Finite Group Databasebeta

← C2×#10592562 #11869549

Subgroups — C2×#10592562 #11869549

Order 1152.

1536 conjugacy classes of subgroups.

The subgroup lattice has 351 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64104C211yesmaximal, characteristic
2C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×C32×#106C211yesmaximal, characteristic, complemented
4C2×#63648C211yesmaximal, characteristic, complemented
5C2×#63647C211yesmaximal, characteristic, complemented
6C2×#63636C211yesmaximal, characteristic, complemented
7C2×#63635C211yesmaximal, characteristic, complemented
8#10592562C218yesmaximal, direct product factor
9C2×#4863—34nomaximal
10C22×C4⋊(C3⋊D3)—21no—
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C4×C3⋊D3—21no—
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×#3752—21no—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×#3750—21no—
20C22×C3⋊(C3⋊C8)C2211yescharacteristic
21#64104—22no—
22#64104C2214yes—
23C4⋊C4×C3⋊D3—22no—
24C4⋊C4×C3⋊D3C2214yescomplemented
25C32×#106C2214yescomplemented
26#63648C2214yescomplemented
27#63647C2214yescomplemented
28#63636C2214yescomplemented
29#63635C2214yescomplemented
30C2×#895—34no—
31C2×D3×C4⋊C4—34no—
32C2×C3×#106D314yescomplemented
33C2×#821—34no—
34C2×(C2×D3)⋊C8—34no—
35C2×#809—34no—
36C2×#808—34no—
37#4863—332no—
38C23×C3⋊D3—21no—
39C23×C3⋊D3D411yescharacteristic
40C22×C32×C4—21no—
41C22×C32×C4—21no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C22×C3⋊Dic3D411yescharacteristic
45C2×C4⋊(C3⋊D3)—22no—
46C2×C4⋊(C3⋊D3)—22no—
47C2×C4⋊(C3⋊D3)—24no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—44no—
50C2×C4⋊(C3⋊D3)C2312yes—
51C2×C4×C3⋊D3—22no—
52C2×C4×C3⋊D3—22no—
53C2×C4×C3⋊D3—24no—
54C2×C4×C3⋊D3—44no—
55C2×C4×C3⋊D3D412yes—
56C2×C4×C3⋊D3C2312yes—
57C2×C32×C8—22no—
58C2×C32×C8C2312yes—
59C32×C4⋊C4—21no—
60C32×C4⋊C4—21no—
61C32×C4⋊C4C2312yes—
62C32×C4⋊C4C2312yes—
63#3752—24no—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)C2312yes—
66#3750—24no—
67C2×C3⋊(C3⋊C8)—22no—
68C2×C3⋊(C3⋊C8)C2312yes—
69C2×#481—91noSylow
70C22×D12—34no—
71C22×D12—64no—
72C22×C4×D3—34no—
73C22×C4×D3—64no—
74C22×C3×C8C2×D314yes—
75C2×C3×C4⋊C4C2×D314yes—
76C2×C3×C4⋊C4C2×D314yes—
77C2×(C2×D3)⋊C4—64no—
78C2×C4⋊Dic3—34no—
79C2×Dic3⋊C4—64no—
80C22×C3⋊C8—34no—
81#895—316no—
82#895—68no—
83D3×C4⋊C4—316no—
84D3×C4⋊C4—68no—
85C3×#106C2×D3116yescomplemented
86#821—316no—
87(C2×D3)⋊C8—316no—
88#809—316no—
89#808—316no—
90C23×C32C2×D411yescharacteristic
91C22×C3⋊D3—22no—
92C22×C3⋊D3—22no—
93C22×C3⋊D3—22no—
94C22×C3⋊D3—42no—
95C22×C3⋊D3—42no—
96C22×C3⋊D3—42no—
97C22×C3⋊D3SD1614yes—
98C22×C3⋊D3C2×D412yes—
99C2×C32×C4—22no—
100C2×C32×C4—22no—
101C2×C32×C4—42no—
102C2×C32×C4—42no—
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4#4112yes—
105C2×C32×C4#4112yes—
106C2×C32×C4C2411yescharacteristic
