Finite Group Databasebeta

← #36352665

Subgroups — #36352665

Order 22144.

250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×Dic346C211yesmaximal, characteristic, complemented
2#26011837C211yesmaximal, characteristic, complemented
3#26011688C211yesmaximal, characteristic, complemented
4#26011236C211yesmaximal, characteristic, complemented
5#26011221C211yesmaximal, characteristic, complemented
6D4⋊#13063436C211yesmaximal, characteristic, complemented
7#459×C173C211yesmaximal, characteristic
8C22×Dic346—21no—
9C2×#14583814—21no—
10#19149679C2211yescharacteristic
11#19149678—21no—
12#19149658—21no—
13#19149656—22no—
14C4×Dic346C2211yescharacteristic
15D4×Dic173—21no—
16C4⋊#13063436C2211yescharacteristic
17#19149600—21no—
18#19149600—22no—
19C4×#13063436C2211yescharacteristic
20C2×D8×C173—21no—
21#127×C173C2211yescharacteristic
22C4×D4×C173C2211yescharacteristic
23C4⋊C8×C173C2211yescharacteristic
24#102×C173—21no—
25C2×Dic346—22no—
26C2×Dic346—21no—
27C2×Dic346—42no—
28C2×Dic346—42no—
29C2×Dic346D411yescharacteristic
30C22×Dic173—22no—
31#14583814—42no—
32C2×#13063436—21no—
33C2×#13063436—21no—
34C4⋊Dic173—21no—
35C4⋊Dic173D411yescharacteristic
36C4⋊Dic173D412yes—
37#14583805—22no—
38#14583805—21no—
39C22⋊Dic173—22no—
40C4×Dic173—21no—
41C2×D4×C173—21no—
42C2×D4×C173—21no—
43C2×D4×C173—21no—
44C2×D4×C173D411yescharacteristic
45C22×C4×C173—21no—
46D8×C173—42no—
47C2×C8×C173—21no—
48C4⋊C4×C173D411yescharacteristic
49C22⋊C4×C173—21no—
50C42×C173C2311yescharacteristic
51Dic346—21no—
52Dic346—44no—
53Dic346—41no—
54Dic346—41no—
55Dic346D812yescomplemented
56C2×Dic173—21no—
57C2×Dic173—22no—
58C2×Dic173—21no—
59C2×Dic173—44no—
60#13063436—41no—
61#13063436—41no—
62C23×C173—21no—
63C23×C173—41no—
64D4×C173—21no—
65D4×C173—42no—
66D4×C173—41no—
67D4×C173—41no—
68D4×C173—41no—
69D4×C173—41no—
70D4×C173SD1612yescomplemented
71C2×C4×C173—21no—
72C2×C4×C173—41no—
73C2×C4×C173—41no—
74C2×C4×C173C2×D411yescharacteristic
75C2×C4×C173C2×D411yescharacteristic
76C2×C4×C173C2×D411yescharacteristic
77C8×C173—41no—
78C22×C173—22no—
79C22×C173—41no—
80C22×C173—41no—
81C22×C173—81no—
82C22×C173—81no—
83C22×C173—81no—
84C22×C173#12011yescharacteristic
85C4×C173—21no—
86C4×C173—41no—
87C4×C173C2×D811yescharacteristic
88C4×C173C2×SD1611yescharacteristic
89C4×C173AGL(1,ℤ/8)11yescharacteristic
90C4×C173#13711yescharacteristic
91Dic173—22no—
92Dic173—42no—
93Dic173—41no—
94C2×C173—42no—
95C2×C173—161no—
96C2×C173#44711yescharacteristic
97C2×C173#44811yescharacteristic
98C2×C173#45411yescharacteristic
99C173#162711yescharacteristic, complemented, Sylow
100#1627—1731nomaximal, Sylow
101D4×Q8—1731no—
102#486—1731no—
103#460—1731no—
104#459D17311yescharacteristic
105#332—1731no—
106Q8⋊C8—1731no—
107D4⋊C8—1731no—
108C22×Q8—3461no—
109C2×SD16—3461no—
110C2×D8—21no—
111C4⋊Q8—3461no—
112C4⋊Q8—1731no—
113#127C2×D17311yescharacteristic
114C22⋊Q8—3462no—
115C22⋊Q8—3461no—
116C4×Q8—1731no—
117C4×D4—3461no—
118C4×D4C2×D17311yescharacteristic
119C4⋊C8—1731no—
120C4⋊C8C2×D17311yescharacteristic
121#102—21no—
122#102—3461no—
123#102—3462no—
124C4×C8—1731no—
125C2×Q8—3462no—
126C2×Q8—3461no—
127C2×Q8—1731no—
128C2×Q8—6922no—
129C2×Q8—6922no—
130C2×D4—21no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4C22⋊D17311yescharacteristic
134C22×C4—21no—
135C22×C4—3462no—
136SD16—6922no—
137D8—42no—
138C2×C8—21no—
139C2×C8—3461no—
140C2×C8—3461no—
141C4⋊C4—3462no—
142C4⋊C4—3461no—
143C4⋊C4—3461no—
144C4⋊C4—1731no—
145C4⋊C4—1732no—
146C4⋊C4C22⋊D17311yescharacteristic
147C22⋊C4—21no—
148C22⋊C4—3462no—
149C42—3461no—
150C42C22×D17311yescharacteristic
151C23—21no—
152C23—41no—
153Q8—3461no—
154Q8—1732no—
155Q8—6924no—
156Q8—6921no—
157Q8—6921no—
158D4—21no—
159D4—42no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—41no—
164D4#1458381412yescomplemented
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—3461no—
169C2×C4—3461no—
170C2×C4—3462no—
171C2×C4—6924no—
172C2×C4D4×D17311yescharacteristic
173C2×C4D4×D17311yescharacteristic
174C2×C4C2×C22⋊D17311yescharacteristic
175C8—41no—
176C8—6921no—
177C8—6921no—
178C22—22no—
179C22—41no—
180C22—41no—
181C22—81no—
182C22—81no—
183C22—81no—
184C22#1914964711yescharacteristic
185C4—21no—
186C4—41no—
187C4—3462no—
188C4—6921no—
189C4—6922no—
190C4D8×D17311yescharacteristic
191C4C2×#1458381411yescharacteristic
192C4#1914970311yescharacteristic
193C4#1914970911yescharacteristic
194C2—42no—
195C2—161no—
196C2#2601162311yescharacteristic
197C2#2601162911yescharacteristic
198C2#2601166211yescharacteristic
subgroupG/H
centerC22#19149647
commutator, cosocleC42×C173C23
FrattiniC42C22×D173
Fitting, prime radical#459×C173C2
socleC22×C173#120
hypercenter#459D173
hypocenterC173#1627
LCSG ▷ C42×C173 ▷ C22×C173 ▷ C173
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. D4×Dic346C2semidirect
2. #26011837C2semidirect
3. #26011688C2semidirect
4. #26011236C2semidirect
5. #26011221C2semidirect
6. D4⋊#13063436C2semidirect
55. Dic346D8semidirect
70. D4×C173SD16semidirect
99. C173#1627semidirect
164. D4#14583814semidirect

Maximal subgroups

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

subgroupindex
D4×Dic3462
#260118372
#260116882
#260112362
#260112212
D4⋊#130634362
#459×C1732
#1627173