Finite Group Databasebeta

← #21455985

Subgroups — #21455985

Order 7808.

386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 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#16840293C211yesmaximal, characteristic
2C2×Q8×Dic61C211yesmaximal, characteristic, complemented
3#16840098C211yesmaximal, characteristic, complemented
4#16840078C211yesmaximal, characteristic
5#16840071C212yesmaximal, complemented
6#16839982C212yesmaximal, complemented
7#16839918C211yesmaximal, characteristic, complemented
8#16839866C212yesmaximal, complemented
9#16839863C212yesmaximal, complemented
10#16839816C211yesmaximal, characteristic, complemented
11C61×#448C211yesmaximal, characteristic
12C2×#11758202C2212yes—
13#14519770—21no—
14#14519768C2211yescharacteristic
15#14519764C2211yescharacteristic
16#14519758—21no—
17#14519756C2211yescharacteristic
18Q8×Dic61—21no—
19Q8×Dic61—21no—
20Q8×Dic61C2212yes—
21Q8×Dic61C2212yes—
22#14519742C2211yescharacteristic
23D4×Dic61—21no—
24D4×Dic61C2211yescharacteristic
25#14519733—21no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61C2211yescharacteristic
28C2×C4×Dic61—21no—
29C2×C4×Dic61C2211yescharacteristic
30#14519711C2212yes—
31#14519708C2212yes—
32#14519706C2212yes—
33#14519702C2212yes—
34#14519701C2212yes—
35#14519698C2212yes—
36C22⋊#92418C2211yescharacteristic
37#14519687C2212yes—
38C22×Q8×C61C2211yescharacteristic
39C2×SD16×C61C2212yes—
40#121×C61C2211yescharacteristic
41#103×C61C2212yes—
42C22⋊C8×C61C2211yescharacteristic
43C2×Q8×C61—24no—
44C2×Q8×C61—21no—
45C2×Q8×C61C2312yes—
46C2×D4×C61—21no—
47C2×D4×C61C2311yescharacteristic
48C22×C4×C61—21no—
49C22×C4×C61C2311yescharacteristic
50C22×Dic61—21no—
51C22×Dic61—21no—
52C22×Dic61D411yescharacteristic
53C22×Dic61D411yescharacteristic
54C2×Dic122C2311yescharacteristic
55SD16×C61—24no—
56C2×C8×C61C2312yes—
57C4⋊C4×C61C2311yescharacteristic
58C22⋊C4×C61—21no—
59C22⋊Dic61—21no—
60C22⋊Dic61—21no—
61C22⋊Dic61—21no—
62C22⋊Dic61—21no—
63#11758202—24no—
64C4⋊Dic61—21no—
65C4⋊Dic61—22no—
66C4⋊Dic61—22no—
67C4⋊Dic61—21no—
68C4⋊Dic61C2312yes—
69C4⋊Dic61C2311yescharacteristic
70#11758196—21no—
71#11758196—21no—
72#11758196—21no—
73C4×Dic61—22no—
74C4×Dic61—22no—
75C4×Dic61—21no—
76C4×Dic61D411yescharacteristic
77C4×Dic61D411yescharacteristic
78C4×Dic61C2311yescharacteristic
79C4×Dic61C2311yescharacteristic
80C2×#92418C2312yes—
81C23×C61—21no—
82C23×C61C2×D411yescharacteristic
83Q8×C61—24no—
84Q8×C61—22no—
85Q8×C61#4114yes—
86D4×C61—22no—
87D4×C61—42no—
88C2×C4×C61—24no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—21no—
92C2×C4×C61C2×D411yescharacteristic
93C2×C4×C61C2411yescharacteristic
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—21no—
97C2×Dic61—21no—
98C2×Dic61—41no—
99C2×Dic61—42no—
100C2×Dic61—42no—
101C2×Dic61C2×D411yescharacteristic
102C2×Dic61C2×D411yescharacteristic
103C2×Dic61C2×D411yescharacteristic
104C2×Dic61C2×D411yescharacteristic
105Dic122—22no—
106C8×C61—22no—
107#92418—22no—
108C22×C61—21no—
109C22×C61—21no—
110C22×C61—41no—
111C22×C61—41no—
112C22×C61—41no—
113C22×C61#13712yes—
114C22×C61C22×D411yescharacteristic
