Finite Group Databasebeta

← C2×#10589124 #11796830

Subgroups — C2×#10589124 #11796830

Order 1152.

529 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#904C211yesmaximal, characteristic
2C2×#63644C211yesmaximal, characteristic, complemented
3C2×C3×#812C211yesmaximal, characteristic, complemented
4#10589124C214yesmaximal, direct product factor
5C2×#4566—31nomaximal
6C2×#4518—31nomaximal
7C2×C3×#235—21no—
8C22×C32×C8C2211yescharacteristic
9C2×C4⋊(C3⋊Dic3)—21no—
10C2×C3×Dic12C411yescharacteristic, complemented
11C3×#904—21no—
12C3×#904—21no—
13C3×#904C412yescomplemented
14C3×#904C2212yes—
15C2×C3×D24C411yescharacteristic, complemented
16C2×C3×#204—21no—
17#63644—21no—
18#63644C2212yescomplemented
19C3×#812—21no—
20C3×#812C2212yescomplemented
21C2×C3×C3⋊C16—21no—
22C2×C3×#135—31no—
23C2×#904D311yescharacteristic
24C2×C3×M32—31no—
25C2×#817—31no—
26C2×#817—31no—
27C2×#817—61no—
28C2×#812D311yescharacteristic, complemented
29#4566—34no—
30#4518—34no—
31C22×C32×C4D411yescharacteristic
32C22×C3⋊Dic3—41no—
33C2×C3×#67—41no—
34C3×#235—22no—
35C3×#235—22no—
36C3×#235—41no—
37C3×#235—41no—
38C2×C3×D12—21no—
39C2×C3×C4×D3—41no—
40C2×C3×Dic6—21no—
41C2×C32×C8C2×C411yescharacteristic
42C2×C32×C8C2×C411yescharacteristic
43C2×C32×C8D411yescharacteristic
44C2×C32×C8D411yescharacteristic
45C2×C32×C8D411yescharacteristic
46C2×C32×C8C2311yescharacteristic
47C4⋊(C3⋊Dic3)—22no—
48C4⋊(C3⋊Dic3)—41no—
49C3×Dic12—21no—
50C3×Dic12C2×C412yescomplemented
51C3×D24—21no—
52C3×D24C2×C412yescomplemented
53C3×#204—22no—
54C3×#204—22no—
55C3×C3⋊C16—22no—
56C2×#360—91noSylow
57C2×C3×#41—61no—
58C2×#235—21no—
59C3×#135—32no—
60C3×#135—32no—
61C3×#135—61no—
62C3×#135—61no—
63C2×C3×Q16—31no—
64C2×C3×SD16—61no—
65C2×C3×D8—31no—
66C22×C3×C8—21no—
67C22×C3×C8C2×D311yescharacteristic
68C22×C3×C8C2×D311yescharacteristic
69C2×C4⋊Dic3—62no—
70C2×C4⋊Dic3—61no—
71C2×C4⋊Dic3—61no—
72C2×Dic12Dic311yescharacteristic, complemented
73#904—21no—
74#904—21no—
75#904Dic312yescomplemented
76#904C2×D312yes—
77C2×D24Dic311yescharacteristic, complemented
78C2×#204—21no—
79C3×M32—32no—
80C3×M32—61no—
81C2×C3×C16—61no—
82#817—32no—
83#817—32no—
84#817—62no—
85#817—62no—
86#817—61no—
87#817—61no—
88#812—21no—
89#812C2×D312yescomplemented
90C2×C3⋊C16—21no—
91C23×C32D811yescharacteristic
92C22×C3×D3—41no—
93C2×C32×C4C22⋊C411yescharacteristic
94C2×C32×C4C22⋊C411yescharacteristic
95C2×C32×C4D811yescharacteristic
96C2×C32×C4SD1611yescharacteristic
97C2×C32×C4SD1611yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C3⋊Dic3—42no—
100C2×C3⋊Dic3—82no—
101C3×#67—42no—
102C3×#67—42no—
103C2×C3×Dic3—41no—
104C3×D12—22no—
105C3×D12—41no—
106C3×C4×D3—42no—
107C3×C4×D3—42no—
108C3×Dic6—22no—
109C3×Dic6—41no—
110C32×C8C22⋊C411yescharacteristic
111C32×C8C22⋊C411yescharacteristic
112C32×C8C22×C411yescharacteristic
113C32×C8C2×D411yescharacteristic
114C2×#135—31no—
115C2×M32—31no—
116C2×#106—91no—
117#360—94no—
118C3×#41—62no—
119C3×#41—62no—
120C3×#41—121no—
121C3×#41—121no—
122C2×C3×Q8—61no—
123C2×C3×D4—61no—
124C2×C3×D4—121no—
125C22×C3×C4—21no—
126C22×C3×C4—121no—
127C22×C3×C4D1211yescharacteristic
128C22×C3×C4#6711yescharacteristic
129C2×#67—41no—
130C22×Dic3—122no—
131C22×Dic3—121no—
132C22×Dic3—121no—
133#235—22no—
134#235—22no—
135#235—41no—
136#235—41no—
137C2×D12—21no—
138C2×C4×D3—41no—
