Finite Group Databasebeta

← #29579490

Subgroups — #29579490

Order 15616.

406 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 119 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×#16840113C211yesmaximal, characteristic
2#21444505C211yesmaximal, characteristic
3#21444501C211yesmaximal, characteristic
4#21444492C211yesmaximal, characteristic
5#21444492C211yesmaximal, characteristic
6#21444111C211yesmaximal, characteristic
7C61×#1848C211yesmaximal, characteristic
8C2×#14519777C2211yescharacteristic
9C2×#14519777C2211yescharacteristic
10#16840113—22no—
11#16840113C414yes—
12#16839815C2211yescharacteristic
13#16839815C2211yescharacteristic
14C2×#14519702—22no—
15#16839510—22no—
16#16839509—22no—
17#16839509—22no—
18#16839507—22no—
19#16839484—22no—
20C2×#108×C61—22no—
21C61×#423C2211yescharacteristic
22C61×#423C2211yescharacteristic
23C2×C4×C8×C61C2211yescharacteristic
24C22×Dic122—21no—
25C22×Dic122—21no—
26#14519777—21no—
27#14519777—21no—
28#14519777—21no—
29#14519777—21no—
30#14519777—21no—
31#14519777—21no—
32#14519777C2×C412yes—
33#14519777C2×C412yes—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61—21no—
38C4⋊#92418D412yes—
39C4⋊#92418D412yes—
40#14519702—28no—
41C22⋊#92418—21no—
42C22⋊#92418—21no—
43C4×#92418—21no—
44C4×#92418—21no—
45C2×M16×C61—21no—
46C2×M16×C61—21no—
47C22×C8×C61D412yes—
48C2×C42×C61C2311yescharacteristic
49#108×C61—44no—
50C4⋊C8×C61—21no—
51C4⋊C8×C61—21no—
52C4⋊C8×C61—21no—
53C4⋊C8×C61—21no—
54C4×C8×C61C2×C412yes—
55C4×C8×C61D412yes—
56C22×C4×C61C2×D411yescharacteristic
57C22×C4×C61#4111yescharacteristic
58C22×C4×C61#4111yescharacteristic
59C22×Dic61—41no—
60C22×Dic61—41no—
61C2×Dic122—22no—
62C2×Dic122—22no—
63C2×Dic122—42no—
64C2×Dic122—42no—
65C2×Dic122—41no—
66C2×Dic122—41no—
67C2×Dic122—82no—
68M16×C61—42no—
69M16×C61—42no—
70C2×C8×C61—22no—
71C2×C8×C61—22no—
72C2×C8×C61—41no—
73C2×C8×C61—41no—
74C2×C8×C61C22⋊C414yes—
75C42×C61C22×C411yescharacteristic
76C42×C61C2×D411yescharacteristic
77C42×C61C2×D411yescharacteristic
78C42×C61C2×D411yescharacteristic
79C4⋊Dic61—22no—
80C4⋊Dic61—22no—
81C4⋊Dic61—22no—
82C4⋊Dic61—22no—
83C4⋊Dic61—41no—
84C4⋊Dic61—41no—
85C4⋊Dic61—41no—
86C4⋊Dic61—41no—
87C2×#92418—22no—
88C2×#92418—22no—
89C23×C61#12411yescharacteristic
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61C2×C22⋊C411yescharacteristic
93C2×C4×C61C4×D411yescharacteristic
94C2×C4×C61C4×D411yescharacteristic
95C2×C4×C61#12111yescharacteristic
96C2×C4×C61#12111yescharacteristic
97C2×C4×C61#12711yescharacteristic
98C2×C4×C61AGL(1,ℤ/8)12yes—
99C2×C4×C61#13712yes—
100C2×Dic61—42no—
101C2×Dic61—42no—
102C2×Dic61—82no—
103C2×Dic61—82no—
104Dic122—44no—
105Dic122—82no—
106Dic122—81no—
107Dic122—81no—
108Dic122—82no—
109C8×C61—24no—
110C8×C61—81no—
111C8×C61—81no—
112#92418—42no—
113#92418—42no—
114#9775—611nomaximal, Sylow
115C22×C61—21no—
116C22×C61—21no—
117C22×C61#39011yescharacteristic
118C22×C61#48912yes—
119C4×C61—21no—
120C4×C61—21no—
121C4×C61#41712yes—
122C4×C61#47112yes—
123C4×C61#47312yes—
124C4×C61#49611yescharacteristic
125C4×C61#49711yescharacteristic
126Dic61—82no—
127Dic61—82no—
128C2×#487—611no—
129#1848D6111yescharacteristic
130#1549—611no—
131#1548—611no—
132#1546—611no—
133#1546—611no—
134#1452—611no—
