Finite Group Databasebeta

← #487×D251 #44560673

Subgroups — #487×D251 #44560673

Order 32128.

424 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C4⋊Q8×D251C211yesmaximal, characteristic
2C4⋊Q8×D251C211yesmaximal, characteristic
3#30632039C211yesmaximal, characteristic, complemented
4#30632038C211yesmaximal, characteristic, complemented
5#30632037C211yesmaximal, characteristic, complemented
6#30632036C214yesmaximal, complemented
7#103×D251C214yesmaximal
8C4×C8×D251C211yesmaximal, characteristic
9#487×C251C211yesmaximal, characteristic, complemented
10C2×Q8×D251—21no—
11C2×Q8×D251C2212yes—
12C2×C8×D251C2212yes—
13#22548715C2211yescharacteristic
14#22548715C2211yescharacteristic
15#22548714—21no—
16#22548714—21no—
17#22548714—21no—
18#22548714C2212yes—
19#22548713—21no—
20#22548713C2212yes—
21C4⋊C4×D251—21no—
22C4⋊C4×D251—21no—
23C4⋊C4×D251—21no—
24C4⋊C4×D251C2212yes—
25C42×D251C2211yescharacteristic
26#22548640C2214yes—
27#22548639C2214yes—
28#22548638C2214yes—
29C4×C251⋊C8C2211yescharacteristic
30C8×Dic251C2212yes—
31C4⋊Q8×C251C2211yescharacteristic
32C4⋊Q8×C251C2211yescharacteristic
33#103×C251C2214yes—
34C4×C8×C251C2211yescharacteristic
35C2×Dic502—22no—
36C2×Dic502—22no—
37C2×Dic502—21no—
38C2×Dic502C2312yes—
39Q8×D251—28no—
40Q8×D251—44no—
41C2×C4×D251—22no—
42C2×C4×D251—22no—
43C2×C4×D251D411yescharacteristic
44C2×C4×D251D411yescharacteristic
45C2×C4×D251C2311yescharacteristic
46C2×C251⋊C8C2312yes—
47C8×D251—24no—
48C4⋊Dic251—21no—
49C4⋊Dic251—21no—
50C4⋊Dic251—21no—
51C4⋊Dic251C2312yes—
52Dic251⋊C4—22no—
53Dic251⋊C4—22no—
54Dic251⋊C4—22no—
55Dic251⋊C4—22no—
56C4×Dic251D411yescharacteristic
57C4×Dic251D411yescharacteristic
58C4×Dic251C2311yescharacteristic
59C2×Q8×C251—21no—
60C2×Q8×C251C2312yes—
61C2×C8×C251C2312yes—
62C4⋊C4×C251—21no—
63C4⋊C4×C251—21no—
64C4⋊C4×C251—21no—
65C4⋊C4×C251C2312yes—
66C42×C251C2311yescharacteristic
67C22×D251C2×D411yescharacteristic
68Dic502—24no—
69Dic502—42no—
70Dic502—44no—
71Dic502—44no—
72C2×Dic251—22no—
73C2×Dic251—22no—
74C2×Dic251C2×D411yescharacteristic
75C2×Dic251C2×D411yescharacteristic
76C2×Dic251C2×D411yescharacteristic
77C4×D251—44no—
78C4×D251—44no—
79C4×D251SD1614yes—
80C4×D251Q1614yes—
81C4×D251#4114yes—
82C251⋊C8—22no—
83Q8×C251—24no—
84Q8×C251—42no—
85C2×C4×C251—22no—
86C2×C4×C251—22no—
87C2×C4×C251C2×D411yescharacteristic
88C2×C4×C251C2×D411yescharacteristic
89C2×C4×C251C2411yescharacteristic
90C8×C251—22no—
91C22×C251C22×D411yescharacteristic
92C2×D251#12412yes—
93C2×D251C2×SD1612yes—
94C2×D251C2×Q1612yes—
95C4×C251—42no—
96C4×C251—42no—
97C4×C251C2×SD1612yes—
98C4×C251C2×Q1612yes—
99C4×C251C2×#4112yes—
100Dic251—42no—
101Dic251—42no—
102Dic251#12412yes—
103Dic251C2×SD1612yes—
104Dic251C2×Q1612yes—
105C2×C251C2×#12411yescharacteristic
106C2×C251C22×SD1611yescharacteristic
107C2×C251C22×Q1611yescharacteristic
