Finite Group Databasebeta

← #15755592

Subgroups — #15755592

Order 3328.

678 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114816C211yesmaximal, characteristic, complemented
2#13114816C211yesmaximal, characteristic, complemented
3C2×#11718117C212yesmaximal
4#13112679C212yesmaximal, complemented
5C2×C13×#388C211yesmaximal, characteristic
6C22×C13×C4⋊C4C411yescharacteristic
7C22×C13×C22⋊C4C411yescharacteristic
8C22×C13×C22⋊C4C411yescharacteristic
9C22×C13×C22⋊C4C2211yescharacteristic
10C22×C42×C13C2211yescharacteristic
11C13×#388—21no—
12C13×#388—21no—
13C13×#388—21no—
14C13×#388—21no—
15C2×C13×#95C411yescharacteristic
16C2×C13×#95C2211yescharacteristic
17C2×C22⋊#1055C2212yes—
18C2×C22⋊#1055C2212yes—
19C2×C4⋊#1055—21no—
20C2×C4⋊#1055—21no—
21#11718117—24no—
22#11718116—21no—
23#11718116—21no—
24C25×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13C2×C411yescharacteristic
27C23×C4×C13C2×C411yescharacteristic
28C23×C4×C13C2×C411yescharacteristic
29C23×C4×C13C2×C411yescharacteristic
30C23×C4×C13C2311yescharacteristic
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—42no—
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—42no—
43C2×C13×C22⋊C4—42no—
44C2×C13×C22⋊C4D412yes—
45C2×C13×C22⋊C4Q812yes—
46C2×C42×C13—42no—
47C2×C42×C13D411yescharacteristic
48C2×C42×C13D411yescharacteristic
49C2×C42×C13D411yescharacteristic
50C2×C42×C13D411yescharacteristic
51C22×#1055—22no—
52C22×#1055—22no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95—21no—
57C22⋊#1055—22no—
58C22⋊#1055—22no—
59C22⋊#1055—22no—
60C22⋊#1055—22no—
61C4⋊#1055—42no—
62C4⋊#1055—42no—
63#8561—131nomaximal, Sylow
64C24×C13—21no—
65C24×C13—21no—
66C24×C13—22no—
67C24×C13—22no—
68C24×C13—41no—
69C24×C13—41no—
70C24×C13—41no—
71C24×C13—41no—
72C24×C13C4⋊C412yes—
73C24×C13C22×C411yescharacteristic
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—22no—
77C22×C4×C13—22no—
78C22×C4×C13—22no—
79C22×C4×C13—22no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—22no—
83C22×C4×C13—22no—
84C22×C4×C13—41no—
85C22×C4×C13—41no—
86C22×C4×C13—41no—
87C22×C4×C13—41no—
88C22×C4×C13—41no—
89C22×C4×C13—41no—
90C22×C4×C13—41no—
91C22×C4×C13—41no—
92C22×C4×C13—41no—
93C22×C4×C13—41no—
94C22×C4×C13C22⋊C411yescharacteristic
95C22×C4×C13C22⋊C411yescharacteristic
96C22×C4×C13C22⋊C411yescharacteristic
97C22×C4×C13C22⋊C411yescharacteristic
98C22×C4×C13C4⋊C412yes—
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×Q811yescharacteristic
103C22×C4×C13#4111yescharacteristic
104C22×C4×C13#4111yescharacteristic
105C13×C4⋊C4—42no—
106C13×C4⋊C4—42no—
107C13×C22⋊C4—22no—
108C13×C22⋊C4—22no—
109C13×C22⋊C4—22no—
110C13×C22⋊C4—22no—
111C13×C22⋊C4—42no—
112C13×C22⋊C4—42no—
113C13×C22⋊C4—42no—
114C13×C22⋊C4—42no—
115C42×C13—22no—
116C42×C13—22no—
117C42×C13—41no—
118C42×C13—41no—
119C2×#1055—42no—
120C2×#1055—42no—
121C2×#1055—42no—
122C2×#1055—42no—
123C2×#1055—42no—
124C2×#1055—42no—
125C2×#388D1311yescharacteristic
126#1797—131no—
127#1797—131no—
128C2×#323—132no—
129#1280—132no—
130C23×C13—21no—
131C23×C13—21no—
132C23×C13—21no—
133C23×C13—21no—
134C23×C13—22no—
135C23×C13—24no—
136C23×C13—42no—
137C23×C13—42no—
138C23×C13—42no—
139C23×C13—42no—
