Finite Group Databasebeta

← #22614415

Subgroups — #22614415

Order 9344.

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

normal subgroups only

This group has 512 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×#14556567C211yesmaximal, characteristic
2C2×C4⋊C4×D73C211yesmaximal, characteristic
3#17988528C214yesmaximal, complemented
4#17988494C211yesmaximal, characteristic, complemented
5#17988453C211yesmaximal, characteristic, complemented
6#17988452C211yesmaximal, characteristic, complemented
7#17988449C214yesmaximal
8C4×#11924005C211yesmaximal, characteristic
9#391×C73C211yesmaximal, characteristic, complemented
10C22×C4×D73C2212yes—
11C22×C4×D73C2211yescharacteristic
12#14556567—24no—
13C2×C4⋊Dic73C2211yescharacteristic
14C2×C4⋊Dic73C2211yescharacteristic
15C2×#11924007C2212yes—
16C2×#11924007C2212yes—
17C4⋊C4×D73—24no—
18C2×#11924005C2212yes—
19C2×#11924005C2212yes—
20C2×C4×Dic73C2211yescharacteristic
21#14556498C2212yes—
22#14556498C2214yes—
23#14556498C2214yes—
24#14556498C2214yes—
25C22×Q8×C73C2211yescharacteristic
26C2×C4⋊C4×C73C2211yescharacteristic
27C2×C42×C73C2211yescharacteristic
28#95×C73C2214yes—
29C23×D73C2311yescharacteristic
30C22×Dic73C2312yes—
31C22×Dic73C2312yes—
32C22×Dic73C2312yes—
33C22×Dic73C2311yescharacteristic
34C2×C4×D73—22no—
35C2×C4×D73—22no—
36C2×C4×D73—24no—
37C2×C4×D73—28no—
38C2×C4×D73D414yes—
39C4⋊Dic73—22no—
40C4⋊Dic73—22no—
41#11924007—24no—
42#11924007—24no—
43#11924005—24no—
44#11924005—24no—
45C4×Dic73—22no—
46C2×Q8×C73—22no—
47C2×Q8×C73—22no—
48C2×Q8×C73—22no—
49C22×C4×C73C2312yes—
50C22×C4×C73C2312yes—
51C22×C4×C73C2312yes—
52C22×C4×C73C2311yescharacteristic
53C4⋊C4×C73—22no—
54C42×C73—22no—
55C23×C73C2411yescharacteristic
56C22×D73—21no—
57C22×D73—21no—
58C22×D73—22no—
59C22×D73C2×D412yes—
60C22×D73#4114yes—
61Q8×C73—44no—
62C2×C4×C73—22no—
63C2×C4×C73—22no—
64C2×C4×C73—22no—
65C2×C4×C73—22no—
66C2×C4×C73—22no—
67C2×C4×C73—22no—
68C2×C4×C73—24no—
69C2×C4×C73—22no—
70C2×C4×C73C2×D412yes—
71C2×C4×C73#4112yes—
72C2×C4×C73#4112yes—
73C2×Dic73—21no—
74C2×Dic73—21no—
75C2×Dic73—22no—
76C2×Dic73—22no—
77C2×Dic73—22no—
78C2×Dic73—22no—
79C2×Dic73—24no—
80C2×Dic73—24no—
81C2×Dic73—22no—
82C2×Dic73C2×D412yes—
83C4×D73—28no—
84C4×D73—48no—
85C22×C73C22×D411yescharacteristic
86C22×C73C2×#4112yes—
87C22×C73C2×#4111yescharacteristic
88C22×C73C2×#4111yescharacteristic
89C22×C732−1+412yes—
90C2×D73—22no—
91C2×D73—22no—
92C2×D73—24no—
93C2×D73—24no—
94C2×D73#12414yes—
95C4×C73—42no—
96C4×C73—42no—
97C4×C73—42no—
98C4×C73#12314yes—
99Dic73—22no—
100Dic73—42no—
101Dic73—42no—
102Dic73—42no—
