Finite Group Databasebeta

← #21444231

Subgroups — #21444231

Order 7808.

234 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 67 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#16840299C211yesmaximal, characteristic
2C4⋊C8×D61C211yesmaximal, characteristic, complemented
3C4×#11758189C211yesmaximal, characteristic, complemented
4Q8⋊#92418C211yesmaximal, characteristic, complemented
5#16839491C211yesmaximal, characteristic, complemented
6#16839489C211yesmaximal, characteristic, complemented
7C61×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#11758189—21no—
9C2×C8×D61—21no—
10#14519772—21no—
11#14519768C411yescharacteristic
12#14519766C411yescharacteristic
13#14519762—21no—
14#14519753C411yescharacteristic
15#14519752C411yescharacteristic
16C4×D244—21no—
17C4×D244C2211yescharacteristic
18#14519734—21no—
19C42×D61C2211yescharacteristic
20C4⋊#92418C2211yescharacteristic
21#14519706—21no—
22#14519687—21no—
23C4×#92418C2211yescharacteristic
24C4×Q8×C61C2211yescharacteristic
25C4⋊C8×C61C2211yescharacteristic
26C4×C8×C61C2211yescharacteristic
27C2×Q8×C61C2×C411yescharacteristic
28C2×D244—21no—
29C2×D244C2×C411yescharacteristic
30C2×C4×D61—21no—
31C2×C4×D61C2×C411yescharacteristic
32C2×C4×D61D411yescharacteristic
33C2×C4×D61D411yescharacteristic
34C2×C8×C61—21no—
35C2×C8×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61C2×C411yescharacteristic
38C42×C61—21no—
39C42×C61C2311yescharacteristic
40#11758198—21no—
41#11758198—21no—
42#11758198—21no—
43#11758198—21no—
44#11758198—21no—
45C4⋊Dic61—21no—
46C4⋊Dic61C2×C411yescharacteristic
47#11758196—21no—
48#11758196—21no—
49C4×Dic61C2×C411yescharacteristic
50C4×Dic61D411yescharacteristic
51C4×Dic61D411yescharacteristic
52C2×#92418—21no—
53C2×#92418—21no—
54#11758189—24no—
55C8×D61—42no—
56C22×D61—21no—
57C22×D61C22⋊C411yescharacteristic
58Q8×C61—21no—
59Q8×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61—21no—
62C2×C4×C61C22×C411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C2×C4×C61C2×D411yescharacteristic
65C2×Dic61—21no—
66C2×Dic61C22⋊C411yescharacteristic
67C2×Dic61C22⋊C411yescharacteristic
68C2×Dic61C22⋊C411yescharacteristic
69D244—21no—
70D244—21no—
71D244—42no—
72C4×D61—22no—
73C4×D61—21no—
74C4×D61—21no—
75C4×D61—21no—
76C4×D61—21no—
77C4×D61—41no—
78C4×D61—41no—
79C8×C61—22no—
80C8×C61—41no—
81#92418—22no—
82#92418—41no—
83C22×C61C2×C22⋊C411yescharacteristic
84C2×D61—21no—
85C2×D61—21no—
86C2×D61—41no—
87C2×D61—41no—
88C2×D61—41no—
89C2×D61#10412yes—
90C4×C61—21no—
91C4×C61—41no—
92C4×C61—41no—
93C4×C61#13111yescharacteristic
94C4×C61#13111yescharacteristic
95C4×C61AGL(1,ℤ/8)11yescharacteristic
96C4×C61#13711yescharacteristic
97Dic61—21no—
98Dic61—21no—
99Dic61—21no—
100Dic61—41no—
101#1483—611nomaximal, Sylow
102C2×C61#40811yescharacteristic
103C2×C61#41711yescharacteristic
104C2×C61C2×#10411yescharacteristic
105D61—22no—
106D61—81no—
107#529—611no—
108C2×C4⋊C8—611no—
109C4×M16—611no—
110Q8⋊C8—611no—
111Q8⋊C8D6111yescharacteristic, complemented
112D4⋊C8—611no—
113D4⋊C8—611no—
114C61#148311yescharacteristic, complemented, Sylow
115C2×M16—1221no—
116C22×C8—1221no—
117#126—1221no—
118#125—611no—
119#124—611no—
120#123—1221no—
121C22⋊Q8—611no—
122#121—611no—
123C4×Q8C2×D6111yescharacteristic
124C4×D4—611no—
125C4×D4—1221no—
126#117—1221no—
127C2×C42—611no—
128C4⋊C8—611no—
129C4⋊C8—1221no—
130C4⋊C8C2×D6111yescharacteristic
131#97—1221no—
132C4×C8—611no—
133C4×C8C2×D6111yescharacteristic
134C2×Q8C4×D6111yescharacteristic
135C2×D4—611no—
136C2×D4—1221no—
137C22×C4—611no—
138C22×C4—611no—
139C22×C4—611no—
140C22×C4—1221no—
141M16—1224no—
142C2×C8—21no—
143C2×C8—21no—
144C2×C8—1221no—
145C2×C8—1221no—
146C2×C8—2442no—
147C4⋊C4—21no—
148C4⋊C4—611no—
149C4⋊C4—1221no—
150C4⋊C4—1221no—
151C4⋊C4—1221no—
152C4⋊C4C4×D6111yescharacteristic
153C22⋊C4—1221no—
154C22⋊C4—1221no—
155C22⋊C4—1221no—
156C22⋊C4—1221no—
157C22⋊C4—1221no—
158C42—21no—
159C42—611no—
160C42—611no—
161C42—611no—
162C42C22×D6111yescharacteristic
163C23—611no—
164C23—1221no—
165Q8—21no—
166Q8—21no—
167D4—1221no—
168D4—1221no—
169D4—2442no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—611no—
173C2×C4—611no—
174C2×C4—611no—
175C2×C4—1222no—
176C2×C4—1221no—
177C2×C4—1221no—
178C2×C4—1221no—
179C2×C4—1221no—
180C2×C4—1221no—
181C2×C4—2441no—
182C2×C4—2441no—
183C2×C4C2×C4×D6111yescharacteristic
184C2×C4D4×D6111yescharacteristic
185C2×C4D4×D6111yescharacteristic
186C8—22no—
187C8—41no—
188C8—1222no—
189C8—2441no—
190C22—612no—
191C22—1221no—
192C22—1221no—
193C22—2441no—
194C22—2441no—
195C22—2441no—
196C22C22⋊C4×D6111yescharacteristic
197C4—21no—
198C4—41no—
199C4—41no—
200C4—1221no—
201C4—1221no—
202C4—1221no—
203C4—2441no—
204C4#1451978311yescharacteristic
205C4#1451978511yescharacteristic
206C4#1451980411yescharacteristic
207C4#1451980911yescharacteristic
208C2—1222no—
209C2—4881no—
210C2#1683972711yescharacteristic
211C2#1683976211yescharacteristic
212C2#104×D6111yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×Q8⋊C8C2
socleC22×C61C2×C22⋊C4
hypercenterQ8⋊C8D61
hypocenterC61#1483
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. C4⋊C8×D61C2semidirect
3. C4×#11758189C2semidirect
4. Q8⋊#92418C2semidirect
5. #16839491C2semidirect
6. #16839489C2semidirect
7. C61×Q8⋊C8C2semidirect
111. Q8⋊C8D61semidirect
114. C61#1483semidirect