Finite Group Databasebeta

← C2×#10590073 #11783145

Subgroups — C2×#10590073 #11783145

Order 1152.

734 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C22×#3792C211yesmaximal, characteristic
2C2×#63957C212yesmaximal
3#10590073C214yesmaximal, direct product factor
4C23×C3⋊Dic3C2211yescharacteristic
5C2×#3792—22no—
6C2×#3792—22no—
7C2×#3792C412yescomplemented
8C2×#3792C2212yes—
9C22×#622C412yescomplemented
10C2×C3×#217—22no—
11C2×#3724—22no—
12#63957—22no—
13#63957—22no—
14#63957C414yescomplemented
15#63957C2214yes—
16C2×Dic32C414yescomplemented
17C2×#877—62no—
18C24×C32D411yescharacteristic
19C22×C3⋊Dic3C2×C411yescharacteristic
20C22×C3⋊Dic3C2×C411yescharacteristic
21C22×C3⋊Dic3C2×C412yes—
22C22×C3⋊Dic3C2×C412yes—
23C22×C3⋊Dic3D411yescharacteristic
24C22×C3⋊Dic3D412yes—
25C22×C3⋊Dic3D412yes—
26C22×C3⋊Dic3Q811yescharacteristic
27C22×C3⋊Dic3Q811yescharacteristic
28C22×C3⋊Dic3C2311yescharacteristic
29C22×C3×Dic3—24no—
30#3792—24no—
31#3792—24no—
32C2×#622—22no—
33C2×#622—22no—
34C2×#622C2×C414yescomplemented
35C3×#217—24no—
36C3×#217—24no—
37#3724—24no—
38#3724—24no—
39Dic32—24no—
40Dic32C2×C418yescomplemented
41C2×H(3,ℤ/4)—91nomaximal, Sylow
42C23×Dic3—62no—
43C2×C3×C22⋊C4—62no—
44C2×#217—22no—
45C2×Dic3⋊C4—64no—
46C2×C4×Dic3—64no—
47#877—64no—
48#877—64no—
49#877—64no—
50#877—64no—
51C23×C32—42no—
52C23×C32C22⋊C412yes—
53C23×C32C22⋊C412yes—
54C23×C32C4⋊C411yescharacteristic
55C23×C32C4⋊C411yescharacteristic
56C23×C32C2×D411yescharacteristic
57C2×C3⋊Dic3C4211yescharacteristic
58C2×C3⋊Dic3C4212yes—
59C2×C3⋊Dic3C4211yescharacteristic
60C2×C3⋊Dic3C22⋊C412yes—
61C2×C3⋊Dic3C22⋊C412yes—
62C2×C3⋊Dic3C22⋊C411yescharacteristic
63C2×C3⋊Dic3C22⋊C411yescharacteristic
64C2×C3⋊Dic3C22⋊C412yes—
65C2×C3⋊Dic3C4⋊C411yescharacteristic
66C2×C3⋊Dic3C4⋊C411yescharacteristic
67C2×C3⋊Dic3C4⋊C412yes—
68C2×C3⋊Dic3C4⋊C412yes—
69C2×C3⋊Dic3C4⋊C412yes—
70C2×C3⋊Dic3C4⋊C412yes—
71C2×C3⋊Dic3C22×C411yescharacteristic
72C2×C3⋊Dic3C22×C412yes—
73C2×C3⋊Dic3C2×D412yes—
74C2×C3⋊Dic3C2×Q811yescharacteristic
75C2×C3×Dic3—28no—
76C2×C3×Dic3—48no—
77#622—24no—
78C22×M16—91no—
79C2×#117—92no—
80H(3,ℤ/4)—94no—
81C24×C3—22no—
82C22×C3×C4—64no—
83C22×Dic3—24no—
84C22×Dic3—62no—
85C22×Dic3—62no—
86C22×Dic3—62no—
87C22×Dic3—62no—
88C22×Dic3—62no—
89C22×Dic3—62no—
90C22×Dic3—62no—
91C22×Dic3—62no—
92C22×Dic3—62no—
93C22×Dic3—62no—
94C22×Dic3—62no—
95C22×Dic3—62no—
96C22×Dic3—62no—
97C22×Dic3—62no—
98C3×C22⋊C4—64no—
99C3×C22⋊C4—64no—
100#217—24no—
101#217—24no—
102Dic3⋊C4—68no—
103Dic3⋊C4—68no—
104C4×Dic3—68no—
105C4×Dic3—68no—
106C22×C32—24no—
107C22×C32—22no—
108C22×C32—42no—
109C22×C32—41no—
110C22×C32—41no—
111C22×C32#9512yes—
112C22×C32#9511yescharacteristic
113C22×C32#9511yescharacteristic
114C22×C32C2×C22⋊C412yes—
115C22×C32C2×C4⋊C411yescharacteristic
116C3⋊Dic3#9511yescharacteristic
117C3⋊Dic3#9512yes—
118C3⋊Dic3#9511yescharacteristic
119C3⋊Dic3C2×C4211yescharacteristic
120C3⋊Dic3C2×C22⋊C411yescharacteristic
121C3⋊Dic3C2×C4⋊C412yes—
122C3×Dic3—48no—
123C23×C4—91no—
124C2×M16—92no—
125C2×M16—92no—
126C2×M16—182no—
127C2×M16—182no—
128C22×C8—92no—
129#117—94no—
130#117—94no—
131#117—182no—
132#117—182no—
133C2×C4⋊C4—182no—
134C2×C22⋊C4—62no—
135C2×C42—94no—
136C23×C3—22no—
137C23×C3—22no—
