Finite Group Databasebeta

← #21446871

Subgroups — #21446871

Order 7808.

380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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
2C2×#14519802C211yesmaximal, characteristic, complemented
3#16840331C211yesmaximal, characteristic, complemented
4#16839780C211yesmaximal, characteristic, complemented
5#16839766C211yesmaximal, characteristic, complemented
6#16839532C211yesmaximal, characteristic, complemented
7C61×#410C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C22×D244C2211yescharacteristic
10#14519808—21no—
11#14519807—21no—
12#14519803—21no—
13#14519802—22no—
14#14519802—21no—
15#14519802—22no—
16#14519797—22no—
17C2×#11758201—21no—
18C2×#11758199—21no—
19C2×#11758194C2211yescharacteristic
20C2×#11758194C2211yescharacteristic
21#14519774—21no—
22#14519765—21no—
23#14519752—22no—
24#14519747—22no—
25#14519705—22no—
26#14519697—22no—
27C2×#41×C61C2211yescharacteristic
28#117×C61C2211yescharacteristic
29#117×C61C2211yescharacteristic
30#99×C61—22no—
31C23×D61—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×C61D411yescharacteristic, complemented
39C22×C4×C61—21no—
40C22×C4×C61C2311yescharacteristic
41C2×C22⋊D61—21no—
42#11758222—21no—
43#11758222—21no—
44#11758222—21no—
45#11758222—21no—
46C2×D244—21no—
47C2×D244—21no—
48C2×D244—21no—
49C2×D244—21no—
50C2×D244—21no—
51C2×D244—24no—
52C2×D244D412yes—
53C2×D244D411yescharacteristic
54C2×C4×D61—21no—
55C2×Dic122D411yescharacteristic
56C4⋊C4×C61—21no—
57C4⋊C4×C61—21no—
58C22⋊C4×C61—21no—
59C22⋊C4×C61D412yes—
60C42×C61—21no—
61C42×C61—21no—
62#11758202—22no—
63#11758201—22no—
64#11758201—24no—
65#11758200—22no—
66#11758199—24no—
67#11758199—22no—
68#11758198—24no—
69#11758194—21no—
70#11758194—21no—
71#11758194—21no—
72#11758194D412yescomplemented
73C2×#92418—21no—
74C2×#92418D412yescomplemented
75C23×C61—21no—
76C23×C61C2×D411yescharacteristic
77C22×D61—22no—
78C22×D61—21no—
79C22×D61—41no—
80C22×D61—41no—
81C22×D61—82no—
82Q8×C61—21no—
83Q8×C61—21no—
84D4×C61—21no—
85D4×C61—21no—
86D4×C61—41no—
87D4×C61—41no—
88C2×C4×C61—22no—
89C2×C4×C61—21no—
90C2×C4×C61—41no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61C2×D411yescharacteristic
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61C2×D411yescharacteristic
97C2×C4×C61C2×D411yescharacteristic
98C2×C4×C61#4111yescharacteristic
99C22⋊D61—41no—
100C22⋊D61—41no—
101C2×Dic61—21no—
102D244—22no—
103D244—21no—
104D244—22no—
105D244—21no—
106D244—41no—
107D244—41no—
108D244—84no—
109C4×D61—41no—
110C4×D61—41no—
111Dic122—21no—
112Dic122—21no—
113#92418—22no—
114#92418—22no—
115C22×C61—41no—
116C22×C61—41no—
117C22×C61—81no—
118C22×C61#12011yescharacteristic
119C22×C61#12111yescharacteristic
120C22×C61#12711yescharacteristic
121C2×D61—42no—
122C2×D61—44no—
123C2×D61—41no—
124C2×D61—42no—
125C2×D61—82no—
126C2×D61—82no—
127C4×C61—42no—
128C4×C61—41no—
129C4×C61—81no—
130C4×C61#12011yescharacteristic
131C4×C61#12011yescharacteristic
132C4×C61#12111yescharacteristic
133C4×C61#12111yescharacteristic
134Dic61—41no—
135#2008—611nomaximal, Sylow
136C2×C61—21no—
137C2×C61—21no—
138C2×C61—21no—
