Finite Group Databasebeta

← C2×#10593299 #11861026

Subgroups — C2×#10593299 #11861026

Order 1152.

738 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64223C211yesmaximal, characteristic
2C2×#63805C212yesmaximal, complemented
3C2×C8×#157C211yesmaximal, characteristic, complemented
4C2×#63733C211yesmaximal, characteristic, complemented
5C2×#63731C212yesmaximal, complemented
6#10593299C218yesmaximal, direct product factor
7C2×#3798C2212yes—
8C2×C4×#157C2211yescharacteristic
9C2×#3787C2211yescharacteristic
10C2×#3776C411yescharacteristic, complemented
11C2×#3775C412yescomplemented
12C2×#3774C411yescharacteristic, complemented
13#64223C414yescomplemented
14#64223C2214yes—
15C2×C8×C3⋊D3C2211yescharacteristic
16C2×C3×ΓL(1,𝔽25)—22no—
17C2×#3712C2212yes—
18C2×D3×C3⋊C8—22no—
19#63805—24no—
20#63805C2218yescomplemented
21C8×#157C2214yescomplemented
22#63733C2214yescomplemented
23#63731C2218yescomplemented
24C2×#907—62no—
25C22×#157—21no—
26C2×C4×C3⋊D3C2311yescharacteristic
27C2×C3×C4×D3—22no—
28C2×#627C2×C412yes—
29C2×#626—22no—
30C2×#625C2×C412yes—
31#3798—22no—
32#3798—22no—
33#3798C2×C414yes—
34#3798C2314yes—
35C2×#622C2×C411yescharacteristic
36C2×#622C2×C411yescharacteristic
37C4×#157—21no—
38C4×#157C2312yes—
39#3787C2×C412yes—
40#3787C2312yes—
41#3776C2×C414yescomplemented
42#3775C2×C418yescomplemented
43#3774C2×C414yescomplemented
44C2×C32×C8D411yescharacteristic
45C2×C3⋊(C3⋊C8)D411yescharacteristic
46C8×C3⋊D3D412yes—
47C8×C3⋊D3C2312yes—
48C2×C3×C3⋊C8—22no—
49C3×ΓL(1,𝔽25)—28no—
50#3712—22no—
51#3712C2314yes—
52D3×C3⋊C8—28no—
53C2×#443—91nomaximal, Sylow
54C2×#235—62no—
55C2×C3×M16—62no—
56C22×C3⋊C8—62no—
57#907—68no—
58#907—68no—
59C2×ΓL(1,𝔽25)—22no—
60C2×ΓL(1,𝔽25)—62no—
61C2×D3×C8—62no—
62C2×D3×C8—62no—
63C22×C3⋊D3#4111yescharacteristic
64C22×C3×D3—22no—
65C2×#157—24no—
66C2×#157—22no—
67C2×C32×C4C2×D411yescharacteristic
68C2×C3⋊Dic3C22×C411yescharacteristic
69C4×C3⋊D3C22×C411yescharacteristic
70C4×C3⋊D3C2×D411yescharacteristic
71C4×C3⋊D3#4111yescharacteristic
72C4×C3⋊D3C2411yescharacteristic
73C2×C3×Dic3—22no—
74C3×C4×D3—24no—
75C3×C4×D3—24no—
76#627—22no—
77#627C22×C414yes—
78#626—24no—
79#626—24no—
80#625—22no—
81#625C22×C414yes—
82#622C22×C412yes—
83#622C22×C412yes—
84C32×C8C2×D412yes—
85C3⋊(C3⋊C8)C2×D412yes—
86C3×C3⋊C8—24no—
87C2×#135—91no—
88C2×#131—92no—
89#443—98no—
90C2×#108—91no—
91C2×#104—92no—
92C2×C4×C8—91no—
93C22×C3×C4—62no—
94C2×#67—62no—
95C2×#67—62no—
96#235—64no—
97#235—64no—
98#235—64no—
99#235—64no—
100C2×D12—62no—
101C2×C4×D3—22no—
102C2×C4×D3—62no—
103C2×Dic6—62no—
104C3×M16—68no—
105C2×C3×C8—22no—
106C2×C3×C8—62no—
107C2×C3⋊C8—22no—
108C2×C3⋊C8—62no—
109C2×C3⋊C8—68no—
110ΓL(1,𝔽25)—28no—
111ΓL(1,𝔽25)—64no—
112ΓL(1,𝔽25)—64no—
113D3×C8—64no—
114D3×C8—64no—
115D3×C8—68no—
116C22×C32C4×D411yescharacteristic
117C2×C3⋊D3—22no—
118C2×C3⋊D3C4×D411yescharacteristic
119C2×C3⋊D3C2×#4111yescharacteristic
120C2×C3×D3—24no—
121C2×C3×D3—44no—
122#157—24no—
123C32×C4C4×D411yescharacteristic
124C32×C4C22×D411yescharacteristic
125C3⋊Dic3C4×D411yescharacteristic
126C3⋊Dic3C23×C411yescharacteristic
127C3×Dic3—24no—
128C2×#41—92no—
129#135—94no—
130#135—94no—
131C2×Q16—91no—
