Finite Group Databasebeta

← #21446249

Subgroups — #21446249

Order 7808.

360 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 99 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×#11758189C211yesmaximal, characteristic
2C2×#14519753C211yesmaximal, characteristic
3C2×#14519701C211yesmaximal, characteristic, complemented
4#16839619C211yesmaximal, characteristic
5#16839525C211yesmaximal, characteristic, complemented
6#16839524C211yesmaximal, characteristic, complemented
7C2×#103×C61C211yesmaximal, characteristic, complemented
8C22×C4×D61C2211yescharacteristic
9C2×#11758189—22no—
10C2×#11758189—22no—
11C2×#11758189—22no—
12C22×#92418C2211yescharacteristic
13#14519753—22no—
14#14519753C414yescomplemented
15C2×C4⋊Dic61C2211yescharacteristic
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758196—21no—
18C2×#11758198—21no—
19C2×#11758198—21no—
20#14519701—22no—
21#14519684—21no—
22C22×Q8×C61C2211yescharacteristic
23C22×C8×C61C2211yescharacteristic
24C2×C4⋊C4×C61C2211yescharacteristic
25#103×C61—22no—
26C23×D61D411yescharacteristic
27C2×Q8×C61—21no—
28C2×Q8×C61—21no—
29C2×Q8×C61—21no—
30C2×Q8×C61—21no—
31C2×Q8×C61—21no—
32C2×Q8×C61C2×C412yes—
33C22×C4×C61—21no—
34C22×C4×C61—21no—
35C22×C4×C61C2311yescharacteristic
36C22×Dic61—21no—
37C22×Dic61—21no—
38C22×Dic61D411yescharacteristic
39C2×C4×D61—21no—
40C2×C4×D61—21no—
41C2×C4×D61—21no—
42C2×C4×D61—21no—
43C2×C4×D61C2×C412yes—
44C2×C4×D61D412yes—
45C2×C8×C61—21no—
46C2×C8×C61—21no—
47C2×C8×C61D412yes—
48C4⋊C4×C61—21no—
49C4⋊C4×C61—21no—
50#11758198—24no—
51#11758198—42no—
52C4⋊Dic61—21no—
53C4⋊Dic61—21no—
54C4⋊Dic61—21no—
55C4⋊Dic61C2×C412yes—
56#11758196—24no—
57C2×#92418—21no—
58C2×#92418—21no—
59C2×#92418D412yes—
60#11758189—28no—
61C23×C61C2×D411yescharacteristic
62C22×D61—21no—
63C22×D61—21no—
64C22×D61—21no—
65C22×D61—21no—
66C22×D61—21no—
67C22×D61—21no—
68C22×D61C22⋊C412yes—
69Q8×C61—22no—
70Q8×C61—22no—
71Q8×C61—41no—
72Q8×C61—41no—
73C2×C4×C61—22no—
74C2×C4×C61—41no—
75C2×C4×C61—41no—
76C2×C4×C61—41no—
77C2×C4×C61—41no—
78C2×C4×C61—41no—
79C2×C4×C61C22×C411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61#4111yescharacteristic
84C2×C4×C61#4111yescharacteristic
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—22no—
88C2×Dic61—41no—
89C2×Dic61—41no—
90C2×Dic61—41no—
91C2×Dic61—41no—
92C2×Dic61—41no—
93C2×Dic61C22⋊C412yes—
94C4×D61—22no—
95C4×D61—22no—
96C4×D61—22no—
97C4×D61—22no—
98C8×C61—22no—
99#92418—22no—
100C22×C61C2×C22⋊C411yescharacteristic
101C22×C61#12111yescharacteristic
102C22×C61#12111yescharacteristic
103C22×C61AGL(1,ℤ/8)11yescharacteristic
104C22×C61#13711yescharacteristic
105C22×C61#13711yescharacteristic
106C22×C61#13711yescharacteristic
107C2×D61—22no—
108C2×D61—22no—
109C2×D61—22no—
110C2×D61—41no—
111C2×D61—41no—
112C2×D61—41no—
113C2×D61—41no—
114C4×C61—42no—
115C4×C61—81no—
116C4×C61C4×D411yescharacteristic
117C4×C61C4×D411yescharacteristic
118C4×C61#12011yescharacteristic
119C4×C61#12311yescharacteristic
120Dic61—22no—
121Dic61—42no—
122Dic61—81no—
123#1894—611nomaximal, Sylow
124C2×C61#38611yescharacteristic
125C2×C61#41711yescharacteristic
126C2×C61#41911yescharacteristic
