Finite Group Databasebeta

← #22618001

Subgroups — #22618001

Order 9344.

380 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14556581C211yesmaximal, characteristic
3#17988529C212yesmaximal
4#17988527C211yesmaximal, characteristic
5#17988526C211yesmaximal, characteristic
6#17988521C212yesmaximal
7#17988520C212yesmaximal
8#17988518C211yesmaximal, characteristic
9#17988518C212yesmaximal
10#17988451C211yesmaximal, characteristic
11#398×C73C211yesmaximal, characteristic
12#14556582—24no—
13#14556581—24no—
14C2×C4⋊Dic73C2212yes—
15C2×C4⋊Dic73C2211yescharacteristic
16C2×C4⋊Dic73C2211yescharacteristic
17C2×#11924007C2211yescharacteristic
18C2×#11924007C2212yes—
19C2×#11924007C2211yescharacteristic
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2211yescharacteristic
22C2×#11924007C2212yes—
23C2×#11924007C2212yes—
24C2×C4×Dic73C2211yescharacteristic
25#14556498C2211yescharacteristic
26#14556498C2212yes—
27#14556498C2212yes—
28#14556498C2212yes—
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C2×C4⋊C4×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2211yescharacteristic
34C2×C4⋊C4×C73C2212yes—
35#95×C73C2211yescharacteristic
36#95×C73C2212yes—
37C22×Dic73C2312yes—
38C22×Dic73C2311yescharacteristic
39C22×Dic73C2312yes—
40C22×Dic73C2311yescharacteristic
41C22×Dic73C2311yescharacteristic
42C22×Dic73C2311yescharacteristic
43C4⋊Dic73—22no—
44C4⋊Dic73—22no—
45C4⋊Dic73—24no—
46#11924007—22no—
47#11924007—22no—
48#11924007—22no—
49#11924007—22no—
50#11924007—24no—
51#11924007—42no—
52#11924007—42no—
53C4×Dic73D414yes—
54C22×C4×C73C2312yes—
55C22×C4×C73C2311yescharacteristic
56C22×C4×C73C2312yes—
57C22×C4×C73C2311yescharacteristic
58C22×C4×C73C2311yescharacteristic
59C4⋊C4×C73—22no—
60C4⋊C4×C73—22no—
61C4⋊C4×C73—42no—
62C23×C73C2411yescharacteristic
63C2×C4×C73—22no—
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—22no—
72C2×C4×C73—21no—
73C2×C4×C73—22no—
74C2×C4×C73—22no—
75C2×C4×C73C2×D412yes—
76C2×Dic73—21no—
77C2×Dic73—21no—
78C2×Dic73—22no—
79C2×Dic73—21no—
80C2×Dic73—21no—
81C2×Dic73—22no—
82C2×Dic73—21no—
83C2×Dic73—22no—
84C2×Dic73—22no—
85C2×Dic73—21no—
86C2×Dic73—22no—
87C2×Dic73—24no—
88C2×Dic73—22no—
89C2×Dic73C2×D412yes—
90C2×Dic73C2×D412yes—
91C22×C73C22×D411yescharacteristic
92C22×C73H(5,𝔽2)11yescharacteristic
93C22×C732−1+412yes—
94C22×C732−1+411yescharacteristic
95C22×C732−1+412yes—
96C4×C73—22no—
97C4×C73—41no—
98C4×C73—41no—
99C4×C73—42no—
100C4×C73—42no—
101Dic73—22no—
102Dic73—22no—
103Dic73—41no—
104Dic73—42no—
105Dic73—41no—
106Dic73—42no—
107C2×C73#53611yescharacteristic
108C2×C73#53611yescharacteristic
109C2×C73#53711yescharacteristic
110C2×C73#56312yes—
111C2×C73#56412yes—
112#2822—731nomaximal, Sylow
113C73#282211yescharacteristic, complemented, Sylow
114C2×#125—731no—
115C2×#125—731no—
116#400—731no—
117#400—731no—
118#400—732no—
119#398—731no—
120#398—732no—
121#398—732no—
122#398—732no—
123#398D7311yescharacteristic
124#382—731no—
125#125—1464no—
126#125—1464no—
127C2×C4⋊C4—732no—
128C2×C4⋊C4—732no—
129C2×C4⋊C4—731no—
130C2×C4⋊C4—731no—
131C2×C4⋊C4—732no—
132C2×C4⋊C4—731no—
133C2×C4⋊C4—731no—
134C2×C4⋊C4—731no—
135C2×C4⋊C4—732no—
136C2×C4⋊C4—731no—
137C2×C4⋊C4C2×D7311yescharacteristic
138C2×C4⋊C4C2×D7311yescharacteristic
139C2×C4⋊C4C2×D7312yes—
140C2×C42—731no—
141#95—732no—
142#95—731no—
143#95—732no—
144#95—732no—
145#95—732no—
146#95—732no—
147#95—732no—
148#95C2×D7311yescharacteristic
149#95C2×D7312yes—
150C22×C4—731no—
151C22×C4—731no—
152C22×C4—732no—
153C22×C4—731no—
154C22×C4—732no—
155C22×C4—731no—
156C22×C4C22×D7312yes—
157C22×C4C22×D7311yescharacteristic
158C22×C4C22×D7311yescharacteristic
159C22×C4C22×D7312yes—
160C22×C4C22×D7311yescharacteristic
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—42no—
164C4⋊C4—2922no—
165C4⋊C4—2922no—
166C4⋊C4—1462no—
167C4⋊C4—1462no—
168C4⋊C4—1462no—
169C4⋊C4—1464no—
170C4⋊C4—1462no—
171C4⋊C4—1464no—
172C4⋊C4—1462no—
173C4⋊C4—1462no—
174C42—734no—
175C23C23×D7311yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—732no—
189C2×C4—732no—
190C2×C4—1461no—
191C2×C4—1462no—
192C2×C4—1461no—
193C2×C4—1461no—
194C2×C4—1462no—
195C2×C4—1462no—
196C2×C4—1461no—
197C2×C4—1462no—
198C2×C4—1464no—
199C2×C4—1462no—
200C2×C4—1461no—
201C2×C4—1461no—
202C2×C4—1462no—
203C2×C4D4×D7312yes—
204C22C2×D4×D7311yescharacteristic
205C22#1455663611yescharacteristic
206C22#1455663812yes—
207C22#1455663811yescharacteristic
208C22#1455663912yes—
209C4—22no—
210C4—41no—
211C4—41no—
212C4—42no—
213C4—42no—
214C4—2921no—
215C4—2922no—
216C4—2921no—
217C4—2922no—
218C4—1462no—
219C4—1462no—
220C2#1798915911yescharacteristic
221C2#1798916211yescharacteristic
222C2#1798916611yescharacteristic
223C2#1798933812yes—
224C2C73⋊#56412yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#398×C73C2
hypercenter#398D73
hypocenterC73#2822
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
113. C73#2822semidirect