Finite Group Databasebeta

← #21446900

Subgroups — #21446900

Order 7808.

406 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 95 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×#11758200C211yesmaximal, characteristic
2C2×#14519775C211yesmaximal, characteristic, complemented
3C2×#14519702C211yesmaximal, characteristic, complemented
4C2×#14519701C211yesmaximal, characteristic, complemented
5#16839665C211yesmaximal, characteristic
6#16839516C211yesmaximal, characteristic, complemented
7C22×SD16×C61C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C2×#11758200—22no—
10C2×#11758200—22no—
11C2×#11758200—22no—
12C22×#92418C2211yescharacteristic
13#14519775—22no—
14#14519775—22no—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×#11758196—22no—
17C2×C22⋊Dic61—22no—
18C2×C4×Dic61C2211yescharacteristic
19#14519702—22no—
20#14519701—22no—
21C22×Q8×C61C2211yescharacteristic
22C22×D4×C61C2211yescharacteristic
23C2×SD16×C61—22no—
24C2×SD16×C61—22no—
25C2×SD16×C61—22no—
26C22×C8×C61C2211yescharacteristic
27C24×C61—21no—
28C2×Q8×C61—21no—
29C2×Q8×C61—21no—
30C2×Q8×C61—21no—
31C2×Q8×C61—21no—
32C2×Q8×C61—21no—
33C2×Q8×C61D412yes—
34C2×D4×C61—21no—
35C2×D4×C61—21no—
36C2×D4×C61—21no—
37C2×D4×C61—21no—
38C2×D4×C61—21no—
39C2×D4×C61D412yes—
40C22×C4×C61—21no—
41C22×C4×C61C2311yescharacteristic
42C22×Dic61—21no—
43C22×Dic61—21no—
44C22×Dic61D412yes—
45C2×Dic122—21no—
46C2×Dic122—21no—
47C2×Dic122—21no—
48C2×Dic122—21no—
49C2×Dic122—21no—
50C2×Dic122D412yes—
51SD16×C61—28no—
52C2×C8×C61—21no—
53C2×C8×C61—21no—
54C2×C8×C61D412yes—
55C22⋊Dic61—44no—
56#11758200—28no—
57C4⋊Dic61—21no—
58C4⋊Dic61—21no—
59#11758196—28no—
60C4×Dic61—21no—
61C4×Dic61—21no—
62C2×#92418—21no—
63C2×#92418—21no—
64C2×#92418D412yes—
65C23×C61—22no—
66C23×C61—41no—
67C23×C61—41no—
68C23×C61—42no—
69C23×C61—42no—
70C23×C61C2×D411yescharacteristic
71Q8×C61—22no—
72Q8×C61—22no—
73Q8×C61—41no—
74Q8×C61—41no—
75D4×C61—22no—
76D4×C61—22no—
77D4×C61—41no—
78D4×C61—41no—
79C2×C4×C61—22no—
80C2×C4×C61—41no—
81C2×C4×C61—41no—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61#4111yescharacteristic
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—41no—
92C2×Dic61—41no—
93C2×Dic61—41no—
94C2×Dic61—42no—
95C2×Dic61SD1614yescomplemented
96Dic122—22no—
97Dic122—22no—
98Dic122—41no—
99Dic122—41no—
100C8×C61—22no—
101#92418—22no—
102C22×C61—42no—
103C22×C61—44no—
104C22×C61—82no—
105C22×C61—81no—
106C22×C61—81no—
107C22×C61#12011yescharacteristic
108C22×C61#12111yescharacteristic
109C22×C61#12711yescharacteristic
110C22×C61C2×SD1612yes—
111C22×C61#13712yes—
112C4×C61—42no—
113C4×C61#12011yescharacteristic
114C4×C61#12011yescharacteristic
115C4×C61#12111yescharacteristic
116C4×C61#12111yescharacteristic
117Dic61—24no—
118Dic61—42no—
119Dic61—81no—
120#2013—611nomaximal, Sylow
121C2×C61—82no—
122C2×C61#39211yescharacteristic
