Finite Group Databasebeta

← #21446875

Subgroups — #21446875

Order 7808.

380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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#16840562C211yesmaximal, characteristic, complemented
2C2×#14519805C211yesmaximal, characteristic, complemented
3#16840331C211yesmaximal, characteristic, complemented
4#16839778C211yesmaximal, characteristic, complemented
5#16839768C211yesmaximal, characteristic, complemented
6#16839735C211yesmaximal, characteristic, complemented
7C61×#344C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C2×#11758222C2211yescharacteristic
10C22×D244C2211yescharacteristic
11#14519810—21no—
12#14519810—21no—
13#14519805—22no—
14#14519805—21no—
15#14519805—21no—
16#14519805—22no—
17#14519799—22no—
18C2×#11758190—21no—
19C2×D488—21no—
20#14519774—21no—
21#14519765—21no—
22#14519752—22no—
23#14519747—22no—
24#14519736C2211yescharacteristic
25#14519703—22no—
26#14519699—22no—
27#14519691—22no—
28C2×M16×C61C2211yescharacteristic
29C2×M16×C61C2211yescharacteristic
30#117×C61C2211yescharacteristic
31C23×D61—21no—
32C22×C4×C61C2311yescharacteristic
33C2×C22⋊D61—21no—
34C2×C22⋊D61—21no—
35#11758222—21no—
36#11758222—21no—
37#11758222—21no—
38#11758222—21no—
39#11758222—21no—
40#11758222—21no—
41#11758222—21no—
42#11758222—21no—
43C2×D244—21no—
44C2×D244—21no—
45C2×D244—21no—
46C2×D244—21no—
47C2×D244—21no—
48C2×D244—24no—
49C2×D244D412yes—
50C2×D244D411yescharacteristic
51C2×D244D411yescharacteristic, complemented
52C2×C4×D61—21no—
53C2×C4×D61—21no—
54C2×Dic122D411yescharacteristic
55C2×Dic122D411yescharacteristic, complemented
56M16×C61—21no—
57M16×C61—21no—
58M16×C61—21no—
59M16×C61D412yescomplemented
60C2×C8×C61—21no—
61C2×C8×C61D412yescomplemented
62C4⋊C4×C61—21no—
63C22⋊C4×C61D412yes—
64C42×C61—21no—
65C22⋊Dic61—21no—
66#11758198—24no—
67C4⋊Dic61—21no—
68C4×Dic61—21no—
69Dic244—22no—
70D488—24no—
71D488—22no—
72#11758190—22no—
73#11758190—22no—
74#11758190—24no—
75C23×C61C2×D411yescharacteristic
76C22×D61—22no—
77C22×D61—21no—
78C22×D61—21no—
79C22×D61—41no—
80C22×D61—41no—
81C22×D61—82no—
82C2×C4×C61—22no—
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61#4111yescharacteristic
89C22⋊D61—41no—
90C22⋊D61—41no—
91C22⋊D61—41no—
92C22⋊D61—41no—
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—41no—
96D244—22no—
97D244—21no—
98D244—21no—
99D244—21no—
100D244—22no—
101D244—21no—
102D244—41no—
103D244—41no—
104D244—84no—
105C4×D61—41no—
106C4×D61—41no—
107C4×D61—41no—
108C4×D61—41no—
109Dic122—21no—
110Dic122—21no—
111Dic122—21no—
112Dic122—21no—
113C8×C61—22no—
114C8×C61—22no—
115C22×C61—41no—
116C22×C61#12011yescharacteristic
117C22×C61#12111yescharacteristic
118C22×C61#12711yescharacteristic
119C2×D61—42no—
120C2×D61—44no—
121C2×D61—41no—
122C2×D61—41no—
123C2×D61—42no—
124C2×D61—82no—
125C2×D61—82no—
126C2×D61—81no—
127C4×C61—42no—
128C4×C61#12011yescharacteristic
129C4×C61#12011yescharacteristic
130C4×C61#12111yescharacteristic
131C4×C61#12111yescharacteristic
132Dic61—41no—
133Dic61—41no—
134Dic61—81no—
135#2008—611nomaximal, Sylow
136C2×C61—21no—
137C2×C61—21no—
138C2×C61—21no—
139C2×C61#39211yescharacteristic
140D61—81no—
141D61—82no—
142D61—81no—
143#575—611no—
