Finite Group Databasebeta

← #22625207

Subgroups — #22625207

Order 9344.

322 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 64 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
1#17989557C211yesmaximal, characteristic, complemented
2C2×C22⋊#10596833C211yesmaximal, characteristic, complemented
3#17989431C212yesmaximal, complemented
4#17989430C212yesmaximal, complemented
5C2×#14556563C211yesmaximal, characteristic
6C2×#11924037—21no—
7C22×#10596833—21no—
8C22⋊#10596833—21no—
9C22⋊#10596833—21no—
10C22⋊#10596833C2212yes—
11C22⋊#10596833C2212yes—
12C22×C22⋊D73C411yescharacteristic
13C22×C22⋊D73C411yescharacteristic
14C23×Dic73C2211yescharacteristic
15#14556563—21no—
16#14556563—21no—
17#14556563—21no—
18#14556563—21no—
19C2×#11924007C411yescharacteristic
20C2×C22⋊Dic73C2211yescharacteristic
21C2×#11924005C2211yescharacteristic
22C22×D4×C73C411yescharacteristic
23#11924037—42no—
24C2×#10596833—22no—
25C2×#10596833—22no—
26C2×#10596833—42no—
27C23×D73C2×C411yescharacteristic
28C2×C22⋊D73—21no—
29C2×C22⋊D73—21no—
30C2×C22⋊D73—21no—
31C2×C22⋊D73—21no—
32C2×C22⋊D73—42no—
33C2×C22⋊D73—42no—
34C22×Dic73—42no—
35C22×Dic73C2×C411yescharacteristic
36C22×Dic73C2×C411yescharacteristic
37C22×Dic73D411yescharacteristic
38C22×Dic73D411yescharacteristic
39C22×Dic73D411yescharacteristic
40C22×Dic73D411yescharacteristic
41C22×Dic73C2311yescharacteristic
42#11924007—21no—
43#11924007—21no—
44C22⋊Dic73—21no—
45C22⋊Dic73—21no—
46#11924005—21no—
47#11924005—21no—
48C24×C73C2×C411yescharacteristic
49C24×C73C2×C411yescharacteristic
50C2×D4×C73—21no—
51C2×D4×C73—21no—
52C2×D4×C73—42no—
53C22×C4×C73C2×C411yescharacteristic
54C23×C73—22no—
55C23×C73—22no—
56C23×C73—21no—
57C23×C73—22no—
58C23×C73—41no—
59C23×C73—41no—
60C23×C73—41no—
61C23×C73C22⋊C411yescharacteristic
62C23×C73C22⋊C411yescharacteristic
63C23×C73C22×C411yescharacteristic
64C22×D73—21no—
65C22×D73—22no—
66C22×D73—41no—
67C22×D73—41no—
68D4×C73—42no—
69D4×C73—42no—
70C2×C4×C73—21no—
71C2×C4×C73—41no—
72C22⋊D73—42no—
73C22⋊D73—42no—
74C22⋊D73—42no—
75C22⋊D73—42no—
76C2×Dic73—22no—
77C2×Dic73—22no—
78C2×Dic73—22no—
79C2×Dic73—21no—
80C2×Dic73—41no—
81C2×Dic73—41no—
82C2×Dic73—41no—
83C2×Dic73—41no—
84C2×Dic73C22⋊C411yescharacteristic
85C2×Dic73C22⋊C411yescharacteristic
86C2×Dic73C2×D411yescharacteristic
87C2×Dic73C2×D411yescharacteristic
88#10596833—42no—
89#10596833—42no—
90C22×C73—21no—
91C22×C73—21no—
92C22×C73—21no—
93C22×C73—21no—
94C22×C73—21no—
95C22×C73—21no—
96C22×C73—21no—
97C22×C73—44no—
98C22×C73—41no—
99C22×C73—41no—
100C22×C73—41no—
101C22×C73—82no—
102C22×C73#10012yes—
103C22×C73C2×C22⋊C411yescharacteristic
104C22×C73#13112yes—
105C2×D73—41no—
106C2×D73—41no—
107C2×D73—41no—
108C2×D73—82no—
109C4×C73—41no—
110Dic73—21no—
111Dic73—21no—
112Dic73—21no—
113Dic73—41no—
