Finite Group Databasebeta

← #22625701

Subgroups — #22625701

Order 9344.

388 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 100 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×#14556653C212yesmaximal
2#17989546C211yesmaximal, characteristic, complemented
3C4×C4⋊#64408C211yesmaximal, characteristic, complemented
4#17989460C212yesmaximal, complemented
5C4×D4×D73C211yesmaximal, characteristic
6C2×#11924036C2212yes—
7C2×C4⋊#64408C2212yes—
8C2×C4×#64408—21no—
9#14556653C418yescomplemented
10#14556646—21no—
11#14556646—21no—
12(C2×#64408)⋊C4—21no—
13C2×D4×D73C2211yescharacteristic
14C22×C4×D73—21no—
15C4×D292C411yescharacteristic, complemented
16D4×Dic73C411yescharacteristic, complemented
17#14556553C411yescharacteristic, complemented
18C4×C22⋊D73—21no—
19#14556551—21no—
20C4⋊C4×D73C2211yescharacteristic
21C22⋊C4×D73—21no—
22C42×D73C2211yescharacteristic
23C4×D4×C73C411yescharacteristic, complemented
24C22×#64408—22no—
25#11924036—22no—
26#11924036C2×C414yescomplemented
27C2×#10596833—22no—
28C4⋊#64408—22no—
29C4⋊#64408C2×C414yescomplemented
30C4×#64408—42no—
31C23×D73—21no—
32C2×D292C2×C411yescharacteristic
33C2×C22⋊D73—21no—
34D4×D73—22no—
35D4×D73C2×C414yes—
36C22×Dic73—21no—
37C2×C4×D73—21no—
38C2×C4×D73—21no—
39C2×C4×D73—21no—
40C2×C4×D73—44no—
41C2×C4×D73D411yescharacteristic
42C2×C4×D73D411yescharacteristic
43C2×C4×D73C2311yescharacteristic
44C4⋊Dic73C2×C411yescharacteristic
45#11924007—21no—
46C22⋊Dic73—21no—
47#11924005—21no—
48#11924005—21no—
49C4×Dic73C2×C411yescharacteristic
50C4×Dic73D411yescharacteristic
51C4×Dic73D411yescharacteristic
52C2×D4×C73C2×C411yescharacteristic
53C22×C4×C73—21no—
54C4⋊C4×C73C2×C411yescharacteristic
55C22⋊C4×C73—21no—
56C42×C73C2×C411yescharacteristic
57C23×C73—21no—
58C22×D73—21no—
59C22×D73—24no—
60C22×D73—42no—
61C22×D73—41no—
62C22×D73—41no—
63C22×D73C2×D411yescharacteristic
64C2×#64408—24no—
65C2×#64408—42no—
66C2×#64408—42no—
67D4×C73—21no—
68D4×C73C4212yescomplemented
69C2×C4×C73—21no—
70C2×C4×C73—42no—
71C2×C4×C73C22⋊C411yescharacteristic
72C2×C4×C73C22⋊C411yescharacteristic
73C2×C4×C73C22×C411yescharacteristic
74C22⋊D73—24no—
75C2×Dic73—21no—
76C2×Dic73—42no—
77C2×Dic73C22⋊C411yescharacteristic
78C2×Dic73C22⋊C411yescharacteristic
79C2×Dic73C2×D411yescharacteristic
80D292—21no—
81D292C4212yescomplemented
82C4×D73—22no—
83C4×D73—21no—
84C4×D73—21no—
85C4×D73—42no—
86C4×D73—42no—
87C4×D73—42no—
88C4×D73C22×C412yes—
89C4×D73#4112yes—
90#10596833—24no—
91C22×C73—22no—
92C22×C73—41no—
93C22×C73—41no—
94C22×C73C2×C22⋊C411yescharacteristic
95C2×D73—22no—
96C2×D73—41no—
97C2×D73—41no—
98C2×D73—44no—
99C2×D73—44no—
100C2×D73C4×D412yes—
101C2×D73AGL(1,ℤ/8)12yes—
102C2×D73AGL(1,ℤ/8)11yescharacteristic
103C2×D73#13711yescharacteristic
104#64408—44no—
105C4×C73—21no—
106C4×C73—21no—
107C4×C73—41no—
108C4×C73C2×C4211yescharacteristic
109C4×C73#11711yescharacteristic
110Dic73—21no—
111Dic73—21no—
112Dic73—41no—
113Dic73C4×D412yes—
114C2×C73—42no—
115C2×C73C4×C22⋊C411yescharacteristic
