Finite Group Databasebeta

← #29593262

Subgroups — #29593262

Order 15616.

306 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 57 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#21456709C211yesmaximal, characteristic
2#21448021C211yesmaximal, characteristic, complemented
3#21447260C211yesmaximal, characteristic
4#21443838C211yesmaximal, characteristic, complemented
5#21443837C211yesmaximal, characteristic, complemented
6#21443744C211yesmaximal, characteristic
7C61×#2235C211yesmaximal, characteristic, complemented
8#16840335—21no—
9#16840105—21no—
10#16840102—21no—
11#16840018—21no—
12#16840003C2211yescharacteristic
13#16839919—21no—
14#16839916—21no—
15#16839761—21no—
16#16839728C2211yescharacteristic
17#16839587—21no—
18#16839565—21no—
19C22⋊#11758185C2211yescharacteristic
20#16839531—21no—
21#16839527C2211yescharacteristic
22C61×#467C2211yescharacteristic
23C2×#107×C61C2211yescharacteristic
24C61×#367—21no—
25C61×#358—21no—
26C61×C22⋊C16C2211yescharacteristic
27C2×#11758222D411yescharacteristic
28C2×Q8×D61—21no—
29C2×Dic244D411yescharacteristic
30C2×#11758202—21no—
31C2×#11758194—21no—
32C2×#11758194D411yescharacteristic
33#14519776—41no—
34#14519763—41no—
35#14519762—41no—
36#14519759—41no—
37#14519757—21no—
38#14519756—21no—
39#14519753—21no—
40#14519735—21no—
41C2×#11758185—21no—
42#14519711D411yescharacteristic
43#14519708—21no—
44#14519702—21no—
45#14519701—21no—
46#14519700—21no—
47#14519700—41no—
48#14519697—41no—
49#14519689—21no—
50#14519689—21no—
51C2×Q16×C61D411yescharacteristic
52C22×C8×C61C2311yescharacteristic
53C22⋊Q8×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C16×C61—21no—
56#107×C61—21no—
57#107×C61—21no—
58#107×C61D411yescharacteristic
59#103×C61—21no—
60C2×Q8×C61—21no—
61C22×C4×C61—41no—
62C22×C4×C61C2×D411yescharacteristic
63C2×C22⋊D61—21no—
64Q8×D61—81no—
65Q8×D61—81no—
66#11758222—41no—
67#11758222—41no—
68C2×D244D811yescharacteristic
69C2×C4×D61—21no—
70C2×C4×D61—41no—
71C2×Dic122—21no—
72C2×Dic122—41no—
73C2×Dic122D811yescharacteristic
74Q16×C61—41no—
75C2×C8×C61—41no—
76C2×C8×C61C2×D411yescharacteristic
77C2×C8×C61C2×D411yescharacteristic
78C4⋊C4×C61—21no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—41no—
82C22⋊C4×C61—41no—
83C22⋊Dic61—41no—
84#11758202—81no—
85#11758198—41no—
86#11758198—41no—
87#11758198—41no—
88C4⋊Dic61—21no—
89C4⋊Dic61—41no—
90#11758196—41no—
91#11758196—41no—
92C4×Dic61—41no—
93#11758194—41no—
94#11758194—41no—
95#11758194—41no—
96C2×#92418—21no—
97C2×#92418—41no—
98Dic244—41no—
99C16×C61—41no—
100#11758185—41no—
101C23×C61AGL(1,ℤ/8)11yescharacteristic
102C22×D61—21no—
103Q8×C61—41no—
104Q8×C61—41no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—81no—
110C2×C4×C61—161no—
111C2×C4×C61#12011yescharacteristic
112C2×C4×C61C2×D811yescharacteristic
113C22⋊D61—81no—
114C2×Dic61—21no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117D244—41no—
118C4×D61—41no—
119C4×D61—41no—
120C4×D61—82no—
121Dic122—41no—
122Dic122—41no—
123Dic122—41no—
124Dic122—82no—
125C8×C61—21no—
126C8×C61—21no—
127#92418—41no—
128#92418—81no—
129#12286—611nomaximal, Sylow
130C22×C61—21no—
131C22×C61—21no—
132C22×C61—21no—
133C22×C61#44711yescharacteristic
134C2×D61—41no—
135C2×D61—41no—
136C2×D61—41no—
137C4×C61—21no—
138C4×C61—81no—
139C4×C61—81no—
140C4×C61—161no—
141C4×C61#45511yescharacteristic
142C4×C61#45811yescharacteristic
143Dic61—41no—
144Dic61—81no—
145Dic61—81no—
146#3202—611no—
147#2236—611no—
