Finite Group Databasebeta

← #15865611

Subgroups — #15865611

Order 3328.

1122 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718794C211yesmaximal, characteristic
2C2×#11718663C211yesmaximal, characteristic
3C2×#11718783C211yesmaximal, characteristic, complemented
4#13117452C211yesmaximal, characteristic, complemented
5#13117429C211yesmaximal, characteristic
6#13115531C212yesmaximal, complemented
7#13115524C212yesmaximal, complemented
8#13115517C212yesmaximal, complemented
9#13115510C212yesmaximal, complemented
10C2×#11718121C211yesmaximal, characteristic, complemented
11C13×#1736C211yesmaximal, characteristic, complemented
12C22×#6127C2211yescharacteristic
13C22×C13×M16C2211yescharacteristic
14C2×C13×#117C2211yescharacteristic
15C22×C13×C4⋊C4C2211yescharacteristic
16C2×#88180C2211yescharacteristic
17C22×C4⋊Dic13C2211yescharacteristic
18C23×#1055C2211yescharacteristic
19#11718874—22no—
20#11718794C418yescomplemented
21#11718783—24no—
22C2×#88061C2212yes—
23C2×#88056C2212yes—
24C2×#88055C2212yes—
25C2×C8×Dic13C2212yes—
26#11718663—24no—
27#11718649C2212yes—
28#11718648—21no—
29#11718648—21no—
30#11718635C2212yes—
31#11718634C2212yes—
32#11718634C2212yes—
33C2×#88050C2211yescharacteristic
34C2×#88050C2211yescharacteristic
35C2×#88049C2211yescharacteristic
36C2×#88049C2211yescharacteristic
37#11718603—22no—
38#11718589—21no—
39#11718589—21no—
40C13×#340C2212yes—
41C13×#340C2212yes—
42#11718121C2212yes—
43#11718121C2212yes—
44C23×C4×C13—21no—
45C23×C4×C13C2311yescharacteristic
46C22×C22⋊D13—21no—
47C23×Dic13—21no—
48C2×#6127—22no—
49C2×#6127—22no—
50C2×#6127—22no—
51C2×#6127—22no—
52C2×#6127—22no—
53C2×#6127C2×C414yes—
54C22×D52C2311yescharacteristic
55C22×C4×D13—21no—
56C22×Dic26C2311yescharacteristic
57C2×C13×M16—22no—
58C2×C13×M16—22no—
59C2×C13×M16C2×C414yes—
60C22×C8×C13C2312yes—
61C13×#117—22no—
62C13×#117—22no—
63C2×C13×C4⋊C4—22no—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4C2312yes—
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C22⋊C4—21no—
70C2×C42×C13—21no—
71C2×C22⋊Dic13D412yes—
72C2×#6103—22no—
73C2×#6103—22no—
74#88180—22no—
75#88180—22no—
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13—22no—
78C2×C4⋊Dic13C2×C414yes—
79C2×C4⋊Dic13D411yescharacteristic
80C2×C4⋊Dic13D411yescharacteristic
81C2×C4⋊Dic13C2312yes—
82C2×#6101—22no—
83C2×#6101—22no—
84C2×C4×Dic13C2312yes—
85C22×#1055—22no—
86C22×#1055—22no—
87C22×#1055D414yes—
88C22×#1055C2311yescharacteristic
89C22×#1055C2311yescharacteristic
90#88071—22no—
91#88071—22no—
92#88071—22no—
93#88071—22no—
94#88061C2×C418yescomplemented
95#88056C2×C418yescomplemented
96#88055—24no—
97C8×Dic13—24no—
98#88050—22no—
99#88050—22no—
100#88049—22no—
101#88049—22no—
102#21092—131nomaximal, Sylow
103C24×C13C2×D411yescharacteristic
104C23×D13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—21no—
107C22×C4×C13—22no—
108C22×C4×C13—42no—
109C22×C4×C13—81no—
110C22×C4×C13—81no—
111C22×C4×C13C22×C412yes—
112C22×C4×C13C2×D411yescharacteristic
113C22×C4×C13C2×D412yes—
114C22×C4×C13#4112yes—
115C22×C4×C13#4112yes—
116C22×C4×C13#4112yes—
117C22×C4×C13#4112yes—
118C22×C4×C13C2411yescharacteristic
