Finite Group Databasebeta

← #15914509

Subgroups — #15914509

Order 3328.

778 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718745C211yesmaximal, characteristic
2#13120010C211yesmaximal, characteristic
3#13117926C211yesmaximal, characteristic, complemented
4#13116320C212yesmaximal, complemented
5#13116219C212yesmaximal
6#13115785C211yesmaximal, characteristic, complemented
7#13115601C212yesmaximal, complemented
8#13115554C211yesmaximal, characteristic, complemented
9#13115455C212yesmaximal
10C4×#88061C211yesmaximal, characteristic
11C2×C13×#500C211yesmaximal, characteristic, complemented
12C2×C13×C4⋊Q8C2211yescharacteristic
13C2×C13×C4⋊Q8C2211yescharacteristic
14C2×C4×D52C2211yescharacteristic
15C13×#500—24no—
16C2×C13×#107C2212yes—
17C2×C13×#107C2212yes—
18C2×C4×C8×C13C2211yescharacteristic
19#11718892—22no—
20#11718891—22no—
21C2×#88061C2211yescharacteristic
22C2×#88061C2211yescharacteristic
23C2×#88054C2212yes—
24#11718745—24no—
25#11718649C2212yes—
26#11718648—21no—
27#11718648—21no—
28#11718646—21no—
29#11718646C2212yes—
30#11718638C2212yes—
31C4⋊C4×Dic13—21no—
32C4⋊C4×Dic13C2212yes—
33C2×#88049C2212yes—
34C2×#88048C2212yes—
35C4×C4⋊Dic13C2211yescharacteristic
36C4×C4⋊Dic13C2211yescharacteristic
37C2×C4⋊#1055C2211yescharacteristic
38#11718143C2211yescharacteristic
39#11718143C2211yescharacteristic
40#11718142C2212yes—
41#11718121C2212yes—
42#11718121C2212yes—
43C22×Q8×C13—21no—
44C22×Q8×C13—21no—
45C22×D52C2311yescharacteristic
46C22×C4×D13—21no—
47C22×C8×C13C2311yescharacteristic
48C22×C8×C13C2311yescharacteristic
49C13×C4⋊Q8—22no—
50C13×C4⋊Q8—22no—
51C13×C4⋊Q8—22no—
52C13×C4⋊Q8D414yes—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4C2312yes—
56C2×C13×C4⋊C4C2312yes—
57C2×C42×C13C2311yescharacteristic
58C2×#6103—21no—
59C2×#6103—22no—
60C2×#6103—22no—
61C2×C4⋊Dic13—22no—
62C2×C4⋊Dic13D411yescharacteristic
63C2×C4⋊Dic13D411yescharacteristic
64C2×C4⋊Dic13C2311yescharacteristic
65C2×C4⋊Dic13C2311yescharacteristic
66C2×C4⋊Dic13C2311yescharacteristic
67C2×C4×Dic13—21no—
68C2×C4×Dic13—22no—
69C2×C4×Dic13C2312yes—
70C22×#1055C2312yes—
71C4×D52—22no—
72C4×D52—22no—
73C13×#107—24no—
74C13×#107—24no—
75C4×C8×C13—22no—
76#88071—21no—
77#88071—22no—
78#88071—22no—
79#88071—22no—
80#88071—22no—
81#88071D412yes—
82#88061—22no—
83#88061Q814yescomplemented
84#88054—24no—
85#88049—24no—
86#88048—24no—
87C4⋊#1055—22no—
88#25450—131nomaximal, Sylow
89C23×D13—21no—
90C2×Q8×C13—24no—
91C2×Q8×C13—42no—
92C2×Q8×C13—81no—
93C2×Q8×C13—81no—
94C2×Q8×C13—81no—
95C2×Q8×C13—81no—
96C22×C4×C13—22no—
97C22×C4×C13—22no—
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2411yescharacteristic
101C22×Dic13—21no—
