Finite Group Databasebeta

← #15751901

Subgroups — #15751901

Order 3328.

478 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 87 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#13116169C211yesmaximal, characteristic, complemented
2#13116164C211yesmaximal, characteristic, complemented
3#13115918C211yesmaximal, characteristic
4#13112659C211yesmaximal, characteristic, complemented
5#13112659C211yesmaximal, characteristic, complemented
6#13112657C211yesmaximal, characteristic
7C13×#2727C211yesmaximal, characteristic
8C2×C13×#126—21no—
9C22×#6105—21no—
10C2×#88123C2211yescharacteristic
11C13×#399—21no—
12C13×#396—21no—
13C13×#394—21no—
14C13×#390C2211yescharacteristic
15C13×#389—21no—
16C13×#389C2211yescharacteristic
17C13×#389C2211yescharacteristic
18C13×#388—21no—
19C2×#88050—21no—
20C2×#88048—21no—
21C2×#88047—21no—
22#11718121—21no—
23#11718121—21no—
24#11718116C2211yescharacteristic
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×D4×C13D411yescharacteristic
28C22×Dic26—21no—
29C13×#126—42no—
30C13×#126—42no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C13×C4⋊C4D411yescharacteristic
39C2×C13×C4⋊C4D411yescharacteristic
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C42×C13—21no—
47C2×C42×C13C2311yescharacteristic
48C2×#6105—42no—
49C2×#6105—42no—
50C2×#6105—42no—
51C2×C4⋊Dic13—21no—
52C2×C4⋊Dic13—21no—
53C22×#1055—21no—
54C22×#1055—21no—
55C22×#1055—21no—
56#88123—42no—
57C13×#95—21no—
58C13×#95—21no—
59C13×#95—21no—
60#88050—42no—
61#88048—42no—
62#88047—42no—
63#7780—131nomaximal, Sylow
64C24×C13—21no—
65C2×D4×C13—21no—
66C2×D4×C13—21no—
67C2×D4×C13—41no—
68C2×D4×C13—41no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×Dic13—41no—
78C2×Dic26—22no—
79C2×Dic26—41no—
80C2×Dic26—41no—
81C2×Dic26—41no—
82C2×Dic26—41no—
83C2×Dic26—41no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4—21no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—42no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—81no—
96C13×C4⋊C4SD1612yescomplemented
97C13×C22⋊C4—42no—
98C13×C22⋊C4—42no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—41no—
101C13×C22⋊C4—41no—
102C13×C22⋊C4—41no—
103C13×C22⋊C4—81no—
104C13×C22⋊C4—81no—
105C42×C13—41no—
106C42×C13—42no—
107#6105—48no—
108C4⋊Dic13—22no—
109C4⋊Dic13—22no—
110C4⋊Dic13—41no—
111C4⋊Dic13—41no—
112C2×#1055—22no—
113C2×#1055—22no—
114C2×#1055—22no—
115C2×#1055—41no—
116C2×#1055—41no—
117C2×#1055—41no—
118C2×#1055—41no—
119C2×#1055—41no—
120C2×#1055—41no—
121#2727D1311yescharacteristic
122#2058—131no—
123#2057—131no—
124#2013—131no—
125#1271—131no—
126#1271—131no—
127#1270—131no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13—41no—
134C23×C13—41no—
135C23×C13#12011yescharacteristic
136D4×C13—42no—
137D4×C13—81no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—22no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13C2×SD1611yescharacteristic
160C2×C4×C13#13511yescharacteristic
161C2×C4×C13#13511yescharacteristic
162C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C13#13711yescharacteristic
165C2×Dic13—42no—
166C2×Dic13—81no—
167C2×Dic13—81no—
168Dic26—42no—
169Dic26—42no—
170Dic26—81no—
171Dic26—81no—
172#1055—42no—
173#1055—42no—
174#1055—42no—
175C22×SD16—261no—
176C2×C4⋊Q8—131no—
177C2×#126—21no—
178C2×#107—261no—
179C2×#106—261no—
180C2×#103—261no—
181#399—21no—
182#396—21no—
183#394—21no—
184#390C2×D1311yescharacteristic
185#389—21no—
186#389C2×D1311yescharacteristic
187#389C2×D1311yescharacteristic
188#388—21no—
189#340—261no—
190#340—261no—
191#336—131no—
192#336—131no—
193#336—131no—
194C22×C13—81no—
195C22×C13—81no—
196C22×C13—81no—
197C22×C13—81no—
198C22×C13—81no—
199C22×C13—81no—
200C22×C13—81no—
201C22×C13#44911yescharacteristic
202C22×C13#45011yescharacteristic
203C22×C13#45211yescharacteristic
204C22×C13#45311yescharacteristic
205C22×C13#45611yescharacteristic
