Finite Group Databasebeta

← #21446687

Subgroups — #21446687

Order 7808.

304 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C22×#11758202C211yesmaximal, characteristic
2C2×#14519708C211yesmaximal, characteristic
3C2×#14519702C211yesmaximal, characteristic
4C2×#14519687C211yesmaximal, characteristic
5#16839669C211yesmaximal, characteristic
6#16839667C211yesmaximal, characteristic
7C2×#103×C61C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C2×#11758202—22no—
10C2×#11758202—22no—
11C2×#11758202C414yescomplemented
12C22×#92418C2211yescharacteristic
13C2×C4⋊Dic61C2211yescharacteristic
14C2×C4×Dic61C2211yescharacteristic
15#14519708—22no—
16#14519702—22no—
17#14519687—22no—
18#14519684—22no—
19#14519684—22no—
20C22×Q8×C61C2211yescharacteristic
21C22×C8×C61C2211yescharacteristic
22C2×C4⋊C4×C61C2211yescharacteristic
23#103×C61—22no—
24C2×Q8×C61—21no—
25C2×Q8×C61—21no—
26C2×Q8×C61—21no—
27C2×Q8×C61—21no—
28C2×Q8×C61—21no—
29C2×Q8×C61C2×C412yes—
30C22×C4×C61—21no—
31C22×C4×C61—21no—
32C22×C4×C61C2311yescharacteristic
33C22×Dic61—21no—
34C22×Dic61—21no—
35C22×Dic61D412yes—
36C2×Dic122—21no—
37C2×Dic122—21no—
38C2×Dic122—21no—
39C2×Dic122—21no—
40C2×Dic122—21no—
41C2×Dic122C2×C412yes—
42C2×C8×C61—21no—
43C2×C8×C61—21no—
44C2×C8×C61D412yes—
45C4⋊C4×C61—21no—
46C4⋊C4×C61—21no—
47#11758202—28no—
48C4⋊Dic61—21no—
49C4⋊Dic61—21no—
50C4×Dic61—21no—
51C4×Dic61—21no—
52C2×#92418C2×C412yes—
53C2×#92418D412yes—
54C2×#92418D412yes—
55C23×C61C2×D411yescharacteristic
56Q8×C61—22no—
57Q8×C61—22no—
58Q8×C61—41no—
59Q8×C61—41no—
60C2×C4×C61—22no—
61C2×C4×C61—41no—
62C2×C4×C61—41no—
63C2×C4×C61—41no—
64C2×C4×C61—42no—
65C2×C4×C61C22×C411yescharacteristic
66C2×C4×C61C2×D411yescharacteristic
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61#4111yescharacteristic
70C2×C4×C61#4111yescharacteristic
71C2×Dic61—22no—
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—41no—
76C2×Dic61—41no—
77C2×Dic61—41no—
78C2×Dic61—42no—
79Dic122—22no—
80Dic122—22no—
81Dic122—41no—
82Dic122—41no—
83C8×C61—22no—
84#92418C22⋊C414yes—
85C22×C61C4×D411yescharacteristic
86C22×C61#12111yescharacteristic
87C22×C61#12711yescharacteristic
88C22×C61#13712yes—
89C22×C61#13712yes—
90C4×C61—42no—
91C4×C61—81no—
92C4×C61C2×C22⋊C411yescharacteristic
93C4×C61C4×D411yescharacteristic
94C4×C61#12111yescharacteristic
95C4×C61#12411yescharacteristic
96Dic61—42no—
97Dic61—42no—
98Dic61—81no—
99#1971—611nomaximal, Sylow
100C2×C61#39011yescharacteristic
101C2×C61#44112yes—
102C2×C61#47012yes—
103C2×C61#49711yescharacteristic
104C2×C61#49711yescharacteristic
105C22×Q16—611no—
106C2×#106—611no—
107C2×#103—611no—
108C2×#103D6111yescharacteristic
109C2×#97—611no—
110#391—611no—
111#391—611no—
112C61#197111yescharacteristic, complemented, Sylow
113C22×Q8—611no—
114C22×Q8C2×D6111yescharacteristic
115C2×Q16—614no—
116C2×Q16—1222no—
117C2×Q16—1222no—
118C22×C8—611no—
119C22×C8C2×D6111yescharacteristic
120C2×C4⋊C4—611no—
121C2×C4⋊C4C2×D6111yescharacteristic
122C2×C42—611no—
123#106—1222no—
124#103—22no—
125#103—1222no—
126#97—1222no—
127#95—1222no—
128#95—1222no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—612no—
135C2×Q8—1221no—
136C2×Q8—1221no—
137C2×Q8—1221no—
138C2×Q8—1221no—
139C2×Q8—1221no—
140C2×Q8C4×D6112yes—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—612no—
144C22×C4—1221no—
145C22×C4—1221no—
146C22×C4C22×D6111yescharacteristic
147Q16—1228no—
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—612no—
151C2×C8—612no—
152C2×C8—612no—
153C2×C8C22⋊D6112yes—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—1221no—
157C4⋊C4—1221no—
158C42—1221no—
159C42—1221no—
160C23D4×D6111yescharacteristic
161Q8—22no—
162Q8—22no—
163Q8—41no—
164Q8—41no—
165Q8—1222no—
166Q8—1222no—
167Q8—2441no—
168Q8—2441no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—42no—
174C2×C4—1222no—
175C2×C4—1222no—
176C2×C4—1222no—
177C2×C4—1222no—
178C2×C4—2442no—
179C2×C4—2441no—
180C2×C4—2441no—
181C2×C4—2441no—
182C2×C4C2×C4×D6111yescharacteristic
183C2×C4#1175822211yescharacteristic
184C2×C4D4×D6111yescharacteristic
185C2×C4D4×D6111yescharacteristic
186C2×C4#1175822411yescharacteristic
187C2×C4C2×C22⋊D6111yescharacteristic
188C8—22no—
189C8—614no—
190C22#1451973711yescharacteristic
191C22#1451975011yescharacteristic
192C22#1451977311yescharacteristic
193C22#1451980612yes—
194C22#1451980912yes—
195C4—42no—
196C4—81no—
197C4—4881no—
198C4—2442no—
199C4—2442no—
200C4C22⋊C4×D6111yescharacteristic
201C4C4×C22⋊D6111yescharacteristic
202C4#1451974911yescharacteristic
203C4#1451976311yescharacteristic
204C2#1683966211yescharacteristic
205C2#1683986612yes—
206C2#1684001912yes—
207C2#1684015311yescharacteristic
208C2#1684015511yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#103×C61C2
socleC23×C61C2×D4
hypercenterC2×#103D61
hypocenterC61#1971
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
11. C2×#11758202C4semidirect
112. C61#1971semidirect