Finite Group Databasebeta

← #22615714

Subgroups — #22615714

Order 9344.

526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14556574C211yesmaximal, characteristic
2C22×C4⋊Dic73C211yesmaximal, characteristic, complemented
3#17988527C212yesmaximal, complemented
4#17988524C212yesmaximal, complemented
5#17988519C212yesmaximal, complemented
6#17988514C212yesmaximal, complemented
7#17988464C212yesmaximal
8#17988462C212yesmaximal, complemented
9#381×C73C211yesmaximal, characteristic, complemented
10C22×C22⋊D73C2211yescharacteristic
11C23×Dic73C2212yes—
12#14556574—24no—
13C2×C4⋊Dic73—24no—
14C2×C4⋊Dic73C2212yes—
15C2×C4⋊Dic73C2212yes—
16C2×C4⋊Dic73C2214yes—
17C2×#11924007C2211yescharacteristic
18C2×#11924007C2211yescharacteristic
19C2×C22⋊Dic73C2211yescharacteristic
20C2×#11924005C2211yescharacteristic
21C2×#11924005C2211yescharacteristic
22C2×#11924005C2214yes—
23#14556498C2214yes—
24#14556498C2214yes—
25C23×C4×C73C2211yescharacteristic
26C2×C22⋊C4×C73C2212yes—
27#95×C73C2212yes—
28#95×C73C2212yes—
29C23×D73C2311yescharacteristic
30C2×C22⋊D73—22no—
31C2×C22⋊D73—24no—
32C22×Dic73—24no—
33C22×Dic73—44no—
34C22×Dic73C2311yescharacteristic
35C22×Dic73C2311yescharacteristic
36C22×Dic73C2314yes—
37C22×Dic73C2311yescharacteristic
38C4⋊Dic73—24no—
39C4⋊Dic73—24no—
40C4⋊Dic73—44no—
41#11924007—22no—
42#11924007—22no—
43C22⋊Dic73—22no—
44#11924005—22no—
45#11924005—22no—
46#11924005—44no—
47C24×C73C2311yescharacteristic
48C22×C4×C73—24no—
49C22×C4×C73D414yes—
50C22×C4×C73C2314yes—
51C22×C4×C73C2311yescharacteristic
52C22×C4×C73C2311yescharacteristic
53C22⋊C4×C73—24no—
54C23×C73—22no—
55C23×C73—22no—
56C23×C73C2×D412yes—
57C23×C73#4114yes—
58C23×C73C2411yescharacteristic
59C22×D73—21no—
60C22×D73—22no—
61C22×D73—22no—
62C22×D73—22no—
63C2×C4×C73—28no—
64C2×C4×C73—22no—
65C2×C4×C73—22no—
66C2×C4×C73—24no—
67C2×C4×C73—24no—
68C2×C4×C73—24no—
69C2×C4×C73C2×D412yes—
70C2×C4×C73C2×D412yes—
71C22⋊D73—44no—
72C2×Dic73—21no—
73C2×Dic73—21no—
74C2×Dic73—21no—
75C2×Dic73—24no—
76C2×Dic73—22no—
77C2×Dic73—24no—
78C2×Dic73—22no—
79C2×Dic73—24no—
80C2×Dic73—22no—
81C2×Dic73—48no—
82C22×C73—22no—
83C22×C73—22no—
84C22×C73—28no—
85C22×C73#12314yes—
86C22×C73C22×D411yescharacteristic
87C22×C73C2×#4112yes—
88C22×C73H(5,𝔽2)12yes—
89C22×C732−1+412yes—
90C2×D73—41no—
91C2×D73—41no—
92C2×D73—41no—
93C2×D73—44no—
94C4×C73—22no—
95C4×C73—22no—
96C4×C73—44no—
97Dic73—41no—
98Dic73—41no—
99Dic73—44no—
100Dic73—41no—
101C2×C73—24no—
102C2×C73C2×#12311yescharacteristic
103C2×C73#53511yescharacteristic
104C2×C73#53611yescharacteristic
105C2×C73#53914yes—
106D73—81no—
107#2623—731nomaximal, Sylow
108C73#262311yescharacteristic, complemented, Sylow
109C2×#123—731no—
110C22×C4⋊C4—731no—
111#400—732no—
112#399—732no—
113#398—732no—
114#397—732no—
115#386—732no—
116#385—732no—
117#381D7311yescharacteristic, complemented
118C22×D4—731no—
119C23×C4—732no—
120C23×C4C2×D7311yescharacteristic
121#123—1464no—
122C2×C4⋊C4—734no—
123C2×C4⋊C4—732no—
124C2×C4⋊C4—732no—
125C2×C4⋊C4—731no—
126C2×C4⋊C4—731no—
127C2×C4⋊C4—1464no—
128C2×C22⋊C4—734no—
129C2×C22⋊C4—731no—
130C2×C22⋊C4—731no—
131C2×C22⋊C4—731no—
132C2×C22⋊C4C2×D7312yes—
133#95—734no—
134#95—734no—
135#95C2×D7312yes—
136#95C2×D7312yes—
137C24—731no—
138C24C22×D7311yescharacteristic
139C2×D4—1462no—
140C2×D4—1464no—
141C22×C4—24no—
142C22×C4—2924no—
143C22×C4—731no—
144C22×C4—731no—
145C22×C4—734no—
146C22×C4—731no—
147C22×C4—1464no—
148C22×C4D29214yes—
149C22×C4C22×D7314yes—
150C22×C4C22×D7311yescharacteristic
151C22×C4C22×D7311yescharacteristic
152C4⋊C4—2924no—
153C4⋊C4—1462no—
154C4⋊C4—1462no—
155C4⋊C4—1464no—
156C4⋊C4—1464no—
157C22⋊C4—24no—
158C22⋊C4—2924no—
159C22⋊C4—1462no—
160C22⋊C4—1462no—
161C22⋊C4—1462no—
162C23—22no—
163C23—22no—
164C23—1461no—
165C23—1462no—
166C23—1462no—
167C23—1462no—
168C23C2×D29212yes—
169C23#1192402714yes—
170C23C23×D7311yescharacteristic
171D4—2924no—
172C2×C4—28no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—24no—
178C2×C4—2928no—
179C2×C4—1461no—
180C2×C4—1461no—
181C2×C4—1464no—
182C2×C4—1461no—
183C2×C4—1462no—
184C2×C4—1464no—
185C2×C4—1462no—
186C2×C4—1464no—
187C2×C4—1462no—
188C2×C4C2×D29212yes—
189C2×C4C2×D29212yes—
190C22—22no—
191C22—22no—
192C22—28no—
193C22—2921no—
194C22—2921no—
195C22—2924no—
196C22—2921no—
197C22#1455657514yes—
198C22C22×D29211yescharacteristic
199C22C2×#1192402712yes—
200C22#1455663712yes—
201C22#1455663812yes—
202C4—22no—
203C4—22no—
204C4—44no—
205C4—2924no—
206C4—2921no—
207C4—2921no—
208C4—2921no—
209C2—24no—
210C2—5841no—
211C2C2×#1455657511yescharacteristic
212C2#1798915611yescharacteristic
213C2#1798916311yescharacteristic
214C2#1798918114yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#381×C73C2
hypercenter#381D73
hypocenterC73#2623
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊Dic73C2semidirect
3. #17988527C2semidirect
4. #17988524C2semidirect
5. #17988519C2semidirect
6. #17988514C2semidirect
8. #17988462C2semidirect
9. #381×C73C2semidirect
108. C73#2623semidirect
117. #381D73semidirect