114Dic73#9912yes—
115C2×C73—22no—
116C2×C73—22no—
117C2×C73—41no—
118C2×C73—81no—
119C2×C73#40811yescharacteristic
120C2×C73C2×#9911yescharacteristic
121C2×C73C2×#10011yescharacteristic
122D73—81no—
123#1471—731nomaximal, Sylow
124C73#147111yescharacteristic, complemented, Sylow
125C2×#121—731no—
126#407—731no—
127C2×C22⋊C8—731no—
128#323—732no—
129#323—732no—
130C22×D4—731no—
131C22×D4—731no—
132C22×D4#6440811yescharacteristic
133C23×C4—731no—
134C2×M16—1461no—
135C22×C8—1461no—
136#121—1461no—
137#121—1461no—
138#121—1461no—
139#121—1461no—
140C2×C4⋊C4—731no—
141C2×C22⋊C4—731no—
142C2×C22⋊C4—731no—
143C22⋊C8—732no—
144C22⋊C8—732no—
145C22⋊C8—1461no—
146C22⋊C8—1461no—
147C24—731no—
148C24C2×#6440811yescharacteristic
149C24C2×#6440811yescharacteristic
150C2×D4—21no—
151C2×D4—21no—
152C2×D4—42no—
153C2×D4—2922no—
154C2×D4—2922no—
155C2×D4—1461no—
156C2×D4—1461no—
157C2×D4—1461no—
158C2×D4—1461no—
159C22×C4—2922no—
160C22×C4—731no—
161C22×C4—731no—
162C22×C4—731no—
163C22×C4—731no—
164C22×C4—731no—
165C22×C4—731no—
166C22×C4—731no—
167C22×C4C2×#6440811yescharacteristic
168M16—2922no—
169C2×C8—2922no—
170C2×C8—1462no—
171C2×C8—1462no—
172C4⋊C4—1461no—
173C4⋊C4—1461no—
174C22⋊C4—1461no—
175C22⋊C4—1461no—
176C22⋊C4—1461no—
177C22⋊C4—1461no—
178C23—22no—
179C23—22no—
180C23—21no—
181C23—22no—
182C23—41no—
183C23—41no—
184C23—41no—
185C23—2921no—
186C23—2921no—
187C23—1461no—
188C23—1462no—
189C23C22⋊#6440811yescharacteristic
190C23C22⋊#6440811yescharacteristic
191C23C22×#6440811yescharacteristic
192D4—42no—
193D4—42no—
194D4—2922no—
195D4—2922no—
196D4—2922no—
197D4—2922no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4—2921no—
201C2×C4—2921no—
202C2×C4—2921no—
203C2×C4—2921no—
204C2×C4—731no—
205C2×C4—731no—
206C2×C4—731no—
207C2×C4—731no—
208C2×C4—1461no—
209C2×C4—1462no—
210C2×C4—1462no—
211C2×C4—1462no—
212C8—2922no—
213C8—2922no—
214C22—21no—
215C22—21no—
216C22—21no—
217C22—21no—
218C22—21no—
219C22—21no—
220C22—21no—
221C22—44no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—82no—
226C22—2921no—
227C22—2921no—
228C22—2921no—
229C22—5842no—
230C22#1455665112yes—
231C22C2×C22⋊#6440811yescharacteristic
232C22#1455667812yes—
233C4—41no—
234C4—2921no—
235C4—732no—
236C4—1461no—
237C4—1461no—
238C4—1461no—
239C2—22no—
240C2—22no—
241C2—41no—
242C2—81no—
243C2—5841no—
244C2#1798956011yescharacteristic
245C2D73⋊#9911yescharacteristic
246C2C2×#1455665111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC23×C73C22×C4
FrattiniC23C22×#64408
FittingC22×D4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC22×D4#64408
hypocenterC73#1471
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #17989557C2semidirect
2. C2×C22⋊#10596833C2semidirect
3. #17989431C2semidirect
4. #17989430C2semidirect
124. C73#1471semidirect