Finite Group Databasebeta

← #36361938

Subgroups — #36361938

Order 22144.

504 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 177 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×#19149678C211yesmaximal, characteristic
2C2×#19149677C211yesmaximal, characteristic
3#26011398C211yesmaximal, characteristic
4#26011397C211yesmaximal, characteristic
5#26011396C211yesmaximal, characteristic
6#26011395C214yesmaximal
7#26011355C214yesmaximal
8C42×Dic173C211yesmaximal, characteristic
9#391×C173C211yesmaximal, characteristic
10C22×Dic346C2212yes—
11C22×Dic346C2211yescharacteristic
12#19149678—24no—
13#19149677—24no—
14C2×C4⋊Dic173C2211yescharacteristic
15C2×#14583805C2212yes—
16C2×#14583805C2212yes—
17C2×#14583805C2212yes—
18C2×C4×Dic173C2212yes—
19C2×C4×Dic173C2211yescharacteristic
20C2×C4×Dic173C2211yescharacteristic
21C2×C4×Dic173C2212yes—
22#19149586C2214yes—
23#19149586C2214yes—
24#19149586C2214yes—
25C22×Q8×C173C2211yescharacteristic
26C2×C4⋊C4×C173C2211yescharacteristic
27C2×C42×C173C2211yescharacteristic
28#95×C173C2214yes—
29C2×Dic346—24no—
30C2×Dic346—28no—
31C2×Dic346—22no—
32C2×Dic346—22no—
33C2×Dic346—22no—
34C22×Dic173C2312yes—
35C22×Dic173C2312yes—
36C22×Dic173C2312yes—
37C22×Dic173C2311yescharacteristic
38C22×Dic173C2311yescharacteristic
39C4⋊Dic173—22no—
40#14583805—24no—
41#14583805—24no—
42#14583805—24no—
43C4×Dic173—24no—
44C4×Dic173—22no—
45C4×Dic173D414yes—
46C4×Dic173Q818yescomplemented
47C2×Q8×C173—22no—
48C2×Q8×C173—22no—
49C2×Q8×C173—22no—
50C22×C4×C173C2312yes—
51C22×C4×C173C2312yes—
52C22×C4×C173C2312yes—
53C22×C4×C173C2311yescharacteristic
54C4⋊C4×C173—22no—
55C42×C173—22no—
56Dic346—44no—
57Dic346—48no—
58C2×Dic173—22no—
59C2×Dic173—22no—
60C2×Dic173—22no—
61C2×Dic173—22no—
62C2×Dic173—24no—
63C2×Dic173—22no—
64C2×Dic173—22no—
65C2×Dic173C2×D412yes—
66C2×Dic173C2×D412yes—
67C2×Dic173C2×Q814yes—
68C2×Dic173C2×Q814yes—
69C2×Dic173#4114yes—
70C23×C173C2411yescharacteristic
71Q8×C173—44no—
72C2×C4×C173—22no—
73C2×C4×C173—22no—
74C2×C4×C173—22no—
75C2×C4×C173—22no—
76C2×C4×C173—24no—
77C2×C4×C173—22no—
78C2×C4×C173—22no—
79C2×C4×C173C2×D412yes—
80C2×C4×C173C2×Q814yes—
81C2×C4×C173#4112yes—
82C2×C4×C173#4112yes—
83C22×C173C22×D411yescharacteristic
84C22×C173C22×Q812yes—
85C22×C173C2×#4112yes—
86C22×C173C2×#4111yescharacteristic
87C22×C173C2×#4111yescharacteristic
88C4×C173—24no—
89C4×C173—42no—
90C4×C173—42no—
91C4×C173#12414yes—
92Dic173—24no—
93Dic173—42no—
94Dic173—42no—
95Dic173#12414yes—
96Dic173C4⋊Q814yes—
97C2×C173C2×#12411yescharacteristic
98C2×C173C2×#12411yescharacteristic
99C2×C173C2×C4⋊Q811yescharacteristic
