Finite Group Databasebeta

← C2×#19127883 #24916804

Subgroups — C2×#19127883 #24916804

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×#14581823C212yesmaximal, complemented
3#19127883C218yesmaximal, direct product factor
4C2×#14581720C212yesmaximal, complemented
5C2×#14581711C211yesmaximal, characteristic, complemented
6C2×C4⋊Q8×C83C211yesmaximal, characteristic, complemented
7#14581840—24no—
8#14581840—22no—
9#14581840C2214yes—
10C2×#13050591—22no—
11C2×#13050590—22no—
12C2×#13050590C2212yes—
13C2×Q8×D83—22no—
14#14581823—24no—
15#14581823C2218yescomplemented
16C2×#13050580—22no—
17C2×#13050577—22no—
18C2×#13050574C2212yes—
19#14581720C2218yescomplemented
20#14581711C2214yescomplemented
21C22×Q8×C83C2211yescharacteristic
22C22×Q8×C83C2211yescharacteristic
23C4⋊Q8×C83—22no—
24C4⋊Q8×C83C2214yescomplemented
25C2×C4⋊C4×C83—22no—
26C2×C42×C83C2211yescharacteristic
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×Dic166D412yes—
37Q8×D83—28no—
38Q8×D83—28no—
39C2×D332—22no—
40C2×D332D412yes—
41C2×C22⋊D83—22no—
42C2×C4×D83—24no—
43C2×C4×D83—22no—
44#13050580—28no—
45#13050577—28no—
46#13050574—22no—
47#13050574C2314yes—
48C2×C83⋊C8—22no—
49C2×Q8×C83—22no—
50C2×Q8×C83—22no—
51C2×Q8×C83—21no—
52C2×Q8×C83—22no—
53C2×Q8×C83—22no—
54C2×Q8×C83D412yes—
55C2×Q8×C83C2312yes—
56C2×Q8×C83C2312yes—
57C22×C4×C83—21no—
58C22×C4×C83—21no—
59C22×C4×C83D412yes—
60C22×C4×C83C2311yescharacteristic
61C4⋊C4×C83—28no—
62C42×C83—21no—
63C42×C83C2312yes—
64C23×C83C2×D411yescharacteristic
65C22×D83—22no—
66Q8×C83—24no—
67Q8×C83—24no—
68Q8×C83—24no—
69Q8×C83—42no—
70C2×C4×C83—24no—
71C2×C4×C83—22no—
72C2×C4×C83—22no—
73C2×C4×C83—22no—
74C2×C4×C83—22no—
75C2×C4×C83—41no—
76C2×C4×C83—41no—
77C2×C4×C83C2×D412yes—
78C2×C4×C83C2×D412yes—
79C2×C4×C83C2×D414yes—
80C2×C4×C83C2×D411yescharacteristic
81C2×C4×C83C2411yescharacteristic
82C22⋊D83—24no—
83C22⋊D83—24no—
84C2×Dic83—22no—
85D332—28no—
86D332—22no—
87D332C2×D414yes—
88C4×D83—216no—
89C4×D83—24no—
90C4×D83—24no—
91Dic166—28no—
92Dic166—22no—
93Dic166C2×D414yes—
94C83⋊C8—24no—
95C22×C83—22no—
96C22×C83#12011yescharacteristic
97C22×C83#12011yescharacteristic
98C22×C83C22×D411yescharacteristic
99C2×D83—24no—
100C2×D83—44no—
101C4×C83—24no—
102C4×C83—24no—
103C4×C83—42no—
104C4×C83#12012yes—
105C4×C83C22×D412yes—
106Dic83—24no—
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⋊Q8D8311yescharacteristic, complemented
117#456—838no—
118C2×#104—832no—
119C2×#101—831no—
1202−1+4—834no—
1212−1+4—1664no—
1222−1+4—1662no—
123C2×#41—832no—
124C2×#41—1662no—
125C2×#41—1662no—
126C22×Q8—1662no—
127C22×Q8C2×D8311yescharacteristic
128C22×Q8C2×D8311yescharacteristic
129#137—838no—
130#137—1664no—
131C2×Q16—1662no—
132C2×SD16—1662no—
133C2×M16—832no—
134C4⋊Q8—22no—
135C4⋊Q8C2×D8314yescomplemented
136C2×C4⋊C4—22no—
137C2×C42C2×D8311yescharacteristic
138#104—838no—
139#101—834no—
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—21no—
151C2×Q8—22no—
152C2×Q8—22no—
153C2×Q8—832no—
154C2×Q8—1662no—
155C2×Q8—1668no—
156C2×Q8—1668no—
157C2×Q8C22⋊D8312yes—
158C2×Q8C22×D8312yes—
159C2×Q8C22×D8312yes—
160C2×D4—832no—
161C2×D4—1662no—
162C2×D4—1662no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—1664no—
166C22×C4—1662no—
167C22×C4C22⋊D8312yes—
168C22×C4C22×D8311yescharacteristic
169Q16—1668no—
170SD16—1668no—
171M16—834no—
172M16—1662no—
173C2×C8—1662no—
174C4⋊C4—28no—
175C42—21no—
176C42C22×D8312yes—
177C23—1662no—
178C23C2×C22⋊D8311yescharacteristic
179Q8—24no—
180Q8—24no—
181Q8—24no—
182Q8—42no—
183Q8—834no—
184Q8—1668no—
185Q8—1662no—
186D4—834no—
187D4—1668no—
188D4—1664no—
189D4—1664no—
190D4—1662no—
191C2×C4—24no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—16616no—
199C2×C4—1662no—
200C2×C4—1664no—
201C2×C4—1664no—
202C2×C4D4×D8312yes—
203C2×C4D4×D8312yes—
204C2×C4C2×C22⋊D8314yes—
205C2×C4C2×C22⋊D8311yescharacteristic
206C2×C4C23×D8311yescharacteristic
207C8—1664no—
208C22—22no—
209C22—3324no—
210C22—1664no—
211C22#1458176011yescharacteristic
212C22#1458176011yescharacteristic
213C22C22×C22⋊D8311yescharacteristic
214C4—24no—
215C4—24no—
216C4—42no—
217C4—1664no—
218C4#1458176012yes—
219C4C2×D4×D8312yes—
220C2—21no—
221C2—21no—
222C2—3324no—
223C2#1912788312yesdirect product factor
224C2C2×#1458176011yescharacteristic
subgroupG/H
centerC22#14581760
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
FittingC2×C4⋊Q8×C83C2
socleC22×C83#120
prime radicalC2×#14581840C2
hypercenterC2×C4⋊Q8D83
hypocenterC83C2×#456
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#14581823C2semidirect
3. #19127883C2direct (N × H)
4. C2×#14581720C2semidirect
5. C2×#14581711C2semidirect
6. C2×C4⋊Q8×C83C2semidirect
15. #14581823C22semidirect
19. #14581720C22semidirect
20. #14581711C22semidirect
24. C4⋊Q8×C83C22semidirect
109. C2×C83#456semidirect
113. C83C2×#456semidirect
116. C2×C4⋊Q8D83semidirect
135. C4⋊Q8C2×D83semidirect
223. C2#19127883direct (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×#145818232
#191278832
C2×#145817202
C2×#145817112
C2×C4⋊Q8×C832
C2×#45683