Finite Group Databasebeta

← #22615753

Subgroups — #22615753

Order 9344.

488 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14556548C211yesmaximal, characteristic
2#17988525C212yesmaximal, complemented
3#17988522C212yesmaximal
4#17988506C212yesmaximal, complemented
5#17988498C212yesmaximal
6#17988483C212yesmaximal, complemented
7#17988453C211yesmaximal, characteristic, complemented
8#17988444C212yesmaximal
9C2×C4⋊Q8×C73C211yesmaximal, characteristic, complemented
10C22×C4×D73C2211yescharacteristic
11#14556548—24no—
12C2×C4⋊Dic73C2212yes—
13C2×#11924007C2211yescharacteristic
14C2×#11924007C2211yescharacteristic
15C2×#11924007C2214yes—
16C2×#11924005C2211yescharacteristic
17C2×#11924005C2211yescharacteristic
18C2×#11924005C2214yes—
19C2×C4×Dic73C2211yescharacteristic
20#14556498C2214yes—
21#14556498C2212yes—
22#14556498C2212yes—
23#14556498C2214yes—
24C22×Q8×C73C2212yes—
25C4⋊Q8×C73—24no—
26C2×C4⋊C4×C73C2212yes—
27C2×C4⋊C4×C73C2212yes—
28C2×C42×C73C2211yescharacteristic
29C23×D73C2311yescharacteristic
30C22×Dic73C2311yescharacteristic
31C22×Dic73C2314yes—
32C22×Dic73C2311yescharacteristic
33C22×Dic73C2311yescharacteristic
34C2×C4×D73—22no—
35C2×C4×D73—22no—
36C2×C4×D73Q814yescomplemented
37C4⋊Dic73—24no—
38#11924007—22no—
39#11924007—22no—
40#11924007—44no—
41#11924005—22no—
42#11924005—22no—
43#11924005—44no—
44C4×Dic73—22no—
45C2×Q8×C73—24no—
46C2×Q8×C73—44no—
47C22×C4×C73C2314yes—
48C22×C4×C73C2311yescharacteristic
49C22×C4×C73C2311yescharacteristic
50C22×C4×C73C2311yescharacteristic
51C4⋊C4×C73—24no—
52C4⋊C4×C73—24no—
53C42×C73D414yes—
54C23×C73C2411yescharacteristic
55C22×D73—21no—
56C22×D73—21no—
57C22×D73—22no—
58C22×D73—22no—
59C22×D73C2×Q812yes—
60Q8×C73—48no—
61C2×C4×C73—22no—
62C2×C4×C73—22no—
63C2×C4×C73—24no—
64C2×C4×C73—24no—
65C2×C4×C73—24no—
66C2×C4×C73C2×D412yes—
67C2×C4×C73C2×D412yes—
68C2×C4×C73C2×D412yes—
69C2×C4×C73C2×Q812yes—
70C2×C4×C73#4112yes—
71C2×Dic73—21no—
72C2×Dic73—21no—
73C2×Dic73—21no—
74C2×Dic73—21no—
75C2×Dic73—24no—
76C2×Dic73—24no—
77C2×Dic73—22no—
78C2×Dic73—22no—
79C2×Dic73—24no—
80C2×Dic73C2×Q812yes—
81C4×D73—28no—
82C22×C73C22×D411yescharacteristic
83C22×C73C22×Q811yescharacteristic
84C22×C73C2×#4111yescharacteristic
85C22×C73H(5,𝔽2)12yes—
86C22×C732−1+412yes—
87C2×D73—22no—
88C2×D73—24no—
89C2×D73—41no—
90C2×D73—41no—
91C2×D73—42no—
92C4×C73—22no—
93C4×C73—22no—
94C4×C73—44no—
95C4×C73C22⋊Q814yes—
96Dic73—22no—
97Dic73—41no—
98Dic73—41no—
99Dic73—44no—
100C2×C73C2×C22⋊Q811yescharacteristic
101C2×C73#53511yescharacteristic
102C2×C73#53611yescharacteristic
