Finite Group Databasebeta

← #29583107

Subgroups — #29583107

Order 15616.

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

normal subgroups only

This group has 416 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
1#21454197C211yesmaximal, characteristic
2#21446796C211yesmaximal, characteristic
3#21444384C212yesmaximal
4#21443678C212yesmaximal
5C61×#1276C211yesmaximal, characteristic
6#16840319C2211yescharacteristic
7C2×#14519777—21no—
8#16839786C2211yescharacteristic
9#16839668—24no—
10#16839628—21no—
11#16839628C2212yes—
12#16839522—21no—
13#16839522—21no—
14#16839500—24no—
15C61×#431C2212yes—
16C43×C61C2211yescharacteristic
17C22×Dic122—22no—
18C2×#11758194—21no—
19#14519777—42no—
20#14519777—42no—
21#14519777Q812yescomplemented
22#14519769—21no—
23#14519756—22no—
24C4×Dic122—22no—
25#14519736—21no—
26C2×C4⋊Dic61—22no—
27C2×C4⋊Dic61—22no—
28C4⋊#92418—22no—
29#14519684—24no—
30#14519684—22no—
31#14519684D414yes—
32C2×C42×C61—22no—
33C2×C42×C61D411yescharacteristic
34C2×C42×C61D411yescharacteristic
35C2×C42×C61C2311yescharacteristic
36C4⋊C8×C61—22no—
37C22⋊C8×C61—22no—
38C4×C8×C61—22no—
39C22×C4×C61—21no—
40C22×C4×C61—21no—
41C22×C4×C61C2×D412yes—
42C22×C4×C61C2×D411yescharacteristic
43C22×Dic61—24no—
44C2×Dic122—22no—
45C2×Dic122—48no—
46C2×Dic122—44no—
47C2×C8×C61—42no—
48C42×C61—21no—
49C42×C61—21no—
50C42×C61—44no—
51C42×C61SD1612yes—
52C42×C61Q1612yes—
53C42×C61C2×Q811yescharacteristic
54C42×C61#4112yes—
55C42×C61#4111yescharacteristic
56C22⋊Dic61—41no—
57C4⋊Dic61—22no—
58C4⋊Dic61—22no—
59C4⋊Dic61—44no—
60C4⋊Dic61—42no—
61C4⋊Dic61—42no—
62#11758196—42no—
63C4×Dic61—41no—
64#11758194—41no—
65#11758194—41no—
66C2×#92418—41no—
67C23×C61#12011yescharacteristic
68C2×C4×C61—24no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—42no—
72C2×C4×C61—42no—
73C2×C4×C61C22⋊Q812yes—
74C2×C4×C61C22⋊Q811yescharacteristic
75C2×C4×C61#12412yes—
76C2×C4×C61#12411yescharacteristic
77C2×C4×C61C2×SD1611yescharacteristic
78C2×C4×C61C2×Q1611yescharacteristic
79C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
80C2×C4×C61#13711yescharacteristic
81C2×Dic61—48no—
82C2×Dic61—42no—
83C2×Dic61—44no—
84Dic122—88no—
85Dic122—82no—
86C8×C61—82no—
87#92418—81no—
88#10363—611nomaximal, Sylow
89C22×C61—22no—
90C22×C61#39311yescharacteristic
91C22×C61#45011yescharacteristic
92C22×C61#45111yescharacteristic
93C4×C61—24no—
94C4×C61—22no—
95C4×C61—22no—
96C4×C61—42no—
97C4×C61#47511yescharacteristic
98C4×C61#47711yescharacteristic
99C4×C61#48711yescharacteristic
100C4×C61#48911yescharacteristic
101Dic61—84no—
102Dic61—82no—
103#2862—611no—
104#1994—611no—
105#1518—612no—
106#1286—612no—
107#1276D6111yescharacteristic
108C2×C61—21no—
109C2×C61—21no—
110C2×C61#202411yescharacteristic
111C2×C61#203112yes—
112#533—611no—
113C2×C4⋊Q8—1221no—
114#431C2×D6112yes—
115#423—611no—
116#391—1224no—
117#382—612no—
118#382—1221no—
119C43C2×D6111yescharacteristic
120#339—1221no—
121#339—1221no—
122#328—1224no—
123C61#1036311yescharacteristic, complemented, Sylow
124C22×Q8—1222no—
125C2×M16—1221no—
126C4⋊Q8—612no—
127C4⋊Q8—2442no—
128C4⋊Q8—2442no—
129#125—1221no—
130C22⋊Q8—1222no—
131C4×Q8—1222no—
132#117—1221no—
133C2×C4⋊C4—1222no—
134C2×C4⋊C4—1222no—
135C2×C42—22no—
136C2×C42D24411yescharacteristic
137C2×C42D24411yescharacteristic
138C2×C42C22×D6111yescharacteristic
139C4⋊C8—22no—
140C4⋊C8—1222no—
141C22⋊C8—22no—
142C4×C8—22no—
143#95—614no—
144#95—1224no—
145#95—1222no—
146C2×Q8—1222no—
147C2×Q8—2444no—
148C2×Q8—2448no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—1224no—
152C22×C4C2×D24411yescharacteristic
153C22×C4D4×D6112yes—
154M16—2441no—
155M16—2441no—
156C2×C8—42no—
157C2×C8—2441no—
158C4⋊C4—1222no—
159C4⋊C4—1222no—
160C4⋊C4—2444no—
161C4⋊C4—2442no—
162C4⋊C4—2442no—
163C4⋊C4—2442no—
164C22⋊C4—2441no—
165C42—21no—
166C42—21no—
167C42—44no—
168C42—2441no—
169C42#1175819012yes—
170C42Dic24412yes—
171C42#1175822212yes—
172C42#1175822411yescharacteristic
173C42Q8×D6111yescharacteristic
174C23#1451974711yescharacteristic
175Q8—4882no—
176Q8—4888no—
177C2×C4—24no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—2448no—
183C2×C4—2444no—
184C2×C4—2442no—
185C2×C4#1451975512yes—
186C2×C4#1451975711yescharacteristic
187C2×C4#1451976312yes—
188C2×C4#1451976511yescharacteristic
189C2×C4C2×#1175819011yescharacteristic
190C2×C4C2×Dic24411yescharacteristic
191C2×C4#1451980511yescharacteristic
192C2×C4#1451981011yescharacteristic
193C8—82no—
194C8—4881no—
195C22—22no—
196C22#1683967511yescharacteristic
197C22#1683991511yescharacteristic
198C22#1683992011yescharacteristic
199C4—24no—
200C4—22no—
201C4—22no—
202C4—42no—
203C4—4884no—
204C4—4882no—
205C4#1684004811yescharacteristic
206C4#1684005811yescharacteristic
207C4#1684011311yescharacteristic
208C4#1684012211yescharacteristic
209C2—21no—
210C2—21no—
211C2#2144696111yescharacteristic
212C2#2144699212yes—
subgroupG/H
centerC22#16839675
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1276C2
socleC22×C61#393
prime radicalC23×C61#120
hypercenter#1276D61
hypocenterC61#10363
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
21. #14519777Q8semidirect
123. C61#10363semidirect

Maximal subgroups

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

subgroupindex
#214541972
#214467962
#214443842
#214436782
C61×#12762
#1036361