Finite Group Databasebeta

← #16799249

Subgroups — #16799249

Order 3328.

1046 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×#11719051C211yesmaximal, characteristic, complemented
2C2×#11719125C211yesmaximal, characteristic, complemented
3#13130959C212yesmaximal
4#13130935C212yesmaximal, complemented
5#13130907C212yesmaximal, complemented
6#13130905C212yesmaximal, complemented
7C4×#88112C211yesmaximal, characteristic, complemented
8C4×#88111C211yesmaximal, characteristic, complemented
9C4×C22⋊#1057C211yesmaximal, characteristic, complemented
10C42×#1057C211yesmaximal, characteristic, complemented
11C4×#88135C211yesmaximal, characteristic
12C2×C4×C22⋊D13C411yescharacteristic
13C22×C4×Dic13C2211yescharacteristic
14C2×#88135C411yescharacteristic
15C2×#88135C2211yescharacteristic
16C2×C42×D13C2211yescharacteristic
17C2×C22⋊#1057C2212yes—
18C2×C22⋊#1057C2212yes—
19#11719125—24no—
20C2×#88112C2212yes—
21C2×#88112C2212yes—
22C2×#88111C2212yes—
23C2×#88111C2212yes—
24C2×C4⋊#1057C2212yes—
25C2×C4×#1057C2211yescharacteristic
26C2×C4×#1057C2211yescharacteristic
27C2×C4×#1057C2211yescharacteristic
28C2×C4×#1057C2212yes—
29C2×C4×#1057C2212yes—
30C2×C4×#1057C2211yescharacteristic
31#11719051—24no—
32C4×C13×C22⋊C4C411yescharacteristic
33C22⋊C4×Dic13C411yescharacteristic
34C22⋊C4×Dic13C2211yescharacteristic
35C4×#6103C411yescharacteristic
36C4×#6101C411yescharacteristic
37C42×Dic13C2211yescharacteristic
38#11718327C411yescharacteristic
39#11718327C2211yescharacteristic
40#11718310C411yescharacteristic
41#11718310C2211yescharacteristic
42#11718290C2212yes—
43#11718290C2212yes—
44#11718290C2212yes—
45C23×C4×C13C2×C411yescharacteristic
46C22×C22⋊D13C2×C411yescharacteristic
47C23×Dic13C2×C411yescharacteristic
48C23×Dic13C2311yescharacteristic
49C22×C4×D13C2×C411yescharacteristic
50C22×C4×D13C2×C411yescharacteristic
51C22×C4×D13C2311yescharacteristic
52C22×#1057C2312yes—
53C22×#1057C2312yes—
54C22×#1057C2312yes—
55C22×#1057C2312yes—
56C2×C13×C22⋊C4C2×C411yescharacteristic
57C2×C13×C22⋊C4C2×C411yescharacteristic
58C2×C42×C13C2×C411yescharacteristic
59C2×C42×C13C2×C411yescharacteristic
60C2×C22⋊Dic13C2×C411yescharacteristic
61C4×C22⋊D13—24no—
62C2×#6103C2×C411yescharacteristic
63C2×#6103C2×C411yescharacteristic
64C2×#6103C2×C411yescharacteristic
65C2×#6101C2×C411yescharacteristic
66C2×#6101C2×C411yescharacteristic
67C2×#6101C2×C411yescharacteristic
68C2×C4×Dic13—22no—
69C2×C4×Dic13—22no—
70C2×C4×Dic13C2×C411yescharacteristic
71C2×C4×Dic13C2×C411yescharacteristic
72C2×C4×Dic13C2×C411yescharacteristic
73C2×C4×Dic13C2×C411yescharacteristic
74C2×C4×Dic13C2×C411yescharacteristic
75C2×C4×Dic13C2×C411yescharacteristic
76C2×C4×Dic13C2311yescharacteristic
77C2×C4×Dic13C2311yescharacteristic
78C2×C4×Dic13C2311yescharacteristic
79C2×C4×Dic13C2311yescharacteristic
80C2×C4×Dic13C2311yescharacteristic
81#88135—24no—
82#88135C818yescomplemented
83C42×D13—22no—
84C42×D13—22no—
85C22⋊#1057—24no—
86C22⋊#1057—24no—
87#88112—24no—
88#88112—24no—
89#88111—24no—
90#88111—24no—
91C4⋊#1057—24no—
