Finite Group Databasebeta

← #29581349

Subgroups — #29581349

Order 15616.

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

normal subgroups only

This group has 500 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
1C2×#16840172C212yesmaximal
2#21446638C211yesmaximal, characteristic
3C2×#16839504C212yesmaximal
4#21443700C211yesmaximal, characteristic
5C61×#2822C211yesmaximal, characteristic
6C2×#14519777C2211yescharacteristic
7#16840172—24no—
8#16840172—24no—
9C2×#14519710—22no—
10C2×#14519708—22no—
11C2×#14519700—22no—
12C2×#14519688C2211yescharacteristic
13C2×#14519688C2212yes—
14#16839504—24no—
15C2×#125×C61C2212yes—
16C61×#400—22no—
17C61×#398—22no—
18C61×#398—22no—
19C61×#382C2211yescharacteristic
20C22×Dic122—21no—
21C22×#92418—22no—
22C22×#92418—21no—
23#14519777—22no—
24#14519777—21no—
25#14519777D412yes—
26C2×C4⋊Dic61—22no—
27#14519710—28no—
28#14519708—28no—
29#14519700—44no—
30#14519688—22no—
31#14519688—22no—
32#14519688D414yes—
33#125×C61—22no—
34#125×C61—22no—
35#125×C61—22no—
36#125×C61—22no—
37C2×C4⋊C4×C61—22no—
38C2×C4⋊C4×C61—22no—
39C2×C4⋊C4×C61—22no—
40C2×C4⋊C4×C61D412yes—
41C2×C4⋊C4×C61D412yes—
42C2×C4⋊C4×C61D412yes—
43C2×C42×C61C2311yescharacteristic
44#95×C61—24no—
45#95×C61—22no—
46#95×C61—22no—
47C22×C4×C61—22no—
48C22×C4×C61—22no—
49C22×C4×C61—22no—
50C22×C4×C61C2×D412yes—
51C22×C4×C61C2×D411yescharacteristic
52C22×Dic61—41no—
53C2×Dic122—22no—
54C2×Dic122—42no—
55C2×Dic122—42no—
56C2×Dic122—41no—
57C4⋊C4×C61—22no—
58C4⋊C4×C61—22no—
59C4⋊C4×C61—22no—
60C4⋊C4×C61—22no—
61C4⋊C4×C61—42no—
62C4⋊C4×C61—42no—
63C4⋊C4×C61—42no—
64C4⋊C4×C61—42no—
65C4⋊C4×C61—42no—
66C4⋊C4×C61—82no—
67C42×C61C2×D411yescharacteristic
68C42×C61C2×D412yes—
69C42×C61#4111yescharacteristic
70C4⋊Dic61—24no—
71C4⋊Dic61—42no—
72C2×#92418—28no—
73C2×#92418—24no—
74C2×#92418—22no—
75C2×#92418—41no—
76C2×#92418—41no—
77C23×C61#12011yescharacteristic
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—24no—
81C2×C4×C61—42no—
82C2×C4×C61—42no—
83C2×C4×C61—42no—
84C2×C4×C61—42no—
85C2×C4×C61—42no—
86C2×C4×C61—44no—
87C2×C4×C61—44no—
88C2×C4×C61#12012yes—
89C2×C4×C61#12111yescharacteristic
90C2×C4×C61#12112yes—
91C2×C4×C61#12711yescharacteristic
92C2×Dic61—42no—
93C2×Dic61—81no—
94C2×Dic61—81no—
95Dic122—44no—
96Dic122—82no—
97#92418—28no—
98#92418—42no—
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—
110C4×C61—82no—
111Dic61—82no—
112C2×#501—612no—
113#2822D6111yescharacteristic
114#1960—611no—
115C2×#330—612no—
116#1295—611no—
117C2×C61#166012yes—
118C2×C61#166312yes—
119C2×C61#200512yes—
120C2×C61#200611yescharacteristic
121C2×C4⋊Q8—611no—
122C2×#125C2×D6112yes—
123#501—1224no—
124#501—1224no—
125C2×#107—1222no—
126C2×#106—1222no—
127C2×#103—1222no—
128C2×#97—612no—
129C2×#97—611no—
130#400—22no—
131#398—22no—
132#398—22no—
133#382C2×D6111yescharacteristic
134#330—1224no—
135C61#1008711yescharacteristic, complemented, Sylow
136C22×Q8—1221no—
137C22×C8—1222no—
138C22×C8—1221no—
139C4⋊Q8—612no—
140C4⋊Q8—1222no—
141C4⋊Q8—1221no—
142#125—22no—
143#125—22no—
144#125—22no—
145#125—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—1222no—
150C2×C4⋊C4C22⋊D6112yes—
151C2×C4⋊C4C22⋊D6112yes—
152C2×C4⋊C4C22⋊D6112yes—
153C2×C42C22×D6111yescharacteristic
154#107—1228no—
155#106—1228no—
156#103—2444no—
157#97—614no—
158#97—1222no—
159#97—1222no—
160#95—24no—
161#95—22no—
162#95—22no—
163C2×Q8—1222no—
164C2×Q8—2442no—
165C2×Q8—2442no—
166C2×Q8—2441no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—2441no—
171C22×C4C2×C22⋊D6112yes—
172C22×C4C2×C22⋊D6111yescharacteristic
173C2×C8—1228no—
174C2×C8—1224no—
175C2×C8—1222no—
176C2×C8—2441no—
177C2×C8—2441no—
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—42no—
183C4⋊C4—42no—
184C4⋊C4—42no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C4⋊C4—82no—
188C4⋊C4—1224no—
189C4⋊C4—2442no—
190C42D4×D6111yescharacteristic
191C42D4×D6112yes—
192C42#1175822411yescharacteristic
193C23#1451974611yescharacteristic
194Q8—4882no—
195Q8—2444no—
196C2×C4—24no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—44no—
200C2×C4—44no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—4881no—
207C2×C4—4881no—
208C2×C4—2442no—
209C2×C4#1451974512yes—
210C2×C4#1451974811yescharacteristic
211C2×C4#1451974912yes—
212C2×C4#1451977311yescharacteristic
213C8—1228no—
214C8—2442no—
215C22#1683967011yescharacteristic
216C22#1683993011yescharacteristic
217C22#1683993511yescharacteristic
218C22#1683994514yes—
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—82no—
224C4—82no—
225C4—82no—
226C4—4882no—
227C2#2144513012yes—
228C2#2144514712yes—
229C2#2144685312yes—
230C2#2144686111yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2822C2
socle, prime radicalC23×C61#120
hypercenter#2822D61
hypocenterC61#10087
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2822

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×#168401722
#214466382
C2×#168395042
#214437002
C61×#28222
#1008761