Finite Group Databasebeta

← #21457006

Subgroups — #21457006

Order 7808.

368 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 113 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#16840307C211yesmaximal, characteristic
2C2×#14519768C211yesmaximal, characteristic, complemented
3#16840170C212yesmaximal, complemented
4#16840125C212yesmaximal, complemented
5#16840081C211yesmaximal, characteristic, complemented
6#16840078C211yesmaximal, characteristic, complemented
7#16840075C211yesmaximal, characteristic, complemented
8#16840065C212yesmaximal, complemented
9#16840064C212yesmaximal, complemented
10#16839816C211yesmaximal, characteristic, complemented
11C61×#480C211yesmaximal, characteristic, complemented
12C2×#11758224—21no—
13#14519776C2211yescharacteristic
14#14519773C2211yescharacteristic
15#14519768—21no—
16#14519768—21no—
17#14519768C2212yes—
18#14519768C2212yes—
19#14519763—21no—
20#14519751C2211yescharacteristic
21#14519749—21no—
22D4×Dic61C2211yescharacteristic
23#14519739C2211yescharacteristic
24#14519737—21no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61C2211yescharacteristic
27C2×#11758196—21no—
28C2×C4×Dic61C2211yescharacteristic
29#14519710C2212yes—
30#14519709C2212yes—
31#14519708C2212yes—
32#14519706C2212yes—
33#14519699C2212yes—
34#14519698C2212yes—
35#14519697C2212yes—
36C22⋊#92418C2211yescharacteristic
37#14519687C2212yes—
38#121×C61C2211yescharacteristic
39C2×C4⋊C4×C61C2211yescharacteristic
40#107×C61C2212yes—
41#102×C61C2212yes—
42C22⋊C8×C61C2211yescharacteristic
43C2×D4×C61—21no—
44C2×D4×C61C2311yescharacteristic
45C22×C4×C61—21no—
46C22×C4×C61C2311yescharacteristic
47C2×C22⋊D61—21no—
48C2×C22⋊D61—21no—
49C2×C22⋊D61—21no—
50C22×Dic61—21no—
51C22×Dic61—21no—
52C22×Dic61D411yescharacteristic
53C22×Dic61D411yescharacteristic
54#11758224—44no—
55C2×D244C2311yescharacteristic
56C2×C4×D61—21no—
57C2×Dic122—21no—
58C2×C8×C61C2312yes—
59C4⋊C4×C61—21no—
60C4⋊C4×C61C2312yes—
61C4⋊C4×C61C2311yescharacteristic
62C22⋊C4×C61—21no—
63C22⋊Dic61—21no—
64#11758198—21no—
65#11758198—21no—
66C4⋊Dic61—21no—
67C4⋊Dic61—22no—
68C4⋊Dic61—22no—
69C4⋊Dic61C2312yes—
70C4⋊Dic61C2311yescharacteristic
71#11758196—22no—
72#11758196—22no—
73#11758196—21no—
74C4×Dic61D411yescharacteristic
75C4×Dic61D411yescharacteristic
76C4×Dic61C2311yescharacteristic
77C4×Dic61C2311yescharacteristic
78C2×#92418C2312yes—
79C23×C61—21no—
80C23×C61C2×D411yescharacteristic
81C22×D61—21no—
82D4×C61—22no—
83D4×C61—42no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—21no—
87C2×C4×C61—42no—
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61C2411yescharacteristic
90C22⋊D61—42no—
91C22⋊D61—42no—
92C22⋊D61—42no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—21no—
96C2×Dic61—41no—
97C2×Dic61—42no—
98C2×Dic61—42no—
99C2×Dic61C2×D411yescharacteristic
100C2×Dic61C2×D411yescharacteristic
101C2×Dic61C2×D411yescharacteristic
102C2×Dic61C2×D411yescharacteristic
103D244—22no—
104C4×D61—42no—
105Dic122—42no—
106C8×C61—22no—
107#92418—22no—
108C22×C61—21no—
109C22×C61—21no—
110C22×C61—41no—
111C22×C61—41no—
112C22×C61—41no—
113C22×C61AGL(1,ℤ/8)12yes—
114C22×C61C22×D411yescharacteristic
115C2×D61—41no—
116C2×D61—41no—
117C2×D61—41no—
118C4×C61—21no—
