Finite Group Databasebeta

← #29589450

Subgroups — #29589450

Order 15616.

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

normal subgroups only

This group has 280 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#21454466C211yesmaximal, characteristic
2#21447628C212yesmaximal, complemented
3#21443771C212yesmaximal, complemented
4#21443757C211yesmaximal, characteristic
5C61×#1321C211yesmaximal, characteristic
6#41×Dic61C411yescharacteristic
7#16839820—22no—
8#16839816—22no—
9#16839790C2211yescharacteristic
10#16839788C411yescharacteristic
11#16839729C411yescharacteristic
12M16×Dic61C2211yescharacteristic
13C2×#14519687C411yescharacteristic
14#16839582—22no—
15#16839544C2212yes—
16#16839539—22no—
17C61×#408C2211yescharacteristic
18C61×#349C2212yes—
19C2×#11758194C2×C411yescharacteristic
20C22×#92418C2×C411yescharacteristic
21Q8×Dic61—21no—
22D4×Dic61—21no—
23D4×Dic61—22no—
24#14519736—21no—
25#14519736C2×C411yescharacteristic
26C2×C4×Dic61—21no—
27C2×C4×Dic61C2×C411yescharacteristic
28#14519717—22no—
29#14519706—22no—
30#14519706—22no—
31C22⋊#92418—22no—
32#14519687—21no—
33#14519687—21no—
34#14519687D412yes—
35C8×Dic61D412yes—
36C2×#41×C61C2×C411yescharacteristic
37C2×M16×C61C2311yescharacteristic
38C22×C8×C61C2×C411yescharacteristic
39M32×C61—22no—
40C22⋊C8×C61—22no—
41#41×C61—41no—
42#41×C61—41no—
43C2×Q8×C61M1611yescharacteristic
44C2×D4×C61—21no—
45C2×D4×C61M1611yescharacteristic
46C22×C4×C61—21no—
47C22×C4×C61C22×C411yescharacteristic
48C22×Dic61—22no—
49C22×Dic61—21no—
50M16×C61—41no—
51C2×C8×C61—21no—
52C2×C8×C61—41no—
53C2×C8×C61C2×D412yes—
54C22⋊Dic61—22no—
55C22⋊Dic61M1612yes—
56C4⋊Dic61—22no—
57C4⋊Dic61—21no—
58C4×Dic61—22no—
59C4×Dic61—21no—
60C4×Dic61—21no—
61C4×Dic61C22⋊C411yescharacteristic
62C4×Dic61C22⋊C411yescharacteristic
63#11758194—41no—
64C2×#92418—21no—
65C2×#92418—41no—
66C2×#92418C22⋊C412yes—
67C16×C61—42no—
68#11758185—42no—
69C23×C61—21no—
70C23×C61C2×M1611yescharacteristic
71Q8×C61—41no—
72D4×C61—41no—
73D4×C61—42no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—41no—
78C2×C4×C61—41no—
79C2×C4×C61C2×C22⋊C411yescharacteristic
80C2×C4×C61C2×M1611yescharacteristic
81C2×Dic61—21no—
82C2×Dic61—22no—
83C2×Dic61—21no—
84C2×Dic61—81no—
85C2×Dic61—82no—
86C8×C61—22no—
87C8×C61—41no—
88#92418—22no—
89#92418—41no—
90#11523—611nomaximal, Sylow
91C22×C61—21no—
92C22×C61—41no—
93C22×C61—42no—
94C22×C61—41no—
95C22×C61#40711yescharacteristic
96C4×C61—21no—
97C4×C61—41no—
98C4×C61#41011yescharacteristic
99C4×C61#41311yescharacteristic
100Dic61—42no—
101Dic61—41no—
102Dic61—41no—
103#2923—611no—
104#2165—612no—
105#1328—612no—
106#1321—611no—
107#1321D6111yescharacteristic
108C2×C61—21no—
109C2×C61—41no—
110C2×C61—81no—
111C2×C61#146411yescharacteristic
112C4×#41—611no—
113#433—1222no—
114#432—1222no—
115#424—611no—
116#424—611no—
117#408—611no—
118#408C2×D6111yescharacteristic
119C4×M16—611no—
120C2×#97—611no—
121#364—1222no—
122#349—612no—
123#349C2×D6112yes—
124#347—1222no—
125C61#1152311yescharacteristic, complemented, Sylow
126C2×#41C4×D6111yescharacteristic
127C2×M16—611no—
128C2×M16C22×D6111yescharacteristic
129C22×C8—611no—
130C22×C8C4×D6111yescharacteristic
131C4×Q8—1221no—
132C4×D4—1222no—
133C4×D4—1221no—
134#117—611no—
135#117—1221no—
136C2×C42—611no—
137C2×C42—1221no—
138M32—22no—
139M32—1222no—
140C4⋊C8—1222no—
141C4⋊C8—1222no—
142C22⋊C8—22no—
143C22⋊C8—1222no—
144#97—612no—
145#97—1221no—
146#97—1221no—
147C4×C8—612no—
148#41—41no—
149#41—41no—
150C2×Q8#1175818911yescharacteristic
151C2×D4—21no—
152C2×D4#1175818911yescharacteristic
153C22×C4—21no—
154C22×C4—1222no—
155C22×C4—1221no—
156C22×C4C2×C4×D6111yescharacteristic
157M16—41no—
158M16—2441no—
159C2×C8—21no—
160C2×C8—41no—
161C2×C8—612no—
162C2×C8—1221no—
163C2×C8—2441no—
164C2×C8D4×D6112yes—
165C4⋊C4—1222no—
166C4⋊C4—1221no—
167C22⋊C4—612no—
168C22⋊C4—1222no—
169C42—611no—
170C42—611no—
171C42—1222no—
172C42—1221no—
173C42—1221no—
174C16—42no—
175C16—2442no—
176C23—21no—
177C23M16×D6111yescharacteristic
178Q8—41no—
179D4—41no—
180D4—42no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—1221no—
187C2×C4—1221no—
188C2×C4—1222no—
189C2×C4—4881no—
190C2×C4—4882no—
191C2×C4C22⋊C4×D6111yescharacteristic
192C2×C4C2×#1175818911yescharacteristic
193C8—22no—
194C8—41no—
195C8—1222no—
196C8—2441no—
197C22—21no—
198C22—41no—
199C22—42no—
200C22—41no—
201C22#1683972411yescharacteristic
202C4—21no—
203C4—41no—
204C4—2441no—
205C4—2442no—
206C4—2441no—
207C4#1683973411yescharacteristic
208C4#1683974311yescharacteristic
209C2—21no—
210C2—41no—
211C2—81no—
212C2#2144415011yescharacteristic
subgroupG/H
centerC4#16839734
commutatorC22×C4×C61C22×C4
FrattiniC2×M16C22×D61
FittingC61×#1321C2
socleC2×C61#1464
prime radicalC2×#41×C61C2×C4
cosocleC2×M16×C61C23
hypercenter#1321D61
hypocenterC61#11523
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1321

Complements

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

NH ≅ G/Ntype
2. #21447628C2semidirect
3. #21443771C2semidirect
125. C61#11523semidirect

Maximal subgroups

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

subgroupindex
#214544662
#214476282
#214437712
#214437572
C61×#13212
#1152361