Finite Group Databasebeta

← C2×#13092605 #15682782

Subgroups — C2×#13092605 #15682782

Order 2944.

1018 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10625155C211yesmaximal, characteristic, complemented
2C2×#10625053C212yesmaximal, complemented
3C2×#10625108C211yesmaximal, characteristic, complemented
4#13092605C218yesmaximal, direct product factor
5C2×#10624988C212yesmaximal, complemented
6C2×C23×#99C211yesmaximal, characteristic, complemented
7C24×D23C2211yescharacteristic, complemented
8C22×D4×C23C2211yescharacteristic
9C22×C22⋊D23—21no—
10C22×C22⋊D23—21no—
11C22×C22⋊D23C2212yes—
12#10625155—22no—
13#10625155—24no—
14#10625155C2214yescomplemented
15C2×#67290—22no—
16C2×D4×D23—22no—
17C2×#67288—21no—
18C22×D92—22no—
19C2×C22⋊C4×C23C2212yescomplemented
20C2×C22⋊Dic23C2211yescharacteristic, complemented
21#10625108—22no—
22#10625108C2214yescomplemented
23C2×(C2×D23)⋊C4—21no—
24C2×(C2×D23)⋊C4—22no—
25#10625053—24no—
26#10625053C2218yescomplemented
27C23×#99C2214yescomplemented
28#10624988C2218yescomplemented
29C24×C23D411yescharacteristic, complemented
30C24×C23C2311yescharacteristic
31C23×D23—22no—
32C23×D23—21no—
33C23×D23—21no—
34C23×D23—22no—
35C23×D23—21no—
36C23×D23—44no—
37C23×D23D412yescomplemented
38C23×D23C2312yescomplemented
39C2×D4×C23—22no—
40C2×D4×C23—22no—
41C2×D4×C23D412yescomplemented
42C2×D4×C23C2312yes—
43C22×C4×C23—22no—
44C22×C4×C23D411yescharacteristic, complemented
45C2×C22⋊D23—22no—
46C2×C22⋊D23—24no—
47C2×C22⋊D23—22no—
48C2×C22⋊D23—22no—
49C2×C22⋊D23—22no—
50C2×C22⋊D23—22no—
51C2×C22⋊D23—24no—
52C2×C22⋊D23—24no—
53C2×C22⋊D23—44no—
54C2×C22⋊D23D414yescomplemented
55C2×C22⋊D23C2314yes—
56C22×Dic23—21no—
57C22×Dic23—21no—
58C22×Dic23D412yescomplemented
59#67290—28no—
60#67290—28no—
61D4×D23—28no—
62D4×D23—28no—
63#67288—24no—
64#67288—24no—
65C2×D92—21no—
66C2×D92—28no—
67C2×D92—48no—
68C2×C4×D23—22no—
69C2×Dic46—21no—
70C22⋊C4×C23—22no—
71C22⋊C4×C23C2314yescomplemented
72C22⋊Dic23—21no—
73C22⋊Dic23C2312yescomplemented
74(C2×D23)⋊C4—24no—
75(C2×D23)⋊C4—28no—
76C23×C23—21no—
77C23×C23—21no—
78C23×C23—42no—
79C23×C23—42no—
80C23×C23C2×D411yescharacteristic
81C23×C23C2×D411yescharacteristic
82C23×C23C2×D412yes—
83C23×C23C2×D412yes—
84C23×C23C2×D412yescomplemented
85C23×C23C2411yescharacteristic
86C22×D23—28no—
87C22×D23—24no—
88C22×D23—22no—
89C22×D23—24no—
90C22×D23—22no—
91C22×D23—24no—
92C22×D23—22no—
93C22×D23—44no—
94C22×D23—48no—
95C22×D23—44no—
96C22×D23—42no—
97C22×D23—44no—
98C22×D23—42no—
99C22×D23—41no—
100C22×D23—41no—
101C22×D23—44no—
102C22×D23—82no—
103C22×D23C2×D414yescomplemented
104D4×C23—24no—
105D4×C23—24no—
106C2×C4×C23—21no—
107C2×C4×C23—21no—
108C2×C4×C23—24no—
109C2×C4×C23—44no—
110C2×C4×C23C2×D412yescomplemented
