Finite Group Databasebeta

← #29584790

Subgroups — #29584790

Order 15616.

292 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 87 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#21446799C211yesmaximal, characteristic
2#21445972C211yesmaximal, characteristic
3#21444477C211yesmaximal, characteristic
4#21444474C211yesmaximal, characteristic
5#21443714C211yesmaximal, characteristic
6#21443647C211yesmaximal, characteristic
7C61×#1301C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16839815C2211yescharacteristic
10C2×C4⋊#92418C2211yescharacteristic
11C2×#14519706—21no—
12C2×#14519706—21no—
13#16839608C2211yescharacteristic
14#16839523—21no—
15#16839523—21no—
16#16839510—21no—
17#16839510—21no—
18#16839509—21no—
19#16839507—21no—
20C61×#431C2211yescharacteristic
21C61×#423C2211yescharacteristic
22C2×C4⋊C8×C61C2211yescharacteristic
23C22×#92418—21no—
24#14519777D411yescharacteristic
25#14519777D411yescharacteristic
26#14519769—21no—
27#14519756—21no—
28#14519756—21no—
29C4×Dic122—21no—
30C4×Dic122—21no—
31#14519736—21no—
32C2×C4×Dic61D411yescharacteristic
33C2×C4×Dic61D411yescharacteristic
34C4⋊#92418—21no—
35C4⋊#92418—21no—
36C4⋊#92418—21no—
37#14519706—42no—
38#14519706—42no—
39C22⋊#92418—21no—
40C4×#92418—21no—
41#14519684—21no—
42#14519684—21no—
43C2×M16×C61—21no—
44C22×C8×C61—21no—
45C2×C42×C61C2311yescharacteristic
46C4⋊C8×C61—21no—
47C4⋊C8×C61—21no—
48C4⋊C8×C61—21no—
49C4⋊C8×C61—21no—
50C4⋊C8×C61—21no—
51C22⋊C8×C61—21no—
52C4×C8×C61—21no—
53C22×C4×C61C2×D411yescharacteristic
54C22×C4×C61#4111yescharacteristic
55C22×C4×C61#4111yescharacteristic
56C22×Dic61—21no—
57C22×Dic61—21no—
58C2×Dic122—21no—
59C2×Dic122—21no—
60M16×C61—41no—
61M16×C61—41no—
62C2×C8×C61—41no—
63C2×C8×C61—41no—
64C2×C8×C61—41no—
65C2×C8×C61—41no—
66C2×C8×C61—41no—
67C42×C61C2×D411yescharacteristic
68C42×C61#4111yescharacteristic
69C42×C61#4111yescharacteristic
70C42×C61#4111yescharacteristic
71C22⋊Dic61—41no—
72C4⋊Dic61—21no—
73C4⋊Dic61—21no—
74C4⋊Dic61—21no—
75C4⋊Dic61—21no—
76#11758196—41no—
77#11758196—41no—
78C4×Dic61—21no—
79C4×Dic61—21no—
80C4×Dic61—41no—
81C4×Dic61SD1612yes—
82C4×Dic61Q1612yes—
83C2×#92418—41no—
84C2×#92418—41no—
85C2×#92418—41no—
86C2×#92418—41no—
87C23×C61#12311yescharacteristic
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61#12111yescharacteristic
91C2×C4×C61#12311yescharacteristic
92C2×C4×C61#12311yescharacteristic
93C2×C4×C61#12411yescharacteristic
94C2×C4×C61#12611yescharacteristic
95C2×C4×C61#12611yescharacteristic
96C2×C4×C61C2×SD1611yescharacteristic
97C2×C4×C61C2×Q1611yescharacteristic
98C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
99C2×C4×C61#13711yescharacteristic
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—41no—
103C2×Dic61—41no—
104C2×Dic61—41no—
105C2×Dic61—41no—
106C2×Dic61—41no—
107C2×Dic61—41no—
108Dic122—81no—
109Dic122—81no—
110C8×C61—81no—
111C8×C61—81no—
112C8×C61—81no—
113#92418—81no—
114#92418—81no—
115#10628—611nomaximal, Sylow
116C22×C61—21no—
117C22×C61—21no—
118C22×C61#39711yescharacteristic
119C22×C61#48311yescharacteristic
120C22×C61#48411yescharacteristic
121C4×C61—21no—
122C4×C61—21no—
123C4×C61—21no—
124C4×C61—21no—
125C4×C61#46011yescharacteristic
126C4×C61#46211yescharacteristic
127C4×C61#48711yescharacteristic
128C4×C61#48911yescharacteristic
129Dic61—42no—
130Dic61—42no—
131Dic61—81no—
132Dic61—81no—
133#1995—611no—
