Finite Group Databasebeta

← #21445768

Subgroups — #21445768

Order 7808.

548 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 97 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#16839744C212yesmaximal, complemented
3#16839730C212yesmaximal, complemented
4#16839729C211yesmaximal, characteristic, complemented
5C61×#413C211yesmaximal, characteristic, complemented
6#14519825—21no—
7#14519824—22no—
8#14519823—22no—
9#14519822—21no—
10#14519822C414yes—
11C2×#11758222—22no—
12C2×#11758222C2212yes—
13#41×D61—24no—
14C2×#11758194C2211yescharacteristic, complemented
15C22×#92418C2211yescharacteristic, complemented
16#14519695—22no—
17#14519693—22no—
18C22⋊#92418—22no—
19#14519689—24no—
20C2×#41×C61C2211yescharacteristic
21C2×M16×C61C2212yescomplemented
22#101×C61—21no—
23#100×C61—21no—
24#41×C61—22no—
25#41×C61—22no—
26C2×Q8×C61D411yescharacteristic
27C2×D4×C61C2×C412yes—
28C2×D4×C61D411yescharacteristic
29C22×C4×C61D412yes—
30C22×C4×C61C2311yescharacteristic
31C2×C22⋊D61—24no—
32C2×C22⋊D61C2×C414yes—
33#11758226—24no—
34Q8×D61—24no—
35#11758224—24no—
36#11758224—28no—
37D4×D61—24no—
38D4×D61—28no—
39#11758222—24no—
40#11758222—24no—
41#11758222—24no—
42#11758222—22no—
43#11758222—22no—
44#11758222—22no—
45#11758222—22no—
46C2×D244—22no—
47C2×D244D412yes—
48C2×C4×D61—24no—
49C2×C4×D61D414yes—
50C2×Dic122—22no—
51C2×Dic122D412yes—
52M16×C61—22no—
53M16×C61—22no—
54C2×C8×C61—22no—
55#11758194—22no—
56C2×#92418—22no—
57C2×#92418—21no—
58C2×#92418—21no—
59C23×C61C22⋊C412yes—
60C23×C61C22×C411yescharacteristic
61C22×D61—24no—
62C22×D61C22⋊C414yes—
63Q8×C61—22no—
64D4×C61—24no—
65D4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61C22⋊C412yes—
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D412yes—
71C2×C4×C61C2×D412yes—
72C2×C4×C61C2×D411yescharacteristic
73C22⋊D61—28no—
74C22⋊D61—24no—
75C22⋊D61—24no—
76C2×Dic61—24no—
77C2×Dic61C22⋊C414yes—
78D244—24no—
79D244—22no—
80D244—22no—
81C4×D61—28no—
82C4×D61—24no—
83C4×D61—24no—
84Dic122—24no—
85Dic122—22no—
86Dic122—22no—
87C8×C61—42no—
88#92418—41no—
89#92418—41no—
90C22×C61—22no—
91C22×C61—41no—
92C22×C61—42no—
93C22×C61C2×C22⋊C412yes—
94C22×C61C2×C22⋊C411yescharacteristic
95C2×D61—24no—
96C2×D61—44no—
97C2×D61—84no—
98C4×C61—22no—
99C4×C61#12012yes—
100C4×C61#12011yescharacteristic
101C4×C61#12011yescharacteristic
102Dic61—24no—
103#1791—611nomaximal, Sylow
104C2×C61—22no—
105C2×C61—21no—
106C2×C61—42no—
107C2×C61#37911yescharacteristic
108D61—44no—
109#585—611no—
110#413—612no—
111#413D6111yescharacteristic, complemented
112#408—611no—
113#408—612no—
114C61#179111yescharacteristic, complemented, Sylow
1152−1+4—1222no—
1162−1+4—1221no—
117H(5,𝔽2)—614no—
118H(5,𝔽2)—1222no—
119H(5,𝔽2)—1221no—
120C2×#41—612no—
121C2×#41—1224no—
122C2×#41—1222no—
123C2×#41C2×D6111yescharacteristic
124C2×M16—611no—
125C2×M16C2×D6112yescomplemented
126C22×C8—611no—
127#101—21no—
128#101—1222no—
129#100—21no—
130#100—1222no—
131C22⋊C8—1224no—
132C22⋊C8—1222no—
133#41—22no—
134#41—22no—
135#41—1224no—
136#41—1224no—
137#41—1228no—
138#41—1224no—
139#41—1224no—
140#41—1224no—
141#41—1222no—
142#41—1222no—
143#41—1222no—
144#41—1222no—
145C2×Q8—612no—
146C2×Q8—1222no—
147C2×Q8—1224no—
148C2×Q8C22⋊D6111yescharacteristic
149C2×D4—614no—
150C2×D4—612no—
151C2×D4—1222no—
152C2×D4—1228no—
153C2×D4—1224no—
154C2×D4—1224no—
155C2×D4C4×D6112yes—
156C2×D4C22⋊D6111yescharacteristic
157C22×C4—614no—
158C22×C4—1224no—
159C22×C4D24412yes—
160C22×C4C22×D6111yescharacteristic
161M16—22no—
162M16—22no—
163M16—1222no—
164C2×C8—22no—
165C2×C8—1221no—
166C2×C8—1221no—
167C2×C8—1222no—
168C23—614no—
169C23—1224no—
170C23#1175819812yes—
171C23C2×C4×D6111yescharacteristic
172Q8—22no—
173Q8—1224no—
174Q8—1222no—
175Q8—1222no—
176D4—24no—
177D4—22no—
178D4—1224no—
179D4—1228no—
180D4—1224no—
181D4—1224no—
182D4—1222no—
183D4—1222no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—614no—
187C2×C4—1228no—
188C2×C4—1224no—
189C2×C4—1224no—
190C2×C4—1224no—
191C2×C4#1175819812yes—
192C2×C4C2×D24411yescharacteristic
193C2×C4D4×D6112yes—
194C2×C4D4×D6112yes—
195C2×C4C2×C22⋊D6111yescharacteristic
196C8—42no—
197C8—2441no—
198C8—2441no—
199C22—22no—
200C22—41no—
201C22—42no—
202C22—1224no—
203C22—4884no—
204C22—2444no—
205C22C22⋊C4×D6112yes—
206C22C2×#1175819811yescharacteristic
207C4—22no—
208C4—1224no—
209C4#1451974512yes—
210C4#1451974711yescharacteristic
211C4#1451974711yescharacteristic
212C2—21no—
213C2—22no—
214C2—42no—
215C2—2444no—
216C2#1683961711yescharacteristic
subgroupG/H
centerC4#14519747
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#413C2
socleC2×C61#379
hypercenter#413D61
hypocenterC61#1791
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #16839744C2semidirect
3. #16839730C2semidirect
4. #16839729C2semidirect
5. C61×#413C2semidirect
14. C2×#11758194C22semidirect
15. C22×#92418C22semidirect
21. C2×M16×C61C22semidirect
111. #413D61semidirect
114. C61#1791semidirect
125. C2×M16C2×D61semidirect