Finite Group Databasebeta

← #21455095

Subgroups — #21455095

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×#14519823C211yesmaximal, characteristic
2C22×#11758201C211yesmaximal, characteristic, complemented
3#16840336C211yesmaximal, characteristic, complemented
4#16839923C214yesmaximal, complemented
5#16839911C214yesmaximal, complemented
6#16839768C211yesmaximal, characteristic, complemented
7#16839758C211yesmaximal, characteristic, complemented
8#16839730C211yesmaximal, characteristic, complemented
9C2×#137×C61C211yesmaximal, characteristic, complemented
10#14519823—24no—
11#14519823—24no—
12C2×#11758226C2212yes—
13C2×#11758222—21no—
14C2×#11758222C2211yescharacteristic
15C22×D244—21no—
16C22×D244C2211yescharacteristic
17C2×D4×D61—22no—
18C2×D4×D61C2212yes—
19C2×#11758201—24no—
20C2×#11758201C2214yescomplemented
21C22×#92418C2211yescharacteristic, complemented
22#14519775—21no—
23#14519766—21no—
24#14519760—22no—
25#14519753C2214yescomplemented
26#14519736C2211yescharacteristic, complemented
27#14519701C2212yescomplemented
28#14519699C2214yescomplemented
29#14519698C2212yescomplemented
30#14519689C2214yescomplemented
31C2×#41×C61C2211yescharacteristic
32C22×Q8×C61C2211yescharacteristic, complemented
33#137×C61—24no—
34C2×Q16×C61C2212yescomplemented
35C2×SD16×C61C2212yescomplemented
36C2×M16×C61C2211yescharacteristic, complemented
37C23×D61—21no—
38C23×D61—22no—
39#41×C61—22no—
40#41×C61D414yes—
41C2×Q8×C61—21no—
42C2×Q8×C61—22no—
43C2×Q8×C61—22no—
44C2×Q8×C61C2312yes—
45C2×Q8×C61C2311yescharacteristic
46C2×D4×C61—21no—
47C2×D4×C61C2311yescharacteristic
48C22×C4×C61—21no—
49C22×C4×C61—21no—
50C22×C4×C61C2311yescharacteristic
51C2×C22⋊D61—22no—
52C2×C22⋊D61D412yes—
53#11758226—24no—
54#11758226—24no—
55D4×D61—216no—
56D4×D61—24no—
57D4×D61—24no—
58#11758222—28no—
59#11758222—22no—
60#11758222—22no—
61C2×D244—28no—
62C2×D244—22no—
63C2×D244—21no—
64C2×D244—22no—
65C2×D244D411yescharacteristic
66C2×D244D414yes—
67C2×D244C2312yes—
68C2×C4×D61—22no—
69C2×C4×D61C2312yes—
70C2×Dic122D411yescharacteristic
71Q16×C61—24no—
72SD16×C61—24no—
73M16×C61—22no—
74C2×C8×C61C2312yes—
75C22⋊Dic61—21no—
76#11758201—28no—
77#11758198—24no—
78C4⋊Dic61C2312yes—
79#11758196—24no—
80C4×Dic61—21no—
81C2×#92418—22no—
82C2×#92418C2312yes—
83C23×C61—21no—
84C23×C61C2×D411yescharacteristic
85C22×D61—22no—
86C22×D61—28no—
87C22×D61—24no—
88C22×D61—84no—
89C22×D61—82no—
90C22×D61C2×D412yes—
91Q8×C61—21no—
92Q8×C61—22no—
93Q8×C61—22no—
94Q8×C61—42no—
95Q8×C61C2×D412yes—
96D4×C61—24no—
97D4×C61—21no—
98D4×C61C2×D412yes—
99C2×C4×C61—21no—
100C2×C4×C61—24no—
101C2×C4×C61—22no—
102C2×C4×C61—42no—
103C2×C4×C61C2×D411yescharacteristic
104C2×C4×C61C2×D412yes—
105C2×C4×C61C2×D412yes—
106C2×C4×C61C2411yescharacteristic
107C22⋊D61—28no—
108C22⋊D61—24no—
109C2×Dic61—22no—
110C2×Dic61C2×D412yes—
111D244—28no—
112D244—22no—
113D244—24no—
114D244—22no—
115D244C2×D414yes—
116C4×D61—28no—
117C4×D61—22no—
118C4×D61—22no—
119Dic122—22no—
120C8×C61—22no—
121#92418—22no—
122C22×C61—22no—
123C22×C61—22no—
124C22×C61—42no—
125C22×C61#12012yes—
126C22×C61C22×D411yescharacteristic
127C2×D61—22no—
128C2×D61—24no—
129C2×D61—24no—
130C2×D61—44no—
131C2×D61—84no—
132C2×D61—88no—
133C4×C61—22no—
134C4×C61—42no—
135C4×C61#12012yes—
136C4×C61C22×D411yescharacteristic
137C4×C61C22×D411yescharacteristic
138Dic61—22no—
139Dic61—42no—
140#3009—611nomaximal, Sylow
141C2×C61—22no—
142C2×C61—42no—
143C2×C61C2×#12011yescharacteristic
144C2×C61#57712yes—
