Finite Group Databasebeta

← #21446503

Subgroups — #21446503

Order 7808.

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

normal subgroups only

This group has 292 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
1C2×#14519699C211yesmaximal, characteristic
2C2×#14519697C211yesmaximal, characteristic
3C2×C8×Dic61C211yesmaximal, characteristic, complemented
4#16839663C211yesmaximal, characteristic
5#16839661C211yesmaximal, characteristic, complemented
6#16839524C211yesmaximal, characteristic, complemented
7C61×#340C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10C2×C4⋊Dic61—21no—
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758198—21no—
13C2×#11758198—21no—
14C2×C4×Dic61C2211yescharacteristic
15#14519699—22no—
16#14519697C414yescomplemented
17C8×Dic61—22no—
18#14519684—21no—
19C22×C8×C61C2211yescharacteristic
20C2×C4⋊C4×C61C2211yescharacteristic
21C2×C4⋊C4×C61C2211yescharacteristic
22C23×D61—21no—
23C22×C4×C61—21no—
24C22×C4×C61—21no—
25C22×C4×C61C2311yescharacteristic
26C22×Dic61—21no—
27C22×Dic61D411yescharacteristic
28C22×Dic61D411yescharacteristic
29C2×D244—21no—
30C2×D244—21no—
31C2×D244—21no—
32C2×D244—21no—
33C2×D244—21no—
34C2×D244C2×C412yes—
35C2×C8×C61—21no—
36C2×C8×C61—21no—
37C2×C8×C61D412yes—
38C4⋊C4×C61—21no—
39C4⋊C4×C61—21no—
40C4⋊C4×C61—21no—
41C4⋊C4×C61C2×C412yes—
42#11758198—42no—
43#11758198—42no—
44C4⋊Dic61—21no—
45C4⋊Dic61—21no—
46C4⋊Dic61—42no—
47C4×Dic61—21no—
48C4×Dic61—21no—
49C2×#92418—21no—
50C2×#92418—21no—
51C2×#92418C2×C412yes—
52C23×C61C2×D411yescharacteristic
53C22×D61—22no—
54C22×D61—41no—
55C22×D61—41no—
56C22×D61—41no—
57C22×D61—41no—
58C22×D61—41no—
59C22×D61—41no—
60C2×C4×C61—22no—
61C2×C4×C61—41no—
62C2×C4×C61—41no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61—41no—
66C2×C4×C61C22×C411yescharacteristic
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61#4111yescharacteristic
69C2×C4×C61#4111yescharacteristic
70C2×C4×C61#4111yescharacteristic
71C2×C4×C61#4111yescharacteristic
72C2×Dic61—21no—
73C2×Dic61—21no—
74C2×Dic61—21no—
75C2×Dic61—21no—
76C2×Dic61—41no—
77C2×Dic61—41no—
78C2×Dic61—41no—
79C2×Dic61D812yes—
80C2×Dic61SD1612yes—
81D244—22no—
82D244—22no—
83D244—41no—
84D244—41no—
85C8×C61—22no—
86#92418—22no—
87C22×C61C4×D411yescharacteristic
88C22×C61#12111yescharacteristic
89C22×C61#12411yescharacteristic
90C22×C61C2×D811yescharacteristic
91C22×C61C2×SD1611yescharacteristic
92C22×C61#13511yescharacteristic
93C22×C61#13511yescharacteristic
94C2×D61—42no—
95C2×D61—42no—
96C2×D61—42no—
97C2×D61—81no—
98C2×D61—81no—
99C2×D61—81no—
100C2×D61—81no—
101C4×C61—42no—
102C4×C61—81no—
103C4×C61#11711yescharacteristic
104C4×C61C4×D411yescharacteristic
105C4×C61#12311yescharacteristic
106C4×C61#12611yescharacteristic
107Dic61—22no—
108Dic61—22no—
109Dic61—81no—
110#1934—611nomaximal, Sylow
111C2×C61#38811yescharacteristic
112C2×C61C4×D811yescharacteristic
113C2×C61C4×SD1611yescharacteristic
114C2×C61#46511yescharacteristic
