Finite Group Databasebeta

← #22598635

Subgroups — #22598635

Order 9088.

358 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 121 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#17986476C211yesmaximal, characteristic
2#17986337C212yesmaximal
3#17986303C212yesmaximal, complemented
4#17986206C212yesmaximal, complemented
5#17986154C212yesmaximal
6#17986104C212yesmaximal, complemented
7C4×#11765855C212yesmaximal, complemented
8#17986060C211yesmaximal, characteristic
9#541×C71C211yesmaximal, characteristic
10C22×Dic142C2211yescharacteristic
11C2×#11765855C2212yes—
12C2×#11765855C2212yes—
13C4×Dic142C2212yes—
14C4×Dic142C2212yes—
15#14556093—22no—
16#14556087C2211yescharacteristic
17#14556084—22no—
18#14556061C2212yes—
19#14556059C2212yes—
20C4⋊(C71⋊C8)C2212yes—
21#14556052C2212yes—
22#14556052C2212yes—
23#14556051C2212yes—
24#14556051C2212yes—
25C22⋊(C71⋊C8)C2212yes—
26#14556039C2211yescharacteristic
27C4×C71⋊C8C2211yescharacteristic
28C4⋊Q8×C71C2211yescharacteristic
29#126×C71—22no—
30#125×C71—22no—
31#125×C71C2211yescharacteristic
32C22⋊Q8×C71C2212yes—
33C4×Q8×C71C2212yes—
34#117×C71C2211yescharacteristic
35C2×Dic142—21no—
36C2×Dic142—24no—
37C2×Dic142C2312yes—
38C22×Dic71—21no—
39#11765855—24no—
40#11765855—24no—
41C2×C71⋊C8C2312yes—
42C2×C71⋊C8C2312yes—
43C4⋊Dic71C2312yes—
44Dic71⋊C4—22no—
45Dic71⋊C4—22no—
46C22⋊Dic71—21no—
47C4×Dic71—22no—
48C4×Dic71—22no—
49C4×Dic71—21no—
50C2×Q8×C71C2312yes—
51C22×C4×C71C2311yescharacteristic
52C4⋊C4×C71—22no—
53C4⋊C4×C71—22no—
54C4⋊C4×C71—22no—
55C4⋊C4×C71—22no—
56C4⋊C4×C71D412yes—
57C4⋊C4×C71C2312yes—
58C22⋊C4×C71—22no—
59C22⋊C4×C71D412yes—
60C42×C71—22no—
61C42×C71C2311yescharacteristic
62C42×C71C2311yescharacteristic
63C23×C71C2×D411yescharacteristic
64Q8×C71—22no—
65Q8×C71—22no—
66C2×C4×C71—22no—
67C2×C4×C71—22no—
68C2×C4×C71—22no—
69C2×C4×C71C2×D412yes—
70C2×C4×C71C2×D412yes—
71C2×C4×C71C2×D411yescharacteristic
72C2×C4×C71C2411yescharacteristic
73C2×Dic71—24no—
74C2×Dic71—22no—
75C2×Dic71—22no—
76Dic142—24no—
77Dic142—22no—
78Dic142#4114yes—
79C71⋊C8—22no—
80C71⋊C8—22no—
81C22×C71—21no—
82C22×C71—22no—
83C22×C71C22×D411yescharacteristic
84C4×C71—21no—
85C4×C71—22no—
86C4×C71—22no—
87C4×C71—42no—
88C4×C71—42no—
89C4×C71C2×#4112yes—
90Dic71—24no—
91Dic71—42no—
92C2×C71—41no—
93C2×C71#52511yescharacteristic
94C2×C71#57812yes—
95#3127—711nomaximal, Sylow
96C71#312711yescharacteristic, complemented, Sylow
97#541D7111yescharacteristic
98#519—711no—
99#485—712no—
100#479—712no—
101#462—712no—
102#451—712no—
103#441—712no—
104C4×Q16—712no—
105#433—711no—
106C22×Q8—711no—
107C2×Q16—712no—
108C2×Q16—712no—
109C4⋊Q8C2×D7111yescharacteristic
110#126—22no—
111#125—22no—
112#125C2×D7111yescharacteristic
113C22⋊Q8C2×D7112yes—
114C4×Q8—712no—
115C4×Q8—712no—
116C4×Q8—1422no—
117C4×Q8C2×D7112yes—
118#117—711no—
119#117—1422no—
120#117C2×D7111yescharacteristic
121#107—712no—
122#106—712no—
123C4⋊C8—712no—
124#103—712no—
125#103—712no—
126#103—712no—
127#103—712no—
128C22⋊C8—712no—
129#97—711no—
130C4×C8—711no—
131C2×Q8—712no—
132C2×Q8—1424no—
133C2×Q8—1421no—
134C2×Q8C22×D7112yes—
135C22×C4—1421no—
136C22×C4C22×D7111yescharacteristic
137Q16—1424no—
138Q16—1424no—
139C2×C8—712no—
140C2×C8—712no—
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—22no—
144C4⋊C4—22no—
145C4⋊C4—712no—
146C4⋊C4—1422no—
147C4⋊C4—1422no—
148C4⋊C4C22⋊D7112yes—
149C4⋊C4C22×D7112yes—
150C22⋊C4—22no—
151C22⋊C4—1421no—
152C22⋊C4C22⋊D7112yes—
153C42—22no—
154C42—1421no—
155C42—1422no—
156C42—1422no—
157C42C22×D7111yescharacteristic
158C42C22×D7111yescharacteristic
159C23C2×C22⋊D7111yescharacteristic
160Q8—22no—
161Q8—22no—
162Q8—714no—
163Q8—1424no—
164Q8—1422no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—1422no—
169C2×C4—1424no—
170C2×C4—1422no—
171C2×C4C2×C22⋊D7112yes—
172C2×C4C2×C22⋊D7112yes—
173C2×C4C2×C22⋊D7111yescharacteristic
174C2×C4C23×D7111yescharacteristic
175C8—1422no—
176C8—1422no—
177C22—21no—
178C22—22no—
179C22C22×C22⋊D7111yescharacteristic
180C4—21no—
181C4—22no—
182C4—22no—
183C4—42no—
184C4—42no—
185C4—2842no—
186C4—1424no—
187C4#41×D7112yes—
188C2—41no—
189C2#1798650611yescharacteristic
190C2#1798681412yes—
subgroupG/H
centerC22C22×C22⋊D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#541×C71C2
socleC22×C71C22×D4
hypercenter#541D71
hypocenterC71#3127
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
3. #17986303C2semidirect
4. #17986206C2semidirect
6. #17986104C2semidirect
7. C4×#11765855C2semidirect
96. C71#3127semidirect