Finite Group Databasebeta

← #21461984

Subgroups — #21461984

Order 7808.

336 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 72 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×#14519842C212yesmaximal, complemented
2C2×#14519841C212yesmaximal, complemented
3C4×#11758213C211yesmaximal, characteristic, complemented
4C4×C4⋊#6923C211yesmaximal, characteristic, complemented
5#16840311C211yesmaximal, characteristic
6C2×#11758213C2212yes—
7C2×C4⋊#6923—21no—
8C2×C4×#6923C2212yes—
9#14519842—24no—
10#14519841—24no—
11#14519832—21no—
12C4×#92420—21no—
13(C2×#6923)⋊C4—21no—
14C2×#11758226C2211yescharacteristic
15C2×#11758224C2211yescharacteristic
16#14519775C411yescharacteristic, complemented
17#14519773C411yescharacteristic, complemented
18#14519765C411yescharacteristic, complemented
19#14519750—21no—
20#14519750—21no—
21#14519737—21no—
22#14519737—21no—
23C42×D61C2211yescharacteristic
24#124×C61C411yescharacteristic, complemented
25C22×#6923—22no—
26C2×Q8×C61C2×C411yescharacteristic
27C2×D4×C61C2×C411yescharacteristic
28C2×C22⋊D61—21no—
29C2×C22⋊D61—21no—
30C2×C22⋊D61—21no—
31C22×Dic61—21no—
32#11758226—22no—
33#11758226—22no—
34#11758224—22no—
35#11758224—22no—
36C2×D244—21no—
37C2×D244C2×C411yescharacteristic
38C2×C4×D61—21no—
39C2×C4×D61D411yescharacteristic
40C2×C4×D61D411yescharacteristic
41C2×C4×D61C2311yescharacteristic
42C2×Dic122C2×C411yescharacteristic
43C2×#92420—22no—
44C4⋊#6923—24no—
45C4×#6923—22no—
46C4×#6923—22no—
47#11758213—22no—
48#11758213D414yescomplemented
49C22⋊C4×C61—21no—
50C22⋊C4×C61—21no—
51C42×C61C2×C411yescharacteristic
52#11758198—21no—
53#11758198—21no—
54#11758196—21no—
55#11758196—21no—
56C4×Dic61C2×C411yescharacteristic
57C4×Dic61D411yescharacteristic
58C4×Dic61D411yescharacteristic
59C23×C61—21no—
60C22×D61—21no—
61C22×D61C2×D411yescharacteristic
62C2×#6923—24no—
63C2×#6923—42no—
64C2×#6923—42no—
65Q8×C61—22no—
66D4×C61—22no—
67C2×C4×C61—21no—
68C2×C4×C61C22⋊C411yescharacteristic
69C2×C4×C61C22⋊C411yescharacteristic
70C2×C4×C61C22×C411yescharacteristic
71C22⋊D61—42no—
72C22⋊D61—41no—
73C22⋊D61—41no—
74C22⋊D61—42no—
75C2×Dic61—21no—
76C2×Dic61—42no—
77C2×Dic61C22⋊C411yescharacteristic
78C2×Dic61C22⋊C411yescharacteristic
79C2×Dic61C2×D411yescharacteristic
80D244—22no—
81D244—41no—
82D244—41no—
83C4×D61—22no—
84C4×D61—41no—
85C4×D61—42no—
86C4×D61C2×D412yes—
87C4×D61#4112yes—
88Dic122—22no—
89#92420—24no—
90C22×C61—41no—
91C22×C61—41no—
92C22×C61—41no—
93C22×C61C2×C22⋊C411yescharacteristic
94C2×D61—21no—
95C2×D61—21no—
96C2×D61—41no—
97C2×D61—41no—
98C2×D61—41no—
99C2×D61#12411yescharacteristic
100C2×D61#12711yescharacteristic
101#6923—44no—
102C4×C61—21no—
103C4×C61—21no—
104C4×C61—41no—
105C4×C61C4×D412yes—
106Dic61—21no—
107Dic61—41no—
108Dic61#10412yescomplemented
