Finite Group Databasebeta

← #21458561

Subgroups — #21458561

Order 7808.

338 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 123 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
1Q8×Dic122C211yesmaximal, characteristic, complemented
2#16840485C211yesmaximal, characteristic
3#16840122C212yesmaximal
4#16840113C211yesmaximal, characteristic, complemented
5#16840053C211yesmaximal, characteristic
6#16840048C212yesmaximal, complemented
7#16839985C212yesmaximal
8#16839973C211yesmaximal, characteristic, complemented
9#16839870C212yesmaximal, complemented
10C4×#11758190C211yesmaximal, characteristic
11C61×#446C211yesmaximal, characteristic, complemented
12C2×Dic244C2212yes—
13C2×#11758190C2211yescharacteristic
14#14519777C2211yescharacteristic
15#14519777C2212yes—
16#14519777C2211yescharacteristic
17#14519776—21no—
18#14519776—22no—
19#14519772—22no—
20#14519765C2212yes—
21#14519753—21no—
22Q8×Dic61—21no—
23C4×Dic122C2211yescharacteristic
24C4×Dic122C2212yes—
25C4×Dic122C2212yes—
26C4×D244C2211yescharacteristic
27#14519735—21no—
28#14519709C2211yescharacteristic
29#14519709C2212yes—
30#14519702C2212yes—
31#14519702C2212yes—
32#14519702C2211yescharacteristic
33#14519702C2212yes—
34#14519699C2212yes—
35#14519699C2211yescharacteristic
36C4×Q8×C61C2211yescharacteristic
37C4⋊C8×C61C2211yescharacteristic
38C4⋊C8×C61C2212yes—
39#97×C61C2212yes—
40C4×C8×C61C2211yescharacteristic
41C2×Q8×C61D411yescharacteristic
42C2×D244C2311yescharacteristic
43C2×C4×D61—21no—
44C2×Dic122—22no—
45C2×Dic122—21no—
46C2×Dic122C2312yes—
47C2×Dic122C2311yescharacteristic
48C2×C8×C61C2311yescharacteristic
49C2×C8×C61C2311yescharacteristic
50C2×C8×C61C2312yes—
51C4⋊C4×C61D411yescharacteristic
52C4⋊C4×C61D412yes—
53C42×C61C2311yescharacteristic
54C42×C61C2312yes—
55#11758198—22no—
56#11758198—21no—
57#11758198—22no—
58C4⋊Dic61—21no—
59C4⋊Dic61—22no—
60C4⋊Dic61—21no—
61C4⋊Dic61—21no—
62C4⋊Dic61C2312yes—
63C4⋊Dic61C2311yescharacteristic
64C4⋊Dic61C2311yescharacteristic
65#11758196—22no—
66#11758196—22no—
67#11758196—21no—
68C4×Dic61—22no—
69C4×Dic61—22no—
70C4×Dic61—21no—
71Dic244—24no—
72#11758190—22no—
73C22×D61—21no—
74Q8×C61—22no—
75C2×C4×C61C2×D412yes—
76C2×C4×C61C2×D412yes—
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2411yescharacteristic
80C2×Dic61—21no—
81C2×Dic61—21no—
82C2×Dic61—22no—
83C2×Dic61—21no—
84C2×Dic61—22no—
85D244—21no—
86D244—21no—
87C4×D61—42no—
88Dic122—21no—
89Dic122—22no—
90Dic122—22no—
91Dic122—82no—
92Dic122—81no—
93Dic122#4112yes—
94C8×C61—21no—
95C8×C61—22no—
96C8×C61—21no—
97C22×C61C22×D411yescharacteristic
98C2×D61—41no—
99C2×D61—41no—
100C2×D61—41no—
101C4×C61—22no—
102C4×C61—22no—
103C4×C61—21no—
104C4×C61#13712yes—
105C4×C61C2×#4111yescharacteristic
106C4×C612−1+411yescharacteristic
107Dic61—22no—