140C23×C13—41no—
141C23×C13—41no—
142C23×C13—41no—
143C23×C13—41no—
144C23×C13—41no—
145C23×C13—41no—
146C23×C13—42no—
147C23×C13—82no—
148C23×C13—82no—
149C23×C13—82no—
150C23×C13—82no—
151C23×C13C2×C22⋊C411yescharacteristic
152C23×C13C2×C4⋊C411yescharacteristic
153C23×C13#11711yescharacteristic
154C23×C13#13112yes—
155C23×C13#13112yes—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—21no—
164C2×C4×C13—22no—
165C2×C4×C13—21no—
166C2×C4×C13—21no—
167C2×C4×C13—21no—
168C2×C4×C13—21no—
169C2×C4×C13—21no—
170C2×C4×C13—21no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—44no—
176C2×C4×C13—44no—
177C2×C4×C13—42no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—42no—
181C2×C4×C13—41no—
182C2×C4×C13—41no—
183C2×C4×C13—41no—
184C2×C4×C13—41no—
185C2×C4×C13—41no—
186C2×C4×C13—41no—
187C2×C4×C13—82no—
188C2×C4×C13—82no—
189C2×C4×C13#9912yes—
190C2×C4×C13#10012yes—
191C2×C4×C13#12111yescharacteristic
192C2×C4×C13#12111yescharacteristic
193C2×C4×C13C22⋊Q811yescharacteristic
194C2×C4×C13C22⋊Q811yescharacteristic
195#1055—82no—
196#1055—82no—
197C22×C4⋊C4Dic1311yescharacteristic
198C22×C22⋊C4Dic1311yescharacteristic
199C22×C22⋊C4Dic1311yescharacteristic
200C22×C22⋊C4C2×D1311yescharacteristic
201C22×C42C2×D1311yescharacteristic
202C2×C4⋊C8—261no—
203C2×C4⋊C8—261no—
204C2×C22⋊C8—132no—
205C2×C22⋊C8—132no—
206#388—21no—
207#388—21no—
208#388—21no—
209#388—21no—
210C2×#95Dic1311yescharacteristic
211C2×#95C2×D1311yescharacteristic
212#336—261no—
213#336—261no—
214#323—264no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—21no—
219C22×C13—22no—
220C22×C13—22no—
221C22×C13—22no—
222C22×C13—22no—
223C22×C13—42no—
224C22×C13—42no—
225C22×C13—42no—
226C22×C13—84no—
227C22×C13—84no—
228C22×C13—81no—
229C22×C13—81no—
230C22×C13—81no—
231C22×C13—81no—
232C22×C13#38011yescharacteristic
233C22×C13#40811yescharacteristic
234C22×C13#40811yescharacteristic
235C22×C13C2×#9911yescharacteristic
236C22×C13#41011yescharacteristic
237C22×C13C2×#10011yescharacteristic
238C22×C13#41311yescharacteristic
239C22×C13#42412yes—
240C22×C13#43312yes—
241C4×C13—21no—
242C4×C13—21no—
243C4×C13—21no—
244C4×C13—21no—
245C4×C13—22no—
246C4×C13—22no—
247C4×C13—42no—
248C4×C13—41no—
249C4×C13—41no—
250C4×C13—81no—
251C4×C13—81no—
252C25C2×Dic1311yescharacteristic
253C23×C4C2×Dic1311yescharacteristic
254C23×C4C2×Dic1311yescharacteristic
255C23×C4C2×Dic1311yescharacteristic
256C23×C4C2×Dic1311yescharacteristic
257C23×C4C2×Dic1311yescharacteristic
258C23×C4C22×D1311yescharacteristic
259C22×C8—262no—
260C22×C8—262no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—42no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—42no—
273C2×C22⋊C4—42no—
274C2×C22⋊C4Dic2612yes—
275C2×C22⋊C4D5212yes—
276C2×C42—42no—
277C2×C42C22⋊D1311yescharacteristic
278C2×C42C22⋊D1311yescharacteristic
279C2×C42C22⋊D1311yescharacteristic
280C2×C42C22⋊D1311yescharacteristic
281C4⋊C8—522no—
282C4⋊C8—522no—
283C22⋊C8—262no—
284C22⋊C8—262no—
285C22⋊C8—262no—
286C22⋊C8—262no—
287#95—21no—
288#95—21no—
289#95—21no—
290#95—21no—
291C2×C13—22no—
292C2×C13—22no—
293C2×C13—82no—
294C2×C13#146811yescharacteristic
295C2×C13#146911yescharacteristic
296C2×C13#147111yescharacteristic
