Finite Group Databasebeta

← #29593934

Subgroups — #29593934

Order 15616.

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

normal subgroups only

This group has 296 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#21448055C211yesmaximal, characteristic, complemented
3#21447957C211yesmaximal, characteristic, complemented
4#21445348C211yesmaximal, characteristic, complemented
5#21443800C211yesmaximal, characteristic, complemented
6#21443785C211yesmaximal, characteristic, complemented
7C61×#1360C211yesmaximal, characteristic, complemented
8#16840494—21no—
9#16840167C2211yescharacteristic
10#16840148—21no—
11#16840058—21no—
12#16839986—21no—
13#16839974—21no—
14#16839955—21no—
15#16839892C2211yescharacteristic
16#16839863—21no—
17C4×D488C2211yescharacteristic
18#16839588—21no—
19#16839566—21no—
20#16839564—21no—
21#16839563—21no—
22#16839538C2211yescharacteristic
23#16839510—21no—
24C61×#495C2211yescharacteristic
25C61×C4⋊C16C2211yescharacteristic
26C61×#334C2211yescharacteristic
27C2×#11758201—21no—
28C2×D488D411yescharacteristic
29C2×#11758199—21no—
30#14519777—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#14519711—21no—
43#14519711—21no—
44#14519711—41no—
45#14519711D411yescharacteristic
46C4⋊#92418D411yescharacteristic
47#14519706—21no—
48#14519702—41no—
49#14519701—21no—
50#14519699—21no—
51#14519698—21no—
52#14519687—21no—
53C2×Q16×C61D411yescharacteristic
54C2×SD16×C61—21no—
55C2×D8×C61D411yescharacteristic
56#124×C61—21no—
57C2×C16×C61—21no—
58C4⋊C8×C61—21no—
59C4×C8×C61C2311yescharacteristic
60C2×Q8×C61—21no—
61C2×D4×C61—21no—
62C2×C22⋊D61—41no—
63C2×C22⋊D61—41no—
64C22×Dic61—41no—
65C2×D244—21no—
66C2×C4×D61—41no—
67C2×Dic122—41no—
68C2×Dic122D811yescharacteristic
69Q16×C61—41no—
70SD16×C61—41no—
71SD16×C61—41no—
72D8×C61—41no—
73C2×C8×C61—41no—
74C2×C8×C61C2×D411yescharacteristic
75C2×C8×C61C2×D411yescharacteristic
76C22⋊C4×C61—41no—
77C22⋊C4×C61—41no—
78C42×C61C2×D411yescharacteristic
79C22⋊Dic61—41no—
80#11758201—81no—
81#11758199—81no—
82#11758198—41no—
83#11758198—41no—
84#11758198—41no—
85C4⋊Dic61—21no—
86C4⋊Dic61—41no—
87C4⋊Dic61—41no—
88C4⋊Dic61—41no—
89C4⋊Dic61D811yescharacteristic
90#11758196—21no—
91C4×Dic61—21no—
92C4×Dic61—41no—
93C2×#92418—21no—
94D488—21no—
95D488—21no—
96C16×C61—41no—
97#11758185—41no—
98C23×C61—41no—
99C22×D61—41no—
100Q8×C61—41no—
101Q8×C61—41no—
102D4×C61—41no—
103D4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61#12011yescharacteristic
106C2×C4×C61C2×D811yescharacteristic
107C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
108C22⋊D61—82no—
109C22⋊D61—161no—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—41no—
113C2×Dic61—81no—
114C2×Dic61—161no—
115D244—41no—
116D244—41no—
117C4×D61—161no—
118Dic122—41no—
119Dic122—161no—
120C8×C61—21no—
121C8×C61—81no—
122C8×C61#13511yescharacteristic
123C8×C61#13711yescharacteristic
124#92418—41no—
125#12388—611nomaximal, Sylow
126C22×C61—81no—
127C22×C61—81no—
128C22×C61—81no—
129C22×C61#44711yescharacteristic
130C2×D61—81no—
131C2×D61—81no—
132C2×D61—81no—
133C4×C61—21no—
134C4×C61—21no—
135C4×C61—81no—
136C4×C61#45211yescharacteristic
137C4×C61#45511yescharacteristic
138Dic61—41no—
139Dic61—41no—
140Dic61—81no—
141Dic61—161no—
142#3403—611no—
143#2243—611no—
144#2224—611no—
145#1696—611no—
146#1360D6111yescharacteristic, complemented
147#1338—611no—
