Finite Group Databasebeta

← C2×#10592717 #11860042

Subgroups — C2×#10592717 #11860042

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
1C2×C32×C4×D4C211yesmaximal, characteristic
2C22×#3754C211yesmaximal, characteristic
3C2×C4×#634C211yesmaximal, characteristic, complemented
4C2×#63659C211yesmaximal, characteristic
5#10592717C218yesmaximal, direct product factor
6C2×#63637C211yesmaximal, characteristic, complemented
7C2×#63634C211yesmaximal, characteristic, complemented
8C2×#63630C211yesmaximal, characteristic, complemented
9C2×#5018—34nomaximal
10C22×C32×D4C2211yescharacteristic
11C23×C32×C4—21no—
12C22×#634C2211yescharacteristic
13C32×C4×D4—22no—
14C32×C4×D4C2214yes—
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C32×C22⋊C4—21no—
17C2×C32×C42C2211yescharacteristic
18C2×#3754C418yescomplemented
19C2×#3754C2214yes—
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×#3750—21no—
22C2×C4×C3⋊Dic3—21no—
23C22×C3⋊(C3⋊C8)C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25C4×#634—22no—
26C4×#634C2214yescomplemented
27#63659C2214yes—
28#63637C2214yescomplemented
29#63634C2214yescomplemented
30#63630C2214yescomplemented
31C2×C3×C4×D4D314yes—
32C22×#214—34no—
33C2×C4×Dic6—34no—
34C2×#832—34no—
35#5018—332no—
36C2×#810—34no—
37C2×#807—34no—
38C2×#803—34no—
39C24×C32—21no—
40C2×C32×D4—21no—
41C2×C32×D4—22no—
42C2×C32×D4C2×C414yes—
43C2×C32×D4C2312yes—
44C22×C32×C4—21no—
45C22×C32×C4—24no—
46C22×C32×C4—44no—
47C22×C32×C4D411yescharacteristic
48C22×C32×C4D411yescharacteristic
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3—21no—
51C22×C3⋊Dic3—21no—
52C2×#634—21no—
53C2×#634—22no—
54C2×#634C2×C414yescomplemented
55C2×#634C2312yes—
56C32×C4⋊C4—21no—
57C32×C4⋊C4C2312yes—
58C32×C22⋊C4—24no—
59C32×C42D412yes—
60C32×C42C2312yes—
61#3754C2×C4116yescomplemented
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)C2312yes—
64#3750—24no—
65C4×C3⋊Dic3—24no—
66C2×C3⋊(C3⋊C8)—22no—
67C2×C3⋊(C3⋊C8)C2×C414yescomplemented
68C2×C3⋊(C3⋊C8)C2312yes—
69C2×C3⋊(C3⋊C8)C2312yes—
70C2×#440—91noSylow
71C22×C3×D4C2×D314yes—
72C23×C3×C4—24no—
73C22×Dic6—34no—
74C3×C4×D4—28no—
75C3×C4×D4C2×D3116yes—
76C2×C3×C4⋊C4C2×D314yes—
77C2×C3×C22⋊C4—24no—
78C2×C3×C42C2×D314yes—
79C2×#214—332no—
80C2×#214—316no—
81C2×C4⋊Dic3—34no—
82C2×Dic3⋊C4—64no—
83C2×C4×Dic3—64no—
84C22×C3⋊C8—34no—
85C22×C3⋊C8—34no—
86C4×Dic6—316no—
87C4×Dic6—68no—
88#832—316no—
89#810—316no—
90#807—316no—
91#803—316no—
92C23×C32—24no—
93C23×C32—22no—
94C23×C32—42no—
95C23×C32—42no—
96C23×C32C2×D411yescharacteristic
97C32×D4—24no—
98C32×D4—22no—
99C32×D4C22×C414yes—
100C2×C32×C4—22no—
101C2×C32×C4—22no—
102C2×C32×C4—22no—
103C2×C32×C4—48no—
104C2×C32×C4—42no—
105C2×C32×C4C22×C412yes—
106C2×C32×C4C2×D412yes—
