Finite Group Databasebeta

← #21452549

Subgroups — #21452549

Order 7808.

612 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 137 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×#14519773C211yesmaximal, characteristic
2C2×#14519758C211yesmaximal, characteristic, complemented
3#16839680C212yesmaximal, complemented
4#16839678C212yesmaximal, complemented
5#16839678C212yesmaximal, complemented
6#16839647C212yesmaximal, complemented
7#16839641C212yesmaximal, complemented
8#16839639C212yesmaximal, complemented
9C61×#386C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11C22×C22⋊D61C2212yes—
12C22×C22⋊D61C2212yes—
13C23×Dic61C2211yescharacteristic
14#14519773—24no—
15#14519758—24no—
16C2×C4⋊Dic61C2212yes—
17C2×#11758196C2212yes—
18C2×C22⋊Dic61C2212yes—
19C2×C22⋊Dic61C2211yescharacteristic
20C2×#11758198C2212yes—
21C2×#11758198C2212yes—
22C2×#11758198C2212yes—
23C2×#11758198C2212yes—
24C2×C4×Dic61C2211yescharacteristic
25#14519684C2212yes—
26#14519684C2212yes—
27#14519684C2212yes—
28C22×D4×C61C2211yescharacteristic
29C23×C4×C61C2211yescharacteristic
30C2×C22⋊C4×C61C2212yes—
31C2×C22⋊C4×C61C2211yescharacteristic
32#95×C61C2212yes—
33C24×C61C2311yescharacteristic
34C24×C61C2311yescharacteristic
35C23×D61C2312yes—
36C2×D4×C61—41no—
37C2×D4×C61—41no—
38C2×D4×C61D414yes—
39C22×C4×C61—41no—
40C22×C4×C61—42no—
41C22×C4×C61C2312yes—
42C22×C4×C61C2312yes—
43C22×C4×C61C2311yescharacteristic
44C2×C22⋊D61—24no—
45C2×C22⋊D61—24no—
46C2×C22⋊D61—24no—
47C2×C22⋊D61—24no—
48C2×C22⋊D61—42no—
49C2×C22⋊D61—42no—
50C22×Dic61—22no—
51C22×Dic61—41no—
52C22×Dic61—41no—
53C22×Dic61C2312yes—
54C22×Dic61C2312yes—
55C22×Dic61C2312yes—
56C2×D244—22no—
57C2×D244—41no—
58C2×D244—41no—
59C22⋊C4×C61—41no—
60C22⋊C4×C61—42no—
61C22⋊Dic61—22no—
62C22⋊Dic61—24no—
63#11758198—42no—
64#11758198—42no—
65#11758198—42no—
66#11758198—42no—
67C4⋊Dic61—24no—
68#11758196—24no—
69C4×Dic61—22no—
70C23×C61—22no—
71C23×C61—22no—
72C23×C61—22no—
73C23×C61—21no—
74C23×C61—21no—
75C23×C61—21no—
76C23×C61—22no—
77C23×C61—21no—
78C23×C61C2×D412yes—
79C23×C61C2×D412yes—
80C23×C61C2411yescharacteristic
81C22×D61—22no—
82C22×D61—22no—
83C22×D61—22no—
84C22×D61—22no—
85C22×D61—22no—
86C22×D61—22no—
87C22×D61—22no—
88D4×C61—44no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61—22no—
97C2×C4×C61—44no—
98C2×C4×C61C2×D412yes—
99C22⋊D61—48no—
100C22⋊D61—48no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—22no—
108C2×Dic61—22no—
109C2×Dic61—44no—
110C2×Dic61#4114yes—
111D244—44no—
112C22×C61—22no—
113C22×C61—22no—
114C22×C61—24no—
115C22×C61—24no—
116C22×C61—42no—
117C22×C61—42no—
118C22×C61—41no—
119C22×C61—41no—
120C22×C61—41no—
121C22×C61—41no—
122C22×C61C22×D411yescharacteristic
123C22×C61C2×#4112yes—
124C22×C61H(5,𝔽2)11yescharacteristic
125C22×C61H(5,𝔽2)11yescharacteristic
126C22×C61H(5,𝔽2)12yes—
127C2×D61—42no—
128C2×D61—42no—
129C2×D61—42no—
130C2×D61—42no—
131C2×D61—42no—
132C2×D61—42no—
133C2×D61—42no—
134C4×C61—22no—
135C4×C61—42no—
136C4×C61—42no—
137Dic61—24no—
138Dic61—42no—
139Dic61—42no—
140#2709—611nomaximal, Sylow
141C2×C61—42no—
142C2×C61—42no—
143C2×C61#53411yescharacteristic