92C4×#1057—24no—
93C4×#1057—22no—
94C4×#1057—22no—
95C4×#1057—24no—
96C4×#1057—22no—
97C4×#1057D414yescomplemented
98C13×#95C2×C411yescharacteristic
99C13×#95C2×C411yescharacteristic
100#88071C2×C411yescharacteristic
101#88071C2×C411yescharacteristic
102#88071C2×C411yescharacteristic
103#88071C2×C411yescharacteristic
104#21264—131nomaximal, Sylow
105C24×C13C22×C411yescharacteristic
106C23×D13C22×C411yescharacteristic
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13C22×C411yescharacteristic
111C22×C4×C13C22×C411yescharacteristic
112C22×C4×C13C22×C411yescharacteristic
113C22×C4×C13C22×C411yescharacteristic
114C22×C4×C13C22×C411yescharacteristic
115C22×C4×C13C22×C411yescharacteristic
116C2×C22⋊D13—22no—
117C2×C22⋊D13—22no—
118C2×C22⋊D13C2×C814yes—
119C22×Dic13—22no—
120C22×Dic13—22no—
121C22×Dic13—21no—
122C22×Dic13—22no—
123C22×Dic13—22no—
124C22×Dic13—21no—
125C22×Dic13C2×C814yes—
126C22×Dic13C22×C411yescharacteristic
127C22×Dic13C22×C411yescharacteristic
128C22×Dic13C22×C411yescharacteristic
129C22×Dic13C22×C411yescharacteristic
130C22×Dic13C22×C411yescharacteristic
131C22×Dic13C22×C411yescharacteristic
132C22×Dic13C2411yescharacteristic
133C2×C4×D13—22no—
134C2×C4×D13—22no—
135C2×C4×D13—22no—
136C2×C4×D13—22no—
137C2×C4×D13—22no—
138C2×C4×D13—21no—
139C2×C4×D13—22no—
140C2×C4×D13—21no—
141C2×C4×D13—22no—
142C2×C4×D13C2×C814yes—
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×C22⋊C4—22no—
156C13×C22⋊C4C2×C814yes—
157C42×C13—22no—
158C42×C13—22no—
159C22⋊Dic13—22no—
160#6103—22no—
161#6103—22no—
162#6103C2×C814yes—
163#6101—22no—
164#6101—22no—
165#6101C2×C814yes—
166C4×Dic13—22no—
167C4×Dic13—22no—
168C4×Dic13—22no—
169C4×Dic13—22no—
170C4×Dic13—21no—
171C4×Dic13—21no—
172C4×Dic13—22no—
173C4×Dic13—21no—
174C4×Dic13—21no—
175C4×Dic13C2×C814yes—
176C4×Dic13M1614yes—
177C4×Dic13C2×D412yes—
178C4×Dic13#4114yes—
179C4×Dic13#4112yes—
180C2×#431—131no—
181C2×#431—131no—
182C42×D4—131no—
183#1954—132no—
184#1939—132no—
185#1923—132no—
186#1923—132no—
187C4×C4⋊C8—131no—
188C4×C22⋊C8—131no—
189C4×C22⋊C8—131no—
190C42×C8—131no—
191C23×C13—21no—
192C23×C13—21no—
193C23×C13—21no—
194C23×C13—21no—
195C23×C13—21no—
196C23×C13—21no—
197C23×C13C22×C812yes—
198C23×C13C23×C411yescharacteristic
199C22×D13—21no—
200C22×D13—21no—
201C22×D13—21no—
202C22×D13—21no—
203C22×D13—21no—
204C22×D13—21no—
205C22×D13C22×C812yes—
206C2×C4×C13—21no—
207C2×C4×C13—21no—
208C2×C4×C13—21no—
209C2×C4×C13—21no—
210C2×C4×C13—21no—
211C2×C4×C13—21no—
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×C13C22×C812yes—
222C2×C4×C13C22×C812yes—
223C2×C4×C13C2×M1612yes—
224C2×C4×C13#13112yes—
225C22⋊D13—28no—
226C2×Dic13—21no—
227C2×Dic13—21no—
228C2×Dic13—21no—
229C2×Dic13—21no—
230C2×Dic13—28no—
231C2×Dic13—21no—
232C2×Dic13—21no—
233C2×Dic13—21no—
234C2×Dic13—21no—
235C2×Dic13—21no—
236C2×Dic13—21no—
237C2×Dic13—42no—
238C2×Dic13—42no—
239C2×Dic13#11712yes—
240C2×Dic13C4×D412yes—
241C2×Dic13C22×C812yes—
242C2×Dic13C22×C812yes—
243C2×Dic13C22×C812yes—
244C2×Dic13C2×M1612yes—
245C2×Dic13C2×M1612yes—
