Finite Group Databasebeta

← #21455365

Subgroups — #21455365

Order 7808.

472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14519808C211yesmaximal, characteristic, complemented
2C2×#14519797C211yesmaximal, characteristic
3#16840242C211yesmaximal, characteristic, complemented
4#16839981C212yesmaximal, complemented
5#16839974C212yesmaximal, complemented
6#16839969C212yesmaximal, complemented
7#16839964C212yesmaximal, complemented
8#16839789C211yesmaximal, characteristic, complemented
9#16839763C211yesmaximal, characteristic, complemented
10C2×#14519701C211yesmaximal, characteristic, complemented
11C61×#536C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13#14519808—24no—
14#14519797—24no—
15C2×#11758202C2211yescharacteristic
16C2×#11758202C2212yes—
17C2×#11758200C2211yescharacteristic
18C2×#11758201C2211yescharacteristic
19C2×#11758201C2212yes—
20C2×#11758199C2211yescharacteristic
21C2×#11758194C2211yescharacteristic
22C22×#92418C2211yescharacteristic
23C4×Dic122C2212yes—
24C4×D244C2212yes—
25#14519737—22no—
26#14519735—21no—
27C2×C4⋊Dic61C2211yescharacteristic
28C4⋊C4×D61—21no—
29C4⋊#92418C2212yes—
30C4⋊#92418C2212yes—
31#14519701C2212yes—
32#14519701C2212yes—
33#14519701C2212yes—
34#14519698C2212yes—
35C2×#41×C61C2211yescharacteristic
36C22×Q8×C61C2211yescharacteristic
37C4⋊Q8×C61C2212yes—
38#124×C61C2212yes—
39#123×C61—22no—
40C22⋊Q8×C61—21no—
41C22⋊Q8×C61—21no—
42#117×C61C2211yescharacteristic
43#41×C61—22no—
44#41×C61—22no—
45C2×Q8×C61—21no—
46C2×Q8×C61—22no—
47C2×Q8×C61—22no—
48C2×Q8×C61C2312yes—
49C2×Q8×C61C2311yescharacteristic
50C2×D4×C61—21no—
51C2×D4×C61C2311yescharacteristic
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61C2311yescharacteristic
55C2×C22⋊D61—21no—
56C22×Dic61—21no—
57#11758222—22no—
58#11758222D414yes—
59C2×D244C2311yescharacteristic
60C2×C4×D61—21no—
61C2×C4×D61—22no—
62C2×Dic122C2311yescharacteristic
63C4⋊C4×C61—22no—
64C4⋊C4×C61—22no—
65C4⋊C4×C61D411yescharacteristic
66C4⋊C4×C61D411yescharacteristic
67C22⋊C4×C61—22no—
68C22⋊C4×C61—22no—
69C22⋊C4×C61D412yes—
70C42×C61C2312yes—
71#11758202—24no—
72#11758202—22no—
73#11758201—24no—
74#11758201—22no—
75#11758200—22no—
76#11758199—22no—
77#11758198—22no—
78C4⋊Dic61—21no—
79C4⋊Dic61C2312yes—
80#11758196—22no—
81C4×Dic61—22no—
82#11758194—22no—
83C2×#92418—22no—
84C2×#92418C2312yes—
85C2×#92418C2311yescharacteristic
86C2×#92418C2311yescharacteristic
87C23×C61—21no—
88C23×C61C2×D411yescharacteristic
89C22×D61—21no—
90Q8×C61—22no—
91Q8×C61—21no—
92Q8×C61—22no—
93Q8×C61—21no—
94Q8×C61—42no—
95D4×C61—21no—
96D4×C61—21no—
97D4×C61—42no—
98C2×C4×C61—22no—
99C2×C4×C61—21no—
100C2×C4×C61—42no—
101C2×C4×C61—42no—
102C2×C4×C61C2×D412yes—
103C2×C4×C61C2×D412yes—
104C2×C4×C61C2×D411yescharacteristic
105C2×C4×C61C2×D412yes—
106C2×C4×C61#4112yes—
107C2×C4×C61C2411yescharacteristic
108C22⋊D61—24no—
109C2×Dic61—21no—
110C2×Dic61—22no—
111C2×Dic61—81no—
112D244—21no—
113D244C2×D412yes—
114C4×D61—24no—
115C4×D61—82no—
116Dic122—21no—
117Dic122C2×D412yes—
118#92418—21no—
119#92418—21no—
120#92418—22no—
121C22×C61—21no—
122C22×C61—21no—
123C22×C61—41no—
124C22×C61—41no—
125C22×C61—41no—
126C22×C61#12112yes—
127C22×C61C22×D411yescharacteristic
128C2×D61—22no—
129C2×D61—41no—
130C2×D61—41no—
131C4×C61—22no—
132C4×C61—22no—
133C4×C61—41no—
134C4×C61—42no—
135C4×C61#12112yes—
136C4×C61C22×D411yescharacteristic
137C4×C61C2×#4111yescharacteristic