108D251#48714yesdirect product factor
109C251C2×#48711yescharacteristic, complemented, Sylow
110C2×#487—2511nomaximal, Sylow
111C2×C4⋊Q8—2511no—
112C2×C4⋊Q8—2511no—
113#487—2511no—
114#487—2511no—
115#487—2514no—
116#487—2511no—
117#487D25111yescharacteristic, direct product factor
118C2×#103—2514no—
119C2×C4×C8—2511no—
120C22×Q8—5021no—
121C22×Q8—2512no—
122C22×C8—2512no—
123C4⋊Q8—5021no—
124C4⋊Q8—5021no—
125C4⋊Q8—5021no—
126C4⋊Q8—5021no—
127C4⋊Q8—2512no—
128C4⋊Q8—2512no—
129C4⋊Q8—2511no—
130C4⋊Q8—2511no—
131C4⋊Q8C2×D25111yescharacteristic
132C4⋊Q8C2×D25111yescharacteristic
133C2×C4⋊C4—5021no—
134C2×C4⋊C4—5021no—
135C2×C4⋊C4—5021no—
136C2×C4⋊C4—2512no—
137C2×C42—2511no—
138#103—2514no—
139#103—2514no—
140#103—2514no—
141#103C2×D25114yes—
142C4×C8—2512no—
143C4×C8—2511no—
144C4×C8C2×D25111yescharacteristic
145C2×Q8—21no—
146C2×Q8—10044no—
147C2×Q8—5022no—
148C2×Q8—5022no—
149C2×Q8—5028no—
150C2×Q8—5021no—
151C2×Q8—2512no—
152C2×Q8C22×D25112yes—
153C22×C4—5022no—
154C22×C4—5022no—
155C22×C4—2511no—
156C22×C4—2511no—
157C22×C4—2511no—
158C2×C8—5024no—
159C2×C8—2512no—
160C2×C8C22×D25112yes—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—5022no—
165C4⋊C4—5022no—
166C4⋊C4—5022no—
167C4⋊C4—5022no—
168C4⋊C4—5021no—
169C4⋊C4—5021no—
170C4⋊C4—5021no—
171C4⋊C4—2512no—
172C4⋊C4C22×D25112yes—
173C42—2511no—
174C42—2511no—
175C42—2511no—
176C42C22×D25111yescharacteristic
177C23—2511no—
178Q8—24no—
179Q8—42no—
180Q8—10044no—
181Q8—10044no—
182Q8—10042no—
183Q8—5024no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—10044no—
187C2×C4—10044no—
188C2×C4—5022no—
189C2×C4—5022no—
190C2×C4—2511no—
191C2×C4—2511no—
192C2×C4—2511no—
193C2×C4—2514no—
194C2×C4—2514no—
195C2×C4—2514no—
196C2×C4D4×D25111yescharacteristic
197C2×C4D4×D25111yescharacteristic
198C2×C4C23×D25111yescharacteristic
199C8—22no—
200C8—5022no—
201C22—2512no—
202C22—2512no—
203C22—2512no—
204C22C2×D4×D25111yescharacteristic
205C4—42no—
206C4—42no—
207C4—10042no—
208C4—10042no—
209C4—2512no—
210C4—2512no—
211C4—2512no—
212C4SD16×D25112yes—
213C4Q16×D25112yes—
214C4#41×D25112yes—
215C2—2514no—
216C2#124×D25111yescharacteristic
217C2C2×SD16×D25111yescharacteristic
218C2C2×Q16×D25111yescharacteristic
subgroupG/H
centerC22C2×D4×D251
commutator, cosocleC2×C4×C251C24
FrattiniC2×C4C23×D251
Fitting#487×C251C2
socleC22×C251C22×D4
prime radicalC22×D251C2×D4
hypercenter#487D251
hypocenterC251C2×#487
LCSG ▷ C2×C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #30632039C2semidirect
4. #30632038C2semidirect
5. #30632037C2semidirect
6. #30632036C2semidirect
9. #487×C251C2semidirect
108. D251#487direct (N × H)
109. C251C2×#487semidirect
117. #487D251direct (N × H)

Maximal subgroups

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

subgroupindex
C4⋊Q8×D2512
#306320392
#306320382
#306320372
#306320362
#103×D2512
C4×C8×D2512
#487×C2512
C2×#487251