Finite Group Databasebeta

← #16790852

Subgroups — #16790852

Order 3328.

294 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 92 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
1D13⋊#365C212yesmaximal
2#13130773C211yesmaximal, characteristic
3#13130638C211yesmaximal, characteristic
4#13129908C212yesmaximal
5D13×#364C211yesmaximal, characteristic
6D13⋊#108C2211yescharacteristic
7#11719092C2211yescharacteristic
8C2×#88102—21no—
9C2×#88101C2212yes—
10#11719089—21no—
11#11719060—21no—
12D13×M32C2212yes—
13C4×C8×D13C2211yescharacteristic
14#11718234—21no—
15#11718220—22no—
16#11718219—22no—
17C13×#364C411yescharacteristic, complemented
18#11718103C412yescomplemented
19#11718055C411yescharacteristic, complemented
20#88237—21no—
21C2×C4⋊#261—22no—
22D13⋊M16—21no—
23C2×C8×D13D411yescharacteristic
24C2×C8×D13C2311yescharacteristic
25C42×D13D411yescharacteristic
26(C2×#261)⋊C4—42no—
27#88104—21no—
28#88103D411yescharacteristic
29#88103D411yescharacteristic
30#88102—41no—
31#88102—41no—
32#88102Q812yes—
33#88101—22no—
34#88101—21no—
35#88101—22no—
36#88100—41no—
37C8×#261—41no—
38C13×M32C2×C412yes—
39C4×C8×C13C2×C411yescharacteristic
40C8×Dic13C2×C411yescharacteristic
41C8×Dic13Q811yescharacteristic
42#88052C2×C412yes—
43C4×#1055Q811yescharacteristic
44#88038—22no—
45C16×D13—22no—
46#13187—131nomaximal, Sylow
47C22×#261—42no—
48C2×C4×D13—21no—
49C2×C4×D13C2×D411yescharacteristic
50C22⋊#261—41no—
51#6122—41no—
52C4⋊#261—22no—
53C4⋊#261—42no—
54C4⋊#261—42no—
55C4×#261—41no—
56#6118—21no—
57#6118—21no—
58D13⋊C8—41no—
59C2×C8×C13C4⋊C411yescharacteristic
60C2×C8×C13C22×C411yescharacteristic
61C42×C13C4⋊C411yescharacteristic
62C4×Dic13—21no—
63C4×Dic13C4⋊C411yescharacteristic
64C2×#1055C4⋊C411yescharacteristic
65C2×#1055C2×Q811yescharacteristic
66C8×D13SD1611yescharacteristic
67C8×D13SD1611yescharacteristic
68C8×D13SD1611yescharacteristic
69C8×D13SD1611yescharacteristic
70C8×D13C2×D411yescharacteristic
71C8×D13C2×Q811yescharacteristic
72C8×D13#4111yescharacteristic
73C8×D13#4111yescharacteristic
74C13×C16—22no—
75#6090—22no—
76C2×#365—132no—
77C2×#364—131no—
78#1846—131no—
79#1772—131no—
80#1386—132no—
81C22×D13AGL(1,ℤ/8)11yescharacteristic
82C2×#261—42no—
83C2×#261—84no—
84C2×#261—82no—
85C2×C4×C13—21no—
86C2×C4×C13C2×C4⋊C411yescharacteristic
87C2×Dic13—21no—
88C2×Dic13#13711yescharacteristic
89C4×D13—42no—
90C4×D13#12111yescharacteristic
91C4×D13C22⋊Q811yescharacteristic
92C4×D13C2×SD1611yescharacteristic
93C4×D13C2×SD1611yescharacteristic
94#1057—41no—
95#1057—41no—
96C8×C13#10611yescharacteristic
97C8×C13#10611yescharacteristic
98C8×C13C4×D411yescharacteristic
99C8×C13C4×Q811yescharacteristic
100#1055#10611yescharacteristic
101#1055#10611yescharacteristic
102#1055#12511yescharacteristic
103#1055C4⋊Q811yescharacteristic
104C2×M32—132no—
105C2×#108—131no—
106#427—131no—
107C2×#107—261no—
108C2×#106—132no—
109#405—261no—
