Finite Group Databasebeta

← C4×#64118 #11860379

Subgroups — C4×#64118 #11860379

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×#64118C211yesmaximal, characteristic
2C4×#3828C211yesmaximal, characteristic
3C2×C4×#634C211yesmaximal, characteristic, complemented
4C32×C4×M16C211yesmaximal, characteristic, complemented
5#10592832C211yesmaximal, characteristic
6#10592820C211yesmaximal, characteristic, complemented
7#10592819C211yesmaximal, characteristic, complemented
8#10592415C212yesmaximal, complemented
9#10592409C212yesmaximal, complemented
10C4×#3746C212yesmaximal, complemented
11C4×#3744C212yesmaximal, complemented
12C4×#909—34nomaximal
13C2×#3828C2211yescharacteristic
14C22×#634C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16C2×C32×M16C2211yescharacteristic
17C2×C32×C42C2211yescharacteristic
18C4×#638—21no—
19C4×#638—21no—
20#64135C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×#3750—21no—
23C2×C4×C3⋊Dic3—21no—
24#64118C418yesdirect product factor
25C2×#3746C2212yes—
26C2×#3744C2212yes—
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29#64081—21no—
30C42×C3⋊D3—21no—
31C4×#634—21no—
32C4×#634—21no—
33C4×#634C2212yes—
34C4×#634C2212yes—
35C4×#634C2211yescharacteristic
36C4×#634C2211yescharacteristic
37C32×#97C2212yes—
38C32×C4×C8C2212yes—
39#63648C2212yes—
40#63645C2212yes—
41#63644C2212yes—
42#63643C2212yes—
43#63643C2212yes—
44#63643C2212yes—
45C2×#909—34no—
46C4×#235—34no—
47C2×C4×Dic6—34no—
48C3×C4×M16D314yescomplemented
49#5133—34no—
50#5121—34no—
51#5120—34no—
52#4716—38no—
53#4710—38no—
54C4×Dic12—38no—
55C4×#204—38no—
56C22×C32×C4D411yescharacteristic
57C22×C32×C4D411yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C2×#638—21no—
60C22×C3⋊Dic3—21no—
61C22×C3⋊Dic3—21no—
62#3828—22no—
63#3828C2×C414yes—
64C2×C4⋊(C3⋊D3)C2311yescharacteristic
65C2×C4×C3⋊D3—21no—
66C2×C4×C3⋊D3—21no—
67C2×C4×C3⋊D3—21no—
68C2×#634—21no—
69C2×#634—22no—
70C2×#634C2×C414yescomplemented
71C2×#634C2312yes—
72C2×#634C2311yescharacteristic
73C32×M16—22no—
74C32×M16C2×C414yescomplemented
75C2×C32×C8C2312yes—
76C2×C32×C8C2312yes—
77C32×C42D411yescharacteristic
78C32×C42D411yescharacteristic
79C32×C42C2311yescharacteristic
80C32×C42C2311yescharacteristic
81#3757—21no—
82#3752—21no—
83#3752—21no—
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)C2312yes—
86C4⋊(C3⋊Dic3)C2311yescharacteristic
87C4⋊(C3⋊Dic3)C2311yescharacteristic
88#3750—22no—
89#3750—22no—
90#3750—21no—
91#3750—21no—
92C4×C3⋊Dic3—22no—
93C4×C3⋊Dic3—22no—
94C4×C3⋊Dic3—21no—
95C4×C3⋊Dic3—21no—
96C4×C3⋊Dic3—21no—
97#3746C2×C418yescomplemented
98#3744C2×C418yescomplemented
99C4×#137—91noSylow
100C2×#235—34no—
101C22×Dic6—34no—
102C2×C3×M16C2×D314yes—
103C2×C3×M16C2×D314yes—
104C2×C3×C42C2×D314yes—
105C4×#67—64no—
106C4×#67—64no—
107#926—34no—
108C2×C4⋊Dic3—34no—
109C2×Dic3⋊C4—64no—
110C2×C4×Dic3—64no—
111#909—332no—
112C2×Dic12—38no—
113C2×#204—38no—
114C4×D12—34no—
115C4×D12—34no—
116#872—64no—
117C42×D3—64no—
118C4×Dic6—38no—
119C4×Dic6—34no—
120C4×Dic6—38no—
121C4×Dic6—34no—
122C4×Dic6—64no—
123C4×Dic6—64no—
124C3×#97C2×D318yes—
125C3×C4×C8C2×D318yes—
126#821—38no—
127#818—38no—
128#817—38no—
129#816—38no—
130#816—38no—
131#816—38no—
132C23×C32C2×D411yescharacteristic
133C22×C3⋊D3—21no—
134C2×C32×C4—22no—
135C2×C32×C4—41no—
136C2×C32×C4C22×C412yes—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4112yes—
