Finite Group Databasebeta

← #21455117

Subgroups — #21455117

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×#14519807C211yesmaximal, characteristic, complemented
3C22×Dic244C211yesmaximal, characteristic, complemented
4#16840338C211yesmaximal, characteristic, complemented
5#16839925C214yesmaximal, complemented
6#16839919C214yesmaximal, complemented
7#16839770C211yesmaximal, characteristic, complemented
8#16839728C211yesmaximal, characteristic, complemented
9C61×#416C211yesmaximal, characteristic, complemented
10#14519824—24no—
11#14519824—24no—
12C2×#11758222—21no—
13C2×#11758222C2211yescharacteristic
14C2×#11758224—22no—
15C2×#11758224C2212yes—
16C22×Dic122—21no—
17C22×Dic122C2211yescharacteristic
18C22×Dic122C2211yescharacteristic
19C2×Q8×D61C2212yes—
20#14519807—24no—
21C2×Dic244—24no—
22C2×Dic244C2214yes—
23C2×#11758202C2212yes—
24C2×#11758200C2212yes—
25C2×#11758194C2211yescharacteristic
26#14519777—21no—
27#14519765—21no—
28#14519761—22no—
29#14519757C2214yes—
30#14519700C2214yes—
31#14519689C2214yes—
32C2×#41×C61C2211yescharacteristic
33C22×C8×C61C2211yescharacteristic
34#117×C61C2211yescharacteristic
35#103×C61C2212yes—
36#102×C61C2212yes—
37#41×C61—22no—
38#41×C61D414yes—
39C2×Q8×C61C2311yescharacteristic
40C2×D4×C61—21no—
41C2×D4×C61C2311yescharacteristic
42C22×C4×C61—21no—
43C22×C4×C61C2311yescharacteristic
44C2×C22⋊D61—22no—
45C2×C22⋊D61D412yes—
46C22×Dic61—21no—
47C22×Dic61—22no—
48C22×Dic61—21no—
49Q8×D61—24no—
50Q8×D61—24no—
51#11758224—216no—
52#11758224—24no—
53#11758224—24no—
54#11758222—28no—
55#11758222—22no—
56#11758222—22no—
57C2×D244D411yescharacteristic
58C2×C4×D61—22no—
59C2×C4×D61C2312yes—
60C2×Dic122—28no—
61C2×Dic122—21no—
62C2×Dic122—22no—
63C2×Dic122—22no—
64C2×Dic122—22no—
65C2×Dic122—22no—
66C2×Dic122—21no—
67C2×Dic122D411yescharacteristic
68C2×Dic122D414yes—
69C2×Dic122C2312yes—
70C2×Dic122C2312yes—
71C2×C8×C61—22no—
72C2×C8×C61C2312yes—
73C4⋊C4×C61C2312yes—
74C22⋊C4×C61—21no—
75C42×C61—21no—
76#11758202—24no—
77#11758200—24no—
78#11758198—24no—
79C4⋊Dic61—24no—
80#11758194—22no—
81C2×#92418C2312yes—
82Dic244—28no—
83C23×C61—21no—
84C23×C61C2×D411yescharacteristic
85C22×D61C2×D412yes—
86Q8×C61—21no—
87Q8×C61C2×D412yes—
88D4×C61—24no—
89D4×C61—21no—
90D4×C61C2×D412yes—
91C2×C4×C61—21no—
92C2×C4×C61—24no—
93C2×C4×C61—22no—
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2×D412yes—
96C2×C4×C61C2×D412yes—
97C2×C4×C61C2411yescharacteristic
98C22⋊D61—28no—
99C22⋊D61—24no—
100C2×Dic61—28no—
101C2×Dic61—24no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—42no—
105C2×Dic61C2×D412yes—
106D244—22no—
107C4×D61—28no—
108C4×D61—22no—
109C4×D61—22no—
110Dic122—28no—
111Dic122—22no—
112Dic122—24no—
113Dic122—22no—
114Dic122—22no—
115Dic122—22no—
116Dic122—42no—
117Dic122C2×D414yes—
118C8×C61—22no—
119#92418—22no—
120C22×C61—22no—
121C22×C61—22no—
122C22×C61—42no—
123C22×C61#12012yes—
124C22×C61C22×D411yescharacteristic
125C2×D61—22no—
126C2×D61—24no—
127C4×C61—22no—
128C4×C61—42no—
129C4×C61#12012yes—
