Finite Group Databasebeta

← C2×#10592588 #11860039

Subgroups — C2×#10592588 #11860039

Order 1152.

1632 conjugacy classes of subgroups.

The subgroup lattice has 333 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3744C211yesmaximal, characteristic
2C2×#64102C211yesmaximal, characteristic
3C2×#64096C211yesmaximal, characteristic, complemented
4C2×C32×#107C211yesmaximal, characteristic, complemented
5C2×#63642C211yesmaximal, characteristic, complemented
6C2×#63637C211yesmaximal, characteristic, complemented
7C2×#63636C211yesmaximal, characteristic
8#10592588C218yesmaximal, direct product factor
9C2×#4889—34nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C4×C3⋊D3—21no—
12C22×#634C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×#3752—21no—
17C2×#3750—21no—
18C2×C4×C3⋊Dic3—21no—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C22×C3⋊(C3⋊C8)C2211yescharacteristic
21C2×#3744C418yescomplemented
22C2×#3744C2214yes—
23#64102—22no—
24#64102C2214yes—
25#64096—22no—
26#64096C2214yescomplemented
27C32×#107C2214yescomplemented
28#63642C2214yescomplemented
29#63637C2214yescomplemented
30#63636C2214yes—
31C22×#204—34no—
32C2×#893—34no—
33C2×#887—34no—
34C2×C3×#107D314yescomplemented
35C2×#815—34no—
36C2×#810—34no—
37C2×#809—34no—
38#4889—332no—
39C23×C3⋊D3—21no—
40C22×C32×C4—21no—
41C22×C32×C4—21no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C22×C3⋊Dic3D411yescharacteristic
45C22×C3⋊Dic3D411yescharacteristic
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—22no—
48C2×C4⋊(C3⋊D3)C2×C414yes—
49C2×C4⋊(C3⋊D3)C2312yes—
50C2×C4×C3⋊D3—24no—
51C2×C4×C3⋊D3—44no—
52C2×#634—21no—
53C2×#634—22no—
54C2×#634C2×C414yescomplemented
55C2×#634C2312yes—
56C2×C32×C8C2×C414yescomplemented
57C2×C32×C8C2312yes—
58C32×C4⋊C4—21no—
59C32×C4⋊C4—21no—
60C32×C4⋊C4C2312yes—
61C32×C4⋊C4C2312yes—
62#3752—24no—
63#3750—24no—
64C4×C3⋊Dic3—24no—
65C4×C3⋊Dic3D412yes—
66C4×C3⋊Dic3C2312yes—
67C2×C3⋊(C3⋊C8)—22no—
68C2×C3⋊(C3⋊C8)C2312yes—
69#3744C2×C4116yescomplemented
70C2×#440—91noSylow
71C22×D12—34no—
72C22×C4×D3—64no—
73C22×Dic6—34no—
74C22×C3×C8C2×D314yes—
75C2×C3×C4⋊C4C2×D314yes—
76C2×C3×C4⋊C4C2×D314yes—
77C2×(C2×D3)⋊C4—64no—
78C2×Dic3⋊C4—64no—
79C2×C4×Dic3—34no—
80C2×C4×Dic3—64no—
81C22×C3⋊C8—34no—
82C2×#204—332no—
83C2×#204—316no—
84#893—316no—
85#893—68no—
86#887—316no—
87#887—68no—
88C3×#107C2×D3116yescomplemented
89#815—316no—
90#810—316no—
91#809—316no—
92C23×C32C2×D411yescharacteristic
93C22×C3⋊D3—24no—
94C22×C3⋊D3—22no—
95C22×C3⋊D3—42no—
96C22×C3⋊D3—42no—
97C2×C32×C4—22no—
98C2×C32×C4—22no—
99C2×C32×C4—42no—
100C2×C32×C4—42no—
101C2×C32×C4C22×C412yes—
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4#4112yes—
104C2×C32×C4C2411yescharacteristic
105C2×C3⋊Dic3—24no—
106C2×C3⋊Dic3—22no—
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3C2×D412yes—
