Finite Group Databasebeta

← #15767327

Subgroups — #15767327

Order 3328.

560 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 119 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#13120950C211yesmaximal, characteristic
2#13115029C212yesmaximal
3#13112715C212yesmaximal
4#13112679C211yesmaximal, characteristic
5C13×#1442C211yesmaximal, characteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C2×#88178—21no—
8C2×C13×#95—21no—
9C2×C13×#95—21no—
10C2×C13×#95C2211yescharacteristic
11C2×C13×#95C2211yescharacteristic
12#11718873—21no—
13#11718873C2212yes—
14C2×C22⋊#1055C2212yes—
15C2×#88048—22no—
16#11718322—22no—
17#11718317—22no—
18#11718121—22no—
19C23×C4×C13—21no—
20C23×C4×C13—21no—
21C23×C4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13C2311yescharacteristic
24C22×Dic26—21no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—42no—
27C2×C22⋊Dic13—22no—
28C2×C4⋊Dic13—21no—
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13D412yes—
32C2×C4⋊Dic13D412yes—
33#88178—42no—
34#88178—42no—
35C2×#6101—22no—
36C22×#1055—22no—
37C13×#95—22no—
38C13×#95—21no—
39C13×#95—42no—
40C13×#95—42no—
41C13×#95Q812yescomplemented
42#88071—22no—
43#88071—22no—
44C22⋊#1055—22no—
45C22⋊#1055Q814yescomplemented
46#88048—44no—
47#10568—131nomaximal, Sylow
48C24×C13C2×D411yescharacteristic
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—22no—
54C22×C4×C13—22no—
55C22×C4×C13—41no—
56C22×C4×C13—41no—
57C22×C4×C13—41no—
58C22×C4×C13—41no—
59C22×C4×C13—41no—
60C22×C4×C13—41no—
61C22×C4×C13—41no—
62C22×C4×C13—41no—
63C22×C4×C13—41no—
64C22×C4×C13—41no—
65C22×C4×C13—41no—
66C22×C4×C13—41no—
67C22×C4×C13—41no—
68C22×C4×C13—41no—
69C22×C4×C13—41no—
70C22×C4×C13—41no—
71C22×C4×C13—41no—
72C22×C4×C13—41no—
73C22×C4×C13SD1612yes—
74C22×C4×C13SD1612yes—
75C22×C4×C13C2×D412yes—
76C22×C4×C13C2×Q811yescharacteristic
77C22×C4×C13C2×Q812yes—
78C22×C4×C13#4111yescharacteristic
79C22×Dic13—22no—
80C22×Dic13—22no—
81C2×Dic26—42no—
82C2×Dic26—81no—
83C2×Dic26—81no—
84C13×C4⋊C4—24no—
85C13×C4⋊C4—42no—
86C22⋊Dic13—42no—
87C22⋊Dic13—42no—
88C4⋊Dic13—42no—
89C4⋊Dic13—42no—
90C4⋊Dic13—42no—
91C4⋊Dic13—81no—
92C4⋊Dic13—81no—
93#6101—44no—
94C2×#1055—24no—
95C2×#1055—42no—
96C2×#1055—42no—
97#2659—131no—
98#1853—132no—
99#1442D1311yescharacteristic
100#1294—132no—
101#1280—131no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13#12011yescharacteristic
107C23×C13C22⋊Q811yescharacteristic
108C23×C13C4⋊Q811yescharacteristic
109C23×C13C2×SD1611yescharacteristic
110C23×C13C2×SD1611yescharacteristic
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—42no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13—81no—
133C2×C4×C13—81no—
134C2×C4×C13—81no—
135C2×C4×C13—81no—
136C2×C4×C13—81no—
137C2×C4×C13—81no—
138C2×C4×C13—81no—
139C2×C4×C13—81no—
140C2×C4×C13—81no—
141C2×C4×C13—81no—
142C2×C4×C13C22⋊Q812yes—
143C2×C4×C13C4⋊Q812yes—
144C2×Dic13—42no—
145C2×Dic13—42no—
146C2×Dic13—42no—
147C2×Dic13—42no—
148C2×Dic13—42no—
149C2×Dic13—42no—
150Dic26—84no—
151#1055—44no—
152C2×C22⋊Q8—261no—
153C22×C4⋊C4C2×D1311yescharacteristic
154C2×#106—262no—
155C2×C22⋊C8—132no—
156#398—262no—
157#395—262no—
158#380—132no—
159#380—261no—
160C2×#95—21no—
161C2×#95—21no—
162C2×#95C2×D1311yescharacteristic
163C2×#95C2×D1311yescharacteristic
164#340—262no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13#39511yescharacteristic
178C22×C13#44811yescharacteristic
179C22×C13#45011yescharacteristic
180C22×C13#45411yescharacteristic
181C22×C13#45511yescharacteristic
182C22×C13B(4,𝔽2)11yescharacteristic
183C22×C13#45811yescharacteristic
