Finite Group Databasebeta

← C2×#14271351 #16828877

Subgroups — C2×#14271351 #16828877

Order 3712.

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×#11745359C211yesmaximal, characteristic, complemented
2C2×#11745244C212yesmaximal, complemented
3C2×#11745299C211yesmaximal, characteristic, complemented
4#14271351C218yesmaximal, direct product factor
5C2×#11745154C212yesmaximal, complemented
6C2×C29×#99C211yesmaximal, characteristic, complemented
7C24×D29C2211yescharacteristic, complemented
8C22×D4×C29C2211yescharacteristic
9C22×C22⋊D29—21no—
10C22×C22⋊D29—21no—
11C22×C22⋊D29C2212yes—
12#11745359—22no—
13#11745359—24no—
14#11745359C2214yescomplemented
15C2×#90807—22no—
16C2×D4×D29—22no—
17C2×#90805—21no—
18C22×D116—22no—
19C2×C22⋊C4×C29C2212yescomplemented
20C2×C22⋊Dic29C2211yescharacteristic, complemented
21#11745299—22no—
22#11745299C2214yescomplemented
23C2×#90781—21no—
24C2×#90781—22no—
25#11745244—24no—
26#11745244C2218yescomplemented
27C29×#99C2214yescomplemented
28#11745154C2218yescomplemented
29C24×C29D411yescharacteristic, complemented
30C24×C29C2311yescharacteristic
31C23×D29—22no—
32C23×D29—21no—
33C23×D29—21no—
34C23×D29—21no—
35C23×D29—22no—
36C23×D29—44no—
37C23×D29D412yescomplemented
38C23×D29C2312yescomplemented
39C2×D4×C29—22no—
40C2×D4×C29—22no—
41C2×D4×C29D412yescomplemented
42C2×D4×C29C2312yes—
43C22×C4×C29—22no—
44C22×C4×C29D411yescharacteristic, complemented
45C2×C22⋊D29—22no—
46C2×C22⋊D29—24no—
47C2×C22⋊D29—22no—
48C2×C22⋊D29—22no—
49C2×C22⋊D29—22no—
50C2×C22⋊D29—22no—
51C2×C22⋊D29—24no—
52C2×C22⋊D29—24no—
53C2×C22⋊D29—44no—
54C2×C22⋊D29D414yescomplemented
55C2×C22⋊D29C2314yes—
56C22×Dic29—21no—
57C22×Dic29—21no—
58C22×Dic29D412yescomplemented
59#90807—28no—
60#90807—28no—
61D4×D29—28no—
62D4×D29—28no—
63#90805—24no—
64#90805—24no—
65C2×D116—21no—
66C2×D116—28no—
67C2×D116—48no—
68C2×C4×D29—22no—
69C2×Dic58—21no—
70C22⋊C4×C29—22no—
71C22⋊C4×C29C2314yescomplemented
72C22⋊Dic29—21no—
73C22⋊Dic29C2312yescomplemented
74#90781—24no—
75#90781—28no—
76C23×C29—21no—
77C23×C29—21no—
78C23×C29—42no—
79C23×C29—42no—
80C23×C29C2×D411yescharacteristic
81C23×C29C2×D411yescharacteristic
82C23×C29C2×D412yes—
83C23×C29C2×D412yes—
84C23×C29C2×D412yescomplemented
85C23×C29C2411yescharacteristic
86C22×D29—28no—
87C22×D29—24no—
88C22×D29—22no—
89C22×D29—24no—
90C22×D29—22no—
91C22×D29—24no—
92C22×D29—22no—
93C22×D29—44no—
94C22×D29—48no—
95C22×D29—44no—
96C22×D29—42no—
97C22×D29—44no—
98C22×D29—42no—
99C22×D29—41no—
100C22×D29—41no—
101C22×D29—44no—
102C22×D29—82no—
103C22×D29C2×D414yescomplemented
104D4×C29—24no—
105D4×C29—24no—
106C2×C4×C29—21no—
107C2×C4×C29—21no—
108C2×C4×C29—24no—
109C2×C4×C29—44no—
110C2×C4×C29C2×D412yescomplemented
111C22⋊D29—28no—
