Finite Group Databasebeta

← C2×#11740563 #13560353

Subgroups — C2×#11740563 #13560353

Order 1792.

3666 conjugacy classes of subgroups; only the 667 normal subgroups are shown.

normal subgroups only

This group has 3666 conjugacy classes of subgroups — too many to draw. Only its 667 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×C7×#126C211yesmaximal, characteristic, complemented
2C22×#6437C211yesmaximal, characteristic, complemented
3#11740563C2116yesmaximal, direct product factor
4C2×#89763C216yesmaximal, complemented
5C2×#89732C216yesmaximal, complemented
6C2×#89709C211yesmaximal, characteristic, complemented
7C23×C22⋊D7C2214yes—
8C23×D28C2216yes—
9C2×C7×#126—28no—
10C2×C7×#126C2218yescomplemented
11C22×C7×C4⋊C4C2213yes—
12C22×C7×C22⋊C4C2213yes—
13C22×C42×C7C2211yescharacteristic
14C22×(C2×D7)⋊C4C22112yes—
15C2×#6437—28no—
16C2×#6437C2218yescomplemented
17C2×C7⋊#95C2216yes—
18#89763C22148yescomplemented
19#89732C22148yescomplemented
20#89709C2218yescomplemented
21C2×#2818—71nomaximal, Sylow
22C25×C7C2311yescharacteristic
23C24×D7C2314yes—
24C23×C4×C7C2313yes—
25C23×C4×C7C2313yes—
26C22×C22⋊D7—424no—
27C22×C22⋊D7C23116yes—
28C23×Dic7C2314yes—
29C22×D28—224no—
30C22×D28—424no—
31C22×D28C23124yes—
32C7×#126—232no—
33C2×C7×C4⋊C4—212no—
34C2×C7×C4⋊C4C23112yes—
35C2×C7×C22⋊C4—212no—
36C2×C7×C22⋊C4C23112yes—
37C2×C42×C7D418yescomplemented
38C2×C42×C7C2314yes—
39C2×(C2×D7)⋊C4—424no—
40C2×(C2×D7)⋊C4C23148yes—
41#6437—232no—
42C7⋊#95C23124yes—
43C22×#127—71no—
44C22×#126D711yescharacteristic, complemented
45#2818—716no—
46C2×#394—76no—
47C2×#392—76no—
48C2×#383—71no—
49C24×C7—22no—
50C24×C7—212no—
51C24×C7C2412yes—
52C24×C7C2411yescharacteristic
53C23×D7—28no—
54C23×D7—224no—
55C23×D7—224no—
56C23×D7C2418yes—
57C22×C4×C7—212no—
58C22×C4×C7—26no—
59C22×C4×C7—212no—
60C22×C4×C7C2×D4112yes—
61C22×C4×C7C2416yes—
62C22×C4×C7C2416yes—
63C2×C22⋊D7—448no—
64C2×C22⋊D7—464no—
65C22×Dic7—224no—
66C22×Dic7C2418yes—
67C2×D28—248no—
68C2×D28—448no—
69C2×D28—496no—
70C7×C4⋊C4—224no—
71C7×C22⋊C4—224no—
72C42×C7C2×D4116yescomplemented
73(C2×D7)⋊C4—448no—
74C23×D4—74no—
75C23×D4—76no—
76C2×#127—78no—
77C2×#127—148no—
78C2×#126—28no—
79C2×#126C2×D718yescomplemented
80C22×C4⋊C4C2×D713yes—
81C22×C22⋊C4—712no—
82C22×C22⋊C4C2×D713yes—
83C22×C42C2×D711yescharacteristic
84#394—748no—
85#392—748no—
86#383—78no—
87C2×#95—76no—
88C23×C7—22no—
89C23×C7—212no—
90C23×C7—412no—
91C23×C7—416no—
92C23×C7C22×D412yes—
93C23×C7H(5,𝔽2)112yes—
94C23×C7C2511yescharacteristic
95C22×D7—28no—
96C22×D7—224no—
97C22×D7—224no—
98C22×D7—448no—
99C22×D7—416no—
100C22×D7—448no—
101C2×C4×C7—224no—
102C2×C4×C7—212no—
103C2×C4×C7—26no—
104C2×C4×C7—212no—
105C2×C4×C7—412no—
106C2×C4×C7C22×D4112yes—
107C22⋊D7—464no—
108C2×Dic7—224no—
109C2×Dic7—416no—
110D28—496no—
111C25—74no—
112C25C22×D711yescharacteristic
