Finite Group Databasebeta

← C2×#10593376 #11868419

Subgroups — C2×#10593376 #11868419

Order 1152.

710 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 710 conjugacy classes of subgroups — too many to draw. Only its 143 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×C4×#627C211yesmaximal, characteristic
2C2×#63873C211yesmaximal, characteristic
3C2×C4⋊#622C211yesmaximal, characteristic
4C2×#63742C212yesmaximal
5C2×#63740C212yesmaximal
6#10593376C218yesmaximal, direct product factor
7C22×C3×Dic6—21no—
8C22×#627C2211yescharacteristic
9C22×#622C2212yes—
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C2×C3×C4×Dic3—21no—
12C2×#3724—21no—
13C2×#3724C2212yes—
14C2×#3724C2211yescharacteristic
15C2×Dic3⋊Dic3—21no—
16C4×#627—22no—
17C4×#627C2214yes—
18#63873—22no—
19#63873C2214yes—
20C4⋊#622C2214yes—
21#63742C2218yes—
22#63740C2218yes—
23C2×#944—61no—
24C2×C4×Dic6—61no—
25C22×C32×C4D411yescharacteristic
26C22×C3⋊Dic3D411yescharacteristic
27C22×C3⋊Dic3C2311yescharacteristic
28C22×C3×Dic3—21no—
29C22×C3×Dic3—21no—
30C22×C3×Dic3—22no—
31C2×C3×Dic6—24no—
32C2×C3×Dic6—44no—
33C2×#627—21no—
34C2×#627—22no—
35C2×#627Q814yescomplemented
36C2×#627C2312yes—
37C2×#622—24no—
38C2×#622C2314yes—
39C4×C3⋊Dic3D412yes—
40C4×C3⋊Dic3C2312yes—
41C3×C4×Dic3—24no—
42#3724—22no—
43#3724—24no—
44#3724—21no—
45#3724C2314yes—
46#3724C2312yes—
47Dic3⋊Dic3—24no—
48C2×#475—91nomaximal, Sylow
49C22×C3×Q8—61no—
50C22×Dic6—21no—
51C22×Dic6—61no—
52C2×C3×C42—61no—
53#944—64no—
54#944—64no—
55C2×C4⋊Dic3—61no—
56C2×Dic3⋊C4—61no—
57C2×Dic3⋊C4—62no—
58C2×Dic3⋊C4—61no—
59C2×Dic3⋊C4—62no—
60C2×C4×Dic3—21no—
61C2×C4×Dic3—61no—
62C2×C4×Dic3—61no—
63C4×Dic6—64no—
64C4×Dic6—64no—
65C23×C32C2×D411yescharacteristic
66C2×C32×C4SD1614yes—
67C2×C32×C4C2×D412yes—
68C2×C3⋊Dic3—22no—
69C2×C3⋊Dic3C2×D412yes—
70C2×C3⋊Dic3C2×D411yescharacteristic
71C2×C3⋊Dic3C2×Q812yes—
72C2×C3⋊Dic3#4112yes—
73C2×C3⋊Dic3C2411yescharacteristic
74C2×C3×Dic3—24no—
75C2×C3×Dic3—22no—
76C2×C3×Dic3—22no—
77C2×C3×Dic3—24no—
78C2×C3×Dic3—44no—
79C2×C3×Dic3—42no—
80C3×Dic6—48no—
81#627—24no—
82#627—22no—
83#627C2×Q814yescomplemented
84#622—24no—
85C2×C4⋊Q8—91no—
86C2×C4×Q8—91no—
87#475—98no—
88C2×#106—92no—
89C2×C4⋊C8—91no—
90C2×#103—92no—
91C2×C3×Q8—64no—
92C2×C3×Q8—124no—
93C22×C3×C4—21no—
94C22×C3×C4—21no—
95C22×C3×C4—61no—
96C22×C3×C4—61no—
97C22×C3×C4—62no—
98C22×Dic3—21no—
99C22×Dic3—21no—
100C22×Dic3—22no—
101C22×Dic3—61no—
102C22×Dic3—61no—
103C22×Dic3—61no—
104C22×Dic3—61no—
105C2×Dic6—24no—
106C2×Dic6—44no—
107C2×Dic6—62no—
108C2×Dic6—64no—
109C2×Dic6—62no—
110C2×Dic6—64no—
111C3×C42—64no—
112C4⋊Dic3—64no—
113Dic3⋊C4—62no—
114Dic3⋊C4—64no—
115Dic3⋊C4—64no—
116Dic3⋊C4—62no—
117Dic3⋊C4—64no—
118Dic3⋊C4—68no—
119C4×Dic3—24no—
120C4×Dic3—62no—
121C4×Dic3—62no—
122C4×Dic3—62no—
123C4×Dic3—62no—
124C22×C32C22⋊Q812yes—
125C22×C32C2×SD1612yes—
126C22×C32#13712yes—
127C22×C32C22×D411yescharacteristic
128C32×C4C2×SD1614yes—
129C3⋊Dic3—22no—
130C3⋊Dic3C22⋊Q812yes—
131C3⋊Dic3C22×Q811yescharacteristic
132C3⋊Dic3C2×#4111yescharacteristic
