Finite Group Databasebeta

← #37509390

Subgroups — #37509390

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×#19153111C211yesmaximal, characteristic
2#26038916C211yesmaximal, characteristic
3#26038448C211yesmaximal, characteristic
4C2×#19153031C211yesmaximal, characteristic
5#26038200C211yesmaximal, characteristic
6#26038198C211yesmaximal, characteristic
7#419×C179C211yesmaximal, characteristic
8C22×Dic358C2211yescharacteristic
9C2×#15668243C2211yescharacteristic
10#19153111—22no—
11#19153111C414yescomplemented
12C4×Dic358—22no—
13#19153078—22no—
14#19153072C2211yescharacteristic
15#19153069—22no—
16C2×Dic179⋊C4—22no—
17C2×C4×Dic179C2211yescharacteristic
18#19153037—22no—
19#19153031—22no—
20C22×Q8×C179C2211yescharacteristic
21C2×M16×C179C2211yescharacteristic
22#117×C179C2211yescharacteristic
23#103×C179—22no—
24C2×Dic358—21no—
25C2×Dic358—21no—
26C2×Dic358—21no—
27C2×Dic358—21no—
28C2×Dic358C2×C412yes—
29C2×Dic358D412yes—
30C22×Dic179—21no—
31C22×Dic179D412yes—
32#15668243—21no—
33#15668243—21no—
34C2×C179⋊C8—21no—
35C4⋊Dic179D412yes—
36Dic179⋊C4—24no—
37Dic179⋊C4—28no—
38C22⋊Dic179—21no—
39C4×Dic179—24no—
40C4×Dic179—21no—
41C4×Dic179—21no—
42C4×Dic179C2×C412yes—
43C2×Q8×C179—21no—
44C2×Q8×C179—21no—
45C2×Q8×C179—21no—
46C2×Q8×C179—21no—
47C2×Q8×C179—21no—
48C2×Q8×C179C2×C412yes—
49C22×C4×C179—21no—
50C22×C4×C179C2311yescharacteristic
51M16×C179—21no—
52M16×C179—21no—
53C2×C8×C179—21no—
54C4⋊C4×C179D412yes—
55C22⋊C4×C179—21no—
56C42×C179—21no—
57Dic358—22no—
58Dic358—22no—
59Dic358—22no—
60Dic358—22no—
61C2×Dic179—24no—
62C2×Dic179—22no—
63C2×Dic179—22no—
64C2×Dic179—22no—
65C2×Dic179—22no—
66C2×Dic179C22⋊C414yes—
67C179⋊C8—41no—
68C23×C179C2×D411yescharacteristic
69Q8×C179—22no—
70Q8×C179—22no—
71Q8×C179—41no—
72Q8×C179—41no—
73C2×C4×C179—22no—
74C2×C4×C179—22no—
75C2×C4×C179—41no—
76C2×C4×C179—41no—
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—42no—
89C4×C179—42no—
90C4×C179C4×D411yescharacteristic
91C4×C179C4×D411yescharacteristic
92C4×C179#12111yescharacteristic
93C4×C179#12111yescharacteristic
94Dic179—24no—
95Dic179—24no—
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#419D17911yescharacteristic
107C2×#101—1791no—
108#339—1791no—
109#339—1791no—
110C22×Q8—1791no—
111C22×Q8C2×D17911yescharacteristic
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×C42—1791no—
123#103—22no—
124#103—3582no—
125#101—3582no—
126C2×Q8—21no—
127C2×Q8—21no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—3581no—
132C2×Q8—3581no—
133C2×Q8—3581no—
134C2×Q8—3581no—
135C2×Q8—1792no—
136C2×Q8—1792no—
137C2×Q8C4×D17912yes—
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⋊C4C22⋊D17912yes—
152C22⋊C4—21no—
153C22⋊C4—3581no—
154C42—21no—
155C42—3584no—
156C42—3581no—
157C42—3581no—
158C42—1792no—
159C23D4×D17911yescharacteristic
160Q8—22no—
161Q8—22no—
162Q8—41no—
163Q8—41no—
164Q8—3582no—
165Q8—3582no—
166Q8—3582no—
167Q8—3582no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—3584no—
173C2×C4—3582no—
174C2×C4—3582no—
175C2×C4—3582no—
176C2×C4—3582no—
177C2×C4—1794no—
178C2×C4C2×C4×D17911yescharacteristic
179C2×C4D4×D17911yescharacteristic
180C2×C4D4×D17911yescharacteristic
181C2×C4C2×C22⋊D17911yescharacteristic
182C2×C4#1566825811yescharacteristic
183C2×C4#1566825911yescharacteristic
184C8—41no—
185C8—7161no—
186C22—22no—
187C22C22⋊C4×D17911yescharacteristic
188C22#1915308111yescharacteristic
189C22#1915309511yescharacteristic
190C4—42no—
191C4—42no—
192C4—3584no—
193C4—3584no—
194C4—7162no—
195C4(C22⋊D179)⋊C411yescharacteristic
196C4C4×C22⋊D17911yescharacteristic
197C4#1915308411yescharacteristic
198C4#1915308611yescharacteristic
199C2—21no—
200C2—21no—
201C2#2603831511yescharacteristic
202C2#2603862012yes—
subgroupG/H
centerC22#19153081
commutatorC2×C4×C179C22×C4
FrattiniC22×C4C22×D179
Fitting#419×C179C2
socleC22×C179#120
prime radicalC23×C179C2×D4
cosocleC22×C4×C179C23
hypercenter#419D179
hypocenterC179#1886
LCSG ▷ C2×C4×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
11. #19153111C4semidirect
101. C179#1886semidirect

Maximal subgroups

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

subgroupindex
C2×#191531112
#260389162
#260384482
C2×#191530312
#260382002
#260381982
#419×C1792
#1886179