Finite Group Databasebeta

← C2×#11740636 #13560354

Subgroups — C2×#11740636 #13560354

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×#127C211yesmaximal, characteristic, complemented
2C22×#6439C211yesmaximal, characteristic, complemented
3C2×#89995C216yesmaximal, complemented
4C2×#89994C216yesmaximal, complemented
5#11740636C2116yesmaximal, direct product factor
6C2×#89709C211yesmaximal, characteristic, complemented
7C23×C7×D4C2216yes—
8C23×C22⋊D7C2214yes—
9C2×C7×#127—28no—
10C2×C7×#127C2218yescomplemented
11C22×C42×C7C2211yescharacteristic
12C22×C22⋊Dic7C22112yes—
13C22×(C2×D7)⋊C4C2213yes—
14C22×Dic7⋊C4C2213yes—
15C2×#6439—28no—
16C2×#6439C2218yescomplemented
17#89995C22148yescomplemented
18#89994C22148yescomplemented
19C2×C7⋊#95C2216yes—
20#89709C2218yescomplemented
21C2×#2818—71nomaximal, Sylow
22C25×C7C2314yes—
23C24×D7C2311yescharacteristic
24C22×C7×D4—224no—
25C22×C7×D4—424no—
26C22×C7×D4C23124yes—
27C23×C4×C7C2313yes—
28C22×C22⋊D7—424no—
29C22×C22⋊D7C23116yes—
30C23×Dic7C2313yes—
31C23×Dic7C2314yes—
32C7×#127—232no—
33C2×C42×C7D418yescomplemented
34C2×C42×C7C2314yes—
35C2×C22⋊Dic7—424no—
36C2×C22⋊Dic7C23148yes—
37C2×(C2×D7)⋊C4—212no—
38C2×(C2×D7)⋊C4C23112yes—
39C2×Dic7⋊C4—212no—
40C2×Dic7⋊C4C23112yes—
41#6439—232no—
42C7⋊#95C23124yes—
43C22×#127D711yescharacteristic, complemented
44C22×#126—71no—
45#2818—716no—
46C2×#394—76no—
47C2×#392—76no—
48C2×#383—71no—
49C24×C7—28no—
50C24×C7—224no—
51C24×C7—224no—
52C24×C7C2418yes—
53C24×C7C2411yescharacteristic
54C23×D7—22no—
55C23×D7—212no—
56C23×D7C2412yes—
57C2×C7×D4—248no—
58C2×C7×D4—448no—
59C2×C7×D4—496no—
60C22×C4×C7—212no—
61C22×C4×C7C2×D4112yes—
62C22×C4×C7C2416yes—
63C2×C22⋊D7—448no—
64C2×C22⋊D7—464no—
65C22×Dic7—26no—
66C22×Dic7—212no—
67C22×Dic7—224no—
68C22×Dic7C2418yes—
69C22×Dic7C2416yes—
70C42×C7C2×D4116yescomplemented
71C22⋊Dic7—448no—
72(C2×D7)⋊C4—224no—
73Dic7⋊C4—224no—
74C23×D4—74no—
75C23×D4C2×D716yes—
76C2×#127—28no—
77C2×#127C2×D718yescomplemented
78C2×#126—78no—
79C2×#126—148no—
80C22×C4⋊C4—73no—
81C22×C22⋊C4—73no—
82C22×C22⋊C4—712no—
83C22×C42C2×D711yescharacteristic
84#394—748no—
85#392—748no—
86#383—78no—
87C2×#95—76no—
88C23×C7—28no—
89C23×C7—224no—
90C23×C7—224no—
91C23×C7—448no—
92C23×C7—416no—
93C23×C7—448no—
94C23×C7C22×D412yes—
95C23×C7H(5,𝔽2)112yes—
96C23×C7C2511yescharacteristic
97C22×D7—22no—
98C22×D7—212no—
99C22×D7—412no—
100C22×D7—416no—
101C7×D4—496no—
102C2×C4×C7—224no—
103C2×C4×C7—212no—
104C2×C4×C7C22×D4112yes—
105C22⋊D7—464no—
106C2×Dic7—26no—
107C2×Dic7—212no—
108C2×Dic7—224no—
109C2×Dic7—412no—
110C2×Dic7—416no—
111C25—71no—
112C25C22×D714yes—
113C22×D4—224no—
114C22×D4—424no—
115C22×D4—716no—
116C22×D4—2824no—
117C22×D4C22×D7124yes—
118C23×C4—73no—
119C23×C4—74no—
120C23×C4C22×D713yes—