107C2×C32×C4C2×D412yes—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4#4112yes—
110C2×C32×C4C2411yescharacteristic
111C2×C3⋊Dic3—24no—
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—42no—
115#634—24no—
116#634—22no—
117#634C22×C414yescomplemented
118C3⋊(C3⋊C8)—22no—
119C3⋊(C3⋊C8)C22×C414yescomplemented
120C22×SD16—91no—
121C2×C4×Q8—91no—
122C2×C4×D4C3⋊D311yescharacteristic
123#440—98no—
124C2×#107—91no—
125C2×#103—91no—
126C2×#102—91no—
127C2×#97—91no—
128C24×C3—24no—
129C2×C3×D4—28no—
130C2×C3×D4—24no—
131C2×C3×D4C4×D3116yes—
132C2×C3×D4C22×D318yes—
133C22×C3×C4—24no—
134C22×C3×C4—216no—
135C22×C3×C4—416no—
136C22×C3×C4#6714yes—
137C22×C3×C4#6714yes—
138C22×C3×C4C22×D314yes—
139C22×Dic3—64no—
140C22×Dic3—64no—
141C2×Dic6—316no—
142C2×Dic6—38no—
143C2×Dic6—68no—
144C2×Dic6—64no—
145C3×C4⋊C4—24no—
146C3×C4⋊C4C22×D318yes—
147C3×C22⋊C4—216no—
148C3×C42#6718yes—
149C3×C42C22×D318yes—
150#214—364no—
151C4⋊Dic3—38no—
152C4⋊Dic3—64no—
153Dic3⋊C4—616no—
154C4×Dic3—616no—
155C2×C3⋊C8—316no—
156C2×C3⋊C8—38no—
157C2×C3⋊C8—38no—
158C2×C3⋊C8—68no—
159C22×C32—24no—
160C22×C32—42no—
161C22×C32—42no—
162C22×C32—48no—
163C22×C32C4×D412yes—
164C22×C32AGL(1,ℤ/8)12yes—
165C22×C32#13712yes—
166C22×C32C22×D411yescharacteristic
167C32×C4—22no—
168C32×C4—22no—
169C32×C4—42no—
170C32×C4C4×D412yes—
171C32×C4C23×C411yescharacteristic
172C32×C4C2×#4111yescharacteristic
173C3⋊Dic3—24no—
174C3⋊Dic3—42no—
175C22×Q8—91no—
176C22×D4C2×C3⋊D311yescharacteristic
177C23×C4—21no—
178C2×SD16—98no—
179C2×SD16—94no—
180C22×C8—91no—
181C22×C8—91no—
182C4×Q8—94no—
183C4×Q8—182no—
184C4×D4—22no—
185C4×D4C2×C3⋊D314yes—
186C2×C4⋊C4—91no—
187C2×C4⋊C4—181no—
188C2×C4⋊C4C2×C3⋊D311yescharacteristic
189C2×C22⋊C4—21no—
190C2×C42—181no—
191C2×C42C2×C3⋊D311yescharacteristic
192#107—94no—
193#103—94no—
194#102—94no—
195#97—94no—
196C23×C3—216no—
197C23×C3—28no—
198C23×C3—48no—
199C23×C3—48no—
200C23×C3C2×#6714yes—
201C3×D4—216no—
202C3×D4—28no—
203C3×D4C2×C4×D3116yes—
204C2×C3×C4—28no—
205C2×C3×C4—28no—
206C2×C3×C4—28no—
207C2×C3×C4—432no—
208C2×C3×C4—48no—
209C2×C3×C4C2×C4×D318yes—
210C2×C3×C4#23518yes—
211C2×C3×C4C2×#6718yes—
212C2×C3×C4C2×#6718yes—
213C2×C3×C4C2×#6714yes—
214C2×C3×C4C23×D314yes—
215C2×Dic3—616no—
216C2×Dic3—68no—
217C2×Dic3—68no—
218C2×Dic3—128no—
219Dic6—316no—
220Dic6—616no—
221Dic6—68no—
222C3⋊C8—316no—
223C3⋊C8—68no—
224C2×C32—44no—
225C2×C32#44014yescomplemented
226C2×C32C2×C4×D411yescharacteristic
227C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
228C2×C32C2×#13711yescharacteristic
229C24—21no—
230C2×Q8—92no—
231C2×Q8—94no—
232C2×Q8—182no—
233C2×Q8—181no—
234C2×D4—22no—
235C2×D4—21no—
236C2×D4C4×C3⋊D314yes—
237C2×D4C22×C3⋊D312yes—
238C22×C4—21no—
239C22×C4—24no—
240C22×C4—44no—
241C22×C4—181no—
