Finite Group Databasebeta

← C2×#14272202 #16836243

Subgroups — C2×#14272202 #16836243

Order 3712.

544 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 170 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×Q8×#1181C211yesmaximal, characteristic, complemented
2C2×D4×#1181C211yesmaximal, characteristic
3#14272202C218yesmaximal, direct product factor
4C2×#11745210C211yesmaximal, characteristic, complemented
5C2×#11745225C211yesmaximal, characteristic, complemented
6C2×#11745223C211yesmaximal, characteristic
7C2×#11745208C211yesmaximal, characteristic, complemented
8C2×SD16×D29C211yesmaximal, characteristic
9C23×#1181—21no—
10C2×Q8×D29C2211yescharacteristic
11C2×D4×D29C2211yescharacteristic
12C2×C22⋊#1181—21no—
13Q8×#1181—22no—
14Q8×#1181C2214yescomplemented
15D4×#1181—22no—
16D4×#1181C2214yes—
17C2×C4⋊#1181—21no—
18C2×C4⋊#1181C2211yescharacteristic
19C2×C4⋊#1181C2211yescharacteristic
20C2×C4×#1181—21no—
21C2×C4×#1181C2211yescharacteristic
22C2×D29⋊C8C2211yescharacteristic
23C2×SD16×C29C411yescharacteristic, complemented
24C2×#90784C411yescharacteristic, complemented
25C2×#90783C411yescharacteristic, complemented
26SD16×D29C414yescomplemented
27SD16×D29C2214yes—
28C2×#90773C411yescharacteristic, complemented
29C2×C8×D29C2211yescharacteristic
30#11745225C2214yescomplemented
31#11745223C2214yes—
32#11745210C2214yescomplemented
33#11745208C2214yescomplemented
34C23×D29—21no—
35C22×#1181—21no—
36C22×#1181—21no—
37C22×#1181—24no—
38C22×#1181—44no—
39C22×#1181D411yescharacteristic
40C22×#1181D411yescharacteristic
41C2×Q8×C29C2×C411yescharacteristic, complemented
42C2×D4×C29C2×C411yescharacteristic
43C2×C22⋊D29—21no—
44Q8×D29—21no—
45Q8×D29—21no—
46Q8×D29C2×C412yescomplemented
47Q8×D29C2312yes—
48D4×D29—21no—
49D4×D29—21no—
50D4×D29C2×C412yes—
51D4×D29C2312yes—
52C2×D116C2×C411yescharacteristic
53C2×C4×D29—21no—
54C2×C4×D29C2311yescharacteristic
55C2×Dic58—21no—
56C2×Dic58C2×C411yescharacteristic, complemented
57C22⋊#1181—24no—
58C2×#6599—21no—
59C4⋊#1181—24no—
60C4⋊#1181—21no—
61C4⋊#1181—21no—
62C4⋊#1181C2312yes—
63C4⋊#1181C2312yes—
64C4×#1181—24no—
65C4×#1181D412yes—
66C4×#1181C2312yes—
67D29⋊C8—21no—
68D29⋊C8C2312yes—
69SD16×C29C2×C414yescomplemented
70C2×C8×C29C2×C411yescharacteristic, complemented
71#90784C2×C414yescomplemented
72#90783C2×C414yescomplemented
73C2×#6597C2×C411yescharacteristic, complemented
74#90773C2×C414yescomplemented
75C8×D29C2×C412yescomplemented
76C8×D29C2312yes—
77C23×C29—21no—
78C22×D29—21no—
79C22×D29—22no—
80C22×D29—22no—
81C22×D29—42no—
82C22×D29—42no—
83C22×D29C2×D411yescharacteristic
84C2×#1181—22no—
85C2×#1181—22no—
86C2×#1181—22no—
87C2×#1181—22no—
88C2×#1181—48no—
89C2×#1181—42no—
90C2×#1181—42no—
