Finite Group Databasebeta

← #15763057

Subgroups — #15763057

Order 3328.

430 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123197C211yesmaximal, characteristic
2#13114952C211yesmaximal, characteristic
3C4⋊C8×Dic13C211yesmaximal, 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×C8×Dic13—21no—
13#11718646—21no—
14#11718646—21no—
15#11718638C412yes—
16#11718634—21no—
17#11718634—21no—
18#11718596C2211yescharacteristic
19C42×Dic13C2211yescharacteristic
20C2×C4⋊#1055C2211yescharacteristic
21C2×C4⋊#1055C2211yescharacteristic
22#11718142—21no—
23#11718142—21no—
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—
51C8×Dic13—42no—
52C4⋊#1055—21no—
53C4⋊#1055—21no—
54C4⋊#1055—21no—
55C4⋊#1055Q812yes—
56#9901—131nomaximal, Sylow
57C22×C4×C13—22no—
58C22×C4×C13C22×C411yescharacteristic
59C22×C4×C13C2×D411yescharacteristic
60C22×C4×C13C2×D411yescharacteristic
61C22×Dic13—22no—
62C22×Dic13C22⋊C411yescharacteristic
63C22×Dic13C22⋊C411yescharacteristic
64C22×Dic13C22⋊C411yescharacteristic
65C22×Dic13C22⋊C411yescharacteristic
66C2×C8×C13—22no—
67C2×C8×C13—41no—
68C2×C8×C13—41no—
69C2×C8×C13—41no—
70C2×C8×C13—41no—
71C2×C8×C13—41no—
72C13×C4⋊C4—42no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C42×C13C2×Q811yescharacteristic
78C42×C13C2×Q811yescharacteristic
79C42×C13#4111yescharacteristic
80C42×C13#4111yescharacteristic
81C4⋊Dic13—41no—
82C4⋊Dic13—41no—
83C4⋊Dic13—41no—
84C4⋊Dic13—41no—
85C4⋊Dic13—44no—
86C4⋊Dic13—42no—
87#6101—44no—
88C4×Dic13—21no—
89C4×Dic13—21no—
90C4×Dic13—21no—
91C4×Dic13—21no—
92C4×Dic13—21no—
93C4×Dic13—21no—
94C4×Dic13—21no—
95C4×Dic13—21no—
96C4×Dic13—22no—
97C4×Dic13—22no—
98C2×#1055—22no—
99C2×#1055—41no—
100C2×#1055—41no—
101C2×#1055—41no—
102C2×#1055—41no—
103C2×#1055—41no—
104#2859—131no—
105#1831—131no—
106C4×C4⋊C8—131no—
107#1296—131no—
108#1296—131no—
109#1296—131no—
110#1296D1311yescharacteristic
111C23×C13C2×C22⋊C411yescharacteristic
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13C4×Q811yescharacteristic
118C2×C4×C13C4×Q811yescharacteristic
119C2×C4×C13C22⋊Q811yescharacteristic
120C2×C4×C13C22⋊Q811yescharacteristic
121C2×C4×C13#12411yescharacteristic
122C2×C4×C13C4⋊Q811yescharacteristic
123C2×C4×C13#13511yescharacteristic
124C2×C4×C13#13511yescharacteristic
125C2×C4×C13#13511yescharacteristic
126C2×C4×C13#13511yescharacteristic
127C2×C4×C13#13511yescharacteristic
128C2×C4×C13#13511yescharacteristic
129C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C13#13711yescharacteristic
131C2×Dic13—21no—
132C2×Dic13—21no—
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—42no—
142C2×Dic13—42no—
143C2×Dic13—42no—
144C2×Dic13#10012yes—
145C2×Dic13#10112yes—
146C8×C13—42no—
147C8×C13—81no—
148#1055—42no—
149#1055—81no—
150C2×#125—132no—
151C2×C4⋊C8—131no—
152C2×C4⋊C8—131no—
153C2×C4⋊C8C2×D1311yescharacteristic
154C2×C4⋊C8C2×D1311yescharacteristic
155C2×C4×C8—261no—
156#389—261no—
157#389—261no—
158#389—261no—
159#389—261no—
160#384—131no—
161#384C2×D1311yescharacteristic
162#382—132no—
163C43—131no—
164#336—261no—
165#336—261no—
166#336—261no—
167C22×C13#39111yescharacteristic
168C22×C13C2×#10011yescharacteristic
169C22×C13C2×#10111yescharacteristic
170C22×C13#41611yescharacteristic
171C22×C13#41611yescharacteristic
172C22×C13#41611yescharacteristic
173C22×C13#41711yescharacteristic
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—82no—
177C4×C13#47811yescharacteristic
178C4×C13#47811yescharacteristic
179C4×C13#47911yescharacteristic
180C4×C13#47911yescharacteristic
181C4×C13#48811yescharacteristic
182C4×C13#48811yescharacteristic
183C4×C13#49911yescharacteristic
