Finite Group Databasebeta

← #21447180

Subgroups — #21447180

Order 7808.

228 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 65 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×#14519712C211yesmaximal, characteristic, complemented
2#16839802C211yesmaximal, characteristic, complemented
3#16839790C211yesmaximal, characteristic, complemented
4#16839768C211yesmaximal, characteristic
5C2×#14519697C211yesmaximal, characteristic
6C2×#14519693C211yesmaximal, characteristic
7C61×#343C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10C22×#92418C2211yescharacteristic
11#14519736C2211yescharacteristic
12#14519712—22no—
13#14519710—21no—
14#14519708—21no—
15#14519706—22no—
16#14519699—21no—
17#14519699—21no—
18#14519697—22no—
19#14519693—22no—
20C2×M16×C61C2211yescharacteristic
21C2×M16×C61C2211yescharacteristic
22C2×C4⋊C4×C61C2211yescharacteristic
23C23×D61—21no—
24C22×C4×C61—21no—
25C22×C4×C61C2311yescharacteristic
26C2×D244—21no—
27C2×D244—21no—
28C2×D244—21no—
29C2×D244—21no—
30C2×D244—21no—
31C2×D244Q812yes—
32M16×C61—21no—
33M16×C61—21no—
34M16×C61—21no—
35M16×C61—21no—
36C2×C8×C61—21no—
37C2×C8×C61—21no—
38C4⋊C4×C61—21no—
39C4⋊C4×C61—21no—
40C22⋊Dic61—21no—
41C4⋊Dic61D411yescharacteristic
42C4⋊Dic61D411yescharacteristic
43C4×Dic61—21no—
44#11758194—21no—
45#11758194D412yes—
46C2×#92418—21no—
47C2×#92418—21no—
48C2×#92418—21no—
49C2×#92418D412yes—
50C23×C61#4111yescharacteristic
51C22×D61—22no—
52C22×D61—41no—
53C22×D61—41no—
54C22×D61—81no—
55C22×D61—81no—
56C2×C4×C61—41no—
57C2×C4×C61—81no—
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2×Q811yescharacteristic
62C2×C4×C61#4111yescharacteristic
63C2×C4×C61#4111yescharacteristic
64C2×Dic61—21no—
65C2×Dic61—21no—
66D244—22no—
67D244—22no—
68D244—41no—
69D244—41no—
70C8×C61—41no—
71C8×C61—41no—
72#92418—22no—
73#92418—22no—
74C22×C61—21no—
75C22×C61—21no—
76C22×C61#12111yescharacteristic
77C22×C61C22⋊Q811yescharacteristic
78C22×C61#12611yescharacteristic
79C2×D61—42no—
80C2×D61—82no—
81C2×D61—81no—
82C2×D61—81no—
83C2×D61—82no—
84C4×C61—81no—
85C4×C61#12111yescharacteristic
86C4×C61#12111yescharacteristic
87C4×C61C22⋊Q811yescharacteristic
88C4×C61C22⋊Q811yescharacteristic
89Dic61—41no—
90Dic61—41no—
91#2063—611nomaximal, Sylow
92C2×C61—21no—
93C2×C61—21no—
94C2×C61#39611yescharacteristic
95C2×C61#47111yescharacteristic
96C2×C61#47211yescharacteristic
97D61—82no—
98C2×#108—611no—
99#428—611no—
100#424—611no—
101#418—611no—
102C2×#102—611no—
103C2×#100—611no—
104#343D6111yescharacteristic, complemented
105C61#206311yescharacteristic, complemented, Sylow
106C22×D4—611no—
107C2×M16—611no—
108C2×M16C2×D6111yescharacteristic
109C2×M16C2×D6111yescharacteristic
110C22×C8—611no—
111#117—611no—
112C2×C4⋊C4C2×D6111yescharacteristic
113#108—1222no—
114#107—1221no—
115#106—1221no—
116C4⋊C8—1222no—
117#102—1222no—
118#102—1221no—
119#102—1221no—
120#100—1222no—
121C24—1221no—
122C2×D4—612no—
123C2×D4—1221no—
124C2×D4—1221no—
125C2×D4—1221no—
126C2×D4—1221no—
127C2×D4—1221no—
128C22×C4—21no—
129C22×C4C22×D6111yescharacteristic
130M16—21no—
131M16—21no—
132M16—21no—
133M16—21no—
134M16—612no—
135M16—1221no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—612no—
139C2×C8—1221no—
140C2×C8—1221no—
141C2×C8—1221no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—611no—
145C4⋊C4—611no—
146C22⋊C4—1221no—
147C42—1221no—
148C23—1222no—
149C23—4881no—
150C23—4881no—
151C23—2441no—
152C23—2441no—
153C23#1175822211yescharacteristic
154D4—1222no—
155D4—1222no—
156D4—2441no—
157D4—2441no—
158C2×C4—41no—
159C2×C4—81no—
160C2×C4—1221no—
161C2×C4—1221no—
162C2×C4#1175822211yescharacteristic
163C2×C4#1175822211yescharacteristic
164C2×C4D4×D6111yescharacteristic
165C2×C4D4×D6111yescharacteristic
166C2×C4D4×D6111yescharacteristic
167C2×C4Q8×D6111yescharacteristic
168C8—41no—
169C8—41no—
170C8—1222no—
171C8—1222no—
172C22—21no—
173C22—21no—
174C22—4882no—
175C22—4882no—
176C22—4881no—
177C22—4881no—
178C22—2442no—
179C22#1451975011yescharacteristic
180C22#1451975511yescharacteristic
181C22#1451977111yescharacteristic
182C4—81no—
183C4—2441no—
184C4—2441no—
185C4#1451975011yescharacteristic
186C4#1451975011yescharacteristic
187C4#1451975511yescharacteristic
188C4#1451975511yescharacteristic
189C2—21no—
190C2—21no—
191C2—4882no—
192C2#1683968611yescharacteristic
193C2#1684002811yescharacteristic
194C2#1684003111yescharacteristic
subgroupG/H
centerC22#14519750
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#343C2
socleC22×C61#121
hypercenter#343D61
hypocenterC61#2063
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. C2×#14519712C2semidirect
2. #16839802C2semidirect
3. #16839790C2semidirect
7. C61×#343C2semidirect
104. #343D61semidirect
105. C61#2063semidirect