Finite Group Databasebeta

← #15766537

Subgroups — #15766537

Order 3328.

408 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#11718510C211yesmaximal, characteristic
2#13114829C211yesmaximal, characteristic
3#13113606C211yesmaximal, characteristic
4#13113509C211yesmaximal, characteristic
5#13113507C211yesmaximal, characteristic
6#13113232C211yesmaximal, characteristic
7C13×#1301C211yesmaximal, characteristic
8C22×Dic52—21no—
9C2×#88123C2211yescharacteristic
10C2×C4×Dic26C2211yescharacteristic
11C13×#431C2211yescharacteristic
12C13×#423C2211yescharacteristic
13C2×C13×C4⋊C8C2211yescharacteristic
14C2×#88064—21no—
15C2×#88056—21no—
16#11718586C2211yescharacteristic
17#11718585C2211yescharacteristic
18#11718510—22no—
19#11718510—22no—
20#11718146—21no—
21#11718078—22no—
22#11718074—22no—
23#11718072—22no—
24#11718048—22no—
25C22×Dic26—21no—
26C22×Dic26D411yescharacteristic
27C2×C13×M16—21no—
28C22×C8×C13—21no—
29C2×C42×C13C2311yescharacteristic
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13D411yescharacteristic
33C2×#6101—21no—
34C2×C4×Dic13—21no—
35C2×#6099—21no—
36C2×Dic52—24no—
37C2×Dic52—42no—
38C2×Dic52—42no—
39#88123—21no—
40#88123—21no—
41#88123—21no—
42#88123D412yes—
43C4×Dic26—21no—
44C4×Dic26—21no—
45C4×Dic26—21no—
46C4×Dic26—21no—
47C13×C4⋊C8—21no—
48C13×C4⋊C8—21no—
49C13×C4⋊C8—21no—
50C13×C4⋊C8—21no—
51C13×C4⋊C8D412yes—
52C13×C22⋊C8—21no—
53C4×C8×C13—21no—
54C22⋊#1055—21no—
55#88064—42no—
56#88056—24no—
57C4⋊#1055—21no—
58C4⋊#1055—21no—
59C4⋊#1055D412yes—
60C4×#1055—21no—
61#10447—131nomaximal, Sylow
62C22×C4×C13C2×D411yescharacteristic
63C22×C4×C13#4111yescharacteristic
64C22×C4×C13#4111yescharacteristic
65C22×Dic13—21no—
66C22×Dic13—21no—
67C22×Dic13—41no—
68C2×Dic26—21no—
69C2×Dic26—21no—
70C2×Dic26—21no—
71C2×Dic26—21no—
72C2×Dic26—21no—
73C2×Dic26—22no—
74C2×Dic26—41no—
75C2×Dic26—41no—
76C2×Dic26—41no—
77C2×Dic26—41no—
78C2×Dic26—41no—
79C2×Dic26SD1612yes—
80C13×M16—41no—
81C13×M16—41no—
82C2×C8×C13—22no—
83C2×C8×C13—41no—
84C2×C8×C13—41no—
85C2×C8×C13—41no—
86C2×C8×C13—41no—
87C42×C13C2×D411yescharacteristic
88C42×C13C2×D411yescharacteristic
89C42×C13C2×D411yescharacteristic
90C42×C13#4111yescharacteristic
91C4⋊Dic13—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13—22no—
94C4⋊Dic13—22no—
95C4⋊Dic13—41no—
96C4⋊Dic13—41no—
97#6101—41no—
98#6101—41no—
99C4×Dic13—41no—
100C4×Dic13—41no—
101#6099—41no—
102#6099—41no—
103C2×#1055—22no—
104C2×#1055—41no—
105Dic52—48no—
106C2×#462—131no—
107#1801—131no—
108#1570—131no—
109#1546—131no—
110#1546—131no—
111#1479—131no—
112#1301D1311yescharacteristic
113C23×C13#12311yescharacteristic
114C2×C4×C13—22no—
115C2×C4×C13—41no—
116C2×C4×C13#12011yescharacteristic
117C2×C4×C13#12111yescharacteristic
118C2×C4×C13#12111yescharacteristic
119C2×C4×C13#12111yescharacteristic
120C2×C4×C13#12311yescharacteristic
121C2×C4×C13#12411yescharacteristic
122C2×C4×C13C2×SD1611yescharacteristic
123C2×C4×C13#13511yescharacteristic
124C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
126C2×Dic13—22no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—42no—
131C2×Dic13—81no—
132C2×Dic13—81no—
133C2×Dic13—81no—
134Dic26—22no—
135Dic26—22no—
136Dic26—41no—
137Dic26—41no—
138Dic26—42no—
139Dic26—42no—
140Dic26—81no—
141Dic26—81no—
142C8×C13—42no—
143C8×C13—81no—
144C8×C13—81no—
145#1055—42no—
146#1055—81no—
147C22×Q16—261no—
148C2×C4⋊Q8—131no—
149C2×C4×Q8—131no—
150#462—262no—
151#462—262no—
152#431—131no—
153#431C2×D1311yescharacteristic
154#423—131no—
155#423C2×D1311yescharacteristic
156C2×C4⋊C8C2×D1311yescharacteristic
157C2×#103—261no—
158C2×#101—261no—
159#343—261no—
160#334—262no—
161#332—262no—
162#332—262no—