103C2×C73C2×#12311yescharacteristic
104C2×C73C2×#12411yescharacteristic
105C2×C73#53611yescharacteristic
106C2×C73#55212yes—
107C2×C73#55212yes—
108D73—24no—
109#2503—731nomaximal, Sylow
110C73#250311yescharacteristic, complemented, Sylow
111C2×C22⋊Q8—731no—
112C22×C4⋊C4—731no—
113#400—734no—
114#391—731no—
115#391D7311yescharacteristic, complemented
116#382—731no—
117#382—731no—
118#381—734no—
119C4×C22⋊C4—731no—
120C22×Q8C2×D7311yescharacteristic
121C23×C4—731no—
122C23×C4—732no—
123C22⋊Q8—1464no—
124C2×C4⋊C4—731no—
125C2×C4⋊C4—732no—
126C2×C4⋊C4—731no—
127C2×C4⋊C4—732no—
128C2×C4⋊C4—1464no—
129C2×C4⋊C4C2×D7311yescharacteristic
130C2×C22⋊C4—732no—
131C2×C22⋊C4—732no—
132C2×C42—731no—
133C2×C42C2×D7311yescharacteristic
134#95—732no—
135#95—734no—
136#95—734no—
137#95—734no—
138#95C2×D7314yes—
139C24—731no—
140C2×Q8—22no—
141C2×Q8—22no—
142C2×Q8—22no—
143C22×C4—731no—
144C22×C4—734no—
145C22×C4—732no—
146C22×C4—732no—
147C22×C4—732no—
148C22×C4—1464no—
149C22×C4—1468no—
150C22×C4—1462no—
151C22×C4—1462no—
152C22×C4C22×D7312yes—
153C22×C4C22×D7312yes—
154C22×C4C22×D7312yes—
155C22×C4C22×D7311yescharacteristic
156C4⋊C4—22no—
157C4⋊C4—1464no—
158C4⋊C4—1464no—
159C4⋊C4—1462no—
160C4⋊C4—1462no—
161C22⋊C4—1464no—
162C22⋊C4—1464no—
163C42—22no—
164C42—1462no—
165C23—732no—
166C23—734no—
167C23—1461no—
168C23—1461no—
169C23—1462no—
170C23C23×D7311yescharacteristic
171Q8—44no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—24no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—2928no—
181C2×C4—732no—
182C2×C4—1462no—
183C2×C4—1462no—
184C2×C4—1462no—
185C2×C4—1464no—
186C2×C4—1462no—
187C2×C4—1464no—
188C2×C4—1462no—
189C2×C4—1461no—
190C2×C4—1461no—
191C2×C4—1468no—
192C2×C4D4×D7312yes—
193C2×C4#1192402712yes—
194C2×C4#1192402812yes—
195C22—734no—
196C22—1462no—
197C22—1464no—
198C22—1464no—
199C22—1462no—
200C22C2×D4×D7311yescharacteristic
201C22#41×D7312yes—
202C22C2×#1192402711yescharacteristic
203C22C2×#1192402811yescharacteristic
204C22#1455663912yes—
205C4—42no—
206C4—42no—
207C4—42no—
208C4—2922no—
209C4—2922no—
210C4—2922no—
211C4—1462no—
212C4#1455657314yes—
213C2—1464no—
214C2C2×#1455657311yescharacteristic
215C2#124×D7311yescharacteristic
216C2#1798916211yescharacteristic
217C2#1798927112yes—
218C2#1798927812yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#391×C73C2
hypercenter#391D73
hypocenterC73#2503
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
3. #17988528C2semidirect
4. #17988494C2semidirect
5. #17988453C2semidirect
6. #17988452C2semidirect
9. #391×C73C2semidirect
110. C73#2503semidirect
115. #391D73semidirect