Finite Group Databasebeta

← #22619428

Subgroups — #22619428

Order 9344.

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

normal subgroups only

This group has 500 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
1C2×#14556622C211yesmaximal, characteristic, complemented
2C2×#14556619C211yesmaximal, characteristic
3C2×#14556580C211yesmaximal, characteristic, complemented
4#17989055C211yesmaximal, characteristic, complemented
5#17988812C214yesmaximal, complemented
6#17988805C214yesmaximal, complemented
7#17988610C211yesmaximal, characteristic, complemented
8#17988591C211yesmaximal, characteristic, complemented
9#419×C73C211yesmaximal, characteristic, complemented
10C2×#11924028C2211yescharacteristic
11C22×D292C2211yescharacteristic
12#14556622—24no—
13#14556619—24no—
14C2×#11924018C2212yescomplemented
15C2×#11924017C2212yes—
16C2×#11924015C2212yescomplemented
17C2×D584C2212yes—
18C2×#11924012C2211yescharacteristic
19#14556580—21no—
20#14556580—21no—
21#14556580C2214yes—
22#14556556C2212yescomplemented
23#14556553C2212yescomplemented
24#14556551—22no—
25#14556548—21no—
26C2×#11924005—22no—
27C2×C4×Dic73C2211yescharacteristic
28C42×D73—21no—
29#14556520C2214yescomplemented
30#14556511C2214yes—
31C22×Q8×C73C2211yescharacteristic
32C2×M16×C73C2211yescharacteristic
33#117×C73C2211yescharacteristic
34#103×C73C2214yescomplemented
35C23×D73—21no—
36#11924028—22no—
37#11924028D414yes—
38C2×Dic146C2311yescharacteristic
39C2×D292—22no—
40C2×D292—22no—
41C2×D292—21no—
42C2×D292C2312yes—
43C2×D292C2311yescharacteristic
44C2×C22⋊D73—21no—
45C22×Dic73D412yes—
46C2×C4×D73—21no—
47C2×C4×D73—22no—
48#11924018—24no—
49#11924017—24no—
50#11924015—24no—
51D584—24no—
52#11924012—22no—
53C2×#10596831C2312yes—
54#11924007—22no—
55#11924005—24no—
56#11924005—24no—
57#11924005—22no—
58C4×Dic73—22no—
59C4×Dic73D411yescharacteristic
60C4×Dic73D411yescharacteristic
61C4×Dic73C2312yes—
62C2×Q8×C73—21no—
63C2×Q8×C73—22no—
64C2×Q8×C73—22no—
65C2×Q8×C73C2312yes—
66C22×C4×C73—21no—
67C22×C4×C73C2311yescharacteristic
68M16×C73—22no—
69C2×C8×C73C2312yes—
70C4⋊C4×C73C2312yes—
71C22⋊C4×C73—21no—
72C42×C73—21no—
73C23×C73C2×D411yescharacteristic
74C22×D73—21no—
75C22×D73—22no—
76C22×D73—44no—
77C22×D73—42no—
78Q8×C73—22no—
79Q8×C73—22no—
80Q8×C73—42no—
81C2×C4×C73—22no—
82C2×C4×C73—22no—
83C2×C4×C73—42no—
84C2×C4×C73C2×D411yescharacteristic
85C2×C4×C73C2×D412yes—
86C2×C4×C73#4112yes—
87C2×C4×C73C2411yescharacteristic
88C22⋊D73—24no—
89C2×Dic73—21no—
90C2×Dic73—42no—
91C2×Dic73C2×D412yes—
92C2×Dic73C2×D412yes—
93D292—22no—
94D292—21no—
95D292—22no—
96D292—42no—
97D292C2×D412yes—
98C4×D73—24no—
99C4×D73—44no—
100Dic146—21no—
101Dic146C2×D412yes—
102C8×C73—22no—
103#10596831—22no—
104C22×C73—22no—
105C22×C73#12112yes—
106C22×C73C22×D411yescharacteristic
107C2×D73—22no—
108C2×D73—42no—
109C2×D73—42no—
110C2×D73—44no—
111C2×D73—84no—
112C4×C73—42no—
113C4×C73—42no—
114C4×C73#12112yes—
115C4×C73C22×D411yescharacteristic
116C4×C73C2×#4111yescharacteristic
117Dic73—22no—
118Dic73—22no—
119Dic73—22no—
120C2×C73—22no—
