Finite Group Databasebeta

← SD16×Q32 #492578

Subgroups — SD16×Q32 #492578

Order 512.

437 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 437 conjugacy classes of subgroups — too many to draw. Only its 134 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
1Q8×Q32C211yesmaximal, characteristic, complemented
2D4×Q32C211yesmaximal, characteristic
3SD16×Q16C212yesmaximal
4#12504C211yesmaximal, characteristic, complemented
5#12452C211yesmaximal, characteristic
6#12440C211yesmaximal, characteristic, complemented
7#12421C212yesmaximal, complemented
8#12374C212yesmaximal
9#12358C212yesmaximal, complemented
10C16×SD16C211yesmaximal, characteristic
11C8×Q32C211yesmaximal, characteristic, complemented
12C22×Q32—21no—
13Q8×Q16C2212yes—
14Q8×SD16—22no—
15D4×Q16C2212yes—
16#2252—21no—
17#2252C2211yescharacteristic
18#2247C2211yescharacteristic
19#2241C2212yes—
20#2227—22no—
21#2227C2212yes—
22#2216—21no—
23#2209C2212yes—
24#2188—22no—
25Q8×C16C2211yescharacteristic
26C4×Q32—21no—
27C4×Q32C2211yescharacteristic
28D4×C16C2211yescharacteristic
29#1707C2212yes—
30#1675C2212yes—
31#1672—22no—
32#1670C2212yes—
33#1645—22no—
34#1637—22no—
35C8×Q16C2212yes—
36C8×SD16C2211yescharacteristic
37#1371C2211yescharacteristic
38#1367C2211yescharacteristic
39#1365C2212yes—
40#1362C2212yes—
41Q8⋊C16C2211yescharacteristic
42#1332C2212yes—
43D4⋊C16C2211yescharacteristic
44C8×C16C2211yescharacteristic
45C22×Q16—22no—
46Q82—22no—
47D4×Q8—22no—
48C2×Q32—22no—
49C2×Q32—21no—
50C2×Q32—21no—
51C2×Q32—44no—
52C2×Q32D411yescharacteristic
53C22×C16—21no—
54#500—22no—
55#500C2312yes—
56#498—22no—
57#498—42no—
58#494C2312yes—
59#487—22no—
60#477—22no—
61#477—42no—
62#476—22no—
63#476—42no—
64#475—22no—
65#475—42no—
66#467—22no—
67#462—22no—
68#451—42no—
69C8×Q8—22no—
70C8×Q8C2311yescharacteristic
71C4×Q16—22no—
72C4×Q16C2312yes—
73C4×SD16—42no—
74C4×SD16D411yescharacteristic
75C8×D4C2311yescharacteristic
76#366—21no—
77#366—21no—
78#366—22no—
79#366D411yescharacteristic
80C4⋊C16—21no—
81C4⋊C16C2311yescharacteristic
82C4⋊C16C2311yescharacteristic
83#358—22no—
84#358—22no—
85#358—42no—
86#358D412yes—
87C22⋊C16—21no—
88C4×C16—21no—
89C4×C16C2311yescharacteristic
90C4×C16C2311yescharacteristic
91#335C2312yes—
92#334D411yescharacteristic
93#333—22no—
94#332—22no—
95Q8⋊C8—22no—
96Q8⋊C8D411yescharacteristic
97D4⋊C8D411yescharacteristic
98C82C2311yescharacteristic
99C22×Q8—42no—
100C2×Q16—22no—
101C2×Q16—22no—
102C2×Q16—42no—
103C2×Q16—44no—
104C2×Q16—82no—
105C2×Q16C2×D412yes—
106C2×SD16D811yescharacteristic
107C22×C8—21no—
108C4⋊Q8—22no—
109C4⋊Q8—22no—
110C4⋊Q8—42no—
111C4⋊Q8—42no—
112C4⋊Q8—42no—
113C4⋊Q8—82no—
114C22⋊Q8—42no—
115C22⋊Q8—82no—
116C4×Q8—22no—
117C4×Q8—42no—
118C4×Q8—42no—
119C4×Q8C2×D411yescharacteristic
120C4×D4—42no—
121C4×D4C2×D411yescharacteristic
122Q32—44no—
123Q32—42no—
124Q32—81no—
125Q32SD1614yesdirect product factor
126C2×C16—21no—
127C2×C16—21no—
128C2×C16—21no—
129C2×C16—42no—
130C2×C16C2×D411yescharacteristic
131C2×C16C2×D411yescharacteristic
132#107—22no—
133#107—22no—
