Finite Group Databasebeta

← C4×#64151 #11860367

Subgroups — C4×#64151 #11860367

Order 1152.

1452 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×Q8C211yesmaximal, characteristic, complemented
2C2×#64151C211yesmaximal, characteristic
3C4×#3828C211yesmaximal, characteristic
4#10592924C211yesmaximal, characteristic, complemented
5#10592729C212yesmaximal, complemented
6C4×#3756C212yesmaximal, complemented
7#10592725C212yesmaximal, complemented
8C4×#3755C212yesmaximal, complemented
9#10592665C211yesmaximal, characteristic
10#10592663C211yesmaximal, characteristic, complemented
11C4×#3748C211yesmaximal, characteristic, complemented
12C4×#942—34nomaximal
13C22×C32×Q8C2211yescharacteristic
14C2×#3828C2211yescharacteristic
15C32×C4×Q8—21no—
16C32×C4×Q8—21no—
17C32×C4×Q8C2212yes—
18C32×C4×Q8C2212yes—
19C2×C32×C4⋊C4—21no—
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C32×C42—21no—
22C2×C32×C42C2211yescharacteristic
23C2×#3756C2212yes—
24#64151C418yesdirect product factor
25C2×#3755C2212yes—
26C4×#638—21no—
27C4×#638—21no—
28#64135C2211yescharacteristic
29C2×#3748C2211yescharacteristic
30C2×#3748C2211yescharacteristic
31C4×C4⋊(C3⋊D3)C2211yescharacteristic
32C4×C4⋊(C3⋊D3)C2211yescharacteristic
33#64081—21no—
34C42×C3⋊D3—21no—
35C4×#634C2211yescharacteristic
36C4×#634C2211yescharacteristic
37#63662C2212yes—
38#63662C2212yes—
39#63637C2212yes—
40#63636C2212yes—
41#63635C2212yes—
42#63634C2212yes—
43#63630C2212yes—
44C4×C3⋊(C3⋊C8)C2212yes—
45C2×C3×C4×Q8D314yescomplemented
46C2×#942—34no—
47C4×#235—34no—
48#5225—34no—
49#5030—38no—
50C4×#216—38no—
51#5026—38no—
52C4×#215—38no—
53#4966—34no—
54#4964—34no—
55C4×#208—34no—
56C2×C32×Q8—21no—
57C2×C32×Q8—22no—
58C2×C32×Q8C2×C414yescomplemented
59C2×C32×Q8C2312yes—
60C22×C32×C4—21no—
61C22×C32×C4—21no—
62C22×C32×C4D411yescharacteristic
63C22×C32×C4D411yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C2×#638—21no—
66#3828—22no—
67#3828C2×C414yes—
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×C4×C3⋊D3—21no—
70C2×C4×C3⋊D3—21no—
71C2×C4×C3⋊D3—21no—
72C2×#634C2311yescharacteristic
73C32×C4⋊C4—22no—
74C32×C4⋊C4—22no—
75C32×C4⋊C4—21no—
76C32×C4⋊C4C2312yes—
77C32×C42—22no—
78C32×C42—22no—
79C32×C42D411yescharacteristic
80C32×C42D411yescharacteristic
81C32×C42C2311yescharacteristic
82C32×C42C2311yescharacteristic
83#3757—21no—
84#3756C2×C418yescomplemented
85#3755C2×C418yescomplemented
86#3752—21no—
87#3752—21no—
88C4⋊(C3⋊Dic3)C2311yescharacteristic
89C4⋊(C3⋊Dic3)C2311yescharacteristic
90#3750—21no—