123C2×C61#44812yes—
124C2×C61#46112yes—
125C2×C61#49211yescharacteristic
126C2×C61#49711yescharacteristic
127C22×SD16—611no—
128C22×SD16D6111yescharacteristic
129C2×C4⋊Q8—611no—
130C2×#103—611no—
131C2×#103—611no—
132#390—611no—
133#336—611no—
134C61#201311yescharacteristic, complemented, Sylow
135C22×Q8—611no—
136C22×Q8C2×D6111yescharacteristic
137C22×D4C2×D6111yescharacteristic
138C2×SD16—22no—
139C2×SD16—22no—
140C2×SD16—22no—
141C2×SD16—1222no—
142C2×SD16—1222no—
143C2×SD16—1222no—
144C22×C8—611no—
145C22×C8C2×D6111yescharacteristic
146C4⋊Q8—1222no—
147C4⋊Q8—1222no—
148C2×C4⋊C4—611no—
149C2×C4⋊C4—1222no—
150C2×C22⋊C4—1222no—
151C2×C42—611no—
152#103—1222no—
153#103—1222no—
154C24—21no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—612no—
161C2×Q8—1221no—
162C2×Q8—1221no—
163C2×Q8—1221no—
164C2×Q8—1221no—
165C2×Q8—1221no—
166C2×Q8C22⋊D6112yes—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4C22⋊D6112yes—
173C22×C4—21no—
174C22×C4—612no—
175C22×C4—1221no—
176C22×C4—1221no—
177C22×C4C22×D6111yescharacteristic
178SD16—28no—
179SD16—1228no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—612no—
183C2×C8—1221no—
184C2×C8—1221no—
185C2×C8C22⋊D6112yes—
186C4⋊C4—1228no—
187C4⋊C4—1221no—
188C4⋊C4—1221no—
189C22⋊C4—2444no—
190C42—1221no—
191C42—1221no—
192C23—22no—
193C23—41no—
194C23—41no—
195C23—42no—
196C23—42no—
197C23D4×D6111yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—41no—
201Q8—41no—
202Q8—1222no—
203Q8—1222no—
204Q8—2441no—
205Q8—2441no—
206D4—22no—
207D4—22no—
208D4—41no—
209D4—41no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—614no—
214C2×C4—1222no—
215C2×C4—1222no—
216C2×C4—1222no—
217C2×C4—2441no—
218C2×C4—2442no—
219C2×C4—2441no—
220C2×C4—2441no—
221C2×C4D4×D6111yescharacteristic
222C2×C4D4×D6111yescharacteristic
223C2×C4#1175822411yescharacteristic
224C2×C4C2×C22⋊D6111yescharacteristic
225C2×C4C2×C22⋊D6111yescharacteristic
226C2×C4C2×C22⋊D6111yescharacteristic
227C8—22no—
228C8—1222no—
229C22—44no—
230C22—42no—
231C22—81no—
232C22—81no—
233C22—82no—
234C22#1451974511yescharacteristic
235C22#1451974911yescharacteristic
236C22#1451977311yescharacteristic
237C22SD16×D6112yes—
238C22#1451980612yes—
239C4—42no—
240C4—1224no—
241C4—4881no—
242C4—2442no—
243C4#1451974511yescharacteristic
244C4#1451974611yescharacteristic
245C4#1451974811yescharacteristic
246C4#1451974911yescharacteristic
247C2—82no—
248C2#1683967011yescharacteristic
249C2#1683989912yes—
250C2#1683996512yes—
251C2#1684013311yescharacteristic
252C2#1684015311yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC22×SD16×C61C2
socleC23×C61C2×D4
hypercenterC22×SD16D61
hypocenterC61#2013
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#14519775C2semidirect
3. C2×#14519702C2semidirect
4. C2×#14519701C2semidirect
6. #16839516C2semidirect
95. C2×Dic61SD16semidirect
134. C61#2013semidirect