Finite Group Databasebeta

← #29593944

Subgroups — #29593944

Order 15616.

302 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 61 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#21458910C211yesmaximal, characteristic
2#21447963C211yesmaximal, characteristic, complemented
3#21445334C211yesmaximal, characteristic, complemented
4#21443862C211yesmaximal, characteristic, complemented
5#21443802C211yesmaximal, characteristic, complemented
6#21443787C211yesmaximal, characteristic, complemented
7C61×#2243C211yesmaximal, characteristic, complemented
8#16840494—21no—
9#16840148—21no—
10#16839986—21no—
11#16839974—21no—
12#16839969—21no—
13#16839955—21no—
14#16839892C2211yescharacteristic
15#16839863—21no—
16C4×D488C2211yescharacteristic
17#16839589—21no—
18C4⋊#11758185C2211yescharacteristic
19#16839562—21no—
20#16839513C2211yescharacteristic
21#16839508—21no—
22C61×#500C2211yescharacteristic
23C61×#495C2211yescharacteristic
24C61×#358—21no—
25C61×#357—21no—
26C61×#346C2211yescharacteristic
27C2×#11758202—41no—
28C2×#11758201—21no—
29C2×D488D411yescharacteristic
30C2×#11758199—21no—
31#14519773—21no—
32#14519766—21no—
33#14519763—41no—
34#14519761—41no—
35#14519759—41no—
36Q8×Dic61—21no—
37C4×Dic122D411yescharacteristic
38C4×D244—21no—
39D4×Dic61—21no—
40#14519737—41no—
41C2×#11758185—21no—
42#14519711D411yescharacteristic
43C4⋊#92418—21no—
44C4⋊#92418D411yescharacteristic
45#14519706—21no—
46#14519701—21no—
47#14519701—41no—
48#14519699—21no—
49#14519698—21no—
50#14519687—21no—
51C2×Q16×C61D411yescharacteristic
52C2×SD16×C61—21no—
53C2×D8×C61D411yescharacteristic
54C4⋊Q8×C61—21no—
55#124×C61—21no—
56C2×C16×C61—21no—
57#107×C61—21no—
58#107×C61—21no—
59C4×C8×C61C2311yescharacteristic
60C2×Q8×C61—21no—
61C2×Q8×C61—41no—
62C2×D4×C61—21no—
63C2×C22⋊D61—41no—
64C2×C22⋊D61—41no—
65C22×Dic61—41no—
66C2×D244—21no—
67C2×C4×D61—41no—
68C2×Dic122D811yescharacteristic
69Q16×C61—41no—
70SD16×C61—41no—
71SD16×C61—41no—
72D8×C61—41no—
73C2×C8×C61C2×D411yescharacteristic
74C2×C8×C61C2×D411yescharacteristic
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77C22⋊C4×C61—41no—
78C22⋊C4×C61—41no—
79C42×C61C2×D411yescharacteristic
80C22⋊Dic61—41no—
81#11758202—82no—
82#11758201—81no—
83#11758199—81no—
84#11758198—41no—
85#11758198—41no—
86#11758198—41no—
87C4⋊Dic61—21no—
88C4⋊Dic61—41no—
89C4⋊Dic61D811yescharacteristic
90#11758196—21no—
91C4×Dic61—21no—
92C4×Dic61—41no—
93C2×#92418—21no—
94C2×#92418—41no—
95D488—21no—
96D488—21no—
97C16×C61—41no—
98#11758185—41no—
99C23×C61—41no—
100C22×D61—41no—
101Q8×C61—41no—
102Q8×C61—41no—
103Q8×C61—81no—
104Q8×C61—81no—
105D4×C61—41no—
106D4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—81no—
109C2×C4×C61#12011yescharacteristic
110C2×C4×C61C2×D811yescharacteristic
111C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
112C22⋊D61—82no—
113C22⋊D61—161no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—41no—
117C2×Dic61—161no—
118D244—41no—
119D244—41no—
120C4×D61—161no—
121Dic122—41no—
122C8×C61—21no—
123C8×C61#13511yescharacteristic
124C8×C61#13711yescharacteristic
125#92418—41no—
126#92418—81no—
127#12390—611nomaximal, Sylow
128C22×C61—81no—
129C22×C61—81no—
130C22×C61—81no—
131C22×C61#44711yescharacteristic
132C2×D61—81no—
133C2×D61—81no—
134C2×D61—81no—
135C4×C61—21no—
136C4×C61—21no—
137C4×C61—81no—
138C4×C61—161no—
139C4×C61#45211yescharacteristic
140C4×C61#45511yescharacteristic
141Dic61—41no—
142Dic61—41no—
143Dic61—81no—
144#3403—611no—