138Dic61—22no—
139Dic61—42no—
140#3046—611nomaximal, Sylow
141C2×C61—22no—
142C2×C61—81no—
143C2×C61C2×#12111yescharacteristic
144C2×C61#57711yescharacteristic
145C2×C61#57811yescharacteristic
146D61—42no—
147C2×#137—611no—
148C2×#135—611no—
149#536D6111yescharacteristic, complemented
150#520—611no—
151#464—612no—
152#463—612no—
153#462—612no—
154#461—612no—
155#424—611no—
156#417—611no—
157C2×#103—611no—
158C61#304611yescharacteristic, complemented, Sylow
159C2×#41—611no—
160C2×#41C2×D6111yescharacteristic
161C22×Q8C2×D6111yescharacteristic
162#137—1224no—
163#135—1224no—
164C2×Q16—611no—
165C2×Q16—612no—
166C2×SD16—611no—
167C2×SD16—612no—
168C2×SD16—611no—
169C2×D8—611no—
170C2×M16—611no—
171C22×C8—611no—
172C4⋊Q8C2×D6112yes—
173#124C2×D6112yes—
174#123—22no—
175C22⋊Q8—21no—
176C22⋊Q8—21no—
177C4×Q8—612no—
178C4×D4—612no—
179C4×D4—1222no—
180#117—1221no—
181#117C2×D6111yescharacteristic
182C2×C4⋊C4—611no—
183C2×C4⋊C4—1221no—
184C4⋊C8—612no—
185C4⋊C8—612no—
186#103—612no—
187#103—612no—
188#103—612no—
189#102—612no—
190#41—22no—
191#41—22no—
192#41—614no—
193#41—1222no—
194C2×Q8—21no—
195C2×Q8—22no—
196C2×Q8—22no—
197C2×Q8—611no—
198C2×Q8C22×D6112yes—
199C2×Q8C22×D6111yescharacteristic
200C2×D4—21no—
201C2×D4—611no—
202C2×D4—1221no—
203C2×D4C22×D6111yescharacteristic
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—1221no—
207C22×C4—1221no—
208C22×C4—1222no—
209C22×C4C22×D6111yescharacteristic
210Q16—1222no—
211Q16—1224no—
212SD16—1222no—
213SD16—1222no—
214SD16—1224no—
215D8—1222no—
216M16—1222no—
217C2×C8—612no—
218C2×C8—611no—
219C2×C8—611no—
220C2×C8—1222no—
221C4⋊C4—22no—
222C4⋊C4—22no—
223C4⋊C4—612no—
224C4⋊C4—1221no—
225C4⋊C4—1222no—
226C4⋊C4C22⋊D6111yescharacteristic
227C4⋊C4C22⋊D6111yescharacteristic
228C22⋊C4—22no—
229C22⋊C4—22no—
230C22⋊C4—1222no—
231C22⋊C4C22⋊D6112yes—
232C42—1222no—
233C42C22×D6112yes—
234C23—21no—
235C23—1221no—
236C23C2×C22⋊D6111yescharacteristic
237Q8—22no—
238Q8—21no—
239Q8—22no—
240Q8—21no—
241Q8—42no—
242Q8—612no—
243Q8—1221no—
244D4—21no—
245D4—21no—
246D4—42no—
247D4—612no—
248D4—1224no—
249D4—1221no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—1221no—
255C2×C4—1224no—
256C2×C4—1222no—
257C2×C4—4882no—
258C2×C4—4881no—
259C2×C4D4×D6112yes—
260C2×C4#1175822412yes—
261C2×C4C2×C22⋊D6112yes—
262C2×C4C2×C22⋊D6112yes—
263C2×C4C2×C22⋊D6111yescharacteristic
264C2×C4C23×D6111yescharacteristic
265C8—1221no—
266C8—1221no—
267C8—1222no—
268C22—21no—
269C22—21no—
270C22—41no—
271C22—41no—
272C22—41no—
273C22—1222no—
274C22—2441no—
275C22—2441no—
276C22#1451974812yes—
277C22C22×C22⋊D6111yescharacteristic
278C4—22no—
279C4—22no—
280C4—41no—
281C4—42no—
282C4—1222no—
283C4—2442no—
284C4#1451974812yes—
285C4C2×D4×D6111yescharacteristic
286C4C2×#1175822411yescharacteristic
287C2—22no—
288C2—81no—
289C2—2442no—
290C2C2×#1451974811yescharacteristic
291C2#1684057011yescharacteristic
292C2#1684057711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#536C2
socleC22×C61C22×D4
hypercenter#536D61
hypocenterC61#3046
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C2×#14519808C2semidirect
3. #16840242C2semidirect
4. #16839981C2semidirect
5. #16839974C2semidirect
6. #16839969C2semidirect
7. #16839964C2semidirect
8. #16839789C2semidirect
9. #16839763C2semidirect
10. C2×#14519701C2semidirect
11. C61×#536C2semidirect
149. #536D61semidirect
158. C61#3046semidirect