Finite Group Databasebeta

← #37509448

Subgroups — #37509448

Order 22912.

358 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 93 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#26038950C211yesmaximal, characteristic
2C2×#19153041C212yesmaximal, complemented
3#26038403C211yesmaximal, characteristic, complemented
4#26038199C212yesmaximal, complemented
5C2×#117×C179C211yesmaximal, characteristic, complemented
6C2×#15668259C2211yescharacteristic
7C2×#15668243C2212yes—
8#19153096—21no—
9#19153092C412yescomplemented
10#19153087C412yescomplemented
11#19153082—21no—
12C4×C22⋊D179—22no—
13#19153072C2211yescharacteristic
14#19153041—24no—
15C22⋊(C179⋊C8)—22no—
16C23×C4×C179C2211yescharacteristic
17#117×C179—24no—
18C2×C4⋊C4×C179—21no—
19C2×C22⋊C4×C179—21no—
20C2×C42×C179C2212yes—
21#15668259—22no—
22#15668259—22no—
23C2×Dic358C2×C411yescharacteristic
24C2×D716C2×C411yescharacteristic
25C2×C22⋊D179—22no—
26C2×C22⋊D179—21no—
27C2×C4×D179—21no—
28#15668243—22no—
29#15668243—22no—
30C2×C179⋊C8—22no—
31C4⋊Dic179C2×C412yes—
32Dic179⋊C4—22no—
33C22⋊Dic179—22no—
34C22⋊Dic179—21no—
35(C2×D179)⋊C4—22no—
36C4×Dic179—21no—
37C24×C179D411yescharacteristic
38C22×C4×C179—22no—
39C22×C4×C179—22no—
40C22×C4×C179—22no—
41C22×C4×C179C2×C412yes—
42C22×C4×C179D411yescharacteristic
43C22×C4×C179D412yes—
44C22×C4×C179C2311yescharacteristic
45C4⋊C4×C179—24no—
46C22⋊C4×C179—24no—
47C42×C179—22no—
48C42×C179D414yescomplemented
49C22×D179—21no—
50Dic358—22no—
51D716—22no—
52C22⋊D179—44no—
53C22⋊D179—41no—
54C22⋊D179—41no—
55C2×Dic179—22no—
56C2×Dic179—21no—
57C4×D179—42no—
58C179⋊C8—42no—
59C23×C179—21no—
60C23×C179—21no—
61C23×C179—42no—
62C23×C179C22⋊C412yes—
63C23×C179C2×D411yescharacteristic
64C2×C4×C179—21no—
65C2×C4×C179—21no—
66C2×C4×C179—24no—
67C2×C4×C179—24no—
68C2×C4×C179—24no—
69C2×C4×C179—44no—
70C2×C4×C179C22⋊C412yes—
71C2×C4×C179C22×C411yescharacteristic
72C2×C4×C179C2×D412yes—
73C2×C4×C179C2×D411yescharacteristic
74C2×C4×C179#4112yes—
75C22×C179—22no—
76C22×C179—22no—
77C22×C179—22no—
78C22×C179—22no—
79C22×C179—42no—
80C22×C179—42no—
81C22×C179C2×C22⋊C411yescharacteristic
82C22×C179#12011yescharacteristic
83C22×C179#12311yescharacteristic
84C2×D179—41no—
85C2×D179—42no—
86C4×C179—22no—
87C4×C179—44no—
88C4×C179C4×D412yes—
89C4×C179#12112yes—
90Dic179—41no—
91Dic179—42no—
92C2×C179—21no—
93C2×C179—21no—
94C2×C179—42no—
95C2×C179#38611yescharacteristic
96C2×C179#42112yes—
97D179—81no—
98C179#189711yescharacteristic, complemented, Sylow
99#1897—1791nomaximal, Sylow
100#525—1791no—
101C2×#117D17911yescharacteristic, complemented
102C2×#104—1792no—
103#407—1791no—
104#339—1792no—
105C2×#41—1791no—
106C23×C4C2×D17911yescharacteristic
107C2×M16—1792no—
108#123—3581no—
109C22⋊Q8—1792no—
110#121—1792no—
111#120—3581no—
112C4×D4—3582no—
113#117—24no—
114#117—1791no—
115C2×C4⋊C4—21no—
116C2×C22⋊C4—21no—
117C2×C42C2×D17912yes—
118#104—3584no—
119C22⋊C8—3582no—
120C24C22⋊D17911yescharacteristic
121#41—3582no—
122#41—3582no—
123C2×Q8—1791no—
124C2×D4—3582no—
125C2×D4—3581no—
126C2×D4—1791no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—3581no—
131C22×C4C4×D17912yes—
132C22×C4C22⋊D17911yescharacteristic
133C22×C4D71612yes—
134C22×C4C22×D17911yescharacteristic
135M16—3582no—
136M16—3582no—
137C2×C8—3582no—
138C4⋊C4—24no—
139C4⋊C4—3582no—
140C4⋊C4—1792no—
141C22⋊C4—24no—
142C22⋊C4—3582no—
143C22⋊C4—3581no—
144C22⋊C4—3582no—
145C42—22no—
146C42—3581no—
147C42C22⋊D17914yescomplemented
148C23—21no—
149C23—21no—
150C23—42no—
151C23—3581no—
152C23(C2×D179)⋊C412yes—
153C23C2×C22⋊D17911yescharacteristic
154Q8—3582no—
155D4—3582no—
156D4—7164no—
157D4—7161no—
158D4—7161no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—24no—
164C2×C4—44no—
165C2×C4—3582no—
166C2×C4—3581no—
167C2×C4—7162no—
168C2×C4(C2×D179)⋊C412yes—
169C2×C4C2×C4×D17911yescharacteristic
170C2×C4C2×C22⋊D17912yes—
171C2×C4C2×D71611yescharacteristic
172C2×C4#1566825912yes—
173C8—7162no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—7161no—
181C22—7162no—
182C22C2×(C2×D179)⋊C411yescharacteristic
183C22#1915308211yescharacteristic
184C22#1915309611yescharacteristic
185C4—22no—
186C4—44no—
187C4—7161no—
188C4—7162no—
189C4C4×C22⋊D17912yes—
190C4#1915308712yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—14321no—
195C2#2603831811yescharacteristic
196C2#2603845712yes—
subgroupG/H
centerC2×C4C2×D716
commutatorC2×C4×C179C22×C4
FrattiniC22×C4C22×D179
FittingC2×#117×C179C2
socleC22×C179C2×C22⋊C4
prime radical#26038950C2
cosocleC22×C4×C179C23
hypercenterC2×#117D179
hypocenterC179#1897
LCSG ▷ C2×C4×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×#19153041C2semidirect
3. #26038403C2semidirect
4. #26038199C2semidirect
5. C2×#117×C179C2semidirect
9. #19153092C4semidirect
10. #19153087C4semidirect
48. C42×C179D4semidirect
98. C179#1897semidirect
101. C2×#117D179semidirect
147. C42C22⋊D179semidirect

Maximal subgroups

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

subgroupindex
#260389502
C2×#191530412
#260384032
#260381992
C2×#117×C1792
#1897179