Finite Group Databasebeta

← #21451614

Subgroups — #21451614

Order 7808.

548 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14519750C211yesmaximal, characteristic
2C2×#14519735C211yesmaximal, characteristic, complemented
3#16839699C211yesmaximal, characteristic, complemented
4#16839698C211yesmaximal, characteristic, complemented
5#16839688C211yesmaximal, characteristic, complemented
6#16839680C212yesmaximal, complemented
7#16839678C212yesmaximal, complemented
8#16839662C212yesmaximal, complemented
9#16839659C212yesmaximal, complemented
10#16839621C211yesmaximal, characteristic, complemented
11C61×#397C211yesmaximal, characteristic, complemented
12C22×D244C2211yescharacteristic
13C22×C22⋊D61C2211yescharacteristic
14C22×C22⋊D61C2211yescharacteristic
15C22×C4×D61C2211yescharacteristic
16#14519750—24no—
17#14519735—24no—
18C2×C4⋊Dic61C2211yescharacteristic
19C2×C4⋊Dic61C2212yes—
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2212yes—
22C2×#11758196C2212yes—
23C2×C22⋊Dic61C2212yes—
24C2×#11758198C2212yes—
25C2×#11758198C2211yescharacteristic
26C2×#11758198C2212yes—
27C2×#11758198C2212yes—
28C2×#11758198C2212yes—
29C2×C4×Dic61C2212yes—
30#14519684C2211yescharacteristic
31#14519684C2212yes—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C22⋊C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2212yes—
35#95×C61C2212yes—
36#95×C61C2211yescharacteristic
37C24×C61C2311yescharacteristic
38C23×D61C2311yescharacteristic
39C23×D61C2311yescharacteristic
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2312yes—
42C22×C4×C61C2312yes—
43C22×C4×C61C2311yescharacteristic
44C2×C22⋊D61—22no—
45C2×C22⋊D61—22no—
46C2×C22⋊D61—24no—
47C2×C22⋊D61—42no—
48C22×Dic61C2311yescharacteristic
49C22×Dic61C2312yes—
50C22×Dic61C2312yes—
51C22×Dic61C2311yescharacteristic
52C2×D244—22no—
53C2×D244—42no—
54C2×C4×D61—24no—
55C2×C4×D61D414yes—
56C4⋊C4×C61—22no—
57C22⋊C4×C61—22no—
58C22⋊C4×C61—42no—
59C22⋊Dic61—42no—
60#11758198—24no—
61#11758198—22no—
62#11758198—42no—
63#11758198—42no—
64#11758198—42no—
65C4⋊Dic61—22no—
66C4⋊Dic61—42no—
67#11758196—22no—
68#11758196—24no—
69#11758196—42no—
70C4×Dic61—24no—
71C23×C61—21no—
72C23×C61—22no—
73C23×C61—22no—
74C23×C61—21no—
75C23×C61—21no—
76C23×C61C2411yescharacteristic
77C22×D61—22no—
78C22×D61—21no—
79C22×D61—22no—
80C22×D61—21no—
81C22×D61—21no—
82C22×D61—22no—
83C22×D61—21no—
84C22×D61—22no—
85C22×D61—21no—
86C22×D61C2×D412yes—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—21no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61C2×D412yes—
97C22⋊D61—44no—
98C22⋊D61—44no—
99C2×Dic61—22no—
100C2×Dic61—21no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61C2×D412yes—
108C2×Dic61#4114yes—
109D244—44no—
110C4×D61—28no—
111C22×C61—41no—
112C22×C61—41no—
113C22×C61—41no—
114C22×C61—42no—
115C22×C61—42no—
116C22×C61C22×D411yescharacteristic
117C22×C61C2×#4112yes—
118C22×C61H(5,𝔽2)11yescharacteristic
119C22×C61H(5,𝔽2)12yes—
120C22×C612−1+411yescharacteristic
121C2×D61—22no—
122C2×D61—22no—
123C2×D61—22no—
124C2×D61—42no—
125C2×D61—42no—
126C2×D61—41no—
127C2×D61—41no—
128C2×D61—41no—
129C2×D61—42no—
130C2×D61—42no—
131C4×C61—22no—
132C4×C61—41no—
133C4×C61—42no—
134C4×C61—42no—
135Dic61—42no—
136Dic61—41no—
137Dic61—42no—
138Dic61#12314yes—