113C22×D4—716no—
114C22×D4—724no—
115C22×D4—1424no—
116C22×D4—2824no—
117C22×D4—2824no—
118C23×C4—74no—
119C23×C4C22×D713yes—
120C23×C4C22×D713yes—
121#127—1432no—
122#126—232no—
123C2×C4⋊C4—212no—
124C2×C4⋊C4C22×D7112yes—
125C2×C22⋊C4—212no—
126C2×C22⋊C4—748no—
127C2×C22⋊C4—2824no—
128C2×C22⋊C4C22×D7112yes—
129C2×C42C22⋊D718yescomplemented
130C2×C42C22×D714yes—
131#95—724no—
132C22×C7—46no—
133C22×C7—48no—
134C22×C7—88no—
135C22×C7#535112yes—
136C22×C7#560116yes—
137C22×C7C23×D411yescharacteristic
138C22×C7C2×H(5,𝔽2)16yes—
139C2×D7—424no—
140C2×D7—48no—
141C2×D7—424no—
142C2×D7—832no—
143C4×C7—212no—
144C4×C7—46no—
145Dic7—48no—
146C24—212no—
147C24—22no—
148C24—78no—
149C24—1424no—
150C24—1424no—
151C24—148no—
152C24C23×D712yes—
153C24C23×D711yescharacteristic
154C2×D4—1448no—
155C2×D4—2848no—
156C2×D4—2896no—
157C2×D4—2848no—
158C2×D4—2864no—
159C22×C4—212no—
160C22×C4—212no—
161C22×C4—26no—
162C22×C4—78no—
163C22×C4—1424no—
164C22×C4C2×C22⋊D7112yes—
165C22×C4C23×D716yes—
166C22×C4C23×D716yes—
167C4⋊C4—224no—
168C22⋊C4—224no—
169C22⋊C4—2848no—
170C42C2×C22⋊D7116yescomplemented
171C2×C7—82no—
172C2×C7#281818yescomplemented
173C2×C7C2×#53513yes—
174C2×C7C2×#56014yes—
175D7—88no—
176C23—212no—
177C23—22no—
178C23—416no—
179C23—412no—
180C23—1424no—
181C23—1424no—
182C23—148no—
183C23—2816no—
184C23—2848no—
185C23—2848no—
186C23#6553112yes—
187C23C22×C22⋊D712yes—
188C23C24×D711yescharacteristic
189D4—2896no—
190D4—2864no—
191C2×C4—224no—
192C2×C4—212no—
193C2×C4—212no—
194C2×C4—26no—
195C2×C4—412no—
196C2×C4—1424no—
197C2×C4—2816no—
198C2×C4C22×C22⋊D7112yes—
199C7C2×#281811yescharacteristic, complemented, Sylow
200C22—46no—
201C22—48no—
202C22—88no—
203C22—2824no—
204C22—288no—
205C22—2824no—
206C22—5632no—
207C22#90402116yes—
208C22#90521112yes—
209C22C2×#655316yes—
210C22C23×C22⋊D711yescharacteristic
211C4—212no—
212C4—46no—
213C4—288no—
214C2—82no—
215C2—568no—
216C2#1174056318yesdirect product factor
217C2C2×#9040214yes—
218C2C2×#9052113yes—
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC22×C7×#126C2
socleC24×C7C24
hypercenterC22×#126D7
hypocenterC7C2×#2818
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
1. C22×C7×#126C2semidirect
2. C22×#6437C2semidirect
3. #11740563C2direct (N × H)
4. C2×#89763C2semidirect
5. C2×#89732C2semidirect
6. C2×#89709C2semidirect
10. C2×C7×#126C22semidirect
16. C2×#6437C22semidirect
18. #89763C22semidirect
19. #89732C22semidirect
20. #89709C22semidirect
37. C2×C42×C7D4semidirect
44. C22×#126D7semidirect
72. C42×C7C2×D4semidirect
79. C2×#126C2×D7semidirect
129. C2×C42C22⋊D7semidirect
170. C42C2×C22⋊D7semidirect
172. C2×C7#2818semidirect
199. C7C2×#2818semidirect
216. C2#11740563direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1262
C22×#64372
#117405632
C2×#897632
C2×#897322
C2×#897092
C2×#28187