Finite Group Databasebeta

← #21446934

Subgroups — #21446934

Order 7808.

362 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 73 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×#14519807C211yesmaximal, characteristic, complemented
2C2×#14519802C211yesmaximal, characteristic
3C22×#11758190C211yesmaximal, characteristic, complemented
4C2×#14519695C211yesmaximal, characteristic, complemented
5C2×#14519693C211yesmaximal, characteristic, complemented
6#16839527C211yesmaximal, characteristic, complemented
7C61×#408C211yesmaximal, characteristic, complemented
8C22×Dic122C2211yescharacteristic
9C22×D244C2211yescharacteristic
10#14519807—22no—
11#14519807—22no—
12#14519802—22no—
13#14519802—22no—
14C2×#11758202—21no—
15C2×#11758190—22no—
16C2×#11758190—22no—
17C2×#11758190—22no—
18C2×#11758200—21no—
19C2×#11758201—21no—
20C2×#11758199—21no—
21C2×#11758194C2211yescharacteristic
22C2×#11758194C2211yescharacteristic
23#14519695—22no—
24#14519693—22no—
25C2×#41×C61C2211yescharacteristic
26C2×M16×C61C2211yescharacteristic
27C22×C8×C61C2211yescharacteristic
28C22⋊C8×C61—22no—
29C23×D61—21no—
30#41×C61—21no—
31#41×C61—21no—
32#41×C61—21no—
33#41×C61—21no—
34C2×Q8×C61D411yescharacteristic
35C2×D4×C61—21no—
36C2×D4×C61D411yescharacteristic
37C22×C4×C61—21no—
38C22×C4×C61C2311yescharacteristic
39C22×Dic61—21no—
40C2×D244—21no—
41C2×D244—21no—
42C2×D244—21no—
43C2×D244—21no—
44C2×D244—21no—
45C2×D244D412yes—
46C2×Dic122—21no—
47C2×Dic122—21no—
48C2×Dic122—21no—
49C2×Dic122—21no—
50C2×Dic122—21no—
51C2×Dic122D412yes—
52M16×C61—21no—
53M16×C61—21no—
54C2×C8×C61—21no—
55C2×C8×C61—21no—
56C2×C8×C61—21no—
57C2×C8×C61D412yes—
58#11758202—24no—
59#11758201—24no—
60#11758200—24no—
61#11758199—24no—
62#11758194—21no—
63#11758194—21no—
64#11758194D412yes—
65#11758194D412yes—
66C2×#92418—21no—
67C2×#92418—21no—
68#11758190—28no—
69C23×C61—21no—
70C23×C61#4111yescharacteristic
71C22×D61—22no—
72C22×D61—41no—
73C22×D61—41no—
74C22×D61—82no—
75Q8×C61—21no—
76Q8×C61—21no—
77D4×C61—21no—
78D4×C61—21no—
79D4×C61—41no—
80D4×C61—41no—
81C2×C4×C61—21no—
82C2×C4×C61—41no—
83C2×C4×C61—41no—
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61C2×D411yescharacteristic
90C2×Dic61—22no—
91C2×Dic61—41no—
92C2×Dic61—41no—
93D244—22no—
94D244—22no—
95D244—41no—
96D244—41no—
97Dic122—22no—
98Dic122—22no—
99Dic122—41no—
100Dic122—41no—
101C8×C61—22no—
102C8×C61—41no—
103#92418—22no—
104#92418—22no—
105C22×C61—22no—
106C22×C61—41no—
107C22×C61—42no—
108C22×C61#12111yescharacteristic
109C22×C61#12111yescharacteristic
110C22×C61#12111yescharacteristic
111C2×D61—42no—
112C2×D61—82no—
113C2×D61—82no—
114C2×D61—82no—
115C4×C61—41no—
116C4×C61#12011yescharacteristic
117C4×C61#12011yescharacteristic
118C4×C61#12011yescharacteristic
119C4×C61#12711yescharacteristic
120Dic61—42no—
121#2019—611nomaximal, Sylow
122C2×C61—21no—
123C2×C61—21no—
124C2×C61—81no—
125C2×C61#39211yescharacteristic