143C2×C32×C4C2411yescharacteristic
144#638—24no—
145C2×C3⋊Dic3—24no—
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3—21no—
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3—21no—
151C2×C3⋊Dic3—42no—
152C4⋊(C3⋊D3)—21no—
153C4⋊(C3⋊D3)C22×C412yes—
154C4×C3⋊D3—24no—
155C4×C3⋊D3—42no—
156C4×C3⋊D3—42no—
157#634—24no—
158#634—22no—
159#634—21no—
160#634C22×C414yes—
161#634C22×C412yes—
162C32×C8—22no—
163C32×C8C22×C414yes—
164C2×#137—91no—
165C4×#41—91no—
166C2×C4×Q8—91no—
167#441—92no—
168#440—92no—
169C4×Q16—92no—
170C4×SD16—92no—
171#428—91no—
172#419—91no—
173#417—91no—
174C4×M16C3⋊D311yescharacteristic, complemented
175C22×C3×C4D1214yes—
176C22×C3×C4D1214yes—
177C22×C3×C4C22×D314yes—
178C2×#67—64no—
179C22×Dic3—64no—
180C22×Dic3—64no—
181#235—316no—
182#235—68no—
183C2×D12—34no—
184C2×C4×D3—64no—
185C2×C4×D3—64no—
186C2×C4×D3—64no—
187C2×Dic6—316no—
188C2×Dic6—38no—
189C2×Dic6—34no—
190C2×Dic6—64no—
191C2×Dic6—68no—
192C3×M16—28no—
193C3×M16C4×D3116yescomplemented
194C2×C3×C8C22×D318yes—
195C2×C3×C8C22×D318yes—
196C3×C42D1214yes—
197C3×C42D1214yes—
198C3×C42C22×D314yes—
199C3×C42C22×D314yes—
200#217—64no—
201(C2×D3)⋊C4—64no—
202(C2×D3)⋊C4—64no—
203C4⋊Dic3—34no—
204C4⋊Dic3—34no—
205C4⋊Dic3—38no—
206C4⋊Dic3—64no—
207Dic3⋊C4—68no—
208Dic3⋊C4—68no—
209Dic3⋊C4—64no—
210Dic3⋊C4—64no—
211C4×Dic3—68no—
212C4×Dic3—68no—
213C4×Dic3—64no—
214C4×Dic3—64no—
215C4×Dic3—64no—
216Dic12—332no—
217#204—332no—
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—21no—
226C32×C4—21no—
227C32×C4—21no—
228C32×C4C4×D412yes—
229C32×C4#13712yescomplemented
230C32×C4C23×C411yescharacteristic
231C32×C4C2×#4111yescharacteristic
232C3⋊Dic3—24no—
233C3⋊Dic3—22no—
234C3⋊Dic3—41no—
235C3⋊Dic3—41no—
236C3⋊Dic3—42no—
237C2×#41—91no—
238C22×Q8—91no—
239#137—98no—
240C2×Q16—92no—
241C2×SD16—92no—
242C2×M16C2×C3⋊D311yescharacteristic
243C2×M16C2×C3⋊D311yescharacteristic
244C4×Q8—92no—
245C4×Q8—92no—
246C4×Q8—91no—
247C4×Q8—91no—
248C4×Q8—181no—
249C4×Q8—181no—
250C4×D4—91no—
251C4×D4—91no—
252C4×D4—181no—
253C4×D4—181no—
254#117—91no—
255#117—181no—
256C2×C4⋊C4—91no—
257C2×C4⋊C4—181no—
258C2×C42—181no—
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#97C2×C3⋊D312yes—
268C4×C8C2×C3⋊D312yes—
269C23×C3C2×D1214yes—
270C22×D3—64no—
271C2×C3×C4—28no—
272C2×C3×C4—44no—
273C2×C3×C4C2×C4×D318yes—
274C2×C3×C4C2×D1214yes—
275C2×C3×C4C2×D1214yes—
276C2×C3×C4C2×D1214yes—
277C2×C3×C4C2×D1214yes—
278C2×C3×C4C2×D1214yes—
279C2×C3×C4#23518yes—
280C2×C3×C4C23×D314yes—
281#67—616no—
282C2×Dic3—616no—
283C2×Dic3—68no—
284C2×Dic3—64no—
285C2×Dic3—68no—
286C2×Dic3—64no—
287C2×Dic3—64no—
288C2×Dic3—128no—
289D12—38no—
290D12—64no—
291C4×D3—616no—
292C4×D3—128no—
293C4×D3—128no—
294Dic6—316no—
295Dic6—38no—
296Dic6—616no—
297Dic6—68no—
298Dic6—64no—
299C3×C8—28no—
300C3×C8C2×C4×D3116yes—
301C2×C32—22no—
302C2×C32C2×C4×D411yescharacteristic
303C2×C32C2×#13711yescharacteristic
304C2×C32#57511yescharacteristic
305C3⋊D3—42no—
306#41—94no—
307#41—182no—
308C2×Q8—92no—
309C2×Q8—91no—
310C2×Q8—94no—
311C2×Q8—181no—
312C2×Q8—182no—
313C2×D4—91no—
314C2×D4—181no—
315C22×C4—181no—
316C22×C4—181no—
317C22×C4—181no—
318C22×C4—181no—
319C22×C4—181no—
320C22×C4C4⋊(C3⋊D3)11yescharacteristic
321C22×C4C4⋊(C3⋊D3)11yescharacteristic
322C22×C4C22×C3⋊D311yescharacteristic
323Q16—98no—
