Finite Group Databasebeta

← C2×#13092606 #15682784

Subgroups — C2×#13092606 #15682784

Order 2944.

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

normal subgroups only

This group has 794 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
2C2×#10625100C212yesmaximal, complemented
3#13092606C218yesmaximal, direct product factor
4C2×#10625016C211yesmaximal, characteristic, complemented
5C2×#10624988C212yesmaximal, complemented
6C2×C23×#123C211yesmaximal, characteristic, complemented
7C22×D4×C23C2211yescharacteristic
8C23×C4×C23C2211yescharacteristic, complemented
9C22×C22⋊D23—21no—
10C22×C22⋊D23C2212yes—
11#10625155—22no—
12#10625155—24no—
13#10625155C2214yes—
14C2×#67290—22no—
15C2×D4×D23—22no—
16C2×#67288—21no—
17C23×#123—22no—
18C23×#123C2214yescomplemented
19C2×C4⋊C4×C23—21no—
20C2×C22⋊C4×C23—21no—
21C2×C22⋊C4×C23C2211yescharacteristic, complemented
22C2×C22⋊Dic23C2212yescomplemented
23#10625100—24no—
24#10625100C2218yescomplemented
25C2×(C2×D23)⋊C4—22no—
26C2×Dic23⋊C4—22no—
27#10625016C2214yescomplemented
28#10624988C2218yescomplemented
29C24×C23D411yescharacteristic
30C24×C23C2311yescharacteristic
31C23×D23—21no—
32C23×D23D412yes—
33C2×D4×C23—22no—
34C2×D4×C23—22no—
35C2×D4×C23D412yes—
36C2×D4×C23C2312yes—
37C22×C4×C23—22no—
38C22×C4×C23—22no—
39C22×C4×C23—21no—
40C22×C4×C23—21no—
41C22×C4×C23—21no—
42C22×C4×C23D411yescharacteristic
43C22×C4×C23C2312yescomplemented
44C2×C22⋊D23—22no—
45C2×C22⋊D23—24no—
46C2×C22⋊D23—22no—
47C2×C22⋊D23—22no—
48C2×C22⋊D23—22no—
49C2×C22⋊D23—22no—
50C2×C22⋊D23—24no—
51C2×C22⋊D23D414yes—
52C2×C22⋊D23C2314yes—
53C22×Dic23—21no—
54C22×Dic23—22no—
55C22×Dic23D412yes—
56#67290—28no—
57#67290—28no—
58D4×D23—28no—
59D4×D23—28no—
60#67288—24no—
61#67288—24no—
62C2×D92—21no—
63C2×C4×D23—22no—
64C2×Dic46—21no—
65C4⋊C4×C23—24no—
66C22⋊C4×C23—24no—
67C22⋊C4×C23—21no—
68C22⋊C4×C23C2312yescomplemented
69C22⋊Dic23—22no—
70C22⋊Dic23C2314yescomplemented
71(C2×D23)⋊C4—28no—
72Dic23⋊C4—28no—
73C23×C23—21no—
74C23×C23—21no—
75C23×C23—42no—
76C23×C23—42no—
77C23×C23C2×D412yes—
78C23×C23C2×D412yes—
79C23×C23C2×D411yescharacteristic
80C23×C23C2×D412yes—
81C23×C23C2×D411yescharacteristic
82C23×C23C2411yescharacteristic
83C22×D23—22no—
84C22×D23—24no—
85C22×D23—22no—
86C22×D23—44no—
87C22×D23—82no—
88C22×D23C2×D414yes—
89D4×C23—24no—
90D4×C23—24no—
91C2×C4×C23—21no—
92C2×C4×C23—21no—
93C2×C4×C23—24no—
94C2×C4×C23—22no—
95C2×C4×C23—22no—
96C2×C4×C23—42no—
97C2×C4×C23—42no—
98C2×C4×C23—41no—
99C2×C4×C23—41no—
100C2×C4×C23C2×D412yes—
101C22⋊D23—28no—
102C22⋊D23—24no—
103C22⋊D23—24no—
104C22⋊D23—24no—
105C22⋊D23—24no—
106C2×Dic23—24no—
107C2×Dic23—22no—
108C2×Dic23—22no—
109C2×Dic23—24no—
110C2×Dic23—44no—
111C2×Dic23C2×D414yes—
112D92—24no—
113C4×D23—28no—
114Dic46—24no—
115C2×#458—231nomaximal, Sylow
116C22×C23—24no—
117C22×C23—22no—
118C22×C23—22no—
119C22×C23—42no—
120C22×C23—41no—
121C22×C23—41no—
122C22×C23—42no—
123C22×C23—42no—
124C22×C23—81no—
125C22×C23#12012yes—
126C22×C23#12011yescharacteristic
127C22×C23#12011yescharacteristic
128C22×C23C22×D412yes—
129C22×C23C22×D411yescharacteristic
130C2×D23—24no—
131C2×D23—44no—
132C2×D23—44no—
133C2×D23—82no—
134C2×D23—84no—
135C4×C23—22no—
136C4×C23—42no—
137C4×C23—42no—
138Dic23—24no—
139Dic23—44no—
140C2×H(5,𝔽2)—231no—
141C2×#123—232no—
142C2×#123D2311yescharacteristic, complemented
143#458—238no—
144C2×#99—231no—
145C2×#99—232no—
146C2×C23—22no—
147C2×C23—21no—
148C2×C23—22no—
149C2×C23—21no—
150C2×C23—42no—
151C2×C23#45812yescomplemented
152C2×C23C2×#12011yescharacteristic
153D23—44no—
154H(5,𝔽2)—234no—
