Finite Group Databasebeta

← #22625442

Subgroups — #22625442

Order 9344.

260 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 68 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#17989592C211yesmaximal, characteristic, complemented
2#17989588C211yesmaximal, characteristic, complemented
3#17989446C212yesmaximal, complemented
4#17989445C212yesmaximal, complemented
5#17989134C211yesmaximal, characteristic
6C2×#11924038—21no—
7C2×#11924036—21no—
8#14556658—21no—
9#14556658C2212yes—
10#14556658C2212yes—
11C4⋊#10596833—21no—
12C2×#11924028—21no—
13#14556590C2211yescharacteristic
14#14556587C2211yescharacteristic
15#14556577—21no—
16#14556566C411yescharacteristic
17#14556564—21no—
18#14556562C411yescharacteristic
19C4×D292C411yescharacteristic
20C4×C22⋊D73—21no—
21C42×D73C2211yescharacteristic
22C4×D4×C73C411yescharacteristic
23#11924038—42no—
24#11924036—42no—
25C2×#10596833—22no—
26C2×#10596833—22no—
27#11924028—42no—
28#11924028—42no—
29C2×Dic146—21no—
30C2×D292—21no—
31C2×D292C2×C411yescharacteristic
32C2×C22⋊D73—21no—
33C2×C22⋊D73—21no—
34C2×C22⋊D73—21no—
35C2×C4×D73—21no—
36C2×C4×D73C2×C411yescharacteristic
37C2×C4×D73D411yescharacteristic
38C2×C4×D73D411yescharacteristic
39C4⋊Dic73C2×C411yescharacteristic
40#11924007—21no—
41C22⋊Dic73—21no—
42#11924005—21no—
43#11924005—21no—
44C4×Dic73D411yescharacteristic
45C4×Dic73D411yescharacteristic
46C4×Dic73C2311yescharacteristic
47C2×D4×C73C2×C411yescharacteristic
48C22×C4×C73—21no—
49C4⋊C4×C73C2×C411yescharacteristic
50C22⋊C4×C73—21no—
51C42×C73C2×C411yescharacteristic
52C23×C73—21no—
53C22×D73—21no—
54C22×D73C22⋊C411yescharacteristic
55D4×C73—41no—
56C2×C4×C73—21no—
57C2×C4×C73—42no—
58C2×C4×C73C22⋊C411yescharacteristic
59C2×C4×C73C22⋊C411yescharacteristic
60C2×C4×C73C22×C411yescharacteristic
61C22⋊D73—42no—
62C22⋊D73—41no—
63C22⋊D73—41no—
64C22⋊D73—41no—
65C22⋊D73—41no—
66C2×Dic73—21no—
67C2×Dic73C22⋊C411yescharacteristic
68C2×Dic73C2×D411yescharacteristic
69C2×Dic73C2×D411yescharacteristic
70D292—41no—
71D292—42no—
72C4×D73—21no—
73C4×D73—21no—
74C4×D73—41no—
75C4×D73—42no—
76C4×D73D812yes—
77C4×D73SD1612yes—
78Dic146—41no—
79Dic146—41no—
80#10596833—42no—
81#10596833—42no—
82C22×C73—41no—
83C22×C73—41no—
84C22×C73—41no—
85C22×C73C2×C22⋊C411yescharacteristic
86C2×D73—21no—
87C2×D73—21no—
88C2×D73—41no—
89C2×D73—41no—
90C2×D73—41no—
91C2×D73#10212yes—
92C4×C73—21no—
93C4×C73—21no—
94C4×C73—41no—
95C4×C73#10212yes—
96Dic73—21no—
97Dic73—41no—
98Dic73C2×D811yescharacteristic
99Dic73C2×SD1611yescharacteristic
100Dic73AGL(1,ℤ/8)11yescharacteristic
101Dic73#13711yescharacteristic
102C2×C73—81no—
103C2×C73#41311yescharacteristic
104C2×C73C2×#10211yescharacteristic
105C2×C73#41711yescharacteristic
106D73—22no—
107D73—81no—
108#1547—731nomaximal, Sylow
109C73#154711yescharacteristic, complemented, Sylow
110#532—731no—
111#423—731no—
112C2×C4⋊C8—731no—
113#332—732no—
114#331—732no—
115C2×#41—1461no—
116C2×M16—1461no—
117C22×C8—1461no—
118C4⋊Q8—731no—
119#127—731no—
120#124—1461no—
121#121—731no—
122#121—731no—
123#121—1461no—
124C4×D4—731no—
125C4×D4—1461no—
126C4×D4#6440811yescharacteristic
127C2×C42—731no—
128C4⋊C8—732no—
129C4⋊C8—732no—
130C4⋊C8—1461no—
131C4⋊C8—1461no—
132#41—2922no—
133#41—2922no—
134C2×Q8—1461no—
135C2×D4—731no—
136C2×D4—1461no—
137C2×D4—1461no—
138C2×D4—1461no—
139C2×D4—1461no—
140C2×D4C2×#6440811yescharacteristic
141C22×C4—21no—
142C22×C4—731no—
143C22×C4—731no—
144C22×C4—731no—
145C22×C4—1461no—
146M16—2922no—
147C2×C8—2922no—
148C2×C8—1462no—
149C2×C8—1462no—
150C4⋊C4—731no—
151C4⋊C4—1461no—
152C4⋊C4C2×#6440811yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—1461no—
155C22⋊C4—1461no—
156C22⋊C4—1461no—
157C42—731no—
158C42—731no—
159C42—731no—
160C42C2×#6440811yescharacteristic
161C23—21no—
162C23—731no—
163C23—1461no—
164Q8—2921no—
165Q8—2921no—
166D4—41no—
167D4—2921no—
168D4—2922no—
169D4—2922no—
170D4—2921no—
171D4—2921no—
172D4—2921no—
173D4—2921no—
174C2×C4—21no—
175C2×C4—42no—
176C2×C4—2921no—
177C2×C4—2922no—
178C2×C4—731no—
179C2×C4—731no—
180C2×C4—732no—
181C2×C4—732no—
182C2×C4—731no—
183C2×C4—1461no—
184C2×C4—1461no—
185C2×C4—1461no—
186C2×C4C22⋊#6440811yescharacteristic
187C2×C4C22⋊#6440811yescharacteristic
188C2×C4C22×#6440811yescharacteristic
189C8—2922no—
190C8—2922no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—2921no—
195C22—2921no—
196C22—2921no—
197C22—732no—
198C22—1461no—
199C22—1461no—
200C22C2×C22⋊#6440811yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—2921no—
205C4—731no—
206C4—731no—
207C4—731no—
208C4—731no—
209C4—1461no—
210C4#1455665312yes—
211C2—81no—
212C2—5841no—
213C2—1462no—
214C2#1798957311yescharacteristic
215C2C2×#1455665311yescharacteristic
216C2#1798957811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC4×D4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC4×D4#64408
hypocenterC73#1547
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #17989592C2semidirect
2. #17989588C2semidirect
3. #17989446C2semidirect
4. #17989445C2semidirect
109. C73#1547semidirect