Finite Group Databasebeta

← #13242010

Subgroups — #13242010

Order 1792.

462 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C4×#6432C211yesmaximal, characteristic
2C7×#1767C211yesmaximal, characteristic
3#11727147C211yesmaximal, characteristic
4#11725286C214yesmaximal
5C2×#6432C411yescharacteristic
6C2×C4×Dic14C412yes—
7C2×C7×C4⋊C8—21no—
8C2×C7×#97—21no—
9C43×C7C2211yescharacteristic
10#89707C411yescharacteristic
11C4×C4⋊Dic7—21no—
12C4×C4⋊Dic7—21no—
13#89701C2212yes—
14#89700—21no—
15#89700—21no—
16C7×#336C2212yes—
17#89319—21no—
18#89319—21no—
19#89319C2212yes—
20#7624—71nomaximal, Sylow
21C22×Dic14C2×C412yes—
22C22×C7×C8—22no—
23C2×C42×C7C2×C411yescharacteristic
24C2×C42×C7C2×C411yescharacteristic
25C2×C42×C7D411yescharacteristic
26C2×C42×C7D411yescharacteristic
27C2×C42×C7D411yescharacteristic
28C2×C42×C7D411yescharacteristic
29C2×C42×C7C2311yescharacteristic
30C2×C4⋊Dic7—21no—
31C2×C4⋊Dic7—21no—
32C2×C4⋊Dic7—21no—
33C2×C4⋊Dic7—21no—
34C2×C4⋊Dic7C2×C412yes—
35C2×Dic7⋊C4—22no—
36C2×C4×Dic7—22no—
37C22×C7⋊C8—22no—
38#6432—24no—
39C4×Dic14—44no—
40C7×C4⋊C8—24no—
41C7×#97—42no—
42C7⋊#95—22no—
43C7⋊#95—22no—
44C4×C4⋊Q8—71no—
45#1839—71no—
46#1767D711yescharacteristic
47#1272—74no—
48C22×C4×C7C22⋊C411yescharacteristic
49C22×C4×C7C22⋊C411yescharacteristic
50C22×C4×C7C22⋊C411yescharacteristic
51C22×C4×C7C22⋊C411yescharacteristic
52C22×C4×C7C22×C411yescharacteristic
53C22×C4×C7C2×D411yescharacteristic
54C22×C4×C7C2×D411yescharacteristic
55C22×Dic7—22no—
56C22×Dic7—22no—
57C2×Dic14—22no—
58C2×Dic14—42no—
59C2×Dic14—42no—
60C2×Dic14M1614yes—
61C2×C7×C8—24no—
62C2×C7×C8—42no—
63C2×C7×C8—42no—
64C42×C7—22no—
65C42×C7—22no—
66C42×C7—22no—
67C42×C7—22no—
68C42×C7—41no—
69C42×C7—41no—
70C42×C7SD1612yes—
71C42×C7Q1612yes—
72C4⋊Dic7—24no—
73C4⋊Dic7—24no—
74C4⋊Dic7—42no—
75C4⋊Dic7—42no—
76C4⋊Dic7—42no—
77Dic7⋊C4—44no—
78C4×Dic7—44no—
79C2×C7⋊C8—42no—
80C2×C7⋊C8—42no—
81C2×C7⋊C8—42no—
82C2×C4⋊Q8—71no—
83C2×C4×Q8—72no—
84C2×C4⋊C8—21no—
85C2×#97—21no—
86#391—72no—
87#389—141no—
88#389—141no—
89#384—71no—
90C4×C4⋊C4—141no—
91C4×C4⋊C4—141no—
92C43C2×D711yescharacteristic
93#336—72no—
94#336—141no—
95#336—141no—
96#336C2×D712yes—
97C23×C7C2×C22⋊C411yescharacteristic
98C2×C4×C7—21no—
99C2×C4×C7—21no—
100C2×C4×C7—21no—
101C2×C4×C7—21no—
102C2×C4×C7—21no—
103C2×C4×C7—21no—
104C2×C4×C7—21no—
105C2×C4×C7—21no—
106C2×C4×C7—21no—
107C2×C4×C7—21no—
108C2×C4×C7—21no—
109C2×C4×C7—21no—
110C2×C4×C7—21no—
111C2×C4×C7—21no—
112C2×C4×C7#10012yes—
113C2×C4×C7#10312yes—
114C2×C4×C7#10312yes—
115C2×C4×C7#10412yes—
116C2×C4×C7C2×M1612yes—
117C2×C4×C7C2×SD1611yescharacteristic
118C2×C4×C7C2×Q1611yescharacteristic
119C2×C4×C7#13712yes—
120C2×Dic7—24no—
121C2×Dic7—42no—
122C2×Dic7—42no—
123C2×Dic7—42no—
124C2×Dic7—42no—
125C2×Dic7—42no—
126Dic14—44no—
127Dic14—44no—
128C7×C8—44no—
129C7⋊C8—82no—
130C22×Q8—72no—
131C22×C8—22no—
132C22×C8—142no—
133C4⋊Q8—144no—
134C4×Q8—284no—
135C2×C4⋊C4—72no—
136C2×C4⋊C4—141no—
137C2×C4⋊C4—141no—
138C2×C4⋊C4—142no—
139C2×C4⋊C4—141no—
140C2×C4⋊C4—141no—
