Finite Group Databasebeta

← C2×#10592458 #11868231

Subgroups — C2×#10592458 #11868231

Order 1152.

1440 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic
2C2×#64097C211yesmaximal, characteristic, complemented
3C2×C32×#102C211yesmaximal, characteristic
4C2×#63659C211yesmaximal, characteristic
5C2×#63645C211yesmaximal, characteristic, complemented
6C2×#63641C211yesmaximal, characteristic, complemented
7C2×#63634C211yesmaximal, characteristic, complemented
8#10592458C218yesmaximal, direct product factor
9C2×#4759—34nomaximal
10C22×C32×D4C2211yescharacteristic
11C23×C3⋊Dic3—21no—
12C22×#634—21no—
13C22×C32×C8C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×#3757—21no—
16D4×C3⋊Dic3—22no—
17D4×C3⋊Dic3C2214yes—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×#3750—21no—
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23#64097—22no—
24#64097C2214yescomplemented
25C32×#102C2214yes—
26#63659C2214yes—
27#63645C2214yescomplemented
28#63641C2214yescomplemented
29#63634C2214yescomplemented
30C2×D4×Dic3—34no—
31C2×#888—34no—
32C2×C3×#102D314yes—
33C2×#832—34no—
34C2×#818—34no—
35C2×Dic3⋊C8—34no—
36C2×#807—34no—
37#4759—332no—
38C24×C32—21no—
39C2×C32×D4—21no—
40C2×C32×D4—22no—
41C2×C32×D4Q814yescomplemented
42C2×C32×D4C2312yes—
43C22×C32×C4—21no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C22×C3⋊Dic3—21no—
47C22×C3⋊Dic3—24no—
48C22×C3⋊Dic3—44no—
49C22×C3⋊Dic3D411yescharacteristic
50C22×C3⋊Dic3D411yescharacteristic
51C2×#634—24no—
52C2×#634—44no—
53C2×C32×C8—22no—
54C2×C32×C8C2312yes—
55C32×C4⋊C4—21no—
56C32×C4⋊C4C2312yes—
57#3757—24no—
58C4⋊(C3⋊Dic3)—21no—
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)C2312yes—
61C4⋊(C3⋊Dic3)C2312yes—
62#3750—24no—
63C4×C3⋊Dic3D412yes—
64C4×C3⋊Dic3C2312yes—
65C2×C3⋊(C3⋊C8)—22no—
66C2×C3⋊(C3⋊C8)C2312yes—
67C2×#474—91noSylow
68C22×C3×D4C2×D314yes—
69C23×Dic3—64no—
70C22×Dic6—64no—
71C22×C3×C8C2×D314yes—
72C2×C3×C4⋊C4C2×D314yes—
73C2×#217—64no—
74D4×Dic3—316no—
75D4×Dic3—68no—
76C2×C4⋊Dic3—34no—
77C2×C4⋊Dic3—34no—
78C2×Dic3⋊C4—64no—
79C2×C4×Dic3—34no—
80C22×C3⋊C8—34no—
81#888—316no—
82#888—68no—
83C3×#102C2×D3116yes—
84#832—316no—
85#818—316no—
86Dic3⋊C8—316no—
87#807—316no—
88C23×C32—24no—
89C23×C32—22no—
90C23×C32—42no—
91C23×C32—42no—
92C23×C32C2×D411yescharacteristic
93C32×D4—24no—
94C32×D4—22no—
95C32×D4C2×Q814yescomplemented
96C2×C32×C4—22no—
97C2×C32×C4—42no—
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×Q812yes—
100C2×C32×C4#4112yes—
101C2×C32×C4C2411yescharacteristic
102C2×C3⋊Dic3—22no—
103C2×C3⋊Dic3—22no—
