Finite Group Databasebeta

← #11740484

Subgroups — #11740484

Order 896.

452 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 161 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
1C2×C7×#125C211yesmaximal, characteristic
2C2×C4×Dic14C211yesmaximal, characteristic
3#89756C214yesmaximal
4#89750C214yesmaximal
5#89749C211yesmaximal, characteristic
6#89748C211yesmaximal, characteristic
7#89746C211yesmaximal, characteristic
8#89746C211yesmaximal, characteristic
9C4×C4⋊Dic7C211yesmaximal, characteristic
10C22×Dic14C2211yescharacteristic
11C7×#125—24no—
12C2×C7×C4⋊C4C2211yescharacteristic
13C2×C7×C4⋊C4C2211yescharacteristic
14C2×C7×C4⋊C4C2212yes—
15C2×C7×C4⋊C4C2212yes—
16C2×C42×C7C2211yescharacteristic
17C2×C4⋊Dic7C2211yescharacteristic
18C2×C4⋊Dic7C2212yes—
19C2×Dic7⋊C4C2212yes—
20C2×Dic7⋊C4C2214yes—
21C2×C4×Dic7C2212yes—
22C2×C4×Dic7C2211yescharacteristic
23C2×C4×Dic7C2211yescharacteristic
24C4×Dic14—24no—
25C7⋊#95C2212yes—
26C7⋊#95C2214yes—
27C7⋊#95C2214yes—
28C7⋊#95C2214yes—
29#2565—71nomaximal, Sylow
30C22×C4×C7C2312yes—
31C22×C4×C7C2312yes—
32C22×C4×C7C2311yescharacteristic
33C22×C4×C7C2311yescharacteristic
34C22×C4×C7C2311yescharacteristic
35C22×Dic7C2312yes—
36C22×Dic7C2312yes—
37C22×Dic7C2312yes—
38C22×Dic7C2312yes—
39C2×Dic14—22no—
40C2×Dic14—22no—
41C2×Dic14Q814yes—
42C7×C4⋊C4—24no—
43C7×C4⋊C4—24no—
44C7×C4⋊C4—22no—
45C7×C4⋊C4—22no—
46C42×C7D414yes—
47C4⋊Dic7—22no—
48C4⋊Dic7—24no—
49Dic7⋊C4—24no—
50Dic7⋊C4—28no—
51C4×Dic7—24no—
52C4×Dic7—22no—
53C4×Dic7—22no—
54C2×#125D711yescharacteristic
55C2×C4×Q8—71no—
56#398—74no—
57#391—71no—
58#391—71no—
59#387—74no—
60#384—71no—
61#382—71no—
62C4×C4⋊C4—71no—
63C23×C7C2411yescharacteristic
64C2×C4×C7—22no—
65C2×C4×C7—22no—
66C2×C4×C7—22no—
67C2×C4×C7—22no—
68C2×C4×C7—24no—
69C2×C4×C7—24no—
70C2×C4×C7C2×D412yes—
71C2×C4×C7C2×D412yes—
72C2×C4×C7C2×D412yes—
73C2×C4×C7C2×Q812yes—
74C2×C4×C7#4112yes—
75C2×Dic7—22no—
76C2×Dic7—22no—
77C2×Dic7—22no—
78C2×Dic7—22no—
79C2×Dic7—22no—
80C2×Dic7—22no—
81C2×Dic7—24no—
82C2×Dic7—22no—
83C2×Dic7—22no—
84C2×Dic7C2×Q814yes—
85C2×Dic7#4114yes—
86Dic14—28no—
87C22×Q8—71no—
88#125—24no—
89C4×Q8—144no—
90C2×C4⋊C4—72no—
91C2×C4⋊C4—71no—
92C2×C4⋊C4—74no—
93C2×C4⋊C4—72no—
94C2×C4⋊C4C2×D711yescharacteristic
95C2×C4⋊C4C2×D711yescharacteristic
96C2×C4⋊C4C2×D712yes—
97C2×C4⋊C4C2×D712yes—
98C2×C42—72no—
99C2×C42—71no—
100C2×C42—71no—
101C2×C42C2×D711yescharacteristic
102#95—72no—
103#95—74no—
104#95—74no—
105#95—74no—
106C22×C7C22×D411yescharacteristic
107C22×C7C22×Q811yescharacteristic
108C22×C7C2×#4111yescharacteristic
109C22×C7C2×#4112yes—
110C22×C72−1+412yes—
111C4×C7—22no—
112C4×C7—22no—
113C4×C7—42no—
114C4×C7—42no—
115C4×C7C22⋊Q814yes—
116Dic7—24no—
117Dic7—24no—
118Dic7—42no—
119Dic7—42no—
120C2×Q8—74no—
121C2×Q8—142no—
122C2×Q8—142no—
123C22×C4—72no—
124C22×C4—72no—
125C22×C4—72no—
126C22×C4—72no—
127C22×C4C22×D712yes—
128C22×C4C22×D712yes—
129C22×C4C22×D711yescharacteristic
130C22×C4C22×D711yescharacteristic
131C22×C4C22×D711yescharacteristic
132C4⋊C4—24no—
133C4⋊C4—24no—
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—148no—
137C4⋊C4—144no—
138C4⋊C4—144no—
139C4⋊C4—142no—
140C42—142no—
141C42—142no—
142C42—144no—
143C42C22⋊D714yes—
144C2×C7C2×C22⋊Q811yescharacteristic
145C2×C7#53211yescharacteristic
146C2×C7#53611yescharacteristic
147C2×C7#55212yes—
148C2×C7#55712yes—
149C23C23×D711yescharacteristic
150Q8—148no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—24no—
154C2×C4—24no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—74no—
158C2×C4—74no—
159C2×C4—142no—
160C2×C4—142no—
161C2×C4—142no—
162C2×C4—142no—
163C2×C4—142no—
164C2×C4—142no—
165C2×C4—144no—
166C2×C4—142no—
167C2×C4—142no—
168C2×C4Q8×D712yes—
169C2×C4#116112yes—
170C2×C4C2×C22⋊D712yes—
171C2×C4C2×C22⋊D712yes—
172C2×C4C2×C22⋊D712yes—
173C7#256511yescharacteristic, complemented, Sylow
174C22C2×Q8×D711yescharacteristic
175C22C2×#116111yescharacteristic
176C22D7×#4112yes—
177C22#655412yes—
178C22C22×C22⋊D711yescharacteristic
179C4—22no—
180C4—22no—
181C4—42no—
182C4—42no—
183C4—144no—
184C4—144no—
185C4—282no—
186C4—282no—
187C4#650914yes—
188C2#9037612yes—
189C2#9038512yes—
190C2C2×#650911yescharacteristic
191C2#9051611yescharacteristic
192C2#9052311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D7
commutator, socle, prime radical, cosocleC23×C7C24
FittingC2×C7×#125C2
hypercenterC2×#125D7
hypocenterC7#2565
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
173. C7#2565semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#1252
C2×C4×Dic142
#897562
#897502
#897492
#897482
#897462
C4×C4⋊Dic72
#25657