Finite Group Databasebeta

← #21446997

Subgroups — #21446997

Order 7808.

278 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 63 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×#14519691C211yesmaximal, characteristic
3C2×#14519691C211yesmaximal, characteristic
4C2×#14519691C211yesmaximal, characteristic
5#16839529C211yesmaximal, characteristic, complemented
6#16839528C211yesmaximal, characteristic, complemented
7C61×#342C211yesmaximal, characteristic, complemented
8C22×C22⋊D61C2211yescharacteristic
9#14519756—22no—
10#14519754—22no—
11#14519754—22no—
12C2×C22⋊Dic61C2211yescharacteristic
13C2×C22⋊Dic61C2211yescharacteristic
14C2×C22⋊Dic61C2211yescharacteristic
15#14519691—22no—
16#14519691—22no—
17#14519691—22no—
18C2×C22⋊C4×C61C2211yescharacteristic
19C2×C22⋊C4×C61C2211yescharacteristic
20C2×C22⋊C4×C61C2211yescharacteristic
21C24×C61C2311yescharacteristic
22C23×D61Q811yescharacteristic, complemented
23C22×C4×C61—21no—
24C22×C4×C61—21no—
25C22×C4×C61—21no—
26C2×C22⋊D61—21no—
27C2×C22⋊D61—21no—
28C2×C22⋊D61—21no—
29C2×C22⋊D61—21no—
30C2×C22⋊D61—21no—
31C2×C22⋊D61—21no—
32C22×Dic61—21no—
33C22×Dic61—21no—
34C22×Dic61—21no—
35C22×Dic61Q811yescharacteristic, complemented
36C2×Dic122—22no—
37C22⋊C4×C61—21no—
38C22⋊C4×C61—21no—
39C22⋊C4×C61—21no—
40C22⋊C4×C61—21no—
41C22⋊C4×C61—21no—
42C22⋊C4×C61D412yes—
43C22⋊Dic61—21no—
44C22⋊Dic61—21no—
45C22⋊Dic61—21no—
46C22⋊Dic61—21no—
47C22⋊Dic61D412yes—
48C22⋊Dic61D412yes—
49C4⋊Dic61—22no—
50#11758196—24no—
51C23×C61—81no—
52C23×C61C2×D411yescharacteristic
53C23×C61C2×D411yescharacteristic
54C23×C61C2×D411yescharacteristic
55C23×C61C2×Q811yescharacteristic
56C23×C61#4111yescharacteristic
57C23×C61#4111yescharacteristic
58C23×C61#4111yescharacteristic
59C22×D61—21no—
60C22×D61—21no—
61C22×D61—21no—
62C22×D61—81no—
63C2×C4×C61—22no—
64C2×C4×C61—41no—
65C2×C4×C61—41no—
66C2×C4×C61—81no—
67C2×C4×C61—81no—
68C2×C4×C61—81no—
69C22⋊D61—41no—
70C22⋊D61—41no—
71C22⋊D61—41no—
72C22⋊D61—41no—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—21no—
76C2×Dic61—21no—
77C2×Dic61—21no—
78C2×Dic61—41no—
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#12011yescharacteristic
91C22×C61C22⋊Q811yescharacteristic
92C22×C61C22⋊Q811yescharacteristic
93C22×C61C22⋊Q811yescharacteristic
94C22×C61#12411yescharacteristic
95C22×C61#12411yescharacteristic
96C22×C61#12411yescharacteristic
97C2×D61—41no—
98C2×D61—81no—
99C2×D61—81no—
100C2×D61—81no—
101C4×C61—42no—
102C4×C61—81no—
103C4×C61—81no—
104Dic61—42no—
105Dic61—42no—
106Dic61—41no—
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#39311yescharacteristic
117D61—81no—
118#543—611no—
119C2×#99—611no—
120C2×#99—611no—
121C2×#99—611no—
122#342—611no—
123#342—611no—
124#342D6111yescharacteristic, complemented
125C61#203211yescharacteristic, complemented, Sylow
126C22×D4—611no—
127C22⋊Q8—1222no—
128C22⋊Q8—1222no—
129C22⋊Q8—1222no—
130C2×C22⋊C4—611no—
131C2×C22⋊C4—611no—
132C2×C22⋊C4—611no—
133C2×C22⋊C4C2×D6111yescharacteristic
134C2×C22⋊C4C2×D6111yescharacteristic
135C2×C22⋊C4C2×D6111yescharacteristic
136#99—1222no—
137#99—1222no—
138#99—1222no—
139C24—611no—
140C24C22×D6111yescharacteristic
141C2×Q8—1222no—
142C2×D4—1221no—
143C2×D4—1221no—
144C2×D4—1221no—
145C2×D4—1221no—
146C2×D4—1221no—
147C2×D4—1221no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—611no—
152C22×C4—1221no—
153C22×C4—1221no—
154C22×C4—1221no—
155C4⋊C4—1224no—
156C4⋊C4—1222no—
157C22⋊C4—21no—
158C22⋊C4—21no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—612no—
163C22⋊C4—612no—
164C22⋊C4—1221no—
165C22⋊C4—1221no—
166C22⋊C4—1221no—
167C22⋊C4—1221no—
168C22⋊C4D24412yes—
169C23—81no—
170C23—1221no—
171C23—1221no—
172C23—1221no—
173C23—4881no—
174C23C2×D24411yescharacteristic
175C23#1175822211yescharacteristic
176C23#1175822211yescharacteristic
177C23D4×D6111yescharacteristic
178C23D4×D6111yescharacteristic
179C23#1175822411yescharacteristic
180C23Q8×D6111yescharacteristic
181Q8—4882no—
182D4—2441no—
183D4—2441no—
184D4—2441no—
185D4—2441no—
186C2×C4—22no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—81no—
190C2×C4—81no—
191C2×C4—81no—
192C2×C4—1222no—
193C2×C4—1222no—
194C2×C4—1221no—
195C2×C4—1221no—
196C2×C4—1221no—
197C2×C4—4881no—
198C2×C4—4881no—
199C2×C4—4881no—
200C2×C4—2441no—
201C22—41no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—4881no—
209C22—4881no—
210C22—4881no—
211C22—2441no—
212C22#1451974711yescharacteristic
213C22#1451975511yescharacteristic
214C22#1451975511yescharacteristic
215C22#1451975711yescharacteristic
216C22#1451976311yescharacteristic
217C22#1451976311yescharacteristic
218C22#1451976511yescharacteristic
219C4—42no—
220C4—81no—
221C4—81no—
222C4—4881no—
223C4—2442no—
224C4—2442no—
225C4—2441no—
226C2—21no—
227C2—21no—
228C2—21no—
229C2—21no—
230C2—21no—
231C2—21no—
232C2—21no—
233C2—4881no—
234C2#1683967511yescharacteristic
subgroupG/H
centerC2#16839675
commutatorC24×C61C23
FrattiniC24C22×D61
FittingC61×#342C2
socleC2×C61#393
hypercenter#342D61
hypocenterC61#2032
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
1. #16840388C2semidirect
5. #16839529C2semidirect
6. #16839528C2semidirect
7. C61×#342C2semidirect
22. C23×D61Q8semidirect
35. C22×Dic61Q8semidirect
124. #342D61semidirect
125. C61#2032semidirect