184C22×C13#47511yescharacteristic
185C22×C13#47611yescharacteristic
186C22×C13#49811yescharacteristic
187C22×C13#50111yescharacteristic
188C4×C13—22no—
189C4×C13—22no—
190C4×C13—42no—
191C4×C13—42no—
192C4×C13—82no—
193C4×C13—82no—
194Dic13—82no—
195Dic13—82no—
196C22×Q8—261no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4C22⋊D1311yescharacteristic
200C23×C4C22⋊D1311yescharacteristic
201C23×C4C22×D1311yescharacteristic
202C22×C8—262no—
203C22⋊Q8—522no—
204C22⋊Q8—522no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—42no—
207C2×C4⋊C4—132no—
208C2×C4⋊C4—132no—
209C2×C4⋊C4—262no—
210C2×C4⋊C4—261no—
211C2×C4⋊C4—261no—
212C2×C4⋊C4—261no—
213C2×C22⋊C4—262no—
214#106—524no—
215C22⋊C8—134no—
216C22⋊C8—262no—
217#95—21no—
218#95—22no—
219#95—42no—
220#95—42no—
221#95—262no—
222#95—262no—
223#95Dic2612yescomplemented
224C2×C13—21no—
225C2×C13—21no—
226C2×C13—21no—
227C2×C13—21no—
228C2×C13#159911yescharacteristic
229C2×C13#160111yescharacteristic
230C2×C13#160811yescharacteristic
231C2×C13#161611yescharacteristic
232C2×C13#205811yescharacteristic
233C2×C13#206111yescharacteristic
234C2×C13#206211yescharacteristic
235C24C2×C22⋊D1311yescharacteristic
236C2×Q8—522no—
237C2×Q8—1041no—
238C2×Q8—1041no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—262no—
264C22×C4—262no—
265C22×C4#610512yes—
266C22×C4#610612yes—
267C22×C4C2×Dic2611yescharacteristic
268C22×C4#612711yescharacteristic
269C22×C4D4×D1312yes—
270C22×C4Q8×D1312yes—
271C2×C8—264no—
272C2×C8—522no—
273C2×C8—522no—
274C4⋊C4—24no—
275C4⋊C4—42no—
276C4⋊C4—522no—
277C4⋊C4—522no—
278C4⋊C4—524no—
279C4⋊C4—522no—
280C4⋊C4—1041no—
281C4⋊C4—1041no—
282C22⋊C4—522no—
283C22⋊C4—522no—
284C13#1056811yescharacteristic, complemented, Sylow
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23#8817811yescharacteristic
290C23C2×#610511yescharacteristic
291C23#8819111yescharacteristic
292C23C2×#610611yescharacteristic
293C23#8819811yescharacteristic
294C23#8820311yescharacteristic
295C23#8820511yescharacteristic
296Q8—1044no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—522no—
327C2×C4—522no—
328C2×C4—522no—
329C2×C4—522no—
330C2×C4—522no—
331C2×C4—522no—
332C2×C4#8814212yes—
333C2×C4#8815012yes—
334C8—524no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22#1171864011yescharacteristic
348C22#1171866911yescharacteristic
349C22#1171868111yescharacteristic
350C22#1171869311yescharacteristic
351C22#1171870111yescharacteristic
352C22#1171870711yescharacteristic
353C22#1171871411yescharacteristic
354C22#1171872211yescharacteristic
355C22#1171872311yescharacteristic
356C22#1171872611yescharacteristic
357C22#1171874011yescharacteristic
358C4—22no—
359C4—22no—
360C4—42no—
361C4—42no—
362C4—82no—
363C4—82no—
364C4—1042no—
365C4—1042no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—21no—
370C2#1311377511yescharacteristic
371C2#1311378711yescharacteristic
372C2#1311382611yescharacteristic
373C2#1311387211yescharacteristic
374C2#1311616911yescharacteristic
375C2#1311618611yescharacteristic
376C2#1311618911yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#1442C2
socleC23×C13#120
prime radicalC24×C13C2×D4
hypercenter#1442D13
hypocenterC13#10568
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1442

Complements

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

NH ≅ G/Ntype
41. C13×#95Q8semidirect
45. C22⋊#1055Q8semidirect
223. #95Dic26semidirect
284. C13#10568semidirect

Maximal subgroups

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

subgroupindex
#131209502
#131150292
#131127152
#131126792
C13×#14422
#1056813