Finite Group Databasebeta

← #21458136

Subgroups — #21458136

Order 7808.

388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 123 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#16840469C211yesmaximal, characteristic, complemented
2#16840417C211yesmaximal, characteristic
3#16840113C211yesmaximal, characteristic, complemented
4#16840093C212yesmaximal, complemented
5#16840053C211yesmaximal, characteristic, complemented
6#16840020C212yesmaximal, complemented
7#16839973C211yesmaximal, characteristic, complemented
8#16839926C212yesmaximal, complemented
9C4×#11758190C211yesmaximal, characteristic, complemented
10#16839764C212yesmaximal, complemented
11C61×#436C211yesmaximal, characteristic, complemented
12C2×#11758222C2212yes—
13C2×Dic244C2212yes—
14C2×#11758190C2211yescharacteristic
15#14519777C2211yescharacteristic
16#14519777C2211yescharacteristic
17#14519768—21no—
18#14519759—22no—
19#14519756C2212yes—
20#14519756C2212yes—
21#14519754—22no—
22#14519748—21no—
23C4×Dic122C2211yescharacteristic
24C4×D244C2211yescharacteristic
25D4×Dic61—21no—
26C2×C4⋊Dic61C2212yes—
27C4⋊C4×D61—21no—
28#14519709C2212yes—
29#14519709C2211yescharacteristic
30#14519702C2212yes—
31#14519702C2212yes—
32#14519702C2211yescharacteristic
33#14519702C2212yes—
34#14519699C2211yescharacteristic
35#14519699C2212yes—
36C2×M16×C61C2212yes—
37C4×D4×C61C2211yescharacteristic
38C4⋊C8×C61C2211yescharacteristic
39C22⋊C8×C61C2212yes—
40C4×C8×C61C2211yescharacteristic
41C2×D4×C61D411yescharacteristic
42C22×C4×C61C2312yes—
43C2×C22⋊D61—22no—
44C22×Dic61—22no—
45#11758222—24no—
46#11758222—42no—
47C2×D244C2311yescharacteristic
48C2×C4×D61—22no—
49C2×C4×D61—21no—
50C2×Dic122—21no—
51C2×Dic122C2312yes—
52C2×Dic122C2311yescharacteristic
53M16×C61—42no—
54C2×C8×C61C2311yescharacteristic
55C2×C8×C61C2311yescharacteristic
56C2×C8×C61C2312yes—
57C4⋊C4×C61D411yescharacteristic
58C22⋊C4×C61D412yes—
59C42×C61C2311yescharacteristic
60C22⋊Dic61—22no—
61C22⋊Dic61—22no—
62#11758198—21no—
63C4⋊Dic61—21no—
64C4⋊Dic61—22no—
65C4⋊Dic61—21no—
66C4⋊Dic61—21no—
67C4⋊Dic61C2311yescharacteristic
68C4⋊Dic61C2312yes—
69C4⋊Dic61C2311yescharacteristic
70#11758196—22no—
71#11758196—21no—
72#11758196—22no—
73C4×Dic61—21no—
74Dic244—42no—
75#11758190—22no—
76C23×C61C2×D412yes—
77C22×D61—21no—
78D4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61C2×D412yes—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2411yescharacteristic
85C22⋊D61—44no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—82no—
92D244—21no—
93D244#4112yes—
94C4×D61—44no—
95C4×D61—42no—
96Dic122—21no—
97Dic122—22no—
98Dic122—21no—
99Dic122—22no—
100Dic122—81no—
101C8×C61—21no—
102C8×C61—22no—
103C8×C61—21no—
104C22×C61—22no—
105C22×C61—22no—
106C22×C61—22no—
107C22×C61C22×D411yescharacteristic
108C2×D61—22no—
109C2×D61—41no—
110C2×D61—41no—
111C4×C61—22no—
112C4×C61—21no—
113C4×C61#13712yes—
114C4×C61C2×#4111yescharacteristic
115C4×C61H(5,𝔽2)11yescharacteristic
116Dic61—42no—
117Dic61—41no—
118Dic61—41no—
119Dic61—42no—
