Finite Group Databasebeta

← #21458156

Subgroups — #21458156

Order 7808.

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

normal subgroups only

This group has 398 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#16840473C211yesmaximal, characteristic, complemented
2#16840432C211yesmaximal, characteristic
3#16840074C212yesmaximal, complemented
4#16840054C211yesmaximal, characteristic, complemented
5#16840007C212yesmaximal, complemented
6#16839959C211yesmaximal, characteristic, complemented
7#16839925C212yesmaximal, complemented
8C4×Dic244C211yesmaximal, characteristic, complemented
9#16839841C211yesmaximal, characteristic, complemented
10#16839760C212yesmaximal, complemented
11C61×#486C211yesmaximal, characteristic, complemented
12C2×#11758224C2212yes—
13C2×Dic244C2211yescharacteristic
14C2×#11758200C2212yes—
15C2×#11758189C2212yes—
16#14519773—21no—
17#14519768—21no—
18#14519757C2212yes—
19#14519753—22no—
20#14519749—22no—
21#14519748C2212yes—
22C4×Dic122C2211yescharacteristic
23C4×Dic122C2211yescharacteristic
24C4×D244C2211yescharacteristic
25D4×Dic61—21no—
26#14519739—21no—
27C4⋊C4×D61C2212yes—
28#14519711C2211yescharacteristic
29#14519710C2212yes—
30C4⋊#92418C2211yescharacteristic
31#14519702C2211yescharacteristic
32#14519702C2211yescharacteristic
33#14519700C2212yes—
34#14519698C2212yes—
35#14519689C2212yes—
36C4⋊Q8×C61C2211yescharacteristic
37#127×C61C2211yescharacteristic
38#102×C61C2212yes—
39#102×C61C2212yes—
40C4×C8×C61C2211yescharacteristic
41C2×Q8×C61—21no—
42C2×D4×C61—21no—
43C2×D4×C61—21no—
44C2×D4×C61C2312yes—
45C2×C22⋊D61—22no—
46C2×C22⋊D61—22no—
47C22×Dic61—22no—
48#11758224—24no—
49#11758224—42no—
50C2×D244D411yescharacteristic
51C2×C4×D61—22no—
52C2×C4×D61C2312yes—
53C2×Dic122C2311yescharacteristic
54C2×Dic122C2311yescharacteristic
55C2×C8×C61C2311yescharacteristic
56C2×C8×C61C2311yescharacteristic
57C4⋊C4×C61—21no—
58C4⋊C4×C61C2312yes—
59C42×C61C2311yescharacteristic
60C22⋊Dic61—22no—
61#11758200—42no—
62#11758198—22no—
63#11758198D412yes—
64C4⋊Dic61—22no—
65C4⋊Dic61D411yescharacteristic
66C4⋊Dic61C2311yescharacteristic
67C4⋊Dic61C2311yescharacteristic
68#11758196—21no—
69#11758196—21no—
70#11758196—22no—
71C4×Dic61—21no—
72C4×Dic61—21no—
73C2×#92418C2312yes—
74Dic244—22no—
75#11758189—42no—
76C23×C61—22no—
77C22×D61C2×D412yes—
78Q8×C61—81no—
79D4×C61—22no—
80D4×C61—22no—
81D4×C61—42no—
82D4×C61—81no—
83C2×C4×C61—22no—
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2411yescharacteristic
87C22⋊D61—44no—
88C22⋊D61—82no—
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—44no—
94C2×Dic61C2×D412yes—
95D244—22no—
96C4×D61—22no—
97C4×D61—22no—
98C4×D61—82no—
99Dic122—21no—
100Dic122—21no—
101Dic122—21no—
102Dic122#4112yes—
103C8×C61—21no—
104C8×C61—21no—
105#92418—22no—
106C22×C61—42no—
107C22×C61—42no—
108C22×C61—42no—
109C22×C61C22×D411yescharacteristic
110C2×D61—22no—
111C2×D61—22no—
112C2×D61—22no—
113C4×C61—21no—
114C4×C61—42no—
115C4×C61#13712yes—
116C4×C61C2×#4111yescharacteristic
117C4×C61H(5,𝔽2)11yescharacteristic
118Dic61—22no—
