Finite Group Databasebeta

← #21458633

Subgroups — #21458633

Order 7808.

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

normal subgroups only

This group has 350 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#16840497C211yesmaximal, characteristic
2#16840124C212yesmaximal, complemented
3#16840110C211yesmaximal, characteristic
4#16840054C211yesmaximal, characteristic, complemented
5#16840039C212yesmaximal, complemented
6#16839984C212yesmaximal, complemented
7#16839962C211yesmaximal, characteristic
8#16839893C211yesmaximal, characteristic, complemented
9#16839860C212yesmaximal, complemented
10C4×#11758202C211yesmaximal, characteristic, complemented
11Q82×C61C211yesmaximal, characteristic, complemented
12C2×#11758202C2211yescharacteristic
13C2×#11758201C2212yes—
14#14519774C2211yescharacteristic
15#14519766—21no—
16#14519765C2212yes—
17#14519762—22no—
18C4×Dic122C2211yescharacteristic
19C4×D244C2212yes—
20#14519739—21no—
21#14519710C2211yescharacteristic
22#14519710C2212yes—
23C4⋊#92418C2211yescharacteristic
24C4⋊#92418C2212yes—
25#14519701C2211yescharacteristic
26#14519700C2212yes—
27#14519700C2211yescharacteristic
28#14519697C2212yes—
29#14519697C2212yes—
30#14519697C2212yes—
31#14519688C2212yes—
32C4×#92418C2211yescharacteristic
33C4⋊Q8×C61—21no—
34C4⋊Q8×C61—22no—
35C4⋊Q8×C61C2212yes—
36C4⋊Q8×C61C2211yescharacteristic
37C4×Q8×C61—21no—
38C4×Q8×C61C2211yescharacteristic
39C4×Q8×C61C2212yes—
40C4×Q8×C61C2211yescharacteristic
41C2×Q8×C61—21no—
42C2×Q8×C61—22no—
43C2×Q8×C61D411yescharacteristic
44C2×Q8×C61C2311yescharacteristic
45C2×D244—21no—
46C2×D244—21no—
47C2×D244C2312yes—
48C2×C4×D61—22no—
49C2×Dic122C2311yescharacteristic
50C4⋊C4×C61—22no—
51C4⋊C4×C61—21no—
52C4⋊C4×C61—21no—
53C4⋊C4×C61—22no—
54C4⋊C4×C61D411yescharacteristic
55C4⋊C4×C61D412yes—
56C4⋊C4×C61C2311yescharacteristic
57C4⋊C4×C61C2312yes—
58C42×C61—22no—
59C42×C61—21no—
60C42×C61C2311yescharacteristic
61C42×C61C2312yes—
62#11758202—22no—
63#11758201—24no—
64#11758198—22no—
65#11758198—22no—
66#11758198—22no—
67C4⋊Dic61C2311yescharacteristic
68#11758196—21no—
69C4×Dic61—21no—
70C2×#92418C2311yescharacteristic
71C2×#92418C2311yescharacteristic
72C2×#92418C2312yes—
73C22×D61—22no—
74Q8×C61—22no—
75Q8×C61—21no—
76Q8×C61—82no—
77Q8×C61—81no—
78Q8×C61#4112yes—
79C2×C4×C61—21no—
80C2×C4×C61—22no—
81C2×C4×C61—21no—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D412yes—
84C2×C4×C61C2×D412yes—
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2411yescharacteristic
87C2×Dic61—21no—
88C2×Dic61—21no—
89D244—22no—
90D244—22no—
91D244—42no—
92D244—81no—
93C4×D61—82no—
94Dic122—21no—
95Dic122—21no—
96#92418—22no—
97#92418—21no—
98#92418—21no—
99C22×C61C22×D411yescharacteristic
100C2×D61—42no—
101C2×D61—42no—
102C2×D61—42no—
103C4×C61—22no—
104C4×C61—22no—
105C4×C61—22no—
106C4×C61—21no—
107C4×C61—41no—
108C4×C61—42no—
