Finite Group Databasebeta

← #21446513

Subgroups — #21446513

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×#14519698C211yesmaximal, characteristic
2C2×#14519687C211yesmaximal, characteristic, complemented
3#16839665C211yesmaximal, characteristic
4#16839658C211yesmaximal, characteristic, complemented
5#16839525C211yesmaximal, characteristic, complemented
6#16839524C211yesmaximal, characteristic, complemented
7C2×#102×C61C211yesmaximal, characteristic
8C22×#92418C2211yescharacteristic
9C2×C4⋊Dic61C2211yescharacteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×#11758196—21no—
12C2×C22⋊Dic61—21no—
13C2×C22⋊Dic61—21no—
14C2×C4×Dic61C2211yescharacteristic
15#14519698C414yescomplemented
16#14519687—22no—
17#14519684—21no—
18C22×D4×C61C2211yescharacteristic
19C22×C8×C61C2211yescharacteristic
20C2×C4⋊C4×C61C2211yescharacteristic
21#102×C61—22no—
22C24×C61—21no—
23C2×D4×C61—21no—
24C2×D4×C61—21no—
25C2×D4×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61—21no—
28C2×D4×C61C2×C412yes—
29C22×C4×C61—21no—
30C22×C4×C61C2311yescharacteristic
31C22×Dic61—21no—
32C22×Dic61—21no—
33C22×Dic61D411yescharacteristic
34C22×Dic61D411yescharacteristic
35C2×C8×C61—21no—
36C2×C8×C61—21no—
37C2×C8×C61D412yes—
38C4⋊C4×C61—21no—
39C4⋊C4×C61—21no—
40C22⋊Dic61—42no—
41C22⋊Dic61—42no—
42C4⋊Dic61—21no—
43C4⋊Dic61—21no—
44C4⋊Dic61—21no—
45C4⋊Dic61C2×C412yes—
46#11758196—42no—
47C4×Dic61—21no—
48C4×Dic61—21no—
49C2×#92418—21no—
50C2×#92418—21no—
51C2×#92418C2×C412yes—
52C23×C61—22no—
53C23×C61—41no—
54C23×C61—41no—
55C23×C61—41no—
56C23×C61—41no—
57C23×C61—41no—
58C23×C61—41no—
59C23×C61C2×D411yescharacteristic
60D4×C61—22no—
61D4×C61—22no—
62D4×C61—41no—
63D4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61C22×C411yescharacteristic
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61#4111yescharacteristic
70C2×C4×C61#4111yescharacteristic
71C2×C4×C61#4111yescharacteristic
72C2×C4×C61#4111yescharacteristic
73C2×Dic61—22no—
74C2×Dic61—21no—
75C2×Dic61—21no—
76C2×Dic61—21no—
77C2×Dic61—21no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—41no—
81C2×Dic61—41no—
82C2×Dic61—41no—
83C2×Dic61—41no—
84C2×Dic61—41no—
85C8×C61—22no—
86#92418—22no—
87C22×C61—42no—
88C22×C61—42no—
89C22×C61—42no—
90C22×C61—81no—
91C22×C61—81no—
92C22×C61—81no—
93C22×C61—81no—
94C22×C61C4×D411yescharacteristic
95C22×C61#12111yescharacteristic
96C22×C61#12411yescharacteristic
97C22×C61AGL(1,ℤ/8)11yescharacteristic
98C22×C61AGL(1,ℤ/8)11yescharacteristic
99C22×C61AGL(1,ℤ/8)11yescharacteristic
100C22×C61#13711yescharacteristic
101C4×C61—81no—
102C4×C61#11711yescharacteristic
103C4×C61C4×D411yescharacteristic
104C4×C61#12311yescharacteristic
105C4×C61#12611yescharacteristic
106Dic61—42no—
107Dic61—41no—
108Dic61—41no—
109Dic61—81no—
110#1936—611nomaximal, Sylow
111C2×C61—82no—
112C2×C61#38811yescharacteristic
113C2×C61#44011yescharacteristic
114C2×C61#44211yescharacteristic
