Finite Group Databasebeta

← #21445790

Subgroups — #21445790

Order 7808.

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

normal subgroups only

This group has 588 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×#14519823C211yesmaximal, characteristic
2#16839778C212yesmaximal, complemented
3#16839768C212yesmaximal, complemented
4#16839736C211yesmaximal, characteristic, complemented
5C61×#413C211yesmaximal, characteristic, complemented
6#14519823—24no—
7#14519823—24no—
8C2×#11758226—21no—
9C2×#11758222C412yescomplemented
10C2×#11758222C2211yescharacteristic
11C22×D244C412yescomplemented
12C22×D244C2211yescharacteristic
13C2×D4×D61—22no—
14C2×D4×D61—21no—
15#14519736C2212yescomplemented
16#14519703—24no—
17#14519699—24no—
18#14519692—22no—
19C2×#41×C61C2211yescharacteristic
20C2×M16×C61C2212yescomplemented
21#101×C61—21no—
22#100×C61—21no—
23C23×D61—22no—
24C23×D61—21no—
25#41×C61—22no—
26#41×C61—22no—
27C2×Q8×C61D411yescharacteristic
28C2×D4×C61D412yes—
29C2×D4×C61D411yescharacteristic
30C22×C4×C61C2×C412yes—
31C22×C4×C61C2311yescharacteristic
32C2×C22⋊D61—22no—
33C2×C22⋊D61—21no—
34#11758226—28no—
35D4×D61—216no—
36D4×D61—28no—
37#11758222—22no—
38#11758222—24no—
39#11758222—24no—
40#11758222D414yes—
41C2×D244—22no—
42C2×D244—21no—
43C2×D244—22no—
44C2×D244—24no—
45C2×D244—24no—
46C2×D244C2×C411yescharacteristic
47C2×D244C2×C412yes—
48C2×D244D414yes—
49C2×C4×D61—22no—
50C2×C4×D61—21no—
51C2×Dic122C2×C411yescharacteristic
52M16×C61—22no—
53M16×C61—22no—
54C2×C8×C61—22no—
55C22⋊Dic61—22no—
56C4⋊Dic61—22no—
57C4×Dic61—22no—
58C23×C61C22⋊C412yes—
59C23×C61C2×D411yescharacteristic
60C22×D61—22no—
61C22×D61—21no—
62C22×D61—28no—
63C22×D61—24no—
64C22×D61—82no—
65C22×D61—84no—
66Q8×C61—22no—
67D4×C61—24no—
68D4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61C22⋊C412yes—
72C2×C4×C61C22×C411yescharacteristic
73C2×C4×C61C2×D412yes—
74C2×C4×C61C2×D412yes—
75C2×C4×C61C2×D411yescharacteristic
76C22⋊D61—28no—
77C22⋊D61—24no—
78C2×Dic61—21no—
79C2×Dic61—42no—
80D244—28no—
81D244—21no—
82D244—22no—
83D244—24no—
84D244C22⋊C412yes—
85D244C22⋊C414yes—
86C4×D61—28no—
87C4×D61—24no—
88Dic122—21no—
89Dic122C22⋊C412yes—
90C8×C61—42no—
91C22×C61—22no—
92C22×C61—41no—
93C22×C61—42no—
94C22×C61C2×C22⋊C411yescharacteristic
95C22×C61#12012yes—
96C2×D61—24no—
97C2×D61—22no—
98C2×D61—44no—
99C2×D61—42no—
100C2×D61—84no—
101C2×D61—88no—
102C4×C61—22no—
103C4×C61C2×C22⋊C411yescharacteristic
104C4×C61C2×C22⋊C411yescharacteristic
105C4×C61#12012yes—
106Dic61—22no—
107Dic61—82no—
108#1795—611nomaximal, Sylow
109C2×C61—22no—
110C2×C61—21no—
111C2×C61—42no—
112C2×C61#37911yescharacteristic
113D61—44no—
114D61—42no—
115C2×H(5,𝔽2)—611no—
116#421—612no—
117#418—612no—
118#413D6111yescharacteristic, complemented
119#410—611no—
120C61#179511yescharacteristic, complemented, Sylow
121H(5,𝔽2)—1224no—
122H(5,𝔽2)—1224no—
123C2×#41—612no—
124C2×#41—611no—
125C2×#41—1221no—
126C2×#41C2×D6111yescharacteristic
127C22×D4—612no—
128C22×D4—611no—
129C22×D4—1222no—
130C22×D4—1221no—
131C2×M16C2×D6112yescomplemented
132#117—612no—
133#104—1224no—
134#102—1224no—
135#101—21no—
136#100—21no—
137#99—1222no—
138C24—1222no—
139C24—1221no—
140#41—22no—
141#41—22no—
142#41—614no—
143#41—1224no—
144#41—1224no—
145#41—1228no—
146#41—1222no—
147C2×Q8—611no—
148C2×Q8C22⋊D6111yescharacteristic
149C2×D4—612no—
150C2×D4—611no—
151C2×D4—614no—
152C2×D4—1224no—
153C2×D4—1224no—
154C2×D4—12216no—
155C2×D4—1228no—
156C2×D4—1222no—
157C2×D4—1221no—
158C2×D4—1222no—
159C2×D4—1222no—
160C2×D4—1221no—
161C2×D4D24412yes—
162C2×D4C22⋊D6111yescharacteristic
163C22×C4—1222no—
164C22×C4—1221no—
165C22×C4C4×D6112yes—
166C22×C4C22×D6111yescharacteristic
167M16—22no—
168M16—22no—
169C2×C8—22no—
170C4⋊C4—1222no—
171C22⋊C4—1222no—
172C42—1222no—
173C23—1228no—
174C23—1224no—
175C23—1222no—
176C23—1221no—
177C23—4882no—
178C23—4884no—
179C23#1175819812yes—
180C23C2×D24411yescharacteristic
181Q8—22no—
182Q8—612no—
183Q8—1221no—
184D4—24no—
185D4—22no—
186D4—614no—
187D4—612no—
188D4—1228no—
189D4—1228no—
190D4—1224no—
191D4—1221no—
192D4—1222no—
193D4—1224no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—1228no—
197C2×C4—1221no—
198C2×C4—1224no—
199C2×C4—2442no—
200C2×C4#1175819812yes—
201C2×C4C2×C4×D6111yescharacteristic
202C2×C4D4×D6112yes—
203C2×C4D4×D6112yes—
204C2×C4C2×C22⋊D6111yescharacteristic
205C8—42no—
206C22—22no—
207C22—41no—
208C22—42no—
209C22—1224no—
210C22—1222no—
211C22—4884no—
212C22—4888no—
213C22—2444no—
214C22—2442no—
215C22C2×#1175819811yescharacteristic
216C22#1451974712yes—
217C4—22no—
218C4—1222no—
219C4—4882no—
220C4C22⋊C4×D6111yescharacteristic
221C4C22⋊C4×D6111yescharacteristic
222C4#1451974512yes—
223C2—22no—
224C2—21no—
225C2—42no—
226C2—2444no—
227C2—2442no—
228C2#1683961711yescharacteristic
subgroupG/H
centerC2#16839617
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#413C2
socleC2×C61#379
hypercenter#413D61
hypocenterC61#1795
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #16839778C2semidirect
3. #16839768C2semidirect
4. #16839736C2semidirect
5. C61×#413C2semidirect
9. C2×#11758222C4semidirect
11. C22×D244C4semidirect
15. #14519736C22semidirect
20. C2×M16×C61C22semidirect
118. #413D61semidirect
120. C61#1795semidirect
131. C2×M16C2×D61semidirect