Finite Group Databasebeta

← #29593785

Subgroups — #29593785

Order 15616.

336 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 59 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#21457623C211yesmaximal, characteristic
2#21447987C212yesmaximal, complemented
3#21443858C211yesmaximal, characteristic, complemented
4#21443796C212yesmaximal, complemented
5C61×#1716C211yesmaximal, characteristic, complemented
6#16840575—22no—
7#16840034—22no—
8#16839944—21no—
9#16839944—21no—
10#16839880C2212yes—
11#16839584—22no—
12#16839583C2212yes—
13#16839571—22no—
14C61×#498—21no—
15C61×#498C2211yescharacteristic
16C61×#494C2211yescharacteristic
17C61×#487—21no—
18C61×#322C2211yescharacteristic
19#14519825—21no—
20#14519825—21no—
21#14519809—42no—
22#14519809—42no—
23#14519808—22no—
24#14519808—22no—
25#14519800—42no—
26#14519799D412yes—
27Q16×D61—42no—
28#14519783—22no—
29#14519717—22no—
30#14519713D412yes—
31#14519705—22no—
32#14519696—21no—
33#14519696—21no—
34C2×Q16×C61—22no—
35C4⋊Q8×C61—21no—
36C4⋊Q8×C61D411yescharacteristic
37C4⋊Q8×C61D411yescharacteristic
38#106×C61—22no—
39#106×C61—42no—
40#103×C61—42no—
41C4×C8×C61—21no—
42C4×C8×C61C2311yescharacteristic
43C2×Q8×C61—21no—
44C2×Q8×C61—21no—
45C2×Q8×C61—41no—
46#11758226—42no—
47#11758226—42no—
48Q8×D61—42no—
49Q8×D61—42no—
50#11758222—22no—
51#11758222—81no—
52#11758222—81no—
53Q16×C61—42no—
54Q16×C61—42no—
55C2×C8×C61—22no—
56C2×C8×C61C2×D412yes—
57C4⋊C4×C61—41no—
58C4⋊C4×C61—41no—
59C4⋊C4×C61—41no—
60C4⋊C4×C61—41no—
61C42×C61C2×D411yescharacteristic
62#11758202—42no—
63#11758202—42no—
64#11758201—42no—
65#11758201—42no—
66#11758194—22no—
67Dic244SD1612yes—
68D488SD1612yes—
69#11758190—22no—
70#11758189—42no—
71C8×D61—42no—
72#11758185—42no—
73Q8×C61—42no—
74Q8×C61—42no—
75Q8×C61—82no—
76C2×C4×C61—21no—
77C2×C4×C61—41no—
78C2×C4×C61—41no—
79C2×C4×C61—81no—
80C2×C4×C61#12011yescharacteristic
81C22⋊D61—42no—
82D244—22no—
83D244—81no—
84D244—81no—
85C4×D61—42no—
86C4×D61—82no—
87C4×D61—82no—
88Dic122—22no—
89Dic122—81no—
90Dic122—81no—
91C8×C61—42no—
92C8×C61C2×SD1612yes—
93C8×C61AGL(1,ℤ/8)12yes—
94#92418—42no—
95#12367—611nomaximal, Sylow
96C22×C61#45311yescharacteristic
97C2×D61—42no—
98C4×C61—22no—
99C4×C61—81no—
100C4×C61—81no—
101C4×C61—161no—
102C4×C61#45012yes—
103Dic61—42no—
104#3293—611no—
105#2230—612no—
106#1716D6111yescharacteristic, complemented
107#1358—611no—
108#1336—612no—
109C2×C61—21no—
110C2×C61#162911yescharacteristic
111D61—82no—
112#578—1222no—
113#498—21no—
114#498C2×D6111yescharacteristic
115#494C2×D6111yescharacteristic
116#487—21no—
117#473—1222no—
118#456—1221no—
119#456—1221no—
120#443—612no—
121#365—1222no—
122#364—612no—
123#360—1222no—
124#322C2×D6111yescharacteristic
125C61#1236711yescharacteristic, complemented, Sylow
1262−1+4—1221no—
1272−1+4—1221no—
128#137—1222no—
129#137—1222no—
130#137—2442no—
131#137—2442no—
132#135—612no—
133#135—2442no—
134C2×Q16—22no—
135C2×Q16—2442no—
136#131—1222no—
137C4⋊Q8—21no—
138C4⋊Q8C22⋊D6111yescharacteristic
139C4⋊Q8C22⋊D6111yescharacteristic
140M32—1222no—
141#108—612no—
142#106—22no—
143#106—42no—
144#104—1222no—
145#103—42no—
146#101—1221no—
147#101—1221no—
148C4×C8—21no—
149C4×C8C22×D6111yescharacteristic
150#41—1222no—
151#41—4881no—
152#41—4881no—
153#41—2442no—
154#41—2442no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—41no—
158C2×Q8—2442no—
159C2×Q8—2442no—
160Q16—42no—
161Q16—42no—
162Q16—612no—
163Q16—2442no—
164Q16—2442no—
165SD16—1222no—
166SD16—2442no—
167SD16—2442no—
168D8—612no—
169M16—1222no—
170M16—2442no—
171C2×C8—22no—
172C2×C8—2442no—
173C2×C8D4×D6112yes—
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—41no—
178C42C2×C22⋊D6111yescharacteristic
179C16—2442no—
180Q8—42no—
181Q8—42no—
182Q8—82no—
183Q8—1222no—
184Q8—4881no—
185Q8—4881no—
186D4—1222no—
187D4—4881no—
188D4—4881no—
189D4—2442no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—81no—
194C2×C4—4882no—
195C2×C4—4882no—
196C2×C4—2442no—
197C2×C4#1451974511yescharacteristic
198C8—42no—
199C8—2442no—
200C8SD16×D6112yes—
201C8#1451980412yes—
202C22—2442no—
203C22#1683992911yescharacteristic
204C4—22no—
205C4—81no—
206C4—81no—
207C4—161no—
208C4—2442no—
209C4#1683991112yes—
210C2—21no—
211C2—4882no—
212C2#2144493311yescharacteristic
subgroupG/H
centerC2#21444933
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1716C2
socleC2×C61#1629
prime radical#21457623C2
hypercenter#1716D61
hypocenterC61#12367
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1716

Complements

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

NH ≅ G/Ntype
2. #21447987C2semidirect
3. #21443858C2semidirect
4. #21443796C2semidirect
5. C61×#1716C2semidirect
106. #1716D61semidirect
125. C61#12367semidirect

Maximal subgroups

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

subgroupindex
#214576232
#214479872
#214438582
#214437962
C61×#17162
#1236761