Finite Group Databasebeta

← #22615806

Subgroups — #22615806

Order 9344.

416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14556581C211yesmaximal, characteristic
2C2×Q8×Dic73C211yesmaximal, characteristic
3#17988529C212yesmaximal
4#17988527C211yesmaximal, characteristic
5#17988526C211yesmaximal, characteristic
6#17988520C212yesmaximal
7#17988506C211yesmaximal, characteristic
8#17988473C212yesmaximal
9#17988469C212yesmaximal
10#17988454C211yesmaximal, characteristic
11#395×C73C211yesmaximal, characteristic
12#14556581—24no—
13Q8×Dic73—24no—
14C2×C4⋊Dic73C2211yescharacteristic
15C2×C4⋊Dic73C2212yes—
16C2×C4⋊Dic73C2211yescharacteristic
17C2×#11924007C2211yescharacteristic
18C2×#11924007C2212yes—
19C2×#11924007C2211yescharacteristic
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2211yescharacteristic
22C2×C4×Dic73C2212yes—
23C2×C4×Dic73C2211yescharacteristic
24#14556498C2212yes—
25#14556498C2211yescharacteristic
26#14556498C2212yes—
27#14556498C2212yes—
28#14556498C2212yes—
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C22×Q8×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2212yes—
34C2×C4⋊C4×C73C2211yescharacteristic
35#95×C73C2211yescharacteristic
36#95×C73C2212yes—
37C22×Dic73C2312yes—
38C22×Dic73C2312yes—
39C22×Dic73C2311yescharacteristic
40C22×Dic73C2311yescharacteristic
41C22×Dic73C2311yescharacteristic
42C22×Dic73C2311yescharacteristic
43C4⋊Dic73—22no—
44C4⋊Dic73—24no—
45C4⋊Dic73—22no—
46#11924007—22no—
47#11924007—24no—
48#11924007—22no—
49#11924007—22no—
50#11924007—22no—
51C4×Dic73—24no—
52C4×Dic73D414yes—
53C2×Q8×C73—22no—
54C2×Q8×C73—24no—
55C22×C4×C73C2312yes—
56C22×C4×C73C2311yescharacteristic
57C22×C4×C73C2311yescharacteristic
58C22×C4×C73C2311yescharacteristic
59C22×C4×C73C2312yes—
60C4⋊C4×C73—22no—
61C4⋊C4×C73—24no—
62C23×C73C2411yescharacteristic
63Q8×C73—28no—
64C2×C4×C73—22no—
65C2×C4×C73—22no—
66C2×C4×C73—22no—
67C2×C4×C73—21no—
68C2×C4×C73—21no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73—21no—
72C2×C4×C73—22no—
73C2×C4×C73—21no—
74C2×C4×C73—22no—
75C2×C4×C73C2×D412yes—
76C2×C4×C73#4114yes—
77C2×Dic73—21no—
78C2×Dic73—21no—
79C2×Dic73—22no—
80C2×Dic73—22no—
81C2×Dic73—21no—
82C2×Dic73—21no—
83C2×Dic73—22no—
84C2×Dic73—22no—
85C2×Dic73—21no—
86C2×Dic73—24no—
87C2×Dic73—21no—
88C2×Dic73—22no—
89C2×Dic73—22no—
90C2×Dic73C2×D412yes—
91C2×Dic73C2×D412yes—
92C22×C73C22×D411yescharacteristic
93C22×C73C2×#4112yes—
94C22×C732−1+411yescharacteristic
95C22×C732−1+411yescharacteristic
96C22×C732−1+412yes—
97C4×C73—22no—
98C4×C73—24no—
99C4×C73—41no—
100C4×C73—41no—
101C4×C73—42no—
102Dic73—22no—
103Dic73—22no—
104Dic73—41no—
105Dic73—41no—
106Dic73—42no—
107Dic73—42no—
108C2×C73#52511yescharacteristic
109C2×C73#53611yescharacteristic
110C2×C73#53611yescharacteristic
111C2×C73#54112yes—
112C2×C73#54112yes—
113#2634—731nomaximal, Sylow
114C73#263411yescharacteristic, complemented, Sylow
115C2×#125—731no—
116C2×C4×Q8—731no—
117#400—731no—
118#400—731no—
119#400—732no—
120#398—732no—
121#395—731no—
122#395D7311yescharacteristic
123#387—732no—
124#387—732no—
125#383—731no—
126C22×Q8C2×D7311yescharacteristic
127#125—1464no—
128C4×Q8—1464no—
129C2×C4⋊C4—732no—
130C2×C4⋊C4—731no—
131C2×C4⋊C4—731no—
132C2×C4⋊C4—731no—
133C2×C4⋊C4—731no—
134C2×C4⋊C4—731no—
135C2×C4⋊C4—731no—
136C2×C4⋊C4—732no—
137C2×C4⋊C4C2×D7311yescharacteristic
138C2×C4⋊C4C2×D7312yes—
139C2×C42—731no—
140C2×C42—732no—
141#95—732no—
142#95—731no—
143#95—732no—
144#95—732no—
145#95—732no—
146#95—732no—
147#95—732no—
148#95—732no—
149#95C2×D7311yescharacteristic
150#95C2×D7312yes—
151C2×Q8—22no—
152C2×Q8—24no—
153C22×C4—731no—
154C22×C4—731no—
155C22×C4—732no—
156C22×C4—732no—
157C22×C4—731no—
158C22×C4—731no—
159C22×C4C22×D7312yes—
160C22×C4C22×D7311yescharacteristic
161C22×C4C22×D7311yescharacteristic
162C22×C4C22×D7311yescharacteristic
163C22×C4C22×D7312yes—
164C4⋊C4—22no—
165C4⋊C4—24no—
166C4⋊C4—1462no—
167C4⋊C4—1462no—
168C4⋊C4—1462no—
169C4⋊C4—1464no—
170C4⋊C4—1462no—
171C4⋊C4—1462no—
172C4⋊C4—1462no—
173C4⋊C4—1464no—
174C42—734no—
175C42—1464no—
176C23C23×D7311yescharacteristic
177Q8—28no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—732no—
190C2×C4—732no—
191C2×C4—1462no—
192C2×C4—1461no—
193C2×C4—1461no—
194C2×C4—1462no—
195C2×C4—1462no—
196C2×C4—1461no—
197C2×C4—1461no—
198C2×C4—1464no—
199C2×C4—1462no—
200C2×C4—1462no—
201C2×C4—1461no—
202C2×C4—1461no—
203C2×C4—1462no—
204C2×C4D4×D7312yes—
205C2×C4#1192402714yes—
206C22C2×D4×D7311yescharacteristic
207C22C2×#1192402712yes—
208C22#1455663811yescharacteristic
209C22#1455663911yescharacteristic
210C22#1455663912yes—
211C4—22no—
212C4—24no—
213C4—41no—
214C4—42no—
215C4—41no—
216C4—2921no—
217C4—2922no—
218C4—2922no—
219C4—2921no—
220C4—1462no—
221C4—1462no—
222C2#1798909311yescharacteristic
223C2#1798916011yescharacteristic
224C2#1798916211yescharacteristic
225C2#1798919712yes—
226C2#1798919812yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#395×C73C2
hypercenter#395D73
hypocenterC73#2634
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
114. C73#2634semidirect