Finite Group Databasebeta

← C2×#10590256 #11858722

Subgroups — C2×#10590256 #11858722

Order 1152.

1305 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C42×C3⋊D3C211yesmaximal, characteristic
2C2×C3×C4⋊(C3⋊C8)C212yesmaximal, complemented
3C2×#63557C212yesmaximal
4C2×#63553C212yesmaximal, complemented
5#10590256C218yesmaximal, direct product factor
6C2×#4833—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×C4⋊(C3⋊C8)C2218yescomplemented
18#63557C2218yes—
19#63553C2218yescomplemented
20C2×C42×D3—32no—
21C2×C42×D3—61no—
22C2×C3×C4⋊C8—32no—
23C2×(C2×D3)⋊C8—34no—
24C2×C8×Dic3—34no—
25C2×C4⋊(C3⋊C8)D312yescomplemented
26#4833—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⋊D3C818yescomplemented
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×#431—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×C4⋊C8—38no—
71(C2×D3)⋊C8—316no—
72C8×Dic3—316no—
73C4⋊(C3⋊C8)C2×D318yescomplemented
74C23×C32C22×C411yescharacteristic
75C22×C3⋊D3—22no—
76C22×C3⋊D3—22no—
77C22×C3⋊D3C2×C814yes—
78C22×C3⋊D3C22×C412yes—
79C2×C32×C4—22no—
80C2×C32×C4C2×C814yes—
81C2×C32×C4C22×C412yes—
82C2×C32×C4C22×C411yescharacteristic
83C2×C32×C4C22×C412yes—
84C2×C32×C4#4114yes—
85C2×C32×C4C2411yescharacteristic
86C2×C3⋊Dic3—22no—
87C2×C3⋊Dic3C2×C814yes—
88C2×C3⋊Dic3M1614yes—
89C2×C3⋊Dic3C22×C412yes—
90C2×C3⋊Dic3C22×C412yes—
91C2×C3⋊Dic3C22×C412yes—
92C4×C3⋊D3—24no—
93C4×C3⋊D3—24no—
94C4×C3⋊D3—28no—
95C4×C3⋊D3C2×C8116yescomplemented
96C3×C3⋊C8—28no—
97C22×C42—91no—
98#431—98no—
99C2×C4⋊C8—32no—
100C2×C22⋊C8—92no—
101C2×C4×C8—92no—
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—316no—
117C2×C4×D3—38no—
118C2×C4×D3—38no—
119C2×C4×D3—34no—
120C2×C4×D3—34no—
121C2×C4×D3—64no—
122C2×C4×D3—62no—
123C2×C4×D3—64no—
124C2×C4×D3—62no—
125C2×C4×D3—68no—
126C2×C4×D3—68no—
127C2×C4×D3—68no—
128C2×C4×D3—68no—
129C2×C4×D3—64no—
130C2×C4×D3—64no—
131C2×C3×C8—38no—
132C2×C3×C8—68no—
133C3×C42—22no—
134C3×C42—22no—
135C3×C42C4×D314yes—
136C3×C42C22×D314yes—
137C4×Dic3—34no—
138C4×Dic3—38no—
139C4×Dic3—38no—
140C4×Dic3—34no—
141C4×Dic3—62no—
142C4×Dic3—64no—
143C4×Dic3—64no—
144C4×Dic3—62no—
145C2×C3⋊C8—28no—
146C2×C3⋊C8C22×D318yes—
147C22×C32#11712yes—
148C22×C32C22×C812yes—
149C22×C32C2×M1612yes—
150C22×C32C23×C411yescharacteristic
151C2×C3⋊D3—22no—
152C2×C3⋊D3—22no—
153C2×C3⋊D3—28no—
154C2×C3⋊D3C22×C814yes—
155C32×C4—22no—
156C32×C4#11712yes—
157C32×C4C22×C814yes—
158C32×C4C2×#4112yes—
159C3⋊Dic3—22no—
160C3⋊Dic3C22×C814yes—
161C3⋊Dic3C2×M1614yes—
162C23×C4—91no—
163C23×C4—91no—
164C23×C4—91no—
165C22×C8—34no—
166C2×C42—91no—
167C2×C42—91no—
168C2×C42—91no—
169C2×C42—94no—
170C2×C42—94no—
171C2×C42D3211yescharacteristic
172C4⋊C8—38no—
173C22⋊C8—98no—
174C4×C8—98no—
175C23×C3—21no—
176C23×C3C2×C4×D312yes—
177C22×D3—38no—
178C22×D3—34no—
179C22×D3—64no—
180C22×D3—62no—
181C22×D3—64no—
182C22×D3—64no—
183C22×D3—64no—
184C22×D3—64no—
185C2×C3×C4—24no—
186C2×C3×C4—24no—
187C2×C3×C4—21no—
188C2×C3×C4—24no—
189C2×C3×C4—24no—
190C2×C3×C4—22no—
191C2×C3×C4—22no—
192C2×C3×C4—21no—
193C2×C3×C4D3×C818yes—
194C2×C3×C4C2×C4×D314yes—
195C2×C3×C4C2×C4×D312yes—
196C2×C3×C4C2×C4×D314yes—
197C2×C3×C4#23714yes—
198C2×C3×C4#23914yes—
199C2×C3×C4C23×D312yes—
200C2×Dic3—38no—
201C2×Dic3—38no—
202C2×Dic3—34no—
203C2×Dic3—34no—