130C4×C61C22×D411yescharacteristic
131C4×C61C22×D411yescharacteristic
132Dic61—22no—
133Dic61—24no—
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#416D6111yescharacteristic, complemented
149#408—611no—
150C61#301111yescharacteristic, complemented, Sylow
1512−1+4—1224no—
1522−1+4—1224no—
153C2×#41—611no—
154C2×#41—612no—
155C2×#41—1221no—
156C2×#41—1222no—
157C2×#41C2×D6111yescharacteristic
158C22×Q8—612no—
159C22×Q8—611no—
160C22×Q8—611no—
161C22×Q8—1221no—
162#137—1224no—
163C2×Q16—612no—
164C2×Q16—614no—
165C2×Q16—1224no—
166C2×SD16—612no—
167C2×M16—611no—
168C22×C8C2×D6111yescharacteristic
169C4⋊Q8—1221no—
170#124—1221no—
171#123—1222no—
172C22⋊Q8—614no—
173#117C2×D6111yescharacteristic
174#103—614no—
175#103C2×D6112yes—
176#102C2×D6112yes—
177C22⋊C8—614no—
178#41—22no—
179#41—1228no—
180#41—1224no—
181#41—12216no—
182#41—1224no—
183#41—1222no—
184#41—1222no—
185#41D24414yes—
186C2×Q8—611no—
187C2×Q8—614no—
188C2×Q8—612no—
189C2×Q8—612no—
190C2×Q8—1222no—
191C2×Q8—1228no—
192C2×Q8—1224no—
193C2×Q8—1224no—
194C2×Q8—1222no—
195C2×Q8—1221no—
196C2×Q8—1221no—
197C2×Q8—1222no—
198C2×Q8—1222no—
199C2×Q8C22×D6111yescharacteristic
200C2×D4—21no—
201C2×D4—612no—
202C2×D4—611no—
203C2×D4—1222no—
204C2×D4C22×D6111yescharacteristic
205C22×C4—21no—
206C22×C4—612no—
207C22×C4—1222no—
208C22×C4—1222no—
209C22×C4—1221no—
210C22×C4—1221no—
211C22×C4C22×D6111yescharacteristic
212Q16—1228no—
213Q16—1224no—
214SD16—1224no—
215M16—1222no—
216C2×C8—22no—
217C2×C8—612no—
218C2×C8C22×D6112yes—
219C4⋊C4—1224no—
220C4⋊C4C22×D6112yes—
221C22⋊C4—21no—
222C22⋊C4—1224no—
223C42—21no—
224C23—21no—
225C23—612no—
226C23D4×D6111yescharacteristic
227Q8—21no—
228Q8—614no—
229Q8—1228no—
230Q8—1222no—
231Q8—1222no—
232Q8—1224no—
233Q8—1222no—
234Q8—1222no—
235Q8—2442no—
236Q8C2×D24412yes—
237D4—24no—
238D4—21no—
239D4—1228no—
240D4—1224no—
241D4—1222no—
242D4C2×D24412yes—
243C2×C4—21no—
244C2×C4—24no—
245C2×C4—22no—
246C2×C4—612no—
247C2×C4—1228no—
248C2×C4—1228no—
249C2×C4—1222no—
250C2×C4—1224no—
251C2×C4—1222no—
252C2×C4—1222no—
253C2×C4—1222no—
254C2×C4—2442no—
255C2×C4C2×D24412yes—
256C2×C4D4×D6112yes—
257C2×C4D4×D6111yescharacteristic
258C2×C4C23×D6111yescharacteristic
259C8—22no—
260C8—1222no—
261C22—22no—
262C22—22no—
263C22—42no—
264C22—1222no—
265C22—1224no—
266C22#1451974712yes—
267C22C2×D4×D6111yescharacteristic
268C4—22no—
269C4—42no—
270C4—1222no—
271C4—1224no—
272C4—2442no—
273C4#1451974712yes—
274C4C2×D4×D6111yescharacteristic
275C4C22×D24411yescharacteristic
276C2—22no—
277C2—42no—
278C2—2442no—
279C2C2×#1451974711yescharacteristic
280C2#1684057612yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#416C2
socleC22×C61C22×D4
hypercenter#416D61
hypocenterC61#3011
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. C2×#14519807C2semidirect
3. C22×Dic244C2semidirect
4. #16840338C2semidirect
5. #16839925C2semidirect
6. #16839919C2semidirect
7. #16839770C2semidirect
8. #16839728C2semidirect
9. C61×#416C2semidirect
148. #416D61semidirect
150. C61#3011semidirect