102C22×Dic13—21no—
103C22×Dic13—21no—
104C22×Dic13C2×D412yes—
105C22×Dic13C2×D412yes—
106C2×D52—21no—
107C2×D52—21no—
108C2×D52—21no—
109C2×D52—21no—
110C2×D52—21no—
111C2×D52C2×Q812yes—
112C2×C4×D13—42no—
113C2×C4×D13—42no—
114C2×C4×D13—42no—
115C2×C8×C13—21no—
116C2×C8×C13—21no—
117C2×C8×C13—21no—
118C2×C8×C13—21no—
119C2×C8×C13C2×Q812yes—
120C2×C8×C13#4112yes—
121C13×C4⋊C4—24no—
122C13×C4⋊C4—22no—
123C13×C4⋊C4—22no—
124C13×C4⋊C4—22no—
125C13×C4⋊C4—42no—
126C13×C4⋊C4C2×D414yes—
127C42×C13C2×D412yes—
128C42×C13#4112yes—
129#6103—42no—
130#6103—82no—
131#6103—82no—
132C4⋊Dic13—22no—
133C4⋊Dic13—22no—
134C4⋊Dic13—21no—
135C4⋊Dic13—21no—
136C4⋊Dic13—21no—
137C4⋊Dic13—21no—
138C4⋊Dic13—21no—
139C4⋊Dic13—82no—
140C4⋊Dic13C2×Q812yes—
141C4×Dic13—22no—
142C4×Dic13—22no—
143C4×Dic13—42no—
144C4×Dic13—82no—
145C2×#1055—22no—
146C2×#1055—22no—
147C2×#1055—22no—
148C2×#500D1311yescharacteristic, complemented
149C2×#476—131no—
150#2563—131no—
151#2369—131no—
152#2085—132no—
153#2067—132no—
154#1987—131no—
155#1949—132no—
156#1939—131no—
157#1925—132no—
158C4×#102—131no—
159C23×C13C22×D411yescharacteristic
160C22×D13—22no—
161C22×D13—41no—
162C22×D13—41no—
163C22×D13—41no—
164C22×D13—41no—
165C22×D13—41no—
166C22×D13—41no—
167Q8×C13—84no—
168Q8×C13—84no—
169C2×C4×C13—21no—
170C2×C4×C13—21no—
171C2×C4×C13—24no—
172C2×C4×C13—42no—
173C2×C4×C13—42no—
174C2×C4×C13—42no—
175C2×C4×C13—42no—
176C2×C4×C13—42no—
177C2×C4×C13#12112yes—
178C2×C4×C13#12112yes—
179C2×C4×C13#13512yes—
180C2×C4×C13#13712yes—
181C2×C4×C13C22×D411yescharacteristic
182C2×C4×C13C22×Q811yescharacteristic
183C2×C4×C13C2×#4111yescharacteristic
184C2×C4×C13C2×#4111yescharacteristic
185C2×C4×C132−1+411yescharacteristic
186C2×C4×C132−1+411yescharacteristic
187C2×Dic13—22no—
188C2×Dic13—22no—
189C2×Dic13—22no—
190C2×Dic13—22no—
191C2×Dic13—22no—
192C2×Dic13—22no—
193C2×Dic13—22no—
194C2×Dic13—41no—
195C2×Dic13—41no—
196C2×Dic13—41no—
197C2×Dic13—41no—
198C2×Dic13—41no—
199C2×Dic13—41no—
200C2×Dic13—41no—
201C2×Dic13—41no—
202D52—22no—
203D52—22no—
204D52—41no—
205D52—41no—
206C4×D13—84no—
207C8×C13—22no—
208C8×C13—22no—
209#1055—42no—
210C2×C4⋊Q8C2×D1311yescharacteristic
211C2×C4⋊Q8C2×D1311yescharacteristic
212C2×C4×D4—131no—
213#500—24no—
214#476—264no—
215C2×#107C2×D1312yes—
216C2×#107C2×D1312yes—
217C2×#106—132no—
218C2×C4⋊C8—132no—
219C2×C4⋊C8—131no—
220C2×#102—131no—
221C2×#102—131no—
222C2×#102—132no—
223C2×C4×C8C2×D1311yescharacteristic
224#393—262no—
225#391—262no—
226#390—132no—
227#389—132no—
228#389—261no—
229#382—132no—
230#380—261no—
231#380—261no—
232C4×C4⋊C4—131no—
233C4×C4⋊C4—132no—
234C4×C4⋊C4—131no—
235C4×C4⋊C4—261no—
236#340—131no—
