Finite Group Databasebeta

← #22619589

Subgroups — #22619589

Order 9344.

484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14556597C211yesmaximal, characteristic, complemented
2#17989165C212yesmaximal, complemented
3#17988842C212yesmaximal, complemented
4#17988837C212yesmaximal, complemented
5#17988813C214yesmaximal, complemented
6C2×#14556523C211yesmaximal, characteristic, complemented
7#17988588C212yesmaximal, complemented
8C2×#135×C73C211yesmaximal, characteristic, complemented
9C2×#11924028C2211yescharacteristic
10#14556597—24no—
11C2×#11924012C2211yescharacteristic
12C2×#11924011C2212yes—
13C2×C8×D73C2212yes—
14#14556570—22no—
15#14556567C2214yes—
16#14556565—22no—
17#14556563—24no—
18#14556562C2214yes—
19C2×C4⋊Dic73C2212yes—
20#14556523C2212yes—
21#14556523C2212yes—
22#14556515C2214yes—
23#14556512C2214yes—
24C2×#41×C73C2212yes—
25#135×C73—24no—
26C2×Q16×C73C2211yescharacteristic
27C2×SD16×C73C2212yes—
28C2×D8×C73C2211yescharacteristic
29C22×C8×C73C2211yescharacteristic
30#11924028—22no—
31#11924028—22no—
32C2×Dic146D411yescharacteristic
33C2×D292D411yescharacteristic
34C2×C22⋊D73—24no—
35C2×C22⋊D73D412yes—
36C22×Dic73—22no—
37C2×C4×D73C2312yes—
38#11924012—22no—
39#11924011—24no—
40C2×#10596831C2312yes—
41C8×D73—24no—
42C4⋊Dic73—22no—
43C4⋊Dic73C2314yes—
44#11924007—24no—
45C22⋊Dic73—24no—
46#11924005—24no—
47#41×C73—24no—
48#41×C73—24no—
49C2×Q8×C73C2312yes—
50C2×D4×C73—22no—
51C2×D4×C73C2312yes—
52C22×C4×C73—22no—
53C22×C4×C73C2311yescharacteristic
54Q16×C73—22no—
55SD16×C73—24no—
56D8×C73—22no—
57C2×C8×C73D414yescomplemented
58C2×C8×C73C2311yescharacteristic
59C2×C8×C73C2311yescharacteristic
60C23×C73—22no—
61C23×C73C2×D411yescharacteristic
62C22×D73C2×D412yes—
63Q8×C73—22no—
64Q8×C73—22no—
65D4×C73—22no—
66D4×C73—22no—
67D4×C73—44no—
68C2×C4×C73—22no—
69C2×C4×C73—44no—
70C2×C4×C73C2×D411yescharacteristic
71C2×C4×C73C2×D412yes—
72C2×C4×C73#4112yes—
73C2×C4×C73C2411yescharacteristic
74C22⋊D73—24no—
75C22⋊D73—84no—
76C2×Dic73—24no—
77C2×Dic73—82no—
78C2×Dic73C2×D412yes—
79D292—22no—
80C4×D73—22no—
81C4×D73—22no—
82Dic146—22no—
83C8×C73C2×D412yes—
84C8×C73C2×D412yes—
85#10596831—22no—
86C22×C73—22no—
87C22×C73—42no—
88C22×C73—42no—
89C22×C73—42no—
90C22×C73#12112yes—
91C22×C73C22×D411yescharacteristic
92C2×D73—22no—
93C2×D73—24no—
94C4×C73—42no—
95C4×C73#12112yes—
96C4×C73C22×D411yescharacteristic
97C4×C73C2×#4111yescharacteristic
98Dic73—22no—
99Dic73—44no—
100C2×C73—22no—
101C2×C73—82no—
102C2×C73C2×#12111yescharacteristic
103C2×C73#57712yes—
104D73—42no—
105#3060—731nomaximal, Sylow
106C73#306011yescharacteristic, complemented, Sylow
107C2×#135D7311yescharacteristic, complemented
108C2×#131—731no—
109#537—732no—
110#470—732no—
111#469—732no—
112#465—734no—
113C2×#106—731no—
114#417—732no—
115C2×#41—731no—
116C2×#41C2×D7312yes—
117#135—24no—
118C2×Q16C2×D7311yescharacteristic
119C2×SD16C2×D7312yes—
120C2×D8C2×D7311yescharacteristic
121#131—1464no—
122C2×M16—731no—
123C2×M16—732no—
124C22×C8—732no—
125C22×C8C2×D7311yescharacteristic
126C22⋊Q8—734no—
127C22⋊Q8—1462no—
128#121—734no—
129#121—1462no—
130#121—1464no—
131C2×C4⋊C4—732no—
132#106—732no—
133#106—732no—
134#103—734no—
135#102—734no—
136#41—24no—
137#41—24no—
138#41—1462no—
139#41—1462no—
140C2×Q8—731no—
141C2×Q8C22×D7312yes—
142C2×D4—22no—
143C2×D4—732no—
144C2×D4—731no—
145C2×D4—1464no—
146C2×D4C22×D7312yes—
147C22×C4—22no—
148C22×C4—732no—
149C22×C4—1462no—
150C22×C4C22×D7311yescharacteristic
151Q16—22no—
152SD16—24no—
153D8—22no—
154M16—1462no—
155M16—1464no—
156C2×C8—732no—
157C2×C8—1464no—
158C2×C8C22⋊D7314yescomplemented
159C2×C8C22×D7311yescharacteristic
160C2×C8C22×D7311yescharacteristic
161C4⋊C4—734no—
162C4⋊C4—1464no—
163C4⋊C4—1462no—
164C22⋊C4—1464no—
165C22⋊C4—1464no—
166C23—22no—
167C23—732no—
168C23D4×D7311yescharacteristic
169Q8—22no—
170Q8—22no—
171Q8—1462no—
172D4—22no—
173D4—22no—
174D4—44no—
175D4—5844no—
176D4—1464no—
177D4—1462no—
178C2×C4—22no—
179C2×C4—44no—
180C2×C4—5842no—
181C2×C4—732no—
182C2×C4—1464no—
183C2×C4—1462no—
184C2×C4—1462no—
185C2×C4D4×D7311yescharacteristic
186C2×C4C2×C22⋊D7312yes—
187C2×C4#1192402712yes—
188C2×C4C23×D7311yescharacteristic
189C8—1462no—
190C8C2×C22⋊D7312yes—
191C8C2×C22⋊D7312yes—
192C22—22no—
193C22—42no—
194C22—42no—
195C22—42no—
196C22—1464no—
197C22—1462no—
198C22#1455656212yes—
199C22C2×D4×D7311yescharacteristic
200C4—42no—
201C4—2924no—
202C4—1462no—
203C4#1455656212yes—
204C4C22×C22⋊D7311yescharacteristic
205C4C2×#1192402711yescharacteristic
206C2—22no—
207C2—82no—
208C2—2922no—
209C2C2×#1455656211yescharacteristic
210C2#1798939412yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×#135×C73C2
socleC22×C73C22×D4
hypercenterC2×#135D73
hypocenterC73#3060
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#14556597C2semidirect
2. #17989165C2semidirect
3. #17988842C2semidirect
4. #17988837C2semidirect
5. #17988813C2semidirect
6. C2×#14556523C2semidirect
7. #17988588C2semidirect
8. C2×#135×C73C2semidirect
57. C2×C8×C73D4semidirect
106. C73#3060semidirect
107. C2×#135D73semidirect
158. C2×C8C22⋊D73semidirect