204C2×Dic3—34no—
205C2×Dic3—64no—
206C2×Dic3—64no—
207C2×Dic3—62no—
208C2×Dic3—62no—
209C2×Dic3—62no—
210C2×Dic3—64no—
211C2×Dic3—64no—
212C4×D3—332no—
213C4×D3—616no—
214C4×D3—616no—
215C4×D3—616no—
216C4×D3—68no—
217C4×D3—68no—
218C4×D3—68no—
219C4×D3—64no—
220C4×D3—64no—
221C3×C8—68no—
222C3⋊C8—28no—
223C2×C32#43114yescomplemented
224C2×C32C2×#11711yescharacteristic
225C2×C32C23×C811yescharacteristic
226C2×C32C22×M1611yescharacteristic
227C3⋊D3—24no—
228C24—91no—
229C22×C4—91no—
230C22×C4—91no—
231C22×C4—98no—
232C22×C4—94no—
233C22×C4—91no—
234C22×C4—92no—
235C22×C4—94no—
236C22×C4—92no—
237C22×C4—184no—
238C22×C4—184no—
239C22×C4#62411yescharacteristic
240C22×C4#62411yescharacteristic
241C22×C4C2×D3211yescharacteristic
242C2×C8—38no—
243C2×C8—68no—
244C42—92no—
245C42—92no—
246C42—94no—
247C42—94no—
248C42#62412yes—
249C42C2×D3212yes—
250C22×C3—21no—
251C22×C3—22no—
252C22×C3—22no—
253C22×C3—22no—
254C22×C3#89214yes—
255C22×C3C2×D3×C814yes—
256C22×C3D3×M1614yes—
257C22×C3C22×C4×D312yes—
258C2×D3—38no—
259C2×D3—64no—
260C2×D3—64no—
261C2×D3—64no—
262C2×D3—616no—
263C2×D3—64no—
264C2×D3—64no—
265C2×D3—616no—
266C3×C4—24no—
267C3×C4—24no—
268C3×C4—22no—
269C3×C4—24no—
270C3×C4—22no—
271C3×C4#89214yes—
272C3×C4C2×D3×C818yes—
273C3×C4C2×#23712yes—
274C3×C4C2×#23912yes—
275Dic3—38no—
276Dic3—38no—
277Dic3—64no—
278Dic3—64no—
279Dic3—64no—
280Dic3—64no—
281C32C2×#43111yescharacteristic, complemented, Sylow
282C23—92no—
283C23—94no—
284C23—182no—
285C23—182no—
286C23C2×#62411yescharacteristic
287C2×C4—22no—
288C2×C4—92no—
289C2×C4—92no—
290C2×C4—94no—
291C2×C4—94no—
292C2×C4—916no—
293C2×C4—92no—
294C2×C4—188no—
295C2×C4—182no—
296C2×C4—184no—
297C2×C4—184no—
298C2×C4#371014yes—
299C2×C4#379614yes—
300C2×C4C2×#62412yes—
301C2×C4C2×#62412yes—
302C2×C4C2×#62411yescharacteristic
303C2×C4C22×D3211yescharacteristic
304C8—68no—
305C2×C3—21no—
306C2×C3—24no—
307C2×C3—21no—
308C2×C3—21no—
309C2×C3#483318yescomplemented
310C2×C3C2×#89212yes—
311C2×C3C22×D3×C812yes—
312C2×C3C2×D3×M1612yes—
313D3—68no—
314D3—68no—
315C22—94no—
316C22—182no—
317C22—188no—
318C22—182no—
319C22C2×#371012yes—
320C22#6381812yes—
321C22#6384912yes—
322C22C22×#62411yescharacteristic
323C4—22no—
324C4—94no—
325C4—94no—
326C4—182no—
327C4C2×#371014yes—
328C4#6384912yes—
329C4C2×#379612yes—
330C3—21no—
331C3C2×#483312yescomplemented
332C2—184no—
333C2#1059025614yesdirect product factor
334C2C22×#371011yescharacteristic
335C2C2×#6381811yescharacteristic
336C2C2×#6384911yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC2×C32C23×C8
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC23×C32C22×C4
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C32×C4C24
hypercenterC2×C42D32
hypocenterC32C2×#431
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4⋊(C3⋊C8)C2semidirect
4. C2×#63553C2semidirect
5. #10590256C2direct (N × H)
17. C3×C4⋊(C3⋊C8)C22semidirect
19. #63553C22semidirect
25. C2×C4⋊(C3⋊C8)D3semidirect
36. C2×C4×C3⋊D3C8semidirect
73. C4⋊(C3⋊C8)C2×D3semidirect
95. C4×C3⋊D3C2×C8semidirect
223. C2×C32#431semidirect
281. C32C2×#431semidirect
309. C2×C3#4833semidirect
331. C3C2×#4833semidirect
333. C2#10590256direct (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×C4⋊(C3⋊C8)2
C2×#635572
C2×#635532
#105902562
C2×#48333