Finite Group Databasebeta

← #21446882

Subgroups — #21446882

Order 7808.

348 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 71 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#16840562C211yesmaximal, characteristic
2C2×#14519810C211yesmaximal, characteristic, complemented
3#16840338C211yesmaximal, characteristic, complemented
4#16839778C211yesmaximal, characteristic, complemented
5#16839772C211yesmaximal, characteristic, complemented
6#16839735C211yesmaximal, characteristic, complemented
7C61×#344C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C2×#11758222C2211yescharacteristic
10C22×Dic122C2211yescharacteristic
11#14519810—22no—
12#14519810—21no—
13#14519810—21no—
14#14519810—22no—
15#14519805—21no—
16#14519805—21no—
17#14519799—22no—
18C2×Dic244—21no—
19C2×#11758190—21no—
20#14519777—21no—
21#14519765—21no—
22#14519761—22no—
23#14519757—22no—
24#14519736C2211yescharacteristic
25#14519703—22no—
26#14519702—22no—
27#14519691—22no—
28C2×M16×C61C2211yescharacteristic
29C2×M16×C61C2211yescharacteristic
30#117×C61C2211yescharacteristic
31C22×C4×C61C2311yescharacteristic
32C2×C22⋊D61—21no—
33C2×C22⋊D61—21no—
34C22×Dic61—21no—
35#11758222—21no—
36#11758222—21no—
37#11758222—21no—
38#11758222—21no—
39#11758222—21no—
40#11758222—21no—
41#11758222—21no—
42#11758222—21no—
43C2×D244D411yescharacteristic
44C2×D244D411yescharacteristic
45C2×C4×D61—21no—
46C2×C4×D61—21no—
47C2×Dic122—21no—
48C2×Dic122—21no—
49C2×Dic122—21no—
50C2×Dic122—21no—
51C2×Dic122—21no—
52C2×Dic122D412yes—
53C2×Dic122D411yescharacteristic
54C2×Dic122D411yescharacteristic
55M16×C61—21no—
56M16×C61—21no—
57M16×C61—21no—
58M16×C61D412yes—
59C2×C8×C61—21no—
60C2×C8×C61D412yes—
61C4⋊C4×C61—21no—
62C22⋊C4×C61D412yes—
63C42×C61—21no—
64C22⋊Dic61—21no—
65#11758198—24no—
66C4⋊Dic61—24no—
67C4⋊Dic61—21no—
68C4×Dic61—21no—
69Dic244—24no—
70Dic244—22no—
71D488—22no—
72#11758190—24no—
73#11758190—22no—
74#11758190—22no—
75C23×C61C2×D411yescharacteristic
76C22×D61—21no—
77C22×D61—21no—
78C2×C4×C61—22no—
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61#4111yescharacteristic
85C22⋊D61—41no—
86C22⋊D61—41no—
87C22⋊D61—41no—
88C22⋊D61—41no—
89C2×Dic61—21no—
90C2×Dic61—22no—
91C2×Dic61—21no—
92C2×Dic61—41no—
93C2×Dic61—41no—
94C2×Dic61—41no—
95D244—21no—
96D244—21no—
97D244—21no—
98D244—21no—
99C4×D61—41no—
100C4×D61—41no—
101C4×D61—41no—
102C4×D61—41no—
103Dic122—22no—
104Dic122—21no—
105Dic122—21no—
106Dic122—21no—
107Dic122—22no—
108Dic122—21no—
109Dic122—41no—
110Dic122—41no—
111C8×C61—22no—
112C8×C61—22no—
113C22×C61—41no—
114C22×C61#12011yescharacteristic
115C22×C61#12111yescharacteristic
116C22×C61#12711yescharacteristic
117C2×D61—42no—
118C2×D61—41no—
119C2×D61—41no—
120C2×D61—81no—
121C4×C61—42no—
122C4×C61#12011yescharacteristic
123C4×C61#12011yescharacteristic
124C4×C61#12111yescharacteristic
125C4×C61#12111yescharacteristic
126Dic61—42no—
127Dic61—41no—
128Dic61—41no—
129Dic61—81no—
130#2009—611nomaximal, Sylow
131C2×C61—21no—
132C2×C61—21no—
133C2×C61—21no—
