Finite Group Databasebeta

← C2×#10593385 #11868420

Subgroups — C2×#10593385 #11868420

Order 1152.

710 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 710 conjugacy classes of subgroups — too many to draw. Only its 135 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×#63919C211yesmaximal, characteristic
2C2×#63838C211yesmaximal, characteristic
3C2×#63779C211yesmaximal, characteristic
4C2×#63742C212yesmaximal
5C2×#63740C212yesmaximal
6#10593385C218yesmaximal, direct product factor
7C22×#627—21no—
8C22×#627C2211yescharacteristic
9C22×#622C2212yes—
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C2×C3×C4⋊Dic3—21no—
12C2×C3×Dic3⋊C4—21no—
13C2×#3724C2212yes—
14C2×#3724C2211yescharacteristic
15C2×Dic32—21no—
16#63919—22no—
17#63919C2214yes—
18#63838—22no—
19#63838C2214yes—
20#63779C2214yes—
21#63742C2218yes—
22#63740C2218yes—
23C2×#888—61no—
24C2×#887—61no—
25C22×C32×C4D411yescharacteristic
26C22×C3⋊Dic3D411yescharacteristic
27C22×C3⋊Dic3C2311yescharacteristic
28C22×C3×Dic3—21no—
29C22×C3×Dic3—21no—
30C22×C3×Dic3—22no—
31C2×#627—21no—
32C2×#627—22no—
33C2×#627—24no—
34C2×#627—44no—
35C2×#627Q814yescomplemented
36C2×#627C2312yes—
37C2×#622—24no—
38C2×#622C2314yes—
39C4×C3⋊Dic3D412yes—
40C4×C3⋊Dic3C2312yes—
41C3×C4⋊Dic3—24no—
42C3×Dic3⋊C4—24no—
43#3724—21no—
44#3724—22no—
45#3724C2312yes—
46#3724C2314yes—
47Dic32—24no—
48C2×#475—91nomaximal, Sylow
49C22×Dic6—61no—
50C22×Dic6—62no—
51C2×C3×C4⋊C4—61no—
52C2×C3×C4⋊C4—61no—
53C2×C4⋊Dic3—21no—
54C2×Dic3⋊C4—21no—
55C2×Dic3⋊C4—61no—
56C2×Dic3⋊C4—62no—
57C2×C4×Dic3—61no—
58C2×C4×Dic3—61no—
59C2×C4×Dic3—61no—
60C2×C4×Dic3—61no—
61#888—64no—
62#888—64no—
63#887—64no—
64#887—64no—
65C23×C32C2×D411yescharacteristic
66C2×C32×C4—22no—
67C2×C32×C4C2×D412yes—
68C2×C3⋊Dic3SD1614yes—
69C2×C3⋊Dic3C2×D411yescharacteristic
70C2×C3⋊Dic3C2×D412yes—
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—
80#627—24no—
81#627—22no—
82#627—48no—
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—
91C22×C3×C4—21no—
92C22×C3×C4—21no—
93C22×C3×C4—61no—
94C22×C3×C4—61no—
95C22×C3×C4—62no—
96C22×Dic3—21no—
97C22×Dic3—21no—
98C22×Dic3—22no—
99C22×Dic3—61no—
100C22×Dic3—61no—
101C22×Dic3—61no—
102C22×Dic3—61no—
103C2×Dic6—62no—
104C2×Dic6—64no—
105C2×Dic6—62no—
106C2×Dic6—64no—
107C2×Dic6—68no—
108C2×Dic6—128no—
109C3×C4⋊C4—64no—
110C3×C4⋊C4—64no—
111C4⋊Dic3—24no—
112Dic3⋊C4—24no—
113Dic3⋊C4—62no—
114Dic3⋊C4—64no—
115Dic3⋊C4—62no—
116Dic3⋊C4—64no—
117C4×Dic3—62no—
118C4×Dic3—62no—
119C4×Dic3—62no—
120C4×Dic3—62no—
121C4×Dic3—64no—
122C4×Dic3—64no—
123C22×C32C22⋊Q812yes—
124C22×C32C2×SD1612yes—
125C22×C32#13712yes—
126C22×C32C22×D411yescharacteristic
127C32×C4—22no—
128C3⋊Dic3C22⋊Q812yes—
129C3⋊Dic3C2×SD1614yes—
130C3⋊Dic3C22×Q811yescharacteristic
131C3⋊Dic3C2×#4111yescharacteristic
132C3×Dic3—24no—
133C3×Dic3—44no—
134C3×Dic3—42no—
135C22×Q8—91no—
136C22×Q8—181no—
137C22×C8—92no—