100C2×C173#53312yes—
101C2×C173#53312yes—
102C173#286211yescharacteristic, complemented, Sylow
103#2862—1731nomaximal, Sylow
104C2×C4⋊Q8—1731no—
105C2×C4⋊Q8—1731no—
106#391—1731no—
107#391—1731no—
108#391—1731no—
109#391—1734no—
110#391D17311yescharacteristic
111#382—1734no—
112C43—1731no—
113C22×Q8—1731no—
114C22×Q8—1732no—
115C22×Q8C2×D17311yescharacteristic
116C4⋊Q8—3464no—
117C4⋊Q8—3464no—
118C2×C4⋊C4—1732no—
119C2×C4⋊C4—1732no—
120C2×C4⋊C4—1732no—
121C2×C4⋊C4—1731no—
122C2×C4⋊C4C2×D17311yescharacteristic
123C2×C42—1732no—
124C2×C42—1731no—
125C2×C42—1731no—
126C2×C42—1732no—
127C2×C42C2×D17311yescharacteristic
128#95—1734no—
129#95—1734no—
130#95—1734no—
131#95C2×D17314yes—
132C2×Q8—22no—
133C2×Q8—22no—
134C2×Q8—22no—
135C2×Q8—3464no—
136C2×Q8—3468no—
137C2×Q8—3462no—
138C2×Q8—3462no—
139C2×Q8—3462no—
140C22×C4—1732no—
141C22×C4—1732no—
142C22×C4—1732no—
143C22×C4—1731no—
144C22×C4—1731no—
145C22×C4C22×D17312yes—
146C22×C4C22×D17312yes—
147C22×C4C22×D17312yes—
148C22×C4C22×D17311yescharacteristic
149C4⋊C4—22no—
150C4⋊C4—3464no—
151C4⋊C4—3464no—
152C4⋊C4—3464no—
153C4⋊C4—3462no—
154C42—22no—
155C42—3464no—
156C42—3462no—
157C42—1734no—
158C42—1738no—
159C23C23×D17311yescharacteristic
160Q8—44no—
161Q8—6928no—
162Q8—6924no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—24no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—3462no—
171C2×C4—3462no—
172C2×C4—3462no—
173C2×C4—3462no—
174C2×C4—3464no—
175C2×C4—3462no—
176C2×C4—3462no—
177C2×C4—1734no—
178C2×C4—1732no—
179C2×C4—1732no—
180C2×C4—1734no—
181C2×C4—1734no—
182C2×C4D4×D17312yes—
183C2×C4Q8×D17314yes—
184C2×C4#1458382512yes—
185C2×C4#1458382612yes—
186C22C2×D4×D17311yescharacteristic
187C22C2×Q8×D17312yes—
188C22#41×D17312yes—
189C22C2×#1458382511yescharacteristic
190C22C2×#1458382611yescharacteristic
191C4—24no—
192C4—42no—
193C4—42no—
194C4—3464no—
195C4—1734no—
196C4—1734no—
197C4—6922no—
198C4—6922no—
199C4#1914966514yes—
200C2#124×D17311yescharacteristic
201C2C2×#1914966511yescharacteristic
202C2C4⋊Q8×D17311yescharacteristic
203C2#2601204312yes—
204C2#2601204512yes—
subgroupG/H
center, FrattiniC23C23×D173
commutator, socle, prime radical, cosocleC23×C173C24
Fitting#391×C173C2
hypercenter#391D173
hypocenterC173#2862
LCSG ▷ C23×C173 ▷ C173
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
46. C4×Dic173Q8semidirect
102. C173#2862semidirect

Maximal subgroups

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

subgroupindex
C2×#191496782
C2×#191496772
#260113982
#260113972
#260113962
#260113952
#260113552
C42×Dic1732
#391×C1732
#2862173