127C2×C61#46811yescharacteristic
128C2×C61#46811yescharacteristic
129C2×C61#47011yescharacteristic
130C2×C61#47011yescharacteristic
131D61—42no—
132C22×M16—611no—
133C2×C22⋊Q8—611no—
134C2×#103—611no—
135C2×#103D6111yescharacteristic, complemented
136#380—611no—
137#340—611no—
138#340—611no—
139C61#189411yescharacteristic, complemented, Sylow
140C22×Q8C2×D6111yescharacteristic
141C23×C4—611no—
142C2×M16—1222no—
143C2×M16—1222no—
144C2×M16—1222no—
145C22×C8—611no—
146C22×C8C2×D6111yescharacteristic
147C22⋊Q8—614no—
148C22⋊Q8—1222no—
149C2×C4⋊C4—611no—
150C2×C4⋊C4—611no—
151C2×C4⋊C4—1221no—
152C2×C4⋊C4C2×D6111yescharacteristic
153C2×C22⋊C4—1221no—
154C2×C22⋊C4—1221no—
155#103—22no—
156#103—1222no—
157#95—1221no—
158C24—611no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8C4×D6112yes—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—611no—
168C22×C4—612no—
169C22×C4—612no—
170C22×C4—1221no—
171C22×C4—1221no—
172C22×C4—1221no—
173C22×C4—1221no—
174C22×C4—1221no—
175C22×C4—1221no—
176C22×C4C22×D6111yescharacteristic
177M16—1228no—
178C2×C8—21no—
179C2×C8—21no—
180C2×C8—612no—
181C2×C8—1221no—
182C2×C8—1221no—
183C2×C8C22⋊D6112yes—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4—612no—
187C4⋊C4—1224no—
188C4⋊C4—1221no—
189C4⋊C4—1221no—
190C4⋊C4—1221no—
191C22⋊C4—1224no—
192C22⋊C4—2442no—
193C23—612no—
194C23—1221no—
195C23—1221no—
196C23—1221no—
197C23—1221no—
198C23—1221no—
199C23—1221no—
200C23D4×D6111yescharacteristic
201Q8—22no—
202Q8—22no—
203Q8—41no—
204Q8—41no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—612no—
212C2×C4—1221no—
213C2×C4—1221no—
214C2×C4—1222no—
215C2×C4—1222no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4—2441no—
220C2×C4—2441no—
221C2×C4—2441no—
222C2×C4—2441no—
223C2×C4—2441no—
224C2×C4C2×C4×D6111yescharacteristic
225C2×C4#1175822211yescharacteristic
226C2×C4D4×D6111yescharacteristic
227C2×C4D4×D6111yescharacteristic
228C2×C4#1175822411yescharacteristic
229C2×C4C2×C22⋊D6111yescharacteristic
230C8—22no—
231C8—1222no—
232C22—1222no—
233C22—1222no—
234C22—1222no—
235C22—2441no—
236C22—2441no—
237C22—2441no—
238C22—2441no—
239C22C22⋊C4×D6111yescharacteristic
240C22#1451974811yescharacteristic
241C22#1451975011yescharacteristic
242C22#1451980411yescharacteristic
243C22#1451980611yescharacteristic
244C22#1451980911yescharacteristic
245C22#1451980911yescharacteristic
246C4—42no—
247C4—81no—
248C4—1222no—
249C4—4881no—
250C4—2442no—
251C4#1451973711yescharacteristic
252C4C4×C22⋊D6111yescharacteristic
253C4#1451974511yescharacteristic
254C4#1451975911yescharacteristic
255C2—2442no—
256C2#1683963811yescharacteristic
257C2#1683976211yescharacteristic
258C2#1683976911yescharacteristic
259C2#1684000511yescharacteristic
260C2#1684001111yescharacteristic
261C2#1684001711yescharacteristic
262C2#1684001911yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#103×C61C2
socleC23×C61C2×D4
hypercenterC2×#103D61
hypocenterC61#1894
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. C2×#14519701C2semidirect
5. #16839525C2semidirect
6. #16839524C2semidirect
7. C2×#103×C61C2semidirect
14. #14519753C4semidirect
135. C2×#103D61semidirect
139. C61#1894semidirect