Finite Group Databasebeta

← #21454300

Subgroups — #21454300

Order 7808.

704 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 209 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#16840528C212yesmaximal, complemented
3#16839746C211yesmaximal, characteristic, complemented
4#16839743C214yesmaximal, complemented
5C2×#14519695C212yesmaximal, complemented
6#101×D61C214yesmaximal, complemented
7C61×#413C211yesmaximal, characteristic, complemented
8#14519824—24no—
9#14519824—24no—
10C2×#11758222C412yes—
11C2×#11758222C2211yescharacteristic
12C2×#11758224C414yes—
13C2×#11758224C2212yes—
14C22×Dic122C412yes—
15C22×Dic122C2211yescharacteristic
16C2×Q8×D61C2212yes—
17#14519785—24no—
18#14519783—24no—
19C2×#11758194C2212yes—
20M16×D61C2218yes—
21#14519696C2212yes—
22#14519695C2218yes—
23#14519694C2212yes—
24C2×#41×C61C2211yescharacteristic
25C2×M16×C61C2212yes—
26#101×C61C2212yes—
27#100×C61C2212yes—
28#41×C61—22no—
29#41×C61—22no—
30C2×Q8×C61C2311yescharacteristic
31C2×D4×C61C2×C412yes—
32C2×D4×C61C2311yescharacteristic
33C22×C4×C61C2×C412yes—
34C22×C4×C61C2311yescharacteristic
35C2×C22⋊D61C2×C414yes—
36C2×C22⋊D61C2×C412yes—
37C22×Dic61C2×C414yes—
38C22×Dic61C2×C412yes—
39Q8×D61—28no—
40#11758224—216no—
41#11758224—28no—
42#11758222—24no—
43#11758222—24no—
44#11758222D414yes—
45#11758222D414yes—
46C2×D244C2×C411yescharacteristic
47C2×C4×D61C2×C414yes—
48C2×C4×D61C2312yes—
49C2×Dic122—22no—
50C2×Dic122—22no—
51C2×Dic122—24no—
52C2×Dic122—24no—
53C2×Dic122C2×C414yes—
54C2×Dic122C2×C412yes—
55C2×Dic122C2×C411yescharacteristic
56C2×Dic122C2312yes—
57M16×C61—22no—
58M16×C61C2314yes—
59C2×C8×C61—22no—
60#11758194—22no—
61#11758194C2314yes—
62C2×#92418—22no—
63#11758189—28no—
64C8×D61—28no—
65C23×C61C22×C412yes—
66C23×C61C22×C411yescharacteristic
67C22×D61C22×C412yes—
68Q8×C61—22no—
69D4×C61—24no—
70D4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61C22×C412yes—
74C2×C4×C61C22×C411yescharacteristic
75C2×C4×C61C2×D412yes—
76C2×C4×C61C2×D412yes—
77C2×C4×C61C2411yescharacteristic
78C22⋊D61—28no—
79C22⋊D61C22⋊C418yes—
80C2×Dic61—24no—
81C2×Dic61—28no—
82C2×Dic61C22×C414yes—
83C2×Dic61C22×C412yes—
84D244C22⋊C412yes—
85D244C22⋊C412yes—
86C4×D61—28no—
87C4×D61C2×D418yes—
88Dic122—22no—
89Dic122—22no—
90Dic122—24no—
91Dic122—28no—
92Dic122C22⋊C412yes—
93Dic122C22⋊C412yes—
94C8×C61—24no—
95#92418—24no—
96C22×C61—22no—
97C22×C61—41no—
98C22×C61—42no—
99C22×C61C2×C22⋊C412yes—
100C22×C61C23×C411yescharacteristic
101C2×D61—42no—
102C2×D61C2×C22⋊C414yes—
103C4×C61—22no—
104C4×C61C2×C22⋊C411yescharacteristic
105C4×C61C2×C22⋊C411yescharacteristic
106C4×C61C22×D412yes—
107Dic61—24no—
108Dic61C2×C22⋊C414yes—
