Finite Group Databasebeta

← #29591514

Subgroups — #29591514

Order 15616.

352 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 85 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#21456399C211yesmaximal, characteristic
2#21447573C211yesmaximal, characteristic, complemented
3#21444576C211yesmaximal, characteristic, complemented
4#21443877C211yesmaximal, characteristic, complemented
5#21443866C211yesmaximal, characteristic, complemented
6#21443864C211yesmaximal, characteristic, complemented
7C61×#1365C211yesmaximal, characteristic, complemented
8#16840313—21no—
9C2×#14519716—21no—
10#16840139C2211yescharacteristic
11#16840110—21no—
12#16839999—21no—
13#16839999C412yes—
14#16839844—21no—
15#16839844C412yes—
16#16839784—21no—
17C4×C8×D61C2211yescharacteristic
18C4⋊#11758185C2211yescharacteristic
19#16839580—21no—
20#16839515C2211yescharacteristic
21#16839514—21no—
22C61×#500C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×#11758226—41no—
26C2×D488—21no—
27C2×D488C2×C412yes—
28C2×#11758189—41no—
29C2×C8×D61C2×C411yescharacteristic
30C2×C8×D61D411yescharacteristic
31#14519774—21no—
32#14519766—41no—
33#14519752—22no—
34#14519752—41no—
35#14519739—22no—
36#14519739—41no—
37C42×D61D411yescharacteristic
38#14519716—42no—
39C2×#11758185—21no—
40C4⋊#92418—21no—
41#14519706—41no—
42#14519697—22no—
43#14519697—22no—
44C4×#92418D411yescharacteristic
45C8×Dic61C2×C411yescharacteristic
46C8×Dic61D411yescharacteristic
47C4⋊Q8×C61—21no—
48C2×C16×C61—21no—
49#107×C61—21no—
50#107×C61C2×C412yes—
51C4⋊C8×C61—21no—
52C4×C8×C61C2311yescharacteristic
53C2×Q8×C61—41no—
54#11758226—84no—
55C2×D244—22no—
56C2×D244—42no—
57C2×D244—41no—
58C2×D244—41no—
59C2×C4×D61—42no—
60C2×C4×D61C22⋊C411yescharacteristic
61C2×C4×D61D811yescharacteristic
62C2×C4×D61SD1611yescharacteristic
63C2×C8×C61—41no—
64C2×C8×C61C22×C411yescharacteristic
65C2×C8×C61C2×D411yescharacteristic
66C4⋊C4×C61—22no—
67C4⋊C4×C61—41no—
68C42×C61C2×D411yescharacteristic
69#11758198—42no—
70#11758198—42no—
71C4×Dic61C22⋊C411yescharacteristic
72C4×Dic61D811yescharacteristic
73C4×Dic61SD1611yescharacteristic
74C2×#92418—41no—
75C2×#92418C22⋊C411yescharacteristic
76C2×#92418C22⋊C411yescharacteristic
77D488—42no—
78D488—41no—
79D488—41no—
80#11758189—82no—
81C8×D61—21no—
82C8×D61—21no—
83C8×D61—41no—
84C16×C61—41no—
85#11758185—41no—
86C22×D61—42no—
87C22×D61#10211yescharacteristic
88Q8×C61—82no—
89C2×C4×C61—42no—
90C2×C4×C61C2×C22⋊C411yescharacteristic
91C2×C4×C61C2×D811yescharacteristic
92C2×C4×C61C2×SD1611yescharacteristic
93C2×Dic61#10211yescharacteristic
94C2×Dic61#10211yescharacteristic
95C2×Dic61#10211yescharacteristic
96D244—42no—
97D244—42no—
98D244—82no—
99D244—84no—
100D244—81no—
101D244—81no—
102C4×D61—21no—
103C4×D61—21no—
104C4×D61—21no—
105C4×D61—21no—
106C4×D61—22no—
107C4×D61—84no—
108C8×C61—21no—
109C8×C61—81no—
110C8×C61AGL(1,ℤ/8)11yescharacteristic
111C8×C61#13711yescharacteristic
112#92418—21no—
113#92418—21no—
114#92418—81no—
115#11986—611nomaximal, Sylow
116C22×C61C2×#10211yescharacteristic
117C2×D61—21no—
118C2×D61—21no—
119C2×D61—21no—
120C2×D61—82no—
121C2×D61—82no—
122C2×D61—82no—
123C4×C61—21no—
124C4×C61—82no—
125C4×C61#41311yescharacteristic
126C4×C61#41711yescharacteristic
127C4×C61#50911yescharacteristic
128C4×C61#51011yescharacteristic
129Dic61—21no—
130Dic61—21no—
131Dic61#36112yes—
132#3169—611no—
133#2150—611no—
134#1567—611no—
