Finite Group Databasebeta

← #21446481

Subgroups — #21446481

Order 7808.

232 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 77 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
1#16839805C211yesmaximal, characteristic, complemented
2#16839766C211yesmaximal, characteristic
3C2×#14519699C211yesmaximal, characteristic
4C2×#14519693C211yesmaximal, characteristic
5#16839530C211yesmaximal, characteristic, complemented
6#16839527C211yesmaximal, characteristic, complemented
7C61×#405C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10C2×#11758194C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12#14519710—21no—
13#14519708—21no—
14#14519699—21no—
15#14519699—21no—
16#14519697—21no—
17#14519697—21no—
18#14519693C414yescomplemented
19C2×M16×C61C2211yescharacteristic
20C22×C8×C61C2211yescharacteristic
21#117×C61C2211yescharacteristic
22#97×C61—21no—
23C4×C8×C61—21no—
24C23×D61—21no—
25C22×C4×C61C2311yescharacteristic
26C22×Dic61—21no—
27C2×D244—21no—
28C2×D244—21no—
29C2×D244—21no—
30C2×D244—21no—
31C2×D244—21no—
32C2×D244C2×C412yes—
33M16×C61—21no—
34M16×C61C2×C412yes—
35C2×C8×C61—21no—
36C2×C8×C61—21no—
37C2×C8×C61—21no—
38C2×C8×C61D411yescharacteristic
39C2×C8×C61D411yescharacteristic
40C4⋊C4×C61D411yescharacteristic
41C4⋊C4×C61D411yescharacteristic
42C22⋊C4×C61—21no—
43C42×C61—21no—
44C4⋊Dic61—21no—
45C4⋊Dic61—21no—
46#11758194—21no—
47#11758194—21no—
48#11758194—21no—
49#11758194C2×C412yes—
50C2×#92418—21no—
51C2×#92418—21no—
52C23×C61#4111yescharacteristic
53C22×D61—22no—
54C22×D61—41no—
55C22×D61—41no—
56C22×D61—81no—
57C22×D61—81no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61C22×C411yescharacteristic
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61#4111yescharacteristic
64C2×C4×C61#4111yescharacteristic
65C2×C4×C61#4111yescharacteristic
66C2×Dic61—41no—
67C2×Dic61—81no—
68D244—22no—
69D244—22no—
70D244—41no—
71D244—41no—
72C8×C61—22no—
73C8×C61—21no—
74C8×C61—21no—
75#92418—22no—
76#92418—41no—
77C22×C61—21no—
78C22×C61—21no—
79C22×C61#11711yescharacteristic
80C22×C61#12111yescharacteristic
81C22×C61#12611yescharacteristic
82C2×D61—42no—
83C2×D61—82no—
84C2×D61—81no—
85C2×D61—81no—
86C2×D61—82no—
87C4×C61—41no—
88C4×C61—41no—
89C4×C61C4×D411yescharacteristic
90C4×C61C4×D411yescharacteristic
91C4×C61#12311yescharacteristic
92C4×C61#12411yescharacteristic
93Dic61—81no—
94#1931—611nomaximal, Sylow
95C2×C61—21no—
96C2×C61—21no—
97C2×C61#38811yescharacteristic
98C2×C61#47111yescharacteristic
99C2×C61#47211yescharacteristic
100D61—82no—
101#428—611no—
102#418—611no—
103C2×#102—611no—
104C2×#100—611no—
105#405D6111yescharacteristic, complemented
106#343—611no—
107#341—611no—
108C61#193111yescharacteristic, complemented, Sylow
109C22×D4—611no—
110C2×M16—611no—
111C2×M16—611no—
112C2×M16C2×D6111yescharacteristic
113C22×C8C2×D6111yescharacteristic
114#117C2×D6111yescharacteristic
115C2×C4⋊C4—611no—
116#107—1221no—
117#106—1221no—
118#102—1221no—
119#102—1221no—
120#102—1221no—
121#102—1221no—
122#100—614no—
123#97—21no—
124C4×C8—21no—
125C24—1221no—
126C2×D4—612no—
127C2×D4—1221no—
128C2×D4—1221no—
129C2×D4—1221no—
130C2×D4—1221no—
131C2×D4—1221no—
132C22×C4—1221no—
133C22×C4C22×D6111yescharacteristic
134M16—21no—
135M16—612no—
136M16—1221no—
137M16—1221no—
138M16—1221no—
139M16C4×D6112yes—
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—1221no—
144C2×C8—1221no—
145C2×C8C22⋊D6111yescharacteristic
146C2×C8C22⋊D6111yescharacteristic
147C4⋊C4—1221no—
148C4⋊C4—1221no—
149C4⋊C4D24411yescharacteristic
150C4⋊C4D24411yescharacteristic
151C22⋊C4—21no—
152C42—21no—
153C23—1222no—
154C23—4881no—
155C23—4881no—
156C23—2441no—
157C23—2441no—
158C23#1175822211yescharacteristic
159D4—1222no—
160D4—1222no—
161D4—2441no—
162D4—2441no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—4881no—
166C2×C4—2441no—
167C2×C4C2×C4×D6111yescharacteristic
168C2×C4C2×D24411yescharacteristic
169C2×C4#1175822211yescharacteristic
170C2×C4#1175822211yescharacteristic
171C2×C4#1175822211yescharacteristic
172C2×C4C2×C22⋊D6111yescharacteristic
173C8—22no—
174C8—21no—
175C8—21no—
176C8—1222no—
177C8—2441no—
178C22—21no—
179C22—21no—
180C22—4882no—
181C22—4882no—
182C22—4881no—
183C22—4881no—
184C22—2442no—
185C22#1451973411yescharacteristic
186C22#1451975111yescharacteristic
187C22#1451977111yescharacteristic
188C4—41no—
189C4—41no—
190C4—4881no—
191C4C4×C22⋊D6111yescharacteristic
192C4C4×D24411yescharacteristic
193C4#1451976011yescharacteristic
194C4#1451976511yescharacteristic
195C2—21no—
196C2—21no—
197C2—4882no—
198C2#1683965311yescharacteristic
199C2#1684002511yescharacteristic
200C2#1684003211yescharacteristic
subgroupG/H
centerC22#14519751
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#405C2
socleC22×C61#121
hypercenter#405D61
hypocenterC61#1931
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #405

Complements

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

NH ≅ G/Ntype
1. #16839805C2semidirect
5. #16839530C2semidirect
6. #16839527C2semidirect
7. C61×#405C2semidirect
18. #14519693C4semidirect
105. #405D61semidirect
108. C61#1931semidirect