Finite Group Databasebeta

← #16799251

Subgroups — #16799251

Order 3328.

998 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719125C211yesmaximal, characteristic, complemented
2C2×#11719119C211yesmaximal, characteristic, complemented
3#13130960C212yesmaximal
4#13130938C212yesmaximal, complemented
5#13130910C212yesmaximal, complemented
6#13130909C212yesmaximal, complemented
7C4×#88112C211yesmaximal, characteristic, complemented
8C4×C22⋊#1057C211yesmaximal, characteristic, complemented
9C4×C22⋊#1057C211yesmaximal, characteristic, complemented
10C4×#88110C211yesmaximal, characteristic, complemented
11C4×D4×Dic13C211yesmaximal, characteristic
12C2×C4×D4×C13C411yescharacteristic
13C2×D4×Dic13C411yescharacteristic
14C2×D4×Dic13C2211yescharacteristic
15C22×C4×Dic13C2211yescharacteristic
16C22×C4×Dic13C2211yescharacteristic
17C2×C22⋊#1057C2212yes—
18C2×C22⋊#1057C2212yes—
19C2×C22⋊#1057C2212yes—
20C2×C22⋊#1057C2212yes—
21#11719125—24no—
22C2×#88112C2212yes—
23C2×#88112C2212yes—
24C2×#88110C2212yes—
25C2×#88110C2212yes—
26#11719119—24no—
27C2×C4⋊#1057C2212yes—
28C2×C4×#1057C2211yescharacteristic
29C2×C4×#1057C2211yescharacteristic
30C2×C4×#1057C2211yescharacteristic
31C2×C4×#1057C2211yescharacteristic
32C4×C22⋊Dic13C411yescharacteristic
33C4×C22⋊Dic13C411yescharacteristic
34C4⋊C4×Dic13C411yescharacteristic
35C4⋊C4×Dic13C2211yescharacteristic
36C22⋊C4×Dic13C411yescharacteristic
37C22⋊C4×Dic13C411yescharacteristic
38C22⋊C4×Dic13C2211yescharacteristic
39C22⋊C4×Dic13C2211yescharacteristic
40C4×C4⋊Dic13C411yescharacteristic
41C42×Dic13C2211yescharacteristic
42#11718290C2212yes—
43#11718290C2212yes—
44#11718290C2212yes—
45C22×D4×C13C2×C411yescharacteristic
46C23×C4×C13C2×C411yescharacteristic
47C23×C4×C13C2×C411yescharacteristic
48C23×Dic13C2×C411yescharacteristic
49C23×Dic13C2×C411yescharacteristic
50C23×Dic13C2311yescharacteristic
51C23×Dic13C2311yescharacteristic
52C22×#1057C2312yes—
53C22×#1057C2312yes—
54C22×#1057C2312yes—
55C22×#1057C2312yes—
56C4×D4×C13—24no—
57C2×C13×C4⋊C4C2×C411yescharacteristic
58C2×C13×C22⋊C4C2×C411yescharacteristic
59C2×C13×C22⋊C4C2×C411yescharacteristic
60C2×C42×C13C2×C411yescharacteristic
61C2×C22⋊Dic13C2×C411yescharacteristic
62C2×C22⋊Dic13C2×C411yescharacteristic
63C2×C22⋊Dic13C2×C411yescharacteristic
64C2×C22⋊Dic13C2×C411yescharacteristic
65D4×Dic13—24no—
66D4×Dic13—24no—
67C2×C4⋊Dic13C2×C411yescharacteristic
68C2×C4⋊Dic13C2×C411yescharacteristic
69C2×C4×Dic13—22no—
70C2×C4×Dic13—22no—
71C2×C4×Dic13—22no—
72C2×C4×Dic13—22no—
73C2×C4×Dic13C2×C411yescharacteristic
74C2×C4×Dic13C2×C411yescharacteristic
75C2×C4×Dic13C2×C411yescharacteristic
76C2×C4×Dic13C2×C411yescharacteristic