120Dic61—41no—
121#3331—611nomaximal, Sylow
122C2×C61—42no—
123C2×C61#54611yescharacteristic
124C2×C61C2×#13711yescharacteristic
125C2×C61#57711yescharacteristic
126D61—42no—
127#554—611no—
128#547—611no—
129#487—611no—
130#483—612no—
131#476—611no—
132#470—612no—
133#462—611no—
134#452—612no—
135C4×SD16—611no—
136#436D6111yescharacteristic, complemented
137#417—612no—
138C61#333111yescharacteristic, complemented, Sylow
139C2×#41—612no—
140C2×Q16—612no—
141C2×SD16—611no—
142C2×M16C2×D6112yes—
143C4⋊Q8—611no—
144C4⋊Q8—611no—
145#125—1221no—
146#123—1222no—
147C22⋊Q8—612no—
148C22⋊Q8—612no—
149C22⋊Q8—1222no—
150#121—1221no—
151C4×Q8—611no—
152C4×D4—611no—
153C4×D4—1221no—
154C4×D4C2×D6111yescharacteristic
155C2×C4⋊C4—612no—
156C2×C4⋊C4—1221no—
157#106—611no—
158#106—612no—
159C4⋊C8C2×D6111yescharacteristic
160#103—612no—
161#103—612no—
162#103—611no—
163#103—612no—
164#102—611no—
165#102—612no—
166C22⋊C8C2×D6112yes—
167C4×C8C2×D6111yescharacteristic
168#41—1224no—
169#41—2442no—
170C2×Q8—612no—
171C2×Q8—611no—
172C2×Q8—1221no—
173C2×D4—611no—
174C2×D4—1222no—
175C2×D4D24411yescharacteristic
176C22×C4—1222no—
177C22×C4—1221no—
178C22×C4—1222no—
179C22×C4C22×D6112yes—
180Q16—2442no—
181SD16—1222no—
182M16—42no—
183C2×C8C22×D6111yescharacteristic
184C2×C8C22×D6111yescharacteristic
185C2×C8C22×D6112yes—
186C4⋊C4—611no—
187C4⋊C4—612no—
188C4⋊C4—611no—
189C4⋊C4—1222no—
190C4⋊C4—1222no—
191C4⋊C4—1221no—
192C4⋊C4—1221no—
193C4⋊C4—1222no—
194C4⋊C4—1221no—
195C4⋊C4—1221no—
196C4⋊C4D24411yescharacteristic
197C22⋊C4—1222no—
198C22⋊C4—1222no—
199C22⋊C4—1221no—
200C22⋊C4D24412yes—
201C42—1221no—
202C42C22×D6111yescharacteristic
203C23—1221no—
204C23C2×D24412yes—
205Q8—1221no—
206Q8—1222no—
207Q8—1221no—
208Q8—1222no—
209Q8—4881no—
210D4—22no—
211D4—612no—
212D4—1221no—
213D4—2444no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—1221no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4—4882no—
222C2×C4—2444no—
223C2×C4—2442no—
224C2×C4C2×D24411yescharacteristic
225C2×C4C2×D24412yes—
226C2×C4C2×D24411yescharacteristic
227C2×C4C23×D6111yescharacteristic
228C8—21no—
229C8—21no—
230C8—22no—
231C22—22no—
232C22—22no—
233C22—22no—
234C22—1222no—
235C22—2441no—
236C22—2441no—
237C22C22×D24411yescharacteristic
238C4—21no—
239C4—22no—
240C4—2441no—
241C4—2441no—
242C4—2442no—
243C4—2442no—
244C4—2441no—
245C4#1451981012yes—
246C4#41×D6111yescharacteristic
247C4#1451982211yescharacteristic
248C2—42no—
249C2—2442no—
250C2#1684040711yescharacteristic
251C2C2×#1451981011yescharacteristic
252C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#436C2
socleC22×C61C22×D4
hypercenter#436D61
hypocenterC61#3331
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #16840469C2semidirect
3. #16840113C2semidirect
4. #16840093C2semidirect
5. #16840053C2semidirect
6. #16840020C2semidirect
7. #16839973C2semidirect
8. #16839926C2semidirect
9. C4×#11758190C2semidirect
10. #16839764C2semidirect
11. C61×#436C2semidirect
136. #436D61semidirect
138. C61#3331semidirect