Finite Group Databasebeta

← #22619291

Subgroups — #22619291

Order 9344.

762 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 145 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×#14556636C211yesmaximal, characteristic, complemented
2#17989387C212yesmaximal, complemented
3#17989154C211yesmaximal, characteristic, complemented
4#17988767C214yesmaximal, complemented
5#17988757C214yesmaximal, complemented
6#17988603C212yesmaximal, complemented
7C2×#100×C73C211yesmaximal, characteristic, complemented
8#14556636—24no—
9#14556636—22no—
10#14556636C2214yes—
11C2×#11924028C2212yes—
12C2×#11924028C2211yescharacteristic, complemented
13C2×#11924027—22no—
14C22×C22⋊D73—22no—
15C2×D4×D73—22no—
16#14556624—22no—
17#14556624C2214yescomplemented
18#14556619—22no—
19#14556619C2214yescomplemented
20#14556613—24no—
21#14556587C2212yescomplemented
22#14556578C2212yescomplemented
23#14556562—22no—
24#14556560—22no—
25#14556550C2211yescharacteristic, complemented
26#14556517C2218yescomplemented
27C22×D4×C73C2211yescharacteristic
28C2×M16×C73C2212yescomplemented
29#100×C73C2214yescomplemented
30C23×D73—22no—
31#11924028—22no—
32#11924028—22no—
33#11924028—22no—
34#11924028—22no—
35#11924028D414yescomplemented
36#11924028C2314yes—
37#11924027—28no—
38#11924027—28no—
39C2×Dic146D412yescomplemented
40C2×Dic146C2311yescharacteristic, complemented
41C2×D292D412yescomplemented
42C2×D292C2311yescharacteristic, complemented
43C2×C22⋊D73—24no—
44C2×C22⋊D73—28no—
45C2×C22⋊D73—22no—
46C2×C22⋊D73—28no—
47C2×C22⋊D73—21no—
48C2×C22⋊D73—24no—
49D4×D73—28no—
50D4×D73—28no—
51C22×Dic73—22no—
52C2×C4×D73—22no—
53C2×C4×D73—21no—
54Dic292—24no—
55#11924017—24no—
56#11924017—24no—
57D584—24no—
58C4⋊Dic73—21no—
59C22⋊Dic73—21no—
60C22⋊Dic73—24no—
61C4×Dic73C2312yescomplemented
62C24×C73D412yes—
63C2×D4×C73—22no—
64C2×D4×C73—22no—
65C2×D4×C73D412yes—
66C2×D4×C73C2312yes—
67C22×C4×C73C2311yescharacteristic
68M16×C73—22no—
69M16×C73C2314yescomplemented
70C2×C8×C73—22no—
71C23×C73—22no—
72C23×C73—22no—
73C23×C73—82no—
74C23×C73C2×D414yes—
75C23×C73C2×D411yescharacteristic
76C22×D73—22no—
77C22×D73—28no—
78C22×D73—21no—
79C22×D73—84no—
80D4×C73—24no—
81D4×C73—24no—
82C2×C4×C73C2×D412yes—
83C2×C4×C73C2×D412yes—
84C2×C4×C73C2×D411yescharacteristic
85C2×C4×C73C2411yescharacteristic
86C22⋊D73—216no—
87C22⋊D73—24no—
88C22⋊D73—24no—
89C22⋊D73—41no—
90C22⋊D73—41no—
91C22⋊D73—84no—
92C2×Dic73—28no—
93C2×Dic73—22no—
94C2×Dic73—22no—
95C2×Dic73—21no—
96D292—22no—
97D292—22no—
98D292C2×D414yes—
99C4×D73—24no—
100C4×D73—24no—
101C4×D73—42no—
102Dic146—22no—
103Dic146—22no—
104Dic146C2×D414yes—
105C8×C73—24no—
106C22×C73—24no—
107C22×C73—41no—
108C22×C73—44no—
109C22×C73—44no—
110C22×C73—82no—
111C22×C73#12011yescharacteristic
112C22×C73#12011yescharacteristic
113C22×C73C22×D411yescharacteristic
114C2×D73—24no—
115C2×D73—44no—
116C2×D73—42no—
117C2×D73—41no—
118C2×D73—88no—
119C4×C73#12012yes—
120C4×C73C22×D412yes—
121Dic73—24no—
122Dic73—42no—
123Dic73—41no—
124C2×C73—21no—
125C2×C73—21no—
126C2×C73—21no—
127C2×C73—44no—
128C2×C73C2×#12011yescharacteristic
129D73—44no—
130D73—81no—
131#3019—731nomaximal, Sylow
132C73#301911yescharacteristic, complemented, Sylow
133C2×H(5,𝔽2)—731no—
134#575—732no—