121C2×C73C2×#12111yescharacteristic
122C2×C73#57512yes—
123D73—42no—
124D73—82no—
125#3040—731nomaximal, Sylow
126C73#304011yescharacteristic, complemented, Sylow
127C2×#137—731no—
128C2×AGL(1,ℤ/8)—731no—
129C2×#124—731no—
130C4×#41—731no—
131#464—734no—
132#463—734no—
133#423—731no—
134#419D7311yescharacteristic, complemented
135#418—731no—
136C2×#41—731no—
137C22×Q8C2×D7311yescharacteristic
138C22×D4—731no—
139#137—1464no—
140AGL(1,ℤ/8)—1464no—
141C2×Q16—732no—
142C2×SD16—732no—
143C2×SD16—732no—
144C2×D8—732no—
145C2×M16—731no—
146C2×M16C2×D7311yescharacteristic
147#124—734no—
148#124—1461no—
149#124—1461no—
150C4×Q8—732no—
151C4×D4—732no—
152C4×D4—1462no—
153#117—1461no—
154#117C2×D7311yescharacteristic
155C2×C22⋊C4—1462no—
156C2×C42—731no—
157C2×C42—1461no—
158C4⋊C8—734no—
159#103C2×D7314yescomplemented
160#102—734no—
161C24—1461no—
162#41—734no—
163#41—1462no—
164C2×Q8—21no—
165C2×Q8—22no—
166C2×Q8—22no—
167C2×Q8—731no—
168C2×Q8C22×D7312yes—
169C2×D4—731no—
170C2×D4—732no—
171C2×D4—1461no—
172C2×D4—1461no—
173C2×D4—1462no—
174C2×D4—1462no—
175C22×C4—21no—
176C22×C4—732no—
177C22×C4—1462no—
178C22×C4—1461no—
179C22×C4C22×D7311yescharacteristic
180Q16—1464no—
181SD16—1464no—
182SD16—1464no—
183D8—1464no—
184M16—22no—
185M16—1462no—
186C2×C8—732no—
187C2×C8C22×D7312yes—
188C4⋊C4—1462no—
189C4⋊C4C22×D7312yes—
190C22⋊C4—21no—
191C22⋊C4—1464no—
192C22⋊C4—1464no—
193C22⋊C4—1462no—
194C42—21no—
195C42—731no—
196C42—731no—
197C42—732no—
198C42—1462no—
199C23—2924no—
200C23—2922no—
201C23—1462no—
202C23—1461no—
203C23D4×D7311yescharacteristic
204Q8—22no—
205Q8—22no—
206Q8—42no—
207Q8—732no—
208Q8—1461no—
209D4—2922no—
210D4—732no—
211D4—1464no—
212D4—1462no—
213D4—1462no—
214D4—1461no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—42no—
218C2×C4—2924no—
219C2×C4—2922no—
220C2×C4—732no—
221C2×C4—732no—
222C2×C4—1461no—
223C2×C4—1464no—
224C2×C4D4×D7311yescharacteristic
225C2×C4D4×D7312yes—
226C2×C4#1192402812yes—
227C2×C4C23×D7311yescharacteristic
228C8—22no—
229C8—1462no—
230C22—22no—
231C22—2922no—
232C22—2924no—
233C22—2922no—
234C22—5844no—
235C22—1462no—
236C22#1455656412yes—
237C22C2×D4×D7311yescharacteristic
238C4—42no—
239C4—42no—
240C4—1462no—
241C4—1462no—
242C4—1462no—
243C4#1455656412yes—
244C4C2×D4×D7311yescharacteristic
245C4C2×#1192402811yescharacteristic
246C2—22no—
247C2—2922no—
248C2—5842no—
249C2C2×#1455656411yescharacteristic
250C2#1798938612yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#419×C73C2
socleC22×C73C22×D4
hypercenter#419D73
hypocenterC73#3040
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. C2×#14556622C2semidirect
3. C2×#14556580C2semidirect
4. #17989055C2semidirect
5. #17988812C2semidirect
6. #17988805C2semidirect
7. #17988610C2semidirect
8. #17988591C2semidirect
9. #419×C73C2semidirect
14. C2×#11924018C22semidirect
16. C2×#11924015C22semidirect
22. #14556556C22semidirect
23. #14556553C22semidirect
29. #14556520C22semidirect
34. #103×C73C22semidirect
126. C73#3040semidirect
134. #419D73semidirect
159. #103C2×D73semidirect