Finite Group Databasebeta

← #21456210

Subgroups — #21456210

Order 7808.

424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 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#16840308C211yesmaximal, characteristic
2C2×#14519776C211yesmaximal, characteristic, complemented
3#16840123C212yesmaximal, complemented
4#16840120C212yesmaximal, complemented
5#16840111C212yesmaximal, complemented
6#16840107C212yesmaximal, complemented
7#16839764C211yesmaximal, characteristic, complemented
8#16839763C211yesmaximal, characteristic, complemented
9#16839761C211yesmaximal, characteristic, complemented
10M16×Dic61C211yesmaximal, characteristic, complemented
11C61×#417C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13C22×Dic122—21no—
14C2×#11758194C2211yescharacteristic
15#14519776—21no—
16#14519776—21no—
17#14519776C2212yes—
18#14519776C2212yes—
19#14519775C2211yescharacteristic
20#14519773C2211yescharacteristic
21#14519766C2211yescharacteristic
22#14519764C2211yescharacteristic
23#14519749—21no—
24#14519749—21no—
25C4×C22⋊D61—21no—
26C4×C22⋊D61—21no—
27C2×C4⋊Dic61C2211yescharacteristic
28C2×#11758196—21no—
29C2×C4×Dic61C2211yescharacteristic
30#14519702C2212yes—
31#14519701C2212yes—
32#14519700C2212yes—
33#14519699C2212yes—
34#14519698C2212yes—
35#14519697C2212yes—
36#14519687C2212yes—
37C8×Dic61C2212yes—
38C2×#41×C61C2211yescharacteristic
39C2×M16×C61C2211yescharacteristic
40C2×C4⋊C4×C61C2211yescharacteristic
41#103×C61C2212yes—
42#102×C61C2212yes—
43#41×C61—22no—
44#41×C61—22no—
45C2×Q8×C61C2311yescharacteristic
46C2×D4×C61—21no—
47C2×D4×C61C2311yescharacteristic
48C22×C4×C61—21no—
49C22×C4×C61—21no—
50C22×C4×C61C2311yescharacteristic
51C2×C22⋊D61—21no—
52C2×C22⋊D61—21no—
53C2×C22⋊D61—21no—
54C22×Dic61—21no—
55C22×Dic61D411yescharacteristic
56C22×Dic61D411yescharacteristic
57#11758222—22no—
58#11758222—22no—
59C2×D244C2311yescharacteristic
60C2×C4×D61—21no—
61C2×Dic122—22no—
62C2×Dic122—22no—
63C2×Dic122—44no—
64C2×Dic122C2311yescharacteristic
65M16×C61—22no—
66C2×C8×C61C2312yes—
67C4⋊C4×C61—21no—
68C4⋊C4×C61C2312yes—
69C22⋊Dic61—21no—
70C22⋊Dic61—21no—
71#11758198—21no—
72#11758198—21no—
73C4⋊Dic61—21no—
74C4⋊Dic61C2312yes—
75#11758196—22no—
76#11758196—22no—
77#11758196—21no—
78#11758196—21no—
79C4×Dic61D411yescharacteristic
80C4×Dic61D411yescharacteristic
81C4×Dic61C2311yescharacteristic
82C4×Dic61C2311yescharacteristic
83#11758194—22no—
84C2×#92418C2312yes—
85C23×C61—21no—
86C23×C61C2×D411yescharacteristic
87C22×D61—21no—
88Q8×C61—21no—
89Q8×C61—21no—
90D4×C61—21no—
91D4×C61—21no—
92D4×C61—42no—
93C2×C4×C61—21no—
94C2×C4×C61—22no—
95C2×C4×C61—42no—
96C2×C4×C61—42no—
97C2×C4×C61C2×D411yescharacteristic
98C2×C4×C61#4112yes—
99C2×C4×C61#4112yes—
100C2×C4×C61C2411yescharacteristic
101C22⋊D61—42no—
102C22⋊D61—42no—
103C22⋊D61—42no—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—21no—
108C2×Dic61—42no—
109C2×Dic61C2×D411yescharacteristic
110C2×Dic61C2×D411yescharacteristic
111C2×Dic61C2×D411yescharacteristic
112C2×Dic61C2×D411yescharacteristic
113D244—21no—
114D244—21no—
115C4×D61—42no—
116Dic122—21no—
117Dic122—21no—
118Dic122—44no—
119Dic122—44no—
120C8×C61—22no—
121#92418—22no—
122C22×C61—21no—
123C22×C61—21no—
124C22×C61—41no—
125C22×C61—41no—
126C22×C61—41no—
127C22×C61#12412yes—
128C22×C61C22×D411yescharacteristic
129C2×D61—41no—
130C2×D61—41no—
131C2×D61—41no—
132C4×C61—41no—
133C4×C61—42no—
134C4×C61#12412yes—
135C4×C61C2×#4111yescharacteristic
136C4×C61C2×#4111yescharacteristic
