Finite Group Databasebeta

← #15907784

Subgroups — #15907784

Order 3328.

842 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119759C211yesmaximal, characteristic
2C4⋊C4×D52C211yesmaximal, characteristic
3#13116270C212yesmaximal, complemented
4#13116034C212yesmaximal, complemented
5#13115629C211yesmaximal, characteristic
6#13115142C212yesmaximal, complemented
7#13114963C211yesmaximal, characteristic, complemented
8#13114921C212yesmaximal, complemented
9#13114842C211yesmaximal, characteristic, complemented
10C4×#88050C211yesmaximal, characteristic, complemented
11C13×#1948C211yesmaximal, characteristic, complemented
12C2×#88151C2212yes—
13C2×C4⋊C4×D13C2212yes—
14C2×C4×D52—21no—
15C2×C4×D52C2211yescharacteristic
16C2×C4×Dic26C2211yescharacteristic
17C2×C13×#106C2212yes—
18C2×C13×C4⋊C8C2211yescharacteristic
19C13×#384C2211yescharacteristic
20C4×C13×C4⋊C4C2211yescharacteristic
21C2×#88060C2212yes—
22C2×#88060C2212yes—
23C2×#88056C2212yes—
24#11718655—22no—
25#11718649—21no—
26#11718648C2212yes—
27#11718648C2212yes—
28#11718646—21no—
29C2×#88050C2211yescharacteristic
30C2×#88050C2211yescharacteristic
31#11718596C2211yescharacteristic
32#11718589—21no—
33C2×C4×#1055C2211yescharacteristic
34#11718329—22no—
35C13×#340C2212yes—
36#11718143C2212yes—
37#11718121C2212yes—
38#11718121C2211yescharacteristic
39#11718121C2211yescharacteristic
40#11718121C2212yes—
41C22×D52D411yescharacteristic
42C22×C4×D13—22no—
43C22×C4×D13C2312yes—
44C22×Dic26C2311yescharacteristic
45C22×C8×C13C2312yes—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4C2311yescharacteristic
49C2×C13×C4⋊C4C2312yes—
50C2×C13×C4⋊C4C2311yescharacteristic
51C2×C42×C13—21no—
52C2×C42×C13C2311yescharacteristic
53C2×#6103—22no—
54C2×#6103—22no—
55C2×#6103—22no—
56C2×#6103D412yes—
57C2×C4⋊Dic13—21no—
58C2×C4⋊Dic13—22no—
59C2×C4⋊Dic13—21no—
60C2×C4⋊Dic13D411yescharacteristic
61C2×C4⋊Dic13C2311yescharacteristic
62C2×C4⋊Dic13C2312yes—
63C2×#6101—21no—
64C2×#6101—22no—
65C2×C4×Dic13—21no—
66C22×#1055C2311yescharacteristic
67C22×#1055C2311yescharacteristic
68#88151—24no—
69#88151—42no—
70C4⋊C4×D13—24no—
71C4⋊C4×D13—42no—
72C4×D52—22no—
73C4×D52—22no—
74C4×D52—44no—
75C4×Dic26—22no—
76C4×Dic26—22no—
77C13×#106—42no—
78C13×C4⋊C8—22no—
79C13×#95—21no—
80#88071—22no—
81#88071—22no—
82#88060—42no—
83#88060—42no—
84#88056—42no—
85#88050—22no—
86#88050—22no—
87C4×#1055—22no—
88#24969—131nomaximal, Sylow
89C23×D13C2×D412yes—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—22no—
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13C2411yescharacteristic
96C22×Dic13—21no—
97C22×Dic13—21no—
98C22×Dic13—22no—
99C22×Dic13C2×D412yes—
100C2×D52—22no—
101C2×D52—22no—
102C2×D52SD1614yes—
103C2×C4×D13—22no—
104C2×C4×D13—22no—
