Finite Group Databasebeta

← #15756250

Subgroups — #15756250

Order 3328.

642 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718310C211yesmaximal, characteristic
2#13114902C212yesmaximal
3#13112679C211yesmaximal, characteristic
4#13112678C212yesmaximal
5C13×#1280C211yesmaximal, characteristic
6C22×#6101C411yescharacteristic
7C22×#6101C411yescharacteristic
8C22×C4×Dic13C411yescharacteristic
9C22×C4×Dic13C411yescharacteristic
10C22×C4×Dic13C2211yescharacteristic
11C2×C13×C22⋊C8C2212yes—
12C2×C13×#95C2211yescharacteristic
13C2×#88071C2211yescharacteristic
14C2×C22⋊#1055C2212yes—
15#11718310—22no—
16#11718310—22no—
17#11718142—22no—
18#11718142—22no—
19C23×C4×C13C2×C411yescharacteristic
20C23×C4×C13C2×C411yescharacteristic
21C23×C4×C13C2311yescharacteristic
22C23×Dic13C2×C411yescharacteristic
23C23×Dic13C2×C411yescharacteristic
24C23×Dic13C2×C411yescharacteristic
25C23×Dic13C2×C411yescharacteristic
26C22×C8×C13—22no—
27C2×#6101—22no—
28C2×#6101—22no—
29C2×#6101—22no—
30C2×#6101—22no—
31C2×#6101—22no—
32C2×#6101C814yescomplemented
33C2×C4×Dic13—22no—
34C2×C4×Dic13—21no—
35C2×C4×Dic13—21no—
36C2×C4×Dic13—21no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13—21no—
39C2×C4×Dic13—21no—
40C2×C4×Dic13—42no—
41C2×C4×Dic13—42no—
42C2×C4×Dic13D412yes—
43C2×C4×Dic13D412yes—
44C22×#1055—22no—
45C13×C22⋊C8—22no—
46C13×C22⋊C8—22no—
47C13×#95—22no—
48#88071—22no—
49C22⋊#1055—22no—
50C22⋊#1055—22no—
51#8701—131nomaximal, Sylow
52C24×C13C22×C411yescharacteristic
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—41no—
58C22×C4×C13—41no—
59C22×C4×C13—41no—
60C22×C4×C13—41no—
61C22×C4×C13—41no—
62C22×C4×C13—41no—
63C22×C4×C13C2×C812yes—
64C22×C4×C13M1612yes—
65C22×C4×C13C2×D412yes—
66C22×C4×C13#4112yes—
67C22×C4×C13#4111yescharacteristic
68C22×C4×C13#4111yescharacteristic
69C22×Dic13—21no—
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13—21no—
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—22no—
76C22×Dic13—22no—
77C22×Dic13—21no—
78C22×Dic13—21no—
79C22×Dic13—21no—
80C22×Dic13—21no—
81C22×Dic13—41no—
82C22×Dic13—41no—
83C22×Dic13—41no—
84C22×Dic13—41no—
85C22×Dic13C22⋊C412yes—
86C22×Dic13C22⋊C411yescharacteristic
87C22×Dic13C22⋊C411yescharacteristic
88C22×Dic13C2×C812yes—
89C22×Dic13C2×C812yes—
90C22×Dic13M1612yes—
91C22×Dic13M1612yes—
92C2×C8×C13—42no—
93C2×C8×C13—42no—
94C2×C8×C13—42no—
95#6101—28no—
96#6101—28no—
97C4×Dic13—22no—
98C4×Dic13—22no—
99C4×Dic13—22no—
100C4×Dic13—22no—
101C4×Dic13—42no—
102C4×Dic13—42no—
103C4×Dic13—42no—
104C4×Dic13—42no—
105C2×#1055—42no—
106C2×#1055—42no—
107C2×#1055—42no—
108C2×C4×C4⋊C4—131no—
109#1817—132no—
110#1280—132no—
111#1280—131no—
112#1280D1311yescharacteristic
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13C2×C22⋊C411yescharacteristic
118C23×C13#11711yescharacteristic
119C23×C13#11711yescharacteristic
120C23×C13C22×C811yescharacteristic
121C23×C13C2×M1611yescharacteristic
122C23×C13C2×M1611yescharacteristic
123C23×C13C2×M1611yescharacteristic
124C2×C4×C13—22no—
125C2×C4×C13—22no—
126C2×C4×C13—22no—
127C2×C4×C13—22no—
128C2×C4×C13—41no—
129C2×C4×C13—42no—
130C2×C4×C13—41no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—42no—
138C2×C4×C13—42no—
139C2×C4×C13#12312yes—
140C2×C4×C13#12312yes—
141C2×Dic13—24no—
142C2×Dic13—24no—
143C2×Dic13—22no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—22no—
147C2×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13—22no—
150C2×Dic13—22no—
151C2×Dic13—22no—
152C2×Dic13—22no—
153C2×Dic13—22no—
154C2×Dic13—22no—
155C2×Dic13—42no—
156C2×Dic13—42no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—41no—
161C2×Dic13—42no—
162C2×Dic13—42no—
163C2×Dic13C22⋊C814yes—
164C2×Dic13#10012yes—
165C2×Dic13#10112yes—
166C8×C13—82no—
167#1055—82no—
168C22×C4⋊C4—131no—
169C22×C4⋊C4—131no—
170C22×C42—131no—
171C22×C42—131no—
172C22×C42—131no—
173C2×C22⋊C8—132no—
174C2×C22⋊C8C2×D1312yes—
175C4×C4⋊C4—262no—
176C4×C4⋊C4—262no—
177C2×#95—131no—
178C2×#95C2×D1311yescharacteristic
179#336—262no—
180#336—262no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13#38111yescharacteristic
194C22×C13C2×C22⋊C811yescharacteristic
195C22×C13#40711yescharacteristic
196C22×C13#41011yescharacteristic
