Finite Group Databasebeta

← #13245231

Subgroups — #13245231

Order 1792.

812 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 147 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×C7×#540C211yesmaximal, characteristic
2#11729351C214yesmaximal, complemented
3#11729325C212yesmaximal, complemented
4C7×#540—28no—
5C2×C7×#127C411yescharacteristic
6C2×C7×#125C411yescharacteristic
7C2×C7×#123—22no—
8C2×C7×#121—22no—
9C2×C7×#121C412yes—
10C2×C4×C7×D4C2212yes—
11C2×C7×#117C2211yescharacteristic
12#89697C2214yes—
13D4⋊(C7⋊C8)—28no—
14#89323—22no—
15#89320—22no—
16#8326—71nomaximal, Sylow
17C22×C7×D4—22no—
18C22×C7×D4—22no—
19C22×C7×D4C2×C412yes—
20C23×C4×C7—22no—
21C23×C4×C7C2×C411yescharacteristic
22C7×#127—24no—
23C7×#125—24no—
24C7×#123—216no—
25C7×#121—216no—
26C7×#121—24no—
27C7×#121—24no—
28C4×C7×D4—24no—
29C4×C7×D4D418yes—
30C7×#117—24no—
31C2×C7×C4⋊C4—22no—
32C2×C7×C4⋊C4C2×C412yes—
33C2×C7×C4⋊C4D412yes—
34C2×C7×C22⋊C4—22no—
35C2×C7×C22⋊C4—22no—
36C2×C7×C22⋊C4D412yes—
37C2×C42×C7C2×C411yescharacteristic
38C2×C42×C7C2311yescharacteristic
39C22⋊(C7⋊C8)—24no—
40C4⋊(C7⋊C8)—24no—
41C4×C7⋊C8—24no—
42C2×#540D711yescharacteristic
43#1478—74no—
44#1458—72no—
45C24×C7—22no—
46C24×C7C22⋊C411yescharacteristic
47C2×C7×D4—28no—
48C2×C7×D4—28no—
49C2×C7×D4—22no—
50C2×C7×D4—28no—
51C2×C7×D4—84no—
52C2×C7×D4—84no—
53C2×C7×D4C22⋊C414yes—
54C22×C4×C7—22no—
55C22×C4×C7—22no—
56C22×C4×C7—24no—
57C22×C4×C7—28no—
58C22×C4×C7—84no—
59C22×C4×C7C22⋊C411yescharacteristic
60C22×C4×C7C22⋊C412yes—
61C22×C4×C7C22×C411yescharacteristic
62C22×C4×C7C2×D412yes—
63C7×C4⋊C4—28no—
64C7×C4⋊C4—22no—
65C7×C4⋊C4—24no—
66C7×C4⋊C4C22⋊C414yes—
67C7×C22⋊C4—28no—
68C7×C22⋊C4—28no—
69C7×C22⋊C4—24no—
70C42×C7—22no—
71C42×C7C2×D414yes—
72C2×C7⋊C8—44no—
73#540—28no—
74C2×#127Dic711yescharacteristic
75C2×#125Dic711yescharacteristic
76C2×#123—22no—
77C2×#121—22no—
78C2×#121Dic712yes—
79C2×C4×D4C2×D712yes—
80C2×#117C2×D711yescharacteristic
81#431—74no—
82D4⋊C8—148no—
83#324—142no—
84#323—142no—
85C23×C7—21no—
86C23×C7—24no—
87C23×C7—22no—
88C23×C7—44no—
89C23×C7—44no—
90C23×C7—42no—
91C23×C7—44no—
92C23×C7C2×C22⋊C411yescharacteristic
93C7×D4—28no—
94C7×D4—44no—
95C7×D4—88no—
96C7×D4—88no—
97C2×C4×C7—22no—
98C2×C4×C7—21no—
99C2×C4×C7—24no—
100C2×C4×C7—22no—
101C2×C4×C7—42no—
102C2×C4×C7—44no—
103C2×C4×C7—44no—
104C2×C4×C7—42no—
105C2×C4×C7—88no—
106C2×C4×C7C2×C22⋊C412yes—
107C2×C4×C7#12014yes—
108C2×C4×C7#13114yes—
109C7⋊C8—84no—
110C22×D4—22no—
111C22×D4—22no—
112C22×D4C2×Dic712yes—
