Finite Group Databasebeta

← #21447183

Subgroups — #21447183

Order 7808.

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

normal subgroups only

This group has 208 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
2#16839789C211yesmaximal, characteristic
3#16839770C211yesmaximal, characteristic
4C2×#14519700C211yesmaximal, characteristic
5C2×#14519695C211yesmaximal, characteristic
6#16839531C211yesmaximal, characteristic
7C61×#428C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10C2×#11758194C2211yescharacteristic
11C22×#92418C2211yescharacteristic
12#14519712—22no—
13C4⋊#92418—22no—
14#14519700—21no—
15#14519700—21no—
16#14519700—22no—
17#14519695—22no—
18C2×M16×C61C2211yescharacteristic
19#117×C61C2211yescharacteristic
20C2×C4⋊C4×C61C2211yescharacteristic
21#107×C61—21no—
22#106×C61—21no—
23C22×C4×C61—21no—
24C22×C4×C61C2311yescharacteristic
25C22×Dic61—21no—
26C2×Dic122—21no—
27C2×Dic122—21no—
28C2×Dic122—21no—
29C2×Dic122—21no—
30C2×Dic122—21no—
31C2×Dic122Q812yes—
32M16×C61—21no—
33M16×C61D412yes—
34C2×C8×C61—21no—
35C4⋊C4×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61D411yescharacteristic
38C4⋊C4×C61D411yescharacteristic
39C22⋊C4×C61—21no—
40C42×C61—21no—
41#11758194—21no—
42#11758194—21no—
43#11758194—21no—
44#11758194—21no—
45C2×#92418—21no—
46C2×#92418—21no—
47C2×#92418—21no—
48C2×#92418—21no—
49C2×#92418D412yes—
50C23×C61#4111yescharacteristic
51C2×C4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—41no—
54C2×C4×C61—81no—
55C2×C4×C61C2×D411yescharacteristic
56C2×C4×C61C2×D411yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61C2×Q811yescharacteristic
59C2×C4×C61#4111yescharacteristic
60C2×C4×C61#4111yescharacteristic
61C2×Dic61—22no—
62C2×Dic61—41no—
63C2×Dic61—41no—
64Dic122—22no—
65Dic122—22no—
66Dic122—41no—
67Dic122—41no—
68C8×C61—22no—
69#92418—22no—
70#92418—41no—
71#92418—41no—
72C22×C61—21no—
73C22×C61—21no—
74C22×C61#12111yescharacteristic
75C22×C61C22⋊Q811yescharacteristic
76C22×C61#12611yescharacteristic
77C4×C61—41no—
78C4×C61—41no—
79C4×C61—81no—
80C4×C61#12111yescharacteristic
81C4×C61#12111yescharacteristic
82C4×C61C22⋊Q811yescharacteristic
83C4×C61C22⋊Q811yescharacteristic
84Dic61—42no—
85#2064—611nomaximal, Sylow
86C2×C61—21no—
87C2×C61—21no—
88C2×C61#39611yescharacteristic
89C2×C61#47111yescharacteristic
90C2×C61#47311yescharacteristic
91C2×#108—611no—
92#428D6111yescharacteristic
93#424—611no—
94#419—611no—
95C2×#103—611no—
96C2×#101—611no—
97#343—611no—
98C61#206411yescharacteristic, complemented, Sylow
99C22×Q8—611no—
100C2×M16—611no—
101C2×M16—611no—
102C2×M16C2×D6111yescharacteristic
103C22×C8—611no—
104#117C2×D6111yescharacteristic
105C2×C4⋊C4C2×D6111yescharacteristic
106#108—1222no—
107#107—21no—
108#106—21no—
109C4⋊C8—1222no—
110#103—1222no—
111#103—1221no—
112#103—1221no—
113#101—1222no—
114C2×Q8—612no—
115C2×Q8—1221no—
116C2×Q8—1221no—
117C2×Q8—1221no—
118C2×Q8—1221no—
119C2×Q8—1221no—
120C22×C4—21no—
121C22×C4—1221no—
122C22×C4C22×D6111yescharacteristic
123M16—21no—
124M16—1221no—
125M16—1221no—
126M16—1221no—
127M16—1221no—
128M16D24412yes—
129C2×C8—21no—
130C2×C8—612no—
131C2×C8—1221no—
132C2×C8—1221no—
133C2×C8—1221no—
134C2×C8—1221no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4C22⋊D6111yescharacteristic
138C4⋊C4C22⋊D6111yescharacteristic
139C22⋊C4—21no—
140C42—21no—
141C23#1175822411yescharacteristic
142Q8—1222no—
143Q8—1222no—
144Q8—2441no—
145Q8—2441no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—41no—
149C2×C4—81no—
150C2×C4—1222no—
151C2×C4—2441no—
152C2×C4—2441no—
153C2×C4C2×D24411yescharacteristic
154C2×C4#1175822211yescharacteristic
155C2×C4D4×D6111yescharacteristic
156C2×C4Q8×D6111yescharacteristic
157C2×C4#1175822611yescharacteristic
158C2×C4C2×C22⋊D6111yescharacteristic
159C8—22no—
160C8—1222no—
161C8—2441no—
162C8—2441no—
163C22—21no—
164C22—21no—
165C22#1451974911yescharacteristic
166C22#1451975711yescharacteristic
167C22#1451977211yescharacteristic
168C4—41no—
169C4—41no—
170C4—81no—
171C4—2442no—
172C4#1451975111yescharacteristic
173C4#1451975211yescharacteristic
174C4#1451975311yescharacteristic
175C4#1451975511yescharacteristic
176C2—21no—
177C2—21no—
178C2#1683968411yescharacteristic
179C2#1684002311yescharacteristic
180C2#1684003511yescharacteristic
subgroupG/H
centerC22#14519749
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#428C2
socleC22×C61#121
hypercenter#428D61
hypocenterC61#2064
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
98. C61#2064semidirect