Finite Group Databasebeta

← #22589617

Subgroups — #22589617

Order 9088.

254 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 67 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#17986047C211yesmaximal, characteristic, complemented
2#17986016C211yesmaximal, characteristic
3#17986008C211yesmaximal, characteristic, complemented
4#17985983C211yesmaximal, characteristic
5C2×#14556047C211yesmaximal, characteristic, complemented
6#17985771C211yesmaximal, characteristic, complemented
7C2×#137×C71C211yesmaximal, characteristic
8C2×#11765849C2211yescharacteristic
9C2×#11765849C2211yescharacteristic
10C2×#11765849C2211yescharacteristic
11#14556087C2211yescharacteristic
12#14556063—22no—
13#14556055—22no—
14#14556052—22no—
15#14556047—22no—
16#14556047—21no—
17#14556045—21no—
18C2×#41×C71C2211yescharacteristic
19C22×Q8×C71C2211yescharacteristic
20#137×C71—22no—
21#137×C71—22no—
22C2×Q16×C71—21no—
23C2×SD16×C71—21no—
24C2×M16×C71C2211yescharacteristic
25#11765849—21no—
26#11765849—21no—
27#11765849—21no—
28#11765849—21no—
29#11765849—21no—
30#11765849D412yes—
31C2×C71⋊C8—21no—
32C2×C71⋊C8—21no—
33C2×C71⋊C8—21no—
34C4⋊Dic71—21no—
35C22⋊Dic71—21no—
36C4×Dic71—21no—
37#41×C71—21no—
38#41×C71—21no—
39#41×C71—21no—
40#41×C71—21no—
41C2×Q8×C71—21no—
42C2×Q8×C71—21no—
43C2×Q8×C71—21no—
44C2×Q8×C71—21no—
45C2×Q8×C71—21no—
46C2×Q8×C71D411yescharacteristic
47C2×Q8×C71D412yes—
48C2×D4×C71—21no—
49C2×D4×C71D411yescharacteristic
50C22×C4×C71—21no—
51C22×C4×C71—21no—
52C22×C4×C71C2311yescharacteristic
53Q16×C71—24no—
54SD16×C71—24no—
55M16×C71—21no—
56M16×C71D412yes—
57C2×C8×C71—21no—
58C23×C71—21no—
59C23×C71#4111yescharacteristic
60Q8×C71—22no—
61Q8×C71—21no—
62Q8×C71—21no—
63Q8×C71—22no—
64Q8×C71—41no—
65Q8×C71—41no—
66D4×C71—21no—
67D4×C71—21no—
68D4×C71—41no—
69D4×C71—41no—
70C2×C4×C71—22no—
71C2×C4×C71—21no—
72C2×C4×C71—41no—
73C2×C4×C71—41no—
74C2×C4×C71—41no—
75C2×C4×C71—41no—
76C2×C4×C71C2×D411yescharacteristic
77C2×C4×C71C2×D411yescharacteristic
78C2×C4×C71C2×D411yescharacteristic
79C2×C4×C71C2×D411yescharacteristic
80C2×C4×C71#4111yescharacteristic
81C2×C4×C71#4111yescharacteristic
82C2×Dic71—41no—
83C8×C71—22no—
84C71⋊C8—22no—
85C71⋊C8—41no—
86C71⋊C8—41no—
87C22×C71—41no—
88C22×C71—41no—
89C22×C71—81no—
90C22×C71#12111yescharacteristic
91C22×C71#12311yescharacteristic
92C22×C71#12411yescharacteristic
93C4×C71—41no—
94C4×C71—42no—
95C4×C71#12011yescharacteristic
96C4×C71#12111yescharacteristic
97C4×C71#12111yescharacteristic
98C4×C71#12311yescharacteristic
99Dic71—81no—
100C2×C71—21no—
101C2×C71—21no—
102C2×C71—21no—
103C2×C71—81no—
104C2×C71#39411yescharacteristic
105#2049—711nomaximal, Sylow
106C71#204911yescharacteristic, complemented, Sylow
107C2×#137D7111yescharacteristic
108#430—711no—
109#421—711no—
110#419—711no—
111#413—711no—
112C2×#101—711no—
113#344—711no—
114C2×#41C2×D7111yescharacteristic
115C22×Q8C2×D7111yescharacteristic
116#137—22no—
117#137—22no—
118C2×Q16—21no—
119C2×SD16—21no—
120C2×M16—711no—
121C2×M16—711no—
122C2×M16—711no—
123C2×M16C2×D7111yescharacteristic
124#117—711no—
125#108—1422no—
126#104—1422no—
127#103—1422no—
128#101—1422no—
129#101—1421no—
130#100—1421no—
131#41—21no—
132#41—21no—
133#41—21no—
134#41—21no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8C22⋊D7111yescharacteristic
141C2×Q8C22⋊D7112yes—
142C2×D4—21no—
143C2×D4C22⋊D7111yescharacteristic
144C22×C4—21no—
145C22×C4—21no—
146C22×C4C22×D7111yescharacteristic
147Q16—24no—
148SD16—24no—
149M16—21no—
150M16—712no—
151M16—1421no—
152M16—1421no—
153M16—1421no—
154M16—1421no—
155M16—1421no—
156M16C22⋊D7112yes—
157C2×C8—21no—
158C2×C8—1421no—
159C2×C8—1421no—
160C2×C8—1421no—
161C4⋊C4—1421no—
162C22⋊C4—1421no—
163C42—1421no—
164C23—21no—
165C23#1176586411yescharacteristic
166Q8—22no—
167Q8—21no—
168Q8—21no—
169Q8—22no—
170Q8—41no—
171Q8—41no—
172D4—21no—
173D4—21no—
174D4—41no—
175D4—41no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—2841no—
183C2×C4D4×D7111yescharacteristic
184C2×C4C2×C22⋊D7111yescharacteristic
185C2×C4C2×C22⋊D7111yescharacteristic
186C2×C4C2×C22⋊D7111yescharacteristic
187C2×C4#1176586411yescharacteristic
188C2×C4#1176586411yescharacteristic
189C8—22no—
190C8—2841no—
191C8—2841no—
192C8—1422no—
193C22—41no—
194C22—41no—
195C22—81no—
196C22#1455610011yescharacteristic
197C22#1455610911yescharacteristic
198C22#1455611511yescharacteristic
199C4—41no—
200C4—42no—
201C4—5681no—
202C4#1455609711yescharacteristic
203C4#1455609911yescharacteristic
204C4#1455610011yescharacteristic
205C4#1455610911yescharacteristic
206C2—21no—
207C2—21no—
208C2—21no—
209C2—81no—
210C2#1798591311yescharacteristic
subgroupG/H
centerC2#17985913
commutatorC22×C4×C71C23
FrattiniC22×C4C22×D71
FittingC2×#137×C71C2
socleC2×C71#394
hypercenterC2×#137D71
hypocenterC71#2049
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. #17986047C2semidirect
3. #17986008C2semidirect
5. C2×#14556047C2semidirect
6. #17985771C2semidirect
106. C71#2049semidirect