Finite Group Databasebeta

← #29569314

Subgroups — #29569314

Order 15616.

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

normal subgroups only

This group has 394 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#21452851C211yesmaximal, characteristic
2#21447383C212yesmaximal
3#21447357C211yesmaximal, characteristic
4#21443641C212yesmaximal
5C61×#1272C211yesmaximal, characteristic
6C2×#14519775—21no—
7C2×#14519710—21no—
8C2×#14519701—21no—
9#16839692—21no—
10#16839683—22no—
11#16839660C2212yes—
12#16839647—22no—
13#16839632C2211yescharacteristic
14#16839525—22no—
15#16839525—22no—
16#16839517C2211yescharacteristic
17C61×#391C2211yescharacteristic
18C61×#336C2212yes—
19C22×Dic122—21no—
20C22×#92418—21no—
21#14519775—42no—
22#14519775—42no—
23C2×C4⋊Dic61—21no—
24C2×C4⋊Dic61—22no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61D412yes—
27C2×C4⋊Dic61D412yes—
28C2×#11758196—22no—
29C2×#11758196—22no—
30C2×C4×Dic61—21no—
31#14519710—42no—
32#14519701—42no—
33#14519684—22no—
34#14519684—21no—
35#14519684—22no—
36C22×Q8×C61D411yescharacteristic
37C22×C8×C61—22no—
38C2×C4⋊C4×C61D411yescharacteristic
39C2×C42×C61C2311yescharacteristic
40#95×C61—22no—
41C2×Q8×C61—21no—
42C2×Q8×C61—41no—
43C2×Q8×C61—41no—
44C2×Q8×C61SD1612yes—
45C22×C4×C61—21no—
46C22×C4×C61—21no—
47C22×C4×C61C2×D411yescharacteristic
48C22×C4×C61C2×D412yes—
49C22×Dic61—22no—
50C22×Dic61—22no—
51C22×Dic61—41no—
52C2×Dic122—42no—
53C2×Dic122—81no—
54C2×Dic122—81no—
55C2×C8×C61—42no—
56C2×C8×C61—42no—
57C2×C8×C61—42no—
58C4⋊C4×C61—41no—
59C42×C61—41no—
60C4⋊Dic61—22no—
61C4⋊Dic61—42no—
62C4⋊Dic61—41no—
63C4⋊Dic61—41no—
64C4⋊Dic61—44no—
65C4⋊Dic61—81no—
66C4⋊Dic61Q1614yes—
67#11758196—44no—
68#11758196—42no—
69#11758196—42no—
70C4×Dic61—42no—
71C2×#92418—22no—
72C2×#92418—41no—
73C2×#92418—41no—
74C23×C61#12011yescharacteristic
75Q8×C61—42no—
76Q8×C61—81no—
77C2×C4×C61—21no—
78C2×C4×C61—22no—
79C2×C4×C61—21no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—41no—
83C2×C4×C61—41no—
84C2×C4×C61—41no—
85C2×C4×C61—42no—
86C2×C4×C61C2×SD1611yescharacteristic
87C2×C4×C61C2×Q1612yes—
88C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
89C2×C4×C61#13712yes—
90C2×Dic61—24no—
91C2×Dic61—42no—
92C2×Dic61—42no—
93C2×Dic61—42no—
94C2×Dic61—42no—
95C2×Dic61—42no—
96C2×Dic61—81no—
97C2×Dic61—82no—
98Dic122—84no—
99C8×C61—82no—
100#92418—42no—
101#7829—611nomaximal, Sylow
102C22×C61#45011yescharacteristic
103C22×C61#45112yes—
104C22×C61#45311yescharacteristic
105C22×C61#45412yes—
106C22×C61#45811yescharacteristic
107C4×C61—21no—
108C4×C61—21no—
109C4×C61—22no—
110C4×C61—22no—
111C4×C61—42no—
112C4×C61—81no—
113Dic61—44no—
114Dic61—82no—
115Dic61—161no—
116#2734—611no—
117#2100—612no—
