Finite Group Databasebeta

← #13251207

Subgroups — #13251207

Order 1792.

486 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 123 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
1C7×#2546C211yesmaximal, characteristic
2#11739881C211yesmaximal, characteristic
3#11729527C212yesmaximal
4#11729391C211yesmaximal, characteristic
5#11725426C212yesmaximal
6C2×C7×C4⋊Q8—21no—
7C2×C7×C4⋊Q8C2211yescharacteristic
8C2×C4×C7×Q8C2211yescharacteristic
9C7×#398C414yes—
10C7×#391—21no—
11C7×#389—22no—
12C4×C7×C4⋊C4C2211yescharacteristic
13C2×#6410—21no—
14#89796—24no—
15#89698—22no—
16#89697C2212yes—
17#89696C2212yes—
18#89342—24no—
19#89325—21no—
20#9402—71nomaximal, Sylow
21C22×C7×Q8—21no—
22C22×C7×Q8D411yescharacteristic
23C7×C4⋊Q8—22no—
24C7×C4⋊Q8—22no—
25C7×C4⋊Q8—44no—
26C4×C7×Q8—22no—
27C4×C7×Q8—22no—
28C2×C7×C4⋊C4—21no—
29C2×C7×C4⋊C4—24no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4C2×C412yes—
32C2×C7×C4⋊C4C2×C412yes—
33C2×C7×C4⋊C4D411yescharacteristic
34C2×C42×C7—21no—
35C2×C42×C7D412yes—
36C2×C42×C7C2311yescharacteristic
37C2×#1136—22no—
38C7×#95—24no—
39C7×#95C2×C412yes—
40#6410—42no—
41C22⋊(C7⋊C8)—22no—
42C4⋊(C7⋊C8)—24no—
43C4⋊(C7⋊C8)—22no—
44C4⋊(C7⋊C8)—22no—
45C4⋊(C7⋊C8)D414yes—
46#6377—24no—
47C4×C7⋊C8—22no—
48#2983—71no—
49#2546D711yescharacteristic
50#1801—71no—
51#1546—72no—
52#1303—72no—
53C2×C7×Q8—22no—
54C2×C7×Q8—21no—
55C2×C7×Q8—22no—
56C2×C7×Q8—21no—
57C2×C7×Q8—42no—
58C2×C7×Q8—42no—
59C2×C7×Q8—41no—
60C2×C7×Q8—41no—
61C22×C4×C7—22no—
62C22×C4×C7—22no—
63C22×C4×C7C22⋊C412yes—
64C22×C4×C7C22⋊C412yes—
65C22×C4×C7C22×C411yescharacteristic
66C22×C4×C7C2×D411yescharacteristic
67C22×C4×C7C2×D411yescharacteristic
68C7×C4⋊C4—24no—
69C7×C4⋊C4—24no—
70C7×C4⋊C4—22no—
71C7×C4⋊C4—24no—
72C7×C4⋊C4—48no—
73C7×C4⋊C4—41no—
74C7×C4⋊C4—41no—
75C42×C7—22no—
76C42×C7—22no—
77C42×C7—42no—
78C42×C7C2×D412yes—
79C42×C7#4112yes—
80#1136—42no—
81#1136—42no—
82C2×C7⋊C8—24no—
83C2×C7⋊C8—42no—
84C2×C4⋊Q8—21no—
85C2×C4⋊Q8C2×D711yescharacteristic
86C2×C4×Q8C2×D711yescharacteristic
87#446—144no—
88#432—142no—
89#431—72no—
90#423—72no—
91C2×#101—141no—
92#398Dic714yes—
93#391—21no—
94#389—22no—
95C4×C4⋊C4C2×D711yescharacteristic
96#343—141no—
97#332—144no—
98C23×C7C2×C22⋊C411yescharacteristic
99C7×Q8—42no—
100C7×Q8—42no—
101C7×Q8—82no—
102C7×Q8—82no—
103C2×C4×C7—22no—
104C2×C4×C7—24no—
105C2×C4×C7—22no—
106C2×C4×C7—22no—
107C2×C4×C7—22no—
108C2×C4×C7—22no—
109C2×C4×C7—41no—
110C2×C4×C7—42no—
111C2×C4×C7—42no—
112C2×C4×C7—42no—
113C2×C4×C7—42no—
114C2×C4×C7—42no—
115C2×C4×C7—42no—
116C2×C4×C7C4×D412yes—
117C2×C4×C7#12011yescharacteristic
118C2×C4×C7#12112yes—
119C2×C4×C7#12311yescharacteristic
120C2×C4×C7AGL(1,ℤ/8)12yes—
121C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C7#13711yescharacteristic
123C7⋊C8—44no—
124C7⋊C8—82no—
125C22×Q8—21no—
126C22×Q8C22⋊D711yescharacteristic