206C22×C13#45611yescharacteristic
207C22×C13B(4,𝔽2)11yescharacteristic
208C4×C13—21no—
209C4×C13—21no—
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—21no—
213C4×C13—21no—
214C4×C13—42no—
215C4×C13—81no—
216C4×C13—81no—
217C4×C13—81no—
218C4×C13—81no—
219Dic13—82no—
220C22×Q8—261no—
221C22×D4C22⋊D1311yescharacteristic
222C2×SD16—522no—
223C2×SD16—522no—
224C2×SD16—522no—
225C22×C8—261no—
226C22×C8—261no—
227C22×C8—261no—
228C4⋊Q8—522no—
229#126—42no—
230#126—42no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—261no—
236C2×C4⋊C4—261no—
237C2×C4⋊C4C22⋊D1311yescharacteristic
238C2×C4⋊C4C22⋊D1311yescharacteristic
239C2×C4⋊C4C22⋊D1311yescharacteristic
240C2×C4⋊C4C22⋊D1311yescharacteristic
241C2×C4⋊C4C22⋊D1311yescharacteristic
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C42—21no—
249C2×C42C22×D1311yescharacteristic
250#107—522no—
251#106—522no—
252#103—522no—
253#95—21no—
254#95—21no—
255#95—21no—
256C2×C13—161no—
257C2×C13#160011yescharacteristic
258C2×C13#160311yescharacteristic
259C2×C13#160411yescharacteristic
260C2×C13#163111yescharacteristic
261C2×C13#165011yescharacteristic
262C2×C13#165411yescharacteristic
263C2×C13#166011yescharacteristic
264C24—21no—
265C2×Q8—262no—
266C2×Q8—521no—
267C2×Q8—521no—
268C2×Q8—521no—
269C2×Q8—521no—
270C2×Q8—521no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—41no—
274C2×D4—41no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—521no—
281C22×C4C2×C22⋊D1311yescharacteristic
282C22×C4C2×C22⋊D1311yescharacteristic
283C22×C4C2×C22⋊D1311yescharacteristic
284SD16—528no—
285C2×C8—262no—
286C2×C8—262no—
287C2×C8—262no—
288C2×C8—521no—
289C2×C8—521no—
290C2×C8—521no—
291C2×C8—521no—
292C2×C8—521no—
293C2×C8—521no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—42no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—81no—
306C4⋊C4—262no—
307C4⋊C4—262no—
308C4⋊C4—521no—
309C4⋊C4—521no—
310C4⋊C4#610512yescomplemented
311C22⋊C4—42no—
312C22⋊C4—42no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—81no—
318C22⋊C4—81no—
319C42—41no—
320C42—42no—
321C13#778011yescharacteristic, complemented, Sylow
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23#8820711yescharacteristic
330Q8—522no—
331Q8—522no—
332Q8—1041no—
333Q8—1041no—
334D4—42no—
335D4—81no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—522no—
358C2×C4—1041no—
359C2×C4—1041no—
360C2×C4#8818611yescharacteristic
361C2×C4C2×#610511yescharacteristic
362C2×C4#8820311yescharacteristic
363C2×C4#8820411yescharacteristic
364C2×C4#8820411yescharacteristic
365C2×C4#8820511yescharacteristic
366C8—522no—
367C8—522no—
368C8—522no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22#1171887911yescharacteristic
377C22#1171889911yescharacteristic
378C22#1171890011yescharacteristic
379C22#1171890211yescharacteristic
380C22#1171890511yescharacteristic
381C22#1171890711yescharacteristic
382C22#1171890711yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—42no—
390C4—81no—
391C4—81no—
392C4—81no—
393C4—81no—
394C4—1042no—
395C2—161no—
396C2#1311378211yescharacteristic
397C2#1311379911yescharacteristic
398C2#1311380511yescharacteristic
399C2#1311396311yescharacteristic
400C2#1311409211yescharacteristic
401C2#1311412011yescharacteristic
402C2#1311414711yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2727C2
socleC23×C13#120
prime radicalC22×D4×C13D4
hypercenter#2727D13
hypocenterC13#7780
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2727

Complements

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

NH ≅ G/Ntype
1. #13116169C2semidirect
2. #13116164C2semidirect
4. #13112659C2semidirect
5. #13112659C2semidirect
96. C13×C4⋊C4SD16semidirect
310. C4⋊C4#6105semidirect
321. C13#7780semidirect

Maximal subgroups

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

subgroupindex
#131161692
#131161642
#131159182
#131126592
#131126572
C13×#27272
#778013