134#107—42no—
135#107C2×D412yes—
136#106—42no—
137#106—42no—
138#106—42no—
139#106—42no—
140#106D811yescharacteristic
141C4⋊C8—21no—
142C4⋊C8—22no—
143C4⋊C8—42no—
144C4⋊C8C2×D411yescharacteristic
145C4⋊C8C2×D411yescharacteristic
146#103—22no—
147#103—42no—
148#103—42no—
149#103—42no—
150#103—82no—
151#103D811yescharacteristic
152#102—42no—
153#102D811yescharacteristic
154C22⋊C8—21no—
155C4×C8—21no—
156C4×C8—42no—
157C4×C8C2×D411yescharacteristic
158C4×C8C2×D411yescharacteristic
159C4×C8C2411yescharacteristic
160C2×Q8—22no—
161C2×Q8—42no—
162C2×Q8—42no—
163C2×Q8—82no—
164C2×Q8—82no—
165C2×Q8—84no—
166C2×Q8—162no—
167C2×Q8C2×D811yescharacteristic
168C2×D4C2×D811yescharacteristic
169C22×C4—21no—
170C22×C4—82no—
171Q16—22no—
172Q16—42no—
173Q16—42no—
174Q16—82no—
175Q16—84no—
176Q16C2×SD1614yes—
177SD16Q3214yesdirect product factor
178C2×C8—21no—
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—41no—
182C2×C8—41no—
183C2×C8—42no—
184C2×C8C2×D811yescharacteristic
185C2×C8C2×D811yescharacteristic
186C2×C8C22×D411yescharacteristic
187C2×C8H(5,𝔽2)11yescharacteristic
188C4⋊C4—21no—
189C4⋊C4—22no—
190C4⋊C4—42no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—82no—
196C4⋊C4—82no—
197C4⋊C4—82no—
198C4⋊C4C2×D811yescharacteristic
199C4⋊C4C2×D811yescharacteristic
200C22⋊C4—21no—
201C22⋊C4—82no—
202C42—21no—
203C42—42no—
204C42—82no—
205C42C22×D411yescharacteristic
206C16—21no—
207C16—41no—
208C16—41no—
209C16—41no—
210C16C2×SD1612yes—
211C23—21no—
212Q8—21no—
213Q8—24no—
214Q8—42no—
215Q8—82no—
216Q8—82no—
217Q8—162no—
218Q8—164no—
219Q8—322no—
220Q8C2×Q3212yescomplemented
221D4—21no—
222D4C2×Q3212yes—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—42no—
230C2×C4—82no—
231C2×C4—82no—
232C2×C4—164no—
233C2×C4D4211yescharacteristic
234C2×C4C22×D811yescharacteristic
235C2×C4#57611yescharacteristic
236C8—21no—
237C8—21no—
238C8—41no—
239C8—41no—
240C8—41no—
241C8—82no—
242C8C2×Q3212yescomplemented
243C8C22×SD1611yescharacteristic
244C8#57711yescharacteristic
245C22—22no—
246C22—41no—
247C22—41no—
248C22D4×D811yescharacteristic
249C4—22no—
250C4—21no—
251C4—41no—
252C4—44no—
253C4—41no—
254C4—82no—
255C4—162no—
256C4—162no—
257C4D4×SD1611yescharacteristic
258C4#329011yescharacteristic
259C4C22×Q3211yescharacteristic
260C4#341711yescharacteristic
261C2—42no—
262C2D8×SD1611yescharacteristic
263C2D4×Q3211yescharacteristic
264C2#3385911yescharacteristic
subgroupG/H
center, socleC22D4×D8
commutator, Frattini, cosocleC4×C8C24
prime radicalC2×D4C2×D8
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C42 ◁ C8×SD16 ◁ G
LECSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. Q8×Q32C2semidirect
4. #12504C2semidirect
6. #12440C2semidirect
7. #12421C2semidirect
9. #12358C2semidirect
11. C8×Q32C2semidirect
125. Q32SD16direct (N × H)
177. SD16Q32direct (N × H)
220. Q8C2×Q32semidirect
242. C8C2×Q32semidirect

Maximal subgroups

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

subgroupindex
Q8×Q322
D4×Q322
SD16×Q162
#125042
#124522
#124402
#124212
#123742
#123582
C16×SD162
C8×Q322