Finite Group Databasebeta

← #29599103

Subgroups — #29599103

Order 15616.

370 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 97 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#21456343C211yesmaximal, characteristic
2#21447540C212yesmaximal
3#21446690C211yesmaximal, characteristic
4#21443925C212yesmaximal
5C61×#1377C211yesmaximal, characteristic
6C22×Dic244C2211yescharacteristic
7#16840319—21no—
8#16840171—24no—
9#16839800—21no—
10#16839800C2212yes—
11C2×#14519709C2211yescharacteristic
12C2×#14519702—21no—
13#16839668—21no—
14#16839567—24no—
15C2×M32×C61C2212yes—
16C2×#97×C61C2211yescharacteristic
17C22×Dic122—21no—
18C2×Dic244—22no—
19C2×Dic244—22no—
20C2×Dic244—21no—
21C2×Dic244Q812yescomplemented
22#14519777—22no—
23#14519769—22no—
24#14519756—42no—
25C4×Dic122—42no—
26#14519736—22no—
27C2×C4⋊Dic61—21no—
28#14519711—22no—
29#14519711D414yes—
30#14519709—22no—
31#14519709—22no—
32#14519709—22no—
33#14519702—42no—
34#14519684—42no—
35C22×C8×C61D411yescharacteristic
36C22×C8×C61C2311yescharacteristic
37C2×C42×C61D411yescharacteristic
38M32×C61—22no—
39M32×C61—22no—
40C2×C16×C61—22no—
41#97×C61—22no—
42C22×C4×C61D812yes—
43C22×C4×C61C2×D411yescharacteristic
44C22×Dic61—41no—
45C22×Dic61—41no—
46C2×Dic122—22no—
47C2×Dic122—41no—
48C2×Dic122—41no—
49C2×Dic122—41no—
50C2×Dic122—41no—
51C2×Dic122—42no—
52C2×Dic122—41no—
53C2×C8×C61—21no—
54C2×C8×C61—21no—
55C2×C8×C61SD1612yes—
56C2×C8×C61C2×D412yes—
57C2×C8×C61C2×Q811yescharacteristic
58C2×C8×C61#4112yes—
59C2×C8×C61#4111yescharacteristic
60C42×C61—21no—
61C42×C61—21no—
62C22⋊Dic61—42no—
63C4⋊Dic61—24no—
64C4⋊Dic61—42no—
65C4⋊Dic61—41no—
66C4⋊Dic61—41no—
67#11758196—44no—
68C4×Dic61—42no—
69Dic244—24no—
70Dic244—42no—
71C16×C61—42no—
72C23×C61C2×D811yescharacteristic
73C2×C4×C61—22no—
74C2×C4×C61—42no—
75C2×C4×C61#12011yescharacteristic
76C2×C4×C61C22⋊Q811yescharacteristic
77C2×C4×C61#12411yescharacteristic
78C2×C4×C61C2×SD1611yescharacteristic
79C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
80C2×C4×C61#13711yescharacteristic
81C2×Dic61—44no—
82C2×Dic61—42no—
83C2×Dic61—81no—
84C2×Dic61—81no—
85C2×Dic61—82no—
86C2×Dic61—81no—
87Dic122—42no—
88Dic122—42no—
89Dic122—84no—
90Dic122—81no—
91Dic122—81no—
92C8×C61—22no—
93C8×C61C22⋊Q812yes—
94C8×C61#12412yes—
95#13368—611nomaximal, Sylow
96C22×C61—22no—
97C22×C61#44711yescharacteristic
98C22×C61#47411yescharacteristic
99C22×C61#48611yescharacteristic
100C4×C61—42no—
101C4×C61#39311yescharacteristic
102C4×C61#44811yescharacteristic
103C4×C61#47611yescharacteristic
104C4×C61#48911yescharacteristic
105Dic61—84no—
106Dic61—82no—
107Dic61—161no—
108#3162—611no—
109#2141—612no—
110#1971—611no—
111#1386—612no—
112#1377D6111yescharacteristic
113C2×C61—21no—
114C2×C61—21no—
115C2×C61#202311yescharacteristic
