Finite Group Databasebeta

← #29593868

Subgroups — #29593868

Order 15616.

350 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 65 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#21457477C211yesmaximal, characteristic
2#21448058C211yesmaximal, characteristic, complemented
3#21447968C211yesmaximal, characteristic, complemented
4#21443861C211yesmaximal, characteristic, complemented
5#21443788C211yesmaximal, characteristic, complemented
6#21443777C211yesmaximal, characteristic, complemented
7C61×#1693C211yesmaximal, characteristic, complemented
8C2×#14519810—21no—
9#16840421—21no—
10#16840146C2211yescharacteristic
11#16840008—21no—
12#16839985—21no—
13#16839920—21no—
14#16839909—21no—
15C4×Dic244C2211yescharacteristic
16#16839587—21no—
17C4⋊#11758185C2211yescharacteristic
18#16839565—21no—
19#16839565—21no—
20#16839562—21no—
21#16839538C2211yescharacteristic
22C61×#500C2211yescharacteristic
23C61×#461—21no—
24C61×#436C2211yescharacteristic
25C61×#334C2211yescharacteristic
26C61×#332—21no—
27C2×#11758222—21no—
28C22×Dic122—21no—
29#14519810—42no—
30#14519810—42no—
31C2×Dic244—21no—
32C2×Dic244D411yescharacteristic
33C2×Dic244D411yescharacteristic
34C2×#11758190—21no—
35C2×#11758190—21no—
36C2×D488D411yescharacteristic
37#14519765—21no—
38#14519763—41no—
39#14519756—21no—
40#14519755—41no—
41#14519751—21no—
42#14519749—41no—
43C4×Dic122—21no—
44#14519737—41no—
45C2×#11758185—21no—
46C2×#11758185—21no—
47#14519711D411yescharacteristic
48#14519702—21no—
49#14519702—21no—
50#14519699—21no—
51C2×SD16×C61—41no—
52C2×M16×C61—21no—
53C4⋊Q8×C61—21no—
54C4×D4×C61D411yescharacteristic
55#107×C61—21no—
56#107×C61—21no—
57C4⋊C8×C61—21no—
58C4⋊C8×C61D411yescharacteristic
59#103×C61—41no—
60C22⋊C8×C61—21no—
61C4×C8×C61C2311yescharacteristic
62C2×Q8×C61—41no—
63C2×D4×C61D811yescharacteristic
64C22×C4×C61—21no—
65C2×C22⋊D61—41no—
66C2×C22⋊D61—41no—
67C22×Dic61—41no—
68#11758222—42no—
69#11758222—81no—
70C2×D244—21no—
71C2×C4×D61—41no—
72C2×Dic122—21no—
73C2×Dic122—21no—
74C2×Dic122—42no—
75C2×Dic122—41no—
76C2×Dic122—81no—
77SD16×C61—82no—
78M16×C61—41no—
79M16×C61—41no—
80C2×C8×C61—21no—
81C2×C8×C61—41no—
82C2×C8×C61C2×D411yescharacteristic
83C2×C8×C61C2×D411yescharacteristic
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61D811yescharacteristic
87C22⋊C4×C61—21no—
88C42×C61C2×D411yescharacteristic
89C22⋊Dic61—41no—
90#11758198—41no—
91#11758198—41no—
92#11758198—41no—
93C4⋊Dic61—21no—
94#11758196—41no—
95#11758196—41no—
96C4×Dic61—41no—
97Dic244—21no—
98Dic244—41no—
99Dic244—42no—
100Dic244SD1612yescomplemented
101D488—41no—
102#11758190—42no—
103#11758190—41no—
104#11758190—41no—
105#11758185—41no—
106#11758185—41no—
107C23×C61—21no—
108C22×D61—41no—
109Q8×C61—81no—
110Q8×C61—81no—
111D4×C61—41no—
112C2×C4×C61—21no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—81no—
116C2×C4×C61#12011yescharacteristic
117C2×C4×C61C2×D811yescharacteristic
118C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
119C22⋊D61—82no—
120C22⋊D61—82no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—82no—
125D244—41no—
126D244—41no—
127C4×D61—82no—
128Dic122—22no—
129Dic122—41no—
130Dic122—41no—
131Dic122—41no—
132Dic122—82no—
133C8×C61—21no—
134C8×C61—41no—
135C8×C61—81no—
136C8×C61C2×SD1611yescharacteristic
137C8×C61AGL(1,ℤ/8)11yescharacteristic
138#12379—611nomaximal, Sylow
139C22×C61—41no—
140C22×C61—41no—
141C22×C61—41no—
142C22×C61#44711yescharacteristic
143C2×D61—81no—
144C2×D61—81no—
145C2×D61—81no—
146C4×C61—21no—
147C4×C61—21no—
148C4×C61—41no—
149C4×C61—161no—
150C4×C61#45011yescharacteristic
151C4×C61#45511yescharacteristic
152Dic61—42no—
153Dic61—81no—
154Dic61—81no—
155#3277—611no—
156#2243—611no—
157#2227—611no—
158#1693D6111yescharacteristic, complemented
159#1360—611no—
