Finite Group Databasebeta

← #15862389

Subgroups — #15862389

Order 3328.

1514 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×Dic13C211yesmaximal, characteristic
2C22×#88054C211yesmaximal, characteristic, complemented
3C2×#11718894C211yesmaximal, characteristic
4#13117239C211yesmaximal, characteristic, complemented
5#13114849C212yesmaximal, complemented
6#13114844C212yesmaximal, complemented
7#13114839C212yesmaximal, complemented
8#13114834C212yesmaximal, complemented
9#13114553C211yesmaximal, characteristic, complemented
10#13114552C211yesmaximal, characteristic, complemented
11C2×C13×#416C211yesmaximal, characteristic
12C22×C13×#41C2211yescharacteristic
13C23×C8×C13C2211yescharacteristic
14C2×C13×#117C2211yescharacteristic
15#41×Dic13—24no—
16#41×Dic13C418yescomplemented
17C2×Q8×Dic13C2211yescharacteristic
18C2×Q8×Dic13C2211yescharacteristic
19C2×D4×Dic13—21no—
20C2×D4×Dic13—21no—
21C2×D4×Dic13C2211yescharacteristic
22C2×D4×Dic13C2211yescharacteristic
23C2×#88180—21no—
24C2×#88180C2211yescharacteristic
25C2×#88180C2211yescharacteristic
26C22×C4×Dic13—21no—
27C22×C4×Dic13C2211yescharacteristic
28C23×#1055C2211yescharacteristic
29C13×#416—24no—
30C2×C13×#103C2212yes—
31C2×C13×#102C2212yes—
32#11718894—24no—
33C2×#88075C2212yes—
34C2×#88072C2212yes—
35C2×#88054—24no—
36C2×#88054C2212yes—
37C2×#88054C2212yes—
38#11718638C2212yes—
39#11718637C2212yes—
40#11718603—21no—
41#11718603—21no—
42C4×#6101—21no—
43C4×#6101—21no—
44#11718143C2212yes—
45#11718143C2212yes—
46#11718121C2212yes—
47#11718121C2212yes—
48C2×C13×#41—22no—
49C2×C13×#41—22no—
50C2×C13×#41—22no—
51C2×C13×#41C2×C414yes—
52C2×C13×#41D414yes—
53C2×C13×#41Q814yes—
54C22×Q8×C13C2311yescharacteristic
55C22×D4×C13—21no—
56C22×D4×C13C2311yescharacteristic
57C23×C4×C13—21no—
58C23×C4×C13C2311yescharacteristic
59C23×Dic13—21no—
60C23×Dic13—21no—
61C23×Dic13D411yescharacteristic
62C23×Dic13D411yescharacteristic
63C22×C8×C13—22no—
64C22×C8×C13—22no—
65C22×C8×C13—22no—
66C22×C8×C13C2312yes—
67C13×#117—22no—
68C13×#117—22no—
69C2×C13×C4⋊C4C2312yes—
70C2×C13×C22⋊C4—21no—
71C2×C42×C13—21no—
72C2×C22⋊Dic13—21no—
73C2×C22⋊Dic13—21no—
74C2×C22⋊Dic13—21no—
75C2×C22⋊Dic13—21no—
76Q8×Dic13—22no—
77Q8×Dic13—22no—
78Q8×Dic13C2×C414yes—
79Q8×Dic13C2×C414yes—
80D4×Dic13—28no—
81D4×Dic13—28no—
82D4×Dic13—22no—
83D4×Dic13—22no—
84D4×Dic13C2×C414yes—
85D4×Dic13C2×C414yes—
86#88180—22no—
87#88180—28no—
88#88180—22no—
89#88180—22no—
90#88180C2×C414yes—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13C2312yes—
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×#6101—22no—
97C2×#6101—22no—
98C2×C4×Dic13—21no—
99C2×C4×Dic13—21no—
100C2×C4×Dic13—21no—
101C2×C4×Dic13—28no—
102C2×C4×Dic13—21no—
103C2×C4×Dic13C2×C414yes—