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—42no—
106C2×C3⋊Dic3—42no—
107C2×C3⋊Dic3—48no—
108C2×C3⋊Dic3D814yes—
109C2×C3⋊Dic3C2×D412yes—
110C2×C3⋊Dic3C2×D412yes—
111#634—48no—
112C32×C8—22no—
113C3⋊(C3⋊C8)—22no—
114C2×C4⋊Q8—91no—
115C2×C4×D4—91no—
116#474—98no—
117C2×#107—91no—
118C2×#107—91no—
119C2×C4⋊C8—91no—
120C2×#102—91no—
121C2×#102C3⋊D311yescharacteristic
122C24×C3—24no—
123C2×C3×D4—24no—
124C2×C3×D4—28no—
125C2×C3×D4Dic6116yescomplemented
126C2×C3×D4C22×D318yes—
127C22×C3×C4—24no—
128C22×C3×C4C22×D314yes—
129C22×Dic3—34no—
130C22×Dic3—34no—
131C22×Dic3—616no—
132C22×Dic3—64no—
133C22×Dic3—64no—
134C22×Dic3—1216no—
135C2×Dic6—616no—
136C2×Dic6—1216no—
137C2×C3×C8—28no—
138C2×C3×C8C22×D318yes—
139C3×C4⋊C4—24no—
140C3×C4⋊C4C22×D318yes—
141#217—616no—
142C4⋊Dic3—38no—
143C4⋊Dic3—38no—
144C4⋊Dic3—64no—
145C4⋊Dic3—64no—
146Dic3⋊C4—616no—
147C4×Dic3—38no—
148C4×Dic3—38no—
149C2×C3⋊C8—38no—
150C2×C3⋊C8—68no—
151C22×C32—24no—
152C22×C32—42no—
153C22×C32—42no—
154C22×C32—48no—
155C22×C32C22⋊Q812yes—
156C22×C32C2×D812yes—
157C22×C32#13712yes—
158C22×C32C22×D411yescharacteristic
159C32×C4—42no—
160C32×C4C22⋊Q812yes—
161C32×C4C22×Q811yescharacteristic
162C32×C4C2×#4111yescharacteristic
163C3⋊Dic3—22no—
164C3⋊Dic3—42no—
165C3⋊Dic3—42no—
166C3⋊Dic3C2×D814yes—
167C22×Q8—181no—
168C22×D4C2×C3⋊D311yescharacteristic
169C23×C4—181no—
170C22×C8—91no—
171C22×C8C2×C3⋊D311yescharacteristic
172C4⋊Q8—94no—
173C4⋊Q8—182no—
174C4×D4—94no—
175C4×D4—182no—
176C2×C4⋊C4—91no—
177C2×C4⋊C4—91no—
178C2×C4⋊C4—181no—
179C2×C4⋊C4C2×C3⋊D311yescharacteristic
180C2×C22⋊C4—181no—
181C2×C42—91no—
182#107—94no—
183#107—94no—
184C4⋊C8—94no—
185#102—94no—
186#102C2×C3⋊D314yes—
187C23×C3—216no—
188C23×C3—28no—
189C23×C3—48no—
190C23×C3—48no—
191C23×C3D3×D414yes—
192C3×D4—216no—
193C3×D4—28no—
194C3×D4C2×Dic6116yescomplemented
195C2×C3×C4—28no—
196C2×C3×C4—48no—
197C2×C3×C4C2×Dic618yes—
198C2×C3×C4D3×D414yes—
199C2×C3×C4#23718yes—
200C2×C3×C4C23×D314yes—
201C2×Dic3—316no—
202C2×Dic3—38no—
203C2×Dic3—38no—
204C2×Dic3—68no—
205C2×Dic3—68no—
206C2×Dic3—68no—
207C2×Dic3—1232no—
208C2×Dic3—128no—
209C2×Dic3—128no—
210Dic6—1232no—
211C3×C8—28no—
212C3⋊C8—68no—
213C2×C32—44no—
214C2×C32#47414yescomplemented
215C2×C32C2×C22⋊Q811yescharacteristic
216C2×C32C22×D811yescharacteristic
217C2×C32C2×#13711yescharacteristic
218C24—21no—
219C2×Q8—184no—
220C2×Q8—364no—
221C2×D4—21no—
222C2×D4—22no—
223C2×D4#63414yescomplemented
224C2×D4C22×C3⋊D312yes—
225C22×C4—21no—
226C22×C4—91no—
227C22×C4—91no—
228C22×C4—184no—
229C22×C4—181no—
