Finite Group Databasebeta

← #37510103

Subgroups — #37510103

Order 22912.

350 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 71 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#26039237C212yesmaximal, complemented
2#26038407C211yesmaximal, characteristic, complemented
3#26038406C212yesmaximal, complemented
4C179⋊#338C211yesmaximal, characteristic, complemented
5#575×C179C211yesmaximal, characteristic, complemented
6C2×#15668259C2211yescharacteristic
7#19153144—22no—
8#19153143—22no—
9#19153139—22no—
10#19153138—22no—
11#19153133—24no—
12C2×#15668243C2212yes—
13C22×C179⋊C8C2211yescharacteristic
14C22⋊(C179⋊C8)—24no—
15(C2×D179)⋊C8—22no—
16C2×#41×C179C2212yes—
17#137×C179—22no—
18AGL(1,ℤ/8)×C179—22no—
19#135×C179—22no—
20C2×M16×C179C2211yescharacteristic
21#15668259—22no—
22#15668259—22no—
23C2×Dic358D411yescharacteristic
24C2×D716D411yescharacteristic
25C2×C22⋊D179—21no—
26C2×C4×D179—21no—
27#15668249—24no—
28#15668247—24no—
29#15668246—24no—
30#15668244—24no—
31#15668243—22no—
32#15668243—22no—
33C2×C179⋊C8—21no—
34C2×C179⋊C8—22no—
35C2×C179⋊C8D414yes—
36#41×C179—22no—
37#41×C179—22no—
38#41×C179—22no—
39#41×C179—22no—
40C2×Q8×C179D412yes—
41C2×D4×C179—22no—
42C2×D4×C179D412yes—
43C22×C4×C179—22no—
44C22×C4×C179C2311yescharacteristic
45Q16×C179—22no—
46SD16×C179—24no—
47D8×C179—22no—
48M16×C179—22no—
49C2×C8×C179D412yes—
50C22×D179—21no—
51Dic358—22no—
52D716—22no—
53C22⋊D179—42no—
54C2×Dic179—21no—
55C4×D179—41no—
56C4×D179—41no—
57C179⋊C8—24no—
58C179⋊C8—41no—
59C23×C179—22no—
60C23×C179#4111yescharacteristic
61Q8×C179—22no—
62Q8×C179—22no—
63D4×C179—22no—
64D4×C179—22no—
65D4×C179—42no—
66D4×C179—42no—
67C2×C4×C179—22no—
68C2×C4×C179—42no—
69C2×C4×C179—42no—
70C2×C4×C179C2×D411yescharacteristic
71C2×C4×C179C2×D412yes—
72C2×C4×C179C2×D412yes—
73C2×C4×C179C2×D411yescharacteristic
74C8×C179—22no—
75C22×C179—41no—
76C22×C179—44no—
77C22×C179—42no—
78C22×C179#12111yescharacteristic
79C22×C179#12112yes—
80C2×D179—42no—
81C2×D179—41no—
82C4×C179—42no—
83C4×C179#12012yes—
84C4×C179#12011yescharacteristic
85C4×C179#12711yescharacteristic
86Dic179—41no—
87C2×C179—21no—
88C2×C179—22no—
89C2×C179—82no—
90C2×C179#39211yescharacteristic
91D179—81no—
92C179#201711yescharacteristic, complemented, Sylow
93#2017—1791nomaximal, Sylow
94#575—1792no—
95#575D17911yescharacteristic, complemented
96#408—1792no—
97#408—1791no—
98#338—1791no—
99C2×#41—1791no—
100C2×#41C2×D17912yes—
101#137—22no—
102#137—3582no—
103#137—3582no—
104AGL(1,ℤ/8)—22no—
105AGL(1,ℤ/8)—3582no—
106AGL(1,ℤ/8)—3582no—
107#135—22no—
108#135—3584no—
109C2×M16—1792no—
110C2×M16C2×D17911yescharacteristic
111C22×C8—1791no—
112C22⋊C8—3584no—
113C22⋊C8—3582no—
114#41—22no—
115#41—22no—
116#41—22no—
117#41—22no—
118#41—3582no—
119#41—3582no—
120C2×Q8—1791no—
121C2×Q8C22⋊D17912yes—
122C2×D4—22no—
123C2×D4—3581no—
124C2×D4—1791no—
125C2×D4C22⋊D17912yes—
126C22×C4—22no—
127C22×C4—3581no—
128C22×C4C22×D17911yescharacteristic
129Q16—22no—
130Q16—3584no—
131SD16—24no—
132SD16—3584no—
133SD16—3584no—
134D8—22no—
135D8—3584no—
136M16—22no—
137M16—3582no—
138M16—3582no—
139C2×C8—3582no—
140C2×C8—3581no—
141C2×C8—1794no—
142C2×C8C22⋊D17912yes—
143C23—22no—
144C23—3581no—
145C23#1566825811yescharacteristic
146Q8—22no—
147Q8—22no—
148Q8—3582no—
149D4—22no—
150D4—22no—
151D4—42no—
152D4—42no—
153D4—3582no—
154D4—7162no—
155C2×C4—22no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—3581no—
159C2×C4—7161no—
160C2×C4—7161no—
161C2×C4D4×D17911yescharacteristic
162C2×C4D4×D17912yes—
163C2×C4C2×C22⋊D17912yes—
164C2×C4C2×C22⋊D17911yescharacteristic
165C8—22no—
166C8—3584no—
167C8—7161no—
168C22—41no—
169C22—44no—
170C22—42no—
171C22—7162no—
172C22—7161no—
173C22#1915308411yescharacteristic
174C22#1915308512yes—
175C4—42no—
176C4—7161no—
177C4#1915308112yes—
178C4#1915308211yescharacteristic
179C4#1915310911yescharacteristic
180C2—22no—
181C2—21no—
182C2—82no—
183C2—14321no—
184C2#2603834711yescharacteristic
subgroupG/H
centerC4#19153109
commutator, cosocleC22×C4×C179C23
FrattiniC22×C4C22×D179
Fitting#575×C179C2
socleC2×C179#392
hypercenter#575D179
hypocenterC179#2017
LCSG ▷ C22×C4×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #26039237C2semidirect
2. #26038407C2semidirect
3. #26038406C2semidirect
4. C179⋊#338C2semidirect
5. #575×C179C2semidirect
92. C179#2017semidirect
95. #575D179semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#260392372
#260384072
#260384062
C179⋊#3382
#575×C1792
#2017179