104C2×C4×Dic13D411yescharacteristic
105C2×C4×Dic13D411yescharacteristic
106C2×C4×Dic13D414yes—
107C2×C4×Dic13C2311yescharacteristic
108C2×C4×Dic13C2311yescharacteristic
109C22×#1055—22no—
110C22×#1055—22no—
111C22×#1055—22no—
112C22×#1055C2312yes—
113C13×#103—24no—
114C13×#102—24no—
115#88075—24no—
116#88072—24no—
117#88071—22no—
118#88071—22no—
119#88054—24no—
120#88054—24no—
121#20645—131nomaximal, Sylow
122C24×C13—21no—
123C24×C13C2×D411yescharacteristic
124C13×#41—28no—
125C13×#41—28no—
126C13×#41—28no—
127C13×#41C4⋊C4116yescomplemented
128C2×Q8×C13—21no—
129C2×Q8×C13—21no—
130C2×Q8×C13—21no—
131C2×Q8×C13C22×C412yes—
132C2×Q8×C13C2×D412yes—
133C2×Q8×C13C2×Q812yes—
134C2×D4×C13—24no—
135C2×D4×C13—24no—
136C2×D4×C13—24no—
137C2×D4×C13—21no—
138C2×D4×C13—21no—
139C2×D4×C13—21no—
140C2×D4×C13C22×C412yes—
141C2×D4×C13C2×D412yes—
142C2×D4×C13C2×Q812yes—
143C22×C4×C13—21no—
144C22×C4×C13—24no—
145C22×C4×C13—24no—
146C22×C4×C13—24no—
147C22×C4×C13—22no—
148C22×C4×C13C22×C412yes—
149C22×C4×C13C2×D412yes—
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D412yes—
152C22×C4×C13C2×Q812yes—
153C22×C4×C13#4112yes—
154C22×C4×C13#4112yes—
155C22×C4×C13C2411yescharacteristic
156C22×Dic13—24no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—24no—
160C22×Dic13—24no—
161C22×Dic13—22no—
162C22×Dic13—42no—
163C22×Dic13—44no—
164C22×Dic13—44no—
165C22×Dic13C22⋊C414yes—
166C22×Dic13C22⋊C414yes—
167C22×Dic13C2×D411yescharacteristic
168C22×Dic13C2×D411yescharacteristic
169C22×Dic13C2×D411yescharacteristic
170C22×Dic13C2×D411yescharacteristic
171C2×C8×C13—22no—
172C2×C8×C13—22no—
173C2×C8×C13—22no—
174C2×C8×C13—44no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—22no—
177C13×C22⋊C4—42no—
178C42×C13—42no—
179C22⋊Dic13—24no—
180C22⋊Dic13—24no—
181C22⋊Dic13—24no—
182C22⋊Dic13—42no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—24no—
186C4⋊Dic13—24no—
187C4⋊Dic13—22no—
188C4⋊Dic13—22no—
189C4⋊Dic13C22×C412yes—
190C4⋊Dic13C22×C412yes—
191#6101—44no—
192#6101—44no—
193C4×Dic13—24no—
194C4×Dic13—24no—
195C4×Dic13—24no—
196C4×Dic13—42no—
197C4×Dic13C22⋊C414yes—
198C4×Dic13C22⋊C414yes—
199C4×Dic13C22×C412yes—
200C4×Dic13C22×C412yes—
201C4×Dic13C2×D412yes—
202C4×Dic13C2×D412yes—
203C2×#1055—22no—
204C2×#1055—22no—
205C2×#1055—22no—
206C2×#1055—44no—
207C2×C4×#41—131no—
208C22×C4⋊C8—131no—
209C2×#416—131no—
210C2×#416D1311yescharacteristic
211#2285—131no—
212#1805—132no—
213#1804—132no—
214#1803—132no—
215#1802—132no—
216#1735—131no—
217#1735—131no—
218C23×C13—22no—
219C23×C13—22no—
220C23×C13—22no—
221C23×C13—22no—
222C23×C13—22no—
223C23×C13—42no—
224C23×C13—42no—
225C23×C13C2×C22⋊C412yes—
226C23×C13#12112yes—
227C23×C13C22⋊Q812yes—
228C23×C13C22×D411yescharacteristic
