Finite Group Databasebeta

← #21446298

Subgroups — #21446298

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×#14519805C211yesmaximal, characteristic
2#16840528C211yesmaximal, characteristic, complemented
3#16839780C211yesmaximal, characteristic, complemented
4#16839766C211yesmaximal, characteristic, complemented
5C2×#14519693C211yesmaximal, characteristic, complemented
6#16839520C211yesmaximal, characteristic, complemented
7C61×#344C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C22×D244C2211yescharacteristic
10#14519805—22no—
11#14519805—22no—
12C2×#11758190C412yescomplemented
13C2×D488C412yescomplemented
14#14519785—22no—
15#14519783—22no—
16C2×#11758194C2211yescharacteristic
17C2×#11758194C2211yescharacteristic
18M16×D61—22no—
19#14519705—22no—
20#14519697—22no—
21#14519693—22no—
22C2×M16×C61C2211yescharacteristic
23C2×M16×C61C2211yescharacteristic
24#117×C61C2211yescharacteristic
25C23×D61—21no—
26C22×C4×C61C2311yescharacteristic
27C2×C22⋊D61—21no—
28#11758222—21no—
29#11758222—21no—
30#11758222D412yes—
31#11758222D412yes—
32C2×D244—21no—
33C2×D244—21no—
34C2×D244—21no—
35C2×D244—21no—
36C2×D244—21no—
37C2×D244C2×C412yes—
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×C61C2×C412yes—
47C4⋊C4×C61—21no—
48C22⋊C4×C61—21no—
49C42×C61—21no—
50#11758194—21no—
51#11758194—21no—
52#11758194—21no—
53#11758194—21no—
54C2×#92418—21no—
55C2×#92418D412yes—
56D488—24no—
57#11758190—24no—
58#11758189—24no—
59C8×D61—24no—
60C23×C61#4111yescharacteristic
61C22×D61—21no—
62C22×D61—22no—
63C22×D61—41no—
64C22×D61—41no—
65C22×D61—82no—
66C2×C4×C61—41no—
67C2×C4×C61C22×C411yescharacteristic
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61#4111yescharacteristic
73C22⋊D61—22no—
74C22⋊D61—22no—
75C2×Dic61—21no—
76D244—22no—
77D244—21no—
78D244—22no—
79D244—41no—
80D244—41no—
81D244C22⋊C412yes—
82C4×D61—22no—
83C4×D61—22no—
84Dic122—21no—
85Dic122C22⋊C412yes—
86C8×C61—22no—
87C8×C61—22no—
88#92418—22no—
89#92418—41no—
90C22×C61—41no—
91C22×C61C4×D411yescharacteristic
92C22×C61#12111yescharacteristic
93C22×C61#12311yescharacteristic
94C2×D61—22no—
95C2×D61—42no—
96C2×D61—81no—
97C2×D61—82no—
98C2×D61—82no—
99C2×D61—82no—
100C4×C61—81no—
101C4×C61C2×C22⋊C411yescharacteristic
102C4×C61C4×D411yescharacteristic
103C4×C61#12011yescharacteristic
104C4×C61#12111yescharacteristic
105Dic61—22no—
106#1903—611nomaximal, Sylow
107C2×C61—21no—
108C2×C61—21no—
109C2×C61—21no—
110C2×C61#38611yescharacteristic
111D61—42no—
112D61—82no—
113C2×AGL(1,ℤ/8)—611no—
114#568—611no—
115#421—611no—
116#418—611no—
117C2×#100—611no—
118#344D6111yescharacteristic, complemented
119#338—611no—
120C61#190311yescharacteristic, complemented, Sylow
121C2×#41—611no—
122C22×D4—611no—
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#117C2×D6111yescharacteristic
135#104—1222no—
136#102—1222no—
137#100—1222no—
138C24—1221no—
139#41—612no—
140#41—612no—
141#41—1221no—
142#41—1221no—
143C2×Q8—611no—
144C2×D4—611no—
145C2×D4—612no—
146C2×D4—1221no—
147C2×D4—1221no—
148C2×D4—1221no—
149C2×D4—1221no—
150C2×D4—1221no—
151C2×D4—1221no—
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—
164M16D24412yes—
165C2×C8—21no—
166C2×C8—612no—
167C2×C8—1224no—
168C2×C8—1221no—
169C2×C8C4×D6112yes—
170C4⋊C4—21no—
171C22⋊C4—21no—
172C42—21no—
173C23—1221no—
174C23—1222no—
175C23—4882no—
176C23—2441no—
177C23—2441no—
178C23#1175822211yescharacteristic
179Q8—612no—
180Q8—1221no—
181D4—612no—
182D4—1222no—
183D4—1222no—
184D4—1222no—
185D4—1221no—
186D4—1222no—
187D4—2441no—
188D4—2441no—
189C2×C4—41no—
190C2×C4—1221no—
191C2×C4—1222no—
192C2×C4—1222no—
193C2×C4C2×C4×D6111yescharacteristic
194C2×C4C2×D24411yescharacteristic
195C2×C4D4×D6111yescharacteristic
196C2×C4D4×D6111yescharacteristic
197C2×C4D4×D6111yescharacteristic
198C2×C4#1175822611yescharacteristic
199C8—22no—
200C8—22no—
201C8—1222no—
202C8—2441no—
203C22—41no—
204C22—1222no—
205C22—4882no—
206C22—4882no—
207C22—4882no—
208C22—4881no—
209C22—2442no—
210C22C4×D24411yescharacteristic
211C22#1451975011yescharacteristic
212C22#1451976211yescharacteristic
213C4—81no—
214C4—1222no—
215C4C22⋊C4×D6111yescharacteristic
216C4#1451973911yescharacteristic
217C4#1451974711yescharacteristic
218C4#1451975211yescharacteristic
219C2—21no—
220C2—21no—
221C2—21no—
222C2—4882no—
223C2—2442no—
224C2#1683964011yescharacteristic
subgroupG/H
centerC2#16839640
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#344C2
socleC2×C61#386
hypercenter#344D61
hypocenterC61#1903
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
2. #16840528C2semidirect
3. #16839780C2semidirect
4. #16839766C2semidirect
5. C2×#14519693C2semidirect
6. #16839520C2semidirect
7. C61×#344C2semidirect
12. C2×#11758190C4semidirect
13. C2×D488C4semidirect
118. #344D61semidirect
120. C61#1903semidirect