Finite Group Databasebeta

← #21446689

Subgroups — #21446689

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×#14519701C211yesmaximal, characteristic
4C2×#14519700C211yesmaximal, characteristic
5C2×#14519688C211yesmaximal, characteristic
6#16839668C211yesmaximal, characteristic
7C61×#391C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C2×#11758202—22no—
10C2×#11758202—22no—
11C2×#11758202C414yescomplemented
12C22×#92418C2211yescharacteristic
13C22×#92418C2211yescharacteristic
14C2×C4⋊Dic61C2211yescharacteristic
15#14519708—22no—
16#14519701—22no—
17#14519700—22no—
18#14519688—22no—
19#14519684—22no—
20C22×Q8×C61C2211yescharacteristic
21C2×C4⋊C4×C61C2211yescharacteristic
22C2×C42×C61C2211yescharacteristic
23#95×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×C61D412yes—
33C22×C4×C61C2311yescharacteristic
34C22×Dic61—21no—
35C22×Dic61—21no—
36C2×Dic122—21no—
37C2×Dic122—21no—
38C2×Dic122—21no—
39C2×Dic122—21no—
40C2×Dic122—21no—
41C2×Dic122C2×C412yes—
42C4⋊C4×C61—21no—
43C4⋊C4×C61—21no—
44C42×C61—21no—
45C42×C61—21no—
46#11758202—28no—
47C4⋊Dic61—21no—
48C4⋊Dic61—21no—
49C2×#92418—21no—
50C2×#92418—21no—
51C2×#92418C2×C412yes—
52C2×#92418D412yes—
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—22no—
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—41no—
65C2×C4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61—42no—
68C2×C4×C61C22×C411yescharacteristic
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61#4111yescharacteristic
73C2×C4×C61#4111yescharacteristic
74C2×Dic61—22no—
75C2×Dic61—41no—
76C2×Dic61—41no—
77C2×Dic61—41no—
78C2×Dic61—42no—
79Dic122—22no—
80Dic122—22no—
81Dic122—41no—
82Dic122—41no—
83#92418—22no—
84#92418C22⋊C414yes—
85C22×C61C4×D411yescharacteristic
86C22×C61#12111yescharacteristic
87C22×C61#12711yescharacteristic
88C22×C61#13712yes—
89C22×C61#13712yes—
90C4×C61—42no—
91C4×C61—42no—
92C4×C61—81no—
93C4×C61C2×C22⋊C411yescharacteristic
94C4×C61C4×D411yescharacteristic
95C4×C61#12111yescharacteristic
96C4×C61#12411yescharacteristic
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×#103—611no—
109C2×#97—611no—
110#391—611no—
111#391D6111yescharacteristic
112C61#197111yescharacteristic, complemented, Sylow
113C22×Q8—611no—
114C22×Q8C2×D6111yescharacteristic
115C2×Q16—614no—
116C2×Q16—1222no—
117C2×Q16—1222no—
118C22×C8—611no—
119C22×C8—611no—
120C2×C4⋊C4—611no—
121C2×C4⋊C4C2×D6111yescharacteristic
122C2×C42C2×D6111yescharacteristic
123#106—1222no—
124#103—1222no—
125#103—1222no—
126#97—1222no—
127#95—22no—
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—1221no—
144C22×C4—1221no—
145C22×C4C22⋊D6112yes—
146C22×C4C22×D6111yescharacteristic
147Q16—1228no—
148C2×C8—612no—
149C2×C8—612no—
150C2×C8—612no—
151C2×C8—612no—
152C2×C8—1221no—
153C2×C8—1221no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—1221no—
157C4⋊C4—1221no—
158C42—21no—
159C42—21no—
160C23C2×C22⋊D6111yescharacteristic
161Q8—22no—
162Q8—22no—
163Q8—41no—
164Q8—41no—
165Q8—1222no—
166Q8—1222no—
167Q8—2441no—
168Q8—2441no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—42no—
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×C4D4×D6111yescharacteristic
187C2×C4#1175822411yescharacteristic
188C8—614no—
189C8—1222no—
190C22C4×C22⋊D6111yescharacteristic
191C22#1451974911yescharacteristic
192C22#1451977311yescharacteristic
193C22#1451980712yes—
194C22#1451980812yes—
195C4—42no—
196C4—42no—
197C4—81no—
198C4—4881no—
199C4—2442no—
200C4C22⋊C4×D6111yescharacteristic
201C4#1451973711yescharacteristic
202C4#1451975011yescharacteristic
203C4#1451976311yescharacteristic
204C2#1683966211yescharacteristic
205C2#1683986712yes—
206C2#1684001812yes—
207C2#1684015411yescharacteristic
208C2#1684015711yescharacteristic
subgroupG/H
centerC23C2×C22⋊D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#391C2
socleC23×C61C2×D4
hypercenter#391D61
hypocenterC61#1971
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

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