113C23×C4—22no—
114C23×C4C2×Dic711yescharacteristic
115#127—24no—
116#125—24no—
117#123—216no—
118#121—216no—
119#121—24no—
120#121—24no—
121C4×D4—24no—
122C4×D4C22⋊D718yes—
123#117—24no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4C2×Dic712yes—
126C2×C4⋊C4C22⋊D712yes—
127C2×C22⋊C4—22no—
128C2×C22⋊C4—22no—
129C2×C22⋊C4C22⋊D712yes—
130C2×C42C2×Dic711yescharacteristic
131C2×C42C22×D711yescharacteristic
132C4⋊C8—144no—
133C22⋊C8—144no—
134C4×C8—144no—
135C22×C7—22no—
136C22×C7—44no—
137C22×C7—42no—
138C22×C7—44no—
139C22×C7—41no—
140C22×C7—44no—
141C22×C7—82no—
142C22×C7—88no—
143C22×C7#37911yescharacteristic
144C22×C7#40812yes—
145C4×C7—24no—
146C4×C7—44no—
147C4×C7—42no—
148C4×C7—41no—
149C4×C7#40814yes—
150C24—22no—
151C24C22⋊Dic711yescharacteristic
152C2×D4—28no—
153C2×D4—28no—
154C2×D4—28no—
155C2×D4—22no—
156C2×D4—84no—
157C2×D4—84no—
158C2×D4C22⋊Dic714yes—
159C22×C4—22no—
160C22×C4—24no—
161C22×C4—22no—
162C22×C4—28no—
163C22×C4—84no—
164C22×C4C22⋊Dic711yescharacteristic
165C22×C4C22⋊Dic712yes—
166C22×C4C22×Dic711yescharacteristic
167C22×C4C2×C22⋊D712yes—
168C2×C8—284no—
169C4⋊C4—28no—
170C4⋊C4—22no—
171C4⋊C4—24no—
172C4⋊C4C22⋊Dic714yes—
173C22⋊C4—28no—
174C22⋊C4—28no—
175C22⋊C4—24no—
176C42—22no—
177C42C2×C22⋊D714yes—
178C2×C7—22no—
179C2×C7—81no—
180C2×C7—84no—
181C2×C7#178011yescharacteristic
182C2×C7#179512yes—
183C23—21no—
184C23—24no—
185C23—22no—
186C23—44no—
187C23—44no—
188C23—42no—
189C23—44no—
190C23C2×C22⋊Dic711yescharacteristic
191D4—28no—
192D4—44no—
193D4—88no—
194D4—88no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—24no—
199C2×C4—42no—
200C2×C4—44no—
201C2×C4—44no—
202C2×C4—42no—
203C2×C4—88no—
204C2×C4#651114yes—
205C2×C4C2×C22⋊Dic712yes—
206C2×C4#651614yes—
207C8—564no—
208C7#832611yescharacteristic, complemented, Sylow
209C22—22no—
210C22—41no—
211C22—44no—
212C22—44no—
213C22—44no—
214C22—42no—
215C22—82no—
216C22—88no—
217C22#9000612yes—
218C22#9001911yescharacteristic
219C4—24no—
220C4—41no—
221C4—44no—
222C4—42no—
223C4#9000614yes—
224C2—22no—
225C2—84no—
226C2—81no—
227C2#1172989011yescharacteristic
228C2#1172989512yes—
subgroupG/H
centerC22#90019
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
Fitting, prime radicalC2×C7×#540C2
socleC22×C7#379
cosocleC2×C42×C7C23
hypercenterC2×#540D7
hypocenterC7#8326
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
2. #11729351C2semidirect
3. #11729325C2semidirect
208. C7#8326semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5402
#117293512
#117293252
#83267