112C22⋊D29—24no—
113C22⋊D29—24no—
114C22⋊D29—24no—
115C22⋊D29—24no—
116C22⋊D29—48no—
117C2×Dic29—24no—
118C2×Dic29—22no—
119C2×Dic29—22no—
120C2×Dic29—22no—
121C2×Dic29—42no—
122C2×Dic29C2×D414yescomplemented
123D116—24no—
124D116—416no—
125C4×D29—28no—
126Dic58—24no—
127C2×B(4,𝔽2)—291nomaximal, Sylow
128C22×C29—22no—
129C22×C29—24no—
130C22×C29—22no—
131C22×C29—41no—
132C22×C29—42no—
133C22×C29—41no—
134C22×C29—42no—
135C22×C29—42no—
136C22×C29—81no—
137C22×C29#12012yes—
138C22×C29#12011yescharacteristic
139C22×C29#12011yescharacteristic
140C22×C29C22×D411yescharacteristic
141C22×C29C22×D412yes—
142C2×D29—28no—
143C2×D29—24no—
144C2×D29—24no—
145C2×D29—42no—
146C2×D29—44no—
147C2×D29—48no—
148C2×D29—44no—
149C2×D29—42no—
150C2×D29—44no—
151C2×D29—44no—
152C2×D29—44no—
153C2×D29—82no—
154C2×D29—84no—
155C4×C29—22no—
156C4×C29—44no—
157Dic29—24no—
158Dic29—42no—
159C2×H(5,𝔽2)—291no—
160C2×#120—291no—
161C2×#120—292no—
162B(4,𝔽2)—298no—
163C2×#99—292no—
164C2×#99D2911yescharacteristic, complemented
165C2×C29—21no—
166C2×C29—22no—
167C2×C29—22no—
168C2×C29—21no—
169C2×C29—42no—
170C2×C29B(4,𝔽2)12yescomplemented
171C2×C29C2×#12011yescharacteristic
172D29—44no—
173D29—44no—
174C25—291no—
175H(5,𝔽2)—294no—
176H(5,𝔽2)—584no—
177H(5,𝔽2)—582no—
178C2×#41—582no—
179C2×#41—581no—
180C22×D4—292no—
181C22×D4—582no—
182C22×D4—582no—
183C22×D4—581no—
184C22×D4—581no—
185C22×D4C2×D2911yescharacteristic
186#120—294no—
187#120—298no—
188#120—584no—
189#120—582no—
190C2×C22⋊C4—291no—
191C2×C22⋊C4—582no—
192C2×C22⋊C4—581no—
193C2×C22⋊C4C2×D2912yescomplemented
194#99—298no—
195#99C2×D2914yescomplemented
196C29C2×B(4,𝔽2)11yescharacteristic, complemented, Sylow
197C24—292no—
198C24—292no—
199C24—581no—
200C24—581no—
201C24—582no—
202C24—581no—
203C24—582no—
204C24—1164no—
205C24D11611yescharacteristic, complemented
206C24C22×D2911yescharacteristic
207#41—584no—
208#41—588no—
209#41—588no—
210#41—584no—
211C2×Q8—581no—
212C2×D4—22no—
213C2×D4—22no—
214C2×D4—294no—
215C2×D4—294no—
216C2×D4—581no—
217C2×D4—588no—
218C2×D4—588no—
219C2×D4—588no—
220C2×D4—582no—
221C2×D4—584no—
222C2×D4—582no—
223C2×D4—582no—
224C2×D4—584no—
225C2×D4—582no—
226C2×D4—582no—
227C2×D4—584no—
228C2×D4—1168no—
229C2×D4—1164no—
230C2×D4D11612yescomplemented
231C2×D4C22×D2912yes—
232C22×C4—22no—
233C22×C4—292no—
234C22×C4—582no—
235C22×C4—581no—
236C22×C4—581no—
237C22×C4D11611yescharacteristic, complemented
238C22⋊C4—22no—
239C22⋊C4—292no—
240C22⋊C4—588no—
241C22⋊C4—581no—
242C22⋊C4—584no—
243C22⋊C4C22×D2914yescomplemented
244C23—21no—
245C23—21no—
246C23—42no—
247C23—42no—
248C23—294no—
249C23—588no—
250C23—584no—
251C23—584no—
252C23—582no—
253C23—584no—
254C23—582no—
255C23—582no—
256C23—1164no—
257C23—1162no—