229Q8×C13—22no—
230Q8×C13—22no—
231Q8×C13—22no—
232Q8×C13C2×C4⋊C414yes—
233D4×C13—216no—
234D4×C13—22no—
235D4×C13—22no—
236D4×C13—22no—
237D4×C13C2×C4⋊C414yes—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
241C2×C4×C13—216no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13C2×C22⋊C412yes—
246C2×C4×C13C2×C4⋊C414yes—
247C2×C4×C13#11714yes—
248C2×C4×C13#12114yes—
249C2×C4×C13#12112yes—
250C2×C4×C13C22⋊Q814yes—
251C2×C4×C13C22⋊Q812yes—
252C2×C4×C13C23×C411yescharacteristic
253C2×C4×C13C22×D411yescharacteristic
254C2×C4×C13C22×D411yescharacteristic
255C2×C4×C13C22×Q811yescharacteristic
256C2×C4×C13C2×#4111yescharacteristic
257C2×C4×C13C2×#4111yescharacteristic
258C2×Dic13—22no—
259C2×Dic13—22no—
260C2×Dic13—22no—
261C2×Dic13—28no—
262C2×Dic13—22no—
263C2×Dic13—22no—
264C2×Dic13—44no—
265C2×Dic13—48no—
266C2×Dic13—42no—
267C2×Dic13—42no—
268C2×Dic13—48no—
269C2×Dic13—42no—
270C2×Dic13—42no—
271C2×Dic13—42no—
272C2×Dic13C2×C22⋊C412yes—
273C2×Dic13C2×C22⋊C412yes—
274C2×Dic13C2×C22⋊C412yes—
275C2×Dic13C2×C22⋊C412yes—
276C2×Dic13#13514yes—
277C8×C13—42no—
278#1055—42no—
279C22×#41C2×D1311yescharacteristic
280C23×C8—131no—
281C23×C8C2×D1311yescharacteristic
282C4×#41—138no—
283C4×#41—264no—
284C2×C4×Q8—131no—
285C2×C4×Q8—131no—
286C2×C4×D4—131no—
287C2×C4×D4—131no—
288C2×C4×D4—261no—
289C2×C4×D4—261no—
290C2×#117—131no—
291C2×#117—131no—
292C2×#117—261no—
293C2×#117C2×D1311yescharacteristic
294C22×C42—131no—
295C22×C42—261no—
296C2×C4⋊C8—132no—
297C2×C4⋊C8—132no—
298C2×C4⋊C8—264no—
299#416—24no—
300#416—264no—
301C2×#103—132no—
302C2×#103C2×D1312yes—
303C2×#102—132no—
304C2×#102C2×D1312yes—
305#384—132no—
306#382—132no—
307#380—261no—
308#380—261no—
309C4×C4⋊C4—261no—
310C4×C4⋊C4—261no—
311#340—132no—
312#340—132no—
313#340—132no—
314#340—132no—
315C22×C13—24no—
316C22×C13—22no—
317C22×C13—22no—
318C22×C13—24no—
319C22×C13—24no—
320C22×C13—44no—
321C22×C13—42no—
322C22×C13—42no—
323C22×C13—44no—
324C22×C13#38014yes—
325C22×C13C22×C22⋊C411yescharacteristic
326C22×C13C2×#12111yescharacteristic
327C22×C13C2×C22⋊Q811yescharacteristic
328C22×C13C2×#13512yes—
329C22×C13#57512yes—
330C4×C13—24no—
331C4×C13—82no—
332C4×C13#38014yes—
333C4×C13C22×C4⋊C411yescharacteristic
334C4×C13C2×#11711yescharacteristic
335C4×C13C2×#12111yescharacteristic
336C4×C13C2×C22⋊Q811yescharacteristic
337Dic13—22no—
338Dic13—22no—
339Dic13—22no—
340Dic13—42no—
341Dic13—42no—
342Dic13—82no—
343Dic13#41614yescomplemented
344C2×#41—22no—
345C2×#41—22no—
346C2×#41—22no—
347C2×#41Dic2614yes—
348C2×#41C4×D1314yes—
349C2×#41C22⋊D1314yes—
350C22×Q8C22×D1311yescharacteristic
351C22×D4—21no—
352C22×D4C22×D1311yescharacteristic
353C23×C4—21no—
354C23×C4—131no—
355C23×C4—131no—
356C23×C4—261no—
357C23×C4—261no—
