Finite Group Databasebeta

← C2×#10590707 #11858440

Subgroups — C2×#10590707 #11858440

Order 1152.

1089 conjugacy classes of subgroups.

The subgroup lattice has 355 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×C8C211yesmaximal, characteristic
2C2×#63841C212yesmaximal
3C2×#63645C211yesmaximal, characteristic, complemented
4C2×C3×#818C211yesmaximal, characteristic, complemented
5C2×#63573C212yesmaximal, complemented
6#10590707C218yesmaximal, direct product factor
7C2×#5106—31nomaximal
8C2×#4880—31nomaximal
9C22×C3×C4×D3C2211yescharacteristic
10C22×C32×C8C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2212yes—
12C2×C3×C4⋊Dic3C2212yes—
13C22×C3×C3⋊C8C2211yescharacteristic
14C2×C3×D3×C8C418yescomplemented
15C2×C3×D3×C8C2214yes—
16C2×(C2×D3)⋊Dic3—22no—
17C2×Dic32—22no—
18#63841—24no—
19#63841C2218yes—
20#63645C2214yescomplemented
21C3×#818C2214yescomplemented
22#63573C2218yescomplemented
23C23×C3×C8—31no—
24C2×#926—32no—
25C22×D3×C8D311yescharacteristic
26C2×#892—32no—
27C2×C3×#107—31no—
28#5106—38no—
29C2×#818—31no—
30C2×#818—31no—
31C2×#818—61no—
32C2×#818D311yescharacteristic, complemented
33C2×#817—32no—
34C2×#808—32no—
35#4880—38no—
36C23×C3×D3D411yescharacteristic
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3—22no—
39C22×C3×Dic3—22no—
40C22×C3×Dic3D411yescharacteristic
41C2×C3×C4×D3C2×C414yes—
42C2×C3×C4×D3D412yes—
43C2×C3×C4×D3Q814yes—
44C2×C3×C4×D3C2312yes—
45C2×C32×C8C2×C414yes—
46C2×C32×C8C2312yes—
47C4⋊(C3⋊Dic3)—22no—
48C4⋊(C3⋊Dic3)C2314yes—
49C3×C4⋊Dic3—22no—
50C3×C4⋊Dic3C2314yes—
51C2×C3×C3⋊C8C2×C414yes—
52C2×C3×C3⋊C8C2312yes—
53C3×D3×C8C2×C4116yescomplemented
54(C2×D3)⋊Dic3—28no—
55Dic32—28no—
56C2×#427—91noSylow
57C23×C3×C4—31no—
58C22×C4×D3C2×D311yescharacteristic
59C22×C3×C8—21no—
60C22×C3×C8—31no—
61C22×C3×C8—38no—
62C22×C3×C8—34no—
63C22×C3×C8C2×D311yescharacteristic
64C22×C3×C8C2×D311yescharacteristic
65C2×C3×C4⋊C4—32no—
66C2×#217—62no—
67C2×(C2×D3)⋊C4—62no—
68#926—38no—
69#926—64no—
70C2×C4⋊Dic3—32no—
71C2×C4⋊Dic3—32no—
72C2×C4⋊Dic3—62no—
73C2×C4⋊Dic3C2×D312yes—
74C2×C4×Dic3—62no—
75C2×C4×Dic3—62no—
76C22×C3⋊C8C2×D311yescharacteristic
77C2×D3×C8Dic318yescomplemented
78C2×D3×C8C2×D314yes—
79#892—38no—
80#892—64no—
81C3×#107—34no—
82#818—34no—
83#818—34no—
84#818—64no—
85#818C2×D314yescomplemented
86#817—38no—
87#808—38no—
88C23×C32C2×D411yescharacteristic
89C22×C3×D3—22no—
90C22×C3×D3—22no—
91C22×C3×D3C4⋊C414yes—
92C22×C3×D3C2×D412yes—
93C2×C32×C4C22×C412yes—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×Q812yes—
96C2×C32×C4C2411yescharacteristic
97C2×C3⋊Dic3—24no—
98C2×C3⋊Dic3—44no—
99C2×C3×Dic3—24no—
100C2×C3×Dic3—44no—
101C2×C3×Dic3C4⋊C414yes—
102C2×C3×Dic3C2×D412yes—
103C3×C4×D3C4⋊C418yes—
104C3×C4×D3C22×C414yes—
105C3×C4×D3C2×Q814yes—
106C32×C8C22×C414yes—
107C3×C3⋊C8C22×C414yes—
108C23×C8—31no—
109C2×#117—92no—
110#427—98no—
111C2×#107—31no—
112C2×#107—91no—
113C2×#106—92no—
114C24×C3—31no—
115C23×D3D1211yescharacteristic