116C2×C73#41711yescharacteristic
117C2×C73#41811yescharacteristic
118D73—42no—
119D73#44012yes—
120D73#44212yes—
121#1762—731nomaximal, Sylow
122C73#176211yescharacteristic, complemented, Sylow
123C2×C4×D4—731no—
124C2×#102—732no—
125C2×#97—731no—
126C4×C4⋊C4—731no—
127#340—732no—
128C22×D4—731no—
129C23×C4—1461no—
130C22×C8—732no—
131C4×D4—731no—
132C4×D4—731no—
133C4×D4—731no—
134C4×D4—1461no—
135C4×D4—1461no—
136C4×D4#6440811yescharacteristic, complemented
137C2×C4⋊C4—732no—
138C2×C4⋊C4—731no—
139C2×C22⋊C4—1461no—
140C2×C42—731no—
141C2×C42—1461no—
142#102—738no—
143#97—1461no—
144#97—1461no—
145#95—1461no—
146C24—1461no—
147C2×D4—734no—
148C2×D4—731no—
149C2×D4—1462no—
150C2×D4—1461no—
151C2×D4C2×#6440811yescharacteristic
152C22×C4—21no—
153C22×C4—2924no—
154C22×C4—731no—
155C22×C4—731no—
156C22×C4—731no—
157C22×C4—1461no—
158C22×C4—1461no—
159C22×C4—1461no—
160C22×C4—1462no—
161C22×C4—1461no—
162C2×C8—734no—
163C2×C8—1462no—
164C2×C8—1462no—
165C4⋊C4—734no—
166C4⋊C4—731no—
167C4⋊C4—1461no—
168C4⋊C4—1462no—
169C4⋊C4C2×#6440811yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—1461no—
172C22⋊C4—1461no—
173C22⋊C4—1461no—
174C42—2922no—
175C42—731no—
176C42—731no—
177C42—731no—
178C42C2×#6440811yescharacteristic
179C23—21no—
180C23—2922no—
181C23—2921no—
182C23—2921no—
183C23—731no—
184C23—1464no—
185C23—1461no—
186D4—21no—
187D4—732no—
188D4—1464no—
189D4—1461no—
190D4C4×#6440812yescomplemented
191C2×C4—21no—
192C2×C4—42no—
193C2×C4—2922no—
194C2×C4—2922no—
195C2×C4—2922no—
196C2×C4—2922no—
197C2×C4—2922no—
198C2×C4—2922no—
199C2×C4—731no—
200C2×C4—732no—
201C2×C4—732no—
202C2×C4—731no—
203C2×C4—731no—
204C2×C4—1461no—
205C2×C4—1462no—
206C2×C4—1461no—
207C2×C4—1464no—
208C2×C4—1461no—
209C2×C4C22⋊#6440811yescharacteristic
210C2×C4C22⋊#6440811yescharacteristic
211C2×C4C22×#6440811yescharacteristic
212C8—1464no—
213C22—22no—
214C22—41no—
215C22—41no—
216C22—2924no—
217C22—2924no—
218C22—2921no—
219C22—2921no—
220C22—732no—
221C22—731no—
222C22—731no—
223C22—732no—
224C22—1462no—
225C22C2×C22⋊#6440811yescharacteristic
226C4—21no—
227C4—21no—
228C4—41no—
229C4—2924no—
230C4—2921no—
231C4—732no—
232C4—1461no—
233C4—1461no—
234C4C2×C4×#6440811yescharacteristic
235C4#1455667011yescharacteristic
236C2—42no—
237C2—2922no—
238C2—732no—
239C2—732no—
240C2C4×C22⋊#6440811yescharacteristic
241C2#1798957811yescharacteristic
242C2#1798957911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC4×C73C2×C42
FrattiniC2×C4C22×#64408
FittingC4×D4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC4×D4#64408
hypocenterC73#1762
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #17989546C2semidirect
3. C4×C4⋊#64408C2semidirect
4. #17989460C2semidirect
9. #14556653C4semidirect
15. C4×D292C4semidirect
16. D4×Dic73C4semidirect
17. #14556553C4semidirect
23. C4×D4×C73C4semidirect
26. #11924036C2×C4semidirect
29. C4⋊#64408C2×C4semidirect
68. D4×C73C42semidirect
81. D292C42semidirect
122. C73#1762semidirect
136. C4×D4#64408semidirect
190. D4C4×#64408semidirect