109#2889—611nomaximal, Sylow
110C2×C61—21no—
111C2×C61—22no—
112C2×C61—42no—
113C2×C61C22×C22⋊C411yescharacteristic
114D61—24no—
115C2×2−1+4—611no—
116#568—612no—
117#413—611no—
118#413—614no—
119#413D6111yescharacteristic, complemented
120C2×#101—612no—
121C2×#101—614no—
122C61#288911yescharacteristic, complemented, Sylow
1232−1+4—1224no—
1242−1+4—1224no—
125C2×#41—614no—
126C2×#41—612no—
127C2×#41—612no—
128C2×#41—611no—
129C2×#41C2×D6111yescharacteristic
130C22×Q8—612no—
131C22×Q8—612no—
132C22×Q8—611no—
133#131—1224no—
134#131—1224no—
135C2×M16—612no—
136C2×M16—618no—
137C2×M16C2×D6112yes—
138#101—612no—
139#101—618no—
140#101C2×D6112yes—
141#100—612no—
142#100C2×D6112yes—
143#41—22no—
144#41—22no—
145#41—614no—
146#41—614no—
147#41—1224no—
148#41—1224no—
149#41—1228no—
150#41—12216no—
151C2×Q8—611no—
152C2×Q8—614no—
153C2×Q8—612no—
154C2×Q8—612no—
155C2×Q8—1224no—
156C2×Q8—1224no—
157C2×Q8—1228no—
158C2×Q8—1222no—
159C2×Q8—1222no—
160C2×Q8C22×D6111yescharacteristic
161C2×D4—612no—
162C2×D4—614no—
163C2×D4—611no—
164C2×D4C4×D6112yes—
165C2×D4C22×D6111yescharacteristic
166C22×C4—612no—
167C22×C4—614no—
168C22×C4—612no—
169C22×C4—614no—
170C22×C4C4×D6112yes—
171C22×C4C22×D6111yescharacteristic
172M16—22no—
173M16—614no—
174M16—1228no—
175M16—1222no—
176M16C22×D6114yes—
177C2×C8—22no—
178C2×C8—1228no—
179C2×C8—1222no—
180C23—612no—
181C23C2×C4×D6112yes—
182C23C2×C4×D6111yescharacteristic
183Q8—22no—
184Q8—612no—
185Q8—612no—
186Q8—1228no—
187Q8—1224no—
188Q8—1222no—
189Q8—1222no—
190D4—24no—
191D4—22no—
192D4—618no—
193D4—612no—
194D4—612no—
195D4—1228no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—612no—
199C2×C4—618no—
200C2×C4—614no—
201C2×C4—1228no—
202C2×C4—1228no—
203C2×C4—1224no—
204C2×C4C2×C4×D6112yes—
205C2×C4C2×C4×D6111yescharacteristic
206C2×C4D4×D6112yes—
207C2×C4D4×D6112yes—
208C2×C4C23×D6111yescharacteristic
209C8—24no—
210C8—1224no—
211C22—22no—
212C22—41no—
213C22—42no—
214C22—614no—
215C22—2442no—
216C22C22⋊C4×D6112yes—
217C22C22×C4×D6111yescharacteristic
218C4—22no—
219C4—614no—
220C4—1224no—
221C4C22⋊C4×D6111yescharacteristic
222C4C22⋊C4×D6111yescharacteristic
223C4C2×D4×D6112yes—
224C2—21no—
225C2—22no—
226C2—42no—
227C2—1224no—
228C2C2×C22⋊C4×D6111yescharacteristic
subgroupG/H
centerC2C2×C22⋊C4×D61
commutatorC22×C61C23×C4
FrattiniC2×C4C23×D61
FittingC61×#413C2
socleC2×C61C22×C22⋊C4
hypercenter#413D61
hypocenterC61#2889
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #16840528C2semidirect
3. #16839746C2semidirect
4. #16839743C2semidirect
5. C2×#14519695C2semidirect
6. #101×D61C2semidirect
7. C61×#413C2semidirect
119. #413D61semidirect
122. C61#2889semidirect