Finite Group Databasebeta

← #13519969

Subgroups — #13519969

Order 1792.

1800 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
1C2×C7×#564C211yesmaximal, characteristic
2#11740472C213yesmaximal
3#11740471C216yesmaximal
4#11740470C216yesmaximal
5#11740469C216yesmaximal
6#11740468C216yesmaximal
7Dic7×#125C213yesmaximal
8C7×#564C4116yescomplemented
9C2×C7×#125C2213yes—
10C2×C7×#125C2216yes—
11C2×C7×#125C2216yes—
12#89757C2213yes—
13#89757C2213yes—
14#89757C2216yes—
15#89757C2216yes—
16#89757C2216yes—
17#89757C2216yes—
18#89753C2216yes—
19#89753C2216yes—
20#89753C2216yes—
21#89753C2216yes—
22#89753C2216yes—
23#89753C2216yes—
24#89753C2216yes—
25#89753C2216yes—
26#89753C2216yes—
27#89753C2216yes—
28C4⋊C4×Dic7C2216yes—
29C4⋊C4×Dic7C2213yes—
30C4⋊C4×Dic7C2216yes—
31C4⋊C4×Dic7C2213yes—
32C4⋊C4×Dic7C2216yes—
33C4⋊C4×Dic7C2216yes—
34#89709C2212yes—
35#89708C2213yes—
36#89707C2212yes—
37C4×C4⋊Dic7C2216yes—
38#89704C2216yes—
39C42×Dic7C2211yescharacteristic
40#34530—71nomaximal, Sylow
41C7×#125C2×C4124yes—
42C7×#125C2×C4148yes—
43C7×#125C2×C4148yes—
44C2×C7×C4⋊C4C2316yes—
45C2×C7×C4⋊C4C2313yes—
46C2×C7×C4⋊C4C2316yes—
47C2×C7×C4⋊C4C2313yes—
48C2×C7×C4⋊C4C2316yes—
49C2×C7×C4⋊C4C2316yes—
50C2×C42×C7C2311yescharacteristic
51C2×C42×C7C2312yes—
52C2×C42×C7C2312yes—
53C2×C4⋊Dic7C2316yes—
54C2×C4⋊Dic7C2316yes—
55C2×C4⋊Dic7C2316yes—
56C2×C4⋊Dic7C2316yes—
57C2×C4⋊Dic7C2313yes—
58C2×C4⋊Dic7C2313yes—
59C2×C4×Dic7C2313yes—
60C2×C4×Dic7C2316yes—
61C2×C4×Dic7C2313yes—
62C2×C4×Dic7C2316yes—
63C2×C4×Dic7C2316yes—
64C2×C4×Dic7C2316yes—
65C7⋊#95C2316yes—
66C7⋊#95C2316yes—
67C7⋊#95C2316yes—
68C7⋊#95C2316yes—
69C7⋊#95C2316yes—
70C7⋊#95C2316yes—
71C7⋊#95C2316yes—
72C7⋊#95C2316yes—
73C7⋊#95C2316yes—
74C7⋊#95C2316yes—
75C2×#564D711yescharacteristic
76#2382—73no—
77#2371—76no—
78#2370—76no—
79#2336—76no—
80#2330—76no—
81C4×#125—73no—
82C22×C4×C7C2416yes—
83C22×C4×C7C2413yes—
84C22×C4×C7C2416yes—
85C22×Dic7C2416yes—
86C22×Dic7C2416yes—
87C22×Dic7C2411yescharacteristic
88C22×Dic7C2413yes—
89C7×C4⋊C4C22×C4124yes—
90C7×C4⋊C4C22×C4112yes—
91C7×C4⋊C4C22×C4124yes—
92C7×C4⋊C4C22×C4112yes—
93C7×C4⋊C4C22×C4124yes—
94C7×C4⋊C4C22×C4124yes—
95C42×C7C22×C414yes—
96C42×C7C22×C418yes—
97C42×C7C22×C418yes—
98C4⋊Dic7—212no—
99C4⋊Dic7—43no—
100C4⋊Dic7—46no—
101C4⋊Dic7—46no—
102C4⋊Dic7—46no—
103C4⋊Dic7—43no—
104C4×Dic7—26no—
105C4×Dic7—212no—
106C4×Dic7—46no—
107C4×Dic7—43no—
108C4×Dic7—46no—
109C4×Dic7—46no—
110#564Dic7116yescomplemented
111C2×#125C2×D713yes—
112C2×#125C2×D716yes—
113C2×#125C2×D716yes—
114#389—73no—
115#389—73no—
116#389—76no—
117#389—76no—
118#389—76no—
119#389—76no—
120#387—76no—
121#387—76no—
122#387—76no—
123#387—76no—
124#387—76no—
125#387—76no—
126#387—76no—
127#387—76no—
128#387—76no—
129#387—76no—
130#384—72no—
131#383—72no—
132#382—73no—
133C4×C4⋊C4—76no—
134C4×C4⋊C4—73no—
135C4×C4⋊C4—76no—
136C4×C4⋊C4—73no—
137C4×C4⋊C4—76no—
138C4×C4⋊C4—76no—
139C4×C4⋊C4—76no—
140#376—76no—
141C43—71no—