121#127—232no—
122#126—1432no—
123C2×C4⋊C4—712no—
124C2×C4⋊C4—1412no—
125C2×C22⋊C4—712no—
126C2×C22⋊C4—748no—
127C2×C22⋊C4—1412no—
128C2×C22⋊C4—2824no—
129C2×C42C22⋊D718yescomplemented
130C2×C42C22×D714yes—
131#95—724no—
132C22×C7—424no—
133C22×C7—48no—
134C22×C7—424no—
135C22×C7—832no—
136C22×C7#535112yes—
137C22×C7#560116yes—
138C22×C7C23×D411yescharacteristic
139C22×C7C2×H(5,𝔽2)16yes—
140C2×D7—46no—
141C2×D7—48no—
142C2×D7—88no—
143C4×C7—212no—
144Dic7—46no—
145Dic7—48no—
146C24—224no—
147C24—224no—
148C24—28no—
149C24—72no—
150C24—1412no—
151C24—142no—
152C24C23×D718yes—
153C24C23×D711yescharacteristic
154C2×D4—248no—
155C2×D4—448no—
156C2×D4—496no—
157C2×D4—2848no—
158C2×D4—2864no—
159C22×C4—212no—
160C22×C4—78no—
161C22×C4—76no—
162C22×C4—1412no—
163C22×C4—1424no—
164C22×C4—146no—
165C22×C4C2×C22⋊D7112yes—
166C22×C4C23×D716yes—
167C4⋊C4—1424no—
168C22⋊C4—1424no—
169C22⋊C4—2848no—
170C42C2×C22⋊D7116yescomplemented
171C2×C7—88no—
172C2×C7#281818yescomplemented
173C2×C7C2×#53513yes—
174C2×C7C2×#56014yes—
175D7—82no—
176C23—224no—
177C23—224no—
178C23—28no—
179C23—416no—
180C23—448no—
181C23—448no—
182C23—1412no—
183C23—142no—
184C23—2816no—
185C23—2812no—
186C23#6548112yes—
187C23C22×C22⋊D712yes—
188C23C24×D711yescharacteristic
189D4—496no—
190D4—2864no—
191C2×C4—224no—
192C2×C4—212no—
193C2×C4—1412no—
194C2×C4—1424no—
195C2×C4—146no—
196C2×C4—2816no—
197C2×C4—2812no—
198C2×C4C22×C22⋊D7112yes—
199C7C2×#281811yescharacteristic, complemented, Sylow
200C22—48no—
201C22—424no—
202C22—424no—
203C22—832no—
204C22—288no—
205C22—286no—
206C22—568no—
207C22#90411116yes—
208C22#90496112yes—
209C22C2×#654816yes—
210C22C23×C22⋊D711yescharacteristic
211C4—212no—
212C4—288no—
213C4—286no—
214C2—88no—
215C2—562no—
216C2#1174063618yesdirect product factor
217C2C2×#9041114yes—
218C2C2×#9049613yes—
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC22×C7×#127C2
socleC24×C7C24
hypercenterC22×#127D7
hypocenterC7C2×#2818
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×#127

Complements

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

NH ≅ G/Ntype
1. C22×C7×#127C2semidirect
2. C22×#6439C2semidirect
3. C2×#89995C2semidirect
4. C2×#89994C2semidirect
5. #11740636C2direct (N × H)
6. C2×#89709C2semidirect
10. C2×C7×#127C22semidirect
16. C2×#6439C22semidirect
17. #89995C22semidirect
18. #89994C22semidirect
20. #89709C22semidirect
33. C2×C42×C7D4semidirect
43. C22×#127D7semidirect
70. C42×C7C2×D4semidirect
77. C2×#127C2×D7semidirect
129. C2×C42C22⋊D7semidirect
170. C42C2×C22⋊D7semidirect
172. C2×C7#2818semidirect
199. C7C2×#2818semidirect
216. C2#11740636direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1272
C22×#64392
C2×#899952
C2×#899942
#117406362
C2×#897092
C2×#28187