197C22×C13#41011yescharacteristic
198C22×C13C2×#10011yescharacteristic
199C22×C13C2×#10111yescharacteristic
200C22×C13#43111yescharacteristic
201C22×C13#43111yescharacteristic
202C22×C13#43211yescharacteristic
203C22×C13#43211yescharacteristic
204C4×C13—22no—
205C4×C13—22no—
206C4×C13—42no—
207C4×C13—42no—
208Dic13—24no—
209Dic13—22no—
210Dic13—22no—
211Dic13—42no—
212Dic13—42no—
213C23×C4—131no—
214C23×C4—131no—
215C23×C4—131no—
216C23×C4—131no—
217C23×C4C4×D1311yescharacteristic
218C23×C4C4×D1311yescharacteristic
219C23×C4C22×D1311yescharacteristic
220C22×C8—22no—
221C22×C8—262no—
222C2×C4⋊C4—134no—
223C2×C4⋊C4—262no—
224C2×C4⋊C4—262no—
225C2×C4⋊C4—262no—
226C2×C4⋊C4—262no—
227C2×C4⋊C4—262no—
228C2×C42—132no—
229C2×C42—132no—
230C2×C42—262no—
231C2×C42—261no—
232C2×C42—261no—
233C2×C42—261no—
234C2×C42—261no—
235C2×C42—261no—
236C2×C42—261no—
237C2×C42—522no—
238C2×C42—522no—
239C22⋊C8—22no—
240C22⋊C8—22no—
241C22⋊C8—262no—
242C22⋊C8—262no—
243#95—22no—
244#95—262no—
245C2×C13—21no—
246C2×C13—21no—
247C2×C13—21no—
248C2×C13—21no—
249C2×C13#146011yescharacteristic
250C2×C13#146111yescharacteristic
251C2×C13#146611yescharacteristic
252C2×C13#146711yescharacteristic
253C2×C13#181711yescharacteristic
254C2×C13#182011yescharacteristic
255C2×C13#182111yescharacteristic
256C24C2×C4×D1311yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—131no—
268C22×C4—131no—
269C22×C4—132no—
270C22×C4—132no—
271C22×C4—132no—
272C22×C4—132no—
273C22×C4—132no—
274C22×C4—262no—
275C22×C4—262no—
276C22×C4—261no—
277C22×C4—261no—
278C22×C4—261no—
279C22×C4—261no—
280C22×C4—261no—
281C22×C4—261no—
282C22×C4—261no—
283C22×C4—261no—
284C22×C4—261no—
285C22×C4—261no—
286C22×C4—521no—
287C22×C4—521no—
288C22×C4—521no—
289C22×C4—521no—
290C22×C4C8×D1312yes—
291C22×C4#609412yes—
292C22×C4#612712yes—
293C22×C4D4×D1312yes—
294C22×C4#612911yescharacteristic
295C22×C4#613111yescharacteristic
296C2×C8—42no—
297C2×C8—42no—
298C2×C8—42no—
299C2×C8—522no—
300C2×C8—522no—
301C2×C8—522no—
302C4⋊C4—268no—
303C4⋊C4—268no—
304C42—262no—
305C42—262no—
306C42—262no—
307C42—262no—
308C42—522no—
309C42—522no—
310C42—522no—
311C42—522no—
312C13#870111yescharacteristic, complemented, Sylow
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23#8812611yescharacteristic
318C23C22⋊C4×D1311yescharacteristic
319C23#8814611yescharacteristic
320C23C2×C8×D1311yescharacteristic
321C23C2×#609411yescharacteristic
322C23M16×D1311yescharacteristic
323C23M16×D1311yescharacteristic
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—132no—
340C2×C4—132no—
341C2×C4—134no—
342C2×C4—264no—
343C2×C4—264no—
344C2×C4—261no—
345C2×C4—261no—
346C2×C4—262no—
347C2×C4—262no—
348C2×C4—262no—
349C2×C4—261no—
350C2×C4—261no—
351C2×C4—262no—
352C2×C4—262no—
353C2×C4—262no—
354C2×C4—262no—
355C2×C4—262no—
356C2×C4—522no—
357C2×C4—522no—
358C2×C4—521no—
359C2×C4—521no—
360C2×C4—521no—
361C2×C4—521no—
362C2×C4—522no—
363C2×C4—522no—
364C2×C4#8813712yes—
365C2×C4#8814812yes—
366C8—82no—
367C8—1042no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22#1171832511yescharacteristic
381C22#1171834611yescharacteristic
382C22#1171836611yescharacteristic
383C22D13×C22⋊C811yescharacteristic
384C22#1171838711yescharacteristic
385C22#1171840111yescharacteristic
386C22#1171840111yescharacteristic
387C22D13×#10011yescharacteristic
388C22D13×#10111yescharacteristic
389C22#1171849411yescharacteristic
390C22#1171849611yescharacteristic
391C4—22no—
392C4—22no—
393C4—42no—
394C4—42no—
395C4—264no—
396C4—262no—
397C4—262no—
398C4—522no—
399C4—522no—
400C2—21no—
401C2—21no—
402C2—21no—
403C2—21no—
404C2#1311315511yescharacteristic
405C2#1311315811yescharacteristic
406C2#1311317511yescharacteristic
407C2#1311317811yescharacteristic
408C2#1311490311yescharacteristic
409C2#1311491211yescharacteristic
410C2#1311491511yescharacteristic
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#8701
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
32. C2×#6101C8semidirect
312. C13#8701semidirect

Maximal subgroups

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

subgroupindex
C2×#117183102
#131149022
#131126792
#131126782
C13×#12802
#870113