Finite Group Databasebeta

← #15767597

Subgroups — #15767597

Order 3328.

306 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 97 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#13115826C211yesmaximal, characteristic
2#13115612C211yesmaximal, characteristic
3#13113606C211yesmaximal, characteristic
4#13113586C211yesmaximal, characteristic
5#13113521C211yesmaximal, characteristic
6#13112711C211yesmaximal, characteristic
7C2×C13×#332C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×#88059—21no—
12#11718586C2211yescharacteristic
13#11718585C2211yescharacteristic
14#11718585C2211yescharacteristic
15C4×#6099C2211yescharacteristic
16C13×#332—22no—
17#11718144—21no—
18#11718139—21no—
19#11718139—21no—
20#11718122—21no—
21#11718122—21no—
22#11718072—21no—
23#11718072—22no—
24#11718071—21no—
25C22×Q8×C13—21no—
26C22×C8×C13—21no—
27C22×C8×C13—21no—
28C13×C4⋊Q8—21no—
29C13×C4⋊Q8—21no—
30C13×C4⋊Q8—21no—
31C13×C4⋊Q8—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4Q812yes—
34C2×C42×C13C2311yescharacteristic
35C2×#6099—21no—
36C2×#6099—21no—
37C2×#6099D411yescharacteristic
38C2×#6099D411yescharacteristic
39C13×C4⋊C8—21no—
40C13×C4⋊C8—21no—
41C13×C4⋊C8—21no—
42C13×C4⋊C8D412yes—
43C22⋊#1055—21no—
44#88059—42no—
45C4⋊#1055—21no—
46C4⋊#1055—21no—
47C4⋊#1055—21no—
48C4⋊#1055—21no—
49C4⋊#1055D411yescharacteristic
50C4⋊#1055D411yescharacteristic
51#88043—21no—
52C4×#1055—21no—
53C4×#1055—21no—
54#10610—131nomaximal, Sylow
55C2×Q8×C13—41no—
56C2×Q8×C13—41no—
57C2×Q8×C13—81no—
58C2×Q8×C13—81no—
59C22×C4×C13—22no—
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13C2×Q811yescharacteristic
62C22×C4×C13#4111yescharacteristic
63C2×C8×C13—22no—
64C2×C8×C13—41no—
65C2×C8×C13—41no—
66C2×C8×C13—41no—
67C2×C8×C13—81no—
68C13×C4⋊C4—22no—
69C13×C4⋊C4—22no—
70C13×C4⋊C4—41no—
71C13×C4⋊C4—41no—
72C42×C13C2×D411yescharacteristic
73C42×C13C2×D411yescharacteristic
74C42×C13#4111yescharacteristic
75C42×C13#4111yescharacteristic
76#6099—21no—
77#6099—21no—
78#6099—21no—
79#6099—41no—
80#6099—41no—
81#6099—41no—
82#6099—41no—
83#6099SD1612yes—
84C2×#1055—21no—
85C2×#1055—21no—
86C2×#1055—21no—
87C2×#1055—21no—
88C2×#1055—41no—
89C2×#1055—41no—
90#1997—131no—
91#1950—131no—
92#1570—131no—
93#1565—131no—
94#1549—131no—
95C2×#332D1311yescharacteristic
96#1292—131no—
97C23×C13C22⋊Q811yescharacteristic
98Q8×C13—82no—
99Q8×C13—81no—
100Q8×C13—81no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—41no—
104C2×C4×C13—42no—
105C2×C4×C13—82no—
106C2×C4×C13#12111yescharacteristic
107C2×C4×C13#12111yescharacteristic
108C2×C4×C13#12111yescharacteristic
109C2×C4×C13C22⋊Q811yescharacteristic
110C2×C4×C13C22⋊Q811yescharacteristic
111C2×C4×C13#12611yescharacteristic
112C2×C4×C13C2×SD1611yescharacteristic
113C2×C4×C13#13511yescharacteristic
114C2×C4×C13#13711yescharacteristic
115C2×C4×C13#13711yescharacteristic
116C8×C13—42no—
117C8×C13—81no—
118#1055—22no—
119#1055—41no—
120#1055—41no—
121#1055—41no—
122#1055—81no—
123#1055—81no—
124C2×C4⋊Q8C2×D1311yescharacteristic
125#431—131no—
126C2×#108—261no—
127#423—131no—
128#423—131no—
129C2×C4⋊C8C2×D1311yescharacteristic
130C2×C4⋊C8C2×D1311yescharacteristic
131C4×M16—131no—
132#343—261no—
133#343—261no—
134#341—261no—
135#335—261no—
136#334—261no—
137#334—262no—
138#332—22no—
139#332—261no—
140#332—261no—
141C22×C13—21no—
