Finite Group Databasebeta

← C2×#10590658 #11858223

Subgroups — C2×#10590658 #11858223

Order 1152.

1449 conjugacy classes of subgroups.

The subgroup lattice has 343 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C8×C3⋊D3C211yesmaximal, characteristic
2C2×C4×#624C211yesmaximal, characteristic
3C22×#3710C211yesmaximal, characteristic
4C2×C3×Dic3⋊C8C212yesmaximal, complemented
5C2×Dic3⋊(C3⋊C8)C212yesmaximal, complemented
6#10590658C218yesmaximal, direct product factor
7C2×D3×C4⋊C8—32nomaximal
8C22×C4×C3⋊D3C2211yescharacteristic
9C22×#624C411yescharacteristic
10C22×#624C411yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C2×C8×C3⋊D3—24no—
14C2×C8×C3⋊D3C2214yes—
15C2×C3×C4×Dic3C2212yes—
16C22×C3×C3⋊C8C2212yes—
17C2×Dic32C412yes—
18C4×#624C414yes—
19C4×#624C2214yes—
20C2×#3710—24no—
21C2×#3710C2214yes—
22C3×Dic3⋊C8C2218yescomplemented
23Dic3⋊(C3⋊C8)C2218yescomplemented
24C22×D3×C8—32no—
25C22×D3×C8—32no—
26C22×D3×C8—61no—
27C2×C42×D3—32no—
28C2×C3×C4⋊C8—32no—
29C2×Dic3⋊C8—32no—
30C2×Dic3⋊C8D312yescomplemented
31C2×C4⋊(C3⋊C8)—32no—
32D3×C4⋊C8—316no—
33C23×C3⋊D3C2×C411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3C2×C411yescharacteristic
36C2×C4×C3⋊D3C2×C412yes—
37C2×C4×C3⋊D3D414yes—
38C2×C4×C3⋊D3Q814yes—
39C2×C4×C3⋊D3C2312yes—
40C22×C3×Dic3C2×C412yes—
41C22×C3×Dic3C2×C412yes—
42C2×#624—24no—
43C2×#624C818yescomplemented
44C2×#624C2×C414yes—
45C2×#624C2×C414yes—
46C2×C32×C8—22no—
47C2×C32×C8C2312yes—
48C2×C3⋊(C3⋊C8)—22no—
49C2×C3⋊(C3⋊C8)C2312yes—
50C8×C3⋊D3—28no—
51C3×C4×Dic3C2×C414yes—
52C3×C4×Dic3C2314yes—
53C2×C3×C3⋊C8—24no—
54C2×C3×C3⋊C8C2314yes—
55Dic32C2×C418yes—
56#3710—28no—
57C22×C4⋊C8—91noSylow
58C22×C4×D3—32no—
59C22×C4×D3—32no—
60C22×C4×D3—32no—
61C22×C4×D3—61no—
62C22×C3×C8—21no—
63C22×C3×C8—32no—
64C22×C3×C8C2×D312yes—
65C2×C3×C42—32no—
66C2×C4×Dic3—32no—
67C2×C4×Dic3—32no—
68C2×C4×Dic3C2×D312yes—
69C22×C3⋊C8—32no—
70C22×C3⋊C8—61no—
71C22×C3⋊C8C2×D312yes—
72C2×D3×C8—38no—
73C2×D3×C8—38no—
74C2×D3×C8—64no—
75C2×D3×C8—68no—
76C2×D3×C8—68no—
77C2×D3×C8—68no—
78C42×D3—38no—
79C42×D3—38no—
80C3×C4⋊C8—38no—
81Dic3⋊C8—38no—
82Dic3⋊C8C2×D318yescomplemented
83C4⋊(C3⋊C8)—38no—
84C23×C32C22×C411yescharacteristic
85C22×C3⋊D3C4⋊C414yes—
86C22×C3⋊D3C2×C814yes—
87C22×C3⋊D3M1614yes—
88C22×C3⋊D3C22×C412yes—
89C2×C32×C4C22×C411yescharacteristic
90C2×C32×C4C2×D412yes—
91C2×C32×C4C2×Q812yes—
92C2×C32×C4C2411yescharacteristic
93C2×C3⋊Dic3C4⋊C414yes—
94C2×C3⋊Dic3C22×C412yes—
95C4×C3⋊D3C4⋊C418yes—
96C4×C3⋊D3C2×D414yes—
97C4×C3⋊D3C2×Q814yes—
98C2×C3×Dic3—24no—
99C2×C3×Dic3C2×C818yescomplemented
100C2×C3×Dic3C22×C414yes—
101C2×C3×Dic3C22×C414yes—
102#624—28no—
103#624C2×C8116yescomplemented
104C32×C8—22no—
105C3⋊(C3⋊C8)—22no—
106C3×C3⋊C8—24no—
107C23×C8—91no—
108C23×C8—91no—
