Finite Group Databasebeta

← #21455482

Subgroups — #21455482

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#16840021C212yesmaximal, complemented
5#16840016C212yesmaximal, complemented
6#16839992C214yesmaximal, complemented
7#16839761C212yesmaximal, complemented
8C2×#106×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#106×C61C2212yes—
29#106×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—22no—
87C22×C61#12112yes—
88C22×C61C22×D411yescharacteristic
89C2×D61—22no—
90C2×D61—24no—
91C2×D61—42no—
92C2×D61—42no—
93C2×D61—42no—
94C4×C61—44no—
95C4×C61#12112yes—
96C4×C61C22×D411yescharacteristic
97C4×C61C2×#4111yescharacteristic
98Dic61—22no—
99Dic61—42no—
100#3060—611nomaximal, Sylow
101C2×C61—22no—
102C2×C61C2×#12111yescharacteristic
103C2×C61#57712yes—
104D61—42no—
105D61—82no—
106C2×#135—611no—
107C2×#131—611no—
108#537—612no—
109#470—612no—
110#469—612no—
111#465—614no—
112C2×#106D6111yescharacteristic, complemented
113#417—612no—
114C61#306011yescharacteristic, complemented, Sylow
115C2×#41—611no—
116C2×#41—612no—
117#135—1224no—
118C2×Q16—611no—
119C2×SD16—612no—
120C2×D8—611no—
121#131—1224no—
122C2×M16—611no—
123C2×M16—612no—
124C22×C8—612no—
125C22×C8C2×D6111yescharacteristic
126C22⋊Q8—614no—
127C22⋊Q8—1222no—
128#121—614no—
129#121—1222no—
130#121—1224no—
131C2×C4⋊C4C2×D6112yes—
132#106C2×D6112yes—
133#106C2×D6112yes—
134#103—614no—
135#102—614no—
136#41—1222no—
137#41—1222no—
138#41—1224no—
139#41—1224no—
140C2×Q8—611no—
141C2×Q8—612no—
142C2×D4—612no—
143C2×D4—611no—
144C2×D4—612no—
145C2×D4—1224no—
146C2×D4—1222no—
147C22×C4—22no—
148C22×C4—612no—
149C22×C4—1222no—
150C22×C4C22×D6111yescharacteristic
151Q16—1222no—
152SD16—1224no—
153D8—1222no—
154M16—1222no—
155M16—1224no—
156C2×C8—612no—
157C2×C8—1224no—
158C2×C8D24414yescomplemented
159C2×C8C22×D6111yescharacteristic
160C2×C8C22×D6111yescharacteristic
161C4⋊C4—22no—
162C4⋊C4—1224no—
163C4⋊C4C22×D6114yes—
164C22⋊C4—1224no—
165C22⋊C4—1224no—
166C23—612no—
167C23—1222no—
168C23D4×D6111yescharacteristic
169Q8—1222no—
170Q8—1222no—
171Q8—1222no—
172D4—1224no—
173D4—1222no—
174D4—1222no—
175D4—1222no—
176D4—4884no—
177D4—2444no—
178C2×C4—24no—
179C2×C4—82no—
180C2×C4—612no—
181C2×C4—1222no—
182C2×C4—1222no—
183C2×C4—1222no—
184C2×C4—2444no—
185C2×C4C2×D24412yes—
186C2×C4D4×D6111yescharacteristic
187C2×C4#1175822612yes—
188C2×C4C23×D6111yescharacteristic
189C8—1222no—
190C8C2×D24412yes—
191C8C2×D24412yes—
192C22—22no—
193C22—1222no—
194C22—1224no—
195C22—2442no—
196C22—2442no—
197C22—2442no—
198C22#1451975212yes—
199C22C2×D4×D6111yescharacteristic
200C4—44no—
201C4—1222no—
202C4—2442no—
203C4#1451975212yes—
204C4C22×D24411yescharacteristic
205C4C2×#1175822611yescharacteristic
206C2—22no—
207C2—4882no—
208C2—2442no—
209C2C2×#1451975211yescharacteristic
210C2#1684056812yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#106×C61C2
socleC22×C61C22×D4
hypercenterC2×#106D61
hypocenterC61#3060
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
1. C2×#14519799C2semidirect
2. C2×#14519783C2semidirect
3. #16840343C2semidirect
4. #16840021C2semidirect
5. #16840016C2semidirect
6. #16839992C2semidirect
7. #16839761C2semidirect
8. C2×#106×C61C2semidirect
45. C2×C8×C61D4semidirect
112. C2×#106D61semidirect
114. C61#3060semidirect
158. C2×C8D244semidirect