91#3750—21no—
92C4×C3⋊Dic3—21no—
93C4×C3⋊Dic3—21no—
94C4×C3⋊Dic3—21no—
95#3748—22no—
96#3748C2×C414yescomplemented
97C2×C3⋊(C3⋊C8)C2312yes—
98C2×C3⋊(C3⋊C8)C2312yes—
99C4×#137—91noSylow
100C22×C3×Q8C2×D314yes—
101C2×#235—34no—
102C3×C4×Q8—24no—
103C3×C4×Q8—24no—
104C3×C4×Q8C2×D318yes—
105C3×C4×Q8C2×D318yes—
106C2×C3×C4⋊C4—24no—
107C2×C3×C4⋊C4C2×D314yes—
108C2×C3×C42—24no—
109C2×C3×C42C2×D314yes—
110C2×#216—38no—
111#942—332no—
112C2×#215—38no—
113C4×#67—64no—
114C4×#67—64no—
115#926—34no—
116C2×#208—34no—
117C2×#208—34no—
118C4×D12—34no—
119C4×D12—34no—
120#872—64no—
121C42×D3—64no—
122C4×Dic6—34no—
123C4×Dic6—34no—
124#835—38no—
125#835—38no—
126#810—38no—
127#809—38no—
128#808—38no—
129#807—38no—
130#803—38no—
131C4×C3⋊C8—38no—
132C23×C32C2×D411yescharacteristic
133C22×C3⋊D3—21no—
134C32×Q8—24no—
135C32×Q8—22no—
136C32×Q8C22×C414yes—
137C2×C32×C4—24no—
138C2×C32×C4—22no—
139C2×C32×C4—22no—
140C2×C32×C4—22no—
141C2×C32×C4—41no—
142C2×C32×C4—42no—
143C2×C32×C4C22×C412yes—
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4#4112yes—
150C2×C32×C4C2411yescharacteristic
151#638—24no—
152C2×C3⋊Dic3—21no—
153C2×C3⋊Dic3—21no—
154C2×C3⋊Dic3—21no—
155C4⋊(C3⋊D3)—21no—
156C4⋊(C3⋊D3)C22×C412yes—
157C4×C3⋊D3—24no—
158C4×C3⋊D3—42no—
159C4×C3⋊D3—42no—
160#634—21no—
161#634C22×C412yes—
162C3⋊(C3⋊C8)—22no—
163C3⋊(C3⋊C8)C22×C414yes—
164C2×#137—91no—
165C4×#41—91no—
166C2×C4×Q8C3⋊D311yescharacteristic, complemented
167#441—92no—
168#440—92no—
169C4×Q16—92no—
170C4×SD16—92no—
171#428—91no—
172#419—91no—
173#417—91no—
174C4×M16—91no—
175C2×C3×Q8—28no—
176C2×C3×Q8—24no—
177C2×C3×Q8C4×D3116yescomplemented
178C2×C3×Q8C22×D318yes—
179C22×C3×C4—24no—
180C22×C3×C4—24no—
181C22×C3×C4#6714yes—
182C22×C3×C4#6714yes—
183C22×C3×C4C22×D314yes—
184C2×#67—64no—
185#235—316no—
186#235—68no—
187C2×D12—34no—
188C2×C4×D3—64no—
189C2×C4×D3—64no—
190C2×C4×D3—64no—
191C2×Dic6—34no—
192C3×C4⋊C4—28no—
193C3×C4⋊C4—28no—
194C3×C4⋊C4—24no—
195C3×C4⋊C4C22×D318yes—
196C3×C42—28no—
197C3×C42—28no—
198C3×C42#6714yes—
199C3×C42#6714yes—
200C3×C42C22×D314yes—
201C3×C42C22×D314yes—
202#217—64no—
203#216—332no—
204#215—332no—
205(C2×D3)⋊C4—64no—
206(C2×D3)⋊C4—64no—
207C4⋊Dic3—34no—
208C4⋊Dic3—34no—
209Dic3⋊C4—64no—
210Dic3⋊C4—64no—
211C4×Dic3—64no—
212C4×Dic3—64no—
213C4×Dic3—64no—
214#208—316no—
215#208—68no—
216C2×C3⋊C8—38no—
217C2×C3⋊C8—38no—
218C22×C32—21no—
219C22×C32—21no—
220C22×C32C4×D412yes—
221C22×C32C22×D411yescharacteristic
222C2×C3⋊D3—22no—
223C2×C3⋊D3—41no—
224C2×C3⋊D3—41no—
225C32×C4—24no—
