Finite Group Databasebeta

← #21446304

Subgroups — #21446304

Order 7808.

346 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 85 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×#14519803C211yesmaximal, characteristic
2#16840237C211yesmaximal, characteristic, complemented
3#16839778C211yesmaximal, characteristic, complemented
4#16839735C211yesmaximal, characteristic, complemented
5#16839534C211yesmaximal, characteristic, complemented
6#16839518C211yesmaximal, characteristic, complemented
7C61×#418C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519803—22no—
10#14519803—22no—
11C2×#11758200C412yescomplemented
12C2×#11758199C412yescomplemented
13C2×#11758194C2211yescharacteristic
14D4×Dic61—22no—
15D4×Dic61—22no—
16#14519736C2211yescharacteristic
17#14519736C2211yescharacteristic
18C2×C22⋊Dic61—22no—
19#14519703—22no—
20#14519691—22no—
21C22×D4×C61C2211yescharacteristic
22C2×M16×C61C2211yescharacteristic
23#117×C61C2211yescharacteristic
24#102×C61—22no—
25C24×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61—21no—
28C2×D4×C61—21no—
29C2×D4×C61C2×C412yes—
30C2×D4×C61D412yes—
31C2×D4×C61D412yes—
32C22×C4×C61C2311yescharacteristic
33C2×C22⋊D61—21no—
34C22×Dic61—24no—
35#11758222—21no—
36#11758222—21no—
37#11758222—21no—
38#11758222—21no—
39C2×D244C2×C411yescharacteristic, complemented
40C2×C4×D61—21no—
41C2×Dic122C2×C411yescharacteristic, complemented
42M16×C61—21no—
43M16×C61—21no—
44C2×C8×C61—21no—
45C4⋊C4×C61—21no—
46C22⋊C4×C61—21no—
47C42×C61—21no—
48C22⋊Dic61—24no—
49C22⋊Dic61—21no—
50C22⋊Dic61D412yes—
51#11758200—24no—
52#11758199—24no—
53C4⋊Dic61—21no—
54C4⋊Dic61—21no—
55C4×Dic61—21no—
56C4×Dic61D412yes—
57#11758194—21no—
58#11758194—21no—
59C2×#92418C2×C412yescomplemented
60C23×C61—22no—
61C23×C61—22no—
62C23×C61—22no—
63C23×C61—82no—
64C23×C61C2×D411yescharacteristic
65C22×D61—21no—
66D4×C61—22no—
67D4×C61—22no—
68D4×C61—22no—
69D4×C61C22⋊C414yes—
70C2×C4×C61—41no—
71C2×C4×C61C22×C411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61#4111yescharacteristic
76C2×C4×C61#4111yescharacteristic
77C22⋊D61—41no—
78C22⋊D61—41no—
79C2×Dic61—21no—
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61—84no—
83D244—21no—
84D244—21no—
85C4×D61—41no—
86C4×D61—41no—
87Dic122—21no—
88Dic122—21no—
89C8×C61—41no—
90#92418—22no—
91C22×C61—24no—
92C22×C61—41no—
93C22×C61—44no—
94C22×C61—82no—
95C22×C61—82no—
96C22×C61C4×D411yescharacteristic
97C22×C61#12011yescharacteristic
98C22×C61#12111yescharacteristic
99C2×D61—41no—
100C2×D61—81no—
101C4×C61—81no—
102C4×C61C2×C22⋊C411yescharacteristic
103C4×C61C4×D411yescharacteristic
104C4×C61#12111yescharacteristic
105C4×C61#12311yescharacteristic
106Dic61—42no—
107Dic61—42no—
108Dic61—41no—
109#1904—611nomaximal, Sylow
110C2×C61—21no—
111C2×C61—21no—
112C2×C61—21no—
113C2×C61—44no—
