Finite Group Databasebeta

← #22589618

Subgroups — #22589618

Order 9088.

254 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 63 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×#14556159C211yesmaximal, characteristic
2#17986047C211yesmaximal, characteristic, complemented
3#17986017C211yesmaximal, characteristic
4#17985981C211yesmaximal, characteristic
5C2×#14556047C211yesmaximal, characteristic, complemented
6#17985769C211yesmaximal, characteristic, complemented
7#419×C71C211yesmaximal, characteristic, complemented
8C2×#11765865C2211yescharacteristic
9#14556159—22no—
10#14556159—22no—
11C2×#11765855—21no—
12C2×#11765852—21no—
13C2×#11765849C2211yescharacteristic
14C2×#11765849C2211yescharacteristic
15C2×#11765849C2211yescharacteristic
16#14556063—22no—
17#14556056—22no—
18#14556047—22no—
19#14556046—21no—
20#14556044—21no—
21C22×Q8×C71C2211yescharacteristic
22C2×M16×C71C2211yescharacteristic
23#117×C71C2211yescharacteristic
24#103×C71—22no—
25#11765865—21no—
26#11765865—21no—
27#11765865—21no—
28#11765865—21no—
29C2×Dic142D411yescharacteristic
30C2×D284D411yescharacteristic
31C2×C22⋊D71—21no—
32C2×C4×D71—21no—
33#11765855—24no—
34#11765852—24no—
35#11765849—21no—
36#11765849—21no—
37#11765849—21no—
38#11765849—21no—
39#11765849D412yes—
40#11765849D412yes—
41C2×C71⋊C8—21no—
42C2×C71⋊C8—21no—
43C2×C71⋊C8—21no—
44C2×Q8×C71—21no—
45C2×Q8×C71—21no—
46C2×Q8×C71—21no—
47C2×Q8×C71—21no—
48C2×Q8×C71—21no—
49C2×Q8×C71D412yes—
50C22×C4×C71—21no—
51C22×C4×C71C2311yescharacteristic
52M16×C71—21no—
53M16×C71—21no—
54C2×C8×C71—21no—
55C4⋊C4×C71—21no—
56C22⋊C4×C71—21no—
57C42×C71—21no—
58C23×C71#4111yescharacteristic
59C22×D71—21no—
60Q8×C71—22no—
61Q8×C71—22no—
62Q8×C71—41no—
63Q8×C71—41no—
64C2×C4×C71—22no—
65C2×C4×C71—41no—
66C2×C4×C71—41no—
67C2×C4×C71—41no—
68C2×C4×C71C2×D411yescharacteristic
69C2×C4×C71C2×D411yescharacteristic
70C2×C4×C71C2×D411yescharacteristic
71C2×C4×C71C2×D411yescharacteristic
72C2×C4×C71#4111yescharacteristic
73C2×C4×C71#4111yescharacteristic
74C22⋊D71—41no—
75C22⋊D71—41no—
76C2×Dic71—21no—
77D284—21no—
78D284—21no—
79C4×D71—41no—
80C4×D71—41no—
81Dic142—21no—
82Dic142—21no—
83C8×C71—41no—
84C71⋊C8—22no—
85C71⋊C8—22no—
86C71⋊C8—41no—
87C22×C71—41no—
88C22×C71#12111yescharacteristic
89C22×C71#12311yescharacteristic
90C22×C71#12411yescharacteristic
91C2×D71—41no—
92C2×D71—81no—
93C4×C71—42no—
94C4×C71—81no—
95C4×C71#12011yescharacteristic
96C4×C71#12111yescharacteristic
97C4×C71#12111yescharacteristic
98C4×C71#12311yescharacteristic
99Dic71—41no—
100C2×C71—21no—
101C2×C71—21no—
102C2×C71—21no—
103C2×C71#39411yescharacteristic
104D71—81no—
105#2049—711nomaximal, Sylow
106C71#204911yescharacteristic, complemented, Sylow
107C2×#137—711no—
108#430—711no—
109#421—711no—
110#419D7111yescharacteristic, complemented
111#413—711no—
112C2×#101—711no—
113#344—711no—
114C2×#41—711no—
115C22×Q8C2×D7111yescharacteristic
116#137—1422no—
117#137—1422no—
118C2×Q16—1421no—
119C2×SD16—1421no—
120C2×M16—711no—
121C2×M16—711no—
122C2×M16—711no—
123C2×M16C2×D7111yescharacteristic
124#117C2×D7111yescharacteristic
125#108—1422no—
126#104—1422no—
127#103—22no—
128#101—1421no—
129#101—1422no—
130#100—1421no—
131#41—1421no—
132#41—1421no—
133#41—1421no—
134#41—1421no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—711no—
141C2×Q8C22⋊D7112yes—
142C2×D4—711no—
143C2×D4—1421no—
144C22×C4—21no—
145C22×C4—1421no—
146C22×C4C22×D7111yescharacteristic
147Q16—1424no—
148SD16—1424no—
149M16—21no—
150M16—21no—
151M16—712no—
152M16—712no—
153M16—1421no—
154M16—1421no—
155M16—1421no—
156M16—1421no—
157C2×C8—21no—
158C2×C8—1421no—
159C2×C8—1421no—
160C2×C8—1421no—
161C4⋊C4—21no—
162C22⋊C4—21no—
163C42—21no—
164C23—1421no—
165C23#1176586411yescharacteristic
166Q8—22no—
167Q8—22no—
168Q8—41no—
169Q8—41no—
170Q8—1421no—
171Q8—1421no—
172D4—2841no—
173D4—2841no—
174D4—1421no—
175D4—1421no—
176C2×C4—22no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—2841no—
181C2×C4—2841no—
182C2×C4—1421no—
183C2×C4D4×D7111yescharacteristic
184C2×C4D4×D7111yescharacteristic
185C2×C4D4×D7111yescharacteristic
186C2×C4C2×C22⋊D7111yescharacteristic
187C2×C4#1176586511yescharacteristic
188C2×C4#1176586511yescharacteristic
189C8—41no—
190C8—2841no—
191C8—1422no—
192C8—1422no—
193C22—41no—
194C22—2841no—
195C22—5681no—
196C22#1455610011yescharacteristic
197C22#1455611011yescharacteristic
198C22#1455611411yescharacteristic
199C4—42no—
200C4—81no—
201C4—2841no—
202C4#1455609611yescharacteristic
203C4#1455610111yescharacteristic
204C4#1455610111yescharacteristic
205C4#1455611111yescharacteristic
206C2—21no—
207C2—21no—
208C2—21no—
209C2—5681no—
210C2#1798591411yescharacteristic
subgroupG/H
centerC2#17985914
commutatorC22×C4×C71C23
FrattiniC22×C4C22×D71
Fitting#419×C71C2
socleC2×C71#394
hypercenter#419D71
hypocenterC71#2049
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
2. #17986047C2semidirect
5. C2×#14556047C2semidirect
6. #17985769C2semidirect
7. #419×C71C2semidirect
106. C71#2049semidirect
110. #419D71semidirect