Finite Group Databasebeta

← #15763068

Subgroups — #15763068

Order 3328.

438 conjugacy classes of subgroups.

The subgroup lattice has 352 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×#88144—21no—
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C13×#384C2211yescharacteristic
12C2×#88055—21no—
13C2×#88054—21no—
14C2×#88054—21no—
15#11718646—21no—
16#11718646C412yes—
17#11718638—21no—
18#11718634—21no—
19#11718634C412yes—
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—42no—
45#88144—42no—
46C13×C4⋊C8—21no—
47C13×C4⋊C8—21no—
48C13×C4⋊C8—21no—
49C13×C4⋊C8Q812yes—
50#88071—22no—
51#88071—22no—
52#88055—42no—
53#88054—42no—
54#88054—42no—
55C4⋊#1055—21no—
56C4⋊#1055—21no—
57C4⋊#1055—21no—
58C4⋊#1055Q812yes—
59#9904—131nomaximal, Sylow
60C22×C4×C13—22no—
61C22×C4×C13C22×C411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×Dic13—22no—
65C22×Dic13C22⋊C411yescharacteristic
66C22×Dic13C22⋊C411yescharacteristic
67C22×Dic13C22⋊C411yescharacteristic
68C22×Dic13C22⋊C411yescharacteristic
69C2×C8×C13—22no—
70C2×C8×C13—41no—
71C2×C8×C13—41no—
72C2×C8×C13—41no—
73C2×C8×C13—41no—
74C2×C8×C13—41no—
75C13×C4⋊C4—42no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C42×C13C2×Q811yescharacteristic
81C42×C13C2×Q811yescharacteristic
82C42×C13#4111yescharacteristic
83C42×C13#4111yescharacteristic
84C4⋊Dic13—41no—
85C4⋊Dic13—41no—
86C4⋊Dic13—41no—
87C4⋊Dic13—41no—
88C4⋊Dic13—44no—
89C4⋊Dic13—42no—
90#6101—44no—
91C4×Dic13—21no—
92C4×Dic13—21no—
93C4×Dic13—21no—
94C4×Dic13—21no—
95C4×Dic13—21no—
96C4×Dic13—21no—
97C4×Dic13—41no—
98C4×Dic13—41no—
99C4×Dic13D812yes—
100C4×Dic13SD1612yes—
101C2×#1055—22no—
102C2×#1055—41no—
103C2×#1055—41no—
104C2×#1055—41no—
105C2×#1055—41no—
106C2×#1055—41no—
107#2859—131no—
108#1842—131no—
109#1767—131no—
110#1296—131no—
111#1296—131no—
112#1296—131no—
113#1296D1311yescharacteristic
114C23×C13C2×C22⋊C411yescharacteristic
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13C4×Q811yescharacteristic
121C2×C4×C13C4×Q811yescharacteristic
122C2×C4×C13C22⋊Q811yescharacteristic
123C2×C4×C13C22⋊Q811yescharacteristic
124C2×C4×C13#12411yescharacteristic
125C2×C4×C13C4⋊Q811yescharacteristic
126C2×C4×C13C2×D811yescharacteristic
127C2×C4×C13C2×SD1611yescharacteristic
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×C4×C13#13711yescharacteristic
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—21no—
144C2×Dic13—42no—
145C2×Dic13—42no—
146C2×Dic13—42no—
147C2×Dic13#10212yes—
148C2×Dic13#10212yes—
149C8×C13—42no—
150C8×C13—81no—
151#1055—42no—
152#1055—81no—
153C2×#125—261no—
154C2×C4⋊C8—131no—
155C2×C4⋊C8—131no—
156C2×C4⋊C8—261no—
157C2×C4⋊C8—261no—
158C2×C4⋊C8C2×D1311yescharacteristic
159C2×C4⋊C8C2×D1311yescharacteristic
160C2×#97—261no—
161#389—132no—
162#389—132no—
163#389—261no—
164#389—261no—
165#384—131no—
166#384C2×D1311yescharacteristic
167#382—261no—
168C43—131no—
169#336—261no—
170C22×C13#39111yescharacteristic
171C22×C13#41311yescharacteristic
172C22×C13#41311yescharacteristic
173C22×C13C2×#10211yescharacteristic
174C22×C13#41711yescharacteristic
175C22×C13#41711yescharacteristic
176C22×C13#41911yescharacteristic
177C4×C13—21no—
178C4×C13—21no—
179C4×C13—82no—
180C4×C13#47411yescharacteristic
181C4×C13#47411yescharacteristic
182C4×C13#47511yescharacteristic
183C4×C13#47511yescharacteristic
184C4×C13#49011yescharacteristic
185C4×C13#49111yescharacteristic
186C4×C13#50111yescharacteristic
187C4×C13#50111yescharacteristic
188Dic13—22no—
189Dic13—22no—
190Dic13—41no—
191Dic13—41no—
