Finite Group Databasebeta

← #15756265

Subgroups — #15756265

Order 3328.

680 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C4⋊C4×D13C211yesmaximal, characteristic
2#13114813C211yesmaximal, characteristic
3C4×#88060C211yesmaximal, characteristic
4#13112677C211yesmaximal, characteristic, complemented
5#13112676C211yesmaximal, characteristic, complemented
6#13112675C211yesmaximal, characteristic, complemented
7C13×#1279C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×D13C411yescharacteristic
9C2×C4⋊C4×D13C411yescharacteristic
10C2×C42×D13—21no—
11C2×C42×D13C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13C2×C4×C8×C13C2211yescharacteristic
14C4×C13×C4⋊C4C2211yescharacteristic
15C2×#88060—21no—
16C2×#88060—21no—
17C4⋊C4×Dic13C411yescharacteristic
18C4⋊C4×Dic13C411yescharacteristic
19C4×C4⋊Dic13C2211yescharacteristic
20C4×#6101—21no—
21C2×C4⋊#1055C2211yescharacteristic
22C2×C4×#1055C2211yescharacteristic
23D13×#95—21no—
24#11718310—21no—
25#11718142—21no—
26#11718142—21no—
27C22×C4×D13—21no—
28C22×C4×D13—21no—
29C22×C4×D13C2×C411yescharacteristic
30C22×C4×D13D411yescharacteristic
31C22×C4×D13D411yescharacteristic
32C22×C8×C13—21no—
33C22×C8×C13—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C42×C13—21no—
37C2×C42×C13C2311yescharacteristic
38C2×C4⋊Dic13C2×C411yescharacteristic
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×#6101—21no—
41C2×#6101—21no—
42C2×C4×Dic13—21no—
43C2×C4×Dic13—21no—
44C2×C4×Dic13—21no—
45C2×C4×Dic13C2×C411yescharacteristic
46C2×C4×Dic13D411yescharacteristic
47C2×C4×Dic13D411yescharacteristic
48C22×#1055—21no—
49C22×#1055—21no—
50C4⋊C4×D13—22no—
51C4⋊C4×D13—22no—
52C4⋊C4×D13—22no—
53C4⋊C4×D13C814yescomplemented
54C42×D13—21no—
55C42×D13—21no—
56C42×D13—21no—
57C42×D13—21no—
58C42×D13—42no—
59C42×D13—42no—
60C13×C4⋊C8—21no—
61C13×C4⋊C8—21no—
62C4×C8×C13—21no—
63C4×C8×C13—21no—
64C13×#95—21no—
65#88071—21no—
66#88071—21no—
67#88071—21no—
68#88060—24no—
69#88060—42no—
70C4⋊#1055—21no—
71C4⋊#1055—21no—
72C4×#1055—21no—
73C4×#1055—21no—
74#8706—131nomaximal, Sylow
75C23×D13C22⋊C411yescharacteristic
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13C22×C411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×Dic13—21no—
82C22×Dic13—21no—
83C22×Dic13C22⋊C411yescharacteristic
84C22×Dic13C22⋊C411yescharacteristic
85C22×Dic13C22⋊C411yescharacteristic
86C2×C4×D13—21no—
87C2×C4×D13—21no—
88C2×C4×D13—21no—
89C2×C4×D13—21no—
90C2×C4×D13—21no—
91C2×C4×D13—21no—
92C2×C4×D13—21no—
93C2×C4×D13—21no—
94C2×C4×D13—24no—
95C2×C4×D13—24no—
96C2×C4×D13—22no—
97C2×C4×D13—21no—
98C2×C4×D13—21no—
99C2×C4×D13—41no—
100C2×C4×D13—42no—
101C2×C4×D13—42no—
102C2×C4×D13—42no—
103C2×C4×D13—42no—
104C2×C4×D13C2×C812yes—
105C2×C4×D13M1612yes—
106C2×C4×D13D812yes—
107C2×C4×D13SD1612yes—
108C2×C8×C13—22no—
109C2×C8×C13—41no—
110C2×C8×C13—41no—