110C2×C3⋊Dic3C2×D412yes—
111C4⋊(C3⋊D3)—24no—
112C4⋊(C3⋊D3)—22no—
113C4⋊(C3⋊D3)C22×C414yes—
114C4×C3⋊D3—48no—
115#634—24no—
116#634—22no—
117#634C22×C414yescomplemented
118C32×C8C22×C414yescomplemented
119C3⋊(C3⋊C8)—22no—
120C22×SD16—91no—
121C2×C4×Q8—91no—
122C2×C4×D4—91no—
123#440—98no—
124C2×#107C3⋊D311yescharacteristic, complemented
125C2×#103—91no—
126C2×#102—91no—
127C2×#97—91no—
128C23×D3—64no—
129C22×C3×C4—24no—
130C22×C3×C4—24no—
131C22×C3×C4C22×D314yes—
132C22×Dic3—34no—
133C22×Dic3—34no—
134C22×Dic3—64no—
135C2×D12—316no—
136C2×D12—38no—
137C2×D12—64no—
138C2×D12—68no—
139C2×C4×D3—616no—
140C2×C4×D3—1216no—
141C2×Dic6—316no—
142C2×Dic6—38no—
143C2×Dic6—64no—
144C2×Dic6—68no—
145C2×C3×C8C4×D3116yescomplemented
146C2×C3×C8C22×D318yes—
147C3×C4⋊C4—24no—
148C3×C4⋊C4—24no—
149C3×C4⋊C4C22×D318yes—
150C3×C4⋊C4C22×D318yes—
151(C2×D3)⋊C4—616no—
152Dic3⋊C4—616no—
153C4×Dic3—38no—
154C4×Dic3—38no—
155C4×Dic3—616no—
156C2×C3⋊C8—38no—
157C2×C3⋊C8—68no—
158#204—364no—
159C22×C32C4×D412yes—
160C22×C32AGL(1,ℤ/8)12yes—
161C22×C32#13712yes—
162C22×C32C22×D411yescharacteristic
163C2×C3⋊D3—24no—
164C2×C3⋊D3—42no—
165C2×C3⋊D3—42no—
166C2×C3⋊D3—48no—
167C32×C4—42no—
168C32×C4—42no—
169C32×C4C4×D412yes—
170C32×C4C23×C411yescharacteristic
171C32×C4C2×#4111yescharacteristic
172C3⋊Dic3—24no—
173C3⋊Dic3—22no—
174C3⋊Dic3—22no—
175C22×Q8—91no—
176C22×D4—91no—
177C23×C4—181no—
178C2×SD16—98no—
179C2×SD16—94no—
180C22×C8—91no—
181C22×C8C2×C3⋊D311yescharacteristic
182C4×Q8—94no—
183C4×Q8—182no—
184C4×D4—94no—
185C4×D4—182no—
186C2×C4⋊C4—181no—
187C2×C4⋊C4C2×C3⋊D311yescharacteristic
188C2×C4⋊C4C2×C3⋊D311yescharacteristic
189C2×C22⋊C4—181no—
190C2×C42—91no—
191C2×C42—181no—
192#107C2×C3⋊D314yescomplemented
193#103—94no—
194#102—94no—
195#97—94no—
196C23×C3D3×D414yes—
197C22×D3—616no—
198C22×D3—68no—
199C22×D3—128no—
200C22×D3—128no—
201C2×C3×C4—28no—
202C2×C3×C4—28no—
203C2×C3×C4—48no—
204C2×C3×C4—48no—
205C2×C3×C4C2×C4×D318yes—
206C2×C3×C4D3×D414yes—
207C2×C3×C4#23918yes—
208C2×C3×C4C23×D314yes—
209C2×Dic3—38no—
210C2×Dic3—38no—
211C2×Dic3—616no—
212C2×Dic3—68no—
213C2×Dic3—68no—
214C2×Dic3—68no—
215D12—316no—
216D12—616no—
217D12—68no—
218C4×D3—1232no—
219Dic6—316no—
220Dic6—616no—
221Dic6—68no—
222C3×C8C2×C4×D3116yescomplemented
223C3⋊C8—68no—
224C2×C32#44014yescomplemented
225C2×C32C2×C4×D411yescharacteristic
226C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
227C2×C32C2×#13711yescharacteristic
228C3⋊D3—44no—
229C24—181no—
230C2×Q8—92no—
231C2×Q8—94no—
232C2×Q8—181no—
233C2×Q8—182no—
234C2×D4—92no—
235C2×D4—94no—
236C2×D4—181no—
237C2×D4—182no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—91no—
241C22×C4—91no—
242C22×C4—184no—
243C22×C4—181no—
244C22×C4—364no—
245C22×C4C22×C3⋊D311yescharacteristic
246SD16—916no—