118#2095—611no—
119#1272D6111yescharacteristic
120#1271—612no—
121C2×C61#161311yescharacteristic
122C2×C61#161712yes—
123C2×C61#163311yescharacteristic
124C2×C61#163712yes—
125C2×C61#165711yescharacteristic
126C2×C4⋊Q8—1221no—
127C2×#107—1221no—
128C2×#103—1221no—
129#398—1221no—
130#395—1222no—
131#391C2×D6111yescharacteristic
132#389—612no—
133#387—1222no—
134#384—611no—
135#340—1222no—
136#340—1222no—
137#336—611no—
138#336C2×D6112yes—
139C61#782911yescharacteristic, complemented, Sylow
140C22×Q8—1221no—
141C22×Q8D24411yescharacteristic
142C22×C8—22no—
143C22×C8—1221no—
144C4⋊Q8—2442no—
145C4⋊Q8—2442no—
146C2×C4⋊C4—612no—
147C2×C4⋊C4—612no—
148C2×C4⋊C4—1221no—
149C2×C4⋊C4—1222no—
150C2×C4⋊C4—1222no—
151C2×C4⋊C4—1221no—
152C2×C4⋊C4—1222no—
153C2×C4⋊C4D24411yescharacteristic
154C2×C42—1221no—
155C2×C42C22×D6111yescharacteristic
156#107—2442no—
157#103—2442no—
158#95—22no—
159#95—1221no—
160#95—1222no—
161#95—1222no—
162C2×Q8—21no—
163C2×Q8—41no—
164C2×Q8—41no—
165C2×Q8—4881no—
166C2×Q8—4881no—
167C2×Q8—2442no—
168C2×Q8#1175819012yes—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—1222no—
172C22×C4—1222no—
173C22×C4—2441no—
174C22×C4C2×D24411yescharacteristic
175C22×C4D4×D6112yes—
176C2×C8—42no—
177C2×C8—42no—
178C2×C8—42no—
179C2×C8—1222no—
180C2×C8—2441no—
181C2×C8—2441no—
182C4⋊C4—41no—
183C4⋊C4—614no—
184C4⋊C4—1222no—
185C4⋊C4—4881no—
186C4⋊C4—2441no—
187C4⋊C4—2441no—
188C4⋊C4—2444no—
189C4⋊C4—2442no—
190C4⋊C4—2444no—
191C4⋊C4—2442no—
192C4⋊C4—2442no—
193C42—41no—
194C42—2442no—
195C23#1451974711yescharacteristic
196Q8—42no—
197Q8—81no—
198Q8—4884no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—42no—
207C2×C4—41no—
208C2×C4—1224no—
209C2×C4—4882no—
210C2×C4—4881no—
211C2×C4—2442no—
212C2×C4—2442no—
213C2×C4—2442no—
214C2×C4—2442no—
215C2×C4—2442no—
216C2×C4C2×#1175819011yescharacteristic
217C2×C4Q16×D6112yes—
218C2×C4#1451980511yescharacteristic
219C2×C4#1451980612yes—
220C8—82no—
221C8—2442no—
222C22#1683991511yescharacteristic
223C22#1683991912yes—
224C22#1683993211yescharacteristic
225C22#1683993612yes—
226C22#1683995311yescharacteristic
227C4—21no—
228C4—21no—
229C4—22no—
230C4—22no—
231C4—42no—
232C4—81no—
233C4—9761no—
234C4—4882no—
235C4—2444no—
236C2#2144484111yescharacteristic
237C2#2144486212yes—
238C2#2144496011yescharacteristic
239C2#2144498612yes—
240C2#2144511811yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1272C2
socle, prime radicalC23×C61#120
hypercenter#1272D61
hypocenterC61#7829
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
139. C61#7829semidirect

Maximal subgroups

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

subgroupindex
#214528512
#214473832
#214473572
#214436412
C61×#12722
#782961