Finite Group Databasebeta

← C2×#10593358 #11873558

Subgroups — C2×#10593358 #11873558

Order 1152.

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

normal subgroups only

This group has 746 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×#63915C211yesmaximal, characteristic
2C2×#63873C211yesmaximal, characteristic, complemented
3C2×#63777C211yesmaximal, characteristic, complemented
4C2×#63740C212yesmaximal, complemented
5C2×#63739C212yesmaximal
6#10593358C218yesmaximal, direct product factor
7C22×C3×Dic6—21no—
8C22×#627C2211yescharacteristic
9C22×#625C2211yescharacteristic
10C22×#622C2212yes—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×C3×(C2×D3)⋊C4—21no—
13C2×#3724—21no—
14C2×#3724C2212yes—
15C2×(C2×D3)⋊Dic3—21no—
16#63915—22no—
17#63915C2214yes—
18#63873—22no—
19#63873C2214yescomplemented
20#63777C2214yescomplemented
21#63740C2218yescomplemented
22#63739C2218yes—
23C2×#944—61no—
24C2×#885—61no—
25C23×C3×D3—21no—
26C22×C32×C4D411yescharacteristic
27C22×C3⋊Dic3D411yescharacteristic
28C22×C3⋊Dic3C2311yescharacteristic
29C22×C3×Dic3—21no—
30C22×C3×Dic3—22no—
31C2×C3×Dic6—24no—
32C2×C3×Dic6—44no—
33C2×#627—24no—
34C2×#627—21no—
35C2×#627C2312yes—
36C2×#625—24no—
37C2×#625—21no—
38C2×#625C2312yes—
39C2×#622—24no—
40C2×#622C2314yes—
41C4×C3⋊Dic3D412yes—
42C4×C3⋊Dic3C2312yes—
43C3×(C2×D3)⋊C4—24no—
44#3724—22no—
45#3724—24no—
46#3724C2314yes—
47(C2×D3)⋊Dic3—24no—
48C2×#489—91nomaximal, Sylow
49C22×C3×Q8—61no—
50C22×#67—61no—
51C22×Dic6—21no—
52C22×Dic6—61no—
53C2×C3×C22⋊C4—61no—
54C2×#217—61no—
55#944—64no—
56#944—64no—
57C2×(C2×D3)⋊C4—21no—
58C2×(C2×D3)⋊C4—61no—
59C2×Dic3⋊C4—62no—
60C2×Dic3⋊C4—62no—
61C2×C4×Dic3—61no—
62C2×C4×Dic3—61no—
63#885—64no—
64#885—64no—
65C23×C32C2×D411yescharacteristic
66C22×C3×D3—22no—
67C22×C3×D3—42no—
68C22×C3×D3—42no—
69C22×C3×D3—42no—
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—24no—
79C2×C3×Dic3—42no—
80C2×C3×Dic3—44no—
81C3×Dic6—48no—
82#627—24no—
83#627—42no—
84#625—24no—
85#625—42no—
86#622—24no—
87C2×C4⋊Q8—91no—
88C2×#124—91no—
89#489—98no—
90C2×#103—92no—
91C2×#102—92no—
92C2×#97—91no—
93C24×C3—61no—
94C23×D3—21no—
95C2×C3×Q8—64no—
96C2×C3×Q8—124no—
97C22×C3×C4—21no—
98C22×C3×C4—21no—
99C22×C3×C4—62no—
100C22×C3×C4—61no—
101C2×#67—62no—
102C2×#67—62no—
103C2×#67—124no—
104C22×Dic3—22no—
105C22×Dic3—21no—
106C22×Dic3—61no—
107C22×Dic3—61no—
108C22×Dic3—61no—
109C22×Dic3—61no—
110C2×Dic6—24no—
111C2×Dic6—44no—
112C2×Dic6—62no—
113C2×Dic6—62no—
114C2×Dic6—124no—
115C3×C22⋊C4—64no—
116#217—64no—
117(C2×D3)⋊C4—24no—
118(C2×D3)⋊C4—64no—
119Dic3⋊C4—64no—
120Dic3⋊C4—64no—
121Dic3⋊C4—68no—
122C4×Dic3—62no—
123C4×Dic3—62no—
124C4×Dic3—62no—
125C4×Dic3—62no—
126C22×C32#12412yes—
127C22×C32AGL(1,ℤ/8)12yes—
128C22×C32#13712yes—
129C22×C32C22×D411yescharacteristic
130C2×C3×D3—42no—
131C2×C3×D3—42no—
132C2×C3×D3—42no—
133C2×C3×D3—84no—
134C32×C4—22no—
135C3⋊Dic3—22no—
136C3⋊Dic3#12412yes—
137C3⋊Dic3C2×#4112yes—
138C3×Dic3—42no—
139C3×Dic3—44no—
140C22×Q8—61no—
141C22×Q8—91no—
142C22×D4—91no—
143C22×C8—92no—
144C4⋊Q8—94no—
145C4⋊Q8—182no—
146#124—94no—
147#124—182no—
148C2×C4⋊C4—92no—
149C2×C4⋊C4—181no—
150C2×C22⋊C4—61no—
151C2×C22⋊C4—181no—
