Finite Group Databasebeta

← C2×#30631819 #44559539

Subgroups — C2×#30631819 #44559539

Order 32128.

1048 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C22×D4×D251C211yesmaximal, characteristic, complemented
2C22×#16860795C211yesmaximal, characteristic, complemented
3C2×#22548686C211yesmaximal, characteristic, complemented
4#30631819C218yesmaximal, direct product factor
5C2×#22548637C211yesmaximal, characteristic, complemented
6C2×#22548636C211yesmaximal, characteristic, complemented
7C2×(C2×D251)⋊C8C211yesmaximal, characteristic, complemented
8C22×D8×C251C211yesmaximal, characteristic, complemented
9C24×D251—21no—
10C22×D1004C2211yescharacteristic
11C22×C22⋊D251—21no—
12C22×C22⋊D251—21no—
13C2×D4×D251—24no—
14C2×D4×D251—22no—
15C2×D4×D251—24no—
16C2×D4×D251C2214yescomplemented
17C22×C4×D251C2211yescharacteristic
18C2×#16860795—24no—
19C2×#16860795C2214yescomplemented
20C22×C251⋊C8C2211yescharacteristic, complemented
21#22548686—22no—
22#22548686C2214yescomplemented
23C2×C4⋊Dic251C2211yescharacteristic, complemented
24C2×C22⋊Dic251—21no—
25#22548637C2214yescomplemented
26#22548636C2214yescomplemented
27(C2×D251)⋊C8C2214yescomplemented
28C22×D4×C251C2211yescharacteristic
29C22×D4×C251C2211yescharacteristic, complemented
30C2×D8×C251—24no—
31C2×D8×C251C2214yescomplemented
32C22×C8×C251C2211yescharacteristic, complemented
33C23×D251—28no—
34C23×D251—24no—
35C23×D251—21no—
36C23×D251—44no—
37C23×D251—44no—
38C23×D251D411yescharacteristic
39C2×D1004—21no—
40C2×D1004—22no—
41C2×D1004D414yescomplemented
42C2×D1004C2312yes—
43C2×C22⋊D251—28no—
44C2×C22⋊D251—24no—
45C2×C22⋊D251—24no—
46C2×C22⋊D251—44no—
47D4×D251—216no—
48D4×D251—28no—
49D4×D251—28no—
50C22×Dic251—21no—
51C22×Dic251D411yescharacteristic
52C2×C4×D251—22no—
53C2×C4×D251—22no—
54C2×C4×D251D412yes—
55C2×C4×D251C2312yes—
56#16860795—28no—
57C2×C251⋊C8—22no—
58C2×C251⋊C8C2312yescomplemented
59C4⋊Dic251—21no—
60C4⋊Dic251C2312yescomplemented
61C22⋊Dic251—24no—
62C24×C251—21no—
63C24×C251—21no—
64C2×D4×C251—21no—
65C2×D4×C251—22no—
66C2×D4×C251—22no—
67C2×D4×C251—22no—
68C2×D4×C251—21no—
69C2×D4×C251D414yescomplemented
70C2×D4×C251C2312yes—
71C2×D4×C251C2312yescomplemented
72C22×C4×C251C2311yescharacteristic
73D8×C251—28no—
74C2×C8×C251—22no—
75C2×C8×C251C2312yescomplemented
76C22×D251—22no—
77C22×D251—22no—
78C22×D251—216no—
79C22×D251—24no—
80C22×D251—22no—
81C22×D251—48no—
82C22×D251—432no—
83C22×D251—42no—
84C22×D251—42no—
85C22×D251—48no—
86C22×D251D814yescomplemented
87C22×D251C2×D412yes—
88D1004—24no—
89D1004—22no—
90D1004C2×D414yescomplemented
91C22⋊D251—216no—
92C22⋊D251—48no—
93C2×Dic251—22no—
94C2×Dic251—22no—
95C2×Dic251—42no—
96C2×Dic251C2×D412yes—
97C4×D251—24no—
98C4×D251—22no—
99C4×D251—22no—
100C251⋊C8—22no—
101C23×C251—24no—
102C23×C251—22no—
103C23×C251—22no—
104C23×C251—42no—