111C22⋊D23—28no—
112C22⋊D23—24no—
113C22⋊D23—24no—
114C22⋊D23—24no—
115C22⋊D23—24no—
116C22⋊D23—48no—
117C2×Dic23—24no—
118C2×Dic23—22no—
119C2×Dic23—22no—
120C2×Dic23—22no—
121C2×Dic23—42no—
122C2×Dic23C2×D414yescomplemented
123D92—24no—
124D92—416no—
125C4×D23—28no—
126Dic46—24no—
127C2×B(4,𝔽2)—231nomaximal, Sylow
128C22×C23—22no—
129C22×C23—24no—
130C22×C23—22no—
131C22×C23—41no—
132C22×C23—42no—
133C22×C23—41no—
134C22×C23—42no—
135C22×C23—42no—
136C22×C23—81no—
137C22×C23#12012yes—
138C22×C23#12011yescharacteristic
139C22×C23#12011yescharacteristic
140C22×C23C22×D411yescharacteristic
141C22×C23C22×D412yes—
142C2×D23—28no—
143C2×D23—24no—
144C2×D23—24no—
145C2×D23—42no—
146C2×D23—44no—
147C2×D23—48no—
148C2×D23—44no—
149C2×D23—42no—
150C2×D23—44no—
151C2×D23—44no—
152C2×D23—44no—
153C2×D23—82no—
154C2×D23—84no—
155C4×C23—22no—
156C4×C23—44no—
157Dic23—24no—
158Dic23—42no—
159C2×H(5,𝔽2)—231no—
160C2×#120—231no—
161C2×#120—232no—
162B(4,𝔽2)—238no—
163C2×#99—232no—
164C2×#99D2311yescharacteristic, complemented
165C2×C23—21no—
166C2×C23—22no—
167C2×C23—22no—
168C2×C23—21no—
169C2×C23—42no—
170C2×C23B(4,𝔽2)12yescomplemented
171C2×C23C2×#12011yescharacteristic
172D23—44no—
173D23—44no—
174C25—231no—
175H(5,𝔽2)—234no—
176H(5,𝔽2)—464no—
177H(5,𝔽2)—462no—
178C2×#41—462no—
179C2×#41—461no—
180C22×D4—232no—
181C22×D4—462no—
182C22×D4—462no—
183C22×D4—461no—
184C22×D4—461no—
185C22×D4C2×D2311yescharacteristic
186#120—234no—
187#120—238no—
188#120—464no—
189#120—462no—
190C2×C22⋊C4—231no—
191C2×C22⋊C4—462no—
192C2×C22⋊C4—461no—
193C2×C22⋊C4C2×D2312yescomplemented
194#99—238no—
195#99C2×D2314yescomplemented
196C23C2×B(4,𝔽2)11yescharacteristic, complemented, Sylow
197C24—232no—
198C24—232no—
199C24—461no—
200C24—461no—
201C24—462no—
202C24—461no—
203C24—462no—
204C24—924no—
205C24D9211yescharacteristic, complemented
206C24C22×D2311yescharacteristic
207#41—464no—
208#41—468no—
209#41—468no—
210#41—464no—
211C2×Q8—461no—
212C2×D4—22no—
213C2×D4—22no—
214C2×D4—234no—
215C2×D4—234no—
216C2×D4—461no—
217C2×D4—468no—
218C2×D4—468no—
219C2×D4—468no—
220C2×D4—462no—
221C2×D4—464no—
222C2×D4—462no—
223C2×D4—462no—
224C2×D4—464no—
225C2×D4—462no—
226C2×D4—462no—
227C2×D4—464no—
228C2×D4—928no—
229C2×D4—924no—
230C2×D4D9212yescomplemented
231C2×D4C22×D2312yes—
232C22×C4—22no—
233C22×C4—232no—
234C22×C4—462no—
235C22×C4—461no—
236C22×C4—461no—
237C22×C4D9211yescharacteristic, complemented
238C22⋊C4—22no—
239C22⋊C4—232no—
240C22⋊C4—468no—
241C22⋊C4—461no—
242C22⋊C4—464no—
243C22⋊C4C22×D2314yescomplemented
244C23—21no—
245C23—21no—
246C23—42no—
247C23—42no—
248C23—234no—
249C23—468no—
250C23—464no—
251C23—464no—
252C23—462no—
253C23—462no—
254C23—464no—
255C23—462no—
256C23—924no—
