Finite Group Databasebeta

← #21456874

Subgroups — #21456874

Order 7808.

388 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 117 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#16840338C211yesmaximal, characteristic, complemented
2#16840149C211yesmaximal, characteristic, complemented
3#16840134C211yesmaximal, characteristic, complemented
4#16840132C211yesmaximal, characteristic, complemented
5#16840119C211yesmaximal, characteristic, complemented
6#16839977C212yesmaximal, complemented
7#16839967C212yesmaximal, complemented
8#16839905C212yesmaximal, complemented
9#16839900C212yesmaximal, complemented
10#16839823C211yesmaximal, characteristic, complemented
11C61×#540C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13C22×Dic122C2211yescharacteristic
14C2×#11758200C2212yes—
15C2×#11758200C2212yes—
16C2×#11758200C2212yes—
17C2×#11758199C2212yes—
18#14519777C2211yescharacteristic
19#14519777C2211yescharacteristic
20#14519765C2211yescharacteristic
21#14519765C2211yescharacteristic
22#14519761—22no—
23#14519757—22no—
24C4⋊#92418C2212yes—
25#14519700C2212yes—
26#14519700C2212yes—
27#14519700C2212yes—
28#14519697C2212yes—
29C22⋊#92418C2212yes—
30#14519688C2211yescharacteristic
31C4×#92418C2211yescharacteristic
32#127×C61C2211yescharacteristic
33#125×C61C2211yescharacteristic
34#123×C61—22no—
35#121×C61—22no—
36#121×C61C2212yes—
37C4×D4×C61C2212yes—
38#117×C61C2211yescharacteristic
39C2×D4×C61—22no—
40C2×D4×C61—22no—
41C2×D4×C61C2312yes—
42C22×C4×C61—22no—
43C22×C4×C61C2311yescharacteristic
44C2×C22⋊D61—21no—
45C22×Dic61—21no—
46#11758222—42no—
47C2×D244C2311yescharacteristic
48C2×C4×D61—21no—
49C2×Dic122—21no—
50C2×Dic122—42no—
51C2×Dic122C2311yescharacteristic
52C2×Dic122C2311yescharacteristic
53C2×Dic122C2311yescharacteristic
54C4⋊C4×C61—22no—
55C4⋊C4×C61D412yes—
56C4⋊C4×C61C2312yes—
57C22⋊C4×C61—22no—
58C22⋊C4×C61—22no—
59C22⋊C4×C61D412yes—
60C42×C61C2311yescharacteristic
61C42×C61C2311yescharacteristic
62#11758200—42no—
63#11758200—42no—
64#11758200—42no—
65#11758199—42no—
66#11758198—22no—
67#11758198—22no—
68C4⋊Dic61—22no—
69C4⋊Dic61—22no—
70C2×#92418C2312yes—
71C2×#92418C2312yes—
72C23×C61—22no—
73C23×C61C2×D411yescharacteristic
74C22×D61—21no—
75D4×C61—22no—
76D4×C61—22no—
77D4×C61—82no—
78D4×C61—82no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—82no—
82C2×C4×C61C2×D412yes—
83C2×C4×C61C2×D412yes—
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2411yescharacteristic
86C22⋊D61—42no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—42no—
91D244—22no—
92C4×D61—42no—
93Dic122—22no—
94Dic122—22no—
95Dic122—22no—
96Dic122—42no—
97#92418—22no—
98#92418—22no—
99C22×C61—21no—
100C22×C61—22no—
101C22×C61—42no—
102C22×C61—42no—
103C22×C61—42no—
104C22×C61C22×D411yescharacteristic
105C2×D61—41no—
106C2×D61—42no—
107C4×C61—21no—
108C4×C61—22no—
109C4×C61—22no—
110C4×C61—42no—
