Finite Group Databasebeta

← #21455092

Subgroups — #21455092

Order 7808.

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

normal subgroups only

This group has 752 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×#14519822C211yesmaximal, characteristic
2C2×#14519808C211yesmaximal, characteristic, complemented
3#16840336C211yesmaximal, characteristic, complemented
4#16839921C214yesmaximal, complemented
5#16839911C214yesmaximal, complemented
6#16839767C211yesmaximal, characteristic, complemented
7#16839759C211yesmaximal, characteristic, complemented
8#16839728C211yesmaximal, characteristic, complemented
9C22×SD16×C61C211yesmaximal, characteristic, complemented
10#14519822—24no—
11#14519822—24no—
12C2×#11758222C2211yescharacteristic
13C2×#11758222C2211yescharacteristic
14C2×#11758224—21no—
15C2×#11758224C2212yes—
16C22×C22⋊D61—22no—
17C2×D4×D61—21no—
18C2×D4×D61C2212yes—
19#14519808—24no—
20C2×#11758202C2212yescomplemented
21C2×#11758201C2212yescomplemented
22C2×#11758194C2211yescharacteristic, complemented
23#14519775—21no—
24#14519766—21no—
25#14519760—22no—
26#14519753C2214yescomplemented
27#14519736C2211yescharacteristic, complemented
28#14519702C2212yescomplemented
29#14519699C2212yescomplemented
30#14519698C2214yescomplemented
31#14519689C2214yescomplemented
32C22×Q8×C61C2211yescharacteristic, complemented
33C22×D4×C61C2211yescharacteristic
34C2×SD16×C61—24no—
35C2×SD16×C61C2214yescomplemented
36C22×C8×C61C2211yescharacteristic, complemented
37C24×C61—21no—
38C23×D61—22no—
39C2×Q8×C61—21no—
40C2×Q8×C61—22no—
41C2×Q8×C61—22no—
42C2×Q8×C61C2312yes—
43C2×D4×C61—21no—
44C2×D4×C61—22no—
45C2×D4×C61D414yes—
46C2×D4×C61C2312yes—
47C22×C4×C61—21no—
48C22×C4×C61C2311yescharacteristic
49C2×C22⋊D61—216no—
50C2×C22⋊D61—21no—
51C2×C22⋊D61—22no—
52C2×C22⋊D61—22no—
53C2×C22⋊D61D412yes—
54C22×Dic61—22no—
55#11758224—28no—
56#11758224—24no—
57#11758224—24no—
58D4×D61—28no—
59D4×D61—24no—
60D4×D61—24no—
61#11758222—22no—
62#11758222—22no—
63#11758222—22no—
64#11758222D414yes—
65C2×D244D411yescharacteristic
66C2×D244C2311yescharacteristic
67C2×C4×D61—21no—
68C2×C4×D61C2312yes—
69C2×Dic122D411yescharacteristic
70C2×Dic122C2311yescharacteristic
71SD16×C61—28no—
72C2×C8×C61—22no—
73C2×C8×C61C2312yes—
74C22⋊Dic61—21no—
75#11758202—24no—
76#11758201—24no—
77#11758198—24no—
78C4⋊Dic61C2312yes—
79#11758196—24no—
80C4×Dic61—21no—
81#11758194—22no—
82C2×#92418C2312yes—
83C23×C61—22no—
84C23×C61—24no—
85C23×C61—82no—
86C23×C61C2×D411yescharacteristic
87C22×D61—21no—
88C22×D61—28no—
89C22×D61—84no—
90C22×D61C2×D412yes—
91Q8×C61—22no—
92Q8×C61—22no—
93Q8×C61—42no—
94D4×C61—24no—
95D4×C61—22no—
96D4×C61C2×D414yes—
97C2×C4×C61—22no—
98C2×C4×C61—42no—
99C2×C4×C61C2×D411yescharacteristic
100C2×C4×C61C2×D412yes—
101C2×C4×C61C2×D412yes—
102C2×C4×C61C2411yescharacteristic
103C22⋊D61—28no—
104C22⋊D61—28no—
105C22⋊D61—24no—
106C22⋊D61—24no—
107C2×Dic61—28no—
108C2×Dic61—21no—
109C2×Dic61—22no—
110C2×Dic61C2×D412yes—
111D244—22no—
112D244—21no—
113D244C2×D412yes—
114C4×D61—24no—
115C4×D61—22no—
116C4×D61—22no—
117Dic122—22no—
118Dic122—21no—
119Dic122C2×D412yes—
120C8×C61—22no—
121#92418—22no—
122C22×C61—22no—
123C22×C61—24no—
124C22×C61—44no—
125C22×C61—84no—
126C22×C61#12012yes—
127C22×C61C22×D411yescharacteristic
128C2×D61—22no—
129C2×D61—22no—
130C2×D61—24no—
131C2×D61—42no—
132C2×D61—88no—
133C4×C61—42no—
134C4×C61#12012yes—
135C4×C61C22×D411yescharacteristic
136C4×C61C22×D411yescharacteristic
137Dic61—22no—
138Dic61—22no—
139Dic61—42no—
140#3009—611nomaximal, Sylow
141C2×C61—22no—
142C2×C61—44no—
