Finite Group Databasebeta

← #21446903

Subgroups — #21446903

Order 7808.

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

normal subgroups only

This group has 406 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×#11758190C211yesmaximal, characteristic
2C22×#11758201C211yesmaximal, characteristic
3C2×#14519775C211yesmaximal, characteristic, complemented
4C2×#14519700C211yesmaximal, characteristic, complemented
5#16839663C211yesmaximal, characteristic
6#16839516C211yesmaximal, characteristic, complemented
7C2×#103×C61C211yesmaximal, characteristic, complemented
8C22×Dic122C2211yescharacteristic
9C22×D244C2211yescharacteristic
10C2×#11758190—22no—
11C2×#11758190—22no—
12C2×#11758190—22no—
13C2×#11758201—22no—
14C2×#11758201—22no—
15C2×#11758201—22no—
16C22×#92418C2211yescharacteristic
17#14519775—22no—
18#14519775—22no—
19C2×#11758196—22no—
20C2×#11758198—22no—
21C2×C4×Dic61C2211yescharacteristic
22#14519700—22no—
23C22×Q8×C61C2211yescharacteristic
24C22×C8×C61C2211yescharacteristic
25C2×C4⋊C4×C61C2211yescharacteristic
26#103×C61—22no—
27C23×D61—21no—
28C2×Q8×C61—21no—
29C2×Q8×C61—21no—
30C2×Q8×C61—21no—
31C2×Q8×C61—21no—
32C2×Q8×C61—21no—
33C2×Q8×C61D412yes—
34C22×C4×C61—21no—
35C22×C4×C61—21no—
36C22×C4×C61C2311yescharacteristic
37C22×Dic61—21no—
38C22×Dic61D412yes—
39C2×D244—21no—
40C2×D244—21no—
41C2×D244—21no—
42C2×D244—21no—
43C2×D244—21no—
44C2×D244D412yes—
45C2×Dic122—21no—
46C2×Dic122—21no—
47C2×Dic122—21no—
48C2×Dic122—21no—
49C2×Dic122—21no—
50C2×Dic122D412yes—
51C2×C8×C61—21no—
52C2×C8×C61—21no—
53C2×C8×C61D412yes—
54C4⋊C4×C61—21no—
55C4⋊C4×C61—21no—
56#11758201—28no—
57#11758198—44no—
58#11758196—28no—
59C4×Dic61—21no—
60C4×Dic61—21no—
61C2×#92418—21no—
62C2×#92418—21no—
63C2×#92418D412yes—
64#11758190—28no—
65C23×C61C2×D411yescharacteristic
66C22×D61—22no—
67C22×D61—41no—
68C22×D61—41no—
69C22×D61—42no—
70C22×D61—42no—
71Q8×C61—22no—
72Q8×C61—22no—
73Q8×C61—41no—
74Q8×C61—41no—
75C2×C4×C61—22no—
76C2×C4×C61—41no—
77C2×C4×C61—41no—
78C2×C4×C61—41no—
79C2×C4×C61—42no—
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61#4111yescharacteristic
86C2×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—41no—
90C2×Dic61—41no—
91C2×Dic61SD1614yescomplemented
92D244—22no—
93D244—22no—
94D244—41no—
95D244—41no—
96Dic122—22no—
97Dic122—22no—
98Dic122—41no—
99Dic122—41no—
100C8×C61—22no—
101#92418—22no—
102C22×C61#12011yescharacteristic
103C22×C61#12111yescharacteristic
104C22×C61#12711yescharacteristic
105C22×C61C2×SD1612yes—
106C22×C61#13712yes—
107C2×D61—42no—
108C2×D61—44no—
109C2×D61—82no—
110C2×D61—81no—
111C2×D61—81no—
112C4×C61—42no—
113C4×C61—81no—
114C4×C61#12011yescharacteristic
115C4×C61#12011yescharacteristic
116C4×C61#12111yescharacteristic
117C4×C61#12111yescharacteristic
118Dic61—24no—
119Dic61—42no—
120#2013—611nomaximal, Sylow
121C2×C61#39211yescharacteristic
122C2×C61#44812yes—
123C2×C61#46112yes—
124C2×C61#49211yescharacteristic
125C2×C61#49711yescharacteristic
126D61—82no—
127C22×SD16—611no—
128C22×SD16—611no—
129C2×C4⋊Q8—611no—
130C2×#103—611no—
131C2×#103D6111yescharacteristic, complemented
132#390—611no—
133#336—611no—
134C61#201311yescharacteristic, complemented, Sylow
135C22×Q8—611no—
136C22×Q8C2×D6111yescharacteristic
137C22×D4—611no—
138C2×SD16—1222no—
139C2×SD16—1222no—
140C2×SD16—1222no—
141C2×SD16—1222no—
142C2×SD16—1222no—
143C2×SD16—1222no—
144C22×C8—611no—
145C22×C8C2×D6111yescharacteristic
146C4⋊Q8—1222no—
147C4⋊Q8—1222no—
148C2×C4⋊C4—1222no—
149C2×C4⋊C4C2×D6111yescharacteristic
150C2×C22⋊C4—1222no—
151C2×C42—611no—
152#103—22no—
153#103—1222no—
154C24—1221no—
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×Q8D24412yes—
167C2×D4—612no—
168C2×D4—1221no—
169C2×D4—1221no—
170C2×D4—1221no—
171C2×D4—1221no—
172C2×D4—1221no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—612no—
176C22×C4—1221no—
177C22×C4C22×D6111yescharacteristic
178SD16—1228no—
179SD16—1228no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—612no—
183C2×C8—1221no—
184C2×C8—1221no—
185C2×C8C22⋊D6112yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—1228no—
189C22⋊C4—2444no—
190C42—1221no—
191C42—1221no—
192C23—1222no—
193C23—2442no—
194C23—2441no—
195C23—2441no—
196C23—2442no—
197C23D4×D6111yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—41no—
201Q8—41no—
202Q8—1222no—
203Q8—1222no—
204Q8—2441no—
205Q8—2441no—
206D4—1222no—
207D4—1222no—
208D4—2441no—
209D4—2441no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—614no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4—2441no—
220C2×C4—2441no—
221C2×C4C2×D24411yescharacteristic
222C2×C4#1175822211yescharacteristic
223C2×C4D4×D6111yescharacteristic
224C2×C4D4×D6111yescharacteristic
225C2×C4D4×D6111yescharacteristic
226C2×C4C2×C22⋊D6111yescharacteristic
227C8—22no—
228C8—1222no—
229C22—4881no—
230C22—4881no—
231C22—4882no—
232C22—2444no—
233C22—2442no—
234C22#1451974711yescharacteristic
235C22#1451975011yescharacteristic
236C22#1451977311yescharacteristic
237C22SD16×D6112yes—
238C22#1451980912yes—
239C4—42no—
240C4—81no—
241C4—1224no—
242C4—2442no—
243C4#1451974511yescharacteristic
244C4#1451974711yescharacteristic
245C4#1451975011yescharacteristic
246C4#1451975111yescharacteristic
247C2—4882no—
248C2#1683967111yescharacteristic
249C2#1683990212yes—
250C2#1683996612yes—
251C2#1684013311yescharacteristic
252C2#1684015511yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#103×C61C2
socleC23×C61C2×D4
hypercenterC2×#103D61
hypocenterC61#2013
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
3. C2×#14519775C2semidirect
4. C2×#14519700C2semidirect
6. #16839516C2semidirect
7. C2×#103×C61C2semidirect
91. C2×Dic61SD16semidirect
131. C2×#103D61semidirect
134. C61#2013semidirect