Finite Group Databasebeta

← #15766050

Subgroups — #15766050

Order 3328.

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

normal subgroups only

This group has 416 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
1#13118130C211yesmaximal, characteristic
2#13115818C211yesmaximal, characteristic
3#13113335C211yesmaximal, characteristic
4#13112739C211yesmaximal, characteristic
5#13112738C211yesmaximal, characteristic
6#13112664C211yesmaximal, characteristic
7C13×#1503C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C2×C4×Dic26—21no—
10C13×#431C2211yescharacteristic
11C4×C13×C4⋊C4C2211yescharacteristic
12#11718645—21no—
13#11718640—21no—
14C4×C4⋊Dic13C2211yescharacteristic
15#11718593C2211yescharacteristic
16C4×#6101—21no—
17#11718586C2211yescharacteristic
18#11718585C2211yescharacteristic
19#11718318—21no—
20#11718317—21no—
21C13×#328—21no—
22C13×#328—21no—
23#11718130—21no—
24#11718130—21no—
25#11718124—21no—
26#11718124—21no—
27C22×Dic26—21no—
28C13×C4⋊Q8Q811yescharacteristic, complemented
29C13×C4⋊Q8Q811yescharacteristic, complemented
30C13×#125—21no—
31C13×C22⋊Q8—21no—
32C13×C22⋊Q8—21no—
33C4×Q8×C13—21no—
34C4×Q8×C13—21no—
35C13×#117—21no—
36C2×C13×C4⋊C4—21no—
37C2×C42×C13—21no—
38C2×C42×C13C2311yescharacteristic
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C2×#6101—21no—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×#6101—21no—
45C2×C4×Dic13—21no—
46C2×C4×Dic13D411yescharacteristic
47C2×C4×Dic13D411yescharacteristic
48C2×#6099—21no—
49C4×Dic26—42no—
50C4×Dic26—42no—
51C13×C4⋊C8—21no—
52C13×C22⋊C8—21no—
53C4×C8×C13—21no—
54C13×#95D411yescharacteristic
55C13×#95D411yescharacteristic
56#88071—21no—
57#88071—21no—
58#88071—21no—
59#88071—21no—
60#88071D411yescharacteristic
61#88071D411yescharacteristic
62C22⋊#1055—21no—
63C4⋊#1055—21no—
64C4⋊#1055—21no—
65C4⋊#1055—21no—
66C4×#1055—21no—
67#10371—131nomaximal, Sylow
68C2×Q8×C13—21no—
69C2×Q8×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—21no—
78C22×Dic13—21no—
79C2×Dic26—42no—
80C2×Dic26—42no—
81C2×Dic26—42no—
82C2×C8×C13—41no—
83C13×C4⋊C4—21no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4—21no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—42no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C22⋊C4—41no—
91C42×C13—41no—
92C42×C13—41no—
93C42×C13—41no—
94C42×C13C2×Q811yescharacteristic
95C42×C13#4111yescharacteristic
96C42×C13#4111yescharacteristic
97C42×C13#4111yescharacteristic
98C4⋊Dic13—42no—
99C4⋊Dic13—42no—
100#6101—42no—
101#6101—42no—
102#6101—42no—
103#6101—42no—
104C4×Dic13—21no—
105C4×Dic13—21no—
106C4×Dic13—41no—
107C4×Dic13—41no—
108C4×Dic13SD1612yes—
109C4×Dic13Q1612yes—
110#6099—41no—
111#6099—41no—
112C2×#1055—41no—
113C2×#1055—41no—
114#2399—131no—
115#1995—131no—
116#1503—131no—
117#1503D1311yescharacteristic
118#1303—131no—
119#1303—131no—
120#1274—131no—
121C23×C13#12011yescharacteristic
122Q8×C13—81no—
123Q8×C13—81no—
124C2×C4×C13—22no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13C22⋊Q811yescharacteristic
135C2×C4×C13C22⋊Q811yescharacteristic
136C2×C4×C13C22⋊Q811yescharacteristic
137C2×C4×C13#12411yescharacteristic
138C2×C4×C13#12411yescharacteristic
139C2×C4×C13#12411yescharacteristic
140C2×C4×C13C2×SD1611yescharacteristic
141C2×C4×C13C2×Q1611yescharacteristic
142C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C13#13711yescharacteristic
144C2×Dic13—22no—
145C2×Dic13—22no—
146C2×Dic13—22no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156Dic26—48no—
157C8×C13—81no—
158#1055—81no—
159#1055—81no—
160#533C2×D1311yescharacteristic
161C2×C4×Q8—261no—
162#431—131no—
163#431C2×D1311yescharacteristic
164#423—131no—
165#398—261no—
166#398—261no—
167#395—261no—
168#395—261no—
169C4×C4⋊C4—131no—
170C4×C4⋊C4—261no—
171C4×C4⋊C4C2×D1311yescharacteristic
172#376—131no—
173#339—261no—
174#339—261no—
175#328—21no—
176#328—21no—
177#328—261no—
178#328—261no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13#39311yescharacteristic
