Finite Group Databasebeta

← #21446869

Subgroups — #21446869

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
1C2×#14519802C211yesmaximal, characteristic, complemented
2#16840326C211yesmaximal, characteristic, complemented
3#16839779C211yesmaximal, characteristic, complemented
4#16839768C211yesmaximal, characteristic, complemented
5#16839736C211yesmaximal, characteristic, complemented
6#16839533C211yesmaximal, characteristic, complemented
7C61×#575C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9#14519802—22no—
10#14519802—22no—
11C2×#11758201—21no—
12C2×#11758199—21no—
13C2×#11758194C2211yescharacteristic
14#14519773—21no—
15#14519766—21no—
16#14519751—22no—
17#14519745—22no—
18#14519736C2211yescharacteristic
19#14519736C2211yescharacteristic
20#14519704—22no—
21#14519699—22no—
22#14519692—22no—
23C2×#41×C61C2211yescharacteristic
24C2×#41×C61C2211yescharacteristic
25#137×C61—21no—
26#137×C61—21no—
27AGL(1,ℤ/8)×C61—21no—
28AGL(1,ℤ/8)×C61—21no—
29#135×C61—22no—
30C2×M16×C61C2211yescharacteristic
31C23×D61—21no—
32#41×C61—21no—
33#41×C61—21no—
34#41×C61—21no—
35#41×C61—21no—
36#41×C61—21no—
37#41×C61—21no—
38#41×C61—21no—
39#41×C61—21no—
40C2×Q8×C61D411yescharacteristic
41C2×Q8×C61D411yescharacteristic, complemented
42C2×D4×C61—21no—
43C2×D4×C61—21no—
44C2×D4×C61D411yescharacteristic
45C2×D4×C61D411yescharacteristic, complemented
46C22×C4×C61—21no—
47C22×C4×C61—21no—
48C22×C4×C61C2311yescharacteristic
49C2×C22⋊D61—24no—
50C2×D244—21no—
51C2×D244—21no—
52C2×D244—21no—
53C2×D244—21no—
54C2×D244—21no—
55C2×D244D412yes—
56Q16×C61—22no—
57SD16×C61—22no—
58SD16×C61—22no—
59D8×C61—22no—
60M16×C61—21no—
61M16×C61—21no—
62C2×C8×C61D412yescomplemented
63C22⋊Dic61—21no—
64C22⋊Dic61D412yes—
65#11758201—24no—
66#11758199—24no—
67#11758198—24no—
68C4⋊Dic61—21no—
69C4⋊Dic61—21no—
70C4×Dic61—21no—
71C4×Dic61—21no—
72#11758194—21no—
73#11758194D412yescomplemented
74C2×#92418—21no—
75C23×C61—21no—
76C23×C61—21no—
77C23×C61C2×D411yescharacteristic
78C22×D61—22no—
79C22×D61—41no—
80C22×D61—41no—
81C22×D61—82no—
82Q8×C61—21no—
83Q8×C61—21no—
84Q8×C61—21no—
85Q8×C61—21no—
86D4×C61—21no—
87D4×C61—21no—
88D4×C61—21no—
89D4×C61—21no—
90D4×C61—41no—
91D4×C61—41no—
92D4×C61—41no—
93D4×C61—41no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61C2×D411yescharacteristic
101C2×C4×C61C2×D411yescharacteristic
102C2×C4×C61C2×D411yescharacteristic
103C2×C4×C61C2×D411yescharacteristic
104C2×C4×C61C2×D411yescharacteristic
105C2×C4×C61#4111yescharacteristic
106C22⋊D61—84no—
107C2×Dic61—22no—
108C2×Dic61—41no—
109D244—22no—
110D244—22no—
111D244—41no—
112D244—41no—
113C8×C61—22no—
114#92418—22no—
115C22×C61—41no—
116C22×C61—42no—
117C22×C61—41no—
118C22×C61—41no—
119C22×C61—81no—
120C22×C61#12011yescharacteristic
121C22×C61#12111yescharacteristic
122C22×C61#12711yescharacteristic
123C2×D61—44no—
124C2×D61—42no—
125C2×D61—82no—
126C2×D61—82no—
127C4×C61—41no—
128C4×C61—41no—
129C4×C61#12011yescharacteristic
130C4×C61#12011yescharacteristic
131C4×C61#12111yescharacteristic
132C4×C61#12111yescharacteristic
133Dic61—42no—
134Dic61—81no—
135#2008—611nomaximal, Sylow
136C2×C61—21no—
137C2×C61—21no—
138C2×C61—21no—
139C2×C61—81no—
140C2×C61—81no—
141C2×C61#39211yescharacteristic
142D61—82no—
