Finite Group Databasebeta

← C2×#10589123 #11796832

Subgroups — C2×#10589123 #11796832

Order 1152.

509 conjugacy classes of subgroups.

The subgroup lattice has 381 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#904C211yesmaximal, characteristic
2C2×#63639C211yesmaximal, characteristic, complemented
3C2×C3×#817C211yesmaximal, characteristic, complemented
4#10589123C214yesmaximal, direct product factor
5C2×#4566—31nomaximal
6C2×#4488—31nomaximal
7C2×C3×#235—21no—
8C22×C32×C8C2211yescharacteristic
9C2×C3×C4⋊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#63639—21no—
18#63639C2212yescomplemented
19C2×C3⋊(C3⋊C16)—21no—
20C3×#817—21no—
21C3×#817C2212yescomplemented
22C2×C3×#135—31no—
23C2×#904D311yescharacteristic
24C2×C3×#106—31no—
25C2×#817D311yescharacteristic, complemented
26C2×#812—31no—
27C2×#812—31no—
28C2×#812—61no—
29#4566—34no—
30#4488—34no—
31C22×C32×C4D411yescharacteristic
32C2×C3×#67—41no—
33C22×C3×Dic3—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
47C3×C4⋊Dic3—22no—
48C3×C4⋊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×C3×C4⋊C4—61no—
70C2×C4⋊Dic3—21no—
71C2×Dic12Dic311yescharacteristic, complemented
72#904—21no—
73#904—21no—
74#904Dic312yescomplemented
75#904C2×D312yes—
76C2×D24Dic311yescharacteristic, complemented
77C2×#204—21no—
78C3×#106—32no—
79C3×#106—61no—
80#817—21no—
81#817C2×D312yescomplemented
82#812—32no—
83#812—32no—
84#812—62no—
85#812—62no—
86#812—61no—
87#812—61no—
88C2×C3⋊C16—62no—
89C2×C3⋊C16—61no—
90C2×C3⋊C16—61no—
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
99C3×#67—42no—
100C3×#67—42no—
101C2×C3×Dic3—41no—
102C2×C3×Dic3—42no—
103C2×C3×Dic3—82no—
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—91no—
116C2×#106—31no—
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×C4—121no—
128C22×C3×C4#6711yescharacteristic
129C22×C3×C4#6711yescharacteristic
130C2×#67—41no—
131C22×Dic3—41no—
132#235—22no—
133#235—22no—
134#235—41no—
135#235—41no—
136C2×D12—21no—
137C2×C4×D3—41no—
138C2×Dic6—21no—
139C3×Q16—32no—
140C3×Q16—61no—
141C3×SD16—62no—
142C3×SD16—62no—
143C3×D8—32no—
144C3×D8—61no—
145C2×C3×C8—21no—
146C2×C3×C8—21no—
147C2×C3×C8—21no—
148C2×C3×C8—21no—
149C2×C3×C8—21no—
150C2×C3×C8—21no—
151C2×C3×C8C4×D311yescharacteristic
152C2×C3×C8C4×D311yescharacteristic
153C2×C3×C8D1211yescharacteristic
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×C8C22×D311yescharacteristic
162C2×C3×C8C22×D311yescharacteristic
163C3×C4⋊C4—62no—
164C3×C4⋊C4—121no—
165C4⋊Dic3—22no—
166C4⋊Dic3—41no—
167Dic12—21no—
168Dic12C2×Dic312yescomplemented
169D24—21no—
170D24C2×Dic312yescomplemented
171#204—22no—
172#204—22no—
173C3⋊C16—64no—
174C3⋊C16—62no—
175C3⋊C16—62no—
176C22×C32—22no—
177C22×C32#10211yescharacteristic
178C22×C32#10211yescharacteristic
179C22×C32C2×D811yescharacteristic
180C2×C3×D3—42no—
181C2×C3×D3—82no—
182C32×C4#10211yescharacteristic
183C32×C4#10211yescharacteristic
184C32×C4C2×C22⋊C411yescharacteristic
185C32×C4C2×SD1611yescharacteristic
186C3×Dic3—42no—
187C3×Dic3—82no—
188C2×#41—61no—
189#135—32no—
190#135—32no—
191#135—61no—
192#135—61no—
193C2×Q16—31no—
194C2×SD16—61no—
195C2×D8—31no—
196C22×C8D3211yescharacteristic
197C2×C4⋊C4—61no—
198M32—92no—
199M32—181no—
200C2×C16—181no—
201#106—32no—
202#106—61no—
203C23×C3—21no—
204C23×C3—121no—
205C23×C3#21311yescharacteristic
206C23×C3#21311yescharacteristic
207C22×D3—41no—
208C3×Q8—62no—
209C3×Q8—121no—
210C3×D4—62no—
211C3×D4—122no—
212C3×D4—122no—
213C3×D4—121no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—121no—
221C2×C3×C4—122no—
222C2×C3×C4—122no—
223C2×C3×C4—122no—
224C2×C3×C4—242no—
225C2×C3×C4(C2×D3)⋊C411yescharacteristic
226C2×C3×C4(C2×D3)⋊C411yescharacteristic
227C2×C3×C4#21311yescharacteristic
228C2×C3×C4#21311yescharacteristic
229C2×C3×C4#21411yescharacteristic
230C2×C3×C4#21411yescharacteristic
231C2×C3×C4#21511yescharacteristic
232C2×C3×C4#21511yescharacteristic
233C2×C3×C4#21711yescharacteristic
234C2×C3×C4#21711yescharacteristic
235C2×C3×C4C2×#6711yescharacteristic
236C2×C3×C4C2×#6711yescharacteristic