182C22×C13#45011yescharacteristic
183C22×C13#45111yescharacteristic
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—21no—
188C4×C13—42no—
189C4×C13—81no—
190C4×C13—81no—
191C4×C13—81no—
192C4×C13#47511yescharacteristic
193C4×C13#47711yescharacteristic
194C4×C13#48711yescharacteristic
195C4×C13#48911yescharacteristic
196Dic13—42no—
197Dic13—42no—
198Dic13—42no—
199Dic13—81no—
200C22×Q8—261no—
201C2×M16—261no—
202C4⋊Q8Dic2611yescharacteristic, complemented
203C4⋊Q8Dic2611yescharacteristic, complemented
204#125—21no—
205C22⋊Q8—21no—
206C22⋊Q8—21no—
207C4×Q8—21no—
208C4×Q8—21no—
209C4×Q8—522no—
210C4×Q8—522no—
211#117—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4—261no—
215C2×C4⋊C4—261no—
216C2×C4⋊C4—261no—
217C2×C4⋊C4—261no—
218C2×C4⋊C4—261no—
219C2×C42—21no—
220C2×C42—131no—
221C2×C42—131no—
222C2×C42—261no—
223C2×C42C22×D1311yescharacteristic
224C4⋊C8—21no—
225C4⋊C8—261no—
226C4⋊C8—261no—
227C4⋊C8—261no—
228C22⋊C8—21no—
229C22⋊C8—261no—
230C4×C8—21no—
231C4×C8—261no—
232#95—131no—
233#95—131no—
234#95—261no—
235#95—261no—
236#95—261no—
237#95—261no—
238#95C22⋊D1311yescharacteristic
239#95C22⋊D1311yescharacteristic
240C2×C13—21no—
241C2×C13—21no—
242C2×C13#202411yescharacteristic
243C2×C13#203111yescharacteristic
244C2×C13#203111yescharacteristic
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—522no—
248C2×Q8—522no—
249C2×Q8—522no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—261no—
253C22×C4—261no—
254C22×C4—261no—
255C22×C4—261no—
256C22×C4D4×D1311yescharacteristic
257C22×C4D4×D1311yescharacteristic
258C22×C4C2×C22⋊D1311yescharacteristic
259M16—521no—
260M16—521no—
261C2×C8—41no—
262C2×C8—521no—
263C2×C8—521no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—42no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—522no—
272C4⋊C4—522no—
273C4⋊C4—522no—
274C4⋊C4—522no—
275C4⋊C4—522no—
276C4⋊C4—522no—
277C22⋊C4—41no—
278C42—41no—
279C42—41no—
280C42—41no—
281C42—132no—
282C42—132no—
283C42—261no—
284C42—261no—
285C42—521no—
286C42—521no—
287C42C2×Dic2611yescharacteristic
288C42#612711yescharacteristic
289C42#612911yescharacteristic
290C42#612911yescharacteristic
291C13#1037111yescharacteristic, complemented, Sylow
292C23#8819111yescharacteristic
293Q8—81no—
294Q8—81no—
295Q8—528no—
296C2×C4—22no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—262no—
307C2×C4—262no—
308C2×C4—262no—
309C2×C4—521no—
310C2×C4—521no—
311C2×C4—521no—
312C2×C4—521no—
313C2×C4—521no—
314C2×C4—521no—
315C2×C4—521no—
316C2×C4—521no—
317C2×C4—521no—
318C2×C4#8813211yescharacteristic
319C2×C4#8813211yescharacteristic
320C2×C4#8813911yescharacteristic
321C2×C4#8813911yescharacteristic
322C2×C4SD16×D1311yescharacteristic
323C2×C4#8816811yescharacteristic
324C2×C4Q16×D1311yescharacteristic
325C2×C4#8817211yescharacteristic
326C2×C4#8817811yescharacteristic
327C2×C4#8819011yescharacteristic
328C8—81no—
329C8—1041no—
330C8—1041no—
331C22—21no—
332C22—21no—
333C22#1171860811yescharacteristic
334C22#1171883011yescharacteristic
335C22#1171884711yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—42no—
341C4—81no—
342C4—81no—
343C4—81no—
344C4—522no—
345C4—522no—
346C4—522no—
347C4—1041no—
348C4#1171845211yescharacteristic
349C4#1171845311yescharacteristic
350C4#1171845511yescharacteristic
351C4#1171845611yescharacteristic
352C2—21no—
353C2—21no—
354C2#1311597511yescharacteristic
355C2#1311600811yescharacteristic
356C2#1311601011yescharacteristic
subgroupG/H
centerC2×C4#88139
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1503C2
socleC22×C13#393
prime radicalC23×C13#120
hypercenter#1503D13
hypocenterC13#10371
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
28. C13×C4⋊Q8Q8semidirect
29. C13×C4⋊Q8Q8semidirect
202. C4⋊Q8Dic26semidirect
203. C4⋊Q8Dic26semidirect
291. C13#10371semidirect

Maximal subgroups

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

subgroupindex
#131181302
#131158182
#131133352
#131127392
#131127382
#131126642
C13×#15032
#1037113