145D61—42no—
146D61—44no—
147C2×H(5,𝔽2)—611no—
148C2×#137D6111yescharacteristic, complemented
149C22×SD16—611no—
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—1221no—
162C2×#41C2×D6111yescharacteristic
163C22×Q8C2×D6111yescharacteristic, complemented
164C22×D4—612no—
165C22×D4—611no—
166C22×D4—1221no—
167C22×D4—1222no—
168#137—24no—
169C2×Q16C2×D6112yescomplemented
170C2×SD16—614no—
171C2×SD16—1224no—
172C2×SD16C2×D6112yescomplemented
173C2×M16C2×D6111yescharacteristic, complemented
174C22×C8—611no—
175C4⋊Q8—1221no—
176#124—1221no—
177#123—1222no—
178C22⋊Q8—614no—
179#117—611no—
180#103—612no—
181#102—612no—
182#102—614no—
183C22⋊C8—614no—
184C24—1222no—
185C24—1221no—
186#41—22no—
187#41—1228no—
188#41—1224no—
189#41—1224no—
190#41—1222no—
191#41—1222no—
192#41C22⋊D6114yes—
193C2×Q8—21no—
194C2×Q8—22no—
195C2×Q8—22no—
196C2×Q8—611no—
197C2×Q8C22×D6112yes—
198C2×Q8C22×D6111yescharacteristic
199C2×D4—21no—
200C2×D4—612no—
201C2×D4—614no—
202C2×D4—611no—
203C2×D4—612no—
204C2×D4—1222no—
205C2×D4—1228no—
206C2×D4—1222no—
207C2×D4—1224no—
208C2×D4—12216no—
209C2×D4—1224no—
210C2×D4—1221no—
211C2×D4—1222no—
212C2×D4C22×D6111yescharacteristic
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—612no—
216C22×C4—1222no—
217C22×C4C22×D6111yescharacteristic
218Q16—24no—
219SD16—24no—
220SD16—1228no—
221M16—22no—
222C2×C8—612no—
223C2×C8—1222no—
224C2×C8C22×D6112yes—
225C4⋊C4—612no—
226C4⋊C4—1224no—
227C22⋊C4—1224no—
228C22⋊C4—1221no—
229C42—1221no—
230C23—21no—
231C23—612no—
232C23—1228no—
233C23—1224no—
234C23—1222no—
235C23—4882no—
236C23—4884no—
237C23D4×D6111yescharacteristic
238Q8—21no—
239Q8—22no—
240Q8—22no—
241Q8—42no—
242Q8—1222no—
243Q8C2×C22⋊D6112yes—
244D4—24no—
245D4—21no—
246D4—614no—
247D4—1228no—
248D4—1228no—
249D4—1224no—
250D4—1222no—
251D4—1224no—
252D4—1222no—
253D4C2×C22⋊D6112yes—
254C2×C4—21no—
255C2×C4—24no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—612no—
259C2×C4—1228no—
260C2×C4—1222no—
261C2×C4—1222no—
262C2×C4—1222no—
263C2×C4D4×D6112yes—
264C2×C4D4×D6111yescharacteristic
265C2×C4C2×C22⋊D6112yes—
266C2×C4C23×D6111yescharacteristic
267C8—22no—
268C8—1222no—
269C22—22no—
270C22—22no—
271C22—42no—
272C22—1224no—
273C22—1222no—
274C22—1224no—
275C22—4884no—
276C22—4888no—
277C22—2444no—
278C22#1451974512yes—
279C22C2×D4×D6111yescharacteristic
280C4—22no—
281C4—42no—
282C4—1222no—
283C4—2442no—
284C4#1451974512yes—
285C4C2×D4×D6111yescharacteristic
286C4C22×C22⋊D6111yescharacteristic
287C2—22no—
288C2—42no—
289C2—2442no—
290C2—2444no—
291C2C2×#1451974511yescharacteristic
292C2#1684057112yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#137×C61C2
socleC22×C61C22×D4
hypercenterC2×#137D61
hypocenterC61#3009
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
2. C22×#11758201C2semidirect
3. #16840336C2semidirect
4. #16839923C2semidirect
5. #16839911C2semidirect
6. #16839768C2semidirect
7. #16839758C2semidirect
8. #16839730C2semidirect
9. C2×#137×C61C2semidirect
20. C2×#11758201C22semidirect
21. C22×#92418C22semidirect
25. #14519753C22semidirect
26. #14519736C22semidirect
27. #14519701C22semidirect
28. #14519699C22semidirect
29. #14519698C22semidirect
30. #14519689C22semidirect
32. C22×Q8×C61C22semidirect
34. C2×Q16×C61C22semidirect
35. C2×SD16×C61C22semidirect
36. C2×M16×C61C22semidirect
148. C2×#137D61semidirect
156. C61#3009semidirect
163. C22×Q8C2×D61semidirect
169. C2×Q16C2×D61semidirect
172. C2×SD16C2×D61semidirect
173. C2×M16C2×D61semidirect