Finite Group Databasebeta

← #13251167

Subgroups — #13251167

Order 1792.

506 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 139 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#11739880C211yesmaximal, 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—
14Q8×C7⋊C8—24no—
15#89697—22no—
16#89697C2212yes—
17#89696C2212yes—
18#89342—24no—
19#89325—21no—
20#9394—71nomaximal, Sylow
21C22×C7×Q8—21no—
22C22×C7×Q8D411yescharacteristic
23C7×C4⋊Q8—22no—
24C7×C4⋊Q8—22no—
25C7×C4⋊Q8—42no—
26C7×C4⋊Q8—42no—
27C4×C7×Q8—22no—
28C4×C7×Q8—22no—
29C2×C7×C4⋊C4—21no—
30C2×C7×C4⋊C4—24no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4C2×C412yes—
33C2×C7×C4⋊C4C2×C412yes—
34C2×C7×C4⋊C4D411yescharacteristic
35C2×C42×C7—21no—
36C2×C42×C7D412yes—
37C2×C42×C7C2311yescharacteristic
38C2×#1136—22no—
39C7×#95—24no—
40C7×#95C2×C412yes—
41#6410—42no—
42C22⋊(C7⋊C8)—22no—
43C4⋊(C7⋊C8)—24no—
44C4⋊(C7⋊C8)—22no—
45C4⋊(C7⋊C8)—22no—
46C4⋊(C7⋊C8)D414yes—
47C4×C7⋊C8—24no—
48C4×C7⋊C8—22no—
49#2982—71no—
50#2546D711yescharacteristic
51#1801—71no—
52#1546—72no—
53#1303—72no—
54C2×C7×Q8—22no—
55C2×C7×Q8—22no—
56C2×C7×Q8—42no—
57C2×C7×Q8—41no—
58C2×C7×Q8—41no—
59C2×C7×Q8—42no—
60C2×C7×Q8D812yes—
61C2×C7×Q8SD1612yes—
62C22×C4×C7—22no—
63C22×C4×C7—22no—
64C22×C4×C7C22⋊C412yes—
65C22×C4×C7C22⋊C412yes—
66C22×C4×C7C22×C411yescharacteristic
67C22×C4×C7C2×D411yescharacteristic
68C22×C4×C7C2×D411yescharacteristic
69C7×C4⋊C4—24no—
70C7×C4⋊C4—24no—
71C7×C4⋊C4—22no—
72C7×C4⋊C4—24no—
73C7×C4⋊C4—48no—
74C7×C4⋊C4—41no—
75C7×C4⋊C4—41no—
76C42×C7—22no—
77C42×C7—22no—
78C42×C7—41no—
79C42×C7—41no—
80C42×C7C2×D412yes—
81C42×C7#4112yes—
82#1136—42no—
83#1136—42no—
84C2×C7⋊C8—24no—
85C2×C7⋊C8—42no—
86C2×C4⋊Q8—21no—
87C2×C4⋊Q8C2×D711yescharacteristic
88C2×C4×Q8C2×D711yescharacteristic
89C8×Q8—144no—
90#431—72no—
91#431—142no—
92#423—72no—
93C2×#101—141no—
94#398Dic714yes—
95#391—21no—
96#389—22no—
97C4×C4⋊C4C2×D711yescharacteristic
98#343—141no—
99#332—144no—
100C23×C7C2×C22⋊C411yescharacteristic
101C7×Q8—24no—
102C7×Q8—24no—
103C7×Q8—82no—
104C7×Q8—82no—
105C2×C4×C7—22no—
106C2×C4×C7—22no—
107C2×C4×C7—22no—
108C2×C4×C7—24no—
109C2×C4×C7—22no—
110C2×C4×C7—41no—
111C2×C4×C7—42no—
112C2×C4×C7—42no—
113C2×C4×C7—42no—
114C2×C4×C7—42no—
115C2×C4×C7—42no—
116C2×C4×C7—42no—
117C2×C4×C7#10214yes—
118C2×C4×C7C4×D412yes—
119C2×C4×C7#12011yescharacteristic
120C2×C4×C7#12112yes—
121C2×C4×C7#12311yescharacteristic
122C2×C4×C7C2×D811yescharacteristic
123C2×C4×C7C2×SD1611yescharacteristic
124C2×C4×C7#13512yes—
125C7⋊C8—44no—
126C7⋊C8—82no—
127C22×Q8—21no—
128C22×Q8C22⋊D711yescharacteristic
129C2×M16—142no—
130C4⋊Q8—22no—
131C4⋊Q8—22no—