105C2×C4×D13—22no—
106C2×C4×D13—22no—
107C2×C4×D13—22no—
108C2×C4×D13—22no—
109C2×C4×D13—44no—
110C2×C4×D13—44no—
111C2×C4×D13—82no—
112C2×Dic26—21no—
113C2×Dic26—21no—
114C2×Dic26—21no—
115C2×Dic26—21no—
116C2×Dic26—21no—
117C2×Dic26#4112yes—
118C2×C8×C13—22no—
119C2×C8×C13—22no—
120C2×C8×C13—22no—
121C13×C4⋊C4—21no—
122C13×C4⋊C4—22no—
123C13×C4⋊C4—21no—
124C13×C4⋊C4—21no—
125C13×C4⋊C4—22no—
126C13×C4⋊C4—42no—
127C13×C4⋊C4—81no—
128C13×C4⋊C4#4112yes—
129C42×C13—42no—
130C42×C13#4112yes—
131C42×C13#4112yes—
132#6103—24no—
133#6103—44no—
134#6103—44no—
135#6103—82no—
136C4⋊Dic13—22no—
137C4⋊Dic13—21no—
138C4⋊Dic13—21no—
139C4⋊Dic13—22no—
140C4⋊Dic13—22no—
141C4⋊Dic13—44no—
142C4⋊Dic13—42no—
143C4⋊Dic13—81no—
144#6101—44no—
145#6101—42no—
146C4×Dic13—42no—
147C2×#1055—21no—
148C2×#1055—21no—
149C2×#1055—21no—
150C2×#1055—21no—
151C2×#1055—21no—
152C2×#1055—21no—
153#2538—131no—
154D4×C4⋊C4—131no—
155#2077—132no—
156#2035—132no—
157#1954—131no—
158#1948D1311yescharacteristic, complemented
159#1872—132no—
160#1834—131no—
161#1823—132no—
162#1803—131no—
163C4×#103—131no—
164C23×C13C22×D411yescharacteristic
165C22×D13—22no—
166C22×D13—22no—
167C22×D13—22no—
168C22×D13—22no—
169C22×D13—22no—
170C22×D13—22no—
171C22×D13C2×SD1614yes—
172C2×C4×C13—21no—
173C2×C4×C13—21no—
174C2×C4×C13—22no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—42no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—42no—
181C2×C4×C13—42no—
182C2×C4×C13—41no—
183C2×C4×C13#12312yes—
184C2×C4×C13#12312yes—
185C2×C4×C13C2×SD1612yes—
186C2×C4×C13#13712yes—
187C2×C4×C13C2×#4111yescharacteristic
188C2×C4×C13C2×#4111yescharacteristic
189C2×C4×C13C2×#4111yescharacteristic
190C2×C4×C13C2×#4111yescharacteristic
191C2×C4×C13H(5,𝔽2)11yescharacteristic
192C2×C4×C13H(5,𝔽2)11yescharacteristic
193C2×Dic13—22no—
194C2×Dic13—22no—
195C2×Dic13—22no—
196C2×Dic13—22no—
197C2×Dic13—41no—
198C2×Dic13—41no—
199C2×Dic13—41no—
200C2×Dic13—42no—
201C2×Dic13—42no—
202C2×Dic13—42no—
203C2×Dic13—41no—
204C2×Dic13—41no—
205D52—28no—
206C4×D13—42no—
207C4×D13—42no—
208C4×D13—42no—
209C4×D13—42no—
210C4×D13—88no—
211Dic26—22no—
212Dic26—22no—
213Dic26—41no—
214Dic26—41no—
215C8×C13—42no—
216#1055—41no—
217#1055—41no—
218C2×C22⋊Q8—132no—
219C2×C4×Q8—131no—
220C2×C4×D4—131no—
221C2×C4×D4—261no—
222C22×C4⋊C4—132no—
223C2×#106C2×D1312yes—
224C2×C4⋊C8C2×D1311yescharacteristic
225C2×#103—131no—
226C2×#103—131no—
227C2×#103—132no—
228C2×C22⋊C8—132no—
229C2×C22⋊C8—132no—
230C2×C4×C8—131no—
231#396—262no—
232#390—261no—
233#389—261no—
234#389—261no—
235#385—262no—
236#384—131no—
237#384C2×D1311yescharacteristic
238#380—132no—
239#380—132no—
240C4×C4⋊C4C2×D1311yescharacteristic
241#340—132no—
242#340—131no—
243#340—132no—
244#340—131no—
