Finite Group Databasebeta

← #13254791

Subgroups — #13254791

Order 1792.

476 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 103 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
1#11739892C212yesmaximal
2#11735924C211yesmaximal, characteristic
3C7×#1985C211yesmaximal, characteristic
4#11728183C212yesmaximal
5#11725466C211yesmaximal, characteristic
6C2×C4×C7×Q8C2211yescharacteristic
7#90161C2212yes—
8C2×C7×C4⋊C8C2211yescharacteristic
9C2×C7×#97C2211yescharacteristic
10#90000—22no—
11#89878—22no—
12#89803—22no—
13C4×#1144—24no—
14#89793—22no—
15#89742—22no—
16#89697C2212yes—
17#89474—22no—
18#89474—22no—
19C7×#336—22no—
20#89279—24no—
21#10037—71nomaximal, Sylow
22C22×C7×Q8D411yescharacteristic
23C22×C7×C8—21no—
24C22×C7×C8D412yes—
25C4×C7×Q8—22no—
26C4×C7×Q8—22no—
27C2×C7×C4⋊C4—21no—
28C2×C7×C4⋊C4D411yescharacteristic
29C2×C42×C7—21no—
30C2×C42×C7C2311yescharacteristic
31C2×#1144—24no—
32#6489—22no—
33#6487—22no—
34#6487—22no—
35#6433—22no—
36#6432D412yes—
37#6432D412yes—
38C4×Dic14—22no—
39C4×Dic14—22no—
40C7×C4⋊C8—22no—
41C7×#97—22no—
42#6409—24no—
43C22⋊(C7⋊C8)—22no—
44#6392—22no—
45#6392—22no—
46#6391—24no—
47#6384—24no—
48#6381—24no—
49C4⋊(C7⋊C8)—22no—
50C4×C7⋊C8D414yes—
51#3162—71no—
52#3104—72no—
53#1985D711yescharacteristic
54#1481—72no—
55#1275—71no—
56C2×C7×Q8—22no—
57C2×C7×Q8—42no—
58C22×C4×C7—21no—
59C22×C4×C7—21no—
60C22×C4×C7C2×D411yescharacteristic
61C22×C4×C7C2×D411yescharacteristic
62C22×C4×C7#4111yescharacteristic
63C2×Dic14—22no—
64C2×Dic14—22no—
65C2×C7×C8—22no—
66C2×C7×C8—22no—
67C2×C7×C8—41no—
68C2×C7×C8—42no—
69C2×C7×C8Q1614yescomplemented
70C7×C4⋊C4—22no—
71C7×C4⋊C4—42no—
72C42×C7—41no—
73C42×C7—41no—
74C42×C7C2×D412yes—
75C42×C7C2×D412yes—
76C22⋊Dic7—42no—
77#1144—48no—
78C4⋊Dic7—22no—
79C4⋊Dic7—22no—
80C4⋊Dic7—22no—
81C4⋊Dic7—22no—
82Dic7⋊C4—42no—
83Dic7⋊C4—42no—
84C4×Dic7—42no—
85C2×C7⋊C8—24no—
86#533—72no—
87C2×C4×Q8C2×D711yescharacteristic
88#501—142no—
89#501—142no—
90#484—142no—
91#477—142no—
92#462—142no—
93#451—142no—
94C4×Q16—144no—
95#431—72no—
96#427—142no—
97C2×C4⋊C8C2×D711yescharacteristic
98C2×#97C2×D711yescharacteristic
99#336—22no—
100Q8⋊C8—144no—
101C23×C7#12111yescharacteristic
102C7×Q8—24no—
103C7×Q8—42no—
104C2×C4×C7—22no—
105C2×C4×C7—41no—
106C2×C4×C7—41no—
107C2×C4×C7—41no—
108C2×C4×C7—41no—
109C2×C4×C7—42no—
110C2×C4×C7—41no—
111C2×C4×C7#12012yes—
112C2×C4×C7#12011yescharacteristic
113C2×C4×C7#12112yes—
114C2×C4×C7#12711yescharacteristic
115C2×C4×C7C2×Q1612yes—
116C2×C4×C7#13712yes—
117C2×Dic7—42no—
118C2×Dic7—42no—
119Dic14—44no—
120Dic14—44no—
121C7×C8—24no—
122C7×C8—81no—
123C7⋊C8—44no—
124C22×Q8D2811yescharacteristic
125C2×Q16—144no—
126C22×C8—21no—
