Finite Group Databasebeta

← #15892907

Subgroups — #15892907

Order 3328.

880 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88184C211yesmaximal, characteristic
2#13116393C211yesmaximal, characteristic, complemented
3#13116365C211yesmaximal, characteristic, complemented
4#13116308C211yesmaximal, characteristic, complemented
5#13116262C212yesmaximal, complemented
6#13116240C211yesmaximal, characteristic, complemented
7#13116018C212yesmaximal
8C4×#88047C212yesmaximal, complemented
9C4×#88049C212yesmaximal, complemented
10C4×C22⋊#1055C211yesmaximal, characteristic, complemented
11C13×#2285C211yesmaximal, characteristic, complemented
12C2×C13×#117—21no—
13C22×C42×C13C2211yescharacteristic
14C2×#88184C2211yescharacteristic
15C2×C4×C22⋊D13—21no—
16C2×C4×D52C2211yescharacteristic
17C13×#384C2211yescharacteristic
18C13×#384C2211yescharacteristic
19C13×#382—21no—
20C13×#380—21no—
21C13×#380C2212yes—
22C4×C13×C4⋊C4—21no—
23C4×C13×C4⋊C4C2212yes—
24#11718874—21no—
25#11718873C2211yescharacteristic
26C2×C22⋊#1055C2212yes—
27C2×#88049C2212yes—
28C2×#88049C2212yes—
29C2×#88047C2212yes—
30C2×#88047C2212yes—
31#11718601—21no—
32#11718600C2211yescharacteristic
33C4×#6103—21no—
34C4×C4⋊Dic13C2211yescharacteristic
35#11718589C2211yescharacteristic
36C2×C4×#1055C2212yes—
37#11718121C2212yes—
38#11718121C2212yes—
39#11718121C2212yes—
40#11718121C2212yes—
41#11718116C2211yescharacteristic
42#11718116C2211yescharacteristic
43C23×C4×C13D411yescharacteristic
44C23×C4×C13D411yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C22×C22⋊D13—21no—
47C22×D52C2311yescharacteristic
48C22×C4×D13—21no—
49C13×#117—44no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4C2312yes—
55C2×C13×C4⋊C4C2312yes—
56C2×C13×C22⋊C4—22no—
57C2×C42×C13—24no—
58C2×C42×C13—22no—
59C2×C42×C13D411yescharacteristic
60C2×C42×C13D411yescharacteristic
61C2×C42×C13C2311yescharacteristic
62C2×C42×C13C2311yescharacteristic
63C2×C22⋊Dic13—21no—
64#88184—22no—
65#88184—22no—
66C4×C22⋊D13—44no—
67C2×#6103—21no—
68C2×#6103—21no—
69C2×#6103—21no—
70C2×#6103—21no—
71C2×C4⋊Dic13C2311yescharacteristic
72C2×C4⋊Dic13C2311yescharacteristic
73C2×C4⋊Dic13C2311yescharacteristic
74C2×#6101—21no—
75C2×C4×Dic13—21no—
76C22×#1055C2312yes—
77C22×#1055C2312yes—
78C4×D52—24no—
79C13×#95—22no—
80C13×#95—22no—
81#88071—21no—
82#88071—21no—
83#88071—21no—
84C22⋊#1055—24no—
85#88049—24no—
86#88049—24no—
87#88047—24no—
88#88047—24no—
89C4×#1055—24no—
90#23754—131nomaximal, Sylow
91C24×C13C2×D411yescharacteristic
92C23×D13—21no—
93C22×C4×C13—22no—
94C22×C4×C13—22no—
95C22×C4×C13—22no—
96C22×C4×C13—22no—
97C22×C4×C13—22no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—22no—
101C22×C4×C13—22no—
102C22×C4×C13—22no—
103C22×C4×C13—41no—
104C22×C4×C13D814yes—
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2×D411yescharacteristic
