Finite Group Databasebeta

← #13251660

Subgroups — #13251660

Order 1792.

454 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 115 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×#2983C211yesmaximal, characteristic
2#11739926C211yesmaximal, characteristic
3#11729391C211yesmaximal, characteristic
4#11728524C212yesmaximal
5#11725544C212yesmaximal
6C2×C4×C7×Q8C2211yescharacteristic
7C2×C4×Dic14C2211yescharacteristic
8C7×#446—24no—
9C7×#432—22no—
10C7×#431C2212yes—
11#90002—21no—
12C2×#6410—21no—
13#89758C412yes—
14#89751C412yes—
15#89745—21no—
16#89708C2211yescharacteristic
17#89705—22no—
18#89696C2212yes—
19#89325—21no—
20#89251—24no—
21#9488—71nomaximal, Sylow
22C22×C7×Q8D411yescharacteristic
23C22×Dic14C2×C411yescharacteristic
24C4×C7×Q8—22no—
25C4×C7×Q8—22no—
26C2×C7×C4⋊C4C2×C412yes—
27C2×C7×C4⋊C4D411yescharacteristic
28C2×C42×C7D412yes—
29C2×C42×C7C2311yescharacteristic
30C2×C4⋊Dic7—21no—
31C2×C4⋊Dic7C2×C411yescharacteristic
32C2×Dic7⋊C4—22no—
33C2×Dic7⋊C4—21no—
34C2×C4×Dic7—21no—
35C2×#1136—22no—
36C4×Dic14—22no—
37C4×Dic14—22no—
38C7×C4⋊C8—24no—
39C7×C4⋊C8—22no—
40C7×C22⋊C8—22no—
41C7×#97—24no—
42C4×C7×C8D414yes—
43#6410—42no—
44C7⋊#95—22no—
45C7⋊#95—22no—
46C7⋊#95—22no—
47C7⋊#95—21no—
48C7⋊#95C2×C412yes—
49C4⋊(C7⋊C8)—22no—
50C4⋊(C7⋊C8)—22no—
51#2983D711yescharacteristic
52#2581—71no—
53#1801—71no—
54#1487—72no—
55#1286—72no—
56C2×C7×Q8—22no—
57C2×C7×Q8—21no—
58C2×C7×Q8—21no—
59C2×C7×Q8—22no—
60C22×C4×C7C22⋊C412yes—
61C22×C4×C7C22⋊C412yes—
62C22×C4×C7C22×C411yescharacteristic
63C22×C4×C7C2×D411yescharacteristic
64C22×C4×C7C2×D411yescharacteristic
65C22×Dic7—21no—
66C22×Dic7—22no—
67C22×Dic7—21no—
68C2×Dic14—22no—
69C2×Dic14—42no—
70C2×C7×C8—24no—
71C7×C4⋊C4—24no—
72C7×C4⋊C4—22no—
73C42×C7—22no—
74C42×C7—22no—
75C42×C7C2×D412yes—
76C42×C7#4112yes—
77C4⋊Dic7—22no—
78C4⋊Dic7—41no—
79C4⋊Dic7—41no—
80Dic7⋊C4—44no—
81Dic7⋊C4—41no—
82Dic7⋊C4—41no—
83C4×Dic7—42no—
84#1136—42no—
85#1136—42no—
86C2×C7⋊C8—42no—
87C2×C4×Q8—71no—
88C2×C4×Q8C2×D711yescharacteristic
89#446—24no—
90#432—22no—
91#431C2×D712yes—
92#423—72no—
93C2×#101—141no—
94#400—72no—
95#395—72no—
96#391—141no—
97#389—141no—
98#387—142no—
99#382—71no—
100#343—141no—
101Q8⋊C8—144no—
102C23×C7C2×C22⋊C411yescharacteristic
103C7×Q8—42no—
104C7×Q8—42no—
105C2×C4×C7—22no—
106C2×C4×C7—22no—
107C2×C4×C7—22no—
108C2×C4×C7—22no—
109C2×C4×C7—41no—
110C2×C4×C7—41no—
111C2×C4×C7—42no—
112C2×C4×C7C4×D412yes—
113C2×C4×C7#12011yescharacteristic
114C2×C4×C7#12112yes—
115C2×C4×C7#12311yescharacteristic
116C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C7#13712yes—
118C2×C4×C7#13711yescharacteristic
119C2×Dic7—22no—
120C2×Dic7—41no—
121C2×Dic7—41no—
122C2×Dic7—42no—
123C2×Dic7—42no—
124C2×Dic7—42no—
125C2×Dic7—41no—
126C2×Dic7—42no—
127Dic14—24no—
128Dic14—42no—
129C7×C8—44no—
130C7⋊C8—82no—
131C22×Q8—71no—