142C22×C13—21no—
143C22×C13#39611yescharacteristic
144C22×C13#47511yescharacteristic
145C22×C13#47911yescharacteristic
146C4×C13—21no—
147C4×C13—21no—
148C4×C13—21no—
149C4×C13—82no—
150C4×C13#46111yescharacteristic
151C4×C13#46411yescharacteristic
152C4×C13#46511yescharacteristic
153C4×C13#47011yescharacteristic
154C4×C13#47111yescharacteristic
155C4×C13#47211yescharacteristic
156C22×Q8—21no—
157C2×M16—131no—
158C2×M16—131no—
159C2×M16—261no—
160C2×M16—261no—
161C22×C8—21no—
162C22×C8—21no—
163C4⋊Q8—21no—
164C4⋊Q8—21no—
165C4⋊Q8—21no—
166C4⋊Q8—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4Dic2612yes—
169C2×C42C22×D1311yescharacteristic
170#108—522no—
171C4⋊C8—21no—
172C4⋊C8—21no—
173C4⋊C8—21no—
174C4⋊C8—131no—
175C4⋊C8—131no—
176C4⋊C8—261no—
177C4⋊C8—261no—
178C4⋊C8—261no—
179C4⋊C8—261no—
180C4⋊C8C22⋊D1312yes—
181C22⋊C8—261no—
182#97—261no—
183C4×C8—261no—
184C4×C8—261no—
185C2×C13—21no—
186C2×C13—21no—
187C2×C13#206311yescharacteristic
188C2×C13#206611yescharacteristic
189C2×C13#207011yescharacteristic
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8—81no—
193C2×Q8—81no—
194C22×C4—22no—
195C22×C4C2×Dic2611yescharacteristic
196C22×C4D4×D1311yescharacteristic
197C22×C4#612911yescharacteristic
198M16—132no—
199M16—261no—
200M16—261no—
201M16—261no—
202M16—521no—
203M16—521no—
204M16—521no—
205M16—521no—
206C2×C8—22no—
207C2×C8—41no—
208C2×C8—41no—
209C2×C8—41no—
210C2×C8—81no—
211C2×C8—261no—
212C2×C8—261no—
213C2×C8—261no—
214C2×C8—261no—
215C2×C8—521no—
216C2×C8—521no—
217C4⋊C4—22no—
218C4⋊C4—22no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C42#612711yescharacteristic
222C42D4×D1311yescharacteristic
223C42#612911yescharacteristic
224C42C2×C22⋊D1311yescharacteristic
225C13#1061011yescharacteristic, complemented, Sylow
226C23#8813211yescharacteristic
227Q8—82no—
228Q8—81no—
229Q8—81no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—42no—
234C2×C4—82no—
235C2×C4#8813211yescharacteristic
236C2×C4#8813311yescharacteristic
237C2×C4#8813811yescharacteristic
238C2×C4SD16×D1311yescharacteristic
239C2×C4#8816911yescharacteristic
240C2×C4#8817211yescharacteristic
241C2×C4#8817311yescharacteristic
242C2×C4#8817811yescharacteristic
243C2×C4#8819211yescharacteristic
244C2×C4#8819311yescharacteristic
245C8—42no—
246C8—81no—
247C8—262no—
248C8—521no—
249C8—521no—
250C8—521no—
251C8—1041no—
252C8—1041no—
253C22—21no—
254C22—21no—
255C22#1171845211yescharacteristic
256C22#1171845711yescharacteristic
257C22#1171860911yescharacteristic
258C4—21no—
259C4—21no—
260C4—21no—
261C4—82no—
262C4#1171846811yescharacteristic
263C4#1171847711yescharacteristic
264C4#1171882111yescharacteristic
265C4#1171882311yescharacteristic
266C4#1171883811yescharacteristic
267C4#1171884611yescharacteristic
268C2—21no—
269C2—21no—
270C2#1311619411yescharacteristic
271C2#1311621311yescharacteristic
272C2#1311623711yescharacteristic
subgroupG/H
centerC22#11718609
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#332C2
socleC22×C13#396
prime radicalC23×C13C22⋊Q8
hypercenterC2×#332D13
hypocenterC13#10610
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
225. C13#10610semidirect

Maximal subgroups

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

subgroupindex
#131158262
#131156122
#131136062
#131135862
#131135212
#131127112
C2×C13×#3322
#1061013