77C2×C4×Dic13C2×C411yescharacteristic
78C2×C4×Dic13C2×C411yescharacteristic
79C2×C4×Dic13C2×C411yescharacteristic
80C2×C4×Dic13C2311yescharacteristic
81C2×C4×Dic13C2311yescharacteristic
82C2×C4×Dic13C2311yescharacteristic
83C2×C4×Dic13C2311yescharacteristic
84C2×C4×Dic13C2311yescharacteristic
85C22⋊#1057—24no—
86C22⋊#1057—24no—
87C22⋊#1057—24no—
88C22⋊#1057—24no—
89#88112—24no—
90#88112—24no—
91#88110—24no—
92#88110—24no—
93C4⋊#1057—24no—
94C4×#1057—22no—
95C4×#1057—22no—
96C4×#1057—22no—
97C4×#1057D414yescomplemented
98#88071C2×C411yescharacteristic
99#88071C2×C411yescharacteristic
100#88071C2×C411yescharacteristic
101#88071C2×C411yescharacteristic
102#88071C2×C411yescharacteristic
103#88071C2×C411yescharacteristic
104#21265—131nomaximal, Sylow
105C24×C13C22×C411yescharacteristic
106C24×C13C22×C411yescharacteristic
107C2×D4×C13—22no—
108C2×D4×C13—22no—
109C2×D4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13M1614yes—
116C22×C4×C13C22×C411yescharacteristic
117C22×C4×C13C22×C411yescharacteristic
118C22×C4×C13C22×C411yescharacteristic
119C22×C4×C13C22×C411yescharacteristic
120C22×C4×C13C22×C411yescharacteristic
121C22×Dic13—22no—
122C22×Dic13—22no—
123C22×Dic13—22no—
124C22×Dic13—22no—
125C22×Dic13—22no—
126C22×Dic13—21no—
127C22×Dic13—21no—
128C22×Dic13—22no—
129C22×Dic13—22no—
130C22×Dic13—21no—
131C22×Dic13—21no—
132C22×Dic13—22no—
133C22×Dic13—22no—
134C22×Dic13M1614yes—
135C22×Dic13C22×C411yescharacteristic
136C22×Dic13C22×C411yescharacteristic
137C22×Dic13C22×C411yescharacteristic
138C22×Dic13C22×C411yescharacteristic
139C22×Dic13C22×C411yescharacteristic
140C22×Dic13C22×C411yescharacteristic
141C22×Dic13C22×C411yescharacteristic
142C22×Dic13C2411yescharacteristic
143C2×#1057—22no—
144C2×#1057—22no—
145C2×#1057—22no—
146C2×#1057—22no—
147C2×#1057—22no—
148C2×#1057—22no—
149C2×#1057—22no—
150C2×#1057—22no—
151C2×#1057—22no—
152C2×#1057—22no—
153C2×#1057C2×D414yes—
154C2×#1057#4114yes—
155C13×C4⋊C4—22no—
156C13×C22⋊C4—22no—
157C13×C22⋊C4—22no—
158C42×C13—22no—
159C22⋊Dic13—22no—
160C22⋊Dic13—22no—
161C22⋊Dic13—22no—
162C22⋊Dic13—22no—
163C4⋊Dic13—22no—
164C4⋊Dic13—22no—
165C4×Dic13—22no—
166C4×Dic13—22no—
167C4×Dic13—22no—
168C4×Dic13—22no—
169C4×Dic13—22no—
170C4×Dic13—22no—
171C4×Dic13—22no—
172C4×Dic13—21no—
173C4×Dic13—21no—
174C4×Dic13—22no—
175C4×Dic13—21no—
176C4×Dic13—21no—
177C4×Dic13C2×D412yes—
178C4×Dic13#4114yes—
179C4×Dic13#4112yes—
180C2×#431—131no—
181C2×#431—131no—
182C42×D4—131no—
183#1955—132no—
184#1940—132no—
185#1924—132no—
186#1924—132no—
187C4×C4⋊C8—131no—
188C4×C22⋊C8—131no—
189C4×C22⋊C8—131no—
190C4×#97—131no—
191C23×C13—21no—
192C23×C13—21no—
