Finite Group Databasebeta

← #15752140

Subgroups — #15752140

Order 3328.

362 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 85 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#13122800C211yesmaximal, characteristic
2#13116393C211yesmaximal, characteristic
3#13116245C211yesmaximal, characteristic
4#13112662C211yesmaximal, characteristic
5#13112661C211yesmaximal, characteristic
6#13112658C211yesmaximal, characteristic
7C13×#2072C211yesmaximal, characteristic
8C2×C13×#103—21no—
9C13×#391C2211yescharacteristic
10C13×#384C2211yescharacteristic
11#11718891—21no—
12#11718645—21no—
13C2×#88050—21no—
14#11718590C2211yescharacteristic
15#11718589C2211yescharacteristic
16#11718322—21no—
17#11718317—21no—
18#11718315—21no—
19#11718308—21no—
20C13×#340—21no—
21C13×#336C2211yescharacteristic
22#11718121—21no—
23#11718121—21no—
24#11718121—21no—
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×Q8×C13D411yescharacteristic
28C22×Dic26D411yescharacteristic
29C22×C8×C13—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C42×C13C2311yescharacteristic
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13D411yescharacteristic
38C2×C4⋊Dic13D411yescharacteristic
39C2×C4⋊Dic13D411yescharacteristic
40C2×#6101—21no—
41C2×#6101—21no—
42C2×#6101—21no—
43C2×C4×Dic13—21no—
44C22×#1055—21no—
45C22×#1055—21no—
46C13×#103—42no—
47C13×#95—21no—
48C13×#95—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88050—42no—
56#7816—131nomaximal, Sylow
57C2×Q8×C13—21no—
58C2×Q8×C13—41no—
59C2×Q8×C13—41no—
60C2×Q8×C13SD1612yes—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—41no—
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×Dic13—21no—
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13—21no—
71C2×Dic26—21no—
72C2×Dic26—21no—
73C2×Dic26—41no—
74C2×Dic26—41no—
75C2×C8×C13—41no—
76C2×C8×C13—41no—
77C2×C8×C13—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C42×C13—41no—
85C4⋊Dic13—21no—
86C4⋊Dic13—41no—
87C4⋊Dic13—41no—
88C4⋊Dic13—81no—
89C4⋊Dic13—81no—
90C4⋊Dic13Q1612yes—
91#6101—41no—
92#6101—41no—
93#6101—81no—
94#6101—81no—
95C4×Dic13—81no—
96C2×#1055—41no—
97C2×#1055—41no—
98C2×#1055—41no—
99C2×#1055—41no—
100C2×#1055—41no—
101C2×#1055—41no—
102#2806—131no—
103#2099—131no—
104#2072—131no—
105#2072D1311yescharacteristic
106#1272—131no—
107#1272—131no—
108#1271—131no—
109C23×C13#12011yescharacteristic
110Q8×C13—42no—
111Q8×C13—81no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—22no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—81no—
125C2×C4×C13—81no—
126C2×C4×C13—81no—
127C2×C4×C13C2×SD1611yescharacteristic
128C2×C4×C13C2×Q1611yescharacteristic
129C2×C4×C13#13511yescharacteristic
130C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C13#13711yescharacteristic
132C2×C4×C13#13711yescharacteristic
133C2×Dic13—22no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145Dic26—42no—
146Dic26—81no—
147C8×C13—81no—
148#1055—81no—
149#1055—81no—
150C2×#103—21no—
151C2×#103—261no—
152#398—261no—
153#398—261no—
154#395—261no—
155#391—131no—
156#391—261no—
157#391C2×D1311yescharacteristic
158#389—131no—
159#389—261no—
160#387—261no—
161#384C2×D1311yescharacteristic
162#340—21no—
163#340—261no—
164#340—261no—
165#340—261no—
166#336—131no—
167#336—131no—
168#336C2×D1311yescharacteristic
169C22×C13#44811yescharacteristic
170C22×C13#44911yescharacteristic
171C22×C13#45111yescharacteristic
172C22×C13#45411yescharacteristic
173C22×C13#45511yescharacteristic
174C22×C13#45511yescharacteristic
