Finite Group Databasebeta

← #29583507

Subgroups — #29583507

Order 15616.

386 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 91 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#21453887C211yesmaximal, characteristic
2#21446787C212yesmaximal
3C2×#16839503C212yesmaximal
4#21443700C211yesmaximal, characteristic
5C61×#1836C211yesmaximal, characteristic
6C2×#14519769C2212yes—
7C2×#14519688C2212yes—
8#16839702—22no—
9#16839694—22no—
10#16839692—22no—
11#16839524—22no—
12#16839524—22no—
13#16839503—24no—
14C2×#97×C61C2211yescharacteristic
15C61×#384C2211yescharacteristic
16C61×#382C2211yescharacteristic
17C61×#340—22no—
18C22×#92418—22no—
19#14519769—22no—
20#14519769—22no—
21#14519769—22no—
22#14519769—22no—
23C2×C4⋊Dic61—22no—
24C2×C4⋊Dic61D412yes—
25C2×C4⋊Dic61D412yes—
26C2×#11758196—22no—
27C2×#11758196—22no—
28#14519688—22no—
29#14519688—22no—
30#14519684—24no—
31#14519684—22no—
32C22×C8×C61—21no—
33C2×C4⋊C4×C61—21no—
34C2×C4⋊C4×C61—22no—
35C2×C4⋊C4×C61D412yes—
36C2×C42×C61C2311yescharacteristic
37#97×C61—21no—
38#97×C61D412yes—
39#95×C61—22no—
40C22×C4×C61—22no—
41C22×C4×C61—41no—
42C22×C4×C61C2×D412yes—
43C22×C4×C61C2×D411yescharacteristic
44C22×Dic61—22no—
45C22×Dic61—22no—
46C2×C8×C61—22no—
47C2×C8×C61—41no—
48C2×C8×C61—41no—
49C4⋊C4×C61—42no—
50C4⋊C4×C61—44no—
51C4⋊C4×C61—42no—
52C42×C61C2×D411yescharacteristic
53C42×C61#4111yescharacteristic
54C42×C61#4112yes—
55C4⋊Dic61—22no—
56C4⋊Dic61—22no—
57C4⋊Dic61—22no—
58C4⋊Dic61—22no—
59C4⋊Dic61—82no—
60#11758196—42no—
61#11758196—42no—
62#11758196—42no—
63#11758196—42no—
64C2×#92418—24no—
65C2×#92418—42no—
66C2×#92418—42no—
67C23×C61#12011yescharacteristic
68C2×C4×C61—22no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—22no—
72C2×C4×C61—42no—
73C2×C4×C61—42no—
74C2×C4×C61—42no—
75C2×C4×C61—82no—
76C2×C4×C61—81no—
77C2×C4×C61#12111yescharacteristic
78C2×C4×C61#12112yes—
79C2×C4×C61#12312yes—
80C2×C4×C61#12411yescharacteristic
81C2×Dic61—42no—
82C2×Dic61—42no—
83C2×Dic61—42no—
84C2×Dic61—42no—
85C2×Dic61—42no—
86C2×Dic61—42no—
87C8×C61—42no—
88#92418—44no—
89#10428—611nomaximal, Sylow
90C22×C61#39411yescharacteristic
91C22×C61#45412yes—
92C22×C61#45411yescharacteristic
93C22×C61#45511yescharacteristic
94C22×C61#45612yes—
95C4×C61—22no—
96C4×C61—22no—
97C4×C61—21no—
98C4×C61—21no—
99C4×C61—82no—
100C4×C61—161no—
101Dic61—82no—
102Dic61—82no—
103#2822—611no—
104#1992—612no—
105#1836D6111yescharacteristic
106C2×#330—612no—
107#1295—611no—
108C2×C61#165811yescharacteristic
109C2×C61#166311yescharacteristic
110C2×C61#166412yes—
111C2×C61#203812yes—
112C2×C61#204011yescharacteristic
113C2×#125—612no—
114C2×#97—612no—
115C2×#97C2×D6111yescharacteristic
116#400—1222no—
117#398—1222no—
118#398—1222no—
119#384C2×D6111yescharacteristic
120#382C2×D6111yescharacteristic
121#340—22no—
122#340—1222no—
123#340—1222no—
124#330—1224no—
125C61#1042811yescharacteristic, complemented, Sylow
126C22×C8—21no—
127C22×C8—1222no—
128#125—1222no—
129#125—1222no—
130#125—1222no—
131#125—1222no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—612no—
135C2×C4⋊C4—612no—
136C2×C4⋊C4—1222no—
137C2×C4⋊C4—1222no—
138C2×C4⋊C4—1222no—
139C2×C4⋊C4C22⋊D6112yes—
140C2×C42C22×D6111yescharacteristic
141#97—21no—
142#97—1222no—
143#97—1222no—
144#97D24412yes—
145#95—22no—
146#95—1224no—
147#95—1222no—
148C22×C4—22no—
149C22×C4—41no—
150C22×C4—1222no—
151C22×C4—1222no—
152C22×C4D4×D6112yes—
153C22×C4C2×C22⋊D6111yescharacteristic
154C2×C8—22no—
155C2×C8—41no—
156C2×C8—41no—
157C2×C8—1224no—
158C2×C8—2442no—
159C2×C8—2442no—
160C4⋊C4—42no—
161C4⋊C4—44no—
162C4⋊C4—42no—
163C4⋊C4—1222no—
164C4⋊C4—1222no—
165C4⋊C4—1222no—
166C4⋊C4—1222no—
167C4⋊C4—4882no—
168C4⋊C4—2442no—
169C4⋊C4—2442no—
170C4⋊C4—2442no—
171C4⋊C4—2442no—
172C42C2×D24411yescharacteristic
173C42#1175822211yescharacteristic
174C42#1175822612yes—
175C23#1451974511yescharacteristic
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—82no—
184C2×C4—81no—
185C2×C4—2442no—
186C2×C4—2442no—
187C2×C4—2442no—
188C2×C4—2442no—
189C2×C4—2442no—
190C2×C4—2442no—
191C2×C4#1451975111yescharacteristic
192C2×C4#1451975212yes—
193C2×C4#1451976212yes—
194C2×C4#1451976611yescharacteristic
195C8—42no—
196C8—2444no—
197C22#1683967911yescharacteristic
198C22#1683993312yes—
199C22#1683993411yescharacteristic
200C22#1683993911yescharacteristic
201C22#1683994312yes—
202C4—22no—
203C4—22no—
204C4—21no—
205C4—21no—
206C4—82no—
207C4—161no—
208C4—4882no—
209C4—4882no—
210C2#2144512011yescharacteristic
211C2#2144514511yescharacteristic
212C2#2144515212yes—
213C2#2144703812yes—
214C2#2144704811yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1836C2
socle, prime radicalC23×C61#120
hypercenter#1836D61
hypocenterC61#10428
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1836

Complements

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

NH ≅ G/Ntype
125. C61#10428semidirect

Maximal subgroups

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

subgroupindex
#214538872
#214467872
C2×#168395032
#214437002
C61×#18362
#1042861