Finite Group Databasebeta

← C2×#26011840 #36363872

Subgroups — C2×#26011840 #36363872

Order 22144.

424 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 157 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#26011840C218yesmaximal, direct product factor
4C2×#19149604C211yesmaximal, characteristic
5C2×#19149603C211yesmaximal, characteristic
6C2×#19149602C211yesmaximal, characteristic
7C2×C8×Dic173C211yesmaximal, characteristic
8C2×#103×C173C211yesmaximal, characteristic
9C22×Dic346—21no—
10C22×Dic346C2211yescharacteristic
11C22×#13063436C2211yescharacteristic
12#19149678—22no—
13#19149678C2214yes—
14#19149677—22no—
15#19149677C2214yes—
16C2×C4⋊Dic173C2211yescharacteristic
17C2×#14583805—21no—
18C2×#14583805—21no—
19C2×#14583805—21no—
20C2×C4×Dic173C2211yescharacteristic
21#19149604C2214yes—
22#19149603C2214yes—
23#19149602C2214yes—
24C8×Dic173C2214yes—
25C22×Q8×C173C2211yescharacteristic
26C22×C8×C173C2211yescharacteristic
27C2×C4⋊C4×C173C2211yescharacteristic
28#103×C173C2214yes—
29C2×Dic346—24no—
30C2×Dic346—21no—
31C2×Dic346—22no—
32C2×Dic346—22no—
33C2×Dic346—44no—
34C2×Dic346C2312yes—
35C22×Dic173—21no—
36C22×Dic173—21no—
37C22×Dic173D411yescharacteristic
38C22×Dic173D411yescharacteristic
39C2×#13063436—22no—
40C2×#13063436C2312yes—
41C4⋊Dic173—21no—
42C4⋊Dic173C2312yes—
43#14583805—24no—
44#14583805—24no—
45#14583805—24no—
46C4×Dic173D412yes—
47C4×Dic173C2312yes—
48C2×Q8×C173—21no—
49C2×Q8×C173—22no—
50C2×Q8×C173—22no—
51C2×Q8×C173C2312yes—
52C22×C4×C173—21no—
53C22×C4×C173—21no—
54C22×C4×C173C2311yescharacteristic
55C2×C8×C173—22no—
56C2×C8×C173C2312yes—
57C4⋊C4×C173—21no—
58C4⋊C4×C173C2312yes—
59Dic346—22no—
60Dic346—22no—
61Dic346—42no—
62Dic346—48no—
63C2×Dic173—22no—
64C2×Dic173—22no—
65C2×Dic173—42no—
66C2×Dic173—42no—
67C2×Dic173SD1614yes—
68C2×Dic173Q1614yes—
69C2×Dic173C2×D412yes—
70C2×Dic173C2×D412yes—
71#13063436—22no—
72C23×C173C2×D411yescharacteristic
73Q8×C173—22no—
74Q8×C173—22no—
75Q8×C173—42no—
76C2×C4×C173—22no—
77C2×C4×C173—22no—
78C2×C4×C173—42no—
79C2×C4×C173—42no—
80C2×C4×C173C2×D411yescharacteristic
81C2×C4×C173#4112yes—
82C2×C4×C173#4112yes—
83C2×C4×C173C2411yescharacteristic
84C8×C173—22no—
85C22×C173#12412yes—
86C22×C173C2×SD1612yes—
87C22×C173C2×Q1612yes—
88C22×C173C22×D411yescharacteristic
89C4×C173—42no—
90C4×C173—42no—
91C4×C173#12412yes—
92C4×C173C2×#4111yescharacteristic
93C4×C173C2×#4111yescharacteristic
94Dic173—42no—
95Dic173—42no—
96Dic173C2×SD1614yes—
97Dic173C2×Q1614yes—
98C2×C173#48714yescomplemented
99C2×C173C2×#12411yescharacteristic
100C2×C173C22×SD1611yescharacteristic
101C2×C173C22×Q1611yescharacteristic
