Finite Group Databasebeta

← C2×#23777894 #35196105

Subgroups — C2×#23777894 #35196105

Order 20224.

6338 conjugacy classes of subgroups.

The subgroup lattice has 224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777894C2132yesmaximal, direct product factor
2C2×C79⋊#564C213yesmaximal, complemented
3C2×#19099290C2112yesmaximal, complemented
4C2×#19099172C2112yesmaximal
5C2×#19099119C213yesmaximal
6C2×#564×C79C211yesmaximal, characteristic, complemented
7C79⋊#564C22148yescomplemented
8#19099290C221192yescomplemented
9#19099172C221192yes—
10#19099119C22148yes—
11C2×#14579160C2216yes—
12C2×#14579160C22112yes—
13C2×#14579156C22112yes—
14C2×#14579155C2214yes—
15C2×#14579153C2213yes—
16C2×#14579152C22112yes—
17C2×#14579151C22112yes—
18C2×#14579151C22112yes—
19C2×#14579151C22112yes—
20C2×#14579139C22112yes—
21C2×C4×Dic158C22112yes—
22C2×#14579126C22112yes—
23C2×#14579126C22112yes—
24C2×#14579119C2216yes—
25C2×C42×D79C2211yescharacteristic
26#564×C79C22116yescomplemented
27C2×#125×C79C2213yes—
28C2×#125×C79C22112yes—
29C22×Dic158C23112yes—
30C22×C4×D79C2313yes—
31#14579160C23196yes—
32#14579160C23148yes—
33#14579156C23196yes—
34#14579155C23132yes—
35#14579153C23124yes—
36#14579152C23196yes—
37#14579151C23196yes—
38#14579151C23196yes—
39#14579151C23196yes—
40#14579139C23196yes—
41C4×Dic158C23196yes—
42#14579126C23196yes—
43#14579126C23196yes—
44#14579119C23148yes—
45C2×C4⋊Dic79C2316yes—
46C2×C4⋊Dic79C23112yes—
47C2×Dic79⋊C4C23112yes—
48C2×Dic79⋊C4C23112yes—
49C2×Dic79⋊C4C23112yes—
50C2×Dic79⋊C4C23112yes—
51C2×(C2×D79)⋊C4C23112yes—
52C2×C4×Dic79C2313yes—
53C2×C4×Dic79C23112yes—
54C2×C4×Dic79C23112yes—
55C42×D79C2318yes—
56#125×C79C23196yes—
57#125×C79C23124yes—
58C2×C4⋊C4×C79C2316yes—
59C2×C4⋊C4×C79C23112yes—
60C2×C4⋊C4×C79C23112yes—
61C2×C42×C79C2311yescharacteristic
62C2×C42×C79C2314yes—
63C23×D79C2411yescharacteristic
64C2×Dic158—248no—
65C2×Dic158C24148yes—
66C22×Dic79C24112yes—
67C22×Dic79C2413yes—
68C2×C4×D79—212no—
69C2×C4×D79C24112yes—
70C4⋊Dic79C24124yes—
71C4⋊Dic79C24148yes—
72Dic79⋊C4C24148yes—
73Dic79⋊C4C24148yes—
74Dic79⋊C4C24148yes—
75Dic79⋊C4C24148yes—
76(C2×D79)⋊C4C24148yes—
77C4×Dic79C24112yes—
78C4×Dic79C24148yes—
79C4×Dic79C24148yes—
80C22×C4×C79C24112yes—
81C22×C4×C79C2413yes—
82C4⋊C4×C79C24124yes—
83C4⋊C4×C79C24148yes—
84C4⋊C4×C79C24148yes—
85C42×C79C2414yes—
86C42×C79C24116yes—
87C23×C79C2511yescharacteristic
88C22×D79—26no—
89C22×D79C2512yes—
90C2×C4×C79—26no—
91C2×C4×C79—224no—
92C2×C4×C79C25124yes—
93C2×C4×C79C2516yes—
94C2×Dic79—224no—
95C2×Dic792−1+4112yes—
96C2×Dic79C25124yes—
97C2×Dic79C2516yes—
98C4×D79—224no—
99Dic158—296no—
100C22×C79C2×2−1+416yes—
101C22×C79C2611yescharacteristic
102C2×D79—26no—
103C2×D79—44no—
104C4×C79—224no—
105C4×C79—26no—
106Dic79—224no—
107Dic79C2×2−1+4112yes—
108C2×#3556—791nomaximal, Sylow
109C2×C79#355614yescomplemented
110C2×C79C22×2−1+413yes—
111D79—42no—
112#3556—7932no—
113C2×#564—793no—