119C2×C22⋊D13—24no—
120C2×C22⋊D13—42no—
121C2×C22⋊D13—42no—
122C22×Dic13—21no—
123C22×Dic13—22no—
124C22×Dic13—24no—
125C22×Dic13—81no—
126C22×Dic13—81no—
127C22×Dic13C2×D412yes—
128C22×Dic13C2×D412yes—
129#6127—28no—
130#6127—28no—
131#6127—44no—
132#6127—44no—
133C2×D52—21no—
134C2×D52—21no—
135C2×D52—21no—
136C2×D52—21no—
137C2×D52—21no—
138C2×D52C22×C412yes—
139C2×C4×D13—24no—
140C2×C4×D13—42no—
141C2×C4×D13—42no—
142C2×Dic26—21no—
143C2×Dic26—21no—
144C2×Dic26—21no—
145C2×Dic26—21no—
146C2×Dic26—21no—
147C2×Dic26C22×C412yes—
148C13×M16—28no—
149C2×C8×C13—22no—
150C2×C8×C13—22no—
151C2×C8×C13C22×C414yes—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—22no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—42no—
159C13×C22⋊C4—42no—
160C42×C13—42no—
161C22⋊Dic13—24no—
162#6103—82no—
163#6103—82no—
164C4⋊Dic13—24no—
165C4⋊Dic13—22no—
166C4⋊Dic13—22no—
167C4⋊Dic13—22no—
168C4⋊Dic13C22×C414yes—
169#6101—82no—
170#6101—82no—
171C4×Dic13—22no—
172C4×Dic13—22no—
173C2×#1055—28no—
174C2×#1055—21no—
175C2×#1055—21no—
176C2×#1055—21no—
177C2×#1055—21no—
178C2×#1055C2×D412yes—
179C2×#1055C2×D412yes—
180C2×#417—131no—
181C2×#416—131no—
182C2×#405—131no—
183#2316—131no—
184#2311—131no—
185#1936—132no—
186#1935—132no—
187#1934—132no—
188#1933—132no—
189#1736D1311yescharacteristic, complemented
190C2×#340—131no—
191C23×C13—21no—
192C23×C13—21no—
193C23×C13—21no—
194C23×C13—21no—
195C23×C13C4×D412yes—
196C23×C13#12112yes—
197C23×C13#12412yes—
198C23×C13C22×D411yescharacteristic
199C22×D13—22no—
200C22×D13—41no—
201C22×D13—41no—
202C22×D13—41no—
203C22×D13—41no—
204C22×D13—41no—
205C22×D13—41no—
206C2×C4×C13—41no—
207C2×C4×C13—41no—
208C2×C4×C13—42no—
209C2×C4×C13—41no—
210C2×C4×C13—42no—
211C2×C4×C13—41no—
212C2×C4×C13—42no—
213C2×C4×C13—41no—
214C2×C4×C13—41no—
215C2×C4×C13—84no—
216C2×C4×C13#11714yes—
217C2×C4×C13C4×D414yes—
218C2×C4×C13C4×D412yes—
219C2×C4×C13#12112yes—
220C2×C4×C13#12314yes—
221C2×C4×C13#12412yes—
222C2×C4×C13#12614yes—
223C2×C4×C13C23×C411yescharacteristic
224C2×C4×C13C22×D411yescharacteristic
225C2×C4×C13C2×#4111yescharacteristic
226C2×C4×C13C2×#4111yescharacteristic
227C2×C4×C13C2×#4111yescharacteristic
228C2×C4×C13C2×#4111yescharacteristic
229C22⋊D13—48no—
230C2×Dic13—24no—
231C2×Dic13—22no—
232C2×Dic13—22no—
233C2×Dic13—22no—
234C2×Dic13—22no—
235C2×Dic13—22no—
236C2×Dic13—22no—
237C2×Dic13—22no—
238C2×Dic13—41no—
239C2×Dic13—41no—
240C2×Dic13—42no—
241C2×Dic13—42no—
242C2×Dic13—84no—
243D52—22no—
244D52—22no—
245D52—41no—
246D52—41no—
247C4×D13—48no—
248Dic26—22no—
249Dic26—22no—
250Dic26—41no—
251Dic26—41no—
252C8×C13—24no—
253#1055—22no—
254#1055—22no—
255C22×#41—131no—
256C22×M16C2×D1311yescharacteristic
257C23×C8—131no—
258C2×#117—131no—
259C2×#117C2×D1311yescharacteristic
260C22×C4⋊C4—131no—
261C22×C4⋊C4C2×D1311yescharacteristic
262#417—138no—
263#416—264no—
264C2×#103—132no—
265C2×#103—131no—
266C2×#103—131no—
267C2×#102—132no—
268C2×#102—131no—
269C2×#102—131no—
270#405—264no—
271C2×#97—132no—
272C2×C4×C8—132no—
273#391—132no—
274#390—132no—
275#389—132no—
276#389—132no—
277#389—261no—
278#389—261no—
279#386—262no—
280#380—262no—
281#380—261no—
