Finite Group Databasebeta

← #15875026

Subgroups — #15875026

Order 3328.

836 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718748C211yesmaximal, characteristic
2#13117300C211yesmaximal, characteristic
3#13115789C211yesmaximal, characteristic, complemented
4#13115597C211yesmaximal, characteristic, complemented
5#13115571C212yesmaximal, complemented
6#13115532C212yesmaximal
7#13115463C212yesmaximal
8#13115428C212yesmaximal, complemented
9#13114833C211yesmaximal, characteristic
10#13114689C211yesmaximal, characteristic, complemented
11C4×C13×C4⋊Q8C211yesmaximal, characteristic, complemented
12C2×C13×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C13—21no—
14C2×C4×D52C2211yescharacteristic
15C2×#88126—21no—
16C13×#391—21no—
17C13×#389—21no—
18C13×#389C2212yes—
19C13×#384C2211yescharacteristic
20C4×C13×C4⋊C4—21no—
21C4×C13×C4⋊C4C2212yes—
22C43×C13C2211yescharacteristic
23#11718748C418yescomplemented
24C2×#88049C2212yes—
25C2×#88049C2212yes—
26C2×#88048C2212yes—
27C2×#88047C2212yes—
28#11718601—21no—
29#11718601—21no—
30#11718600C2211yescharacteristic
31#11718600C2211yescharacteristic
32C4×#6103—21no—
33C4×C4⋊Dic13C2211yescharacteristic
34#11718589C2211yescharacteristic
35#11718589C2211yescharacteristic
36C2×C4⋊#1055C2211yescharacteristic
37C2×C4⋊#1055C2211yescharacteristic
38C2×#88043C2212yes—
39#11718121C2212yes—
40#11718121C2212yes—
41#11718121C2212yes—
42#11718121C2212yes—
43#11718116C2212yes—
44C22×Q8×C13—21no—
45C22×D52C2311yescharacteristic
46C22×C4×D13—21no—
47C13×C4⋊Q8—22no—
48C13×C4⋊Q8C2×C414yes—
49C4×Q8×C13—44no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—22no—
54C2×C13×C4⋊C4C2312yes—
55C2×C13×C4⋊C4C2312yes—
56C2×C42×C13—22no—
57C2×C42×C13D411yescharacteristic
58C2×C42×C13D411yescharacteristic
59C2×C42×C13D411yescharacteristic
60C2×C42×C13D411yescharacteristic
61C2×C42×C13C2311yescharacteristic
62C2×C42×C13C2311yescharacteristic
63C2×C42×C13C2311yescharacteristic
64C2×#6103—21no—
65C2×#6103—21no—
66C2×#6103—21no—
67C2×#6103—21no—
68C2×#6103—21no—
69C2×C4⋊Dic13C2311yescharacteristic
70C2×C4⋊Dic13C2311yescharacteristic
71C2×C4⋊Dic13C2311yescharacteristic
72C2×#6101—21no—
73C2×#6101—21no—
74C2×C4×Dic13—21no—
75C22×#1055C2312yes—
76C22×#1055C2312yes—
77C4×D52—22no—
78C4×D52C2×C414yes—
79#88126—44no—
80C13×#95—22no—
81C13×#95—22no—
82#88071—21no—
83#88071—21no—
84#88071—21no—
85#88049—42no—
86#88049C2×C418yes—
87#88048—42no—
88#88047C2×C418yes—
89C4⋊#1055—22no—
90C4⋊#1055C2×C414yes—
91#88043—42no—
92#22116—131nomaximal, Sylow
93C23×D13—21no—
94C2×Q8×C13—24no—
95C2×Q8×C13—42no—
96C2×Q8×C13—42no—
97C22×C4×C13—22no—
98C22×C4×C13—22no—
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13C2411yescharacteristic
106C22×Dic13—21no—
107C22×Dic13—21no—
108C22×Dic13—21no—
109C2×D52—21no—