226C32×C4—21no—
227C32×C4—21no—
228C32×C4—21no—
229C32×C4—42no—
230C32×C4C4×D412yes—
231C32×C4#13712yescomplemented
232C32×C4C23×C411yescharacteristic
233C32×C4C2×#4111yescharacteristic
234C3⋊Dic3—22no—
235C3⋊Dic3—41no—
236C3⋊Dic3—41no—
237C2×#41—91no—
238C22×Q8C2×C3⋊D311yescharacteristic
239#137—98no—
240C2×Q16—92no—
241C2×SD16—92no—
242C2×M16—91no—
243C2×M16—91no—
244C4×Q8—21no—
245C4×Q8—21no—
246C4×Q8—91no—
247C4×Q8—91no—
248C4×Q8C2×C3⋊D312yes—
249C4×Q8C2×C3⋊D312yes—
250C4×D4—91no—
251C4×D4—91no—
252C4×D4—181no—
253C4×D4—181no—
254#117—91no—
255#117—181no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4C2×C3⋊D311yescharacteristic
258C2×C42—21no—
259C2×C42—181no—
260C2×C42C2×C3⋊D311yescharacteristic
261#107—92no—
262#106—92no—
263#103—92no—
264#103—92no—
265#103—92no—
266#102—92no—
267#97—92no—
268C4×C8—92no—
269C23×C3C2×#6714yes—
270C22×D3—64no—
271C3×Q8—216no—
272C3×Q8—28no—
273C3×Q8C2×C4×D3116yes—
274C2×C3×C4—216no—
275C2×C3×C4—28no—
276C2×C3×C4—28no—
277C2×C3×C4—28no—
278C2×C3×C4—44no—
279C2×C3×C4—48no—
280C2×C3×C4C2×C4×D318yes—
281C2×C3×C4#23518yes—
282C2×C3×C4C2×#6714yes—
283C2×C3×C4C2×#6714yes—
284C2×C3×C4C2×#6714yes—
285C2×C3×C4C2×#6714yes—
286C2×C3×C4C2×#6714yes—
287C2×C3×C4C23×D314yes—
288#67—616no—
289C2×Dic3—64no—
290C2×Dic3—64no—
291C2×Dic3—64no—
292D12—38no—
293D12—64no—
294C4×D3—616no—
295C4×D3—128no—
296C4×D3—128no—
297Dic6—38no—
298Dic6—64no—
299C3⋊C8—316no—
300C3⋊C8—68no—
301C2×C32—22no—
302C2×C32C2×C4×D411yescharacteristic
303C2×C32C2×#13711yescharacteristic
304C2×C32#57511yescharacteristic
305C3⋊D3—42no—
306#41—94no—
307#41—182no—
308C2×Q8—22no—
309C2×Q8—21no—
310C2×Q8—91no—
311C2×Q8C4×C3⋊D314yescomplemented
312C2×Q8C22×C3⋊D312yes—
313C2×D4—91no—
314C2×D4—181no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—181no—
318C22×C4—181no—
319C22×C4—181no—
320C22×C4#63811yescharacteristic
321C22×C4#63811yescharacteristic
322C22×C4C22×C3⋊D311yescharacteristic
323Q16—98no—
324SD16—98no—
325M16—94no—
326M16—182no—
327C2×C8—92no—
328C2×C8—92no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—21no—
332C4⋊C4—91no—
333C4⋊C4—91no—
334C4⋊C4—181no—
335C4⋊C4—181no—
336C4⋊C4C22×C3⋊D312yes—
337C22⋊C4—181no—
338C22⋊C4—181no—
339C22⋊C4—181no—
340C42—22no—
341C42—22no—
342C42—181no—
343C42—181no—
344C42—181no—
345C42#63811yescharacteristic
346C42#63811yescharacteristic
347C42C22×C3⋊D311yescharacteristic
348C42C22×C3⋊D311yescharacteristic
349C22×C3—24no—
350C22×C3—24no—
351C22×C3C4×#6718yes—
352C22×C3C22×#6714yes—
353C2×D3—68no—
354C2×D3—124no—