109C22×C42—91no—
110C2×C4⋊C8—32no—
111C2×C4⋊C8—98no—
112C2×C4⋊C8—92no—
113C23×D3—32no—
114C23×D3—61no—
115C22×C3×C4—21no—
116C22×C3×C4—32no—
117C22×C3×C4—32no—
118C22×C3×C4C22×D312yes—
119C22×Dic3—32no—
120C22×Dic3—61no—
121C22×Dic3C4×D312yes—
122C22×Dic3C4×D312yes—
123C2×C4×D3—34no—
124C2×C4×D3—38no—
125C2×C4×D3—38no—
126C2×C4×D3—34no—
127C2×C4×D3—316no—
128C2×C4×D3—38no—
129C2×C4×D3—38no—
130C2×C4×D3—64no—
131C2×C4×D3—62no—
132C2×C4×D3—62no—
133C2×C4×D3—64no—
134C2×C4×D3—68no—
135C2×C3×C8—24no—
136C2×C3×C8—24no—
137C2×C3×C8—22no—
138C2×C3×C8—34no—
139C2×C3×C8—64no—
140C2×C3×C8C22×D314yes—
141C3×C42—34no—
142C3×C42—34no—
143C4×Dic3—38no—
144C4×Dic3—38no—
145C4×Dic3C4×D314yes—
146C4×Dic3C22×D314yes—
147C2×C3⋊C8—24no—
148C2×C3⋊C8—34no—
149C2×C3⋊C8—62no—
150C2×C3⋊C8—64no—
151C2×C3⋊C8—64no—
152C2×C3⋊C8C22×D314yes—
153D3×C8—616no—
154D3×C8—616no—
155D3×C8—616no—
156C22×C32C2×C4⋊C412yes—
157C22×C32C22×C812yes—
158C22×C32C2×M1612yes—
159C22×C32C23×C411yescharacteristic
160C2×C3⋊D3C4⋊C8116yescomplemented
161C2×C3⋊D3C2×C4⋊C414yes—
162C2×C3⋊D3C22×C814yes—
163C2×C3⋊D3C2×M1614yes—
164C32×C4C2×C4⋊C412yes—
165C32×C4C22×D411yescharacteristic
166C32×C4C22×Q811yescharacteristic
167C3⋊Dic3C2×C4⋊C414yes—
168C3×Dic3—24no—
169C3×Dic3C22×C818yescomplemented
170C23×C4—91no—
171C23×C4—91no—
172C23×C4—91no—
173C22×C8—32no—
174C22×C8—94no—
175C22×C8—91no—
176C22×C8—94no—
177C22×C8—184no—
178C22×C8—184no—
179C22×C8D3211yescharacteristic
180C2×C42—32no—
181C2×C42—94no—
182C2×C42—94no—
183C2×C42—92no—
184C4⋊C8—38no—
185C4⋊C8—98no—
186C23×C3—21no—
187C23×C3C2×C4×D312yes—
188C22×D3—38no—
189C22×D3—38no—
190C22×D3—38no—
191C22×D3—34no—
192C22×D3—64no—
193C22×D3—64no—
194C22×D3—64no—
195C22×D3—62no—
196C2×C3×C4—21no—
197C2×C3×C4—22no—
198C2×C3×C4—21no—
199C2×C3×C4—22no—
200C2×C3×C4—38no—
201C2×C3×C4—34no—
202C2×C3×C4—34no—
203C2×C3×C4—64no—
204C2×C3×C4C2×C4×D312yes—
205C2×C3×C4D3×D414yes—
206C2×C3×C4D3×Q814yes—
207C2×C3×C4C23×D312yes—
208C2×Dic3—24no—
209C2×Dic3—38no—
210C2×Dic3—34no—
211C2×Dic3—64no—
212C2×Dic3—62no—
213C2×Dic3D3×C818yescomplemented
214C2×Dic3C2×C4×D314yes—
215C2×Dic3C2×C4×D314yes—
216C4×D3—316no—
217C4×D3—38no—
218C4×D3—38no—
219C4×D3—332no—
220C4×D3—68no—
221C4×D3—64no—
222C4×D3—64no—
223C4×D3—616no—
224C3×C8—24no—
225C3×C8—24no—
226C3×C8—64no—
227C3⋊C8—24no—
228C3⋊C8—64no—
229C3⋊C8—64no—
230C2×C32C2×C4⋊C814yescomplemented
231C2×C32C22×C4⋊C411yescharacteristic
232C2×C32C23×C811yescharacteristic
233C2×C32C22×M1611yescharacteristic
234C3⋊D3C2×C4⋊C818yescomplemented
235C24—91no—
236C22×C4—32no—
237C22×C4—32no—
238C22×C4—94no—
239C22×C4—98no—
240C22×C4—94no—
241C22×C4—91no—
242C22×C4—92no—
243C22×C4—94no—
244C22×C4—92no—
245C22×C4—94no—
246C22×C4—184no—
247C22×C4C2×D3211yescharacteristic
