Finite Group Databasebeta

← #22615813

Subgroups — #22615813

Order 9344.

416 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 131 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×#14556582C211yesmaximal, characteristic
2C2×#14556556C211yesmaximal, characteristic
3#17988529C212yesmaximal
4#17988525C211yesmaximal, characteristic
5#17988519C211yesmaximal, characteristic
6#17988517C211yesmaximal, characteristic
7#17988508C212yesmaximal
8#17988470C212yesmaximal
9#17988469C212yesmaximal
10#17988454C211yesmaximal, characteristic
11#400×C73C211yesmaximal, characteristic
12C22×Dic146C2211yescharacteristic
13#14556582—24no—
14#14556556—24no—
15C2×C4⋊Dic73C2212yes—
16C2×C4⋊Dic73C2212yes—
17C2×C4⋊Dic73C2211yescharacteristic
18C2×#11924007C2212yes—
19C2×#11924007C2212yes—
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2211yescharacteristic
22C2×C4×Dic73C2211yescharacteristic
23C2×C4×Dic73C2211yescharacteristic
24C2×C4×Dic73C2211yescharacteristic
25#14556498C2212yes—
26#14556498C2212yes—
27#14556498C2211yescharacteristic
28#14556498C2212yes—
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C2×C4⋊C4×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2211yescharacteristic
34#95×C73C2211yescharacteristic
35#95×C73C2212yes—
36#95×C73C2212yes—
37C2×Dic146—22no—
38C2×Dic146—22no—
39C2×Dic146—22no—
40C22×Dic73C2312yes—
41C22×Dic73C2311yescharacteristic
42C22×Dic73C2312yes—
43C22×Dic73C2311yescharacteristic
44C22×Dic73C2311yescharacteristic
45C22×Dic73C2311yescharacteristic
46C4⋊Dic73—22no—
47C4⋊Dic73—24no—
48C4⋊Dic73—24no—
49#11924007—22no—
50#11924007—24no—
51#11924007—22no—
52#11924007—24no—
53C4×Dic73—22no—
54C4×Dic73—22no—
55C4×Dic73D414yes—
56C22×C4×C73C2312yes—
57C22×C4×C73C2311yescharacteristic
58C22×C4×C73C2312yes—
59C22×C4×C73C2311yescharacteristic
60C22×C4×C73C2311yescharacteristic
61C4⋊C4×C73—22no—
62C4⋊C4×C73—22no—
63C23×C73C2411yescharacteristic
64C2×C4×C73—21no—
65C2×C4×C73—21no—
66C2×C4×C73—22no—
67C2×C4×C73—21no—
68C2×C4×C73—22no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73—24no—
72C2×C4×C73—22no—
73C2×C4×C73—22no—
74C2×C4×C73C2×D412yes—
75C2×C4×C73#4112yes—
76C2×Dic73—21no—
77C2×Dic73—21no—
78C2×Dic73—21no—
79C2×Dic73—21no—
80C2×Dic73—22no—
81C2×Dic73—21no—
82C2×Dic73—22no—
83C2×Dic73—22no—
84C2×Dic73—22no—
85C2×Dic73—22no—
86C2×Dic73—22no—
87C2×Dic73—22no—
88C2×Dic73—22no—
89C2×Dic73C2×D412yes—
90C2×Dic73C2×D412yes—
91C2×Dic73#4112yes—
92Dic146—28no—
93C22×C73C22×D411yescharacteristic
94C22×C73C2×#4111yescharacteristic
95C22×C73C2×#4111yescharacteristic
96C22×C732−1+412yes—
97C22×C732−1+412yes—
98C4×C73—22no—
99C4×C73—22no—
100C4×C73—42no—
101C4×C73—41no—
102C4×C73—42no—
103Dic73—22no—
104Dic73—22no—
105Dic73—22no—
106Dic73—42no—
107Dic73—41no—
108Dic73—42no—
109C2×C73#52511yescharacteristic
110C2×C73#53611yescharacteristic
111C2×C73#53611yescharacteristic
112C2×C73#54112yes—
113C2×C73#54112yes—
114#2634—731nomaximal, Sylow
115C73#263411yescharacteristic, complemented, Sylow
116C2×#125—731no—
117C2×C4×Q8—731no—
118#400—731no—
119#400—732no—
120#400D7311yescharacteristic
121#398—731no—
122#398—731no—
123#395—732no—
124#387—732no—
125#387—732no—
126#383—731no—
127C22×Q8—731no—
128#125—1464no—
129C4×Q8—1464no—
130C2×C4⋊C4—731no—
131C2×C4⋊C4—731no—
132C2×C4⋊C4—732no—
133C2×C4⋊C4—732no—
134C2×C4⋊C4—731no—
135C2×C4⋊C4—732no—
136C2×C4⋊C4—732no—
137C2×C4⋊C4C2×D7311yescharacteristic
138C2×C4⋊C4C2×D7311yescharacteristic
139C2×C42—731no—
140C2×C42—731no—
141C2×C42—731no—
142#95—732no—
143#95—732no—
144#95—731no—
145#95—732no—
146#95—732no—
147#95—732no—
148#95—732no—
149#95C2×D7311yescharacteristic
150#95C2×D7312yes—
151#95C2×D7312yes—
152C2×Q8—1462no—
153C2×Q8—1462no—
154C2×Q8—1462no—
155C22×C4—731no—
156C22×C4—731no—
157C22×C4—731no—
158C22×C4—732no—
159C22×C4—731no—
160C22×C4—732no—
161C22×C4C22×D7312yes—
162C22×C4C22×D7311yescharacteristic
163C22×C4C22×D7312yes—
164C22×C4C22×D7311yescharacteristic
165C22×C4C22×D7311yescharacteristic
166C4⋊C4—22no—
167C4⋊C4—22no—
168C4⋊C4—1462no—
169C4⋊C4—1464no—
170C4⋊C4—1464no—
171C4⋊C4—1464no—
172C4⋊C4—1462no—
173C4⋊C4—1462no—
174C4⋊C4—1464no—
175C42—734no—
176C42—1462no—
177C42—1462no—
178C23C23×D7311yescharacteristic
179Q8—1468no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—24no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—732no—
191C2×C4—732no—
192C2×C4—732no—
193C2×C4—1461no—
194C2×C4—1462no—
195C2×C4—1462no—
196C2×C4—1462no—
197C2×C4—1462no—
198C2×C4—1462no—
199C2×C4—1462no—
200C2×C4—1462no—
201C2×C4—1461no—
202C2×C4—1461no—
203C2×C4—1461no—
204C2×C4—1461no—
205C2×C4—1462no—
206C2×C4D4×D7312yes—
207C2×C4#1192402912yes—
208C22C2×D4×D7311yescharacteristic
209C22#41×D7311yescharacteristic
210C22C2×#1192402911yescharacteristic
211C22#1455663812yes—
212C22#1455663812yes—
213C4—22no—
214C4—22no—
215C4—42no—
216C4—41no—
217C4—42no—
218C4—2921no—
219C4—2922no—
220C4—2922no—
221C4—1462no—
222C4—1462no—
223C4—1462no—
224C2#1798910011yescharacteristic
225C2#1798915711yescharacteristic
226C2#1798915911yescharacteristic
227C2#1798919412yes—
228C2#1798920012yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#400×C73C2
hypercenter#400D73
hypocenterC73#2634
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
115. C73#2634semidirect