134C2×C61#39211yescharacteristic
135D61—81no—
136D61—81no—
137#575—611no—
138C2×#137—611no—
139#536—611no—
140#421—611no—
141#419—611no—
142#410—611no—
143#344D6111yescharacteristic, complemented
144C61#200911yescharacteristic, complemented, Sylow
145C2×#41—611no—
146C2×#41—611no—
147C22×Q8—611no—
148#137—1222no—
149#137—1221no—
150#137—1221no—
151#137—1222no—
152AGL(1,ℤ/8)—1221no—
153AGL(1,ℤ/8)—1221no—
154#135—1222no—
155C2×Q16—1221no—
156C2×SD16—1221no—
157C2×M16C2×D6111yescharacteristic
158C2×M16C2×D6111yescharacteristic
159C4⋊Q8—1221no—
160#124—1221no—
161#123—1222no—
162C22⋊Q8—1222no—
163#117—611no—
164#117C2×D6111yescharacteristic
165#104—1222no—
166#103—1222no—
167#99—1222no—
168#41—1221no—
169#41—1221no—
170#41—1221no—
171#41—1221no—
172#41—1221no—
173#41—1221no—
174#41—1221no—
175#41—1221no—
176C2×Q8—612no—
177C2×Q8—611no—
178C2×Q8—611no—
179C2×Q8—1221no—
180C2×Q8—1221no—
181C2×Q8—1221no—
182C2×Q8—1221no—
183C2×Q8—1221no—
184C2×D4—611no—
185C2×D4—611no—
186C2×D4—1221no—
187C2×D4—1221no—
188C22×C4—1221no—
189C22×C4—1221no—
190C22×C4—1221no—
191C22×C4C22×D6111yescharacteristic
192Q16—1224no—
193Q16—1222no—
194SD16—1224no—
195SD16—1222no—
196SD16—1222no—
197D8—1222no—
198M16—21no—
199M16—21no—
200M16—21no—
201M16D24412yes—
202C2×C8—21no—
203C2×C8D24412yes—
204C4⋊C4—21no—
205C4⋊C4—1224no—
206C4⋊C4—1221no—
207C22⋊C4—1224no—
208C22⋊C4—1221no—
209C22⋊C4D24412yes—
210C42—21no—
211C42—1221no—
212C23—1221no—
213C23—1221no—
214C23C2×D24411yescharacteristic
215Q8—1222no—
216Q8—1221no—
217Q8—1221no—
218Q8—1221no—
219Q8—1222no—
220Q8—1221no—
221Q8—2441no—
222Q8—2441no—
223D4—1221no—
224D4—1221no—
225D4—1221no—
226D4—1221no—
227D4—2441no—
228D4—2441no—
229D4—2441no—
230D4—2441no—
231C2×C4—22no—
232C2×C4—1222no—
233C2×C4—1221no—
234C2×C4—1221no—
235C2×C4—2441no—
236C2×C4—2441no—
237C2×C4—2441no—
238C2×C4—2441no—
239C2×C4—2441no—
240C2×C4—2441no—
241C2×C4—2441no—
242C2×C4C2×D24411yescharacteristic
243C2×C4C2×D24411yescharacteristic
244C2×C4D4×D6111yescharacteristic
245C2×C4D4×D6111yescharacteristic
246C2×C4D4×D6111yescharacteristic
247C2×C4#1175822611yescharacteristic
248C8—22no—
249C8—22no—
250C22—41no—
251C22—4881no—
252C22—2442no—
253C22—2441no—
254C22—2441no—
255C22#1451974711yescharacteristic
256C22#1451975211yescharacteristic
257C22#1451977411yescharacteristic
258C4—42no—
259C4—4881no—
260C4—2441no—
261C4—2441no—
262C4—2442no—
263C4#1451974711yescharacteristic
264C4#1451974711yescharacteristic
265C4#1451975211yescharacteristic
266C4#1451975211yescharacteristic
267C2—21no—
268C2—21no—
269C2—21no—
270C2—4881no—
271C2—4881no—
272C2#1683967211yescharacteristic
subgroupG/H
centerC2#16839672
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#344C2
socleC2×C61#392
hypercenter#344D61
hypocenterC61#2009
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
2. C2×#14519810C2semidirect
3. #16840338C2semidirect
4. #16839778C2semidirect
5. #16839772C2semidirect
6. #16839735C2semidirect
7. C61×#344C2semidirect
143. #344D61semidirect
144. C61#2009semidirect