Finite Group Databasebeta

← #354×D61 #21447478

Subgroups — #354×D61 #21447478

Order 7808.

284 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 57 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#124×D61C211yesmaximal, characteristic
2#99×D61C212yesmaximal
3#16839557C211yesmaximal, characteristic, complemented
4#16839556C212yesmaximal, complemented
5C61×#354C211yesmaximal, characteristic, complemented
6C2×Q8×D61C411yescharacteristic, complemented
7C2×D4×D61C2211yescharacteristic
8#14519766C411yescharacteristic, complemented
9#14519765C411yescharacteristic, complemented
10#14519764C2211yescharacteristic
11#14519763—22no—
12C22⋊C4×D61—22no—
13C22⋊C4×D61—22no—
14C42×D61C411yescharacteristic, complemented
15#14519692C2212yes—
16#14519691—22no—
17#124×C61C2211yescharacteristic
18#99×C61C2212yes—
19C23×D61D412yes—
20C2×Q8×C61C2×C411yescharacteristic, complemented
21C2×D4×C61C2311yescharacteristic
22C2×C22⋊D61D412yes—
23Q8×D61—41no—
24Q8×D61—41no—
25D4×D61—41no—
26D4×D61—41no—
27C2×D244C2×C411yescharacteristic
28C2×C4×D61—21no—
29C2×C4×D61—21no—
30C2×C4×D61—42no—
31C2×C4×D61C2×C411yescharacteristic
32C2×Dic122—21no—
33C2×Dic122C2×C411yescharacteristic, complemented
34C22⋊C4×C61—22no—
35C22⋊C4×C61—22no—
36C42×C61C2×C411yescharacteristic, complemented
37C22⋊Dic61—22no—
38C22⋊Dic61—22no—
39#11758198—22no—
40#11758198—22no—
41#11758198—42no—
42C4×Dic61—21no—
43C4×Dic61C2×C411yescharacteristic, complemented
44C23×C61C2×D412yes—
45C22×D61—22no—
46C22×D61—22no—
47C22×D61—44no—
48C22×D61C22⋊C411yescharacteristic
49C22×D61C22⋊C412yes—
50Q8×C61—41no—
51D4×C61—41no—
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—42no—
55C2×C4×C61C22×C411yescharacteristic
56C22⋊D61—42no—
57C2×Dic61—21no—
58C2×Dic61—21no—
59C2×Dic61—42no—
60C2×Dic61C22⋊C411yescharacteristic
61D244—41no—
62C4×D61—21no—
63C4×D61—21no—
64C4×D61—42no—
65C4×D61—41no—
66C4×D61—41no—
67C4×D61—84no—
68Dic122—42no—
69Dic122—41no—
70C22×C61—22no—
71C22×C61—42no—
72C22×C61C2×C22⋊C411yescharacteristic
73C2×D61—22no—
74C2×D61—22no—
75C2×D61—44no—
76C2×D61—42no—
77C2×D61—82no—
78C2×D61#9911yescharacteristic
79C2×D61#9911yescharacteristic
80C4×C61—21no—
81C4×C61—41no—
82C4×C61—41no—
83C4×C61—82no—
84Dic61—21no—
85Dic61—41no—
86Dic61—41no—
87Dic61—82no—
88C2×#354—611nomaximal, Sylow
89C2×C61—21no—
90C2×C61—42no—
91C2×C61C2×#9911yescharacteristic
92D61—21no—
93D61—42no—
94D61#35412yesdirect product factor
95C2×#124—611no—
96C2×#99—612no—
97#354—611no—
98#354—612no—
99#354D6111yescharacteristic, direct product factor
100C61C2×#35411yescharacteristic, complemented, Sylow
101C22×Q8—611no—
102C22×D4—611no—
103#124—611no—
104#124—611no—
105#124—611no—
106#124—1222no—
107#124C2×D6111yescharacteristic
108C2×C22⋊C4—1222no—
109C2×C22⋊C4—1222no—
110C2×C42—611no—
111#99—612no—
112#99—1222no—
113#99C2×D6112yes—
114C24—612no—
115C2×Q8—611no—
116C2×Q8—1221no—
117C2×Q8—2441no—
118C2×Q8—2441no—
119C2×Q8C4×D6111yescharacteristic, complemented
120C2×D4—612no—
121C2×D4—611no—
122C2×D4—2441no—
123C2×D4—2441no—
124C2×D4C22×D6111yescharacteristic
125C22×C4—611no—
126C22×C4—1221no—
127C22×C4—1221no—
128C22×C4—2442no—
129C22⋊C4—22no—
130C22⋊C4—22no—
131C22⋊C4—1222no—
132C22⋊C4—1222no—
133C22⋊C4—1222no—
134C22⋊C4—1222no—
135C22⋊C4—2442no—
136C42—611no—
137C42—1221no—
138C42C4×D6111yescharacteristic, complemented
139C23—611no—
140C23—612no—
141C23—1222no—
142C23—1222no—
143C23—2444no—
144C23D4×D6112yes—
145Q8—41no—
146Q8—2441no—
147Q8—2442no—
148D4—41no—
149D4—2441no—
150D4—2442no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—42no—
154C2×C4—611no—
155C2×C4—1221no—
156C2×C4—1221no—
157C2×C4—1221no—
158C2×C4—1221no—
159C2×C4—4884no—
160C2×C4—2441no—
161C2×C4—2441no—
162C2×C4—2442no—
163C2×C4—2442no—
164C2×C4C2×C4×D6111yescharacteristic
165C22—22no—
166C22—42no—
167C22—611no—
168C22—611no—
169C22—1222no—
170C22—1222no—
171C22—4882no—
172C22—2442no—
173C22—2444no—
174C22C22⋊C4×D6111yescharacteristic
175C4—21no—
176C4—41no—
177C4—41no—
178C4—82no—
179C4—1221no—
180C4—4882no—
181C4—2441no—
182C4—2441no—
183C2—21no—
184C2—42no—
185C2—612no—
186C2—1221no—
187C2—2442no—
188C2#99×D6111yescharacteristic
subgroupG/H
centerC2#99×D61
commutatorC2×C4×C61C22×C4
FrattiniC2×D4C22×D61
FittingC61×#354C2
socleC2×C61C2×#99
hypercenter#354D61
hypocenterC61C2×#354
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
3. #16839557C2semidirect
4. #16839556C2semidirect
5. C61×#354C2semidirect
6. C2×Q8×D61C4semidirect
8. #14519766C4semidirect
9. #14519765C4semidirect
14. C42×D61C4semidirect
20. C2×Q8×C61C2×C4semidirect
33. C2×Dic122C2×C4semidirect
36. C42×C61C2×C4semidirect
43. C4×Dic61C2×C4semidirect
94. D61#354direct (N × H)
99. #354D61direct (N × H)
100. C61C2×#354semidirect
119. C2×Q8C4×D61semidirect
138. C42C4×D61semidirect