Finite Group Databasebeta

← #22619732

Subgroups — #22619732

Order 9344.

376 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 145 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×C4×Dic146C211yesmaximal, characteristic
2#17988891C214yesmaximal, complemented
3#17988879C212yesmaximal, complemented
4#17988869C212yesmaximal, complemented
5#17988630C212yesmaximal
6#17988611C211yesmaximal, characteristic
7#17988595C212yesmaximal
8#533×C73C211yesmaximal, characteristic
9C22×Dic146C2211yescharacteristic
10C2×#11924012C2212yes—
11C4×Dic146—21no—
12C4×Dic146—21no—
13C4×Dic146C2212yes—
14C4×Dic146C2212yes—
15C2×C4⋊Dic73C2211yescharacteristic
16C2×#11924007—21no—
17C2×C4×Dic73—21no—
18#14556524C2214yes—
19#14556522C2214yes—
20C4⋊#10596831C2212yes—
21C4⋊#10596831C2212yes—
22#14556514C2214yes—
23#14556514C2214yes—
24C4⋊Q8×C73C2211yescharacteristic
25C4⋊Q8×C73C2211yescharacteristic
26#125×C73C2212yes—
27C22⋊Q8×C73—21no—
28C22⋊Q8×C73—21no—
29C4×Q8×C73—21no—
30C4×Q8×C73—21no—
31#117×C73C2212yes—
32C2×C42×C73C2211yescharacteristic
33C2×Dic146—21no—
34C2×Dic146—22no—
35C2×Dic146Q814yescomplemented
36C2×Dic146C2312yes—
37C22×Dic73—21no—
38C22×Dic73—21no—
39#11924012—24no—
40C2×#10596831C2314yes—
41C4⋊Dic73—21no—
42C4⋊Dic73C2312yes—
43#11924007—22no—
44#11924007—22no—
45C4×Dic73—22no—
46C4×Dic73—22no—
47C2×Q8×C73—21no—
48C2×Q8×C73—21no—
49C22×C4×C73D411yescharacteristic
50C22×C4×C73D411yescharacteristic
51C22×C4×C73C2311yescharacteristic
52C4⋊C4×C73—22no—
53C4⋊C4×C73—22no—
54C4⋊C4×C73—21no—
55C4⋊C4×C73—21no—
56C4⋊C4×C73C2312yes—
57C4⋊C4×C73C2312yes—
58C22⋊C4×C73—22no—
59C42×C73—22no—
60C42×C73D411yescharacteristic
61C42×C73D411yescharacteristic
62C42×C73C2311yescharacteristic
63C42×C73C2311yescharacteristic
64C23×C73C2×D411yescharacteristic
65Q8×C73—42no—
66Q8×C73—42no—
67C2×C4×C73—22no—
68C2×C4×C73—22no—
69C2×C4×C73—22no—
70C2×C4×C73—41no—
71C2×C4×C73C2×D411yescharacteristic
72C2×C4×C73C2×D411yescharacteristic
73C2×C4×C73C2×D411yescharacteristic
74C2×C4×C73C2×D411yescharacteristic
75C2×C4×C73C2×D411yescharacteristic
76C2×C4×C73C2×Q812yes—
77C2×C4×C73#4112yes—
78C2×C4×C73C2411yescharacteristic
79C2×Dic73—24no—
80C2×Dic73—22no—
81C2×Dic73—22no—
82C2×Dic73—42no—
83Dic146—24no—
84Dic146—22no—
85Dic146C2×Q814yes—
86#10596831—24no—
87C22×C73—21no—
88C22×C73—21no—
89C22×C73C22⋊Q812yes—
90C22×C73C22×D411yescharacteristic
91C4×C73—21no—
92C4×C73—21no—
93C4×C73—21no—
94C4×C73—42no—
95C4×C73—42no—
96C4×C73C22⋊Q812yes—
97C4×C73#13712yes—
98C4×C73C22×Q811yescharacteristic
99C4×C73C2×#4111yescharacteristic
100Dic73—24no—
101Dic73—42no—
102C2×C73—22no—
