Finite Group Databasebeta

← #21458638

Subgroups — #21458638

Order 7808.

350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 115 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#16840498C211yesmaximal, characteristic
2#16840492C211yesmaximal, characteristic, complemented
3#16840120C212yesmaximal, complemented
4#16840054C211yesmaximal, characteristic, complemented
5#16840040C212yesmaximal, complemented
6#16839983C212yesmaximal, complemented
7#16839959C211yesmaximal, characteristic
8#16839892C211yesmaximal, characteristic, complemented
9#16839859C212yesmaximal, complemented
10C4×Dic244C211yesmaximal, characteristic, complemented
11C61×#486C211yesmaximal, characteristic
12C2×Dic244C2211yescharacteristic
13C2×#11758200C2212yes—
14#14519776—21no—
15#14519776C2212yes—
16#14519775—22no—
17#14519764—21no—
18#14519764C2212yes—
19#14519758—22no—
20C4×Dic122C2211yescharacteristic
21C4×Dic122C2211yescharacteristic
22C4×Dic122C2211yescharacteristic
23#14519742—21no—
24#14519742C2212yes—
25D4×Dic61—21no—
26D4×Dic61C2212yes—
27#14519711C2211yescharacteristic
28#14519710C2212yes—
29C4⋊#92418C2211yescharacteristic
30#14519706C2212yes—
31#14519702C2211yescharacteristic
32#14519702C2211yescharacteristic
33#14519700C2212yes—
34#14519698C2212yes—
35#14519687C2212yes—
36C4⋊Q8×C61C2211yescharacteristic
37#127×C61C2211yescharacteristic
38#102×C61C2212yes—
39#102×C61C2212yes—
40C4×C8×C61C2211yescharacteristic
41C2×Q8×C61—21no—
42C2×D4×C61—21no—
43C2×D4×C61—21no—
44C2×D4×C61C2312yes—
45C22×Dic61—22no—
46C2×Dic122—22no—
47C2×Dic122D411yescharacteristic
48C2×Dic122C2311yescharacteristic
49C2×Dic122C2311yescharacteristic
50C2×C8×C61C2311yescharacteristic
51C2×C8×C61C2311yescharacteristic
52C4⋊C4×C61—21no—
53C4⋊C4×C61C2312yes—
54C42×C61C2311yescharacteristic
55C22⋊Dic61—22no—
56C22⋊Dic61—22no—
57C22⋊Dic61—22no—
58#11758200—24no—
59C4⋊Dic61D411yescharacteristic
60C4⋊Dic61C2311yescharacteristic
61C4⋊Dic61C2311yescharacteristic
62#11758196—21no—
63#11758196—21no—
64#11758196—22no—
65#11758196—22no—
66#11758196D412yes—
67C4×Dic61—21no—
68C4×Dic61—21no—
69C4×Dic61—22no—
70C4×Dic61C2312yes—
71C2×#92418C2312yes—
72Dic244—22no—
73C23×C61—22no—
74Q8×C61—81no—
75D4×C61—22no—
76D4×C61—22no—
77D4×C61—42no—
78D4×C61—81no—
79C2×C4×C61—22no—
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2411yescharacteristic
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—82no—
88C2×Dic61C2×D412yes—
89C2×Dic61C2×D412yes—
90Dic122—22no—
91Dic122—21no—
92Dic122—21no—
93Dic122—21no—
94Dic122—82no—
95Dic122#4112yes—
96C8×C61—21no—
97C8×C61—21no—
98#92418—22no—
99C22×C61—42no—
100C22×C61—42no—
101C22×C61—42no—
102C22×C61C22×D411yescharacteristic
103C4×C61—21no—
104C4×C61—42no—
105C4×C61#13712yes—
106C4×C61C2×#4111yescharacteristic
107C4×C612−1+411yescharacteristic
