Finite Group Databasebeta

← #22615899

Subgroups — #22615899

Order 9344.

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

normal subgroups only

This group has 352 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
1C73⋊#401C212yesmaximal
2#17988529C212yesmaximal
3#17988526C212yesmaximal
4#17988525C212yesmaximal
5#17988493C211yesmaximal, characteristic
6#17988492C211yesmaximal, characteristic
7#17988492C211yesmaximal, characteristic
8#17988486C211yesmaximal, characteristic
9#17988483C211yesmaximal, characteristic
10#17988433C211yesmaximal, characteristic
11#389×C73C211yesmaximal, characteristic
12C22×Dic146C2211yescharacteristic
13C2×C4⋊Dic73C2211yescharacteristic
14C2×C4⋊Dic73C2212yes—
15C2×#11924007C2212yes—
16C2×C4×Dic73C2211yescharacteristic
17C2×C4×Dic73C2211yescharacteristic
18#14556498C2211yescharacteristic
19#14556498C2211yescharacteristic
20#14556498C2211yescharacteristic
21#14556498C2211yescharacteristic
22#14556498C2212yes—
23#14556498C2212yes—
24#14556498C2212yes—
25#14556498C2212yes—
26#14556498C2212yes—
27#14556498C2212yes—
28#14556498C2212yes—
29#14556498C2212yes—
30C2×C4⋊C4×C73C2211yescharacteristic
31C2×C4⋊C4×C73C2211yescharacteristic
32C2×C4⋊C4×C73C2212yes—
33C2×C42×C73C2211yescharacteristic
34#95×C73C2212yes—
35C2×Dic146—22no—
36C2×Dic146—22no—
37C2×Dic146—22no—
38C22×Dic73C2311yescharacteristic
39C22×Dic73C2311yescharacteristic
40C22×Dic73C2312yes—
41C22×Dic73C2311yescharacteristic
42C22×Dic73C2311yescharacteristic
43C22×Dic73C2312yes—
44C4⋊Dic73—22no—
45C4⋊Dic73—42no—
46#11924007—42no—
47C4×Dic73—22no—
48C4×Dic73—22no—
49C22×C4×C73C2311yescharacteristic
50C22×C4×C73C2312yes—
51C22×C4×C73C2312yes—
52C22×C4×C73C2311yescharacteristic
53C22×C4×C73C2311yescharacteristic
54C4⋊C4×C73—22no—
55C4⋊C4×C73—22no—
56C4⋊C4×C73—42no—
57C42×C73—22no—
58C23×C73C2411yescharacteristic
59C2×C4×C73—21no—
60C2×C4×C73—21no—
61C2×C4×C73—22no—
62C2×C4×C73—22no—
63C2×C4×C73—21no—
64C2×C4×C73—22no—
65C2×C4×C73—22no—
66C2×C4×C73—21no—
67C2×C4×C73—22no—
68C2×C4×C73—22no—
69C2×C4×C73—21no—
70C2×C4×C73—21no—
71C2×C4×C73#4112yes—
72C2×C4×C73#4112yes—
73C2×C4×C73#4112yes—
74C2×Dic73—21no—
75C2×Dic73—21no—
76C2×Dic73—21no—
77C2×Dic73—21no—
78C2×Dic73—22no—
79C2×Dic73—22no—
80C2×Dic73—22no—
81C2×Dic73—22no—
82C2×Dic73—21no—
83C2×Dic73—22no—
84C2×Dic73—21no—
85C2×Dic73—21no—
86C2×Dic73—21no—
87C2×Dic73—21no—
88C2×Dic73—21no—
89C2×Dic73—21no—
90C2×Dic73—21no—
91C2×Dic73—22no—
92Dic146—44no—
93C22×C73C2×#4111yescharacteristic
94C22×C73C2×#4111yescharacteristic
95C22×C73C2×#4111yescharacteristic
96C22×C73H(5,𝔽2)11yescharacteristic
97C22×C732−1+411yescharacteristic
98C22×C732−1+411yescharacteristic
99C22×C732−1+411yescharacteristic
100C4×C73—41no—
101C4×C73—42no—
102C4×C73—41no—
103C4×C73—42no—