257C23—922no—
258C23—924no—
259C23—924no—
260C23—924no—
261C23—928no—
262C23—921no—
263C23—922no—
264C23—921no—
265C23—1842no—
266C23C2×D9211yescharacteristic
267C23C2×D9211yescharacteristic
268C23C2×D9212yescomplemented
269C23D4×D2312yes—
270C23D4×D2312yes—
271C23C23×D2311yescharacteristic
272Q8—464no—
273D4—24no—
274D4—24no—
275D4—464no—
276D4—468no—
277D4—464no—
278D4—464no—
279D4—464no—
280D4—464no—
281D4—9216no—
282D4—928no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—24no—
286C2×C4—44no—
287C2×C4—234no—
288C2×C4—468no—
289C2×C4—464no—
290C2×C4—462no—
291C2×C4—462no—
292C2×C4—462no—
293C2×C4—922no—
294C2×C4C2×D9212yescomplemented
295C22—24no—
296C22—22no—
297C22—22no—
298C22—41no—
299C22—42no—
300C22—41no—
301C22—42no—
302C22—42no—
303C22—81no—
304C22—468no—
305C22—464no—
306C22—464no—
307C22—924no—
308C22—924no—
309C22—922no—
310C22—924no—
311C22—928no—
312C22—922no—
313C22—924no—
314C22—924no—
315C22—1842no—
316C22—1844no—
317C22#1062505311yescharacteristic
318C22#1062505312yes—
319C22#1062505311yescharacteristic
320C22C22×D9211yescharacteristic
321C22C2×D4×D2312yes—
322C4—22no—
323C4—44no—
324C4—464no—
325C4—922no—
326C2—22no—
327C2—21no—
328C2—21no—
329C2—22no—
330C2—42no—
331C2—924no—
332C2—924no—
333C2#1309260512yesdirect product factor
334C2C2×#1062505311yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC23×C23C24
FrattiniC23C23×D23
FittingC2×C23×#99C2
socleC22×C23#120
hypercenterC2×#99D23
hypocenterC23C2×B(4,𝔽2)
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
1. C2×#10625155C2semidirect
2. C2×#10625053C2semidirect
3. C2×#10625108C2semidirect
4. #13092605C2direct (N × H)
5. C2×#10624988C2semidirect
6. C2×C23×#99C2semidirect
7. C24×D23C22semidirect
14. #10625155C22semidirect
19. C2×C22⋊C4×C23C22semidirect
20. C2×C22⋊Dic23C22semidirect
22. #10625108C22semidirect
26. #10625053C22semidirect
27. C23×#99C22semidirect
28. #10624988C22semidirect
29. C24×C23D4semidirect
37. C23×D23D4semidirect
38. C23×D23C23semidirect
41. C2×D4×C23D4semidirect
44. C22×C4×C23D4semidirect
54. C2×C22⋊D23D4semidirect
58. C22×Dic23D4semidirect
71. C22⋊C4×C23C23semidirect
73. C22⋊Dic23C23semidirect
84. C23×C23C2×D4semidirect
103. C22×D23C2×D4semidirect
110. C2×C4×C23C2×D4semidirect
122. C2×Dic23C2×D4semidirect
164. C2×#99D23semidirect
170. C2×C23B(4,𝔽2)semidirect
193. C2×C22⋊C4C2×D23semidirect
195. #99C2×D23semidirect
196. C23C2×B(4,𝔽2)semidirect
205. C24D92semidirect
230. C2×D4D92semidirect
237. C22×C4D92semidirect
243. C22⋊C4C22×D23semidirect
268. C23C2×D92semidirect
294. C2×C4C2×D92semidirect
333. C2#13092605direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106251552
C2×#106250532
C2×#106251082
#130926052
C2×#106249882
C2×C23×#992
C2×B(4,𝔽2)23