132C2×SD16—92no—
133C2×D8—91no—
134#131—98no—
135#131—184no—
136C2×M16—62no—
137C2×M16—92no—
138C22×C8—91no—
139C22×C8—91no—
140C22×C8—182no—
141C2×C42—91no—
142#108—94no—
143#104—98no—
144C4×C8—94no—
145C23×C3—62no—
146C22×D3—22no—
147C22×D3—62no—
148C2×C3×C4—22no—
149C2×C3×C4—64no—
150C2×C3×C4—64no—
151C2×C3×C4—62no—
152#67—64no—
153#67—64no—
154#67—64no—
155#67—64no—
156C2×Dic3—22no—
157C2×Dic3—62no—
158D12—64no—
159D12—64no—
160C4×D3—24no—
161C4×D3—24no—
162C4×D3—62no—
163C4×D3—62no—
164C4×D3—62no—
165C4×D3—62no—
166Dic6—64no—
167Dic6—64no—
168C3×C8—24no—
169C3×C8—64no—
170C3⋊C8—24no—
171C3⋊C8—64no—
172C2×C32#44312yescomplemented
173C2×C32C2×C4×D411yescharacteristic
174C3⋊D3—21no—
175C3⋊D3—21no—
176C3×D3—44no—
177#41—94no—
178#41—94no—
179#41—182no—
180#41—182no—
181C2×Q8—92no—
182C2×D4—92no—
183C2×D4—182no—
184C22×C4—62no—
185C22×C4—91no—
186C22×C4—181no—
187Q16—94no—
188SD16—98no—
189D8—94no—
190M16—68no—
191M16—94no—
192M16—182no—
193C2×C8—62no—
194C2×C8—92no—
195C2×C8—91no—
196C2×C8—91no—
197C2×C8—92no—
198C2×C8—91no—
199C2×C8—92no—
200C2×C8—92no—
201C2×C8—188no—
202C2×C8GO+(4,𝔽2)11yescharacteristic
203C42—92no—
204C42—181no—
205C22×C3—22no—
206C22×C3—64no—
207C22×C3—124no—
208C2×D3—24no—
209C2×D3—44no—
210C2×D3—62no—
211C2×D3—62no—
212C2×D3—124no—
213C3×C4—22no—
214C3×C4—22no—
215C3×C4—64no—
216Dic3—24no—
217Dic3—62no—
218Dic3—62no—
219C32C2×#44311yescharacteristic, complemented, Sylow
220C23—62no—
221C23—91no—
222Q8—94no—
223Q8—182no—
224D4—94no—
225D4—184no—
226D4—184no—
227D4—182no—
228C2×C4—62no—
229C2×C4—64no—
230C2×C4—64no—
231C2×C4—91no—
232C2×C4—91no—
233C2×C4—91no—
234C2×C4—91no—
235C2×C4—91no—
236C2×C4—182no—
237C2×C4—184no—
238C2×C4C2×GO+(4,𝔽2)11yescharacteristic
239C8—64no—
240C8—92no—
241C8—92no—
242C8—92no—
243C8C2×GO+(4,𝔽2)12yes—
244C2×C3—24no—
245C2×C3—22no—
246C2×C3—124no—
247D3—44no—
248D3—122no—
249D3—122no—
250C22—64no—
251C22—91no—
252C22—91no—
253C22—124no—
254C22—182no—
255C22C4×GO+(4,𝔽2)11yescharacteristic
256C4—64no—
257C4—91no—
258C4—91no—
259C4—184no—
260C4C4×GO+(4,𝔽2)11yescharacteristic
261C4C22×GO+(4,𝔽2)11yescharacteristic
262C3—22no—
263C2—124no—
264C2—181no—
265C2—181no—
266C2#1059329912yesdirect product factor
267C2C2×C4×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
centerC2×C4C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FrattiniC4C22×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32C4×D4
prime radicalC2×#64223C2
cosocleC4×C3⋊D3C24
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32C2×#443
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63805C2semidirect
3. C2×C8×#157C2semidirect
4. C2×#63733C2semidirect
5. C2×#63731C2semidirect
6. #10593299C2direct (N × H)
10. C2×#3776C4semidirect
11. C2×#3775C4semidirect
12. C2×#3774C4semidirect
13. #64223C4semidirect
20. #63805C22semidirect
21. C8×#157C22semidirect
22. #63733C22semidirect
23. #63731C22semidirect
41. #3776C2×C4semidirect
42. #3775C2×C4semidirect
43. #3774C2×C4semidirect
172. C2×C32#443semidirect
219. C32C2×#443semidirect
266. C2#10593299direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#642232
C2×#638052
C2×C8×#1572
C2×#637332
C2×#637312
#105932992
C2×#4439