Finite Group Databasebeta

← C2×#20295683 #28376496

Subgroups — C2×#20295683 #28376496

Order 13952.

1620 conjugacy classes of subgroups; only the 573 normal subgroups are shown.

normal subgroups only

This group has 1620 conjugacy classes of subgroups — too many to draw. Only its 573 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×Q8×D109C211yesmaximal, characteristic, complemented
2#20295683C2116yesmaximal, direct product factor
3C2×#16812686C213yesmaximal, complemented
4C2×#16812678C213yesmaximal, complemented
5C2×#16812670C213yesmaximal, complemented
6C2×Q8×Dic109C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊D109C213yesmaximal, complemented
8C22×#41×C109C211yesmaximal, characteristic, complemented
9C22×Dic218C2213yes—
10C2×Q8×D109—28no—
11C2×Q8×D109C2218yescomplemented
12C22×C22⋊D109C2213yes—
13C22×C4×D109C2213yes—
14#16812686C22124yescomplemented
15#16812678C22124yescomplemented
16#16812670C22124yescomplemented
17Q8×Dic109C2218yescomplemented
18C4×C22⋊D109C22124yescomplemented
19C2×C4⋊Dic109C2213yes—
20C2×#13182008C2213yes—
21C2×C22⋊Dic109C2213yes—
22C2×C22⋊Dic109C2216yes—
23C2×#13182006C2211yescharacteristic
24C2×C4×Dic109C2213yes—
25C2×#41×C109—28no—
26C2×#41×C109C2218yescomplemented
27C22×Q8×C109C2211yescharacteristic
28C22×D4×C109C2213yes—
29C23×C4×C109C2213yes—
30C23×D109C2311yescharacteristic
31C2×Dic218—212no—
32C2×Dic218C23112yes—
33Q8×D109—232no—
34C2×C22⋊D109—212no—
35C2×C22⋊D109C23112yes—
36C22×Dic109C2311yescharacteristic
37C22×Dic109C2313yes—
38C22×Dic109C2313yes—
39C2×C4×D109—212no—
40C2×C4×D109C23112yes—
41C4⋊Dic109C23112yes—
42#13182008C23112yes—
43C22⋊Dic109C23112yes—
44C22⋊Dic109C23124yes—
45#13182006C2314yes—
46C4×Dic109C23112yes—
47C24×C109C2313yes—
48#41×C109—232no—
49C2×Q8×C109D418yescomplemented
50C2×Q8×C109C2314yes—
51C2×D4×C109—212no—
52C2×D4×C109C23112yes—
53C22×C4×C109—212no—
54C22×C4×C109C2311yescharacteristic
55C22×C4×C109C23112yes—
56C22×C4×C109C2313yes—
57C23×C109—26no—
58C23×C109—26no—
59C23×C109—26no—
60C23×C109C2416yes—
61C23×C109C2411yescharacteristic
62C22×D109—22no—
63C22×D109—22no—
64C22×D109#4114yescomplemented
65C22×D109C2412yes—
66Q8×C109C2×D4116yescomplemented
67D4×C109—224no—
68C2×C4×C109—22no—
69C2×C4×C109—224no—
70C2×C4×C109C2×D4112yes—
71C2×C4×C109C2412yes—
72C2×C4×C109C2416yes—
73C22⋊D109—224no—
74C2×Dic109—26no—
75C2×Dic109—26no—
76C2×Dic109—22no—
77C2×Dic109C2412yes—
78C2×Dic109C2416yes—
79C2×Dic109C2416yes—
80C4×D109—224no—
81Dic218—224no—
82C22×C109—26no—
83C22×C109—26no—
84C22×C109—26no—
85C22×C109—412no—
86C22×C109C22×D412yes—
87C22×C109C2×#4112yes—
88C22×C1092−1+412yes—
89C22×C109C2511yescharacteristic
90C2×D109—28no—
91C2×D109—22no—
92C2×D109—22no—
93C2×D109C2×#4114yescomplemented
94C4×C109—22no—
95C4×C109C22×D4112yes—
96Dic109—26no—
97Dic109—26no—
98Dic109—22no—
99C2×C109—46no—
100C2×C109#54814yescomplemented
101C2×C109C23×D411yescharacteristic
102C2×C109C22×#4111yescharacteristic
103C2×C109C2×2−1+411yescharacteristic
104D109—24no—
105C2×#548—1091nomaximal, Sylow
106C109C2×#54811yescharacteristic, complemented, Sylow
107C22×#41D10911yescharacteristic, complemented
108C23×Q8—1091no—