139C2×Dic6—21no—
140C3×Q16—32no—
141C3×Q16—61no—
142C3×SD16—62no—
143C3×SD16—62no—
144C3×D8—32no—
145C3×D8—61no—
146C2×C3×C8—21no—
147C2×C3×C8—21no—
148C2×C3×C8—21no—
149C2×C3×C8—21no—
150C2×C3×C8—21no—
151C2×C3×C8—21no—
152C2×C3×C8C4×D311yescharacteristic
153C2×C3×C8C4×D311yescharacteristic
154C2×C3×C8D1211yescharacteristic
155C2×C3×C8C2×Dic311yescharacteristic
156C2×C3×C8C2×Dic311yescharacteristic
157C2×C3×C8#6711yescharacteristic
158C2×C3×C8#6711yescharacteristic
159C2×C3×C8#6711yescharacteristic
160C2×C3×C8#6711yescharacteristic
161C2×C3×C8#6711yescharacteristic
162C2×C3×C8C22×D311yescharacteristic
163C2×C3×C8C22×D311yescharacteristic
164C4⋊Dic3—64no—
165C4⋊Dic3—62no—
166C4⋊Dic3—62no—
167C4⋊Dic3—122no—
168C4⋊Dic3—121no—
169C4⋊Dic3—121no—
170Dic12—21no—
171Dic12C2×Dic312yescomplemented
172D24—21no—
173D24C2×Dic312yescomplemented
174#204—22no—
175#204—22no—
176C3×C16—62no—
177C3⋊C16—22no—
178C22×C32—22no—
179C22×C32#10211yescharacteristic
180C22×C32#10211yescharacteristic
181C22×C32C2×D811yescharacteristic
182C2×C3×D3—42no—
183C2×C3×D3—82no—
184C32×C4#10211yescharacteristic
185C32×C4#10211yescharacteristic
186C32×C4C2×C22⋊C411yescharacteristic
187C32×C4C2×SD1611yescharacteristic
188C3⋊Dic3—82no—
189C3×Dic3—42no—
190C2×#41—61no—
191#135—32no—
192#135—32no—
193#135—61no—
194#135—61no—
195C2×Q16—31no—
196C2×SD16—61no—
197C2×D8—31no—
198C22×C8D3211yescharacteristic
199C2×C4⋊C4—181no—
200M32—32no—
201M32—61no—
202C2×C16—61no—
203#106—92no—
204#106—181no—
205C23×C3—21no—
206C23×C3—121no—
207C23×C3D2411yescharacteristic
208C23×C3#21311yescharacteristic
209C22×D3—41no—
210C3×Q8—62no—
211C3×Q8—121no—
212C3×D4—62no—
213C3×D4—122no—
214C3×D4—122no—
215C3×D4—121no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—121no—
223C2×C3×C4—122no—
224C2×C3×C4—122no—
225C2×C3×C4#20411yescharacteristic
226C2×C3×C4#20411yescharacteristic
227C2×C3×C4D2411yescharacteristic
228C2×C3×C4(C2×D3)⋊C411yescharacteristic
229C2×C3×C4(C2×D3)⋊C411yescharacteristic
230C2×C3×C4#21311yescharacteristic
231C2×C3×C4#21411yescharacteristic
232C2×C3×C4#21411yescharacteristic
233C2×C3×C4#21711yescharacteristic
234C2×C3×C4#21711yescharacteristic
235C2×C3×C4C2×D1211yescharacteristic
236C2×C3×C4C2×#6711yescharacteristic
237#67—42no—
238#67—42no—
239C2×Dic3—41no—
240C2×Dic3—124no—
241C2×Dic3—122no—
242C2×Dic3—122no—
243C2×Dic3—244no—
244C2×Dic3—242no—
245C2×Dic3—242no—
246D12—22no—
247D12—41no—
248C4×D3—42no—
249C4×D3—42no—
250Dic6—22no—
251Dic6—41no—
252C3×C8—21no—
253C3×C8—21no—
254C3×C8—21no—
255C3×C8—21no—
256C3×C8(C2×D3)⋊C411yescharacteristic
257C3×C8(C2×D3)⋊C411yescharacteristic
258C3×C8#21711yescharacteristic
259C3×C8#21711yescharacteristic
260C3×C8C2×C4×D311yescharacteristic
261C3×C8C22×Dic311yescharacteristic
262C3×C8C2×#6711yescharacteristic
263C3×C8C2×#6711yescharacteristic
264C2×C32—21no—
265C2×C32—21no—
266C2×C32#36012yescomplemented
267C2×C32C2×#10211yescharacteristic
268C3×D3—82no—
269#41—62no—
270#41—62no—
271#41—121no—
272#41—121no—
273C2×Q8—61no—
274C2×D4—61no—
275C2×D4—121no—
276C22×C4—121no—
277C22×C4—361no—
278C22×C4#62611yescharacteristic
279Q16—32no—
280Q16—61no—
281SD16—62no—
282SD16—62no—
283D8—32no—
284D8—61no—
285C2×C8D3×Dic311yescharacteristic
286C2×C8D3×Dic311yescharacteristic
287C2×C8#62511yescharacteristic
288C2×C8#62511yescharacteristic
