Finite Group Databasebeta

← #29594144

Subgroups — #29594144

Order 15616.

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

normal subgroups only

This group has 256 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#21447967C211yesmaximal, characteristic, complemented
2#21447855C211yesmaximal, characteristic
3#21445411C211yesmaximal, characteristic, complemented
4C8×D488C211yesmaximal, characteristic, complemented
5#21443876C211yesmaximal, characteristic, complemented
6#21443866C211yesmaximal, characteristic, complemented
7C61×#1367C211yesmaximal, characteristic, complemented
8C2×D976—21no—
9#16840167C2211yescharacteristic
10#16840139C2211yescharacteristic
11#16840135—21no—
12#16840109—21no—
13C4×D488C2211yescharacteristic
14C8×D244—21no—
15#16839590—21no—
16#16839564—21no—
17#16839564—21no—
18#16839515C2211yescharacteristic
19#16839491—21no—
20C61×C4⋊C16C2211yescharacteristic
21C61×C4⋊C16C2211yescharacteristic
22C82×C61C2211yescharacteristic
23C2×#11758190—42no—
24C2×D488—21no—
25C2×D488—21no—
26C2×D488D411yescharacteristic
27C2×C8×D61—41no—
28#14519777—21no—
29#14519774—21no—
30C4×D244—21no—
31D976—42no—
32#14519711—21no—
33#14519711—21no—
34#14519711D411yescharacteristic
35C4⋊#92418—21no—
36#14519699—21no—
37#14519699—41no—
38#14519699—41no—
39#14519689—41no—
40C2×C16×C61—21no—
41C2×C16×C61—21no—
42C4×C8×C61D411yescharacteristic
43C4×C8×C61D411yescharacteristic
44C4×C8×C61C2311yescharacteristic
45C2×D244—21no—
46C2×D244—41no—
47C2×D244—41no—
48C2×D244—41no—
49C2×C4×D61—41no—
50C2×Dic122—41no—
51C2×C8×C61—21no—
52C2×C8×C61D811yescharacteristic
53C2×C8×C61D811yescharacteristic
54C2×C8×C61C2×D411yescharacteristic
55C2×C8×C61#4111yescharacteristic
56C42×C61C2×D411yescharacteristic
57#11758198—41no—
58C4⋊Dic61—21no—
59C4⋊Dic61—41no—
60C4⋊Dic61—41no—
61C2×#92418—41no—
62D488—21no—
63D488—41no—
64D488—41no—
65D488—81no—
66D488SD1612yescomplemented
67#11758190—84no—
68C8×D61—82no—
69C16×C61—41no—
70C16×C61—41no—
71C22×D61—41no—
72C22×D61—81no—
73C2×C4×C61#12111yescharacteristic
74C2×C4×C61C2×D811yescharacteristic
75C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
76C2×Dic61—41no—
77C2×Dic61—81no—
78D244—22no—
79D244—41no—
80D244—82no—
81D244—81no—
82D244—81no—
83D244—81no—
84D244—81no—
85C4×D61—81no—
86C4×D61—81no—
87Dic122—82no—
88C8×C61—22no—
89C8×C61—21no—
90C8×C61—21no—
91C8×C61—21no—
92C8×C61C2×SD1611yescharacteristic
93C8×C61#13511yescharacteristic
94#92418—81no—
95#12418—611nomaximal, Sylow
96C22×C61#45911yescharacteristic
97C2×D61—42no—
98C2×D61—81no—
99C2×D61—81no—
100C2×D61—161no—
101C2×D61—161no—
102C2×D61—161no—
103C4×C61—21no—
104C4×C61#46511yescharacteristic
105C4×C61#47111yescharacteristic
106C4×C61#50811yescharacteristic
107C4×C61#50911yescharacteristic
108Dic61—81no—
109Dic61—161no—
110#2226—611no—
111#2206—611no—
112#1706—611no—
113C8×D8—611no—
114#1367D6111yescharacteristic, complemented
115#1365—611no—
116#1361—611no—
117C2×C61#166511yescharacteristic
