Finite Group Databasebeta

← #21446345

Subgroups — #21446345

Order 7808.

344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 79 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#16840528C211yesmaximal, characteristic, complemented
2#16840331C211yesmaximal, characteristic
3#16839768C211yesmaximal, characteristic, complemented
4#16839766C211yesmaximal, characteristic, complemented
5#16839735C211yesmaximal, characteristic, complemented
6#16839518C211yesmaximal, characteristic, complemented
7C61×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C22×D244C2211yescharacteristic
10#14519785—22no—
11#14519783—22no—
12C2×#11758194C2211yescharacteristic
13M16×D61—22no—
14#14519774C412yescomplemented
15#14519765C412yescomplemented
16#14519752—22no—
17#14519747—22no—
18#14519736C2211yescharacteristic
19#14519699—22no—
20#14519697—22no—
21#14519691—22no—
22C2×M16×C61C2211yescharacteristic
23#117×C61C2211yescharacteristic
24#117×C61C2211yescharacteristic
25C23×D61—21no—
26C22×C4×C61C2311yescharacteristic
27C2×C22⋊D61D412yes—
28#11758222—21no—
29#11758222—21no—
30#11758222—21no—
31#11758222—21no—
32C2×D244—21no—
33C2×D244—21no—
34C2×D244—21no—
35C2×D244—21no—
36C2×D244—21no—
37C2×D244—24no—
38C2×D244C2×C412yes—
39C2×D244C2×C411yescharacteristic
40C2×C4×D61D412yes—
41C2×Dic122C2×C411yescharacteristic
42M16×C61—21no—
43M16×C61—21no—
44C2×C8×C61D412yescomplemented
45C4⋊C4×C61—21no—
46C4⋊C4×C61—21no—
47C22⋊C4×C61—21no—
48C22⋊C4×C61—21no—
49C42×C61—21no—
50C42×C61C2×C412yes—
51C22⋊Dic61—21no—
52#11758198—24no—
53C4⋊Dic61—21no—
54C4×Dic61—21no—
55#11758194—21no—
56#11758194—21no—
57C2×#92418D412yescomplemented
58#11758189—24no—
59C8×D61—24no—
60C23×C61C2×D411yescharacteristic
61C22×D61—22no—
62C22×D61—41no—
63C22×D61—41no—
64C22×D61—82no—
65C22×D61C22⋊C412yes—
66C2×C4×C61—22no—
67C2×C4×C61—41no—
68C2×C4×C61C22×C411yescharacteristic
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61#4111yescharacteristic
73C2×C4×C61#4111yescharacteristic
74C22⋊D61—22no—
75C22⋊D61—22no—
76C2×Dic61—41no—
77C2×Dic61C22⋊C412yes—
78D244—21no—
79D244—21no—
80D244—22no—
81D244—22no—
82D244—41no—
83D244—41no—
84D244—84no—
85C4×D61—22no—
86C4×D61—22no—
87Dic122—21no—
88Dic122—21no—
89C8×C61—22no—
90#92418—22no—
91C22×C61—41no—
92C22×C61C2×C22⋊C411yescharacteristic
93C22×C61#12111yescharacteristic
94C22×C61#12111yescharacteristic
95C2×D61—22no—
96C2×D61—42no—
97C2×D61—44no—
98C2×D61—42no—
99C2×D61—82no—
100C2×D61—82no—
101C4×C61—42no—
102C4×C61—81no—
103C4×C61C4×D411yescharacteristic
104C4×C61C4×D411yescharacteristic
105C4×C61#12011yescharacteristic
106C4×C61#12311yescharacteristic
107Dic61—22no—
108Dic61—81no—
109#1910—611nomaximal, Sylow
110C2×C61—21no—
111C2×C61—21no—
112C2×C61—21no—
113C2×C61#38611yescharacteristic
114D61—42no—