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13C2×D411yescharacteristic
109C22×C4×C13C2×D411yescharacteristic
110C22×C4×C13C2411yescharacteristic
111C2×C22⋊D13—24no—
112C2×C22⋊D13—42no—
113C2×C22⋊D13—42no—
114C22×Dic13—21no—
115C22×Dic13—21no—
116C22×Dic13—21no—
117C2×D52—22no—
118C2×D52—22no—
119C2×D52—21no—
120C2×D52#4112yes—
121C2×C4×D13—42no—
122C2×C4×D13—42no—
123C2×C4×D13—42no—
124C13×C4⋊C4—22no—
125C13×C4⋊C4—22no—
126C13×C4⋊C4—22no—
127C13×C4⋊C4—22no—
128C13×C4⋊C4—42no—
129C13×C4⋊C4—42no—
130C13×C4⋊C4—42no—
131C13×C4⋊C4—42no—
132C13×C22⋊C4—44no—
133C42×C13—22no—
134C42×C13—22no—
135C42×C13—22no—
136C42×C13—44no—
137C42×C13#4114yes—
138C22⋊Dic13—42no—
139#6103—24no—
140#6103—42no—
141#6103—42no—
142#6103—42no—
143C4⋊Dic13—21no—
144C4⋊Dic13—22no—
145C4⋊Dic13—22no—
146C4⋊Dic13#4112yes—
147#6101—42no—
148C4×Dic13—42no—
149C2×#1055—22no—
150C2×#1055—22no—
151C2×#1055—22no—
152C2×#1055—22no—
153C2×#1055—22no—
154C2×#1055#4114yes—
155C4×#121—131no—
156#2285D1311yescharacteristic, complemented
157#2099—131no—
158#2093—131no—
159#2083—131no—
160#2075—132no—
161#2071—131no—
162#2033—132no—
163C4×#107—132no—
164C4×#102—132no—
165C4×C22⋊C8—131no—
166C23×C13—21no—
167C23×C13—21no—
168C23×C13—21no—
169C23×C13—21no—
170C23×C13—21no—
171C23×C13—21no—
172C23×C13C2×D812yes—
173C23×C13C22×D411yescharacteristic
174C22×D13—22no—
175C22×D13—41no—
176C22×D13—41no—
177C22×D13—41no—
178C22×D13—41no—
179C22×D13—41no—
180C22×D13—41no—
181C2×C4×C13—21no—
182C2×C4×C13—21no—
183C2×C4×C13—21no—
184C2×C4×C13—21no—
185C2×C4×C13—21no—
186C2×C4×C13—21no—
187C2×C4×C13—28no—
188C2×C4×C13—21no—
189C2×C4×C13—21no—
190C2×C4×C13—21no—
191C2×C4×C13—44no—
192C2×C4×C13—42no—
193C2×C4×C13—42no—
194C2×C4×C13—42no—
195C2×C4×C13—42no—
196C2×C4×C13—42no—
197C2×C4×C13—42no—
198C2×C4×C13—42no—
199C2×C4×C13—42no—
200C2×C4×C13#12312yes—
201C2×C4×C13#12312yes—
202C2×C4×C13C2×D812yes—
203C2×C4×C13C2×D812yes—
204C2×C4×C13#13512yes—
205C2×C4×C13#13712yes—
206C2×C4×C13C2×#4112yes—
207C2×C4×C13C2×#4111yescharacteristic
208C2×C4×C13C2×#4111yescharacteristic
209C2×C4×C13C2×#4112yes—
210C22⋊D13—48no—
211C2×Dic13—22no—
212C2×Dic13—41no—
213C2×Dic13—41no—
214C2×Dic13—41no—
215C2×Dic13—41no—
216C2×Dic13—41no—
217C2×Dic13—41no—
218C2×Dic13—41no—
219C2×Dic13—41no—
220D52—24no—
221D52—42no—
222C4×D13—84no—
223#1055—24no—
224#1055—42no—
225C2×#121—131no—
226C2×C4×D4—131no—
227C2×C4×D4—261no—
228C2×#117—21no—
229C22×C42C2×D1311yescharacteristic
230C2×#107—132no—
231C2×#107—132no—
232C2×#102—132no—
233C2×#102—132no—
234C2×C22⋊C8—132no—
235C2×C4×C8—132no—
236#390—131no—
237#389—131no—
238#388—261no—
239#386—261no—
240#384C2×D1311yescharacteristic
241#384C2×D1311yescharacteristic
242#382—21no—
243#380—21no—
244#380—131no—
245#380C2×D1312yes—
246C4×C4⋊C4—21no—
247C4×C4⋊C4—131no—