282#380—261no—
283#340—132no—
284#340—132no—
285#340C2×D1312yes—
286#340C2×D1312yes—
287C22×C13—22no—
288C22×C13—22no—
289C22×C13—22no—
290C22×C13—22no—
291C22×C13—22no—
292C22×C13—22no—
293C22×C13#38814yes—
294C22×C13C2×C4×D411yescharacteristic
295C22×C13C2×#12111yescharacteristic
296C22×C13C2×#12411yescharacteristic
297C22×C13#57611yescharacteristic
298C22×C13#57711yescharacteristic
299C22×C13#57711yescharacteristic
300C22×C13#57811yescharacteristic
301C2×D13—42no—
302C2×D13—42no—
303C2×D13—42no—
304C2×D13—81no—
305C2×D13—81no—
306C2×D13—81no—
307C2×D13—81no—
308C4×C13—82no—
309C4×C13—81no—
310C4×C13—81no—
311C4×C13#38814yes—
312C4×C13C2×#11711yescharacteristic
313C4×C13C2×C4×D411yescharacteristic
314C4×C13C2×#12311yescharacteristic
315C4×C13C2×#12611yescharacteristic
316Dic13—44no—
317Dic13—42no—
318Dic13—42no—
319Dic13—42no—
320C2×#41—134no—
321C2×#41—262no—
322C2×#41—262no—
323C2×#41—262no—
324C2×#41—262no—
325C2×#41—262no—
326C22×Q8—131no—
327C22×D4—131no—
328C22×D4—261no—
329C23×C4—21no—
330C23×C4—261no—
331C23×C4—261no—
332C23×C4C22×D1311yescharacteristic
333C2×M16—22no—
334C2×M16—22no—
335C2×M16C4×D1314yes—
336C22×C8—134no—
337C22×C8—131no—
338C22×C8—131no—
339C22×C8—262no—
340C22×C8—262no—
341C22×C8C22×D1312yes—
342#117—22no—
343#117—22no—
344#117—262no—
345#117—262no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—134no—
350C2×C4⋊C4—132no—
351C2×C4⋊C4—131no—
352C2×C4⋊C4—131no—
353C2×C4⋊C4—261no—
354C2×C4⋊C4—262no—
355C2×C4⋊C4—262no—
356C2×C4⋊C4—262no—
357C2×C4⋊C4C22×D1312yes—
358C2×C4⋊C4C22×D1311yescharacteristic
359C2×C4⋊C4C22×D1311yescharacteristic
360C2×C22⋊C4—21no—
361C2×C22⋊C4—132no—
362C2×C22⋊C4—262no—
363C2×C22⋊C4—262no—
364C2×C42—21no—
365C2×C42—132no—
366#103—138no—
367#103—262no—
368#103—262no—
369#102—138no—
370#102—262no—
371#102—262no—
372#97—264no—
373C4×C8—264no—
374#95—262no—
375#95—262no—
376#95—262no—
377#95—262no—
378C2×C13—24no—
379C2×C13C2×#38811yescharacteristic
380C2×C13#294611yescharacteristic
381C2×C13#294711yescharacteristic
382C2×C13#306011yescharacteristic
383C2×C13#306111yescharacteristic
384C2×C13#313611yescharacteristic
385C2×C13#313711yescharacteristic
386D13—82no—
387C24—261no—
388C24D4×D1311yescharacteristic
389#41—268no—
390#41—268no—
391#41—524no—
392#41—524no—
393C2×Q8—132no—
394C2×Q8—261no—
395C2×Q8—261no—
396C2×Q8—261no—
397C2×Q8—261no—
398C2×Q8—261no—
399C2×D4—132no—
400C2×D4—264no—
401C2×D4—261no—
402C2×D4—261no—
403C2×D4—261no—
404C2×D4—261no—
405C2×D4—261no—
406C2×D4—522no—
407C2×D4—522no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—42no—
412C22×C4—81no—
413C22×C4—81no—
414C22×C4—132no—
415C22×C4—132no—
416C22×C4—261no—
417C22×C4—262no—
418C22×C4—264no—
419C22×C4—264no—
420C22×C4—522no—
421C22×C4—522no—
422C22×C4—1041no—
423C22×C4—1041no—
424C22×C4C2×C4×D1312yes—
425C22×C4#612712yes—
426C22×C4#612712yes—
427C22×C4D4×D1312yes—
428C22×C4D4×D1311yescharacteristic
429C22×C4#612912yes—
430C22×C4#613112yes—
431C22×C4C23×D1311yescharacteristic
432M16—28no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—132no—
436C2×C8—132no—
437C2×C8—268no—
438C2×C8—261no—
439C2×C8—261no—
440C2×C8—261no—
441C2×C8—261no—