355C2×D3—124no—
356C3×C4—216no—
357C3×C4—24no—
358C3×C4—24no—
359C3×C4—24no—
360C3×C4—48no—
361C3×C4C4×#6718yes—
362C3×C4#94218yescomplemented
363C3×C4C22×C4×D314yes—
364C3×C4C2×#23514yes—
365Dic3—68no—
366Dic3—124no—
367Dic3—124no—
368C32C4×#13711yescharacteristic, complemented, Sylow
369C23—181no—
370C23C2×#63811yescharacteristic
371Q8—22no—
372Q8—24no—
373Q8—92no—
374Q8—181no—
375Q8C2×C4×C3⋊D314yes—
376D4—92no—
377D4—184no—
378D4—181no—
379C2×C4—22no—
380C2×C4—24no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—181no—
386C2×C4—184no—
387C2×C4—181no—
388C2×C4—181no—
389C2×C4—362no—
390C2×C4—362no—
391C2×C4C2×C4×C3⋊D312yes—
392C2×C4#382812yes—
393C2×C4C2×#63811yescharacteristic
394C2×C4C2×#63811yescharacteristic
395C2×C4C2×#63811yescharacteristic
396C2×C4C2×#63811yescharacteristic
397C2×C4C2×#63811yescharacteristic
398C2×C4C23×C3⋊D311yescharacteristic
399C8—94no—
400C8—182no—
401C2×C3—28no—
402C2×C3C2×C4×#6714yes—
403C2×C3C2×#94214yes—
404C2×C3#582214yes—
405D3—128no—
406C22—21no—
407C22—21no—
408C22—182no—
409C22—361no—
410C22—361no—
411C22C4×#63812yes—
412C22C22×#63811yescharacteristic
413C4—24no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—42no—
418C4—182no—
419C4—361no—
420C4—361no—
421C4C4×#63812yes—
422C4#6415112yesdirect product factor
423C4C22×C4×C3⋊D311yescharacteristic
424C4C2×#382811yescharacteristic
425C3C4×#94214yescomplemented
426C2—22no—
427C2—362no—
428C2C2×C4×#63811yescharacteristic
429C2C2×#6415111yescharacteristic
430C2#1059629311yescharacteristic
subgroupG/H
centerC2×C4C2×#638
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×C4×Q8C2
socleC22×C32C22×D4
prime radicalC2×#3828C22
cosocleC2×C32×C4C24
hypercenterC2×C4×Q8C3⋊D3
hypocenterC32C4×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×Q8C2semidirect
4. #10592924C2semidirect
5. #10592729C2semidirect
6. C4×#3756C2semidirect
7. #10592725C2semidirect
8. C4×#3755C2semidirect
10. #10592663C2semidirect
11. C4×#3748C2semidirect
24. #64151C4direct (N × H)
45. C2×C3×C4×Q8D3semidirect
58. C2×C32×Q8C2×C4semidirect
84. #3756C2×C4semidirect
85. #3755C2×C4semidirect
96. #3748C2×C4semidirect
166. C2×C4×Q8C3⋊D3semidirect
177. C2×C3×Q8C4×D3semidirect
231. C32×C4#137semidirect
311. C2×Q8C4×C3⋊D3semidirect
362. C3×C4#942semidirect
368. C32C4×#137semidirect
422. C4#64151direct (N × H)
425. C3C4×#942semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×Q82
C2×#641512
C4×#38282
#105929242
#105927292
C4×#37562
#105927252
C4×#37552
#105926652
#105926632
C4×#37482
C4×#9423