242C22×C4—181no—
243C22×C4#63811yescharacteristic
244C22×C4#63811yescharacteristic
245C22×C4C22×C3⋊D311yescharacteristic
246SD16—916no—
247C2×C8—92no—
248C2×C8—94no—
249C2×C8—92no—
250C2×C8—182no—
251C4⋊C4—21no—
252C4⋊C4—92no—
253C4⋊C4—181no—
254C4⋊C4—184no—
255C4⋊C4C22×C3⋊D312yes—
256C22⋊C4—24no—
257C42—184no—
258C42#63812yes—
259C42C22×C3⋊D312yes—
260C22×C3—216no—
261C22×C3—432no—
262C22×C3—48no—
263C22×C3—48no—
264C22×C3C4×#6718yes—
265C22×C3#93218yes—
266C22×C3#95118yes—
267C22×C3C22×#6714yes—
268C3×C4—28no—
269C3×C4—28no—
270C3×C4—48no—
271C3×C4C4×#6718yes—
272C3×C4C22×C4×D314yes—
273C3×C4C2×#23514yes—
274Dic3—616no—
275Dic3—128no—
276C32C2×#44011yescharacteristic, complemented, Sylow
277C23—22no—
278C23—24no—
279C23—42no—
280C23—42no—
281C23C2×#63811yescharacteristic
282Q8—94no—
283Q8—182no—
284Q8—184no—
285D4—22no—
286D4—24no—
287D4C2×C4×C3⋊D314yes—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—48no—
292C2×C4—42no—
293C2×C4—182no—
294C2×C4—184no—
295C2×C4—182no—
296C2×C4—362no—
297C2×C4C2×C4×C3⋊D312yes—
298C2×C4#382812yes—
299C2×C4C2×#63812yes—
300C2×C4C2×#63812yes—
301C2×C4C2×#63811yescharacteristic
302C2×C4C23×C3⋊D311yescharacteristic
303C8—94no—
304C8—182no—
305C2×C3—416no—
306C2×C3#5018116yescomplemented
307C2×C3C2×C4×#6714yes—
308C2×C3C2×#93214yes—
309C2×C3C2×#95114yes—
310C22—24no—
311C22—42no—
312C22—42no—
313C22—48no—
314C22C4×#63812yes—
315C22#6414112yes—
316C22#6416012yes—
317C22C22×#63811yescharacteristic
318C4—22no—
319C4—22no—
320C4—42no—
321C4—184no—
322C4—362no—
323C4C4×#63812yes—
324C4C22×C4×C3⋊D311yescharacteristic
325C4C2×#382811yescharacteristic
326C3C2×#501814yescomplemented
327C2—44no—
328C2#1059271714yesdirect product factor
329C2C2×C4×#63811yescharacteristic
330C2C2×#6414111yescharacteristic
331C2C2×#6416011yescharacteristic
subgroupG/H
centerC23C2×#638
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×C4×D4C2
socleC23×C32C2×D4
prime radicalC22×C32×D4C22
cosocleC2×C32×C4C24
hypercenterC2×C4×D4C3⋊D3
hypocenterC32C2×#440
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
3. C2×C4×#634C2semidirect
5. #10592717C2direct (N × H)
6. C2×#63637C2semidirect
7. C2×#63634C2semidirect
8. C2×#63630C2semidirect
18. C2×#3754C4semidirect
26. C4×#634C22semidirect
28. #63637C22semidirect
29. #63634C22semidirect
30. #63630C22semidirect
54. C2×#634C2×C4semidirect
61. #3754C2×C4semidirect
67. C2×C3⋊(C3⋊C8)C2×C4semidirect
117. #634C22×C4semidirect
119. C3⋊(C3⋊C8)C22×C4semidirect
225. C2×C32#440semidirect
276. C32C2×#440semidirect
306. C2×C3#5018semidirect
326. C3C2×#5018semidirect
328. C2#10592717direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C22×#37542
C2×C4×#6342
C2×#636592
#105927172
C2×#636372
C2×#636342
C2×#636302
C2×#50183