Finite Group Databasebeta

← #15756244

Subgroups — #15756244

Order 3328.

598 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718309C211yesmaximal, characteristic
2#13114902C212yesmaximal
3#13112679C211yesmaximal, characteristic
4#13112678C212yesmaximal
5C13×#1280C211yesmaximal, characteristic
6C22×C4×Dic13C411yescharacteristic
7C22×C4×Dic13C411yescharacteristic
8C22×C4×Dic13C2211yescharacteristic
9C2×C13×C22⋊C8C2212yes—
10C2×C13×#95C2211yescharacteristic
11C2×#88071C411yescharacteristic
12C2×#88071C411yescharacteristic
13C2×#88071C2211yescharacteristic
14C2×C22⋊#1055C2212yes—
15#11718309—24no—
16#11718142—24no—
17C23×C4×C13C2×C411yescharacteristic
18C23×C4×C13C2×C411yescharacteristic
19C23×C4×C13C2311yescharacteristic
20C23×Dic13C2×C411yescharacteristic
21C23×Dic13C2×C411yescharacteristic
22C23×Dic13C2×C411yescharacteristic
23C23×Dic13C2×C411yescharacteristic
24C22×C8×C13—22no—
25C2×C4×Dic13—22no—
26C2×C4×Dic13—22no—
27C2×C4×Dic13—21no—
28C2×C4×Dic13—21no—
29C2×C4×Dic13—22no—
30C2×C4×Dic13—22no—
31C2×C4×Dic13—22no—
32C2×C4×Dic13—22no—
33C2×C4×Dic13C814yescomplemented
34C2×C4×Dic13D414yes—
35C22×#1055—22no—
36C13×C22⋊C8—22no—
37C13×C22⋊C8—22no—
38C13×#95—22no—
39#88071—22no—
40#88071—22no—
41#88071—22no—
42C22⋊#1055—22no—
43C22⋊#1055—22no—
44#8699—131nomaximal, Sylow
45C24×C13C22×C411yescharacteristic
46C22×C4×C13—21no—
47C22×C4×C13—21no—
48C22×C4×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13—41no—
51C22×C4×C13—41no—
52C22×C4×C13—41no—
53C22×C4×C13—41no—
54C22×C4×C13—41no—
55C22×C4×C13—41no—
56C22×C4×C13C2×C812yes—
57C22×C4×C13M1612yes—
58C22×C4×C13C2×D412yes—
59C22×C4×C13#4112yes—
60C22×C4×C13#4111yescharacteristic
61C22×C4×C13#4111yescharacteristic
62C22×Dic13—21no—
63C22×Dic13—21no—
64C22×Dic13—21no—
65C22×Dic13—21no—
66C22×Dic13—21no—
67C22×Dic13—21no—
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13—41no—
73C22×Dic13—41no—
74C22×Dic13—41no—
75C22×Dic13—41no—
76C22×Dic13—41no—
77C22×Dic13—41no—
78C22×Dic13C22⋊C412yes—
79C22×Dic13C22⋊C412yes—
80C22×Dic13C2×C812yes—
81C22×Dic13C2×C812yes—
82C22×Dic13M1612yes—
83C22×Dic13M1612yes—
84C2×C8×C13—42no—
85C2×C8×C13—42no—
86C2×C8×C13—42no—
87C4×Dic13—28no—
88C4×Dic13—24no—
89C4×Dic13—24no—
90C4×Dic13—28no—
91C2×#1055—42no—
92C2×#1055—42no—
93C2×#1055—42no—
94C2×#376—131no—
95#1817—132no—
96#1280—132no—
97#1280—131no—
98#1280D1311yescharacteristic
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13C2×C22⋊C411yescharacteristic
104C23×C13#11711yescharacteristic
105C23×C13#11711yescharacteristic
106C23×C13C22×C811yescharacteristic
107C23×C13C2×M1611yescharacteristic
108C23×C13C2×M1611yescharacteristic
109C23×C13C2×M1611yescharacteristic
110C2×C4×C13—22no—
111C2×C4×C13—22no—
112C2×C4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13—41no—
115C2×C4×C13—42no—
116C2×C4×C13—41no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13#12312yes—
126C2×C4×C13#12312yes—
127C2×Dic13—22no—
128C2×Dic13—22no—
129C2×Dic13—22no—
130C2×Dic13—22no—
131C2×Dic13—22no—
132C2×Dic13—22no—
133C2×Dic13—22no—
134C2×Dic13—22no—
135C2×Dic13—22no—
136C2×Dic13—22no—
137C2×Dic13—22no—
138C2×Dic13—42no—
139C2×Dic13—42no—
140C2×Dic13—42no—
141C2×Dic13—42no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—42no—
147C2×Dic13—42no—
148C2×Dic13C22⋊C814yes—
149C8×C13—82no—
150#1055—82no—
151C22×C42—131no—
152C22×C42—131no—
153C22×C42—131no—
154C2×C22⋊C8—132no—
155C2×C22⋊C8C2×D1312yes—
156#376—264no—
157C2×#95—131no—
158C2×#95—131no—
159C2×#95—131no—
160C2×#95C2×D1311yescharacteristic
161#336—264no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13#38111yescharacteristic
175C22×C13C2×C22⋊C811yescharacteristic
176C22×C13#40711yescharacteristic
177C22×C13#41011yescharacteristic
178C22×C13#41011yescharacteristic
179C22×C13#41311yescharacteristic
180C22×C13#41311yescharacteristic
181C22×C13#43111yescharacteristic
182C22×C13#43111yescharacteristic
