Finite Group Databasebeta

← #30605252

Subgroups — #30605252

Order 15616.

324 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 58 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#21462190C211yesmaximal, characteristic, complemented
2#21461750C211yesmaximal, characteristic, complemented
3#21460794C211yesmaximal, characteristic, complemented
4#21460793C211yesmaximal, characteristic, complemented
5#21460790C211yesmaximal, characteristic, complemented
6#21460789C211yesmaximal, characteristic, complemented
7#21456554C211yesmaximal, characteristic
8#16840684—21no—
9#16840659C2211yescharacteristic
10#16840659C2211yescharacteristic
11#16840654—21no—
12#16840644—21no—
13#16840633—21no—
14#16840631C2211yescharacteristic
15#16840630C2211yescharacteristic
16#16840309—21no—
17#16840159C411yescharacteristic, complemented
18#16840137C411yescharacteristic, complemented
19#16840107—21no—
20#16840016C2211yescharacteristic
21#16840014—21no—
22#16840012C2211yescharacteristic
23#16839875C411yescharacteristic, complemented
24#16839872—21no—
25#16839714C2211yescharacteristic
26C61×#442C411yescharacteristic, complemented
27D61⋊M16—21no—
28#14519856—21no—
29#14519851—21no—
30#14519851—21no—
31C2×#11758222—41no—
32C2×D488C2×C411yescharacteristic
33C2×#11758199—21no—
34C2×#11758189D411yescharacteristic
35C2×#11758189C2311yescharacteristic
36#14519776—21no—
37#14519773—21no—
38#14519763—41no—
39#14519752—21no—
40#14519750—41no—
41#14519748—21no—
42C4×D244—21no—
43C4×C22⋊D61—41no—
44C42×D61D411yescharacteristic
45#14519709C2×C411yescharacteristic
46#14519708—21no—
47#14519699—21no—
48#14519698—21no—
49#14519697—21no—
50#14519688D411yescharacteristic
51C8×Dic61C2×C411yescharacteristic
52C8×Dic61D411yescharacteristic
53C2×D8×C61C2×C411yescharacteristic
54C4×D4×C61—21no—
55#106×C61C2×C411yescharacteristic
56#102×C61—21no—
57#97×C61C2×C411yescharacteristic
58C2×D4×C61—21no—
59C22×C4×C61—41no—
60C2×C22⋊D61—41no—
61C2×C22⋊D61—41no—
62C2×C22⋊D61—41no—
63#11758222—84no—
64C2×D244—21no—
65C2×D244—41no—
66C2×C4×D61—21no—
67C2×C4×D61—41no—
68C2×C4×D61C2×D411yescharacteristic
69C2×Dic122—41no—
70C22⋊#6923—41no—
71#11758217—41no—
72C4⋊#6923—41no—
73C4×#6923—41no—
74#11758213—41no—
75D61⋊C8—41no—
76D8×C61—41no—
77C2×C8×C61C22⋊C411yescharacteristic
78C2×C8×C61C22×C411yescharacteristic
79C4⋊C4×C61—21no—
80C22⋊C4×C61—41no—
81C42×C61C22⋊C411yescharacteristic
82C22⋊Dic61—41no—
83#11758199—42no—
84#11758198—41no—
85#11758198—41no—
86C4⋊Dic61—21no—
87#11758196—41no—
88C4×Dic61—21no—
89C4×Dic61C22⋊C411yescharacteristic
90C2×#92418C22⋊C411yescharacteristic
91C2×#92418C2×D411yescharacteristic
92D488—41no—
93#11758189—41no—
94#11758189—41no—
95#11758187—41no—
96#11758187—41no—
97C23×C61—41no—
98C22×D61—41no—
99C22×D61AGL(1,ℤ/8)11yescharacteristic
100C2×#6923—81no—
101D4×C61—41no—
102D4×C61—41no—
103C2×C4×C61—21no—
104C2×C4×C61—41no—
105C2×C4×C61—82no—
106C2×C4×C61C2×C22⋊C411yescharacteristic
107C22⋊D61—82no—
108C22⋊D61—82no—
109C22⋊D61—82no—
110C2×Dic61—21no—
111C2×Dic61—41no—
112C2×Dic61AGL(1,ℤ/8)11yescharacteristic
113D244—41no—
114D244—41no—
115D244—82no—
116C4×D61—21no—
117C4×D61—21no—
118C4×D61—42no—
119C4×D61—82no—
120Dic122—82no—
121#92420—81no—
122C8×C61—21no—
123C8×C61—21no—
124#92418—21no—
125#92418—21no—
126#11837—611nomaximal, Sylow
127C22×C61—81no—
128C22×C61—81no—
129C22×C61—81no—
130C22×C61#41811yescharacteristic
131C2×D61—21no—
132C2×D61—41no—
133C2×D61—81no—
134C2×D61—81no—
135C2×D61—81no—
136#6923—161no—
137C4×C61—41no—
138C4×C61—81no—
139C4×C61#41011yescharacteristic
