Finite Group Databasebeta

← #29599695

Subgroups — #29599695

Order 15616.

484 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 79 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#21453765C211yesmaximal, characteristic
2#21446100C212yesmaximal
3#21443944C211yesmaximal, characteristic
4#21443938C212yesmaximal
5C61×#1856C211yesmaximal, characteristic
6C2×#14519692C2212yes—
7#16839701—21no—
8#16839674—22no—
9#16839668—21no—
10#16839642C2212yes—
11#16839637—22no—
12#16839634—22no—
13#16839529—22no—
14C61×#518C2211yescharacteristic
15C61×#428—21no—
16C2×#100×C61C2211yescharacteristic
17C61×#390C2211yescharacteristic
18C61×#339—21no—
19C22×Dic122—21no—
20C23×Dic61D412yes—
21C2×C4⋊Dic61—21no—
22C2×C4⋊Dic61—21no—
23C2×#11758196—42no—
24C2×C22⋊Dic61—22no—
25C2×C22⋊Dic61—22no—
26C2×C22⋊Dic61D412yes—
27#14519692—22no—
28#14519692Q814yescomplemented
29#14519684—22no—
30#14519684—21no—
31#14519684—22no—
32#14519684—22no—
33#14519684—42no—
34C22×D4×C61C2311yescharacteristic
35C2×M16×C61—21no—
36C4×D4×C61—41no—
37C4×D4×C61—41no—
38#117×C61—21no—
39C2×C4⋊C4×C61D411yescharacteristic
40C2×C22⋊C4×C61—22no—
41C2×C22⋊C4×C61—22no—
42C2×C42×C61D411yescharacteristic
43#107×C61—41no—
44#106×C61—41no—
45#100×C61—21no—
46#100×C61Q812yescomplemented
47C24×C61C2×D412yes—
48C2×D4×C61—41no—
49C2×D4×C61—41no—
50C2×D4×C61C2×Q811yescharacteristic
51C2×D4×C61C2×Q812yes—
52C2×D4×C61#4111yescharacteristic
53C22×C4×C61—21no—
54C22×C4×C61—21no—
55C22×C4×C61—22no—
56C22×C4×C61—22no—
57C22×C4×C61C2×D411yescharacteristic
58C22×Dic61—22no—
59C22×Dic61—22no—
60C22×Dic61—42no—
61C22×Dic61—42no—
62C22×Dic61—82no—
63C2×Dic122—42no—
64C2×Dic122—81no—
65C2×Dic122—81no—
66M16×C61—22no—
67M16×C61—41no—
68C2×C8×C61—41no—
69C4⋊C4×C61—21no—
70C4⋊C4×C61—21no—
71C4⋊C4×C61—41no—
72C22⋊C4×C61—44no—
73C22⋊C4×C61—42no—
74C22⋊C4×C61—41no—
75C42×C61—41no—
76C42×C61—41no—
77C22⋊Dic61—24no—
78C22⋊Dic61—42no—
79C22⋊Dic61—42no—
80C22⋊Dic61—82no—
81C4⋊Dic61—81no—
82C4⋊Dic61—81no—
83#11758196—84no—
84C23×C61—22no—
85C23×C61—22no—
86C23×C61—42no—
87C23×C61—42no—
88C23×C61#12011yescharacteristic
89C23×C61C22⋊Q812yes—
90C23×C61C4⋊Q812yes—
91D4×C61—41no—
92D4×C61—42no—
93D4×C61—41no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—22no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61—42no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61—82no—
104C2×C4×C61—82no—
105C2×C4×C61C22⋊Q811yescharacteristic
106C2×C4×C61C4⋊Q811yescharacteristic
107C2×Dic61—42no—
108C2×Dic61—44no—
109C2×Dic61—42no—
110C2×Dic61—42no—
111C2×Dic61—42no—
112C2×Dic61—44no—
113C2×Dic61—42no—
114C2×Dic61—42no—
115C2×Dic61—82no—
116C2×Dic61—82no—
117C2×Dic61—82no—
118Dic122—84no—
119C8×C61—42no—
120#13463—611nomaximal, Sylow
121C22×C61—21no—
122C22×C61—21no—
123C22×C61—22no—
124C22×C61—22no—
125C22×C61—42no—
126C22×C61—42no—
127C22×C61—42no—
128C22×C61—42no—
129C22×C61—82no—
130C22×C61#39511yescharacteristic
131C22×C61B(4,𝔽2)11yescharacteristic
132C22×C61#45811yescharacteristic
133C4×C61—21no—
134C4×C61—21no—
135C4×C61—42no—
136C4×C61—81no—
137C4×C61—81no—
138C4×C61—81no—
139Dic61—82no—
140Dic61—84no—
141Dic61—82no—
142#2804—611no—
143#1867—612no—
144#1856D6111yescharacteristic
145#1393—611no—
146#1390—612no—
147C2×C61—21no—
148C2×C61—21no—