297C2×C13#147311yescharacteristic
298C2×C13#179811yescharacteristic
299C2×C13#179911yescharacteristic
300C2×C13#180011yescharacteristic
301C24—21no—
302C24—21no—
303C24—22no—
304C24—22no—
305C24—41no—
306C24—41no—
307C24—41no—
308C24—41no—
309C24C4⋊Dic1312yes—
310C24C22×Dic1311yescharacteristic
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—21no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4C4⋊Dic1312yes—
332C22×C4C22⋊Dic1311yescharacteristic
333C22×C4C22⋊Dic1311yescharacteristic
334C22×C4C22⋊Dic1311yescharacteristic
335C22×C4C22⋊Dic1311yescharacteristic
336C22×C4C2×Dic2611yescharacteristic
337C22×C4C2×D5211yescharacteristic
338C22×C4#612711yescharacteristic
339C22×C4#612711yescharacteristic
340C22×C4C2×C22⋊D1311yescharacteristic
341C22×C4C2×C22⋊D1311yescharacteristic
342C2×C8—522no—
343C2×C8—522no—
344C2×C8—522no—
345C2×C8—522no—
346C2×C8—522no—
347C2×C8—522no—
348C4⋊C4—42no—
349C4⋊C4—42no—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—42no—
355C22⋊C4—42no—
356C22⋊C4—42no—
357C22⋊C4—42no—
358C42—22no—
359C42—22no—
360C42—41no—
361C42—41no—
362C13#856111yescharacteristic, complemented, Sylow
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—22no—
368C23—24no—
369C23—42no—
370C23—42no—
371C23—42no—
372C23—42no—
373C23—42no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—82no—
381C23—82no—
382C23—82no—
383C23—82no—
384C23C2×C4⋊Dic1311yescharacteristic
385C23#8818011yescharacteristic
386C23#8820212yes—
387C23#8820212yes—
388C23C2×C22⋊Dic1311yescharacteristic
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—22no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—44no—
409C2×C4—44no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4#8807312yes—
423C2×C4#8807412yes—
424C2×C4#8817811yescharacteristic
425C2×C4#8817811yescharacteristic
426C2×C4#8818411yescharacteristic
427C2×C4#8818411yescharacteristic
428C8—1042no—
429C8—1042no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—84no—
442C22—84no—
443C22—81no—
444C22—81no—
445C22—81no—
446C22—81no—
447C22#1171866012yes—
448C22#1171866112yes—
449C22#1171887311yescharacteristic
450C22C2×#8807311yescharacteristic
451C22C2×#8807411yescharacteristic
452C22#1171889511yescharacteristic
453C22#1171889511yescharacteristic
454C22#1171889811yescharacteristic
455C22#1171890111yescharacteristic
456C4—22no—
457C4—22no—
458C4—21no—
459C4—21no—
460C4—21no—
461C4—21no—
462C4—41no—
463C4—41no—
464C4—42no—
465C4—81no—
466C4—81no—
467C2—22no—
468C2—22no—
469C2—82no—
470C2#1311318411yescharacteristic
471C2#1311318811yescharacteristic
472C2#1311319611yescharacteristic
473C2#1311320511yescharacteristic
474C2#1311482011yescharacteristic
475C2#1311482411yescharacteristic
476C2#1311482811yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#388C2
socleC23×C13C2×C22⋊C4
prime radicalC25×C13C2×C4
cosocleC23×C4×C13C23
hypercenterC2×#388D13
hypocenterC13#8561
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. #13114816C2semidirect
2. #13114816C2semidirect
4. #13112679C2semidirect
362. C13#8561semidirect

Maximal subgroups

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

subgroupindex
#131148162
C2×#117181172
#131126792
C2×C13×#3882
#856113