127C2×M16—142no—
128C4⋊Q8—22no—
129C4⋊Q8—22no—
130C4⋊Q8—44no—
131C4×Q8—22no—
132C4×Q8—22no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—24no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4C2×Dic712yes—
137C2×C4⋊C4C2×Dic712yes—
138C2×C4⋊C4C22⋊D711yescharacteristic
139C2×C42—21no—
140C2×C42C22⋊D712yes—
141C2×C42C22×D711yescharacteristic
142C4⋊C8—74no—
143C4⋊C8—144no—
144C4⋊C8—142no—
145C4⋊C8—142no—
146#101—282no—
147C22⋊C8—142no—
148#97—144no—
149C4×C8—142no—
150#95—24no—
151#95C2×Dic712yes—
152C22×C7—21no—
153C22×C7—21no—
154C22×C7#38611yescharacteristic
155C22×C7#41711yescharacteristic
156C22×C7#41811yescharacteristic
157C4×C7—21no—
158C4×C7—22no—
159C4×C7—44no—
160C4×C7—42no—
161C4×C7—42no—
162C4×C7—82no—
163C4×C7#45612yes—
164C4×C7#46812yes—
165C4×C7#46912yes—
166C2×Q8—22no—
167C2×Q8—22no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—42no—
171C2×Q8—42no—
172C2×Q8—41no—
173C2×Q8—41no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4C22⋊Dic712yes—
177C22×C4C22⋊Dic712yes—
178C22×C4C22×Dic711yescharacteristic
179C22×C4C2×C22⋊D711yescharacteristic
180C22×C4C2×C22⋊D711yescharacteristic
181M16—282no—
182M16—282no—
183C2×C8—144no—
184C2×C8—282no—
185C4⋊C4—24no—
186C4⋊C4—24no—
187C4⋊C4—22no—
188C4⋊C4—24no—
189C4⋊C4—48no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C42—22no—
193C42—22no—
194C42—42no—
195C42D4×D712yes—
196C42#115912yes—
197C2×C7—21no—
198C2×C7—21no—
199C2×C7#188611yescharacteristic
200C2×C7#189511yescharacteristic
201C2×C7#191511yescharacteristic
202C23C2×C22⋊Dic711yescharacteristic
203Q8—42no—
204Q8—42no—
205Q8—82no—
206Q8—82no—
207C2×C4—22no—
208C2×C4—24no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4#649512yes—
221C2×C4D4×Dic712yes—
222C2×C4#649811yescharacteristic
223C2×C4#650011yescharacteristic
224C2×C4#650212yes—
225C2×C4#651211yescharacteristic
226C2×C4#651411yescharacteristic
227C8—284no—
228C8—562no—
229C7#940211yescharacteristic, complemented, Sylow
230C22—21no—
231C22—21no—
232C22#8998711yescharacteristic
233C22#8999211yescharacteristic
234C22#9000411yescharacteristic
235C4—21no—
236C4—22no—
237C4—44no—
238C4—42no—
239C4—42no—
240C4—82no—
241C4#8981112yes—
242C4#8981412yes—
243C4#8986712yes—
244C2—21no—
245C2—21no—
246C2#1172943611yescharacteristic
247C2#1172953811yescharacteristic
248C2#1172962011yescharacteristic
subgroupG/H
centerC22#89992
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#2546C2
socleC22×C7#386
prime radicalC23×C7C2×C22⋊C4
cosocleC2×C42×C7C23
hypercenter#2546D7
hypocenterC7#9402
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2546

Complements

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

NH ≅ G/Ntype
229. C7#9402semidirect

Maximal subgroups

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

subgroupindex
C7×#25462
#117398812
#117295272
#117293912
#117254262
#94027