115C2×C61#46611yescharacteristic
116C2×C61#48611yescharacteristic
117C2×C61#48811yescharacteristic
118D61—82no—
119C2×#102—611no—
120C2×#102—611no—
121C2×C4×C8—611no—
122#390—611no—
123#389—611no—
124#340—611no—
125#340D6111yescharacteristic, complemented
126C61#193411yescharacteristic, complemented, Sylow
127C22×D4—611no—
128C22×C8—611no—
129C22×C8C2×D6111yescharacteristic
130C2×C4⋊C4—611no—
131C2×C4⋊C4—1221no—
132C2×C4⋊C4C2×D6111yescharacteristic
133C2×C4⋊C4C2×D6111yescharacteristic
134C2×C22⋊C4—1221no—
135C2×C22⋊C4—1221no—
136C2×C42—611no—
137#102—614no—
138#102—1222no—
139C4×C8—1222no—
140#95—1221no—
141C24—1221no—
142C2×D4—612no—
143C2×D4—1221no—
144C2×D4—1221no—
145C2×D4—1221no—
146C2×D4—1221no—
147C2×D4—1221no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—611no—
151C22×C4—611no—
152C22×C4—1221no—
153C22×C4C22×D6111yescharacteristic
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—612no—
157C2×C8—1221no—
158C2×C8—1221no—
159C2×C8D24412yes—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—1221no—
164C4⋊C4—1221no—
165C4⋊C4—2442no—
166C4⋊C4C4×D6112yes—
167C22⋊C4—2442no—
168C22⋊C4—2442no—
169C42—1221no—
170C42—1221no—
171C23—1222no—
172C23—2441no—
173C23—2441no—
174C23—2441no—
175C23—2441no—
176C23—2441no—
177C23—2441no—
178C23D4×D6111yescharacteristic
179D4—1222no—
180D4—1222no—
181D4—2441no—
182D4—2441no—
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—612no—
190C2×C4—612no—
191C2×C4—1221no—
192C2×C4—1221no—
193C2×C4—1221no—
194C2×C4—1221no—
195C2×C4—2441no—
196C2×C4—2441no—
197C2×C4—2441no—
198C2×C4C2×C4×D6111yescharacteristic
199C2×C4C2×D24411yescharacteristic
200C2×C4#1175822211yescharacteristic
201C2×C4#1175822411yescharacteristic
202C2×C4#1175822411yescharacteristic
203C2×C4#1175822611yescharacteristic
204C8—22no—
205C8—1222no—
206C22—4881no—
207C22—4881no—
208C22—4881no—
209C22—4881no—
210C22—2442no—
211C22—2442no—
212C22—2442no—
213C22#1451973711yescharacteristic
214C22#1451975211yescharacteristic
215C22#1451976311yescharacteristic
216C22D8×D6111yescharacteristic
217C22SD16×D6111yescharacteristic
218C22#1451979811yescharacteristic
219C22#1451980011yescharacteristic
220C4—42no—
221C4—81no—
222C4—1222no—
223C4—1222no—
224C4—4881no—
225C4#1451973511yescharacteristic
226C4C4×D24411yescharacteristic
227C4#1451976111yescharacteristic
228C4#1451977211yescharacteristic
229C2—4882no—
230C2#1683965411yescharacteristic
231C2#1683984211yescharacteristic
232C2#1683984711yescharacteristic
233C2#1683999211yescharacteristic
234C2#1683999911yescharacteristic
235C2#1684010711yescharacteristic
236C2#1684011811yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#340C2
socleC23×C61C2×D4
hypercenter#340D61
hypocenterC61#1934
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
3. C2×C8×Dic61C2semidirect
5. #16839661C2semidirect
6. #16839524C2semidirect
7. C61×#340C2semidirect
16. #14519697C4semidirect
125. #340D61semidirect
126. C61#1934semidirect