248C2×C8—22no—
249C2×C8—34no—
250C2×C8—64no—
251C2×C8—92no—
252C2×C8—188no—
253C2×C8—188no—
254C2×C8—182no—
255C2×C8C2×D3212yes—
256C42—34no—
257C42—34no—
258C42—98no—
259C22×C3—22no—
260C22×C3—21no—
261C22×C3—22no—
262C22×C3—22no—
263C22×C3D3×C4⋊C414yes—
264C22×C3C2×D3×C814yes—
265C22×C3D3×M1614yes—
266C22×C3C22×C4×D312yes—
267C2×D3—38no—
268C2×D3—38no—
269C2×D3—38no—
270C2×D3—332no—
271C2×D3—64no—
272C2×D3—616no—
273C2×D3—64no—
274C2×D3—64no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—22no—
278C3×C4—38no—
279C3×C4—64no—
280C3×C4D3×C4⋊C414yes—
281C3×C4C2×D3×D412yes—
282C3×C4C2×D3×Q812yes—
283Dic3—24no—
284Dic3—38no—
285Dic3—64no—
286Dic3C2×D3×C818yescomplemented
287C32C22×C4⋊C811yescharacteristic, complemented, Sylow
288C23—94no—
289C23—92no—
290C23—94no—
291C23—94no—
292C23C4×D3211yescharacteristic
293C2×C4—38no—
294C2×C4—34no—
295C2×C4—34no—
296C2×C4—64no—
297C2×C4—916no—
298C2×C4—92no—
299C2×C4—94no—
300C2×C4—94no—
301C2×C4—94no—
302C2×C4—98no—
303C2×C4—188no—
304C2×C4#379712yes—
305C2×C4C4×D3211yescharacteristic
306C2×C4#381112yes—
307C2×C4C22×D3211yescharacteristic
308C8—22no—
309C8—64no—
310C8—182no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—24no—
315C2×C3D3×C4⋊C818yescomplemented
316C2×C3C2×D3×C4⋊C412yes—
317C2×C3C22×D3×C812yes—
318C2×C3C2×D3×M1612yes—
319D3—316no—
320D3—68no—
321C22—94no—
322C22—94no—
323C22—94no—
324C22—916no—
325C22D32×C812yes—
326C22#6379112yes—
327C22#6388312yes—
328C22C2×C4×D3211yescharacteristic
329C4—38no—
330C4—64no—
331C4—94no—
332C4#6388312yes—
333C4C2×#379711yescharacteristic
334C4C2×#381111yescharacteristic
335C3—21no—
336C3C2×D3×C4⋊C812yescomplemented
337C2—98no—
338C2#1059065814yesdirect product factor
339C2C2×D32×C811yescharacteristic
340C2C2×#6379111yescharacteristic
341C2C2×#6388311yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC2×C32C23×C8
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C22×C4
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C22×C4⋊C8
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
4. C2×C3×Dic3⋊C8C2semidirect
5. C2×Dic3⋊(C3⋊C8)C2semidirect
6. #10590658C2direct (N × H)
22. C3×Dic3⋊C8C22semidirect
23. Dic3⋊(C3⋊C8)C22semidirect
30. C2×Dic3⋊C8D3semidirect
43. C2×#624C8semidirect
82. Dic3⋊C8C2×D3semidirect
99. C2×C3×Dic3C2×C8semidirect
103. #624C2×C8semidirect
160. C2×C3⋊D3C4⋊C8semidirect
169. C3×Dic3C22×C8semidirect
213. C2×Dic3D3×C8semidirect
230. C2×C32C2×C4⋊C8semidirect
234. C3⋊D3C2×C4⋊C8semidirect
286. Dic3C2×D3×C8semidirect
287. C32C22×C4⋊C8semidirect
315. C2×C3D3×C4⋊C8semidirect
336. C3C2×D3×C4⋊C8semidirect
338. C2#10590658direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C8×C3⋊D32
C2×C4×#6242
C22×#37102
C2×C3×Dic3⋊C82
C2×Dic3⋊(C3⋊C8)2
#105906582
C2×D3×C4⋊C83