Finite Group Databasebeta

← #29597979

Subgroups — #29597979

Order 15616.

314 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#16839579C211yesmaximal, characteristic
2#21447538C211yesmaximal, characteristic
3C2×#16839539C211yesmaximal, characteristic
4#21446688C211yesmaximal, characteristic
5#21446573C211yesmaximal, characteristic
6#21443917C211yesmaximal, characteristic
7C61×#1386C211yesmaximal, characteristic
8C22×Dic244C2211yescharacteristic
9C2×#14519717C2211yescharacteristic
10C2×#14519713C2211yescharacteristic
11#16839789—21no—
12C2×#14519700—21no—
13C2×#14519687C2211yescharacteristic
14#16839667—21no—
15#16839579—22no—
16#16839565C414yescomplemented
17#16839539—22no—
18#16839521—21no—
19C2×M32×C61C2211yescharacteristic
20C61×#427C2211yescharacteristic
21C2×#106×C61C2211yescharacteristic
22C22×Dic122—21no—
23C2×Dic244—21no—
24C2×Dic244—21no—
25C2×Dic244—21no—
26C2×Dic244—21no—
27C2×Dic244—21no—
28C2×Dic244C2×C412yes—
29C2×#11758194—21no—
30C22×#92418D411yescharacteristic
31C2×C4×Dic61D411yescharacteristic
32#14519717—21no—
33#14519717—21no—
34C2×#11758185C2×C412yes—
35#14519713—21no—
36#14519713—21no—
37C4⋊#92418—42no—
38#14519700—42no—
39#14519687—21no—
40#14519687—21no—
41#14519684—42no—
42C22×C8×C61C2311yescharacteristic
43#117×C61—21no—
44C2×C4⋊C4×C61—21no—
45M32×C61—21no—
46M32×C61D412yes—
47C2×C16×C61—21no—
48#107×C61C2×C412yes—
49#106×C61—21no—
50#106×C61—21no—
51#106×C61—21no—
52C22×C4×C61—41no—
53C22×C4×C61C2×D411yescharacteristic
54C22×Dic61—21no—
55C22×Dic61—41no—
56C2×Dic122—22no—
57C2×Dic122—41no—
58C2×Dic122—41no—
59C2×Dic122—41no—
60C2×Dic122—41no—
61C2×Dic122—41no—
62C2×C8×C61C22×C411yescharacteristic
63C2×C8×C61C2×D411yescharacteristic
64C2×C8×C61#4111yescharacteristic
65C2×C8×C61#4111yescharacteristic
66C2×C8×C61#4111yescharacteristic
67C2×C8×C61#4111yescharacteristic
68C4⋊C4×C61—22no—
69C4⋊C4×C61—41no—
70C4⋊C4×C61—41no—
71C22⋊C4×C61—41no—
72C42×C61—41no—
73C4×Dic61—21no—
74C4×Dic61—21no—
75#11758194—41no—
76#11758194—41no—
77C2×#92418—21no—
78C2×#92418—21no—
79C2×#92418—21no—
80C2×#92418—41no—
81Dic244—22no—
82Dic244—22no—
83Dic244—41no—
84Dic244—41no—
85C16×C61—22no—
86#11758185—22no—
87C23×C61AGL(1,ℤ/8)11yescharacteristic
88C2×C4×C61—42no—
89C2×C4×C61—82no—
90C2×C4×C61—81no—
91C2×C4×C61C4×D411yescharacteristic
92C2×C4×C61#12111yescharacteristic
93C2×C4×C61#12411yescharacteristic
94C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
95C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
96C2×C4×C61#13711yescharacteristic
97C2×Dic61—42no—
98C2×Dic61—42no—
99C2×Dic61—41no—
100C2×Dic61—81no—
101C2×Dic61—81no—
102Dic122—42no—
103Dic122—42no—
104Dic122—81no—
105Dic122—81no—
106C8×C61#11711yescharacteristic
107C8×C61C4×D411yescharacteristic
108C8×C61#12311yescharacteristic
109C8×C61#12611yescharacteristic
110#92418—41no—
111#92418—81no—
112#13154—611nomaximal, Sylow
113C22×C61—22no—
114C22×C61#44211yescharacteristic
115C22×C61#46811yescharacteristic
116C22×C61#49011yescharacteristic
117C4×C61—82no—
118C4×C61—161no—
119C4×C61#38811yescharacteristic
120C4×C61#44011yescharacteristic
121C4×C61#46911yescharacteristic
122C4×C61#48911yescharacteristic
123Dic61—81no—
124Dic61—82no—
125C2×#362—611no—
126#2141—611no—
127C2×#347—611no—
128#1971—611no—
