Finite Group Databasebeta

← #21446920

Subgroups — #21446920

Order 7808.

370 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 93 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×Dic244C211yesmaximal, characteristic
2C22×#11758202C211yesmaximal, characteristic
3C2×#14519775C211yesmaximal, characteristic
4C2×#14519700C211yesmaximal, characteristic
5#16839667C211yesmaximal, characteristic
6#16839516C211yesmaximal, characteristic
7C2×#103×C61C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C22×Dic122C2211yescharacteristic
10C2×Dic244—22no—
11C2×Dic244—22no—
12C2×Dic244—22no—
13C2×#11758202—22no—
14C2×#11758202—22no—
15C2×#11758202—22no—
16C22×#92418C2211yescharacteristic
17#14519775—22no—
18#14519775—22no—
19C2×#11758196—22no—
20C2×C4×Dic61C2211yescharacteristic
21#14519700—22no—
22#14519684—22no—
23C22×Q8×C61C2211yescharacteristic
24C22×C8×C61C2211yescharacteristic
25C2×C4⋊C4×C61C2211yescharacteristic
26#103×C61—22no—
27C2×Q8×C61—21no—
28C2×Q8×C61—21no—
29C2×Q8×C61—21no—
30C2×Q8×C61—21no—
31C2×Q8×C61—21no—
32C2×Q8×C61D412yes—
33C22×C4×C61—21no—
34C22×C4×C61—21no—
35C22×C4×C61C2311yescharacteristic
36C22×Dic61—21no—
37C22×Dic61—21no—
38C22×Dic61D412yes—
39C2×Dic122—21no—
40C2×Dic122—21no—
41C2×Dic122—21no—
42C2×Dic122—21no—
43C2×Dic122—21no—
44C2×Dic122—21no—
45C2×Dic122—21no—
46C2×Dic122—21no—
47C2×Dic122—21no—
48C2×Dic122—21no—
49C2×Dic122D412yes—
50C2×Dic122D412yes—
51C2×C8×C61—21no—
52C2×C8×C61—21no—
53C2×C8×C61D412yes—
54C4⋊C4×C61—21no—
55C4⋊C4×C61—21no—
56#11758202—28no—
57#11758196—28no—
58C4×Dic61—21no—
59C4×Dic61—21no—
60C2×#92418—21no—
61C2×#92418—21no—
62C2×#92418D412yes—
63Dic244—28no—
64C23×C61C2×D411yescharacteristic
65Q8×C61—22no—
66Q8×C61—22no—
67Q8×C61—41no—
68Q8×C61—41no—
69C2×C4×C61—22no—
70C2×C4×C61—41no—
71C2×C4×C61—41no—
72C2×C4×C61—41no—
73C2×C4×C61—42no—
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61#4111yescharacteristic
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—41no—
85C2×Dic61—41no—
86C2×Dic61—41no—
87C2×Dic61—41no—
88C2×Dic61Q1614yescomplemented
89Dic122—22no—
90Dic122—22no—
91Dic122—22no—
92Dic122—22no—
93Dic122—41no—
94Dic122—41no—
95Dic122—41no—
96Dic122—41no—
97C8×C61—22no—
98#92418—22no—
99C22×C61#12011yescharacteristic
100C22×C61#12111yescharacteristic
101C22×C61#12711yescharacteristic
102C22×C61C2×Q1612yes—
103C22×C61#13712yes—
104C4×C61—42no—
105C4×C61—81no—
106C4×C61#12011yescharacteristic
107C4×C61#12011yescharacteristic
108C4×C61#12111yescharacteristic
109C4×C61#12111yescharacteristic
110Dic61—24no—
111Dic61—42no—
112Dic61—42no—
113#2016—611nomaximal, Sylow
114C2×C61#39211yescharacteristic
115C2×C61#45112yes—
116C2×C61#46212yes—
117C2×C61#49411yescharacteristic
118C2×C61#49711yescharacteristic
119C22×Q16—611no—
120C22×Q16—611no—
121C2×C4⋊Q8—611no—
122C2×#103—611no—
123C2×#103D6111yescharacteristic
124#391—611no—
125#336—611no—
126C61#201611yescharacteristic, complemented, Sylow
127C22×Q8—611no—
128C22×Q8—611no—
129C22×Q8C2×D6111yescharacteristic
130C2×Q16—1222no—
131C2×Q16—1222no—
132C2×Q16—1222no—
133C2×Q16—1222no—
134C2×Q16—1222no—
135C2×Q16—1222no—
136C22×C8—611no—
137C22×C8C2×D6111yescharacteristic
138C4⋊Q8—1222no—
139C4⋊Q8—1222no—
140C2×C4⋊C4—1222no—
141C2×C4⋊C4C2×D6111yescharacteristic
142C2×C42—611no—
143#103—22no—
144#103—1222no—
145#95—1222no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—612no—
152C2×Q8—612no—
153C2×Q8—1221no—
154C2×Q8—1221no—
155C2×Q8—1221no—
156C2×Q8—1221no—
157C2×Q8—1221no—
158C2×Q8—1221no—
159C2×Q8—1221no—
160C2×Q8—1221no—
161C2×Q8—1221no—
162C2×Q8—1221no—
163C2×Q8D24412yes—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—612no—
167C22×C4—1221no—
168C22×C4—1221no—
169C22×C4C22×D6111yescharacteristic
170Q16—1228no—
171Q16—1228no—
172C2×C8—21no—
173C2×C8—21no—
174C2×C8—612no—
175C2×C8—1221no—
176C2×C8—1221no—
177C2×C8C22⋊D6112yes—
178C4⋊C4—21no—
179C4⋊C4—21no—
180C4⋊C4—1228no—
181C42—1221no—
182C42—1221no—
183C23D4×D6111yescharacteristic
184Q8—22no—
185Q8—22no—
186Q8—41no—
187Q8—41no—
188Q8—1222no—
189Q8—1222no—
190Q8—1222no—
191Q8—1222no—
192Q8—2441no—
193Q8—2441no—
194Q8—2441no—
195Q8—2441no—
196C2×C4—22no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—42no—
201C2×C4—614no—
202C2×C4—1222no—
203C2×C4—1222no—
204C2×C4—1222no—
205C2×C4—1222no—
206C2×C4—2441no—
207C2×C4—2441no—
208C2×C4—2441no—
209C2×C4—2441no—
210C2×C4C2×D24411yescharacteristic
211C2×C4#1175822211yescharacteristic
212C2×C4D4×D6111yescharacteristic
213C2×C4D4×D6111yescharacteristic
214C2×C4D4×D6111yescharacteristic
215C2×C4C2×C22⋊D6111yescharacteristic
216C8—22no—
217C8—1222no—
218C22#1451974711yescharacteristic
219C22#1451975011yescharacteristic
220C22#1451977311yescharacteristic
221C22Q16×D6112yes—
222C22#1451980612yes—
223C4—42no—
224C4—81no—
225C4—1224no—
226C4—2442no—
227C4—2442no—
228C4#1451974511yescharacteristic
229C4#1451974711yescharacteristic
230C4#1451975011yescharacteristic
231C4#1451975111yescharacteristic
232C2#1683967111yescharacteristic
233C2#1683991912yes—
234C2#1683997112yes—
235C2#1684014011yescharacteristic
236C2#1684015311yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#103×C61C2
socleC23×C61C2×D4
hypercenterC2×#103D61
hypocenterC61#2016
LCSG ▷ C22×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
88. C2×Dic61Q16semidirect
126. C61#2016semidirect