109C4×C61#13712yes—
110C4×C61C2×#4111yescharacteristic
111C4×C612−1+411yescharacteristic
112Dic61—41no—
113Dic61—41no—
114#3375—611nomaximal, Sylow
115C2×C61#54811yescharacteristic
116C2×C61C2×#13711yescharacteristic
117C2×C61#57611yescharacteristic
118D61—82no—
119#559—611no—
120Q82D6111yescharacteristic, complemented
121#489—612no—
122#486—611no—
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—21no—
134C4⋊Q8—22no—
135C4⋊Q8C2×D6112yes—
136C4⋊Q8C2×D6111yescharacteristic
137#127—611no—
138#124—612no—
139#124—1221no—
140#123—1222no—
141C4×Q8—21no—
142C4×Q8—611no—
143C4×Q8C2×D6111yescharacteristic
144C4×Q8C2×D6112yes—
145C4×Q8C2×D6111yescharacteristic
146C4×D4—612no—
147C4×D4—1221no—
148#107—611no—
149#107—612no—
150C4⋊C8—611no—
151C4⋊C8—612no—
152#103—611no—
153#103—611no—
154#103—612no—
155#102—612no—
156#102—612no—
157#102—612no—
158#97—612no—
159C4×C8—611no—
160C2×Q8—22no—
161C2×Q8—21no—
162C2×Q8—611no—
163C2×Q8C22⋊D6111yescharacteristic
164C2×Q8C22×D6111yescharacteristic
165C2×D4—612no—
166C2×D4—1221no—
167C2×D4—1221no—
168C22×C4—1222no—
169Q16—1222no—
170SD16—1224no—
171C2×C8—611no—
172C2×C8—611no—
173C2×C8—612no—
174C4⋊C4—22no—
175C4⋊C4—21no—
176C4⋊C4—22no—
177C4⋊C4—21no—
178C4⋊C4—611no—
179C4⋊C4—1221no—
180C4⋊C4C22⋊D6111yescharacteristic
181C4⋊C4C22⋊D6112yes—
182C4⋊C4C22×D6112yes—
183C4⋊C4C22×D6111yescharacteristic
184C22⋊C4—1222no—
185C22⋊C4—1222no—
186C22⋊C4—1222no—
187C42—22no—
188C42—21no—
189C42—1221no—
190C42C22×D6111yescharacteristic
191C42C22×D6112yes—
192C23—1222no—
193Q8—22no—
194Q8—21no—
195Q8—82no—
196Q8—81no—
197Q8—1221no—
198Q8—1221no—
199Q8#1175822612yes—
200D4—1222no—
201D4—1222no—
202D4—4881no—
203D4—2442no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—1221no—
208C2×C4—1221no—
209C2×C4—4882no—
210C2×C4C2×C22⋊D6112yes—
211C2×C4C2×C22⋊D6112yes—
212C2×C4C2×C22⋊D6111yescharacteristic
213C2×C4C2×C22⋊D6111yescharacteristic
214C2×C4C23×D6111yescharacteristic
215C8—1222no—
216C8—1221no—
217C8—1221no—
218C22—2442no—
219C22—2442no—
220C22—2442no—
221C22C22×C22⋊D6111yescharacteristic
222C4—22no—
223C4—22no—
224C4—21no—
225C4—22no—
226C4—41no—
227C4—42no—
228C4—2441no—
229C4—2441no—
230C4#1451980812yes—
231C4C2×#1175822611yescharacteristic
232C4#1451982511yescharacteristic
233C2—4882no—
234C2#1684042311yescharacteristic
235C2C2×#1451980811yescharacteristic
236C2#1684056511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingQ82×C61C2
socleC22×C61C22×D4
hypercenterQ82D61
hypocenterC61#3375
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ Q82

Complements

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

NH ≅ G/Ntype
2. #16840124C2semidirect
4. #16840054C2semidirect
5. #16840039C2semidirect
6. #16839984C2semidirect
8. #16839893C2semidirect
9. #16839860C2semidirect
10. C4×#11758202C2semidirect
11. Q82×C61C2semidirect
120. Q82D61semidirect
130. C61#3375semidirect