248C4×C4⋊C4C2×D1312yes—
249C4×C22⋊C4—261no—
250#340—132no—
251#340—132no—
252#340—132no—
253#340—132no—
254#336—131no—
255#336—131no—
256C22×C13—22no—
257C22×C13—22no—
258C22×C13—22no—
259C22×C13—41no—
260C22×C13—41no—
261C22×C13—41no—
262C22×C13—41no—
263C22×C13C2×#12311yescharacteristic
264C22×C13#52511yescharacteristic
265C22×C13#53211yescharacteristic
266C22×C13C22×D811yescharacteristic
267C22×C13C2×#13511yescharacteristic
268C22×C13C2×#13711yescharacteristic
269C22×C13#57511yescharacteristic
270C2×D13—42no—
271C2×D13—42no—
272C2×D13—42no—
273C2×D13—81no—
274C2×D13—81no—
275C2×D13—81no—
276C2×D13—81no—
277C4×C13—22no—
278C4×C13—22no—
279C4×C13—22no—
280C4×C13—41no—
281C4×C13—82no—
282C4×C13—82no—
283C4×C13#48014yes—
284C4×C13#52912yes—
285C4×C13#52912yes—
286Dic13—42no—
287Dic13—81no—
288Dic13—81no—
289C22×D4—131no—
290C22×D4—261no—
291C23×C4—261no—
292C23×C4C22⋊D1311yescharacteristic
293C23×C4C22⋊D1311yescharacteristic
294C23×C4C22×D1311yescharacteristic
295C22×C8—132no—
296C22×C8—132no—
297#121—262no—
298#121—262no—
299C4×D4—264no—
300C4×D4—524no—
301#117—44no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—131no—
307C2×C4⋊C4—131no—
308C2×C4⋊C4—131no—
309C2×C4⋊C4—261no—
310C2×C4⋊C4C22×D1312yes—
311C2×C4⋊C4C22×D1312yes—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—261no—
314C2×C22⋊C4—261no—
315C2×C22⋊C4—261no—
316C2×C22⋊C4—261no—
317C2×C22⋊C4—261no—
318C2×C42—24no—
319C2×C42—22no—
320C2×C42—261no—
321C2×C42C22⋊D1311yescharacteristic
322C2×C42C22⋊D1311yescharacteristic
323C2×C42C22×D1311yescharacteristic
324C2×C42C22×D1311yescharacteristic
325#107—264no—
326#107—264no—
327#102—264no—
328#102—264no—
329C22⋊C8—264no—
330C4×C8—264no—
331#95—22no—
332#95—22no—
333#95—261no—
334#95—261no—
335#95—261no—
336C2×C13—42no—
337C2×C13#239511yescharacteristic
338C2×C13C2×#48011yescharacteristic
339C2×C13#309111yescharacteristic
340C2×C13#310011yescharacteristic
341C2×C13#310711yescharacteristic
342C2×C13#316911yescharacteristic
343C2×C13#317211yescharacteristic
344D13—82no—
345C24—261no—
346C24C2×C22⋊D1311yescharacteristic
347C2×D4—132no—
348C2×D4—264no—
349C2×D4—262no—
350C2×D4—262no—
351C2×D4—261no—
352C2×D4—522no—
353C2×D4—522no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—41no—
365C22×C4—261no—
366C22×C4—261no—
367C22×C4—261no—
368C22×C4—522no—
369C22×C4—522no—
370C22×C4—522no—
371C22×C4#610414yes—
372C22×C4C2×C22⋊D1311yescharacteristic
373C22×C4C2×C22⋊D1311yescharacteristic
374C22×C4C2×C22⋊D1311yescharacteristic
375C22×C4C2×C22⋊D1311yescharacteristic
376C22×C4C2×C22⋊D1311yescharacteristic
377C22×C4C23×D1311yescharacteristic
378C2×C8—134no—
379C2×C8—262no—
380C2×C8—262no—
381C2×C8—262no—
382C2×C8—262no—
383C2×C8—262no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—42no—
389C4⋊C4—42no—
390C4⋊C4—42no—
391C4⋊C4—42no—
392C4⋊C4—132no—