137Dic61—21no—
138Dic61—21no—
139Dic61—41no—
140Dic61—42no—
141Dic61AGL(1,ℤ/8)12yes—
142Dic61#13712yes—
143#3141—611nomaximal, Sylow
144C2×C61—22no—
145C2×C61—81no—
146C2×C61C2×#12411yescharacteristic
147C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
148C2×C61C2×#13711yescharacteristic
149D61—81no—
150#532—611no—
151C2×C4⋊Q8—611no—
152#489—612no—
153#489—612no—
154#487—612no—
155#486—612no—
156#417—611no—
157#417—611no—
158#417—611no—
159#417D6111yescharacteristic, complemented
160C4×M16—611no—
161C61#314111yescharacteristic, complemented, Sylow
162C2×#41—611no—
163C2×#41C2×D6111yescharacteristic
164C22×Q8—1221no—
165C2×M16—611no—
166C2×M16C2×D6111yescharacteristic
167C4⋊Q8—612no—
168C4⋊Q8—612no—
169C4⋊Q8—611no—
170C4⋊Q8—1221no—
171C4⋊Q8—1221no—
172#127—611no—
173#124—611no—
174#124—611no—
175#121—1221no—
176#121—1221no—
177C4×D4—1221no—
178C4×D4—1221no—
179C2×C4⋊C4—611no—
180C2×C4⋊C4—1221no—
181C2×C4⋊C4C2×D6111yescharacteristic
182C2×C42—611no—
183#103—612no—
184#103—612no—
185#103—612no—
186#103C2×D6112yes—
187#102—612no—
188#102—612no—
189#102—612no—
190#102C2×D6112yes—
191#97—612no—
192C4×C8—612no—
193#41—22no—
194#41—22no—
195#41—1222no—
196#41—1222no—
197C2×Q8—611no—
198C2×Q8—1222no—
199C2×Q8—1222no—
200C2×Q8—2444no—
201C2×Q8C22×D6111yescharacteristic
202C2×D4—21no—
203C2×D4—611no—
204C2×D4—1221no—
205C2×D4—1221no—
206C2×D4—1221no—
207C2×D4C22×D6111yescharacteristic
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—611no—
211C22×C4—611no—
212C22×C4—1221no—
213C22×C4—1221no—
214C22×C4C22×D6111yescharacteristic
215M16—22no—
216M16—1222no—
217C2×C8—612no—
218C2×C8C22×D6112yes—
219C4⋊C4—21no—
220C4⋊C4—612no—
221C4⋊C4—1222no—
222C4⋊C4—1222no—
223C4⋊C4—1221no—
224C4⋊C4—1221no—
225C4⋊C4—1221no—
226C4⋊C4C22×D6112yes—
227C22⋊C4—1221no—
228C22⋊C4—1221no—
229C22⋊C4—1221no—
230C22⋊C4—1221no—
231C42—611no—
232C42—611no—
233C42—611no—
234C42—611no—
235C23—21no—
236C23—1221no—
237C23D4×D6111yescharacteristic
238Q8—21no—
239Q8—21no—
240Q8—1221no—
241Q8—1221no—
242Q8—2444no—
243Q8—2444no—
244D4—21no—
245D4—21no—
246D4—42no—
247D4—1221no—
248D4—1221no—
249D4—2442no—
250D4—2442no—
251D4—2442no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—611no—
257C2×C4—611no—
258C2×C4—611no—
259C2×C4—611no—
260C2×C4—1222no—
261C2×C4—1222no—
262C2×C4—1221no—
263C2×C4—1222no—
264C2×C4—2442no—
265C2×C4—2442no—
266C2×C4#1175822212yes—
267C2×C4D4×D6111yescharacteristic
268C2×C4#1175822412yes—
269C2×C4C23×D6111yescharacteristic
270C8—22no—
271C8—1222no—
272C22—21no—
273C22—21no—
274C22—41no—
275C22—41no—
276C22—41no—
277C22—2441no—
278C22—2441no—
279C22—2441no—
280C22#1451976312yes—
281C22C2×D4×D6111yescharacteristic
282C4—41no—
283C4—42no—
284C4—612no—
285C4—612no—
286C4—1221no—
287C4—1221no—
288C4—2441no—
289C4—2442no—
290C4#1451976312yes—
291C4C2×#1175822411yescharacteristic
292C4C2×#1175822211yescharacteristic
293C2—22no—
294C2—81no—
295C2—4881no—
296C2C2×#1451976311yescharacteristic
297C2AGL(1,ℤ/8)×D6111yescharacteristic
298C2#137×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#417C2
socleC22×C61C22×D4
hypercenter#417D61
hypocenterC61#3141
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. C2×#14519776C2semidirect
3. #16840123C2semidirect
4. #16840120C2semidirect
5. #16840111C2semidirect
6. #16840107C2semidirect
7. #16839764C2semidirect
8. #16839763C2semidirect
9. #16839761C2semidirect
10. M16×Dic61C2semidirect
11. C61×#417C2semidirect
159. #417D61semidirect
161. C61#3141semidirect