143#575D6111yescharacteristic, complemented
144C2×AGL(1,ℤ/8)—611no—
145#535—611no—
146#421—611no—
147#418—611no—
148#410—611no—
149#344—611no—
150C61#200811yescharacteristic, complemented, Sylow
151C2×#41C2×D6111yescharacteristic
152C2×#41C2×D6111yescharacteristic
153C22×D4—611no—
154#137—21no—
155#137—21no—
156AGL(1,ℤ/8)—21no—
157AGL(1,ℤ/8)—21no—
158AGL(1,ℤ/8)—1222no—
159AGL(1,ℤ/8)—1222no—
160#135—22no—
161C2×SD16—1221no—
162C2×D8—1221no—
163C2×M16—611no—
164C2×M16C2×D6111yescharacteristic
165#127—1221no—
166#124—1221no—
167#121—1222no—
168#120—1222no—
169#117—611no—
170#117—611no—
171#104—1222no—
172#102—1222no—
173#99—1222no—
174C24—1221no—
175#41—21no—
176#41—21no—
177#41—21no—
178#41—21no—
179#41—21no—
180#41—21no—
181#41—21no—
182#41—21no—
183C2×Q8C22⋊D6111yescharacteristic
184C2×Q8C22⋊D6111yescharacteristic, complemented
185C2×D4—21no—
186C2×D4—21no—
187C2×D4—612no—
188C2×D4—1224no—
189C2×D4—1221no—
190C2×D4—1221no—
191C2×D4—1221no—
192C2×D4—1221no—
193C2×D4—1221no—
194C2×D4C22⋊D6111yescharacteristic
195C2×D4C22⋊D6111yescharacteristic, complemented
196C22×C4—21no—
197C22×C4—21no—
198C22×C4C22×D6111yescharacteristic
199Q16—22no—
200SD16—22no—
201SD16—22no—
202SD16—1224no—
203D8—22no—
204D8—1224no—
205M16—21no—
206M16—21no—
207M16—612no—
208M16—1221no—
209C2×C8—1221no—
210C2×C8C22⋊D6112yescomplemented
211C4⋊C4—1221no—
212C4⋊C4—1221no—
213C22⋊C4—612no—
214C22⋊C4—1224no—
215C22⋊C4—1221no—
216C42—1221no—
217C42—1221no—
218C23—21no—
219C23—21no—
220C23—1222no—
221C23—4882no—
222C23—2441no—
223C23—2441no—
224C23D4×D6111yescharacteristic
225Q8—21no—
226Q8—21no—
227Q8—21no—
228Q8—21no—
229D4—21no—
230D4—21no—
231D4—21no—
232D4—21no—
233D4—41no—
234D4—41no—
235D4—41no—
236D4—41no—
237D4—1222no—
238D4—1222no—
239D4—4884no—
240D4—2441no—
241D4—2441no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—1222no—
249C2×C4—2441no—
250C2×C4D4×D6111yescharacteristic
251C2×C4D4×D6111yescharacteristic
252C2×C4#1175822411yescharacteristic
253C2×C4C2×C22⋊D6111yescharacteristic
254C2×C4C2×C22⋊D6111yescharacteristic
255C2×C4C2×C22⋊D6111yescharacteristic
256C8—22no—
257C8—1222no—
258C22—41no—
259C22—42no—
260C22—41no—
261C22—41no—
262C22—81no—
263C22—4882no—
264C22—4882no—
265C22—2444no—
266C22—2442no—
267C22#1451974511yescharacteristic
268C22#1451974911yescharacteristic
269C22#1451977311yescharacteristic
270C4—41no—
271C4—41no—
272C4—4881no—
273C4—2442no—
274C4#1451974511yescharacteristic
275C4#1451974611yescharacteristic
276C4#1451974811yescharacteristic
277C4#1451974911yescharacteristic
278C2—21no—
279C2—21no—
280C2—21no—
281C2—81no—
282C2—81no—
283C2—4882no—
284C2#1683967011yescharacteristic
subgroupG/H
centerC2#16839670
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#575C2
socleC2×C61#392
hypercenter#575D61
hypocenterC61#2008
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. C2×#14519802C2semidirect
2. #16840326C2semidirect
3. #16839779C2semidirect
4. #16839768C2semidirect
5. #16839736C2semidirect
6. #16839533C2semidirect
7. C61×#575C2semidirect
41. C2×Q8×C61D4semidirect
45. C2×D4×C61D4semidirect
62. C2×C8×C61D4semidirect
73. #11758194D4semidirect
143. #575D61semidirect
150. C61#2008semidirect
184. C2×Q8C22⋊D61semidirect
195. C2×D4C22⋊D61semidirect
210. C2×C8C22⋊D61semidirect