Finite Group Databasebeta

← #15751865

Subgroups — #15751865

Order 3328.

380 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 79 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#13122827C211yesmaximal, characteristic
2#13116166C211yesmaximal, characteristic
3#13116079C211yesmaximal, characteristic
4#13112660C211yesmaximal, characteristic
5#13112659C211yesmaximal, characteristic
6#13112658C211yesmaximal, characteristic
7C13×#2057C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C13×#107—21no—
10C13×#389C2211yescharacteristic
11C2×#88075—21no—
12C2×#88075—21no—
13#11718647—21no—
14#11718643—21no—
15#11718642—21no—
16#11718639—21no—
17C2×#88048—21no—
18#11718589C2211yescharacteristic
19#11718589C2211yescharacteristic
20#11718320—21no—
21#11718316—21no—
22C13×#340—21no—
23C13×#336C2211yescharacteristic
24#11718121—21no—
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×Q8×C13—21no—
28C22×C8×C13—21no—
29C13×C4⋊Q8—42no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C42×C13C2311yescharacteristic
36C2×C4⋊Dic13D411yescharacteristic
37C2×C4⋊Dic13D411yescharacteristic
38C2×C4⋊Dic13D411yescharacteristic
39C2×C4⋊Dic13D411yescharacteristic
40C2×#6101—21no—
41C2×#6101—21no—
42C2×C4×Dic13—21no—
43C22×#1055—21no—
44C22×#1055—21no—
45C13×#107—42no—
46C13×#95—21no—
47#88075—42no—
48#88075—42no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#88048—42no—
59#7775—131nomaximal, Sylow
60C2×Q8×C13—22no—
61C2×Q8×C13—41no—
62C2×Q8×C13—41no—
63C2×Q8×C13—41no—
64C2×Q8×C13—41no—
65C2×Q8×C13—41no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—41no—
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×Dic13—21no—
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—21no—
76C2×C8×C13—22no—
77C2×C8×C13—41no—
78C2×C8×C13—41no—
79C13×C4⋊C4—22no—
80C13×C4⋊C4—22no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—41no—
88C42×C13—41no—
89C4⋊Dic13—21no—
90C4⋊Dic13—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13—41no—
94C4⋊Dic13—41no—
95#6101—41no—
96#6101—41no—
97#6101—41no—
98#6101—41no—
99C4×Dic13—81no—
100C2×#1055—22no—
101C2×#1055—41no—
102C2×#1055—41no—
103C2×#1055—41no—
104C2×#1055—41no—
105C2×#1055—41no—
106#2810—131no—
107#2058—131no—
108#2057D1311yescharacteristic
109#2043—131no—
110#1271—131no—
111#1271—131no—
112#1271—131no—
113C23×C13#12011yescharacteristic
114Q8×C13—42no—
115Q8×C13—42no—
116Q8×C13—81no—
117Q8×C13—81no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—42no—
131C2×C4×C13—81no—
132C2×C4×C13—81no—
133C2×C4×C13#13511yescharacteristic
134C2×C4×C13#13511yescharacteristic
135C2×C4×C13#13511yescharacteristic
136C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C13#13711yescharacteristic
138C2×C4×C13#13711yescharacteristic
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C8×C13—42no—
152#1055—42no—
153#1055—81no—
154C2×C4⋊Q8C2×D1311yescharacteristic
155C2×#107—21no—
156C2×#106—261no—
157C2×#103—261no—
158C2×#103—261no—
159#400—261no—
160#400—261no—
161#400—261no—
162#389—131no—
163#389—131no—
164#389C2×D1311yescharacteristic
165#387—261no—
166#387—261no—
167#387—261no—
168#340—21no—
169#340—261no—
170#336—131no—
171#336—131no—
172#336C2×D1311yescharacteristic
173C22×C13#44911yescharacteristic
174C22×C13#45211yescharacteristic
175C22×C13#45211yescharacteristic
176C22×C13#45411yescharacteristic
177C22×C13#45611yescharacteristic
178C22×C13#45611yescharacteristic
