Finite Group Databasebeta

← #34034024

Subgroups — #34034024

Order 18688.

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

normal subgroups only

This group has 204 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#22627153C211yesmaximal, characteristic, complemented
2#22627152C211yesmaximal, characteristic, complemented
3#22626994C211yesmaximal, characteristic, complemented
4#22626984C211yesmaximal, characteristic, complemented
5#22626983C211yesmaximal, characteristic, complemented
6#22626950C211yesmaximal, characteristic, complemented
7#22626333C211yesmaximal, characteristic
8#17989709—21no—
9#17989708—21no—
10#17989691C2211yescharacteristic
11#17989691C2211yescharacteristic
12#17989688—21no—
13#17989687—21no—
14#17989682C2211yescharacteristic
15#17989671C2211yescharacteristic
16#17989631C2211yescharacteristic
17#17989629C2211yescharacteristic
18#17989515C411yescharacteristic
19#17989502C411yescharacteristic
20#17989501C411yescharacteristic
21#17989474C2211yescharacteristic
22#17989018C411yescharacteristic
23#14556688—21no—
24#14556688—21no—
25#14556688—41no—
26#14556687—41no—
27#14556686—41no—
28#14556686D411yescharacteristic
29#14556686D411yescharacteristic
30C2×#11924040—41no—
31C4×#10596842—21no—
32#14556679—21no—
33#14556678—21no—
34#14556664C2×C411yescharacteristic
35#14556662C2×C411yescharacteristic
36#14556662C2×C411yescharacteristic
37#14556656—21no—
38#14556655—21no—
39C8×#64408C2311yescharacteristic
40#14556614C2×C411yescharacteristic
41#14556610C2×C411yescharacteristic
42#14556537C811yescharacteristic, complemented
43#14556536C811yescharacteristic, complemented
44#14556532C811yescharacteristic, complemented
45C16×D73C2×C411yescharacteristic
46SD32×C73C811yescharacteristic, complemented
47C2×#10596842—41no—
48#11924040—21no—
49#11924040—21no—
50#11924040—41no—
51#11924040—41no—
52#11924038—21no—
53#11924038—21no—
54#11924038—41no—
55#11924037—41no—
56#11924036—41no—
57#11924036C2×D411yescharacteristic
58C2×#10596833—41no—
59C4×#64408#4111yescharacteristic
60#11924031—21no—
61#11924029—21no—
62#11924027—21no—
63Dic292C2×C811yescharacteristic
64#11924016—21no—
65#11924015—21no—
66D584C2×C811yescharacteristic
67C8×D73C22×C411yescharacteristic
68#11924003C2×C811yescharacteristic
69Q16×C73C2×C811yescharacteristic
70D8×C73C2×C811yescharacteristic
71C16×C73C2×C811yescharacteristic
72C2×#64408—21no—
73#10596842—81no—
74Q8×C73—21no—
75D4×C73—21no—
76C22⋊D73—41no—
77C2×Dic73—41no—
78D292—21no—
79D292—41no—
80C4×D73—41no—
81C4×D73C4×D411yescharacteristic
82Dic146—21no—
83#10596833—41no—
84#10596833—41no—
85#10596833AGL(1,ℤ/8)11yescharacteristic
86#10596833AGL(1,ℤ/8)11yescharacteristic
87C8×C73C22×C811yescharacteristic
88#10596831#13111yescharacteristic
89C22×C73—41no—
90C2×D73—41no—
91C2×D73#44411yescharacteristic
92#64408—41no—
93C4×C73—41no—
94C4×C73C8×D411yescharacteristic
95Dic73—41no—
96Dic73#44211yescharacteristic
97#12068—731nomaximal, Sylow
98C2×C73—81no—
99C2×C73#158011yescharacteristic
100D73—21no—
101D73—81no—
102#2179—731no—
103#2171—731no—
104#2171—731no—
105#1369—731no—
106#1336—731no—
107#1336—731no—
108#1313—731no—
109C73#1206811yescharacteristic, complemented, Sylow
110#508—731no—
111#504—1461no—
112#504—1461no—
113#443—731no—
114#443—731no—
115#368—731no—
116#364—731no—
117#364—731no—
118#359—731no—
119#359—731no—
120#350—1461no—
121#350—1461no—
122#346—731no—
123#346—731no—
124#322—731no—
125#135—731no—
126#135—731no—
127#131—1461no—
128#131—1461no—
129Q32—731no—
130SD32—731no—
131SD32#1059684211yescharacteristic, complemented
132D16—731no—
133M32—2921no—
134M32—2921no—
135M32—1461no—
136M32—1461no—
137C2×C16—2921no—
138C2×C16—2921no—
139C2×C16—731no—
140C2×C16—731no—
141C2×C16—731no—
142C2×C16—731no—
143#108—731no—
144#108—731no—
145#104—1461no—
146#104—1461no—
147C4×C8—731no—
148C4×C8—1461no—
149#41—1461no—
150#41—1461no—
151Q16—731no—
152Q16C2×#1059684211yescharacteristic
153SD16—1461no—
154SD16—1461no—
155D8—731no—
156D8C2×#1059684211yescharacteristic
157M16—2921no—
158M16—2921no—
159M16—1461no—
160M16—1461no—
161C2×C8—2921no—
162C2×C8—2921no—
163C2×C8—2921no—
164C2×C8—731no—
165C2×C8—731no—
166C42—731no—
167C16—2921no—
168C16—2921no—
169C16—731no—
170C16—1461no—
171C16—1461no—
172C16—1461no—
173C16C2×#1059684211yescharacteristic
174Q8—21no—
175Q8—1461no—
176D4—21no—
177D4—2921no—
178D4—2921no—
179D4—1461no—
180C2×C4—2921no—
181C2×C4—2921no—
182C2×C4—731no—
183C2×C4—1461no—
184C8—2921no—
185C8—2921no—
186C8—5841no—
187C8—731no—
188C8—731no—
189C8—731no—
190C8C22×#1059684211yescharacteristic
191C22—41no—
192C22—2921no—
193C22—731no—
194C4—41no—
195C4—2921no—
196C4—2921no—
197C4—731no—
198C4D4×#1059684211yescharacteristic
199C2—81no—
200C2—5841no—
201C2—1461no—
202C2#2262706211yescharacteristic
subgroupG/H
centerC2#22627062
commutatorC8×C73C22×C8
FrattiniC8C22×#10596842
FittingSD32×C73C8
socleC2×C73#1580
prime radical#17989018C4
cosocleC8×#64408C23
hypercenterSD32#10596842
hypocenterC73#12068
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
1. #22627153C2semidirect
2. #22627152C2semidirect
3. #22626994C2semidirect
4. #22626984C2semidirect
5. #22626983C2semidirect
6. #22626950C2semidirect
42. #14556537C8semidirect
43. #14556536C8semidirect
44. #14556532C8semidirect
46. SD32×C73C8semidirect
109. C73#12068semidirect
131. SD32#10596842semidirect

Maximal subgroups

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

subgroupindex
#226271532
#226271522
#226269942
#226269842
#226269832
#226269502
#226263332
#1206873