143C2×C61C2×#12011yescharacteristic
144C2×C61#57712yes—
145D61—42no—
146D61—42no—
147C2×H(5,𝔽2)—611no—
148C2×#137—611no—
149C22×SD16D6111yescharacteristic, complemented
150#536—611no—
151#452—614no—
152#450—614no—
153#418—611no—
154#416—611no—
155#408—611no—
156C61#300911yescharacteristic, complemented, Sylow
157H(5,𝔽2)—1224no—
158H(5,𝔽2)—1224no—
159C2×#41—611no—
160C2×#41—612no—
161C2×#41—611no—
162C2×#41—1221no—
163C22×Q8C2×D6111yescharacteristic, complemented
164C22×D4—612no—
165C22×D4—1221no—
166C22×D4—1222no—
167C22×D4C2×D6111yescharacteristic
168#137—1224no—
169C2×Q16—612no—
170C2×SD16—24no—
171C2×SD16—612no—
172C2×SD16C2×D6114yescomplemented
173C2×M16—611no—
174C22×C8C2×D6111yescharacteristic, complemented
175C4⋊Q8—1221no—
176#124—1221no—
177#123—1222no—
178C22⋊Q8—614no—
179#117—611no—
180#103—612no—
181#102—614no—
182#102—612no—
183C22⋊C8—614no—
184C24—21no—
185C24—1222no—
186#41—614no—
187#41—1224no—
188#41—1228no—
189#41—1224no—
190#41—1222no—
191#41—1222no—
192#41—1222no—
193C2×Q8—21no—
194C2×Q8—22no—
195C2×Q8—22no—
196C2×Q8—611no—
197C2×Q8—611no—
198C2×Q8C22×D6112yes—
199C2×D4—21no—
200C2×D4—22no—
201C2×D4—612no—
202C2×D4—611no—
203C2×D4—611no—
204C2×D4—1222no—
205C2×D4—1224no—
206C2×D4—1228no—
207C2×D4—1222no—
208C2×D4—12216no—
209C2×D4—1221no—
210C2×D4—1224no—
211C2×D4C22⋊D6114yes—
212C2×D4C22×D6112yes—
213C22×C4—21no—
214C22×C4—612no—
215C22×C4—1222no—
216C22×C4—1221no—
217C22×C4C22×D6111yescharacteristic
218Q16—1224no—
219SD16—28no—
220SD16—1224no—
221M16—1222no—
222C2×C8—22no—
223C2×C8—612no—
224C2×C8C22×D6112yes—
225C4⋊C4—612no—
226C4⋊C4—1224no—
227C22⋊C4—1224no—
228C22⋊C4—1221no—
229C42—1221no—
230C23—22no—
231C23—24no—
232C23—82no—
233C23—612no—
234C23—1228no—
235C23—1221no—
236C23—4884no—
237C23D4×D6111yescharacteristic
238Q8—22no—
239Q8—22no—
240Q8—42no—
241Q8—612no—
242Q8—1221no—
243Q8—1222no—
244D4—22no—
245D4—24no—
246D4—612no—
247D4—1228no—
248D4—1228no—
249D4—1224no—
250D4—1224no—
251D4—1221no—
252D4—1222no—
253D4C2×C22⋊D6114yes—
254C2×C4—22no—
255C2×C4—42no—
256C2×C4—612no—
257C2×C4—1228no—
258C2×C4—1221no—
259C2×C4—1222no—
260C2×C4—1222no—
261C2×C4—1224no—
262C2×C4—1222no—
263C2×C4D4×D6112yes—
264C2×C4D4×D6111yescharacteristic
265C2×C4C2×C22⋊D6112yes—
266C2×C4C23×D6111yescharacteristic
267C8—22no—
268C8—1222no—
269C22—22no—
270C22—24no—
271C22—44no—
272C22—84no—
273C22—1222no—
274C22—1222no—
275C22—1224no—
276C22—4888no—
277C22—2442no—
278C22#1451974512yes—
279C22C2×D4×D6111yescharacteristic
280C4—42no—
281C4—1222no—
282C4—1222no—
283C4—2442no—
284C4#1451974512yes—
285C4C2×D4×D6111yescharacteristic
286C4C22×C22⋊D6111yescharacteristic
287C2—22no—
288C2—44no—
289C2—2442no—
290C2—2442no—
291C2C2×#1451974511yescharacteristic
292C2#1684056812yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC22×SD16×C61C2
socleC22×C61C22×D4
hypercenterC22×SD16D61
hypocenterC61#3009
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#14519808C2semidirect
3. #16840336C2semidirect
4. #16839921C2semidirect
5. #16839911C2semidirect
6. #16839767C2semidirect
7. #16839759C2semidirect
8. #16839728C2semidirect
9. C22×SD16×C61C2semidirect
20. C2×#11758202C22semidirect
21. C2×#11758201C22semidirect
22. C2×#11758194C22semidirect
26. #14519753C22semidirect
27. #14519736C22semidirect
28. #14519702C22semidirect
29. #14519699C22semidirect
30. #14519698C22semidirect
31. #14519689C22semidirect
32. C22×Q8×C61C22semidirect
35. C2×SD16×C61C22semidirect
36. C22×C8×C61C22semidirect
149. C22×SD16D61semidirect
156. C61#3009semidirect
163. C22×Q8C2×D61semidirect
172. C2×SD16C2×D61semidirect
174. C22×C8C2×D61semidirect