Finite Group Databasebeta

← #13264647

Subgroups — #13264647

Order 1792.

280 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 71 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#11735985C211yesmaximal, characteristic
2C7×#1841C211yesmaximal, characteristic
3#11727618C211yesmaximal, characteristic
4#11725290C212yesmaximal
5#11725288C212yesmaximal
6#90161—21no—
7C4×C7×M16C2211yescharacteristic
8#89909—21no—
9#89909C2212yes—
10#89488—21no—
11#89488C412yescomplemented
12#89471C411yescharacteristic, complemented
13#89453—21no—
14#89452C411yescharacteristic, complemented
15C7×#344—21no—
16C7×#339—21no—
17C7×#338C2211yescharacteristic
18C7×H(3,ℤ/4)C2211yescharacteristic
19#89348C2212yes—
20#89261—21no—
21#89258—21no—
22#11838—71nomaximal, Sylow
23C2×C7×M16—21no—
24C2×C7×M16D411yescharacteristic
25C2×C7×M16C2311yescharacteristic
26C7×#117—21no—
27C2×C42×C7D411yescharacteristic
28#6489—41no—
29#6487—22no—
30#6487—41no—
31C2×Dic28—21no—
32C2×Dic28C2×C412yes—
33#6433—41no—
34#6432—21no—
35#6432—21no—
36C4×Dic14—22no—
37C4×Dic14—41no—
38C7×#97C2×C411yescharacteristic
39C7×#97D411yescharacteristic
40C4×C7×C8C2×C411yescharacteristic
41C4×C7×C8D411yescharacteristic
42#6391—21no—
43#6391C2×C412yes—
44#6390—22no—
45#6390—22no—
46#6386—22no—
47#3185—71no—
48#2165—71no—
49#1841D711yescharacteristic
50#1342—72no—
51#1340—72no—
52C22×C4×C7—21no—
53C22×C4×C7C2×D411yescharacteristic
54C2×Dic14—22no—
55C2×Dic14—41no—
56C7×M16—41no—
57C7×M16—41no—
58C7×M16—41no—
59C7×M16—41no—
60C2×C7×C8—41no—
61C2×C7×C8C22⋊C411yescharacteristic
62C2×C7×C8C22⋊C411yescharacteristic
63C2×C7×C8C22×C411yescharacteristic
64C2×C7×C8C2×D411yescharacteristic
65C7×C4⋊C4—41no—
66C7×C22⋊C4—41no—
67C42×C7—21no—
68C42×C7—41no—
69C42×C7C22⋊C411yescharacteristic
70C42×C7C22⋊C411yescharacteristic
71C22⋊Dic7—42no—
72C4⋊Dic7—22no—
73C4⋊Dic7—41no—
74C4⋊Dic7—41no—
75C4⋊Dic7—41no—
76Dic7⋊C4—42no—
77Dic7⋊C4—42no—
78C4×Dic7—42no—
79Dic28—42no—
80Dic28—42no—
81C7⋊C16—42no—
82#533—141no—
83#498—71no—
84#494—71no—
85#487—141no—
86#470—72no—
87#470—141no—
88#441—72no—
89#441—141no—
90C4×M16C2×D711yescharacteristic
91#364—141no—
92#349—72no—
93#347—141no—
94#344—21no—
95#339—21no—
96#338C2×D711yescharacteristic
97H(3,ℤ/4)C2×D711yescharacteristic
98C23×C7AGL(1,ℤ/8)11yescharacteristic
99C2×C4×C7—21no—
100C2×C4×C7—21no—
101C2×C4×C7—21no—
102C2×C4×C7—21no—
103C2×C4×C7—42no—
104C2×C4×C7—81no—
105C2×C4×C7C2×C22⋊C411yescharacteristic
106C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
107C2×Dic7—42no—
108C2×Dic7—42no—
109Dic14—42no—
110Dic14—42no—
111Dic14—82no—
112C7×C8—21no—
113C7×C8—21no—
114C7×C8—21no—
115C7×C8—21no—