111C2×C8×C13—41no—
112C2×C8×C13—41no—
113C2×C8×C13—41no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4C2×C812yes—
117C13×C4⋊C4M1612yes—
118C42×C13—41no—
119C42×C13—41no—
120C42×C13#4111yescharacteristic
121C42×C13#4111yescharacteristic
122C42×C13#4111yescharacteristic
123C42×C13#4111yescharacteristic
124C4⋊Dic13—21no—
125C4⋊Dic13—21no—
126C4⋊Dic13C2×C812yes—
127C4⋊Dic13M1612yes—
128#6101—24no—
129#6101—24no—
130C4×Dic13—21no—
131C4×Dic13—21no—
132C4×Dic13—21no—
133C4×Dic13—21no—
134C4×Dic13—21no—
135C4×Dic13—21no—
136C4×Dic13—41no—
137C4×Dic13—41no—
138C4×Dic13—42no—
139C4×Dic13—42no—
140C2×#1055—22no—
141C2×#1055—41no—
142C2×#1055—41no—
143C2×#1055—41no—
144C2×#1055—41no—
145C2×#1055—41no—
146C2×C4×C4⋊C4—131no—
147#1797—131no—
148C4×C22⋊C8—131no—
149#1279—131no—
150#1279—131no—
151#1279—131no—
152#1279D1311yescharacteristic, complemented
153C23×C13C2×C22⋊C411yescharacteristic
154C22×D13—21no—
155C22×D13—21no—
156C22×D13—21no—
157C22×D13—21no—
158C22×D13C22⋊C812yes—
159C22×D13#10212yes—
160C22×D13#10412yes—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—22no—
164C2×C4×C13—22no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13#11711yescharacteristic
170C2×C4×C13#11711yescharacteristic
171C2×C4×C13#12311yescharacteristic
172C2×C4×C13#12311yescharacteristic
173C2×C4×C13#12311yescharacteristic
174C2×C4×C13#12311yescharacteristic
175C2×C4×C13C22×C811yescharacteristic
176C2×C4×C13C2×M1611yescharacteristic
177C2×C4×C13C2×M1611yescharacteristic
178C2×C4×C13C2×M1611yescharacteristic
179C2×C4×C13C2×D811yescharacteristic
180C2×C4×C13C2×SD1611yescharacteristic
181C2×C4×C13#13711yescharacteristic
182C2×C4×C13#13711yescharacteristic
183C2×Dic13—21no—
184C2×Dic13—21no—
185C2×Dic13—21no—
186C2×Dic13—21no—
187C2×Dic13—21no—
188C2×Dic13—22no—
189C2×Dic13—22no—
190C2×Dic13—21no—
191C2×Dic13—21no—
192C2×Dic13—41no—
193C2×Dic13—41no—
194C2×Dic13—41no—
195C2×Dic13—41no—
196C2×Dic13C22⋊C812yes—
197C2×Dic13#10212yes—
198C4×D13—22no—
199C4×D13—22no—
200C4×D13—22no—
201C4×D13—22no—
202C4×D13—22no—
203C4×D13—22no—
204C4×D13—22no—
205C4×D13—22no—
206C4×D13—42no—
207C4×D13—42no—
208C4×D13—48no—
209C4×D13—48no—
210C8×C13—42no—
211C8×C13—81no—
212#1055—42no—
213#1055—81no—
214C22×C4⋊C4—131no—
215C22×C4⋊C4—131no—
216C22×C42—131no—
217C22×C42—261no—
218C2×C4⋊C8—131no—
219C2×C4⋊C8C2×D1311yescharacteristic
220C2×C22⋊C8—261no—
221C2×C22⋊C8—261no—
222C2×C4×C8—131no—
223C2×C4×C8C2×D1311yescharacteristic
224C4×C4⋊C4—131no—
225C4×C4⋊C4—131no—
226C4×C4⋊C4—131no—
227C4×C4⋊C4—261no—
228C4×C4⋊C4—261no—
229C4×C4⋊C4C2×D1311yescharacteristic
230C2×#95—261no—
231#336—261no—
232#336—261no—
233C22×C13#38111yescharacteristic
234C22×C13C2×C22⋊C811yescharacteristic
235C22×C13#40711yescharacteristic
236C22×C13C2×#10211yescharacteristic
237C22×C13#41911yescharacteristic
238C22×C13C2×#10411yescharacteristic