119Dic61—22no—
120Dic61—41no—
121Dic61—41no—
122Dic61—41no—
123#3333—611nomaximal, Sylow
124C2×C61—82no—
125C2×C61#54611yescharacteristic
126C2×C61C2×#13711yescharacteristic
127C2×C61#57611yescharacteristic
128D61—42no—
129#554—611no—
130#550—611no—
131#486D6111yescharacteristic, complemented
132#480—612no—
133#477—611no—
134#468—612no—
135#460—611no—
136#452—612no—
137C4×Q16—611no—
138#436—611no—
139#417—612no—
140C61#333311yescharacteristic, complemented, Sylow
141C2×#41—612no—
142C2×Q16—611no—
143C2×SD16—612no—
144C2×M16—612no—
145C4⋊Q8C2×D6111yescharacteristic
146#127—1221no—
147#127C2×D6111yescharacteristic
148#125—1221no—
149C22⋊Q8—612no—
150C22⋊Q8—1222no—
151#121—612no—
152#121—1222no—
153C4×Q8—611no—
154C4×Q8—611no—
155C4×D4—611no—
156C4×D4—1221no—
157C4×D4—1221no—
158C2×C4⋊C4—612no—
159#107—611no—
160#107—612no—
161C4⋊C8—611no—
162#103—611no—
163#103—611no—
164#103—612no—
165#102—612no—
166#102C2×D6112yes—
167#102C2×D6112yes—
168C22⋊C8—612no—
169C4×C8C2×D6111yescharacteristic
170#41—1224no—
171#41—2442no—
172C2×Q8—21no—
173C2×Q8—611no—
174C2×Q8—611no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—611no—
178C2×D4—1222no—
179C2×D4—1222no—
180C2×D4C22×D6112yes—
181C22×C4—612no—
182C22×C4—1222no—
183C22×C4—1222no—
184Q16—1222no—
185SD16—2442no—
186M16—2442no—
187C2×C8—612no—
188C2×C8C22×D6111yescharacteristic
189C2×C8C22×D6111yescharacteristic
190C4⋊C4—21no—
191C4⋊C4—611no—
192C4⋊C4—611no—
193C4⋊C4—611no—
194C4⋊C4—1222no—
195C4⋊C4—1222no—
196C4⋊C4—1221no—
197C4⋊C4—1221no—
198C4⋊C4C22×D6112yes—
199C22⋊C4—612no—
200C22⋊C4—1222no—
201C22⋊C4—1222no—
202C42—1221no—
203C42—1221no—
204C42C22×D6111yescharacteristic
205C23—22no—
206C23—612no—
207Q8—81no—
208Q8—612no—
209Q8—1221no—
210Q8—1221no—
211Q8—1221no—
212D4—22no—
213D4—22no—
214D4—42no—
215D4—81no—
216D4—1222no—
217D4—4882no—
218D4—2444no—
219C2×C4—22no—
220C2×C4—612no—
221C2×C4—1221no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4—1221no—
225C2×C4—1221no—
226C2×C4—1221no—
227C2×C4—4882no—
228C2×C4—2444no—
229C2×C4D4×D6111yescharacteristic
230C2×C4D4×D6111yescharacteristic
231C2×C4C23×D6111yescharacteristic
232C8—21no—
233C8—21no—
234C8—1222no—
235C22—42no—
236C22—42no—
237C22—42no—
238C22—1222no—
239C22—1222no—
240C22—1222no—
241C22C2×D4×D6111yescharacteristic
242C4—21no—
243C4—42no—
244C4—1222no—
245C4—1222no—
246C4—2441no—
247C4—2441no—
248C4—2441no—
249C4#1451980612yes—
250C4#41×D6111yescharacteristic
251C4#1451982311yescharacteristic
252C2—82no—
253C2—2442no—
254C2#1684040511yescharacteristic
255C2C2×#1451980611yescharacteristic
256C2#1684056311yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#486C2
socleC22×C61C22×D4
hypercenter#486D61
hypocenterC61#3333
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #16840473C2semidirect
3. #16840074C2semidirect
4. #16840054C2semidirect
5. #16840007C2semidirect
6. #16839959C2semidirect
7. #16839925C2semidirect
8. C4×Dic244C2semidirect
9. #16839841C2semidirect
10. #16839760C2semidirect
11. C61×#486C2semidirect
131. #486D61semidirect
140. C61#3333semidirect