Finite Group Databasebeta

← #15757916

Subgroups — #15757916

Order 3328.

800 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 143 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×#11718640C211yesmaximal, characteristic
2#13117454C211yesmaximal, characteristic
3#13114772C212yesmaximal
4#13112716C212yesmaximal
5C2×C13×#324C211yesmaximal, characteristic
6C23×Dic26C2211yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C2×#88180—21no—
9C22×#6101—21no—
10C2×C13×C22⋊C8C2212yes—
11#11718873—21no—
12#11718873C2212yes—
13C2×#88071—21no—
14C2×#88071C2211yescharacteristic
15C2×#88056—24no—
16#11718646—24no—
17#11718640—22no—
18#11718640C414yescomplemented
19C13×#324—22no—
20C23×C4×C13D411yescharacteristic
21C23×C4×C13D411yescharacteristic
22C23×C4×C13C2311yescharacteristic
23C23×Dic13—21no—
24C23×Dic13—21no—
25C22×Dic26—22no—
26C22×Dic26—22no—
27C22×Dic26—21no—
28C22×Dic26—44no—
29C22×Dic26C2×C412yes—
30C22×C8×C13—22no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4C2×C412yes—
34C2×C13×C4⋊C4D412yes—
35C2×C22⋊Dic13—22no—
36#88180—42no—
37#88180—42no—
38C2×C4⋊Dic13—22no—
39C2×C4⋊Dic13—22no—
40C2×C4⋊Dic13D414yes—
41C2×#6101—24no—
42C2×#6101—44no—
43C2×C4×Dic13—22no—
44C13×C22⋊C8—22no—
45C13×C22⋊C8—22no—
46#88071—22no—
47#88071—24no—
48#88071—21no—
49#88071—22no—
50#88071C2×C412yes—
51#88056—48no—
52#9015—131nomaximal, Sylow
53C24×C13C2×D411yescharacteristic
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—42no—
61C22×C4×C13—42no—
62C22×C4×C13C22⋊C412yes—
63C22×C4×C13C22⋊C412yes—
64C22×C4×C13SD1612yes—
65C22×C4×C13Q1612yes—
66C22×C4×C13C22×C411yescharacteristic
67C22×C4×C13C2×D412yes—
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13#4112yes—
70C22×Dic13—24no—
71C22×Dic13—24no—
72C22×Dic13—22no—
73C22×Dic13—22no—
74C22×Dic13—24no—
75C22×Dic13—42no—
76C22×Dic13—42no—
77C22×Dic13—41no—
78C22×Dic13—41no—
79C22×Dic13—41no—
80C22×Dic13—41no—
81C2×Dic26—28no—
82C2×Dic26—24no—
83C2×Dic26—44no—
84C2×Dic26—48no—
85C2×Dic26—44no—
86C2×Dic26—44no—
87C2×Dic26—42no—
88C2×C8×C13—44no—
89C2×C8×C13—42no—
90C13×C4⋊C4—24no—
91C13×C4⋊C4—24no—
92C22⋊Dic13—42no—
93C22⋊Dic13—42no—
94C4⋊Dic13—44no—
95C4⋊Dic13—44no—
96C4⋊Dic13—82no—
97#6101—48no—
98C4×Dic13—44no—
99C2×#395—131no—
100#2316—131no—
101#1787—132no—
102C2×#324D1311yescharacteristic
103#1294—132no—
104C23×C13—22no—
105C23×C13—22no—
106C23×C13C2×C22⋊C411yescharacteristic
107C23×C13#12011yescharacteristic
108C23×C13#12311yescharacteristic
109C23×C13C2×SD1611yescharacteristic
110C23×C13C2×Q1611yescharacteristic
111C23×C13AGL(1,ℤ/8)11yescharacteristic
112C23×C13#13711yescharacteristic
113C2×C4×C13—22no—
114C2×C4×C13—22no—
115C2×C4×C13—22no—
116C2×C4×C13—22no—
117C2×C4×C13—24no—
118C2×C4×C13—22no—
119C2×C4×C13—22no—
120C2×C4×C13—22no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—81no—
127C2×C4×C13#10314yescomplemented
128C2×C4×C13C4×D412yes—
129C2×C4×C13#12112yes—
130C2×Dic13—24no—
131C2×Dic13—24no—
132C2×Dic13—42no—
133C2×Dic13—42no—
134C2×Dic13—44no—
135C2×Dic13—44no—
136C2×Dic13—44no—
137C2×Dic13—42no—
138C2×Dic13—42no—
139C2×Dic13—44no—
140C2×Dic13—44no—
141C2×Dic13—44no—
142C2×Dic13—44no—
143Dic26—28no—
144Dic26—48no—
145Dic26—44no—
146C8×C13—82no—
147C23×Q8—131no—
148C2×#117—261no—
149C22×C4⋊C4—261no—
150C22×C4⋊C4C2×D1311yescharacteristic
151C2×#103—264no—
152C2×C22⋊C8C2×D1312yes—
153#395—134no—
154#395—262no—
155#389—264no—
156#380—132no—
157#380—261no—
158C2×#95—131no—
159C2×#95—261no—
160#324—22no—
161C22×C13—22no—
162C22×C13—22no—
163C22×C13—22no—
164C22×C13—22no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13#38611yescharacteristic
170C22×C13C2×#10311yescharacteristic
171C22×C13#41711yescharacteristic
172C22×C13#45011yescharacteristic
173C22×C13#45111yescharacteristic