111C4×C61H(5,𝔽2)12yes—
112Dic61—41no—
113Dic61—41no—
114Dic61—41no—
115#3221—611nomaximal, Sylow
116C2×C61—41no—
117C2×C61—82no—
118C2×C61#53511yescharacteristic
119C2×C61#57712yes—
120D61—81no—
121#540D6111yescharacteristic, complemented
122#536—611no—
123#496—611no—
124#492—611no—
125#491—611no—
126#488—611no—
127#463—612no—
128#461—612no—
129#449—612no—
130#448—612no—
131#433—611no—
132C61#322111yescharacteristic, complemented, Sylow
133C2×#41—611no—
134C22×Q8—611no—
135C2×SD16—612no—
136C2×SD16—612no—
137C2×SD16—612no—
138C2×D8—612no—
139C4⋊Q8—611no—
140C4⋊Q8—611no—
141#127C2×D6111yescharacteristic
142#125C2×D6111yescharacteristic
143#124—611no—
144#124—611no—
145#123—22no—
146#123—1222no—
147C22⋊Q8—1222no—
148#121—22no—
149#121C2×D6112yes—
150C4×D4C2×D6112yes—
151#117C2×D6111yescharacteristic
152C4⋊C8—612no—
153#103—612no—
154#103—612no—
155#103—612no—
156#102—612no—
157C22⋊C8—612no—
158#97—611no—
159C4×C8—611no—
160#41—2442no—
161C2×Q8—611no—
162C2×Q8—611no—
163C2×Q8—611no—
164C2×Q8—1221no—
165C2×Q8—2442no—
166C2×D4—22no—
167C2×D4—22no—
168C2×D4—611no—
169C2×D4—1221no—
170C2×D4C22×D6112yes—
171C22×C4—22no—
172C22×C4—1221no—
173C22×C4—1221no—
174C22×C4C22×D6111yescharacteristic
175SD16—2442no—
176SD16—2442no—
177SD16—2442no—
178D8—2442no—
179C2×C8—612no—
180C2×C8—612no—
181C4⋊C4—22no—
182C4⋊C4—1222no—
183C4⋊C4—1222no—
184C4⋊C4C22⋊D6112yes—
185C4⋊C4C22×D6112yes—
186C22⋊C4—22no—
187C22⋊C4—22no—
188C22⋊C4—1222no—
189C22⋊C4—1222no—
190C22⋊C4C22⋊D6112yes—
191C42C22×D6111yescharacteristic
192C42C22×D6111yescharacteristic
193C23—22no—
194C23—1221no—
195C23C2×C22⋊D6111yescharacteristic
196Q8—1222no—
197Q8—1222no—
198Q8—1222no—
199Q8—2442no—
200D4—22no—
201D4—22no—
202D4—82no—
203D4—82no—
204D4—1222no—
205D4—2442no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—82no—
209C2×C4—1221no—
210C2×C4—1221no—
211C2×C4—1221no—
212C2×C4—2442no—
213C2×C4—2442no—
214C2×C4C2×C22⋊D6112yes—
215C2×C4C2×C22⋊D6112yes—
216C2×C4C2×C22⋊D6111yescharacteristic
217C2×C4C23×D6111yescharacteristic
218C8—1222no—
219C8—1222no—
220C22—22no—
221C22—21no—
222C22—42no—
223C22—42no—
224C22—42no—
225C22—2442no—
226C22—2441no—
227C22C22×C22⋊D6111yescharacteristic
228C4—22no—
229C4—22no—
230C4—21no—
231C4—42no—
232C4—2441no—
233C4—2441no—
234C4—2441no—
235C4#1451982312yes—
236C2—41no—
237C2—82no—
238C2—4881no—
239C2#1684032611yescharacteristic
240C2#1684057312yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#540C2
socleC22×C61C22×D4
hypercenter#540D61
hypocenterC61#3221
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #16840338C2semidirect
2. #16840149C2semidirect
3. #16840134C2semidirect
4. #16840132C2semidirect
5. #16840119C2semidirect
6. #16839977C2semidirect
7. #16839967C2semidirect
8. #16839905C2semidirect
9. #16839900C2semidirect
10. #16839823C2semidirect
11. C61×#540C2semidirect
121. #540D61semidirect
132. C61#3221semidirect