239C22×C13#42111yescharacteristic
240C2×D13—22no—
241C2×D13—22no—
242C2×D13—22no—
243C2×D13—22no—
244C2×D13—22no—
245C2×D13—22no—
246C2×D13D4⋊C814yes—
247C4×C13—21no—
248C4×C13—21no—
249C4×C13—42no—
250C4×C13—42no—
251C4×C13#43111yescharacteristic
252C4×C13#43111yescharacteristic
253C4×C13#43211yescharacteristic
254C4×C13#43211yescharacteristic
255C4×C13#48011yescharacteristic
256C4×C13#48011yescharacteristic
257C4×C13#48311yescharacteristic
258C4×C13#48311yescharacteristic
259Dic13—22no—
260Dic13—22no—
261Dic13—41no—
262Dic13—42no—
263Dic13—42no—
264C23×C4—131no—
265C23×C4—131no—
266C23×C4—131no—
267C23×C4—261no—
268C23×C4—261no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—261no—
272C22×C8—261no—
273C2×C4⋊C4—131no—
274C2×C4⋊C4—131no—
275C2×C4⋊C4—134no—
276C2×C4⋊C4—262no—
277C2×C4⋊C4—262no—
278C2×C4⋊C4—261no—
279C2×C4⋊C4—261no—
280C2×C4⋊C4—262no—
281C2×C4⋊C4C4×D1311yescharacteristic
282C2×C4⋊C4C4×D1311yescharacteristic
283C2×C42—21no—
284C2×C42—131no—
285C2×C42—131no—
286C2×C42—131no—
287C2×C42—261no—
288C2×C42—261no—
289C2×C42—261no—
290C2×C42—261no—
291C2×C42—261no—
292C2×C42—261no—
293C2×C42—261no—
294C2×C42—522no—
295C2×C42—522no—
296C2×C42C22×D1311yescharacteristic
297C4⋊C8—21no—
298C4⋊C8—21no—
299C4⋊C8—261no—
300C4⋊C8—261no—
301C22⋊C8—264no—
302C22⋊C8—522no—
303C4×C8—21no—
304C4×C8—21no—
305C4×C8—261no—
306C4×C8—261no—
307#95—21no—
308#95—261no—
309#95—261no—
310#95—261no—
311C2×C13C2×D4⋊C811yescharacteristic
312C2×C13#147911yescharacteristic
313C2×C13#148611yescharacteristic
314C2×C13#149111yescharacteristic
315C2×C13#181711yescharacteristic
316C2×C13#182311yescharacteristic
317C2×C13#182611yescharacteristic
318D13—24no—
319C24—131no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—131no—
323C22×C4—131no—
324C22×C4—132no—
325C22×C4—132no—
326C22×C4—132no—
327C22×C4—132no—
328C22×C4—131no—
329C22×C4—262no—
330C22×C4—264no—
331C22×C4—264no—
332C22×C4—261no—
333C22×C4—261no—
334C22×C4—261no—
335C22×C4—261no—
336C22×C4—261no—
337C22×C4—261no—
338C22×C4—261no—
339C22×C4—261no—
340C22×C4—261no—
341C22×C4—261no—
342C22×C4—261no—
343C22×C4—261no—
344C22×C4—521no—
345C22×C4—522no—
346C22×C4—522no—
347C22×C4—522no—
348C22×C4—522no—
349C22×C4C2×C4×D1311yescharacteristic
350C22×C4D4×D1311yescharacteristic
351C22×C4D4×D1311yescharacteristic
352C2×C8—22no—
353C2×C8—41no—
354C2×C8—41no—
355C2×C8—41no—
356C2×C8—41no—
357C2×C8—41no—
358C2×C8—262no—
359C2×C8—521no—
360C2×C8—521no—
361C2×C8—521no—
362C2×C8—521no—
363C2×C8—521no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—132no—
367C4⋊C4—132no—
368C4⋊C4—264no—
369C4⋊C4—264no—
370C4⋊C4—261no—
371C4⋊C4—261no—
372C4⋊C4C8×D1312yes—
373C4⋊C4#609412yes—
374C42—41no—
375C42—41no—
376C42—261no—
377C42—261no—
378C42—261no—
379C42—261no—
380C42—261no—
381C42—261no—
382C42—522no—
383C42—522no—
384C42—521no—
385C42—521no—