91C2×#1181C2×D412yes—
92C2×#1181C2×D412yes—
93Q8×C29—21no—
94Q8×C29C22×C412yescomplemented
95D4×C29—21no—
96D4×C29C22×C412yes—
97C2×C4×C29—21no—
98C2×C4×C29C22×C411yescharacteristic
99C22⋊D29—22no—
100C22⋊D29—22no—
101C2×Dic29—21no—
102C2×Dic29#4111yescharacteristic
103D116—21no—
104D116C22×C412yes—
105C4×D29—22no—
106C4×D29—22no—
107C4×D29C22×C411yescharacteristic
108C4×D29C2×D411yescharacteristic
109C4×D29#4111yescharacteristic
110C4×D29C2411yescharacteristic
111Dic58—21no—
112Dic58—22no—
113Dic58—22no—
114Dic58C22×C412yescomplemented
115#6599—22no—
116C8×C29C22×C412yescomplemented
117#6597C22×C412yescomplemented
118C2×#440—291nomaximal, Sylow
119C22×C29—22no—
120C22×C29—42no—
121C22×C29C4×D411yescharacteristic
122C2×D29—22no—
123C2×D29—42no—
124C2×D29—42no—
125C2×D29—42no—
126C2×D29—44no—
127C2×D29C4×D411yescharacteristic
128C2×D29AGL(1,ℤ/8)12yes—
129C2×D29#13712yes—
130C2×D29C22×D411yescharacteristic
131#1181—22no—
132#1181—22no—
133#1181—42no—
134#1181—42no—
135C4×C29—22no—
136C4×C29C4×D411yescharacteristic
137C4×C29C23×C411yescharacteristic
138Dic29—22no—
139Dic29C4×D411yescharacteristic
140Dic29C2×#4111yescharacteristic
141C22×SD16—291no—
142C2×C4×Q8—291no—
143C2×C4×D4—291no—
144#440—298no—
145C2×#107—291no—
146C2×#103—291no—
147C2×#102—291no—
148C2×#97—291no—
149C2×C29—42no—
150C2×C29#44012yescomplemented
151C2×C29C2×C4×D411yescharacteristic
152D29—42no—
153D29#44012yescomplemented
154D29C2×AGL(1,ℤ/8)11yescharacteristic
155D29C2×#13711yescharacteristic
156C22×Q8—291no—
157C22×D4—291no—
158C23×C4—581no—
159C2×SD16—291no—
160C2×SD16—291no—
161C2×SD16—294no—
162C2×SD16—294no—
163C2×SD16—291no—
164C2×SD16#118111yescharacteristic, complemented
165C22×C8—291no—
166C22×C8—291no—
167C4×Q8—294no—
168C4×Q8—582no—
169C4×D4—294no—
170C4×D4—582no—
171C2×C4⋊C4—291no—
172C2×C4⋊C4—291no—
173C2×C4⋊C4—581no—
174C2×C22⋊C4—581no—
175C2×C42—291no—
176C2×C42—581no—
177#107—294no—
178#103—294no—
179#102—294no—
180#97—294no—
181C29C2×#44011yescharacteristic, complemented, Sylow
182C24—581no—
183C2×Q8—292no—
184C2×Q8—292no—
185C2×Q8—291no—
186C2×Q8—581no—
187C2×Q8—581no—
188C2×Q8—581no—
189C2×Q8C2×#118111yescharacteristic, complemented
190C2×D4—292no—
191C2×D4—292no—
192C2×D4—291no—
193C2×D4—581no—
194C2×D4—581no—
195C2×D4—581no—
196C2×D4C2×#118111yescharacteristic
197C22×C4—291no—
198C22×C4—291no—
199C22×C4—291no—
200C22×C4—581no—
201C22×C4—584no—
202C22×C4—581no—
203C22×C4—581no—
204C22×C4—1164no—
205SD16—294no—
206SD16—294no—
207SD16—294no—
208SD16C2×#118114yescomplemented
209C2×C8—291no—
210C2×C8—292no—
211C2×C8—292no—
212C2×C8—292no—
213C2×C8—581no—
214C2×C8—581no—
215C2×C8C2×#118111yescharacteristic, complemented
216C4⋊C4—292no—
217C4⋊C4—292no—
218C4⋊C4—581no—