116C22×C3×C4—21no—
117C22×C3×C4—31no—
118C22×C3×C4—34no—
119C22×C3×C4—32no—
120C22×C3×C4—34no—
121C22×C3×C4—32no—
122C22×C3×C4—62no—
123C22×C3×C4C22×D311yescharacteristic
124C22×C3×C4C22×D311yescharacteristic
125C22×Dic3—22no—
126C22×Dic3—62no—
127C22×Dic3—62no—
128C22×Dic3—122no—
129C22×Dic3D1211yescharacteristic
130C2×C4×D3Dic614yes—
131C2×C4×D3D1212yes—
132C2×C4×D3C2×Dic314yes—
133C2×C4×D3C22×D312yes—
134C2×C3×C8—24no—
135C2×C3×C8—22no—
136C2×C3×C8—34no—
137C2×C3×C8—32no—
138C2×C3×C8—316no—
139C2×C3×C8C4×D314yes—
140C2×C3×C8C2×Dic314yes—
141C2×C3×C8C22×D312yes—
142C2×C3×C8C22×D312yes—
143C3×C4⋊C4—34no—
144C3×C4⋊C4—62no—
145#217—68no—
146(C2×D3)⋊C4—68no—
147C4⋊Dic3—22no—
148C4⋊Dic3—34no—
149C4⋊Dic3—34no—
150C4⋊Dic3—64no—
151C4⋊Dic3—62no—
152C4⋊Dic3—62no—
153C4⋊Dic3—122no—
154C4⋊Dic3C22×D314yes—
155C4×Dic3—68no—
156C4×Dic3—68no—
157C2×C3⋊C8C2×Dic314yes—
158C2×C3⋊C8C22×D312yes—
159D3×C8C2×Dic3116yescomplemented
160C22×C32C2×C4⋊C412yes—
161C22×C32#13512yes—
162C22×C32#13512yes—
163C22×C32C22×D411yescharacteristic
164C2×C3×D3—22no—
165C2×C3×D3—22no—
166C2×C3×D3—28no—
167C2×C3×D3C2×C4⋊C414yes—
168C32×C4C2×C4⋊C412yes—
169C32×C4C23×C411yescharacteristic
170C32×C4C22×Q811yescharacteristic
171C3⋊Dic3—44no—
172C3×Dic3—44no—
173C3×Dic3C2×C4⋊C414yes—
174C23×C4—31no—
175C22×C8—31no—
176C22×C8—38no—
177C22×C8—34no—
178C22×C8D3211yescharacteristic
179#117—98no—
180#117—184no—
181C2×C4⋊C4—32no—
182C2×C4⋊C4—92no—
183C2×C22⋊C4—182no—
184C2×C42—182no—
185#107—34no—
186#107—94no—
187#106—98no—
188C23×C3—21no—
189C23×C3—34no—
190C23×C3—32no—
191C23×C3—62no—
192C23×C3—62no—
193C23×C3C2×D1211yescharacteristic
194C23×C3D3×D411yescharacteristic
195C22×D3—22no—
196C22×D3—22no—
197C22×D3C4⋊Dic314yes—
198C22×D3C2×D1212yes—
199C2×C3×C4—21no—
200C2×C3×C4—22no—
201C2×C3×C4—21no—
202C2×C3×C4—22no—
203C2×C3×C4—34no—
204C2×C3×C4—32no—
205C2×C3×C4—38no—
206C2×C3×C4—34no—
207C2×C3×C4—34no—
208C2×C3×C4—64no—
209C2×C3×C4—124no—
210C2×C3×C4C2×Dic612yes—
211C2×C3×C4C2×C4×D312yes—
212C2×C3×C4C2×D1211yescharacteristic
213C2×C3×C4D3×D411yescharacteristic
214C2×C3×C4D3×Q812yes—
215C2×C3×C4C22×Dic312yes—
216C2×C3×C4C23×D311yescharacteristic
217C2×C3×C4C23×D311yescharacteristic
218C2×Dic3—24no—
219C2×Dic3—44no—
220C2×Dic3—64no—
221C2×Dic3—64no—
222C2×Dic3—124no—
223C2×Dic3—124no—
224C2×Dic3—124no—
225C2×Dic3—244no—
226C2×Dic3C4⋊Dic314yes—
227C2×Dic3C2×D1212yes—
228C4×D3C4⋊Dic318yes—
229C4×D3C2×Dic614yes—
230C4×D3C22×Dic314yes—
231C3×C8—24no—
232C3×C8—34no—
233C3×C8C2×C4×D314yes—
234C3×C8C22×Dic314yes—
235C3⋊C8C22×Dic314yes—
236C2×C32#42714yescomplemented
237C2×C32C22×C4⋊C411yescharacteristic
238C2×C32C2×#13511yescharacteristic
239C2×C32C2×#13511yescharacteristic
240C3×D3—24no—
241C24—31no—
242C22×C4—31no—
243C22×C4—32no—
244C22×C4—34no—
245C22×C4—32no—
246C22×C4—34no—
247C22×C4—62no—
248C22×C4—182no—
249C22×C4C2×D3211yescharacteristic
250C2×C8—32no—
251C2×C8—34no—
252C2×C8—316no—
253C2×C8D3×Dic314yes—
254C2×C8C2×D3212yes—
