Finite Group Databasebeta

← #29583512

Subgroups — #29583512

Order 15616.

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

normal subgroups only

This group has 402 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×#1847C211yesmaximal, characteristic
6C2×#14519769C2212yes—
7C2×#14519688C2212yes—
8#16839702—22no—
9#16839694—22no—
10#16839692—21no—
11#16839692—21no—
12#16839524—22no—
13#16839524—22no—
14#16839503—24no—
15C2×#107×C61—21no—
16C2×#106×C61—21no—
17C2×#97×C61C2211yescharacteristic
18C61×#384C2211yescharacteristic
19C61×#382C2211yescharacteristic
20C22×#92418—22no—
21#14519769—22no—
22#14519769—22no—
23#14519769—22no—
24#14519769—22no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61D412yes—
28C2×C4⋊Dic61D412yes—
29C2×#11758196—22no—
30C2×#11758196—22no—
31#14519688—22no—
32#14519688—22no—
33#14519684—22no—
34#14519684—22no—
35#14519684—21no—
36#14519684—21no—
37C22×C8×C61—21no—
38C2×C4⋊C4×C61—22no—
39C2×C4⋊C4×C61—21no—
40C2×C4⋊C4×C61D411yescharacteristic
41C2×C4⋊C4×C61D411yescharacteristic
42C2×C42×C61C2311yescharacteristic
43#107×C61—42no—
44#106×C61—42no—
45#97×C61—21no—
46#97×C61D412yes—
47#95×C61—22no—
48C22×C4×C61—21no—
49C22×C4×C61—21no—
50C22×C4×C61—41no—
51C22×C4×C61C2×D412yes—
52C22×C4×C61C2×D411yescharacteristic
53C22×Dic61—22no—
54C22×Dic61—22no—
55C2×C8×C61—22no—
56C2×C8×C61—22no—
57C2×C8×C61—22no—
58C4⋊C4×C61—41no—
59C4⋊C4×C61—41no—
60C4⋊C4×C61—41no—
61C4⋊C4×C61—41no—
62C4⋊C4×C61—44no—
63C42×C61C2×D411yescharacteristic
64C42×C61#4111yescharacteristic
65C42×C61#4112yes—
66C4⋊Dic61—22no—
67C4⋊Dic61—22no—
68C4⋊Dic61—22no—
69C4⋊Dic61—22no—
70C4⋊Dic61—81no—
71C4⋊Dic61—81no—
72#11758196—42no—
73#11758196—42no—
74#11758196—42no—
75#11758196—42no—
76C2×#92418—24no—
77C2×#92418—42no—
78C2×#92418—42no—
79C23×C61#12011yescharacteristic
80C2×C4×C61—21no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—21no—
84C2×C4×C61—41no—
85C2×C4×C61—41no—
86C2×C4×C61—42no—
87C2×C4×C61—42no—
88C2×C4×C61—81no—
89C2×C4×C61—82no—
90C2×C4×C61#12111yescharacteristic
91C2×C4×C61#12112yes—
92C2×C4×C61#12312yes—
93C2×C4×C61#12411yescharacteristic
94C2×Dic61—42no—
95C2×Dic61—42no—
96C2×Dic61—42no—
97C2×Dic61—42no—
98C2×Dic61—42no—
99C2×Dic61—42no—
100C8×C61—24no—
101#92418—44no—
102#10429—611nomaximal, Sylow
103C22×C61#39411yescharacteristic
104C22×C61#45311yescharacteristic
105C22×C61#45412yes—
106C22×C61#45612yes—
107C22×C61#45611yescharacteristic
108C4×C61—22no—
109C4×C61—22no—
110C4×C61—21no—
111C4×C61—21no—
112C4×C61—81no—
113C4×C61—81no—
114C4×C61—161no—
115Dic61—82no—
116Dic61—82no—
117#2822—611no—
118#1992—612no—
119#1847D6111yescharacteristic
120C2×#330—612no—
121#1295—611no—
122C2×C61#165711yescharacteristic
123C2×C61#166011yescharacteristic
124C2×C61#166312yes—
125C2×C61#203812yes—
126C2×C61#203911yescharacteristic
127C2×#125—612no—
128C2×#107—21no—
129C2×#106—21no—
130C2×#97—612no—
131C2×#97C2×D6111yescharacteristic
132#400—1222no—
133#398—1222no—
134#398—1221no—
135#398—1221no—
136#384C2×D6111yescharacteristic
137#382C2×D6111yescharacteristic
138#340—1222no—
139#340—1222no—
140#330—1224no—
141C61#1042911yescharacteristic, complemented, Sylow
142C22×C8—21no—
143C22×C8—1222no—
144#125—1222no—
145#125—1222no—
146#125—1222no—
147#125—1222no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—612no—
151C2×C4⋊C4—612no—
152C2×C4⋊C4—1221no—
153C2×C4⋊C4—1221no—
154C2×C4⋊C4—1222no—
155C2×C4⋊C4—1222no—
156C2×C4⋊C4C22⋊D6111yescharacteristic
157C2×C4⋊C4C22⋊D6111yescharacteristic
158C2×C42C22×D6111yescharacteristic
159#107—42no—
160#106—42no—
161#97—21no—
162#97—1222no—
163#97—1222no—
164#97D24412yes—
165#95—22no—
166#95—1222no—
167#95—1222no—
168#95—1221no—
169#95—1221no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—41no—
173C22×C4—1222no—
174C22×C4—1222no—
175C22×C4D4×D6112yes—
176C22×C4C2×C22⋊D6111yescharacteristic
177C2×C8—22no—
178C2×C8—22no—
179C2×C8—22no—
180C2×C8—1224no—
181C2×C8—2442no—
182C2×C8—2442no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C4⋊C4—41no—
186C4⋊C4—41no—
187C4⋊C4—44no—
188C4⋊C4—1222no—
189C4⋊C4—1222no—
190C4⋊C4—1222no—
191C4⋊C4—1222no—
192C4⋊C4—4881no—
193C4⋊C4—4881no—
194C4⋊C4—2442no—
195C4⋊C4—2442no—
196C4⋊C4—2442no—
197C4⋊C4—2442no—
198C42C2×D24411yescharacteristic
199C42#1175822211yescharacteristic
200C42#1175822612yes—
201C23#1451974511yescharacteristic
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4—81no—
211C2×C4—82no—
212C2×C4—2442no—
213C2×C4—2442no—
214C2×C4—2442no—
215C2×C4—2442no—
216C2×C4—2442no—
217C2×C4—2442no—
218C2×C4#1451975111yescharacteristic
219C2×C4#1451975212yes—
220C2×C4#1451976212yes—
221C2×C4#1451976611yescharacteristic
222C8—24no—
223C8—2444no—
224C22#1683967911yescharacteristic
225C22#1683992911yescharacteristic
226C22#1683993312yes—
227C22#1683994312yes—
228C22#1683994411yescharacteristic
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—81no—
234C4—81no—
235C4—161no—
236C4—4882no—
237C4—4882no—
238C2#2144511511yescharacteristic
239C2#2144512811yescharacteristic
240C2#2144514612yes—
241C2#2144703812yes—
242C2#2144704311yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1847C2
socle, prime radicalC23×C61#120
hypercenter#1847D61
hypocenterC61#10429
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1847

Complements

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

NH ≅ G/Ntype
141. C61#10429semidirect

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×#18472
#1042961