115C4×C61—24no—
116C4×C61—21no—
117C4×C61—41no—
118C4×C61C2×#4112yes—
119Dic61—21no—
120Dic61—21no—
121Dic61—21no—
122Dic61—21no—
123Dic61—41no—
124Dic61—42no—
125Dic61—41no—
126#3117—611nomaximal, Sylow
127C2×C61—22no—
128C2×C61—81no—
129C2×C61#52511yescharacteristic
130C2×C61C2×#13711yescharacteristic
131C2×C61#57511yescharacteristic
132#529—611no—
133C2×C4×Q8—611no—
134#484—611no—
135#481—611no—
136#479—612no—
137#464—612no—
138#451—611no—
139#448D6111yescharacteristic
140#441—612no—
141#440—612no—
142#432—611no—
143C61#311711yescharacteristic, complemented, Sylow
144C22×Q8C2×D6111yescharacteristic
145C2×Q16—612no—
146C2×SD16C2×D6112yes—
147#126—1221no—
148#125—611no—
149#124—611no—
150#123—1221no—
151C22⋊Q8—611no—
152#121C2×D6111yescharacteristic
153C4×Q8—612no—
154C4×Q8—612no—
155C4×Q8—611no—
156C4×Q8—1221no—
157C4×Q8—1221no—
158C4×D4—611no—
159C4×D4—1221no—
160#117—1221no—
161C2×C4⋊C4—611no—
162C2×C4⋊C4—1221no—
163C2×C42—611no—
164C2×C42—1221no—
165#107—612no—
166#106—612no—
167C4⋊C8—612no—
168#103—612no—
169#103—612no—
170#103C2×D6112yes—
171#102—612no—
172C22⋊C8—611no—
173C22⋊C8C2×D6111yescharacteristic
174#97—612no—
175C2×Q8—24no—
176C2×Q8—21no—
177C2×Q8—611no—
178C2×Q8C22×D6112yes—
179C2×D4—21no—
180C2×D4C22×D6111yescharacteristic
181C22×C4—21no—
182C22×C4—611no—
183C22×C4—611no—
184C22×C4—1221no—
185C22×C4—1221no—
186C22×C4C22×D6111yescharacteristic
187Q16—1224no—
188SD16—24no—
189C2×C8—612no—
190C2×C8C22×D6112yes—
191C4⋊C4—612no—
192C4⋊C4—611no—
193C4⋊C4—1222no—
194C4⋊C4—1222no—
195C4⋊C4—1221no—
196C4⋊C4—1221no—
197C4⋊C4—1221no—
198C4⋊C4—1221no—
199C4⋊C4—1221no—
200C4⋊C4C22×D6111yescharacteristic
201C22⋊C4—21no—
202C22⋊C4—1221no—
203C22⋊C4—1221no—
204C22⋊C4—1221no—
205C22⋊C4—1221no—
206C42—611no—
207C42—611no—
208C42—611no—
209C42—611no—
210C42—1222no—
211C42—1222no—
212C42—1221no—
213C23—21no—
214C23D4×D6111yescharacteristic
215Q8—24no—
216Q8—22no—
217Q8—1222no—
218Q8#1175822414yes—
219D4—22no—
220D4—42no—
221C2×C4—24no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—611no—
226C2×C4—611no—
227C2×C4—611no—
228C2×C4—611no—
229C2×C4—1222no—
230C2×C4—1222no—
231C2×C4—1221no—
232C2×C4—1221no—
233C2×C4—2441no—
234C2×C4—2442no—
235C2×C4—2442no—
236C2×C4D4×D6111yescharacteristic
237C2×C4C23×D6111yescharacteristic
238C8—22no—
239C8—1222no—
240C22—21no—
241C22—21no—
242C22—41no—
243C22—41no—
244C22—41no—
245C22#1451980612yes—
246C22C2×D4×D6111yescharacteristic
247C4—24no—
248C4—21no—
249C4—41no—
250C4—1221no—
251C4—1221no—
252C4—1221no—
253C4—1221no—
254C4—2441no—
255C4—2442no—
256C4—2441no—
257C4C2×#1175822412yes—
258C2—22no—
259C2—81no—
260C2#1684026811yescharacteristic
261C2C2×#1451980611yescharacteristic
262C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#448C2
socleC22×C61C22×D4
hypercenter#448D61
hypocenterC61#3117
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
2. C2×Q8×Dic61C2semidirect
3. #16840098C2semidirect
5. #16840071C2semidirect
6. #16839982C2semidirect
7. #16839918C2semidirect
8. #16839866C2semidirect
9. #16839863C2semidirect
10. #16839816C2semidirect
143. C61#3117semidirect