Finite Group Databasebeta

← #22625317

Subgroups — #22625317

Order 9344.

334 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 62 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#17989559C211yesmaximal, characteristic, complemented
2C2×(C2×#64408)⋊C4C211yesmaximal, characteristic, complemented
3#17989441C212yesmaximal, complemented
4#17989438C212yesmaximal, complemented
5#17989094C211yesmaximal, characteristic
6C23×#64408—21no—
7C2×#11924037—21no—
8#14556648—21no—
9#14556648C2212yes—
10(C2×#64408)⋊C4—21no—
11(C2×#64408)⋊C4C2212yes—
12C22×C4×D73C2211yescharacteristic
13#14556572—21no—
14#14556567C411yescharacteristic, complemented
15#14556567C2211yescharacteristic
16#14556562C411yescharacteristic, complemented
17#14556562C2211yescharacteristic
18#14556559—21no—
19C4×C22⋊D73—21no—
20C4×C22⋊D73—21no—
21#14556550C411yescharacteristic, complemented
22C2×#41×C73C411yescharacteristic, complemented
23C22×#64408—24no—
24C22×#64408—22no—
25C22×#64408—42no—
26C22×#64408—42no—
27#11924037—42no—
28C2×#10596833—22no—
29C23×D73D411yescharacteristic
30C2×C22⋊D73—21no—
31C2×C22⋊D73—21no—
32C22×Dic73D411yescharacteristic
33C2×C4×D73—42no—
34C2×C4×D73C2×C411yescharacteristic
35C2×C4×D73D411yescharacteristic
36C2×C4×D73D411yescharacteristic
37C2×C4×D73C2311yescharacteristic
38C4⋊Dic73C2×C411yescharacteristic, complemented
39C4⋊Dic73C2×C411yescharacteristic, complemented
40#11924007—21no—
41#11924007—21no—
42C22⋊Dic73—21no—
43C22⋊Dic73—21no—
44C22⋊Dic73—21no—
45#11924005—21no—
46#11924005—21no—
47C4×Dic73—21no—
48#41×C73—42no—
49C2×Q8×C73C2×C411yescharacteristic, complemented
50C2×D4×C73—21no—
51C2×D4×C73C2×C411yescharacteristic, complemented
52C22×C4×C73—21no—
53C22×C4×C73C2×C411yescharacteristic
54C23×C73—21no—
55C23×C73C22⋊C411yescharacteristic
56C22×D73—22no—
57C22×D73—22no—
58C22×D73—21no—
59C22×D73—21no—
60C22×D73C22⋊C411yescharacteristic
61C22×D73C2×D411yescharacteristic
62C2×#64408—24no—
63C2×#64408—48no—
64C2×#64408—42no—
65C2×#64408—42no—
66Q8×C73—41no—
67D4×C73—41no—
68D4×C73—42no—
69C2×C4×C73—22no—
70C2×C4×C73—21no—
71C2×C4×C73—42no—
72C2×C4×C73C22⋊C411yescharacteristic
73C2×C4×C73C22×C411yescharacteristic
74C22⋊D73—42no—
75C22⋊D73—41no—
76C22⋊D73—41no—
77C2×Dic73—22no—
78C2×Dic73—21no—
79C2×Dic73—21no—
80C2×Dic73C22⋊C411yescharacteristic
81C2×Dic73C2×D411yescharacteristic
82C4×D73—41no—
83C4×D73—41no—
84C4×D73—41no—
85C4×D73—41no—
86#10596833—42no—
87C22×C73—21no—
88C22×C73—21no—
89C22×C73—41no—
90C22×C73—41no—
91C22×C73—41no—
92C22×C73#9912yes—
93C22×C73C2×C22⋊C411yescharacteristic
94C2×D73—24no—
95C2×D73—24no—
96C2×D73—21no—
97C2×D73—21no—
98C2×D73—21no—
99C2×D73—21no—
100C2×D73#10412yes—
101C2×D73AGL(1,ℤ/8)11yescharacteristic
102C2×D73#13711yescharacteristic
103#64408—44no—
104C4×C73—21no—
105C4×C73—21no—
106C4×C73—41no—
107Dic73—21no—
108Dic73—21no—
109Dic73—41no—
110Dic73—41no—
111C2×C73—22no—
112C2×C73—81no—
113C2×C73C2×#9911yescharacteristic
