Finite Group Databasebeta

← #21446175

Subgroups — #21446175

Order 7808.

374 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#11758190C211yesmaximal, characteristic
2C2×#14519742C211yesmaximal, characteristic, complemented
3C2×#14519700C211yesmaximal, characteristic, complemented
4C2×#14519697C211yesmaximal, characteristic
5#16839663C211yesmaximal, characteristic
6#16839516C211yesmaximal, characteristic, complemented
7C61×#340C211yesmaximal, characteristic, complemented
8C22×Dic122C2211yescharacteristic
9C22×D244C2211yescharacteristic
10C2×#11758190—22no—
11C2×#11758190—22no—
12C2×#11758190C414yescomplemented
13C22×#92418C2211yescharacteristic
14#14519742—22no—
15#14519742—22no—
16C2×#11758196—21no—
17C2×#11758198—21no—
18C2×#11758198—21no—
19C2×C4×Dic61—21no—
20C2×C4×Dic61C2211yescharacteristic
21#14519700—22no—
22#14519697—22no—
23C22×C8×C61C2211yescharacteristic
24C2×C4⋊C4×C61C2211yescharacteristic
25C2×C4⋊C4×C61C2211yescharacteristic
26C23×D61—21no—
27C22×C4×C61—21no—
28C22×C4×C61—21no—
29C22×C4×C61C2311yescharacteristic
30C22×Dic61—21no—
31C22×Dic61D411yescharacteristic
32C22×Dic61D411yescharacteristic
33C2×D244—21no—
34C2×D244—21no—
35C2×D244—21no—
36C2×D244—21no—
37C2×D244—21no—
38C2×D244C2×C412yes—
39C2×Dic122—21no—
40C2×Dic122—21no—
41C2×Dic122—21no—
42C2×Dic122C2×C412yes—
43C2×Dic122D412yes—
44C2×Dic122D412yes—
45C2×C8×C61—21no—
46C2×C8×C61—21no—
47C2×C8×C61C2×C412yes—
48C4⋊C4×C61—21no—
49C4⋊C4×C61—21no—
50C4⋊C4×C61—21no—
51C4⋊C4×C61D412yes—
52#11758198—42no—
53#11758198—42no—
54#11758196—24no—
55C4×Dic61—24no—
56C4×Dic61—21no—
57C4×Dic61—21no—
58C2×#92418—21no—
59C2×#92418—21no—
60C2×#92418—21no—
61#11758190—28no—
62C23×C61C2×D411yescharacteristic
63C22×D61—22no—
64C22×D61—41no—
65C22×D61—41no—
66C22×D61—41no—
67C22×D61—41no—
68C22×D61—41no—
69C22×D61—41no—
70C2×C4×C61—22no—
71C2×C4×C61—41no—
72C2×C4×C61—41no—
73C2×C4×C61—41no—
74C2×C4×C61—41no—
75C2×C4×C61—41no—
76C2×C4×C61C22×C411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61#4111yescharacteristic
81C2×C4×C61#4111yescharacteristic
82C2×Dic61—22no—
83C2×Dic61—21no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61SD1612yescomplemented
91D244—22no—
92D244—22no—
93D244—41no—
94D244—41no—
95Dic122—22no—
96Dic122—22no—
97Dic122—22no—
98Dic122C22⋊C414yescomplemented
99C8×C61—22no—
100#92418—41no—
101C22×C61C4×D411yescharacteristic
102C22×C61#12011yescharacteristic
103C22×C61#12111yescharacteristic
104C22×C61C2×SD1611yescharacteristic
105C22×C61#13511yescharacteristic
106C22×C61AGL(1,ℤ/8)11yescharacteristic
107C22×C61#13711yescharacteristic
108C2×D61—42no—
109C2×D61—42no—
110C2×D61—42no—
111C2×D61—81no—
112C2×D61—81no—
113C2×D61—81no—
114C2×D61—81no—
115C4×C61—42no—
116C4×C61—81no—
117C4×C61C2×C22⋊C411yescharacteristic
118C4×C61C4×D411yescharacteristic
119C4×C61#12111yescharacteristic
120C4×C61#12311yescharacteristic
121Dic61—24no—
122Dic61—22no—
123Dic61—41no—
124#1880—611nomaximal, Sylow
125C2×C61#38611yescharacteristic
126C2×C61C4×SD1611yescharacteristic
127C2×C61#44011yescharacteristic
128C2×C61#44811yescharacteristic
129C2×C61#44911yescharacteristic
130C2×C61#46011yescharacteristic