108Dic61—22no—
109Dic61—22no—
110Dic61—22no—
111Dic61—41no—
112Dic61—41no—
113Dic61—41no—
114#3375—611nomaximal, Sylow
115C2×C61—82no—
116C2×C61#54811yescharacteristic
117C2×C61C2×#13711yescharacteristic
118C2×C61#57611yescharacteristic
119#559—611no—
120Q82—611no—
121#489—612no—
122#486D6111yescharacteristic
123#477—611no—
124#474—612no—
125#464—612no—
126#460—611no—
127#446—611no—
128#440—612no—
129C4×Q16—611no—
130C61#337511yescharacteristic, complemented, Sylow
131C2×Q16—611no—
132C2×SD16—612no—
133C4⋊Q8—612no—
134C4⋊Q8—1221no—
135C4⋊Q8—1222no—
136C4⋊Q8C2×D6111yescharacteristic
137#127C2×D6111yescharacteristic
138#124—612no—
139#124—1221no—
140#123—1222no—
141C4×Q8—611no—
142C4×Q8—612no—
143C4×Q8—611no—
144C4×Q8—611no—
145C4×Q8—1221no—
146C4×D4—612no—
147C4×D4—1221no—
148#107—611no—
149#107—612no—
150C4⋊C8—612no—
151C4⋊C8—611no—
152#103—611no—
153#103—611no—
154#103—612no—
155#102—612no—
156#102C2×D6112yes—
157#102C2×D6112yes—
158#97—612no—
159C4×C8C2×D6111yescharacteristic
160C2×Q8—21no—
161C2×Q8—611no—
162C2×Q8—611no—
163C2×Q8—611no—
164C2×Q8—1222no—
165C2×D4—21no—
166C2×D4—21no—
167C2×D4C22×D6112yes—
168C22×C4—1222no—
169Q16—1222no—
170SD16—1224no—
171C2×C8—612no—
172C2×C8C22×D6111yescharacteristic
173C2×C8C22×D6111yescharacteristic
174C4⋊C4—21no—
175C4⋊C4—612no—
176C4⋊C4—611no—
177C4⋊C4—611no—
178C4⋊C4—611no—
179C4⋊C4—1222no—
180C4⋊C4—1222no—
181C4⋊C4—1221no—
182C4⋊C4—1221no—
183C4⋊C4C22×D6112yes—
184C22⋊C4—1222no—
185C22⋊C4—1222no—
186C22⋊C4—1222no—
187C42—612no—
188C42—1222no—
189C42—1221no—
190C42—1221no—
191C42C22×D6111yescharacteristic
192C23—22no—
193Q8—81no—
194Q8—612no—
195Q8—1221no—
196Q8—1222no—
197Q8—1221no—
198Q8—1221no—
199Q8—4882no—
200D4—22no—
201D4—22no—
202D4—42no—
203D4—81no—
204C2×C4—22no—
205C2×C4—612no—
206C2×C4—612no—
207C2×C4—1221no—
208C2×C4—1221no—
209C2×C4—1221no—
210C2×C4—1221no—
211C2×C4—4882no—
212C2×C4D4×D6111yescharacteristic
213C2×C4D4×D6111yescharacteristic
214C2×C4C23×D6111yescharacteristic
215C8—21no—
216C8—21no—
217C8—1222no—
218C22—42no—
219C22—42no—
220C22—42no—
221C22C2×D4×D6111yescharacteristic
222C4—21no—
223C4—42no—
224C4—1222no—
225C4—1222no—
226C4—1222no—
227C4—2441no—
228C4—2441no—
229C4—2441no—
230C4#1451980612yes—
231C4#41×D6111yescharacteristic
232C4#1451982411yescharacteristic
233C2—82no—
234C2#1684042011yescharacteristic
235C2C2×#1451980611yescharacteristic
236C2#1684056311yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#486C2
socleC22×C61C22×D4
hypercenter#486D61
hypocenterC61#3375
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #16840492C2semidirect
3. #16840120C2semidirect
4. #16840054C2semidirect
5. #16840040C2semidirect
6. #16839983C2semidirect
8. #16839892C2semidirect
9. #16839859C2semidirect
10. C4×Dic244C2semidirect
130. C61#3375semidirect