141C2×C42—142no—
142C2×C42C4×D711yescharacteristic
143C2×C42C4×D711yescharacteristic
144C2×C42D2811yescharacteristic
145C2×C42D2811yescharacteristic
146C2×C42C22⋊D711yescharacteristic
147C2×C42C22⋊D711yescharacteristic
148C2×C42C22×D711yescharacteristic
149C4⋊C8—24no—
150#97—42no—
151#95—142no—
152#95—142no—
153C22×C7#40711yescharacteristic
154C22×C7#41011yescharacteristic
155C22×C7C2×#10011yescharacteristic
156C22×C7C2×#10311yescharacteristic
157C22×C7#41911yescharacteristic
158C22×C7C2×#10411yescharacteristic
159C22×C7#42111yescharacteristic
160C4×C7—22no—
161C4×C7—22no—
162C4×C7—22no—
163C4×C7—22no—
164C4×C7—21no—
165C4×C7—21no—
166C4×C7—22no—
167C4×C7—22no—
168Dic7—44no—
169Dic7—82no—
170C2×Q8—74no—
171C2×Q8—142no—
172C2×Q8—282no—
173C2×Q8—282no—
174C22×C4—142no—
175C22×C4—142no—
176C22×C4(C2×D7)⋊C411yescharacteristic
177C22×C4(C2×D7)⋊C411yescharacteristic
178C22×C4(C2×D7)⋊C411yescharacteristic
179C22×C4(C2×D7)⋊C411yescharacteristic
180C22×C4C2×C4×D711yescharacteristic
181C22×C4C2×D2811yescharacteristic
182C22×C4C2×C22⋊D711yescharacteristic
183C2×C8—24no—
184C2×C8—42no—
185C2×C8—42no—
186C2×C8—282no—
187C2×C8—282no—
188C2×C8—282no—
189C4⋊C4—144no—
190C4⋊C4—144no—
191C4⋊C4—282no—
192C4⋊C4—282no—
193C4⋊C4—282no—
194C4⋊C4—284no—
195C42—22no—
196C42—22no—
197C42—22no—
198C42—22no—
199C42—41no—
200C42—41no—
201C42—284no—
202C42#114212yes—
203C42#114412yes—
204C2×C7#146611yescharacteristic
205C2×C7#148711yescharacteristic
206C2×C7#149111yescharacteristic
207C2×C7#150311yescharacteristic
208C2×C7#151511yescharacteristic
209C2×C7#153011yescharacteristic
210C2×C7#154811yescharacteristic
211C23C2×(C2×D7)⋊C411yescharacteristic
212Q8—284no—
213Q8—284no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—144no—
229C2×C4—282no—
230C2×C4—282no—
231C2×C4—282no—
232C2×C4—282no—
233C2×C4—282no—
234C2×C4#637912yes—
235C2×C4#638412yes—
236C2×C4#638412yes—
237C2×C4#639712yes—
238C2×C4D7×M1612yes—
239C2×C4#647212yes—
240C2×C4C2×#114211yescharacteristic
241C2×C4C2×#114411yescharacteristic
242C8—44no—
243C8—562no—
244C7#762411yescharacteristic, complemented, Sylow
245C22C2×#637911yescharacteristic
246C22C2×#638411yescharacteristic
247C22#8977811yescharacteristic
248C22#8989211yescharacteristic
249C22#8989811yescharacteristic
250C22C2×#639711yescharacteristic
251C22#8991111yescharacteristic
252C4—21no—
253C4—21no—
254C4—22no—
255C4—22no—
256C4—22no—
257C4—22no—
258C4—22no—
259C4—22no—
260C4—284no—
261C4—562no—
262C2#1172722511yescharacteristic
263C2#1172755211yescharacteristic
264C2#1172761111yescharacteristic
265C2#1172825411yescharacteristic
266C2#1172826111yescharacteristic
267C2#1172858111yescharacteristic
268C2#1172859111yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#1767C2
socle, prime radicalC23×C7C2×C22⋊C4
cosocleC2×C42×C7C23
hypercenter#1767D7
hypocenterC7#7624
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
244. C7#7624semidirect

Maximal subgroups

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

subgroupindex
C4×#64322
C7×#17672
#117271472
#117252862
#76247