Finite Group Databasebeta

← #29594137

Subgroups — #29594137

Order 15616.

240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 71 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#21447962C211yesmaximal, characteristic, complemented
2#21447860C211yesmaximal, characteristic
3#21445411C211yesmaximal, characteristic
4C8×Dic244C211yesmaximal, characteristic, complemented
5#21443873C211yesmaximal, characteristic, complemented
6#21443866C211yesmaximal, characteristic
7C61×#1367C211yesmaximal, characteristic, complemented
8C2×#14519722—21no—
9#16840167C2211yescharacteristic
10#16840139C2211yescharacteristic
11#16840135—21no—
12#16840109—21no—
13C8×Dic122—21no—
14C4×Dic244C2211yescharacteristic
15#16839590—21no—
16#16839567—21no—
17#16839564—21no—
18#16839515C2211yescharacteristic
19#16839494—21no—
20C61×C4⋊C16C2211yescharacteristic
21C61×C4⋊C16C2211yescharacteristic
22C82×C61C2211yescharacteristic
23C2×Dic244D411yescharacteristic
24C2×#11758190—41no—
25C2×#11758190—41no—
26C2×D488—21no—
27C2×D488—21no—
28#14519777—21no—
29#14519774—21no—
30C4×Dic122—21no—
31#14519722—42no—
32#14519711—21no—
33#14519711—21no—
34#14519711D411yescharacteristic
35C4⋊#92418—21no—
36#14519706—41no—
37#14519702—21no—
38#14519699—42no—
39C8×Dic61—41no—
40C2×C16×C61—21no—
41C2×C16×C61—21no—
42C4×C8×C61D411yescharacteristic
43C4×C8×C61D411yescharacteristic
44C4×C8×C61C2311yescharacteristic
45C2×D244—41no—
46C2×D244—41no—
47C2×D244—41no—
48C2×Dic122—21no—
49C2×Dic122—41no—
50C2×C8×C61—21no—
51C2×C8×C61D811yescharacteristic
52C2×C8×C61D811yescharacteristic
53C2×C8×C61C2×D411yescharacteristic
54C2×C8×C61#4111yescharacteristic
55C42×C61C2×D411yescharacteristic
56C4⋊Dic61—21no—
57C4⋊Dic61—41no—
58C4⋊Dic61—41no—
59#11758196—41no—
60C4×Dic61—41no—
61C2×#92418—41no—
62Dic244—21no—
63Dic244SD1612yescomplemented
64D488—41no—
65D488—41no—
66D488—81no—
67#11758190—82no—
68#11758190—82no—
69C16×C61—41no—
70C16×C61—41no—
71C22×D61—81no—
72C2×C4×C61#12111yescharacteristic
73C2×C4×C61C2×D811yescharacteristic
74C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
75C2×Dic61—41no—
76C2×Dic61—41no—
77C2×Dic61—81no—
78D244—82no—
79D244—81no—
80D244—81no—
81D244—81no—
82D244—81no—
83Dic122—22no—
84Dic122—41no—
85Dic122—81no—
86Dic122—81no—
87C8×C61—21no—
88C8×C61—21no—
89C8×C61—41no—
90C8×C61SD3212yescomplemented
91C8×C61C2×SD1611yescharacteristic
92C8×C61#13511yescharacteristic
93#92418—81no—
94#12417—611nomaximal, Sylow
95C22×C61#45911yescharacteristic
96C2×D61—161no—
97C2×D61—161no—
98C2×D61—161no—
99C4×C61—21no—
100C4×C61#46511yescharacteristic
101C4×C61#47111yescharacteristic
102C4×C61C2×SD3211yescharacteristic
103C4×C61#50911yescharacteristic
104Dic61—42no—
105Dic61—81no—
106Dic61—161no—
107#2225—611no—
108#2207—611no—
109#1706—611no—
110C8×Q16—611no—
111#1367D6111yescharacteristic, complemented
112#1364—611no—
113#1361—611no—
