Finite Group Databasebeta

← #21446996

Subgroups — #21446996

Order 7808.

278 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 65 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
1#16840388C211yesmaximal, characteristic, complemented
2C2×#14519692C211yesmaximal, characteristic
3C2×#14519692C211yesmaximal, characteristic
4#16839529C211yesmaximal, characteristic, complemented
5#16839528C211yesmaximal, characteristic, complemented
6#16839528C211yesmaximal, characteristic, complemented
7C2×#99×C61C211yesmaximal, characteristic
8#14519756—22no—
9#14519754—22no—
10#14519754—22no—
11C2×C22⋊Dic61C2211yescharacteristic
12C2×C22⋊Dic61C2211yescharacteristic
13C2×C22⋊Dic61C2211yescharacteristic
14C2×C22⋊Dic61C2211yescharacteristic
15#14519692—22no—
16#14519692—22no—
17C22×D4×C61C2211yescharacteristic
18C2×C22⋊C4×C61C2211yescharacteristic
19C2×C22⋊C4×C61C2211yescharacteristic
20#99×C61—22no—
21C24×C61Q811yescharacteristic, complemented
22C24×C61C2311yescharacteristic
23C2×D4×C61—21no—
24C2×D4×C61—21no—
25C2×D4×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61—21no—
28C2×D4×C61—21no—
29C22×C4×C61—21no—
30C22×C4×C61—21no—
31C22×C4×C61Q811yescharacteristic, complemented
32C22×Dic61—21no—
33C22×Dic61—21no—
34C22×Dic61—21no—
35C22×Dic61—21no—
36C2×Dic122—22no—
37C22⋊C4×C61—21no—
38C22⋊C4×C61—21no—
39C22⋊C4×C61—21no—
40C22⋊C4×C61D412yes—
41C22⋊Dic61—21no—
42C22⋊Dic61—21no—
43C22⋊Dic61—21no—
44C22⋊Dic61—21no—
45C22⋊Dic61—21no—
46C22⋊Dic61—21no—
47C22⋊Dic61D412yes—
48C22⋊Dic61D412yes—
49C4⋊Dic61—22no—
50#11758196—24no—
51C23×C61—21no—
52C23×C61—21no—
53C23×C61—21no—
54C23×C61—81no—
55C23×C61—81no—
56C23×C61C2×D411yescharacteristic
57C23×C61C2×D411yescharacteristic
58C23×C61C2×D411yescharacteristic
59C23×C61C2×Q811yescharacteristic
60C23×C61#4111yescharacteristic
61C23×C61#4111yescharacteristic
62C23×C61#4111yescharacteristic
63D4×C61—41no—
64D4×C61—41no—
65D4×C61—41no—
66D4×C61—41no—
67C2×C4×C61—22no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—41no—
72C2×C4×C61—81no—
73C2×C4×C61—81no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61—41no—
77C2×Dic61—41no—
78C2×Dic61—81no—
79C2×Dic61—81no—
80C2×Dic61—81no—
81C2×Dic61—81no—
82Dic122—82no—
83C22×C61—41no—
84C22×C61—41no—
85C22×C61—41no—
86C22×C61—41no—
87C22×C61—41no—
88C22×C61—41no—
89C22×C61—41no—
90C22×C61—41no—
91C22×C61—81no—
92C22×C61—81no—
93C22×C61—81no—
94C22×C61#12011yescharacteristic
95C22×C61C22⋊Q811yescharacteristic
96C22×C61C22⋊Q811yescharacteristic
97C22×C61C22⋊Q811yescharacteristic
98C22×C61#12411yescharacteristic
99C22×C61#12411yescharacteristic
100C22×C61#12411yescharacteristic
101C4×C61—42no—
102C4×C61—41no—
103C4×C61—81no—
104Dic61—42no—
105Dic61—42no—
106Dic61—81no—
107Dic61—81no—
108#2032—611nomaximal, Sylow
109C2×C61—21no—
110C2×C61—21no—
111C2×C61—21no—
112C2×C61—21no—
113C2×C61—21no—
114C2×C61—21no—
115C2×C61—21no—
116C2×C61—81no—
117C2×C61#39311yescharacteristic
118#543—611no—
119C2×#99—611no—
120C2×#99—611no—
121C2×#99D6111yescharacteristic
122#342—611no—
123#342—611no—
124#342—611no—
125C61#203211yescharacteristic, complemented, Sylow
126C22×D4C2×D6111yescharacteristic
127C22⋊Q8—1222no—
128C22⋊Q8—1222no—
129C22⋊Q8—1222no—
130C2×C22⋊C4—611no—
131C2×C22⋊C4—611no—
132C2×C22⋊C4—611no—
133C2×C22⋊C4—611no—
134C2×C22⋊C4C2×D6111yescharacteristic
135C2×C22⋊C4C2×D6111yescharacteristic
136#99—22no—
137#99—1222no—
138#99—1222no—
139C24Dic12211yescharacteristic, complemented
140C24C22×D6111yescharacteristic
141C2×Q8—1222no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—1221no—
151C22×C4—1221no—
152C22×C4—1221no—
153C22×C4—1221no—
154C22×C4Dic12211yescharacteristic, complemented
155C4⋊C4—1224no—
156C4⋊C4—1222no—
157C22⋊C4—21no—
158C22⋊C4—21no—
159C22⋊C4—21no—
160C22⋊C4—612no—
161C22⋊C4—612no—
162C22⋊C4—1221no—
163C22⋊C4—1221no—
164C22⋊C4—1221no—
165C22⋊C4—1221no—
166C22⋊C4—1221no—
167C22⋊C4—1221no—
168C22⋊C4C22⋊D6112yes—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—81no—
173C23—81no—
174C23C2×Dic12211yescharacteristic
175C23#1175822211yescharacteristic
176C23D4×D6111yescharacteristic
177C23D4×D6111yescharacteristic
178C23#1175822411yescharacteristic
179C23#1175822411yescharacteristic
180C23C2×C22⋊D6111yescharacteristic
181Q8—4882no—
182D4—41no—
183D4—41no—
184D4—41no—
185D4—41no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—81no—
192C2×C4—81no—
193C2×C4—1222no—
194C2×C4—1222no—
195C2×C4—4881no—
196C2×C4—4881no—
197C2×C4—4881no—
198C2×C4—4881no—
199C2×C4—2441no—
200C2×C4—2441no—
201C22—41no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22—81no—
210C22—81no—
211C22—81no—
212C22#1451974511yescharacteristic
213C22#1451975411yescharacteristic
214C22#1451975411yescharacteristic
215C22#1451975611yescharacteristic
216C22#1451976311yescharacteristic
217C22#1451976311yescharacteristic
218C22#1451976411yescharacteristic
219C4—42no—
220C4—41no—
221C4—81no—
222C4—4881no—
223C4—4881no—
224C4—2442no—
225C4—2442no—
226C2—21no—
227C2—21no—
228C2—21no—
229C2—21no—
230C2—21no—
231C2—21no—
232C2—21no—
233C2—81no—
234C2#1683967411yescharacteristic
subgroupG/H
centerC2#16839674
commutatorC24×C61C23
FrattiniC24C22×D61
FittingC2×#99×C61C2
socleC2×C61#393
hypercenterC2×#99D61
hypocenterC61#2032
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
1. #16840388C2semidirect
4. #16839529C2semidirect
5. #16839528C2semidirect
6. #16839528C2semidirect
21. C24×C61Q8semidirect
31. C22×C4×C61Q8semidirect
125. C61#2032semidirect
139. C24Dic122semidirect
154. C22×C4Dic122semidirect