Finite Group Databasebeta

← #37508082

Subgroups — #37508082

Order 22912.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#26039154C211yesmaximal, characteristic, complemented
2#26038811C211yesmaximal, characteristic, complemented
3#26038631C211yesmaximal, characteristic, complemented
4#26038187C211yesmaximal, characteristic, complemented
5D4⋊(C179⋊C8)C211yesmaximal, characteristic, complemented
6#26038166C211yesmaximal, characteristic, complemented
7#459×C179C211yesmaximal, characteristic, complemented
8C2×#15668247—22no—
9C2×#15668244—21no—
10#19153113C2211yescharacteristic
11#19153099—22no—
12#19153087—21no—
13#19153084—21no—
14C4×D716C2211yescharacteristic
15#19153072—21no—
16#19153071—21no—
17C4⋊(C179⋊C8)C2211yescharacteristic
18#19153034—21no—
19C4×C179⋊C8C2211yescharacteristic
20C2×D8×C179—21no—
21#127×C179C2211yescharacteristic
22C4×D4×C179C2211yescharacteristic
23C4⋊C8×C179C2211yescharacteristic
24#102×C179—21no—
25C2×Dic358D412yes—
26C2×D716D411yescharacteristic
27C2×C22⋊D179—22no—
28C2×C4×D179—21no—
29#15668247—44no—
30#15668244—42no—
31C2×C179⋊C8—21no—
32C2×C179⋊C8—21no—
33C4⋊Dic179—21no—
34C4⋊Dic179—21no—
35C4⋊Dic179D411yescharacteristic
36C22⋊Dic179—22no—
37(C2×D179)⋊C4—22no—
38(C2×D179)⋊C4—21no—
39C4×Dic179—22no—
40C2×D4×C179—21no—
41C2×D4×C179—21no—
42C2×D4×C179—21no—
43C2×D4×C179D411yescharacteristic
44C22×C4×C179—21no—
45D8×C179—42no—
46C2×C8×C179—21no—
47C4⋊C4×C179D411yescharacteristic
48C22⋊C4×C179—21no—
49C42×C179C2311yescharacteristic
50C22×D179—21no—
51Dic358—42no—
52D716—21no—
53D716—21no—
54C22⋊D179—82no—
55C2×Dic179—21no—
56C2×Dic179—22no—
57C4×D179—41no—
58C4×D179—41no—
59C179⋊C8—22no—
60C179⋊C8—41no—
61C23×C179—21no—
62C23×C179—41no—
63D4×C179—21no—
64D4×C179—21no—
65D4×C179—42no—
66D4×C179—41no—
67D4×C179—41no—
68D4×C179—41no—
69D4×C179—41no—
70C2×C4×C179—21no—
71C2×C4×C179—41no—
72C2×C4×C179—41no—
73C2×C4×C179C2×D411yescharacteristic
74C2×C4×C179C2×D411yescharacteristic
75C2×C4×C179C2×D411yescharacteristic
76C8×C179—41no—
77C22×C179—41no—
78C22×C179—41no—
79C22×C179—41no—
80C22×C179—81no—
81C22×C179—81no—
82C22×C179—81no—
83C22×C179#12011yescharacteristic
84C2×D179—41no—
85C2×D179—41no—
86C2×D179—41no—
87C4×C179—21no—
88C4×C179—41no—
89C4×C179#13511yescharacteristic
90C4×C179#13511yescharacteristic
91C4×C179AGL(1,ℤ/8)11yescharacteristic
92C4×C179AGL(1,ℤ/8)11yescharacteristic
93Dic179—41no—
94Dic179—42no—
95C2×C179—81no—
96C2×C179—161no—
97C2×C179#44911yescharacteristic
98C2×C179#44911yescharacteristic
99C2×C179#45311yescharacteristic
100D179—81no—
101C179#162411yescharacteristic, complemented, Sylow
102#1624—1791nomaximal, Sylow
103#555—1791no—
104#492—1791no—
105#459—1791no—
106#459D17911yescharacteristic, complemented
107#333—1791no—
108D4⋊C8—1791no—
109D4⋊C8—1791no—
110C2×SD16—3582no—
111C2×D8—21no—
112C2×D8—3581no—
113C4⋊Q8—1791no—
114#127C2×D17911yescharacteristic
115#124—3582no—
116#121—3581no—
117#121—3581no—
118C4×D4—1791no—
119C4×D4C2×D17911yescharacteristic
120#117—3581no—
121#117—3581no—
122C4⋊C8—1791no—
123C4⋊C8C2×D17911yescharacteristic
124#102—21no—
125#102—3581no—
126C4×C8—1791no—
127C2×Q8—1792no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—3582no—
132C2×D4—1791no—
133C2×D4C22⋊D17911yescharacteristic
134C22×C4—21no—
135C22×C4—3581no—
136SD16—7164no—
137D8—42no—
138D8—7162no—
139C2×C8—21no—
140C2×C8—3581no—
141C2×C8—3581no—
142C4⋊C4—3581no—
143C4⋊C4—3581no—
144C4⋊C4—1791no—
145C4⋊C4C22⋊D17911yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—3582no—
148C22⋊C4—3582no—
149C22⋊C4—3581no—
150C42—3582no—
151C42C22×D17911yescharacteristic
152C23—21no—
153C23—41no—
154C23—3581no—
155Q8—7162no—
156D4—21no—
157D4—21no—
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—3581no—
164D4—3581no—
165D4—14322no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—3581no—
170C2×C4—3582no—
171C2×C4—7161no—
172C2×C4—7161no—
173C2×C4D4×D17911yescharacteristic
174C2×C4D4×D17911yescharacteristic
175C2×C4C2×C22⋊D17911yescharacteristic
176C8—41no—
177C8—3582no—
178C8—7161no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—81no—
183C22—81no—
184C22—81no—
185C22—7161no—
186C22—7161no—
187C22—7161no—
188C22#1915308111yescharacteristic
189C4—21no—
190C4—41no—
191C4—7161no—
192C4—7162no—
193C4#1915313211yescharacteristic
194C4#1915313311yescharacteristic
195C4#1915313711yescharacteristic
196C4#1915313911yescharacteristic
197C2—81no—
198C2—161no—
199C2—14321no—
200C2#2603858111yescharacteristic
201C2#2603858211yescharacteristic
202C2#2603860511yescharacteristic
subgroupG/H
centerC22#19153081
commutator, cosocleC42×C179C23
FrattiniC42C22×D179
Fitting#459×C179C2
socleC22×C179#120
hypercenter#459D179
hypocenterC179#1624
LCSG ▷ C42×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #26039154C2semidirect
2. #26038811C2semidirect
3. #26038631C2semidirect
4. #26038187C2semidirect
5. D4⋊(C179⋊C8)C2semidirect
6. #26038166C2semidirect
7. #459×C179C2semidirect
101. C179#1624semidirect
106. #459D179semidirect

Maximal subgroups

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

subgroupindex
#260391542
#260388112
#260386312
#260381872
D4⋊(C179⋊C8)2
#260381662
#459×C1792
#1624179