193C23×C13—21no—
194C23×C13—21no—
195C23×C13—21no—
196C23×C13—21no—
197C23×C13—21no—
198C23×C13—21no—
199C23×C13—21no—
200C23×C13—21no—
201C23×C13—21no—
202C23×C13—21no—
203C23×C13C2×M1612yes—
204C23×C13C2×M1612yes—
205C23×C13C23×C411yescharacteristic
206D4×C13—28no—
207C2×C4×C13—21no—
208C2×C4×C13—21no—
209C2×C4×C13—21no—
210C2×C4×C13—21no—
211C2×C4×C13—28no—
212C2×C4×C13—21no—
213C2×C4×C13—21no—
214C2×C4×C13—21no—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—44no—
219C2×C4×C13#11712yes—
220C2×C4×C13C4×D412yes—
221C2×C4×C13C2×M1612yes—
222C2×C4×C13C2×M1612yes—
223C2×C4×C13#13112yes—
224C2×Dic13—21no—
225C2×Dic13—21no—
226C2×Dic13—21no—
227C2×Dic13—21no—
228C2×Dic13—28no—
229C2×Dic13—21no—
230C2×Dic13—21no—
231C2×Dic13—21no—
232C2×Dic13—21no—
233C2×Dic13—21no—
234C2×Dic13—21no—
235C2×Dic13—21no—
236C2×Dic13—21no—
237C2×Dic13—21no—
238C2×Dic13—21no—
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13—42no—
242C2×Dic13—42no—
243C2×Dic13—42no—
244C2×Dic13—42no—
245C2×Dic13—44no—
246C2×Dic13#11712yes—
247C2×Dic13C4×D412yes—
248C2×Dic13C2×M1612yes—
249C2×Dic13C2×M1612yes—
250C2×Dic13#13112yes—
251C2×Dic13C22×D411yescharacteristic
252C2×Dic13C2×#4111yescharacteristic
253C2×Dic13C2×#4112yes—
254C2×Dic13C2×#4112yes—
255#1057—24no—
256#1057—24no—
257#1057—42no—
258#1057—42no—
259C2×C4×D4—131no—
260C2×C4×D4—131no—
261C2×C4×D4#26111yescharacteristic
262C22×C42—131no—
263C22×C42—131no—
264#431—264no—
265#431—264no—
266C2×C4⋊C8—132no—
267C2×C4⋊C8—132no—
268C2×C4⋊C8—132no—
269C2×C22⋊C8—132no—
270C2×C22⋊C8—132no—
271C2×C22⋊C8—132no—
272C2×C22⋊C8—132no—
273C2×#97—132no—
274C2×#97—132no—
275C2×C4×C8—131no—
276C2×C4×C8—131no—
277C2×C4×C8—131no—
278C2×C4×C8—131no—
279C4×C4⋊C4—131no—
280C4×C4⋊C4—131no—
281C4×C4⋊C4—131no—
282C4×C22⋊C4—131no—
283C4×C22⋊C4—131no—
284C4×C22⋊C4—131no—
285C4×C22⋊C4—131no—
286C4×C22⋊C4—131no—
287C4×C22⋊C4—131no—
288C43—131no—
289#336—132no—
290#336—132no—
291#336—132no—
292C22×C13—22no—
293C22×C13—22no—
294C22×C13—22no—
295C22×C13—22no—
296C22×C13—22no—
297C22×C13—22no—
298C22×C13—41no—
299C22×C13—41no—
300C22×C13—41no—
301C22×C13—41no—
302C22×C13—41no—
303C22×C13—41no—
304C22×C13—41no—
305C22×C13—41no—
306C22×C13C2×#11711yescharacteristic
307C22×C13C2×C4×D411yescharacteristic
308C22×C13C4×#4111yescharacteristic
309C22×C13C22×M1611yescharacteristic
310C22×C13C22×M1611yescharacteristic
311C22×C13C2×#13111yescharacteristic
312C22×C13C2×#13111yescharacteristic
313C4×C13—22no—
314C4×C13—22no—
315C4×C13—41no—
316C4×C13—41no—
317C4×C13#43514yes—
318Dic13—22no—
319Dic13—22no—
320Dic13—41no—
321Dic13—41no—
322Dic13—41no—
323Dic13—41no—
324Dic13#43514yes—
325Dic13#52912yes—
326Dic13#53212yes—