109Dic61#12112yes—
110#1980—611nomaximal, Sylow
111C2×C61—81no—
112C2×C61#39011yescharacteristic
113C2×C61C2×#10411yescharacteristic
114C2×C61#42111yescharacteristic
115D61—21no—
116D61—21no—
117D61—81no—
118#532—611no—
119C2×#104—612no—
120C2×#104—612no—
121C4×M16—611no—
122C4×C4⋊C4—611no—
123C61#198011yescharacteristic, complemented, Sylow
124C2×#41—611no—
125C2×#41—611no—
126C2×M16—612no—
127C4⋊Q8—611no—
128#127—611no—
129#124—611no—
130#124#692311yescharacteristic, complemented
131#121—1221no—
132#121—1221no—
133C4×D4—1221no—
134C4×D4—1221no—
135C2×C4⋊C4—1221no—
136C2×C42—611no—
137C2×C42—612no—
138#104—1224no—
139#104—1224no—
140#97—1221no—
141C4×C8—1221no—
142#95—1221no—
143#41—1222no—
144#41—1222no—
145#41—1222no—
146#41—1222no—
147C2×Q8—611no—
148C2×Q8C2×#692311yescharacteristic
149C2×D4—611no—
150C2×D4—1221no—
151C2×D4—1221no—
152C2×D4—1221no—
153C2×D4—1221no—
154C2×D4C2×#692311yescharacteristic
155C22×C4—611no—
156C22×C4—611no—
157C22×C4—611no—
158C22×C4—1221no—
159C22×C4—1221no—
160C22×C4—1222no—
161M16—614no—
162M16—1222no—
163C2×C8—1222no—
164C4⋊C4—1221no—
165C4⋊C4—1221no—
166C4⋊C4—1224no—
167C22⋊C4—21no—
168C22⋊C4—21no—
169C22⋊C4—1221no—
170C22⋊C4—1221no—
171C42—611no—
172C42—611no—
173C42—611no—
174C42—1222no—
175C42—1222no—
176C42C2×#692311yescharacteristic
177C23—21no—
178C23—611no—
179C23—1221no—
180Q8—22no—
181Q8—1222no—
182D4—22no—
183D4—1222no—
184D4—2441no—
185D4—2441no—
186D4—2442no—
187D4—2442no—
188D4—2441no—
189D4—2441no—
190C2×C4—21no—
191C2×C4—611no—
192C2×C4—611no—
193C2×C4—612no—
194C2×C4—612no—
195C2×C4—611no—
196C2×C4—1222no—
197C2×C4—1224no—
198C2×C4—1221no—
199C2×C4—2441no—
200C2×C4—2442no—
201C2×C4—2442no—
202C2×C4—2442no—
203C2×C4—2442no—
204C2×C4C22⋊#692311yescharacteristic
205C2×C4C22⋊#692311yescharacteristic
206C2×C4C22×#692311yescharacteristic
207C8—1224no—
208C22—41no—
209C22—41no—
210C22—41no—
211C22—611no—
212C22—611no—
213C22—1221no—
214C22—1221no—
215C22—2441no—
216C22—2441no—
217C22—2441no—
218C22C2×C22⋊#692311yescharacteristic
219C4—21no—
220C4—21no—
221C4—41no—
222C4—612no—
223C4—612no—
224C4—1221no—
225C4—2444no—
226C4—2441no—
227C4D4×#692312yes—
228C2—81no—
229C2—1221no—
230C2—1221no—
231C2—4881no—
232C2#1684071411yescharacteristic
233C2D61⋊#10411yescharacteristic
234C2#1684075911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#124×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#124#6923
hypocenterC61#1980
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C2×#14519842C2semidirect
2. C2×#14519841C2semidirect
3. C4×#11758213C2semidirect
4. C4×C4⋊#6923C2semidirect
16. #14519775C4semidirect
17. #14519773C4semidirect
18. #14519765C4semidirect
24. #124×C61C4semidirect
48. #11758213D4semidirect
108. Dic61#104semidirect
123. C61#1980semidirect
130. #124#6923semidirect