Finite Group Databasebeta

← #29592444

Subgroups — #29592444

Order 15616.

484 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 63 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#21447048C211yesmaximal, characteristic, complemented
2#21444753C212yesmaximal, complemented
3#21443822C212yesmaximal, complemented
4#21443763C211yesmaximal, characteristic, complemented
5C61×#2819C211yesmaximal, characteristic, complemented
6#16840343C2211yescharacteristic
7#16839896—22no—
8C2×#14519705—21no—
9#16839761—21no—
10#16839531C2211yescharacteristic
11#16839495—22no—
12#16839488C2212yes—
13C2×#124×C61—21no—
14C61×#394—21no—
15C61×#394C2212yes—
16C61×#393—22no—
17C61×#392—22no—
18C61×#382C2211yescharacteristic
19C2×#11758222—21no—
20C2×#11758199—42no—
21C2×#11758194—21no—
22#14519757—41no—
23#14519752—41no—
24#14519751—22no—
25#14519705—42no—
26#14519700—41no—
27#14519698—42no—
28#14519697—41no—
29C22⋊#92418—22no—
30C22×Q8×C61—21no—
31C22×D4×C61—21no—
32C22×D4×C61—21no—
33C22×D4×C61D412yes—
34#124×C61—42no—
35#124×C61—42no—
36C2×C4⋊C4×C61D411yescharacteristic
37C2×C4⋊C4×C61C2311yescharacteristic
38C2×C22⋊C4×C61—22no—
39C2×C22⋊C4×C61—22no—
40C2×C22⋊C4×C61—22no—
41C2×C22⋊C4×C61—22no—
42C2×C42×C61D411yescharacteristic
43#95×C61—21no—
44#95×C61—22no—
45#95×C61D412yes—
46C24×C61—22no—
47C2×Q8×C61—42no—
48C2×Q8×C61—81no—
49C2×Q8×C61—81no—
50C2×D4×C61—42no—
51C2×D4×C61—42no—
52C2×D4×C61—82no—
53C2×D4×C61—81no—
54C2×D4×C61—81no—
55C2×D4×C61—82no—
56C2×D4×C61—81no—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—22no—
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61C2×D412yes—
62C2×C22⋊D61—41no—
63#11758222—41no—
64#11758222—41no—
65#11758222—41no—
66#11758222—41no—
67C2×D244—21no—
68C2×D244—22no—
69C2×C4×D61—41no—
70C2×Dic122—21no—
71C4⋊C4×C61—41no—
72C4⋊C4×C61—41no—
73C22⋊C4×C61—44no—
74C22⋊C4×C61—42no—
75C22⋊C4×C61—42no—
76C22⋊C4×C61—82no—
77C22⋊C4×C61—82no—
78C42×C61—21no—
79C42×C61D812yescomplemented
80#11758199—84no—
81#11758198—42no—
82C4⋊Dic61—22no—
83#11758194—41no—
84#11758194—41no—
85C2×#92418—42no—
86C2×#92418—41no—
87C23×C61—42no—
88C23×C61—42no—
89C23×C61—42no—
90C23×C61—42no—
91C23×C61—42no—
92C23×C61—42no—
93C23×C61—42no—
94C23×C61#12011yescharacteristic
95C22×D61—41no—
96Q8×C61—84no—
97D4×C61—44no—
98D4×C61—82no—
99D4×C61—84no—
100D4×C61—84no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—22no—
104C2×C4×C61—22no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—42no—
108C2×C4×C61—42no—
109C2×C4×C61—42no—
110C2×C4×C61—42no—
111C2×C4×C61—42no—
112C2×C4×C61—41no—
113C2×C4×C61C2×D811yescharacteristic
114C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
115C22⋊D61—81no—
116C22⋊D61—81no—
117C2×Dic61—41no—
118D244—41no—
119D244—41no—
120D244—82no—
121C4×D61—81no—
122C4×D61—81no—
123Dic122—41no—
124Dic122—41no—
125#92418—81no—
126#92418—82no—
127#12156—611nomaximal, Sylow
128C22×C61—21no—
129C22×C61—21no—
130C22×C61—82no—
131C22×C61—82no—
132C22×C61—82no—
133C22×C61—82no—
134C22×C61—82no—
135C22×C61—82no—
136C22×C61—82no—
137C22×C61#44711yescharacteristic
138C22×C61#45411yescharacteristic
139C22×C61B(4,𝔽2)11yescharacteristic
140C2×D61—81no—
141C2×D61—81no—
142C2×D61—81no—
143C4×C61—21no—
144C4×C61—21no—
145C4×C61—42no—
146C4×C61—42no—
147C4×C61—82no—
148C4×C61—81no—
149Dic61—81no—
150#2819D6111yescharacteristic, complemented
151#2040—611no—
152#1598—612no—