115D61—82no—
116#568—611no—
117#535—611no—
118#418—611no—
119#418—611no—
120#410—611no—
121H(3,ℤ/4)—611no—
122H(3,ℤ/4)D6111yescharacteristic, complemented
123C61#191011yescharacteristic, complemented, Sylow
124C2×#41—611no—
125C22×D4—611no—
126#131—1222no—
127#131—1222no—
128C2×M16—611no—
129C2×M16—1222no—
130C2×M16C2×D6111yescharacteristic
131#127—612no—
132#124—612no—
133#121—1222no—
134#120—1222no—
135#117—611no—
136#117C2×D6111yescharacteristic
137#117C2×D6111yescharacteristic
138#102—1222no—
139#102—1222no—
140#99—1222no—
141C24—1221no—
142#41—1221no—
143#41—1221no—
144#41—1221no—
145#41—1221no—
146C2×Q8—611no—
147C2×D4—612no—
148C2×D4—611no—
149C2×D4—612no—
150C2×D4—1224no—
151C2×D4—1221no—
152C2×D4—1221no—
153C2×D4—1221no—
154C2×D4—1221no—
155C2×D4—1221no—
156C22×C4—612no—
157C22×C4C22×D6111yescharacteristic
158M16—21no—
159M16—21no—
160M16—1224no—
161M16—1221no—
162M16—1221no—
163C2×C8—612no—
164C2×C8—1224no—
165C2×C8D24412yescomplemented
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—1221no—
169C22⋊C4—21no—
170C22⋊C4—21no—
171C22⋊C4—1224no—
172C22⋊C4—1221no—
173C42—21no—
174C42—1221no—
175C42C4×D6112yes—
176C23—612no—
177C23—1222no—
178C23—4882no—
179C23—2441no—
180C23—2441no—
181C23D4×D6111yescharacteristic
182Q8—1221no—
183Q8—1221no—
184D4—1222no—
185D4—1222no—
186D4—1221no—
187D4—1222no—
188D4—1221no—
189D4—1222no—
190D4—4884no—
191D4—2441no—
192D4—2441no—
193C2×C4—22no—
194C2×C4—41no—
195C2×C4—612no—
196C2×C4—1222no—
197C2×C4—1222no—
198C2×C4—2441no—
199C2×C4C2×C4×D6111yescharacteristic
200C2×C4C2×D24411yescharacteristic
201C2×C4#1175822211yescharacteristic
202C2×C4D4×D6111yescharacteristic
203C2×C4D4×D6111yescharacteristic
204C2×C4#1175822611yescharacteristic
205C8—22no—
206C8—1222no—
207C22—41no—
208C22—1222no—
209C22—4882no—
210C22—4882no—
211C22—2444no—
212C22—2442no—
213C22—2442no—
214C22C22⋊C4×D6111yescharacteristic
215C22#1451975011yescharacteristic
216C22#1451975211yescharacteristic
217C4—42no—
218C4—81no—
219C4—1222no—
220C4—4881no—
221C4#1451973911yescharacteristic
222C4C4×D24411yescharacteristic
223C4#1451974711yescharacteristic
224C4#1451976211yescharacteristic
225C2—21no—
226C2—21no—
227C2—21no—
228C2—4882no—
229C2—2442no—
230C2#1683964011yescharacteristic
subgroupG/H
centerC2#16839640
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×H(3,ℤ/4)C2
socleC2×C61#386
hypercenterH(3,ℤ/4)D61
hypocenterC61#1910
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #16840528C2semidirect
3. #16839768C2semidirect
4. #16839766C2semidirect
5. #16839735C2semidirect
6. #16839518C2semidirect
7. C61×H(3,ℤ/4)C2semidirect
14. #14519774C4semidirect
15. #14519765C4semidirect
44. C2×C8×C61D4semidirect
57. C2×#92418D4semidirect
122. H(3,ℤ/4)D61semidirect
123. C61#1910semidirect
165. C2×C8D244semidirect