Finite Group Databasebeta

← #29593597

Subgroups — #29593597

Order 15616.

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

normal subgroups only

This group has 308 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#21458896C211yesmaximal, characteristic
2#21448088C211yesmaximal, characteristic
3#21445310C211yesmaximal, characteristic, complemented
4#21443863C211yesmaximal, characteristic
5#21443800C211yesmaximal, characteristic, complemented
6#21443789C211yesmaximal, characteristic, complemented
7C61×#2209C211yesmaximal, characteristic, complemented
8#16840484—21no—
9C2×#14519723—21no—
10C2×#14519720—21no—
11#16840155—21no—
12#16840146C2211yescharacteristic
13#16840044—21no—
14#16839984—21no—
15#16839980—21no—
16#16839971—21no—
17#16839892C2211yescharacteristic
18#16839861—21no—
19#16839538C2211yescharacteristic
20#16839513C2211yescharacteristic
21#16839508—21no—
22C2×Q32×C61—21no—
23C61×#494C2211yescharacteristic
24C4×Q16×C61C2211yescharacteristic
25C61×C4⋊C16C2211yescharacteristic
26C61×#358—21no—
27C2×Dic244D411yescharacteristic
28C2×#11758202—21no—
29C2×#11758190—21no—
30C2×#11758201—21no—
31C2×D488D411yescharacteristic
32#14519775—21no—
33#14519772—41no—
34#14519771—41no—
35#14519766—21no—
36#14519765—21no—
37#14519755—41no—
38C4×Dic122D411yescharacteristic
39#14519742—21no—
40#14519739—21no—
41#14519734—41no—
42#14519723—42no—
43#14519720—42no—
44C2×#11758185—21no—
45#14519708—41no—
46C4⋊#92418—21no—
47C4⋊#92418D411yescharacteristic
48#14519706—21no—
49#14519700—21no—
50#14519700—41no—
51#14519697—21no—
52#14519687—21no—
53C2×Q16×C61—21no—
54C2×Q16×C61—21no—
55C2×Q16×C61D411yescharacteristic
56C4⋊Q8×C61—21no—
57C4×Q8×C61—21no—
58Q32×C61—42no—
59C2×C16×C61—21no—
60#107×C61D411yescharacteristic
61#103×C61—21no—
62C4×C8×C61C2311yescharacteristic
63C2×Q8×C61—21no—
64C2×Q8×C61—41no—
65C2×D244—21no—
66C2×C4×D61—41no—
67C2×Dic122—21no—
68C2×Dic122D811yescharacteristic
69Q16×C61—21no—
70Q16×C61—21no—
71Q16×C61—41no—
72Q16×C61—41no—
73Q16×C61—41no—
74Q16×C61—41no—
75C2×C8×C61C2×D411yescharacteristic
76C2×C8×C61C2×D411yescharacteristic
77C4⋊C4×C61—21no—
78C4⋊C4×C61—41no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C42×C61—41no—
82C42×C61C2×D411yescharacteristic
83#11758202—81no—
84#11758201—81no—
85#11758198—41no—
86#11758198—41no—
87#11758198—41no—
88#11758198—41no—
89#11758198—41no—
90C4⋊Dic61D811yescharacteristic
91#11758196—21no—
92#11758196—41no—
93#11758196—41no—
94#11758196—41no—
95C4×Dic61—21no—
96C4×Dic61—41no—
97C2×#92418—21no—
98C2×#92418—41no—
99Dic244—41no—
100D488—41no—
101#11758190—41no—
102#11758190—41no—
103C16×C61—41no—
104#11758185—22no—
105C22×D61—41no—
106Q8×C61—41no—
107Q8×C61—41no—
108Q8×C61—81no—
109Q8×C61—81no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—81no—
113C2×C4×C61#12011yescharacteristic
114C2×C4×C61C2×D811yescharacteristic
115C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—41no—
119D244—41no—
120D244—41no—
121C4×D61—82no—
122Dic122—41no—
123Dic122—41no—
124Dic122—41no—
125C8×C61—21no—
126C8×C61#13511yescharacteristic
127C8×C61AGL(1,ℤ/8)11yescharacteristic
128#92418—41no—
129#92418—81no—
130#12339—611nomaximal, Sylow
131C22×C61#44711yescharacteristic
132C2×D61—81no—
133C2×D61—81no—
134C2×D61—81no—
135C4×C61—21no—
136C4×C61—21no—
137C4×C61—81no—
138C4×C61—81no—
139C4×C61—161no—
140C4×C61#44911yescharacteristic
141C4×C61#45311yescharacteristic
142Dic61—41no—
143Dic61—41no—
144Dic61—81no—
145#3402—611no—