174C22×C13#45612yes—
175C22×C13B(4,𝔽2)12yes—
176C22×C13#48311yescharacteristic
177C22×C13#48411yescharacteristic
178C4×C13—24no—
179C4×C13—22no—
180C4×C13—22no—
181C4×C13—42no—
182Dic13—44no—
183Dic13—44no—
184Dic13—84no—
185C22×Q8—132no—
186C22×Q8—261no—
187C22×Q8—262no—
188C22×Q8—262no—
189C22×Q8—524no—
190C23×C4—261no—
191C23×C4—261no—
192C23×C4D5211yescharacteristic
193C23×C4D5211yescharacteristic
194C23×C4C22×D1311yescharacteristic
195C22×C8—22no—
196#117—522no—
197#117—522no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—134no—
201C2×C4⋊C4—262no—
202C2×C4⋊C4—264no—
203C2×C4⋊C4—262no—
204C2×C4⋊C4—524no—
205C2×C4⋊C4C4×D1312yes—
206C2×C4⋊C4C22⋊D1312yes—
207C2×C22⋊C4—262no—
208C2×C42—262no—
209#103—528no—
210C22⋊C8—22no—
211C22⋊C8—22no—
212#95—132no—
213#95—262no—
214#95—264no—
215#95—262no—
216#95—261no—
217C2×C13—21no—
218C2×C13—21no—
219C2×C13—21no—
220C2×C13—21no—
221C2×C13#160412yes—
222C2×C13#160512yes—
223C2×C13#187211yescharacteristic
224C2×C13#188611yescharacteristic
225C2×C13#188911yescharacteristic
226C24C2×D5211yescharacteristic
227C2×Q8—268no—
228C2×Q8—264no—
229C2×Q8—524no—
230C2×Q8—524no—
231C2×Q8—524no—
232C2×Q8—528no—
233C2×Q8—522no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4—264no—
243C22×C4—264no—
244C22×C4—262no—
245C22×C4—262no—
246C22×C4—264no—
247C22×C4—522no—
248C22×C4—522no—
249C22×C4—521no—
250C22×C4—521no—
251C22×C4—521no—
252C22×C4—521no—
253C22×C4#609512yes—
254C22×C4Dic5212yes—
255C22×C4#610312yes—
256C22×C4#610312yes—
257C22×C4C2×C4×D1311yescharacteristic
258C22×C4D4×D1312yes—
259C22×C4#612912yes—
260C22×C4C2×C22⋊D1311yescharacteristic
261C2×C8—44no—
262C2×C8—42no—
263C4⋊C4—24no—
264C4⋊C4—24no—
265C4⋊C4—524no—
266C4⋊C4—524no—
267C4⋊C4—528no—
268C4⋊C4—1042no—
269C22⋊C4—522no—
270C22⋊C4—522no—
271C42—524no—
272C13#901511yescharacteristic, complemented, Sylow
273C23—22no—
274C23—22no—
275C23#8813611yescharacteristic
276C23#8814011yescharacteristic
277C23C2×#609511yescharacteristic
278C23C2×Dic5211yescharacteristic
279C23#8816211yescharacteristic
280C23#8816311yescharacteristic
281C23C2×#610311yescharacteristic
282Q8—268no—
283Q8—528no—
284Q8—524no—
285C2×C4—22no—
286C2×C4—24no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—81no—
299C2×C4—264no—
300C2×C4—264no—
301C2×C4—522no—
302C2×C4—524no—
303C2×C4—524no—
304C2×C4—522no—
305C2×C4—524no—
306C2×C4—524no—
307C2×C4—522no—
308C2×C4—522no—
309C2×C4—524no—
310C2×C4—524no—
311C2×C4—524no—
312C2×C4#8805614yescomplemented
313C2×C4#8813512yes—
314C2×C4#8819312yes—
315C8—82no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—22no—
321C22—22no—
322C22—22no—
323C22—22no—
324C22#1171838211yescharacteristic
325C22#1171838311yescharacteristic
326C22#1171839211yescharacteristic
327C22#1171840011yescharacteristic
328C22#1171840212yes—
329C22#1171841312yes—
330C22#1171861911yescharacteristic
331C22C2×#8805611yescharacteristic
332C22#1171879411yescharacteristic
333C4—24no—
334C4—22no—
335C4—22no—
336C4—42no—
337C4—524no—
338C4—524no—
339C4—1044no—
340C2—21no—
341C2—21no—
342C2—21no—
343C2—21no—
344C2#1311380712yes—
345C2#1311381212yes—
346C2#1311514111yescharacteristic
347C2#1311522711yescharacteristic
348C2#1311524211yescharacteristic
subgroupG/H
centerC23#88136
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#324C2
socleC23×C13#120
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenterC2×#324D13
hypocenterC13#9015
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
18. #11718640C4semidirect
127. C2×C4×C13#103semidirect
272. C13#9015semidirect
312. C2×C4#88056semidirect

Maximal subgroups

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

subgroupindex
C2×#117186402
#131174542
#131147722
#131127162
C2×C13×#3242
#901513