237#340—131no—
238#340—132no—
239#340—132no—
240#336—132no—
241C22×C13C2×#12111yescharacteristic
242C22×C13#54711yescharacteristic
243C22×C13D4×Q811yescharacteristic
244C22×C13C2×#13511yescharacteristic
245C22×C13C2×#13711yescharacteristic
246C22×C13#57611yescharacteristic
247C22×C13#57611yescharacteristic
248C2×D13—42no—
249C2×D13—42no—
250C2×D13—42no—
251C2×D13—81no—
252C2×D13—81no—
253C2×D13—81no—
254C2×D13—81no—
255C4×C13—22no—
256C4×C13—44no—
257C4×C13—82no—
258C4×C13#46414yes—
259C4×C13#53311yescharacteristic
260C4×C13#54111yescharacteristic
261C4×C13#54811yescharacteristic
262C4×C13D4×Q811yescharacteristic
263Dic13—42no—
264Dic13—42no—
265Dic13—42no—
266Dic13—81no—
267Dic13—81no—
268C22×Q8—21no—
269C22×Q8—21no—
270C22×D4—131no—
271C23×C4—261no—
272C22×C8—132no—
273C22×C8C22×D1311yescharacteristic
274C22×C8C22×D1311yescharacteristic
275C4⋊Q8—22no—
276C4⋊Q8—22no—
277C4⋊Q8—22no—
278C4⋊Q8C22⋊D1314yes—
279C4×D4—262no—
280C4×D4—262no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—131no—
284C2×C4⋊C4—131no—
285C2×C4⋊C4—131no—
286C2×C4⋊C4—131no—
287C2×C4⋊C4—131no—
288C2×C4⋊C4—262no—
289C2×C4⋊C4C22×D1312yes—
290C2×C4⋊C4C22×D1312yes—
291C2×C22⋊C4—261no—
292C2×C22⋊C4—262no—
293C2×C22⋊C4—262no—
294C2×C42—132no—
295C2×C42—261no—
296C2×C42—262no—
297C2×C42C22×D1311yescharacteristic
298#107—24no—
299#107—24no—
300#106—264no—
301C4⋊C8—264no—
302C4⋊C8—262no—
303#102—134no—
304#102—262no—
305#102—264no—
306C4×C8—22no—
307#95—132no—
308#95—262no—
309#95—262no—
310#95—262no—
311#95—262no—
312#95—261no—
313C2×C13#242911yescharacteristic
314C2×C13C2×#46411yescharacteristic
315C2×C13#304111yescharacteristic
316C2×C13#334111yescharacteristic
317C2×C13#335711yescharacteristic
318C2×C13#338011yescharacteristic
319C2×C13#338511yescharacteristic
320D13—82no—
321C24—261no—
322C2×Q8—24no—
323C2×Q8—42no—
324C2×Q8—81no—
325C2×Q8—81no—
326C2×Q8—81no—
327C2×Q8—81no—
328C2×D4—132no—
329C2×D4—261no—
330C2×D4—261no—
331C2×D4—261no—
332C2×D4—261no—
333C2×D4—261no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—132no—
337C22×C4—132no—
338C22×C4—261no—
339C22×C4—261no—
340C22×C4—261no—
341C22×C4—522no—
342C22×C4—522no—
343C22×C4—522no—
344C22×C4D4×D1311yescharacteristic
345C22×C4D4×D1311yescharacteristic
346C22×C4C23×D1311yescharacteristic
347C2×C8—21no—
348C2×C8—21no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8—262no—
352C2×C8—262no—
353C2×C8—262no—
354C2×C8Q8×D1312yes—
355C2×C8#613112yes—
356C4⋊C4—24no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4—22no—
360C4⋊C4—42no—
361C4⋊C4—132no—
362C4⋊C4—262no—
363C4⋊C4—262no—
364C4⋊C4—261no—
365C4⋊C4—261no—
366C4⋊C4—261no—
367C4⋊C4—261no—
368C4⋊C4—261no—