155H(5,𝔽2)—464no—
156H(5,𝔽2)—462no—
157C2×#41—462no—
158C2×#41—461no—
159C22×D4—232no—
160C22×D4—462no—
161C22×D4—461no—
162C22×D4C2×D2311yescharacteristic
163C23×C4C2×D2311yescharacteristic, complemented
164#123—22no—
165#123—238no—
166#123—464no—
167#123C2×D2314yescomplemented
168C2×C4⋊C4—21no—
169C2×C4⋊C4—462no—
170C2×C22⋊C4—21no—
171C2×C22⋊C4—232no—
172C2×C22⋊C4—462no—
173C2×C22⋊C4C2×D2311yescharacteristic, complemented
174#99—234no—
175#99—238no—
176C23C2×#45811yescharacteristic, complemented, Sylow
177C24—232no—
178C24—461no—
179C24C22⋊D2311yescharacteristic
180C24C22×D2311yescharacteristic
181#41—464no—
182#41—468no—
183#41—468no—
184#41—464no—
185C2×Q8—461no—
186C2×D4—22no—
187C2×D4—22no—
188C2×D4—234no—
189C2×D4—234no—
190C2×D4—461no—
191C2×D4—468no—
192C2×D4—468no—
193C2×D4—462no—
194C2×D4—464no—
195C2×D4—462no—
196C2×D4—462no—
197C2×D4—462no—
198C2×D4—462no—
199C2×D4—464no—
200C2×D4C22⋊D2312yes—
201C2×D4C22×D2312yes—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—232no—
208C22×C4—462no—
209C22×C4—461no—
210C22×C4—462no—
211C22×C4C22⋊D2311yescharacteristic
212C22×C4C22×D2312yescomplemented
213C4⋊C4—24no—
214C4⋊C4—468no—
215C22⋊C4—24no—
216C22⋊C4—21no—
217C22⋊C4—234no—
218C22⋊C4—468no—
219C22⋊C4—462no—
220C22⋊C4C22×D2312yescomplemented
221C23—21no—
222C23—21no—
223C23—42no—
224C23—42no—
225C23—234no—
226C23—464no—
227C23—462no—
228C23—462no—
229C23—924no—
230C23—1842no—
231C23D4×D2312yes—
232C23D4×D2312yes—
233C23C2×C22⋊D2311yescharacteristic
234C23C2×C22⋊D2312yes—
235C23C2×C22⋊D2311yescharacteristic
236C23C23×D2311yescharacteristic
237Q8—464no—
238D4—24no—
239D4—24no—
240D4—464no—
241D4—468no—
242D4—464no—
243D4—464no—
244D4—464no—
245D4—464no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—24no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—234no—
256C2×C4—468no—
257C2×C4—464no—
258C2×C4—462no—
259C2×C4—462no—
260C2×C4—464no—
261C2×C4—924no—
262C2×C4C2×C22⋊D2312yes—
263C22—22no—
264C22—24no—
265C22—22no—
266C22—42no—
267C22—41no—
268C22—41no—
269C22—42no—
270C22—42no—
271C22—81no—
272C22—464no—
273C22—924no—
274C22—924no—
275C22—1842no—
276C22—1844no—
277C22#1062510811yescharacteristic
278C22#1062510812yes—
279C22#1062510811yescharacteristic
280C22C2×D4×D2312yes—
281C22C22×C22⋊D2311yescharacteristic
282C4—22no—
283C4—42no—
284C4—42no—
285C4—464no—
286C4—924no—
287C2—21no—
288C2—22no—
289C2—21no—
290C2—22no—
291C2—42no—
292C2—924no—
293C2#1309260612yesdirect product factor
294C2C2×#1062510811yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC23×C23C24
FrattiniC23C23×D23
FittingC2×C23×#123C2
socleC22×C23#120
prime radicalC2×#10625155C2
hypercenterC2×#123D23
hypocenterC23C2×#458
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C24 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. C2×#10625100C2semidirect
3. #13092606C2direct (N × H)
4. C2×#10625016C2semidirect
5. C2×#10624988C2semidirect
6. C2×C23×#123C2semidirect
8. C23×C4×C23C22semidirect
18. C23×#123C22semidirect
21. C2×C22⋊C4×C23C22semidirect
22. C2×C22⋊Dic23C22semidirect
24. #10625100C22semidirect
27. #10625016C22semidirect
28. #10624988C22semidirect
43. C22×C4×C23C23semidirect
68. C22⋊C4×C23C23semidirect
70. C22⋊Dic23C23semidirect
142. C2×#123D23semidirect
151. C2×C23#458semidirect
163. C23×C4C2×D23semidirect
167. #123C2×D23semidirect
173. C2×C22⋊C4C2×D23semidirect
176. C23C2×#458semidirect
212. C22×C4C22×D23semidirect
220. C22⋊C4C22×D23semidirect
293. C2#13092606direct (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×#106251002
#130926062
C2×#106250162
C2×#106249882
C2×C23×#1232
C2×#45823