Finite Group Databasebeta

← #37509392

Subgroups — #37509392

Order 22912.

324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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×#19153113C211yesmaximal, characteristic
2#26038916C211yesmaximal, characteristic
3#26038449C211yesmaximal, characteristic
4#26038447C211yesmaximal, characteristic
5C2×#19153031C211yesmaximal, characteristic
6#26038199C211yesmaximal, characteristic
7#339×C179C211yesmaximal, characteristic
8C22×Dic358C2211yescharacteristic
9C22×Dic358C2211yescharacteristic
10C2×#15668243C2211yescharacteristic
11#19153113—22no—
12#19153113C414yescomplemented
13C4×Dic358—22no—
14#19153078—22no—
15#19153072C2211yescharacteristic
16#19153069—22no—
17C2×C4⋊Dic179—22no—
18#19153038—22no—
19#19153036—22no—
20#19153031—22no—
21C2×M16×C179C2211yescharacteristic
22#117×C179C2211yescharacteristic
23C2×C42×C179C2211yescharacteristic
24C2×Dic358—21no—
25C2×Dic358—21no—
26C2×Dic358—21no—
27C2×Dic358—21no—
28C2×Dic358—21no—
29C2×Dic358—21no—
30C2×Dic358—21no—
31C2×Dic358—21no—
32C2×Dic358—21no—
33C2×Dic358C2×C412yes—
34C2×Dic358C2×C412yes—
35C2×Dic358D412yes—
36C22×Dic179—21no—
37C22×Dic179D412yes—
38#15668243—21no—
39#15668243—21no—
40C2×C179⋊C8—21no—
41C4⋊Dic179—28no—
42C4⋊Dic179D412yes—
43Dic179⋊C4—24no—
44C22⋊Dic179—21no—
45C4×Dic179—24no—
46C4×Dic179—21no—
47C22×C4×C179—21no—
48C22×C4×C179C2311yescharacteristic
49M16×C179—21no—
50M16×C179—21no—
51C2×C8×C179—21no—
52C4⋊C4×C179D412yes—
53C22⋊C4×C179—21no—
54C42×C179—21no—
55C42×C179—21no—
56C42×C179C2×C412yes—
57Dic358—22no—
58Dic358—22no—
59Dic358—22no—
60Dic358—22no—
61Dic358—22no—
62Dic358—22no—
63Dic358—41no—
64Dic358—41no—
65C2×Dic179—22no—
66C2×Dic179—22no—
67C2×Dic179—22no—
68C2×Dic179—22no—
69C2×Dic179—41no—
70C2×Dic179—41no—
71C2×Dic179C22⋊C414yes—
72C179⋊C8—41no—
73C23×C179C2×D411yescharacteristic
74C2×C4×C179—24no—
75C2×C4×C179—22no—
76C2×C4×C179—22no—
77C2×C4×C179C22×C411yescharacteristic
78C2×C4×C179C2×D411yescharacteristic
79C2×C4×C179C2×D411yescharacteristic
80C2×C4×C179C2×D411yescharacteristic
81C2×C4×C179#4111yescharacteristic
82C2×C4×C179#4111yescharacteristic
83C8×C179—41no—
84C22×C179—22no—
85C22×C179C2×C22⋊C411yescharacteristic
86C22×C179#12011yescharacteristic
87C22×C179#12311yescharacteristic
88C4×C179—24no—
89C4×C179—42no—
90C4×C179C4×D411yescharacteristic
91C4×C179C4×D411yescharacteristic
92C4×C179#12111yescharacteristic
93C4×C179#12111yescharacteristic
94Dic179—24no—
95Dic179—42no—
96Dic179—42no—
97C2×C179—21no—
98C2×C179—21no—
99C2×C179#38611yescharacteristic
100C2×C179#45612yes—
101C179#188611yescharacteristic, complemented, Sylow
102#1886—1791nomaximal, Sylow
103C2×C4⋊Q8—1791no—
104#519—1791no—
105#419—1791no—
106#419—1791no—
107C2×#101—1791no—
108#339—1791no—
109#339D17911yescharacteristic
110C22×Q8—1791no—
111C22×Q8—1791no—
112C2×M16—1791no—
113C2×M16C2×D17911yescharacteristic
114C4⋊Q8—3582no—
115C4⋊Q8—1794no—
116C4×Q8—3582no—
117C4×Q8—3582no—
118#117—3582no—
119#117—1791no—
120#117C2×D17911yescharacteristic
121C2×C4⋊C4—3582no—
122C2×C42C2×D17911yescharacteristic
123#103—3582no—
124#103—3582no—
125#101—3582no—
126C2×Q8—3581no—
127C2×Q8—3581no—
128C2×Q8—3581no—
129C2×Q8—3581no—
130C2×Q8—3581no—
131C2×Q8—3581no—
132C2×Q8—3581no—
133C2×Q8—3581no—
134C2×Q8—3581no—
135C2×Q8—1792no—
136C2×Q8—1792no—
137C2×Q8—1792no—
138C22×C4—21no—
139C22×C4—3581no—
140C22×C4—1792no—
141C22×C4C22×D17911yescharacteristic
142M16—21no—
143M16—21no—
144M16—3581no—
145M16—3581no—
146C2×C8—21no—
147C2×C8—3581no—
148C4⋊C4—3584no—
149C4⋊C4—3588no—
150C4⋊C4—1792no—
151C4⋊C4D71612yes—
152C22⋊C4—21no—
153C22⋊C4—3581no—
154C42—21no—
155C42—21no—
156C42—3584no—
157C42—3581no—
158C42C4×D17912yes—
159C23D4×D17911yescharacteristic
160Q8—3582no—
161Q8—3582no—
162Q8—3582no—
163Q8—3582no—
164Q8—3582no—
165Q8—3582no—
166Q8—7161no—
167Q8—7161no—
168C2×C4—24no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—3582no—
172C2×C4—3582no—
173C2×C4—3582no—
174C2×C4—3582no—
175C2×C4—1794no—
176C2×C4—7161no—
177C2×C4—7161no—
178C2×C4C2×C4×D17911yescharacteristic
179C2×C4D4×D17911yescharacteristic
180C2×C4D4×D17911yescharacteristic
181C2×C4C2×D71611yescharacteristic
182C2×C4#1566825911yescharacteristic
183C2×C4#1566826011yescharacteristic
184C8—41no—
185C8—7161no—
186C22—22no—
187C22C22⋊C4×D17911yescharacteristic
188C22#1915308311yescharacteristic
189C22#1915309811yescharacteristic
190C4—24no—
191C4—42no—
192C4—3584no—
193C4—7162no—
194C4—7162no—
195C4#1915307511yescharacteristic
196C4C4×D71611yescharacteristic
197C4#1915308611yescharacteristic
198C4#1915308811yescharacteristic
199C2—21no—
200C2—21no—
201C2#2603831711yescharacteristic
202C2#2603862312yes—
subgroupG/H
centerC22#19153083
commutatorC2×C4×C179C22×C4
FrattiniC22×C4C22×D179
Fitting#339×C179C2
socleC22×C179#120
prime radicalC23×C179C2×D4
cosocleC22×C4×C179C23
hypercenter#339D179
hypocenterC179#1886
LCSG ▷ C2×C4×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
12. #19153113C4semidirect
101. C179#1886semidirect

Maximal subgroups

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

subgroupindex
C2×#191531132
#260389162
#260384492
#260384472
C2×#191530312
#260381992
#339×C1792
#1886179