245#340—132no—
246#340C2×D1312yes—
247C22×C13C2×#12311yescharacteristic
248C22×C13#54611yescharacteristic
249C22×C13#54611yescharacteristic
250C22×C13C22×SD1611yescharacteristic
251C22×C13C2×#13711yescharacteristic
252C22×C13#57611yescharacteristic
253C22×C13#57811yescharacteristic
254C2×D13—24no—
255C2×D13—24no—
256C2×D13—24no—
257C2×D13—42no—
258C2×D13—42no—
259C2×D13—42no—
260C2×D13—42no—
261C4×C13—22no—
262C4×C13—42no—
263C4×C13—82no—
264C4×C13—81no—
265C4×C13#48314yes—
266C4×C13#52911yescharacteristic
267C4×C13#54011yescharacteristic
268C4×C13#55311yescharacteristic
269C4×C13#55511yescharacteristic
270Dic13—42no—
271Dic13—42no—
272Dic13—81no—
273Dic13—82no—
274C22×Q8—131no—
275C22×D4—131no—
276C23×C4—132no—
277C23×C4—262no—
278C22×C8—131no—
279C22×C8—131no—
280C22×C8C22×D1312yes—
281C22⋊Q8—264no—
282C22⋊Q8—522no—
283C4×Q8—262no—
284C4×Q8—262no—
285C4×D4—262no—
286C4×D4—262no—
287C4×D4—524no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—131no—
291C2×C4⋊C4—132no—
292C2×C4⋊C4—131no—
293C2×C4⋊C4—264no—
294C2×C4⋊C4—262no—
295C2×C4⋊C4—262no—
296C2×C4⋊C4—261no—
297C2×C4⋊C4—261no—
298C2×C4⋊C4—261no—
299C2×C4⋊C4—522no—
300C2×C4⋊C4C22×D1312yes—
301C2×C4⋊C4C22×D1311yescharacteristic
302C2×C4⋊C4C22×D1311yescharacteristic
303C2×C22⋊C4—132no—
304C2×C22⋊C4—262no—
305C2×C22⋊C4—262no—
306C2×C22⋊C4—262no—
307C2×C42—21no—
308C2×C42—261no—
309C2×C42C22×D1311yescharacteristic
310#106—42no—
311C4⋊C8—22no—
312#103—262no—
313#103—262no—
314#103—522no—
315C22⋊C8—522no—
316C22⋊C8—522no—
317C4×C8—262no—
318#95—21no—
319#95—262no—
320#95—262no—
321C2×C13#242011yescharacteristic
322C2×C13C2×#48311yescharacteristic
323C2×C13#309811yescharacteristic
324C2×C13#329511yescharacteristic
325C2×C13#329811yescharacteristic
326C2×C13#332811yescharacteristic
327C2×C13#333311yescharacteristic
328D13—44no—
329C24—132no—
330C2×Q8—132no—
331C2×Q8—261no—
332C2×Q8—261no—
333C2×Q8—261no—
334C2×Q8—261no—
335C2×Q8—261no—
336C2×D4—134no—
337C2×D4—262no—
338C2×D4—262no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—22no—
342C22×C4—132no—
343C22×C4—261no—
344C22×C4—262no—
345C22×C4—262no—
346C22×C4—262no—
347C22×C4—262no—
348C22×C4—262no—
349C22×C4—262no—
350C22×C4—261no—
351C22×C4—262no—
352C22×C4—524no—
353C22×C4—524no—
354C22×C4—1042no—
355C22×C4D4×D1311yescharacteristic
356C22×C4D4×D1311yescharacteristic
357C22×C4C23×D1311yescharacteristic
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—22no—
361C2×C8—261no—
362C2×C8—261no—
363C2×C8—261no—
364C2×C8—261no—
365C2×C8—261no—
366C2×C8—261no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—22no—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—42no—
373C4⋊C4—81no—
374C4⋊C4—262no—
375C4⋊C4—261no—
376C4⋊C4—262no—
377C4⋊C4—261no—
