Finite Group Databasebeta

← #21446299

Subgroups — #21446299

Order 7808.

324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14519802C211yesmaximal, characteristic
2#16839779C211yesmaximal, characteristic, complemented
3#16839768C211yesmaximal, characteristic, complemented
4C2×#14519693C211yesmaximal, characteristic, complemented
5#16839534C211yesmaximal, characteristic, complemented
6#16839520C211yesmaximal, characteristic, complemented
7C61×#568C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9#14519802—22no—
10#14519802—22no—
11C2×#11758201C412yescomplemented
12C2×#11758199C412yescomplemented
13C2×#11758194C2211yescharacteristic
14C2×#11758194C2211yescharacteristic
15#14519736C2211yescharacteristic
16#14519704—22no—
17#14519699—22no—
18#14519693—22no—
19C2×#41×C61C2211yescharacteristic
20#131×C61—22no—
21#131×C61—22no—
22C2×M16×C61—22no—
23C2×M16×C61C2211yescharacteristic
24C2×M16×C61C2211yescharacteristic
25C23×D61—21no—
26#41×C61—21no—
27#41×C61—21no—
28#41×C61D412yes—
29#41×C61D412yes—
30C2×Q8×C61C2×C411yescharacteristic
31C2×D4×C61—21no—
32C2×D4×C61C2×C411yescharacteristic
33C22×C4×C61—21no—
34C22×C4×C61C2311yescharacteristic
35C2×D244—21no—
36C2×D244—21no—
37C2×D244—21no—
38C2×D244—21no—
39C2×D244—21no—
40C2×D244C2×C412yes—
41M16×C61—24no—
42M16×C61—21no—
43M16×C61—21no—
44M16×C61—21no—
45M16×C61D412yes—
46C2×C8×C61—24no—
47C2×C8×C61—21no—
48C2×C8×C61D412yes—
49C22⋊Dic61—21no—
50#11758201—24no—
51#11758199—24no—
52C4⋊Dic61—21no—
53C4×Dic61—21no—
54#11758194—21no—
55#11758194—21no—
56#11758194—21no—
57#11758194—21no—
58C2×#92418—21no—
59C2×#92418C2×C412yes—
60C23×C61—21no—
61C23×C61#4111yescharacteristic
62C22×D61—22no—
63C22×D61—41no—
64C22×D61—41no—
65C22×D61—82no—
66Q8×C61—21no—
67Q8×C61C22⋊C412yes—
68D4×C61—22no—
69D4×C61—22no—
70D4×C61—21no—
71D4×C61C22⋊C412yes—
72C2×C4×C61—21no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61C22×C411yescharacteristic
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61#4111yescharacteristic
81C2×Dic61—41no—
82D244—22no—
83D244—22no—
84D244—41no—
85D244—41no—
86C8×C61—22no—
87C8×C61—22no—
88#92418—22no—
89#92418—41no—
90C22×C61—22no—
91C22×C61—41no—
92C22×C61—81no—
93C22×C61C4×D411yescharacteristic
94C22×C61#12111yescharacteristic
95C22×C61#12311yescharacteristic
96C2×D61—42no—
97C2×D61—82no—
98C2×D61—82no—
99C2×D61—82no—
100C4×C61—22no—
101C4×C61C2×C22⋊C411yescharacteristic
102C4×C61C4×D411yescharacteristic
103C4×C61#12011yescharacteristic
104C4×C61#12111yescharacteristic
105Dic61—81no—
106#1903—611nomaximal, Sylow
107C2×C61—21no—
108C2×C61—21no—
109C2×C61—21no—
110C2×C61—42no—
111C2×C61#38611yescharacteristic
112D61—82no—
113C2×AGL(1,ℤ/8)—611no—
114#568D6111yescharacteristic, complemented
115#421—611no—
116#418—611no—
117C2×#100—611no—
118#344—611no—
119#338—611no—
120C61#190311yescharacteristic, complemented, Sylow
121C2×#41C2×D6111yescharacteristic
122C22×D4—611no—
123AGL(1,ℤ/8)—1222no—
124AGL(1,ℤ/8)—1222no—
125C2×SD16—612no—
126C2×D8—612no—
127#131—22no—
128#131—22no—
129C2×M16—22no—
130C2×M16—611no—
131C2×M16—611no—
132C2×M16C2×D6111yescharacteristic
133C2×M16C2×D6111yescharacteristic
134#117—611no—
135#104—1222no—
136#102—1222no—
137#100—1222no—
138C24—1221no—
139#41—21no—
140#41—21no—
141#41D24412yes—
142#41C22⋊D6112yes—
143C2×Q8C4×D6111yescharacteristic
144C2×D4—21no—
145C2×D4—612no—
146C2×D4—1221no—
147C2×D4—1221no—
148C2×D4—1221no—
149C2×D4—1221no—
150C2×D4—1221no—
151C2×D4C4×D6111yescharacteristic
152C22×C4—21no—
153C22×C4C22×D6111yescharacteristic
154SD16—1224no—
155D8—1224no—
156M16—24no—
157M16—21no—
158M16—21no—
159M16—21no—
160M16—1221no—
161M16—1221no—
162M16—1221no—
163M16—1221no—
164M16C22⋊D6112yes—
165C2×C8—24no—
166C2×C8—21no—
167C2×C8—612no—
168C2×C8—1221no—
169C2×C8C22⋊D6112yes—
170C4⋊C4—1221no—
171C22⋊C4—1221no—
172C42—1221no—
173C23—21no—
174C23—1222no—
175C23—4882no—
176C23—2441no—
177C23—2441no—
178C23#1175822211yescharacteristic
179Q8—21no—
180Q8#1175819812yes—
181D4—22no—
182D4—22no—
183D4—21no—
184D4—1222no—
185D4—1222no—
186D4—2441no—
187D4—2441no—
188D4#1175819812yes—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—2441no—
193C2×C4C2×C4×D6111yescharacteristic
194C2×C4C2×D24411yescharacteristic
195C2×C4#1175822211yescharacteristic
196C2×C4C2×C22⋊D6111yescharacteristic
197C2×C4C2×C22⋊D6111yescharacteristic
198C2×C4C2×C22⋊D6111yescharacteristic
199C8—22no—
200C8—22no—
201C8—1222no—
202C8—2441no—
203C22—22no—
204C22—41no—
205C22—81no—
206C22—4882no—
207C22—4882no—
208C22—4882no—
209C22—2442no—
210C22C4×C22⋊D6111yescharacteristic
211C22#1451975111yescharacteristic
212C22#1451976011yescharacteristic
213C4—22no—
214C4—4881no—
215C4C2×#1175819811yescharacteristic
216C4C4×C22⋊D6111yescharacteristic
217C4#1451974611yescharacteristic
218C4#1451975111yescharacteristic
219C2—21no—
220C2—21no—
221C2—21no—
222C2—42no—
223C2—4882no—
224C2#1683964111yescharacteristic
subgroupG/H
centerC2#16839641
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#568C2
socleC2×C61#386
hypercenter#568D61
hypocenterC61#1903
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #16839779C2semidirect
3. #16839768C2semidirect
4. C2×#14519693C2semidirect
5. #16839534C2semidirect
6. #16839520C2semidirect
7. C61×#568C2semidirect
11. C2×#11758201C4semidirect
12. C2×#11758199C4semidirect
114. #568D61semidirect
120. C61#1903semidirect