144C2×AGL(1,ℤ/8)—611no—
145#535—611no—
146#421—611no—
147#418—611no—
148#410—611no—
149#344D6111yescharacteristic, complemented
150C61#200811yescharacteristic, complemented, Sylow
151C2×#41—611no—
152C2×#41—611no—
153C22×D4—611no—
154#137—1221no—
155#137—1221no—
156AGL(1,ℤ/8)—1222no—
157AGL(1,ℤ/8)—1221no—
158AGL(1,ℤ/8)—1221no—
159AGL(1,ℤ/8)—1222no—
160#135—1222no—
161C2×SD16—1221no—
162C2×D8—1221no—
163C2×M16C2×D6111yescharacteristic
164C2×M16C2×D6111yescharacteristic
165#127—1221no—
166#124—1221no—
167#121—1222no—
168#120—1222no—
169#117—611no—
170#117C2×D6111yescharacteristic
171#104—1222no—
172#102—1222no—
173#99—1222no—
174C24—1221no—
175#41—1221no—
176#41—1221no—
177#41—1221no—
178#41—1221no—
179#41—1221no—
180#41—1221no—
181#41—1221no—
182#41—1221no—
183C2×Q8—611no—
184C2×Q8—611no—
185C2×D4—612no—
186C2×D4—611no—
187C2×D4—611no—
188C2×D4—1224no—
189C2×D4—1221no—
190C2×D4—1221no—
191C2×D4—1221no—
192C2×D4—1221no—
193C2×D4—1221no—
194C2×D4—1221no—
195C2×D4—1221no—
196C22×C4—1221no—
197C22×C4—1221no—
198C22×C4C22×D6111yescharacteristic
199Q16—1222no—
200SD16—1224no—
201SD16—1222no—
202SD16—1222no—
203D8—1224no—
204D8—1222no—
205M16—21no—
206M16—21no—
207M16—21no—
208M16D24412yescomplemented
209C2×C8—21no—
210C2×C8D24412yescomplemented
211C4⋊C4—21no—
212C4⋊C4—1221no—
213C22⋊C4—1224no—
214C22⋊C4—1221no—
215C22⋊C4D24412yes—
216C42—21no—
217C42—1221no—
218C23—1221no—
219C23—1222no—
220C23—1221no—
221C23—4882no—
222C23—2441no—
223C23—2441no—
224C23C2×D24411yescharacteristic
225Q8—1221no—
226Q8—1221no—
227Q8—1221no—
228Q8—1221no—
229D4—1221no—
230D4—1222no—
231D4—1221no—
232D4—1221no—
233D4—1222no—
234D4—1221no—
235D4—4884no—
236D4—2441no—
237D4—2441no—
238D4—2441no—
239D4—2441no—
240D4—2441no—
241D4—2441no—
242C2×C4—22no—
243C2×C4—1221no—
244C2×C4—1221no—
245C2×C4—2441no—
246C2×C4—2441no—
247C2×C4—2441no—
248C2×C4—2441no—
249C2×C4—2441no—
250C2×C4C2×D24411yescharacteristic
251C2×C4C2×D24411yescharacteristic
252C2×C4D4×D6111yescharacteristic
253C2×C4D4×D6111yescharacteristic
254C2×C4D4×D6111yescharacteristic
255C2×C4#1175822611yescharacteristic
256C8—22no—
257C8—22no—
258C22—41no—
259C22—4881no—
260C22—4882no—
261C22—4882no—
262C22—2442no—
263C22—2444no—
264C22—2441no—
265C22—2441no—
266C22—2442no—
267C22#1451974711yescharacteristic
268C22#1451975211yescharacteristic
269C22#1451977411yescharacteristic
270C4—42no—
271C4—4881no—
272C4—2441no—
273C4—2441no—
274C4#1451974711yescharacteristic
275C4#1451974711yescharacteristic
276C4#1451975211yescharacteristic
277C4#1451975211yescharacteristic
278C2—21no—
279C2—21no—
280C2—21no—
281C2—4882no—
282C2—4881no—
283C2—4881no—
284C2#1683967211yescharacteristic
subgroupG/H
centerC2#16839672
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#344C2
socleC2×C61#392
hypercenter#344D61
hypocenterC61#2008
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
1. #16840562C2semidirect
2. C2×#14519805C2semidirect
3. #16840331C2semidirect
4. #16839778C2semidirect
5. #16839768C2semidirect
6. #16839735C2semidirect
7. C61×#344C2semidirect
51. C2×D244D4semidirect
55. C2×Dic122D4semidirect
59. M16×C61D4semidirect
61. C2×C8×C61D4semidirect
149. #344D61semidirect
150. C61#2008semidirect
208. M16D244semidirect
210. C2×C8D244semidirect