Finite Group Databasebeta

← #21445792

Subgroups — #21445792

Order 7808.

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

normal subgroups only

This group has 536 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
1C2×#14519824C211yesmaximal, characteristic
2#16839780C212yesmaximal, complemented
3#16839770C212yesmaximal, complemented
4#16839746C211yesmaximal, characteristic, complemented
5C61×#410C211yesmaximal, characteristic, complemented
6#14519824—24no—
7#14519824—24no—
8C2×#11758222C412yescomplemented
9C2×#11758222C2211yescharacteristic
10C2×#11758224—22no—
11C2×#11758224—21no—
12C22×Dic122C412yescomplemented
13C22×Dic122C2211yescharacteristic
14C2×Q8×D61—21no—
15C2×#11758194C2212yes—
16#14519705—24no—
17#14519700—24no—
18#14519696—21no—
19#14519694—21no—
20C2×#41×C61C2211yescharacteristic
21#117×C61C2212yes—
22#99×C61—22no—
23#41×C61—22no—
24#41×C61—22no—
25C2×Q8×C61D411yescharacteristic
26C2×D4×C61D412yes—
27C2×D4×C61D411yescharacteristic
28C22×C4×C61C2×C412yes—
29C22×C4×C61C2311yescharacteristic
30C2×C22⋊D61—22no—
31C2×C22⋊D61—21no—
32C22×Dic61—22no—
33C22×Dic61—21no—
34Q8×D61—28no—
35#11758224—216no—
36#11758224—28no—
37#11758222—22no—
38#11758222—24no—
39#11758222—24no—
40#11758222D414yes—
41C2×D244C2×C411yescharacteristic
42C2×C4×D61—22no—
43C2×C4×D61—21no—
44C2×Dic122—22no—
45C2×Dic122—21no—
46C2×Dic122—22no—
47C2×Dic122—24no—
48C2×Dic122—24no—
49C2×Dic122C2×C411yescharacteristic
50C2×Dic122C2×C412yes—
51C2×Dic122D414yes—
52C4⋊C4×C61—22no—
53C22⋊C4×C61—22no—
54C42×C61—22no—
55#11758194—22no—
56#11758194—22no—
57C2×#92418—22no—
58C23×C61C22⋊C412yes—
59C23×C61C2×D411yescharacteristic
60C22×D61—21no—
61Q8×C61—22no—
62D4×C61—24no—
63D4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—42no—
67C2×C4×C61C22⋊C412yes—
68C2×C4×C61C22×C411yescharacteristic
69C2×C4×C61C2×D412yes—
70C2×C4×C61C2×D412yes—
71C2×C4×C61C2×D411yescharacteristic
72C22⋊D61—28no—
73C22⋊D61—24no—
74C2×Dic61—28no—
75C2×Dic61—21no—
76C2×Dic61—22no—
77C2×Dic61—24no—
78D244—21no—
79D244C22⋊C412yes—
80C4×D61—28no—
81C4×D61—24no—
82Dic122—28no—
83Dic122—22no—
84Dic122—21no—
85Dic122—24no—
86Dic122C22⋊C412yes—
87Dic122C22⋊C414yes—
88#92418—42no—
89C22×C61—22no—
90C22×C61—41no—
91C22×C61—42no—
92C22×C61C2×C22⋊C411yescharacteristic
93C22×C61#12012yes—
94C2×D61—22no—
95C2×D61—42no—
96C4×C61—22no—
97C4×C61—82no—
98C4×C61C2×C22⋊C411yescharacteristic
99C4×C61C2×C22⋊C411yescharacteristic
100C4×C61#12012yes—
101Dic61—22no—
102Dic61—24no—
103#1796—611nomaximal, Sylow
104C2×C61—22no—
105C2×C61—21no—
106C2×C61—42no—
107C2×C61#37911yescharacteristic
108D61—42no—
109C2×2−1+4—611no—
110#421—612no—
111#419—612no—
112#413—611no—
113#410D6111yescharacteristic, complemented
114C61#179611yescharacteristic, complemented, Sylow
1152−1+4—1224no—
1162−1+4—1224no—
117C2×#41—612no—
118C2×#41—611no—
119C2×#41—1221no—
120C2×#41—1222no—
121C2×#41C2×D6111yescharacteristic
122C22×Q8—612no—
123C22×Q8—611no—
124C22×Q8—1221no—
125C2×M16—612no—
126#117C2×D6112yes—
127#104—1224no—
128#103—1224no—
129#101—1221no—
130#100—1221no—
131#99—22no—
132#41—22no—
133#41—22no—
134#41—614no—
135#41—1224no—
136#41—1224no—
137#41—12216no—
138#41—1228no—
139#41—1222no—
140C2×Q8—612no—
141C2×Q8—611no—
142C2×Q8—614no—
143C2×Q8—1224no—
144C2×Q8—1224no—
145C2×Q8—1228no—
146C2×Q8—1222no—
147C2×Q8—1221no—
148C2×Q8—1222no—
149C2×Q8D24411yescharacteristic
150C2×D4—611no—
151C2×D4—1222no—
152C2×D4—1221no—
153C2×D4D24411yescharacteristic
154C2×D4C22⋊D6112yes—
155C22×C4—1222no—
156C22×C4—1221no—
157C22×C4—1222no—
158C22×C4—1221no—
159C22×C4C4×D6112yes—
160C22×C4C22×D6111yescharacteristic
161M16—1222no—
162M16—1222no—
163C2×C8—1222no—
164C4⋊C4—22no—
165C22⋊C4—22no—
166C42—22no—
167C23—1221no—
168C23#1175819812yes—
169C23C2×C22⋊D6111yescharacteristic
170Q8—22no—
171Q8—614no—
172Q8—612no—
173Q8—1228no—
174Q8—1222no—
175Q8—1221no—
176Q8—1224no—
177D4—24no—
178D4—22no—
179D4—612no—
180D4—1228no—
181D4—1224no—
182D4—1221no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—42no—
186C2×C4—1228no—
187C2×C4—1228no—
188C2×C4—1221no—
189C2×C4—1222no—
190C2×C4—1224no—
191C2×C4—1224no—
192C2×C4#1175819812yes—
193C2×C4C2×C4×D6111yescharacteristic
194C2×C4C2×D24411yescharacteristic
195C2×C4D4×D6112yes—
196C2×C4D4×D6112yes—
197C8—2442no—
198C22—22no—
199C22—41no—
200C22—42no—
201C22—1222no—
202C22—2442no—
203C22C2×#1175819811yescharacteristic
204C22#1451974512yes—
205C4—22no—
206C4—82no—
207C4—1224no—
208C4—1222no—
209C4C22⋊C4×D6111yescharacteristic
210C4C22⋊C4×D6111yescharacteristic
211C4#1451974712yes—
212C2—22no—
213C2—21no—
214C2—42no—
215C2—2442no—
216C2#1683961711yescharacteristic
subgroupG/H
centerC2#16839617
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#410C2
socleC2×C61#379
hypercenter#410D61
hypocenterC61#1796
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #16839780C2semidirect
3. #16839770C2semidirect
4. #16839746C2semidirect
5. C61×#410C2semidirect
8. C2×#11758222C4semidirect
12. C22×Dic122C4semidirect
113. #410D61semidirect
114. C61#1796semidirect