Finite Group Databasebeta

← #21458459

Subgroups — #21458459

Order 7808.

370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 125 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#16840490C211yesmaximal, characteristic, complemented
2D4×Dic122C211yesmaximal, characteristic
3#16840113C211yesmaximal, characteristic, complemented
4#16840111C212yesmaximal, complemented
5#16840047C211yesmaximal, characteristic, complemented
6#16840046C212yesmaximal, complemented
7#16839967C211yesmaximal, characteristic
8#16839965C212yesmaximal
9C8×Dic122C211yesmaximal, characteristic, complemented
10#16839853C212yesmaximal
11C4×SD16×C61C211yesmaximal, characteristic
12C22×Dic122—21no—
13C2×#11758200C2212yes—
14#14519777C2211yescharacteristic
15#14519777C2211yescharacteristic
16#14519776C2212yes—
17#14519775C2212yes—
18#14519769—21no—
19#14519767—22no—
20#14519756—21no—
21#14519754—22no—
22C4×Dic122—21no—
23C4×Dic122C2211yescharacteristic
24#14519742C2212yes—
25D4×Dic61C2212yes—
26#14519708C2212yes—
27C4⋊#92418C2211yescharacteristic
28#14519706C2212yes—
29#14519702C2212yes—
30#14519702C2212yes—
31#14519701C2212yes—
32#14519700C2212yes—
33C8×Dic61C2212yes—
34C2×SD16×C61C2211yescharacteristic
35C4×Q8×C61C2211yescharacteristic
36C4×D4×C61C2211yescharacteristic
37#106×C61C2211yescharacteristic
38#103×C61C2211yescharacteristic
39#102×C61C2211yescharacteristic
40C4×C8×C61C2211yescharacteristic
41C2×Q8×C61C2311yescharacteristic
42C2×D4×C61C2311yescharacteristic
43C22×C4×C61—21no—
44C22×Dic61—22no—
45C2×Dic122—21no—
46C2×Dic122—22no—
47C2×Dic122—44no—
48C2×Dic122D411yescharacteristic
49C2×Dic122C2312yes—
50SD16×C61—22no—
51C2×C8×C61C2311yescharacteristic
52C2×C8×C61C2311yescharacteristic
53C4⋊C4×C61—21no—
54C4⋊C4×C61C2311yescharacteristic
55C4⋊C4×C61C2311yescharacteristic
56C22⋊C4×C61—21no—
57C42×C61—21no—
58C42×C61C2311yescharacteristic
59C22⋊Dic61—22no—
60#11758200—24no—
61C4⋊Dic61—21no—
62C4⋊Dic61—21no—
63C4⋊Dic61—21no—
64C4⋊Dic61D411yescharacteristic
65C4⋊Dic61C2312yes—
66#11758196—22no—
67#11758196—22no—
68#11758196—22no—
69#11758196—22no—
70#11758196D412yes—
71C4×Dic61—22no—
72C4×Dic61C2312yes—
73C2×#92418C2312yes—
74C23×C61—21no—
75Q8×C61—21no—
76Q8×C61—21no—
77D4×C61—21no—
78D4×C61#4112yes—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—42no—
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2411yescharacteristic
86C2×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61—44no—
89C2×Dic61C2×D412yes—
90C2×Dic61C2×D412yes—
91Dic122—22no—
92Dic122—22no—
93Dic122—42no—
94Dic122—44no—
95Dic122SD1614yescomplemented
96C8×C61—21no—
97C8×C61—21no—
98#92418—22no—
99C22×C61—22no—
100C22×C61—41no—
101C22×C61—41no—
102C22×C61C22×D411yescharacteristic
103C4×C61—21no—
104C4×C61—41no—
105C4×C61—41no—
106C4×C61—41no—
107C4×C61C2×SD1612yes—
108C4×C61C2×#4111yescharacteristic
109C4×C612−1+411yescharacteristic
110Dic61—22no—