118C2×C61#221011yescharacteristic
119C2×C61#221311yescharacteristic
120D61—82no—
121D61—321no—
122C2×D16—1221no—
123#500—611no—
124#493—611no—
125#492—1221no—
126#486—1221no—
127C4×D8—611no—
128C8×D4—1221no—
129#367—1221no—
130C4⋊C16C2×D6111yescharacteristic
131C4⋊C16C2×D6111yescharacteristic
132#357—1221no—
133#357—1221no—
134#335—611no—
135D4⋊C8—1221no—
136C82C2×D6111yescharacteristic
137C61#1241811yescharacteristic, complemented, Sylow
138C2×SD16—2442no—
139C2×D8—611no—
140C2×D8—1221no—
141C2×D8—1221no—
142C22×C8—2441no—
143C4⋊Q8—1221no—
144#127—1221no—
145C4×D4—1221no—
146D16—2442no—
147C2×C16—21no—
148C2×C16—21no—
149#107—611no—
150#107—1221no—
151#107—1221no—
152C4⋊C8—1221no—
153#102—1221no—
154#102—2441no—
155#102—2441no—
156C22⋊C8—2441no—
157C4×C8D24411yescharacteristic
158C4×C8D24411yescharacteristic
159C4×C8C22×D6111yescharacteristic
160C2×Q8—2441no—
161C2×D4—1221no—
162C2×D4—2441no—
163C2×D4—2441no—
164C2×D4—2441no—
165C22×C4—2441no—
166SD16—4884no—
167D8—612no—
168D8—1221no—
169D8—4881no—
170D8—2441no—
171D8—2441no—
172C2×C8—21no—
173C2×C8—4882no—
174C2×C8—2441no—
175C2×C8D48811yescharacteristic
176C2×C8D48811yescharacteristic
177C2×C8D4×D6111yescharacteristic
178C2×C8#1175822611yescharacteristic
179C4⋊C4—1221no—
180C4⋊C4—2441no—
181C4⋊C4—2441no—
182C22⋊C4—2441no—
183C42C2×D24411yescharacteristic
184C16—41no—
185C16—41no—
186C23—4881no—
187C23—2441no—
188Q8—4882no—
189D4—1222no—
190D4—4882no—
191D4—4881no—
192D4—4881no—
193D4—4881no—
194D4—4881no—
195D4—2441no—
196C2×C4—4881no—
197C2×C4—4881no—
198C2×C4—4881no—
199C2×C4—2441no—
200C2×C4#1451975211yescharacteristic
201C2×C4C2×D48811yescharacteristic
202C2×C4#1451980511yescharacteristic
203C8—22no—
204C8—21no—
205C8—21no—
206C8—21no—
207C8—4881no—
208C8SD16×D6111yescharacteristic
209C8#1451979811yescharacteristic
210C22—9761no—
211C22—9761no—
212C22—9761no—
213C22—4881no—
214C22—4881no—
215C22—2442no—
216C22#1683995811yescharacteristic
217C4—21no—
218C4—9761no—
219C4—4881no—
220C4#1683999211yescharacteristic
221C4#1684002611yescharacteristic
222C4#1684019411yescharacteristic
223C4#1684020011yescharacteristic
224C2—19521no—
225C2—4882no—
226C2#2144516111yescharacteristic
227C2#2144787511yescharacteristic
228C2#2144789611yescharacteristic
subgroupG/H
centerC22#16839958
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1367C2
socleC22×C61#459
prime radical#21447855C2
hypercenter#1367D61
hypocenterC61#12418
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C82 ◁ #1367

Complements

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

NH ≅ G/Ntype
1. #21447967C2semidirect
3. #21445411C2semidirect
4. C8×D488C2semidirect
5. #21443876C2semidirect
6. #21443866C2semidirect
7. C61×#1367C2semidirect
66. D488SD16semidirect
114. #1367D61semidirect
137. C61#12418semidirect

Maximal subgroups

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

subgroupindex
#214479672
#214478552
#214454112
C8×D4882
#214438762
#214438662
C61×#13672
#1241861