Finite Group Databasebeta

← #15777065

Subgroups — #15777065

Order 3328.

234 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 69 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#13116881C211yesmaximal, characteristic
2#13114434C211yesmaximal, characteristic, complemented
3D8×#1055C211yesmaximal, characteristic
4#13112899C211yesmaximal, characteristic, complemented
5#13112894C211yesmaximal, characteristic, complemented
6#13112886C211yesmaximal, characteristic, complemented
7C13×#2226C211yesmaximal, characteristic
8C13×#500C2211yescharacteristic
9C4×C13×D8C2211yescharacteristic
10C2×#88067—21no—
11#11718742—21no—
12#11718740—21no—
13D4×#1055—21no—
14#11718360C2211yescharacteristic
15C13×#367—21no—
16C13×C4⋊C16C2211yescharacteristic
17C13×#357—21no—
18D4⋊#1055—21no—
19#11718084—21no—
20C4⋊#6090C2211yescharacteristic
21#11718050C2211yescharacteristic
22C8×#1055C2211yescharacteristic
23C2×C13×D8D411yescharacteristic
24C13×C4⋊Q8—21no—
25C4×D4×C13—21no—
26C22×#1055—41no—
27C2×Dic52—21no—
28C2×Dic52—21no—
29#88123—21no—
30C2×C13×C16—21no—
31C13×#107—21no—
32C13×#107—21no—
33C13×#107D411yescharacteristic
34C13×#102—21no—
35C4×C8×C13C2311yescharacteristic
36#88075—42no—
37C22⋊#1055—41no—
38#88067—42no—
39C2×#6090—21no—
40#88048—41no—
41#88048—41no—
42C4⋊#1055—21no—
43C4×#1055D411yescharacteristic
44C4×#1055D411yescharacteristic
45#12420—131nomaximal, Sylow
46C2×Q8×C13—41no—
47C2×D4×C13—21no—
48C22×C4×C13—41no—
49C2×Dic26—41no—
50C13×D8—21no—
51C13×D8SD1612yes—
52C2×C8×C13C2×D411yescharacteristic
53C2×C8×C13#4111yescharacteristic
54C13×C4⋊C4—21no—
55C13×C4⋊C4—41no—
56C13×C4⋊C4—41no—
57C13×C22⋊C4—41no—
58C42×C13C2×D411yescharacteristic
59C4⋊Dic13—41no—
60C4⋊Dic13—41no—
61C2×#1055—21no—
62C2×#1055—41no—
63C2×#1055—82no—
64C2×#1055D811yescharacteristic
65C2×#1055D811yescharacteristic
66Dic52—41no—
67Dic52—41no—
68Dic52—81no—
69C13×C16—41no—
70#6090—41no—
71#2226D1311yescharacteristic
72#2208—131no—
73#1707—131no—
74C8×D8—131no—
75#1367—131no—
76#1365—131no—
77#1362—131no—
78C23×C13—41no—
79Q8×C13—82no—
80D4×C13—22no—
81D4×C13—41no—
82C2×C4×C13—41no—
83C2×C4×C13—81no—
84C2×C4×C13—81no—
85C2×C4×C13—81no—
86C2×C4×C13#12111yescharacteristic
87C2×C4×C13C2×D811yescharacteristic
88C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
89C2×Dic13—81no—
90Dic26—81no—
91Dic26—81no—
92C8×C13—21no—
93C8×C13C2×SD1611yescharacteristic
94C8×C13#13511yescharacteristic
95#1055—21no—
96#1055—41no—
97#1055—81no—
98#1055SD3212yescomplemented
99C2×SD32—261no—
100#500C2×D1311yescharacteristic
101#498—261no—
102#494—131no—
103#487—261no—
104C4×D8C2×D1311yescharacteristic
105C8×D4—261no—
106#367—21no—
107C4⋊C16—131no—
108C4⋊C16C2×D1311yescharacteristic
109#358—261no—
110#357—21no—
111#335—131no—
112D4⋊C8—261no—
113C82—131no—
114C22×C13—42no—
115C22×C13—81no—
116C22×C13—81no—
117C22×C13#45911yescharacteristic
118C4×C13—21no—
119C4×C13—81no—
120C4×C13—161no—
121C4×C13#46511yescharacteristic
122C4×C13#47111yescharacteristic
123C4×C13C2×SD3211yescharacteristic
124C4×C13#51011yescharacteristic
125Dic13—161no—
126C2×Q16—261no—
127C2×Q16—261no—
128C2×D8C22⋊D1311yescharacteristic
129C22×C8—521no—
130C4⋊Q8—21no—
131C4⋊Q8—261no—
132C4×D4—21no—
133SD32—522no—
134C2×C16—21no—
135C2×C16—261no—
136#107—21no—
137#107—21no—
138#107C22⋊D1311yescharacteristic
139#106—521no—
140#106—521no—
141C4⋊C8—261no—
142#103—522no—
143#102—21no—
144C22⋊C8—521no—
145C4×C8—131no—
146C4×C8—131no—
147C4×C8C22×D1311yescharacteristic
148C2×C13—82no—
149C2×C13#166511yescharacteristic
150C2×C13#220811yescharacteristic
151C2×C13#221211yescharacteristic
152C2×Q8—41no—
153C2×Q8—521no—
154C2×D4—21no—
155C22×C4—41no—
156Q16—521no—
157Q16—521no—
158Q16—1041no—
159D8—21no—
160D8#610612yes—
161C2×C8—131no—
162C2×C8—131no—
163C2×C8—261no—
164C2×C8—521no—
165C2×C8—1042no—
166C2×C8#612911yescharacteristic
167C2×C8C2×C22⋊D1311yescharacteristic
168C4⋊C4—21no—
169C4⋊C4—41no—
170C4⋊C4—41no—
171C4⋊C4—521no—
172C4⋊C4—521no—
173C22⋊C4—41no—
174C42D4×D1311yescharacteristic
175C16—41no—
176C16—521no—
177C13#1242011yescharacteristic, complemented, Sylow
178C23—41no—
179Q8—82no—
180Q8—1041no—
181Q8—1041no—
182D4—22no—
183D4—41no—
184C2×C4—41no—
185C2×C4—81no—
186C2×C4—81no—
187C2×C4—81no—
188C2×C4—1041no—
189C2×C4D8×D1311yescharacteristic
190C2×C4#8816511yescharacteristic
191C2×C4#8819311yescharacteristic
192C8—21no—
193C8—132no—
194C8—261no—
195C8—521no—
196C8—1041no—
197C8C2×#610611yescharacteristic
198C8#8820411yescharacteristic
199C22—42no—
200C22—81no—
201C22—81no—
202C22#1171881111yescharacteristic
203C4—21no—
204C4—81no—
205C4—161no—
206C4—2081no—
207C4D13×SD3211yescharacteristic
208C4#1171857611yescharacteristic
209C4#1171870911yescharacteristic
210C4#1171886411yescharacteristic
211C2—82no—
212C2#1311417911yescharacteristic
213C2#1311687911yescharacteristic
214C2#1311690311yescharacteristic
subgroupG/H
centerC22#11718811
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#2226C2
socleC22×C13#459
prime radicalC2×C13×D8D4
hypercenter#2226D13
hypocenterC13#12420
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2226

Complements

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

NH ≅ G/Ntype
2. #13114434C2semidirect
4. #13112899C2semidirect
5. #13112894C2semidirect
6. #13112886C2semidirect
98. #1055SD32semidirect
177. C13#12420semidirect

Maximal subgroups

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

subgroupindex
#131168812
#131144342
D8×#10552
#131128992
#131128942
#131128862
C13×#22262
#1242013