Finite Group Databasebeta

← #21456212

Subgroups — #21456212

Order 7808.

424 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 141 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
2#16840121C214yesmaximal, complemented
3#16840112C212yesmaximal, complemented
4#16840108C212yesmaximal, complemented
5#16839763C214yesmaximal, complemented
6C4×#11758194C211yesmaximal, characteristic, complemented
7C61×#532C211yesmaximal, characteristic
8C22×Dic122—21no—
9C2×#11758194C2212yes—
10#14519777—21no—
11#14519777—21no—
12#14519777C2212yes—
13#14519777C2212yes—
14C2×C4⋊Dic61—21no—
15C2×C4⋊Dic61C2212yes—
16#14519701C2218yes—
17#14519698C2218yes—
18#14519688C2212yes—
19C4×#92418C2212yes—
20C2×#41×C61C2212yes—
21C4⋊Q8×C61C2211yescharacteristic
22#127×C61C2211yescharacteristic
23#124×C61C2212yes—
24#121×C61—21no—
25#121×C61—21no—
26C4×D4×C61—21no—
27C4×D4×C61—21no—
28C2×C42×C61C2211yescharacteristic
29#41×C61—28no—
30C2×Q8×C61C2312yes—
31C2×D4×C61—22no—
32C2×D4×C61—21no—
33C2×D4×C61—21no—
34C2×D4×C61C2312yes—
35C22×C4×C61—22no—
36C22×C4×C61D411yescharacteristic
37C22×C4×C61D411yescharacteristic
38C22×C4×C61C2311yescharacteristic
39C22×Dic61—22no—
40C2×Dic122—22no—
41C2×Dic122—22no—
42C2×Dic122—44no—
43C4⋊C4×C61—21no—
44C4⋊C4×C61—21no—
45C22⋊C4×C61—22no—
46C22⋊C4×C61—22no—
47C42×C61D411yescharacteristic
48C42×C61D411yescharacteristic
49C42×C61C2311yescharacteristic
50C42×C61C2311yescharacteristic
51C4⋊Dic61—22no—
52C4⋊Dic61—22no—
53C4⋊Dic61—22no—
54C4⋊Dic61C2314yes—
55#11758194—24no—
56C2×#92418C2314yes—
57C23×C61—22no—
58C23×C61C2×D411yescharacteristic
59Q8×C61—24no—
60D4×C61—24no—
61D4×C61—44no—
62D4×C61—42no—
63D4×C61—42no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—44no—
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61#4114yes—
74C2×C4×C61C2411yescharacteristic
75C2×Dic61—24no—
76C2×Dic61—44no—
77Dic122—44no—
78Dic122—44no—
79#92418—24no—
80C22×C61—21no—
81C22×C61—21no—
82C22×C61—42no—
83C22×C61—42no—
84C22×C61—42no—
85C22×C61#12412yes—
86C22×C61C22×D411yescharacteristic
87C4×C61—21no—
88C4×C61—21no—
89C4×C61—42no—
90C4×C61#12412yes—
91C4×C61AGL(1,ℤ/8)12yes—
92C4×C61#13712yes—
93C4×C61C2×#4112yes—
94Dic61—44no—
95#3141—611nomaximal, Sylow
96C2×C61—22no—
97C2×C61—82no—
98C2×C61C2×#12411yescharacteristic
99C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
100C2×C61C2×#13711yescharacteristic
101#532D6111yescharacteristic
102C2×C4⋊Q8—611no—
103#489—614no—
104#487—612no—
105#486—612no—
106#417—614no—
107C4×M16—611no—
108C61#314111yescharacteristic, complemented, Sylow
109C2×#41C2×D6112yes—
110C22×Q8—1221no—
111C2×M16—612no—
112C4⋊Q8—612no—
113C4⋊Q8—612no—
114C4⋊Q8—1221no—
115C4⋊Q8—1221no—
116C4⋊Q8C2×D6111yescharacteristic
117#127C2×D6111yescharacteristic
118#124C2×D6112yes—
119#121—21no—
120#121—21no—
121C4×D4—21no—
122C4×D4—21no—
123C2×C4⋊C4—612no—
124C2×C4⋊C4—1221no—
125C2×C42C2×D6111yescharacteristic
126#103—618no—
127#102—618no—
128#97—612no—
129C4×C8—612no—
130#41—28no—
131C2×Q8—1222no—
132C2×Q8—1222no—
133C2×Q8—2444no—
134C2×Q8C22×D6112yes—
135C2×D4—22no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4C22×D6112yes—
139C22×C4—22no—
140C22×C4—1222no—
141C22×C4C22⋊D6111yescharacteristic
142C22×C4C22⋊D6111yescharacteristic
143C22×C4C22×D6111yescharacteristic
144M16—1224no—
145C2×C8—614no—
146C4⋊C4—21no—
147C4⋊C4—21no—
148C4⋊C4—614no—
149C4⋊C4—1222no—
150C4⋊C4—1222no—
151C4⋊C4—1222no—
152C22⋊C4—22no—
153C22⋊C4—22no—
154C42C22⋊D6111yescharacteristic
155C42C22⋊D6111yescharacteristic
156C42C22×D6111yescharacteristic
157C42C22×D6111yescharacteristic
158C23—22no—
159C23C2×C22⋊D6111yescharacteristic
160Q8—24no—
161Q8—2444no—
162Q8—2444no—
163D4—24no—
164D4—44no—
165D4—42no—
166D4—42no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—44no—
171C2×C4—1224no—
172C2×C4—2444no—
173C2×C4#1175822414yes—
174C2×C4C2×C22⋊D6111yescharacteristic
175C2×C4C2×C22⋊D6111yescharacteristic
176C2×C4C2×C22⋊D6111yescharacteristic
177C2×C4C2×C22⋊D6111yescharacteristic
178C2×C4C2×C22⋊D6111yescharacteristic
179C2×C4C23×D6111yescharacteristic
180C8—1224no—
181C22—21no—
182C22—21no—
183C22—42no—
184C22—42no—
185C22—42no—
186C22#1451976412yes—
187C22C22×C22⋊D6111yescharacteristic
188C4—21no—
189C4—21no—
190C4—42no—
191C4—2444no—
192C4#1451976412yes—
193C4#1451980212yes—
194C4#1451980712yes—
195C4C2×#1175822412yes—
196C2—22no—
197C2—82no—
198C2C2×#1451976411yescharacteristic
199C2C2×#1451980211yescharacteristic
200C2C2×#1451980711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#532C2
socleC22×C61C22×D4
hypercenter#532D61
hypocenterC61#3141
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C2×#14519777C2semidirect
2. #16840121C2semidirect
3. #16840112C2semidirect
4. #16840108C2semidirect
5. #16839763C2semidirect
6. C4×#11758194C2semidirect
108. C61#3141semidirect