114C2×#564D7911yescharacteristic, complemented
115C2×#557—7912no—
116C2×#541—7912no—
117C2×#533—793no—
118C79C2×#355611yescharacteristic, complemented, Sylow
119#564—7948no—
120#564C2×D79116yescomplemented
121#557—79192no—
122#541—79192no—
123#533—7948no—
124C2×C4⋊Q8—796no—
125C2×C4⋊Q8—7912no—
126C2×#126—7912no—
127C2×#126—794no—
128C2×#125—7912no—
129C2×#125—7912no—
130C2×#125—7912no—
131C2×#125—7912no—
132C2×#125—793no—
133C2×#125C2×D7913yes—
134C2×#125C2×D79112yes—
135C2×C22⋊Q8—7912no—
136C2×C4×Q8—7912no—
137C2×C4×Q8—7912no—
138C2×C4×Q8—7912no—
139C2×#117—796no—
140C22×C42—791no—
141C22×Q8—7912no—
142C23×C4—793no—
143C4⋊Q8—7948no—
144C4⋊Q8—7996no—
145#126—7996no—
146#126—7932no—
147#125—7996no—
148#125—7996no—
149#125—7996no—
150#125—7996no—
151#125—7924no—
152#125C22×D79124yes—
153#125C22×D79196yes—
154C22⋊Q8—7996no—
155C4×Q8—7996no—
156C4×Q8—7996no—
157C4×Q8—7996no—
158#117—7948no—
159C2×C4⋊C4—796no—
160C2×C4⋊C4—7912no—
161C2×C4⋊C4—7912no—
162C2×C4⋊C4—7912no—
163C2×C4⋊C4—7912no—
164C2×C4⋊C4—7912no—
165C2×C4⋊C4C22×D7916yes—
166C2×C4⋊C4C22×D79112yes—
167C2×C4⋊C4C22×D79112yes—
168C2×C22⋊C4—7912no—
169C2×C42—7912no—
170C2×C42—793no—
171C2×C42—7912no—
172C2×C42—798no—
173C2×C42C22×D7914yes—
174C2×C42C22×D7911yescharacteristic
175C24—791no—
176C2×Q8—7948no—
177C2×Q8—15848no—
178C22×C4—793no—
179C22×C4—7912no—
180C22×C4—7912no—
181C22×C4—15812no—
182C22×C4C23×D79112yes—
183C22×C4C23×D7913yes—
184C4⋊C4—7948no—
185C4⋊C4—7948no—
186C4⋊C4—7948no—
187C4⋊C4—7948no—
188C4⋊C4—7924no—
189C4⋊C4—7948no—
190C4⋊C4C23×D79124yes—
191C4⋊C4C23×D79148yes—
192C4⋊C4C23×D79148yes—
193C22⋊C4—7948no—
194C42—7912no—
195C42—7948no—
196C42—7948no—
197C42C23×D7914yes—
198C42C23×D79116yes—
199C23—792no—
200C23—1586no—
201C23C24×D7911yescharacteristic
202Q8—15896no—
203C2×C4—26no—
204C2×C4—224no—
205C2×C4—7912no—
206C2×C4—796no—
207C2×C4—7924no—
208C2×C4—15824no—
209C2×C4—15824no—
210C2×C4C24×D79124yes—
211C2×C4C24×D7916yes—
212C22—3164no—
213C22—1586no—
214C222−1+4×D7916yes—
215C22C25×D7911yescharacteristic
216C4—26no—
217C4—224no—
218C4—7912no—
219C4—15824no—
220C2—3162no—
221C2#2377789414yesdirect product factor
222C2C2×2−1+4×D7913yes—
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#564×C79C2
socleC23×C79C25
prime radicalC23×D79C24
hypercenterC2×#564D79
hypocenterC79C2×#3556
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#564

Complements

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

NH ≅ G/Ntype
1. #23777894C2direct (N × H)
2. C2×C79⋊#564C2semidirect
3. C2×#19099290C2semidirect
6. C2×#564×C79C2semidirect
7. C79⋊#564C22semidirect
8. #19099290C22semidirect
26. #564×C79C22semidirect
109. C2×C79#3556semidirect
114. C2×#564D79semidirect
118. C79C2×#3556semidirect
120. #564C2×D79semidirect
221. C2#23777894direct (N × H)

Maximal subgroups

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

subgroupindex
#237778942
C2×C79⋊#5642
C2×#190992902
C2×#190991722
C2×#190991192
C2×#564×C792
C2×#355679