369C4⋊C4—1042no—
370C4⋊C4C2×C22⋊D1314yes—
371C22⋊C4—522no—
372C22⋊C4—1042no—
373C22⋊C4—1042no—
374C42—262no—
375C42—262no—
376C42—522no—
377C42—1042no—
378C42#612912yes—
379C42C2×C22⋊D1312yes—
380C13#2545011yescharacteristic, complemented, Sylow
381C23—262no—
382C23—521no—
383C23—521no—
384C23—521no—
385C23—521no—
386C23—521no—
387C23—521no—
388C23C2×D4×D1311yescharacteristic
389Q8—84no—
390Q8—84no—
391D4—262no—
392D4—262no—
393D4—521no—
394D4—521no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—24no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—262no—
404C2×C4—262no—
405C2×C4—262no—
406C2×C4—262no—
407C2×C4—262no—
408C2×C4—262no—
409C2×C4—262no—
410C2×C4—521no—
411C2×C4—521no—
412C2×C4—521no—
413C2×C4—521no—
414C2×C4—521no—
415C2×C4—521no—
416C2×C4—521no—
417C2×C4—521no—
418C2×C4—1044no—
419C2×C4#8817212yes—
420C2×C4#8817312yes—
421C2×C4#8819312yes—
422C2×C4#8819312yes—
423C2×C4C2×#612911yescharacteristic
424C2×C4C2×Q8×D1311yescharacteristic
425C2×C4C2×#613111yescharacteristic
426C2×C4#8825411yescharacteristic
427C2×C4#8825411yescharacteristic
428C2×C4C22×C22⋊D1311yescharacteristic
429C8—22no—
430C8—22no—
431C8—522no—
432C22—522no—
433C22—522no—
434C22—522no—
435C22—1041no—
436C22—1041no—
437C22—1041no—
438C22—1041no—
439C22#1171943111yescharacteristic
440C22#1171943211yescharacteristic
441C22#1171946211yescharacteristic
442C22#1171946211yescharacteristic
443C22C2×#8817211yescharacteristic
444C22C2×#8817311yescharacteristic
445C22C2×#8819311yescharacteristic
446C4—22no—
447C4—44no—
448C4—82no—
449C4—522no—
450C4—522no—
451C4—522no—
452C4—1041no—
453C4—1041no—
454C4#1171884614yes—
455C4#1171943311yescharacteristic
456C4#1171943611yescharacteristic
457C4Q8×C22⋊D1311yescharacteristic
458C4#1171952211yescharacteristic
459C2—1042no—
460C2#1311843811yescharacteristic
461C2C2×#1171884611yescharacteristic
462C2#1312433611yescharacteristic
463C2#1312725811yescharacteristic
464C2#1312746111yescharacteristic
465C2#1312770511yescharacteristic
466C2#1312775111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#500C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenterC2×#500D13
hypocenterC13#25450
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
3. #13117926C2semidirect
4. #13116320C2semidirect
6. #13115785C2semidirect
7. #13115601C2semidirect
8. #13115554C2semidirect
11. C2×C13×#500C2semidirect
83. #88061Q8semidirect
148. C2×#500D13semidirect
380. C13#25450semidirect

Maximal subgroups

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

subgroupindex
C2×#117187452
#131200102
#131179262
#131163202
#131162192
#131157852
#131156012
#131155542
#131154552
C4×#880612
C2×C13×#5002
#2545013