Finite Group Databasebeta

← #21446870

Subgroups — #21446870

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#16840560C211yesmaximal, characteristic, complemented
2#16840329C211yesmaximal, characteristic, complemented
3#16839778C211yesmaximal, characteristic, complemented
4#16839767C211yesmaximal, characteristic, complemented
5#16839736C211yesmaximal, characteristic, complemented
6#16839534C211yesmaximal, characteristic, complemented
7C2×AGL(1,ℤ/8)×C61C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519808—21no—
10#14519807—21no—
11#14519803—21no—
12#14519802—21no—
13#14519797—22no—
14C2×#11758194C2211yescharacteristic
15#14519773—21no—
16#14519764—21no—
17#14519748—22no—
18#14519746—22no—
19#14519736C2211yescharacteristic
20#14519736C2211yescharacteristic
21#14519703—22no—
22#14519698—22no—
23#14519692—22no—
24C2×#41×C61C2211yescharacteristic
25C22×D4×C61C2211yescharacteristic
26AGL(1,ℤ/8)×C61—22no—
27AGL(1,ℤ/8)×C61—22no—
28C2×SD16×C61—21no—
29C2×D8×C61—21no—
30C2×M16×C61C2211yescharacteristic
31C24×C61—21no—
32#41×C61—21no—
33#41×C61—21no—
34#41×C61—21no—
35#41×C61—21no—
36C2×Q8×C61D411yescharacteristic, complemented
37C2×D4×C61—21no—
38C2×D4×C61—21no—
39C2×D4×C61—21no—
40C2×D4×C61—21no—
41C2×D4×C61—21no—
42C2×D4×C61—21no—
43C2×D4×C61D412yes—
44C2×D4×C61D411yescharacteristic, complemented
45C22×C4×C61—21no—
46C22×C4×C61C2311yescharacteristic
47C2×C22⋊D61—21no—
48C2×C22⋊D61—24no—
49#11758222—21no—
50#11758222—21no—
51#11758222—21no—
52#11758222—21no—
53C2×D244D411yescharacteristic
54C2×C4×D61—21no—
55C2×Dic122D411yescharacteristic
56SD16×C61—24no—
57D8×C61—24no—
58M16×C61—21no—
59M16×C61D412yescomplemented
60C2×C8×C61—21no—
61C22⋊Dic61—24no—
62C22⋊Dic61—21no—
63C22⋊Dic61D412yes—
64#11758202—22no—
65#11758201—22no—
66#11758200—22no—
67#11758199—22no—
68C4⋊Dic61—21no—
69C4⋊Dic61—21no—
70C4×Dic61—21no—
71C4×Dic61—21no—
72#11758194—21no—
73#11758194—21no—
74C2×#92418D412yescomplemented
75C23×C61—22no—
76C23×C61—21no—
77C23×C61—41no—
78C23×C61—41no—
79C23×C61—82no—
80C23×C61C2×D411yescharacteristic
81C22×D61—21no—
82Q8×C61—21no—
83Q8×C61—21no—
84D4×C61—21no—
85D4×C61—21no—
86D4×C61—22no—
87D4×C61—22no—
88D4×C61—41no—
89D4×C61—41no—
90D4×C61—41no—
91D4×C61—41no—
92C2×C4×C61—21no—
93C2×C4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61C2×D411yescharacteristic
97C2×C4×C61C2×D411yescharacteristic
98C2×C4×C61C2×D411yescharacteristic
99C2×C4×C61C2×D411yescharacteristic
100C2×C4×C61#4111yescharacteristic
101C22⋊D61—41no—
102C22⋊D61—41no—
103C22⋊D61—84no—
104C2×Dic61—22no—
105C2×Dic61—21no—
106C2×Dic61—41no—
107D244—21no—
108D244—21no—
109C4×D61—41no—
110C4×D61—41no—
111Dic122—21no—
112Dic122—21no—
113C8×C61—22no—
114#92418—22no—
115C22×C61—41no—
116C22×C61—44no—
117C22×C61—41no—
118C22×C61—42no—
119C22×C61—81no—
120C22×C61—82no—
121C22×C61—82no—
122C22×C61#12011yescharacteristic
123C22×C61#12111yescharacteristic
124C22×C61#12711yescharacteristic
125C2×D61—42no—
126C2×D61—41no—
127C4×C61—41no—
128C4×C61#12011yescharacteristic
129C4×C61#12011yescharacteristic
130C4×C61#12111yescharacteristic
131C4×C61#12111yescharacteristic
132Dic61—42no—