104C4×C73#12614yes—
105Dic73—42no—
106Dic73—41no—
107Dic73—41no—
108Dic73—41no—
109Dic73—41no—
110Dic73—42no—
111C2×C73C2×#12611yescharacteristic
112C2×C73#54111yescharacteristic
113C2×C73#54111yescharacteristic
114C2×C73#54111yescharacteristic
115C2×C73#54211yescharacteristic
116C2×C73#54211yescharacteristic
117C2×C73#54211yescharacteristic
118#2645—731nomaximal, Sylow
119C73#264511yescharacteristic, complemented, Sylow
120#401—732no—
121#400—732no—
122#400—732no—
123#400—732no—
124#391—731no—
125#391—731no—
126#391—731no—
127#389—731no—
128#389—731no—
129#389D7311yescharacteristic
130#376—731no—
131C22×Q8—731no—
132C2×C4⋊C4—732no—
133C2×C4⋊C4—732no—
134C2×C4⋊C4—731no—
135C2×C4⋊C4C2×D7311yescharacteristic
136C2×C4⋊C4C2×D7311yescharacteristic
137C2×C4⋊C4C2×D7312yes—
138C2×C42—731no—
139C2×C42—731no—
140C2×C42C2×D7311yescharacteristic
141#95—731no—
142#95—731no—
143#95—731no—
144#95—731no—
145#95—732no—
146#95—732no—
147#95—732no—
148#95—732no—
149#95—732no—
150#95—732no—
151#95—732no—
152#95—732no—
153#95C2×D7312yes—
154C2×Q8—1462no—
155C2×Q8—1462no—
156C2×Q8—1462no—
157C22×C4—731no—
158C22×C4—731no—
159C22×C4—732no—
160C22×C4—731no—
161C22×C4—731no—
162C22×C4—732no—
163C22×C4C22×D7311yescharacteristic
164C22×C4C22×D7311yescharacteristic
165C22×C4C22×D7312yes—
166C22×C4C22×D7312yes—
167C22×C4C22×D7311yescharacteristic
168C4⋊C4—22no—
169C4⋊C4—22no—
170C4⋊C4—42no—
171C4⋊C4—2922no—
172C4⋊C4—2922no—
173C4⋊C4—1462no—
174C42—22no—
175C42—1462no—
176C42—1462no—
177C23C23×D7311yescharacteristic
178Q8—2924no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—1462no—
192C2×C4—1461no—
193C2×C4—1461no—
194C2×C4—1462no—
195C2×C4—1461no—
196C2×C4—1461no—
197C2×C4—1462no—
198C2×C4—1462no—
199C2×C4—1461no—
200C2×C4—1462no—
201C2×C4—1461no—
202C2×C4—1461no—
203C2×C4—1461no—
204C2×C4—1461no—
205C2×C4—1461no—
206C2×C4—1461no—
207C2×C4—1461no—
208C2×C4—1462no—
209C2×C4#1192402712yes—
210C2×C4#1192402812yes—
211C2×C4#1192402912yes—
212C22C2×#1192402711yescharacteristic
213C22C2×#1192402811yescharacteristic
214C22C2×#1192402911yescharacteristic
215C22#1455663611yescharacteristic
216C22#1455663811yescharacteristic
217C22#1455663811yescharacteristic
218C22#1455663911yescharacteristic
219C4—41no—
220C4—42no—
221C4—41no—
222C4—42no—
223C4—2921no—
224C4—2921no—
225C4—2921no—
226C4—2921no—
227C4—2922no—
228C4—2922no—
229C4#1455658614yes—
230C2C2×#1455658611yescharacteristic
231C2#1798919511yescharacteristic
232C2#1798919711yescharacteristic
233C2#1798920011yescharacteristic
234C2#1798920211yescharacteristic
235C2#1798920411yescharacteristic
236C2#1798921111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#389×C73C2
hypercenter#389D73
hypocenterC73#2645
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
119. C73#2645semidirect