Finite Group Databasebeta

← #15761909

Subgroups — #15761909

Order 3328.

700 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123137C211yesmaximal, characteristic
2#13114598C211yesmaximal, characteristic, complemented
3C2×#11718044C212yesmaximal, complemented
4C2×#11718043C212yesmaximal
5C13×C4⋊#95C211yesmaximal, characteristic, complemented
6C22×C13×C4⋊C4—21no—
7C22×C42×C13C2211yescharacteristic
8C2×#88184C2211yescharacteristic
9C2×#88178C2211yescharacteristic
10C2×#88129C411yescharacteristic, complemented
11C2×C13×#95—21no—
12C2×C13×#95C2212yes—
13#11718874—21no—
14#11718874—21no—
15C2×C22⋊#1055C2212yes—
16#11718601—21no—
17#11718601—21no—
18#11718600C411yescharacteristic, complemented
19#11718597C411yescharacteristic, complemented
20#11718590C411yescharacteristic, complemented
21C2×#88043—21no—
22#11718116—21no—
23#11718044—24no—
24#11718043—24no—
25C23×C4×C13—22no—
26C23×C4×C13D411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C23×C4×C13C2311yescharacteristic
29C22×C22⋊D13—21no—
30C22×D52C2×C411yescharacteristic
31C22×Dic26C2×C411yescharacteristic
32C2×C13×C4⋊C4—24no—
33C2×C13×C4⋊C4—42no—
34C2×C13×C4⋊C4—42no—
35C2×C42×C13—42no—
36C2×C42×C13C2×C411yescharacteristic
37C2×C42×C13C2×C411yescharacteristic
38C2×C42×C13D411yescharacteristic
39C2×C42×C13D411yescharacteristic
40C2×C22⋊Dic13—21no—
41#88184—22no—
42#88184—22no—
43C2×#6103—21no—
44C2×#6103—21no—
45C2×#6103—21no—
46C2×#6103—21no—
47C2×#6103—21no—
48C2×C4⋊Dic13C2×C411yescharacteristic
49C2×C4⋊Dic13C2×C411yescharacteristic
50#88178—22no—
51#88178—22no—
52C2×#6101—21no—
53C22×#1055—22no—
54#88129—42no—
55C13×#95—22no—
56C13×#95—22no—
57C13×#95—42no—
58#88071—21no—
59#88071—21no—
60#88071—21no—
61#88071—21no—
62C22⋊#1055—22no—
63C22⋊#1055D414yes—
64#88043—42no—
65#9682—131nomaximal, Sylow
66C24×C13C2×D411yescharacteristic
67C23×D13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—22no—
71C22×C4×C13—22no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—24no—
75C22×C4×C13—41no—
76C22×C4×C13—41no—
77C22×C4×C13—41no—
78C22×C4×C13—41no—
79C22×C4×C13—42no—
80C22×C4×C13—42no—
81C22×C4×C13—42no—
82C22×C4×C13—42no—
83C22×C4×C13—42no—
84C22×C4×C13—42no—
85C22×C4×C13C22⋊C411yescharacteristic
86C22×C4×C13C22⋊C411yescharacteristic
87C22×C4×C13C22⋊C411yescharacteristic
88C22×C4×C13C22⋊C411yescharacteristic
89C22×C4×C13C22×C411yescharacteristic
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13C2×D412yes—
92C22×C4×C13#4112yes—
93C2×C22⋊D13—41no—
94C2×C22⋊D13—41no—
95C2×C22⋊D13—41no—
96C2×C22⋊D13—41no—
97C2×C22⋊D13—41no—
98C2×C22⋊D13—41no—
99C22×Dic13—21no—
100C22×Dic13—21no—
101C22×Dic13—21no—
102C2×D52—22no—
103C2×D52—41no—
104C2×D52—41no—
105C2×Dic26—22no—
106C2×Dic26—41no—
107C2×Dic26—41no—
108C13×C4⋊C4—48no—
109C42×C13—22no—
110C42×C13—22no—
111C42×C13—41no—
112C42×C13—41no—
113C22⋊Dic13—41no—
114C22⋊Dic13—41no—
115#6103—42no—
116#6103—42no—
117#6103—42no—
118#6103—42no—
119#6103—42no—
120C4⋊Dic13—22no—
121C4⋊Dic13—22no—
122#6101—42no—
123C2×#1055—24no—
124C2×#1055—42no—
125C2×#1055—42no—
126#2850—131no—
127#1749—131no—
128C2×#328—132no—
129C2×#327—132no—
130C4⋊#95D1311yescharacteristic, complemented
131C23×C13—21no—
132C23×C13—21no—
133C23×C13—21no—
134C23×C13—21no—
135C23×C13C2×C22⋊C411yescharacteristic
136C23×C13#12411yescharacteristic
137C23×C13#12711yescharacteristic