442C2×C8C2×C4×D1314yes—
443C4⋊C4—22no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—42no—
450C4⋊C4—134no—
451C4⋊C4—262no—
452C4⋊C4—262no—
453C4⋊C4—264no—
454C4⋊C4—262no—
455C4⋊C4—1042no—
456C4⋊C4—1042no—
457C22⋊C4—42no—
458C22⋊C4—264no—
459C22⋊C4—1042no—
460C22⋊C4—1042no—
461C42—42no—
462C42—262no—
463C42—262no—
464C13#2109211yescharacteristic, complemented, Sylow
465C23—21no—
466C23—21no—
467C23—21no—
468C23—21no—
469C23—262no—
470C23—521no—
471C23—521no—
472C23—521no—
473C23—521no—
474C23—521no—
475C23—521no—
476C23#8813812yes—
477C23#8813912yes—
478C23#8814712yes—
479C23C2×D4×D1311yescharacteristic
480Q8—262no—
481Q8—262no—
482Q8—521no—
483Q8—521no—
484D4—262no—
485D4—262no—
486D4—528no—
487D4—521no—
488D4—521no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—84no—
499C2×C4—262no—
500C2×C4—262no—
501C2×C4—264no—
502C2×C4—262no—
503C2×C4—262no—
504C2×C4—262no—
505C2×C4—262no—
506C2×C4—262no—
507C2×C4—521no—
508C2×C4—521no—
509C2×C4—522no—
510C2×C4—522no—
511C2×C4—528no—
512C2×C4—1044no—
513C2×C4#8812614yes—
514C2×C4#8813514yes—
515C2×C4#8813812yes—
516C2×C4#8813912yes—
517C2×C4#8814712yes—
518C2×C4#8814814yes—
519C2×C4#8815214yes—
520C2×C4C22×C4×D1311yescharacteristic
521C2×C4C2×#612711yescharacteristic
522C2×C4C2×#612711yescharacteristic
523C2×C4C2×D4×D1311yescharacteristic
524C2×C4C2×#612911yescharacteristic
525C2×C4C2×#613111yescharacteristic
526C8—24no—
527C8—262no—
528C8—262no—
529C22—22no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—22no—
535C22—522no—
536C22—522no—
537C22—522no—
538C22—1041no—
539C22—1041no—
540C22—1041no—
541C22—1041no—
542C22#1171833014yes—
543C22C2×#8813811yescharacteristic
544C22C2×#8813911yescharacteristic
545C22C2×#8814711yescharacteristic
546C22#1171947911yescharacteristic
547C22#1171948011yescharacteristic
548C22#1171948311yescharacteristic
549C22#1171948411yescharacteristic
550C4—82no—
551C4—81no—
552C4—81no—
553C4—522no—
554C4—524no—
555C4—522no—
556C4—522no—
557C4#1171833014yes—
558C4C2×#8812611yescharacteristic
559C4C2×#8813511yescharacteristic
560C4C2×#8814811yescharacteristic
561C4C2×#8815211yescharacteristic
562C2—24no—
563C2—1042no—
564C2C2×#1171833011yescharacteristic
565C2#1312366611yescharacteristic
566C2#1312367711yescharacteristic
567C2#1312449711yescharacteristic
568C2#1312450511yescharacteristic
569C2#1312518611yescharacteristic
570C2#1312519711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1736C2
socleC23×C13C22×D4
prime radicalC22×#6127C22
cosocleC22×C4×C13C24
hypercenter#1736D13
hypocenterC13#21092
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
3. C2×#11718783C2semidirect
4. #13117452C2semidirect
6. #13115531C2semidirect
7. #13115524C2semidirect
8. #13115517C2semidirect
9. #13115510C2semidirect
10. C2×#11718121C2semidirect
11. C13×#1736C2semidirect
20. #11718794C4semidirect
94. #88061C2×C4semidirect
95. #88056C2×C4semidirect
189. #1736D13semidirect
464. C13#21092semidirect

Maximal subgroups

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

subgroupindex
C2×#117187942
C2×#117186632
C2×#117187832
#131174522
#131174292
#131155312
#131155242
#131155172
#131155102
C2×#117181212
C13×#17362
#2109213