132C22×Q8D2811yescharacteristic
133C2×M16—142no—
134C4×Q8—22no—
135C4×Q8—22no—
136C4×Q8—142no—
137C4×Q8—142no—
138C2×C4⋊C4—71no—
139C2×C4⋊C4—142no—
140C2×C4⋊C4—141no—
141C2×C4⋊C4—141no—
142C2×C4⋊C4C4×D712yes—
143C2×C4⋊C4D2811yescharacteristic
144C2×C42—141no—
145C2×C42C22⋊D712yes—
146C2×C42C22×D711yescharacteristic
147C4⋊C8—24no—
148C4⋊C8—22no—
149C4⋊C8—142no—
150C4⋊C8—142no—
151#101—282no—
152C22⋊C8—22no—
153#97—24no—
154C4×C8C22⋊D714yes—
155#95—72no—
156#95—142no—
157#95—142no—
158#95—142no—
159#95—141no—
160C22×C7—21no—
161C22×C7—21no—
162C22×C7#38611yescharacteristic
163C22×C7#41711yescharacteristic
164C22×C7#41911yescharacteristic
165C4×C7—22no—
166C4×C7—21no—
167C4×C7—21no—
168C4×C7—42no—
169C4×C7—42no—
170C4×C7#46812yes—
171C4×C7#47012yes—
172Dic7—42no—
173Dic7—82no—
174Dic7—81no—
175C2×Q8—21no—
176C2×Q8—22no—
177C2×Q8—21no—
178C2×Q8—22no—
179C2×Q8—142no—
180C2×Q8—282no—
181C22×C4—141no—
182C22×C4—142no—
183C22×C4—141no—
184C22×C4(C2×D7)⋊C412yes—
185C22×C4(C2×D7)⋊C412yes—
186C22×C4C2×C4×D711yescharacteristic
187C22×C4C2×D2811yescharacteristic
188C22×C4C2×C22⋊D711yescharacteristic
189M16—282no—
190M16—282no—
191C2×C8—24no—
192C2×C8—282no—
193C4⋊C4—24no—
194C4⋊C4—22no—
195C4⋊C4—142no—
196C4⋊C4—284no—
197C4⋊C4—281no—
198C4⋊C4—281no—
199C4⋊C4—281no—
200C4⋊C4—281no—
201C42—22no—
202C42—22no—
203C42—282no—
204C42#115712yes—
205C42C2×C22⋊D712yes—
206C2×C7—21no—
207C2×C7—21no—
208C2×C7#189111yescharacteristic
209C2×C7#189411yescharacteristic
210C2×C7#191211yescharacteristic
211C23C2×(C2×D7)⋊C411yescharacteristic
212Q8—42no—
213Q8—42no—
214Q8—144no—
215Q8—282no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—42no—
223C2×C4—142no—
224C2×C4—281no—
225C2×C4—281no—
226C2×C4—282no—
227C2×C4—282no—
228C2×C4—282no—
229C2×C4—282no—
230C2×C4—281no—
231C2×C4#647111yescharacteristic
232C2×C4#647212yes—
233C2×C4#647211yescharacteristic
234C2×C4C4×C22⋊D712yes—
235C2×C4#649211yescharacteristic
236C2×C4#649312yes—
237C2×C4#651611yescharacteristic
238C8—44no—
239C8—562no—
240C7#948811yescharacteristic, complemented, Sylow
241C22—21no—
242C22—21no—
243C22#8989211yescharacteristic
244C22#8990511yescharacteristic
245C22#8998511yescharacteristic
246C4—21no—
247C4—21no—
248C4—22no—
249C4—42no—
250C4—42no—
251C4—282no—
252C4—562no—
253C4—561no—
254C4#8990612yes—
255C4#8990912yes—
256C2—21no—
257C2—21no—
258C2#1172941711yescharacteristic
259C2#1172974311yescharacteristic
260C2#1172978311yescharacteristic
subgroupG/H
centerC22#89985
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#2983C2
socleC22×C7#386
prime radicalC23×C7C2×C22⋊C4
cosocleC2×C42×C7C23
hypercenter#2983D7
hypocenterC7#9488
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
240. C7#9488semidirect

Maximal subgroups

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

subgroupindex
C7×#29832
#117399262
#117293912
#117285242
#117255442
#94887