Finite Group Databasebeta

← #29581348

Subgroups — #29581348

Order 15616.

500 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#16840168C212yesmaximal
2#21453887C211yesmaximal, characteristic
3C2×#16839503C212yesmaximal
4#21443700C211yesmaximal, characteristic
5C61×#1960C211yesmaximal, characteristic
6C2×#14519769C2212yes—
7#16840168—24no—
8#16840168—24no—
9C2×#14519710—22no—
10C2×#14519708—22no—
11C2×#14519688C2212yes—
12#16839702—22no—
13#16839694—22no—
14#16839692—22no—
15#16839503—24no—
16C2×C4⋊Q8×C61C2211yescharacteristic
17C2×#103×C61—22no—
18C2×#97×C61C2211yescharacteristic
19C61×#382C2211yescharacteristic
20C22×#92418—22no—
21#14519769—22no—
22#14519769—22no—
23#14519769—22no—
24#14519769—22no—
25C2×C4⋊Dic61—22no—
26C2×C4⋊Dic61D412yes—
27C2×C4⋊Dic61D412yes—
28C2×#11758196—22no—
29C2×#11758196—22no—
30#14519710—28no—
31#14519708—28no—
32#14519688—22no—
33#14519688D414yes—
34#14519684—24no—
35#14519684—22no—
36C22×Q8×C61—21no—
37C22×C8×C61—21no—
38C4⋊Q8×C61—22no—
39C4⋊Q8×C61—21no—
40C4⋊Q8×C61D412yes—
41C2×C4⋊C4×C61—22no—
42C2×C4⋊C4×C61D412yes—
43C2×C42×C61C2311yescharacteristic
44#103×C61—44no—
45#97×C61—22no—
46#95×C61—22no—
47C2×Q8×C61—22no—
48C2×Q8×C61—42no—
49C2×Q8×C61—42no—
50C2×Q8×C61—41no—
51C22×C4×C61—22no—
52C22×C4×C61—41no—
53C22×C4×C61C2×D412yes—
54C22×C4×C61C2×D411yescharacteristic
55C22×Dic61—22no—
56C22×Dic61—22no—
57C2×C8×C61—22no—
58C2×C8×C61—41no—
59C2×C8×C61—41no—
60C4⋊C4×C61—24no—
61C4⋊C4×C61—42no—
62C4⋊C4×C61—42no—
63C42×C61C2×D411yescharacteristic
64C42×C61C2×D412yes—
65C42×C61#4111yescharacteristic
66C4⋊Dic61—22no—
67C4⋊Dic61—22no—
68C4⋊Dic61—22no—
69C4⋊Dic61—22no—
70C4⋊Dic61—82no—
71#11758196—42no—
72#11758196—42no—
73#11758196—42no—
74#11758196—42no—
75C2×#92418—28no—
76C2×#92418—24no—
77C23×C61#12011yescharacteristic
78Q8×C61—44no—
79Q8×C61—82no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—24no—
83C2×C4×C61—42no—
84C2×C4×C61—42no—
85C2×C4×C61—44no—
86C2×C4×C61—81no—
87C2×C4×C61—81no—
88C2×C4×C61#12012yes—
89C2×C4×C61#12112yes—
90C2×C4×C61#12111yescharacteristic
91C2×C4×C61#12711yescharacteristic
92C2×Dic61—42no—
93C2×Dic61—42no—
94C2×Dic61—42no—
95C2×Dic61—42no—
96C2×Dic61—44no—
97C8×C61—42no—
98#92418—28no—
99#10087—611nomaximal, Sylow
100C22×C61#39211yescharacteristic
101C22×C61#45311yescharacteristic
102C22×C61#45411yescharacteristic
103C22×C61#45614yes—
104C4×C61—22no—
105C4×C61—22no—
106C4×C61—21no—
107C4×C61—21no—
108C4×C61—82no—
109C4×C61—82no—
110Dic61—82no—
111Dic61—82no—
112C2×#501—612no—
113#2822—611no—
114#1960D6111yescharacteristic
115C2×#330—612no—
116#1295—611no—
117C2×C61#166012yes—
118C2×C61#166312yes—
119C2×C61#200512yes—
120C2×C61#200611yescharacteristic
121C2×C4⋊Q8C2×D6111yescharacteristic
122C2×#125—612no—
123#501—1224no—
124#501—1224no—
125C2×#107—1222no—
126C2×#106—1222no—
127C2×#103—22no—
128C2×#97—612no—
129C2×#97C2×D6111yescharacteristic
130#400—1222no—
131#398—1222no—
132#398—1222no—
133#382C2×D6111yescharacteristic
134#330—1224no—
135C61#1008711yescharacteristic, complemented, Sylow
136C22×Q8—21no—
137C22×C8—21no—
138C22×C8—1222no—
139C4⋊Q8—21no—
140C4⋊Q8—22no—
141C4⋊Q8D24412yes—
142#125—1222no—
143#125—1222no—
144#125—1222no—
145#125—1222no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—612no—
148C2×C4⋊C4—612no—
149C2×C4⋊C4—1222no—
150C2×C4⋊C4—1222no—
151C2×C4⋊C4—1222no—
152C2×C4⋊C4C22⋊D6112yes—
153C2×C42C22×D6111yescharacteristic
154#107—1228no—
155#106—1228no—
156#103—44no—
157#97—22no—
158#97—614no—
159#97—1222no—
160#95—22no—
161#95—1224no—
162#95—1222no—
163C2×Q8—22no—
164C2×Q8—42no—
165C2×Q8—42no—
166C2×Q8—41no—
167C22×C4—22no—
168C22×C4—41no—
169C22×C4—1222no—
170C22×C4—1222no—
171C22×C4D4×D6112yes—
172C22×C4C2×C22⋊D6111yescharacteristic
173C2×C8—22no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—1228no—
177C2×C8—1224no—
178C4⋊C4—24no—
179C4⋊C4—42no—
180C4⋊C4—42no—
181C4⋊C4—1222no—
182C4⋊C4—1222no—
183C4⋊C4—1222no—
184C4⋊C4—1222no—
185C4⋊C4—4882no—
186C4⋊C4—2442no—
187C4⋊C4—2442no—
188C4⋊C4—2442no—
189C4⋊C4—2442no—
190C42C2×D24411yescharacteristic
191C42#1175822211yescharacteristic
192C42D4×D6112yes—
193C23#1451974511yescharacteristic
194Q8—44no—
195Q8—82no—
196C2×C4—24no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—44no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—81no—
203C2×C4—81no—
204C2×C4—2444no—
205C2×C4—2442no—
206C2×C4—2442no—
207C2×C4—2442no—
208C2×C4—2442no—
209C2×C4#1451974712yes—
210C2×C4#1451975012yes—
211C2×C4#1451975111yescharacteristic
212C2×C4#1451977311yescharacteristic
213C8—42no—
214C8—1228no—
215C22#1683967111yescharacteristic
216C22#1683992911yescharacteristic
217C22#1683993411yescharacteristic
218C22#1683994314yes—
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—82no—
224C4—82no—
225C4—4882no—
226C4—4882no—
227C2#2144512812yes—
228C2#2144514512yes—
229C2#2144685612yes—
230C2#2144686011yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1960C2
socle, prime radicalC23×C61#120
hypercenter#1960D61
hypocenterC61#10087
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
135. C61#10087semidirect

Maximal subgroups

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

subgroupindex
C2×#168401682
#214538872
C2×#168395032
#214437002
C61×#19602
#1008761