184C4×C13#49911yescharacteristic
185Dic13—22no—
186Dic13—22no—
187Dic13—41no—
188Dic13—41no—
189Dic13—82no—
190C22×C8—21no—
191C22×C8—21no—
192C22×C8—261no—
193C22×C8—261no—
194#125—524no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—132no—
198C2×C4⋊C4—262no—
199C2×C4⋊C4—262no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4C4×D1312yes—
203C2×C42—131no—
204C2×C42—131no—
205C2×C42—131no—
206C2×C42—131no—
207C2×C42—131no—
208C2×C42—131no—
209C2×C42C22×D1311yescharacteristic
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—132no—
214C4⋊C8—261no—
215C4⋊C8—261no—
216C4⋊C8—261no—
217C4⋊C8Dic2612yes—
218C4×C8—522no—
219#95—262no—
220#95—262no—
221C2×C13#154311yescharacteristic
222C2×C13#154411yescharacteristic
223C2×C13#155111yescharacteristic
224C2×C13#155211yescharacteristic
225C2×C13#198911yescharacteristic
226C2×C13#199111yescharacteristic
227C2×C13#199711yescharacteristic
228C22×C4—22no—
229C22×C4—131no—
230C22×C4—131no—
231C22×C4—131no—
232C22×C4—131no—
233C22×C4—262no—
234C22×C4C2×C4×D1311yescharacteristic
235C22×C4D4×D1311yescharacteristic
236C22×C4D4×D1311yescharacteristic
237C2×C8—22no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—262no—
244C2×C8—521no—
245C2×C8—521no—
246C2×C8—521no—
247C2×C8—521no—
248C2×C8—521no—
249C4⋊C4—42no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—522no—
255C4⋊C4—524no—
256C4⋊C4—524no—
257C4⋊C4—521no—
258C4⋊C4—521no—
259C4⋊C4—521no—
260C4⋊C4—521no—
261C42—262no—
262C42—262no—
263C42—261no—
264C42—261no—
265C42—261no—
266C42—261no—
267C42—261no—
268C42—261no—
269C42—261no—
270C42—261no—
271C42C2×Dic2611yescharacteristic
272C42#612711yescharacteristic
273C42#612911yescharacteristic
274C42Q8×D1311yescharacteristic
275C13#990111yescharacteristic, complemented, Sylow
276C23C22⋊C4×D1311yescharacteristic
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—132no—
283C2×C4—132no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—522no—
295C2×C4—522no—
296C2×C4—522no—
297C2×C4C4×Dic2611yescharacteristic
298C2×C4#8813211yescharacteristic
299C2×C4#8813911yescharacteristic
300C2×C4#8814111yescharacteristic
301C2×C4#8814211yescharacteristic
302C2×C4#8815011yescharacteristic
303C2×C4#8816611yescharacteristic
304C2×C4#8816611yescharacteristic
305C2×C4#8816811yescharacteristic
306C2×C4#8817011yescharacteristic
307C2×C4#8817011yescharacteristic
308C2×C4#8817011yescharacteristic
309C2×C4#8817211yescharacteristic
310C2×C4#8817311yescharacteristic
311C8—42no—
312C8—81no—
313C8—522no—
314C8—1041no—
315C22#1171830711yescharacteristic
316C22D13×#10011yescharacteristic
317C22D13×#10111yescharacteristic
318C22#1171843311yescharacteristic
319C22#1171843311yescharacteristic
320C22#1171846411yescharacteristic
321C22#1171846511yescharacteristic
322C4—21no—
323C4—21no—
324C4—82no—
325C4—262no—
326C4—262no—
327C4—521no—
328C4—521no—
329C4—1042no—
330C4#1171842711yescharacteristic
331C4#1171842911yescharacteristic
332C4#1171846011yescharacteristic
333C4#1171846111yescharacteristic
334C4#1171851911yescharacteristic
335C4#1171853211yescharacteristic
336C4#1171853811yescharacteristic
337C4#1171853911yescharacteristic
338C2#1311349511yescharacteristic
339C2#1311349911yescharacteristic
340C2#1311353011yescharacteristic
341C2#1311353311yescharacteristic
342C2#1311579211yescharacteristic
343C2#1311579911yescharacteristic
344C2#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#9901
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
275. C13#9901semidirect

Maximal subgroups

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

subgroupindex
#131231972
#131149522
C4⋊C8×Dic132
#131127202
#131127192
C13×#12962
#990113