Finite Group Databasebeta

← #21444769

Subgroups — #21444769

Order 7808.

308 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 51 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#16840320C211yesmaximal, characteristic
2#16839901C211yesmaximal, characteristic, complemented
3#16839673C211yesmaximal, characteristic, complemented
4#16839497C211yesmaximal, characteristic, complemented
5#16839496C211yesmaximal, characteristic, complemented
6#16839485C211yesmaximal, characteristic, complemented
7C61×#448C211yesmaximal, characteristic, complemented
8C2×D4×D61—21no—
9C2×#11758201—21no—
10#14519762—21no—
11#14519759—21no—
12#14519751C2211yescharacteristic
13#14519749—21no—
14#14519747—21no—
15#14519745—21no—
16C2×#11758198—21no—
17C2×#11758198C2211yescharacteristic
18#14519701—21no—
19C22⋊#92418C2211yescharacteristic, complemented
20#14519684—21no—
21#14519684C2211yescharacteristic, complemented
22C22×Q8×C61C2211yescharacteristic, complemented
23C2×SD16×C61—21no—
24#121×C61C2211yescharacteristic
25#103×C61—21no—
26C22⋊C8×C61C2211yescharacteristic, complemented
27C23×D61—21no—
28C23×D61D411yescharacteristic
29C2×Q8×C61—21no—
30C2×Q8×C61—21no—
31C2×Q8×C61—42no—
32C2×D4×C61—21no—
33C2×D4×C61D411yescharacteristic
34C22×C4×C61—21no—
35C22×C4×C61C2311yescharacteristic
36C2×C22⋊D61—21no—
37C2×C22⋊D61—21no—
38C2×C22⋊D61—21no—
39C22×Dic61—21no—
40C22×Dic61D411yescharacteristic
41D4×D61—42no—
42D4×D61—42no—
43C2×D244—21no—
44C2×D244D411yescharacteristic
45C2×C4×D61—21no—
46SD16×C61—42no—
47C2×C8×C61—21no—
48C4⋊C4×C61D411yescharacteristic
49C22⋊C4×C61—21no—
50C22⋊Dic61—21no—
51#11758201—42no—
52#11758198—21no—
53#11758198—21no—
54#11758198—21no—
55#11758198—21no—
56#11758198—42no—
57C4⋊Dic61D411yescharacteristic
58#11758196—21no—
59C2×#92418—21no—
60C23×C61—21no—
61C23×C61C2×D411yescharacteristic
62C22×D61—21no—
63C22×D61—21no—
64C22×D61—21no—
65C22×D61—42no—
66C22×D61—41no—
67C22×D61—41no—
68C22×D61—81no—
69C22×D61—81no—
70C22×D61SD1612yescomplemented
71Q8×C61—22no—
72Q8×C61—22no—
73Q8×C61—41no—
74Q8×C61—41no—
75D4×C61—41no—
76D4×C61—41no—
77D4×C61—41no—
78C2×C4×C61—22no—
79C2×C4×C61—21no—
80C2×C4×C61—41no—
81C2×C4×C61—41no—
82C2×C4×C61—41no—
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C22⋊D61—42no—
86C22⋊D61—41no—
87C22⋊D61—41no—
88C22⋊D61—81no—
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—41no—
92C2×Dic61—41no—
93C2×Dic61—41no—
94C2×Dic61—41no—
95D244—41no—
96D244—42no—
97C4×D61—42no—
98C8×C61—41no—
99#92418—41no—
100C22×C61—21no—
101C22×C61—21no—
102C22×C61—41no—
103C22×C61—41no—
104C22×C61—41no—
105C22×C61#12011yescharacteristic
106C22×C61C2×SD1611yescharacteristic
107C22×C61AGL(1,ℤ/8)11yescharacteristic
108C2×D61—22no—
109C2×D61—41no—
110C2×D61—41no—
111C2×D61—42no—
112C2×D61—41no—
113C2×D61—41no—
114C2×D61—41no—
115C2×D61—81no—
116C2×D61—84no—
117C4×C61—21no—
118C4×C61—21no—
119C4×C61—41no—
120C4×C61—42no—
121Dic61—41no—
122Dic61—41no—
123Dic61—81no—
124#1601—611nomaximal, Sylow
125C2×C61—21no—
126C2×C61—21no—
127C2×C61—81no—
128C2×C61#45011yescharacteristic