110C2×C4×C8—131no—
111#382—261no—
112#365—262no—
113#365—262no—
114#364—132no—
115#364—131no—
116#364#26111yescharacteristic, complemented
117#339—261no—
118C22×C13#42811yescharacteristic
119C2×D13—22no—
120C2×D13#46011yescharacteristic
121C2×D13#47611yescharacteristic
122#261—82no—
123#261—162no—
124C4×C13—41no—
125C4×C13#38911yescharacteristic
126C4×C13C2×#10611yescharacteristic
127Dic13—41no—
128Dic13#46111yescharacteristic
129Dic13#47511yescharacteristic
130C2×M16—261no—
131C22×C8—131no—
132C22×C8—131no—
133#117—261no—
134C2×C4⋊C4—262no—
135C2×C42—131no—
136M32—132no—
137M32—262no—
138M32C2×#26112yes—
139C2×C16—262no—
140#108—131no—
141#108—131no—
142#108—261no—
143#107—132no—
144#107—521no—
145#107—521no—
146#106—261no—
147#106—262no—
148#106—262no—
149#97—521no—
150C4×C8—131no—
151C4×C8—131no—
152C4×C8—131no—
153C4×C8—521no—
154C4×C8C2×#26111yescharacteristic
155#95—522no—
156C2×C13—21no—
157C2×C13#194811yescharacteristic
158D13—21no—
159D13#223112yes—
160C22×C4—131no—
161C22×C4—261no—
162C22×C4—522no—
163M16—261no—
164M16—261no—
165M16—521no—
166C2×C8—131no—
167C2×C8—131no—
168C2×C8—131no—
169C2×C8—131no—
170C2×C8—131no—
171C2×C8—131no—
172C2×C8—131no—
173C2×C8—131no—
174C2×C8—131no—
175C2×C8—131no—
176C2×C8—521no—
177C2×C8C4⋊#26111yescharacteristic
178C2×C8C22×#26111yescharacteristic
179C4⋊C4—262no—
180C4⋊C4—522no—
181C4⋊C4—522no—
182C22⋊C4—521no—
183C42—131no—
184C42—261no—
185C42—521no—
186C42C4⋊#26111yescharacteristic
187C16—22no—
188C16—262no—
189C13#1318711yescharacteristic, complemented, Sylow
190C23—131no—
191C2×C4—21no—
192C2×C4—131no—
193C2×C4—131no—
194C2×C4—131no—
195C2×C4—131no—
196C2×C4—131no—
197C2×C4—261no—
198C2×C4—522no—
199C2×C4—522no—
200C2×C4—1042no—
201C2×C4—1044no—
202C2×C4C2×C4⋊#26111yescharacteristic
203C8—131no—
204C8—131no—
205C8—131no—
206C8—131no—
207C8—521no—
208C8—521no—
209C8#8810111yescharacteristic
210C8#8810111yescharacteristic
211C8D4×#26111yescharacteristic
212C8Q8×#26111yescharacteristic
213C22—131no—
214C22—131no—
215C22—262no—
216C22#1171909811yescharacteristic
217C4—41no—
218C4—131no—
219C4—131no—
220C4—521no—
221C4—1042no—
222C4—2082no—
223C4#1171908311yescharacteristic
224C4C2×#8810111yescharacteristic
225C2—21no—
226C2—132no—
227C2—261no—
228C2#1313094811yescharacteristic
subgroupG/H
centerC2#13130948
commutatorC2×C8×C13C22×C4
FrattiniC2×C8C22×#261
FittingC13×#364C4
socleC2×C13#1948
prime radicalC22×D13AGL(1,ℤ/8)
cosocleC2×C8×D13C23
hypercenter#364#261
hypocenterC13#13187
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #364

Complements

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

NH ≅ G/Ntype
17. C13×#364C4semidirect
18. #11718103C4semidirect
19. #11718055C4semidirect
116. #364#261semidirect
189. C13#13187semidirect

Maximal subgroups

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

subgroupindex
D13⋊#3652
#131307732
#131306382
#131299082
D13×#3642
#1318713