Finite Group Databasebeta

← #21444967

Subgroups — #21444967

Order 7808.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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
1#16840415C211yesmaximal, characteristic
2#16840049C211yesmaximal, characteristic, complemented
3#16840049C211yesmaximal, characteristic, complemented
4#16839508C211yesmaximal, characteristic, complemented
5#16839491C211yesmaximal, characteristic, complemented
6#16839491C211yesmaximal, characteristic, complemented
7C61×#487C211yesmaximal, characteristic, complemented
8C2×#11758226—21no—
9#14519762—22no—
10#14519753—21no—
11#14519752—21no—
12C4×D244C2211yescharacteristic
13C4×D244C2211yescharacteristic
14C4⋊C4×D61—21no—
15#14519708—21no—
16#14519708—21no—
17C4⋊#92418C2211yescharacteristic
18C4⋊#92418C2211yescharacteristic
19#14519697—21no—
20#14519697—21no—
21C4⋊Q8×C61C2211yescharacteristic
22C4⋊Q8×C61C2211yescharacteristic
23#103×C61—22no—
24C4×C8×C61C2211yescharacteristic
25C2×Q8×C61—21no—
26C2×Q8×C61—21no—
27#11758226—42no—
28#11758226—42no—
29C2×D244—22no—
30C2×D244D411yescharacteristic
31C2×D244D411yescharacteristic
32C2×C4×D61—22no—
33C2×C4×D61—21no—
34C2×C4×D61—21no—
35C2×C8×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61—21no—
38C4⋊C4×C61—21no—
39C4⋊C4×C61D412yes—
40C42×C61C2311yescharacteristic
41#11758198—22no—
42#11758198—21no—
43#11758198—21no—
44C4⋊Dic61D411yescharacteristic
45C4⋊Dic61D411yescharacteristic
46#11758196—22no—
47C2×#92418—21no—
48C2×#92418—21no—
49C22×D61—21no—
50C22×D61—21no—
51Q8×C61—42no—
52Q8×C61—41no—
53Q8×C61—41no—
54C2×C4×C61—22no—
55C2×C4×C61—41no—
56C2×C4×C61C2×D411yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61C2×D411yescharacteristic
59C2×Dic61—21no—
60C2×Dic61—21no—
61D244—21no—
62D244—21no—
63D244—21no—
64D244—44no—
65D244SD1612yes—
66C4×D61—44no—
67C4×D61—41no—
68C4×D61—41no—
69C4×D61—41no—
70C4×D61—41no—
71C8×C61—41no—
72#92418—41no—
73#92418—41no—
74C22×C61#12011yescharacteristic
75C2×D61—22no—
76C2×D61—41no—
77C2×D61—41no—
78C2×D61—41no—
79C2×D61—41no—
80C2×D61—41no—
81C4×C61—21no—
82C4×C61—42no—
83C4×C61—81no—
84C4×C61C2×SD1611yescharacteristic
85C4×C61#13511yescharacteristic
86C4×C61AGL(1,ℤ/8)11yescharacteristic
87C4×C61#13711yescharacteristic
88Dic61—41no—
89Dic61—41no—
90#1635—611nomaximal, Sylow
91C2×C61#45011yescharacteristic
92C2×C61#45211yescharacteristic
93C2×C61#45411yescharacteristic
94D61—42no—
95D61—81no—
96#547—611no—
97#487D6111yescharacteristic, complemented
98#476—611no—
99#476—611no—
100#332—611no—
101D4⋊C8—611no—
102D4⋊C8—611no—
103C61#163511yescharacteristic, complemented, Sylow
104C2×#41—1221no—
105C4⋊Q8C2×D6111yescharacteristic
106C4⋊Q8C2×D6111yescharacteristic
107#123—1222no—
108C22⋊Q8—1221no—
109#121—1221no—
110C4×D4—611no—
111C4×D4—611no—
112C2×C4⋊C4—1221no—
113#106—1221no—
114#106—1221no—
115C4⋊C8—611no—
116C4⋊C8—611no—
117#103—22no—
118#102—1221no—
119#102—1221no—
120C4×C8C2×D6111yescharacteristic
121#41—2442no—
122#41—2442no—
123C2×Q8—21no—
124C2×Q8—21no—
125C2×D4—611no—
126C2×D4—611no—
127C2×D4—1222no—
128C22×C4—1222no—
129C22×C4—1221no—
130C22×C4—1221no—
131C2×C8—21no—
132C2×C8—1221no—
133C2×C8—1221no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—611no—
138C4⋊C4—611no—
139C4⋊C4—1222no—
140C4⋊C4C22⋊D6112yes—
141C22⋊C4—1222no—
142C22⋊C4—1221no—
143C22⋊C4—1221no—
144C42C22×D6111yescharacteristic
145C23—1221no—
146C23—1221no—
147Q8—42no—
148Q8—41no—
149Q8—41no—
150D4—612no—
151D4—1221no—
152D4—1221no—
153D4—1221no—
154D4—2444no—
155C2×C4—22no—
156C2×C4—41no—
157C2×C4—1221no—
158C2×C4—1221no—
159C2×C4—2444no—
160C2×C4—2441no—
161C2×C4—2441no—
162C2×C4—2441no—
163C2×C4—2441no—
164C2×C4D4×D6111yescharacteristic
165C2×C4D4×D6111yescharacteristic
166C2×C4C2×C22⋊D6111yescharacteristic
167C8—41no—
168C8—2441no—
169C8—2441no—
170C22—1222no—
171C22—2441no—
172C22—2441no—
173C22—2441no—
174C22—2441no—
175C22—2441no—
176C22#1451974511yescharacteristic
177C4—21no—
178C4—42no—
179C4—81no—
180C4—2441no—
181C4—2441no—
182C4SD16×D6111yescharacteristic
183C4#1451980011yescharacteristic
184C4#1451980411yescharacteristic
185C4#1451980911yescharacteristic
186C2—4881no—
187C2—2442no—
188C2#1683991111yescharacteristic
189C2#1683992311yescharacteristic
190C2#1683993411yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#487C2
socleC22×C61#120
hypercenter#487D61
hypocenterC61#1635
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #16840049C2semidirect
3. #16840049C2semidirect
4. #16839508C2semidirect
5. #16839491C2semidirect
6. #16839491C2semidirect
7. C61×#487C2semidirect
97. #487D61semidirect
103. C61#1635semidirect