Finite Group Databasebeta

← #13242003

Subgroups — #13242003

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×#1839C211yesmaximal, characteristic
3#11727145C211yesmaximal, characteristic
4#11725284C214yesmaximal
5C2×#6432C411yescharacteristic
6C2×C4×Dic14—21no—
7C43×C7C2211yescharacteristic
8#89707C411yescharacteristic
9C4×C4⋊Dic7—21no—
10C4×C4⋊Dic7C412yes—
11#89701—21no—
12#89700—21no—
13#89700C2212yes—
14C2×C4⋊(C7⋊C8)—21no—
15C2×#6377—21no—
16C7×#336—21no—
17C7×#336—21no—
18C7×#336C2212yes—
19#89319C2212yes—
20#7622—71nomaximal, Sylow
21C22×Dic14—21no—
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⋊Dic7C2×C412yes—
34C2×C4⋊Dic7C2×C412yes—
35C2×Dic7⋊C4—22no—
36C2×C4×Dic7—22no—
37C22×C7⋊C8—22no—
38#6432—24no—
39C4×Dic14—44no—
40C7⋊#95—22no—
41C7⋊#95—22no—
42C4⋊(C7⋊C8)—24no—
43#6377—42no—
44C4×C4⋊Q8—71no—
45#1839D711yescharacteristic
46#1767—71no—
47#1271—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—24no—
58C2×Dic14—42no—
59C2×Dic14—42no—
60C2×C7×C8—42no—
61C2×C7×C8—42no—
62C2×C7×C8—42no—
63C42×C7—22no—
64C42×C7—22no—
65C42×C7—22no—
66C42×C7—22no—
67C42×C7—41no—
68C42×C7—41no—
69C42×C7SD1612yes—
70C42×C7Q1612yes—
71C4⋊Dic7—24no—
72C4⋊Dic7—22no—
73C4⋊Dic7—42no—
74C4⋊Dic7—42no—
75C4⋊Dic7—42no—
76C4⋊Dic7M1614yes—
77Dic7⋊C4—44no—
78C4×Dic7—44no—
79C2×C7⋊C8—24no—
80C2×C7⋊C8—42no—
81C2×C7⋊C8—42no—
82C2×C4⋊Q8—71no—
83C2×C4×Q8—141no—
84C2×C4⋊C8—141no—
85C2×#97—141no—
86#391—141no—
87#389—72no—
88#389—141no—
89#384—71no—
90C4×C4⋊C4—72no—
91C4×C4⋊C4—141no—
92C43C2×D711yescharacteristic
93#336—21no—
94#336—21no—
95#336—72no—
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#10112yes—
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×C7AGL(1,ℤ/8)12yes—
120C2×Dic7—24no—
121C2×Dic7—42no—
122C2×Dic7—42no—
123C2×Dic7—42no—
124C2×Dic7—42no—
125C2×Dic7—42no—
126Dic14—48no—
127C7×C8—82no—
128C7⋊C8—44no—
129C22×Q8—141no—
130C22×C8—22no—
131C22×C8—142no—
132C4⋊Q8—144no—
133C4×Q8—284no—
134C2×C4⋊C4—72no—
135C2×C4⋊C4—72no—
136C2×C4⋊C4—141no—
137C2×C4⋊C4—141no—
138C2×C4⋊C4—141no—
139C2×C4⋊C4—142no—
140C2×C42—142no—
141C2×C42C4×D711yescharacteristic
142C2×C42C4×D711yescharacteristic
143C2×C42D2811yescharacteristic
144C2×C42D2811yescharacteristic
145C2×C42C22⋊D711yescharacteristic
146C2×C42C22⋊D711yescharacteristic
147C2×C42C22×D711yescharacteristic
148C4⋊C8—144no—
149#97—282no—
150#95—142no—
151#95—142no—
152C22×C7#40711yescharacteristic
153C22×C7#41011yescharacteristic
154C22×C7C2×#10111yescharacteristic
155C22×C7C2×#10311yescharacteristic
156C22×C7#41811yescharacteristic
157C22×C7C2×#10411yescharacteristic
158C22×C7#42111yescharacteristic
159C4×C7—22no—
