Finite Group Databasebeta

← #21457204

Subgroups — #21457204

Order 7808.

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

normal subgroups only

This group has 386 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#16840316C211yesmaximal, characteristic, complemented
2#16840310C211yesmaximal, characteristic
3#16840058C211yesmaximal, characteristic, complemented
4#16840057C211yesmaximal, characteristic, complemented
5#16840040C212yesmaximal, complemented
6#16840007C212yesmaximal, complemented
7#16840005C212yesmaximal, complemented
8#16839965C212yesmaximal, complemented
9#16839959C211yesmaximal, characteristic, complemented
10#16839784C211yesmaximal, characteristic, complemented
11C61×#460C211yesmaximal, characteristic, complemented
12C2×#11758224—21no—
13C2×#11758200C2212yes—
14C2×#11758189C2212yes—
15#14519777C2211yescharacteristic
16#14519776C2211yescharacteristic
17#14519775C2211yescharacteristic
18#14519767—21no—
19#14519764—21no—
20#14519757C2211yescharacteristic
21#14519755—21no—
22#14519753C2211yescharacteristic
23#14519748—21no—
24#14519748C2212yes—
25C4×Dic122—21no—
26C4×Dic122C2211yescharacteristic
27D4×Dic61—21no—
28D4×Dic61C2212yes—
29#14519734—21no—
30C42×D61C2211yescharacteristic
31#14519711C2212yes—
32#14519710C2212yes—
33C4⋊#92418C2211yescharacteristic
34#14519706C2212yes—
35#14519702C2212yes—
36#14519701C2212yes—
37#14519698C2212yes—
38C2×SD16×C61C2212yes—
39#127×C61C2211yescharacteristic
40C4×Q8×C61C2211yescharacteristic
41C4⋊C8×C61C2211yescharacteristic
42#102×C61C2212yes—
43C2×Q8×C61C2311yescharacteristic
44C2×D4×C61—21no—
45C2×D4×C61—21no—
46C2×D4×C61C2312yes—
47C2×C22⋊D61—22no—
48C22×Dic61—22no—
49#11758224—44no—
50C2×C4×D61D411yescharacteristic
51C2×C4×D61D411yescharacteristic
52C2×C4×D61C2311yescharacteristic
53C2×Dic122—21no—
54C2×Dic122—21no—
55C2×Dic122C2311yescharacteristic
56SD16×C61—42no—
57C2×C8×C61C2312yes—
58C4⋊C4×C61—21no—
59C4⋊C4×C61C2311yescharacteristic
60C42×C61—21no—
61C42×C61C2311yescharacteristic
62C22⋊Dic61—22no—
63C22⋊Dic61—22no—
64#11758200—42no—
65#11758198—21no—
66#11758198—21no—
67C4⋊Dic61—21no—
68C4⋊Dic61—21no—
69C4⋊Dic61C2311yescharacteristic
70C4⋊Dic61C2312yes—
71#11758196—21no—
72#11758196—21no—
73#11758196—21no—
74#11758196—21no—
75#11758196—21no—
76C4×Dic61—21no—
77C4×Dic61D411yescharacteristic
78C4×Dic61D411yescharacteristic
79C4×Dic61C2311yescharacteristic
80C2×#92418C2312yes—
81#11758189—42no—
82C23×C61—22no—
83C22×D61C2×D411yescharacteristic
84Q8×C61—21no—
85Q8×C61—21no—
86D4×C61—22no—
87D4×C61—22no—
88D4×C61—42no—
89D4×C61—42no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61C2×D411yescharacteristic
93C2×C4×C61C2×D411yescharacteristic
94C2×C4×C61C2411yescharacteristic
95C22⋊D61—44no—
96C2×Dic61—21no—
97C2×Dic61—21no—
98C2×Dic61—22no—
99C2×Dic61—44no—
100C2×Dic61C2×D411yescharacteristic
101C2×Dic61C2×D411yescharacteristic
102C2×Dic61C2×D411yescharacteristic
103C4×D61—22no—
104C4×D61—21no—
105C4×D61—21no—
106C4×D61—22no—
107Dic122—21no—
108Dic122—21no—
109Dic122—42no—
110Dic122—42no—
111C8×C61—22no—
112#92418—22no—
113C22×C61—42no—
114C22×C61—42no—
115C22×C61—42no—
116C22×C61C22×D411yescharacteristic
117C2×D61—21no—
118C2×D61—21no—
119C2×D61—21no—
120C4×C61—21no—
121C4×C61—41no—
122C4×C61—41no—
123C4×C61#13712yes—
124C4×C61H(5,𝔽2)11yescharacteristic