393C4⋊C4—261no—
394C4⋊C4—262no—
395C4⋊C4—262no—
396C4⋊C4—522no—
397C22⋊C4—44no—
398C22⋊C4—264no—
399C22⋊C4—522no—
400C22⋊C4—522no—
401C22⋊C4—522no—
402C22⋊C4—522no—
403C42—22no—
404C42—22no—
405C42—22no—
406C42—44no—
407C42—522no—
408C42#612714yes—
409C13#2375411yescharacteristic, complemented, Sylow
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—262no—
417C23—521no—
418C23—521no—
419C23—521no—
420C23—521no—
421C23—521no—
422C23—521no—
423C23C2×#610412yes—
424C23C22×C22⋊D1311yescharacteristic
425D4—264no—
426D4—528no—
427D4—522no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—28no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—44no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—262no—
448C2×C4—521no—
449C2×C4—521no—
450C2×C4—521no—
451C2×C4—521no—
452C2×C4—521no—
453C2×C4—521no—
454C2×C4—521no—
455C2×C4—521no—
456C2×C4—1044no—
457C2×C4#8818312yes—
458C2×C4#8818312yes—
459C2×C4C2×#610412yes—
460C2×C4C2×#610412yes—
461C2×C4#8819612yes—
462C2×C4#8820412yes—
463C2×C4C2×#612712yes—
464C2×C4#41×D1311yescharacteristic
465C2×C4#41×D1311yescharacteristic
466C2×C4#41×D1312yes—
467C8—264no—
468C8—522no—
469C22—22no—
470C22—22no—
471C22—22no—
472C22—41no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—522no—
477C22—522no—
478C22—522no—
479C22—1041no—
480C22—1041no—
481C22—1041no—
482C22—1041no—
483C22C2×#8818311yescharacteristic
484C22C22×#610411yescharacteristic
485C22C2×#8819611yescharacteristic
486C22C2×#8820411yescharacteristic
487C22#1171952711yescharacteristic
488C22#1171953311yescharacteristic
489C22#1171953711yescharacteristic
490C4—22no—
491C4—22no—
492C4—22no—
493C4—41no—
494C4—82no—
495C4—82no—
496C4—522no—
497C4—1041no—
498C4—1041no—
499C4#1171862814yes—
500C4#1171923312yes—
501C4#1171923312yes—
502C2—42no—
503C2—1042no—
504C2#1311809311yescharacteristic
505C2C2×#1171862811yescharacteristic
506C2#1312474911yescharacteristic
507C2#1312483211yescharacteristic
508C2#1312490111yescharacteristic
509C2#1312541111yescharacteristic
510C2#1312543611yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2285C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenter#2285D13
hypocenterC13#23754
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ #2285

Complements

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

NH ≅ G/Ntype
2. #13116393C2semidirect
3. #13116365C2semidirect
4. #13116308C2semidirect
5. #13116262C2semidirect
6. #13116240C2semidirect
8. C4×#88047C2semidirect
9. C4×#88049C2semidirect
10. C4×C22⋊#1055C2semidirect
11. C13×#2285C2semidirect
156. #2285D13semidirect
409. C13#23754semidirect

Maximal subgroups

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

subgroupindex
C4×#881842
#131163932
#131163652
#131163082
#131162622
#131162402
#131160182
C4×#880472
C4×#880492
C4×C22⋊#10552
C13×#22852
#2375413