Finite Group Databasebeta

← #21455226

Subgroups — #21455226

Order 7808.

716 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 716 conjugacy classes of subgroups — too many to draw. Only its 145 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
1#16840598C211yesmaximal, characteristic
2#16840338C212yesmaximal, complemented
3#16840333C211yesmaximal, characteristic, complemented
4#16839953C218yesmaximal, complemented
5#16839735C212yesmaximal, complemented
6C61×#410C211yesmaximal, characteristic, complemented
7#14519825—21no—
8#14519824—22no—
9#14519823—22no—
10#14519822—21no—
11#14519822C2214yes—
12C2×#11758222—22no—
13C2×#11758222C2212yes—
14#41×D61—24no—
15C22×Dic122C2211yescharacteristic, complemented
16#14519777—22no—
17#14519775—21no—
18#14519765—22no—
19#14519764—21no—
20#14519761C2218yescomplemented
21#14519758C2214yescomplemented
22#14519757—24no—
23#14519756—22no—
24#14519736C2211yescharacteristic, complemented
25#14519691C2218yescomplemented
26C2×#41×C61C2211yescharacteristic
27#117×C61C2212yescomplemented
28#99×C61C2214yescomplemented
29#41×C61—22no—
30#41×C61—22no—
31C2×Q8×C61D411yescharacteristic
32C2×D4×C61D411yescharacteristic
33C2×D4×C61C2312yes—
34C22×C4×C61D412yes—
35C22×C4×C61C2311yescharacteristic
36C2×C22⋊D61—24no—
37C2×C22⋊D61C2314yes—
38C22×Dic61C2312yes—
39#11758226—24no—
40Q8×D61—24no—
41#11758224—24no—
42#11758224—28no—
43D4×D61—24no—
44D4×D61—28no—
45#11758222—24no—
46#11758222—24no—
47#11758222—22no—
48#11758222—22no—
49#11758222—24no—
50#11758222—22no—
51#11758222—22no—
52C2×D244—22no—
53C2×D244D412yes—
54C2×C4×D61—24no—
55C2×C4×D61D414yes—
56C2×Dic122—22no—
57C2×Dic122—21no—
58C2×Dic122—22no—
59C2×Dic122—21no—
60C2×Dic122—22no—
61C2×Dic122D412yes—
62C4⋊C4×C61—22no—
63C22⋊C4×C61C2314yes—
64C42×C61—22no—
65C22⋊Dic61—24no—
66C22⋊Dic61C2312yes—
67#11758198—28no—
68C4⋊Dic61—21no—
69C4⋊Dic61—28no—
70#11758196—24no—
71C4×Dic61—21no—
72C23×C61C2×D412yes—
73C23×C61C2411yescharacteristic
74C22×D61—24no—
75C22×D61C2×D414yes—
76Q8×C61—22no—
77D4×C61—24no—
78D4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—24no—
82C2×C4×C61C2×D412yes—
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D412yes—
86C2×C4×C61C2×D412yes—
87C22⋊D61—28no—
88C22⋊D61—24no—
89C22⋊D61—24no—
90C2×Dic61—24no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—24no—
94C2×Dic61C2×D414yes—
95D244—24no—
96D244—22no—
97D244—22no—
98C4×D61—28no—
99C4×D61—24no—
100C4×D61—24no—
101Dic122—24no—
102Dic122—22no—
103Dic122—22no—
104Dic122—41no—
105Dic122—42no—
106Dic122—41no—
107C22×C61—22no—
108C22×C61—41no—
109C22×C61—42no—
110C22×C61C22×D412yes—
111C22×C61C22×D411yescharacteristic
112C2×D61—24no—
113C2×D61—44no—
114C2×D61—84no—
115C4×C61—22no—
116C4×C61—44no—
117C4×C61#12011yescharacteristic
118C4×C61#12012yes—
119C4×C61#12011yescharacteristic
120Dic61—24no—
121Dic61—42no—
122Dic61—42no—
123#3028—611nomaximal, Sylow
124C2×C61—21no—
125C2×C61—22no—
126C2×C61—42no—
127C2×C61C2×#12011yescharacteristic