139#2624—611nomaximal, Sylow
140C2×C61—81no—
141C2×C61C2×#12311yescharacteristic
142C2×C61#53511yescharacteristic
143C2×C61#53711yescharacteristic
144C2×C61#54012yes—
145C2×C61#54212yes—
146D61—42no—
147D61—81no—
148C2×#121—611no—
149C2×#117—611no—
150#399—611no—
151#399—611no—
152#397—611no—
153#397D6111yescharacteristic, complemented
154#394—612no—
155#394—612no—
156#390—612no—
157#389—612no—
158#380—611no—
159C61#262411yescharacteristic, complemented, Sylow
160C22×D4—611no—
161C22×D4—611no—
162C22×D4—611no—
163C23×C4—611no—
164#121—1224no—
165#117—1224no—
166C2×C4⋊C4—611no—
167C2×C4⋊C4—611no—
168C2×C4⋊C4—612no—
169C2×C4⋊C4—612no—
170C2×C4⋊C4—612no—
171C2×C4⋊C4C2×D6111yescharacteristic
172C2×C22⋊C4—612no—
173C2×C22⋊C4—611no—
174C2×C22⋊C4—612no—
175C2×C22⋊C4—612no—
176C2×C22⋊C4—612no—
177C2×C22⋊C4—612no—
178C2×C22⋊C4C2×D6111yescharacteristic
179C2×C22⋊C4C2×D6112yes—
180C2×C42—612no—
181#95—611no—
182#95—612no—
183#95C2×D6111yescharacteristic
184#95C2×D6112yes—
185C24—611no—
186C24—611no—
187C24C22×D6111yescharacteristic
188C2×D4—1222no—
189C2×D4—1222no—
190C2×D4—1224no—
191C2×D4—1222no—
192C2×D4—2442no—
193C2×D4—2442no—
194C22×C4—611no—
195C22×C4—614no—
196C22×C4—612no—
197C22×C4—611no—
198C22×C4—612no—
199C22×C4—1224no—
200C22×C4C22×D6112yes—
201C22×C4C22×D6112yes—
202C22×C4C22×D6111yescharacteristic
203C22×C4C22×D6111yescharacteristic
204C4⋊C4—22no—
205C4⋊C4—1224no—
206C4⋊C4—1222no—
207C4⋊C4—1222no—
208C4⋊C4—2442no—
209C4⋊C4—2442no—
210C22⋊C4—22no—
211C22⋊C4—42no—
212C22⋊C4—1224no—
213C22⋊C4—1222no—
214C22⋊C4—2442no—
215C22⋊C4—2442no—
216C22⋊C4—2442no—
217C22⋊C4—2442no—
218C42—1224no—
219C23—21no—
220C23—22no—
221C23—21no—
222C23—22no—
223C23—21no—
224C23—612no—
225C23—1222no—
226C23—1221no—
227C23—1222no—
228C23—1221no—
229C23—1221no—
230C23—1222no—
231C23—1221no—
232C23—1222no—
233C23—1221no—
234C23C23×D6111yescharacteristic
235D4—2444no—
236D4—2444no—
237D4—2444no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—612no—
248C2×C4—614no—
249C2×C4—1228no—
250C2×C4—1222no—
251C2×C4—1221no—
252C2×C4—1222no—
253C2×C4—1222no—
254C2×C4—1222no—
255C2×C4—1222no—
256C2×C4—1222no—
257C2×C4—1222no—
258C2×C4D4×D6112yes—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—42no—
263C22—42no—
264C22—1222no—
265C22—1222no—
266C22—1222no—
267C22—2441no—
268C22—2441no—
269C22—2441no—
270C22—2442no—
271C22—2442no—
272C22—2442no—
273C22—2442no—
274C22C2×D4×D6111yescharacteristic
275C22#41×D6112yes—
276C22#1451982211yescharacteristic
277C22#1451982312yes—
278C22#1451982411yescharacteristic
279C4—22no—
280C4—41no—
281C4—42no—
282C4—42no—
283C4—614no—
284C4—2442no—
285C4—2441no—
286C4—2442no—
287C2—81no—
288C2—4881no—
289C2—2442no—
290C2#123×D6111yescharacteristic
291C2#1684033011yescharacteristic
292C2#1684034111yescharacteristic
293C2#1684036412yes—
294C2#1684037812yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#397C2
hypercenter#397D61
hypocenterC61#2624
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. C2×#14519735C2semidirect
3. #16839699C2semidirect
4. #16839698C2semidirect
5. #16839688C2semidirect
6. #16839680C2semidirect
7. #16839678C2semidirect
8. #16839662C2semidirect
9. #16839659C2semidirect
10. #16839621C2semidirect
11. C61×#397C2semidirect
153. #397D61semidirect
159. C61#2624semidirect