327C22×D4C2×#26111yescharacteristic
328C23×C4—131no—
329C23×C4—131no—
330C23×C4—131no—
331C23×C4—131no—
332C23×C4C2×#26111yescharacteristic
333C23×C4C2×#26111yescharacteristic
334C22×C8—132no—
335C22×C8—132no—
336C22×C8—132no—
337C22×C8—132no—
338C4×D4—24no—
339C4×D4—264no—
340C4×D4—264no—
341C2×C4⋊C4—131no—
342C2×C4⋊C4—131no—
343C2×C4⋊C4C2×#26111yescharacteristic
344C2×C22⋊C4—131no—
345C2×C22⋊C4—131no—
346C2×C22⋊C4—131no—
347C2×C22⋊C4—131no—
348C2×C22⋊C4C2×#26111yescharacteristic
349C2×C22⋊C4C2×#26111yescharacteristic
350C2×C42—131no—
351C2×C42—131no—
352C2×C42—131no—
353C2×C42—131no—
354C2×C42—131no—
355C2×C42—131no—
356C2×C42—131no—
357C2×C42—131no—
358C2×C42—131no—
359C2×C42—131no—
360C2×C42—131no—
361C2×C42—131no—
362C2×C42—262no—
363C2×C42—262no—
364C2×C42—262no—
365C2×C42—262no—
366C2×C42C2×#26111yescharacteristic
367C4⋊C8—264no—
368C4⋊C8—264no—
369C4⋊C8—264no—
370C22⋊C8—264no—
371C22⋊C8—264no—
372C22⋊C8—264no—
373C22⋊C8—264no—
374#97—264no—
375#97—264no—
376C4×C8—134no—
377C4×C8—262no—
378C4×C8—262no—
379C4×C8—262no—
380#95—131no—
381#95—131no—
382#95—131no—
383#95—131no—
384#95—131no—
385#95—131no—
386C2×C13—42no—
387C2×C13—42no—
388C2×C13#229311yescharacteristic
389C2×C13#292011yescharacteristic
390C2×C13#292211yescharacteristic
391C2×C13C2×#43511yescharacteristic
392C2×C13C2×#43511yescharacteristic
393C2×C13#296511yescharacteristic
394C2×C13#296511yescharacteristic
395C24C22×#26111yescharacteristic
396C24C22×#26111yescharacteristic
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—131no—
406C22×C4—131no—
407C22×C4—134no—
408C22×C4—131no—
409C22×C4—131no—
410C22×C4—131no—
411C22×C4—131no—
412C22×C4—131no—
413C22×C4—131no—
414C22×C4—262no—
415C22×C4—262no—
416C22×C4—261no—
417C22×C4—261no—
418C22×C4—262no—
419C22×C4—262no—
420C22×C4—261no—
421C22×C4—261no—
422C22×C4—262no—
423C22×C4—262no—
424C22×C4—262no—
425C22×C4—262no—
426C22×C4—262no—
427C22×C4#612214yes—
428C22×C4C22×#26111yescharacteristic
429C22×C4C22×#26111yescharacteristic
430C22×C4C22×#26111yescharacteristic
431C22×C4C22×#26111yescharacteristic
432C22×C4C22×#26111yescharacteristic
433C2×C8—134no—
434C2×C8—134no—
435C2×C8—262no—
436C2×C8—262no—
437C2×C8—262no—
438C2×C8—262no—
439C2×C8—262no—
440C2×C8—262no—
441C2×C8—262no—
442C2×C8—262no—
443C2×C8—262no—
444C2×C8—262no—
445C4⋊C4—22no—
446C4⋊C4—262no—
447C4⋊C4—262no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—262no—
451C22⋊C4—262no—
452C22⋊C4—262no—
453C22⋊C4—262no—
454C42—22no—
455C42—134no—
456C42—132no—
457C42—132no—
458C42—262no—
459C42—261no—
460C42—261no—
461C42—261no—
462C42—262no—
463C42—261no—
464C42—262no—
465C42—262no—
466C42—262no—
467C42—262no—