142C23×C7C2511yescharacteristic
143C2×C4×C7—23no—
144C2×C4×C7—26no—
145C2×C4×C7—26no—
146C2×C4×C7—26no—
147C2×C4×C7—23no—
148C2×C4×C7—26no—
149C2×C4×C7C23×C416yes—
150C2×C4×C7C23×C4112yes—
151C2×C4×C7C23×C4112yes—
152C2×Dic7—23no—
153C2×Dic7—23no—
154C2×Dic7—26no—
155C2×Dic7—26no—
156C2×Dic7—26no—
157C2×Dic7—26no—
158C2×Dic7—26no—
159C2×Dic7—23no—
160C2×Dic7—26no—
161C2×Dic72−1+416yes—
162#125C2×Dic7124yes—
163#125C2×Dic7148yes—
164#125C2×Dic7148yes—
165C2×C4⋊C4—76no—
166C2×C4⋊C4—73no—
167C2×C4⋊C4—73no—
168C2×C4⋊C4—76no—
169C2×C4⋊C4—76no—
170C2×C4⋊C4—76no—
171C2×C4⋊C4C22×D713yes—
172C2×C4⋊C4C22×D716yes—
173C2×C4⋊C4C22×D716yes—
174C2×C4⋊C4C22×D713yes—
175C2×C4⋊C4C22×D716yes—
176C2×C4⋊C4C22×D716yes—
177C2×C42—73no—
178C2×C42—76no—
179C2×C42—73no—
180C2×C42—76no—
181C2×C42—76no—
182C2×C42—76no—
183C2×C42C22×D711yescharacteristic
184C2×C42C22×D712yes—
185C2×C42C22×D712yes—
186#95—76no—
187#95—76no—
188#95—76no—
189#95—76no—
190#95—76no—
191#95—76no—
192#95—76no—
193#95—76no—
194#95—76no—
195#95—76no—
196C22×C7C24×C411yescharacteristic
197C22×C7C2×2−1+413yes—
198C22×C7#58513yes—
199C4×C7—26no—
200C4×C7—212no—
201C4×C7—212no—
202Dic7—26no—
203Dic7—46no—
204Dic7—46no—
205Dic7—41no—
206C22×C4—73no—
207C22×C4—76no—
208C22×C4—76no—
209C22×C4—71no—
210C22×C4C23×D716yes—
211C22×C4C23×D713yes—
212C22×C4C23×D716yes—
213C4⋊C4—1412no—
214C4⋊C4—286no—
215C4⋊C4—283no—
216C4⋊C4—286no—
217C4⋊C4—286no—
218C4⋊C4—283no—
219C4⋊C4C22×Dic7112yes—
220C4⋊C4C22×Dic7124yes—
221C4⋊C4C22×Dic7124yes—
222C4⋊C4C22×Dic7112yes—
223C4⋊C4C22×Dic7124yes—
224C4⋊C4C22×Dic7124yes—
225C42—146no—
226C42—1412no—
227C42—286no—
228C42—286no—
229C42—283no—
230C42—286no—
231C42C22×Dic714yes—
232C42C22×Dic718yes—
233C42C22×Dic718yes—
234C2×C7C4×2−1+413yes—
235C2×C7#356313yes—
236C2×C7#356711yescharacteristic
237C23C24×D711yescharacteristic
238C2×C4—23no—
239C2×C4—26no—
240C2×C4—26no—
241C2×C4—26no—
242C2×C4—23no—
243C2×C4—26no—
244C2×C4—76no—
245C2×C4—143no—
246C2×C4—143no—
247C2×C4—146no—
248C2×C4—146no—
249C2×C4—146no—
250C2×C4—146no—
251C2×C4—146no—
252C2×C4—143no—
253C2×C4—146no—
254C2×C4C23×Dic716yes—
255C2×C4C23×Dic7112yes—
256C2×C4C23×Dic7112yes—
257C7#3453011yescharacteristic, complemented, Sylow
258C22D7×2−1+413yes—
259C22#9062013yes—
260C22C24×Dic711yescharacteristic
261C4—26no—
262C4—212no—
263C4—212no—
264C4—146no—
265C4—286no—
266C4—281no—
267C4—286no—
268C2#1174420911yescharacteristic
269C2#1174421213yes—
270C2Dic7×2−1+413yes—
subgroupG/H
center, FrattiniC23C24×D7
commutatorC22×C7C24×C4
FittingC2×C7×#564C2
socle, prime radical, cosocleC23×C7C25
hypercenterC2×#564D7
hypocenterC7#34530
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#564

Complements

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

NH ≅ G/Ntype
8. C7×#564C4semidirect
110. #564Dic7semidirect
257. C7#34530semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5642
#117404722
#117404712
#117404702
#117404692
#117404682
Dic7×#1252
#345307