Finite Group Databasebeta

← #21447262

Subgroups — #21447262

Order 7808.

198 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 63 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×#14519710C211yesmaximal, characteristic, complemented
2#16839763C211yesmaximal, characteristic
3#16839729C211yesmaximal, characteristic
4#16839531C211yesmaximal, characteristic, complemented
5#16839530C211yesmaximal, characteristic, complemented
6#16839526C211yesmaximal, characteristic, complemented
7C61×#417C211yesmaximal, characteristic
8C2×#11758194C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10C22×#92418C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12#14519710—22no—
13#14519701—21no—
14#14519698—21no—
15C22⋊#92418—22no—
16C2×#41×C61C2211yescharacteristic
17C2×M16×C61C2211yescharacteristic
18C2×C4⋊C4×C61C2211yescharacteristic
19#103×C61—21no—
20#102×C61—21no—
21#41×C61—21no—
22#41×C61—21no—
23#41×C61—21no—
24#41×C61—21no—
25C2×Q8×C61D411yescharacteristic
26C2×D4×C61—21no—
27C2×D4×C61D411yescharacteristic
28C22×C4×C61—21no—
29C22×C4×C61—21no—
30C22×C4×C61C2311yescharacteristic
31C22×Dic61—21no—
32M16×C61—21no—
33M16×C61—21no—
34C2×C8×C61—21no—
35C4⋊C4×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊Dic61—21no—
38C4⋊Dic61—21no—
39#11758194—21no—
40#11758194—21no—
41#11758194—21no—
42#11758194—21no—
43C2×#92418—21no—
44C2×#92418—21no—
45C2×#92418—21no—
46C2×#92418—21no—
47C2×#92418D412yes—
48C23×C61—21no—
49C23×C61#4111yescharacteristic
50Q8×C61—21no—
51Q8×C61—21no—
52D4×C61—21no—
53D4×C61—21no—
54D4×C61—41no—
55D4×C61—41no—
56C2×C4×C61—21no—
57C2×C4×C61—41no—
58C2×C4×C61—41no—
59C2×C4×C61—41no—
60C2×C4×C61—81no—
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61#4111yescharacteristic
64C2×C4×C61#4111yescharacteristic
65C2×C4×C61#4111yescharacteristic
66C2×C4×C61#4111yescharacteristic
67C2×Dic61—41no—
68C2×Dic61—81no—
69C8×C61—41no—
70#92418—22no—
71#92418—41no—
72#92418—41no—
73C22×C61—21no—
74C22×C61—21no—
75C22×C61—41no—
76C22×C61—41no—
77C22×C61—41no—
78C22×C61#12111yescharacteristic
79C22×C61#12611yescharacteristic
80C22×C61#12611yescharacteristic
81C4×C61—41no—
82C4×C61—81no—
83C4×C61#12311yescharacteristic
84C4×C61#12311yescharacteristic
85C4×C61#12311yescharacteristic
86C4×C61#12411yescharacteristic
87Dic61—81no—
88#2078—611nomaximal, Sylow
89C2×C61—21no—
90C2×C61—21no—
91C2×C61—81no—
92C2×C61#39711yescharacteristic
93C2×C61#47211yescharacteristic
94C2×C61#47311yescharacteristic
95C2×#107—611no—
96#417—611no—
97#417D6111yescharacteristic
98#408—611no—
99#343—611no—
100#343—611no—
101#341—611no—
102C61#207811yescharacteristic, complemented, Sylow
103C2×#41C2×D6111yescharacteristic
104C2×M16—611no—
105C2×M16—611no—
106C2×M16C2×D6111yescharacteristic
107C22×C8—611no—
108C2×C4⋊C4—611no—
109C2×C4⋊C4C2×D6111yescharacteristic
110#107—1222no—
111#103—21no—
112#103—1221no—
113#102—21no—
114#102—1221no—
115C22⋊C8—1222no—
116#41—21no—
117#41—21no—
118#41—21no—
119#41—21no—
120C2×Q8C22⋊D6111yescharacteristic
121C2×D4—21no—
122C2×D4C22⋊D6111yescharacteristic
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—1221no—
126C22×C4C22×D6111yescharacteristic
127M16—21no—
128M16—21no—
129M16—1221no—
130M16—1221no—
131M16—1221no—
132M16—1221no—
133C2×C8—21no—
134C2×C8—612no—
135C2×C8—1221no—
136C2×C8—1221no—
137C2×C8—1221no—
138C2×C8—1221no—
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4—1221no—
142C4⋊C4—1221no—
143C23—21no—
144C23#1175822411yescharacteristic
145Q8—21no—
146Q8—21no—
147D4—21no—
148D4—21no—
149D4—41no—
150D4—41no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—81no—
156C2×C4—4881no—
157C2×C4—2441no—
158C2×C4#1175822211yescharacteristic
159C2×C4#1175822211yescharacteristic
160C2×C4D4×D6111yescharacteristic
161C2×C4#1175822411yescharacteristic
162C2×C4#1175822411yescharacteristic
163C2×C4C2×C22⋊D6111yescharacteristic
164C8—41no—
165C8—1222no—
166C8—2441no—
167C8—2441no—
168C22—21no—
169C22—21no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22#1451974911yescharacteristic
174C22#1451977011yescharacteristic
175C22#1451977011yescharacteristic
176C4—41no—
177C4—81no—
178C4—4881no—
179C4#1451975811yescharacteristic
180C4#1451975911yescharacteristic
181C4#1451976011yescharacteristic
182C4#1451976311yescharacteristic
183C2—21no—
184C2—21no—
185C2—81no—
186C2#1683969011yescharacteristic
187C2#1684003011yescharacteristic
188C2#1684003511yescharacteristic
subgroupG/H
centerC22#14519749
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#417C2
socleC22×C61#121
hypercenter#417D61
hypocenterC61#2078
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. C2×#14519710C2semidirect
4. #16839531C2semidirect
5. #16839530C2semidirect
6. #16839526C2semidirect
102. C61#2078semidirect