160C4×C7—22no—
161C4×C7—22no—
162C4×C7—22no—
163C4×C7—21no—
164C4×C7—21no—
165C4×C7—22no—
166C4×C7—22no—
167Dic7—44no—
168Dic7—82no—
169C2×Q8—144no—
170C2×Q8—282no—
171C2×Q8—282no—
172C22×C4—142no—
173C22×C4—142no—
174C22×C4(C2×D7)⋊C411yescharacteristic
175C22×C4(C2×D7)⋊C411yescharacteristic
176C22×C4(C2×D7)⋊C411yescharacteristic
177C22×C4(C2×D7)⋊C411yescharacteristic
178C22×C4C2×C4×D711yescharacteristic
179C22×C4C2×D2811yescharacteristic
180C22×C4C2×C22⋊D711yescharacteristic
181C2×C8—42no—
182C2×C8—42no—
183C2×C8—42no—
184C2×C8—144no—
185C2×C8—282no—
186C2×C8—282no—
187C4⋊C4—74no—
188C4⋊C4—144no—
189C4⋊C4—142no—
190C4⋊C4—282no—
191C4⋊C4—282no—
192C4⋊C4—282no—
193C4⋊C4—284no—
194C42—22no—
195C42—22no—
196C42—22no—
197C42—22no—
198C42—41no—
199C42—41no—
200C42—284no—
201C42#113212yes—
202C42Dic2812yes—
203C2×C7#146711yescharacteristic
204C2×C7#148711yescharacteristic
205C2×C7#149011yescharacteristic
206C2×C7#150311yescharacteristic
207C2×C7#151411yescharacteristic
208C2×C7#153111yescharacteristic
209C2×C7#154911yescharacteristic
210C23C2×(C2×D7)⋊C411yescharacteristic
211Q8—288no—
212C2×C4—21no—
213C2×C4—21no—
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—144no—
227C2×C4—282no—
228C2×C4—282no—
229C2×C4—282no—
230C2×C4—282no—
231C2×C4—282no—
232C2×C4#639012yes—
233C2×C4#639012yes—
234C2×C4#639812yes—
235C2×C4#639912yes—
236C2×C4C2×#113211yescharacteristic
237C2×C4C2×Dic2811yescharacteristic
238C2×C4D7×M1612yes—
239C2×C4#651212yes—
240C8—82no—
241C8—284no—
242C7#762211yescharacteristic, complemented, Sylow
243C22#8977311yescharacteristic
244C22#8977711yescharacteristic
245C22#8977811yescharacteristic
246C22C2×#639011yescharacteristic
247C22#8989811yescharacteristic
248C22C2×#639811yescharacteristic
249C22C2×#639911yescharacteristic
250C4—22no—
251C4—22no—
252C4—21no—
253C4—21no—
254C4—22no—
255C4—22no—
256C4—22no—
257C4—22no—
258C4—284no—
259C4—562no—
260C2#1172731811yescharacteristic
261C2#1172852411yescharacteristic
262C2#1172853411yescharacteristic
263C2#1172854611yescharacteristic
264C2#1172855311yescharacteristic
265C2#1172856711yescharacteristic
266C2#1172858411yescharacteristic
subgroupG/H
centerC23C2×(C2×D7)⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#1839C2
socle, prime radicalC23×C7C2×C22⋊C4
cosocleC2×C42×C7C23
hypercenter#1839D7
hypocenterC7#7622
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C43 ◁ #1839

Complements

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

NH ≅ G/Ntype
242. C7#7622semidirect

Maximal subgroups

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

subgroupindex
C4×#64322
C7×#18392
#117271452
#117252842
#76227