110C2×D52—21no—
111C2×D52—21no—
112C2×D52—21no—
113C2×D52—21no—
114C2×D52C22×C412yes—
115C2×C4×D13—24no—
116C2×C4×D13—42no—
117C2×C4×D13—42no—
118C13×C4⋊C4—24no—
119C13×C4⋊C4—22no—
120C13×C4⋊C4—22no—
121C13×C4⋊C4—22no—
122C13×C4⋊C4—42no—
123C13×C4⋊C4—44no—
124C13×C4⋊C4—42no—
125C13×C4⋊C4C22×C414yes—
126C42×C13—22no—
127C42×C13—22no—
128C42×C13—22no—
129C42×C13—21no—
130C42×C13—21no—
131C42×C13—21no—
132C42×C13—21no—
133C42×C13—41no—
134C42×C13—44no—
135C42×C13C22×C412yes—
136C42×C13#4112yes—
137#6103—24no—
138#6103—42no—
139#6103—42no—
140#6103—42no—
141#6103—42no—
142C4⋊Dic13—21no—
143C4⋊Dic13—21no—
144C4⋊Dic13—21no—
145C4⋊Dic13—21no—
146C4⋊Dic13—21no—
147C4⋊Dic13C22×C412yes—
148#6101—42no—
149#6101—42no—
150C4×Dic13—42no—
151C2×#1055—22no—
152C2×#1055—22no—
153C2×#1055—22no—
154C2×#1055—22no—
155C2×#1055—22no—
156C2×#1055C22×C414yes—
157C2×#474—131no—
158C4×C4⋊Q8D1311yescharacteristic, complemented
159#2293—131no—
160#1988—131no—
161#1948—131no—
162#1943—132no—
163#1936—132no—
164#1926—132no—
165#1921—132no—
166#1802—131no—
167#1767—131no—
168C23×C13C22×D411yescharacteristic
169C22×D13—22no—
170C22×D13—41no—
171C22×D13—41no—
172C22×D13—41no—
173C22×D13—41no—
174C22×D13—41no—
175C22×D13—41no—
176Q8×C13—48no—
177C2×C4×C13—21no—
178C2×C4×C13—21no—
179C2×C4×C13—21no—
180C2×C4×C13—21no—
181C2×C4×C13—24no—
182C2×C4×C13—21no—
183C2×C4×C13—21no—
184C2×C4×C13—21no—
185C2×C4×C13—21no—
186C2×C4×C13—21no—
187C2×C4×C13—21no—
188C2×C4×C13—21no—
189C2×C4×C13—21no—
190C2×C4×C13—21no—
191C2×C4×C13—42no—
192C2×C4×C13—42no—
193C2×C4×C13—42no—
194C2×C4×C13—42no—
195C2×C4×C13—42no—
196C2×C4×C13C4×D412yes—
197C2×C4×C13C4×D412yes—
198C2×C4×C13AGL(1,ℤ/8)12yes—
199C2×C4×C13AGL(1,ℤ/8)12yes—
200C2×C4×C13#13712yes—
201C2×C4×C13C23×C411yescharacteristic
202C2×C4×C13C2×#4111yescharacteristic
203C2×C4×C13H(5,𝔽2)11yescharacteristic
204C2×C4×C132−1+411yescharacteristic
205C2×C4×C132−1+411yescharacteristic
206C2×C4×C132−1+411yescharacteristic
207C2×Dic13—22no—
208C2×Dic13—41no—
209C2×Dic13—41no—
210C2×Dic13—41no—
211C2×Dic13—41no—
212C2×Dic13—41no—
213C2×Dic13—41no—
214C2×Dic13—41no—
215C2×Dic13—41no—
216D52—22no—
217D52—22no—
218D52—41no—
219D52—41no—
220C4×D13—48no—
221#1055—24no—
222#1055—42no—
223C2×C4⋊Q8C2×D1311yescharacteristic
224C2×C4×Q8—21no—
225C2×C4×D4—131no—
226C2×#117—261no—
227#474—138no—
228C2×#107—132no—
229C2×#106—132no—
230C2×C4⋊C8—131no—
231C2×C4⋊C8—131no—
232C2×#102—132no—
233C2×#102—132no—
234C2×#97—132no—
235#391—21no—
236#390—131no—
237#390—131no—
238#389—21no—
239#389—131no—
240#389—131no—
241#389C2×D1312yes—
242#388—261no—
243#388—261no—
244#384C2×D1311yescharacteristic
245C4×C4⋊C4—21no—
246C4×C4⋊C4—131no—
247C4×C4⋊C4C2×D1312yes—
248C4×C22⋊C4—261no—
249C43C2×D1311yescharacteristic
250#340—132no—
251#340—132no—