135#1365—611no—
136#1365D6111yescharacteristic, complemented
137#1361—611no—
138#1361—611no—
139C2×C61#154711yescharacteristic
140C2×C61#213911yescharacteristic
141C2×C61C2×#36111yescharacteristic
142D61—41no—
143D61—162no—
144#532—1221no—
145C2×M32—1221no—
146#500C2×D6111yescharacteristic
147#493—611no—
148#486—1221no—
149#466—612no—
150#466—1221no—
151C4×D8—612no—
152C4×D8—1221no—
153#423—1221no—
154C2×C4×C8—611no—
155C4⋊C16—611no—
156C4⋊C16—1221no—
157C4⋊C16C2×D6111yescharacteristic
158#335—611no—
159#335—1221no—
160#335C2×D6111yescharacteristic
161C61#1198611yescharacteristic, complemented, Sylow
162C2×#41—2441no—
163C2×D8—612no—
164C2×D8—1221no—
165C2×M16—2441no—
166C22×C8—611no—
167C22×C8—611no—
168C4⋊Q8—21no—
169#127—1221no—
170#124—2441no—
171#121—1222no—
172#121—2441no—
173C4×D4—1222no—
174C4×D4—2441no—
175C2×C42—611no—
176M32—2442no—
177C2×C16—21no—
178C2×C16—1221no—
179#107—21no—
180#107C4×D6112yes—
181C4⋊C8—21no—
182C4⋊C8—1221no—
183C4⋊C8—2441no—
184#102—1222no—
185#102—1222no—
186C4×C8—611no—
187C4×C8—611no—
188C4×C8—611no—
189C4×C8C22×D6111yescharacteristic
190#41—4884no—
191C2×Q8—41no—
192C2×D4—1222no—
193C2×D4—2442no—
194C2×D4—2441no—
195C2×D4—2441no—
196C22×C4—611no—
197C22×C4—611no—
198C22×C4—611no—
199C22×C4—2442no—
200D8—2442no—
201D8—2441no—
202D8—2441no—
203M16—4882no—
204C2×C8—41no—
205C2×C8—611no—
206C2×C8—611no—
207C2×C8—1221no—
208C2×C8—1221no—
209C2×C8—2441no—
210C2×C8—2441no—
211C2×C8C2×C4×D6111yescharacteristic
212C2×C8D4×D6111yescharacteristic
213C4⋊C4—22no—
214C4⋊C4—41no—
215C22⋊C4—2442no—
216C22⋊C4—2442no—
217C42—611no—
218C42—611no—
219C42—611no—
220C42D4×D6111yescharacteristic
221C16—41no—
222C16—2441no—
223C23—611no—
224C23—2442no—
225Q8—82no—
226D4—4882no—
227D4—4884no—
228D4—4881no—
229D4—4881no—
230D4—2442no—
231D4—2442no—
232C2×C4—42no—
233C2×C4—611no—
234C2×C4—611no—
235C2×C4—611no—
236C2×C4—1222no—
237C2×C4—1221no—
238C2×C4—1221no—
239C2×C4—1221no—
240C2×C4—1221no—
241C2×C4—4884no—
242C2×C4C22⋊C4×D6111yescharacteristic
243C2×C4D8×D6111yescharacteristic
244C2×C4SD16×D6111yescharacteristic
245C8—21no—
246C8—81no—
247C8—1221no—
248C8—1221no—
249C8—4881no—
250C8#1451980411yescharacteristic
251C8#1451980911yescharacteristic
252C22—1221no—
253C22—1221no—
254C22—1221no—
255C22—4882no—
256C22—4882no—
257C22—4882no—
258C22#102×D6111yescharacteristic
259C4—21no—
260C4—82no—
261C4—612no—
262C4—1221no—
263C4—1221no—
264C4#1683974511yescharacteristic
265C4#1683976211yescharacteristic
266C4#1684019911yescharacteristic
267C4#1684020411yescharacteristic
268C2—9762no—
269C2—2441no—
270C2#2144449511yescharacteristic
271C2#2144753011yescharacteristic
272C2#361×D6111yescharacteristic
subgroupG/H
centerC22#102×D61
commutatorC2×C8×C61C22×C4
FrattiniC4×C8C22×D61
FittingC61×#1365C2
socleC22×C61C2×#102
prime radical#21456399C2
cosocleC4×C8×C61C23
hypercenter#1365D61
hypocenterC61#11986
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1365

Complements

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

NH ≅ G/Ntype
2. #21447573C2semidirect
3. #21444576C2semidirect
4. #21443877C2semidirect
5. #21443866C2semidirect
6. #21443864C2semidirect
7. C61×#1365C2semidirect
136. #1365D61semidirect
161. C61#11986semidirect

Maximal subgroups

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

subgroupindex
#214563992
#214475732
#214445762
#214438772
#214438662
#214438642
C61×#13652
#1198661