230C22×C4—181no—
231C22×C4—364no—
232C22×C4C22×C3⋊D311yescharacteristic
233C2×C8—22no—
234C2×C8—92no—
235C2×C8—182no—
236C2×C8C22×C3⋊D312yes—
237C4⋊C4—21no—
238C4⋊C4—92no—
239C4⋊C4—92no—
240C4⋊C4—184no—
241C4⋊C4—181no—
242C4⋊C4—181no—
243C4⋊C4C22×C3⋊D312yes—
244C22⋊C4—184no—
245C42—92no—
246C42—92no—
247C22×C3—216no—
248C22×C3—48no—
249C22×C3—48no—
250C22×C3—432no—
251C22×C3#87818yes—
252C22×C3D3×D818yes—
253C22×C3#91518yes—
254C22×C3C2×D3×D414yes—
255C3×C4—48no—
256C3×C4#87818yes—
257C3×C4C22×Dic614yes—
258C3×C4C2×#23714yes—
259Dic3—316no—
260Dic3—68no—
261Dic3—128no—
262Dic3—128no—
263C32C2×#47411yescharacteristic, complemented, Sylow
264C23—24no—
265C23—22no—
266C23—42no—
267C23—42no—
268C23D4×C3⋊D311yescharacteristic
269Q8—368no—
270D4—24no—
271D4—22no—
272D4C2×#63414yescomplemented
273C2×C4—22no—
274C2×C4—42no—
275C2×C4—92no—
276C2×C4—94no—
277C2×C4—92no—
278C2×C4—182no—
279C2×C4—182no—
280C2×C4—182no—
281C2×C4—368no—
282C2×C4—362no—
283C2×C4—362no—
284C2×C4C2×#63412yes—
285C2×C4D4×C3⋊D311yescharacteristic
286C2×C4#383012yes—
287C2×C4C23×C3⋊D311yescharacteristic
288C8—22no—
289C8—182no—
290C2×C3—416no—
291C2×C3#4759116yescomplemented
292C2×C3C2×#87814yes—
293C2×C3C2×D3×D814yes—
294C2×C3C2×#91514yes—
295C22—24no—
296C22—42no—
297C22—42no—
298C22—48no—
299C22#6408712yes—
300C22D8×C3⋊D312yes—
301C22#6412412yes—
302C22C2×D4×C3⋊D311yescharacteristic
303C4—42no—
304C4—94no—
305C4—182no—
306C4—362no—
307C4—362no—
308C4#6408712yes—
309C4C22×#63411yescharacteristic
310C4C2×#383011yescharacteristic
311C3C2×#475914yescomplemented
312C2—44no—
313C2#1059245814yesdirect product factor
314C2C2×#6408711yescharacteristic
315C2C2×D8×C3⋊D311yescharacteristic
316C2C2×#6412411yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#102C2
socleC23×C32C2×D4
prime radicalC22×C32×D4C22
hypercenterC2×#102C3⋊D3
hypocenterC32C2×#474
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×#64097C2semidirect
5. C2×#63645C2semidirect
6. C2×#63641C2semidirect
7. C2×#63634C2semidirect
8. #10592458C2direct (N × H)
24. #64097C22semidirect
27. #63645C22semidirect
28. #63641C22semidirect
29. #63634C22semidirect
41. C2×C32×D4Q8semidirect
95. C32×D4C2×Q8semidirect
125. C2×C3×D4Dic6semidirect
194. C3×D4C2×Dic6semidirect
214. C2×C32#474semidirect
223. C2×D4#634semidirect
263. C32C2×#474semidirect
272. D4C2×#634semidirect
291. C2×C3#4759semidirect
311. C3C2×#4759semidirect
313. C2#10592458direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C2×#640972
C2×C32×#1022
C2×#636592
C2×#636452
C2×#636412
C2×#636342
#105924582
C2×#47593