153#1345—612no—
154#1324—611no—
155C2×C61—21no—
156C2×C61—21no—
157C2×C61—162no—
158C2×C61#159811yescharacteristic
159C2×C61#219911yescharacteristic
160C2×C61#220211yescharacteristic
161D61—161no—
162#537—611no—
163C2×#124—21no—
164#447—1222no—
165C2×#104—1221no—
166#417—1221no—
167#394—21no—
168#394C2×D6112yes—
169#393—22no—
170#392—22no—
171#382C2×D6111yescharacteristic
172#343—611no—
173#327—1222no—
174#324—612no—
175C61#1215611yescharacteristic, complemented, Sylow
176C2×#41—1221no—
177C22×Q8—21no—
178C22×D4—21no—
179C22×D4—21no—
180C22×D4C22⋊D6112yes—
181C2×D8—2442no—
182C2×M16—1221no—
183#124—42no—
184#124—42no—
185C22⋊Q8—2441no—
186#121—1222no—
187#121—2441no—
188C2×C4⋊C4C22⋊D6111yescharacteristic
189C2×C4⋊C4C22×D6111yescharacteristic
190C2×C22⋊C4—22no—
191C2×C22⋊C4—22no—
192C2×C22⋊C4—22no—
193C2×C22⋊C4—22no—
194C2×C42C22⋊D6111yescharacteristic
195#104—2442no—
196#103—2441no—
197#102—2441no—
198#102—2442no—
199C22⋊C8—1222no—
200#95—21no—
201#95—22no—
202#95C22⋊D6112yes—
203C24—22no—
204#41—2441no—
205#41—2441no—
206#41—2441no—
207#41—2441no—
208C2×Q8—42no—
209C2×Q8—81no—
210C2×Q8—81no—
211C2×Q8—1221no—
212C2×D4—42no—
213C2×D4—42no—
214C2×D4—82no—
215C2×D4—81no—
216C2×D4—81no—
217C2×D4—82no—
218C2×D4—81no—
219C2×D4—1222no—
220C2×D4—1221no—
221C2×D4—2441no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—22no—
225C22×C4—2441no—
226C22×C4C2×C22⋊D6111yescharacteristic
227C22×C4C2×C22⋊D6112yes—
228D8—4884no—
229M16—2441no—
230M16—2441no—
231C2×C8—2442no—
232C2×C8—2441no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—1222no—
236C22⋊C4—44no—
237C22⋊C4—42no—
238C22⋊C4—42no—
239C22⋊C4—82no—
240C22⋊C4—82no—
241C22⋊C4—2442no—
242C42—21no—
243C42#1175819912yescomplemented
244C23—42no—
245C23—42no—
246C23—42no—
247C23—42no—
248C23—42no—
249C23—42no—
250C23—42no—
251C23—2441no—
252C23#1451974611yescharacteristic
253Q8—84no—
254Q8—2441no—
255Q8—2441no—
256D4—44no—
257D4—82no—
258D4—84no—
259D4—84no—
260D4—4882no—
261D4—4881no—
262D4—4881no—
263D4—2441no—
264D4—2441no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—4881no—
278C2×C4—4881no—
279C2×C4—2441no—
280C2×C4C2×#1175819911yescharacteristic
281C2×C4#1451980311yescharacteristic
282C8—4881no—
283C8—4882no—
284C22—21no—
285C22—21no—
286C22—82no—
287C22—82no—
288C22—82no—
289C22—82no—
290C22—82no—
291C22—82no—
292C22—82no—
293C22—4881no—
294C22—4881no—
295C22—4881no—
296C22#1683989611yescharacteristic
297C22#1683993511yescharacteristic
298C22#1683994911yescharacteristic
299C4—21no—
300C4—21no—
301C4—42no—
302C4—42no—
303C4—82no—
304C4—81no—
305C4—4881no—
306C2—21no—
307C2—21no—
308C2—162no—
309C2—9761no—
310C2#2144475411yescharacteristic
311C2#2144782011yescharacteristic
312C2#2144783611yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2819C2
socleC22×C61B(4,𝔽2)
hypercenter#2819D61
hypocenterC61#12156
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2819

Complements

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

NH ≅ G/Ntype
1. #21447048C2semidirect
2. #21444753C2semidirect
3. #21443822C2semidirect
4. #21443763C2semidirect
5. C61×#2819C2semidirect
79. C42×C61D8semidirect
150. #2819D61semidirect
175. C61#12156semidirect
243. C42#11758199semidirect

Maximal subgroups

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

subgroupindex
#214470482
#214447532
#214438222
#214437632
C61×#28192
#1215661