127C22×C8C22⋊D712yes—
128C4⋊Q8—72no—
129C4⋊Q8—72no—
130#125—142no—
131C22⋊Q8—142no—
132C22⋊Q8—142no—
133C4×Q8—22no—
134C4×Q8—22no—
135C4×Q8—142no—
136C4×Q8—142no—
137#117—142no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4D2811yescharacteristic
140C2×C42—21no—
141C2×C42C22×D711yescharacteristic
142#107—144no—
143#107—142no—
144#107—142no—
145#106—144no—
146C4⋊C8—22no—
147C4⋊C8—142no—
148#103—144no—
149#103—144no—
150C22⋊C8—142no—
151#97—22no—
152C4×C8—74no—
153C22×C7—21no—
154C22×C7—21no—
155C22×C7#39211yescharacteristic
156C22×C7#46212yes—
157C4×C7—22no—
158C4×C7—22no—
159C4×C7—42no—
160C4×C7—81no—
161C4×C7#45112yes—
162C4×C7#49411yescharacteristic
163C4×C7#49711yescharacteristic
164Dic7—82no—
165Dic7—82no—
166C2×Q8—22no—
167C2×Q8—42no—
168C2×Q8—142no—
169C2×Q8—142no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4C2×D2811yescharacteristic
173C22×C4#115711yescharacteristic
174C22×C4C2×C22⋊D711yescharacteristic
175Q16—288no—
176C2×C8—22no—
177C2×C8—22no—
178C2×C8—41no—
179C2×C8—42no—
180C2×C8—144no—
181C2×C8#114414yescomplemented
182C4⋊C4—22no—
183C4⋊C4—42no—
184C4⋊C4—142no—
185C4⋊C4—142no—
186C4⋊C4—142no—
187C4⋊C4—142no—
188C4⋊C4—282no—
189C4⋊C4—282no—
190C22⋊C4—282no—
191C42—41no—
192C42—41no—
193C42—282no—
194C42D4×D712yes—
195C42D4×D712yes—
196C2×C7—22no—
197C2×C7#201011yescharacteristic
198C2×C7#201611yescharacteristic
199C2×C7#201711yescharacteristic
200C23#649311yescharacteristic
201Q8—24no—
202Q8—42no—
203Q8—284no—
204Q8—284no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—282no—
213C2×C4—282no—
214C2×C4#644512yes—
215C2×C4#644712yes—
216C2×C4#650011yescharacteristic
217C2×C4#650311yescharacteristic
218C2×C4C2×#114412yes—
219C2×C4#651412yes—
220C8—24no—
221C8—81no—
222C8—284no—
223C7#1003711yescharacteristic, complemented, Sylow
224C22—21no—
225C22—21no—
226C22#8973211yescharacteristic
227C22#8980312yes—
228C4—22no—
229C4—22no—
230C4—42no—
231C4—81no—
232C4—562no—
233C4—562no—
234C4#8982212yes—
235C4#8983211yescharacteristic
236C4#8986411yescharacteristic
237C2—22no—
238C2#1172744511yescharacteristic
239C2#1172774711yescharacteristic
240C2#1172776711yescharacteristic
subgroupG/H
centerC2×C4#6503
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1985C2
socleC22×C7#392
prime radicalC23×C7#121
hypercenter#1985D7
hypocenterC7#10037
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1985

Complements

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

NH ≅ G/Ntype
69. C2×C7×C8Q16semidirect
181. C2×C8#1144semidirect
223. C7#10037semidirect

Maximal subgroups

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

subgroupindex
#117398922
#117359242
C7×#19852
#117281832
#117254662
#100377