Finite Group Databasebeta

← #21446480

Subgroups — #21446480

Order 7808.

232 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 75 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#16839766C211yesmaximal, characteristic
2C2×#14519697C211yesmaximal, characteristic
3C2×#14519693C211yesmaximal, characteristic
4#16839718C211yesmaximal, characteristic, complemented
5#16839531C211yesmaximal, characteristic, complemented
6#16839526C211yesmaximal, characteristic, complemented
7C61×#428C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10C2×#11758194C2211yescharacteristic
11C22×#92418C2211yescharacteristic
12#14519697—21no—
13#14519697—21no—
14#14519697—21no—
15#14519697—21no—
16#14519693C414yescomplemented
17#14519688—21no—
18C4×#92418—21no—
19C2×M16×C61C2211yescharacteristic
20#117×C61C2211yescharacteristic
21C2×C4⋊C4×C61C2211yescharacteristic
22#107×C61—21no—
23#106×C61—21no—
24C23×D61—21no—
25C22×C4×C61—21no—
26C22×C4×C61C2311yescharacteristic
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—
36C4⋊C4×C61—21no—
37C4⋊C4×C61—21no—
38C4⋊C4×C61D411yescharacteristic
39C4⋊C4×C61D411yescharacteristic
40C22⋊C4×C61—21no—
41C42×C61—21no—
42#11758194—21no—
43#11758194—21no—
44#11758194—21no—
45#11758194C2×C412yes—
46C2×#92418—21no—
47C2×#92418—21no—
48C2×#92418—21no—
49C2×#92418—21no—
50C2×#92418D411yescharacteristic
51C2×#92418D411yescharacteristic
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×C61—41no—
61C2×C4×C61—81no—
62C2×C4×C61C22×C411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C2×C4×C61C2×D411yescharacteristic
65C2×C4×C61#4111yescharacteristic
66C2×C4×C61#4111yescharacteristic
67C2×C4×C61#4111yescharacteristic
68D244—22no—
69D244—22no—
70D244—41no—
71D244—41no—
72C8×C61—22no—
73#92418—22no—
74#92418—21no—
75#92418—21no—
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×C61—81no—
90C4×C61C4×D411yescharacteristic
91C4×C61C4×D411yescharacteristic
92C4×C61#12311yescharacteristic
93C4×C61#12411yescharacteristic
94#1931—611nomaximal, Sylow
95C2×C61—21no—
96C2×C61—21no—
97C2×C61#38811yescharacteristic
98C2×C61#47111yescharacteristic
99C2×C61#47211yescharacteristic
100D61—82no—
101#428D6111yescharacteristic, complemented
102#418—611no—
103C2×#102—611no—
104C2×#100—611no—
105#405—611no—
106#343—611no—
107#341—611no—
108C61#193111yescharacteristic, complemented, Sylow
109C22×D4—611no—
110C2×M16—611no—
111C2×M16—611no—
112C2×M16C2×D6111yescharacteristic
113C22×C8—611no—
114#117C2×D6111yescharacteristic
115C2×C4⋊C4C2×D6111yescharacteristic
116#107—21no—
117#106—21no—
118#102—1221no—
119#102—1221no—
120#102—1221no—
121#102—1221no—
122#100—614no—
123#97—1221no—
124C4×C8—1221no—
125C24—1221no—
126C2×D4—612no—
127C2×D4—1221no—
128C2×D4—1221no—
129C2×D4—1221no—
130C2×D4—1221no—
131C2×D4—1221no—
132C22×C4—21no—
133C22×C4C22×D6111yescharacteristic
134M16—21no—
135M16—612no—
136M16—1221no—
137M16—1221no—
138M16—1221no—
139M16C4×D6112yes—
140C2×C8—21no—
141C2×C8—611no—
142C2×C8—611no—
143C2×C8—1221no—
144C2×C8—1221no—
145C2×C8—1221no—
146C2×C8—1221no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4C22⋊D6111yescharacteristic
150C4⋊C4C22⋊D6111yescharacteristic
151C22⋊C4—21no—
152C42—21no—
153C23—1222no—
154C23—4881no—
155C23—4881no—
156C23—2441no—
157C23—2441no—
158C23#1175822411yescharacteristic
159D4—1222no—
160D4—1222no—
161D4—2441no—
162D4—2441no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—81no—
167C2×C4C2×C4×D6111yescharacteristic
168C2×C4#1175822211yescharacteristic
169C2×C4D4×D6111yescharacteristic
170C2×C4#1175822611yescharacteristic
171C2×C4#1175822611yescharacteristic
172C2×C4C2×C22⋊D6111yescharacteristic
173C8—22no—
174C8—1222no—
175C8—1221no—
176C8—1221no—
177C8—2441no—
178C22—21no—
179C22—21no—
180C22—4882no—
181C22—4882no—
182C22—4881no—
183C22—4881no—
184C22—2442no—
185C22#1451973511yescharacteristic
186C22#1451974911yescharacteristic
187C22#1451977211yescharacteristic
188C4—41no—
189C4—41no—
190C4—81no—
191C4C4×C22⋊D6111yescharacteristic
192C4#1451973911yescharacteristic
193C4#1451976211yescharacteristic
194C4#1451976611yescharacteristic
195C2—21no—
196C2—21no—
197C2—4882no—
198C2#1683965211yescharacteristic
199C2#1684002711yescharacteristic
200C2#1684003011yescharacteristic
subgroupG/H
centerC22#14519749
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#428C2
socleC22×C61#121
hypercenter#428D61
hypocenterC61#1931
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
4. #16839718C2semidirect
5. #16839531C2semidirect
6. #16839526C2semidirect
7. C61×#428C2semidirect
16. #14519693C4semidirect
101. #428D61semidirect
108. C61#1931semidirect