Finite Group Databasebeta

← #29593876

Subgroups — #29593876

Order 15616.

344 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 67 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#21458793C211yesmaximal, characteristic
2#21448044C211yesmaximal, characteristic, complemented
3#21445210C211yesmaximal, characteristic, complemented
4#21443866C211yesmaximal, characteristic, complemented
5#21443797C211yesmaximal, characteristic, complemented
6#21443780C211yesmaximal, characteristic, complemented
7C61×#2224C211yesmaximal, characteristic, complemented
8#16840433—21no—
9#16840139C2211yescharacteristic
10#16840137—21no—
11#16839969—21no—
12#16839957—21no—
13#16839956—22no—
14C8×Dic122C2211yescharacteristic
15#16839844—21no—
16#16839562—22no—
17C4×#11758185C2211yescharacteristic
18#16839515C2211yescharacteristic
19#16839508—21no—
20C61×#500C2211yescharacteristic
21C4×D8×C61C2211yescharacteristic
22C61×#366—21no—
23C61×C4⋊C16C2211yescharacteristic
24C61×#357—21no—
25C2×#11758222—41no—
26C2×#11758202—41no—
27C2×D488—21no—
28C2×D488D412yes—
29C2×#11758199—22no—
30#14519774—21no—
31#14519773—22no—
32#14519751—41no—
33#14519750—42no—
34C4×Dic122D411yescharacteristic
35#14519739—22no—
36C2×#11758185—21no—
37C4⋊#92418—21no—
38C4⋊#92418D411yescharacteristic
39#14519706—21no—
40#14519701—41no—
41#14519697—22no—
42C8×Dic61—21no—
43C2×D8×C61D411yescharacteristic
44C4⋊Q8×C61—21no—
45C4×D4×C61—21no—
46C2×C16×C61—21no—
47#107×C61—21no—
48#107×C61—21no—
49#107×C61D411yescharacteristic
50#102×C61—21no—
51C4×C8×C61C2311yescharacteristic
52C2×Q8×C61—41no—
53C2×D4×C61—21no—
54C22×C4×C61—41no—
55C2×C22⋊D61—42no—
56C2×C22⋊D61—42no—
57#11758222—82no—
58#11758222—82no—
59C2×D244—22no—
60C2×D244—41no—
61C2×D244—41no—
62C2×C4×D61—42no—
63C2×Dic122D811yescharacteristic
64D8×C61—21no—
65D8×C61—21no—
66C2×C8×C61C2×D411yescharacteristic
67C2×C8×C61C2×D411yescharacteristic
68C4⋊C4×C61—21no—
69C4⋊C4×C61—41no—
70C4⋊C4×C61—41no—
71C22⋊C4×C61—41no—
72C42×C61C2×D411yescharacteristic
73#11758202—82no—
74#11758199—82no—
75#11758198—42no—
76C4⋊Dic61D811yescharacteristic
77#11758196—21no—
78C4×Dic61—21no—
79C2×#92418—21no—
80C2×#92418—41no—
81D488—42no—
82D488—41no—
83D488—41no—
84C16×C61—41no—
85#11758185—41no—
86C23×C61—41no—
87C22×D61—42no—
88Q8×C61—81no—
89Q8×C61—81no—
90D4×C61—41no—
91D4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—81no—
94C2×C4×C61—81no—
95C2×C4×C61—81no—
96C2×C4×C61#12011yescharacteristic
97C2×C4×C61C2×D811yescharacteristic
98C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
99C22⋊D61—84no—
100C22⋊D61—162no—
101C2×Dic61—21no—
102C2×Dic61—21no—
103D244—42no—
104D244—42no—
105D244—81no—
106D244—81no—
107D244—161no—
108C4×D61—84no—
109Dic122—21no—
110Dic122D1612yes—
111C8×C61—21no—
112C8×C61#13511yescharacteristic
113C8×C61#13711yescharacteristic
114#92418—41no—
115#92418—81no—
116#12380—611nomaximal, Sylow
117C22×C61—81no—
118C22×C61—81no—
119C22×C61—81no—
120C22×C61#44711yescharacteristic
121C2×D61—82no—
122C2×D61—82no—
123C2×D61—82no—
124C4×C61—21no—
125C4×C61—81no—
126C4×C61—161no—
127C4×C61#45211yescharacteristic
128C4×C61#45511yescharacteristic
129C4×C61C2×D1611yescharacteristic
130C4×C61#50911yescharacteristic
131Dic61—22no—
132Dic61—41no—
133#3391—611no—
134#2240—611no—
135#2224D6111yescharacteristic, complemented
