Finite Group Databasebeta

← #21446874

Subgroups — #21446874

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#16840562C211yesmaximal, characteristic, complemented
2C2×#14519803C211yesmaximal, characteristic, complemented
3#16840329C211yesmaximal, characteristic, complemented
4#16839780C211yesmaximal, characteristic, complemented
5#16839735C211yesmaximal, characteristic, complemented
6#16839533C211yesmaximal, characteristic, complemented
7C61×#418C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C2×#11758222C2211yescharacteristic
10#14519810—21no—
11#14519810—21no—
12#14519805—21no—
13#14519805—21no—
14#14519803—22no—
15#14519803—22no—
16#14519799—22no—
17C2×#11758200—21no—
18C2×#11758199—21no—
19C2×#11758194C2211yescharacteristic
20#14519773—21no—
21#14519764—21no—
22#14519748—22no—
23#14519746—22no—
24#14519736C2211yescharacteristic
25#14519705—22no—
26#14519691—22no—
27C22×D4×C61C2211yescharacteristic
28C2×M16×C61C2211yescharacteristic
29#117×C61C2211yescharacteristic
30#102×C61—22no—
31C24×C61—21no—
32C2×D4×C61—21no—
33C2×D4×C61—21no—
34C2×D4×C61—21no—
35C2×D4×C61—21no—
36C2×D4×C61—21no—
37C2×D4×C61D412yes—
38C22×C4×C61C2311yescharacteristic
39C2×C22⋊D61—21no—
40C2×C22⋊D61—21no—
41C2×C22⋊D61—24no—
42#11758222—21no—
43#11758222—21no—
44#11758222—21no—
45#11758222—21no—
46#11758222—21no—
47#11758222—21no—
48#11758222—21no—
49#11758222—21no—
50C2×D244D411yescharacteristic
51C2×D244D411yescharacteristic, complemented
52C2×C4×D61—21no—
53C2×C4×D61—21no—
54C2×Dic122D411yescharacteristic
55C2×Dic122D411yescharacteristic, complemented
56M16×C61—21no—
57M16×C61—21no—
58C2×C8×C61D412yescomplemented
59C4⋊C4×C61—21no—
60C22⋊C4×C61—21no—
61C42×C61—21no—
62C22⋊Dic61—24no—
63C22⋊Dic61D412yes—
64#11758200—24no—
65#11758199—24no—
66C4⋊Dic61—21no—
67C4×Dic61—21no—
68#11758194—21no—
69#11758194D412yescomplemented
70C2×#92418—21no—
71Dic244—22no—
72D488—22no—
73#11758190—22no—
74#11758190—22no—
75C23×C61—22no—
76C23×C61—41no—
77C23×C61—41no—
78C23×C61—82no—
79C23×C61C2×D411yescharacteristic
80C22×D61—21no—
81C22×D61—21no—
82D4×C61—22no—
83D4×C61—22no—
84D4×C61—41no—
85D4×C61—41no—
86C2×C4×C61—41no—
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61#4111yescharacteristic
93C22⋊D61—41no—
94C22⋊D61—41no—
95C22⋊D61—41no—
96C22⋊D61—41no—
97C22⋊D61—84no—
98C2×Dic61—22no—
99C2×Dic61—21no—
100C2×Dic61—21no—
101D244—21no—
102D244—21no—
103D244—21no—
104D244—21no—
105C4×D61—41no—
106C4×D61—41no—
107C4×D61—41no—
108C4×D61—41no—
109Dic122—21no—
110Dic122—21no—
111Dic122—21no—
112Dic122—21no—
113C8×C61—22no—
114#92418—22no—
115C22×C61—41no—
116C22×C61—44no—
117C22×C61—42no—
118C22×C61—82no—
119C22×C61—82no—
120C22×C61#12011yescharacteristic
121C22×C61#12111yescharacteristic
122C22×C61#12711yescharacteristic
123C2×D61—42no—
124C2×D61—41no—
125C2×D61—41no—
126C2×D61—81no—
127C4×C61—81no—
128C4×C61#12011yescharacteristic
129C4×C61#12011yescharacteristic
130C4×C61#12111yescharacteristic
131C4×C61#12111yescharacteristic
132Dic61—42no—
133Dic61—41no—
134Dic61—41no—
135#2008—611nomaximal, Sylow
136C2×C61—21no—
