Finite Group Databasebeta

← #15763076

Subgroups — #15763076

Order 3328.

438 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123197C211yesmaximal, characteristic
2#13114987C211yesmaximal, characteristic
3#13114691C211yesmaximal, characteristic
4#13112720C211yesmaximal, characteristic
5#13112720C211yesmaximal, characteristic
6#13112719C211yesmaximal, characteristic
7C13×#1296C211yesmaximal, characteristic
8C2×#88144C412yes—
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C13×#384C2211yescharacteristic
12C2×#88055—21no—
13C2×#88054—21no—
14C2×#88054—21no—
15#11718646—21no—
16#11718646—21no—
17#11718638C412yes—
18#11718634—21no—
19#11718634—21no—
20#11718596C2211yescharacteristic
21C42×Dic13C2211yescharacteristic
22C2×C4⋊#1055C2211yescharacteristic
23C2×C4⋊#1055C2211yescharacteristic
24#11718142—21no—
25C22×C8×C13—21no—
26C22×C8×C13—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4C2×C412yes—
30C2×C42×C13C2311yescharacteristic
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—22no—
34C2×C4⋊Dic13C2×C412yes—
35C2×#6101—22no—
36C2×C4×Dic13C2×C411yescharacteristic
37C2×C4×Dic13C2×C411yescharacteristic
38C2×C4×Dic13D411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C22×#1055—21no—
43C22×#1055—21no—
44#88144—44no—
45C13×C4⋊C8—21no—
46C13×C4⋊C8—21no—
47C13×C4⋊C8—21no—
48C13×C4⋊C8Q812yes—
49#88071—22no—
50#88071—22no—
51#88055—42no—
52#88054—42no—
53#88054—42no—
54C4⋊#1055—21no—
55C4⋊#1055—21no—
56C4⋊#1055—21no—
57C4⋊#1055Q812yes—
58#9906—131nomaximal, Sylow
59C22×C4×C13—22no—
60C22×C4×C13C22×C411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C22×Dic13—22no—
64C22×Dic13C22⋊C411yescharacteristic
65C22×Dic13C22⋊C411yescharacteristic
66C22×Dic13C22⋊C411yescharacteristic
67C22×Dic13C22⋊C411yescharacteristic
68C2×C8×C13—22no—
69C2×C8×C13—41no—
70C2×C8×C13—41no—
71C2×C8×C13—41no—
72C2×C8×C13—41no—
73C2×C8×C13—41no—
74C13×C4⋊C4—42no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C42×C13C2×Q811yescharacteristic
80C42×C13C2×Q811yescharacteristic
81C42×C13#4111yescharacteristic
82C42×C13#4111yescharacteristic
83C4⋊Dic13—41no—
84C4⋊Dic13—41no—
85C4⋊Dic13—41no—
86C4⋊Dic13—41no—
87C4⋊Dic13—44no—
88C4⋊Dic13—42no—
89#6101—44no—
90C4×Dic13—21no—
91C4×Dic13—21no—
92C4×Dic13—21no—
93C4×Dic13—21no—
94C4×Dic13—21no—
95C4×Dic13—21no—
96C4×Dic13—21no—
97C4×Dic13—21no—
98C4×Dic13—22no—
99C4×Dic13—22no—
100C2×#1055—22no—
101C2×#1055—41no—
102C2×#1055—41no—
103C2×#1055—41no—
104C2×#1055—41no—
105C2×#1055—41no—
106#2859—131no—
107#1842—131no—
108#1767—131no—
109#1296—131no—
110#1296—131no—
111#1296—131no—
112#1296D1311yescharacteristic
113C23×C13C2×C22⋊C411yescharacteristic
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13C4×Q811yescharacteristic
120C2×C4×C13C4×Q811yescharacteristic
121C2×C4×C13C22⋊Q811yescharacteristic
122C2×C4×C13C22⋊Q811yescharacteristic
123C2×C4×C13#12411yescharacteristic
124C2×C4×C13C4⋊Q811yescharacteristic
125C2×C4×C13#13511yescharacteristic
126C2×C4×C13#13511yescharacteristic
127C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C13#13711yescharacteristic
131C2×C4×C13#13711yescharacteristic
132C2×C4×C13#13711yescharacteristic
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—42no—
144C2×Dic13—42no—
145C2×Dic13—42no—
146C2×Dic13#10012yes—
147C2×Dic13#10112yes—
148C8×C13—42no—
149C8×C13—81no—
150#1055—42no—
151#1055—81no—
152C2×#125—132no—
153C2×C4⋊C8—131no—
154C2×C4⋊C8—131no—
155C2×C4⋊C8—261no—
156C2×C4⋊C8—261no—
157C2×C4⋊C8C2×D1311yescharacteristic
158C2×C4⋊C8C2×D1311yescharacteristic
159C2×#97—261no—
160#389—261no—
161#389—261no—
162#389—261no—
163#389—261no—
164#384—131no—
165#384C2×D1311yescharacteristic
166#382—132no—
167C43—131no—
168#336—261no—
169C22×C13#39111yescharacteristic
170C22×C13C2×#10011yescharacteristic
171C22×C13C2×#10111yescharacteristic
172C22×C13#41611yescharacteristic
173C22×C13#41711yescharacteristic
174C22×C13#41711yescharacteristic
175C22×C13#41711yescharacteristic
176C4×C13—21no—
177C4×C13—21no—
178C4×C13—82no—