133Dic61—41no—
134Dic61—81no—
135#2008—611nomaximal, Sylow
136C2×C61—21no—
137C2×C61—21no—
138C2×C61—21no—
139C2×C61—82no—
140C2×C61—81no—
141C2×C61#39211yescharacteristic
142D61—81no—
143#575—611no—
144C2×AGL(1,ℤ/8)D6111yescharacteristic, complemented
145#535—611no—
146#421—611no—
147#418—611no—
148#410—611no—
149#344—611no—
150C61#200811yescharacteristic, complemented, Sylow
151C2×#41—611no—
152C2×#41C2×D6111yescharacteristic
153C22×D4C2×D6111yescharacteristic
154#137—1221no—
155#137—1221no—
156AGL(1,ℤ/8)—22no—
157AGL(1,ℤ/8)—22no—
158AGL(1,ℤ/8)—1221no—
159AGL(1,ℤ/8)—1221no—
160#135—1222no—
161C2×SD16—21no—
162C2×D8—21no—
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—21no—
175#41—21no—
176#41—21no—
177#41—21no—
178#41—21no—
179#41—1221no—
180#41—1221no—
181#41—1221no—
182#41—1221no—
183C2×Q8—611no—
184C2×Q8C22⋊D6111yescharacteristic, complemented
185C2×D4—21no—
186C2×D4—21no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—21no—
190C2×D4—21no—
191C2×D4—611no—
192C2×D4—1224no—
193C2×D4—1221no—
194C2×D4C22⋊D6112yes—
195C2×D4C22⋊D6111yescharacteristic, complemented
196C22×C4—21no—
197C22×C4—1221no—
198C22×C4C22×D6111yescharacteristic
199Q16—1222no—
200SD16—24no—
201SD16—1222no—
202SD16—1222no—
203D8—24no—
204D8—1222no—
205M16—21no—
206M16—1221no—
207M16—1221no—
208M16C22⋊D6112yescomplemented
209C2×C8—21no—
210C2×C8—612no—
211C4⋊C4—1221no—
212C4⋊C4—1221no—
213C22⋊C4—612no—
214C22⋊C4—1224no—
215C22⋊C4—1221no—
216C42—1221no—
217C42—1221no—
218C23—22no—
219C23—21no—
220C23—41no—
221C23—41no—
222C23—82no—
223C23—1221no—
224C23D4×D6111yescharacteristic
225Q8—21no—
226Q8—21no—
227Q8—1221no—
228Q8—1221no—
229D4—21no—
230D4—21no—
231D4—22no—
232D4—22no—
233D4—41no—
234D4—41no—
235D4—41no—
236D4—41no—
237D4—1221no—
238D4—1221no—
239D4—4884no—
240D4—2441no—
241D4—2441no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—1222no—
246C2×C4—1221no—
247C2×C4—2441no—
248C2×C4—2441no—
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—44no—
260C22—41no—
261C22—42no—
262C22—81no—
263C22—82no—
264C22—82no—
265C22—2442no—
266C22—2441no—
267C22#1451974511yescharacteristic
268C22#1451974911yescharacteristic
269C22#1451977311yescharacteristic
270C4—41no—
271C4—4881no—
272C4—2442no—
273C4—2441no—
274C4#1451974511yescharacteristic
275C4#1451974611yescharacteristic
276C4#1451974811yescharacteristic
277C4#1451974911yescharacteristic
278C2—21no—
279C2—21no—
280C2—21no—
281C2—82no—
282C2—81no—
283C2—4881no—
284C2#1683967011yescharacteristic
subgroupG/H
centerC2#16839670
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×AGL(1,ℤ/8)×C61C2
socleC2×C61#392
hypercenterC2×AGL(1,ℤ/8)D61
hypocenterC61#2008
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #16840560C2semidirect
2. #16840329C2semidirect
3. #16839778C2semidirect
4. #16839767C2semidirect
5. #16839736C2semidirect
6. #16839534C2semidirect
7. C2×AGL(1,ℤ/8)×C61C2semidirect
36. C2×Q8×C61D4semidirect
44. C2×D4×C61D4semidirect
59. M16×C61D4semidirect
74. C2×#92418D4semidirect
144. C2×AGL(1,ℤ/8)D61semidirect
150. C61#2008semidirect
184. C2×Q8C22⋊D61semidirect
195. C2×D4C22⋊D61semidirect
208. M16C22⋊D61semidirect