378C4⋊C4—262no—
379C4⋊C4—524no—
380C4⋊C4—524no—
381C4⋊C4—522no—
382C4⋊C4—522no—
383C4⋊C4—1041no—
384C4⋊C4#613112yes—
385C22⋊C4—264no—
386C22⋊C4—524no—
387C22⋊C4—524no—
388C22⋊C4—1042no—
389C42—42no—
390C42—522no—
391C42#612712yes—
392C42#613112yes—
393C13#2496911yescharacteristic, complemented, Sylow
394C23—134no—
395C23—262no—
396C23—262no—
397C23—262no—
398C23—262no—
399C23—262no—
400C23—262no—
401C23C2×D4×D1311yescharacteristic
402Q8—262no—
403Q8—262no—
404Q8—521no—
405Q8—521no—
406D4—268no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—22no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—262no—
419C2×C4—262no—
420C2×C4—262no—
421C2×C4—262no—
422C2×C4—521no—
423C2×C4—521no—
424C2×C4—522no—
425C2×C4—522no—
426C2×C4—522no—
427C2×C4—522no—
428C2×C4—522no—
429C2×C4—521no—
430C2×C4—521no—
431C2×C4—522no—
432C2×C4—521no—
433C2×C4—522no—
434C2×C4—1048no—
435C2×C4#8814812yes—
436C2×C4#8814812yes—
437C2×C4SD16×D1312yes—
438C2×C4#8816912yes—
439C2×C4C2×#612711yescharacteristic
440C2×C4#8825111yescharacteristic
441C2×C4C2×#613111yescharacteristic
442C2×C4C2×#613111yescharacteristic
443C2×C4#41×D1311yescharacteristic
444C2×C4#8825611yescharacteristic
445C8—42no—
446C8—521no—
447C8—521no—
448C22—264no—
449C22—264no—
450C22—264no—
451C22—522no—
452C22—522no—
453C22—522no—
454C22—522no—
455C22C2×#8814811yescharacteristic
456C22#1171931711yescharacteristic
457C22#1171933511yescharacteristic
458C22C2×SD16×D1311yescharacteristic
459C22C2×#8816911yescharacteristic
460C22#1171947911yescharacteristic
461C22#1171948411yescharacteristic
462C4—22no—
463C4—42no—
464C4—82no—
465C4—81no—
466C4—522no—
467C4—522no—
468C4—1042no—
469C4—1041no—
470C4#1171852314yes—
471C4#1171926711yescharacteristic
472C4#1171928511yescharacteristic
473C4#1171940011yescharacteristic
474C4#1171943911yescharacteristic
475C2—524no—
476C2#1311832911yescharacteristic
477C2C2×#1171852311yescharacteristic
478C2#1312481811yescharacteristic
479C2#1312665711yescharacteristic
480C2#1312670411yescharacteristic
481C2#1312711611yescharacteristic
482C2#1312717711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1948C2
socleC23×C13C22×D4
prime radicalC22×D52D4
hypercenter#1948D13
hypocenterC13#24969
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
3. #13116270C2semidirect
4. #13116034C2semidirect
6. #13115142C2semidirect
7. #13114963C2semidirect
8. #13114921C2semidirect
9. #13114842C2semidirect
10. C4×#88050C2semidirect
11. C13×#1948C2semidirect
158. #1948D13semidirect
393. C13#24969semidirect

Maximal subgroups

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

subgroupindex
#131197592
C4⋊C4×D522
#131162702
#131160342
#131156292
#131151422
#131149632
#131149212
#131148422
C4×#880502
C13×#19482
#2496913