102C173C2×#48711yescharacteristic, complemented, Sylow
103C2×#487—1731nomaximal, Sylow
104C2×C4⋊Q8—1731no—
105C2×C4⋊Q8—1731no—
106#487—1738no—
107C2×#103—1731no—
108C2×#103—1731no—
109C2×#103—1731no—
110C2×#103D17311yescharacteristic
111C2×C4×C8—1731no—
112C22×Q8—3461no—
113C22×Q8—1731no—
114C22×Q8C2×D17311yescharacteristic
115C22×C8—1731no—
116C22×C8C2×D17311yescharacteristic
117C4⋊Q8—3462no—
118C4⋊Q8—3462no—
119C4⋊Q8—1734no—
120C4⋊Q8—1734no—
121C2×C4⋊C4—3461no—
122C2×C4⋊C4—3461no—
123C2×C4⋊C4—3461no—
124C2×C4⋊C4—1731no—
125C2×C4⋊C4C2×D17311yescharacteristic
126C2×C42—1731no—
127#103—1734no—
128#103—1734no—
129#103—1734no—
130#103C2×D17314yes—
131C4×C8—1734no—
132C2×Q8—21no—
133C2×Q8—22no—
134C2×Q8—22no—
135C2×Q8—3464no—
136C2×Q8—3461no—
137C2×Q8—3462no—
138C2×Q8—3462no—
139C2×Q8—1732no—
140C2×Q8—6924no—
141C2×Q8C22×D17312yes—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—3461no—
145C22×C4—3461no—
146C22×C4—1731no—
147C22×C4—1731no—
148C22×C4C22×D17311yescharacteristic
149C2×C8—22no—
150C2×C8—3462no—
151C2×C8—1732no—
152C2×C8C22×D17312yes—
153C4⋊C4—21no—
154C4⋊C4—3464no—
155C4⋊C4—3464no—
156C4⋊C4—3464no—
157C4⋊C4—3461no—
158C4⋊C4—1732no—
159C4⋊C4C22×D17312yes—
160C42—1732no—
161C42—1732no—
162C23D4×D17311yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—42no—
166Q8—3462no—
167Q8—3462no—
168Q8—6928no—
169Q8—6922no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—3462no—
175C2×C4—3462no—
176C2×C4—1734no—
177C2×C4—1734no—
178C2×C4—1732no—
179C2×C4—1732no—
180C2×C4—6922no—
181C2×C4—6922no—
182C2×C4D4×D17311yescharacteristic
183C2×C4#1458382512yes—
184C2×C4#1458382612yes—
185C2×C4C23×D17311yescharacteristic
186C8—22no—
187C8—3462no—
188C22#1914966512yes—
189C22SD16×D17312yes—
190C22Q16×D17312yes—
191C22C2×D4×D17311yescharacteristic
192C4—42no—
193C4—42no—
194C4—1734no—
195C4—1734no—
196C4—6922no—
197C4—6922no—
198C4#1914966512yes—
199C4C2×#1458382511yescharacteristic
200C4C2×#1458382611yescharacteristic
201C2#2601184014yesdirect product factor
202C2C2×#1914966511yescharacteristic
203C2C2×SD16×D17311yescharacteristic
204C2C2×Q16×D17311yescharacteristic
subgroupG/H
centerC23D4×D173
commutator, cosocleC2×C4×C173C24
FrattiniC2×C4C23×D173
FittingC2×#103×C173C2
socle, prime radicalC23×C173C2×D4
hypercenterC2×#103D173
hypocenterC173C2×#487
LCSG ▷ C2×C4×C173 ▷ C2×C173 ▷ C173
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. #26011840C2direct (N × H)
98. C2×C173#487semidirect
102. C173C2×#487semidirect
201. C2#26011840direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191496782
C2×#191496772
#260118402
C2×#191496042
C2×#191496032
C2×#191496022
C2×C8×Dic1732
C2×#103×C1732
C2×#487173