149C2×C61—42no—
150C2×C61—42no—
151C2×C61#206211yescharacteristic
152C2×C61#219811yescharacteristic
153C2×C61#219911yescharacteristic
154#518C2×D6111yescharacteristic
155#428—21no—
156C2×#100C2×D6111yescharacteristic
157C2×#99—612no—
158#400—1221no—
159#393—1222no—
160#391—1221no—
161#390C2×D6111yescharacteristic
162#386—612no—
163#385—1222no—
164#385—1222no—
165#342—1222no—
166#339—21no—
167C61#1346311yescharacteristic, complemented, Sylow
168C22×Q8—1221no—
169C22×D4C22×D6111yescharacteristic
170C23×C4—612no—
171C2×M16—21no—
172C4×D4—41no—
173C4×D4—41no—
174#117—21no—
175C2×C4⋊C4—1221no—
176C2×C4⋊C4—1221no—
177C2×C4⋊C4—2442no—
178C2×C4⋊C4C22⋊D6111yescharacteristic
179C2×C22⋊C4—22no—
180C2×C22⋊C4—22no—
181C2×C22⋊C4—612no—
182C2×C22⋊C4—1222no—
183C2×C22⋊C4—1222no—
184C2×C42C22⋊D6111yescharacteristic
185#107—41no—
186#106—41no—
187#100—21no—
188#100Dic12212yescomplemented
189#99—614no—
190#99—1222no—
191#95—1222no—
192#95—1222no—
193#95—1221no—
194#95—1222no—
195#95—2442no—
196C24D4×D6112yes—
197C2×Q8—4881no—
198C2×Q8—4881no—
199C2×Q8—2442no—
200C2×D4—41no—
201C2×D4—41no—
202C2×D4C2×Dic12211yescharacteristic
203C2×D4#1175822211yescharacteristic
204C2×D4Q8×D6112yes—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—1222no—
210C22×C4—1222no—
211C22×C4—4882no—
212C22×C4—2442no—
213C22×C4—2442no—
214C22×C4C2×C22⋊D6111yescharacteristic
215M16—22no—
216M16—41no—
217C2×C8—41no—
218C4⋊C4—21no—
219C4⋊C4—21no—
220C4⋊C4—41no—
221C4⋊C4—4881no—
222C4⋊C4—4881no—
223C4⋊C4—4884no—
224C22⋊C4—44no—
225C22⋊C4—42no—
226C22⋊C4—41no—
227C22⋊C4—1224no—
228C22⋊C4—4882no—
229C22⋊C4—2442no—
230C22⋊C4—2442no—
231C42—41no—
232C42—41no—
233C23—22no—
234C23—22no—
235C23—42no—
236C23—42no—
237C23#1451974511yescharacteristic
238C23#1451975512yes—
239C23#1451977612yes—
240Q8—4884no—
241D4—41no—
242D4—41no—
243D4—42no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—82no—
254C2×C4—82no—
255C2×C4—4882no—
256C2×C4—4882no—
257C2×C4—4882no—
258C2×C4—2444no—
259C2×C4—2442no—
260C2×C4—2442no—
261C2×C4—2442no—
262C2×C4—2442no—
263C2×C4—2444no—
264C2×C4—2442no—
265C2×C4—2442no—
266C2×C4#1451975611yescharacteristic
267C2×C4#1451977511yescharacteristic
268C8—42no—
269C22—21no—
270C22—21no—
271C22—22no—
272C22—22no—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—82no—
278C22#1683968211yescharacteristic
279C22#1683994811yescharacteristic
280C22#1683995111yescharacteristic
281C4—21no—
282C4—21no—
283C4—42no—
284C4—81no—
285C4—81no—
286C4—81no—
287C4—4882no—
288C4—4884no—
289C4—4882no—
290C2—21no—
291C2—21no—
292C2—42no—
293C2—42no—
294C2#2144717211yescharacteristic
295C2#2144781411yescharacteristic
296C2#2144781911yescharacteristic
subgroupG/H
centerC22#16839948
commutator, prime radical, cosocleC22×D4×C61C23
FrattiniC22×D4C22×D61
FittingC61×#1856C2
socleC22×C61B(4,𝔽2)
hypercenter#1856D61
hypocenterC61#13463
LCSG ▷ C22×D4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1856

Complements

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

NH ≅ G/Ntype
28. #14519692Q8semidirect
46. #100×C61Q8semidirect
167. C61#13463semidirect
188. #100Dic122semidirect

Maximal subgroups

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

subgroupindex
#214537652
#214461002
#214439442
#214439382
C61×#18562
#1346361