135#535—731no—
136#455—734no—
137#453—734no—
138#421—732no—
139C2×#100D7311yescharacteristic, complemented
140H(5,𝔽2)—734no—
141H(5,𝔽2)—1464no—
142H(5,𝔽2)—1462no—
143C2×#41—732no—
144C2×#41—731no—
145C2×#41—1462no—
146C22×D4—1462no—
147C22×D4—1462no—
148C22×D4C2×D7311yescharacteristic
149#137—734no—
150#137—1462no—
151AGL(1,ℤ/8)—734no—
152AGL(1,ℤ/8)—1462no—
153#135—1464no—
154C2×M16C2×D7312yescomplemented
155#127—732no—
156#124—732no—
157#121—1462no—
158#120—1462no—
159#117—731no—
160#104—738no—
161#100C2×D7314yescomplemented
162C24—1462no—
163C24D29212yes—
164#41—734no—
165#41—734no—
166#41—1462no—
167#41—1462no—
168#41—1468no—
169#41—1468no—
170#41—1462no—
171#41—1462no—
172C2×Q8—732no—
173C2×Q8—731no—
174C2×D4—22no—
175C2×D4—22no—
176C2×D4—732no—
177C2×D4—731no—
178C2×D4—1468no—
179C2×D4—1468no—
180C2×D4—1461no—
181C2×D4—1464no—
182C2×D4—1464no—
183C2×D4—1468no—
184C2×D4—1462no—
185C2×D4—1468no—
186C2×D4D29212yes—
187C2×D4C22×D7312yes—
188C22×C4—1461no—
189C22×C4—1462no—
190C22×C4—1462no—
191C22×C4C22×D7311yescharacteristic
192Q16—1464no—
193SD16—1464no—
194SD16—1464no—
195D8—1464no—
196M16—22no—
197M16C22×D7314yescomplemented
198C2×C8—22no—
199C4⋊C4—1461no—
200C22⋊C4—1461no—
201C22⋊C4—1464no—
202C42—732no—
203C23—22no—
204C23—22no—
205C23—82no—
206C23—5844no—
207C23—1468no—
208C23—1461no—
209C23—1462no—
210C23C2×D29214yes—
211C23C2×D29211yescharacteristic
212Q8—734no—
213Q8—1462no—
214Q8—1462no—
215D4—24no—
216D4—24no—
217D4—2921no—
218D4—2921no—
219D4—5844no—
220D4—734no—
221D4—14616no—
222D4—1464no—
223D4—1464no—
224D4—1462no—
225D4—1462no—
226C2×C4—2922no—
227C2×C4—1462no—
228C2×C4—1461no—
229C2×C4—1468no—
230C2×C4—1462no—
231C2×C4—1464no—
232C2×C4—1464no—
233C2×C4D4×D7312yes—
234C2×C4D4×D7312yes—
235C2×C4C2×D29211yescharacteristic
236C2×C4C23×D7311yescharacteristic
237C8—24no—
238C22—24no—
239C22—41no—
240C22—44no—
241C22—44no—
242C22—82no—
243C22—2924no—
244C22—2922no—
245C22—2921no—
246C22—5848no—
247C22—1464no—
248C22#1455656111yescharacteristic
249C22#1455656111yescharacteristic
250C22C22×D29211yescharacteristic
251C4—2922no—
252C4—2921no—
253C4—1464no—
254C4#1455656112yes—
255C4C2×D4×D7312yes—
256C2—21no—
257C2—21no—
258C2—21no—
259C2—44no—
260C2—2924no—
261C2—5841no—
262C2C2×#1455656111yescharacteristic
subgroupG/H
centerC2C2×#14556561
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×#100×C73C2
socleC2×C73C2×#120
hypercenterC2×#100D73
hypocenterC73#3019
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C2×#14556636C2semidirect
2. #17989387C2semidirect
3. #17989154C2semidirect
4. #17988767C2semidirect
5. #17988757C2semidirect
6. #17988603C2semidirect
7. C2×#100×C73C2semidirect
12. C2×#11924028C22semidirect
17. #14556624C22semidirect
19. #14556619C22semidirect
21. #14556587C22semidirect
22. #14556578C22semidirect
25. #14556550C22semidirect
26. #14556517C22semidirect
28. C2×M16×C73C22semidirect
29. #100×C73C22semidirect
35. #11924028D4semidirect
39. C2×Dic146D4semidirect
40. C2×Dic146C23semidirect
41. C2×D292D4semidirect
42. C2×D292C23semidirect
61. C4×Dic73C23semidirect
69. M16×C73C23semidirect
132. C73#3019semidirect
139. C2×#100D73semidirect
154. C2×M16C2×D73semidirect
161. #100C2×D73semidirect
197. M16C22×D73semidirect