Finite Group Databasebeta

← C2×#10593356 #11873592

Subgroups — C2×#10593356 #11873592

Order 1152.

850 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 850 conjugacy classes of subgroups — too many to draw. Only its 119 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×#63914C211yesmaximal, characteristic
2C2×#63870C211yesmaximal, characteristic, complemented
3C2×#63777C211yesmaximal, characteristic, complemented
4C2×#63739C212yesmaximal, complemented
5C2×#63739C212yesmaximal, complemented
6#10593356C218yesmaximal, direct product factor
7C22×C3×D12—21no—
8C22×#625—21no—
9C22×#625C2212yes—
10C22×#622C2212yes—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×C3×Dic3⋊C4—21no—
13C2×#3724C2211yescharacteristic
14C2×#3724C2211yescharacteristic
15C2×Dic3⋊Dic3—21no—
16#63914—22no—
17#63914C2214yes—
18#63870—22no—
19#63870C2214yescomplemented
20#63777C2214yescomplemented
21#63739C2218yescomplemented
22#63739C2218yescomplemented
23C2×#940—61no—
24C2×#889—61no—
25C23×C3×D3—22no—
26C22×C32×C4D411yescharacteristic
27C22×C3⋊Dic3D411yescharacteristic
28C22×C3⋊Dic3C2311yescharacteristic
29C22×C3×Dic3—21no—
30C22×C3×Dic3—21no—
31C2×C3×D12—24no—
32C2×C3×D12—44no—
33C2×#625—28no—
34C2×#625—24no—
35C2×#625—22no—
36C2×#625—44no—
37C2×#625C2314yes—
38C2×#622—24no—
39C2×#622C2314yes—
40C4×C3⋊Dic3D412yes—
41C4×C3⋊Dic3C2312yes—
42C3×Dic3⋊C4—24no—
43#3724—21no—
44#3724—21no—
45#3724C2312yes—
46#3724C2312yes—
47Dic3⋊Dic3—24no—
48C2×#490—91nomaximal, Sylow
49C22×C3×D4—61no—
50C22×#67—62no—
51C22×#67—62no—
52C22×D12—21no—
53C2×C3×C4⋊C4—61no—
54#940—64no—
55#940—64no—
56C2×C4⋊Dic3—61no—
57C2×Dic3⋊C4—21no—
58C2×Dic3⋊C4—61no—
59C2×Dic3⋊C4—61no—
60C2×Dic3⋊C4—61no—
61C2×C4×Dic3—61no—
62C2×C4×Dic3—61no—
63#889—64no—
64#889—64no—
65C23×C32C2×D411yescharacteristic
66C22×C3×D3—24no—
67C22×C3×D3—44no—
68C22×C3×D3—44no—
69C22×C3×D3—44no—
70C2×C32×C4—22no—
71C2×C32×C4C2×D412yes—
72C2×C3⋊Dic3—22no—
73C2×C3⋊Dic3C2×D412yes—
74C2×C3⋊Dic3C2×D411yescharacteristic
75C2×C3⋊Dic3#4114yes—
76C2×C3⋊Dic3C2411yescharacteristic
77C2×C3×Dic3—22no—
78C2×C3×Dic3—22no—
79C2×C3×Dic3—42no—
80C2×C3×Dic3—42no—
81C3×D12—48no—
82#625—28no—
83#625—48no—
84#625—44no—
85#622—24no—
86C2×#127—91no—
87C2×#125—91no—
88#490—98no—
89C2×#102—92no—
90C2×#102—92no—
91C2×#97—91no—
92C24×C3—62no—
93C23×D3—22no—
94C2×C3×D4—64no—
95C2×C3×D4—124no—
96C22×C3×C4—21no—
97C22×C3×C4—21no—
98C22×C3×C4—61no—
99C22×C3×C4—61no—
100C2×#67—64no—
101C2×#67—68no—
102C2×#67—64no—
103C2×#67—128no—
104C2×#67—128no—
105C22×Dic3—21no—
106C22×Dic3—21no—
107C22×Dic3—61no—
108C22×Dic3—61no—
109C22×Dic3—61no—
110C22×Dic3—61no—
111C2×D12—24no—
112C2×D12—44no—
113C3×C4⋊C4—64no—
114C4⋊Dic3—64no—
115Dic3⋊C4—24no—
116Dic3⋊C4—62no—
117Dic3⋊C4—62no—
118Dic3⋊C4—64no—
119Dic3⋊C4—62no—
120Dic3⋊C4—62no—
121C4×Dic3—62no—
122C4×Dic3—62no—
123C4×Dic3—62no—
124C4×Dic3—62no—
125C22×C32#12412yes—
126C22×C32AGL(1,ℤ/8)12yes—
127C22×C32AGL(1,ℤ/8)12yes—
128C22×C32C22×D411yescharacteristic
129C2×C3×D3—44no—
130C2×C3×D3—44no—
131C2×C3×D3—44no—
132C2×C3×D3—88no—
133C32×C4—22no—
134C3⋊Dic3—22no—
135C3⋊Dic3#12412yes—
136C3⋊Dic3C2×#4112yes—
137C3×Dic3—42no—
138C3×Dic3—42no—
139C22×D4—61no—
140C22×D4—92no—
141C22×D4—181no—
142C22×C8—92no—
143#127—94no—
144#127—182no—
145#125—94no—
146#125—182no—
147C2×C4⋊C4—61no—