119C4×C61—41no—
120C4×C61—42no—
121C4×C612−1+412yes—
122Dic61—21no—
123Dic61—21no—
124Dic61—21no—
125Dic61—21no—
126Dic61—41no—
127Dic61—42no—
128#3234—611nomaximal, Sylow
129C2×C61—22no—
130C2×C61—81no—
131C2×C61#53611yescharacteristic
132C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
133C2×C61#57511yescharacteristic
134D61—81no—
135#532—611no—
136C2×#125—611no—
137#501—612no—
138#490—612no—
139#481—611no—
140#481—611no—
141#480—611no—
142#480D6111yescharacteristic, complemented
143#478—612no—
144#478—612no—
145#432—611no—
146C61#323411yescharacteristic, complemented, Sylow
147C2×#41—1221no—
148C4⋊Q8—611no—
149#127—611no—
150#125—612no—
151#125—612no—
152#125—1221no—
153#125—1221no—
154#124—1221no—
155#121—611no—
156#121—1221no—
157#121C2×D6111yescharacteristic
158C4×D4—611no—
159C4×D4—611no—
160C4×D4—1221no—
161C2×C4⋊C4—611no—
162C2×C4⋊C4—1221no—
163C2×C4⋊C4—1221no—
164C2×C4⋊C4C2×D6111yescharacteristic
165C2×C42—611no—
166#107—612no—
167#107C2×D6112yes—
168#106—612no—
169#106—612no—
170C4⋊C8—612no—
171#102—612no—
172#102—612no—
173#102—612no—
174#102C2×D6112yes—
175C22⋊C8—611no—
176C22⋊C8C2×D6111yescharacteristic
177#97—612no—
178#41—2444no—
179C2×Q8—1221no—
180C2×D4—21no—
181C2×D4—611no—
182C2×D4—1221no—
183C2×D4—1221no—
184C2×D4—1221no—
185C2×D4C22×D6111yescharacteristic
186C22×C4—21no—
187C22×C4—611no—
188C22×C4—611no—
189C22×C4—1221no—
190C22×C4—1221no—
191C22×C4—1221no—
192C22×C4C22×D6111yescharacteristic
193C2×C8—612no—
194C2×C8C22×D6112yes—
195C4⋊C4—21no—
196C4⋊C4—612no—
197C4⋊C4—611no—
198C4⋊C4—1222no—
199C4⋊C4—1222no—
200C4⋊C4—1222no—
201C4⋊C4—1222no—
202C4⋊C4—1221no—
203C4⋊C4—1221no—
204C4⋊C4C22×D6112yes—
205C4⋊C4C22×D6111yescharacteristic
206C22⋊C4—21no—
207C22⋊C4—1221no—
208C22⋊C4—1221no—
209C22⋊C4—1221no—
210C42—611no—
211C42—611no—
212C42—611no—
213C42—611no—
214C23—21no—
215C23—1221no—
216C23D4×D6111yescharacteristic
217Q8—2442no—
218D4—22no—
219D4—42no—
220D4—1222no—
221D4—2442no—
222D4—2442no—
223D4—2442no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—42no—
228C2×C4—611no—
229C2×C4—611no—
230C2×C4—611no—
231C2×C4—611no—
232C2×C4—1222no—
233C2×C4—1221no—
234C2×C4—1222no—
235C2×C4—2442no—
236C2×C4—2441no—
237C2×C4—2442no—
238C2×C4—2442no—
239C2×C4D4×D6111yescharacteristic
240C2×C4C23×D6111yescharacteristic
241C8—22no—
242C8—1222no—
243C22—21no—
244C22—21no—
245C22—41no—
246C22—41no—
247C22—41no—
248C22—2441no—
249C22—2441no—
250C22—2441no—
251C22#1451980112yes—
252C22C2×D4×D6111yescharacteristic
253C4—21no—
254C4—42no—
255C4—41no—
256C4—1221no—
257C4—1221no—
258C4—1221no—
259C4—1221no—
260C4—2441no—
261C4—2442no—
262C4#1451982412yes—
263C2—22no—
264C2—81no—
265C2—4881no—
266C2#1684033411yescharacteristic
267C2C2×#1451980111yescharacteristic
268C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#480C2
socleC22×C61C22×D4
hypercenter#480D61
hypocenterC61#3234
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×#14519768C2semidirect
3. #16840170C2semidirect
4. #16840125C2semidirect
5. #16840081C2semidirect
6. #16840078C2semidirect
7. #16840075C2semidirect
8. #16840065C2semidirect
9. #16840064C2semidirect
10. #16839816C2semidirect
11. C61×#480C2semidirect
142. #480D61semidirect
146. C61#3234semidirect