258C23—1164no—
259C23—1164no—
260C23—1164no—
261C23—1168no—
262C23—1161no—
263C23—1162no—
264C23—1161no—
265C23—2322no—
266C23C2×D11611yescharacteristic
267C23C2×D11611yescharacteristic
268C23C2×D11612yescomplemented
269C23D4×D2912yes—
270C23D4×D2912yes—
271C23C23×D2911yescharacteristic
272Q8—584no—
273D4—24no—
274D4—24no—
275D4—584no—
276D4—588no—
277D4—584no—
278D4—584no—
279D4—584no—
280D4—584no—
281D4—11616no—
282D4—1168no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—24no—
286C2×C4—44no—
287C2×C4—294no—
288C2×C4—588no—
289C2×C4—584no—
290C2×C4—582no—
291C2×C4—582no—
292C2×C4—582no—
293C2×C4—1162no—
294C2×C4C2×D11612yescomplemented
295C22—24no—
296C22—22no—
297C22—22no—
298C22—41no—
299C22—42no—
300C22—41no—
301C22—42no—
302C22—42no—
303C22—81no—
304C22—588no—
305C22—584no—
306C22—584no—
307C22—1164no—
308C22—1164no—
309C22—1162no—
310C22—1164no—
311C22—1168no—
312C22—1164no—
313C22—1164no—
314C22—1162no—
315C22—2322no—
316C22—2324no—
317C22#1174524411yescharacteristic
318C22#1174524412yes—
319C22#1174524411yescharacteristic
320C22C22×D11611yescharacteristic
321C22C2×D4×D2912yes—
322C4—22no—
323C4—44no—
324C4—584no—
325C4—1162no—
326C2—22no—
327C2—21no—
328C2—21no—
329C2—22no—
330C2—42no—
331C2—1164no—
332C2—1164no—
333C2#1427135112yesdirect product factor
334C2C2×#1174524411yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC23×C29C24
FrattiniC23C23×D29
FittingC2×C29×#99C2
socleC22×C29#120
hypercenterC2×#99D29
hypocenterC29C2×B(4,𝔽2)
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
1. C2×#11745359C2semidirect
2. C2×#11745244C2semidirect
3. C2×#11745299C2semidirect
4. #14271351C2direct (N × H)
5. C2×#11745154C2semidirect
6. C2×C29×#99C2semidirect
7. C24×D29C22semidirect
14. #11745359C22semidirect
19. C2×C22⋊C4×C29C22semidirect
20. C2×C22⋊Dic29C22semidirect
22. #11745299C22semidirect
26. #11745244C22semidirect
27. C29×#99C22semidirect
28. #11745154C22semidirect
29. C24×C29D4semidirect
37. C23×D29D4semidirect
38. C23×D29C23semidirect
41. C2×D4×C29D4semidirect
44. C22×C4×C29D4semidirect
54. C2×C22⋊D29D4semidirect
58. C22×Dic29D4semidirect
71. C22⋊C4×C29C23semidirect
73. C22⋊Dic29C23semidirect
84. C23×C29C2×D4semidirect
103. C22×D29C2×D4semidirect
110. C2×C4×C29C2×D4semidirect
122. C2×Dic29C2×D4semidirect
164. C2×#99D29semidirect
170. C2×C29B(4,𝔽2)semidirect
193. C2×C22⋊C4C2×D29semidirect
195. #99C2×D29semidirect
196. C29C2×B(4,𝔽2)semidirect
205. C24D116semidirect
230. C2×D4D116semidirect
237. C22×C4D116semidirect
243. C22⋊C4C22×D29semidirect
268. C23C2×D116semidirect
294. C2×C4C2×D116semidirect
333. C2#14271351direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117453592
C2×#117452442
C2×#117452992
#142713512
C2×#117451542
C2×C29×#992
C2×B(4,𝔽2)29