Finite Group Databasebeta

← #37510540

Subgroups — #37510540

Order 22912.

254 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 87 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×#19153044C211yesmaximal, characteristic
2C2×#19153038C211yesmaximal, characteristic
3C2×#19153036C211yesmaximal, characteristic
4#26038344C211yesmaximal, characteristic
5#26038308C211yesmaximal, characteristic
6#26038193C211yesmaximal, characteristic
7C2×#106×C179C211yesmaximal, characteristic
8C22×Dic358C2211yescharacteristic
9C22×C179⋊C8C2211yescharacteristic
10C2×C4⋊Dic179C2211yescharacteristic
11C2×Dic179⋊C4—22no—
12C2×C4×Dic179C2211yescharacteristic
13#19153044—22no—
14#19153038—22no—
15#19153036—22no—
16C179⋊#95—22no—
17C22×C8×C179C2211yescharacteristic
18C2×C4⋊C4×C179C2211yescharacteristic
19C2×C4⋊C4×C179C2211yescharacteristic
20#106×C179—22no—
21C2×Dic358—21no—
22C2×Dic358—21no—
23C2×Dic358—21no—
24C2×Dic358—21no—
25C2×Dic358—21no—
26C2×Dic358Q812yes—
27C22×Dic179—21no—
28C22×Dic179—21no—
29C22×Dic179D412yes—
30C2×C179⋊C8—21no—
31C2×C179⋊C8—21no—
32C2×C179⋊C8D412yes—
33C4⋊Dic179—21no—
34C4⋊Dic179—21no—
35Dic179⋊C4—44no—
36C4×Dic179—21no—
37C4×Dic179—21no—
38C22×C4×C179—21no—
39C22×C4×C179—21no—
40C22×C4×C179C2311yescharacteristic
41C2×C8×C179—21no—
42C2×C8×C179—21no—
43C2×C8×C179D412yes—
44C4⋊C4×C179—21no—
45C4⋊C4×C179—21no—
46C4⋊C4×C179—21no—
47C4⋊C4×C179—21no—
48Dic358—22no—
49Dic358—22no—
50Dic358—41no—
51Dic358—41no—
52C2×Dic179—22no—
53C2×Dic179—22no—
54C2×Dic179—22no—
55C2×Dic179—41no—
56C2×Dic179—41no—
57C2×Dic179—41no—
58C2×Dic179—42no—
59C2×Dic179SD1614yes—
60C179⋊C8—22no—
61C23×C179C2×D411yescharacteristic
62C2×C4×C179—41no—
63C2×C4×C179—41no—
64C2×C4×C179—42no—
65C2×C4×C179—42no—
66C2×C4×C179C2×D411yescharacteristic
67C2×C4×C179C2×D411yescharacteristic
68C2×C4×C179C2×Q811yescharacteristic
69C2×C4×C179#4111yescharacteristic
70C2×C4×C179#4111yescharacteristic
71C2×C4×C179#4111yescharacteristic
72C8×C179—22no—
73C22×C179C22⋊Q811yescharacteristic
74C22×C179#12311yescharacteristic
75C22×C179#12711yescharacteristic
76C22×C179C2×SD1612yes—
77C22×C179#13712yes—
78C4×C179—81no—
79C4×C179—81no—
80C4×C179C22⋊Q811yescharacteristic
81C4×C179C22⋊Q811yescharacteristic
82C4×C179#12311yescharacteristic
83C4×C179#12311yescharacteristic
84Dic179—24no—
85Dic179—42no—
86Dic179—81no—
87C2×C179#39911yescharacteristic
88C2×C179#47512yes—
89C2×C179#48312yes—
90C2×C179#49211yescharacteristic
91C2×C179#49711yescharacteristic
92C179#209611yescharacteristic, complemented, Sylow
93#2096—1791nomaximal, Sylow
94C2×#106—1791no—
95C2×#106D17911yescharacteristic
96C2×#103—1791no—
97C2×#103—1791no—
98#391—1791no—
99#384—1791no—
100#336—1791no—
101C22×Q8—1791no—
102C22×C8—1791no—
103C22×C8C2×D17911yescharacteristic
104C2×C4⋊C4—3582no—
105C2×C4⋊C4—1791no—
106C2×C4⋊C4C2×D17911yescharacteristic
107C2×C4⋊C4C2×D17911yescharacteristic
108C2×C42—1791no—
109#106—22no—
110#106—3582no—
111#103—3582no—
112#103—3582no—
113#95—3582no—
114C2×Q8—3581no—
115C2×Q8—3581no—
116C2×Q8—3581no—
117C2×Q8—3581no—
118C2×Q8—3581no—
119C2×Q8—1792no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—3581no—
123C22×C4—3581no—
124C22×C4—1792no—
125C22×C4C22×D17911yescharacteristic
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—3581no—
129C2×C8—3581no—
130C2×C8—1792no—
131C2×C8C22⋊D17912yes—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—3581no—
137C4⋊C4—3581no—
138C4⋊C4—7164no—
139C42—3581no—
140C42—3581no—
141C23D4×D17911yescharacteristic
142Q8—3582no—
143Q8—3582no—
144Q8—7161no—
145Q8—7161no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—42no—
149C2×C4—42no—
150C2×C4—3582no—
151C2×C4—3582no—
152C2×C4—3582no—
153C2×C4—1794no—
154C2×C4—7161no—
155C2×C4—7162no—
156C2×C4—7161no—
157C2×C4—7161no—
158C2×C4D4×D17911yescharacteristic
159C2×C4C2×C22⋊D17911yescharacteristic
160C2×C4Q8×D17911yescharacteristic
161C2×C4#1566825911yescharacteristic
162C2×C4#1566825911yescharacteristic
163C2×C4#1566826011yescharacteristic
164C8—22no—
165C8—3582no—
166C22#1915309111yescharacteristic
167C22#1915309811yescharacteristic
168C22#1915310911yescharacteristic
169C22SD16×D17912yes—
170C22#1915314212yes—
171C4—81no—
172C4—81no—
173C4—3584no—
174C4—14321no—
175C4—7162no—
176C4#1915308911yescharacteristic
177C4#1915309111yescharacteristic
178C4#1915309611yescharacteristic
179C4#1915309811yescharacteristic
180C2#2603837411yescharacteristic
181C2#2603872312yes—
182C2#2603877112yes—
183C2#2603881011yescharacteristic
184C2#2603883011yescharacteristic
subgroupG/H
centerC23D4×D179
commutator, cosocleC22×C4×C179C23
FrattiniC22×C4C22×D179
FittingC2×#106×C179C2
socle, prime radicalC23×C179C2×D4
hypercenterC2×#106D179
hypocenterC179#2096
LCSG ▷ C22×C4×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
92. C179#2096semidirect

Maximal subgroups

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

subgroupindex
C2×#191530442
C2×#191530382
C2×#191530362
#260383442
#260383082
#260381932
C2×#106×C1792
#2096179