137C2×C61—21no—
138C2×C61—21no—
139C2×C61—82no—
140C2×C61#39211yescharacteristic
141D61—81no—
142D61—81no—
143#575—611no—
144C2×AGL(1,ℤ/8)—611no—
145#535—611no—
146#421—611no—
147#418D6111yescharacteristic, complemented
148#410—611no—
149#344—611no—
150C61#200811yescharacteristic, complemented, Sylow
151C2×#41—611no—
152C2×#41—611no—
153C22×D4C2×D6111yescharacteristic
154#137—1221no—
155#137—1221no—
156AGL(1,ℤ/8)—1221no—
157AGL(1,ℤ/8)—1221no—
158AGL(1,ℤ/8)—1222no—
159AGL(1,ℤ/8)—1222no—
160#135—1222no—
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#117C2×D6111yescharacteristic
171#104—1222no—
172#102—22no—
173#99—1222no—
174C24—21no—
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—21no—
186C2×D4—21no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—21no—
190C2×D4—611no—
191C2×D4—611no—
192C2×D4—1224no—
193C2×D4—1221no—
194C2×D4—1221no—
195C2×D4D24412yes—
196C22×C4—1221no—
197C22×C4—1221no—
198C22×C4C22×D6111yescharacteristic
199Q16—1222no—
200SD16—1222no—
201SD16—1222no—
202SD16—1224no—
203D8—1222no—
204D8—1224no—
205M16—21no—
206M16—21no—
207M16—612no—
208M16—1221no—
209C2×C8—1221no—
210C2×C8C22⋊D6112yescomplemented
211C4⋊C4—21no—
212C4⋊C4—1221no—
213C22⋊C4—21no—
214C22⋊C4—612no—
215C22⋊C4—1224no—
216C42—21no—
217C42—1221no—
218C23—22no—
219C23—41no—
220C23—41no—
221C23—82no—
222C23—1221no—
223C23—1221no—
224C23D4×D6111yescharacteristic
225Q8—1221no—
226Q8—1221no—
227Q8—1221no—
228Q8—1221no—
229D4—22no—
230D4—22no—
231D4—41no—
232D4—41no—
233D4—1221no—
234D4—1221no—
235D4—1221no—
236D4—1221no—
237D4—4884no—
238D4—2441no—
239D4—2441no—
240D4—2441no—
241D4—2441no—
242C2×C4—41no—
243C2×C4—1222no—
244C2×C4—1221no—
245C2×C4—1221no—
246C2×C4—2441no—
247C2×C4—2441no—
248C2×C4—2441no—
249C2×C4—2441no—
250C2×C4C2×D24411yescharacteristic
251C2×C4#1175822211yescharacteristic
252C2×C4D4×D6111yescharacteristic
253C2×C4D4×D6111yescharacteristic
254C2×C4D4×D6111yescharacteristic
255C2×C4C2×C22⋊D6111yescharacteristic
256C8—22no—
257C8—1222no—
258C22—41no—
259C22—44no—
260C22—42no—
261C22—82no—
262C22—82no—
263C22—4881no—
264C22—2442no—
265C22—2441no—
266C22—2441no—
267C22#1451974711yescharacteristic
268C22#1451975011yescharacteristic
269C22#1451977311yescharacteristic
270C4—81no—
271C4—2442no—
272C4—2441no—
273C4—2441no—
274C4#1451974511yescharacteristic
275C4#1451974711yescharacteristic
276C4#1451975011yescharacteristic
277C4#1451975111yescharacteristic
278C2—21no—
279C2—21no—
280C2—21no—
281C2—82no—
282C2—4881no—
283C2—4881no—
284C2#1683967111yescharacteristic
subgroupG/H
centerC2#16839671
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#418C2
socleC2×C61#392
hypercenter#418D61
hypocenterC61#2008
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #16840562C2semidirect
2. C2×#14519803C2semidirect
3. #16840329C2semidirect
4. #16839780C2semidirect
5. #16839735C2semidirect
6. #16839533C2semidirect
7. C61×#418C2semidirect
51. C2×D244D4semidirect
55. C2×Dic122D4semidirect
58. C2×C8×C61D4semidirect
69. #11758194D4semidirect
147. #418D61semidirect
150. C61#2008semidirect
210. C2×C8C22⋊D61semidirect