Finite Group Databasebeta

← #21457280

Subgroups — #21457280

Order 7808.

346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 117 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
1#16840383C212yesmaximal, complemented
2#16840058C212yesmaximal, complemented
3#16840043C212yesmaximal, complemented
4#16840008C212yesmaximal, complemented
5#16840003C211yesmaximal, characteristic, complemented
6#16839998C211yesmaximal, characteristic
7#16839985C212yesmaximal, complemented
8#16839978C212yesmaximal, complemented
9C61×#424C211yesmaximal, characteristic, complemented
10C2×Dic244C2211yescharacteristic
11C2×#11758190C2212yes—
12C2×D488C2211yescharacteristic
13#14519777C2212yes—
14#14519772—22no—
15#14519765C2212yes—
16#14519763—22no—
17#14519759—22no—
18#14519756C2212yes—
19#14519755—22no—
20#14519751C2212yes—
21C4×Dic122C2212yes—
22C4×D244C2212yes—
23#14519711C2211yescharacteristic
24#14519711C2211yescharacteristic
25#14519711C2212yes—
26#14519702C2212yes—
27#14519702C2212yes—
28#14519699C2212yes—
29#14519699C2212yes—
30C2×M16×C61C2211yescharacteristic
31C22×C8×C61C2211yescharacteristic
32#117×C61C2211yescharacteristic
33C4⋊C8×C61C2212yes—
34C4⋊C8×C61C2212yes—
35C22×C4×C61C2311yescharacteristic
36C2×C22⋊D61—22no—
37C2×D244C2312yes—
38C2×C4×D61—22no—
39C2×Dic122—22no—
40C2×Dic122C2312yes—
41M16×C61—41no—
42C2×C8×C61—41no—
43C2×C8×C61C2311yescharacteristic
44C2×C8×C61C2311yescharacteristic
45C2×C8×C61C2312yes—
46C4⋊C4×C61D411yescharacteristic
47C4⋊C4×C61D411yescharacteristic
48C22⋊C4×C61D412yes—
49C42×C61C2312yes—
50C22⋊Dic61—22no—
51#11758198—22no—
52#11758198—22no—
53#11758198—22no—
54#11758198—22no—
55C4⋊Dic61—22no—
56C4⋊Dic61C2312yes—
57C4⋊Dic61C2312yes—
58#11758196—22no—
59#11758196—22no—
60C4×Dic61—22no—
61Dic244—41no—
62D488—41no—
63#11758190—42no—
64C23×C61C2×D411yescharacteristic
65C22×D61—22no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61C2×D412yes—
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D412yes—
71C2×C4×C61C2411yescharacteristic
72C22⋊D61—82no—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76D244—22no—
77D244—22no—
78C4×D61—82no—
79Dic122—22no—
80Dic122—22no—
81Dic122—82no—
82C8×C61—22no—
83C8×C61—21no—
84C8×C61—21no—
85C22×C61—21no—
86C22×C61—21no—
87C22×C61—21no—
88C22×C61C22×D411yescharacteristic
89C2×D61—42no—
90C2×D61—42no—
91C2×D61—42no—
92C4×C61—21no—
93C4×C61—22no—
94C4×C61—22no—
95C4×C61H(5,𝔽2)11yescharacteristic
96C4×C612−1+411yescharacteristic
97Dic61—42no—
98Dic61—42no—
99Dic61—42no—
100#3262—611nomaximal, Sylow
101C2×C61—41no—
102C2×C61#53711yescharacteristic
103C2×C61#57611yescharacteristic
104C2×C61#57811yescharacteristic
105D61—82no—
106#542—612no—
107#477—612no—
108#474—612no—
109#468—612no—
110#467—611no—
111#466—611no—
112#464—612no—
113#463—612no—
114#424D6111yescharacteristic, complemented
115C61#326211yescharacteristic, complemented, Sylow
116C2×Q16—611no—
117C2×SD16—612no—
118C2×D8—611no—
119C2×M16C2×D6111yescharacteristic
120C22×C8C2×D6111yescharacteristic
121C4⋊Q8—612no—
122#126—1222no—
123#124—612no—
124#124—1222no—
125#123—1222no—
126C22⋊Q8—612no—
127C22⋊Q8—1222no—
128#121—612no—
129C4×Q8—612no—
130C4×D4—612no—
131#117C2×D6111yescharacteristic
132#107—611no—
133#107—611no—
134#107—612no—
135C4⋊C8C2×D6112yes—
136C4⋊C8C2×D6112yes—
137#103—612no—
138#103—612no—
139#102—612no—
140#102—612no—
141C2×Q8—612no—
142C2×Q8—1222no—
143C2×D4—612no—
144C2×D4—1222no—
145C22×C4—1222no—
146C22×C4C22×D6111yescharacteristic
147Q16—2441no—
148SD16—2442no—
149D8—2441no—
150M16—41no—
151C2×C8—41no—
152C2×C8C22×D6111yescharacteristic
153C2×C8C22×D6112yes—
154C2×C8C22×D6111yescharacteristic
155C4⋊C4—612no—
156C4⋊C4—612no—
157C4⋊C4—1222no—
158C4⋊C4—1222no—
159C4⋊C4—1222no—
160C4⋊C4D24411yescharacteristic
161C4⋊C4D24411yescharacteristic
162C22⋊C4—1222no—
163C22⋊C4—1222no—
164C22⋊C4—1222no—
165C22⋊C4—1222no—
166C22⋊C4—1222no—
167C22⋊C4D24412yes—
168C42—1222no—
169C42C22×D6112yes—
170C23—1222no—
171C23C2×D24411yescharacteristic
172Q8—1222no—
173Q8—1222no—
174Q8—4882no—
175D4—1222no—
176D4—1222no—
177D4—4882no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—1222no—
181C2×C4—1222no—
182C2×C4—1222no—
183C2×C4—4882no—
184C2×C4C2×D24412yes—
185C2×C4C2×D24412yes—
186C2×C4C2×D24411yescharacteristic
187C2×C4C23×D6111yescharacteristic
188C8—21no—
189C8—21no—
190C8—22no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—2442no—
195C22—2442no—
196C22—2442no—
197C22C22×D24411yescharacteristic
198C4—22no—
199C4—22no—
200C4—21no—
201C4—2442no—
202C4—2442no—
203C4—2442no—
204C4#1451982211yescharacteristic
205C4#1451982511yescharacteristic
206C2—41no—
207C2—4882no—
208C2#1684034311yescharacteristic
209C2#1684056711yescharacteristic
210C2#1684057911yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#424C2
socleC22×C61C22×D4
hypercenter#424D61
hypocenterC61#3262
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #16840383C2semidirect
2. #16840058C2semidirect
3. #16840043C2semidirect
4. #16840008C2semidirect
5. #16840003C2semidirect
7. #16839985C2semidirect
8. #16839978C2semidirect
9. C61×#424C2semidirect
114. #424D61semidirect
115. C61#3262semidirect