183C22×C13#43211yescharacteristic
184C22×C13#43211yescharacteristic
185C4×C13—22no—
186C4×C13—22no—
187C4×C13—42no—
188C4×C13—42no—
189Dic13—24no—
190Dic13—42no—
191Dic13—42no—
192Dic13—42no—
193C23×C4—131no—
194C23×C4—131no—
195C23×C4—131no—
196C23×C4—131no—
197C23×C4C4×D1311yescharacteristic
198C23×C4C4×D1311yescharacteristic
199C23×C4C22×D1311yescharacteristic
200C22×C8—22no—
201C22×C8—262no—
202C2×C42—134no—
203C2×C42—134no—
204C2×C42—262no—
205C2×C42—262no—
206C2×C42—262no—
207C2×C42—262no—
208C2×C42—262no—
209C2×C42—262no—
210C2×C42—261no—
211C2×C42—261no—
212C22⋊C8—22no—
213C22⋊C8—22no—
214C22⋊C8—262no—
215C22⋊C8—262no—
216#95—22no—
217#95—262no—
218#95—262no—
219#95—262no—
220C2×C13—21no—
221C2×C13—21no—
222C2×C13—21no—
223C2×C13—21no—
224C2×C13#145811yescharacteristic
225C2×C13#145811yescharacteristic
226C2×C13#146411yescharacteristic
227C2×C13#146411yescharacteristic
228C2×C13#181711yescharacteristic
229C2×C13#182011yescharacteristic
230C2×C13#182211yescharacteristic
231C24C2×C4×D1311yescharacteristic
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—132no—
243C22×C4—132no—
244C22×C4—132no—
245C22×C4—132no—
246C22×C4—132no—
247C22×C4—132no—
248C22×C4—261no—
249C22×C4—261no—
250C22×C4—261no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4—261no—
254C22×C4—261no—
255C22×C4—261no—
256C22×C4—261no—
257C22×C4—261no—
258C22×C4—521no—
259C22×C4—521no—
260C22×C4—521no—
261C22×C4—521no—
262C22×C4—521no—
263C22×C4—521no—
264C22×C4C8×D1312yes—
265C22×C4#609412yes—
266C22×C4#612712yes—
267C22×C4D4×D1312yes—
268C22×C4#612911yescharacteristic
269C22×C4#613111yescharacteristic
270C2×C8—42no—
271C2×C8—42no—
272C2×C8—42no—
273C2×C8—522no—
274C2×C8—522no—
275C2×C8—522no—
276C42—268no—
277C42—268no—
278C42—264no—
279C42—264no—
280C13#869911yescharacteristic, complemented, Sylow
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23#8812611yescharacteristic
286C23C22⋊C4×D1311yescharacteristic
287C23#8814611yescharacteristic
288C23C2×C8×D1311yescharacteristic
289C23C2×#609411yescharacteristic
290C23M16×D1311yescharacteristic
291C23M16×D1311yescharacteristic
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—134no—
308C2×C4—262no—
309C2×C4—262no—
310C2×C4—262no—
311C2×C4—262no—
312C2×C4—262no—
313C2×C4—262no—
314C2×C4—262no—
315C2×C4—262no—
316C2×C4—262no—
317C2×C4—262no—
318C2×C4—262no—
319C2×C4—522no—
320C2×C4—522no—
321C2×C4—522no—
322C2×C4—522no—
323C2×C4—521no—
324C2×C4—521no—
325C2×C4—521no—
326C2×C4—521no—
327C2×C4—522no—
328C2×C4—522no—
329C2×C4#8813712yes—
330C2×C4#8814812yes—
331C8—82no—
332C8—1042no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22#1171832511yescharacteristic
346C22#1171834611yescharacteristic
347C22#1171836611yescharacteristic
348C22D13×C22⋊C811yescharacteristic
349C22#1171838711yescharacteristic
350C22#1171840111yescharacteristic
351C22#1171840111yescharacteristic
352C22#1171840611yescharacteristic
353C22#1171841211yescharacteristic
354C22#1171849411yescharacteristic
355C22#1171849611yescharacteristic
356C4—22no—
357C4—22no—
358C4—42no—
359C4—42no—
360C4—264no—
361C4—522no—
362C4—522no—
363C4—522no—
364C2—21no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2#1311314711yescharacteristic
369C2#1311314911yescharacteristic
370C2#1311316711yescharacteristic
371C2#1311316911yescharacteristic
372C2#1311490311yescharacteristic
373C2#1311491211yescharacteristic
374C2#1311491811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC23×C13C22×C8
FrattiniC23×C4C22×D13
FittingC13×#1280C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22×C4
cosocleC23×C4×C13C23
hypercenter#1280D13
hypocenterC13#8699
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
33. C2×C4×Dic13C8semidirect
280. C13#8699semidirect

Maximal subgroups

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

subgroupindex
C2×#117183092
#131149022
#131126792
#131126782
C13×#12802
#869913