Finite Group Databasebeta

← C2×#10590299 #11858758

Subgroups — C2×#10590299 #11858758

Order 1152.

1225 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C42×C3⋊D3C211yesmaximal, characteristic
2C2×C3×#803C212yesmaximal, complemented
3C2×#63572C212yesmaximal, complemented
4C2×#63557C212yesmaximal
5#10590299C218yesmaximal, direct product factor
6C2×#4705—32nomaximal
7C22×C4×C3⋊D3C411yescharacteristic
8C22×C4×C3⋊D3C411yescharacteristic
9C22×C4×C3⋊D3C2211yescharacteristic
10C2×C32×C42C2211yescharacteristic
11C2×C4×C3⋊Dic3C411yescharacteristic
12C2×C4×C3⋊Dic3C411yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C42×C3⋊D3C414yes—
15C42×C3⋊D3C2214yes—
16C22×C3×C3⋊C8C2214yes—
17C3×#803C2218yescomplemented
18#63572C2218yescomplemented
19#63557C2218yes—
20C2×C42×D3—32no—
21C2×C42×D3—61no—
22C2×C3×#97—32no—
23C2×(C2×D3)⋊C8—34no—
24C2×Dic3⋊C8—34no—
25C2×#803D312yescomplemented
26#4705—316no—
27C23×C3⋊D3C2×C411yescharacteristic
28C22×C32×C4C2×C411yescharacteristic
29C22×C32×C4C2×C411yescharacteristic
30C22×C32×C4C2311yescharacteristic
31C22×C3⋊Dic3C2×C411yescharacteristic
32C22×C3⋊Dic3C2×C411yescharacteristic
33C22×C3⋊Dic3C2×C411yescharacteristic
34C2×C4×C3⋊D3—24no—
35C2×C4×C3⋊D3—24no—
36C2×C4×C3⋊D3—24no—
37C2×C4×C3⋊D3C2×C412yes—
38C2×C4×C3⋊D3C2×C414yes—
39C2×C4×C3⋊D3C2×C414yes—
40C2×C4×C3⋊D3C2312yes—
41C32×C42C2×C412yes—
42C32×C42C2312yes—
43C4×C3⋊Dic3C2×C412yes—
44C4×C3⋊Dic3C2×C414yes—
45C4×C3⋊Dic3C2×C414yes—
46C4×C3⋊Dic3C2312yes—
47C2×C3×C3⋊C8—28no—
48C2×C3×C3⋊C8C2318yes—
49C2×#432—91noSylow
50C22×C4×D3—32no—
51C22×C4×D3—32no—
52C22×C4×D3—32no—
53C22×C4×D3—61no—
54C22×C4×D3—61no—
55C22×C4×D3—61no—
56C22×C3×C8—34no—
57C2×C3×C42—21no—
58C2×C3×C42C2×D312yes—
59C2×C4×Dic3—32no—
60C2×C4×Dic3—32no—
61C2×C4×Dic3—32no—
62C2×C4×Dic3—61no—
63C2×C4×Dic3—61no—
64C2×C4×Dic3—61no—
65C22×C3⋊C8C2×D314yes—
66C42×D3—38no—
67C42×D3—38no—
68C42×D3—64no—
69C42×D3—64no—
70C3×#97—38no—
71(C2×D3)⋊C8—316no—
72Dic3⋊C8—316no—
73#803C2×D318yescomplemented
74C23×C32C22×C411yescharacteristic
75C22×C3⋊D3—22no—
76C22×C3⋊D3—22no—
77C22×C3⋊D3M1614yes—
78C22×C3⋊D3C22×C412yes—
79C2×C32×C4—22no—
80C2×C32×C4—22no—
81C2×C32×C4C22×C412yes—
82C2×C32×C4C22×C412yes—
83C2×C32×C4C22×C411yescharacteristic
84C2×C32×C4#4114yes—
85C2×C32×C4C2411yescharacteristic
86C2×C3⋊Dic3—22no—
87C2×C3⋊Dic3—22no—
88C2×C3⋊Dic3M1614yes—
89C2×C3⋊Dic3C22×C412yes—
90C2×C3⋊Dic3C22×C412yes—
91C2×C3⋊Dic3C22×C412yes—
92C4×C3⋊D3—28no—
93C4×C3⋊D3—24no—
94C4×C3⋊D3—24no—
95C4×C3⋊D3—28no—
96C3×C3⋊C8—28no—
97C22×C42—91no—
98#432—98no—