148C2×C4⋊C4—91no—
149C2×C4⋊C4—91no—
150C2×C4⋊C4—181no—
151C2×C42—91no—
152#102—98no—
153#102—98no—
154#97—94no—
155C23×C3—21no—
156C23×C3—21no—
157C23×C3—64no—
158C23×C3—124no—
159C23×C3—124no—
160C23×C3—124no—
161C22×D3—24no—
162C22×D3—44no—
163C22×D3—44no—
164C22×D3—44no—
165C3×D4—128no—
166C2×C3×C4—24no—
167C2×C3×C4—22no—
168C2×C3×C4—22no—
169C2×C3×C4—42no—
170C2×C3×C4—62no—
171C2×C3×C4—62no—
172C2×C3×C4—122no—
173C2×C3×C4—122no—
174#67—128no—
175#67—128no—
176#67—1216no—
177C2×Dic3—22no—
178C2×Dic3—22no—
179C2×Dic3—42no—
180C2×Dic3—42no—
181C2×Dic3—61no—
182C2×Dic3—61no—
183C2×Dic3—62no—
184C2×Dic3—64no—
185C2×Dic3—64no—
186C2×Dic3—61no—
187C2×Dic3—61no—
188C2×Dic3—62no—
189C2×Dic3—64no—
190C2×Dic3—122no—
191D12—48no—
192C2×C32#49014yescomplemented
193C2×C32C2×#12411yescharacteristic
194C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
195C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
196C3×D3—84no—
197C24—62no—
198C2×D4—64no—
199C2×D4—94no—
200C2×D4—124no—
201C2×D4—188no—
202C2×D4—184no—
203C2×D4—182no—
204C2×D4—364no—
205C22×C4—61no—
206C22×C4—61no—
207C22×C4—91no—
208C22×C4—91no—
209C22×C4GO+(4,𝔽2)11yescharacteristic
210C2×C8—94no—
211C2×C8—184no—
212C4⋊C4—64no—
213C4⋊C4—92no—
214C4⋊C4—92no—
215C4⋊C4—181no—
216C4⋊C4—181no—
217C4⋊C4—184no—
218C42—92no—
219C42—92no—
220C22×C3—21no—
221C22×C3—21no—
222C22×C3—22no—
223C22×C3—22no—
224C22×C3—22no—
225C22×C3—22no—
226C22×C3—22no—
227C22×C3—22no—
228C22×C3—124no—
229C22×C3—124no—
230C22×C3—124no—
231C22×C3—248no—
232C2×D3—44no—
233C2×D3—44no—
234C2×D3—44no—
235C2×D3—88no—
236C3×C4—24no—
237C3×C4—42no—
238C3×C4—122no—
239C3×C4—122no—
240Dic3—42no—
241Dic3—42no—
242Dic3—62no—
243Dic3—62no—
244Dic3—62no—
245Dic3—62no—
246Dic3—64no—
247Dic3—122no—
248C32C2×#49011yescharacteristic, complemented, Sylow
249C23—64no—
250C23—124no—
251C23—124no—
252C23—124no—
253C23C2×GO+(4,𝔽2)11yescharacteristic
254D4—128no—
255D4—188no—
256D4—364no—
257D4—368no—
258C2×C4—22no—
259C2×C4—62no—
260C2×C4—62no—
261C2×C4—91no—
262C2×C4—91no—
263C2×C4—94no—
264C2×C4—92no—
265C2×C4—122no—
266C2×C4—122no—
267C2×C4—182no—
268C2×C4C2×GO+(4,𝔽2)12yes—
269C8—184no—
270C2×C3—24no—
271C2×C3—24no—
272C2×C3—21no—
273C2×C3—21no—
274C2×C3—21no—
275C2×C3—21no—
276C2×C3—21no—
277C2×C3—21no—
278C2×C3—244no—
279D3—84no—
280C22—124no—
281C22—124no—
282C22—124no—
283C22—248no—
284C22#6422112yes—
285C22#6422412yes—
286C22#6423612yes—
287C22C22×GO+(4,𝔽2)11yescharacteristic
288C4—22no—
289C4—92no—
290C4—92no—
291C4—122no—
292C4—122no—
293C4—182no—
294C3—21no—
295C3—21no—
296C2—244no—
297C2#1059335614yesdirect product factor
298C2C2×#6422111yescharacteristic
299C2C2×#6422411yescharacteristic
300C2C2×#6423611yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC2×#63914C2
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#490
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
2. C2×#63870C2semidirect
3. C2×#63777C2semidirect
4. C2×#63739C2semidirect
5. C2×#63739C2semidirect
6. #10593356C2direct (N × H)
19. #63870C22semidirect
20. #63777C22semidirect
21. #63739C22semidirect
22. #63739C22semidirect
192. C2×C32#490semidirect
248. C32C2×#490semidirect
297. C2#10593356direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#639142
C2×#638702
C2×#637772
C2×#637392
#105933562
C2×#4909