219C4⋊C4—581no—
220C4⋊C4—584no—
221C22⋊C4—584no—
222C42—292no—
223C42—292no—
224C42—584no—
225C23—21no—
226C23—291no—
227C23—582no—
228C23—582no—
229C23—581no—
230C23—1162no—
231C23—1162no—
232Q8—21no—
233Q8—292no—
234Q8—582no—
235Q8—582no—
236Q8—581no—
237Q8C22×#118112yescomplemented
238D4—21no—
239D4—292no—
240D4—582no—
241D4—582no—
242D4—581no—
243D4C22×#118112yes—
244C2×C4—21no—
245C2×C4—291no—
246C2×C4—291no—
247C2×C4—291no—
248C2×C4—291no—
249C2×C4—291no—
250C2×C4—292no—
251C2×C4—292no—
252C2×C4—582no—
253C2×C4—582no—
254C2×C4—582no—
255C2×C4—582no—
256C2×C4—581no—
257C2×C4—582no—
258C2×C4—582no—
259C2×C4—1168no—
260C2×C4—1162no—
261C2×C4—1162no—
262C2×C4C22×#118111yescharacteristic
263C8—292no—
264C8—582no—
265C8C22×#118112yescomplemented
266C22—22no—
267C22—42no—
268C22—292no—
269C22—292no—
270C22—291no—
271C22—291no—
272C22—582no—
273C22—1162no—
274C22—1162no—
275C22—1164no—
276C22—1162no—
277C22D4×#118111yescharacteristic
278C4—22no—
279C4—291no—
280C4—291no—
281C4—582no—
282C4—582no—
283C4—582no—
284C4—1162no—
285C4—1162no—
286C4D4×#118111yescharacteristic
287C4C23×#118111yescharacteristic
288C2—42no—
289C2—291no—
290C2—291no—
291C2—292no—
292C2—1162no—
293C2#1427220212yesdirect product factor
294C2C2×D4×#118111yescharacteristic
subgroupG/H
centerC22D4×#1181
commutatorC4×C29C23×C4
FrattiniC4C23×#1181
FittingC2×SD16×C29C4
socleC22×C29C4×D4
prime radicalC2×D4×D29C22
cosocleC4×D29C24
hypercenterC2×SD16#1181
hypocenterC29C2×#440
LCSG ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×Q8×#1181C2semidirect
3. #14272202C2direct (N × H)
4. C2×#11745210C2semidirect
5. C2×#11745225C2semidirect
7. C2×#11745208C2semidirect
14. Q8×#1181C22semidirect
23. C2×SD16×C29C4semidirect
24. C2×#90784C4semidirect
25. C2×#90783C4semidirect
26. SD16×D29C4semidirect
28. C2×#90773C4semidirect
30. #11745225C22semidirect
32. #11745210C22semidirect
33. #11745208C22semidirect
41. C2×Q8×C29C2×C4semidirect
46. Q8×D29C2×C4semidirect
56. C2×Dic58C2×C4semidirect
69. SD16×C29C2×C4semidirect
70. C2×C8×C29C2×C4semidirect
71. #90784C2×C4semidirect
72. #90783C2×C4semidirect
73. C2×#6597C2×C4semidirect
74. #90773C2×C4semidirect
75. C8×D29C2×C4semidirect
94. Q8×C29C22×C4semidirect
114. Dic58C22×C4semidirect
116. C8×C29C22×C4semidirect
117. #6597C22×C4semidirect
150. C2×C29#440semidirect
153. D29#440semidirect
164. C2×SD16#1181semidirect
181. C29C2×#440semidirect
189. C2×Q8C2×#1181semidirect
208. SD16C2×#1181semidirect
215. C2×C8C2×#1181semidirect
237. Q8C22×#1181semidirect
265. C8C22×#1181semidirect
293. C2#14272202direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×#11812
C2×D4×#11812
#142722022
C2×#117452102
C2×#117452252
C2×#117452232
C2×#117452082
C2×SD16×D292
C2×#44029