135C2×C61—22no—
136C2×C61#195911yescharacteristic
137C2×C61#197711yescharacteristic
138C2×C61#197911yescharacteristic
139C2×C4⋊Q8—611no—
140C2×C4⋊Q8—611no—
141#487—614no—
142#487—1222no—
143#431—611no—
144#431—611no—
145C2×#108—22no—
146#423C2×D6111yescharacteristic
147#423C2×D6111yescharacteristic
148C2×#103—1222no—
149C2×C4×C8C2×D6111yescharacteristic
150#333—1222no—
151#332—1222no—
152#332—1222no—
153#332—1222no—
154#322—1222no—
155C61#977511yescharacteristic, complemented, Sylow
156C22×Q8—1221no—
157C22×Q8—1221no—
158C2×M16—21no—
159C2×M16—21no—
160C22×C8C22⋊D6112yes—
161C4⋊Q8—612no—
162C4⋊Q8—612no—
163C4⋊Q8—1221no—
164C4⋊Q8—1221no—
165C4⋊Q8—1221no—
166C4⋊Q8—1221no—
167C4⋊Q8—1221no—
168C4⋊Q8—1221no—
169C2×C4⋊C4—1221no—
170C2×C4⋊C4—1221no—
171C2×C4⋊C4—1221no—
172C2×C4⋊C4—1221no—
173C2×C42C22×D6111yescharacteristic
174#108—44no—
175C4⋊C8—21no—
176C4⋊C8—21no—
177C4⋊C8—21no—
178C4⋊C8—21no—
179C4⋊C8—612no—
180C4⋊C8—612no—
181#103—1228no—
182C22⋊C8—1221no—
183C22⋊C8—1221no—
184C4×C8—1221no—
185C4×C8—1221no—
186C4×C8C4×D6112yes—
187C4×C8D24412yes—
188C2×Q8—1222no—
189C2×Q8—1222no—
190C2×Q8—4882no—
191C2×Q8—2442no—
192C2×Q8—2442no—
193C2×Q8—2441no—
194C2×Q8—2441no—
195C22×C4—2441no—
196C22×C4—2441no—
197C22×C4#1175822611yescharacteristic
198C22×C4#1175822611yescharacteristic
199C22×C4C2×C22⋊D6111yescharacteristic
200M16—42no—
201M16—42no—
202C2×C8—22no—
203C2×C8—22no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8—1222no—
207C2×C8—1222no—
208C2×C8#1175819814yes—
209C4⋊C4—1222no—
210C4⋊C4—1222no—
211C4⋊C4—1222no—
212C4⋊C4—1222no—
213C4⋊C4—2441no—
214C4⋊C4—2441no—
215C4⋊C4—2441no—
216C4⋊C4—2441no—
217C42C2×C4×D6111yescharacteristic
218C42C2×D24411yescharacteristic
219C42D4×D6111yescharacteristic
220C42D4×D6111yescharacteristic
221C23#1451976611yescharacteristic
222Q8—4882no—
223Q8—4882no—
224Q8—4881no—
225Q8—4881no—
226Q8—2444no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—4882no—
230C2×C4—4882no—
231C2×C4—2442no—
232C2×C4—2442no—
233C2×C4C2×#1175819811yescharacteristic
234C2×C4#1451973911yescharacteristic
235C2×C4#1451973911yescharacteristic
236C2×C4#1451975211yescharacteristic
237C2×C4#1451975211yescharacteristic
238C2×C4#1451977311yescharacteristic
239C2×C4#1451980312yes—
240C2×C4#1451980812yes—
241C8—24no—
242C8—81no—
243C8—81no—
244C8—2442no—
245C8—2442no—
246C22—21no—
247C22—21no—
248C22#1683966311yescharacteristic
249C22#1684012412yes—
250C4—21no—
251C4—21no—
252C4—4882no—
253C4—4882no—
254C4#1683976112yes—
255C4#1684002612yes—
256C4#1684003812yes—
257C4#1684014911yescharacteristic
258C4#1684015411yescharacteristic
259C2—22no—
260C2#2144663311yescharacteristic
261C2#2144672011yescharacteristic
262C2#2144673211yescharacteristic
subgroupG/H
centerC22#16839663
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1848C2
socleC22×C61#390
prime radicalC23×C61#124
cosocleC2×C42×C61C23
hypercenter#1848D61
hypocenterC61#9775
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1848

Complements

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

NH ≅ G/Ntype
155. C61#9775semidirect

Maximal subgroups

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

subgroupindex
C2×#168401132
#214445052
#214445012
#214444922
#214441112
C61×#18482
#977561