99C2×C4⋊C8—92no—
100C2×C22⋊C8—92no—
101C2×#97—32no—
102C23×D3—32no—
103C23×D3—61no—
104C22×C3×C4—21no—
105C22×C3×C4—21no—
106C22×C3×C4—21no—
107C22×C3×C4C4×D312yes—
108C22×C3×C4C4×D312yes—
109C22×C3×C4C22×D312yes—
110C22×Dic3—32no—
111C22×Dic3—32no—
112C22×Dic3—32no—
113C22×Dic3—61no—
114C22×Dic3—61no—
115C22×Dic3—61no—
116C2×C4×D3—38no—
117C2×C4×D3—38no—
118C2×C4×D3—34no—
119C2×C4×D3—34no—
120C2×C4×D3—62no—
121C2×C4×D3—64no—
122C2×C4×D3—64no—
123C2×C4×D3—62no—
124C2×C4×D3—68no—
125C2×C4×D3—68no—
126C2×C4×D3—68no—
127C2×C4×D3—68no—
128C2×C4×D3—68no—
129C2×C4×D3—68no—
130C2×C3×C8—38no—
131C2×C3×C8—68no—
132C3×C42—22no—
133C3×C42—22no—
134C3×C42C4×D314yes—
135C3×C42C22×D314yes—
136C4×Dic3—38no—
137C4×Dic3—34no—
138C4×Dic3—38no—
139C4×Dic3—34no—
140C4×Dic3—62no—
141C4×Dic3—64no—
142C4×Dic3—64no—
143C4×Dic3—62no—
144C2×C3⋊C8—28no—
145C2×C3⋊C8C22×D318yes—
146C22×C32#11712yes—
147C22×C32C2×M1612yes—
148C22×C32C2×M1612yes—
149C22×C32C23×C411yescharacteristic
150C2×C3⋊D3—22no—
151C2×C3⋊D3—22no—
152C2×C3⋊D3—28no—
153C2×C3⋊D3C2×M1614yes—
154C32×C4—22no—
155C32×C4—22no—
156C32×C4#11712yes—
157C32×C4C2×#4112yes—
158C3⋊Dic3—22no—
159C3⋊Dic3—22no—
160C3⋊Dic3C2×M1614yes—
161C23×C4—91no—
162C23×C4—91no—
163C23×C4—91no—
164C22×C8—34no—
165C2×C42—91no—
166C2×C42—91no—
167C2×C42—91no—
168C2×C42—94no—
169C2×C42—94no—
170C2×C42D3211yescharacteristic
171C4⋊C8—98no—
172C22⋊C8—98no—
173#97—38no—
174C23×C3—21no—
175C23×C3C2×C4×D312yes—
176C22×D3—38no—
177C22×D3—34no—
178C22×D3—64no—
179C22×D3—62no—
180C22×D3—64no—
181C22×D3—64no—
182C22×D3—64no—
183C22×D3—64no—
184C2×C3×C4—24no—
185C2×C3×C4—24no—
186C2×C3×C4—24no—
187C2×C3×C4—24no—
188C2×C3×C4—21no—
189C2×C3×C4—24no—
190C2×C3×C4—22no—
191C2×C3×C4—22no—
192C2×C3×C4—21no—
193C2×C3×C4C2×C4×D314yes—
194C2×C3×C4C2×C4×D314yes—
195C2×C3×C4C2×C4×D312yes—
196C2×C3×C4#23518yes—
197C2×C3×C4C23×D312yes—
198C2×Dic3—38no—
199C2×Dic3—34no—
200C2×Dic3—34no—
201C2×Dic3—34no—
202C2×Dic3—64no—
203C2×Dic3—62no—
204C2×Dic3—62no—
205C2×Dic3—62no—
206C2×Dic3—64no—
207C2×Dic3—64no—
208C2×Dic3—64no—
209C2×Dic3—64no—
210C4×D3—616no—
211C4×D3—616no—
212C4×D3—616no—
213C4×D3—616no—
214C4×D3—68no—
215C4×D3—68no—
216C4×D3—68no—
217C4×D3—68no—
218C3×C8—68no—
219C3⋊C8—28no—
220C2×C32#43214yescomplemented
221C2×C32C2×#11711yescharacteristic
222C2×C32C22×M1611yescharacteristic
223C2×C32C22×M1611yescharacteristic
224C3⋊D3—24no—
225C24—91no—
226C22×C4—91no—
227C22×C4—91no—
228C22×C4—91no—
229C22×C4—92no—
230C22×C4—94no—
231C22×C4—94no—
232C22×C4—92no—
233C22×C4—184no—
