Finite Group Databasebeta

← #22598466

Subgroups — #22598466

Order 9088.

380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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×C4×Dic142C211yesmaximal, characteristic
2#17986327C212yesmaximal
3#17986281C212yesmaximal, complemented
4#17986206C212yesmaximal, complemented
5#17986154C212yesmaximal
6#17986104C214yesmaximal, complemented
7#17986056C211yesmaximal, characteristic
8#533×C71C211yesmaximal, characteristic
9C22×Dic142C2211yescharacteristic
10C2×#11765855C2214yes—
11C4×Dic142—21no—
12C4×Dic142—21no—
13C4×Dic142C2212yes—
14C4×Dic142C2212yes—
15C2×C4⋊Dic71C2211yescharacteristic
16C2×Dic71⋊C4—21no—
17C2×C4×Dic71—21no—
18#14556059C2214yes—
19C4⋊(C71⋊C8)C2212yes—
20#14556052C2214yes—
21#14556051C2214yes—
22C22⋊(C71⋊C8)C2212yes—
23#14556039C2212yes—
24C4⋊Q8×C71C2211yescharacteristic
25C4⋊Q8×C71C2211yescharacteristic
26#125×C71—21no—
27C22⋊Q8×C71—21no—
28C22⋊Q8×C71C2212yes—
29C4×Q8×C71—21no—
30C4×Q8×C71C2212yes—
31#117×C71—21no—
32C2×C42×C71C2211yescharacteristic
33C2×Dic142—21no—
34C2×Dic142—24no—
35C2×Dic142C2312yes—
36C22×Dic71—21no—
37C22×Dic71—21no—
38#11765855—28no—
39C2×C71⋊C8C2314yes—
40C4⋊Dic71—21no—
41C4⋊Dic71C2312yes—
42Dic71⋊C4—22no—
43Dic71⋊C4—22no—
44C4×Dic71—22no—
45C4×Dic71—22no—
46C2×Q8×C71—21no—
47C2×Q8×C71C2312yes—
48C22×C4×C71D411yescharacteristic
49C22×C4×C71D411yescharacteristic
50C22×C4×C71C2311yescharacteristic
51C4⋊C4×C71—21no—
52C4⋊C4×C71—21no—
53C4⋊C4×C71—21no—
54C4⋊C4×C71—22no—
55C4⋊C4×C71—22no—
56C4⋊C4×C71C2312yes—
57C22⋊C4×C71—22no—
58C42×C71—22no—
59C42×C71D411yescharacteristic
60C42×C71D411yescharacteristic
61C42×C71C2311yescharacteristic
62C42×C71C2311yescharacteristic
63C23×C71C2×D411yescharacteristic
64Q8×C71—24no—
65Q8×C71—42no—
66C2×C4×C71—22no—
67C2×C4×C71—22no—
68C2×C4×C71—22no—
69C2×C4×C71—22no—
70C2×C4×C71—22no—
71C2×C4×C71C2×D411yescharacteristic
72C2×C4×C71C2×D411yescharacteristic
73C2×C4×C71C2×D411yescharacteristic
74C2×C4×C71C2×D411yescharacteristic
75C2×C4×C71C2×D411yescharacteristic
76C2×C4×C71C2411yescharacteristic
77C2×Dic71—24no—
78C2×Dic71—22no—
79C2×Dic71—22no—
80C2×Dic71—42no—
81Dic142—24no—
82Dic142—22no—
83Dic142#4114yes—
84C71⋊C8—24no—
85C22×C71—21no—
86C22×C71—21no—
87C22×C71#13712yes—
88C22×C71C22×D411yescharacteristic
89C4×C71—21no—
90C4×C71—21no—
91C4×C71—21no—
92C4×C71—21no—
93C4×C71—42no—
94C4×C71—42no—
95C4×C71#13712yes—
96C4×C71C2×#4112yes—
97Dic71—24no—
98Dic71—42no—
99C2×C71—22no—
100C2×C71#52511yescharacteristic
101C2×C71C2×#13711yescharacteristic
102C2×C71C2×#13711yescharacteristic
103#3113—711nomaximal, Sylow
104C71#311311yescharacteristic, complemented, Sylow
105#533D7111yescharacteristic
106C2×C4×Q8—711no—
107#483—712no—
108#475—712no—
109#462—712no—
110#451—712no—
111#441—714no—
112#432—711no—
113C22×Q8—711no—
114C2×Q16—714no—
115C4⋊Q8C2×D7111yescharacteristic
116C4⋊Q8C2×D7111yescharacteristic
117#125—21no—
118C22⋊Q8—21no—
119C22⋊Q8C2×D7112yes—
120C4×Q8—21no—
121C4×Q8—712no—
122C4×Q8—712no—
123C4×Q8—1421no—
124C4×Q8—1421no—
125C4×Q8C2×D7112yes—
126#117—21no—
127C2×C4⋊C4—711no—
128C2×C4⋊C4—1421no—
129C2×C42—1421no—
130C2×C42C2×D7111yescharacteristic
131#106—714no—
132C4⋊C8—712no—
133#103—714no—
134#103—714no—
135C22⋊C8—712no—
136#97—712no—
137C2×Q8—21no—
138C2×Q8—712no—
139C2×Q8—1424no—
140C2×Q8—1421no—
141C2×Q8C22×D7112yes—
142C22×C4—1421no—
143C22×C4—1421no—
144C22×C4C22⋊D7111yescharacteristic
145C22×C4C22⋊D7111yescharacteristic
146C22×C4C22×D7111yescharacteristic
147Q16—1428no—
148C2×C8—714no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—712no—
155C4⋊C4—1422no—
156C4⋊C4—1422no—
157C4⋊C4—1421no—
158C4⋊C4C22×D7112yes—
159C22⋊C4—22no—
160C42—22no—
161C42—1422no—
162C42—1422no—
163C42C22⋊D7111yescharacteristic
164C42C22⋊D7111yescharacteristic
165C42C22×D7111yescharacteristic
166C42C22×D7111yescharacteristic
167C23C2×C22⋊D7111yescharacteristic
168Q8—24no—
169Q8—42no—
170Q8—714no—
171Q8—1424no—
172Q8—1422no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—2842no—
179C2×C4—1422no—
180C2×C4—1424no—
181C2×C4—1422no—
182C2×C4C2×C22⋊D7111yescharacteristic
183C2×C4C2×C22⋊D7111yescharacteristic
184C2×C4C2×C22⋊D7111yescharacteristic
185C2×C4C2×C22⋊D7111yescharacteristic
186C2×C4C2×C22⋊D7111yescharacteristic
187C2×C4C23×D7111yescharacteristic
188C8—1424no—
189C22—21no—
190C22—21no—
191C22#1455615912yes—
192C22C22×C22⋊D7111yescharacteristic
193C4—21no—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—42no—
198C4—42no—
199C4—2842no—
200C4—1424no—
201C4#1455615812yes—
202C4#41×D7112yes—
203C2—22no—
204C2#1798650611yescharacteristic
205C2C2×#1455615811yescharacteristic
206C2C2×#1455615911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#533×C71C2
socleC22×C71C22×D4
hypercenter#533D71
hypocenterC71#3113
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
3. #17986281C2semidirect
4. #17986206C2semidirect
6. #17986104C2semidirect
104. C71#3113semidirect