Finite Group Databasebeta

← #21455349

Subgroups — #21455349

Order 7808.

458 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14519808C211yesmaximal, characteristic
2C22×#11758202C211yesmaximal, characteristic, complemented
3#16840338C211yesmaximal, characteristic
4#16839984C214yesmaximal, complemented
5#16839972C214yesmaximal, complemented
6#16839789C211yesmaximal, characteristic, complemented
7#16839770C211yesmaximal, characteristic, complemented
8#16839756C211yesmaximal, characteristic
9C61×#519C211yesmaximal, characteristic, complemented
10C2×#11758222C2211yescharacteristic
11C22×Dic122C2211yescharacteristic
12#14519808—24no—
13C2×#11758202—24no—
14C2×#11758202C2212yes—
15C2×#11758202C2214yes—
16C2×#11758201C2212yes—
17C2×#11758194C2211yescharacteristic
18C22×#92418C2211yescharacteristic
19#14519777C2212yes—
20#14519765C2212yes—
21#14519761—22no—
22#14519757—22no—
23C4⋊#92418C2214yes—
24#14519700C2212yes—
25#14519700C2214yes—
26#14519697C2212yes—
27C22×Q8×C61C2211yescharacteristic
28C4×Q8×C61—22no—
29C4×Q8×C61C2214yes—
30#117×C61—22no—
31#117×C61C2211yescharacteristic
32#117×C61C2211yescharacteristic
33C2×Q8×C61—21no—
34C2×Q8×C61—22no—
35C2×Q8×C61D414yes—
36C2×Q8×C61C2312yes—
37C22×C4×C61—21no—
38C22×C4×C61C2311yescharacteristic
39C2×C22⋊D61—21no—
40C22×Dic61—21no—
41#11758222—22no—
42#11758222—22no—
43C2×D244C2311yescharacteristic
44C2×C4×D61—21no—
45C2×Dic122—22no—
46C2×Dic122—22no—
47C2×Dic122—21no—
48C2×Dic122C2312yes—
49C2×Dic122C2311yescharacteristic
50C4⋊C4×C61—24no—
51C4⋊C4×C61D412yes—
52C4⋊C4×C61C2312yes—
53C22⋊C4×C61—21no—
54C22⋊C4×C61D412yes—
55C42×C61—24no—
56C42×C61—21no—
57C42×C61C2312yes—
58#11758202—24no—
59#11758202—28no—
60#11758201—24no—
61#11758198—24no—
62C4⋊Dic61—24no—
63#11758194—22no—
64C2×#92418—22no—
65C2×#92418C2312yes—
66C2×#92418C2312yes—
67C23×C61C2×D411yescharacteristic
68C22×D61—21no—
69Q8×C61—24no—
70Q8×C61—22no—
71Q8×C61C2×D414yes—
72C2×C4×C61—24no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61C2×D414yes—
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D412yes—
78C2×C4×C61#4112yes—
79C2×C4×C61C2411yescharacteristic
80C22⋊D61—42no—
81C2×Dic61—21no—
82C2×Dic61—22no—
83C2×Dic61—42no—
84D244—21no—
85D244—21no—
86C4×D61—42no—
87Dic122—22no—
88Dic122—21no—
89Dic122—22no—
90Dic122—21no—
91Dic122—42no—
92#92418—22no—
93#92418—22no—
94C22×C61—22no—
95C22×C61#12112yes—
96C22×C61C22×D411yescharacteristic
97C2×D61—41no—
98C2×D61—42no—
99C4×C61—24no—
100C4×C61—24no—
101C4×C61—42no—
102C4×C61#12112yes—
103C4×C61C22×D411yescharacteristic
104C4×C61C2×#4111yescharacteristic
105Dic61—42no—
106Dic61—41no—
107#3044—611nomaximal, Sylow
108C2×C61—22no—
109C2×C61C2×#12111yescharacteristic
110C2×C61#57812yes—
111D61—81no—
112C2×#137—611no—
113C22×Q16—611no—
114#536—611no—
115#519D6111yescharacteristic, complemented
116#464—614no—
117#462—614no—
118#424—611no—
119#419—611no—
120#416—611no—
121C61#304411yescharacteristic, complemented, Sylow
122C2×#41—611no—
123C22×Q8—611no—
124C22×Q8C2×D6111yescharacteristic
125#137—1224no—
126C2×Q16—614no—
127C2×Q16—612no—
128C2×Q16—1224no—
129C2×SD16—612no—
130C2×M16—611no—
131C22×C8—611no—
132C4⋊Q8—612no—
133#124—612no—
134#123—1222no—
135C22⋊Q8—1222no—
136C4×Q8—22no—
137C4×Q8C2×D6114yes—
138#117—22no—
139#117C2×D6111yescharacteristic
140#117C2×D6111yescharacteristic
141C4⋊C8—614no—
142#103—612no—
143#103—614no—
144#102—612no—
145#41—1222no—
146#41—1222no—
147C2×Q8—22no—
148C2×Q8—21no—
149C2×Q8—612no—
150C2×Q8—611no—
151C2×Q8—1221no—
152C2×Q8—1222no—
153C2×Q8—1222no—
154C2×Q8D24414yes—
155C2×Q8C22×D6112yes—
156C2×D4—611no—
157C2×D4—1221no—
158C22×C4—21no—
159C22×C4—1221no—
160C22×C4—1221no—
161C22×C4C22×D6111yescharacteristic
162Q16—1228no—
163Q16—1224no—
164SD16—1224no—
165M16—1222no—
166C2×C8—612no—
167C2×C8—612no—
168C2×C8—1222no—
169C4⋊C4—24no—
170C4⋊C4—1224no—
171C4⋊C4C22⋊D6112yes—
172C4⋊C4C22×D6112yes—
173C22⋊C4—21no—
174C22⋊C4—1224no—
175C22⋊C4C22⋊D6112yes—
176C42—24no—
177C42—21no—
178C42C22×D6112yes—
179C23—1221no—
180C23C2×C22⋊D6111yescharacteristic
181Q8—22no—
182Q8—24no—
183Q8—1222no—
184Q8—1221no—
185Q8—1222no—
186Q8—1221no—
187Q8—2442no—
188Q8C2×D24414yes—
189D4—1221no—
190D4—1221no—
191D4—2442no—
192C2×C4—22no—
193C2×C4—24no—
194C2×C4—22no—
195C2×C4—1222no—
196C2×C4—1221no—
197C2×C4—2442no—
198C2×C4—2442no—
199C2×C4C2×D24412yes—
200C2×C4#1175822212yes—
201C2×C4C2×C22⋊D6114yes—
202C2×C4C2×C22⋊D6111yescharacteristic
203C2×C4C23×D6111yescharacteristic
204C8—1222no—
205C8—1222no—
206C22—22no—
207C22—2441no—
208C22—2442no—
209C22#1451975112yes—
210C22C22×C22⋊D6111yescharacteristic
211C4—24no—
212C4—24no—
213C4—42no—
214C4—2441no—
215C4—2442no—
216C4#1451975112yes—
217C4C22×D24411yescharacteristic
218C4C2×#1175822211yescharacteristic
219C2—22no—
220C2—4881no—
221C2C2×#1451975111yescharacteristic
222C2#1684057712yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#519C2
socleC22×C61C22×D4
hypercenter#519D61
hypocenterC61#3044
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
2. C22×#11758202C2semidirect
4. #16839984C2semidirect
5. #16839972C2semidirect
6. #16839789C2semidirect
7. #16839770C2semidirect
9. C61×#519C2semidirect
115. #519D61semidirect
121. C61#3044semidirect