125C4×C612−1+411yescharacteristic
126Dic61—21no—
127Dic61—21no—
128Dic61—41no—
129Dic61—41no—
130Dic61—42no—
131Dic61AGL(1,ℤ/8)12yes—
132#3254—611nomaximal, Sylow
133C2×C61—82no—
134C2×C61#53711yescharacteristic
135C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
136C2×C61C2×#13711yescharacteristic
137D61—41no—
138#533—611no—
139#532—611no—
140#477—611no—
141#477—611no—
142#474—612no—
143#468—612no—
144#468—612no—
145#461—612no—
146#460—611no—
147#460D6111yescharacteristic, complemented
148#423—611no—
149C61#325411yescharacteristic, complemented, Sylow
150C2×#41—1221no—
151C2×SD16—612no—
152C2×SD16C2×D6112yes—
153C2×M16—612no—
154C4⋊Q8—611no—
155C4⋊Q8—611no—
156C4⋊Q8—611no—
157#127C2×D6111yescharacteristic
158#125—1221no—
159#124—1221no—
160C22⋊Q8—611no—
161C22⋊Q8—611no—
162C22⋊Q8—1221no—
163#121—612no—
164#121—1221no—
165C4×Q8—611no—
166C4×Q8—1221no—
167C4×Q8C2×D6111yescharacteristic
168C4×D4—612no—
169C4×D4—1221no—
170#117—1221no—
171C2×C42—611no—
172#107—612no—
173#107—612no—
174C4⋊C8—612no—
175C4⋊C8—611no—
176C4⋊C8C2×D6111yescharacteristic
177#103—612no—
178#103—612no—
179#102—612no—
180#102C2×D6112yes—
181#41—2444no—
182C2×Q8—611no—
183C2×Q8—1221no—
184C2×Q8—1221no—
185C2×Q8C22×D6111yescharacteristic
186C2×D4—21no—
187C2×D4—21no—
188C2×D4—1222no—
189C2×D4C22×D6112yes—
190C22×C4—611no—
191C22×C4—611no—
192C22×C4—611no—
193C22×C4—1222no—
194SD16—42no—
195SD16—2442no—
196M16—2442no—
197C2×C8—612no—
198C2×C8C22×D6112yes—
199C4⋊C4—21no—
200C4⋊C4—611no—
201C4⋊C4—612no—
202C4⋊C4—1221no—
203C4⋊C4—1221no—
204C4⋊C4—1221no—
205C4⋊C4—1221no—
206C4⋊C4—1221no—
207C4⋊C4—1221no—
208C4⋊C4—1221no—
209C4⋊C4C22×D6111yescharacteristic
210C22⋊C4—1221no—
211C22⋊C4—1221no—
212C22⋊C4—1222no—
213C22⋊C4—1222no—
214C42—21no—
215C42—611no—
216C42—611no—
217C42—611no—
218C42—1221no—
219C42C22×D6111yescharacteristic
220C23—22no—
221C23—611no—
222Q8—21no—
223Q8—21no—
224Q8—1221no—
225Q8—1221no—
226Q8—2442no—
227Q8—2442no—
228D4—22no—
229D4—22no—
230D4—42no—
231D4—42no—
232D4—2444no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—611no—
236C2×C4—611no—
237C2×C4—611no—
238C2×C4—1222no—
239C2×C4—1221no—
240C2×C4—1221no—
241C2×C4—1222no—
242C2×C4—1221no—
243C2×C4—1221no—
244C2×C4—1222no—
245C2×C4—2444no—
246C2×C4D4×D6111yescharacteristic
247C2×C4D4×D6111yescharacteristic
248C2×C4C23×D6111yescharacteristic
249C8—22no—
250C8—1222no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22—1221no—
255C22—1221no—
256C22—1221no—
257C22C2×D4×D6111yescharacteristic
258C4—21no—
259C4—41no—
260C4—41no—
261C4—612no—
262C4—1221no—
263C4—1221no—
264C4—2442no—
265C4—2441no—
266C4—2441no—
267C4#1451980612yes—
268C4#1451982211yescharacteristic
269C4#1451982411yescharacteristic
270C2—82no—
271C2—2441no—
272C2#1684034111yescharacteristic
273C2AGL(1,ℤ/8)×D6111yescharacteristic
274C2C2×#1451980611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#460C2
socleC22×C61C22×D4
hypercenter#460D61
hypocenterC61#3254
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #16840316C2semidirect
3. #16840058C2semidirect
4. #16840057C2semidirect
5. #16840040C2semidirect
6. #16840007C2semidirect
7. #16840005C2semidirect
8. #16839965C2semidirect
9. #16839959C2semidirect
10. #16839784C2semidirect
11. C61×#460C2semidirect
147. #460D61semidirect
149. C61#3254semidirect