136#1674—611no—
137#1361—611no—
138Q8⋊C16—611no—
139#1331—611no—
140C2×C61—161no—
141C2×C61#164111yescharacteristic
142C2×C61#218411yescharacteristic
143C2×C61#219411yescharacteristic
144D61—162no—
145#550—1221no—
146#500C2×D6111yescharacteristic
147#493—611no—
148#493—1221no—
149#462—1221no—
150#459—1222no—
151#459—1221no—
152C8×Q8—611no—
153C4×D8—1221no—
154C4×D8C2×D6111yescharacteristic
155#366—21no—
156C4⋊C16C2×D6111yescharacteristic
157#357—21no—
158#357—1222no—
159C4×C16—611no—
160#335—611no—
161#332—1221no—
162C61#1238011yescharacteristic, complemented, Sylow
163C2×#41—2441no—
164C2×Q16—2441no—
165C2×D8—612no—
166C2×D8—1222no—
167C2×D8—1221no—
168C2×D8C22⋊D6111yescharacteristic
169C4⋊Q8—21no—
170#127—1222no—
171#127—1221no—
172#121—2442no—
173#121—2441no—
174C4×Q8—611no—
175C4×D4—21no—
176C4×D4—1222no—
177C2×C16—21no—
178C2×C16—1221no—
179#107—21no—
180#107—21no—
181#107C22⋊D6111yescharacteristic
182C4⋊C8—611no—
183C4⋊C8—1221no—
184C4⋊C8—1221no—
185#103—2441no—
186#102—21no—
187#102—1222no—
188C4×C8—1221no—
189C4×C8C22×D6111yescharacteristic
190#41—4882no—
191#41—4882no—
192C2×Q8—41no—
193C2×Q8—611no—
194C2×D4—21no—
195C2×D4—1222no—
196C2×D4—2442no—
197C2×D4—2442no—
198C2×D4—2441no—
199C2×D4—2441no—
200C22×C4—41no—
201C22×C4—2442no—
202Q16—4882no—
203D8—21no—
204D8—21no—
205D8—4882no—
206D8—2442no—
207D8—2441no—
208D8—2441no—
209C2×C8—1221no—
210C2×C8—2441no—
211C2×C8D4×D6111yescharacteristic
212C2×C8C2×C22⋊D6111yescharacteristic
213C4⋊C4—21no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—611no—
217C4⋊C4—1221no—
218C22⋊C4—41no—
219C22⋊C4—2442no—
220C42—1221no—
221C42D4×D6111yescharacteristic
222C16—41no—
223C16—2441no—
224C23—41no—
225C23—2442no—
226Q8—81no—
227Q8—81no—
228Q8—612no—
229Q8—1221no—
230D4—41no—
231D4—41no—
232D4—9761no—
233D4—9762no—
234D4—4884no—
235D4—4881no—
236D4—4881no—
237D4—2442no—
238D4—2442no—
239C2×C4—41no—
240C2×C4—81no—
241C2×C4—81no—
242C2×C4—81no—
243C2×C4—1221no—
244C2×C4—1221no—
245C2×C4—4884no—
246C2×C4#1451974511yescharacteristic
247C2×C4D8×D6111yescharacteristic
248C2×C4#1451980111yescharacteristic
249C8—21no—
250C8—4881no—
251C8—2441no—
252C8#1451979711yescharacteristic
253C8#1451980811yescharacteristic
254C22—81no—
255C22—81no—
256C22—81no—
257C22—4882no—
258C22—4882no—
259C22—4882no—
260C22#1683989411yescharacteristic
261C4—21no—
262C4—81no—
263C4—161no—
264C4—1222no—
265C4—2441no—
266C4#1683992211yescharacteristic
267C4#1683993811yescharacteristic
268C4D16×D6111yescharacteristic
269C4#1684019611yescharacteristic
270C2—161no—
271C2—9762no—
272C2#2144501111yescharacteristic
273C2#2144772911yescharacteristic
274C2#2144778711yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2224C2
socleC22×C61#447
prime radical#21458793C2
hypercenter#2224D61
hypocenterC61#12380
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2224

Complements

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

NH ≅ G/Ntype
2. #21448044C2semidirect
3. #21445210C2semidirect
4. #21443866C2semidirect
5. #21443797C2semidirect
6. #21443780C2semidirect
7. C61×#2224C2semidirect
135. #2224D61semidirect
162. C61#12380semidirect

Maximal subgroups

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

subgroupindex
#214587932
#214480442
#214452102
#214438662
#214437972
#214437802
C61×#22242
#1238061