Finite Group Databasebeta

← C2×#19127886 #24916807

Subgroups — C2×#19127886 #24916807

Order 10624.

708 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 708 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×#14581840C211yesmaximal, characteristic
2C2×#14581825C212yesmaximal, complemented
3C2×#14581790C211yesmaximal, characteristic, complemented
4#19127886C218yesmaximal, direct product factor
5C2×#14581718C212yesmaximal, complemented
6C2×#101×C83C211yesmaximal, characteristic, complemented
7#14581840—24no—
8#14581840—22no—
9#14581840C2214yes—
10C2×#13050591—22no—
11C2×#13050590—22no—
12C2×#13050590C2212yes—
13C22×Dic166C2211yescharacteristic
14C2×Q8×D83—22no—
15#14581825—24no—
16#14581825C2218yescomplemented
17C2×Dic332—22no—
18C2×#13050579—22no—
19#14581790—22no—
20#14581790C2214yescomplemented
21C2×Dic83⋊C4—22no—
22C2×C4×Dic83C2211yescharacteristic
23#14581718C2218yescomplemented
24C22×Q8×C83C2211yescharacteristic
25C2×M16×C83C2212yes—
26#101×C83C2214yescomplemented
27#13050591—28no—
28#13050591—28no—
29#13050590—28no—
30#13050590—28no—
31#13050590—22no—
32#13050590—22no—
33#13050590D414yes—
34#13050590C2314yes—
35C2×Dic166—22no—
36C2×Dic166—22no—
37C2×Dic166—22no—
38C2×Dic166—21no—
39C2×Dic166D412yes—
40C2×Dic166C2312yes—
41Q8×D83—28no—
42Q8×D83—28no—
43C2×D332—22no—
44C2×D332D412yes—
45C2×C22⋊D83—22no—
46C22×Dic83—21no—
47C22×Dic83—21no—
48C2×C4×D83—24no—
49C2×C4×D83—22no—
50Dic332—28no—
51#13050579—28no—
52Dic83⋊C4—28no—
53C4×Dic83—21no—
54C4×Dic83C2312yes—
55C2×Q8×C83—22no—
56C2×Q8×C83—22no—
57C2×Q8×C83D412yes—
58C2×Q8×C83C2312yes—
59C22×C4×C83D412yes—
60C22×C4×C83C2311yescharacteristic
61M16×C83—22no—
62M16×C83C2314yes—
63C2×C8×C83—22no—
64C23×C83C2×D411yescharacteristic
65C22×D83—22no—
66Q8×C83—24no—
67Q8×C83—24no—
68C2×C4×C83—22no—
69C2×C4×C83—22no—
70C2×C4×C83C2×D412yes—
71C2×C4×C83C2×D412yes—
72C2×C4×C83C2×D414yes—
73C2×C4×C83C2×D411yescharacteristic
74C2×C4×C83C2411yescharacteristic
75C22⋊D83—24no—
76C22⋊D83—24no—
77C2×Dic83—24no—
78C2×Dic83—22no—
79C2×Dic83—22no—
80C2×Dic83—22no—
81C2×Dic83—41no—
82C2×Dic83—41no—
83D332—28no—
84D332—22no—
85D332C2×D414yes—
86C4×D83—216no—
87C4×D83—24no—
88C4×D83—24no—
89Dic166—28no—
90Dic166—22no—
91Dic166—24no—
92Dic166—42no—
93Dic166C2×D414yes—
94C8×C83—24no—
95C22×C83—22no—
96C22×C83#12011yescharacteristic
97C22×C83#12011yescharacteristic
98C22×C83C22×D411yescharacteristic
99C2×D83—24no—
100C2×D83—44no—
101C4×C83—24no—
102C4×C83#12012yes—
103C4×C83C22×D412yes—
104Dic83—24no—
105Dic83—24no—
106Dic83—42no—
107C2×C83—21no—
108C2×C83—21no—
109C2×C83#45612yescomplemented
110C2×C83C2×#12011yescharacteristic
111D83—44no—
112C2×#456—831nomaximal, Sylow
113C83C2×#45611yescharacteristic, complemented, Sylow
114C2×2−1+4—831no—
115C2×#137—832no—
116C2×C4⋊Q8—831no—