252#340—132no—
253#340—132no—
254#336—132no—
255C22×C13C2×C4×D411yescharacteristic
256C22×C13#53611yescharacteristic
257C22×C13#53711yescharacteristic
258C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
259C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
260C22×C13C2×#13711yescharacteristic
261C22×C13#57511yescharacteristic
262C2×D13—42no—
263C2×D13—42no—
264C2×D13—42no—
265C2×D13—81no—
266C2×D13—81no—
267C2×D13—81no—
268C2×D13—81no—
269C4×C13—22no—
270C4×C13—22no—
271C4×C13—44no—
272C4×C13—41no—
273C4×C13—41no—
274C4×C13—41no—
275C4×C13—82no—
276C4×C13#44214yes—
277C4×C13#51911yescharacteristic
278C4×C13#52011yescharacteristic
279C4×C13#54111yescharacteristic
280C4×C13#54211yescharacteristic
281Dic13—42no—
282Dic13—81no—
283Dic13—81no—
284C22×Q8—21no—
285C22×D4—131no—
286C23×C4—261no—
287C22×C8—132no—
288C22×C8—132no—
289C4⋊Q8—22no—
290C4⋊Q8C4×D1314yes—
291C4×Q8—44no—
292C4×D4—134no—
293C4×D4—262no—
294#117—524no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—131no—
300C2×C4⋊C4—131no—
301C2×C4⋊C4—131no—
302C2×C4⋊C4—261no—
303C2×C4⋊C4—261no—
304C2×C4⋊C4C22×D1312yes—
305C2×C4⋊C4C22×D1312yes—
306C2×C22⋊C4—261no—
307C2×C22⋊C4—261no—
308C2×C22⋊C4—261no—
309C2×C22⋊C4—261no—
310C2×C22⋊C4—261no—
311C2×C42—22no—
312C2×C42—261no—
313C2×C42C22⋊D1311yescharacteristic
314C2×C42C22⋊D1311yescharacteristic
315C2×C42C22⋊D1311yescharacteristic
316C2×C42C22⋊D1311yescharacteristic
317C2×C42C22×D1311yescharacteristic
318C2×C42C22×D1311yescharacteristic
319C2×C42C22×D1311yescharacteristic
320#107—138no—
321#106—522no—
322C4⋊C8—134no—
323C4⋊C8—262no—
324#102—138no—
325#102—522no—
326#97—522no—
327#95—22no—
328#95—22no—
329#95—261no—
330#95—261no—
331#95—261no—
332C2×C13#232311yescharacteristic
333C2×C13C2×#44211yescharacteristic
334C2×C13C4×#13711yescharacteristic
335C2×C13#323511yescharacteristic
336C2×C13#323911yescharacteristic
337C2×C13#325111yescharacteristic
338C2×C13#325411yescharacteristic
339D13—82no—
340C24—261no—
341C2×Q8—24no—
342C2×Q8—42no—
343C2×Q8—42no—
344C2×D4—132no—
345C2×D4—261no—
346C2×D4—261no—
347C2×D4—261no—
348C2×D4—261no—
349C2×D4—261no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—261no—
353C22×C4—264no—
354C22×C4—261no—
355C22×C4—261no—
356C22×C4—522no—
357C22×C4—522no—
358C22×C4C2×C22⋊D1311yescharacteristic
359C22×C4C2×C22⋊D1311yescharacteristic
360C22×C4C2×C22⋊D1311yescharacteristic
361C22×C4C2×C22⋊D1311yescharacteristic
362C22×C4C2×C22⋊D1311yescharacteristic
363C22×C4C2×C22⋊D1311yescharacteristic
364C22×C4C23×D1311yescharacteristic
365C2×C8—134no—
366C2×C8—262no—
367C2×C8—262no—
368C2×C8—262no—
369C2×C8—262no—
370C2×C8—262no—
371C4⋊C4—24no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—44no—
376C4⋊C4—42no—
377C4⋊C4—42no—
378C4⋊C4—132no—
379C4⋊C4—261no—
380C4⋊C4—261no—
