Finite Group Databasebeta

← #21447175

Subgroups — #21447175

Order 7808.

228 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 69 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#16839804C211yesmaximal, characteristic, complemented
3#16839790C211yesmaximal, characteristic, complemented
4#16839767C211yesmaximal, characteristic
5C2×#14519698C211yesmaximal, characteristic
6#16839530C211yesmaximal, characteristic, complemented
7C2×#100×C61C211yesmaximal, characteristic
8C2×#11758194C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10#14519736C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12#14519712—22no—
13#14519711—21no—
14#14519709—21no—
15#14519706—22no—
16#14519698—21no—
17#14519698—21no—
18#14519698—22no—
19C22×D4×C61C2211yescharacteristic
20C2×M16×C61C2211yescharacteristic
21C2×M16×C61C2211yescharacteristic
22#100×C61—22no—
23C24×C61—21no—
24C2×D4×C61—21no—
25C2×D4×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61—21no—
28C2×D4×C61—21no—
29C2×D4×C61Q812yes—
30C22×C4×C61C2311yescharacteristic
31C22×Dic61—21no—
32M16×C61—21no—
33M16×C61—21no—
34M16×C61—21no—
35M16×C61D412yes—
36C2×C8×C61—21no—
37C2×C8×C61—21no—
38C22⋊Dic61—21no—
39C4⋊Dic61—21no—
40C4⋊Dic61—21no—
41C4⋊Dic61D411yescharacteristic
42C4⋊Dic61D411yescharacteristic
43C4×Dic61—21no—
44#11758194—21no—
45#11758194—21no—
46C2×#92418—21no—
47C2×#92418—21no—
48C2×#92418—21no—
49C2×#92418D412yes—
50C23×C61—22no—
51C23×C61—41no—
52C23×C61—41no—
53C23×C61—81no—
54C23×C61—81no—
55C23×C61#4111yescharacteristic
56D4×C61—22no—
57D4×C61—22no—
58D4×C61—41no—
59D4×C61—41no—
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×Q811yescharacteristic
64C2×C4×C61#4111yescharacteristic
65C2×C4×C61#4111yescharacteristic
66C2×Dic61—21no—
67C2×Dic61—21no—
68C2×Dic61—41no—
69C2×Dic61—81no—
70C8×C61—22no—
71C8×C61—41no—
72#92418—22no—
73#92418—41no—
74C22×C61—21no—
75C22×C61—21no—
76C22×C61—42no—
77C22×C61—82no—
78C22×C61—82no—
79C22×C61—81no—
80C22×C61—81no—
81C22×C61#12111yescharacteristic
82C22×C61C22⋊Q811yescharacteristic
83C22×C61#12611yescharacteristic
84C4×C61#12111yescharacteristic
85C4×C61#12111yescharacteristic
86C4×C61C22⋊Q811yescharacteristic
87C4×C61C22⋊Q811yescharacteristic
88Dic61—41no—
89Dic61—41no—
90Dic61—81no—
91#2063—611nomaximal, Sylow
92C2×C61—21no—
93C2×C61—21no—
94C2×C61—82no—
95C2×C61#39611yescharacteristic
96C2×C61#47111yescharacteristic
97C2×C61#47211yescharacteristic
98C2×#108—611no—
99#428—611no—
100#424—611no—
101#418—611no—
102C2×#102—611no—
103C2×#100D6111yescharacteristic
104#343—611no—
105C61#206311yescharacteristic, complemented, Sylow
106C22×D4C2×D6111yescharacteristic
107C2×M16—611no—
108C2×M16C2×D6111yescharacteristic
109C2×M16C2×D6111yescharacteristic
110C22×C8—611no—
111#117—611no—
112C2×C4⋊C4—611no—
113#108—1222no—
114#107—1221no—
115#106—1221no—
116C4⋊C8—1222no—
117#102—1221no—
118#102—1221no—
119#102—1222no—
120#100—22no—
121C24—21no—
122C2×D4—21no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4Dic12212yes—
128C22×C4—1221no—
129C22×C4C22×D6111yescharacteristic
130M16—21no—
131M16—21no—
132M16—21no—
133M16—1221no—
134M16—1221no—
135M16C22⋊D6112yes—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—612no—
139C2×C8—1221no—
140C2×C8—1221no—
141C2×C8—1221no—
142C4⋊C4—611no—
143C4⋊C4—611no—
144C4⋊C4—1221no—
145C4⋊C4—1221no—
146C22⋊C4—1221no—
147C42—1221no—
148C23—22no—
149C23—41no—
150C23—41no—
151C23—81no—
152C23—81no—
153C23#1175822211yescharacteristic
154D4—22no—
155D4—22no—
156D4—41no—
157D4—41no—
158C2×C4—1221no—
159C2×C4—1221no—
160C2×C4—4881no—
161C2×C4—2441no—
162C2×C4C2×Dic12211yescharacteristic
163C2×C4D4×D6111yescharacteristic
164C2×C4D4×D6111yescharacteristic
165C2×C4#1175822411yescharacteristic
166C2×C4#1175822411yescharacteristic
167C2×C4C2×C22⋊D6111yescharacteristic
168C8—22no—
169C8—41no—
170C8—1222no—
171C8—2441no—
172C22—21no—
173C22—21no—
174C22—42no—
175C22—82no—
176C22—82no—
177C22—81no—
178C22—81no—
179C22#1451975011yescharacteristic
180C22#1451975611yescharacteristic
181C22#1451977011yescharacteristic
182C4—4881no—
183C4—2441no—
184C4—2441no—
185C4#1451974811yescharacteristic
186C4#1451974911yescharacteristic
187C4#1451975411yescharacteristic
188C4#1451975411yescharacteristic
189C2—21no—
190C2—21no—
191C2—82no—
192C2#1683968511yescharacteristic
193C2#1684002411yescharacteristic
194C2#1684003111yescharacteristic
subgroupG/H
centerC22#14519750
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#100×C61C2
socleC22×C61#121
hypercenterC2×#100D61
hypocenterC61#2063
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C2×#14519712C2semidirect
2. #16839804C2semidirect
3. #16839790C2semidirect
6. #16839530C2semidirect
105. C61#2063semidirect