468C42—262no—
469C42—262no—
470C13#2126511yescharacteristic, complemented, Sylow
471C23—21no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—21no—
477C23—21no—
478C23—21no—
479C23—21no—
480C23—21no—
481C23—21no—
482C23—21no—
483C23D13⋊M1612yes—
484C23C2×#612212yes—
485C23C23×#26111yescharacteristic
486D4—28no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—28no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—44no—
499C2×C4—132no—
500C2×C4—132no—
501C2×C4—131no—
502C2×C4—131no—
503C2×C4—132no—
504C2×C4—132no—
505C2×C4—132no—
506C2×C4—132no—
507C2×C4—132no—
508C2×C4—268no—
509C2×C4—261no—
510C2×C4—261no—
511C2×C4—261no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—261no—
517C2×C4—261no—
518C2×C4—261no—
519C2×C4—261no—
520C2×C4—261no—
521C2×C4—261no—
522C2×C4—261no—
523C2×C4—261no—
524C2×C4—261no—
525C2×C4—524no—
526C2×C4—522no—
527C2×C4—522no—
528C2×C4—522no—
529C2×C4—522no—
530C2×C4#8823712yes—
531C2×C4#8823812yes—
532C2×C4D4×#26112yes—
533C2×C4C2×#612212yes—
534C2×C4C2×#612212yes—
535C8—264no—
536C8—264no—
537C8—522no—
538C8—522no—
539C22—22no—
540C22—22no—
541C22—22no—
542C22—22no—
543C22—22no—
544C22—22no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22C2×D13⋊M1611yescharacteristic
554C22C2×#8823711yescharacteristic
555C22C2×#8823811yescharacteristic
556C22C2×D4×#26111yescharacteristic
557C22D13⋊#13111yescharacteristic
558C22#41×#26111yescharacteristic
559C22C22×#612211yescharacteristic
560C4—22no—
561C4—22no—
562C4—41no—
563C4—41no—
564C4—134no—
565C4—132no—
566C4—132no—
567C4—262no—
568C4—262no—
569C4—521no—
570C4—521no—
571C4—521no—
572C4—521no—
573C4#1171914414yes—
574C2—42no—
575C2—42no—
576C2#1313129311yescharacteristic
577C2#1313151211yescharacteristic
578C2#1313152011yescharacteristic
579C2C2×#1171914411yescharacteristic
580C2D13⋊#43511yescharacteristic
581C2#1313164511yescharacteristic
582C2#1313164611yescharacteristic
subgroupG/H
centerC22×C4C22×#261
commutator, socleC23×C13C23×C4
FrattiniC23C23×#261
FittingC2×C4×D4×C13C4
prime radicalC22×D4×C13C2×C4
cosocleC22×Dic13C24
hypercenterC2×C4×D4#261
hypocenterC13#21265
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#11719125C2semidirect
2. C2×#11719119C2semidirect
4. #13130938C2semidirect
5. #13130910C2semidirect
6. #13130909C2semidirect
7. C4×#88112C2semidirect
8. C4×C22⋊#1057C2semidirect
9. C4×C22⋊#1057C2semidirect
10. C4×#88110C2semidirect
97. C4×#1057D4semidirect
470. C13#21265semidirect

Maximal subgroups

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

subgroupindex
C2×#117191252
C2×#117191192
#131309602
#131309382
#131309102
#131309092
C4×#881122
C4×C22⋊#10572
C4×#881102
C4×D4×Dic132
#2126513