237#67—42no—
238#67—42no—
239C2×Dic3—41no—
240C2×Dic3—42no—
241C2×Dic3—82no—
242D12—22no—
243D12—41no—
244C4×D3—42no—
245C4×D3—42no—
246Dic6—22no—
247Dic6—41no—
248C3×C8—21no—
249C3×C8—21no—
250C3×C8—21no—
251C3×C8—21no—
252C3×C8(C2×D3)⋊C411yescharacteristic
253C3×C8(C2×D3)⋊C411yescharacteristic
254C3×C8#21711yescharacteristic
255C3×C8#21711yescharacteristic
256C3×C8C2×C4×D311yescharacteristic
257C3×C8C2×D1211yescharacteristic
258C3×C8C22×Dic311yescharacteristic
259C3×C8C2×#6711yescharacteristic
260C2×C32—21no—
261C2×C32—21no—
262C2×C32#36012yescomplemented
263C2×C32C2×#10211yescharacteristic
264C3×D3—82no—
265#41—62no—
266#41—62no—
267#41—121no—
268#41—121no—
269C2×Q8—61no—
270C2×D4—61no—
271C2×D4—121no—
272C22×C4—121no—
273C22×C4—121no—
274C22×C4#62511yescharacteristic
275Q16—32no—
276Q16—61no—
277SD16—62no—
278SD16—62no—
279D8—32no—
280D8—61no—
281C2×C8D3×Dic311yescharacteristic
282C2×C8D3×Dic311yescharacteristic
283C2×C8#62511yescharacteristic
284C2×C8#62611yescharacteristic
285C2×C8#62611yescharacteristic
286C2×C8C2×D3211yescharacteristic
287C4⋊C4—62no—
288C4⋊C4—121no—
289C16—182no—
290C22×C3—22no—
291C22×C3—22no—
292C22×C3—21no—
293C22×C3—21no—
294C22×C3—21no—
295C22×C3—42no—
296C22×C3—122no—
297C22×C3—242no—
298C22×C3#80911yescharacteristic
299C22×C3#80911yescharacteristic
300C22×C3#83211yescharacteristic
301C22×C3#83211yescharacteristic
302C22×C3C2×#21311yescharacteristic
303C22×C3C2×#21311yescharacteristic
304C2×D3—42no—
305C2×D3—82no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—122no—
311C3×C4—242no—
312C3×C4#80911yescharacteristic
313C3×C4#80911yescharacteristic
314C3×C4#83211yescharacteristic
315C3×C4#83211yescharacteristic
316C3×C4C2×(C2×D3)⋊C411yescharacteristic
317C3×C4C2×#21411yescharacteristic
318C3×C4C2×#21511yescharacteristic
319C3×C4C2×#21711yescharacteristic
320Dic3—42no—
321Dic3—82no—
322C32C2×#36011yescharacteristic, complemented, Sylow
323C23—121no—
324C23#371311yescharacteristic
325Q8—62no—
326Q8—121no—
327D4—62no—
328D4—122no—
329D4—122no—
330D4—121no—
331C2×C4—121no—
332C2×C4—122no—
333C2×C4—122no—
334C2×C4—122no—
335C2×C4—242no—
336C2×C4#371311yescharacteristic
337C2×C4#371511yescharacteristic
338C2×C4#371511yescharacteristic
339C2×C4(C2×D3)⋊Dic311yescharacteristic
340C2×C4(C2×D3)⋊Dic311yescharacteristic
341C2×C4C2×#62511yescharacteristic
342C8(C2×D3)⋊Dic311yescharacteristic
343C8(C2×D3)⋊Dic311yescharacteristic
344C8C2×D3×Dic311yescharacteristic
345C8C2×#62611yescharacteristic
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—22no—
352C2×C3—41no—
353C2×C3—41no—
354C2×C3—242no—
355C2×C3#448812yescomplemented
356C2×C3#456612yescomplemented
357C2×C3C2×#80911yescharacteristic
358C2×C3C2×#83211yescharacteristic
359D3—82no—
360C22—22no—
361C22—122no—
362C22—242no—
363C22#6356211yescharacteristic
364C22#6356211yescharacteristic
365C22C2×#371311yescharacteristic
366C4—122no—
367C4—242no—
368C4#6356211yescharacteristic
369C4#6356211yescharacteristic
370C4C2×#371511yescharacteristic
371C4C2×(C2×D3)⋊Dic311yescharacteristic
372C3—21no—
373C3C2×#448811yescharacteristic, complemented
374C3C2×#456611yescharacteristic, complemented
375C2—21no—
376C2—21no—
377C2—242no—
378C2#1058912312yesdirect product factor
379C2C2×#6356211yescharacteristic
subgroupG/H
centerC22#63562
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×#63639C2semidirect
3. C2×C3×#817C2semidirect
4. #10589123C2direct (N × H)
10. C2×C3×Dic12C4semidirect
13. C3×#904C4semidirect
15. C2×C3×D24C4semidirect
18. #63639C22semidirect
21. C3×#817C22semidirect
25. C2×#817D3semidirect
50. C3×Dic12C2×C4semidirect
52. C3×D24C2×C4semidirect
71. C2×Dic12Dic3semidirect
74. #904Dic3semidirect
76. C2×D24Dic3semidirect
81. #817C2×D3semidirect
168. Dic12C2×Dic3semidirect
170. D24C2×Dic3semidirect
262. C2×C32#360semidirect
322. C32C2×#360semidirect
355. C2×C3#4488semidirect
356. C2×C3#4566semidirect
373. C3C2×#4488semidirect
374. C3C2×#4566semidirect
378. C2#10589123direct (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×#636392
C2×C3×#8172
#105891232
C2×#45663
C2×#44883