146#2251—611no—
147#2209D6111yescharacteristic, complemented
148#1690—611no—
149#1360—611no—
150#1338—611no—
151#1334—611no—
152C2×C61#162111yescharacteristic
153C2×C61#219111yescharacteristic
154C2×C61#219511yescharacteristic
155D61—161no—
156#556—1221no—
157C2×Q32—21no—
158C2×Q32—1221no—
159C2×SD32—1221no—
160#497—1221no—
161#495—611no—
162#494C2×D6111yescharacteristic
163#475—1221no—
164#464—1221no—
165#463—1221no—
166#462—1221no—
167#446—611no—
168#440—1221no—
169C4×Q16C2×D6111yescharacteristic
170C4⋊C16C2×D6111yescharacteristic
171#358—21no—
172#346—611no—
173#334—611no—
174#332—1221no—
175C61#1233911yescharacteristic, complemented, Sylow
176C2×Q16—21no—
177C2×Q16—21no—
178C2×Q16—611no—
179C2×Q16—1221no—
180C2×Q16C22⋊D6111yescharacteristic
181C2×SD16—1221no—
182C2×SD16—1221no—
183C2×D8—611no—
184C4⋊Q8—21no—
185C4⋊Q8—1221no—
186#126—2441no—
187#126—2441no—
188#124—1221no—
189#124—1221no—
190C22⋊Q8—2441no—
191C4×Q8—21no—
192C4×Q8—611no—
193C4×Q8—1221no—
194C4×D4—1221no—
195#117—2441no—
196Q32—42no—
197Q32—2442no—
198SD32—2442no—
199C2×C16—21no—
200C2×C16—1221no—
201#107C22⋊D6111yescharacteristic
202#106—2441no—
203C4⋊C8—611no—
204C4⋊C8—1221no—
205C4⋊C8—1221no—
206#103—21no—
207#103—1221no—
208#103—2441no—
209#102—1221no—
210#97—1221no—
211C4×C8C22×D6111yescharacteristic
212C2×Q8—21no—
213C2×Q8—41no—
214C2×Q8—611no—
215C2×Q8—1221no—
216C2×D4—1221no—
217C22×C4—2441no—
218Q16—21no—
219Q16—21no—
220Q16—41no—
221Q16—41no—
222Q16—41no—
223Q16—41no—
224Q16—4881no—
225Q16—2441no—
226SD16—4881no—
227SD16—2441no—
228SD16—2441no—
229D8—2441no—
230C2×C8—1221no—
231C2×C8—2441no—
232C2×C8D4×D6111yescharacteristic
233C2×C8C2×C22⋊D6111yescharacteristic
234C4⋊C4—21no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—611no—
239C4⋊C4—1221no—
240C4⋊C4—2441no—
241C4⋊C4—2441no—
242C4⋊C4—2441no—
243C22⋊C4—2441no—
244C22⋊C4—2441no—
245C22⋊C4—2441no—
246C22⋊C4—2441no—
247C22⋊C4—2441no—
248C42—41no—
249C42—1221no—
250C42—2441no—
251C42D4×D6111yescharacteristic
252C16—41no—
253C16—1222no—
254C23—2441no—
255Q8—41no—
256Q8—41no—
257Q8—81no—
258Q8—81no—
259Q8—2441no—
260Q8—2441no—
261Q8—2441no—
262D4—2441no—
263D4—2441no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—81no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—4882no—
270C2×C4—2441no—
271C2×C4#1451974511yescharacteristic
272C2×C4D8×D6111yescharacteristic
273C2×C4#1451980111yescharacteristic
274C8—21no—
275C8—4881no—
276C8—2441no—
277C8#1451979711yescharacteristic
278C8#1451980311yescharacteristic
279C22—4881no—
280C22—4881no—
281C22—4881no—
282C22#1683989411yescharacteristic
283C4—21no—
284C4—21no—
285C4—81no—
286C4—81no—
287C4—161no—
288C4—4881no—
289C4—2441no—
290C4—2441no—
291C4#1683990511yescharacteristic
292C4#1683992811yescharacteristic
293C2—9761no—
294C2#2144488311yescharacteristic
295C2#2144776811yescharacteristic
296C2#2144779611yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2209C2
socleC22×C61#447
prime radicalC2×D488D4
hypercenter#2209D61
hypocenterC61#12339
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2209

Complements

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

NH ≅ G/Ntype
3. #21445310C2semidirect
5. #21443800C2semidirect
6. #21443789C2semidirect
7. C61×#2209C2semidirect
147. #2209D61semidirect
175. C61#12339semidirect

Maximal subgroups

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

subgroupindex
#214588962
#214480882
#214453102
#214438632
#214438002
#214437892
C61×#22092
#1233961