138C23×C13AGL(1,ℤ/8)11yescharacteristic
139C23×C13AGL(1,ℤ/8)11yescharacteristic
140C23×C13#13711yescharacteristic
141C23×C13#13711yescharacteristic
142C22×D13—41no—
143C22×D13—41no—
144C22×D13—41no—
145C22×D13—41no—
146C22×D13—41no—
147C22×D13—41no—
148C22×D13—41no—
149C2×C4×C13—24no—
150C2×C4×C13—24no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
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—21no—
165C2×C4×C13—42no—
166C2×C4×C13—42no—
167C2×C4×C13—42no—
168C2×C4×C13—42no—
169C2×C4×C13—44no—
170C2×C4×C13—44no—
171C2×C4×C13—44no—
172C2×C4×C13—82no—
173C2×C4×C13—82no—
174C2×C4×C13—82no—
175C2×C4×C13—82no—
176C2×C4×C13#9912yes—
177C2×C4×C13#10412yes—
178C2×C4×C13C4×D412yes—
179C2×C4×C13#12112yes—
180C22⋊D13—81no—
181C22⋊D13—81no—
182C22⋊D13—81no—
183C22⋊D13—81no—
184C2×Dic13—41no—
185C2×Dic13—41no—
186C2×Dic13—41no—
187C2×Dic13—41no—
188C2×Dic13—41no—
189C2×Dic13—41no—
190C2×Dic13—41no—
191C2×Dic13—41no—
192C2×Dic13—41no—
193D52—82no—
194Dic26—82no—
195#1055—44no—
196C2×#124—131no—
197C2×C22⋊Q8—131no—
198C2×#121—131no—
199C22×C4⋊C4—21no—
200C22×C42C2×D1311yescharacteristic
201C2×C22⋊C8—132no—
202C2×#97—261no—
203#391—131no—
204#390—131no—
205#388—261no—
206#388—261no—
207#386—261no—
208#386—261no—
209#382—131no—
210C2×#95—21no—
211C2×#95C2×D1312yes—
212#336—261no—
213#328—264no—
214#327—264no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—21no—
219C22×C13—21no—
220C22×C13—21no—
221C22×C13—21no—
222C22×C13—21no—
223C22×C13—21no—
224C22×C13—21no—
225C22×C13—21no—
226C22×C13—21no—
227C22×C13#39011yescharacteristic
228C22×C13C2×#9911yescharacteristic
229C22×C13#41011yescharacteristic
230C22×C13#41711yescharacteristic
231C22×C13#41711yescharacteristic
232C22×C13C2×#10411yescharacteristic
233C22×C13#42111yescharacteristic
234C22×C13#48911yescharacteristic
235C22×C13#48911yescharacteristic
236C22×C13#49611yescharacteristic
237C22×C13#49711yescharacteristic
238C2×D13—81no—
239C2×D13—81no—
240C2×D13—81no—
241C2×D13—81no—
242C2×D13—81no—
243C2×D13—81no—
244C2×D13—81no—
245C4×C13—22no—
246C4×C13—22no—
247C4×C13—22no—
248C4×C13—22no—
249C4×C13—41no—
250C4×C13—41no—
251C4×C13—84no—
252Dic13—81no—
253Dic13—81no—
254Dic13—81no—
255C22×Q8—131no—
256C22×D4—131no—
257C22×D4—261no—
258C23×C4—22no—
259C23×C4C22⋊D1311yescharacteristic
260C23×C4C22⋊D1311yescharacteristic
261C23×C4C22×D1311yescharacteristic
262C22×C8—262no—
263#124—522no—
264C22⋊Q8—262no—
265C22⋊Q8—262no—
266#121—262no—
267#121—262no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—42no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—131no—
272C2×C4⋊C4—131no—
273C2×C4⋊C4—261no—
274C2×C22⋊C4—261no—
275C2×C22⋊C4—261no—
276C2×C22⋊C4—261no—
277C2×C22⋊C4—261no—
278C2×C22⋊C4—261no—
279C2×C22⋊C4—261no—
280C2×C42—42no—
281C2×C42C4×D1311yescharacteristic
282C2×C42C4×D1311yescharacteristic
283C2×C42D5211yescharacteristic
284C2×C42D5211yescharacteristic
285C22⋊C8—134no—
286C22⋊C8—262no—
287#97—522no—
288#95—22no—
289#95—22no—
290#95—42no—
291#95—261no—
292#95—261no—
293#95—261no—
294#95—261no—
295C2×C13—21no—
296C2×C13—21no—
297C2×C13—21no—
298C2×C13—21no—
299C2×C13#150411yescharacteristic
300C2×C13#150911yescharacteristic
301C2×C13#151211yescharacteristic
302C2×C13#151311yescharacteristic
303C2×C13#195911yescharacteristic
304C2×C13#196411yescharacteristic
305C2×C13#198011yescharacteristic
306D13—161no—
307C24—261no—
