Finite Group Databasebeta

← #21447206

Subgroups — #21447206

Order 7808.

284 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14519711C211yesmaximal, characteristic, complemented
2C2×#14519699C211yesmaximal, characteristic
3C2×#14519699C211yesmaximal, characteristic
4#16839664C211yesmaximal, characteristic
5#16839660C211yesmaximal, characteristic, complemented
6#16839525C211yesmaximal, characteristic, complemented
7C2×C4⋊C8×C61C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9C2×C4⋊Dic61C2211yescharacteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758196—21no—
13C2×#11758198—21no—
14C2×#11758198—21no—
15#14519711—22no—
16#14519699—22no—
17#14519699—22no—
18#14519684—21no—
19C22×C8×C61C2211yescharacteristic
20C22×C8×C61C2211yescharacteristic
21C2×C42×C61C2211yescharacteristic
22C4⋊C8×C61—22no—
23C23×D61—21no—
24C22×C4×C61D411yescharacteristic
25C22×C4×C61D411yescharacteristic
26C22×C4×C61C2311yescharacteristic
27C22×Dic61—21no—
28C22×Dic61—21no—
29C22×Dic61—21no—
30C2×D244—21no—
31C2×D244—21no—
32C2×D244—21no—
33C2×D244—21no—
34C2×D244—21no—
35C2×D244Q812yes—
36C2×C8×C61—21no—
37C2×C8×C61—21no—
38C2×C8×C61—21no—
39C2×C8×C61—21no—
40C2×C8×C61—21no—
41C2×C8×C61D412yes—
42C42×C61—21no—
43C42×C61—21no—
44#11758198—42no—
45#11758198—42no—
46C4⋊Dic61—21no—
47C4⋊Dic61—21no—
48C4⋊Dic61—21no—
49C4⋊Dic61—21no—
50C4⋊Dic61—21no—
51C4⋊Dic61D412yes—
52#11758196—42no—
53C23×C61C2×D411yescharacteristic
54C22×D61—22no—
55C22×D61—41no—
56C22×D61—41no—
57C22×D61—41no—
58C22×D61—41no—
59C22×D61—41no—
60C22×D61—41no—
61C2×C4×C61—21no—
62C2×C4×C61—21no—
63C2×C4×C61—21no—
64C2×C4×C61—21no—
65C2×C4×C61—21no—
66C2×C4×C61D812yes—
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61C2×Q811yescharacteristic
70C2×C4×C61#4111yescharacteristic
71C2×C4×C61#4111yescharacteristic
72C2×C4×C61#4111yescharacteristic
73C2×Dic61—22no—
74C2×Dic61—41no—
75C2×Dic61—41no—
76C2×Dic61—41no—
77C2×Dic61—41no—
78C2×Dic61—41no—
79C2×Dic61—41no—
80C2×Dic61—41no—
81C2×Dic61—41no—
82D244—22no—
83D244—22no—
84D244—41no—
85D244—41no—
86C8×C61—22no—
87C8×C61—41no—
88C22×C61#12111yescharacteristic
89C22×C61#12111yescharacteristic
90C22×C61C22⋊Q811yescharacteristic
91C22×C61C2×D811yescharacteristic
92C22×C61#13511yescharacteristic
93C22×C61AGL(1,ℤ/8)11yescharacteristic
94C22×C61#13711yescharacteristic
95C2×D61—42no—
96C2×D61—42no—
97C2×D61—42no—
98C2×D61—81no—
99C2×D61—81no—
100C2×D61—81no—
101C2×D61—81no—
102C4×C61—22no—
103C4×C61—41no—
104C4×C61#12111yescharacteristic
105C4×C61C22⋊Q811yescharacteristic
106C4×C61C22⋊Q811yescharacteristic
107C4×C61#12611yescharacteristic
108Dic61—42no—
109Dic61—81no—
110Dic61—81no—
111#2067—611nomaximal, Sylow
112C2×C61#39611yescharacteristic
113C2×C61#45911yescharacteristic
114C2×C61#46411yescharacteristic
115C2×C61#46611yescharacteristic
116C2×C61#46811yescharacteristic
117C2×C61#47411yescharacteristic
118C2×C61#47811yescharacteristic