115C2×C61#46811yescharacteristic
116C2×C61#46911yescharacteristic
117C2×C61#48911yescharacteristic
118C2×C61#49011yescharacteristic
119C2×#102—611no—
120C2×#102D6111yescharacteristic
121C2×#97—611no—
122#390—611no—
123#389—611no—
124#340—611no—
125#340—611no—
126C61#193611yescharacteristic, complemented, Sylow
127C22×D4C2×D6111yescharacteristic
128C22×C8—611no—
129C22×C8C2×D6111yescharacteristic
130C2×C4⋊C4—611no—
131C2×C4⋊C4—611no—
132C2×C4⋊C4—1221no—
133C2×C4⋊C4C2×D6111yescharacteristic
134C2×C22⋊C4—1221no—
135C2×C22⋊C4—1221no—
136C2×C42—611no—
137#102—22no—
138#102—614no—
139#97—1222no—
140#95—1221no—
141C24—21no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4C4×D6112yes—
148C22×C4—21no—
149C22×C4—611no—
150C22×C4—611no—
151C22×C4—1221no—
152C22×C4—1221no—
153C22×C4C22×D6111yescharacteristic
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—612no—
157C2×C8—1221no—
158C2×C8—1221no—
159C2×C8C22⋊D6112yes—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—612no—
163C4⋊C4—1221no—
164C4⋊C4—1221no—
165C4⋊C4—1221no—
166C4⋊C4—2442no—
167C22⋊C4—2442no—
168C22⋊C4—2442no—
169C42—1221no—
170C42—1221no—
171C23—22no—
172C23—41no—
173C23—41no—
174C23—41no—
175C23—41no—
176C23—41no—
177C23—41no—
178C23D4×D6111yescharacteristic
179D4—22no—
180D4—22no—
181D4—41no—
182D4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—1222no—
187C2×C4—1221no—
188C2×C4—1221no—
189C2×C4—1221no—
190C2×C4—1221no—
191C2×C4—1221no—
192C2×C4—1221no—
193C2×C4—2441no—
194C2×C4—2441no—
195C2×C4—2441no—
196C2×C4—2441no—
197C2×C4—2441no—
198C2×C4C2×C4×D6111yescharacteristic
199C2×C4#1175822211yescharacteristic
200C2×C4#1175822411yescharacteristic
201C2×C4#1175822411yescharacteristic
202C2×C4#1175822411yescharacteristic
203C2×C4C2×C22⋊D6111yescharacteristic
204C8—22no—
205C8—1222no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—81no—
210C22—81no—
211C22—81no—
212C22—81no—
213C22#1451973711yescharacteristic
214C22#1451974811yescharacteristic
215C22#1451976311yescharacteristic
216C22#1451980111yescharacteristic
217C22#1451980111yescharacteristic
218C22#1451980411yescharacteristic
219C22#1451980611yescharacteristic
220C4—81no—
221C4—4881no—
222C4—2441no—
223C4—2441no—
224C4—2442no—
225C4#1451973311yescharacteristic
226C4C4×C22⋊D6111yescharacteristic
227C4#1451975811yescharacteristic
228C4#1451977011yescharacteristic
229C2—82no—
230C2#1683965011yescharacteristic
231C2#1683985911yescharacteristic
232C2#1683987111yescharacteristic
233C2#1684000511yescharacteristic
234C2#1684001211yescharacteristic
235C2#1684012011yescharacteristic
236C2#1684012511yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#102×C61C2
socleC23×C61C2×D4
hypercenterC2×#102D61
hypocenterC61#1936
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×#14519687C2semidirect
4. #16839658C2semidirect
5. #16839525C2semidirect
6. #16839524C2semidirect
15. #14519698C4semidirect
126. C61#1936semidirect