134#1843—611no—
135#1542—611no—
136#1542—611no—
137#1301—611no—
138#1301D6111yescharacteristic
139#1274—611no—
140C2×C61—21no—
141C2×C61—21no—
142C2×C61#207211yescharacteristic
143C2×C61#208011yescharacteristic
144C2×C61#208011yescharacteristic
145#533—611no—
146#431—611no—
147#431C2×D6111yescharacteristic
148#423C2×D6111yescharacteristic
149C2×C4⋊C8—611no—
150C2×C4⋊C8—1221no—
151C2×C4⋊C8—1221no—
152C2×C4⋊C8C2×D6111yescharacteristic
153#376—611no—
154#339—1221no—
155#339—1221no—
156#333—1221no—
157#333—1221no—
158#332—1221no—
159#332—1221no—
160C61#1062811yescharacteristic, complemented, Sylow
161C2×M16—21no—
162C22×C8—21no—
163C22×C8—1221no—
164C4⋊Q8—611no—
165C4⋊Q8—611no—
166#125—1221no—
167C22⋊Q8—1221no—
168C22⋊Q8—1221no—
169C4×Q8—1221no—
170C4×Q8—1221no—
171#117—1221no—
172C2×C42—611no—
173C2×C42—611no—
174C2×C42C22×D6111yescharacteristic
175C4⋊C8—21no—
176C4⋊C8—21no—
177C4⋊C8—21no—
178C4⋊C8—21no—
179C4⋊C8—21no—
180C4⋊C8—1221no—
181C4⋊C8—1221no—
182C4⋊C8—1221no—
183C4⋊C8—2442no—
184C4⋊C8—2442no—
185C22⋊C8—21no—
186C22⋊C8—1221no—
187C4×C8—21no—
188C4×C8—1221no—
189#95—1221no—
190#95—1221no—
191C2×Q8—1221no—
192C2×Q8—1221no—
193C22×C4—1221no—
194C22×C4—1221no—
195C22×C4#1175822211yescharacteristic
196C22×C4D4×D6111yescharacteristic
197C22×C4#1175822611yescharacteristic
198M16—41no—
199M16—41no—
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—2441no—
206C2×C8—2441no—
207C2×C8—2441no—
208C2×C8—2441no—
209C4⋊C4—1221no—
210C4⋊C4—1221no—
211C4⋊C4—1221no—
212C4⋊C4—1221no—
213C4⋊C4—2441no—
214C4⋊C4—2441no—
215C22⋊C4—2441no—
216C42—612no—
217C42—612no—
218C42—1221no—
219C42—1221no—
220C42—2441no—
221C42#1175822211yescharacteristic
222C42#1175822211yescharacteristic
223C42D4×D6111yescharacteristic
224C42#1175822411yescharacteristic
225C23#1451976211yescharacteristic
226Q8—4881no—
227Q8—4881no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—1222no—
231C2×C4—1222no—
232C2×C4—2441no—
233C2×C4—2441no—
234C2×C4—2441no—
235C2×C4—2441no—
236C2×C4—2441no—
237C2×C4—2441no—
238C2×C4#1451975011yescharacteristic
239C2×C4#1451975911yescharacteristic
240C2×C4#1451976211yescharacteristic
241C2×C4#1451976311yescharacteristic
242C2×C4#1451977111yescharacteristic
243C2×C4#1451977211yescharacteristic
244C2×C4SD16×D6111yescharacteristic
245C2×C4Q16×D6111yescharacteristic
246C2×C4#1451980111yescharacteristic
247C2×C4#1451980611yescharacteristic
248C8—81no—
249C8—81no—
250C8—81no—
251C8—4881no—
252C8—4881no—
253C22—21no—
254C22—21no—
255C22#1683969111yescharacteristic
256C22#1684009411yescharacteristic
257C22#1684009911yescharacteristic
258C4—21no—
259C4—21no—
260C4—21no—
261C4—21no—
262C4—4881no—
263C4—4881no—
264C4—2442no—
265C4—2442no—
266C4#1683996111yescharacteristic
267C4#1683997111yescharacteristic
268C4#1684011111yescharacteristic
269C4#1684012011yescharacteristic
270C2—21no—
271C2—21no—
272C2#2144723111yescharacteristic
273C2#2144727411yescharacteristic
274C2#2144727511yescharacteristic
subgroupG/H
centerC2×C4#14519763
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1301C2
socleC22×C61#397
prime radicalC23×C61#123
hypercenter#1301D61
hypocenterC61#10628
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
160. C61#10628semidirect

Maximal subgroups

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

subgroupindex
#214467992
#214459722
#214444772
#214444742
#214437142
#214436472
C61×#13012
#1062861