117#456—838no—
118C2×#104—832no—
119C2×#101D8311yescharacteristic, complemented
1202−1+4—834no—
1212−1+4—1664no—
1222−1+4—1662no—
123C2×#41—832no—
124C2×#41—1662no—
125C2×#41—1662no—
126C22×Q8—831no—
127C22×Q8—1662no—
128C22×Q8C2×D8311yescharacteristic
129#137—838no—
130#137—1664no—
131C2×Q16—1662no—
132C2×SD16—1662no—
133C2×M16C2×D8312yes—
134C4⋊Q8—834no—
135C4⋊Q8—1662no—
136C2×C4⋊C4—1662no—
137C2×C42—831no—
138#104—838no—
139#101C2×D8314yescomplemented
140#41—834no—
141#41—834no—
142#41—1668no—
143#41—1668no—
144#41—1668no—
145#41—1662no—
146#41—1662no—
147#41—1668no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—832no—
151C2×Q8—832no—
152C2×Q8—1662no—
153C2×Q8—1662no—
154C2×Q8—1662no—
155C2×Q8—1668no—
156C2×Q8—1668no—
157C2×Q8—1661no—
158C2×Q8D33212yes—
159C2×Q8C22×D8312yes—
160C2×D4—832no—
161C2×D4—1662no—
162C2×D4—1662no—
163C22×C4—1664no—
164C22×C4—1661no—
165C22×C4—1661no—
166C22×C4—1662no—
167C22×C4D33212yes—
168C22×C4C22×D8311yescharacteristic
169Q16—1668no—
170SD16—1668no—
171M16—22no—
172M16C22×D8314yes—
173C2×C8—22no—
174C4⋊C4—1668no—
175C42—832no—
176C42—1661no—
177C23—1662no—
178C23C2×D33211yescharacteristic
179Q8—24no—
180Q8—24no—
181Q8—3322no—
182Q8—834no—
183Q8—1668no—
184Q8—1664no—
185Q8—1662no—
186D4—834no—
187D4—1668no—
188D4—1664no—
189D4—1664no—
190D4—1662no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—3321no—
194C2×C4—3321no—
195C2×C4—16616no—
196C2×C4—1662no—
197C2×C4—1664no—
198C2×C4—1662no—
199C2×C4—1662no—
200C2×C4—1664no—
201C2×C4—1664no—
202C2×C4D4×D8312yes—
203C2×C4D4×D8312yes—
204C2×C4C2×D33214yes—
205C2×C4C2×D33211yescharacteristic
206C2×C4C23×D8311yescharacteristic
207C8—24no—
208C22—22no—
209C22—3324no—
210C22—1664no—
211C22#1458176211yescharacteristic
212C22#1458176211yescharacteristic
213C22C22×D33211yescharacteristic
214C4—24no—
215C4—3322no—
216C4—1664no—
217C4—1664no—
218C4#1458176212yes—
219C4C2×D4×D8312yes—
220C2—21no—
221C2—21no—
222C2—3324no—
223C2#1912788612yesdirect product factor
224C2C2×#1458176211yescharacteristic
subgroupG/H
centerC22#14581762
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
FittingC2×#101×C83C2
socleC22×C83#120
prime radicalC2×#14581840C2
hypercenterC2×#101D83
hypocenterC83C2×#456
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#14581825C2semidirect
3. C2×#14581790C2semidirect
4. #19127886C2direct (N × H)
5. C2×#14581718C2semidirect
6. C2×#101×C83C2semidirect
16. #14581825C22semidirect
20. #14581790C22semidirect
23. #14581718C22semidirect
26. #101×C83C22semidirect
109. C2×C83#456semidirect
113. C83C2×#456semidirect
119. C2×#101D83semidirect
139. #101C2×D83semidirect
223. C2#19127886direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145818402
C2×#145818252
C2×#145817902
#191278862
C2×#145817182
C2×#101×C832
C2×#45683