Finite Group Databasebeta

← #21446956

Subgroups — #21446956

Order 7808.

326 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 91 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×#14519777C211yesmaximal, characteristic, complemented
2C2×#14519699C212yesmaximal
3#16839664C211yesmaximal, characteristic
4#16839525C212yesmaximal, complemented
5C61×#336C211yesmaximal, characteristic, complemented
6C22×Dic122—21no—
7C22×D244C2211yescharacteristic
8#14519777—24no—
9C2×C4⋊Dic61—21no—
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2212yes—
12C2×#11758198—21no—
13C2×#11758198—21no—
14#14519699—24no—
15C22×C8×C61C2212yes—
16C2×C42×C61C2211yescharacteristic
17C23×D61—21no—
18C22×C4×C61D411yescharacteristic
19C22×C4×C61D411yescharacteristic
20C22×C4×C61C2311yescharacteristic
21C22×Dic61—22no—
22C22×Dic61—21no—
23C2×D244—22no—
24C2×D244—22no—
25C2×D244—21no—
26C2×D244Q812yescomplemented
27C2×Dic122—24no—
28C2×Dic122—42no—
29C2×Dic122—42no—
30C2×C8×C61—22no—
31C2×C8×C61—22no—
32C2×C8×C61—22no—
33C42×C61—22no—
34#11758198—42no—
35#11758198—42no—
36C4⋊Dic61—24no—
37C4⋊Dic61—22no—
38C4⋊Dic61—22no—
39C4⋊Dic61D414yes—
40C23×C61C2×D411yescharacteristic
41C22×D61—22no—
42C22×D61—41no—
43C22×D61—41no—
44C22×D61—41no—
45C22×D61—41no—
46C22×D61—41no—
47C22×D61—41no—
48C2×C4×C61—21no—
49C2×C4×C61—21no—
50C2×C4×C61—21no—
51C2×C4×C61—21no—
52C2×C4×C61D812yes—
53C2×C4×C61SD1612yes—
54C2×C4×C61C2×D412yes—
55C2×C4×C61C2×Q811yescharacteristic
56C2×C4×C61#4112yes—
57C2×C4×C61#4111yescharacteristic
58C2×Dic61—24no—
59C2×Dic61—42no—
60C2×Dic61—42no—
61C2×Dic61—41no—
62C2×Dic61—41no—
63C2×Dic61—41no—
64D244—24no—
65D244—42no—
66Dic122—48no—
67C8×C61—42no—
68C22×C61#12011yescharacteristic
69C22×C61C22⋊Q811yescharacteristic
70C22×C61#12411yescharacteristic
71C22×C61C2×D811yescharacteristic
72C22×C61C2×SD1611yescharacteristic
73C22×C61AGL(1,ℤ/8)11yescharacteristic
74C22×C61#13711yescharacteristic
75C2×D61—42no—
76C2×D61—42no—
77C2×D61—42no—
78C2×D61—81no—
79C2×D61—81no—
80C2×D61—81no—
81C2×D61—81no—
82C4×C61—22no—
83C4×C61—22no—
84C4×C61C22⋊Q812yes—
85C4×C61#12412yes—
86Dic61—44no—
87Dic61—81no—
88#2023—611nomaximal, Sylow
89C2×C61#39311yescharacteristic
90C2×C61#44711yescharacteristic
91C2×C61#44811yescharacteristic
92C2×C61#47411yescharacteristic
93C2×C61#47611yescharacteristic
94C2×C61#48611yescharacteristic
95C2×C61#48911yescharacteristic
96D61—82no—
97C2×C4⋊Q8—611no—
98C2×#102—612no—
99#390—611no—
100#340—612no—
101#336D6111yescharacteristic, complemented
102C61#202311yescharacteristic, complemented, Sylow
103C22×Q8—1221no—
104C22×D4—611no—
105C22×C8C2×D6112yes—
106C4⋊Q8—1224no—
107C2×C4⋊C4—612no—
108C2×C4⋊C4—611no—
109C2×C4⋊C4—1221no—
110C2×C22⋊C4—1221no—
111C2×C22⋊C4—1221no—
112C2×C42C2×D6111yescharacteristic
113#102—1224no—
114C24—1221no—
115C2×Q8—1224no—
116C2×Q8—2442no—
117C2×Q8—2442no—
118C2×D4—612no—
119C2×D4—1222no—
120C2×D4—1222no—
121C2×D4—1221no—
122C22×C4—1222no—
123C22×C4—1221no—
124C22×C4D24411yescharacteristic
125C22×C4D24411yescharacteristic
126C22×C4C22×D6111yescharacteristic
127C2×C8—22no—
128C2×C8—22no—
129C2×C8—22no—
130C4⋊C4—614no—
131C4⋊C4—1224no—
132C4⋊C4—1222no—
133C4⋊C4—1222no—
134C22⋊C4—2442no—
135C22⋊C4—2442no—
136C42—22no—
137C23—1222no—
138C23—2441no—
139C23—2441no—
140C23—2441no—
141C23—2441no—
142C23—2441no—
143C23—2441no—
144C23C2×D24411yescharacteristic
145Q8—2448no—
146D4—1224no—
147D4—2442no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—1224no—
153C2×C4—2441no—
154C2×C4—2441no—
155C2×C4—2441no—
156C2×C4—2442no—
157C2×C4—2442no—
158C2×C4#1175819012yes—
159C2×C4D48812yes—
160C2×C4#1175822212yes—
161C2×C4D4×D6112yes—
162C2×C4#1175822411yescharacteristic
163C2×C4Q8×D6111yescharacteristic
164C8—42no—
165C22—4881no—
166C22—4881no—
167C22—4881no—
168C22—4881no—
169C22—2442no—
170C22—2442no—
171C22—2442no—
172C22#1451974711yescharacteristic
173C22#1451975711yescharacteristic
174C22#1451976511yescharacteristic
175C22C2×D48811yescharacteristic
176C22C2×#1175819011yescharacteristic
177C22#1451980511yescharacteristic
178C22#1451981011yescharacteristic
179C4—22no—
180C4—22no—
181C4—4881no—
182C4—2444no—
183C4#1451975512yes—
184C4#1451976312yes—
185C2—4882no—
186C2#1683967511yescharacteristic
187C2#1683989811yescharacteristic
188C2#1683990311yescharacteristic
189C2#1684004311yescharacteristic
190C2#1684005311yescharacteristic
191C2#1684010911yescharacteristic
192C2#1684012211yescharacteristic
subgroupG/H
centerC23C2×D244
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#336C2
socleC23×C61C2×D4
hypercenter#336D61
hypocenterC61#2023
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
1. C2×#14519777C2semidirect
4. #16839525C2semidirect
5. C61×#336C2semidirect
26. C2×D244Q8semidirect
101. #336D61semidirect
102. C61#2023semidirect