Finite Group Databasebeta

← #21456731

Subgroups — #21456731

Order 7808.

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

normal subgroups only

This group has 402 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#16840340C212yesmaximal, complemented
2#16840093C212yesmaximal, complemented
3#16840081C212yesmaximal, complemented
4#16840020C211yesmaximal, characteristic, complemented
5#16840015C211yesmaximal, characteristic, complemented
6#16839991C212yesmaximal, complemented
7#16839926C212yesmaximal, complemented
8#16839909C212yesmaximal, complemented
9C61×#408C211yesmaximal, characteristic, complemented
10C2×#11758222C2212yes—
11C2×Dic244C2211yescharacteristic
12C2×#11758190C2212yes—
13C2×D488C2211yescharacteristic
14#14519756C2212yes—
15#14519756C2212yes—
16#14519753—22no—
17#14519751C2212yes—
18#14519751C2212yes—
19#14519749—22no—
20#14519749—22no—
21#14519748—22no—
22C2×C4⋊Dic61C2212yes—
23#14519709C2212yes—
24#14519709C2211yescharacteristic
25#14519709C2211yescharacteristic
26#14519702C2212yes—
27#14519702C2212yes—
28#14519699C2212yes—
29#14519699C2212yes—
30C2×#41×C61C2211yescharacteristic
31C2×M16×C61C2211yescharacteristic
32C22×C8×C61C2211yescharacteristic
33C22⋊C8×C61C2212yes—
34C22⋊C8×C61C2212yes—
35#41×C61—41no—
36#41×C61—41no—
37C2×Q8×C61D411yescharacteristic
38C2×D4×C61D412yes—
39C2×D4×C61D411yescharacteristic
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C2×C22⋊D61—22no—
43C2×C22⋊D61—22no—
44C2×C22⋊D61—22no—
45C22×Dic61—22no—
46#11758222—42no—
47#11758222—42no—
48C2×D244C2312yes—
49C2×C4×D61—22no—
50C2×Dic122C2312yes—
51M16×C61—41no—
52C2×C8×C61—41no—
53C2×C8×C61C2312yes—
54C2×C8×C61C2311yescharacteristic
55C2×C8×C61C2311yescharacteristic
56C22⋊Dic61—22no—
57C22⋊Dic61—22no—
58#11758198—22no—
59#11758198—22no—
60C4⋊Dic61—22no—
61C4⋊Dic61C2312yes—
62C4⋊Dic61C2312yes—
63#11758196—22no—
64#11758196—22no—
65Dic244—41no—
66D488—41no—
67#11758190—42no—
68C23×C61C2×D411yescharacteristic
69C23×C61C2×D412yes—
70C22×D61—22no—
71Q8×C61—41no—
72D4×C61—42no—
73D4×C61—41no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D412yes—
80C2×C4×C61C2411yescharacteristic
81C22⋊D61—44no—
82C22⋊D61—82no—
83C22⋊D61—82no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—82no—
88D244—22no—
89D244—22no—
90C4×D61—44no—
91Dic122—22no—
92Dic122—22no—
93C8×C61—22no—
94C8×C61—21no—
95C8×C61—21no—
96C22×C61—22no—
97C22×C61—21no—
98C22×C61—22no—
99C22×C61—22no—
100C22×C61—22no—
101C22×C61C22×D411yescharacteristic
102C2×D61—42no—
103C2×D61—42no—
104C2×D61—42no—
105C4×C61—22no—
106C4×C61—21no—
107C4×C61H(5,𝔽2)11yescharacteristic
108C4×C61H(5,𝔽2)11yescharacteristic
109Dic61—42no—
110Dic61—42no—
111Dic61—42no—
112#3204—611nomaximal, Sylow
113C2×C61—42no—
114C2×C61—41no—
115C2×C61#53411yescharacteristic
116C2×C61#57712yes—
117D61—82no—
118#537—612no—
119#483—612no—
120#481—612no—
121#470—611no—
122#469—611no—
123#465—612no—
124#452—612no—
125#449—612no—
126#408D6111yescharacteristic, complemented
127C61#320411yescharacteristic, complemented, Sylow
128C2×#41—612no—
129C2×#41C2×D6111yescharacteristic
130C2×Q16—611no—
131C2×SD16—612no—
132C2×D8—611no—
133C2×M16C2×D6111yescharacteristic
134C22×C8C2×D6111yescharacteristic
135C22⋊Q8—612no—
136C22⋊Q8—612no—
137C22⋊Q8—1222no—
138#121—612no—
139#121—612no—
140#121—1222no—
141#121—1222no—
142#121—1222no—
143C2×C4⋊C4—612no—
144#106—612no—
145#106—611no—
146#106—611no—
147#103—612no—
148#103—612no—
149#102—612no—
150#102—612no—
151C22⋊C8C2×D6112yes—
152C22⋊C8C2×D6112yes—
153#41—41no—
154#41—41no—
155#41—2442no—
156#41—2442no—
157C2×Q8—612no—
158C2×Q8D24411yescharacteristic
159C2×D4—612no—
160C2×D4—1222no—
161C2×D4—1222no—
162C2×D4—1222no—
163C2×D4D24411yescharacteristic
164C2×D4D24412yes—
165C22×C4—1222no—
166C22×C4—1222no—
167C22×C4C22×D6112yes—
168C22×C4C22×D6111yescharacteristic
169Q16—2441no—
170SD16—2442no—
171D8—2441no—
172M16—41no—
173C2×C8—41no—
174C2×C8C22×D6111yescharacteristic
175C2×C8C22×D6112yes—
176C2×C8C22×D6111yescharacteristic
177C4⋊C4—612no—
178C4⋊C4—612no—
179C4⋊C4—1222no—
180C4⋊C4—1222no—
181C4⋊C4—1222no—
182C22⋊C4—1222no—
183C22⋊C4—1222no—
184C22⋊C4—1222no—
185C22⋊C4—1222no—
186C23—1222no—
187C23C2×D24411yescharacteristic
188C23C2×D24412yes—
189Q8—41no—
190Q8—1222no—
191Q8—1222no—
192D4—42no—
193D4—41no—
194D4—1222no—
195D4—1222no—
196D4—4882no—
197D4—4882no—
198D4—2444no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—1222no—
204C2×C4—1222no—
205C2×C4—1222no—
206C2×C4—4882no—
207C2×C4—2444no—
208C2×C4C2×D24411yescharacteristic
209C2×C4C2×D24412yes—
210C2×C4C23×D6111yescharacteristic
211C8—22no—
212C8—21no—
213C8—21no—
214C22—22no—
215C22—22no—
216C22—22no—
217C22—22no—
218C22—21no—
219C22—2442no—
220C22—2442no—
221C22—2442no—
222C22C22×D24411yescharacteristic
223C4—22no—
224C4—21no—
225C4—2442no—
226C4—2442no—
227C4—2442no—
228C4#1451982211yescharacteristic
229C4#1451982211yescharacteristic
230C2—42no—
231C2—41no—
232C2—4882no—
233C2#1684032411yescharacteristic
234C2#1684057412yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#408C2
socleC22×C61C22×D4
hypercenter#408D61
hypocenterC61#3204
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #16840340C2semidirect
2. #16840093C2semidirect
3. #16840081C2semidirect
4. #16840020C2semidirect
5. #16840015C2semidirect
6. #16839991C2semidirect
7. #16839926C2semidirect
8. #16839909C2semidirect
9. C61×#408C2semidirect
126. #408D61semidirect
127. C61#3204semidirect