Finite Group Databasebeta

← #21455491

Subgroups — #21455491

Order 7808.

484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14519799C211yesmaximal, characteristic, complemented
2C2×#14519783C211yesmaximal, characteristic, complemented
3#16840343C212yesmaximal, complemented
4#16840009C214yesmaximal, complemented
5#16840004C212yesmaximal, complemented
6#16839999C212yesmaximal, complemented
7#16839761C212yesmaximal, complemented
8C2×#107×C61C211yesmaximal, characteristic, complemented
9C2×#11758222C2211yescharacteristic
10C2×#11758222C2212yes—
11#14519799—24no—
12C2×Dic244C2211yescharacteristic
13C2×#11758190C2212yes—
14C2×D488C2211yescharacteristic
15#14519783—24no—
16C2×#11758194C2211yescharacteristic
17C2×#11758189C2212yes—
18C2×C8×D61C2212yes—
19#14519757—22no—
20#14519757C2214yes—
21#14519752—22no—
22#14519752C2214yes—
23#14519751—24no—
24#14519700C2214yes—
25#14519697C2214yes—
26C22×C8×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2212yes—
28#107×C61C2212yes—
29#107×C61C2212yes—
30C22×C4×C61—22no—
31C22×C4×C61C2311yescharacteristic
32C2×C22⋊D61—22no—
33C2×C22⋊D61D412yes—
34#11758222—22no—
35#11758222—22no—
36#11758222—24no—
37#11758222—24no—
38C2×D244—24no—
39C2×D244D411yescharacteristic
40C2×D244C2312yes—
41C2×C4×D61—22no—
42C2×C4×D61C2312yes—
43C2×Dic122D411yescharacteristic
44C2×Dic122C2312yes—
45C2×C8×C61D414yescomplemented
46C2×C8×C61C2311yescharacteristic
47C2×C8×C61C2311yescharacteristic
48C4⋊C4×C61—22no—
49C4⋊C4×C61C2314yes—
50#11758198—24no—
51#11758198—24no—
52C4⋊Dic61—24no—
53#11758194—22no—
54C2×#92418C2312yes—
55Dic244—22no—
56D488—22no—
57#11758190—24no—
58#11758189—24no—
59C8×D61—24no—
60C23×C61C2×D411yescharacteristic
61C22×D61—22no—
62C22×D61C2×D412yes—
63C2×C4×C61—24no—
64C2×C4×C61—82no—
65C2×C4×C61C2×D411yescharacteristic
66C2×C4×C61C2×D412yes—
67C2×C4×C61#4112yes—
68C2×C4×C61C2411yescharacteristic
69C22⋊D61—24no—
70C22⋊D61—44no—
71C2×Dic61—22no—
72C2×Dic61C2×D412yes—
73D244—22no—
74D244—22no—
75D244—22no—
76D244—84no—
77C4×D61—22no—
78C4×D61—22no—
79C4×D61—44no—
80Dic122—22no—
81Dic122—22no—
82Dic122—22no—
83C8×C61C2×D412yes—
84C8×C61C2×D412yes—
85#92418—22no—
86C22×C61—21no—
87C22×C61—21no—
88C22×C61#12112yes—
89C22×C61C22×D411yescharacteristic
90C2×D61—22no—
91C2×D61—22no—
92C2×D61—22no—
93C2×D61—42no—
94C2×D61—42no—
95C2×D61—42no—
96C4×C61—44no—
97C4×C61#12112yes—
98C4×C61C22×D411yescharacteristic
99C4×C61C2×#4111yescharacteristic
100Dic61—22no—
101Dic61—42no—
102#3061—611nomaximal, Sylow
103C2×C61—22no—
104C2×C61C2×#12111yescharacteristic
105C2×C61#57611yescharacteristic
106C2×C61#57811yescharacteristic
107D61—42no—
108D61—82no—
109C2×#135—611no—
110C2×#131—611no—
111#537—612no—
112#468—614no—
113#467—612no—
114#466—612no—
115C2×#107D6111yescharacteristic, complemented
116#417—612no—
117C61#306111yescharacteristic, complemented, Sylow
118C2×#41—611no—
119C2×#41—612no—
120#135—1224no—
121C2×Q16—611no—
122C2×SD16—612no—
123C2×D8—611no—
124#131—1224no—
125C2×M16—611no—
126C2×M16—612no—
127C22×C8—612no—
128C22×C8C2×D6111yescharacteristic
129C22⋊Q8—614no—
130C22⋊Q8—1222no—
131#121—614no—
132#121—1222no—
133#121—1224no—
134C2×C4⋊C4C2×D6112yes—
135#107C2×D6112yes—
136#107C2×D6112yes—
137#103—614no—
138#102—614no—
139#41—1222no—
140#41—1222no—
141#41—1224no—
142#41—1224no—
143C2×Q8—611no—
144C2×Q8—612no—
145C2×D4—612no—
146C2×D4—611no—
147C2×D4—612no—
148C2×D4—1224no—
149C2×D4—1222no—
150C22×C4—22no—
151C22×C4—612no—
152C22×C4—1222no—
153C22×C4C22×D6111yescharacteristic
154Q16—1222no—
155SD16—1224no—
156D8—1222no—
157M16—1222no—
158M16—1224no—
159C2×C8—612no—
160C2×C8—1224no—
161C2×C8D24414yescomplemented
162C2×C8C22×D6111yescharacteristic
163C2×C8C22×D6111yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—1224no—
166C4⋊C4C22×D6114yes—
167C22⋊C4—1224no—
168C22⋊C4—1224no—
169C23—612no—
170C23—1222no—
171C23D4×D6111yescharacteristic
172Q8—1222no—
173Q8—1222no—
174Q8—1222no—
175D4—1224no—
176D4—1222no—
177D4—1222no—
178D4—1222no—
179D4—4884no—
180D4—2444no—
181C2×C4—24no—
182C2×C4—82no—
183C2×C4—612no—
184C2×C4—1222no—
185C2×C4—1222no—
186C2×C4—1222no—
187C2×C4—2444no—
188C2×C4C2×D24412yes—
189C2×C4D4×D6111yescharacteristic
190C2×C4#1175822612yes—
191C2×C4C23×D6111yescharacteristic
192C8—1222no—
193C8C2×D24412yes—
194C8C2×D24412yes—
195C22—21no—
196C22—21no—
197C22—1222no—
198C22—1222no—
199C22—1222no—
200C22—2442no—
201C22—2442no—
202C22—2442no—
203C22#1451975212yes—
204C22C2×D4×D6111yescharacteristic
205C4—44no—
206C4—1222no—
207C4—2442no—
208C4#1451975212yes—
209C4C22×D24411yescharacteristic
210C4C2×#1175822611yescharacteristic
211C2—22no—
212C2—4882no—
213C2—2442no—
214C2C2×#1451975211yescharacteristic
215C2#1684056311yescharacteristic
216C2#1684057511yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#107×C61C2
socleC22×C61C22×D4
hypercenterC2×#107D61
hypocenterC61#3061
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. C2×#14519799C2semidirect
2. C2×#14519783C2semidirect
3. #16840343C2semidirect
4. #16840009C2semidirect
5. #16840004C2semidirect
6. #16839999C2semidirect
7. #16839761C2semidirect
8. C2×#107×C61C2semidirect
45. C2×C8×C61D4semidirect
115. C2×#107D61semidirect
117. C61#3061semidirect
161. C2×C8D244semidirect