Finite Group Databasebeta

← #15782005

Subgroups — #15782005

Order 3328.

370 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 101 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#13116555C212yesmaximal
2#13115707C211yesmaximal, characteristic
3#13112941C212yesmaximal
4#13112920C211yesmaximal, characteristic
5C13×#3162C211yesmaximal, characteristic
6C13×#533—21no—
7C22×Dic52C2211yescharacteristic
8C13×#501—24no—
9C13×#427—21no—
10C13×#427C2212yes—
11C2×C13×#97C2211yescharacteristic
12C2×#88057C2211yescharacteristic
13C2×#88056—21no—
14C2×#88052C2212yes—
15#11718590—21no—
16#11718084—24no—
17C22×Dic26—21no—
18C22×C8×C13D411yescharacteristic
19C22×C8×C13C2311yescharacteristic
20C13×C4⋊Q8—22no—
21C13×#125—22no—
22C13×C22⋊Q8—42no—
23C4×Q8×C13—42no—
24C13×#117—22no—
25C2×C42×C13D411yescharacteristic
26C2×C4⋊Dic13—21no—
27C2×Dic52—22no—
28C2×Dic52—22no—
29C2×Dic52—21no—
30C2×Dic52Q812yescomplemented
31C13×#107—22no—
32C13×#107D414yes—
33C13×#106—22no—
34C13×#106—22no—
35C13×#97—22no—
36#88071—42no—
37#88057—22no—
38#88056—42no—
39#88052—22no—
40#88052—22no—
41C2×#6090—22no—
42#13368—131nomaximal, Sylow
43C2×Q8×C13—42no—
44C22×C4×C13D812yes—
45C22×C4×C13C2×D411yescharacteristic
46C22×Dic13—41no—
47C22×Dic13—41no—
48C2×Dic26—22no—
49C2×Dic26—41no—
50C2×Dic26—41no—
51C2×Dic26—41no—
52C2×Dic26—41no—
53C2×Dic26—41no—
54C2×C8×C13—21no—
55C2×C8×C13—21no—
56C2×C8×C13SD1612yes—
57C2×C8×C13C2×D412yes—
58C2×C8×C13C2×Q811yescharacteristic
59C2×C8×C13#4112yes—
60C2×C8×C13#4111yescharacteristic
61C13×C4⋊C4—24no—
62C13×C4⋊C4—44no—
63C13×C4⋊C4—42no—
64C13×C22⋊C4—42no—
65C42×C13—21no—
66C42×C13—21no—
67C42×C13—42no—
68C4⋊Dic13—41no—
69C4⋊Dic13—41no—
70Dic52—24no—
71Dic52—42no—
72#6090—42no—
73#3162D1311yescharacteristic
74#2141—132no—
75#1971—131no—
76#1386—132no—
77#1377—131no—
78C23×C13C2×D811yescharacteristic
79Q8×C13—84no—
80C2×C4×C13—22no—
81C2×C4×C13—42no—
82C2×C4×C13—44no—
83C2×C4×C13#12011yescharacteristic
84C2×C4×C13C22⋊Q811yescharacteristic
85C2×C4×C13#12411yescharacteristic
86C2×C4×C13C2×SD1611yescharacteristic
87C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
88C2×C4×C13#13711yescharacteristic
89C2×Dic13—42no—
90C2×Dic13—81no—
91C2×Dic13—81no—
92C2×Dic13—82no—
93C2×Dic13—81no—
94Dic26—42no—
95Dic26—42no—
96Dic26—81no—
97Dic26—81no—
98C8×C13—22no—
99C8×C13C22⋊Q812yes—
100C8×C13#12412yes—
101C22×Q16—131no—
102#533—21no—
103C2×M32—132no—
104#501—24no—
105#427—21no—
106#427C2×D1312yes—
107C2×#106—131no—
108C2×#103—261no—
109C2×#97C2×D1311yescharacteristic
110#391—261no—
111#358—264no—
112C22×C13—22no—
113C22×C13#44711yescharacteristic
114C22×C13#47411yescharacteristic
115C22×C13#48611yescharacteristic
116C4×C13—42no—
117C4×C13—84no—
118C4×C13#39311yescharacteristic