234C22×C4—184no—
235C22×C4—184no—
236C22×C4#62411yescharacteristic
237C22×C4#62411yescharacteristic
238C22×C4C2×D3211yescharacteristic
239C2×C8—38no—
240C2×C8—68no—
241C42—92no—
242C42—94no—
243C42—92no—
244C42—94no—
245C42#62412yes—
246C42C2×D3212yes—
247C22×C3—21no—
248C22×C3—22no—
249C22×C3—22no—
250C22×C3—22no—
251C22×C3#87214yes—
252C22×C3D3×M1614yes—
253C22×C3D3×M1614yes—
254C22×C3C22×C4×D312yes—
255C2×D3—38no—
256C2×D3—64no—
257C2×D3—64no—
258C2×D3—64no—
259C2×D3—616no—
260C2×D3—64no—
261C2×D3—616no—
262C2×D3—64no—
263C3×C4—24no—
264C3×C4—24no—
265C3×C4—24no—
266C3×C4—24no—
267C3×C4—22no—
268C3×C4—22no—
269C3×C4#87214yes—
270C3×C4C2×#23514yes—
271Dic3—38no—
272Dic3—64no—
273Dic3—64no—
274Dic3—64no—
275Dic3—64no—
276Dic3—64no—
277C32C2×#43211yescharacteristic, complemented, Sylow
278C23—92no—
279C23—94no—
280C23—182no—
281C23—182no—
282C23C2×#62411yescharacteristic
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—92no—
286C2×C4—94no—
287C2×C4—92no—
288C2×C4—92no—
289C2×C4—188no—
290C2×C4—188no—
291C2×C4—182no—
292C2×C4—182no—
293C2×C4—184no—
294C2×C4—184no—
295C2×C4#379814yes—
296C2×C4C2×#62412yes—
297C2×C4C2×#62412yes—
298C2×C4C2×#62411yescharacteristic
299C2×C4C22×D3211yescharacteristic
300C8—68no—
301C2×C3—21no—
302C2×C3—24no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3#470518yescomplemented
306C2×C3C2×#87212yes—
307C2×C3C2×D3×M1612yes—
308C2×C3C2×D3×M1612yes—
309D3—68no—
310D3—68no—
311C22—94no—
312C22—182no—
313C22—188no—
314C22—182no—
315C22#6381812yes—
316C22#6381812yes—
317C22#6387412yes—
318C22C22×#62411yescharacteristic
319C4—22no—
320C4—22no—
321C4—94no—
322C4—182no—
323C4—182no—
324C4#6387412yes—
325C4C2×#379812yes—
326C3—21no—
327C3C2×#470512yescomplemented
328C2—184no—
329C2#1059029914yesdirect product factor
330C2C2×#6381811yescharacteristic
331C2C2×#6381811yescharacteristic
332C2C2×#6387411yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC23×C32C22×C4
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C32×C4C24
hypercenterC2×C42D32
hypocenterC32C2×#432
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×#803C2semidirect
3. C2×#63572C2semidirect
5. #10590299C2direct (N × H)
17. C3×#803C22semidirect
18. #63572C22semidirect
25. C2×#803D3semidirect
73. #803C2×D3semidirect
220. C2×C32#432semidirect
277. C32C2×#432semidirect
305. C2×C3#4705semidirect
327. C3C2×#4705semidirect
329. C2#10590299direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C42×C3⋊D32
C2×C3×#8032
C2×#635722
C2×#635572
#105902992
C2×#47053