358C23×C4C22×D1311yescharacteristic
359C22×C8—22no—
360C22×C8—22no—
361C22×C8—22no—
362C22×C8—132no—
363C22×C8—262no—
364C22×C8—262no—
365C22×C8—262no—
366C22×C8C22×D1312yes—
367C4×Q8—134no—
368C4×Q8—134no—
369C4×Q8—262no—
370C4×Q8—262no—
371C4×D4—134no—
372C4×D4—134no—
373C4×D4—262no—
374C4×D4—262no—
375C4×D4—268no—
376C4×D4—268no—
377#117—22no—
378#117—22no—
379#117—134no—
380#117—268no—
381#117—262no—
382#117—262no—
383#117—262no—
384C2×C4⋊C4—131no—
385C2×C4⋊C4—131no—
386C2×C4⋊C4—132no—
387C2×C4⋊C4—261no—
388C2×C4⋊C4—261no—
389C2×C4⋊C4—262no—
390C2×C4⋊C4—262no—
391C2×C4⋊C4C22×D1312yes—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—261no—
394C2×C22⋊C4—261no—
395C2×C22⋊C4—261no—
396C2×C22⋊C4—261no—
397C2×C42—21no—
398C2×C42—134no—
399C2×C42—134no—
400C2×C42—131no—
401C2×C42—131no—
402C2×C42—131no—
403C2×C42—131no—
404C2×C42—268no—
405C2×C42—261no—
406C2×C42—261no—
407C2×C42—261no—
408C2×C42—261no—
409C4⋊C8—264no—
410C4⋊C8—264no—
411#103—24no—
412#103—264no—
413#102—24no—
414#102—264no—
415#95—262no—
416#95—262no—
417C2×C13—24no—
418C2×C13—44no—
419C2×C13C2×#38011yescharacteristic
420C2×C13C2×#41611yescharacteristic
421C2×C13#289611yescharacteristic
422C2×C13#303512yes—
423C2×C13#307612yes—
424C24—21no—
425C24D4×D1311yescharacteristic
426#41—28no—
427#41—28no—
428#41—28no—
429#41#6101116yescomplemented
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8C2×Dic2612yes—
434C2×Q8C2×C4×D1312yes—
435C2×Q8C2×C22⋊D1312yes—
436C2×D4—24no—
437C2×D4—24no—
438C2×D4—24no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4C2×Dic2612yes—
443C2×D4C2×C4×D1312yes—
444C2×D4C2×C22⋊D1312yes—
445C22×C4—21no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—131no—
451C22×C4—134no—
452C22×C4—131no—
453C22×C4—131no—
454C22×C4—131no—
455C22×C4—134no—
456C22×C4—264no—
457C22×C4—264no—
458C22×C4—264no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—262no—
462C22×C4—524no—
463C22×C4—522no—
464C22×C4—524no—
465C22×C4C2×Dic2612yes—
466C22×C4C2×C4×D1312yes—
467C22×C4D4×D1312yes—
468C22×C4D4×D1311yescharacteristic
469C22×C4#612912yes—
470C22×C4#612912yes—
471C22×C4C2×C22⋊D1312yes—
472C22×C4C23×D1311yescharacteristic
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—44no—
477C2×C8—262no—
478C2×C8—262no—
479C2×C8—262no—
480C2×C8—524no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—132no—
484C4⋊C4—132no—
485C4⋊C4—264no—
486C4⋊C4—264no—
487C4⋊C4—261no—
488C4⋊C4—261no—
489C4⋊C4—262no—
490C4⋊C4—262no—
491C4⋊C4—524no—
492C4⋊C4—524no—
493C22⋊C4—42no—
494C22⋊C4—264no—
495C22⋊C4—264no—
496C22⋊C4—264no—
497C22⋊C4—522no—
498C42—42no—
499C42—134no—
500C42—134no—
501C42—132no—
502C42—132no—
503C42—132no—
504C42—132no—
505C42—264no—
506C42—264no—
507C42—264no—
508C42—522no—