119C4×C13#44811yescharacteristic
120C4×C13#47611yescharacteristic
121C4×C13#48911yescharacteristic
122Dic13—82no—
123Dic13—161no—
124C22×Q8—261no—
125C2×Q16—132no—
126C2×Q16—262no—
127C2×Q16—261no—
128C2×Q16—262no—
129C22×C8C22⋊D1311yescharacteristic
130C22×C8C22×D1311yescharacteristic
131C4⋊Q8—22no—
132#125—22no—
133C22⋊Q8—42no—
134C4×Q8—42no—
135#117—22no—
136C2×C4⋊C4—261no—
137C2×C42C22⋊D1311yescharacteristic
138M32—262no—
139M32—262no—
140C2×C16—262no—
141#107—22no—
142#107C22⋊D1314yes—
143#106—22no—
144#106—22no—
145#106—262no—
146#103—522no—
147#97—22no—
148#95—522no—
149C2×C13—21no—
150C2×C13—21no—
151C2×C13#202311yescharacteristic
152C2×C13#219112yes—
153C2×Q8—42no—
154C2×Q8—262no—
155C2×Q8—521no—
156C2×Q8—521no—
157C2×Q8—521no—
158C2×Q8—521no—
159C2×Q8—521no—
160C22×C4—521no—
161C22×C4—521no—
162C22×C4#610412yes—
163C22×C4C2×C22⋊D1311yescharacteristic
164Q16—264no—
165Q16—522no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8#610612yes—
169C2×C8Q8×D1311yescharacteristic
170C2×C8#613112yes—
171C2×C8#613111yescharacteristic
172C2×C8C2×C22⋊D1312yes—
173C4⋊C4—24no—
174C4⋊C4—44no—
175C4⋊C4—42no—
176C4⋊C4—521no—
177C4⋊C4—521no—
178C22⋊C4—42no—
179C42—21no—
180C42—21no—
181C42—42no—
182C16—522no—
183C13#1336811yescharacteristic, complemented, Sylow
184C23C2×#610411yescharacteristic
185Q8—84no—
186Q8—522no—
187Q8—522no—
188Q8—1041no—
189Q8—1041no—
190C2×C4—22no—
191C2×C4—42no—
192C2×C4—44no—
193C2×C4—522no—
194C2×C4—1041no—
195C2×C4—1041no—
196C2×C4—1042no—
197C2×C4—1041no—
198C2×C4#8818611yescharacteristic
199C2×C4C2×#610611yescharacteristic
200C2×C4#8819611yescharacteristic
201C2×C4#8820011yescharacteristic
202C2×C4#8820111yescharacteristic
203C2×C4#8820711yescharacteristic
204C8—22no—
205C8#8820012yes—
206C8#8820112yes—
207C22—22no—
208C22#1171874811yescharacteristic
209C22#1171874911yescharacteristic
210C22#1171887811yescharacteristic
211C4—42no—
212C4—84no—
213C4—1042no—
214C4—2081no—
215C4#1171874511yescharacteristic
216C4#1171875011yescharacteristic
217C4#1171888811yescharacteristic
218C4#1171889211yescharacteristic
219C2—21no—
220C2—21no—
221C2#1311596911yescharacteristic
222C2#1311678712yes—
subgroupG/H
centerC22#11718878
commutator, cosocleC22×C8×C13C23
FrattiniC22×C8C22×D13
FittingC13×#3162C2
socleC22×C13#447
prime radicalC23×C13C2×D8
hypercenter#3162D13
hypocenterC13#13368
LCSG ▷ C22×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ #3162

Complements

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

NH ≅ G/Ntype
30. C2×Dic52Q8semidirect
183. C13#13368semidirect

Maximal subgroups

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

subgroupindex
#131165552
#131157072
#131129412
#131129202
C13×#31622
#1336813