103C2×C73C2×C22⋊Q811yescharacteristic
104C2×C73C2×#13711yescharacteristic
105C2×C73#57511yescharacteristic
106#3078—731nomaximal, Sylow
107C73#307811yescharacteristic, complemented, Sylow
108#533D7311yescharacteristic
109C2×C4×Q8—731no—
110#479—734no—
111#477—732no—
112#475—732no—
113#428—732no—
114#423—731no—
115#419—732no—
116C22×Q8—731no—
117C2×M16—732no—
118C4⋊Q8C2×D7311yescharacteristic
119C4⋊Q8C2×D7311yescharacteristic
120#125C2×D7312yes—
121C22⋊Q8—21no—
122C22⋊Q8—21no—
123C4×Q8—21no—
124C4×Q8—21no—
125C4×Q8—732no—
126C4×Q8—732no—
127C4×Q8—1461no—
128C4×Q8—1461no—
129#117C2×D7312yes—
130C2×C4⋊C4—731no—
131C2×C4⋊C4—1461no—
132C2×C42—1461no—
133C2×C42C2×D7311yescharacteristic
134#107—734no—
135#106—734no—
136C4⋊C8—732no—
137C4⋊C8—732no—
138#103—734no—
139#103—734no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—734no—
143C2×Q8—732no—
144C2×Q8—1461no—
145C2×Q8—1462no—
146C22×C4—1461no—
147C22×C4—1461no—
148C22×C4C22⋊D7311yescharacteristic
149C22×C4C22⋊D7311yescharacteristic
150C22×C4C22×D7311yescharacteristic
151M16—1464no—
152C2×C8—734no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—732no—
158C4⋊C4—1462no—
159C4⋊C4—1462no—
160C4⋊C4—1461no—
161C4⋊C4C22×D7312yes—
162C4⋊C4C22×D7312yes—
163C22⋊C4—22no—
164C42—22no—
165C42—1462no—
166C42—1462no—
167C42C22⋊D7311yescharacteristic
168C42C22⋊D7311yescharacteristic
169C42C22×D7311yescharacteristic
170C42C22×D7311yescharacteristic
171C23C2×C22⋊D7311yescharacteristic
172Q8—42no—
173Q8—42no—
174Q8—734no—
175Q8—1464no—
176Q8—1462no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—41no—
181C2×C4—2922no—
182C2×C4—1462no—
183C2×C4—1464no—
184C2×C4—1462no—
185C2×C4C2×C22⋊D7311yescharacteristic
186C2×C4C2×C22⋊D7311yescharacteristic
187C2×C4C2×C22⋊D7311yescharacteristic
188C2×C4C2×C22⋊D7311yescharacteristic
189C2×C4C2×C22⋊D7311yescharacteristic
190C2×C4Q8×D7312yes—
191C2×C4#1192402912yes—
192C2×C4C23×D7311yescharacteristic
193C8—1464no—
194C22—21no—
195C22—21no—
196C22#1455656712yes—
197C22C22×C22⋊D7311yescharacteristic
198C4—21no—
199C4—21no—
200C4—21no—
201C4—42no—
202C4—42no—
203C4—2922no—
204C4—1464no—
205C4#1455656712yes—
206C4#1455662112yes—
207C4C2×Q8×D7311yescharacteristic
208C4C2×#1192402911yescharacteristic
209C2—22no—
210C2C2×#1455656711yescharacteristic
211C2C2×#1455662111yescharacteristic
212C2#1798938511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#533×C73C2
socleC22×C73C22×D4
hypercenter#533D73
hypocenterC73#3078
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #17988891C2semidirect
3. #17988879C2semidirect
4. #17988869C2semidirect
35. C2×Dic146Q8semidirect
107. C73#3078semidirect