Finite Group Databasebeta

← #21455620

Subgroups — #21455620

Order 7808.

376 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 145 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×C4×Dic122C211yesmaximal, characteristic
2#16840066C214yesmaximal, complemented
3#16840054C212yesmaximal, complemented
4#16840044C212yesmaximal, complemented
5#16839805C212yesmaximal
6#16839786C211yesmaximal, characteristic
7#16839770C212yesmaximal
8C61×#533C211yesmaximal, characteristic
9C22×Dic122C2211yescharacteristic
10C2×#11758194C2212yes—
11C4×Dic122—21no—
12C4×Dic122—21no—
13C4×Dic122C2212yes—
14C4×Dic122C2212yes—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×#11758196—21no—
17C2×C4×Dic61—21no—
18#14519710C2214yes—
19#14519708C2214yes—
20C4⋊#92418C2212yes—
21C4⋊#92418C2212yes—
22#14519700C2214yes—
23#14519700C2214yes—
24C4⋊Q8×C61C2211yescharacteristic
25C4⋊Q8×C61C2211yescharacteristic
26#125×C61C2212yes—
27C22⋊Q8×C61—21no—
28C22⋊Q8×C61—21no—
29C4×Q8×C61—21no—
30C4×Q8×C61—21no—
31#117×C61C2212yes—
32C2×C42×C61C2211yescharacteristic
33C2×Q8×C61—21no—
34C2×Q8×C61—21no—
35C22×C4×C61D411yescharacteristic
36C22×C4×C61D411yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C22×Dic61—21no—
39C22×Dic61—21no—
40C2×Dic122—21no—
41C2×Dic122—22no—
42C2×Dic122Q814yescomplemented
43C2×Dic122C2312yes—
44C4⋊C4×C61—22no—
45C4⋊C4×C61—22no—
46C4⋊C4×C61—21no—
47C4⋊C4×C61—21no—
48C4⋊C4×C61C2312yes—
49C4⋊C4×C61C2312yes—
50C22⋊C4×C61—22no—
51C42×C61—22no—
52C42×C61D411yescharacteristic
53C42×C61D411yescharacteristic
54C42×C61C2311yescharacteristic
55C42×C61C2311yescharacteristic
56C4⋊Dic61—21no—
57C4⋊Dic61C2312yes—
58#11758196—22no—
59#11758196—22no—
60C4×Dic61—22no—
61C4×Dic61—22no—
62#11758194—24no—
63C2×#92418C2314yes—
64C23×C61C2×D411yescharacteristic
65Q8×C61—42no—
66Q8×C61—42no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—41no—
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2×Q812yes—
77C2×C4×C61#4112yes—
78C2×C4×C61C2411yescharacteristic
79C2×Dic61—24no—
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61—42no—
83Dic122—24no—
84Dic122—22no—
85Dic122C2×Q814yes—
86#92418—24no—
87C22×C61—21no—
88C22×C61—21no—
89C22×C61C22⋊Q812yes—
90C22×C61C22×D411yescharacteristic
91C4×C61—21no—
92C4×C61—21no—
93C4×C61—21no—
94C4×C61—42no—
95C4×C61—42no—
96C4×C61C22⋊Q812yes—
97C4×C61#13712yes—
98C4×C61C22×Q811yescharacteristic
99C4×C61C2×#4111yescharacteristic
100Dic61—24no—
101Dic61—42no—
102#3078—611nomaximal, Sylow
103C2×C61—22no—
104C2×C61C2×C22⋊Q811yescharacteristic
105C2×C61C2×#13711yescharacteristic
106C2×C61#57511yescharacteristic
107#533D6111yescharacteristic
108C2×C4×Q8—611no—
109#479—614no—
110#477—612no—
111#475—612no—
112#428—612no—
113#423—611no—
114#419—612no—
115C61#307811yescharacteristic, complemented, Sylow
116C22×Q8—611no—
117C2×M16—612no—
118C4⋊Q8C2×D6111yescharacteristic
119C4⋊Q8C2×D6111yescharacteristic
120#125C2×D6112yes—
121C22⋊Q8—21no—
122C22⋊Q8—21no—
123C4×Q8—21no—
124C4×Q8—21no—
125C4×Q8—612no—
126C4×Q8—612no—
127C4×Q8—1221no—
128C4×Q8—1221no—
129#117C2×D6112yes—
130C2×C4⋊C4—611no—
131C2×C4⋊C4—1221no—
132C2×C42—1221no—
133C2×C42C2×D6111yescharacteristic
134#107—614no—
135#106—614no—
136C4⋊C8—612no—
137C4⋊C8—612no—
138#103—614no—
139#103—614no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—614no—
143C2×Q8—612no—
144C2×Q8—1222no—
145C2×Q8—1221no—
146C22×C4—1221no—
147C22×C4—1221no—
148C22×C4C22⋊D6111yescharacteristic
149C22×C4C22⋊D6111yescharacteristic
150C22×C4C22×D6111yescharacteristic
151M16—1224no—
152C2×C8—614no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—612no—
158C4⋊C4—1221no—
159C4⋊C4—1222no—
160C4⋊C4—1222no—
161C4⋊C4C22×D6112yes—
162C4⋊C4C22×D6112yes—
163C22⋊C4—22no—
164C42—22no—
165C42—1222no—
166C42—1222no—
167C42C22⋊D6111yescharacteristic
168C42C22⋊D6111yescharacteristic
169C42C22×D6111yescharacteristic
170C42C22×D6111yescharacteristic
171C23C2×C22⋊D6111yescharacteristic
172Q8—42no—
173Q8—42no—
174Q8—614no—
175Q8—1222no—
176Q8—1224no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—41no—
181C2×C4—1222no—
182C2×C4—1224no—
183C2×C4—1222no—
184C2×C4—2442no—
185C2×C4Q8×D6112yes—
186C2×C4#1175822612yes—
187C2×C4C2×C22⋊D6111yescharacteristic
188C2×C4C2×C22⋊D6111yescharacteristic
189C2×C4C2×C22⋊D6111yescharacteristic
190C2×C4C2×C22⋊D6111yescharacteristic
191C2×C4C2×C22⋊D6111yescharacteristic
192C2×C4C23×D6111yescharacteristic
193C8—1224no—
194C22—21no—
195C22—21no—
196C22#1451975312yes—
197C22C22×C22⋊D6111yescharacteristic
198C4—21no—
199C4—21no—
200C4—21no—
201C4—42no—
202C4—42no—
203C4—1224no—
204C4—2442no—
205C4#1451975312yes—
206C4#1451980712yes—
207C4C2×Q8×D6111yescharacteristic
208C4C2×#1175822611yescharacteristic
209C2—22no—
210C2C2×#1451975311yescharacteristic
211C2C2×#1451980711yescharacteristic
212C2#1684056011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#533C2
socleC22×C61C22×D4
hypercenter#533D61
hypocenterC61#3078
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #16840066C2semidirect
3. #16840054C2semidirect
4. #16840044C2semidirect
42. C2×Dic122Q8semidirect
115. C61#3078semidirect