148#1333—611no—
149C2×C61—161no—
150C2×C61#164111yescharacteristic
151C2×C61#219111yescharacteristic
152C2×C61#219211yescharacteristic
153D61—161no—
154#559—1221no—
155#500—611no—
156#496—1221no—
157#495C2×D6111yescharacteristic
158#477—1221no—
159#464—1221no—
160#463—1221no—
161#459—1221no—
162#446—611no—
163#440—1221no—
164C4×D8—611no—
165#366—1221no—
166C4⋊C16C2×D6111yescharacteristic
167#358—1221no—
168#357—1221no—
169#357—1221no—
170#346—611no—
171#334C2×D6111yescharacteristic
172#333—1221no—
173C61#1238811yescharacteristic, complemented, Sylow
174C2×Q16D24411yescharacteristic
175C2×SD16—21no—
176C2×SD16—1221no—
177C2×D8—611no—
178C2×D8—1221no—
179C2×D8D24411yescharacteristic
180C4⋊Q8—1221no—
181#127—1221no—
182#124—21no—
183#124—1221no—
184#124—2441no—
185#123—2441no—
186#123—2441no—
187C4×Q8—611no—
188C4×Q8—1221no—
189C4×D4—1221no—
190C4×D4—1221no—
191C4×D4—2441no—
192C2×C16—21no—
193C2×C16—1221no—
194#107—611no—
195#107—1221no—
196#107—1221no—
197#107—2441no—
198C4⋊C8—21no—
199C4⋊C8—611no—
200C4⋊C8—1221no—
201#103—1221no—
202#103—2441no—
203#102—1221no—
204#102—1221no—
205#97—1221no—
206C4×C8C22×D6111yescharacteristic
207C2×Q8—21no—
208C2×Q8—611no—
209C2×Q8—2441no—
210C2×D4—21no—
211C2×D4—1221no—
212C2×D4—2441no—
213C2×D4—2441no—
214C22×C4—2441no—
215C22×C4—2441no—
216Q16—41no—
217SD16—41no—
218SD16—41no—
219SD16—4881no—
220D8—41no—
221D8—1221no—
222D8—1221no—
223D8—4881no—
224C2×C8—41no—
225C2×C8—1221no—
226C2×C8C2×D24411yescharacteristic
227C2×C8D4×D6111yescharacteristic
228C4⋊C4—611no—
229C4⋊C4—1221no—
230C4⋊C4—1221no—
231C4⋊C4—2441no—
232C4⋊C4—2441no—
233C4⋊C4—2441no—
234C22⋊C4—41no—
235C22⋊C4—41no—
236C22⋊C4—2441no—
237C22⋊C4—2441no—
238C22⋊C4—2441no—
239C22⋊C4—2441no—
240C42—1221no—
241C42—2441no—
242C42D4×D6111yescharacteristic
243C16—41no—
244C16—2441no—
245C23—41no—
246C23—2441no—
247Q8—41no—
248Q8—41no—
249Q8—9761no—
250Q8—2441no—
251D4—41no—
252D4—41no—
253D4—9761no—
254D4—4882no—
255D4—2441no—
256D4—2441no—
257C2×C4—41no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—9761no—
261C2×C4—9761no—
262C2×C4—4881no—
263C2×C4—2441no—
264C2×C4#1451974711yescharacteristic
265C2×C4D8×D6111yescharacteristic
266C2×C4#1451980411yescharacteristic
267C8—21no—
268C8—81no—
269C8—2441no—
270C8#1451979611yescharacteristic
271C8#1451980611yescharacteristic
272C22—81no—
273C22—81no—
274C22—81no—
275C22—4881no—
276C22—4881no—
277C22—4881no—
278C22#1683989711yescharacteristic
279C4—21no—
280C4—21no—
281C4—81no—
282C4—9761no—
283C4—4881no—
284C4—2441no—
285C4—2441no—
286C4#1683992511yescharacteristic
287C4#1683994211yescharacteristic
288C2—161no—
289C2—9761no—
290C2#2144501311yescharacteristic
291C2#2144777111yescharacteristic
292C2#2144777711yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1360C2
socleC22×C61#447
prime radical#21458910C2
hypercenter#1360D61
hypocenterC61#12388
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1360

Complements

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

NH ≅ G/Ntype
2. #21448055C2semidirect
3. #21447957C2semidirect
4. #21445348C2semidirect
5. #21443800C2semidirect
6. #21443785C2semidirect
7. C61×#1360C2semidirect
146. #1360D61semidirect
173. C61#12388semidirect

Maximal subgroups

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

subgroupindex
#214589102
#214480552
#214479572
#214453482
#214438002
#214437852
C61×#13602
#1238861