179C4×C13#47811yescharacteristic
180C4×C13#47811yescharacteristic
181C4×C13#47911yescharacteristic
182C4×C13#47911yescharacteristic
183C4×C13#49011yescharacteristic
184C4×C13#49111yescharacteristic
185C4×C13#50111yescharacteristic
186C4×C13#50111yescharacteristic
187Dic13—22no—
188Dic13—22no—
189Dic13—41no—
190Dic13—41no—
191Dic13—82no—
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—261no—
195C22×C8—261no—
196#125—524no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—132no—
200C2×C4⋊C4—262no—
201C2×C4⋊C4—262no—
202C2×C4⋊C4—261no—
203C2×C4⋊C4—261no—
204C2×C4⋊C4C4×D1312yes—
205C2×C42—131no—
206C2×C42—131no—
207C2×C42—131no—
208C2×C42—131no—
209C2×C42—131no—
210C2×C42—131no—
211C2×C42C22×D1311yescharacteristic
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—132no—
216C4⋊C8—261no—
217C4⋊C8—261no—
218C4⋊C8—261no—
219C4⋊C8—522no—
220C4⋊C8—522no—
221C4⋊C8Dic2612yes—
222#97—522no—
223#95—262no—
224#95—262no—
225C2×C13#155111yescharacteristic
226C2×C13#155211yescharacteristic
227C2×C13#156011yescharacteristic
228C2×C13#156111yescharacteristic
229C2×C13#198911yescharacteristic
230C2×C13#199211yescharacteristic
231C2×C13#199711yescharacteristic
232C22×C4—22no—
233C22×C4—131no—
234C22×C4—131no—
235C22×C4—131no—
236C22×C4—131no—
237C22×C4—262no—
238C22×C4C2×C4×D1311yescharacteristic
239C22×C4D4×D1311yescharacteristic
240C22×C4D4×D1311yescharacteristic
241C2×C8—22no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—262no—
248C2×C8—521no—
249C2×C8—521no—
250C2×C8—521no—
251C2×C8—521no—
252C2×C8—521no—
253C4⋊C4—42no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—522no—
259C4⋊C4—524no—
260C4⋊C4—524no—
261C4⋊C4—521no—
262C4⋊C4—521no—
263C4⋊C4—521no—
264C4⋊C4—521no—
265C42—262no—
266C42—262no—
267C42—261no—
268C42—261no—
269C42—261no—
270C42—261no—
271C42—261no—
272C42—261no—
273C42—261no—
274C42—261no—
275C42C2×Dic2611yescharacteristic
276C42#612711yescharacteristic
277C42#612911yescharacteristic
278C42Q8×D1311yescharacteristic
279C13#990611yescharacteristic, complemented, Sylow
280C23C22⋊C4×D1311yescharacteristic
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—132no—
287C2×C4—132no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—522no—
299C2×C4—522no—
300C2×C4—522no—
301C2×C4C4×Dic2611yescharacteristic
302C2×C4#8813211yescharacteristic
303C2×C4#8813911yescharacteristic
304C2×C4#8814111yescharacteristic
305C2×C4#8814211yescharacteristic
306C2×C4#8815011yescharacteristic
307C2×C4#8816511yescharacteristic
308C2×C4#8816511yescharacteristic
309C2×C4#8816811yescharacteristic
310C2×C4#8816911yescharacteristic
311C2×C4#8816911yescharacteristic
312C2×C4#8817011yescharacteristic
313C2×C4#8817211yescharacteristic
314C2×C4#8817311yescharacteristic
315C8—42no—
316C8—81no—
317C8—522no—
318C8—1041no—
319C22#1171830711yescharacteristic
320C22D13×#10011yescharacteristic
321C22D13×#10111yescharacteristic
322C22#1171843211yescharacteristic
323C22#1171843211yescharacteristic
324C22#1171846411yescharacteristic
325C22#1171846511yescharacteristic
326C4—21no—
327C4—21no—
328C4—82no—
329C4—262no—
330C4—262no—
331C4—521no—
332C4—521no—
333C4—1042no—
334C4#1171842411yescharacteristic
335C4#1171842511yescharacteristic
336C4#1171845711yescharacteristic
337C4#1171845811yescharacteristic
338C4#1171851711yescharacteristic
339C4#1171851811yescharacteristic
340C4#1171853711yescharacteristic
341C4#1171855211yescharacteristic
342C2#1311353011yescharacteristic
343C2#1311353511yescharacteristic
344C2#1311356811yescharacteristic
345C2#1311357211yescharacteristic
346C2#1311579011yescharacteristic
347C2#1311580311yescharacteristic
348C2#1311582311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1296C2
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1296D13
hypocenterC13#9906
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
279. C13#9906semidirect

Maximal subgroups

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

subgroupindex
#131231972
#131149872
#131146912
#131127202
#131127192
C13×#12962
#990613