148#2235D6111yescharacteristic, complemented
149#2078—611no—
150#1350—611no—
151#1350—611no—
152#1315—611no—
153C2×C61—41no—
154C2×C61#160711yescharacteristic
155C2×C61#219311yescharacteristic
156C2×C61#219511yescharacteristic
157D61—81no—
158#536—1221no—
159#485—1221no—
160#485—1221no—
161#470—1221no—
162#467—611no—
163#467C2×D6111yescharacteristic
164#451—1221no—
165#451—1221no—
166C2×#107C2×D6111yescharacteristic
167#417—1221no—
168#408—611no—
169#367—21no—
170#366—1221no—
171#358—21no—
172#358—1221no—
173C22⋊C16—611no—
174C22⋊C16C2×D6111yescharacteristic
175#343—1221no—
176#341—611no—
177C61#1228611yescharacteristic, complemented, Sylow
178C2×#41—611no—
179C22×Q8—1221no—
180C2×Q16—611no—
181C2×Q16—1221no—
182C2×Q16C22⋊D6111yescharacteristic
183C2×M16—611no—
184C2×M16—1221no—
185C22×C8C22×D6111yescharacteristic
186C4⋊Q8—2441no—
187#124—2441no—
188#123—2441no—
189#123—2441no—
190C22⋊Q8—21no—
191C22⋊Q8—1221no—
192C22⋊Q8—1221no—
193C22⋊Q8—1221no—
194#117—1221no—
195C2×C4⋊C4—21no—
196C2×C16—21no—
197C2×C16—1221no—
198#107—21no—
199#107—21no—
200#107—611no—
201#107C22⋊D6111yescharacteristic
202#106—1221no—
203#103—21no—
204#103—1221no—
205#103—1221no—
206#103—1221no—
207#103—2441no—
208#102—2441no—
209C22⋊C8—1221no—
210C22⋊C8—1221no—
211#41—2441no—
212#41—2441no—
213C2×Q8—21no—
214C2×Q8—611no—
215C2×Q8—1221no—
216C2×Q8—4881no—
217C2×Q8—4881no—
218C2×Q8—2441no—
219C2×D4—611no—
220C2×D4—1221no—
221C22×C4—41no—
222C22×C4—1221no—
223C22×C4—2441no—
224C22×C4D4×D6111yescharacteristic
225Q16—41no—
226Q16—4881no—
227Q16—2441no—
228M16—2441no—
229M16—2441no—
230M16—2441no—
231C2×C8—41no—
232C2×C8—1221no—
233C2×C8—2441no—
234C2×C8D4×D6111yescharacteristic
235C2×C8C2×C22⋊D6111yescharacteristic
236C4⋊C4—21no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—1221no—
241C4⋊C4—2441no—
242C4⋊C4—2441no—
243C4⋊C4—2441no—
244C22⋊C4—41no—
245C22⋊C4—2441no—
246C22⋊C4—2441no—
247C22⋊C4—2441no—
248C22⋊C4—2441no—
249C42—2441no—
250C16—41no—
251C16—2441no—
252C23—1221no—
253C23#1451980111yescharacteristic
254Q8—41no—
255Q8—41no—
256Q8—4882no—
257Q8—2441no—
258Q8—2441no—
259Q8—2441no—
260D4—4881no—
261D4—2441no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—81no—
267C2×C4—161no—
268C2×C4—1221no—
269C2×C4—4882no—
270C2×C4—2441no—
271C2×C4—2441no—
272C2×C4—2441no—
273C2×C4—2441no—
274C2×C4#1451974511yescharacteristic
275C2×C4D8×D6111yescharacteristic
276C8—21no—
277C8—21no—
278C8—4881no—
279C8—2441no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—2441no—
284C22—2441no—
285C22—2441no—
286C22#1683989411yescharacteristic
287C4—21no—
288C4—81no—
289C4—81no—
290C4—161no—
291C4—4881no—
292C4—4881no—
293C4—2441no—
294C4#1683993811yescharacteristic
295C4#1683995111yescharacteristic
296C2—41no—
297C2—4881no—
298C2#2144480311yescharacteristic
299C2#2144778211yescharacteristic
300C2#2144779411yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#2235C2
socleC22×C61#447
prime radicalC2×#11758222D4
hypercenter#2235D61
hypocenterC61#12286
LCSG ▷ C22×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2235

Complements

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

NH ≅ G/Ntype
2. #21448021C2semidirect
4. #21443838C2semidirect
5. #21443837C2semidirect
7. C61×#2235C2semidirect
148. #2235D61semidirect
177. C61#12286semidirect

Maximal subgroups

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

subgroupindex
#214567092
#214480212
#214472602
#214438382
#214438372
#214437442
C61×#22352
#1228661