132C4⋊Q8—42no—
133C4⋊Q8—42no—
134C4×Q8—22no—
135C4×Q8—22no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—24no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4C2×Dic712yes—
140C2×C4⋊C4C2×Dic712yes—
141C2×C4⋊C4C22⋊D711yescharacteristic
142C2×C42—21no—
143C2×C42C22⋊D712yes—
144C2×C42C22×D711yescharacteristic
145C4⋊C8—74no—
146C4⋊C8—144no—
147C4⋊C8—142no—
148C4⋊C8—142no—
149#101—282no—
150C22⋊C8—142no—
151C4×C8—144no—
152C4×C8—142no—
153#95—24no—
154#95C2×Dic712yes—
155C22×C7—21no—
156C22×C7—21no—
157C22×C7#38611yescharacteristic
158C22×C7C2×#10211yescharacteristic
159C22×C7#41611yescharacteristic
160C4×C7—21no—
161C4×C7—24no—
162C4×C7—22no—
163C4×C7—44no—
164C4×C7—42no—
165C4×C7—82no—
166C4×C7#45612yes—
167C4×C7#46512yes—
168C4×C7#46612yes—
169C2×Q8—22no—
170C2×Q8—22no—
171C2×Q8—41no—
172C2×Q8—41no—
173C2×Q8—42no—
174C2×Q8—42no—
175C2×Q8#114112yes—
176C2×Q8#114212yes—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4C22⋊Dic712yes—
180C22×C4C22⋊Dic712yes—
181C22×C4C22×Dic711yescharacteristic
182C22×C4C2×C22⋊D711yescharacteristic
183C22×C4C2×C22⋊D711yescharacteristic
184M16—282no—
185M16—282no—
186C2×C8—144no—
187C2×C8—282no—
188C4⋊C4—24no—
189C4⋊C4—24no—
190C4⋊C4—22no—
191C4⋊C4—24no—
192C4⋊C4—48no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C42—22no—
196C42—22no—
197C42—41no—
198C42—41no—
199C42D4×D712yes—
200C42#115912yes—
201C2×C7—21no—
202C2×C7—21no—
203C2×C7#188611yescharacteristic
204C2×C7#189311yescharacteristic
205C2×C7#191511yescharacteristic
206C23C2×C22⋊Dic711yescharacteristic
207Q8—24no—
208Q8—24no—
209Q8—82no—
210Q8—82no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—24no—
215C2×C4—22no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4#640614yes—
224C2×C4C2×#114111yescharacteristic
225C2×C4C2×#114211yescharacteristic
226C2×C4D4×Dic712yes—
227C2×C4#649811yescharacteristic
228C2×C4#650011yescharacteristic
229C2×C4#650212yes—
230C2×C4#651312yes—
231C8—284no—
232C8—562no—
233C7#939411yescharacteristic, complemented, Sylow
234C22—21no—
235C22—21no—
236C22C2×#640611yescharacteristic
237C22#8999211yescharacteristic
238C22#9000511yescharacteristic
239C4—24no—
240C4—21no—
241C4—22no—
242C4—44no—
243C4—42no—
244C4—82no—
245C4#8981012yes—
246C4#8981312yes—
247C4#8986712yes—
248C2—21no—
249C2—21no—
250C2#1172943511yescharacteristic
251C2#1172953811yescharacteristic
252C2#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#9394
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
233. C7#9394semidirect

Maximal subgroups

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

subgroupindex
C7×#25462
#117398802
#117295272
#117293912
#117254262
#93947