179C22×C13B(4,𝔽2)11yescharacteristic
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—81no—
187C4×C13—82no—
188C4×C13—81no—
189Dic13—81no—
190Dic13—81no—
191Dic13—81no—
192Dic13—81no—
193C22×Q8—21no—
194C22×C8—21no—
195C22×C8—261no—
196C22×C8—261no—
197C4⋊Q8—42no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—131no—
202C2×C4⋊C4—131no—
203C2×C4⋊C4—131no—
204C2×C4⋊C4—131no—
205C2×C4⋊C4—261no—
206C2×C4⋊C4—261no—
207C2×C4⋊C4C22⋊D1311yescharacteristic
208C2×C4⋊C4C22⋊D1311yescharacteristic
209C2×C42—261no—
210C2×C42C22×D1311yescharacteristic
211#107—42no—
212#106—522no—
213#103—522no—
214#103—522no—
215#95—21no—
216#95—261no—
217#95—261no—
218#95—261no—
219#95—261no—
220#95—261no—
221#95—261no—
222#95—261no—
223#95—261no—
224#95—261no—
225C2×C13#159711yescharacteristic
226C2×C13#160311yescharacteristic
227C2×C13#160311yescharacteristic
228C2×C13#163811yescharacteristic
229C2×C13#165011yescharacteristic
230C2×C13#165211yescharacteristic
231C2×C13#166311yescharacteristic
232C2×Q8—22no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—41no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—41no—
241C22×C4—261no—
242C22×C4—261no—
243C22×C4—261no—
244C22×C4—261no—
245C22×C4D4×D1311yescharacteristic
246C22×C4D4×D1311yescharacteristic
247C22×C4C2×C22⋊D1311yescharacteristic
248C2×C8—22no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—262no—
252C2×C8—521no—
253C2×C8—521no—
254C2×C8—521no—
255C2×C8—521no—
256C2×C8—521no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—261no—
267C4⋊C4—261no—
268C4⋊C4—261no—
269C4⋊C4—261no—
270C4⋊C4—521no—
271C4⋊C4—521no—
272C4⋊C4—521no—
273C4⋊C4—521no—
274C4⋊C4—521no—
275C4⋊C4—521no—
276C42—41no—
277C42—1041no—
278C13#777511yescharacteristic, complemented, Sylow
279C23#8819111yescharacteristic
280Q8—42no—
281Q8—42no—
282Q8—81no—
283Q8—81no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—521no—
300C2×C4—521no—
301C2×C4—521no—
302C2×C4—521no—
303C2×C4—521no—
304C2×C4—521no—
305C2×C4—521no—
306C2×C4—521no—
307C2×C4—521no—
308C2×C4—521no—
309C2×C4—521no—
310C2×C4—521no—
311C2×C4#8816511yescharacteristic
312C2×C4#8816611yescharacteristic
313C2×C4#8817211yescharacteristic
314C2×C4#8817311yescharacteristic
315C2×C4#8819611yescharacteristic
316C2×C4#8820411yescharacteristic
317C8—42no—
318C8—522no—
319C8—1041no—
320C22#1171869311yescharacteristic
321C22#1171870811yescharacteristic
322C22#1171875611yescharacteristic
323C22#1171881911yescharacteristic
324C22#1171884811yescharacteristic
325C22#1171886211yescharacteristic
326C22#1171886611yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—81no—
334C4—82no—
335C4—81no—
336C4—1041no—
337C4—1041no—
338C4—1041no—
339C4—1041no—
340C2#1311376211yescharacteristic
341C2#1311379711yescharacteristic
342C2#1311379811yescharacteristic
343C2#1311400711yescharacteristic
344C2#1311408911yescharacteristic
345C2#1311410511yescharacteristic
346C2#1311416311yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2057C2
socle, prime radicalC23×C13#120
hypercenter#2057D13
hypocenterC13#7775
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2057

Complements

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

NH ≅ G/Ntype
278. C13#7775semidirect

Maximal subgroups

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

subgroupindex
#131228272
#131161662
#131160792
#131126602
#131126592
#131126582
C13×#20572
#777513