114C2×C61#38611yescharacteristic
115D61—81no—
116C2×AGL(1,ℤ/8)—611no—
117#518—611no—
118#421—611no—
119#418D6111yescharacteristic, complemented
120#410—611no—
121#344—611no—
122H(3,ℤ/4)—611no—
123C61#190411yescharacteristic, complemented, Sylow
124C2×#41—611no—
125C22×D4C2×D6111yescharacteristic
126AGL(1,ℤ/8)—1222no—
127AGL(1,ℤ/8)—1222no—
128C2×SD16—612no—
129C2×D8—612no—
130C2×M16—611no—
131C2×M16C2×D6111yescharacteristic
132C4×D4—1222no—
133C4×D4—1222no—
134#117—611no—
135#117—611no—
136#117C2×D6111yescharacteristic
137C2×C22⋊C4—1222no—
138#104—1222no—
139#102—22no—
140#99—1222no—
141C24—21no—
142#41—1221no—
143#41—1221no—
144#41—1221no—
145#41—1221no—
146C2×Q8—611no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4—21no—
150C2×D4—611no—
151C2×D4—1221no—
152C2×D4C4×D6112yes—
153C2×D4D24412yes—
154C2×D4C22⋊D6112yes—
155C22×C4—1224no—
156C22×C4—1221no—
157C22×C4C22×D6111yescharacteristic
158SD16—1224no—
159D8—1224no—
160M16—21no—
161M16—21no—
162M16—1221no—
163M16—1221no—
164C2×C8—21no—
165C2×C8—612no—
166C4⋊C4—21no—
167C4⋊C4—1221no—
168C4⋊C4—1221no—
169C22⋊C4—21no—
170C22⋊C4—612no—
171C22⋊C4—1224no—
172C22⋊C4—1221no—
173C42—21no—
174C42—612no—
175C42—1221no—
176C23—22no—
177C23—22no—
178C23—22no—
179C23—82no—
180C23—1221no—
181C23D4×D6111yescharacteristic
182Q8—1221no—
183Q8—1221no—
184D4—22no—
185D4—22no—
186D4—22no—
187D4—1221no—
188D4—1221no—
189D4—2441no—
190D4—2441no—
191D4#1175819814yes—
192C2×C4—41no—
193C2×C4—1221no—
194C2×C4—1222no—
195C2×C4—1222no—
196C2×C4—4884no—
197C2×C4—2441no—
198C2×C4—2441no—
199C2×C4C2×C4×D6111yescharacteristic
200C2×C4C2×D24411yescharacteristic
201C2×C4D4×D6111yescharacteristic
202C2×C4#1175822411yescharacteristic
203C2×C4#1175822411yescharacteristic
204C2×C4C2×C22⋊D6111yescharacteristic
205C8—41no—
206C8—1222no—
207C22—24no—
208C22—41no—
209C22—44no—
210C22—82no—
211C22—82no—
212C22—4881no—
213C22—2441no—
214C22#1451973711yescharacteristic
215C22#1451974711yescharacteristic
216C22#1451974911yescharacteristic
217C4—81no—
218C4—2442no—
219C4—2442no—
220C4—2441no—
221C4C2×#1175819811yescharacteristic
222C4#1451973711yescharacteristic
223C4#1451974911yescharacteristic
224C4#1451976111yescharacteristic
225C2—21no—
226C2—21no—
227C2—21no—
228C2—44no—
229C2—4881no—
230C2#1683963911yescharacteristic
subgroupG/H
centerC2#16839639
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#418C2
socleC2×C61#386
hypercenter#418D61
hypocenterC61#1904
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. #16840237C2semidirect
3. #16839778C2semidirect
4. #16839735C2semidirect
5. #16839534C2semidirect
6. #16839518C2semidirect
7. C61×#418C2semidirect
11. C2×#11758200C4semidirect
12. C2×#11758199C4semidirect
39. C2×D244C2×C4semidirect
41. C2×Dic122C2×C4semidirect
59. C2×#92418C2×C4semidirect
119. #418D61semidirect
123. C61#1904semidirect