Finite Group Databasebeta

← #21446863

Subgroups — #21446863

Order 7808.

406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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×#14519805C212yesmaximal, complemented
2#16840343C211yesmaximal, characteristic, complemented
3C2×#14519703C212yesmaximal, complemented
4#16839663C211yesmaximal, characteristic, complemented
5C61×#343C211yesmaximal, characteristic, complemented
6C2×#11758222C2212yes—
7C22×D244C2211yescharacteristic
8#14519805—24no—
9#14519805—24no—
10C2×#11758190—22no—
11C2×D488—22no—
12#14519757—22no—
13#14519752—22no—
14#14519751—22no—
15C2×#11758198—22no—
16C2×C4×Dic61C2211yescharacteristic
17#14519703—24no—
18C2×M16×C61C2212yes—
19C2×C4⋊C4×C61C2211yescharacteristic
20C23×D61—21no—
21C22×C4×C61D412yes—
22C22×C4×C61C2311yescharacteristic
23C2×C22⋊D61—22no—
24C22×Dic61—21no—
25#11758222—22no—
26#11758222—22no—
27#11758222—22no—
28#11758222—22no—
29C2×D244—22no—
30C2×D244—22no—
31C2×D244—21no—
32C2×D244—22no—
33C2×D244D412yes—
34C2×D244D412yescomplemented
35C2×C4×D61—22no—
36C2×Dic122D412yes—
37M16×C61—22no—
38M16×C61D414yescomplemented
39C2×C8×C61—22no—
40C4⋊C4×C61—22no—
41#11758198—24no—
42#11758198—44no—
43C4⋊Dic61—22no—
44C4×Dic61—22no—
45D488—28no—
46#11758190—28no—
47C23×C61C2×D411yescharacteristic
48C22×D61—22no—
49C22×D61—22no—
50C22×D61—42no—
51C22×D61—42no—
52C22×D61—41no—
53C22×D61—41no—
54C2×C4×C61—22no—
55C2×C4×C61—42no—
56C2×C4×C61C2×D411yescharacteristic
57C2×C4×C61C2×D412yes—
58C2×C4×C61C2×D412yes—
59C2×C4×C61#4111yescharacteristic
60C22⋊D61—42no—
61C22⋊D61—42no—
62C2×Dic61—22no—
63C2×Dic61—22no—
64C2×Dic61—41no—
65C2×Dic61—41no—
66D244—24no—
67D244—22no—
68D244—22no—
69D244—42no—
70D244—82no—
71C4×D61—42no—
72C4×D61—42no—
73Dic122—22no—
74Dic122—22no—
75C8×C61—24no—
76C22×C61—21no—
77C22×C61—21no—
78C22×C61#12011yescharacteristic
79C22×C61#12111yescharacteristic
80C22×C61#12711yescharacteristic
81C2×D61—44no—
82C2×D61—42no—
83C2×D61—42no—
84C2×D61—42no—
85C2×D61—42no—
86C2×D61—82no—
87C2×D61—81no—
88C2×D61—81no—
89C4×C61—42no—
90C4×C61#12012yes—
91C4×C61#12112yes—
92Dic61—42no—
93Dic61—42no—
94#2006—611nomaximal, Sylow
95C2×C61—21no—
96C2×C61—21no—
97C2×C61#39211yescharacteristic
98C2×C61#45311yescharacteristic
99C2×C61#45411yescharacteristic
100D61—82no—
101D61—82no—
102C2×AGL(1,ℤ/8)—612no—
103#537—611no—
104C2×#104—612no—
105#390—611no—
106#343D6111yescharacteristic, complemented
107C61#200611yescharacteristic, complemented, Sylow
108C2×#41—612no—
109C22×D4—611no—
110AGL(1,ℤ/8)—1224no—
111AGL(1,ℤ/8)—1224no—
112C2×SD16—1222no—
113C2×D8—1222no—
114C2×M16C2×D6112yes—
115C22⋊Q8—1222no—
116#121—1222no—
117#121—1222no—
118C2×C4⋊C4C2×D6111yescharacteristic
119C2×C22⋊C4—1222no—
120C2×C42—611no—
121#104—1224no—
122C24—1221no—
123#41—1222no—
124#41—1222no—
125#41—1222no—
126#41—1222no—
127C2×Q8—612no—
128C2×D4—612no—
129C2×D4—612no—
130C2×D4—1222no—
131C2×D4—1222no—
132C2×D4—1222no—
133C2×D4—1222no—
134C2×D4—1221no—
135C22×C4—1221no—
136C22×C4—1222no—
137C22×C4D24412yes—
138C22×C4C22×D6111yescharacteristic
139SD16—1228no—
140D8—1228no—
141M16—22no—
142M16D24414yescomplemented
143C2×C8—22no—
144C4⋊C4—22no—
145C4⋊C4—1222no—
146C22⋊C4—1224no—
147C22⋊C4—2444no—
148C42—1222no—
149C23—1222no—
150C23—1222no—
151C23—2442no—
152C23—2442no—
153C23—2441no—
154C23—2441no—
155C23C2×D24411yescharacteristic
156Q8—1222no—
157Q8—1222no—
158D4—1222no—
159D4—1224no—
160D4—1222no—
161D4—4882no—
162D4—2442no—
163D4—2442no—
164D4—2442no—
165C2×C4—22no—
166C2×C4—42no—
167C2×C4—1222no—
168C2×C4—1222no—
169C2×C4—2441no—
170C2×C4—2441no—
171C2×C4—2442no—
172C2×C4—2442no—
173C2×C4C2×D24412yes—
174C2×C4D4×D6111yescharacteristic
175C2×C4D4×D6112yes—
176C2×C4#1175822611yescharacteristic
177C8—24no—
178C22—21no—
179C22—21no—
180C22—4882no—
181C22—4881no—
182C22—4881no—
183C22—2444no—
184C22—2442no—
185C22—2442no—
186C22—2442no—
187C22—2442no—
188C22#1451974711yescharacteristic
189C22#1451975211yescharacteristic
190C22#1451977411yescharacteristic
191C4—42no—
192C4—2442no—
193C4—2442no—
194C4#1451974712yes—
195C4#1451975212yes—
196C2—21no—
197C2—21no—
198C2—4882no—
199C2—4882no—
200C2#1683967211yescharacteristic
201C2#1683993211yescharacteristic
202C2#1683993711yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#343C2
socleC22×C61#120
hypercenter#343D61
hypocenterC61#2006
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. C2×#14519805C2semidirect
2. #16840343C2semidirect
3. C2×#14519703C2semidirect
4. #16839663C2semidirect
5. C61×#343C2semidirect
34. C2×D244D4semidirect
38. M16×C61D4semidirect
106. #343D61semidirect
107. C61#2006semidirect
142. M16D244semidirect