128D61—44no—
129#585—611no—
130#536—611no—
131#536—612no—
132#458—618no—
133#410—612no—
134#410D6111yescharacteristic, complemented
135C61#302811yescharacteristic, complemented, Sylow
1362−1+4—1222no—
1372−1+4—1221no—
138H(5,𝔽2)—614no—
139H(5,𝔽2)—1222no—
140H(5,𝔽2)—1221no—
141C2×#41—612no—
142C2×#41—1224no—
143C2×#41—1222no—
144C2×#41C2×D6111yescharacteristic
145C22×Q8—611no—
146C4⋊Q8—1222no—
147C4⋊Q8—1221no—
148#124—1222no—
149#124—1221no—
150#123—614no—
151#123—618no—
152C22⋊Q8—1224no—
153C22⋊Q8—1222no—
154#117—611no—
155#117C2×D6112yescomplemented
156#99—618no—
157#99C2×D6114yescomplemented
158#41—22no—
159#41—22no—
160#41—1224no—
161#41—1224no—
162#41—1228no—
163#41—1224no—
164#41—1224no—
165#41—1222no—
166#41—1222no—
167#41—1224no—
168#41—1222no—
169#41—1222no—
170C2×Q8—612no—
171C2×Q8—1222no—
172C2×Q8—1224no—
173C2×Q8—1221no—
174C2×Q8—1221no—
175C2×Q8—1222no—
176C2×Q8—1222no—
177C2×Q8D24411yescharacteristic
178C2×D4—614no—
179C2×D4—612no—
180C2×D4—1222no—
181C2×D4—1228no—
182C2×D4—1224no—
183C2×D4—1224no—
184C2×D4D24411yescharacteristic
185C2×D4C22×D6112yes—
186C22×C4—614no—
187C22×C4—612no—
188C22×C4—1224no—
189C22×C4D24412yes—
190C22×C4C22×D6111yescharacteristic
191C4⋊C4—22no—
192C4⋊C4—1228no—
193C4⋊C4—1224no—
194C4⋊C4—1221no—
195C22⋊C4—612no—
196C22⋊C4—1228no—
197C22⋊C4—1224no—
198C22⋊C4C22×D6114yes—
199C42—22no—
200C42—1221no—
201C23—614no—
202C23—1224no—
203C23C2×D24412yes—
204C23C23×D6111yescharacteristic
205Q8—22no—
206Q8—1224no—
207Q8—1222no—
208Q8—1222no—
209Q8—2441no—
210Q8—2441no—
211Q8—2442no—
212D4—24no—
213D4—22no—
214D4—1224no—
215D4—1228no—
216D4—1224no—
217D4—1224no—
218D4—1222no—
219D4—1222no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—24no—
223C2×C4—614no—
224C2×C4—1228no—
225C2×C4—1224no—
226C2×C4—1224no—
227C2×C4—1224no—
228C2×C4—1224no—
229C2×C4—1222no—
230C2×C4—1222no—
231C2×C4C2×D24412yes—
232C2×C4C2×D24411yescharacteristic
233C2×C4C2×D24411yescharacteristic
234C2×C4D4×D6112yes—
235C2×C4D4×D6112yes—
236C22—22no—
237C22—41no—
238C22—42no—
239C22—1224no—
240C22—4884no—
241C22—2444no—
242C22C2×D4×D6112yes—
243C22C22×D24411yescharacteristic
244C4—22no—
245C4—44no—
246C4—1224no—
247C4—2442no—
248C4—2442no—
249C4#1451974711yescharacteristic
250C4#1451974711yescharacteristic
251C4#1451974712yes—
252C2—22no—
253C2—21no—
254C2—42no—
255C2—2444no—
256C2C2×#1451974711yescharacteristic
subgroupG/H
centerC2C2×#14519747
commutatorC23×C61C24
FrattiniC23C23×D61
FittingC61×#410C2
socleC2×C61C2×#120
hypercenter#410D61
hypocenterC61#3028
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #16840338C2semidirect
3. #16840333C2semidirect
4. #16839953C2semidirect
5. #16839735C2semidirect
6. C61×#410C2semidirect
15. C22×Dic122C22semidirect
20. #14519761C22semidirect
21. #14519758C22semidirect
24. #14519736C22semidirect
25. #14519691C22semidirect
27. #117×C61C22semidirect
28. #99×C61C22semidirect
134. #410D61semidirect
135. C61#3028semidirect
155. #117C2×D61semidirect
157. #99C2×D61semidirect