289C2×C8#62611yescharacteristic
290C2×C8C2×D3211yescharacteristic
291C4⋊C4—182no—
292C4⋊C4—361no—
293C16—62no—
294C22×C3—24no—
295C22×C3—22no—
296C22×C3—22no—
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—122no—
301C22×C3—242no—
302C22×C3#82111yescharacteristic
303C22×C3#82111yescharacteristic
304C22×C3#83211yescharacteristic
305C22×C3#83211yescharacteristic
306C22×C3C2×D2411yescharacteristic
307C22×C3C2×#21311yescharacteristic
308C2×D3—42no—
309C2×D3—82no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—122no—
315C3×C4#82111yescharacteristic
316C3×C4#82111yescharacteristic
317C3×C4#83211yescharacteristic
318C3×C4#83211yescharacteristic
319C3×C4C2×#20411yescharacteristic
320C3×C4C2×(C2×D3)⋊C411yescharacteristic
321C3×C4C2×#21411yescharacteristic
322C3×C4C2×#21711yescharacteristic
323Dic3—42no—
324Dic3—244no—
325Dic3—242no—
326Dic3—242no—
327C32C2×#36011yescharacteristic, complemented, Sylow
328C23—121no—
329C23#371411yescharacteristic
330Q8—62no—
331Q8—121no—
332D4—62no—
333D4—122no—
334D4—122no—
335D4—121no—
336C2×C4—121no—
337C2×C4—122no—
338C2×C4—122no—
339C2×C4—362no—
340C2×C4—722no—
341C2×C4#371411yescharacteristic
342C2×C4#371611yescharacteristic
343C2×C4#371611yescharacteristic
344C2×C4(C2×D3)⋊Dic311yescharacteristic
345C2×C4(C2×D3)⋊Dic311yescharacteristic
346C2×C4C2×#62611yescharacteristic
347C8(C2×D3)⋊Dic311yescharacteristic
348C8(C2×D3)⋊Dic311yescharacteristic
349C8C2×D3×Dic311yescharacteristic
350C8C2×#62511yescharacteristic
351C2×C3—22no—
352C2×C3—22no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—21no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3—22no—
359C2×C3—242no—
360C2×C3#451812yescomplemented
361C2×C3#456612yescomplemented
362C2×C3C2×#82111yescharacteristic
363C2×C3C2×#83211yescharacteristic
364D3—82no—
365C22—22no—
366C22—122no—
367C22—242no—
368C22#6356311yescharacteristic
369C22#6356311yescharacteristic
370C22C2×#371411yescharacteristic
371C4—122no—
372C4—722no—
373C4#6356311yescharacteristic
374C4#6356311yescharacteristic
375C4C2×#371611yescharacteristic
376C4C2×(C2×D3)⋊Dic311yescharacteristic
377C3—21no—
378C3C2×#451811yescharacteristic, complemented
379C3C2×#456611yescharacteristic, complemented
380C2—21no—
381C2—21no—
382C2—242no—
383C2#1058912412yesdirect product factor
384C2C2×#6356311yescharacteristic
subgroupG/H
centerC22#63563
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC22×C32×C8C22
socleC22×C32#102
prime radicalC2×C3×#904C2
cosocleC2×C32×C8C23
hypercenterC22×C8D32
hypocenterC32C2×#360
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63644C2semidirect
3. C2×C3×#812C2semidirect
4. #10589124C2direct (N × H)
10. C2×C3×Dic12C4semidirect
13. C3×#904C4semidirect
15. C2×C3×D24C4semidirect
18. #63644C22semidirect
20. C3×#812C22semidirect
28. C2×#812D3semidirect
50. C3×Dic12C2×C4semidirect
52. C3×D24C2×C4semidirect
72. C2×Dic12Dic3semidirect
75. #904Dic3semidirect
77. C2×D24Dic3semidirect
89. #812C2×D3semidirect
171. Dic12C2×Dic3semidirect
173. D24C2×Dic3semidirect
266. C2×C32#360semidirect
327. C32C2×#360semidirect
360. C2×C3#4518semidirect
361. C2×C3#4566semidirect
378. C3C2×#4518semidirect
379. C3C2×#4566semidirect
383. C2#10589124direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9042
C2×#636442
C2×C3×#8122
#105891242
C2×#45663
C2×#45183