111Dic61—42no—
112Dic61—42no—
113Dic61C2×SD1614yes—
114#3359—611nomaximal, Sylow
115C2×C61—42no—
116C2×C61#54811yescharacteristic
117C2×C61C22×SD1611yescharacteristic
118C2×C61#57811yescharacteristic
119#557—611no—
120D4×Q8—611no—
121#487—612no—
122#487—611no—
123#475—611no—
124#475—612no—
125#461—612no—
126#461—611no—
127C8×Q8—611no—
128C4×SD16—612no—
129C4×SD16D6111yescharacteristic
130C61#335911yescharacteristic, complemented, Sylow
131C22×Q8—1221no—
132C2×SD16—612no—
133C2×SD16C2×D6111yescharacteristic
134C4⋊Q8—612no—
135C4⋊Q8—612no—
136C4⋊Q8—611no—
137C4⋊Q8—611no—
138#125—1221no—
139#125—1222no—
140C22⋊Q8—1222no—
141C22⋊Q8—1221no—
142C4×Q8—611no—
143C4×Q8—612no—
144C4×Q8—1221no—
145C4×Q8C2×D6111yescharacteristic
146C4×D4—612no—
147C4×D4C2×D6111yescharacteristic
148#106—612no—
149#106C2×D6111yescharacteristic
150C4⋊C8—612no—
151C4⋊C8—611no—
152#103—612no—
153#103—612no—
154#103—612no—
155#103—612no—
156#103C2×D6111yescharacteristic
157#102C2×D6111yescharacteristic
158C4×C8—612no—
159C4×C8C2×D6111yescharacteristic
160C2×Q8—611no—
161C2×Q8—612no—
162C2×Q8—1222no—
163C2×Q8—1221no—
164C2×Q8—2444no—
165C2×Q8C22×D6111yescharacteristic
166C2×D4C22×D6111yescharacteristic
167C22×C4—21no—
168C22×C4—1222no—
169SD16—22no—
170SD16—1224no—
171C2×C8—612no—
172C2×C8C22×D6111yescharacteristic
173C2×C8C22×D6111yescharacteristic
174C4⋊C4—21no—
175C4⋊C4—612no—
176C4⋊C4—611no—
177C4⋊C4—612no—
178C4⋊C4—1222no—
179C4⋊C4—1222no—
180C4⋊C4—1222no—
181C4⋊C4—1222no—
182C4⋊C4—1221no—
183C4⋊C4—1221no—
184C4⋊C4—1221no—
185C4⋊C4C22×D6111yescharacteristic
186C4⋊C4C22×D6111yescharacteristic
187C22⋊C4—21no—
188C22⋊C4—1222no—
189C42—21no—
190C42—612no—
191C42—1222no—
192C42C22×D6111yescharacteristic
193C23—21no—
194Q8—21no—
195Q8—21no—
196Q8—614no—
197Q8—1222no—
198Q8—1222no—
199Q8—2444no—
200Q8—2442no—
201D4—21no—
202D4#1175822212yes—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—612no—
208C2×C4—612no—
209C2×C4—1222no—
210C2×C4—1222no—
211C2×C4—2444no—
212C2×C4D4×D6111yescharacteristic
213C2×C4D4×D6111yescharacteristic
214C2×C4C23×D6111yescharacteristic
215C8—21no—
216C8—21no—
217C8—1222no—
218C22—22no—
219C22—41no—
220C22—41no—
221C22C2×D4×D6111yescharacteristic
222C4—21no—
223C4—41no—
224C4—41no—
225C4—41no—
226C4—614no—
227C4—1222no—
228C4—2442no—
229C4—2442no—
230C4SD16×D6112yes—
231C4C2×#1175822211yescharacteristic
232C4#1451982411yescharacteristic
233C2—42no—
234C2#1684042111yescharacteristic
235C2C2×SD16×D6111yescharacteristic
236C2#1684057611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC4×SD16×C61C2
socleC22×C61C22×D4
hypercenterC4×SD16D61
hypocenterC61#3359
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #16840490C2semidirect
3. #16840113C2semidirect
4. #16840111C2semidirect
5. #16840047C2semidirect
6. #16840046C2semidirect
9. C8×Dic122C2semidirect
95. Dic122SD16semidirect
130. C61#3359semidirect