Finite Group Databasebeta

← #21446302

Subgroups — #21446302

Order 7808.

324 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 79 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#16840528C211yesmaximal, characteristic, complemented
3#16839778C211yesmaximal, characteristic, complemented
4#16839767C211yesmaximal, characteristic, complemented
5#16839534C211yesmaximal, characteristic, complemented
6#16839520C211yesmaximal, characteristic, complemented
7C2×#100×C61C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519803—22no—
10#14519803—22no—
11C2×#11758200C412yescomplemented
12C2×#11758199C412yescomplemented
13#14519785—22no—
14#14519783—22no—
15C2×#11758194C2211yescharacteristic
16C2×#11758194C2211yescharacteristic
17M16×D61—22no—
18#14519736C2211yescharacteristic
19#14519703—22no—
20#14519698—22no—
21C22×D4×C61C2211yescharacteristic
22C2×M16×C61C2211yescharacteristic
23C2×M16×C61C2211yescharacteristic
24#100×C61—22no—
25C24×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61—21no—
28C2×D4×C61—21no—
29C2×D4×C61—21no—
30C2×D4×C61—21no—
31C2×D4×C61C2×C412yes—
32C22×C4×C61C2311yescharacteristic
33C2×C22⋊D61—21no—
34#11758222—21no—
35#11758222—21no—
36#11758222D412yes—
37#11758222D412yes—
38C2×D244C2×C411yescharacteristic
39C2×C4×D61—21no—
40C2×Dic122C2×C411yescharacteristic
41M16×C61—21no—
42M16×C61—21no—
43M16×C61—21no—
44M16×C61D412yes—
45C2×C8×C61—21no—
46C2×C8×C61—21no—
47C22⋊Dic61—21no—
48#11758200—24no—
49#11758199—24no—
50C4⋊Dic61—21no—
51C4×Dic61—21no—
52#11758194—21no—
53#11758194—21no—
54#11758194—21no—
55#11758194—21no—
56C2×#92418C2×C412yes—
57C2×#92418D412yes—
58#11758189—24no—
59C8×D61—24no—
60C23×C61—22no—
61C23×C61—41no—
62C23×C61—41no—
63C23×C61—82no—
64C23×C61#4111yescharacteristic
65C22×D61—21no—
66D4×C61—22no—
67D4×C61—22no—
68D4×C61—41no—
69D4×C61—41no—
70C2×C4×C61C22×C411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61#4111yescharacteristic
76C22⋊D61—22no—
77C22⋊D61—22no—
78C2×Dic61—21no—
79C2×Dic61—41no—
80D244—21no—
81D244C22⋊C412yes—
82C4×D61—22no—
83C4×D61—22no—
84Dic122—21no—
85Dic122C22⋊C412yes—
86C8×C61—22no—
87C8×C61—41no—
88#92418—22no—
89#92418—22no—
90C22×C61—41no—
91C22×C61—42no—
92C22×C61—82no—
93C22×C61—82no—
94C22×C61—82no—
95C22×C61C4×D411yescharacteristic
96C22×C61#12111yescharacteristic
97C22×C61#12311yescharacteristic
98C2×D61—22no—
99C2×D61—81no—
100C4×C61C2×C22⋊C411yescharacteristic
101C4×C61C4×D411yescharacteristic
102C4×C61#12011yescharacteristic
103C4×C61#12111yescharacteristic
104Dic61—22no—
105Dic61—81no—
106#1903—611nomaximal, Sylow
107C2×C61—21no—
108C2×C61—21no—
109C2×C61—21no—
110C2×C61—82no—
111C2×C61#38611yescharacteristic
112D61—42no—
113C2×AGL(1,ℤ/8)—611no—
114#568—611no—
115#421—611no—
116#418—611no—
117C2×#100D6111yescharacteristic, complemented
118#344—611no—
119#338—611no—
120C61#190311yescharacteristic, complemented, Sylow
121C2×#41—611no—
122C22×D4C2×D6111yescharacteristic
123AGL(1,ℤ/8)—1222no—
124AGL(1,ℤ/8)—1222no—
125C2×SD16—612no—
126C2×D8—612no—
127#131—1222no—
128#131—1222no—
129C2×M16—611no—
130C2×M16—611no—
131C2×M16—1222no—
132C2×M16C2×D6111yescharacteristic
133C2×M16C2×D6111yescharacteristic
134#117—611no—
135#104—1222no—
136#102—1222no—
137#100—22no—
138C24—21no—
139#41—612no—
140#41—612no—
141#41—1221no—
142#41—1221no—
143C2×Q8—611no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4—611no—
150C2×D4—1221no—
151C2×D4C4×D6112yes—
152C22×C4—1221no—
153C22×C4C22×D6111yescharacteristic
154SD16—1224no—
155D8—1224no—
156M16—21no—
157M16—21no—
158M16—21no—
159M16—1224no—
160M16—1221no—
161M16—1221no—
162M16—1221no—
163M16—1221no—
164M16C22⋊D6112yes—
165C2×C8—21no—
166C2×C8—21no—
167C2×C8—612no—
168C2×C8—612no—
169C2×C8—1224no—
170C4⋊C4—1221no—
171C22⋊C4—1221no—
172C42—1221no—
173C23—22no—
174C23—41no—
175C23—41no—
176C23—82no—
177C23—1221no—
178C23#1175822211yescharacteristic
179Q8—612no—
180Q8—1221no—
181D4—22no—
182D4—22no—
183D4—41no—
184D4—41no—
185D4—612no—
186D4—1222no—
187D4—1222no—
188D4—1221no—
189C2×C4—1221no—
190C2×C4—1222no—
191C2×C4—1222no—
192C2×C4—2441no—
193C2×C4C2×C4×D6111yescharacteristic
194C2×C4D4×D6111yescharacteristic
195C2×C4D4×D6111yescharacteristic
196C2×C4D4×D6111yescharacteristic
197C2×C4#1175822411yescharacteristic
198C2×C4C2×C22⋊D6111yescharacteristic
199C8—22no—
200C8—41no—
201C8—1222no—
202C8—1222no—
203C22—41no—
204C22—42no—
205C22—82no—
206C22—82no—
207C22—82no—
208C22—1222no—
209C22—4881no—
210C22C4×C22⋊D6111yescharacteristic
211C22#1451975011yescharacteristic
212C22#1451975911yescharacteristic
213C4—1222no—
214C4—4881no—
215C4C22⋊C4×D6111yescharacteristic
216C4#1451973711yescharacteristic
217C4#1451974511yescharacteristic
218C4#1451974811yescharacteristic
219C2—21no—
220C2—21no—
221C2—21no—
222C2—82no—
223C2—2442no—
224C2#1683963811yescharacteristic
subgroupG/H
centerC2#16839638
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#100×C61C2
socleC2×C61#386
hypercenterC2×#100D61
hypocenterC61#1903
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. #16840528C2semidirect
3. #16839778C2semidirect
4. #16839767C2semidirect
5. #16839534C2semidirect
6. #16839520C2semidirect
7. C2×#100×C61C2semidirect
11. C2×#11758200C4semidirect
12. C2×#11758199C4semidirect
117. C2×#100D61semidirect
120. C61#1903semidirect