145#2243D6111yescharacteristic, complemented
146#2226—611no—
147#1694—611no—
148#1360—611no—
149#1338—611no—
150#1333—611no—
151C2×C61—161no—
152C2×C61#164111yescharacteristic
153C2×C61#219011yescharacteristic
154C2×C61#219411yescharacteristic
155D61—161no—
156#559—1221no—
157#500C2×D6111yescharacteristic
158#496—1221no—
159#495C2×D6111yescharacteristic
160#464—1221no—
161#463—1221no—
162#462—1221no—
163#459—1221no—
164#446—611no—
165#440—1221no—
166C4×D8—611no—
167#367—1221no—
168C4⋊C16—611no—
169#358—21no—
170#357—21no—
171#357—1221no—
172#346C2×D6111yescharacteristic
173#334—611no—
174#332—1221no—
175C61#1239011yescharacteristic, complemented, Sylow
176C2×Q16—2441no—
177C2×Q16C22⋊D6111yescharacteristic
178C2×SD16—21no—
179C2×SD16—1221no—
180C2×D8—611no—
181C2×D8—1221no—
182C2×D8C22⋊D6111yescharacteristic
183C4⋊Q8—21no—
184#127—1221no—
185#124—21no—
186#124—1221no—
187#124—2441no—
188#123—2441no—
189#123—2441no—
190C4×Q8—611no—
191C4×Q8—1221no—
192C4×D4—1221no—
193C4×D4—1221no—
194C4×D4—2441no—
195C2×C16—21no—
196C2×C16—1221no—
197#107—21no—
198#107—21no—
199#107—611no—
200C4⋊C8—611no—
201C4⋊C8—1221no—
202C4⋊C8—1221no—
203#103—1221no—
204#103—2441no—
205#102—1221no—
206#102—1221no—
207#97—1221no—
208C4×C8C22×D6111yescharacteristic
209C2×Q8—21no—
210C2×Q8—41no—
211C2×Q8—611no—
212C2×D4—21no—
213C2×D4—1221no—
214C2×D4—2441no—
215C2×D4—2441no—
216C22×C4—2441no—
217C22×C4—2441no—
218Q16—41no—
219Q16—4882no—
220SD16—41no—
221SD16—41no—
222SD16—4881no—
223D8—41no—
224D8—1221no—
225D8—1221no—
226D8—4881no—
227C2×C8—1221no—
228C2×C8—2441no—
229C2×C8D4×D6111yescharacteristic
230C2×C8C2×C22⋊D6111yescharacteristic
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—611no—
234C4⋊C4—1221no—
235C4⋊C4—1221no—
236C4⋊C4—2441no—
237C22⋊C4—41no—
238C22⋊C4—41no—
239C22⋊C4—2441no—
240C22⋊C4—2441no—
241C22⋊C4—2441no—
242C22⋊C4—2441no—
243C42—1221no—
244C42—2441no—
245C42D4×D6111yescharacteristic
246C16—41no—
247C16—2441no—
248C23—41no—
249C23—2441no—
250Q8—41no—
251Q8—41no—
252Q8—81no—
253Q8—81no—
254Q8—2441no—
255D4—41no—
256D4—41no—
257D4—9761no—
258D4—4882no—
259D4—2441no—
260D4—2441no—
261C2×C4—41no—
262C2×C4—81no—
263C2×C4—1221no—
264C2×C4—1221no—
265C2×C4—9761no—
266C2×C4—9761no—
267C2×C4—2441no—
268C2×C4#1451974511yescharacteristic
269C2×C4D8×D6111yescharacteristic
270C2×C4#1451980111yescharacteristic
271C8—21no—
272C8—4881no—
273C8—2441no—
274C8#1451979811yescharacteristic
275C8#1451980611yescharacteristic
276C22—81no—
277C22—81no—
278C22—81no—
279C22—4881no—
280C22—4881no—
281C22—4881no—
282C22#1683989411yescharacteristic
283C4—21no—
284C4—21no—
285C4—81no—
286C4—161no—
287C4—4881no—
288C4—2441no—
289C4—2441no—
290C4#1683992111yescharacteristic
291C4#1683993911yescharacteristic
292C2—161no—
293C2—9761no—
294C2#2144500911yescharacteristic
295C2#2144776311yescharacteristic
296C2#2144778711yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2243C2
socleC22×C61#447
prime radical#21458910C2
hypercenter#2243D61
hypocenterC61#12390
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2243

Complements

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

NH ≅ G/Ntype
2. #21447963C2semidirect
3. #21445334C2semidirect
4. #21443862C2semidirect
5. #21443802C2semidirect
6. #21443787C2semidirect
7. C61×#2243C2semidirect
145. #2243D61semidirect
175. C61#12390semidirect

Maximal subgroups

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

subgroupindex
#214589102
#214479632
#214453342
#214438622
#214438022
#214437872
C61×#22432
#1239061