509C13#2064511yescharacteristic, complemented, Sylow
510C23—22no—
511C23—22no—
512C23—22no—
513C23—22no—
514C23—22no—
515C23—42no—
516C23—42no—
517C23#8813212yes—
518C23C22⋊C4×D1312yes—
519C23#8819312yes—
520C23C2×D4×D1311yescharacteristic
521Q8—22no—
522Q8—22no—
523Q8—22no—
524Q8C2×#610114yes—
525D4—216no—
526D4—22no—
527D4—22no—
528D4—22no—
529D4C2×#610114yes—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—216no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—132no—
538C2×C4—134no—
539C2×C4—132no—
540C2×C4—132no—
541C2×C4—132no—
542C2×C4—268no—
543C2×C4—262no—
544C2×C4—262no—
545C2×C4—262no—
546C2×C4—262no—
547C2×C4—262no—
548C2×C4—528no—
549C2×C4—524no—
550C2×C4—528no—
551C2×C4—522no—
552C2×C4—522no—
553C2×C4—522no—
554C2×C4—522no—
555C2×C4—522no—
556C2×C4#8813114yes—
557C2×C4#8813214yes—
558C2×C4#8813212yes—
559C2×C4C22⋊C4×D1312yes—
560C2×C4C2×#610114yes—
561C2×C4#8819314yes—
562C2×C4#8819312yes—
563C2×C4C22×Dic2611yescharacteristic
564C2×C4C22×C4×D1311yescharacteristic
565C2×C4C2×D4×D1311yescharacteristic
566C2×C4C2×#612911yescharacteristic
567C2×C4C2×#612911yescharacteristic
568C2×C4C22×C22⋊D1311yescharacteristic
569C8—42no—
570C8—522no—
571C22—22no—
572C22—24no—
573C22—22no—
574C22—24no—
575C22—24no—
576C22—42no—
577C22—44no—
578C22—42no—
579C22—44no—
580C22#1171860314yes—
581C22C2×#8813211yescharacteristic
582C22C2×C22⋊C4×D1311yescharacteristic
583C22D13×#13512yes—
584C22#1171947312yes—
585C22C2×#8819311yescharacteristic
586C4—24no—
587C4—82no—
588C4—134no—
589C4—262no—
590C4—262no—
591C4—262no—
592C4—522no—
593C4—522no—
594C4—1042no—
595C4#1171860314yes—
596C4C2×#8813111yescharacteristic
597C4C2×#8813211yescharacteristic
598C4C22×#610111yescharacteristic
599C4C2×#8819311yescharacteristic
600C2—24no—
601C2—44no—
602C2C2×#1171860311yescharacteristic
603C2D13×#41611yescharacteristic
604C2#1312335111yescharacteristic
605C2#1312428712yes—
606C2#1312462012yes—
subgroupG/H
centerC22×C4D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#416C2
socleC23×C13C22×D4
prime radicalC22×C13×#41C22
cosocleC22×C4×C13C24
hypercenterC2×#416D13
hypocenterC13#20645
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. C22×#88054C2semidirect
4. #13117239C2semidirect
5. #13114849C2semidirect
6. #13114844C2semidirect
7. #13114839C2semidirect
8. #13114834C2semidirect
9. #13114553C2semidirect
10. #13114552C2semidirect
16. #41×Dic13C4semidirect
127. C13×#41C4⋊C4semidirect
343. Dic13#416semidirect
429. #41#6101semidirect
509. C13#20645semidirect

Maximal subgroups

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

subgroupindex
C2×#41×Dic132
C22×#880542
C2×#117188942
#131172392
#131148492
#131148442
#131148392
#131148342
#131145532
#131145522
C2×C13×#4162
#2064513