108Dic61—42no—
109Dic61—41no—
110Dic61—41no—
111Dic61—42no—
112#3369—611nomaximal, Sylow
113C2×C61#54811yescharacteristic
114C2×C61C2×#13711yescharacteristic
115C2×C61#57711yescharacteristic
116D61—81no—
117Q82—611no—
118#556—611no—
119#489—612no—
120#487—611no—
121#476—611no—
122#475—612no—
123#464—612no—
124#462—611no—
125#446D6111yescharacteristic, complemented
126#441—612no—
127C4×SD16—611no—
128C61#336911yescharacteristic, complemented, Sylow
129C2×Q16—612no—
130C2×SD16—611no—
131C4⋊Q8—612no—
132C4⋊Q8—611no—
133C4⋊Q8—611no—
134C4⋊Q8—1221no—
135C4⋊Q8—1222no—
136#126—1222no—
137#124—612no—
138C22⋊Q8—1221no—
139C4×Q8—612no—
140C4×Q8—611no—
141C4×Q8—612no—
142C4×Q8—1221no—
143C4×Q8C2×D6111yescharacteristic
144C4×D4—611no—
145#117—1221no—
146#106—611no—
147#106—612no—
148C4⋊C8C2×D6111yescharacteristic
149C4⋊C8C2×D6112yes—
150#103—611no—
151#103—612no—
152#103—612no—
153#103—612no—
154#102—611no—
155#102—612no—
156#97C2×D6112yes—
157C4×C8C2×D6111yescharacteristic
158C2×Q8—611no—
159C2×Q8—612no—
160C2×Q8—1222no—
161C2×Q8—1221no—
162C2×Q8D24411yescharacteristic
163C2×D4—611no—
164C22×C4—1221no—
165Q16—1224no—
166SD16—1222no—
167C2×C8C22×D6111yescharacteristic
168C2×C8C22×D6111yescharacteristic
169C2×C8C22×D6112yes—
170C4⋊C4—611no—
171C4⋊C4—612no—
172C4⋊C4—611no—
173C4⋊C4—1222no—
174C4⋊C4—1222no—
175C4⋊C4—1221no—
176C4⋊C4—1221no—
177C4⋊C4—1222no—
178C4⋊C4—1221no—
179C4⋊C4—1221no—
180C4⋊C4D24411yescharacteristic
181C4⋊C4D24412yes—
182C22⋊C4—1222no—
183C22⋊C4—1221no—
184C22⋊C4—1222no—
185C42—1222no—
186C42—1222no—
187C42—1221no—
188C42C22×D6111yescharacteristic
189C42C22×D6112yes—
190C23—1221no—
191Q8—22no—
192Q8—612no—
193Q8—1221no—
194Q8—1222no—
195Q8—1222no—
196Q8—4882no—
197Q8—4881no—
198D4—1221no—
199D4—1221no—
200C2×C4—1221no—
201C2×C4—1221no—
202C2×C4—1222no—
203C2×C4—1222no—
204C2×C4—1221no—
205C2×C4—2442no—
206C2×C4C2×D24412yes—
207C2×C4C2×D24412yes—
208C2×C4C2×D24411yescharacteristic
209C2×C4C2×D24411yescharacteristic
210C2×C4C23×D6111yescharacteristic
211C8—21no—
212C8—22no—
213C8—21no—
214C22—2441no—
215C22—2441no—
216C22—2441no—
217C22C22×D24411yescharacteristic
218C4—22no—
219C4—22no—
220C4—21no—
221C4—1222no—
222C4—2441no—
223C4—2442no—
224C4—2441no—
225C4—2442no—
226C4#1451981012yes—
227C4#41×D6111yescharacteristic
228C4#1451982511yescharacteristic
229C2—4881no—
230C2#1684042411yescharacteristic
231C2C2×#1451981011yescharacteristic
232C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#446C2
socleC22×C61C22×D4
hypercenter#446D61
hypocenterC61#3369
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. Q8×Dic122C2semidirect
4. #16840113C2semidirect
6. #16840048C2semidirect
8. #16839973C2semidirect
9. #16839870C2semidirect
11. C61×#446C2semidirect
125. #446D61semidirect
128. C61#3369semidirect