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3—42no—
110C2×C3⋊Dic3C2×D412yes—
111C4⋊(C3⋊D3)—22no—
112C4⋊(C3⋊D3)—22no—
113C4⋊(C3⋊D3)—48no—
114C4⋊(C3⋊D3)—42no—
115C4×C3⋊D3—24no—
116C4×C3⋊D3—22no—
117C4×C3⋊D3—22no—
118C4×C3⋊D3—48no—
119C32×C8—22no—
120C3⋊(C3⋊C8)—22no—
121C2×#121—91no—
122C22×C4⋊C4—91no—
123#481—98no—
124C2×#106—91no—
125C2×#106C3⋊D311yescharacteristic, complemented
126C2×#102—91no—
127C2×#102—91no—
128C2×C22⋊C8—91no—
129C23×D3—34no—
130C23×D3—64no—
131C22×C3×C4—24no—
132C22×C3×C4—24no—
133C22×C3×C4C22×D314yes—
134C22×Dic3—34no—
135C22×Dic3—64no—
136C2×D12—38no—
137C2×D12—68no—
138C2×D12—68no—
139C2×D12—616no—
140C2×D12—64no—
141C2×D12—1216no—
142C2×C4×D3—38no—
143C2×C4×D3—38no—
144C2×C4×D3—68no—
145C2×C4×D3—68no—
146C2×C4×D3—616no—
147C2×C4×D3—1216no—
148C2×C3×C8—28no—
149C2×C3×C8C22×D318yes—
150C3×C4⋊C4—24no—
151C3×C4⋊C4—24no—
152C3×C4⋊C4C22×D318yes—
153C3×C4⋊C4C22×D318yes—
154(C2×D3)⋊C4—616no—
155C4⋊Dic3—38no—
156C4⋊Dic3—64no—
157Dic3⋊C4—616no—
158C2×C3⋊C8—38no—
159C2×C3⋊C8—68no—
160C22×C32#12312yes—
161C22×C32C2×SD1612yes—
162C22×C32AGL(1,ℤ/8)12yes—
163C22×C32C22×D411yescharacteristic
164C2×C3⋊D3—22no—
165C2×C3⋊D3—22no—
166C2×C3⋊D3—28no—
167C2×C3⋊D3—42no—
168C2×C3⋊D3—42no—
169C2×C3⋊D3—42no—
170C2×C3⋊D3—84no—
171C2×C3⋊D3C2×SD1614yes—
172C32×C4—42no—
173C32×C4—42no—
174C32×C4#12312yes—
175C32×C4C2×#4111yescharacteristic
176C32×C4C2×#4111yescharacteristic
177C3⋊Dic3—22no—
178C3⋊Dic3—42no—
179C22×D4—91no—
180C22×D4—181no—
181C23×C4—91no—
182C23×C4—181no—
183C22×C8—91no—
184C22×C8C2×C3⋊D311yescharacteristic
185#121—94no—
186#121—182no—
187C2×C4⋊C4—91no—
188C2×C4⋊C4—94no—
189C2×C4⋊C4—182no—
190C2×C4⋊C4—181no—
191C2×C4⋊C4C2×C3⋊D311yescharacteristic
192C2×C4⋊C4C2×C3⋊D311yescharacteristic
193C2×C22⋊C4—181no—
194#106—94no—
195#106C2×C3⋊D314yescomplemented
196#102—94no—
197#102—94no—
198C22⋊C8—94no—
199C23×C3D3×D414yes—
200C22×D3—316no—
201C22×D3—38no—
202C22×D3—68no—
203C22×D3—68no—
204C22×D3—68no—
205C22×D3—128no—
206C22×D3—128no—
207C22×D3—128no—
208C2×C3×C4—28no—
209C2×C3×C4—28no—
210C2×C3×C4—48no—
211C2×C3×C4—48no—
212C2×C3×C4#23518yes—
213C2×C3×C4D3×D414yes—
214C2×C3×C4#23918yes—
215C2×C3×C4C23×D314yes—
216C2×Dic3—38no—
217C2×Dic3—68no—
218C2×Dic3—68no—
219C2×Dic3—128no—
220D12—68no—
221D12—68no—
222D12—1232no—
223D12—128no—
224C4×D3—616no—
225C4×D3—68no—
226C4×D3—68no—
227C4×D3—1232no—
228C3×C8—28no—
229C3⋊C8—68no—
230C2×C32#48114yescomplemented
231C2×C32C2×#12311yescharacteristic
232C2×C32C22×SD1611yescharacteristic
233C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
234C3⋊D3—24no—
235C3⋊D3—82no—
236C24—91no—
237C24—181no—
238C2×D4—92no—
239C2×D4—184no—
240C2×D4—182no—
241C2×D4—181no—
242C2×D4—182no—
243C2×D4—364no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—91no—
247C22×C4—92no—
248C22×C4—92no—
249C22×C4—184no—