160#1334—611no—
161#1330—611no—
162C2×C61—81no—
163C2×C61#163911yescharacteristic
164C2×C61#219011yescharacteristic
165C2×C61#219511yescharacteristic
166D61—161no—
167C2×#137—1221no—
168#548—1221no—
169#500C2×D6111yescharacteristic
170#495—611no—
171#468—1221no—
172#464—1221no—
173#461—21no—
174#451—1221no—
175#449—1221no—
176C4×Q16—611no—
177#436C2×D6111yescharacteristic
178#366—1221no—
179C4⋊C16—611no—
180#358—1221no—
181#358—1221no—
182#357—1221no—
183#346—611no—
184#334C2×D6111yescharacteristic
185#332—21no—
186C61#1237911yescharacteristic, complemented, Sylow
187C2×#41—1221no—
188C22×Q8—1221no—
189#137—2442no—
190#137—2442no—
191C2×Q16—611no—
192C2×Q16—611no—
193C2×Q16—1221no—
194C2×SD16—41no—
195C2×SD16—1221no—
196C2×SD16—1221no—
197C2×D8—611no—
198C2×M16—21no—
199C4⋊Q8—21no—
200#124—1221no—
201#124—2441no—
202C22⋊Q8—1221no—
203C22⋊Q8—2441no—
204#121—1221no—
205#121—2441no—
206C4×Q8—1221no—
207C4×D4—2441no—
208C4×D4C22⋊D6111yescharacteristic
209C2×C16—1221no—
210C2×C16—1221no—
211#107—21no—
212#107—21no—
213#107—611no—
214C4⋊C8—21no—
215C4⋊C8C22⋊D6111yescharacteristic
216#103—41no—
217#103—1221no—
218#103—1221no—
219#102—1221no—
220C22⋊C8—21no—
221C4×C8C22×D6111yescharacteristic
222#41—4881no—
223#41—2442no—
224C2×Q8—41no—
225C2×Q8—1221no—
226C2×Q8—1221no—
227C2×Q8—4881no—
228C2×Q8—2441no—
229C2×Q8—2442no—
230C2×D4—1221no—
231C2×D4—2441no—
232C2×D4—2441no—
233C2×D4#1175819911yescharacteristic
234C22×C4—21no—
235C22×C4—2441no—
236C22×C4—2441no—
237Q16—612no—
238Q16—1221no—
239Q16—2441no—
240Q16—2442no—
241SD16—82no—
242SD16—2442no—
243SD16—2441no—
244SD16—2441no—
245D8—2441no—
246M16—41no—
247M16—41no—
248C2×C8—21no—
249C2×C8—41no—
250C2×C8D4×D6111yescharacteristic
251C2×C8D4×D6111yescharacteristic
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—1221no—
255C4⋊C4—2441no—
256C4⋊C4—2441no—
257C4⋊C4#1175819911yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—2441no—
260C22⋊C4—2441no—
261C22⋊C4—2441no—
262C22⋊C4—2441no—
263C42—2441no—
264C42C2×C22⋊D6111yescharacteristic
265C16—2441no—
266C16—2441no—
267C23—21no—
268C23—2441no—
269Q8—81no—
270Q8—81no—
271Q8—1222no—
272Q8—4882no—
273Q8—2441no—
274Q8—2441no—
275Q8—2441no—
276D4—41no—
277D4—4882no—
278D4—4882no—
279D4—2441no—
280D4—2441no—
281C2×C4—21no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—81no—
285C2×C4—4882no—
286C2×C4—4882no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4#1451974511yescharacteristic
291C2×C4C2×#1175819911yescharacteristic
292C2×C4#1451980211yescharacteristic
293C8—21no—
294C8—41no—
295C8—81no—
296C8SD16×D6111yescharacteristic
297C8#1451980411yescharacteristic
298C22—41no—
299C22—41no—
300C22—41no—
301C22—4881no—
302C22—4881no—
303C22—4881no—
304C22#1683989511yescharacteristic
305C4—21no—
306C4—21no—
307C4—41no—
308C4—161no—
309C4—4881no—
310C4—4881no—
311C4—2442no—
312C4#1683991111yescharacteristic
313C4#1683993811yescharacteristic
314C2—81no—
315C2—9761no—
316C2#2144499611yescharacteristic
317C2#2144776411yescharacteristic
318C2#2144779511yescharacteristic
subgroupG/H
centerC22#16839895
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1693C2
socleC22×C61#447
prime radical#21457477C2
hypercenter#1693D61
hypocenterC61#12379
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #436 ◁ #1693

Complements

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

NH ≅ G/Ntype
2. #21448058C2semidirect
3. #21447968C2semidirect
4. #21443861C2semidirect
5. #21443788C2semidirect
6. #21443777C2semidirect
7. C61×#1693C2semidirect
100. Dic244SD16semidirect
158. #1693D61semidirect
186. C61#12379semidirect

Maximal subgroups

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

subgroupindex
#214574772
#214480582
#214479682
#214438612
#214437882
#214437772
C61×#16932
#1237961