109#548—10916no—
110C2×#124—1093no—
111C2×C22⋊Q8—1093no—
112C2×#121—1093no—
113C2×C4×Q8—1091no—
114C2×C4×D4—1093no—
115C2×#41—28no—
116C2×#41C2×D10918yescomplemented
117C22×Q8—1098no—
118C22×Q8—1093no—
119C22×Q8—2188no—
120C22×Q8C2×D10911yescharacteristic
121C22×D4—1093no—
122C22×D4C2×D10913yes—
123C23×C4—1093no—
124C23×C4C2×D10913yes—
125#124—10924no—
126C22⋊Q8—10924no—
127#121—10924no—
128C4×Q8—1098no—
129C4×D4—10924no—
130C2×C4⋊C4—1093no—
131C2×C4⋊C4—1093no—
132C2×C22⋊C4—1093no—
133C2×C22⋊C4—1096no—
134C2×C22⋊C4—1091no—
135C2×C42—1093no—
136C24—1091no—
137C24C22×D10913yes—
138#41—232no—
139C2×Q8—10912no—
140C2×Q8—21832no—
141C2×Q8—21812no—
142C2×Q8C22⋊D10918yescomplemented
143C2×Q8C22×D10914yes—
144C2×D4—212no—
145C2×D4—10912no—
146C2×D4—21812no—
147C2×D4C22×D109112yes—
148C22×C4—212no—
149C22×C4—1091no—
150C22×C4—1093no—
151C22×C4—1093no—
152C22×C4—10912no—
153C22×C4—21812no—
154C22×C4C22×D109112yes—
155C22×C4C22×D10911yescharacteristic
156C22×C4C22×D10913yes—
157C4⋊C4—10912no—
158C4⋊C4—10912no—
159C22⋊C4—10912no—
160C22⋊C4—10924no—
161C22⋊C4—1094no—
162C42—10912no—
163C23—26no—
164C23—26no—
165C23—26no—
166C23—1094no—
167C23—1092no—
168C23—2182no—
169C23—2182no—
170C23C23×D10916yes—
171C23C23×D10911yescharacteristic
172Q8—21824no—
173Q8C2×C22⋊D109116yescomplemented
174D4—224no—
175D4—21824no—
176C2×C4—22no—
177C2×C4—224no—
178C2×C4—1092no—
179C2×C4—1096no—
180C2×C4—1096no—
181C2×C4—2186no—
182C2×C4—2186no—
183C2×C4—2182no—
184C2×C4—21824no—
185C2×C4C2×C22⋊D109112yes—
186C2×C4C23×D10912yes—
187C2×C4C23×D10916yes—
188C22—26no—
189C22—26no—
190C22—26no—
191C22—412no—
192C22—1094no—
193C22—2188no—
194C22—2182no—
195C22—2182no—
196C22C22×C22⋊D10912yes—
197C22#41×D10912yes—
198C22#1681274612yes—
199C22C24×D10911yescharacteristic
200C4—22no—
201C4—2186no—
202C4—2186no—
203C4—2182no—
204C4C22×C22⋊D109112yes—
205C2—46no—
206C2—2184no—
207C2#2029568314yesdirect product factor
208C2C23×C22⋊D10911yescharacteristic
209C2C2×#41×D10911yescharacteristic
210C2C2×#1681274611yescharacteristic
subgroupG/H
centerC23C23×D109
commutator, cosocleC22×C109C25
FrattiniC22C24×D109
FittingC22×#41×C109C2
socleC23×C109C24
hypercenterC22×#41D109
hypocenterC109C2×#548
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D109C2semidirect
2. #20295683C2direct (N × H)
3. C2×#16812686C2semidirect
4. C2×#16812678C2semidirect
5. C2×#16812670C2semidirect
6. C2×Q8×Dic109C2semidirect
7. C2×C4×C22⋊D109C2semidirect
8. C22×#41×C109C2semidirect
11. C2×Q8×D109C22semidirect
14. #16812686C22semidirect
15. #16812678C22semidirect
16. #16812670C22semidirect
17. Q8×Dic109C22semidirect
18. C4×C22⋊D109C22semidirect
26. C2×#41×C109C22semidirect
49. C2×Q8×C109D4semidirect
64. C22×D109#41semidirect
66. Q8×C109C2×D4semidirect
93. C2×D109C2×#41semidirect
100. C2×C109#548semidirect
106. C109C2×#548semidirect
107. C22×#41D109semidirect
116. C2×#41C2×D109semidirect
142. C2×Q8C22⋊D109semidirect
173. Q8C2×C22⋊D109semidirect
207. C2#20295683direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D1092
#202956832
C2×#168126862
C2×#168126782
C2×#168126702
C2×Q8×Dic1092
C2×C4×C22⋊D1092
C22×#41×C1092
C2×#548109