250C22×C4—182no—
251C22×C4—182no—
252C22×C4—181no—
253C22×C4—364no—
254C22×C4C22×C3⋊D311yescharacteristic
255C2×C8—22no—
256C2×C8—92no—
257C2×C8—182no—
258C2×C8C22×C3⋊D312yes—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—92no—
262C4⋊C4—184no—
263C4⋊C4—181no—
264C4⋊C4C22×C3⋊D312yes—
265C4⋊C4C22×C3⋊D312yes—
266C22⋊C4—184no—
267C22×C3#89418yes—
268C22×C3D3×SD1618yes—
269C22×C3#91418yes—
270C22×C3C2×D3×D414yes—
271C2×D3—316no—
272C2×D3—68no—
273C2×D3—68no—
274C2×D3—632no—
275C2×D3—128no—
276C2×D3—128no—
277C2×D3—128no—
278C2×D3—2416no—
279C3×C4—48no—
280C3×C4—48no—
281C3×C4#89418yes—
282C3×C4C2×#23514yes—
283C3×C4C2×#23914yes—
284Dic3—68no—
285Dic3—128no—
286C32C2×#48111yescharacteristic, complemented, Sylow
287C23—92no—
288C23—94no—
289C23—182no—
290C23—182no—
291C23—182no—
292C23—362no—
293C23—362no—
294C23—362no—
295C23D4×C3⋊D311yescharacteristic
296D4—182no—
297D4—182no—
298D4—368no—
299D4—362no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—92no—
305C2×C4—182no—
306C2×C4—182no—
307C2×C4—184no—
308C2×C4—182no—
309C2×C4—182no—
310C2×C4—368no—
311C2×C4—362no—
312C2×C4#382812yes—
313C2×C4D4×C3⋊D311yescharacteristic
314C2×C4#383212yes—
315C2×C4C23×C3⋊D311yescharacteristic
316C8—22no—
317C8—182no—
318C2×C3#4863116yescomplemented
319C2×C3C2×#89414yes—
320C2×C3C2×D3×SD1614yes—
321C2×C3C2×#91414yes—
322D3—616no—
323D3—248no—
324C22—94no—
325C22—188no—
326C22—182no—
327C22—182no—
328C22—362no—
329C22—362no—
330C22—362no—
331C22—724no—
332C22#6410312yes—
333C22SD16×C3⋊D312yes—
334C22#6412312yes—
335C22C2×D4×C3⋊D311yescharacteristic
336C4—42no—
337C4—42no—
338C4—182no—
339C4—362no—
340C4#6410312yes—
341C4C2×#382811yescharacteristic
342C4C2×#383211yescharacteristic
343C3C2×#486314yescomplemented
344C2—184no—
345C2—722no—
346C2#1059256214yesdirect product factor
347C2C2×#6410311yescharacteristic
348C2C2×SD16×C3⋊D311yescharacteristic
349C2C2×#6412311yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#106C2
socleC23×C32C2×D4
prime radicalC2×#64104C2
hypercenterC2×#106C3⋊D3
hypocenterC32C2×#481
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×C3⋊D3C2semidirect
3. C2×C32×#106C2semidirect
4. C2×#63648C2semidirect
5. C2×#63647C2semidirect
6. C2×#63636C2semidirect
7. C2×#63635C2semidirect
8. #10592562C2direct (N × H)
24. C4⋊C4×C3⋊D3C22semidirect
25. C32×#106C22semidirect
26. #63648C22semidirect
27. #63647C22semidirect
28. #63636C22semidirect
29. #63635C22semidirect
32. C2×C3×#106D3semidirect
85. C3×#106C2×D3semidirect
125. C2×#106C3⋊D3semidirect
195. #106C2×C3⋊D3semidirect
230. C2×C32#481semidirect
286. C32C2×#481semidirect
318. C2×C3#4863semidirect
343. C3C2×#4863semidirect
346. C2#10592562direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641042
C2×C4⋊C4×C3⋊D32
C2×C32×#1062
C2×#636482
C2×#636472
C2×#636362
C2×#636352
#105925622
C2×#48633