114C2×C61#166511yescharacteristic
115C2×C61#220711yescharacteristic
116C2×C61#221211yescharacteristic
117D61—321no—
118C2×SD32—1221no—
119#500—611no—
120#493—611no—
121#492—1221no—
122#486—1221no—
123C8×Q8—1221no—
124C4×Q16—611no—
125#367—1221no—
126C4⋊C16C2×D6111yescharacteristic
127C4⋊C16C2×D6111yescharacteristic
128#358—1221no—
129#357—1221no—
130#335—611no—
131Q8⋊C8—1221no—
132C82C2×D6111yescharacteristic
133C61#1241711yescharacteristic, complemented, Sylow
134C2×Q16—611no—
135C2×SD16—2441no—
136C2×SD16—2441no—
137C2×D8—1221no—
138C2×D8—1221no—
139C4⋊Q8—1221no—
140#127—1221no—
141C4×Q8—1221no—
142SD32—2442no—
143C2×C16—21no—
144C2×C16—21no—
145#107—611no—
146#107—1221no—
147#107—1221no—
148C4⋊C8—1221no—
149C4⋊C8—2441no—
150#103—1221no—
151#102—2442no—
152C4×C8—2441no—
153C4×C8D24411yescharacteristic
154C4×C8D24411yescharacteristic
155C4×C8C22×D6111yescharacteristic
156C2×Q8—1221no—
157C2×Q8—2441no—
158C2×D4—2441no—
159C2×D4—2441no—
160C2×D4—2441no—
161Q16—612no—
162Q16—1221no—
163SD16—4882no—
164SD16—4882no—
165D8—4881no—
166D8—2441no—
167D8—2441no—
168C2×C8—21no—
169C2×C8—2441no—
170C2×C8D48811yescharacteristic
171C2×C8D48811yescharacteristic
172C2×C8D4×D6111yescharacteristic
173C2×C8#1175822611yescharacteristic
174C4⋊C4—1221no—
175C4⋊C4—2441no—
176C4⋊C4—2441no—
177C4⋊C4—2441no—
178C42—2441no—
179C42C2×D24411yescharacteristic
180C16—41no—
181C16—41no—
182C23—4881no—
183Q8—1222no—
184Q8—4881no—
185Q8—4881no—
186Q8—2441no—
187D4—4882no—
188D4—4881no—
189D4—4881no—
190D4—4881no—
191D4—4881no—
192C2×C4—4881no—
193C2×C4—2441no—
194C2×C4—2441no—
195C2×C4#1451975211yescharacteristic
196C2×C4C2×D48811yescharacteristic
197C2×C4#1451980511yescharacteristic
198C8—21no—
199C8—21no—
200C8—41no—
201C8—4881no—
202C8#1451972212yescomplemented
203C8SD16×D6111yescharacteristic
204C8#1451979811yescharacteristic
205C22—9761no—
206C22—9761no—
207C22—9761no—
208C22#1683995811yescharacteristic
209C4—21no—
210C4—9761no—
211C4—4881no—
212C4—2442no—
213C4#1683999211yescharacteristic
214C4#1684002611yescharacteristic
215C4C2×#1451972211yescharacteristic
216C4#1684020011yescharacteristic
217C2—19521no—
218C2#2144516111yescharacteristic
219C2#2144786011yescharacteristic
220C2#2144788911yescharacteristic
subgroupG/H
centerC22#16839958
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1367C2
socleC22×C61#459
prime radical#16840139C22
hypercenter#1367D61
hypocenterC61#12417
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. #21447962C2semidirect
4. C8×Dic244C2semidirect
5. #21443873C2semidirect
7. C61×#1367C2semidirect
63. Dic244SD16semidirect
90. C8×C61SD32semidirect
111. #1367D61semidirect
133. C61#12417semidirect
202. C8#14519722semidirect

Maximal subgroups

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

subgroupindex
#214479622
#214478602
#214454112
C8×Dic2442
#214438732
#214438662
C61×#13672
#1241761