144C2×C61#54012yes—
145C2×C61#54612yes—
146C2×C61#55911yescharacteristic
147C2×C61#56011yescharacteristic
148D61—82no—
149C2×#127—611no—
150C2×#123—611no—
151#394—612no—
152#394—612no—
153#394—612no—
154#387—612no—
155#386—612no—
156#386—612no—
157#386D6111yescharacteristic, complemented
158C61#270911yescharacteristic, complemented, Sylow
159C22×D4—612no—
160C22×D4—612no—
161C22×D4—611no—
162C22×D4C2×D6111yescharacteristic
163C23×C4—611no—
164C23×C4C2×D6111yescharacteristic
165#127—1224no—
166#123—1224no—
167C2×C4⋊C4—612no—
168C2×C4⋊C4—612no—
169C2×C22⋊C4—612no—
170C2×C22⋊C4—611no—
171C2×C22⋊C4—612no—
172C2×C22⋊C4—612no—
173C2×C22⋊C4—612no—
174C2×C22⋊C4—612no—
175C2×C22⋊C4C2×D6112yes—
176C2×C22⋊C4C2×D6111yescharacteristic
177C2×C42—611no—
178#95—612no—
179#95—612no—
180#95—612no—
181#95C2×D6112yes—
182C24—612no—
183C24C22×D6111yescharacteristic
184C24C22×D6111yescharacteristic
185C2×D4—41no—
186C2×D4—41no—
187C2×D4—1224no—
188C2×D4—1224no—
189C2×D4—1224no—
190C2×D4—1224no—
191C2×D4—1222no—
192C2×D4—2441no—
193C2×D4—2441no—
194C2×D4—2442no—
195C2×D4—2442no—
196C2×D4D24414yes—
197C22×C4—42no—
198C22×C4—41no—
199C22×C4—612no—
200C22×C4—612no—
201C22×C4—612no—
202C22×C4—1222no—
203C22×C4—2441no—
204C22×C4—2441no—
205C22×C4C22×D6112yes—
206C22×C4C22×D6112yes—
207C22×C4C22×D6111yescharacteristic
208C4⋊C4—1224no—
209C4⋊C4—1224no—
210C22⋊C4—41no—
211C22⋊C4—42no—
212C22⋊C4—1222no—
213C22⋊C4—1224no—
214C22⋊C4—2442no—
215C22⋊C4—2442no—
216C22⋊C4—2442no—
217C22⋊C4—2442no—
218C42—1222no—
219C23—22no—
220C23—22no—
221C23—21no—
222C23—22no—
223C23—21no—
224C23—22no—
225C23—21no—
226C23—21no—
227C23—1222no—
228C23—1222no—
229C23—1222no—
230C23—1222no—
231C23—1222no—
232C23—1222no—
233C23—1222no—
234C23C2×D24412yes—
235C23C2×D24412yes—
236C23C23×D6111yescharacteristic
237D4—44no—
238D4—2444no—
239D4—2448no—
240D4—2448no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—44no—
250C2×C4—614no—
251C2×C4—1222no—
252C2×C4—1222no—
253C2×C4—1222no—
254C2×C4—1222no—
255C2×C4—1222no—
256C2×C4—1222no—
257C2×C4—1222no—
258C2×C4—1222no—
259C2×C4—2444no—
260C2×C4C2×D24412yes—
261C22—22no—
262C22—22no—
263C22—24no—
264C22—24no—
265C22—41no—
266C22—41no—
267C22—41no—
268C22—41no—
269C22—42no—
270C22—42no—
271C22—2442no—
272C22—2442no—
273C22—2442no—
274C22—2442no—
275C22—2442no—
276C22—2442no—
277C22—2442no—
278C22C22×D24411yescharacteristic
279C22#41×D6112yes—
280C22#1451982211yescharacteristic
281C22#1451982212yes—
282C22#1451982211yescharacteristic
283C4—22no—
284C4—42no—
285C4—42no—
286C4—1224no—
287C4—2442no—
288C4—2442no—
289C2—42no—
290C2—42no—
291C2—4882no—
292C2#1684032411yescharacteristic
293C2#1684036212yes—
294C2#1684040712yes—
295C2#1684049611yescharacteristic
296C2#1684050111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#386C2
hypercenter#386D61
hypocenterC61#2709
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×#14519758C2semidirect
3. #16839680C2semidirect
4. #16839678C2semidirect
5. #16839678C2semidirect
6. #16839647C2semidirect
7. #16839641C2semidirect
8. #16839639C2semidirect
9. C61×#386C2semidirect
157. #386D61semidirect
158. C61#2709semidirect