163Q8⋊C8—262no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13#39411yescharacteristic
167C22×C13#48111yescharacteristic
168C22×C13#48211yescharacteristic
169C4×C13—21no—
170C4×C13—21no—
171C4×C13—21no—
172C4×C13#44911yescharacteristic
173C4×C13#45011yescharacteristic
174C4×C13#46511yescharacteristic
175C4×C13#46911yescharacteristic
176C4×C13#47312yes—
177Dic13—42no—
178Dic13—81no—
179Dic13—82no—
180C22×Q8—131no—
181C22×Q8—261no—
182C2×Q16—264no—
183C2×Q16—522no—
184C2×Q16—522no—
185C2×M16—21no—
186C2×M16—261no—
187C22×C8—21no—
188C4⋊Q8—132no—
189C4⋊Q8—261no—
190C4⋊Q8—261no—
191C4⋊Q8—261no—
192C4×Q8—261no—
193C4×Q8—261no—
194C4×Q8—261no—
195C4×Q8—261no—
196C2×C4⋊C4—131no—
197C2×C4⋊C4—261no—
198C2×C4⋊C4—261no—
199C2×C4⋊C4—261no—
200C2×C42—261no—
201C2×C42C22×D1311yescharacteristic
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8—21no—
206C4⋊C8—132no—
207C4⋊C8—261no—
208C4⋊C8—261no—
209C4⋊C8D5212yes—
210#103—264no—
211#101—522no—
212C22⋊C8—21no—
213C22⋊C8—261no—
214C4×C8—21no—
215C4×C8—261no—
216C2×C13—21no—
217C2×C13—21no—
218C2×C13#203411yescharacteristic
219C2×C13#204711yescharacteristic
220C2×C13#204911yescharacteristic
221C2×Q8—132no—
222C2×Q8—261no—
223C2×Q8—261no—
224C2×Q8—262no—
225C2×Q8—261no—
226C2×Q8—261no—
227C2×Q8—261no—
228C2×Q8—521no—
229C2×Q8—521no—
230C2×Q8—521no—
231C2×Q8—521no—
232C2×Q8—521no—
233C22×C4—261no—
234C22×C4—261no—
235C22×C4—521no—
236C22×C4#612711yescharacteristic
237C22×C4D4×D1311yescharacteristic
238C22×C4#613111yescharacteristic
239Q16—528no—
240M16—41no—
241M16—41no—
242M16—521no—
243M16—521no—
244C2×C8—22no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—262no—
250C2×C8—521no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4—262no—
254C4⋊C4—262no—
255C4⋊C4—521no—
256C4⋊C4—521no—
257C4⋊C4—521no—
258C4⋊C4—521no—
259C42—521no—
260C42—521no—
261C42C2×D5211yescharacteristic
262C42#612711yescharacteristic
263C42D4×D1311yescharacteristic
264C42D4×D1311yescharacteristic
265C13#1044711yescharacteristic, complemented, Sylow
266C23#8814811yescharacteristic
267Q8—262no—
268Q8—262no—
269Q8—521no—
270Q8—521no—
271Q8—522no—
272Q8—522no—
273Q8—1041no—
274Q8—1041no—
275C2×C4—22no—
276C2×C4—41no—
277C2×C4—262no—
278C2×C4—521no—
279C2×C4—521no—
280C2×C4—521no—
281C2×C4—522no—
282C2×C4—1041no—
283C2×C4—1041no—
284C2×C4—1041no—
285C2×C4#8812911yescharacteristic
286C2×C4#8813611yescharacteristic
287C2×C4#8813811yescharacteristic
288C2×C4#8813811yescharacteristic
289C2×C4#8814811yescharacteristic
290C2×C4#8814911yescharacteristic
291C2×C4#8816511yescharacteristic
292C2×C4SD16×D1311yescharacteristic
293C2×C4#8816811yescharacteristic
294C2×C4#8817311yescharacteristic
295C8—42no—
296C8—81no—
297C8—81no—
298C8—522no—
299C8—1041no—
300C22—21no—
301C22—21no—
302C22#1171833311yescharacteristic
303C22#1171852411yescharacteristic
304C22#1171854611yescharacteristic
305C4—21no—
306C4—21no—
307C4—21no—
308C4—522no—
309C4—1042no—
310C4—1041no—
311C4#1171843711yescharacteristic
312C4#1171844311yescharacteristic
313C4#1171846811yescharacteristic
314C4#1171847211yescharacteristic
315C4#1171855712yes—
316C2—21no—
317C2—21no—
318C2#1311602811yescharacteristic
319C2#1311610511yescharacteristic
320C2#1311611911yescharacteristic
subgroupG/H
centerC22#11718333
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1301C2
socleC22×C13#394
prime radicalC23×C13#123
hypercenter#1301D13
hypocenterC13#10447
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
265. C13#10447semidirect

Maximal subgroups

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

subgroupindex
C2×#117185102
#131148292
#131136062
#131135092
#131135072
#131132322
C13×#13012
#1044713