126C2×C61#47112yes—
127D61—82no—
128C2×#137—611no—
129C2×AGL(1,ℤ/8)—611no—
130C22×SD16—611no—
131C2×#101—611no—
132C2×#100—611no—
133#408D6111yescharacteristic, complemented
134#341—611no—
135C61#201911yescharacteristic, complemented, Sylow
136C2×#41C2×D6111yescharacteristic
137C22×Q8—611no—
138C22×D4—611no—
139#137—1222no—
140#137—1222no—
141AGL(1,ℤ/8)—1222no—
142AGL(1,ℤ/8)—1222no—
143C2×Q16—1221no—
144C2×SD16—1222no—
145C2×SD16—1222no—
146C2×SD16—1221no—
147C2×SD16—1221no—
148C2×SD16—1222no—
149C2×D8—1221no—
150C2×M16—611no—
151C2×M16—611no—
152C2×M16C2×D6111yescharacteristic
153C22×C8C2×D6111yescharacteristic
154#101—1222no—
155#100—1222no—
156C22⋊C8—22no—
157C24—1221no—
158#41—21no—
159#41—21no—
160#41—21no—
161#41—21no—
162C2×Q8—612no—
163C2×Q8—1221no—
164C2×Q8—1221no—
165C2×Q8—1221no—
166C2×Q8—1221no—
167C2×Q8—1221no—
168C2×Q8D24411yescharacteristic
169C2×D4—21no—
170C2×D4—612no—
171C2×D4—1221no—
172C2×D4—1221no—
173C2×D4—1221no—
174C2×D4—1221no—
175C2×D4—1221no—
176C2×D4D24411yescharacteristic
177C22×C4—21no—
178C22×C4—1221no—
179C22×C4C22×D6111yescharacteristic
180Q16—1224no—
181SD16—1228no—
182SD16—1224no—
183SD16—1224no—
184D8—1224no—
185M16—21no—
186M16—21no—
187M16—612no—
188M16—612no—
189M16—1221no—
190M16—1221no—
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—21no—
194C2×C8—1221no—
195C2×C8—1221no—
196C2×C8C22⋊D6112yes—
197C23—21no—
198C23—1222no—
199C23—4882no—
200C23—2441no—
201C23—2441no—
202C23#1175822211yescharacteristic
203Q8—21no—
204Q8—21no—
205Q8—1222no—
206Q8—1222no—
207Q8—2441no—
208Q8—2441no—
209D4—21no—
210D4—21no—
211D4—41no—
212D4—41no—
213D4—1222no—
214D4—1222no—
215D4—2441no—
216D4—2441no—
217C2×C4—21no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—1222no—
221C2×C4—2441no—
222C2×C4—2441no—
223C2×C4C2×D24411yescharacteristic
224C2×C4D4×D6111yescharacteristic
225C2×C4D4×D6111yescharacteristic
226C2×C4D4×D6111yescharacteristic
227C2×C4D4×D6111yescharacteristic
228C2×C4C2×C22⋊D6111yescharacteristic
229C8—22no—
230C8—41no—
231C8—1222no—
232C8—1222no—
233C22—22no—
234C22—42no—
235C22—41no—
236C22—4882no—
237C22—4882no—
238C22—4882no—
239C22—2442no—
240C22#1451975011yescharacteristic
241C22#1451975011yescharacteristic
242C22#1451975111yescharacteristic
243C4—41no—
244C4—2442no—
245C4#1451974511yescharacteristic
246C4#1451974711yescharacteristic
247C4#1451974711yescharacteristic
248C4#1451977311yescharacteristic
249C2—21no—
250C2—21no—
251C2—81no—
252C2—4882no—
253C2#1683967111yescharacteristic
254C2#1684002512yes—
subgroupG/H
centerC22#14519751
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#408C2
socleC22×C61#121
hypercenter#408D61
hypocenterC61#2019
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
1. C2×#14519807C2semidirect
3. C22×#11758190C2semidirect
4. C2×#14519695C2semidirect
5. C2×#14519693C2semidirect
6. #16839527C2semidirect
7. C61×#408C2semidirect
133. #408D61semidirect
135. C61#2019semidirect