386C42#612711yescharacteristic
387C42#612711yescharacteristic
388C42#612911yescharacteristic
389C42#613111yescharacteristic
390C13#870611yescharacteristic, complemented, Sylow
391C23—132no—
392C23—132no—
393C23—132no—
394C23—261no—
395C23—261no—
396C23—261no—
397C23—261no—
398C23C22⋊C4×D1311yescharacteristic
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—132no—
408C2×C4—132no—
409C2×C4—261no—
410C2×C4—261no—
411C2×C4—261no—
412C2×C4—261no—
413C2×C4—262no—
414C2×C4—262no—
415C2×C4—262no—
416C2×C4—262no—
417C2×C4—262no—
418C2×C4—262no—
419C2×C4—262no—
420C2×C4—262no—
421C2×C4—261no—
422C2×C4—261no—
423C2×C4—261no—
424C2×C4—262no—
425C2×C4—262no—
426C2×C4—522no—
427C2×C4—522no—
428C2×C4—528no—
429C2×C4—528no—
430C2×C4—521no—
431C2×C4—521no—
432C2×C4—521no—
433C2×C4—521no—
434C2×C4#8812611yescharacteristic
435C2×C4#8813711yescharacteristic
436C2×C4#8813711yescharacteristic
437C2×C4#8814611yescharacteristic
438C2×C4#8814811yescharacteristic
439C2×C4#8814811yescharacteristic
440C2×C4C2×C8×D1311yescharacteristic
441C2×C4C2×#609411yescharacteristic
442C2×C4M16×D1311yescharacteristic
443C2×C4M16×D1311yescharacteristic
444C2×C4D8×D1311yescharacteristic
445C2×C4SD16×D1311yescharacteristic
446C2×C4#8816911yescharacteristic
447C2×C4#8817211yescharacteristic
448C8—42no—
449C8—81no—
450C8—522no—
451C8—1041no—
452C22—134no—
453C22—262no—
454C22—262no—
455C22—262no—
456C22—262no—
457C22—262no—
458C22—262no—
459C22#1171832511yescharacteristic
460C22D13×C22⋊C811yescharacteristic
461C22#1171838711yescharacteristic
462C22D13×#10211yescharacteristic
463C22#1171846311yescharacteristic
464C22D13×#10411yescharacteristic
465C22#1171848211yescharacteristic
466C4—21no—
467C4—21no—
468C4—42no—
469C4—42no—
470C4—262no—
471C4—262no—
472C4—521no—
473C4—522no—
474C4—522no—
475C4#1171834611yescharacteristic
476C4#1171836611yescharacteristic
477C4#1171843511yescharacteristic
478C4#1171846611yescharacteristic
479C4#1171849411yescharacteristic
480C4#1171849611yescharacteristic
481C4#1171852311yescharacteristic
482C4#1171854311yescharacteristic
483C2—264no—
484C2D13×D4⋊C811yescharacteristic
485C2#1311322911yescharacteristic
486C2#1311325911yescharacteristic
487C2#1311328111yescharacteristic
488C2#1311490311yescharacteristic
489C2#1311492111yescharacteristic
490C2#1311493411yescharacteristic
subgroupG/H
centerC22×C4D4×D13
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1279C2
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1279D13
hypocenterC13#8706
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
4. #13112677C2semidirect
5. #13112676C2semidirect
6. #13112675C2semidirect
7. C13×#1279C2semidirect
53. C4⋊C4×D13C8semidirect
152. #1279D13semidirect
390. C13#8706semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊C4×D132
#131148132
C4×#880602
#131126772
#131126762
#131126752
C13×#12792
#870613