192Dic13—82no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—261no—
196C22×C8—261no—
197#125—522no—
198#125—522no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—132no—
202C2×C4⋊C4—262no—
203C2×C4⋊C4—262no—
204C2×C4⋊C4—261no—
205C2×C4⋊C4—261no—
206C2×C4⋊C4C4×D1312yes—
207C2×C42—131no—
208C2×C42—131no—
209C2×C42—131no—
210C2×C42—131no—
211C2×C42—131no—
212C2×C42—131no—
213C2×C42C22×D1311yescharacteristic
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—132no—
218C4⋊C8—261no—
219C4⋊C8—261no—
220C4⋊C8—261no—
221C4⋊C8—522no—
222C4⋊C8—522no—
223C4⋊C8Dic2612yes—
224#97—522no—
225#95—262no—
226#95—262no—
227C2×C13#154711yescharacteristic
228C2×C13#154711yescharacteristic
229C2×C13#155911yescharacteristic
230C2×C13#155911yescharacteristic
231C2×C13#198811yescharacteristic
232C2×C13#199211yescharacteristic
233C2×C13#199811yescharacteristic
234C22×C4—22no—
235C22×C4—131no—
236C22×C4—131no—
237C22×C4—131no—
238C22×C4—131no—
239C22×C4—262no—
240C22×C4C2×C4×D1311yescharacteristic
241C22×C4D4×D1311yescharacteristic
242C22×C4D4×D1311yescharacteristic
243C2×C8—22no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—262no—
250C2×C8—521no—
251C2×C8—521no—
252C2×C8—521no—
253C2×C8—521no—
254C2×C8—521no—
255C4⋊C4—42no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—522no—
261C4⋊C4—524no—
262C4⋊C4—524no—
263C4⋊C4—521no—
264C4⋊C4—521no—
265C4⋊C4—521no—
266C4⋊C4—521no—
267C42—132no—
268C42—132no—
269C42—261no—
270C42—261no—
271C42—261no—
272C42—261no—
273C42—261no—
274C42—261no—
275C42—521no—
276C42—521no—
277C42C2×Dic2611yescharacteristic
278C42#612711yescharacteristic
279C42#612911yescharacteristic
280C42Q8×D1311yescharacteristic
281C13#990411yescharacteristic, complemented, Sylow
282C23C22⋊C4×D1311yescharacteristic
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—132no—
289C2×C4—132no—
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—261no—
299C2×C4—261no—
300C2×C4—522no—
301C2×C4—522no—
302C2×C4—522no—
303C2×C4C4×Dic2611yescharacteristic
304C2×C4#8813211yescharacteristic
305C2×C4#8813911yescharacteristic
306C2×C4#8814111yescharacteristic
307C2×C4#8814211yescharacteristic
308C2×C4#8815011yescharacteristic
309C2×C4D8×D1311yescharacteristic
310C2×C4#8816511yescharacteristic
311C2×C4SD16×D1311yescharacteristic
312C2×C4#8816811yescharacteristic
313C2×C4#8816911yescharacteristic
314C2×C4#8816911yescharacteristic
315C2×C4#8817211yescharacteristic
316C2×C4#8817211yescharacteristic
317C8—42no—
318C8—81no—
319C8—522no—
320C8—1041no—
321C22#1171830711yescharacteristic
322C22#1171840611yescharacteristic
323C22#1171841211yescharacteristic
324C22D13×#10211yescharacteristic
325C22#1171843211yescharacteristic
326C22#1171846311yescharacteristic
327C22#1171846411yescharacteristic
328C4—21no—
329C4—21no—
330C4—82no—
331C4—262no—
332C4—262no—
333C4—521no—
334C4—521no—
335C4—1042no—
336C4#1171842011yescharacteristic
337C4#1171842511yescharacteristic
338C4#1171845211yescharacteristic
339C4#1171845811yescharacteristic
340C4#1171851511yescharacteristic
341C4#1171851711yescharacteristic
342C4#1171853711yescharacteristic
343C4#1171855111yescharacteristic
344C2#1311351011yescharacteristic
345C2#1311351211yescharacteristic
346C2#1311356311yescharacteristic
347C2#1311356511yescharacteristic
348C2#1311578611yescharacteristic
349C2#1311580311yescharacteristic
350C2#1311582711yescharacteristic
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#9904
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
281. C13#9904semidirect

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
#990413