Finite Group Databasebeta

← #29591987

Subgroups — #29591987

Order 15616.

218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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#21447685C211yesmaximal, characteristic
2#21444734C211yesmaximal, characteristic
3#21444639C211yesmaximal, characteristic, complemented
4#21443885C211yesmaximal, characteristic, complemented
5#21443790C211yesmaximal, characteristic, complemented
6#21443787C211yesmaximal, characteristic
7C61×#1313C211yesmaximal, characteristic, complemented
8C2×#14519722C411yescharacteristic
9C8×Dic122—21no—
10C4×Dic244C2211yescharacteristic
11C4×D488C2211yescharacteristic
12#16839841—21no—
13#16839588C411yescharacteristic
14#16839567C411yescharacteristic
15#16839564C411yescharacteristic
16#16839513C2211yescharacteristic
17#16839513C2211yescharacteristic
18#16839494—21no—
19#16839491—21no—
20C61×#346C2211yescharacteristic
21C61×#346C2211yescharacteristic
22C61×#322C2211yescharacteristic
23C2×Dic244C2×C411yescharacteristic
24C2×D488C2×C411yescharacteristic
25C2×#11758189—41no—
26C4×Dic122—21no—
27C4×D244—21no—
28#14519722—22no—
29#14519711C2×C411yescharacteristic
30#14519711C2×C411yescharacteristic
31C4⋊#92418—21no—
32C4⋊#92418—21no—
33#14519706—41no—
34#14519702—21no—
35#14519699—21no—
36#14519689—41no—
37C8×Dic61—41no—
38C2×C16×C61—21no—
39C2×C16×C61C2×C411yescharacteristic
40C2×C16×C61C2×C411yescharacteristic
41C4×C8×C61D411yescharacteristic
42C4×C8×C61D411yescharacteristic
43C4×C8×C61C2311yescharacteristic
44C2×D244—21no—
45C2×C4×D61—41no—
46C2×Dic122—21no—
47C2×C8×C61—21no—
48C2×C8×C61—21no—
49C2×C8×C61C22×C411yescharacteristic
50C2×C8×C61#4111yescharacteristic
51C42×C61C2×D411yescharacteristic
52#11758198—41no—
53C4⋊Dic61—21no—
54C4⋊Dic61—21no—
55#11758196—41no—
56C4×Dic61—41no—
57C2×#92418—41no—
58C2×#92418—41no—
59Dic244—21no—
60Dic244M1612yescomplemented
61D488—21no—
62D488—21no—
63#11758189—82no—
64C16×C61—22no—
65C16×C61—21no—
66C16×C61—21no—
67C22×D61—41no—
68C2×C4×C61C4×D411yescharacteristic
69C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
70C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
71C2×Dic61—41no—
72C2×Dic61—41no—
73C2×Dic61—41no—
74D244—41no—
75D244—41no—
76C4×D61—81no—
77C4×D61—81no—
78Dic122—22no—
79Dic122—41no—
80C8×C61—21no—
81C8×C61—41no—
82C8×C61—41no—
83C8×C61C2×M1611yescharacteristic
84C8×C61#13111yescharacteristic
85#92418—81no—
86#92418—81no—
87#12080—611nomaximal, Sylow
88C22×C61#44211yescharacteristic
89C2×D61—81no—
90C2×D61—81no—
91C2×D61—81no—
92C4×C61—21no—
93C4×C61—21no—
94C4×C61#43511yescharacteristic
95C4×C61#44311yescharacteristic
96Dic61—42no—
97Dic61—81no—
98Dic61—81no—
99#2175—611no—
100#1594—611no—
101#1579—611no—
102#1368—611no—
103#1334—611no—
104#1333—611no—
105#1313D6111yescharacteristic, complemented
106C2×C61#158611yescharacteristic
107C2×C61#218011yescharacteristic
108C2×C61AGL(1,ℤ/16)11yescharacteristic
109D61—161no—
110C2×SD32—611no—
111C8×Q8—1221no—
112C4×Q16—611no—
113C4×D8—611no—
114#436—1221no—
115#366—611no—
116#358—611no—
117#357—611no—
118#346C2×D6111yescharacteristic
119#346C2×D6111yescharacteristic
120#334—611no—
121#334—611no—
122Q8⋊C8—1221no—
123D4⋊C8—1221no—
124#322C2×D6111yescharacteristic
125C61#1208011yescharacteristic, complemented, Sylow
126C2×Q16—611no—
127C2×D8—611no—
128C2×M16—2441no—
129C4×Q8—1221no—
130C4×D4—1221no—
131SD32—1222no—
132C2×C16—21no—
133C2×C16C4×D6111yescharacteristic
134C2×C16C4×D6111yescharacteristic
135#107—611no—
136#107—611no—
137C4⋊C8—1221no—
138C4⋊C8—1221no—
139C4⋊C8—2441no—
140#103—1221no—
141#102—1221no—
142C22⋊C8—2441no—
143C4×C8—2441no—
144C4×C8D24411yescharacteristic
145C4×C8D24411yescharacteristic
146C4×C8C22×D6111yescharacteristic
147C2×Q8—1221no—
148C2×D4—1221no—
149C22×C4—2441no—
150Q16—612no—
151Q16—1221no—
152D8—1221no—
153D8—1221no—
154M16—4882no—
155C2×C8—21no—
156C2×C8—21no—
157C2×C8—2441no—
158C2×C8—2441no—
159C2×C8C2×C4×D6111yescharacteristic
160C2×C8#1175822211yescharacteristic
161C4⋊C4—1221no—
162C4⋊C4—1221no—
163C4⋊C4—2441no—
164C22⋊C4—2441no—
165C42—2441no—
166C42C2×D24411yescharacteristic
167C16—22no—
168C16—21no—
169C16—21no—
170C23—2441no—
171Q8—1222no—
172Q8—2441no—
173D4—2441no—
174D4—2441no—
175C2×C4—4881no—
176C2×C4—4881no—
177C2×C4—2441no—
178C2×C4—2441no—
179C2×C4—2441no—
180C2×C4C4×D24411yescharacteristic
181C2×C4#1451980511yescharacteristic
182C2×C4#1451980511yescharacteristic
183C8—21no—
184C8—41no—
185C8—41no—
186C8—4881no—
187C8—4881no—
188C8M16×D6111yescharacteristic
189C8#1451978511yescharacteristic
190C22—4881no—
191C22—4881no—
192C22—4881no—
193C22#1683987511yescharacteristic
194C4—21no—
195C4—21no—
196C4—4881no—
197C4—4881no—
198C4—2442no—
199C4#1683983511yescharacteristic
200C4#1683988011yescharacteristic
201C2—9761no—
202C2#2144468511yescharacteristic
203C2#2144771211yescharacteristic
204C2#2144771911yescharacteristic
subgroupG/H
centerC22#16839875
commutatorC2×C8×C61C22×C4
FrattiniC4×C8C22×D61
FittingC61×#1313C2
socleC22×C61#442
prime radicalC2×D488C2×C4
cosocleC4×C8×C61C23
hypercenter#1313D61
hypocenterC61#12080
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #322 ◁ #1313

Complements

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

NH ≅ G/Ntype
3. #21444639C2semidirect
4. #21443885C2semidirect
5. #21443790C2semidirect
7. C61×#1313C2semidirect
60. Dic244M16semidirect
105. #1313D61semidirect
125. C61#12080semidirect

Maximal subgroups

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

subgroupindex
#214476852
#214447342
#214446392
#214438852
#214437902
#214437872
C61×#13132
#1208061