308C24C2×C22⋊D1311yescharacteristic
309C2×Q8—262no—
310C2×Q8—521no—
311C2×Q8—521no—
312C2×D4—262no—
313C2×D4—521no—
314C2×D4—521no—
315C2×D4—521no—
316C2×D4—521no—
317C2×D4—521no—
318C2×D4—521no—
319C2×D4—521no—
320C2×D4—521no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—24no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—261no—
339C22×C4—261no—
340C22×C4—261no—
341C22×C4#610311yescharacteristic
342C22×C4#610311yescharacteristic
343C22×C4#610311yescharacteristic
344C22×C4#610311yescharacteristic
345C22×C4C2×C4×D1311yescharacteristic
346C22×C4C2×D5211yescharacteristic
347C22×C4D4×D1312yes—
348C22×C4#613112yes—
349C2×C8—264no—
350C2×C8—522no—
351C2×C8—522no—
352C4⋊C4—48no—
353C4⋊C4—262no—
354C4⋊C4—262no—
355C4⋊C4—522no—
356C22⋊C4—522no—
357C22⋊C4—522no—
358C22⋊C4—521no—
359C22⋊C4—521no—
360C22⋊C4—522no—
361C22⋊C4—522no—
362C22⋊C4—522no—
363C42—22no—
364C42—22no—
365C42—41no—
366C42—41no—
367C13#968211yescharacteristic, complemented, Sylow
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—521no—
373C23—521no—
374C23—521no—
375C23—521no—
376C23—521no—
377C23—521no—
378C23—521no—
379C23C2×#610311yescharacteristic
380C23#8818611yescharacteristic
381C23#8818611yescharacteristic
382C23#8819411yescharacteristic
383C23#8819611yescharacteristic
384C23#8819611yescharacteristic
385C23#8820111yescharacteristic
386Q8—1042no—
387D4—1042no—
388D4—1041no—
389D4—1041no—
390D4—1041no—
391D4—1041no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—82no—
416C2×C4—82no—
417C2×C4—82no—
418C2×C4—82no—
419C2×C4—521no—
420C2×C4—521no—
421C2×C4—521no—
422C2×C4—521no—
423C2×C4—521no—
424C2×C4—521no—
425C2×C4—521no—
426C2×C4—521no—
427C2×C4—521no—
428C2×C4#8804512yes—
429C2×C4#8804612yes—
430C2×C4#8814712yes—
431C2×C4#8814912yes—
432C8—524no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—1041no—
446C22—1041no—
447C22—1041no—
448C22—1041no—
449C22—1041no—
450C22—1041no—
451C22—1041no—
452C22C2×#8804511yescharacteristic
453C22C2×#8804611yescharacteristic
454C22#1171862711yescharacteristic
455C22#1171862711yescharacteristic
456C22#1171864911yescharacteristic
457C22#1171866611yescharacteristic
458C22#1171866711yescharacteristic
459C22#1171873511yescharacteristic
460C22#1171874711yescharacteristic
461C22#1171875011yescharacteristic
462C22#1171875011yescharacteristic
463C4—22no—
464C4—22no—
465C4—22no—
466C4—22no—
467C4—41no—
468C4—41no—
469C4—84no—
470C4—1041no—
471C4—1041no—
472C4—1041no—
473C2—21no—
474C2—21no—
475C2—21no—
476C2—21no—
477C2—2081no—
478C2#1311333811yescharacteristic
479C2#1311335911yescharacteristic
480C2#1311337211yescharacteristic
481C2#1311337711yescharacteristic
482C2#1311565011yescharacteristic
483C2#1311567111yescharacteristic
484C2#1311575411yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×C4⋊#95C2
socleC23×C13C2×C22⋊C4
prime radicalC2×#88184C22
cosocleC23×C4×C13C23
hypercenterC4⋊#95D13
hypocenterC13#9682
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. #13114598C2semidirect
3. C2×#11718044C2semidirect
5. C13×C4⋊#95C2semidirect
10. C2×#88129C4semidirect
18. #11718600C4semidirect
19. #11718597C4semidirect
20. #11718590C4semidirect
130. C4⋊#95D13semidirect
367. C13#9682semidirect

Maximal subgroups

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

subgroupindex
#131231372
#131145982
C2×#117180442
C2×#117180432
C13×C4⋊#952
#968213