246C2×Dic13#13112yes—
247C2×Dic13C22×D411yescharacteristic
248C2×Dic13C2×#4111yescharacteristic
249C2×Dic13C2×#4112yes—
250C2×Dic13C2×#4112yes—
251C4×D13—28no—
252C4×D13—44no—
253C4×D13—42no—
254C4×D13—42no—
255#1057—24no—
256#1057—24no—
257#1057—42no—
258#1057—42no—
259C2×C4×D4—131no—
260C2×C4×D4—131no—
261C2×C4×D4—131no—
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×C4×C8—131no—
274C2×C4×C8—131no—
275C2×C4×C8—131no—
276C2×C4×C8—132no—
277C2×C4×C8—132no—
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#26111yescharacteristic
288C43—131no—
289#336—132no—
290#336—132no—
291#336—132no—
292C22×C13—22no—
293C22×C13—22no—
294C22×C13—22no—
295C22×C13—41no—
296C22×C13—41no—
297C22×C13—41no—
298C22×C13—41no—
299C22×C13C2×#11711yescharacteristic
300C22×C13C2×C4×D411yescharacteristic
301C22×C13C4×#4111yescharacteristic
302C22×C13C23×C811yescharacteristic
303C22×C13C22×M1611yescharacteristic
304C22×C13C2×#13111yescharacteristic
305C22×C13C2×#13111yescharacteristic
306C2×D13—22no—
307C2×D13—22no—
308C2×D13—22no—
309C2×D13—41no—
310C2×D13—41no—
311C2×D13—41no—
312C2×D13—41no—
313C4×C13—22no—
314C4×C13—22no—
315C4×C13—22no—
316C4×C13—41no—
317C4×C13—41no—
318C4×C13#43614yes—
319Dic13—22no—
320Dic13—22no—
321Dic13—41no—
322Dic13—41no—
323Dic13#43114yescomplemented
324Dic13C8×D414yes—
325Dic13#52912yes—
326Dic13#53212yes—
327C22×D4—131no—
328C23×C4—131no—
329C23×C4—131no—
330C23×C4—131no—
331C23×C4—131no—
332C23×C4—131no—
333C23×C4C2×#26111yescharacteristic
334C22×C8—132no—
335C22×C8—132no—
336C22×C8—132no—
337C22×C8—132no—
338C4×D4—138no—
339C4×D4—264no—
340C4×D4—264no—
341C2×C4⋊C4—131no—
342C2×C4⋊C4—131no—
343C2×C4⋊C4—131no—
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—262no—
362C2×C42—262no—
363C2×C42—262no—
364C2×C42—262no—
365C2×C42C2×#26111yescharacteristic
366C2×C42C2×#26111yescharacteristic
367C4⋊C8—264no—
368C4⋊C8—264no—
369C4⋊C8—264no—
370C22⋊C8—264no—
371C22⋊C8—264no—
372C22⋊C8—264no—
373C22⋊C8—264no—
374C4×C8—134no—
375C4×C8—264no—
376C4×C8—262no—
377C4×C8—262no—
378C4×C8—262no—
379C4×C8—264no—
380#95—131no—
381#95—131no—
382#95—131no—
383#95—131no—
384#95C2×#26111yescharacteristic
385#95C2×#26111yescharacteristic
386C2×C13—42no—
387C2×C13#229311yescharacteristic
388C2×C13C2×#43111yescharacteristic
389C2×C13#292211yescharacteristic
390C2×C13C2×C8×D411yescharacteristic
391C2×C13C2×#43611yescharacteristic
392C2×C13C8×#4111yescharacteristic
393C2×C13#296511yescharacteristic
394D13—42no—
395C24—131no—
396C24C22×#26111yescharacteristic
397C2×D4—134no—
398C2×D4—262no—
399C2×D4—262no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—131no—
404C22×C4—131no—
405C22×C4—131no—
406C22×C4—134no—
407C22×C4—131no—
408C22×C4—131no—
409C22×C4—134no—
410C22×C4—131no—
411C22×C4—131no—
412C22×C4—262no—
413C22×C4—262no—
414C22×C4—261no—
415C22×C4—262no—
416C22×C4—261no—
417C22×C4—262no—
418C22×C4—262no—
419C22×C4—262no—
420C22×C4—261no—
421C22×C4—262no—
422C22×C4—261no—
423C22×C4—262no—
424C22×C4—262no—
425C22×C4—262no—
426C22×C4—262no—
427C22×C4C22×#26111yescharacteristic