138C23×C3—22no—
139C23×C3—22no—
140C23×C3—22no—
141C23×C3—22no—
142C23×C3—22no—
143C23×C3—48no—
144C2×C3×C4—68no—
145C2×C3×C4—128no—
146C2×Dic3—28no—
147C2×Dic3—48no—
148C2×Dic3—62no—
149C2×Dic3—62no—
150C2×Dic3—62no—
151C2×Dic3—62no—
152C2×Dic3—62no—
153C2×Dic3—62no—
154C2×Dic3—62no—
155C2×Dic3—62no—
156C2×Dic3—62no—
157C2×Dic3—62no—
158C2×Dic3—62no—
159C2×Dic3—62no—
160C2×Dic3—62no—
161C2×Dic3—62no—
162C2×Dic3—62no—
163C2×Dic3—62no—
164C2×Dic3—62no—
165C2×Dic3—62no—
166C2×Dic3—62no—
167C2×Dic3—62no—
168C2×Dic3—62no—
169C2×Dic3—62no—
170C2×Dic3—62no—
171C2×Dic3—62no—
172C2×Dic3—62no—
173C2×Dic3—62no—
174C2×Dic3—62no—
175C2×Dic3—62no—
176C2×C32—22no—
177C2×C32—22no—
178C2×C32—21no—
179C2×C32—21no—
180C2×C32H(3,ℤ/4)12yescomplemented
181C2×C32C2×#9511yescharacteristic
182C24GO+(4,𝔽2)11yescharacteristic
183C22×C4—64no—
184C22×C4—91no—
185C22×C4—91no—
186C22×C4—92no—
187C22×C4—92no—
188C22×C4—92no—
189C22×C4—92no—
190C22×C4—91no—
191C22×C4—91no—
192C22×C4—91no—
193C22×C4—91no—
194M16—184no—
195M16—184no—
196C2×C8—94no—
197C2×C8—182no—
198C2×C8—182no—
199C4⋊C4—184no—
200C4⋊C4—184no—
201C22⋊C4—64no—
202C22⋊C4—64no—
203C42—98no—
204C42—184no—
205C22×C3—28no—
206C22×C3—22no—
207C22×C3—22no—
208C22×C3—22no—
209C22×C3—22no—
210C22×C3—22no—
211C22×C3—22no—
212C22×C3—22no—
213C22×C3—44no—
214C22×C3—44no—
215C22×C3—44no—
216C22×C3—44no—
217C22×C3—44no—
218C22×C3—44no—
219C3×C4—128no—
220Dic3—48no—
221Dic3—62no—
222Dic3—62no—
223Dic3—62no—
224Dic3—62no—
225Dic3—62no—
226Dic3—62no—
227Dic3—62no—
228Dic3—62no—
229C32C2×H(3,ℤ/4)11yescharacteristic, complemented, Sylow
230C23—42no—
231C23D32⋊C412yes—
232C23D32⋊C412yes—
233C23#377311yescharacteristic
234C23#377311yescharacteristic
235C23C2×GO+(4,𝔽2)11yescharacteristic
236C2×C4—68no—
237C2×C4—92no—
238C2×C4—92no—
239C2×C4—92no—
240C2×C4—92no—
241C2×C4—91no—
242C2×C4—91no—
243C2×C4—91no—
244C2×C4—91no—
245C2×C4—91no—
246C2×C4—92no—
247C2×C4—92no—
248C2×C4—92no—
249C2×C4—92no—
250C2×C4—91no—
251C2×C4—92no—
252C2×C4—91no—
253C2×C4—91no—
254C2×C4—92no—
255C2×C4—128no—
256C8—184no—
257C2×C3—24no—
258C2×C3—24no—
259C2×C3—24no—
260C2×C3—22no—
261C2×C3—42no—
262C2×C3—42no—
263C2×C3—42no—
264C2×C3—42no—
265C22—24no—
266C22—22no—
267C22—41no—
268C22—42no—
269C22—41no—
270C22#6373712yes—
271C22#6373711yescharacteristic
272C22#6373711yescharacteristic
273C22C2×D32⋊C412yes—
274C22C2×#377311yescharacteristic
275C4—91no—
276C4—91no—
277C4—92no—
278C4—91no—
279C4—92no—
280C4—91no—
281C4—128no—
282C3—22no—
283C2—22no—
284C2—21no—
285C2—22no—
286C2—21no—
287C2#1059007312yesdirect product factor
288C2C2×#6373711yescharacteristic
subgroupG/H
centerC22#63737
commutatorC3⋊Dic3C2×C42
FrattiniC23C2×GO+(4,𝔽2)
Fitting, prime radicalC24×C32D4
socleC22×C32#95
cosocleC22×C3⋊Dic3C23
hypercenterC24GO+(4,𝔽2)
hypocenterC32C2×H(3,ℤ/4)
LCSG ▷ C3⋊Dic3 ▷ C32
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
3. #10590073C2direct (N × H)
7. C2×#3792C4semidirect
9. C22×#622C4semidirect
14. #63957C4semidirect
16. C2×Dic32C4semidirect
34. C2×#622C2×C4semidirect
40. Dic32C2×C4semidirect
180. C2×C32H(3,ℤ/4)semidirect
229. C32C2×H(3,ℤ/4)semidirect
287. C2#10590073direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37922
C2×#639572
#105900732
C2×H(3,ℤ/4)9