116C2×C61#219112yes—
117C22×Q16—611no—
118#533—1221no—
119C2×M32C2×D6112yes—
120#501—1224no—
121#427—612no—
122#427—1221no—
123C2×#106—611no—
124C2×#103—1221no—
125C2×#97C2×D6111yescharacteristic
126#391—1221no—
127#358—1224no—
128C61#1336811yescharacteristic, complemented, Sylow
129C22×Q8—1221no—
130C2×Q16—612no—
131C2×Q16—1222no—
132C2×Q16—1222no—
133C2×Q16—1221no—
134C22×C8D24411yescharacteristic
135C22×C8C22×D6111yescharacteristic
136C4⋊Q8—1222no—
137#125—1222no—
138C22⋊Q8—2442no—
139C4×Q8—2442no—
140#117—1222no—
141C2×C4⋊C4—1221no—
142C2×C42D24411yescharacteristic
143M32—22no—
144M32—22no—
145C2×C16—22no—
146#107—614no—
147#107—1222no—
148#106—1222no—
149#106—1222no—
150#106—1222no—
151#103—2442no—
152#97—22no—
153#95—2442no—
154C2×Q8—1222no—
155C2×Q8—2442no—
156C2×Q8—2441no—
157C2×Q8—2441no—
158C2×Q8—2441no—
159C2×Q8—2441no—
160C2×Q8—2441no—
161C22×C4—2441no—
162C22×C4—2441no—
163C22×C4D48812yes—
164C22×C4C2×D24411yescharacteristic
165Q16—1224no—
166Q16—2442no—
167C2×C8—21no—
168C2×C8—21no—
169C2×C8#1175819012yes—
170C2×C8#1175822212yes—
171C2×C8D4×D6112yes—
172C2×C8#1175822411yescharacteristic
173C2×C8Q8×D6111yescharacteristic
174C4⋊C4—1224no—
175C4⋊C4—2444no—
176C4⋊C4—2442no—
177C4⋊C4—2441no—
178C4⋊C4—2441no—
179C22⋊C4—2442no—
180C42—21no—
181C42—21no—
182C42—2442no—
183C16—42no—
184C23C2×D48811yescharacteristic
185Q8—4884no—
186Q8—4881no—
187Q8—4881no—
188Q8—2442no—
189Q8—2442no—
190C2×C4—22no—
191C2×C4—42no—
192C2×C4—4882no—
193C2×C4—4881no—
194C2×C4—4881no—
195C2×C4—4881no—
196C2×C4—2442no—
197C2×C4—2444no—
198C2×C4#1451974711yescharacteristic
199C2×C4#1451975711yescharacteristic
200C2×C4#1451976511yescharacteristic
201C2×C4C2×#1175819011yescharacteristic
202C2×C4#1451980511yescharacteristic
203C2×C4#1451981011yescharacteristic
204C8—22no—
205C8#1451975512yes—
206C8#1451976312yes—
207C22—22no—
208C22#1683989811yescharacteristic
209C22#1684004311yescharacteristic
210C22#1684010911yescharacteristic
211C4—42no—
212C4—9761no—
213C4—4882no—
214C4—4884no—
215C4#1683967511yescharacteristic
216C4#1683990311yescharacteristic
217C4#1684005311yescharacteristic
218C4#1684012211yescharacteristic
219C2—21no—
220C2—21no—
221C2#2144695611yescharacteristic
222C2#2144777212yes—
subgroupG/H
centerC22#16839898
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#1377C2
socleC22×C61#447
prime radicalC23×C61C2×D8
hypercenter#1377D61
hypocenterC61#13368
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ #1377

Complements

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

NH ≅ G/Ntype
21. C2×Dic244Q8semidirect
128. C61#13368semidirect

Maximal subgroups

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

subgroupindex
#214563432
#214475402
#214466902
#214439252
C61×#13772
#1336861