116C7×C8—81no—
117C2×Q16—72no—
118C2×Q16—141no—
119C2×M16—21no—
120C2×M16C22⋊D711yescharacteristic
121C2×M16C22×D711yescharacteristic
122C4⋊Q8—141no—
123C4⋊Q8—141no—
124#125—281no—
125C22⋊Q8—142no—
126C22⋊Q8—281no—
127C4×Q8—142no—
128C4×Q8—281no—
129#117—21no—
130#117—281no—
131C2×C42C22⋊D711yescharacteristic
132M32—142no—
133#106—72no—
134#106—141no—
135#103—142no—
136#103—142no—
137#97C4×D711yescharacteristic
138#97D2811yescharacteristic
139C4×C8C4×D711yescharacteristic
140C4×C8D2811yescharacteristic
141C22×C7—21no—
142C22×C7—41no—
143C22×C7#41811yescharacteristic
144C4×C7—22no—
145C4×C7—21no—
146C4×C7—41no—
147C4×C7—161no—
148C4×C7#41011yescharacteristic
149C4×C7#42111yescharacteristic
150Dic7—82no—
151Dic7—82no—
152C2×Q8—142no—
153C2×Q8—281no—
154C22×C4—21no—
155C22×C4C2×C22⋊D711yescharacteristic
156Q16—282no—
157Q16—282no—
158M16—41no—
159M16—41no—
160M16—41no—
161M16—41no—
162C2×C8—41no—
163C2×C8(C2×D7)⋊C411yescharacteristic
164C2×C8(C2×D7)⋊C411yescharacteristic
165C2×C8C2×C4×D711yescharacteristic
166C2×C8C2×D2811yescharacteristic
167C4⋊C4—41no—
168C4⋊C4—142no—
169C4⋊C4—282no—
170C4⋊C4—281no—
171C4⋊C4—281no—
172C4⋊C4—281no—
173C4⋊C4—282no—
174C22⋊C4—41no—
175C22⋊C4—282no—
176C42—21no—
177C42—41no—
178C42—282no—
179C42(C2×D7)⋊C411yescharacteristic
180C42(C2×D7)⋊C411yescharacteristic
181C16—282no—
182C2×C7—21no—
183C2×C7—41no—
184C2×C7#151411yescharacteristic
185C23#651211yescharacteristic
186Q8—282no—
187Q8—282no—
188Q8—562no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—42no—
194C2×C4—81no—
195C2×C4—282no—
196C2×C4—282no—
197C2×C4C2×(C2×D7)⋊C411yescharacteristic
198C2×C4#651211yescharacteristic
199C8—21no—
200C8—21no—
201C8—21no—
202C8—21no—
203C8—81no—
204C7#1183811yescharacteristic, complemented, Sylow
205C22—21no—
206C22—41no—
207C22#8977311yescharacteristic
208C4—22no—
209C4—21no—
210C4—41no—
211C4—161no—
212C4—562no—
213C4—562no—
214C4#8977711yescharacteristic
215C4#8977811yescharacteristic
216C2—21no—
217C2—41no—
218C2#1172731811yescharacteristic
subgroupG/H
centerC2#11727318
commutatorC2×C7×C8C22×C4
FrattiniC2×M16C22×D7
FittingC7×#1841C2
socleC2×C7#1514
prime radicalC23×C7AGL(1,ℤ/8)
cosocleC2×C7×M16C23
hypercenter#1841D7
hypocenterC7#11838
LCSG ▷ C2×C7×C8 ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #1841

Complements

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

NH ≅ G/Ntype
11. #89488C4semidirect
12. #89471C4semidirect
14. #89452C4semidirect
204. C7#11838semidirect

Maximal subgroups

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

subgroupindex
#117359852
C7×#18412
#117276182
#117252902
#117252882
#118387