105C23×C251—42no—
106C23×C251—42no—
107C23×C251—42no—
108C23×C251—42no—
109C23×C251C2×D411yescharacteristic
110D4×C251—24no—
111D4×C251—22no—
112D4×C251—22no—
113D4×C251—22no—
114D4×C251—42no—
115D4×C251C2×D414yescomplemented
116C2×C4×C251C2×D411yescharacteristic
117C2×C4×C251C2×D412yes—
118C2×C4×C251C2×D412yes—
119C2×C4×C251C2411yescharacteristic
120C8×C251—22no—
121C22×C251—24no—
122C22×C251—42no—
123C22×C251—42no—
124C22×C251—48no—
125C22×C251—42no—
126C22×C251—42no—
127C22×C251—42no—
128C22×C251—84no—
129C22×C251#12012yes—
130C22×C251C2×D812yes—
131C22×C251AGL(1,ℤ/8)12yes—
132C22×C251C22×D411yescharacteristic
133C2×D251—22no—
134C2×D251—22no—
135C2×D251—28no—
136C2×D251—24no—
137C2×D251—432no—
138C2×D251—42no—
139C2×D251—42no—
140C2×D251—48no—
141C2×D251C2×D814yescomplemented
142C4×C251#12012yes—
143C4×C251C22×D411yescharacteristic
144C4×C251C22×D411yescharacteristic
145Dic251—22no—
146Dic251—42no—
147C2×C251—44no—
148C2×C251—82no—
149C2×C251#44714yescomplemented
150C2×C251C2×#12011yescharacteristic
151C2×C251C22×D811yescharacteristic
152C2×C251C2×AGL(1,ℤ/8)11yescharacteristic
153D251—24no—
154D251—44no—
155C251C2×#44711yescharacteristic, complemented, Sylow
156C2×#447—2511nomaximal, Sylow
157C23×D4—2511no—
158C22×D8—2511no—
159C22×D8D25111yescharacteristic, complemented
160C2×#121—2511no—
161#447—2518no—
162C2×#102—2511no—
163C2×#102—2511no—
164C2×C22⋊C8—2511no—
165C25—5021no—
166C22×D4—5024no—
167C22×D4—5021no—
168C22×D4—5024no—
169C22×D4—5022no—
170C22×D4—5021no—
171C22×D4—2514no—
172C22×D4—2511no—
173C22×D4C2×D25111yescharacteristic
174C22×D4C2×D25111yescharacteristic, complemented
175C23×C4—2511no—
176C2×D8—24no—
177C2×D8—5024no—
178C2×D8—2514no—
179C2×D8C2×D25114yescomplemented
180C22×C8—2511no—
181C22×C8C2×D25111yescharacteristic, complemented
182#121—5022no—
183#121—2514no—
184C2×C4⋊C4—2511no—
185C2×C22⋊C4—5021no—
186#102—2514no—
187#102—2514no—
188C22⋊C8—2514no—
189C24—21no—
190C24—21no—
191C24—10044no—
192C24—10044no—
193C24—5028no—
194C24—5024no—
195C24—5021no—
196C24—2511no—
197C2×D4—22no—
198C2×D4—21no—
199C2×D4—22no—
200C2×D4—21no—
201C2×D4—22no—
202C2×D4—10044no—
203C2×D4—50216no—
204C2×D4—5028no—
205C2×D4—5024no—
206C2×D4—5028no—
207C2×D4—5028no—
208C2×D4—5024no—
209C2×D4—5021no—
210C2×D4—5022no—
211C2×D4—2514no—
212C2×D4—2512no—
213C2×D4C22⋊D25114yescomplemented
214C2×D4C22×D25112yes—
215C2×D4C22×D25112yescomplemented
216C22×C4—5021no—
217C22×C4—5022no—
218C22×C4—5022no—
219C22×C4—2511no—
220C22×C4—2512no—
221C22×C4—2512no—
222C22×C4C22×D25111yescharacteristic
223D8—28no—
224D8—5028no—
225C2×C8—22no—
226C2×C8—5022no—
227C2×C8—2512no—
228C2×C8C22×D25112yescomplemented
229C4⋊C4—5021no—
230C4⋊C4—2512no—
231C22⋊C4—5024no—
232C23—22no—
233C23—24no—
234C23—22no—
235C23—42no—
236C23—42no—
237C23—42no—
238C23—42no—
239C23—42no—
240C23—10048no—