114C2×C73#41711yescharacteristic
115C2×C73C2×#10411yescharacteristic
116D73—21no—
117D73—22no—
118D73—21no—
119#1504—731nomaximal, Sylow
120C73#150411yescharacteristic, complemented, Sylow
121#525—731no—
122#407—731no—
123C2×#95—731no—
124#328—732no—
125#327—732no—
126C2×#41#6440811yescharacteristic, complemented
127C23×C4—731no—
128C23×C4—1461no—
129C2×M16—1461no—
130#123—1461no—
131C22⋊Q8—731no—
132C22⋊Q8—731no—
133#121—731no—
134#121—731no—
135#120—1461no—
136C4×D4—1461no—
137C4×D4—1461no—
138#117—731no—
139C22⋊C8—732no—
140C22⋊C8—1461no—
141#95—732no—
142#95—1461no—
143C24—731no—
144#41—42no—
145C2×Q8C2×#6440811yescharacteristic, complemented
146C2×D4—21no—
147C2×D4—1461no—
148C2×D4—1461no—
149C2×D4C2×#6440811yescharacteristic, complemented
150C22×C4—21no—
151C22×C4—2922no—
152C22×C4—2922no—
153C22×C4—2922no—
154C22×C4—731no—
155C22×C4—731no—
156C22×C4—731no—
157C22×C4—731no—
158C22×C4—731no—
159C22×C4—1462no—
160C22×C4—1464no—
161C22×C4C2×#6440811yescharacteristic
162M16—2922no—
163C2×C8—1462no—
164C4⋊C4—731no—
165C4⋊C4—731no—
166C4⋊C4—1461no—
167C4⋊C4—1461no—
168C22⋊C4—1461no—
169C22⋊C4—1461no—
170C22⋊C4—1461no—
171C22⋊C4—1461no—
172C22⋊C4—1461no—
173C42—1461no—
174C23—21no—
175C23—731no—
176C23—731no—
177C23—1461no—
178C23—1462no—
179C23—1461no—
180C23—1462no—
181C23C22⋊#6440811yescharacteristic
182Q8—41no—
183D4—41no—
184D4—42no—
185D4—2921no—
186D4—2921no—
187D4—2922no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—42no—
191C2×C4—2921no—
192C2×C4—2921no—
193C2×C4—2921no—
194C2×C4—2921no—
195C2×C4—2922no—
196C2×C4—2928no—
197C2×C4—2922no—
198C2×C4—731no—
199C2×C4—731no—
200C2×C4—1464no—
201C2×C4—1461no—
202C2×C4—1461no—
203C2×C4—1462no—
204C2×C4C22⋊#6440811yescharacteristic
205C2×C4C22×#6440811yescharacteristic
206C8—2922no—
207C22—21no—
208C22—21no—
209C22—41no—
210C22—41no—
211C22—41no—
212C22—731no—
213C22—731no—
214C22—732no—
215C22—1464no—
216C22—1464no—
217C22—1461no—
218C22—1461no—
219C22—1461no—
220C22—1461no—
221C22#1455664912yes—
222C22C2×C22⋊#6440811yescharacteristic
223C4—21no—
224C4—21no—
225C4—41no—
226C4—2924no—
227C4—2921no—
228C4—2921no—
229C4—1461no—
230C4—1461no—
231C2—22no—
232C2—81no—
233C2—1461no—
234C2—1461no—
235C2—1462no—
236C2C2×#1455664911yescharacteristic
237C2#1798957811yescharacteristic
238C2D73⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC2×#41×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC2×#41#64408
hypocenterC73#1504
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #17989559C2semidirect
2. C2×(C2×#64408)⋊C4C2semidirect
3. #17989441C2semidirect
4. #17989438C2semidirect
14. #14556567C4semidirect
16. #14556562C4semidirect
21. #14556550C4semidirect
22. C2×#41×C73C4semidirect
38. C4⋊Dic73C2×C4semidirect
39. C4⋊Dic73C2×C4semidirect
49. C2×Q8×C73C2×C4semidirect
51. C2×D4×C73C2×C4semidirect
120. C73#1504semidirect
126. C2×#41#64408semidirect
145. C2×Q8C2×#64408semidirect
149. C2×D4C2×#64408semidirect