Finite Group Databasebeta

← #29594139

Subgroups — #29594139

Order 15616.

240 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 65 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#21447958C211yesmaximal, characteristic, complemented
2#21447860C211yesmaximal, characteristic
3#21445412C211yesmaximal, characteristic
4#21444625C211yesmaximal, characteristic, complemented
5#21443882C211yesmaximal, characteristic, complemented
6#21443864C211yesmaximal, characteristic
7C61×#1364C211yesmaximal, characteristic, complemented
8C2×#14519722—21no—
9#16840139C2211yescharacteristic
10#16840136—21no—
11#16840110—21no—
12#16839886—21no—
13C4×Dic244C2211yescharacteristic
14#16839589—21no—
15C4⋊#11758185C2211yescharacteristic
16#16839565—21no—
17#16839564—21no—
18#16839492—21no—
19C8×#92418C2211yescharacteristic
20C61×#500C2211yescharacteristic
21C61×C4⋊C16C2211yescharacteristic
22C61×#335C2211yescharacteristic
23C2×Dic244D411yescharacteristic
24C2×#11758201—41no—
25C2×#11758201—41no—
26C2×D488—21no—
27C2×D488—21no—
28#14519774—21no—
29C4×Dic122—21no—
30#14519722—42no—
31C2×#11758185—21no—
32#14519711D411yescharacteristic
33#14519706—41no—
34#14519702—21no—
35#14519697—42no—
36C4×#92418D411yescharacteristic
37C4×#92418D411yescharacteristic
38C8×Dic61—41no—
39C4⋊Q8×C61—21no—
40C2×C16×C61—21no—
41#107×C61—21no—
42#107×C61—21no—
43C4⋊C8×C61—21no—
44C4×C8×C61C2311yescharacteristic
45C2×Q8×C61—41no—
46C2×D244—41no—
47C2×D244—41no—
48C2×D244—41no—
49C2×Dic122—21no—
50C2×C8×C61—41no—
51C2×C8×C61C2×D411yescharacteristic
52C2×C8×C61#4111yescharacteristic
53C4⋊C4×C61—41no—
54C4⋊C4×C61—41no—
55C42×C61C2×D411yescharacteristic
56#11758201—82no—
57#11758201—82no—
58C4⋊Dic61—21no—
59#11758196—41no—
60C4×Dic61—41no—
61C2×#92418—21no—
62C2×#92418D811yescharacteristic
63C2×#92418D811yescharacteristic
64Dic244—21no—
65Dic244SD1612yescomplemented
66D488—41no—
67D488—41no—
68D488—81no—
69C16×C61—41no—
70#11758185—41no—
71C22×D61—81no—
72Q8×C61—81no—
73Q8×C61—81no—
74C2×C4×C61—81no—
75C2×C4×C61#12111yescharacteristic
76C2×C4×C61C2×D811yescharacteristic
77C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
78C2×Dic61—41no—
79C2×Dic61—41no—
80D244—82no—
81D244—81no—
82D244—81no—
83D244—81no—
84D244—81no—
85Dic122—22no—
86Dic122—41no—
87C8×C61—21no—
88C8×C61—81no—
89C8×C61C2×SD1611yescharacteristic
90C8×C61#13511yescharacteristic
91#92418—21no—
92#92418—41no—
93#92418SD3212yescomplemented
94#12417—611nomaximal, Sylow
95C22×C61#45911yescharacteristic
96C2×D61—161no—
97C2×D61—161no—
98C2×D61—161no—
99C4×C61—21no—
100C4×C61—161no—
101C4×C61#46511yescharacteristic
102C4×C61#47111yescharacteristic
103C4×C61C2×SD3211yescharacteristic
104C4×C61#50911yescharacteristic
105Dic61—42no—
106Dic61—81no—
107#2225—611no—
108#2207—611no—
109#1706—611no—
110C8×Q16—611no—
111#1367—611no—
112#1364D6111yescharacteristic, complemented
113#1361—611no—
114C2×C61#166511yescharacteristic
115C2×C61#220711yescharacteristic
116C2×C61#221211yescharacteristic
117D61—321no—
118C2×SD32—1221no—
119#500C2×D6111yescharacteristic
120#493—611no—
121#492—1221no—
122#486—1221no—
123C8×Q8—1221no—
124C4×Q16—611no—
125#367—1221no—
126C4⋊C16—611no—
127C4⋊C16C2×D6111yescharacteristic
128#358—1221no—
129#357—1221no—
130#335C2×D6111yescharacteristic
131Q8⋊C8—1221no—
132C82—611no—
133C61#1241711yescharacteristic, complemented, Sylow
134C2×Q16—611no—
135C2×SD16—2441no—
136C2×SD16—2441no—
137C2×D8—1221no—
138C2×D8—1221no—
139C4⋊Q8—21no—
140#127—1221no—
141C4×Q8—1221no—
142SD32—2442no—
143C2×C16—21no—
144C2×C16—1221no—
145#107—21no—
146#107—21no—
147#107—611no—
148C4⋊C8—21no—
149C4⋊C8—2441no—
150#103—1221no—
151#102—2442no—
152C4×C8—611no—
153C4×C8—611no—
154C4×C8—2441no—
155C4×C8C22×D6111yescharacteristic
156C2×Q8—41no—
157C2×Q8—1221no—
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—41no—
169C2×C8—611no—
170C2×C8—611no—
171C2×C8—1221no—
172C2×C8#1175822211yescharacteristic
173C2×C8D4×D6111yescharacteristic
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—1221no—
177C4⋊C4—2441no—
178C42—2441no—
179C42D4×D6111yescharacteristic
180C16—41no—
181C16—2441no—
182C23—4881no—
183Q8—81no—
184Q8—81no—
185Q8—1222no—
186Q8—2441no—
187D4—4882no—
188D4—4881no—
189D4—4881no—
190D4—4881no—
191D4—4881no—
192C2×C4—81no—
193C2×C4—2441no—
194C2×C4—2441no—
195C2×C4#1451975011yescharacteristic
196C2×C4D8×D6111yescharacteristic
197C2×C4#1451980411yescharacteristic
198C8—21no—
199C8—81no—
200C8—612no—
201C8—1221no—
202C8—2441no—
203C8SD16×D6111yescharacteristic
204C8#1451980011yescharacteristic
205C22—9761no—
206C22—9761no—
207C22—9761no—
208C22#1683995611yescharacteristic
209C4—21no—
210C4—161no—
211C4—4881no—
212C4—2442no—
213C4#1683999411yescharacteristic
214C4#1684002811yescharacteristic
215C4SD32×D6111yescharacteristic
216C4#1684019611yescharacteristic
217C2—19521no—
218C2#2144516311yescharacteristic
219C2#2144785811yescharacteristic
220C2#2144789111yescharacteristic
subgroupG/H
centerC22#16839956
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1364C2
socleC22×C61#459
prime radical#16840139C22
hypercenter#1364D61
hypocenterC61#12417
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1364

Complements

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

NH ≅ G/Ntype
1. #21447958C2semidirect
4. #21444625C2semidirect
5. #21443882C2semidirect
7. C61×#1364C2semidirect
65. Dic244SD16semidirect
93. #92418SD32semidirect
112. #1364D61semidirect
133. C61#12417semidirect

Maximal subgroups

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

subgroupindex
#214479582
#214478602
#214454122
#214446252
#214438822
#214438642
C61×#13642
#1241761