241C23—100432no—
242C23—10048no—
243C23—10042no—
244C23—10042no—
245C23—50216no—
246C23—5022no—
247C23—5024no—
248C23—5022no—
249C23—5022no—
250C23—2512no—
251C23—2514no—
252C23D4×D25111yescharacteristic
253D4—22no—
254D4—22no—
255D4—22no—
256D4—24no—
257D4—42no—
258D4—10048no—
259D4—50216no—
260D4—5022no—
261D4—5024no—
262D4—2514no—
263D4C2×C22⋊D25114yescomplemented
264C2×C4—10042no—
265C2×C4—5022no—
266C2×C4—5022no—
267C2×C4—5022no—
268C2×C4—5022no—
269C2×C4—5024no—
270C2×C4—2512no—
271C2×C4D4×D25112yes—
272C2×C4D4×D25111yescharacteristic
273C2×C4C2×C22⋊D25112yes—
274C2×C4C23×D25111yescharacteristic
275C8—22no—
276C8—5022no—
277C22—24no—
278C22—42no—
279C22—42no—
280C22—48no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—84no—
285C22—100432no—
286C22—10042no—
287C22—10042no—
288C22—10048no—
289C22—5024no—
290C22—5022no—
291C22—5028no—
292C22—5022no—
293C22—2514no—
294C22#2254868312yes—
295C22D8×D25112yes—
296C22#2254873912yes—
297C22C2×D4×D25111yescharacteristic
298C4—10042no—
299C4—5022no—
300C4#2254868312yes—
301C4C2×D4×D25111yescharacteristic
302C4C22×C22⋊D25111yescharacteristic
303C2—44no—
304C2—82no—
305C2—10044no—
306C2—5024no—
307C2#3063181914yesdirect product factor
308C2C2×#2254868311yescharacteristic
309C2C2×D8×D25111yescharacteristic
310C2C2×#2254873911yescharacteristic
subgroupG/H
centerC23D4×D251
commutator, cosocleC2×C4×C251C24
FrattiniC2×C4C23×D251
FittingC22×D8×C251C2
socleC23×C251C2×D4
hypercenterC22×D8D251
hypocenterC251C2×#447
LCSG ▷ C2×C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×D4×D251C2semidirect
2. C22×#16860795C2semidirect
3. C2×#22548686C2semidirect
4. #30631819C2direct (N × H)
5. C2×#22548637C2semidirect
6. C2×#22548636C2semidirect
7. C2×(C2×D251)⋊C8C2semidirect
8. C22×D8×C251C2semidirect
16. C2×D4×D251C22semidirect
19. C2×#16860795C22semidirect
20. C22×C251⋊C8C22semidirect
22. #22548686C22semidirect
23. C2×C4⋊Dic251C22semidirect
25. #22548637C22semidirect
26. #22548636C22semidirect
27. (C2×D251)⋊C8C22semidirect
29. C22×D4×C251C22semidirect
31. C2×D8×C251C22semidirect
32. C22×C8×C251C22semidirect
41. C2×D1004D4semidirect
58. C2×C251⋊C8C23semidirect
60. C4⋊Dic251C23semidirect
69. C2×D4×C251D4semidirect
71. C2×D4×C251C23semidirect
75. C2×C8×C251C23semidirect
86. C22×D251D8semidirect
90. D1004C2×D4semidirect
115. D4×C251C2×D4semidirect
141. C2×D251C2×D8semidirect
149. C2×C251#447semidirect
155. C251C2×#447semidirect
159. C22×D8D251semidirect
174. C22×D4C2×D251semidirect
179. C2×D8C2×D251semidirect
181. C22×C8C2×D251semidirect
213. C2×D4C22⋊D251semidirect
215. C2×D4C22×D251semidirect
228. C2×C8C22×D251semidirect
263. D4C2×C22⋊D251semidirect
307. C2#30631819direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D2512
C22×#168607952
C2×#225486862
#306318192
C2×#225486372
C2×#225486362
C2×(C2×D251)⋊C82
C22×D8×C2512
C2×#447251