8—91no—
230C22×C8—91no—
231C22×C8—91no—
232C4×Q8—92no—
233C4×Q8C2×C3⋊D312yes—
234C4×D4—22no—
235C4×D4—92no—
236C4×D4—182no—
237C4×D4C2×C3⋊D312yes—
238#117—21no—
239#117—91no—
240#117—181no—
241#117C2×C3⋊D311yescharacteristic
242C2×C42—21no—
243C2×C42—181no—
244C2×C42C2×C3⋊D311yescharacteristic
245#107—92no—
246#106—92no—
247#103—92no—
248#103—92no—
249#102—92no—
250#102—92no—
251C4×C8—92no—
252C4×C8—92no—
253C23×C3—24no—
254C23×C3C2×#6714yes—
255C22×D3—64no—
256C3×Q8—24no—
257C3×Q8C2×C4×D318yes—
258C3×D4—216no—
259C3×D4—24no—
260C3×D4C2×C4×D318yes—
261C2×C3×C4—24no—
262C2×C3×C4—216no—
263C2×C3×C4—216no—
264C2×C3×C4—28no—
265C2×C3×C4—416no—
266C2×C3×C4C2×C4×D318yes—
267C2×C3×C4#23518yes—
268C2×C3×C4C2×#6718yes—
269C2×C3×C4C2×#6714yes—
270C2×C3×C4C2×#6718yes—
271C2×C3×C4C23×D314yes—
272#67—616no—
273C2×Dic3—64no—
274C2×Dic3—68no—
275D12—38no—
276D12—64no—
277C4×D3—616no—
278C4×D3—1216no—
279Dic6—38no—
280Dic6—64no—
281C3⋊C8—38no—
282C3⋊C8—38no—
283C3⋊C8—68no—
284C2×C32—22no—
285C2×C32—42no—
286C2×C32C2×C4×D411yescharacteristic
287C2×C32C2×#13512yes—
288C3⋊D3—42no—
289#41—22no—
290#41—94no—
291#41—182no—
292#41C4×C3⋊D314yescomplemented
293C2×Q8—91no—
294C2×Q8C22×C3⋊D311yescharacteristic
295C2×D4—21no—
296C2×D4—91no—
297C2×D4—181no—
298C2×D4C22×C3⋊D311yescharacteristic
299C22×C4—21no—
300C22×C4—22no—
301C22×C4—181no—
302C22×C4—182no—
303C22×C4#63812yes—
304C22×C4C22×C3⋊D311yescharacteristic
305Q16—94no—
306SD16—94no—
307SD16—94no—
308D8—94no—
309C2×C8—91no—
310C2×C8—91no—
311C2×C8—94no—
312C2×C8—92no—
313C2×C8—182no—
314C4⋊C4—22no—
315C4⋊C4—92no—
316C4⋊C4—182no—
317C4⋊C4C22×C3⋊D312yes—
318C22⋊C4—21no—
319C22⋊C4—22no—
320C22⋊C4—181no—
321C22⋊C4—182no—
322C42—21no—
323C42—22no—
324C42—181no—
325C42—182no—
326C42#63811yescharacteristic
327C42#63811yescharacteristic
328C42C22×C3⋊D312yes—
329C22×C3—28no—
330C22×C3—28no—
331C22×C3—48no—
332C22×C3C4×#6718yes—
333C22×C3C22×#6714yes—
334C2×D3—68no—
335C2×D3—128no—
336C3×C4—28no—
337C3×C4—28no—
338C3×C4—48no—
339C3×C4C4×#6718yes—
340C3×C4#950116yescomplemented
341C3×C4C22×C4×D314yes—
342C3×C4C2×#23514yes—
343Dic3—68no—
344Dic3—128no—
345C32C4×#13511yescharacteristic, complemented, Sylow
346C23—21no—
347C23—181no—
348C23C2×#63811yescharacteristic
349Q8—21no—
350Q8—92no—
351Q8—181no—
352Q8C2×C4×C3⋊D312yes—
353D4—24no—
354D4—21no—
355D4—92no—
356D4—184no—
357D4—181no—
358D4C2×C4×C3⋊D312yes—
359C2×C4—21no—
360C2×C4—24no—
361C2×C4—24no—
362C2×C4—22no—
363C2×C4—44no—
364C2×C4—181no—
365C2×C4—184no—
366C2×C4—182no—
367C2×C4—364no—
368C2×C4C2×C4×C3⋊D312yes—
369C2×C4#382812yes—
370C2×C4C2×#63812yes—
371C2×C4C2×#63811yescharacteristic
372C2×C4C2×#63812yes—
373C2×C4C23×C3⋊D311yescharacteristic
374C8—92no—
375C8—92no—
376C8—182no—
377C2×C3—28no—
378C2×C3—48no—
379C2×C3C2×C4×#6714yes—
380C2×C3C2×#95018yes—
381D3—128no—
382C22—22no—
383C22—22no—
384C22—42no—
385C22—182no—
386C22—362no—
387C22C4×#63812yes—
388C22C22×#63811yescharacteristic
389C4—22no—
390C4—22no—
391C4—42no—
392C4—182no—
393C4—362no—
394C4C4×#63812yes—
395C4#6415914yesdirect product factor
396C4C22×C4×C3⋊D311yescharacteristic
397C4C2×#382811yescharacteristic
398C3C4×#95014yescomplemented
399C2—22no—
400C2—42no—
401C2—362no—
402C2C2×C4×#63811yescharacteristic
403C2C2×#6415912yes—
subgroupG/H
centerC42#638
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×#41C2
socleC22×C32C22×D4
prime radicalC2×#64159C2
cosocleC2×C32×C4C24
hypercenterC4×#41C3⋊D3
hypocenterC32C4×#135
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C42 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C32×C4×#41C2semidirect
3. C4×#3828C2semidirect
4. #10592932C2semidirect
5. C4×#3756C2semidirect
6. C4×#3755C2semidirect
7. C4×#3754C2semidirect
8. C4×#3753C2semidirect
9. #10592701C2semidirect
10. #10592697C2semidirect
11. C2×C4×C3⋊(C3⋊C8)C2semidirect
22. #64159C4direct (N × H)
43. C3×C4×#41D3semidirect
55. C32×#41C2×C4semidirect
65. #3828C2×C4semidirect
80. #3756C2×C4semidirect
81. #3755C2×C4semidirect
82. #3754C2×C4semidirect
83. #3753C2×C4semidirect
90. C2×C3⋊(C3⋊C8)C2×C4semidirect
158. C4×#41C3⋊D3semidirect
168. C3×#41C4×D3semidirect
218. C32×C4#135semidirect
292. #41C4×C3⋊D3semidirect
340. C3×C4#950semidirect
345. C32C4×#135semidirect
395. C4#64159direct (N × H)
398. C3C4×#950semidirect

Maximal subgroups

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

subgroupindex
C32×C4×#412
C2×#641592
C4×#38282
#105929322
C4×#37562
C4×#37552
C4×#37542
C4×#37532
#105927012
#105926972
C2×C4×C3⋊(C3⋊C8)2
C4×#9503