247C2×C8—92no—
248C2×C8—182no—
249C2×C8C4×C3⋊D314yescomplemented
250C2×C8C22×C3⋊D312yes—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—184no—
254C4⋊C4C22×C3⋊D312yes—
255C4⋊C4C22×C3⋊D312yes—
256C22⋊C4—184no—
257C42—92no—
258C42—92no—
259C42—184no—
260C22×C3#89318yes—
261C22×C3#91118yes—
262C22×C3#91818yes—
263C22×C3C2×D3×D414yes—
264C2×D3—616no—
265C2×D3—1232no—
266C2×D3—128no—
267C2×D3—128no—
268C3×C4—48no—
269C3×C4—48no—
270C3×C4#89318yes—
271C3×C4C22×C4×D314yes—
272C3×C4C2×#23914yes—
273Dic3—68no—
274Dic3—616no—
275Dic3—68no—
276C32C2×#44011yescharacteristic, complemented, Sylow
277C23—184no—
278C23—182no—
279C23—362no—
280C23—362no—
281C23D4×C3⋊D311yescharacteristic
282Q8—94no—
283Q8—184no—
284Q8—182no—
285D4—94no—
286D4—184no—
287D4—182no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—92no—
293C2×C4—92no—
294C2×C4—184no—
295C2×C4—182no—
296C2×C4—182no—
297C2×C4—182no—
298C2×C4—368no—
299C2×C4C2×C4×C3⋊D312yes—
300C2×C4D4×C3⋊D311yescharacteristic
301C2×C4#383212yes—
302C2×C4C23×C3⋊D311yescharacteristic
303C8—182no—
304C8C2×C4×C3⋊D314yescomplemented
305C2×C3#4889116yescomplemented
306C2×C3C2×#89314yes—
307C2×C3C2×#91114yes—
308C2×C3C2×#91814yes—
309D3—1216no—
310C22—184no—
311C22—368no—
312C22—362no—
313C22—362no—
314C22#6410212yes—
315C22#6412012yes—
316C22#6412712yes—
317C22C2×D4×C3⋊D311yescharacteristic
318C4—42no—
319C4—42no—
320C4—182no—
321C4—184no—
322C4—182no—
323C4#6410212yes—
324C4C22×C4×C3⋊D311yescharacteristic
325C4C2×#383211yescharacteristic
326C3C2×#488914yescomplemented
327C2—364no—
328C2#1059258814yesdirect product factor
329C2C2×#6410211yescharacteristic
330C2C2×#6412011yescharacteristic
331C2C2×#6412711yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#107C2
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC2×C32×C4C24
hypercenterC2×#107C3⋊D3
hypocenterC32C2×#440
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
3. C2×#64096C2semidirect
4. C2×C32×#107C2semidirect
5. C2×#63642C2semidirect
6. C2×#63637C2semidirect
8. #10592588C2direct (N × H)
21. C2×#3744C4semidirect
26. #64096C22semidirect
27. C32×#107C22semidirect
28. #63642C22semidirect
29. #63637C22semidirect
34. C2×C3×#107D3semidirect
54. C2×#634C2×C4semidirect
56. C2×C32×C8C2×C4semidirect
69. #3744C2×C4semidirect
88. C3×#107C2×D3semidirect
117. #634C22×C4semidirect
118. C32×C8C22×C4semidirect
124. C2×#107C3⋊D3semidirect
145. C2×C3×C8C4×D3semidirect
192. #107C2×C3⋊D3semidirect
222. C3×C8C2×C4×D3semidirect
224. C2×C32#440semidirect
249. C2×C8C4×C3⋊D3semidirect
276. C32C2×#440semidirect
304. C8C2×C4×C3⋊D3semidirect
305. C2×C3#4889semidirect
326. C3C2×#4889semidirect
328. C2#10592588direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37442
C2×#641022
C2×#640962
C2×C32×#1072
C2×#636422
C2×#636372
C2×#636362
#105925882
C2×#48893