103C2×C73#54212yes—
104C2×C73#54412yes—
105D73—42no—
106#2628—731nomaximal, Sylow
107C73#262811yescharacteristic, complemented, Sylow
108C2×C4⋊Q8D7311yescharacteristic, complemented
109C2×#117—731no—
110#400—732no—
111#399—732no—
112#395—732no—
113#393—732no—
114#389—732no—
115#382—731no—
116#380—732no—
117C22×Q8C2×D7312yes—
118C23×C4—731no—
119C4⋊Q8—24no—
120#117—1464no—
121C2×C4⋊C4—734no—
122C2×C4⋊C4—731no—
123C2×C4⋊C4—731no—
124C2×C4⋊C4—732no—
125C2×C4⋊C4C2×D7312yes—
126C2×C4⋊C4C2×D7312yes—
127C2×C22⋊C4—734no—
128C2×C22⋊C4—731no—
129C2×C22⋊C4—731no—
130C2×C42—731no—
131C2×C42C2×D7311yescharacteristic
132#95—734no—
133#95—732no—
134#95—732no—
135#95—734no—
136C24—731no—
137C2×Q8—24no—
138C2×Q8—44no—
139C22×C4—731no—
140C22×C4—734no—
141C22×C4—731no—
142C22×C4—734no—
143C22×C4—731no—
144C22×C4—1462no—
145C22×C4—1462no—
146C22×C4C22×D7314yes—
147C22×C4C22×D7311yescharacteristic
148C22×C4C22×D7311yescharacteristic
149C22×C4C22×D7311yescharacteristic
150C4⋊C4—24no—
151C4⋊C4—24no—
152C4⋊C4—2924no—
153C4⋊C4—1462no—
154C4⋊C4—1462no—
155C4⋊C4—1464no—
156C22⋊C4—2924no—
157C22⋊C4—1462no—
158C22⋊C4—1462no—
159C42—1462no—
160C42C22⋊D7314yes—
161C23—732no—
162C23—1461no—
163C23—1461no—
164C23—1462no—
165C23—1462no—
166C23C23×D7311yescharacteristic
167Q8—48no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—24no—
171C2×C4—24no—
172C2×C4—24no—
173C2×C4—732no—
174C2×C4—1461no—
175C2×C4—1461no—
176C2×C4—1464no—
177C2×C4—1464no—
178C2×C4—1462no—
179C2×C4—1462no—
180C2×C4—1464no—
181C2×C4—1461no—
182C2×C4—1461no—
183C2×C4—1468no—
184C2×C4C2×C22⋊D7312yes—
185C2×C4C2×C22⋊D7312yes—
186C2×C4C2×C22⋊D7312yes—
187C2×C4Q8×D7312yes—
188C2×C4#1192402912yes—
189C22—2921no—
190C22—2921no—
191C22—2922no—
192C22—1464no—
193C22—1462no—
194C22C22×C22⋊D7311yescharacteristic
195C22C2×Q8×D7311yescharacteristic
196C22C2×#1192402911yescharacteristic
197C22#1455663612yes—
198C22#1455663912yes—
199C4—22no—
200C4—22no—
201C4—44no—
202C4—2921no—
203C4—2921no—
204C4—2924no—
205C4—1462no—
206C4#1455656714yes—
207C2—2922no—
208C2C2×#1455656711yescharacteristic
209C2#1798915411yescharacteristic
210C2#1798916111yescharacteristic
211C2#1798921112yes—
212C2#1798921412yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×C4⋊Q8×C73C2
hypercenterC2×C4⋊Q8D73
hypocenterC73#2628
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #17988525C2semidirect
4. #17988506C2semidirect
6. #17988483C2semidirect
7. #17988453C2semidirect
9. C2×C4⋊Q8×C73C2semidirect
36. C2×C4×D73Q8semidirect
107. C73#2628semidirect
108. C2×C4⋊Q8D73semidirect