Finite Group Databasebeta

← #21455287

Subgroups — #21455287

Order 7808.

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

normal subgroups only

This group has 484 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×#14519807C212yesmaximal, complemented
2C2×C4×Dic122C211yesmaximal, characteristic, complemented
3#16839981C214yesmaximal, complemented
4#16839969C212yesmaximal, complemented
5#16839959C212yesmaximal, complemented
6#16839786C211yesmaximal, characteristic, complemented
7#16839763C212yesmaximal, complemented
8C61×#532C211yesmaximal, characteristic
9C22×Dic122C2211yescharacteristic
10#14519807—28no—
11C2×#11758202C2214yes—
12C2×#11758200C2214yes—
13C2×#11758194C2212yes—
14C4×Dic122—21no—
15C4×Dic122—21no—
16C4×Dic122C2212yes—
17C4×Dic122C2212yes—
18C2×C4⋊Dic61C2211yescharacteristic
19C2×#11758196—21no—
20C2×C4×Dic61—21no—
21C4⋊#92418C2212yes—
22C4⋊#92418C2212yes—
23#14519701C2214yes—
24#14519698C2214yes—
25C2×#41×C61C2212yes—
26C4⋊Q8×C61C2211yescharacteristic
27#127×C61C2211yescharacteristic
28#124×C61C2212yes—
29#121×C61—21no—
30#121×C61—21no—
31C4×D4×C61—21no—
32C4×D4×C61—21no—
33C2×C42×C61C2211yescharacteristic
34#41×C61—24no—
35#41×C61—24no—
36C2×Q8×C61C2312yes—
37C2×D4×C61—22no—
38C2×D4×C61—21no—
39C2×D4×C61—21no—
40C2×D4×C61C2312yes—
41C22×C4×C61—22no—
42C22×C4×C61D411yescharacteristic
43C22×C4×C61D411yescharacteristic
44C22×C4×C61C2311yescharacteristic
45C22×Dic61—21no—
46C22×Dic61—21no—
47C2×Dic122—21no—
48C2×Dic122—22no—
49C2×Dic122D414yescomplemented
50C2×Dic122C2312yes—
51C4⋊C4×C61—21no—
52C4⋊C4×C61—21no—
53C22⋊C4×C61—22no—
54C22⋊C4×C61—22no—
55C42×C61D411yescharacteristic
56C42×C61D411yescharacteristic
57C42×C61C2311yescharacteristic
58C42×C61C2311yescharacteristic
59#11758202—28no—
60#11758200—28no—
61C4⋊Dic61—21no—
62C4⋊Dic61C2312yes—
63#11758196—22no—
64#11758196—22no—
65C4×Dic61—22no—
66C4×Dic61—22no—
67#11758194—24no—
68C2×#92418C2314yes—
69C23×C61—22no—
70C23×C61C2×D411yescharacteristic
71Q8×C61—22no—
72Q8×C61—22no—
73D4×C61—22no—
74D4×C61—22no—
75D4×C61—42no—
76D4×C61—44no—
77D4×C61—42no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—41no—
81C2×C4×C61—44no—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2×D412yes—
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61#4112yes—
89C2×C4×C61C2411yescharacteristic
90C2×Dic61—24no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—42no—
94Dic122—24no—
95Dic122—22no—
96Dic122C2×D414yes—
97#92418—24no—
98C22×C61—21no—
99C22×C61—21no—
100C22×C61—42no—
101C22×C61—42no—
102C22×C61—42no—
103C22×C61#12112yes—
104C22×C61C22×D411yescharacteristic
105C4×C61—21no—
106C4×C61—21no—
107C4×C61—21no—
108C4×C61—42no—
109C4×C61#12112yes—
110C4×C61#13712yescomplemented
111C4×C61C22×D411yescharacteristic
112C4×C61C2×#4111yescharacteristic
113Dic61—24no—
114Dic61—42no—
115#3037—611nomaximal, Sylow
116C2×C61—22no—
117C2×C61—82no—
118C2×C61C2×#12111yescharacteristic