119D61—82no—
120C2×#107—611no—
121C2×C4⋊C8D6111yescharacteristic, complemented
122C2×#102—611no—
123C2×#102—611no—
124#390—611no—
125#389—611no—
126#340—611no—
127C61#206711yescharacteristic, complemented, Sylow
128C22×D4—611no—
129C22×C8C2×D6111yescharacteristic
130C22×C8C2×D6111yescharacteristic
131C2×C4⋊C4—611no—
132C2×C4⋊C4—611no—
133C2×C4⋊C4—611no—
134C2×C4⋊C4—1221no—
135C2×C22⋊C4—1221no—
136C2×C22⋊C4—1221no—
137C2×C42C2×D6111yescharacteristic
138#107—1222no—
139C4⋊C8—22no—
140#102—1222no—
141#102—1222no—
142#95—1221no—
143C24—1221no—
144C2×D4—612no—
145C2×D4—1221no—
146C2×D4—1221no—
147C2×D4—1221no—
148C2×D4—1221no—
149C2×D4—1221no—
150C22×C4—1221no—
151C22×C4—1221no—
152C22×C4—1221no—
153C22×C4D24411yescharacteristic
154C22×C4D24411yescharacteristic
155C22×C4C22×D6111yescharacteristic
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—21no—
161C2×C8C22⋊D6112yes—
162C4⋊C4—612no—
163C4⋊C4—1221no—
164C4⋊C4—1221no—
165C4⋊C4—1221no—
166C4⋊C4—1221no—
167C4⋊C4—1221no—
168C4⋊C4—2442no—
169C22⋊C4—2442no—
170C22⋊C4—2442no—
171C42—21no—
172C42—21no—
173C23—1222no—
174C23—2441no—
175C23—2441no—
176C23—2441no—
177C23—2441no—
178C23—2441no—
179C23—2441no—
180C23C2×D24411yescharacteristic
181D4—1222no—
182D4—1222no—
183D4—2441no—
184D4—2441no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—1222no—
191C2×C4—2441no—
192C2×C4—2441no—
193C2×C4—2441no—
194C2×C4—2441no—
195C2×C4—2441no—
196C2×C4—2441no—
197C2×C4—2441no—
198C2×C4—2441no—
199C2×C4D48812yes—
200C2×C4#1175822211yescharacteristic
201C2×C4D4×D6111yescharacteristic
202C2×C4#1175822411yescharacteristic
203C2×C4Q8×D6111yescharacteristic
204C2×C4#1175822611yescharacteristic
205C2×C4C2×C22⋊D6111yescharacteristic
206C8—22no—
207C8—41no—
208C22—4881no—
209C22—4881no—
210C22—4881no—
211C22—4881no—
212C22—2442no—
213C22—2442no—
214C22—2442no—
215C22#1451975111yescharacteristic
216C22#1451975211yescharacteristic
217C22#1451975711yescharacteristic
218C22C2×D48811yescharacteristic
219C22#1451979911yescharacteristic
220C22#1451980511yescharacteristic
221C22#1451981011yescharacteristic
222C4—22no—
223C4—41no—
224C4—4881no—
225C4—4881no—
226C4—2442no—
227C4#1451974911yescharacteristic
228C4#1451975311yescharacteristic
229C4#1451975511yescharacteristic
230C4#1451977211yescharacteristic
231C2—4882no—
232C2#1683968411yescharacteristic
233C2#1683995811yescharacteristic
234C2#1683998511yescharacteristic
235C2#1683999811yescharacteristic
236C2#1684000811yescharacteristic
237C2#1684004311yescharacteristic
238C2#1684006311yescharacteristic
subgroupG/H
centerC23C2×D244
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×C4⋊C8×C61C2
socleC23×C61C2×D4
hypercenterC2×C4⋊C8D61
hypocenterC61#2067
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#14519711C2semidirect
5. #16839660C2semidirect
6. #16839525C2semidirect
7. C2×C4⋊C8×C61C2semidirect
121. C2×C4⋊C8D61semidirect
127. C61#2067semidirect