129#1946—611no—
130#1386D6111yescharacteristic
131#1383—611no—
132C2×C61—21no—
133C2×C61—21no—
134C2×C61#193611yescharacteristic
135C2×C61#218012yes—
136C22×Q16—611no—
137C2×M32—611no—
138C2×M32C2×D6111yescharacteristic
139C2×#108—611no—
140#427C2×D6111yescharacteristic
141C2×#106C2×D6111yescharacteristic
142#424—1221no—
143C2×#103—1221no—
144C2×#97—611no—
145#391—1221no—
146#362—1222no—
147#358—614no—
148#347—1222no—
149#339—1221no—
150C61#1315411yescharacteristic, complemented, Sylow
151C22×Q8—1221no—
152C2×Q16—612no—
153C2×Q16—1221no—
154C2×Q16—1221no—
155C2×Q16—1221no—
156C2×Q16—1221no—
157C2×Q16—1221no—
158C2×M16—1221no—
159C22×C8—611no—
160C22×C8C22×D6111yescharacteristic
161#117—21no—
162C2×C4⋊C4—21no—
163C2×C42—611no—
164M32—21no—
165M32—1221no—
166M32—1221no—
167M32D24412yes—
168C2×C16—21no—
169C2×C16—612no—
170#108—1221no—
171#108—1221no—
172#107C4×D6112yes—
173#106—21no—
174#106—21no—
175#106—21no—
176C4⋊C8—2442no—
177#103—2442no—
178#97—1221no—
179#97—1221no—
180#95—2442no—
181C2×Q8—1222no—
182C2×Q8—2441no—
183C2×Q8—2441no—
184C2×Q8—2441no—
185C2×Q8—2441no—
186C2×Q8—2441no—
187C22×C4—41no—
188C22×C4—1221no—
189C22×C4—2441no—
190C22×C4D4×D6111yescharacteristic
191Q16—1222no—
192Q16—1222no—
193Q16—2441no—
194Q16—2441no—
195M16—2441no—
196M16—2441no—
197C2×C8—1221no—
198C2×C8—1221no—
199C2×C8—1221no—
200C2×C8—2441no—
201C2×C8C2×C4×D6111yescharacteristic
202C2×C8C2×D24411yescharacteristic
203C2×C8#1175822211yescharacteristic
204C2×C8#1175822411yescharacteristic
205C2×C8#1175822411yescharacteristic
206C2×C8#1175822611yescharacteristic
207C4⋊C4—22no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C22⋊C4—41no—
211C42—41no—
212C42—1221no—
213C42—1221no—
214C16—22no—
215C16—1222no—
216C23#1451980111yescharacteristic
217Q8—4881no—
218Q8—4881no—
219Q8—2442no—
220Q8—2442no—
221C2×C4—42no—
222C2×C4—82no—
223C2×C4—81no—
224C2×C4—4881no—
225C2×C4—4881no—
226C2×C4—2442no—
227C2×C4—2441no—
228C2×C4—2442no—
229C2×C4#1451973711yescharacteristic
230C2×C4#1451975211yescharacteristic
231C2×C4#1451976311yescharacteristic
232C2×C4#1451980411yescharacteristic
233C2×C4#1451980411yescharacteristic
234C2×C4#1451980911yescharacteristic
235C8—4881no—
236C8—2441no—
237C8#1451973511yescharacteristic
238C8C4×D24411yescharacteristic
239C8#1451976111yescharacteristic
240C8#1451977211yescharacteristic
241C22—22no—
242C22#1683987111yescharacteristic
243C22#1684000911yescharacteristic
244C22#1684012511yescharacteristic
245C4—82no—
246C4—161no—
247C4—4881no—
248C4—4882no—
249C4#1683965411yescharacteristic
250C4#1683986511yescharacteristic
251C4#1684001611yescharacteristic
252C4#1684012311yescharacteristic
253C2—21no—
254C2—21no—
255C2#2144651711yescharacteristic
256C2#2144770712yes—
subgroupG/H
centerC22#16839871
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1386C2
socleC22×C61#442
prime radicalC23×C61AGL(1,ℤ/8)
cosocleC22×C8×C61C23
hypercenter#1386D61
hypocenterC61#13154
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1386

Complements

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

NH ≅ G/Ntype
16. #16839565C4semidirect
150. C61#13154semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168395792
#214475382
C2×#168395392
#214466882
#214465732
#214439172
C61×#13862
#1315461