119C2×C61C2×#13711yescharacteristic
120C2×C61#57511yescharacteristic
121C2×#137—612no—
122#532D6111yescharacteristic
123C2×C4×Q8—611no—
124#464—614no—
125#462—612no—
126#460—612no—
127#423—611no—
128#417—612no—
129C61#303711yescharacteristic, complemented, Sylow
130C2×#41C2×D6112yes—
131C22×Q8—611no—
132#137—1228no—
133C2×Q16—614no—
134C2×SD16—614no—
135C2×M16—612no—
136C4⋊Q8C2×D6111yescharacteristic
137#127C2×D6111yescharacteristic
138#124C2×D6112yes—
139#121—21no—
140#121—21no—
141C4×Q8—612no—
142C4×Q8—612no—
143C4×Q8—1221no—
144C4×Q8—1221no—
145C4×D4—21no—
146C4×D4—21no—
147C2×C4⋊C4—611no—
148C2×C4⋊C4—1221no—
149C2×C42—1221no—
150C2×C42C2×D6111yescharacteristic
151C4⋊C8—612no—
152C4⋊C8—612no—
153#103—614no—
154#102—614no—
155#41—24no—
156#41—24no—
157C2×Q8—614no—
158C2×Q8—612no—
159C2×Q8—1222no—
160C2×Q8—1221no—
161C2×Q8C22×D6112yes—
162C2×D4—22no—
163C2×D4—21no—
164C2×D4—21no—
165C2×D4C22×D6112yes—
166C22×C4—22no—
167C22×C4—1221no—
168C22×C4—1221no—
169C22×C4C22⋊D6111yescharacteristic
170C22×C4C22⋊D6111yescharacteristic
171C22×C4C22×D6111yescharacteristic
172Q16—1228no—
173SD16—1228no—
174M16—1224no—
175C2×C8—614no—
176C4⋊C4—21no—
177C4⋊C4—21no—
178C4⋊C4—612no—
179C4⋊C4—1221no—
180C4⋊C4—1222no—
181C4⋊C4—1222no—
182C22⋊C4—22no—
183C22⋊C4—22no—
184C42—1222no—
185C42—1222no—
186C42C22⋊D6111yescharacteristic
187C42C22⋊D6111yescharacteristic
188C42C22×D6111yescharacteristic
189C42C22×D6111yescharacteristic
190C23—22no—
191C23C2×C22⋊D6111yescharacteristic
192Q8—22no—
193Q8—22no—
194Q8—614no—
195Q8—1222no—
196Q8—1224no—
197D4—22no—
198D4—22no—
199D4—42no—
200D4—44no—
201D4—42no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—41no—
205C2×C4—44no—
206C2×C4—1222no—
207C2×C4—1224no—
208C2×C4—1222no—
209C2×C4—2442no—
210C2×C4D4×D6112yes—
211C2×C4#1175822412yes—
212C2×C4C2×C22⋊D6111yescharacteristic
213C2×C4C2×C22⋊D6111yescharacteristic
214C2×C4C2×C22⋊D6111yescharacteristic
215C2×C4C2×C22⋊D6111yescharacteristic
216C2×C4C2×C22⋊D6111yescharacteristic
217C2×C4C23×D6111yescharacteristic
218C8—1224no—
219C22—21no—
220C22—21no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22#1451974812yes—
225C22C22×C22⋊D6111yescharacteristic
226C4—21no—
227C4—21no—
228C4—21no—
229C4—42no—
230C4—1224no—
231C4—2442no—
232C4#1451974812yes—
233C4#1451980712yescomplemented
234C4C2×D4×D6111yescharacteristic
235C4C2×#1175822411yescharacteristic
236C2—22no—
237C2—82no—
238C2C2×#1451974811yescharacteristic
239C2C2×#1451980711yescharacteristic
240C2#1684056011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#532C2
socleC22×C61C22×D4
hypercenter#532D61
hypocenterC61#3037
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C2×#14519807C2semidirect
2. C2×C4×Dic122C2semidirect
3. #16839981C2semidirect
4. #16839969C2semidirect
5. #16839959C2semidirect
6. #16839786C2semidirect
7. #16839763C2semidirect
49. C2×Dic122D4semidirect
110. C4×C61#137semidirect
129. C61#3037semidirect
233. C4#14519807semidirect