131C2×C61#46411yescharacteristic
132D61—82no—
133C22×SD16—611no—
134C2×C4×Q8—611no—
135C2×#103—611no—
136C2×#102—611no—
137#390—611no—
138#340D6111yescharacteristic, complemented
139#336—611no—
140C61#188011yescharacteristic, complemented, Sylow
141C22×Q8—611no—
142C22×D4—611no—
143C2×SD16—614no—
144C2×SD16—1222no—
145C2×SD16—1222no—
146C22×C8—611no—
147C22×C8C2×D6111yescharacteristic
148C4×Q8—1222no—
149C4×Q8—1222no—
150C2×C4⋊C4—1221no—
151C2×C4⋊C4C2×D6111yescharacteristic
152C2×C4⋊C4C2×D6111yescharacteristic
153C2×C22⋊C4—1221no—
154C2×C22⋊C4—1221no—
155C2×C42—611no—
156C2×C42—1221no—
157#103—1222no—
158#102—1222no—
159C24—1221no—
160C2×Q8—612no—
161C2×Q8—612no—
162C2×Q8—612no—
163C2×Q8—1221no—
164C2×Q8—1221no—
165C2×Q8—1221no—
166C2×D4—612no—
167C2×D4—1221no—
168C2×D4—1221no—
169C2×D4—1221no—
170C2×D4—1221no—
171C2×D4—1221no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—611no—
175C22×C4—611no—
176C22×C4—1221no—
177C22×C4C22×D6111yescharacteristic
178SD16—1228no—
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—1221no—
182C2×C8—1221no—
183C2×C8—1221no—
184C2×C8C4×D6112yes—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—1224no—
189C4⋊C4D24412yes—
190C22⋊C4—2442no—
191C22⋊C4—2442no—
192C42—1224no—
193C42—1221no—
194C42—1221no—
195C23—1222no—
196C23—2441no—
197C23—2441no—
198C23—2441no—
199C23—2441no—
200C23—2441no—
201C23—2441no—
202C23D4×D6111yescharacteristic
203Q8—614no—
204Q8—1222no—
205Q8—1222no—
206Q8—1222no—
207D4—1222no—
208D4—1222no—
209D4—2441no—
210D4—2441no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—612no—
218C2×C4—1221no—
219C2×C4—1222no—
220C2×C4—1221no—
221C2×C4—1222no—
222C2×C4—1222no—
223C2×C4—1221no—
224C2×C4—1221no—
225C2×C4—1221no—
226C2×C4C2×C4×D6111yescharacteristic
227C2×C4C2×D24411yescharacteristic
228C2×C4#1175822211yescharacteristic
229C2×C4D4×D6111yescharacteristic
230C2×C4D4×D6111yescharacteristic
231C2×C4#1175822611yescharacteristic
232C8—22no—
233C8—2441no—
234C22—4881no—
235C22—4881no—
236C22—4881no—
237C22—4881no—
238C22—2442no—
239C22—2442no—
240C22—2442no—
241C22#1451973911yescharacteristic
242C22#1451974711yescharacteristic
243C22#1451975011yescharacteristic
244C22SD16×D6111yescharacteristic
245C22#1451979811yescharacteristic
246C22#1451980111yescharacteristic
247C22#1451980911yescharacteristic
248C4—42no—
249C4—81no—
250C4—1224no—
251C4—1222no—
252C4—2441no—
253C4C22⋊C4×D6111yescharacteristic
254C4C4×D24411yescharacteristic
255C4#1451975211yescharacteristic
256C4#1451976211yescharacteristic
257C2—4882no—
258C2#1683964011yescharacteristic
259C2#1683984911yescharacteristic
260C2#1683986111yescharacteristic
261C2#1683990211yescharacteristic
262C2#1683990811yescharacteristic
263C2#1683996111yescharacteristic
264C2#1683998711yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#340C2
socleC23×C61C2×D4
hypercenter#340D61
hypocenterC61#1880
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×#14519742C2semidirect
3. C2×#14519700C2semidirect
6. #16839516C2semidirect
7. C61×#340C2semidirect
12. C2×#11758190C4semidirect
90. C2×Dic61SD16semidirect
98. Dic122C22⋊C4semidirect
138. #340D61semidirect
140. C61#1880semidirect