Finite Group Databasebeta

← #22586973

Subgroups — #22586973

Order 9088.

238 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 59 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#17986548C211yesmaximal, characteristic
2#17986054C212yesmaximal, complemented
3#17985739C211yesmaximal, characteristic, complemented
4#17985738C212yesmaximal, complemented
5#329×C71C211yesmaximal, characteristic, complemented
6C2×#11765866C411yescharacteristic
7C2×#11765864C411yescharacteristic
8#14556126C411yescharacteristic
9#14556124C411yescharacteristic
10#14556116C2211yescharacteristic
11#14556101—22no—
12(C22⋊D71)⋊C4—22no—
13C42×D71C2211yescharacteristic
14Dic71⋊C8—22no—
15(C2×D71)⋊C8—22no—
16#14556039C2212yes—
17#124×C71C2211yescharacteristic
18#97×C71C2212yes—
19#11765866—42no—
20#11765864—42no—
21C2×Dic142C2×C411yescharacteristic
22C2×D284—21no—
23C2×D284C2×C411yescharacteristic
24C2×C22⋊D71—21no—
25C2×C22⋊D71—22no—
26C22×Dic71—21no—
27C2×C4×D71—21no—
28C2×C4×D71C2×C411yescharacteristic
29C2×C4×D71D412yes—
30C2×C71⋊C8—22no—
31Dic71⋊C4—22no—
32(C2×D71)⋊C4—22no—
33C4×Dic71C2×C411yescharacteristic
34C4×Dic71D412yes—
35C2×Q8×C71C2×C411yescharacteristic
36C2×D4×C71C2×C411yescharacteristic
37C2×C8×C71—22no—
38C22⋊C4×C71—22no—
39C42×C71C2311yescharacteristic
40C23×C71—21no—
41C22×D71—21no—
42C22×D71C22⋊C411yescharacteristic
43Q8×C71—41no—
44D4×C71—41no—
45C2×C4×C71—21no—
46C2×C4×C71C22×C411yescharacteristic
47C2×C4×C71C2×D412yes—
48C22⋊D71—44no—
49C22⋊D71—42no—
50C2×Dic71—21no—
51C2×Dic71—42no—
52C2×Dic71C22⋊C412yes—
53C2×Dic71C22⋊C411yescharacteristic
54D284—41no—
55D284—42no—
56C4×D71—22no—
57C4×D71—42no—
58C4×D71—42no—
59Dic142—41no—
60C8×C71—42no—
61C71⋊C8—42no—
62C22×C71—41no—
63C22×C71—42no—
64C22×C71C2×C22⋊C411yescharacteristic
65C2×D71—21no—
66C2×D71—22no—
67C2×D71—41no—
68C2×D71—42no—
69C4×C71—21no—
70C4×C71—22no—
71C4×C71—41no—
72Dic71—22no—
73Dic71—41no—
74Dic71#10012yes—
75C2×C71—81no—
76C2×C71C2×#10011yescharacteristic
77C2×C71#42112yes—
78D71—41no—
79D71—81no—
80#1536—711nomaximal, Sylow
81C71#153611yescharacteristic, complemented, Sylow
82#532—711no—
83#432—712no—
84#329—711no—
85#329—712no—
86#329D7111yescharacteristic, complemented
87C2×#41—711no—
88C2×#41—711no—
89C4⋊Q8—711no—
90#127—711no—
91#124—711no—
92#124C2×D7111yescharacteristic
93#121—1422no—
94C4×D4—1422no—
95C2×C42—711no—
96C4⋊C8—1422no—
97C22⋊C8—1422no—
98#97—712no—
99#97C2×D7112yes—
100#41—2842no—
101#41—2842no—
102C2×Q8—711no—
103C2×Q8C4×D7111yescharacteristic
104C2×D4—711no—
105C2×D4—1421no—
106C2×D4—1422no—
107C2×D4—1421no—
108C2×D4C4×D7111yescharacteristic
109C22×C4—712no—
110C22×C4—711no—
111C22×C4—1421no—
112C22×C4—1421no—
113C2×C8—22no—
114C2×C8—1422no—
115C4⋊C4—1422no—
116C22⋊C4—22no—
117C22⋊C4—1422no—
118C42—711no—
119C42—712no—
120C42C22×D7111yescharacteristic
121C23—21no—
122C23—711no—
123C23—1421no—
124Q8—41no—
125Q8—2841no—
126D4—41no—
127D4—2841no—
128D4—2842no—
129D4—2842no—
130D4—2844no—
131C2×C4—21no—
132C2×C4—2842no—
133C2×C4—2842no—
134C2×C4—2842no—
135C2×C4—711no—
136C2×C4—712no—
137C2×C4—1422no—
138C2×C4—1421no—
139C2×C4C2×C4×D7111yescharacteristic
140C2×C4D4×D7112yes—
141C8—42no—
142C8—2842no—
143C22—41no—
144C22—42no—
145C22—2841no—
146C22—2842no—
147C22—1421no—
148C22—1422no—
149C22C22⋊C4×D7111yescharacteristic
150C4—21no—
151C4—22no—
152C4—41no—
153C4—2841no—
154C4—712no—
155C4—1422no—
156C2—81no—
157C2—2841no—
158C2—5681no—
159C2#100×D7111yescharacteristic
160C2#1798601412yes—
subgroupG/H
centerC22C22⋊C4×D71
commutatorC2×C4×C71C22×C4
FrattiniC42C22×D71
Fitting#329×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#329D71
hypocenterC71#1536
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #17986054C2semidirect
3. #17985739C2semidirect
4. #17985738C2semidirect
5. #329×C71C2semidirect
81. C71#1536semidirect
86. #329D71semidirect