Finite Group Databasebeta

← #21455116

Subgroups — #21455116

Order 7808.

700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14519824C211yesmaximal, characteristic
2C2×#14519810C211yesmaximal, characteristic, complemented
3C22×Dic244C211yesmaximal, characteristic, complemented
4#16840333C211yesmaximal, characteristic, complemented
5#16839926C214yesmaximal, complemented
6#16839920C214yesmaximal, complemented
7#16839772C211yesmaximal, characteristic, complemented
8#16839759C211yesmaximal, characteristic, complemented
9C61×#408C211yesmaximal, characteristic, complemented
10#14519824—24no—
11#14519824—24no—
12C2×#11758222C2212yes—
13C2×#11758222C2211yescharacteristic
14C2×#11758224—22no—
15C2×#11758224—21no—
16C22×Dic122C2211yescharacteristic
17C22×Dic122C2212yes—
18C22×Dic122C2211yescharacteristic
19C2×Q8×D61—21no—
20#14519810—24no—
21C2×Dic244—24no—
22C2×Dic244C2214yes—
23C2×Dic244C2212yes—
24C2×#11758190C2212yes—
25#14519775—21no—
26#14519764—21no—
27#14519758—22no—
28#14519756C2214yes—
29#14519736C2211yescharacteristic
30#14519702C2212yes—
31#14519702C2214yes—
32#14519699C2212yes—
33C2×#41×C61C2211yescharacteristic
34C2×M16×C61C2211yescharacteristic
35C22×C8×C61C2211yescharacteristic
36C22⋊C8×C61C2214yes—
37#41×C61—22no—
38#41×C61—22no—
39C2×Q8×C61D411yescharacteristic
40C2×D4×C61D412yes—
41C2×D4×C61D411yescharacteristic
42C22×C4×C61C2312yes—
43C22×C4×C61C2311yescharacteristic
44C2×C22⋊D61—22no—
45C2×C22⋊D61—21no—
46C22×Dic61—22no—
47C22×Dic61—21no—
48C22×Dic61—21no—
49Q8×D61—28no—
50#11758224—216no—
51#11758224—28no—
52#11758222—22no—
53#11758222—24no—
54#11758222—24no—
55#11758222D414yes—
56C2×D244C2311yescharacteristic
57C2×C4×D61—22no—
58C2×C4×D61—21no—
59C2×Dic122—22no—
60C2×Dic122—21no—
61C2×Dic122—22no—
62C2×Dic122—24no—
63C2×Dic122—24no—
64C2×Dic122—22no—
65C2×Dic122—22no—
66C2×Dic122—21no—
67C2×Dic122D414yes—
68C2×Dic122C2312yes—
69C2×Dic122C2311yescharacteristic
70C2×Dic122C2312yes—
71M16×C61—22no—
72C2×C8×C61—22no—
73C2×C8×C61C2312yes—
74C2×C8×C61C2312yes—
75C22⋊Dic61—21no—
76C22⋊Dic61—24no—
77C4⋊Dic61C2312yes—
78#11758196—24no—
79C4×Dic61—21no—
80Dic244—24no—
81Dic244—28no—
82#11758190—24no—
83C23×C61C2×D412yes—
84C23×C61C2×D411yescharacteristic
85C22×D61—21no—
86Q8×C61—22no—
87D4×C61—24no—
88D4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61C2×D412yes—
92C2×C4×C61C2×D411yescharacteristic
93C2×C4×C61C2×D412yes—
94C2×C4×C61C2×D412yes—
95C2×C4×C61C2411yescharacteristic
96C22⋊D61—28no—
97C22⋊D61—24no—
98C2×Dic61—28no—
99C2×Dic61—24no—
100C2×Dic61—21no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—42no—
105D244—21no—
106D244C2×D412yes—
107C4×D61—28no—
108C4×D61—24no—
109Dic122—28no—
110Dic122—24no—
111Dic122—22no—
112Dic122—21no—
113Dic122—22no—
114Dic122—22no—
115Dic122—42no—
116Dic122C2×D412yes—
117Dic122C2×D414yes—
118C8×C61—22no—
119C8×C61—22no—
120C22×C61—22no—
121C22×C61—22no—
122C22×C61—24no—
123C22×C61#12012yes—
124C22×C61C22×D411yescharacteristic
125C2×D61—22no—
126C2×D61—42no—
127C4×C61—22no—
128C4×C61#12012yes—
129C4×C61C22×D411yescharacteristic
130C4×C61C22×D411yescharacteristic
131Dic61—22no—
132Dic61—24no—
133Dic61—42no—