140C4×C61#42111yescharacteristic
141Dic61—22no—
142Dic61—21no—
143Dic61—81no—
144#3184—611no—
145#2165—611no—
146#1841—611no—
147#1341—611no—
148#1341—611no—
149#1339—611no—
150#1339—611no—
151C2×C61—21no—
152C2×C61—161no—
153C2×C61#151411yescharacteristic
154D61—41no—
155D61—161no—
156#532—1221no—
157#498—611no—
158#493—611no—
159#486—1221no—
160#469—611no—
161#469—611no—
162#469—1221no—
163#442—611no—
164#442—1221no—
165#442#692311yescharacteristic, complemented
166C4×M16—611no—
167#364—1221no—
168#349—611no—
169#349—611no—
170#347—1221no—
171#344—1221no—
172#339—1221no—
173#338—611no—
174H(3,ℤ/4)—611no—
175C61#1183711yescharacteristic, complemented, Sylow
176C2×#41—2441no—
177C2×D8—611no—
178C2×D8—1221no—
179C2×D8C2×#692311yescharacteristic
180C2×M16—611no—
181C2×M16—611no—
182C2×M16—1221no—
183C4⋊Q8—1221no—
184#127—1221no—
185#124—2441no—
186#121—1221no—
187#121—1221no—
188#121—2441no—
189C4×D4—21no—
190C4×D4—1221no—
191C4×D4—2441no—
192#117—1221no—
193C2×C42—611no—
194M32—1221no—
195M32—1221no—
196#106—611no—
197#106—1221no—
198#106C2×#692311yescharacteristic
199#102—21no—
200#102—1221no—
201#102—1221no—
202#102—1221no—
203#97—611no—
204#97C2×#692311yescharacteristic
205C4×C8—611no—
206C4×C8—611no—
207#41—4884no—
208C2×Q8—2441no—
209C2×D4—21no—
210C2×D4—1221no—
211C2×D4—2441no—
212C2×D4—2441no—
213C2×D4—2441no—
214C2×D4—2441no—
215C22×C4—41no—
216C22×C4—611no—
217C22×C4—1221no—
218C22×C4—2441no—
219D8—41no—
220D8—2441no—
221D8—2442no—
222M16—2441no—
223M16—2441no—
224M16—2441no—
225M16—2441no—
226C2×C8—611no—
227C2×C8—611no—
228C2×C8—2441no—
229C2×C8C22⋊#692311yescharacteristic
230C2×C8C22×#692311yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—1221no—
233C4⋊C4—2441no—
234C4⋊C4—2441no—
235C22⋊C4—41no—
236C22⋊C4—2441no—
237C22⋊C4—2441no—
238C22⋊C4—2441no—
239C22⋊C4—2441no—
240C42—611no—
241C42—1221no—
242C42—2441no—
243C42C22⋊#692311yescharacteristic
244C16—2441no—
245C16—2441no—
246C23—41no—
247C23—611no—
248C23—2441no—
249Q8—4882no—
250D4—41no—
251D4—41no—
252D4—4882no—
253D4—4882no—
254D4—4882no—
255D4—4882no—
256D4—2441no—
257D4—2441no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—82no—
261C2×C4—611no—
262C2×C4—1221no—
263C2×C4—1221no—
264C2×C4—1221no—
265C2×C4—4882no—
266C2×C4—4881no—
267C2×C4—2442no—
268C2×C4—2441no—
269C2×C4C2×C22⋊#692311yescharacteristic
270C8—21no—
271C8—21no—
272C8—1221no—
273C8—1221no—
274C8—4881no—
275C22—81no—
276C22—81no—
277C22—81no—
278C22—1221no—
279C22—4881no—
280C22—4881no—
281C22—4881no—
282C22—2441no—
283C22#1684075411yescharacteristic
284C4—41no—
285C4—81no—
286C4—1222no—
287C4—1221no—
288C4—9761no—
289C4—4881no—
290C4#1684074111yescharacteristic
291C4#1684075911yescharacteristic
292C2—21no—
293C2—161no—
294C2—9761no—
295C2—2441no—
296C2#2146123811yescharacteristic
subgroupG/H
centerC2#21461238
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#442C4
socleC2×C61#1514
prime radical#21456554C2
cosocleC2×#11758189C23
hypercenter#442#6923
hypocenterC61#11837
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #21462190C2semidirect
2. #21461750C2semidirect
3. #21460794C2semidirect
4. #21460793C2semidirect
5. #21460790C2semidirect
6. #21460789C2semidirect
17. #16840159C4semidirect
18. #16840137C4semidirect
23. #16839875C4semidirect
26. C61×#442C4semidirect
165. #442#6923semidirect
175. C61#11837semidirect

Maximal subgroups

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

subgroupindex
#214621902
#214617502
#214607942
#214607932
#214607902
#214607892
#214565542
#1183761