138C4⋊Q8—94no—
139C4⋊Q8—182no—
140C4×Q8—94no—
141C4×Q8—182no—
142C2×C4⋊C4—61no—
143C2×C4⋊C4—61no—
144C2×C4⋊C4—91no—
145C2×C4⋊C4—92no—
146C2×C42—91no—
147C2×C42—181no—
148#106—98no—
149C4⋊C8—94no—
150#103—98no—
151C23×C3—21no—
152C23×C3—21no—
153C2×C3×C4—24no—
154C2×C3×C4—22no—
155C2×C3×C4—22no—
156C2×C3×C4—42no—
157C2×C3×C4—62no—
158C2×C3×C4—64no—
159C2×C3×C4—62no—
160C2×C3×C4—64no—
161C2×C3×C4—124no—
162C2×C3×C4—122no—
163C2×Dic3—22no—
164C2×Dic3—24no—
165C2×Dic3—22no—
166C2×Dic3—24no—
167C2×Dic3—44no—
168C2×Dic3—42no—
169C2×Dic3—64no—
170C2×Dic3—64no—
171C2×Dic3—62no—
172C2×Dic3—61no—
173C2×Dic3—61no—
174C2×Dic3—62no—
175C2×Dic3—62no—
176C2×Dic3—62no—
177C2×Dic3—62no—
178C2×Dic3—62no—
179C2×Dic3—61no—
180C2×Dic3—61no—
181Dic6—64no—
182Dic6—68no—
183Dic6—64no—
184Dic6—1216no—
185C2×C32#47514yescomplemented
186C2×C32C2×C22⋊Q811yescharacteristic
187C2×C32C22×SD1611yescharacteristic
188C2×C32C2×#13711yescharacteristic
189C2×Q8—92no—
190C2×Q8—94no—
191C2×Q8—181no—
192C2×Q8—182no—
193C2×Q8—184no—
194C2×Q8—364no—
195C22×C4—61no—
196C22×C4—61no—
197C22×C4—62no—
198C22×C4—91no—
199C22×C4—91no—
200C22×C4GO+(4,𝔽2)11yescharacteristic
201C2×C8—94no—
202C2×C8—184no—
203C4⋊C4—64no—
204C4⋊C4—64no—
205C4⋊C4—94no—
206C4⋊C4—92no—
207C4⋊C4—181no—
208C4⋊C4—182no—
209C42—92no—
210C42—92no—
211C42—184no—
212C22×C3—21no—
213C22×C3—21no—
214C22×C3—22no—
215C22×C3—22no—
216C22×C3—22no—
217C22×C3—22no—
218C22×C3—22no—
219C22×C3—22no—
220C3×C4—24no—
221C3×C4—42no—
222C3×C4—64no—
223C3×C4—124no—
224C3×C4—122no—
225Dic3—24no—
226Dic3—44no—
227Dic3—42no—
228Dic3—62no—
229Dic3—61no—
230Dic3—61no—
231Dic3—64no—
232Dic3—62no—
233Dic3—64no—
234Dic3—61no—
235Dic3—61no—
236C32C2×#47511yescharacteristic, complemented, Sylow
237C23C2×GO+(4,𝔽2)11yescharacteristic
238Q8—94no—
239Q8—182no—
240Q8—184no—
241Q8—368no—
242C2×C4—22no—
243C2×C4—62no—
244C2×C4—64no—
245C2×C4—62no—
246C2×C4—64no—
247C2×C4—92no—
248C2×C4—91no—
249C2×C4—91no—
250C2×C4—92no—
251C2×C4—92no—
252C2×C4—94no—
253C2×C4—124no—
254C2×C4—122no—
255C2×C4C2×GO+(4,𝔽2)12yes—
256C8—184no—
257C2×C3—24no—
258C2×C3—24no—
259C2×C3—21no—
260C2×C3—21no—
261C2×C3—21no—
262C2×C3—21no—
263C2×C3—21no—
264C2×C3—21no—
265C22D32⋊Q812yes—
266C22#6422712yes—
267C22#6423912yes—
268C22C22×GO+(4,𝔽2)11yescharacteristic
269C4—22no—
270C4—64no—
271C4—91no—
272C4—91no—
273C4—92no—
274C4—94no—
275C4—124no—
276C4—122no—
277C3—21no—
278C3—21no—
279C2#1059338514yesdirect product factor
280C2C2×D32⋊Q811yescharacteristic
281C2C2×#6422711yescharacteristic
282C2C2×#6423911yescharacteristic
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. #10593385C2direct (N × H)
35. C2×#627Q8semidirect
83. #627C2×Q8semidirect
185. C2×C32#475semidirect
236. C32C2×#475semidirect
279. C2#10593385direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#639192
C2×#638382
C2×#637792
C2×#637422
C2×#637402
#105933852
C2×#4759