139C2×C61—81no—
140C2×C61#39211yescharacteristic
141D61—81no—
142D61—82no—
143#575—611no—
144C2×AGL(1,ℤ/8)—611no—
145#535—611no—
146#421—611no—
147#418—611no—
148#410D6111yescharacteristic, complemented
149#344—611no—
150C61#200811yescharacteristic, complemented, Sylow
151C2×#41—611no—
152C2×#41C2×D6111yescharacteristic
153C22×D4—611no—
154#137—1221no—
155#137—1221no—
156AGL(1,ℤ/8)—1222no—
157AGL(1,ℤ/8)—1222no—
158AGL(1,ℤ/8)—1221no—
159AGL(1,ℤ/8)—1221no—
160#135—1222no—
161C2×SD16—1221no—
162C2×D8—1221no—
163C2×M16—611no—
164C2×M16—611no—
165#127—1221no—
166#124—1221no—
167#121—1222no—
168#120—1222no—
169#117C2×D6111yescharacteristic
170#117C2×D6111yescharacteristic
171#104—1222no—
172#102—1222no—
173#99—22no—
174C24—1221no—
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×Q8D24411yescharacteristic, complemented
185C2×D4—21no—
186C2×D4—612no—
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×D4D24411yescharacteristic, complemented
196C22×C4—21no—
197C22×C4—1221no—
198C22×C4C22×D6111yescharacteristic
199Q16—1222no—
200SD16—1222no—
201SD16—1224no—
202SD16—1222no—
203D8—1224no—
204D8—1222no—
205M16—612no—
206M16—1221no—
207M16—1221no—
208M16—1221no—
209C2×C8—612no—
210C2×C8—1221no—
211C4⋊C4—21no—
212C4⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—1224no—
215C22⋊C4C22⋊D6112yes—
216C42—21no—
217C42—21no—
218C23—21no—
219C23—1222no—
220C23—1221no—
221C23—4882no—
222C23—2441no—
223C23—2441no—
224C23C2×C22⋊D6111yescharacteristic
225Q8—21no—
226Q8—21no—
227Q8—1221no—
228Q8—1221no—
229D4—21no—
230D4—21no—
231D4—41no—
232D4—41no—
233D4—1222no—
234D4—1221no—
235D4—1222no—
236D4—1221no—
237D4—4884no—
238D4—2441no—
239D4—2441no—
240D4—2441no—
241D4—2441no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—1221no—
248C2×C4—2441no—
249C2×C4—2441no—
250C2×C4C2×D24411yescharacteristic
251C2×C4#1175822211yescharacteristic
252C2×C4D4×D6111yescharacteristic
253C2×C4D4×D6111yescharacteristic
254C2×C4D4×D6111yescharacteristic
255C2×C4D4×D6111yescharacteristic
256C8—1222no—
257C8—1222no—
258C22—41no—
259C22—41no—
260C22—81no—
261C22—4882no—
262C22—4882no—
263C22—2442no—
264C22—2444no—
265C22—2441no—
266C22—2442no—
267C22#1451974511yescharacteristic
268C22#1451975111yescharacteristic
269C22#1451977311yescharacteristic
270C4—42no—
271C4—41no—
272C4—81no—
273C4—2441no—
274C4#1451974711yescharacteristic
275C4#1451974711yescharacteristic
276C4#1451975011yescharacteristic
277C4#1451975011yescharacteristic
278C2—21no—
279C2—21no—
280C2—21no—
281C2—81no—
282C2—4882no—
283C2—4881no—
284C2#1683967111yescharacteristic
subgroupG/H
centerC2#16839671
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#410C2
socleC2×C61#392
hypercenter#410D61
hypocenterC61#2008
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #16840560C2semidirect
2. C2×#14519802C2semidirect
3. #16840331C2semidirect
4. #16839780C2semidirect
5. #16839766C2semidirect
6. #16839532C2semidirect
7. C61×#410C2semidirect
36. C2×Q8×C61D4semidirect
38. C2×D4×C61D4semidirect
72. #11758194D4semidirect
74. C2×#92418D4semidirect
148. #410D61semidirect
150. C61#2008semidirect
184. C2×Q8D244semidirect
195. C2×D4D244semidirect