133C3×Dic3—24no—
134C3×Dic3—44no—
135C3×Dic3—42no—
136C22×Q8—61no—
137C22×Q8—91no—
138C22×C8—92no—
139C4⋊Q8—94no—
140C4⋊Q8—182no—
141C4×Q8—94no—
142C4×Q8—182no—
143C2×C4⋊C4—91no—
144C2×C4⋊C4—92no—
145C2×C4⋊C4—181no—
146C2×C4⋊C4—181no—
147C2×C42—61no—
148C2×C42—91no—
149#106—98no—
150C4⋊C8—94no—
151#103—98no—
152C23×C3—21no—
153C23×C3—21no—
154C3×Q8—128no—
155C2×C3×C4—22no—
156C2×C3×C4—22no—
157C2×C3×C4—24no—
158C2×C3×C4—24no—
159C2×C3×C4—62no—
160C2×C3×C4—64no—
161C2×C3×C4—62no—
162C2×C3×C4—64no—
163C2×C3×C4—122no—
164C2×C3×C4—124no—
165C2×Dic3—22no—
166C2×Dic3—24no—
167C2×Dic3—22no—
168C2×Dic3—24no—
169C2×Dic3—44no—
170C2×Dic3—42no—
171C2×Dic3—61no—
172C2×Dic3—62no—
173C2×Dic3—61no—
174C2×Dic3—62no—
175C2×Dic3—62no—
176C2×Dic3—62no—
177C2×Dic3—62no—
178C2×Dic3—61no—
179C2×Dic3—61no—
180C2×Dic3—62no—
181C2×Dic3—64no—
182C2×Dic3—122no—
183Dic6—48no—
184Dic6—64no—
185Dic6—68no—
186Dic6—64no—
187C2×C32#47514yescomplemented
188C2×C32C2×C22⋊Q811yescharacteristic
189C2×C32C22×SD1611yescharacteristic
190C2×C32C2×#13711yescharacteristic
191C2×Q8—64no—
192C2×Q8—92no—
193C2×Q8—94no—
194C2×Q8—124no—
195C2×Q8—181no—
196C2×Q8—182no—
197C22×C4—61no—
198C22×C4—61no—
199C22×C4—62no—
200C22×C4—91no—
201C22×C4—91no—
202C22×C4GO+(4,𝔽2)11yescharacteristic
203C2×C8—94no—
204C2×C8—184no—
205C4⋊C4—94no—
206C4⋊C4—92no—
207C4⋊C4—181no—
208C4⋊C4—182no—
209C4⋊C4—184no—
210C4⋊C4—184no—
211C42—64no—
212C42—92no—
213C42—92no—
214C22×C3—21no—
215C22×C3—21no—
216C22×C3—22no—
217C22×C3—22no—
218C22×C3—22no—
219C22×C3—22no—
220C22×C3—22no—
221C22×C3—22no—
222C3×C4—24no—
223C3×C4—24no—
224C3×C4—64no—
225C3×C4—124no—
226C3×C4—122no—
227Dic3—24no—
228Dic3—44no—
229Dic3—42no—
230Dic3—62no—
231Dic3—61no—
232Dic3—61no—
233Dic3—62no—
234Dic3—61no—
235Dic3—61no—
236Dic3—64no—
237Dic3—122no—
238C32C2×#47511yescharacteristic, complemented, Sylow
239C23C2×GO+(4,𝔽2)11yescharacteristic
240Q8—94no—
241Q8—128no—
242Q8—182no—
243Q8—184no—
244C2×C4—62no—
245C2×C4—64no—
246C2×C4—62no—
247C2×C4—64no—
248C2×C4—91no—
249C2×C4—91no—
250C2×C4—92no—
251C2×C4—92no—
252C2×C4—92no—
253C2×C4—122no—
254C2×C4—124no—
255C2×C4—182no—
256C2×C4#377514yes—
257C2×C4C2×GO+(4,𝔽2)12yes—
258C8—184no—
259C2×C3—24no—
260C2×C3—24no—
261C2×C3—21no—
262C2×C3—21no—
263C2×C3—21no—
264C2×C3—21no—
265C2×C3—21no—
266C2×C3—21no—
267C22D32⋊Q812yes—
268C22#6422612yes—
269C22C2×#377512yes—
270C22C22×GO+(4,𝔽2)11yescharacteristic
271C4—64no—
272C4—91no—
273C4—91no—
274C4—92no—
275C4—122no—
276C4—124no—
277C4—182no—
278C4C2×#377514yes—
279C3—21no—
280C3—21no—
281C2#1059337614yesdirect product factor
282C2C2×D32⋊Q811yescharacteristic
283C2C2×#6422611yescharacteristic
284C2C22×#377511yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#475
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
6. #10593376C2direct (N × H)
35. C2×#627Q8semidirect
83. #627C2×Q8semidirect
187. C2×C32#475semidirect
238. C32C2×#475semidirect
281. C2#10593376direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#6272
C2×#638732
C2×C4⋊#6222
C2×#637422
C2×#637402
#105933762
C2×#4759