381C4⋊C4—261no—
382C4⋊C4—261no—
383C4⋊C4—261no—
384C4⋊C4—522no—
385C4⋊C4—522no—
386C4⋊C4C2×C4×D1314yes—
387C22⋊C4—264no—
388C22⋊C4—522no—
389C22⋊C4—522no—
390C22⋊C4—522no—
391C22⋊C4—522no—
392C42—22no—
393C42—22no—
394C42—22no—
395C42—21no—
396C42—21no—
397C42—21no—
398C42—21no—
399C42—41no—
400C42—44no—
401C42—522no—
402C42C2×C4×D1312yes—
403C42#612712yes—
404C13#2211611yescharacteristic, complemented, Sylow
405C23—262no—
406C23—521no—
407C23—521no—
408C23—521no—
409C23—521no—
410C23—521no—
411C23—521no—
412C23C22×C22⋊D1311yescharacteristic
413Q8—48no—
414D4—262no—
415D4—262no—
416D4—521no—
417D4—521no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—24no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—262no—
438C2×C4—521no—
439C2×C4—521no—
440C2×C4—528no—
441C2×C4—521no—
442C2×C4—521no—
443C2×C4—521no—
444C2×C4—521no—
445C2×C4—521no—
446C2×C4—521no—
447C2×C4C4×C22⋊D1312yes—
448C2×C4C4×C22⋊D1312yes—
449C2×C4#8818612yes—
450C2×C4#8819612yes—
451C2×C4#8820312yes—
452C2×C4C22×C4×D1311yescharacteristic
453C2×C4C2×#612711yescharacteristic
454C2×C4#8825411yescharacteristic
455C2×C4#8825411yescharacteristic
456C2×C4#8825611yescharacteristic
457C2×C4#8825711yescharacteristic
458C8—264no—
459C8—522no—
460C22—522no—
461C22—522no—
462C22—522no—
463C22—1041no—
464C22—1041no—
465C22—1041no—
466C22—1041no—
467C22C2×C4×C22⋊D1311yescharacteristic
468C22C2×#8818611yescharacteristic
469C22C2×#8819611yescharacteristic
470C22#1171952111yescharacteristic
471C22C2×#8820311yescharacteristic
472C22#1171952711yescharacteristic
473C22#1171953811yescharacteristic
474C4—22no—
475C4—22no—
476C4—44no—
477C4—41no—
478C4—41no—
479C4—41no—
480C4—82no—
481C4—522no—
482C4—1041no—
483C4—1041no—
484C4#1171867514yes—
485C4#1171927711yescharacteristic
486C4#1171927911yescharacteristic
487C4#1171928711yescharacteristic
488C4#1171928811yescharacteristic
489C2—1042no—
490C2#1311751211yescharacteristic
491C2C2×#1171867511yescharacteristic
492C2C4×#8819611yescharacteristic
493C2#1312603411yescharacteristic
494C2#1312606611yescharacteristic
495C2#1312619211yescharacteristic
496C2#1312621911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC4×C13×C4⋊Q8C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenterC4×C4⋊Q8D13
hypocenterC13#22116
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13115789C2semidirect
4. #13115597C2semidirect
5. #13115571C2semidirect
8. #13115428C2semidirect
10. #13114689C2semidirect
11. C4×C13×C4⋊Q8C2semidirect
23. #11718748C4semidirect
158. C4×C4⋊Q8D13semidirect
404. C13#22116semidirect

Maximal subgroups

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

subgroupindex
C2×#117187482
#131173002
#131157892
#131155972
#131155712
#131155322
#131154632
#131154282
#131148332
#131146892
C4×C13×C4⋊Q82
#2211613