134Dic61—42no—
135#3011—611nomaximal, Sylow
136C2×C61—22no—
137C2×C61—42no—
138C2×C61C2×#12011yescharacteristic
139C2×C61#57812yes—
140D61—42no—
141C2×2−1+4—611no—
142C2×#137—611no—
143C22×Q16—611no—
144#536—611no—
145#452—614no—
146#451—614no—
147#419—611no—
148#416—611no—
149#408D6111yescharacteristic, complemented
150C61#301111yescharacteristic, complemented, Sylow
1512−1+4—1224no—
1522−1+4—1224no—
153C2×#41—611no—
154C2×#41—612no—
155C2×#41—1222no—
156C2×#41—1221no—
157C2×#41C2×D6111yescharacteristic
158C22×Q8—611no—
159C22×Q8—611no—
160C22×Q8—612no—
161C22×Q8—1221no—
162#137—1224no—
163C2×Q16—614no—
164C2×Q16—612no—
165C2×Q16—1224no—
166C2×SD16—612no—
167C2×M16C2×D6111yescharacteristic
168C22×C8C2×D6111yescharacteristic
169C4⋊Q8—1221no—
170#124—1221no—
171#123—1222no—
172C22⋊Q8—614no—
173#117—611no—
174#103—612no—
175#103—614no—
176#102—612no—
177C22⋊C8C2×D6114yes—
178#41—22no—
179#41—22no—
180#41—614no—
181#41—1224no—
182#41—1224no—
183#41—12216no—
184#41—1228no—
185#41—1222no—
186C2×Q8—614no—
187C2×Q8—612no—
188C2×Q8—611no—
189C2×Q8—612no—
190C2×Q8—1224no—
191C2×Q8—1224no—
192C2×Q8—1228no—
193C2×Q8—1222no—
194C2×Q8—1221no—
195C2×Q8—1221no—
196C2×Q8—1222no—
197C2×Q8—1222no—
198C2×Q8—1222no—
199C2×Q8D24411yescharacteristic
200C2×D4—611no—
201C2×D4—1222no—
202C2×D4—1221no—
203C2×D4D24412yes—
204C2×D4D24411yescharacteristic
205C22×C4—1222no—
206C22×C4—1221no—
207C22×C4—1222no—
208C22×C4—1221no—
209C22×C4—1221no—
210C22×C4C22×D6112yes—
211C22×C4C22×D6111yescharacteristic
212Q16—1228no—
213Q16—1224no—
214SD16—1224no—
215M16—22no—
216C2×C8—22no—
217C2×C8C22×D6112yes—
218C2×C8C22×D6112yes—
219C4⋊C4—612no—
220C4⋊C4—1224no—
221C22⋊C4—1221no—
222C22⋊C4—1224no—
223C42—1221no—
224C23—1221no—
225C23C2×D24412yes—
226C23C2×D24411yescharacteristic
227Q8—22no—
228Q8—614no—
229Q8—612no—
230Q8—1228no—
231Q8—1222no—
232Q8—1221no—
233Q8—1224no—
234Q8—1222no—
235Q8—1222no—
236Q8—2442no—
237D4—24no—
238D4—22no—
239D4—612no—
240D4—1228no—
241D4—1224no—
242D4—1221no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—1228no—
246C2×C4—1228no—
247C2×C4—1222no—
248C2×C4—1221no—
249C2×C4—1224no—
250C2×C4—1224no—
251C2×C4—1222no—
252C2×C4—1222no—
253C2×C4—2442no—
254C2×C4C2×D24412yes—
255C2×C4C2×D24411yescharacteristic
256C2×C4D4×D6112yes—
257C2×C4D4×D6112yes—
258C2×C4C23×D6111yescharacteristic
259C8—22no—
260C8—22no—
261C22—22no—
262C22—22no—
263C22—24no—
264C22—1222no—
265C22—2442no—
266C22#1451974712yes—
267C22C22×D24411yescharacteristic
268C4—22no—
269C4—1224no—
270C4—1222no—
271C4—2442no—
272C4—2442no—
273C4#1451974712yes—
274C4C2×D4×D6111yescharacteristic
275C4C2×D4×D6111yescharacteristic
276C2—22no—
277C2—42no—
278C2—2442no—
279C2C2×#1451974711yescharacteristic
280C2#1684057912yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#408C2
socleC22×C61C22×D4
hypercenter#408D61
hypocenterC61#3011
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
2. C2×#14519810C2semidirect
3. C22×Dic244C2semidirect
4. #16840333C2semidirect
5. #16839926C2semidirect
6. #16839920C2semidirect
7. #16839772C2semidirect
8. #16839759C2semidirect
9. C61×#408C2semidirect
149. #408D61semidirect
150. C61#3011semidirect