324SD16—98no—
325M16—22no—
326M16C4×C3⋊D314yescomplemented
327C2×C8C22×C3⋊D312yes—
328C2×C8C22×C3⋊D312yes—
329C4⋊C4—92no—
330C4⋊C4—91no—
331C4⋊C4—91no—
332C4⋊C4—181no—
333C4⋊C4—182no—
334C4⋊C4—182no—
335C4⋊C4—181no—
336C4⋊C4—181no—
337C22⋊C4—181no—
338C22⋊C4—181no—
339C22⋊C4—181no—
340C42—181no—
341C42—181no—
342C42—182no—
343C42—181no—
344C42—182no—
345C42C4⋊(C3⋊D3)11yescharacteristic
346C42C4⋊(C3⋊D3)11yescharacteristic
347C42C22×C3⋊D311yescharacteristic
348C42C22×C3⋊D311yescharacteristic
349C22×C3—24no—
350C22×C3—24no—
351C22×C3C4×D1218yes—
352C22×C3C22×D1214yes—
353C2×D3—68no—
354C2×D3—124no—
355C2×D3—124no—
356C3×C4—24no—
357C3×C4—24no—
358C3×C4—24no—
359C3×C4C4×D1218yes—
360C3×C4#90918yescomplemented
361C3×C4C22×C4×D314yes—
362C3×C4C2×#23514yes—
363Dic3—616no—
364Dic3—68no—
365Dic3—124no—
366Dic3—124no—
367Dic3—128no—
368C32C4×#13711yescharacteristic, complemented, Sylow
369C23—181no—
370C23C2×C4⋊(C3⋊D3)11yescharacteristic
371Q8—94no—
372Q8—92no—
373Q8—184no—
374Q8—182no—
375Q8—181no—
376D4—92no—
377D4—184no—
378D4—181no—
379C2×C4—22no—
380C2×C4—41no—
381C2×C4—184no—
382C2×C4—181no—
383C2×C4—182no—
384C2×C4—184no—
385C2×C4—181no—
386C2×C4—181no—
387C2×C4—182no—
388C2×C4—362no—
389C2×C4—362no—
390C2×C4—362no—
391C2×C4C2×C4×C3⋊D312yes—
392C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
393C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
394C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
395C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
396C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
397C2×C4#382812yes—
398C2×C4C23×C3⋊D311yescharacteristic
399C8—22no—
400C8C2×C4×C3⋊D314yes—
401C2×C3—28no—
402C2×C3C2×C4×D1214yes—
403C2×C3C2×#90914yes—
404C2×C3#574814yes—
405D3—128no—
406C22—21no—
407C22—21no—
408C22—182no—
409C22—361no—
410C22—361no—
411C22C4×C4⋊(C3⋊D3)12yes—
412C22C22×C4⋊(C3⋊D3)11yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—182no—
417C4—184no—
418C4—361no—
419C4—361no—
420C4—362no—
421C4C4×C4⋊(C3⋊D3)12yes—
422C4#6411812yesdirect product factor
423C4C22×C4×C3⋊D311yescharacteristic
424C4C2×#382811yescharacteristic
425C3C4×#90914yescomplemented
426C2—22no—
427C2—362no—
428C2C2×C4×C4⋊(C3⋊D3)11yescharacteristic
429C2C2×#6411811yescharacteristic
430C2#1059621911yescharacteristic
subgroupG/H
centerC2×C4C2×C4⋊(C3⋊D3)
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×M16C2
socleC22×C32C22×D4
prime radicalC2×#3828C22
cosocleC2×C32×C4C24
hypercenterC4×M16C3⋊D3
hypocenterC32C4×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
3. C2×C4×#634C2semidirect
4. C32×C4×M16C2semidirect
6. #10592820C2semidirect
7. #10592819C2semidirect
8. #10592415C2semidirect
9. #10592409C2semidirect
10. C4×#3746C2semidirect
11. C4×#3744C2semidirect
24. #64118C4direct (N × H)
48. C3×C4×M16D3semidirect
70. C2×#634C2×C4semidirect
74. C32×M16C2×C4semidirect
97. #3746C2×C4semidirect
98. #3744C2×C4semidirect
174. C4×M16C3⋊D3semidirect
193. C3×M16C4×D3semidirect
229. C32×C4#137semidirect
326. M16C4×C3⋊D3semidirect
360. C3×C4#909semidirect
368. C32C4×#137semidirect
422. C4#64118direct (N × H)
425. C3C4×#909semidirect

Maximal subgroups

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

subgroupindex
C2×#641182
C4×#38282
C2×C4×#6342
C32×C4×M162
#105928322
#105928202
#105928192
#105924152
#105924092
C4×#37462
C4×#37442
C4×#9093