Finite Group Databasebeta

← #21446515

Subgroups — #21446515

Order 7808.

284 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 91 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×#14519697C211yesmaximal, characteristic
2C2×#14519697C211yesmaximal, characteristic
3C2×#14519688C211yesmaximal, characteristic, complemented
4#16839664C211yesmaximal, characteristic
5#16839524C211yesmaximal, characteristic, complemented
6#16839524C211yesmaximal, characteristic, complemented
7C61×#389C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10C22×#92418C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758198—21no—
13C2×#11758198—21no—
14#14519697—22no—
15#14519697C414yescomplemented
16#14519688—22no—
17C2×C4⋊C4×C61—21no—
18C2×C4⋊C4×C61C2211yescharacteristic
19C2×C4⋊C4×C61C2211yescharacteristic
20C2×C42×C61C2211yescharacteristic
21#95×C61—21no—
22C23×D61—21no—
23C22×C4×C61—21no—
24C22×C4×C61—21no—
25C22×C4×C61D411yescharacteristic
26C22×C4×C61D411yescharacteristic
27C22×C4×C61C2311yescharacteristic
28C22×Dic61—21no—
29C2×D244—21no—
30C2×D244—21no—
31C2×D244—21no—
32C2×D244—21no—
33C2×D244—21no—
34C2×D244C2×C412yes—
35C4⋊C4×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61—21no—
38C4⋊C4×C61—42no—
39C4⋊C4×C61C2×C412yes—
40C42×C61—21no—
41C42×C61—21no—
42#11758198—42no—
43#11758198—42no—
44C4⋊Dic61—21no—
45C4⋊Dic61—21no—
46C2×#92418—21no—
47C2×#92418—21no—
48C2×#92418—21no—
49C2×#92418—21no—
50C2×#92418C2×C412yes—
51C2×#92418D412yes—
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—21no—
62C2×C4×C61—21no—
63C2×C4×C61—21no—
64C2×C4×C61—21no—
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×C61C22×C411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61#4111yescharacteristic
75C2×C4×C61#4111yescharacteristic
76C2×C4×C61#4111yescharacteristic
77C2×C4×C61#4111yescharacteristic
78C2×Dic61—41no—
79C2×Dic61—41no—
80C2×Dic61—41no—
81D244—22no—
82D244—22no—
83D244—41no—
84D244—41no—
85#92418—22no—
86#92418—22no—
87C22×C61C4×D411yescharacteristic
88C22×C61#12111yescharacteristic
89C22×C61#12411yescharacteristic
90C22×C61AGL(1,ℤ/8)11yescharacteristic
91C22×C61AGL(1,ℤ/8)11yescharacteristic
92C22×C61AGL(1,ℤ/8)11yescharacteristic
93C22×C61#13711yescharacteristic
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—41no—
103C4×C61—41no—
104C4×C61—81no—
105C4×C61#11711yescharacteristic
106C4×C61C4×D411yescharacteristic
107C4×C61#12311yescharacteristic
108C4×C61#12611yescharacteristic
109Dic61—81no—
110#1936—611nomaximal, Sylow
111C2×C61#38811yescharacteristic
112C2×C61#44011yescharacteristic
113C2×C61#44211yescharacteristic
114C2×C61#46811yescharacteristic
115C2×C61#46911yescharacteristic
116C2×C61#48911yescharacteristic
117C2×C61#49011yescharacteristic
118D61—82no—
119C2×#102—611no—
120C2×#102—611no—
121C2×#97—611no—
122#390—611no—
123#389D6111yescharacteristic, complemented
124#340—611no—
125#340—611no—
126C61#193611yescharacteristic, complemented, Sylow
127C22×D4—611no—
128C22×C8—611no—
129C22×C8—611no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—611no—
132C2×C4⋊C4C2×D6111yescharacteristic
133C2×C4⋊C4C2×D6111yescharacteristic
134C2×C22⋊C4—1221no—
135C2×C22⋊C4—1221no—
136C2×C42C2×D6111yescharacteristic
137#102—614no—
138#102—1222no—
139#97—1222no—
140#95—21no—
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—1221no—
151C22×C4C22⋊D6111yescharacteristic
152C22×C4C22⋊D6111yescharacteristic
153C22×C4C22×D6111yescharacteristic
154C2×C8—612no—
155C2×C8—612no—
156C2×C8—1221no—
157C2×C8—1221no—
158C2×C8—1221no—
159C2×C8—1221no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—42no—
164C4⋊C4—1221no—
165C4⋊C4—1221no—
166C4⋊C4C4×D6112yes—
167C22⋊C4—2442no—
168C22⋊C4—2442no—
169C42—21no—
170C42—21no—
171C23—1222no—
172C23—2441no—
173C23—2441no—
174C23—2441no—
175C23—2441no—
176C23—2441no—
177C23—2441no—
178C23C2×C22⋊D6111yescharacteristic
179D4—1222no—
180D4—1222no—
181D4—2441no—
182D4—2441no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—2441no—
196C2×C4—2441no—
197C2×C4—2441no—
198C2×C4C2×C4×D6111yescharacteristic
199C2×C4#1175822211yescharacteristic
200C2×C4D4×D6111yescharacteristic
201C2×C4#1175822411yescharacteristic
202C2×C4#1175822611yescharacteristic
203C2×C4#1175822611yescharacteristic
204C8—1222no—
205C8—1222no—
206C22—4881no—
207C22—4881no—
208C22—4881no—
209C22—4881no—
210C22—2442no—
211C22—2442no—
212C22—2442no—
213C22C4×C22⋊D6111yescharacteristic
214C22#1451974911yescharacteristic
215C22#1451976611yescharacteristic
216C22#1451980211yescharacteristic
217C22#1451980211yescharacteristic
218C22#1451980311yescharacteristic
219C22#1451980811yescharacteristic
220C4—41no—
221C4—41no—
222C4—42no—
223C4—81no—
224C4—4881no—
225C4#1451973511yescharacteristic
226C4#1451973911yescharacteristic
227C4#1451976211yescharacteristic
228C4#1451977211yescharacteristic
229C2—4882no—
230C2#1683965211yescharacteristic
231C2#1683986011yescharacteristic
232C2#1683987211yescharacteristic
233C2#1684001011yescharacteristic
234C2#1684001311yescharacteristic
235C2#1684012411yescharacteristic
236C2#1684012811yescharacteristic
subgroupG/H
centerC23C2×C22⋊D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#389C2
socleC23×C61C2×D4
hypercenter#389D61
hypocenterC61#1936
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
3. C2×#14519688C2semidirect
5. #16839524C2semidirect
6. #16839524C2semidirect
7. C61×#389C2semidirect
15. #14519697C4semidirect
123. #389D61semidirect
126. C61#1936semidirect