129C2×C61#45511yescharacteristic
130C2×C61B(4,𝔽2)11yescharacteristic
131D61—42no—
132D61—81no—
133#534—611no—
134#448—611no—
135#448D6111yescharacteristic, complemented
136#393—611no—
137#327—611no—
138#327—611no—
139#323—611no—
140C61#160111yescharacteristic, complemented, Sylow
141C22×Q8C2×D6111yescharacteristic, complemented
142C22×D4—1221no—
143C2×SD16—21no—
144C2×SD16—1221no—
145#123—1221no—
146#123—1221no—
147#121—611no—
148#121—1221no—
149#121C2×D6111yescharacteristic
150#120—1221no—
151#120—1221no—
152C2×C22⋊C4—611no—
153C2×C22⋊C4—1221no—
154#103—21no—
155#103—1221no—
156C22⋊C8—611no—
157C22⋊C8C2×D6111yescharacteristic, complemented
158#95—611no—
159#95—1221no—
160C24—611no—
161C24—1221no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—42no—
165C2×D4—21no—
166C2×D4—611no—
167C2×D4—1221no—
168C2×D4—1221no—
169C2×D4—1221no—
170C2×D4—1221no—
171C2×D4—2442no—
172C2×D4—2442no—
173C2×D4C22⋊D6111yescharacteristic
174C22×C4—21no—
175C22×C4—611no—
176C22×C4—1221no—
177C22×C4—1221no—
178C22×C4C22×D6111yescharacteristic
179SD16—42no—
180SD16—2442no—
181C2×C8—21no—
182C2×C8—1221no—
183C4⋊C4—611no—
184C4⋊C4—1221no—
185C4⋊C4C22⋊D6111yescharacteristic
186C22⋊C4—21no—
187C22⋊C4—1221no—
188C22⋊C4—1221no—
189C22⋊C4—1221no—
190C22⋊C4—1221no—
191C22⋊C4—1221no—
192C22⋊C4—2442no—
193C23—21no—
194C23—612no—
195C23—1221no—
196C23—1221no—
197C23—1221no—
198C23—4881no—
199C23—4881no—
200C23—2441no—
201C23—2441no—
202C23—2442no—
203C23D4×D6111yescharacteristic
204Q8—22no—
205Q8—22no—
206Q8—41no—
207Q8—41no—
208D4—41no—
209D4—41no—
210D4—41no—
211D4—4881no—
212D4—2441no—
213D4—2442no—
214D4—2442no—
215D4—2441no—
216D4—2441no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—1221no—
223C2×C4—1221no—
224C2×C4—2442no—
225C2×C4—2441no—
226C2×C4—2441no—
227C2×C4—2441no—
228C2×C4—2441no—
229C2×C4D4×D6111yescharacteristic
230C2×C4C2×C22⋊D6111yescharacteristic
231C8—41no—
232C8—2441no—
233C22—21no—
234C22—21no—
235C22—41no—
236C22—41no—
237C22—41no—
238C22—1222no—
239C22—4881no—
240C22—4884no—
241C22—2442no—
242C22—2441no—
243C22—2441no—
244C22—2441no—
245C22—2441no—
246C22—2441no—
247C22#1451974511yescharacteristic
248C22SD16×D6111yescharacteristic
249C22#1451980411yescharacteristic
250C4—21no—
251C4—21no—
252C4—42no—
253C4—41no—
254C4—4881no—
255C4—2441no—
256C4—2441no—
257C2—21no—
258C2—21no—
259C2—81no—
260C2—4881no—
261C2—2442no—
262C2#1683991111yescharacteristic
263C2#1683993811yescharacteristic
264C2#1683994811yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#448C2
socleC22×C61#120
hypercenter#448D61
hypocenterC61#1601
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
2. #16839901C2semidirect
3. #16839673C2semidirect
4. #16839497C2semidirect
5. #16839496C2semidirect
6. #16839485C2semidirect
7. C61×#448C2semidirect
19. C22⋊#92418C22semidirect
21. #14519684C22semidirect
22. C22×Q8×C61C22semidirect
26. C22⋊C8×C61C22semidirect
70. C22×D61SD16semidirect
135. #448D61semidirect
140. C61#1601semidirect
141. C22×Q8C2×D61semidirect
157. C22⋊C8C2×D61semidirect