175C22×C13#45811yescharacteristic
176C4×C13—21no—
177C4×C13—21no—
178C4×C13—21no—
179C4×C13—21no—
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—42no—
183C4×C13—81no—
184C4×C13—161no—
185Dic13—42no—
186Dic13—81no—
187Dic13—81no—
188Dic13—81no—
189C22×Q8—131no—
190C22×Q8C22⋊D1311yescharacteristic
191C22×C8—21no—
192C22×C8—261no—
193C22×C8—261no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—131no—
198C2×C4⋊C4—131no—
199C2×C4⋊C4—131no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4—261no—
203C2×C4⋊C4—261no—
204C2×C4⋊C4—261no—
205C2×C4⋊C4C22⋊D1311yescharacteristic
206C2×C42—261no—
207C2×C42C22×D1311yescharacteristic
208#103—42no—
209#103—522no—
210#95—21no—
211#95—21no—
212#95—261no—
213#95—261no—
214#95—261no—
215#95—261no—
216#95—261no—
217#95—261no—
218C2×C13#160811yescharacteristic
219C2×C13#161211yescharacteristic
220C2×C13#161711yescharacteristic
221C2×C13#162611yescharacteristic
222C2×C13#164411yescharacteristic
223C2×C13#164511yescharacteristic
224C2×C13#166211yescharacteristic
225C2×Q8—21no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—261no—
229C2×Q8—261no—
230C2×Q8—521no—
231C2×Q8—521no—
232C2×Q8#610512yes—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—41no—
236C22×C4—261no—
237C22×C4—261no—
238C22×C4—261no—
239C22×C4—261no—
240C22×C4D4×D1311yescharacteristic
241C22×C4D4×D1311yescharacteristic
242C22×C4C2×C22⋊D1311yescharacteristic
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—521no—
247C2×C8—521no—
248C2×C8—521no—
249C2×C8—521no—
250C2×C8—521no—
251C2×C8—521no—
252C4⋊C4—41no—
253C4⋊C4—42no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—132no—
259C4⋊C4—261no—
260C4⋊C4—521no—
261C4⋊C4—521no—
262C4⋊C4—521no—
263C4⋊C4—521no—
264C4⋊C4—1041no—
265C4⋊C4—1041no—
266C4⋊C4—1041no—
267C4⋊C4—1041no—
268C42—41no—
269C42—1041no—
270C13#781611yescharacteristic, complemented, Sylow
271C23#8819111yescharacteristic
272Q8—42no—
273Q8—81no—
274Q8—522no—
275Q8—1041no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—262no—
292C2×C4—521no—
293C2×C4—521no—
294C2×C4—521no—
295C2×C4—521no—
296C2×C4—521no—
297C2×C4—521no—
298C2×C4—521no—
299C2×C4—521no—
300C2×C4—521no—
301C2×C4—521no—
302C2×C4—521no—
303C2×C4#8816811yescharacteristic
304C2×C4#8817011yescharacteristic
305C2×C4Q16×D1311yescharacteristic
306C2×C4#8817211yescharacteristic
307C2×C4C2×#610511yescharacteristic
308C2×C4#8820511yescharacteristic
309C8—81no—
310C8—1041no—
311C8—1041no—
312C22#1171870111yescharacteristic
313C22#1171871411yescharacteristic
314C22#1171872211yescharacteristic
315C22#1171883311yescharacteristic
316C22#1171884711yescharacteristic
317C22#1171886211yescharacteristic
318C22#1171886311yescharacteristic
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—42no—
326C4—81no—
327C4—161no—
328C4—522no—
329C4—1041no—
330C4—1041no—
331C4—1041no—
332C2#1311382611yescharacteristic
333C2#1311384911yescharacteristic
334C2#1311387611yescharacteristic
335C2#1311393111yescharacteristic
336C2#1311404711yescharacteristic
337C2#1311405511yescharacteristic
338C2#1311415811yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2072C2
socle, prime radicalC23×C13#120
hypercenter#2072D13
hypocenterC13#7816
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2072

Complements

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

NH ≅ G/Ntype
270. C13#7816semidirect

Maximal subgroups

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

subgroupindex
#131228002
#131163932
#131162452
#131126622
#131126612
#131126582
C13×#20722
#781613