152C2×C42—91no—
153#103—98no—
154#102—98no—
155#97—94no—
156C23×C3—21no—
157C23×C3—21no—
158C23×C3—62no—
159C23×C3—122no—
160C23×C3—122no—
161C23×C3—122no—
162C22×D3—22no—
163C22×D3—42no—
164C22×D3—42no—
165C22×D3—42no—
166C3×Q8—128no—
167C2×C3×C4—24no—
168C2×C3×C4—22no—
169C2×C3×C4—22no—
170C2×C3×C4—42no—
171C2×C3×C4—64no—
172C2×C3×C4—62no—
173C2×C3×C4—122no—
174C2×C3×C4—124no—
175#67—124no—
176#67—124no—
177C2×Dic3—24no—
178C2×Dic3—22no—
179C2×Dic3—44no—
180C2×Dic3—42no—
181C2×Dic3—61no—
182C2×Dic3—62no—
183C2×Dic3—61no—
184C2×Dic3—64no—
185C2×Dic3—64no—
186C2×Dic3—61no—
187C2×Dic3—61no—
188C2×Dic3—62no—
189C2×Dic3—64no—
190C2×Dic3—122no—
191Dic6—48no—
192Dic6—124no—
193Dic6—124no—
194C2×C32#48914yescomplemented
195C2×C32C2×#12411yescharacteristic
196C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
197C2×C32C2×#13711yescharacteristic
198C3×D3—82no—
199C24—61no—
200C2×Q8—64no—
201C2×Q8—92no—
202C2×Q8—124no—
203C2×Q8—181no—
204C2×Q8—184no—
205C2×D4—92no—
206C2×D4—184no—
207C2×D4—181no—
208C22×C4—61no—
209C22×C4—62no—
210C22×C4—91no—
211C22×C4—91no—
212C22×C4GO+(4,𝔽2)11yescharacteristic
213C2×C8—94no—
214C2×C8—184no—
215C4⋊C4—94no—
216C4⋊C4—182no—
217C4⋊C4—184no—
218C22⋊C4—64no—
219C22⋊C4—184no—
220C42—92no—
221C42—92no—
222C22×C3—21no—
223C22×C3—21no—
224C22×C3—22no—
225C22×C3—22no—
226C22×C3—22no—
227C22×C3—22no—
228C22×C3—22no—
229C22×C3—22no—
230C22×C3—122no—
231C22×C3—122no—
232C22×C3—122no—
233C22×C3—244no—
234C2×D3—42no—
235C2×D3—42no—
236C2×D3—42no—
237C2×D3—84no—
238C3×C4—24no—
239C3×C4—42no—
240C3×C4—122no—
241C3×C4—124no—
242Dic3—44no—
243Dic3—42no—
244Dic3—62no—
245Dic3—62no—
246Dic3—62no—
247Dic3—62no—
248Dic3—64no—
249Dic3—122no—
250C32C2×#48911yescharacteristic, complemented, Sylow
251C23—62no—
252C23—122no—
253C23—122no—
254C23—122no—
255C23C2×GO+(4,𝔽2)11yescharacteristic
256Q8—128no—
257Q8—184no—
258Q8—362no—
259D4—184no—
260D4—362no—
261C2×C4—22no—
262C2×C4—62no—
263C2×C4—64no—
264C2×C4—91no—
265C2×C4—91no—
266C2×C4—94no—
267C2×C4—92no—
268C2×C4—122no—
269C2×C4—124no—
270C2×C4—182no—
271C2×C4C2×GO+(4,𝔽2)12yes—
272C8—184no—
273C2×C3—24no—
274C2×C3—24no—
275C2×C3—21no—
276C2×C3—21no—
277C2×C3—21no—
278C2×C3—21no—
279C2×C3—21no—
280C2×C3—21no—
281C2×C3—242no—
282D3—82no—
283C22—122no—
284C22—122no—
285C22—122no—
286C22—244no—
287C22#6422112yes—
288C22#6422612yes—
289C22#6423612yes—
290C22C22×GO+(4,𝔽2)11yescharacteristic
291C4—22no—
292C4—92no—
293C4—92no—
294C4—122no—
295C4—124no—
296C4—182no—
297C3—21no—
298C3—21no—
299C2—242no—
300C2#1059335814yesdirect product factor
301C2C2×#6422111yescharacteristic
302C2C2×#6422611yescharacteristic
303C2C2×#6423611yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC22×#625C22
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#489
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×#63873C2semidirect
3. C2×#63777C2semidirect
4. C2×#63740C2semidirect
6. #10593358C2direct (N × H)
19. #63873C22semidirect
20. #63777C22semidirect
21. #63740C22semidirect
194. C2×C32#489semidirect
250. C32C2×#489semidirect
300. C2#10593358direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#639152
C2×#638732
C2×#637772
C2×#637402
C2×#637392
#105933582
C2×#4899