Finite Group Databasebeta

← #36353665

Subgroups — #36353665

Order 22144.

262 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 73 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
1#26011959C211yesmaximal, characteristic
2#26011473C211yesmaximal, characteristic
3#26011464C211yesmaximal, characteristic
4#26011252C211yesmaximal, characteristic, complemented
5#26011250C211yesmaximal, characteristic, complemented
6#26011247C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C173C211yesmaximal, characteristic, complemented
8C2×#14583826C2211yescharacteristic
9C2×#14583810C2211yescharacteristic
10#19149644—21no—
11#19149641—21no—
12#19149639—22no—
13#19149638C2211yescharacteristic
14#19149636C412yescomplemented
15C2×C4×Dic173C2211yescharacteristic
16C42×D173C412yescomplemented
17#19149597—21no—
18#19149595—21no—
19#19149593—22no—
20C2×M16×C173C2211yescharacteristic
21#117×C173C2211yescharacteristic
22#117×C173C2211yescharacteristic
23#14583826—21no—
24#14583826—21no—
25#14583826—21no—
26#14583826—21no—
27C2×Dic346D411yescharacteristic
28C2×D692D411yescharacteristic
29C2×C22⋊D173D412yes—
30C22×Dic173—21no—
31C2×C4×D173—22no—
32C2×C4×D173C2×C412yes—
33#14583810—21no—
34#14583810—21no—
35C2×#13063436—21no—
36C4⋊Dic173—21no—
37#14583805—22no—
38C22⋊Dic173—21no—
39#14583803—22no—
40C4×Dic173—22no—
41C4×Dic173—21no—
42C4×Dic173—21no—
43C4×Dic173C2×C411yescharacteristic
44C4×Dic173C2×C411yescharacteristic
45C22×C4×C173C2311yescharacteristic
46M16×C173—21no—
47M16×C173—21no—
48C2×C8×C173—21no—
49C4⋊C4×C173—21no—
50C4⋊C4×C173—21no—
51C22⋊C4×C173—21no—
52C22⋊C4×C173—21no—
53C42×C173—21no—
54C42×C173C2×C412yes—
55C22×D173C22⋊C412yes—
56Dic346—21no—
57Dic346—21no—
58D692—21no—
59D692—21no—
60C22⋊D173—22no—
61C22⋊D173—22no—
62C2×Dic173—21no—
63C2×Dic173—21no—
64C2×Dic173—42no—
65C2×Dic173—41no—
66C2×Dic173C22⋊C412yes—
67C4×D173—22no—
68C4×D173—22no—
69C4×D173—44no—
70#13063436—41no—
71C23×C173C2×D411yescharacteristic
72C2×C4×C173—22no—
73C2×C4×C173—41no—
74C2×C4×C173C22×C411yescharacteristic
75C2×C4×C173C2×D411yescharacteristic
76C2×C4×C173#4111yescharacteristic
77C2×C4×C173#4111yescharacteristic
78C2×C4×C173#4111yescharacteristic
79C2×C4×C173#4111yescharacteristic
80C8×C173—41no—
81C22×C173—41no—
82C22×C173C2×C22⋊C411yescharacteristic
83C22×C173#12311yescharacteristic
84C22×C173#12311yescharacteristic
85C2×D173—22no—
86C2×D173—42no—
87C4×C173—42no—
88C4×C173—81no—
89C4×C173#11711yescharacteristic
90C4×C173#11711yescharacteristic
91C4×C173#12311yescharacteristic
92C4×C173#12311yescharacteristic
93Dic173—22no—
94Dic173—22no—
95Dic173—41no—
96Dic173—81no—
97C2×C173—21no—
98C2×C173—21no—
99C2×C173—21no—
100C2×C173#38111yescharacteristic
101D173—42no—
102C173#182711yescharacteristic, complemented, Sylow
103#1827—1731nomaximal, Sylow
104C4×#41—1731no—
105#413—1731no—
106#410—1731no—
107#339—1731no—
108#339—1731no—
109H(3,ℤ/4)—1731no—
110H(3,ℤ/4)D17311yescharacteristic, complemented
111C2×#41—1731no—
112C2×M16—1731no—
113C2×M16C2×D17311yescharacteristic
114C4×Q8—3461no—
115C4×D4—3462no—
116C4×D4—3461no—
117#117—1731no—
118#117—1732no—
119#117C2×D17311yescharacteristic
120#117C2×D17311yescharacteristic
121C2×C42—1731no—
122C2×C42—1732no—
123#101—3461no—
124#100—3461no—
125#99—3462no—
126#41—3461no—
127#41—3461no—
128#41—3461no—
129#41—3461no—
130C2×Q8—1731no—
131C2×D4—1732no—
132C2×D4—1731no—
133C22×C4—3462no—
134C22×C4—3461no—
135C22×C4—1732no—
136C22×C4C22×D17311yescharacteristic
137M16—21no—
138M16—21no—
139M16—3461no—
140M16—3461no—
141C2×C8—21no—
142C2×C8—3461no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—3462no—
146C4⋊C4—3461no—
147C22⋊C4—21no—
148C22⋊C4—21no—
149C22⋊C4—3462no—
150C22⋊C4—3461no—
151C42—21no—
152C42—3462no—
153C42—3461no—
154C42—3461no—
155C42—1731no—
156C42—1731no—
157C42C4×D17312yes—
158C23—1732no—
159C23D4×D17311yescharacteristic
160Q8—3461no—
161Q8—3461no—
162D4—3462no—
163D4—3462no—
164D4—3461no—
165D4—3461no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—3461no—
169C2×C4—3462no—
170C2×C4—3462no—
171C2×C4—3461no—
172C2×C4—1732no—
173C2×C4—6924no—
174C2×C4—6922no—
175C2×C4—6921no—
176C2×C4C2×C4×D17311yescharacteristic
177C2×C4D4×D17311yescharacteristic
178C2×C4#1458382511yescharacteristic
179C2×C4#1458382611yescharacteristic
180C2×C4#1458382611yescharacteristic
181C2×C4#1458382711yescharacteristic
182C8—41no—
183C8—6921no—
184C22—41no—
185C22—3462no—
186C22—6922no—
187C22C22⋊C4×D17311yescharacteristic
188C22#1914966111yescharacteristic
189C22#1914966411yescharacteristic
190C4—42no—
191C4—81no—
192C4—3462no—
193C4—3462no—
194C4—13841no—
195C4—6921no—
196C4#1914963611yescharacteristic
197C4#1914963711yescharacteristic
198C4#1914966111yescharacteristic
199C4#1914966411yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—6922no—
204C2#2601135311yescharacteristic
subgroupG/H
centerC4#19149636
commutatorC2×C4×C173C22×C4
FrattiniC22×C4C22×D173
FittingH(3,ℤ/4)×C173C2
socleC2×C173#381
prime radicalC2×#14583826C22
cosocleC22×C4×C173C23
hypercenterH(3,ℤ/4)D173
hypocenterC173#1827
LCSG ▷ C2×C4×C173 ▷ C2×C173 ▷ C173
UCSC1 ◁ C4 ◁ #117 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. #26011252C2semidirect
5. #26011250C2semidirect
6. #26011247C2semidirect
7. H(3,ℤ/4)×C173C2semidirect
14. #19149636C4semidirect
16. C42×D173C4semidirect
102. C173#1827semidirect
110. H(3,ℤ/4)D173semidirect

Maximal subgroups

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

subgroupindex
#260119592
#260114732
#260114642
#260112522
#260112502
#260112472
H(3,ℤ/4)×C1732
#1827173