255C4⋊C4—34no—
256C4⋊C4—62no—
257C4⋊C4—94no—
258C4⋊C4—182no—
259C22⋊C4—188no—
260C42—188no—
261C22×C3—21no—
262C22×C3—22no—
263C22×C3—22no—
264C22×C3—22no—
265C22×C3—34no—
266C22×C3—68no—
267C22×C3—62no—
268C22×C3—62no—
269C22×C3D3×C4⋊C412yes—
270C22×C3#90412yes—
271C22×C3#90412yes—
272C22×C3#91212yes—
273C22×C3#91912yes—
274C22×C3C2×C4⋊Dic312yes—
275C22×C3C22×D1211yescharacteristic
276C22×C3C2×D3×D411yescharacteristic
277C2×D3—22no—
278C2×D3—22no—
279C2×D3—28no—
280C2×D3C2×C4⋊Dic314yes—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—22no—
284C3×C4—34no—
285C3×C4—124no—
286C3×C4D3×C4⋊C412yes—
287C3×C4C2×C4⋊Dic312yes—
288C3×C4C22×Dic611yescharacteristic
289C3×C4C22×C4×D311yescharacteristic
290C3×C4C2×D3×Q811yescharacteristic
291C3×C4C23×Dic311yescharacteristic
292Dic3—44no—
293Dic3—124no—
294Dic3—124no—
295Dic3—244no—
296Dic3C2×C4⋊Dic314yes—
297C32C2×#42711yescharacteristic, complemented, Sylow
298C23—32no—
299C23—34no—
300C23—62no—
301C23—62no—
302C23D3×D1211yescharacteristic
303C2×C4—32no—
304C2×C4—34no—
305C2×C4—34no—
306C2×C4—34no—
307C2×C4—38no—
308C2×C4—64no—
309C2×C4—124no—
310C2×C4—184no—
311C2×C4—364no—
312C2×C4D3×Dic612yes—
313C2×C4D3×D1211yescharacteristic
314C2×C4C2×D3×Dic312yes—
315C2×C4C22×D3211yescharacteristic
316C8—34no—
317C8C2×D3×Dic314yes—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—24no—
322C2×C3—64no—
323C2×C3#488014yescomplemented
324C2×C3#510614yescomplemented
325C2×C3C2×D3×C4⋊C411yescharacteristic
326C2×C3C2×#90411yescharacteristic
327C2×C3C2×#90411yescharacteristic
328C2×C3C2×#91211yescharacteristic
329C2×C3C2×#91911yescharacteristic
330C2×C3C22×C4⋊Dic311yescharacteristic
331D3—24no—
332C22—34no—
333C22—62no—
334C22—62no—
335C22—68no—
336C22#6380712yes—
337C22#6380812yes—
338C22D3×C4⋊Dic312yes—
339C22C2×D3×D1211yescharacteristic
340C4—34no—
341C4—124no—
342C4—364no—
343C4D3×C4⋊Dic312yes—
344C4C2×D3×Dic611yescharacteristic
345C4C22×D3×Dic311yescharacteristic
346C3—21no—
347C3C2×#488011yescharacteristic, complemented
348C3C2×#510611yescharacteristic, complemented
349C2—64no—
350C2#1059070714yesdirect product factor
351C2C2×#6380711yescharacteristic
352C2C2×#6380811yescharacteristic
353C2C2×D3×C4⋊Dic311yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C2×#427
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. C2×#63645C2semidirect
4. C2×C3×#818C2semidirect
5. C2×#63573C2semidirect
6. #10590707C2direct (N × H)
14. C2×C3×D3×C8C4semidirect
20. #63645C22semidirect
21. C3×#818C22semidirect
22. #63573C22semidirect
32. C2×#818D3semidirect
53. C3×D3×C8C2×C4semidirect
77. C2×D3×C8Dic3semidirect
85. #818C2×D3semidirect
159. D3×C8C2×Dic3semidirect
236. C2×C32#427semidirect
297. C32C2×#427semidirect
323. C2×C3#4880semidirect
324. C2×C3#5106semidirect
347. C3C2×#4880semidirect
348. C3C2×#5106semidirect
350. C2#10590707direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×C82
C2×#638412
C2×#636452
C2×C3×#8182
C2×#635732
#105907072
C2×#51063
C2×#48803