Finite Group Databasebeta

← #21447204

Subgroups — #21447204

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×#14519710C211yesmaximal, characteristic, complemented
2C2×C4⋊#92418C211yesmaximal, characteristic, complemented
3C2×#14519697C211yesmaximal, characteristic
4C2×#14519697C211yesmaximal, characteristic
5#16839664C211yesmaximal, characteristic
6#16839524C211yesmaximal, characteristic, complemented
7C61×#389C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10C22×#92418C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758198—21no—
13C2×#11758198—21no—
14#14519710—22no—
15C4⋊#92418—22no—
16#14519697—22no—
17#14519697—22no—
18C2×C4⋊C4×C61—21no—
19C2×C4⋊C4×C61C2211yescharacteristic
20C2×C4⋊C4×C61C2211yescharacteristic
21C2×C42×C61C2211yescharacteristic
22#95×C61—21no—
23C23×D61—21no—
24C22×C4×C61—21no—
25C22×C4×C61—21no—
26C22×C4×C61D411yescharacteristic
27C22×C4×C61D411yescharacteristic
28C22×C4×C61C2311yescharacteristic
29C22×Dic61—21no—
30C2×D244—21no—
31C2×D244—21no—
32C2×D244—21no—
33C2×D244—21no—
34C2×D244—21no—
35C2×D244Q812yes—
36C4⋊C4×C61—21no—
37C4⋊C4×C61—21no—
38C4⋊C4×C61—21no—
39C4⋊C4×C61—42no—
40C4⋊C4×C61D412yes—
41C42×C61—21no—
42C42×C61—21no—
43#11758198—42no—
44#11758198—42no—
45C4⋊Dic61—21no—
46C4⋊Dic61—21no—
47C2×#92418—21no—
48C2×#92418—21no—
49C2×#92418—21no—
50C2×#92418—21no—
51C2×#92418—21no—
52C2×#92418D412yes—
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—22no—
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61—41no—
68C2×C4×C61—41no—
69C2×C4×C61—41no—
70C2×C4×C61—41no—
71C2×C4×C61—41no—
72C2×C4×C61D812yes—
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2×Q811yescharacteristic
76C2×C4×C61#4111yescharacteristic
77C2×C4×C61#4111yescharacteristic
78C2×C4×C61#4111yescharacteristic
79C2×Dic61—41no—
80C2×Dic61—41no—
81C2×Dic61—41no—
82D244—22no—
83D244—22no—
84D244—41no—
85D244—41no—
86#92418—22no—
87#92418—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—42no—
104C4×C61—41no—
105C4×C61—81no—
106C4×C61#12111yescharacteristic
107C4×C61C22⋊Q811yescharacteristic
108C4×C61C22⋊Q811yescharacteristic
109C4×C61#12611yescharacteristic
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⋊C8—611no—
122C2×#102—611no—
123C2×#102—611no—
124#390—611no—
125#389D6111yescharacteristic, complemented
126#340—611no—
127C61#206711yescharacteristic, complemented, Sylow
128C22×D4—611no—
129C22×C8—611no—
130C22×C8—611no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—611no—
133C2×C4⋊C4C2×D6111yescharacteristic
134C2×C4⋊C4C2×D6111yescharacteristic
135C2×C22⋊C4—1221no—
136C2×C22⋊C4—1221no—
137C2×C42C2×D6111yescharacteristic
138#107—1222no—
139C4⋊C8—1222no—
140#102—1222no—
141#102—1222no—
142#95—21no—
143C24—1221no—
144C2×D4—612no—
145C2×D4—1221no—
146C2×D4—1221no—
147C2×D4—1221no—
148C2×D4—1221no—
149C2×D4—1221no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—1221no—
153C22×C4C22⋊D6111yescharacteristic
154C22×C4C22⋊D6111yescharacteristic
155C22×C4C22×D6111yescharacteristic
156C2×C8—612no—
157C2×C8—1221no—
158C2×C8—1221no—
159C2×C8—1221no—
160C2×C8—1221no—
161C2×C8—1221no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—42no—
166C4⋊C4—1221no—
167C4⋊C4—1221no—
168C4⋊C4D24412yes—
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×C22⋊D6111yescharacteristic
181D4—1222no—
182D4—1222no—
183D4—2441no—
184D4—2441no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—2441no—
197C2×C4—2441no—
198C2×C4—2441no—
199C2×C4#1175819912yes—
200C2×C4C2×D24411yescharacteristic
201C2×C4#1175822211yescharacteristic
202C2×C4D4×D6111yescharacteristic
203C2×C4#1175822411yescharacteristic
204C2×C4Q8×D6111yescharacteristic
205C2×C4#1175822611yescharacteristic
206C8—1222no—
207C8—2441no—
208C22—4881no—
209C22—4881no—
210C22—4881no—
211C22—4881no—
212C22—2442no—
213C22—2442no—
214C22—2442no—
215C22#1451974911yescharacteristic
216C22#1451975111yescharacteristic
217C22#1451975311yescharacteristic
218C22C2×#1175819911yescharacteristic
219C22#1451979711yescharacteristic
220C22#1451980211yescharacteristic
221C22#1451980811yescharacteristic
222C4—22no—
223C4—42no—
224C4—41no—
225C4—81no—
226C4—4881no—
227C4#1451975211yescharacteristic
228C4#1451975511yescharacteristic
229C4#1451975711yescharacteristic
230C4#1451977211yescharacteristic
231C2—4882no—
232C2#1683968411yescharacteristic
233C2#1683995711yescharacteristic
234C2#1683998411yescharacteristic
235C2#1683999611yescharacteristic
236C2#1684001011yescharacteristic
237C2#1684003911yescharacteristic
238C2#1684005911yescharacteristic
subgroupG/H
centerC23C2×C22⋊D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#389C2
socleC23×C61C2×D4
hypercenter#389D61
hypocenterC61#2067
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#14519710C2semidirect
2. C2×C4⋊#92418C2semidirect
6. #16839524C2semidirect
7. C61×#389C2semidirect
125. #389D61semidirect
127. C61#2067semidirect