Finite Group Databasebeta

← #13513849

Subgroups — #13513849

Order 1792.

2446 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#117C211yesmaximal, characteristic
2C2×#89983C212yesmaximal
3#11739682C2116yesmaximal, complemented
4#11739600C214yesmaximal, complemented
5#11739539C212yesmaximal
6#11739528C212yesmaximal
7#11739505C214yesmaximal, complemented
8C24×C4×C7C2211yescharacteristic
9C2×C7×#117C4116yescomplemented
10C2×C7×#117C2218yes—
11C22×C7×C4⋊C4C2212yes—
12C22×C7×C22⋊C4C2211yescharacteristic
13C22×C7×C22⋊C4C2211yescharacteristic
14C22×C42×C7C2212yes—
15C22×C22⋊Dic7C2214yes—
16#89984C2218yes—
17#89983C2218yes—
18#89983C2214yes—
19#89983C2214yes—
20C4×C22⋊Dic7C2218yes—
21C2×C7⋊#95C2218yes—
22#89753C22132yescomplemented
23#89722C22116yes—
24C22⋊C4×Dic7C22116yes—
25#89709C2218yescomplemented
26#89708C2218yescomplemented
27C4×C4⋊Dic7C2218yescomplemented
28#89704C2218yescomplemented
29#34177—71nomaximal, Sylow
30C25×C7C2311yescharacteristic
31C23×C4×C7—28no—
32C23×C4×C7C2×C418yes—
33C23×C4×C7C2314yes—
34C23×C4×C7C2311yescharacteristic
35C23×C4×C7C2311yescharacteristic
36C23×C4×C7C2312yes—
37C23×C4×C7C2312yes—
38C23×Dic7C2318yes—
39C7×#117C2×C4164yescomplemented
40C2×C7×C4⋊C4C2×C4116yescomplemented
41C2×C7×C4⋊C4C2318yes—
42C2×C7×C22⋊C4C2×C418yes—
43C2×C7×C22⋊C4C2×C418yes—
44C2×C7×C22⋊C4C2314yes—
45C2×C7×C22⋊C4C2314yes—
46C2×C42×C7C2×C4116yescomplemented
47C2×C42×C7C2314yes—
48C2×C42×C7C2314yes—
49C2×C22⋊Dic7—216no—
50C2×C22⋊Dic7C2318yes—
51C2×C22⋊Dic7C2318yes—
52C2×C4⋊Dic7C23116yes—
53C2×C4×Dic7C23116yes—
54C7⋊#95C23116yes—
55C7⋊#95C23116yes—
56C7⋊#95C23116yes—
57C7⋊#95C23116yes—
58C22×#117D711yescharacteristic
59#2343—716no—
60#2315—72no—
61#2313—74no—
62#2283—74no—
63C2×#381—72no—
64#2273—72no—
65C24×C7—44no—
66C24×C7C22×C414yes—
67C24×C7#4118yes—
68C24×C7C2411yescharacteristic
69C24×C7C2412yes—
70C22×C4×C7—232no—
71C22×C4×C7—24no—
72C22×C4×C7—24no—
73C22×C4×C7—216no—
74C22×C4×C7—44no—
75C22×C4×C7—44no—
76C22×C4×C7C22×C414yes—
77C22×C4×C7C22×C414yes—
78C22×C4×C7C22×C4116yes—
79C22×C4×C7C22×C418yes—
80C22×C4×C7C22×C418yes—
81C22×C4×C7C2412yes—
82C22×C4×C7C2412yes—
83C22×C4×C7C2414yes—
84C22×C4×C7C2414yes—
85C22×Dic7—216no—
86C22×Dic7—416no—
87C22×Dic7C24116yes—
88C7×C4⋊C4C22×C4132yes—
89C7×C22⋊C4C22×C4116yes—
90C7×C22⋊C4C22×C4116yes—
91C42×C7C22×C4116yes—
92C42×C7C22×C4116yes—
93C22⋊Dic7—216no—
94C22⋊Dic7—216no—
95C4⋊Dic7—416no—
96C4×Dic7—416no—
97C24×C4C2×D711yescharacteristic
98C2×#117Dic7116yescomplemented
99C2×#117C2×D718yes—
100C22×C4⋊C4C2×D712yes—
101C22×C22⋊C4—74no—
102C22×C22⋊C4C2×D711yescharacteristic
103C22×C22⋊C4C2×D711yescharacteristic
104C22×C42C2×D712yes—
105#387—732no—
106#385—716no—
107#383—78no—
108#382—78no—
109#381—74no—
110#381—78no—
111#381—74no—
112#380—78no—
113C4×C4⋊C4—78no—
114C4×C22⋊C4—78no—
115C4×C22⋊C4—716no—
116#376—78no—
117C2×#95—78no—
118C23×C7—28no—
119C23×C7—24no—
120C23×C7—48no—
121C23×C7—416no—
122C23×C7#117116yes—
123C23×C7C23×C414yes—
124C23×C7C23×C412yes—
125C23×C7C2×#4114yes—
126C23×C7C2×#4118yes—
127C23×C7C2511yescharacteristic
128C2×C4×C7—28no—
129C2×C4×C7—28no—
130C2×C4×C7—232no—
131C2×C4×C7—24no—
132C2×C4×C7—24no—
133C2×C4×C7—28no—
134C2×C4×C7—28no—
135C2×C4×C7—48no—
136C2×C4×C7—48no—
137C2×C4×C7C23×C414yes—
138C2×C4×C7C23×C418yes—
139C2×C4×C7C23×C418yes—
140C2×C4×C7C23×C414yes—
141C2×Dic7—216no—
142C2×Dic7—232no—
143C2×Dic7—816no—
144C25C22×D711yescharacteristic