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—134no—
446C4⋊C4—262no—
447C4⋊C4—262no—
448C22⋊C4—22no—
449C22⋊C4—134no—
450C22⋊C4—262no—
451C22⋊C4—262no—
452C22⋊C4—262no—
453C22⋊C4D13⋊C814yes—
454C42—22no—
455C42—22no—
456C42—134no—
457C42—134no—
458C42—134no—
459C42—132no—
460C42—132no—
461C42—262no—
462C42—261no—
463C42—261no—
464C42—261no—
465C42—262no—
466C42—261no—
467C42—262no—
468C42—262no—
469C42—262no—
470C13#2126411yescharacteristic, complemented, Sylow
471C23—21no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—21no—
477C23—132no—
478C23—261no—
479C23—261no—
480C23—261no—
481C23—261no—
482C23—261no—
483C23—261no—
484C23C2×D13⋊C812yes—
485C23C23×#26111yescharacteristic
486D4—268no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—44no—
500C2×C4—132no—
501C2×C4—132no—
502C2×C4—132no—
503C2×C4—132no—
504C2×C4—132no—
505C2×C4—131no—
506C2×C4—131no—
507C2×C4—132no—
508C2×C4—132no—
509C2×C4—132no—
510C2×C4—132no—
511C2×C4—132no—
512C2×C4—268no—
513C2×C4—268no—
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—522no—
525C2×C4—522no—
526C2×C4—522no—
527C2×C4—522no—
528C2×C4—524no—
529C2×C4C2×D13⋊C812yes—
530C2×C4C2×D13⋊C812yes—
531C2×C4D13⋊M1612yes—
532C2×C4#8823712yes—
533C2×C4#8823812yes—
534C2×C4D4×#26112yes—
535C8—264no—
536C8—264no—
537C8—522no—
538C8—522no—
539C22—22no—
540C22—22no—
541C22—22no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—262no—
547C22—262no—
548C22—262no—
549C22—521no—
550C22—521no—
551C22—521no—
552C22—521no—
553C22C22×D13⋊C811yescharacteristic
554C22C2×D13⋊M1611yescharacteristic
555C22C2×#8823711yescharacteristic
556C22C2×#8823811yescharacteristic
557C22C2×D4×#26111yescharacteristic
558C22D13⋊#13111yescharacteristic
559C22#41×#26111yescharacteristic
560C4—22no—
561C4—22no—
562C4—22no—
563C4—41no—
564C4—41no—
565C4—134no—
566C4—132no—
567C4—132no—
568C4—134no—
569C4—262no—
570C4—262no—
571C4—521no—
572C4—521no—
573C4#1171906614yes—
574C2—42no—
575C2—522no—
576C2#1313129311yescharacteristic
577C2D13⋊#43111yescharacteristic
578C2#1313151911yescharacteristic
579C2D4×D13⋊C811yescharacteristic
580C2C2×#1171906611yescharacteristic
581C2#1313164111yescharacteristic
582C2#1313164711yescharacteristic
subgroupG/H
centerC22×C4C22×#261
commutatorC22×C13C23×C8
FrattiniC23C23×#261
FittingC4×C13×C22⋊C4C4
socleC23×C13C23×C4
prime radicalC22×C22⋊D13C2×C4
cosocleC22×Dic13C24
hypercenterC4×C22⋊C4#261
hypocenterC13#21264
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11719051C2semidirect
2. C2×#11719125C2semidirect
4. #13130935C2semidirect
5. #13130907C2semidirect
6. #13130905C2semidirect
7. C4×#88112C2semidirect
8. C4×#88111C2semidirect
9. C4×C22⋊#1057C2semidirect
10. C42×#1057C2semidirect
82. #88135C8semidirect
97. C4×#1057D4semidirect
323. Dic13#431semidirect
470. C13#21264semidirect

Maximal subgroups

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

subgroupindex
C2×#117190512
C2×#117191252
#131309592
#131309352
#131309072
#131309052
C4×#881122
C4×#881112
C4×C22⋊#10572
C42×#10572
C4×#881352
#2126413