Finite Group Databasebeta

← #37510104

Subgroups — #37510104

Order 22912.

350 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 69 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#26039239C211yesmaximal, characteristic, complemented
2#26039237C212yesmaximal, complemented
3#26038405C212yesmaximal, complemented
4C179⋊#338C211yesmaximal, characteristic, complemented
5#408×C179C211yesmaximal, characteristic, complemented
6C2×#15668259C2212yes—
7#19153146—22no—
8#19153144—22no—
9#19153143—22no—
10#19153141—22no—
11#19153139—22no—
12#19153138—22no—
13#19153135—22no—
14#19153133—24no—
15C2×#15668243C2212yes—
16(C2×D179)⋊C8—24no—
17C2×#41×C179C2211yescharacteristic
18C2×M16×C179C2211yescharacteristic
19C22×C8×C179C2211yescharacteristic
20C22⋊C8×C179—22no—
21#15668259—22no—
22#15668259—22no—
23#15668259—22no—
24#15668259—22no—
25C2×Dic358D412yes—
26C2×D716D412yes—
27C2×C22⋊D179—22no—
28C2×C4×D179—22no—
29Dic716—22no—
30#15668249—24no—
31#15668248—24no—
32#15668247—24no—
33#15668246—24no—
34D1432—22no—
35#15668244—24no—
36#15668243—22no—
37#15668243—22no—
38C2×C179⋊C8D414yes—
39#41×C179—22no—
40#41×C179—22no—
41C2×Q8×C179D411yescharacteristic
42C2×D4×C179—21no—
43C2×D4×C179D411yescharacteristic
44C22×C4×C179—21no—
45C22×C4×C179C2311yescharacteristic
46M16×C179—22no—
47C2×C8×C179—21no—
48C2×C8×C179—22no—
49C2×C8×C179D412yes—
50C22×D179—22no—
51Dic358—22no—
52Dic358—22no—
53D716—22no—
54D716—22no—
55C22⋊D179—42no—
56C22⋊D179—42no—
57C2×Dic179—22no—
58C4×D179—42no—
59C4×D179—42no—
60C179⋊C8—24no—
61C23×C179—21no—
62C23×C179#4111yescharacteristic
63Q8×C179—22no—
64D4×C179—22no—
65D4×C179—42no—
66C2×C4×C179—21no—
67C2×C4×C179—41no—
68C2×C4×C179—41no—
69C2×C4×C179C2×D412yes—
70C2×C4×C179C2×D412yes—
71C2×C4×C179C2×D411yescharacteristic
72C2×C4×C179C2×D411yescharacteristic
73C8×C179—22no—
74C8×C179—41no—
75C22×C179—41no—
76C22×C179—42no—
77C22×C179—41no—
78C22×C179#12112yes—
79C22×C179#12111yescharacteristic
80C2×D179—44no—
81C2×D179—42no—
82C4×C179—41no—
83C4×C179#12011yescharacteristic
84C4×C179#12012yes—
85C4×C179#12711yescharacteristic
86Dic179—42no—
87C2×C179—22no—
88C2×C179—21no—
89C2×C179—81no—
90C2×C179#39211yescharacteristic
91D179—82no—
92C179#201711yescharacteristic, complemented, Sylow
93#2017—1791nomaximal, Sylow
94#575—1792no—
95#575—1791no—
96#408—1792no—
97#408D17911yescharacteristic, complemented
98#338—1791no—
99C2×#41—1792no—
100C2×#41C2×D17911yescharacteristic
101#137—3582no—
102#137—3582no—
103#137—3582no—
104AGL(1,ℤ/8)—3582no—
105AGL(1,ℤ/8)—3582no—
106AGL(1,ℤ/8)—3582no—
107#135—3584no—
108#135—3582no—
109C2×M16—1792no—
110C2×M16C2×D17911yescharacteristic
111C22×C8C2×D17911yescharacteristic
112C22⋊C8—22no—
113C22⋊C8—3584no—
114#41—22no—
115#41—22no—
116#41—3582no—
117#41—3582no—
118#41—3582no—
119#41—3582no—
120C2×Q8—1792no—
121C2×Q8D71611yescharacteristic
122C2×D4—21no—
123C2×D4—3582no—
124C2×D4—1792no—
125C2×D4D71611yescharacteristic
126C22×C4—21no—
127C22×C4—3582no—
128C22×C4C22×D17911yescharacteristic
129Q16—3582no—
130Q16—3584no—
131SD16—3584no—
132SD16—3584no—
133SD16—3584no—
134D8—3582no—
135D8—3584no—
136M16—22no—
137M16—3582no—
138M16—3582no—
139C2×C8—22no—
140C2×C8—21no—
141C2×C8—1794no—
142C2×C8C22⋊D17912yes—
143C23—21no—
144C23—3582no—
145C23#1566825911yescharacteristic
146Q8—22no—
147Q8—3582no—
148Q8—3582no—
149D4—22no—
150D4—42no—
151D4—3582no—
152D4—3582no—
153D4—7162no—
154D4—7162no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—3582no—
159C2×C4—7162no—
160C2×C4—7162no—
161C2×C4D4×D17912yes—
162C2×C4D4×D17912yes—
163C2×C4C2×C22⋊D17911yescharacteristic
164C2×C4C2×D71611yescharacteristic
165C8—22no—
166C8—41no—
167C8—3584no—
168C22—41no—
169C22—42no—
170C22—41no—
171C22—7164no—
172C22—7162no—
173C22#1915308612yes—
174C22#1915308711yescharacteristic
175C4—41no—
176C4—7162no—
177C4#1915308111yescharacteristic
178C4#1915308312yes—
179C4#1915310911yescharacteristic
180C2—21no—
181C2—22no—
182C2—81no—
183C2—14322no—
184C2#2603834811yescharacteristic
subgroupG/H
centerC4#19153109
commutator, cosocleC22×C4×C179C23
FrattiniC22×C4C22×D179
Fitting#408×C179C2
socleC2×C179#392
hypercenter#408D179
hypocenterC179#2017
LCSG ▷ C22×C4×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #26039239C2semidirect
2. #26039237C2semidirect
3. #26038405C2semidirect
4. C179⋊#338C2semidirect
5. #408×C179C2semidirect
92. C179#2017semidirect
97. #408D179semidirect

Maximal subgroups

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

subgroupindex
#260392392
#260392372
#260384052
C179⋊#3382
#408×C1792
#2017179