145C23×C4—28no—
146C23×C4—78no—
147C23×C4C2×Dic718yes—
148C23×C4C22×D711yescharacteristic
149C23×C4C22×D714yes—
150C23×C4C22×D711yescharacteristic
151C23×C4C22×D712yes—
152C23×C4C22×D712yes—
153#117C2×Dic7164yescomplemented
154C2×C4⋊C4—716no—
155C2×C4⋊C4C2×Dic7116yescomplemented
156C2×C4⋊C4C22×D718yes—
157C2×C22⋊C4—78no—
158C2×C22⋊C4—78no—
159C2×C22⋊C4—1416no—
160C2×C22⋊C4C2×Dic718yes—
161C2×C22⋊C4C2×Dic718yes—
162C2×C22⋊C4C22×D714yes—
163C2×C22⋊C4C22×D714yes—
164C2×C42—716no—
165C2×C42C2×Dic7116yescomplemented
166C2×C42C22×D714yes—
167C2×C42C22×D714yes—
168#95—716no—
169#95—716no—
170#95—716no—
171#95—716no—
172C22×C7—24no—
173C22×C7—28no—
174C22×C7—216no—
175C22×C7—28no—
176C22×C7—416no—
177C22×C7C2×#11718yes—
178C22×C7C2×#11714yes—
179C22×C7C24×C411yescharacteristic
180C22×C7C22×#4112yes—
181C22×C7#58514yes—
182C4×C7—24no—
183C4×C7—24no—
184C4×C7—28no—
185C4×C7—28no—
186Dic7—416no—
187C24—44no—
188C24#115718yes—
189C24C22×Dic714yes—
190C24C23×D711yescharacteristic
191C24C23×D712yes—
192C22×C4—232no—
193C22×C4—24no—
194C22×C4—24no—
195C22×C4—216no—
196C22×C4—44no—
197C22×C4—44no—
198C22×C4—716no—
199C22×C4—1416no—
200C22×C4—2816no—
201C22×C4C22×Dic714yes—
202C22×C4C22×Dic714yes—
203C22×C4C22×Dic7116yes—
204C22×C4C22×Dic718yes—
205C22×C4C22×Dic718yes—
206C22×C4C23×D712yes—
207C22×C4C23×D712yes—
208C22×C4C23×D714yes—
209C22×C4C23×D714yes—
210C4⋊C4—2816no—
211C4⋊C4C22×Dic7132yes—
212C22⋊C4—1416no—
213C22⋊C4—1416no—
214C22⋊C4C22×Dic7116yes—
215C22⋊C4C22×Dic7116yes—
216C42—2816no—
217C42C22×Dic7116yes—
218C42C22×Dic7116yes—
219C2×C7—24no—
220C2×C7—28no—
221C2×C7C22×#11711yescharacteristic
222C2×C7#342812yes—
223C2×C7#349114yes—
224C23—24no—
225C23—28no—
226C23—416no—
227C23—48no—
228C23#6489116yes—
229C23C2×#115714yes—
230C23C2×#115718yes—
231C23C23×Dic714yes—
232C23C23×Dic712yes—
233C23C24×D711yescharacteristic
234C2×C4—28no—
235C2×C4—28no—
236C2×C4—232no—
237C2×C4—24no—
238C2×C4—24no—
239C2×C4—28no—
240C2×C4—28no—
241C2×C4—48no—
242C2×C4—48no—
243C2×C4—1416no—
244C2×C4—1432no—
245C2×C4—5616no—
246C2×C4C23×Dic714yes—
247C2×C4C23×Dic718yes—
248C2×C4C23×Dic718yes—
249C2×C4C23×Dic714yes—
250C7#3417711yescharacteristic, complemented, Sylow
251C22—24no—
252C22—28no—
253C22—216no—
254C22—28no—
255C22—416no—
256C22C2×#648914yes—
257C22C2×#648918yes—
258C22C22×#115712yes—
259C22#9061614yes—
260C22C24×Dic711yescharacteristic
261C4—24no—
262C4—24no—
263C4—28no—
264C4—28no—
265C4—2816no—
266C2—24no—
267C2—28no—
268C2#1174281314yes—
269C2C22×#648911yescharacteristic
270C2#1174432812yes—
subgroupG/H
center, FrattiniC23C24×D7
commutatorC22×C7C24×C4
FittingC22×C7×#117C2
socle, cosocleC23×C7C25
prime radicalC25×C7C23
hypercenterC22×#117D7
hypocenterC7#34177
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
3. #11739682C2semidirect
4. #11739600C2semidirect
7. #11739505C2semidirect
9. C2×C7×#117C4semidirect
22. #89753C22semidirect
25. #89709C22semidirect
26. #89708C22semidirect
27. C4×C4⋊Dic7C22semidirect
28. #89704C22semidirect
39. C7×#117C2×C4semidirect
40. C2×C7×C4⋊C4C2×C4semidirect
46. C2×C42×C7C2×C4semidirect
98. C2×#117Dic7semidirect
153. #117C2×Dic7semidirect
155. C2×C4⋊C4C2×Dic7semidirect
165. C2×C42C2×Dic7semidirect
250. C7#34177semidirect

Maximal subgroups

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

subgroupindex
C22×C7×#1172
C2×#899832
#117396822
#117396002
#117395392
#117395282
#117395052
#341777